We're asked to multiply 65 times 1.
So literally, we just need to multiply 65, and we could write it as a times sign like that or we could write it as a dot like that but this means 65 times 1.
And there's two ways to interpret this.
You could view this as the number 65 one time or you could view this as the number 1 sixty-five times, all added up.
But either way, if you have one 65, this is literally just going to be 65.
Anything times 1 is going to be that anything, whatever this is.
Whatever this is times 1 is going to be that same thing again.
If I have just some kind of placeholder here times 1, that's going to be that same placeholder.
So if I have 3 times 1, I'm going to get 3.
If I have 5 times 1, I'm going to get 5, because literally, all this is saying is 5 one time.
If I put-- I don't know-- 157 times 1, that'll be 157.
I think you get the idea.
This movement isn't about the 99% defeating or toppling the 1%.
You know the next chapter of that story, which is that the 99% create a new 1%.
That's not what it's about.
What we want to create is the more beautiful world our hearts tell us is possible.
A sacred world.
A world that works for everybody.
A world that is healing.
A world of peace.
You can't just say: "we demand a world of peace." Demands have to be specific.
Anything that people can articulate can only be articulated within the language of the current political discourse.
That entire political discourse is already too small.
That's why making explicit demands reduces the movement, and takes the heart out of it.
So, it's a real paradox, and I think the movement actually understands that.
The system isn't working for the 1% either.
You know, if you were a CEO, you would be making the same choices they do.
The institutions have their own logic.
Life is pretty bleak at the top too - and all the baubles of the rich... they are kind of this, uh, phony compensation for the loss of what's really important: the loss of community; the loss of connection; the loss of intimacy. The loss of meaning. Everybody wants to live a life of meaning.
And today, we live in a money economy where we don't really depend on the gifts of anybody.
But, we buy everything.
Therefore, we don't really need anybody, because whoever grew my food, or made my clothes, or built my house... well, if they died, or if I alienate them, or if they don't like me.
I can just pay someone else to do it.
And it's really hard to create community if the underlying knowledge is: "we don't need each other." So people kind of get together and act nice.
Or, maybe they consume together.
But joint consumption doesn't create intimacy.
Only joint creativity and gifts create intimacy and connection.
You have such gifts that are important.
Just like every species has an important gift to give to the ecosystem, and the extinction of any species hurts everybody.
The same is true of each person - that you have a necessary and important gift to give.
And, that for a long time our minds have told us that maybe we are imagining things.
That it's crazy to live according to what you want to give.
But I think now as more and more people are waking up to the truth, that we're here to give, and wake up to that desire.
And wake up to the fact that the other way isn't working anyway - the more reinforcement we have from people around us that this isn't crazy.
That this makes sense.
This is how to live.
And as we get that reinforcement, then our minds and our logic no longer have to fight against the logic of the heart, which wants us to be of service.
This shift of consciousness that inspires such things is universal; it's everybody.
The 99% and 1%, and it's wakening in different people in different ways.
I think love is the felt experience of connection to another being.
An economist says, essentially, "more for you is less for me."
But the lover knows that more for you is more for me too.
If you love somebody their happiness is your happiness.
Their pain is your pain.
Your sense of self expands to include other beings.
That's love - love is the expansion of the self to include the other. And that is a different kind of revolution.
There's no one to fight.
There's no evil to fight.
There's no "other" in this revolution.
Everybody has a unique calling and it's really time to listen to that.
That's what the future is going to be.
It's time to get ready for it, and help contribute to it, and make it happen.
Simplify the rate of cans of soda compared to people.
So this ratio here says that we have 92 cans of soda for every 28 people.
What we want to do is simplify this, and really just putting this ratio, or this fraction, in simplest form.
So the best way to do that is just to figure out what is the largest number, or the largest common factor, of both 92 and 28, and divide both of these numbers by that common factor.
So let's figure out what it is.
And to do that, let's just take the prime factorization of 92, and then we'll do the prime factorization of 28.
So 92 is 2 times 46, which is 2 times 23.
And 23 is a prime number, so we're done.
92 is 2 times 2 times 23.
And if we did the prime factorization of 28, 28 is 2 times 14, which is 2 times 7.
So we can rewrite the 92 cans of soda as 2 times 2 times 23 cans of soda for every 2 times 2 times 7 people.
Now, both of these numbers have a 2 times 2 in it, or they're both divisible by 4.
That is their greatest common factor.
So let's divide both the top number and the bottom number by 4.
So if you divide the top number by 4, or if you divide it by 2 times 2, it will cancel out right over there.
And then if you do the bottom number divided by 4, or 2 times 2, it will cancel out with that 2 times 2.
And we are left with 23 cans of soda for every 7 people, or 7 people for every 23 cans of soda.
And we're done!
We've simplified the rate of cans, or the ratio of cans, of soda compared to people.
I guess they're considering this a rate, so maybe they're saying how quickly do 7 people consume cans over some period, or you can view it as a ratio.
What is the least common multiple, abbreviated as LCM, of 15, 6 and 10?
So the LCM is exactly what the word is saying, it is the least common multiple of these numbers.
And I know that probably did not help you much. But lets actually work trough this problem.
So to do that, lets think of the different multiples of 15, 6 and 10. and then find the smallest multiple, the least multiple they have in common.
So, lets find the multiples of 15.
You have:
1 times 15 is 15, two times 15 is 30, then if you add 15 again you get 45, you add 15 again you get 60, you add 15 again, you get 75, you add 15 again, you get 90, you add 15 again you get 105. and if still none of these are common multiples with these guys over here then you may have to go further, but I will stop here for now.
Now that's the multiples of 15 up through 105.
Obviously, we keep going from there.
Now lets do the multiples of 6.
Let's do the multiples of 6: 1 times 6 is 6, two times 6 is 12, 3 times 6 is 18, 4 times 6 is 24, 5 times 6 is 30, 6 times 6 is 36, 7 times 6 is 42, 8 times 6 is 48, 9 times 6 is 54, 10 times 6 is 60.
60 already looks interesting, because it is a common multiple of both 15 and 60.
Although we have to of them over here.
We have 30 and we have a 30, we have a 60 and a 60.
So the smallest LCM... ...so if we only cared about the least common multiple of 15 and 6.
We would say it is 30.
Lets write that down as an intermediate: the LCM of 15 and 6.
So the least common multiple, the smallest multiple that they have in common we see over here.
15 times 2 is 30 and 6 times 5 is 30.
So this is definitely a common multiple and it is the smallest of all of their LCMs.
60 is also a common multiple, but it is a bigger one.
This is the least common multiple.
So this is 30.
We have not thought of the 10 yet.
So lets bring the 10 in there.
I think you see where this is going.
Let's do the multiples of 10.
They are 10, 20, 30, 40... well, we already went far enough.
Because we already got to 30, and 30 is a common multiple of 15 and 6 and it is the smallest common multiple of all of them.
So it is actually the fact that the LCM of 15, 6 and 10 is equal to 30.
Now, this is one way to find the least common multiple.
Literally, just find and look at the multiples of each of the numbers... and then see what the smallest multiple is they have in common.
Another way to do that, is to look at the prime factorization of each of these numbers and the LCM is the number that has all the elements of the prime factorization of these and nothing else.
So let me show you what I mean by that.
So, you can do it this way or you can say that 15 is the same thing as 3 times 5 and that's it.
That is its prime factorization, 15 is 3 times 5, since both 3 and 5 are prime numbers.
We can say that 6 is the same thing as 2 times 3.
That's it, that is its prime factorization, since both 2 and 3 are prime.
And then we can say that 10 is the same thing as 2 times 5.
Both two and 5 are prime, so we are done factoring it.
So the LCM of 15, 6 and 10, just needs to have all of these prime factors. And what I mean is... to be clear, in order to be divisible by 15 it has to have at least one 3 and at least one 5 in its prime factorization, so it needs to have one 3 and at least one 5.
By having a 3 times 5 in its prime factorization that ensures that this number is divisible by 15.
To be divisible by 6 it has to have at least one 2 and one 3.
So it has to have at least one 2 and we already have a 3 over here so that is all we want.
We just need one 3.
So one 2 and one 3.
That is 2 times 3 and ensures we are divisible by 6.
And let me make it clear, this right here is the 15.
And then to make sure we are divisible by 10, we need to have at least one 2 and one 5.
These two over here make sure we are divisible by 10. and so we have all of them, this 2 x 3 x 5 has all of the prime factors of either 10, 6 or 15, so it is the LCM.
So if we multiply this out, you will get, 2 x 3 is 6, 6 x 5 is 30.
So either way.
Hopefully these kind of resonate with you and you see why they make sense.
This second way is a little bit better, if you are trying to do it for really complex numbers... ...numbers, where you might have to be multiplying for a really long time.
Well, either way, both of these are valid ways of finding the least common multiple.
Welcome to the presentation on multiplying and dividing negative numbers.
Let's get started.
I think you're going to find that multiplying and dividing negative numbers are a lot easier than it might
look initially. You just have to remember a couple of rules.
And I am going to teach probably in the future like I'm actually going to give you more intuition on why there rules work.
So the basic rules are when you multiply two negative numbers, so let's say I had negative 2 times negative 2.
First you just look at each of the numbers as if there was no negative sign.
Well you say well, 2 times 2 that equals 4.
And it turns out that if you have a negative times a negative, that that equals a positive.
So let's write that first rule down.
A negative times a negative equals a positive.
What if it was negative 2 times positive 2?
Well in this case, let's first of all look at the two numbers without signs.
We know that 2 times 2 is 4.
But here we have a negative times a positive 2, and it turns out that when you multiply a negative times a positive you get a negative.
So that's another rule.
Negative times positive is equal to negative.
What happens if you have a positive 2 times a negative 2?
I think you'll probably guess this one right, as you can tell that these two are pretty much the same thing by, I believe it's the transitive property -- no, no I think it's the communicative property.
But 2 times negative 2, this also equals negative 4.
So we have the final rule that a positive times a negative also equals the negative. And actually these second two rules, they're kind of the same thing.
A negative times a positive is a negative, or a positive times a negative is negative.
You could also say that as when the signs are different and you multiply the two numbers, you get a negative number.
And of course, you already know what happens when you have a positive times a positive. Well that's just a positive.
So let's review.
Negative times a negative is a positive. A negative times a positive is a negative. A positive times a negative is a negative.
And positive times each other equals positive.
I think that last little bit completely confused you. Maybe I can simplify it for you.
What if I just told you if when you're multiplying and they're the same signs that gets you a positive result. And different signs gets you a negative result.
So that would be either, let's say a 1 times 1 is equal to 1, or if I said negative 1 times negative 1 is equal to positive 1 as well.
Or if I said 1 times negative 1 is equal to negative 1, or negative 1 times 1 is equal to negative 1.
You see how on the bottom two problems I had two different signs, positive 1 and negative 1?
And the top two problems, this one right here both 1s are positive.
And this one right here both 1s are negative.
So let's do a bunch of problems now, and hopefully it'll hit the point home, and you also could try to do along the practice problems and also give the hints and give you what rules to you so that should help you as well
So if I said negative 4 times positive 3, well 4 times 3 is 12, and we have a negative and a positive.
So different signs mean negative.
So negative 4 times 3 is a negative 12.
That makes sense because we're essentially saying what's negative 4 times itself three times, so it's like negative 4 plus negative 4 plus negative 4, which is negative 12.
If you've seen the video on adding and subtracting negative numbers, you probably should watch first.
Let's do another one.
What if I said minus 2 times minus 7.
And you might want to pause the video at any time to see if you know how to do it and then restart it to see what the answer is.
Well, 2 times 7 is 14, and we have the same sign here, so it's a positive 14 -- normally you wouldn't have to write the positive but that makes it a little bit more explicit.
And what if I had -- let me think -- 9 times negative 5.
Well, 9 times 5 is 45.
And once again, the signs are different so it's a negative.
And then finally what if it I had -- let me think of some good numbers -- minus 6 times minus 11.
Well, 6 times 11 is 66 and then it's a negative and negative, it's a positive.
Let me give you a trick problem.
What is 0 times negative 12?
Well, you might say that the signs are different, but 0 is actually neither positive nor negative.
And 0 times anything is still 0.
It doesn't matter if the thing you multiply it by is a negative number or a positive number.
0 times anything is still 0.
So let's see if we can apply these same rules to division. It actually turns out that the same rules apply.
If I have 9 divided by negative 3.
Well, first we say what's 9 divided by 3?
Well that's 3. And they have different signs, positive 9, negative 3.
So different signs means a negative.
9 divided by negative 3 is equal to negative 3.
What is minus 16 divided by 8?
Well, once again, 16 divided by 8 is 2, but the signs are different.
Negative 16 divided by positive 8, that equals negative 2.
Remember, different signs will get you a negative result.
What is minus 54 divided by minus 6?
Well, 54 divided by 6 is 9.
And since both terms, the divisor and the dividend, are both negative -- negative 54 and negative 6 -- it turns out that the answer is positive. Remember, same signs result in a positive sign.
Obviously, 0 divided by anything is still 0.
That's pretty straightforward. And of course, you can't divide anything by 0
Let's do one more.
What is -- I'm just going to think of random numbers -- 4 divided by negative 1?
Well, 4 divided by 1 is 4, but the signs are different.
So it's negative 4.
I hope that helps.
Now what I want you to do is actually try as many of these multiplying and dividing negative numbers as you can.
And you click on hints and it'll remind you of which rule to use.
In your own time you might want to actually think about why these rules apply and what it means to multiply a negative number times a positive number.
And even more interesting, what it means to multiply a negative number times a negative number.
Good luck.
I will now do a proof of the law of sines.
So, let's see, let me draw an arbitrary triangle.
We know this angle -- well, actually, I'm not going to say what we know or don't know, but the law of sines is just a relationship between different angles and different sides.
Let's say that this angle right here is alpha.
This side here is A.
The length here is A.
Let's say that this side here is beta, and that the length here is B.
So let's see if we can find a relationship that connects A and B, and alpha and beta.
So what can we do?
So let me draw an altitude here.
If I just draw a line from this side coming straight down, and it's going to be perpendicular to this bottom side, which I haven't labeled, but I'll probably, if I have to label it, probably label it C, because that's A and B.
All I know is I went from this vertex and I dropped a line that's perpendicular to this other side.
So what can we do with this line?
Well let me just say that it has length x.
The length of this line is x.
Can we find a relationship between A, the length of this line x, and beta?
Well, sure.
Let's see.
Let me find an appropriate color.
So what's the relationship?
If we look at this angle right here, beta, x is opposite to it and A is the hypotenuse, if we look at this right triangle right here, right?
So what deals with opposite and hypotenuse?
Whenever we do trigonometry, we should always just right soh cah toa at the top of the page.
Soh cah toa.
So what deals with opposite of hypotenuse?
Sine, right?
Soh, and you should probably guess that, because I'm proving the law of sines.
So the sine of beta is equal to the opposite over the hypotenuse.
It's equal to this opposite, which is x, over the hypotenuse, which is A, in this case.
And if we wanted to solve for x, and I'll just do that, because it'll be convenient later, we can multiply both sides of this equation by A and you get A sine of beta is equal to x.
Well, let's see if we can find a relationship between alpha, B, and x.
Well, similarly, if we look at this right triangle, because this is also a right triangle, of course, x here, relative to alpha, is also the opposite side, and B now is the hypotenuse.
So we can also write that sine of alpha -- let me do it in a different color -- is equal to opposite over hypotenuse.
The opposite is x and the hypotenuse is B.
Multiply both sides by B and you get B sine of alpha is equal to x.
So now what do we have?
We have two different ways that we solved for this thing that I dropped down from this side, this x, right?
We have A sine of beta is equal to x.
And then B sine of alpha is equal to x.
Well, if they're both equal to x, then they're both equal to each other.
So let me write that down.
So we know that A sine of beta is equal to x, which is also equal to B sine of beta -- sorry, B sine of alpha.
If we divide both sides of this equation by A, what do we get?
We get sine of beta, right, because the A on this side cancels out, is equal to B sine of alpha over A.
And if we divide both sides of this equation by B, we get sine of beta over B is equal to sine of alpha over A.
So this is the law of sines.
The ratio between the sine of beta and its opposite side -- and it's the side that it corresponds to, this B -- is equal to the ratio of the sine of alpha and its opposite side.
And a lot of times in the books, let's say, if this angle was theta, and this was C, then they would also write that's also equal to the sine of theta over C.
And the proof of adding this here is identical.
We've picked B arbitrarily, B as a side, we could have done the exact same thing with theta and C, but instead of dropping the altitude here, we would have had to drop one of the other altitudes.
But the important thing is we have this ratio.
And of course, you could have written it -- since it's a ratio, you could flip both sides of the ratio -- you could write it B over the sine of B is equal to A over the sine of alpha.
And this is useful, because if you know one side and its corresponding angle, the angle opposite it that kind of opens up into that side, and say you know the other side, then you could figure out the angle that opens up into it.
And that's what's useful about the law of sines.
So maybe now I will do a few law of sines word problems.
I'll see you in the next video.
In the last video we did a couple of lattice multiplication problems and we saw it was pretty straightforward.
You got to do all your multiplication first and then do all of your addition.
Well, let's try to understand why exactly it worked.
It almost seemed like magic.
And to see why it worked I'm going to redo this problem up here and then I'll also try to explain what we did in the longer problems.
So when we multiplied twenty-seven-- so you write your two and your seven just like that-- times forty-eight.
I'm just doing exactly what we did in the previous video.
We drew a lattice, gave the two a column and the seven a column. Just like that.
We gave the four a row and we gave the eight a row.
And then we drew our diagonal.
And the key here is the diagonals, as you can imagine, otherwise we wouldn't be drawing them.
So you have your diagonals.
Now the way to think about it is each of these diagonals are a number place.
So for example, this diagonal right here, that is the ones place.
The next diagonal, I'll do it in this light green color. The next diagonal right here in the light green color, that is the tens place.
Now the next diagonal to the left or above that, depending on how you want to view it,
I'll do in this little pink color right here.
You could guess, that's going to be the hundreds place.
And then, finally, we have this little diagonal there, and I'll do it in this light blue color.
That is the thousands place.
So whenever we multiply one digit times another digit, we just make sure we put it in the right bucket or in the right place.
And you'll see what I mean in a second.
So we did seven times four.
Well, we know that seven times four is twenty-eight.
We just simply wrote a two and an eight just like that.
But what did we really do?
And I guess the best way to think about it, this seven-- this is the seven in twenty-seven.
So it's just a regular seven.
Right?
But this four, it's the four in forty-eight.
So it's not just a regular four, it's really a forty.
Forty-eight can be rewritten as forty plus eight. This four right here actually represents a forty.
So right here we're not really multiplying seven times four, we're actually multiplying seven times forty.
And seven times forty isn't just twenty-eight, it's two hundred eighty.
And two hundred eighty, how can we think about that?
We could say that's two hundreds plus eight tens.
And that's exactly what we wrote right here.
Notice: this column-- I'm sorry, this diagonal right here,
I already told you, it was the tens diagonal.
And we multiplied seven times forty.
We put the eight right here in the tens diagonal.
So that means eight tens.
Seven times forty is two hundreds.
We wrote a two in the hundreds diagonal.
And eight tens.
That's what this two eight here is.
We actually wrote two hundred and eighty.
Let's keep going.
When I multiply two times four.
You might say, oh, two times four, that's eight.
But what am I really doing?
This is the two in twenty-seven.
This is really a twenty and this is really a forty.
So twenty times forty is equal to just eight with two zeros.
Is equal to eight hundred.
And what did we do?
We multiplied two times four and we said, oh, two times four is eight.
We wrote a zero and an eight just like that.
But notice where we wrote the eight.
We wrote the eight in the hundreds diagonal.
Let me make this a different color.
We wrote it in the one hundreds diagonal.
So we literally wrote-- even though it looked like we multiplied two times four and saying it's eight, the way we accounted for it, we really did twenty times forty is equal to eight hundreds.
Remember, this is the hundreds diagonal, this whole thing right there.
And we can keep going.
When you multiply seven times eight.
Remember, this is really seven-- well, this is the seven in twenty-seven, so it's just a regular seven.
This is the eight in forty-eight, so it's just a regular eight. Seven times eight is fifty-six.
You write a six in the ones place.
Fifty-six is just five tens and one six.
So it's five tens in the tens diagonal and one six.
Fifty-six.
Then when you multiply two times eight, notice, that's not really just two times eight.
I mean we did write it's just sixteen when we did the problem over here, but we're actually multiplying twenty.
This is a twenty times eight.
Twenty times eight is equal to one hundred sixty.
Or you could say it's one hundred-- notice the one in the one hundreds diagonal-- and six tens.
That's what one hundred sixty is.
So what we did by doing this lattice multiplication, is we accounted all the digits.
The right digits in the right places.
We put the six in the ones place.
We put the six, the five, and the eight in the tens place.
We put the one, the eight, and the two in the hundreds place.
And we put nothing right now in the thousands place.
Then, now that we're done with all the multiplication, we can actually do our adding up.
And then you just keep adding, and if there's something that goes over to the next place, you just carry that number.
So six in the ones place, well, that's just a six.
Then you go the tens place.
Eight plus five plus six is what?
Eight plus five is thirteen. Plus six is nineteen. But notice, we're in the tens place.
It's nineteen tens or we could say it's nine tens and one hundred.
We carry the one up here, if you can see it, into the hundreds place.
Now we add up all the hundreds.
One hundred plus two hundred plus eight hundred plus one hundred.
Or, what is this?
One thousand two hundred.
So you write two in the hundreds place.
One thousand two hundred is the same thing as two hundreds plus one thousand.
And now you only have one thousand in your thousands diagonal.
And so you write that one right there.
That's exactly how we did it.
The same reasoning applies to the more complex problem.
We can label our places.
This was the ones place right there.
And it made sense.
When we multiplied the nine times the seven, those are just literally nines and sevens.
It's sixty-three.
Six tens and three ones.
This right here is the tens diagonal.
Then we got six tens and three ones.
When we multiplied nine times eighty-- remember, seven hundred eighty-seven, that's the same thing as seven hundreds plus eight tens plus seven, just regular seven ones.
So this nine times eight is really nine times eighty.
Nine times eighty is seven hundred twenty.
Seven hundreds-- this is the hundreds place.
Seven hundreds and twenty-- two tens just right there.
And you can keep going. This up here, this is the thousands place. This is the ten thousands.
I'll write it like that. This is the hundred thousands place.
And then this was the millions place.
So we did all of our multiplication at once, and accounted for things in their proper place based on what those numbers really are. This entry right here, it looks like we just multiplied four times eight and got thirty-two, but we actually were multiplying four hundred-- this is a four hundred-- times eighty.
And four hundred times eighty is equal to three two and three zeros.
It's equal to thirty-two thousand.
And the way we counted for it-- notice, we put a two right there, and what diagonal is that?
That is the thousands diagonal.
So we say it's two thousand and three ten thousands.
So three ten thousands and two thousands.
That's thirty-two thousand.
So hopefully that gives you an understanding.
I mean it's fun to maybe do some lattice multiplication and get practice.
But you know sometimes it looks like this bizarre magical thing.
But hopefully from this video you understand that all it is is just a different way of keeping track of where the ones, tens, and hundreds place are.
With the advantage that it's kind of nice and compartmentalized, it doesn't take up a lot of space.
And, it allows you to do all your multiplication at once, and then, switch your brain into addition and carrying mode.
In the last video we had a three-dimensional surface, where the height z was a function of x and y.
And it gave us surface in three-dimensional space.
Now let's try to get our heads around what the gradient of a function of three variables looks like.
So the easiest one for me to imagine is a scalar field.
So what's a scalar field?
We now have the general tools to really tackle any multiplication problems. So in this video I'm just going to do a ton of examples. So let's start off with-- and I'll start in yellow.
Put the one up there. Eight times three is twenty-four. Twenty-four plus one is twenty-five.
But this eight is an eighty. So let's stick a zero down there. Eight times nine is seventy-two.
Put the one there and put the two up here. Seven times five is thirty-five. Plus two is thirty-seven.
Put the four up there. Eight times nine is seventy-two. Plus four is seventy-six.
Put the zero there, put the three up there. Five times nine is forty-five. Plus the three is forty-eight.
So the number is in the correct ballpark. Now let's do one more here where I'm really going to step up the stakes. Let's do five hundred twenty-three times--
Put the one up there. Eight times five is forty. Plus one is forty-one.
We have to multiply times the ninety and by the seven hundred. So let's do the ninety right there. So it's a ninety, so we'll stick a zero there.
When it was just an eight we just started multiplying here. When it was a ninety, when we were dealing with the tens place, we put a zero there.
Now that we're dealing with something that's in the hundreds we're going to put two zeros there.
And so you have seven-- and let's get rid of this stuff. Seven times three is twenty-one.
Put the one there. Stick the two up there. Seven times two is fourteen.
Put the one up there. Seven times five is thirty-five. Plus one is thirty-six.
Four plus six is ten. It's seventeen. And then we have one plus four is five.
Which whole numbers will make this statement true?
We have the statement here where we have some brackets are less than 7.
So we just have to figure out which whole numbers, if we put them here, are really less than 7.
So let's draw a number line and let's go up to 7.
When we talk about whole numbers, we're talking about the non-negative numbers or numbers that start at zero, and they aren't fractions.
Let me draw them on a number line.
Let's say we have this number line right here.
We'll start at 0.
You could go below 0.
There are negative numbers, but we're not going to concern ourselves with them right now.
So you have 0, 1, 2, 3, 4, 5, 6, 7-- I'll go up a little bit-- 8, 9.
Now we want all of the numbers that are less than 7.
That's what that means.
We could write it like this.
Question mark is less than 7, and what would satisfy question mark?
The hardest thing about these greater than or less than is remembering what the symbol means.
We have the smaller side pointing to the question mark, so that is the smaller number.
We have the larger side of the symbol pointing to the 7, so 7 is going to be the larger of the two numbers.
So what numbers satisfy that?
Well, anything below 7.
Any whole number below 7.
So if we look at 7 on the number line, what are all of the whole numbers that are below 7, that are less than 7?
Well, we have a 6, we have 5, we have 4, 3, 2, 1 or 0.
So you could put any of these numbers here and the statement would be true.
You could write 0 is less than 7.
That's true.
You could write 3 is less than 7.
That's true.
You could write 6 is less than 7, and that would be true.
You could not write that 8 is less than 7, so 8 would not satisfy this.
This is not true.
This is not true, so we cannot write that.
8 is greater than 7.
We need to calculate 9.005 minus 3.6, or we could view it as 9 and 5 thousandths minus 3 and 6 tenths.
Whenever you do a subtracting decimals problem, the most important thing, and this is true when you're adding decimals as well, is you have to line up the decimals.
So this is 9.005 minus 3.6.
So we've lined up the decimals, and now we're ready to subtract.
Now we can subtract.
So we start up here.
We have 5 minus nothing.
You can imagine this 3.6, or this 3 and 6 tenths. We could add two zeroes right here, and it would be the same thing as 3 and 600 thousandths, which is the same thing as 6 tenths.
And when you look at it that way, you'd say, OK, 5 minus 0 is nothing, and you just write a 5 right there.
Or you could have said, if there's nothing there, it would have been 5 minus nothing is 5.
Then you have 0 minus 0, which is just 0.
And then you have a 0 minus 6.
And you can't subtract 6 from 0.
So we need to get something into this space right here, and what we essentially are going to do is regroup.
We're going to take one 1 from the 9, so let's do that.
So let's take one 1 from the 9, so it becomes an 8.
And we need to do something with that one 1.
We're going to put it in the tenths place.
Now remember, one whole is equal to 10 tenths. This is the tenths place.
So then this will become 10.
Sometimes it's taught that you're borrowing the 1, but you're really taking it, and you're actually taking 10 from the place to your left.
So one whole is 10 tenths, we're in the tenths place.
So you have 10 minus 6.
Let me switch colors.
10 minus 6 is 4.
You have your decimal right there, and then you have 8 minus 3 is 5.
So 9.005 minus 3.6 is 5.405.
Brought to you by the PKer team @ www.Viki
Episode 11
She talks in her sleep now .
I'm never going to get sleep.
What the heck am I going to do ?
That's right
I spent the whole night with Seung Jo.
You mean that when I wake up, Seung Jo will be in the same bed as me.
Seung Jo.
It's time to wake up.
Did you sleep well?
Good morning.
It was a disaster sleeping with you last night.
Why?
Because of your terrible sleeping habits.
What are you talking about?
I'm a totally still sleeper.
Stop kidding me.
Wear this one.
I don't want to.
Are you just going to stare at me like that?
Ah, sorry...
You act like it's your own home.
Really?
Is that so? en español it feels different when I'm staying in Seung Jo's apartment. It feels like we're living together.
What kind of fantasy are you having now?
Don't overdo it.
He's never been late for work.
What's the matter? " Oh Han Ni and Baek Seung Jo spent the night together" Did they really spend the night together?
You know that girl from the tennis club.
Oh her?
Hey!
Baek Seung Jo! Since when did you...?
Lucky you
Tell us, tell us the details.
So how was it?
I said to give us some details.
Mother!
What's your problem?
Why are you calling me "Mother"?
You're embar . . .
Mother!
How can you tell so quickly?
The way you disguise yourself so that one can tell in one look... please do something about it!
And what do you think you're doing coming all the way to my school and causing all this?
Ha Ni, how are you feeling, after being sick and all?
I'm alright now.
Really?
That's a relief.
Alright...So how was it?
Huh?
How was it...?
Your voice is very loud.
It was nothing special.
Ah...really?
Seung Jo is that type of man?
That's unbelievable.
Oh yes!
Ha Ni, did you give him the chocolates?
Right! The chocolates!
The chocolates..
I lost the chocolates!
What do you mean you "lost" them?
It is a sign of love.
Where did it go?
What to do?
Baek Seung Jo's chocolates!
Do you see me volumizing the ends?!
Isn't it off the hook! I'm really good at it!
I'll make sure your hair isn't damaged and-- Welcome!
Bong Joon Gu...
What?
Slept together?
Baek Seung Jo and Oh Ha Ni?
My feet just dragged me here...
When I spoke to Ha Ni not long ago she didn't tell me anything like that.
There is no way Ha Ni won't tell me the big news.
Weren't you mistaken and went around in the rain for nothing?
From a kiss to sleeping together...that's great!
Now everything is over.
It's over.
Ah... Joon Gu... Joon...
Nothing happened you said?
Yeah...
A man and a woman spent a whole night together, How is it that nothing happened?
Nothing happened.
Can I tell her?
Jung Ju Ri
You're early today.
The school's a bit talkative today.
You know nothing happened.
True..
There is no way.
Seung Jo...
Do you want to get dinner together after class?
I think I'm going to die because of this upcoming test.
Min Ah, you don't study for exams?
There's no way I can study for all 12 subjects.
If there's no way for Dok Go Min Ah, then it's absolutely impossible for Oh Ha Ni.
Fine, I've made a decision.
I'm only going to study for English.
Only English?
Why?
It's the only subject I'm taking with Seung Jo, so if I fail that as well, then it's all over.
No matter what I get on the other subjects, I'm definitely going to pass English.
Oh Ha Ni, you are now in study mode.
Ah!
I don't have much time. I'm leaving.
It's raining...
Aigoo.
Why is it raining like this?
Oh! Really.
Oh, aren't you the one who works at the restaurant?
Oh right!
What are you doing here? Are you waiting for someone?
Looks like you're not in a good mood.
It's not that I'm in a bad mood.
I am trying to give up my love
My heart feels like it's breaking apart.
What do you mean give up on love?
You shouldn't give up on love.
No, certainly not.
I've only been following for the past few years.
I never even went on a date with her.
This is a very serious matter.
Have you tried confessing your feelings?
Confessing?
Oh, so you don't know how to confess.
Look
This is how you do it.
You grab the girl like this.
You pull her like this, push her up against a wall, and when she looks up, then you say,
" If you can forget me then go ahead," and suddenly kiss her.
If you do it like this the girl won't even be able to think
When they're flustered, they'll suddenly have feelings for you!
That's how you confess.
That's right! A confession.
I won't die from it, so let's try it.
Hyung-nim, thank you!
Oh right!
Timing is very important thing, timing! Brought to you by the PKer team @ www.Viki
Ha Ni, you're here!
Your face doesn't look good.
Even when it's exam week, you two look fine.
Usually, you're supposed to take tests with your every day capabilities.
If you try to study it all at once, then how could they test what you've learned?
Then the test would just be some kind of photographic memory test or something.
Isn't that right Seung Jo?
How did you do on the other tests?
So so.
I will really do my best on the test, so that we can attend the same class next semester together...
This English test is famous for being hard.
What are you going to do?
Weren't you hitting it pretty close in the last test too?
Ha Ni, it would be better if you attend this same class for another year.
You know that girl you saw before,
Ji Yeon, who Seung Jo and I were tutoring.
She's going to be attending our school.
How about you attend the same class next year?
Ha Ni, why are you glaring at me like that?
Your eyes will burst. This is the first time I'm taking a test together with Seung Jo.
Why are you not finishing?
I'm done.
There is still 40 minutes left!
Already?
Seung Jo, wait for a second.
Let's go out together.
It was surprisingly easy, right?
Oh, you didn't even write anything! What are you going to do?
I came because
I have something to tell you.
Oh, really?
What is it?
Even if you don't tell me anything,
I know everything.
You probably don't know how much my heart ached that night.
But no matter how much I thought about it, it didn't seem right.
To be honest,
I can't bring myself to give up on you Ha Ni.
But still, once a guy pulls out his sword, he's got to see it till the very end.
I'm just going to be understanding about everything that's happened.
Ha Ni, I thought about giving you up, but it won't go the way I want.
You don't have to be sorry.
How is it your fault?
It's that fool Baek Seung Jo that's trying to seduce you!
Quite soon
I'm going to beat the crap out of that Baek Seung Jo.
So, forget everything and let's start over,
Ha Ni.
Ha Ni?
Ha Ni, are you sleeping?!
Hey!
Hey, Bong Joon Gu.
Hurry.
What?
Hey, Bong Joon Gu. What are you trying to start over?
That night, nothing happened between them.
He didn't touch a hair on her.
Really?
Yeah, really.
Man, that Baek Seung Jo is a real gentleman!
Wow, you're even complimenting Baek Seung Jo.
Ha Ni!
Let's go!
Oh Ha Ni.
Let's start dating.
Hey, Gi Tae, when did you arrive?
You've come back?
Hey, go and practice. What are you saying so early in the morning? Ha Ni's got someone.
It's not a joke.
I am Kyung Su's friend, and starting next semester
I'll be attending the same school
I'm Kim Gi Tae.
Nice to meet you.
Since you guys are here already, say hello. He is your Tennis club Sunbae,
His name is Kim Gi Tae.
Greet him.
- Hello.
- Hello
If you're done, go and practice Go, go.
You're a funny guy.
Since when do you know Ha Ni, that you want to go out with her as soon as you met her?
Haven't you heard?
Oh Ha Ni and Baek Seung Jo.
I know.
Ha Ni likes Baek Seung Jo, right?
Ever since high school, I've watched over those two.
Huh?
Then, why?
Especially since the two of you aren't dating, that means that I too, have a chance.
Yes? Suddenly...
Was it too fast?
OK, good.
This week-end, let's go on a date.
You need to get to know me as well.
That's how it's going to be.
Then, see you later.
I'm leaving.
Before leaving, let's have a game.
Next time.
She totally froze up.
Hey Ha Ni. Isn't he really good looking?
When we first joined this school, Gi Tae and I were very popular with the female Sunbaes,
Him for his looks, and me for my charisma.
But that Gi Tae, to you . . .
You punks! You won't go practice?! It feels weird.
This is amazing.
Is it real?
Did it really happen?
Did he ask you out?
Isn't this the first time in your life?
You've always been the one doing the chasing!
I heard he was a sunbae?
Who might he be?
I'm curious!
How is he?
Is he tall?
What about his looks?!
You're embarrassed!
He must be good looking.
Hey, Baek Seung Jo knows too?
Right right.
Does Baek Seung Jo know too?
I'm saying, Ha Ni got confessed to by a really cool guy.
Really?
So?
So if you don't do something, Ha Ni and that guy might get together...
You're not worried?
You sure do get excited over nothing.
That's what you wanted to say?
I'm not worried.
Oh? really?
He wants to date you?!
Yes.
But it's not a big deal.
Omo!
Who would like you? How can he be just like his brother!?
The thing I've been fearing has finally come.
Someone as cute as Ha Ni...
I knew I would lose her like this soon enough.
This is all because Seung Jo is dragging his feet.
Stop it dear.
Don't get so worked up.
Stuff like this is all the free will of the person.
What kind of guy is he?
It's a sunbae and he's one year older than me.
We're in the same grade.
Sunbae?!?
My god the most dangerous person is a male Sunbae!
I don't really remember his face.
Ha Ni, haven't you been tricked by a player?
You're all naive and go around smiling at any old guy right?!
No, dad.
I'm not like that.
I have to do whatever I can.
I can't leave it like this. It's gotten much bigger than I expected. Today has been eventful.
Hey you.
I'll see you later.
Oh Ha Ni.
Why did you come...?
You can't forget my face.
So I came to show you my face.
Hey, Baek Seung Jo is working part time at a restaurant?
Huh?
Yes.
Last time I went, you were there too.
I heard that you went there everyday.
I went a few times
You know, I'm pretty damn smart too.
Of course I wasn't as visible due to the all around perfect Baek Seung Jo.
Then are you approaching me because of Seung Jo...
Of course I was provoked a bit by Baek Seung who's good at everything whether it's studying or tennis.
As I was worrying about Baek Seung Jo, it's true that I saw you following him around everywhere.
Suddenly without me even realizing it, little by little,
I started looking at you.
Ah, yes.
You would still step forward despite being rejected by Baek Seung Jo over and over again.
You could say I was touched by that, Oh Ha Ni.
Anyway I was pulled towards you.
Hey, just go out with me.
Don't waste your precious youth on Baek Seung Jo, when you don't even know if he will turn around towards you.
Have an amusing campus life with me.
What do you think?
Even so, I...
I was wondering who it was. It's Gi Tae Sunbae!
Oh, Yoon Hae Ra.
Do you know each other?
I met him often during the tennis matches.
But do you know each other?
I am going out with Oh Ha Ni.
Ah, that's not true.
So, you're going to give up Seung Jo now?
Of course!
Don't just say whatever you want!
Before Kyung Su Sunbae, and now Gi tae Sunbae.
You're so popular Oh Ha Ni!
You suit each other well.
See you later at the club room.
Ok.
See you later.
Sunbae, continue what you were doing.
Make sure to keep it moving straight forward!
I'll be going first.
See you later.
Oh, I can't believe it!
His face is about a... 85%
He seems to have a bright personality and he's enthusiastic.
If he's a law major...
A future politician or lawyer?
Mother.
Oh!
This...
Did you possibly go to school to see that sunbae?
He's Seung Jo's rival, so we need to analyze him real well and plan something.
The way I see it, this guy is much cuter than Seung Jo.
What to do?
If this guy takes your heart,
What would I do?!
Mother.
Not to worry.
I will always think of Seung Jo only.
Ha Ni.
I'll go reject him right now!
I'm deeply touched!
Oh wait! No, don't go.
Ha Ni you shouldn't reject him.
Yes?
Let's try to make Seung Jo jealous.
Eh! That's impossible.
No, no.
He may be acting so cocky all the time, but just wait and see.
Seung Jo will definitely feel himself being pulled towards you!
Because you're always next to him, he is relaxed and doing other things!
But if you suddenly show him another side of you, he will notice his feelings for you.
Will it be alright to use such a dangerous plan like this? Will it be okay?
Will Seung Jo really be jealous?
You don't have to be thinking like that.
Do well.
Gi Tae sunbae is smart, and is very popular with the ladies.
But seeing that he has an interest in you, he does have really unique taste then.
That's a relief.
Then again, one man's trash is another man's treasure.
What are you talking about?
Though I'm like this, aside from you, I'm quite popular with the guys.
Maybe he's got a bad eye or a real weirdo.
That person is just as smart as you are and as good looking as you.
Most of all, compared to you, he is really nice to girls.
I'm in a good mood, because Ha Ni thinks of me like that.
Well Baek Seung Jo, seeing how it is, why don't you pass Ha Ni on to me?
So it was you Sunbae.
There's no need to pass her on. It's not like she belongs to me.
Do as you please. What did he say?
I can't believe him.
Gi Tae Sunbae
Oh yes princess?
Where are we going on this Sunday's date?
I'm okay with anything.
Whether it's the mountain or the sea, I'll go anywhere.
Sunbae, Congratulations. I'm serious!
Seung Jo! If it goes on like this, I'm really going to cheat on him! I won't regret it!
What would you like to order?
One ice tea.
Do you want to kill time with that again?
Today, I didn't came here to see you.
I'm here for an other appointment.
Ha Ni, I'm sorry.
On the way here, there was a traffic jam.
Did you wait long?
No, I just arrived here, too.
Oh, hi Baek Seung Jo.
One coffee for me, with ice.
Yes.
Ice tea and iced coffee.
Wait for a moment please.
Today, it's finally the much anticipated Date day.
The weather today was really nice!
What would you like to do?
Well, I don't really know.
Perhaps, is this your first date?
Huh? No way.
I've gone on dates before.
With Baek Seung Jo?
Yes.
Then again, it's our time to have all the fun in the world.
From now on, I'll take you out a lot.
Yes.
Where should we go?
There's this new rollercoaster, which is really fast. Should we go to the amusement park?
It sounds fun!
What should we do afterwards?
Watch a movie at the drive-in theater and eat something delicious.
Oh I totally like it, the drive-in theater.
I've never been there before.
Excuse me.
Then how about we go to a nice park and ride bikes?
Oh I like that!
Oh let's do that first, then let's go to the amusement park, and the drive-in theater.
Enjoy.
Have you gone to the Namsan Tower?
There's a place there, where you can write your names on a lock and if you do your love will stay true!
Watch your head.
Here, sit.
Oh, let's take another one. Brought to you by the PKer team @ www.Viki If he's this nice to me...
Ha Ni!
Did you have a nice time?
Yes.
Here.
It's been a long time since I had this much fun.
Why is that?
Is it because when you're with Baek Seung Jo, you're nervous?
Well.
How many years have it been that you liked Baek Seung Jo?
What?
More or less 4 years.
Since High school.
I guess this will be a prolonged war for me, then.
What?
No...
If you loved him for 4 years...
Just because I've suddenly appeared before you, doesn't mean your heart is suddenly going to change.
Even if you only think of me from time to time,
I'm satisfied with that.
He's 180 degrees different from Seung Jo. I expected it, but Seung Jo eventually didn't show up.
Ha Ni, let's go!
And if I continue along with this, I'm only using Gi Tae sunbae.
So, my heart aches.
I must end it.
What are you doing?
Ah, Sunbae.
What are you thinking about in a place like this?
Were you looking at something?
No.
You were looking at Seung Jo from here?
Sunbae, I . . .
Oh Ha Ni!
Forget Seung Jo already.
Sunbae, I have something to sa-
Come here.
Ha Ni.
S-sunbae.
- No...
- What is this?
Sunbae!
I think I've seen you before.
What are you trying to do to Ha Ni?
Joon Gu don't!
I was wondering what fool kept hanging around my Ha Ni. You little fearless...
If you compare the time hanging around, then you've done it much longer.
What are you saying? What do you know?
Yes, Bong Joon Gu.
Why don't you give up already?
What?!
Stop it already!
What's going on?
What do you think you're doing in the library?
You two aren't fighting over Oh Ha Ni, right?
Hey Baek Seung Jo, this has nothing to do with you. So, back off.
Despite you guys fighting or shedding blood...
It doesn't really matter, but still.
The only person Ha Ni likes is me.
So isn't it a waste to fight over it?
Seung Jo.
My mother said for us all to eat dinner together.
Let's go.
Slow down.
Baek Seung Jo, you have quite a lot of confidence.
What?
The only person Ha Ni likes is me?
My heart could have changed. You haven't thought about that?
Never.
But, you were a little jealous, right?
If you're going to put on a show...
Why don't you use your brains a bit more.
I can see right through everything you and mother are doing. Dummies.
He already knew everything...
He really can't be tricked.
See how nice it is for us to all gather like this?
You like it too, right Seung Jo?
Living alone I know exactly what you eat.
No matter where you go, eating at home is the best.
That's right.
No matter which restaurant I go to, nothing compares to a home cooked meal.
I thought you said Dduk Bok Gi was the best thing in the world?!
Stupid.
But hey Su Chang, you aren't eating much today.
A new game is coming out so he's been pulling a lot of all nighters, so he's really tired.
Ahjusshi, I'll get some more soup for you.
No, his doctor told him not to eat too much.
No matter how enjoyable your work is, make sure you take of your health first.
Good health is the best thing!
Of course.
Gi Dong shi, you take care of your health too.
Of course!
Healthy is as healthy can be!
They ate up 3 bowls of Bool Nak porridge!
There's no way.
Seriously!
I'll just be leaving then.
I thought you would sleep here tonight and then go...
Seung Jo, I have something to tell you. See me for a bit.
Yes.
You are now an adult, too.
What do you think about your future plans?
It's been some time since you left the house.
I feel like it's about time you start clearing up your thoughts.
No, not yet.
Seung Jo.
I wish you would manage my gaming company.
First, as my right hand man.
Next, as a successor of the company.
What do you think? It's not that you're asking me what I think, but that I should do as you say, isn't it?
So you're just deciding my future as you wish.
No, that's not it.
If you're done talking, I'll get up first.
Okay, go.
I'm going.
Okay.
Go safely.
Just as the holidays were approaching...
Seung Jo suddenly disappeared.
He didn't show up at the tennis courts and even stopped part-timing at the family restaurant.
Where could Seung Jo have gone?
Okay, I'm taking it.
One, two, three... Say cheese!
The trails around here are really nice.
We'll be preparing the bbq while you're gone.
Thank you.
Good-bye.
Hyung!
I've come.
Sticky gum Ha Ni has found Seung Jo's new part time job!
Eun Jo, you came by yourself?
What about mom and dad?
Dad couldn't come because of work and mom said she couldn't leave dad alone.
Mother was really very disappointed.
It's obvious.
The water is really good! The water is really famous, seriously!
Aigoo, Ha Ni!
Ha Ni has come!
Well then, if you need anything else, just call me.
Rest for now.
Yes.
Why did you come so late?
Ah, this must be Eun Jo.
Just as I thought, it was you Sunbae.
Why don't you just open up your own broadcasting company. What are you talking about?
You didn't tell other people too, did you?
Seung Jo!
Have you been well? Oh Eun Jo is here too!
Oh Seung Jo, have you been doing well?
Our villa is right over there.
I want to invite you over for dinner.
Want to come?
You're coming, right?
Eun Jo, hello.
Kyung Soo sunbae! Just to me?! What kind of secret information is this?!
I have something to tell you, come this way.
Ha Ni, Ha Ni.
I'm thinking about closing the deal with Hae Ra this time.
Do you think, you can do that?
So, I really need your help.
You and I have to join forces to stay afloat.
First off, I need you to keep staying near Seung Jo and stop him from approaching Hae Ra.
Sunbae it's Hae Ra that is approaching Seung Jo!
Has Seung Jo ever approached Hae Ra?
Just becoming a couple is important.
I'm going to ask to play a couple game.
And then you can just become a couple.
- You and Seung Jo.
Me and Hae Ra.
- Ay...
Is it that easy? I've tried it this whole time and it's still yet to happen.
Don't worry.
I've planned and prepared everything.
Give me your hand.
Let's try our best in order to achieve our loves!
I feel uneasy for some reason.
What are you doing? I said, let's do fighting!
Fighting.
Hello all my youthful visitors.
You've all come here in order to create memories of your youth.
Will checking out the scenery here and there create memories?! No it won't.
So the couple games start now!
Fool.
The way to play this game... Take a look at the map and see the numbers 1-7?
Those are all places.
The couple that gets a stamp from all those spots first, wins the game.
This is the stamp!
It's not just a treasure hunt...
But a stamp hunt!
Then we have to decide on your partner.
Your partner will be decided fairly...
We'll use this ladder game method.
Why isn't Seung Jo here?
And really it couldn't be helped...
But I will be joining this game in order to keep all of you safe.
It really couldn't be helped.
What the?
Eun Jo, haven't you seen Seung Jo?
I don't know.
Where the heck did he go?
Here you go, this is it.
Hae Ra, what number? Ah! Number 3!
Then I'll be 8. Everyone pick. Brought to you by the PKer team @ www.Viki
I'm dying here.
It's like some villas or something.
Let's see.
Is this here?
I can't tell.
I'm sure it'll show up eventually.
Ha Ni, just wait! I'll definitely protect you!
From now on, I'll never send you off alone!
Let's go.
Why must I do this with Oh Ha Ni?!
Oh! It's there, it's there!
Come quickly!
Wow it seems we're the first ones! Right, right, right?!
Shut up.
Ya, let's do this on good terms.
Why are you being like this too?
Either way I can't even be with Seung Jo after coming this far.
Even elementary kids don't play games like this!
Do your legs hurt?
I'll piggy back you.
Try getting on my back.
Oh really!
Did you set this up?
You picked 3 first.
How could I cheat that?
It's a bug.
I want to quit!
It's not fun.
Who said we're doing this for fun?
The great Yoon Hae Ra can't lose to Oh Ha Ni, right? Seung Jo wouldn't like that either.
We just need 6 more.
Let's hurry up and find it then.
Where can it be?
You're the one that hid the stamps, Sunbae. So how could you not know, Sunbae?!
Since the trees all look the same, it's a little confusing.
What is it?
Since we just got the 4th stamp we just need to go...
Did you hear that?
Just now, that sound...
Wasn't that the sound of a wolf?
Idiot.
Wolves went extinct in our country.
Then...a bear!?
I think I heard Ha Ni's voice.
Thank god! It's probably not following us, right? It is not a relief!
Where are we?
It's alright Eun Jo.
Noona will try to figure out our path.
Don't worry.
Are you alright?
Yes, I am alright Eun Joo.
Stupid!
But...my hat disappeared.
It's my most cherished.
Stay there.
I'll come down there.
Yes.
Eun Joo, be careful!
Where are we supposed to go?
How did this change?
Last night there wasn't any water.
Strange.
Hey, Hae Ra, let's go together.
Oh, hey, Hae Ra!
Let's go together!
Together!
I found it!
The stamp, the stamp!
Where?
Oh, that?!
The stamp!
Let's go, hurry!
Gosh!
This is why there's no reason to like you.
It's alright, I'm going.
Hey Hae Ra...
Seeing a guy like this, doesn't your motherly instincts...
Isn't that Ha Ni's hat?
Did something happen to you, Ha Nl?
Just wait there awhile.
I'll come and rescue you.
Oh that!
Alright this.
Aigoo!
Aigoo!
Got it.
Got it.
Alright, alright!
Oh, Seung Jo!
Oh, really!
Seung Jo.
Seung Joo, give me water..
What happened to Sunbae?
I don't know!
His body build is completely useless!
Seung Jo, the mountains here are pretty rough.
There are animals making noises in the mountains.
Anyways, it was really hard.
Where are Eun Joo and Ha Ni?
They were the first ones to leave.
They're still not back?
Give me water, water...
It got cold.
I am hungry too.
But other than that, the problem is not finding our way back.
There's still no signal.
Cell phones must not even work here.
Here.
Baek Eun Joo!
You are amazing.
That's it!
Preparation.
If you are prepared you'll be happy.
Analogy...
What is it?
Just put this over yourself.
Our Eun Jo sure is reliable.
It feels like being with mini Seung Jo.
First we need to find the canyon.
If we follow the path we came from, then we're going to be able to find a way out.
If we wait, won't Seung Jo come?
You are really stupid!
How will he know that we are here?
Are you cold?
You can hold it.
You're so reliable.
The sun is going to go down, and my feet are killing me. Damn it!
Anyway, I need to go.
Aigoo!
Ha Ni, I am really sorry.
I can't go up in this condition.
Like this..
Like this, definitely
This can't be!
Aigoo!
No!
No!
No!
That can't happen!
Ha Ni!
I love you!
That sound, there it is again!
What do we do!
It's probably a village dog or something!
Isn't that Ha Ni's voice?
Ha Ni!
Ha Ni!
It must be coming this way.
What should we do?
Get behind me.
Hyung!
Eun Jo!
Hyung!
Seung Jo!
Won't anyone help me?
I would be grateful if someone came to help me.
Oh.
Hey.
Grab this.
Isn't that voice Baek Seung Joo?
Hurry and grab this.
Hey.
Why are you butting in?!
Who the hell are you to save me!
Screw off!
Really?
Then, I'm leaving first.
Hey, hey!
Where are you going now?
Fine, we have to save Ha Ni.
Calm down, she's safe. She went to the camp first.
Rea...Really?
It is a relief, you really did well.
It is really a relief!
Hey!
Then... would you help me?
Man I'm dying.
Shut your mouth.
I can't show anyone this side of me.
Especially not to Ha Ni.
Got it?
Anyways, nobody knows that you're here.
Don't worry.
Man, I'm a complete mess.
How can I show this side of me to Baek Seung Jo.
Baek Seung Jo!
I'm going to return the favor.
That's not very appreciative.
Oh...Seung Jo!
Did you come out for a walk?
Yes.
You should've come alone.
Huh?
Saying that you like me and stuff.. don't you know how I feel?
How you feel...
There's no way someone like me...
It was a dream.
I was surprised.
No wonder
It was playing out so smoothly.
If I knew it was a dream...
I should have dreamed a bit longer before waking up.
But... the feeling of his lips Brought to you by the PKer team @ www.Viki
For the first time I want to do something.
I'm going to apply for medical school.
I have a dream too.
Tell me that dream.
That you want to do something with me?
I'll make it come true.
Did you grab your wallet?
A new wife, I'm sure you want to call him honey.
Let me choose what I want to do with my life.
Baek Seung Jo
I've decided to become a doctor.
I will not inherit father's company.
Father!
Father, what's wrong!
Honey!
Are you okay?
This is the first time you want to do something right?
If I do this, Dad will be happy. I have no interest in it but at least he'll be happy.
Add and simplify the answer and write as a mixed number.
So we have two mixed numbers here.
We have a whole number part and a fraction part.
We need to add them.
Now, there's two ways to do this.
You could convert both of these into improper fractions, then add them, and then convert that back into a mixed number.
Or you could just look at this and say, well, you know what?
17 and 2/9 is the exact same thing as 17 plus 2/9, and then 5 and 1/9 is the exact same thing as 5 plus 1/9, so 17 and 2/9 plus 5 and 1/9 is the same thing as 17 plus 2/9 plus 5 plus 1/9.
These two statements are completely equivalent.
And we know that when you're just adding a bunch of numbers, it doesn't matter what order you do it in, so you can swap the order.
So you could say that this is the same thing as 17 plus 5 plus 2/9 plus 1/9.
And we could do this in any order.
And we know what 17 plus 5 is.
We've done that before.
17 plus 5 is 22, so that part right there is 22.
So we have 22 plus-- now what is 2/9 plus 1/9?
Well, they have the same denominator, so it's going to be over 9, and then you add the numerators.
2 plus 1 is 3.
So it's 22 plus 3/9, but this can be simplified.
Both the numerator and the denominator are divisible by 3.
Divide the numerator by 3, you get 1.
Divide the denominator by 3, you get 3.
So this is 22 plus 1/3, which is the exact same thing as 22 and-- let me write it in that other blue color-- which is the exact same thing as 22 and 1/3.
A farmer grows 531 tomatoes and is able to sell 176 of them in three days.
Given that his supply of tomatoes decreases by 176, how many tomatoes does he have remaining at the end of three days?
So he starts with 531 tomatoes let me give myself a little more space to work with -- he starts with 531 tomatoes and he is able to sell 176.
He is essentially going to subtract the 176 that he is selling.
If we want to figure out how many he is left with, we are going to subtract 176.
That's how many he sells in three days.
They're asking us: how many does he have left at the end of three days?
We just have to subtract those 176 from the amount he grew.
It turned into this straight up subtraction problem.
Lets see if we can do it.
If we go straight to the ones place right over here and actually let me do it in parallel because i think that might be interesting over here.
I'm going to do it the way you traditionally do it here on the left and then I'm going to show you what's happening here on the right.
So 531 is the same thing as 500 + 30 + 1 and if you subtract 176 that is the same thing as subtracting 100 and subtracting another 70 and subtracting another 6
I wrote it this way because the 5 in 531 is the same thing as 500
The 3 in 531 is in the tens place so it's really representing 30 the 1 in 531 is in the ones place so it represents one and now it'll be a little bit clearer what we're doing when we're borrowing or regouping on this problem right over here and so let's start off with the ones place one is less than 6
It'd be great if we can regoup some of the value from the rest of the places so we can go straight to the tens place the tens place we can borrow or regroup ten from it so if we take ten from here this becomes 20 we're going to take that 10 and add it to the 1 so this will become 11 we just added 10 we moved over 10 from the tens place to the ones place if you look at it over here you could say:
Look! we're taking 10 from the 30 that becomes a 20 and then the 1 becomes an 11 the way when I was first in school people'd say, "You borrow one from the three" and you kind of just stick that one right over here but what you're really doing is you're taking a 10 from a 30 and making it into a twenty and you're getting a- you're adding the ten to the one getting 11 but either way you'll end up with 11 in the ones place and now you can subtract 11 - 6 is 5 now we go over to the tens place in the tens place we now have 2-7 which is really representing 20-70 well we - thats 70 is bigger than the 20 so we want to add some more to the tens place well we can go the hundreds place to find some more value to regroup so let's see if we can do that we have 500 here so what happens when we take a hundred from that so we're just left with 400 from here and we take that 100 and we put it in the tens place so instead of 20 we now have 120 if you look at it on this problem since we are using the places here we're going to take 100 from the 500 and have 400 and then we're going to take that 100 that we took and take it to the tens place well 100 is 10 tens so we're going to add 10 to this so this is going to become a 12 once again, the way- the kind of more mechanical rope way of thinking about it is that -oh- you took one away from the four and you stick that one in front on the two but you're really taking a 100 from the 500, making it 400 and then adding that 100 to the 20 here and making it 120 but your writing here is a 12 because it is 12 tens you're at the tens place so let me write it down this is the ones place this is tens place and this is the hundreds place so now that our numbers on top in the tens place is bigger than the numbers on the bottom we can subtract so we get 120-70 that is 50 or 12 minus 7 is 5 5 is in the tens place so it's really representing 50 let me circle it with the same colour so you recognise that this 5 is representing 50 then finally we're in the hundreds place so 400 -100 is 300 4-1 is 3 but this 3 represents 300 this 5 represents 50 this 5 represents 5 so we're done we get 355 the farmer is left with 355 tomatoes at the end of 3 days or 300+50+5 tomatoes.
Nice people live here - and smart: well, mostly.
Mm what's this? [Metalloc noise]
Oh, this is Badoo.
Badoo is very happy today.
You're so right!
I just sold my hillside of worthless trees to a company that logs illegally.
They pay really well.
That's the easiest money I've ever made!
I'm rich!
I'm rich!
[electrical saw]
[Squirrel]
Ah.
[Off voice]
That's right, little girl.
Those trees are history.
[Sawing noises - the squirrel yelps]
It's raining hard.
It's been raining hard for four days and four nights.
Early monsoon?
No matter.
Badoo still has some money left.
He's going out to eat.
Here is Tita's food stand.
How about a nice rice dish and an extra large soft drink?
[munching]
[Badoo] .......
When you're rich, you don't have to cook.
That garbage will really block the drain [1:49]
We're asked to compute 3,060 divided by 36.
We want to figure out how many times does 36-- I don't need to write it that big.
We need to figure out how many times does 36 go into 3,060.
Now, this is interesting because we're dividing by a two-digit number, by 36.
We're going to see in this video that the process is the exact same way.
There's just going to be a little bit more mental estimation going on, but we'll do it explicitly here, so hopefully, it won't be too bad.
So we first look at 36, and we say, well, does 36 go into 3?
Well, no.
3 is smaller than 36, so it won't go into 3.
Does 36 go into 30?
No, 30 is still smaller than 36, so it won't go into that.
Does 36 go into 306?
Well, sure.
306 is larger than 36, and if we were to estimate it, 30 would go into 300 ten times, but this is larger than 30, so it's going to go fewer times.
Maybe it's 9.
I'm not sure.
Let's try it out.
Let me try it out over on the side.
What is 36 times 9?
And this is kind of the art of doing these problems when you're dividing a two-digit number into something.
So 6 times 9 is 54.
Regroup, or carry the 5.
3 times 9 is 27, plus 5.
27 plus 5 is 32.
So 36 times 9 is 324.
That's still larger than 306, so we're going to have to go 36 less than that, so we're going to have to do eight times.
So we're going to have to go into it eight times.
And remember, the way I thought about that is I said my first guess was maybe it goes in nine times, but when I tried out 36 times 9, that was still larger than 306.
That got me 324.
Eight times should work, because if you take 36 away, if you only do 8 times 36, that's going to take us below 300.
342, 136 away from that, or another way, 324 minus 36 is going to get us below 300.
So let's try this out and just make sure.
8 times 6 is 48.
Put the 8 there; carry the 4.
8 times 3 is 24 plus 4 is 28.
So 8 times 36 is 288 and it fits.
It's less than 306.
9 would've been too much.
It would've been greater than 306, so now we can just subtract.
We can't just subtract 8 from 6.
We have to do a little bit of regrouping.
Let's get a 10 from the ones place right here, but we can't borrow anything from here or regroup anything from there, so let's go to the hundreds place.
Let's take 1 from the hundreds place, and so this will become a 2, and then this 0 here will become a 10.
Another way to think about it is this is now 10 tens.
We took 100 from there, and we're now writing 100 as 10 tens.
Or another way to think about it is you borrowed a 1, or you took a 1, really.
You took a 1 from the hundreds place.
That made it into a 2, and then you put the 1 out in front of the 0.
That's kind of the process way of thinking about it.
Now, we have this 10 here, and now we can borrow from this 10.
So let's borrow from this 10.
So this 10 can become a 9.
1 is really taken from it, and then this 6 becomes a 16.
Because if you think about it, this 10 was really 10 tens.
It's in the tens place, so when you put a 10 there, it really means 10 tens.
So if you take 1 away from it, this is actually now 90, and we have 10 to give to this 6, and 10 plus 6 is 16, so that's what we're really doing.
But now we're ready to subtract, so we have 16 minus 8 is 8, 9 minus 8 is 1, and 2 minus 2 is 0.
So we have 18 left over, and now we can bring down this 0 right here.
Bring down that 0.
So how many times does 36 go into 180?
And once again, this is going to be estimation.
It's not going to be six times.
6 times 30 would be 180.
6 times 36 would be too big, because 36 is bigger than 30, so let's try 5.
Let's see if 5 works.
So let's see.
5 times 6-- and there's a little trial and error here sometimes.
5 times 6 is 30.
Put the 0; carry the 3.
We don't need that.
That's from last time.
5 times 3 is 15 plus 3 is 18.
It looks like it works out.
You subtract 180 from 180, your get zero, so we have no remainder.
So we're left with 36 goes in 3,060 eighty-five times.
So this is equal to 85.
"Kids react to viral videos."
"This episode:
Nyan Cat"
Oh my God!
Look at the kitty
What is this?
I'm crying
Alright, that's annoying.
How long is this?
Now what are you going to do?
Say something else besides "Meow"
Jeez, cat!
What's the point of this?!
Shut up!
She's adorable!
And she's dancing in the sky.
I just want that kitty.
No, don't go away!
I'm lost.
I'm kind of glad that's over now.
Why do people make this?
That was the funniest video I've ever seen.
"Question Time"
[Fine Bros]
"So, what was happening beginning to end?"
Really?
[Fine Bros] "Yes"
There was a cat, who was farting out a rainbow.
It was running across space pooing out rainbows.
It was going like this.
Meowing
[Fine Bros]
"So you see the cat's face and tail and the rainbow, but what about the body?
[Fine Bros]
"What does the body look like?"
It's a Pop-Tart!
It's a cupcake.
It's like grey part of the cat is the cake and then the pink part's the icing.
A doughnut and then the head looks like a heart.
[Fine Bros]
"Did it do anything else?"
Not that I saw.
No.
I didn't see anything else, I was too busy going, "Oh, when is it going to be over?"
[Fine Bros]
"What were you thinking while watching the video?
What is this?
What is this, I don't get it.
Why was he going "Minnie Mouse" so much times?
God, I would rather shoot myself.
[Fine Bros]
And why was it just showing the same thing over and over and over again?"
I don't know, it wanted to be funny?
Because it's trying to confuse me.
Cause' they couldn't find what else to play on there?
Or maybe because that's how the song was?
Or maybe they want it to irritate people?
Because I think they wanted it to be a pattern.
[Fine Bros]
"And why would someone want that?"
Because patterns aren't boring.
[Fine Bros]
"Doesn't that get boring?"
No!
It's just a kitty, a cute little kitty, people.
She's so adorable.
Didn't you want to kidnap her, people?
"If this video was just playing, forever, how long could you actually sit there before you just walk away?"
I was ready to walk away before that was even done.
I could not sit there longer than that.
30 seconds and then leave.
Less than ten minutes.
Until I die.
[Fine Bros]
"Someone actually uploaded a six hour version of this.
What?
[Fine Bros]
"Someone actually uploaded a six hour version of this.
(laughing)
[Fine Bros]
"Someone actually uploaded a six hour version of this.
What?
How do you upload a six hour version on Youtube?
I wonder how long that took to upload.
[Fine Bros]
"What do you think about that?"
I think they're awesome.
Three words for that person:
Get A LlFE!
Oh no, no, something stupid.
[Fine Bros]
"If you had to give this cat a name, what would you name it?"
Mister Irritating Pants
Rainbow cat Crazy cat
Puffball
Rapunzel.
Cute, snuggly, and soft.
[Fine Bros]
"Why is this video so popular?"
Well, it is funny but what's the point to it?
Because society is crazy.
Cause' they don't have a life.
Any video that's catchy or funny or interesting to watch will be viral.
Why do they love it?
[Fine Bros]
"I was gonna ask you!"
Why do they love it?
I wanna ask you! [Fine Bros]
"Ask them."
Why do you love this, people?
I want to know.
[Fine Bros]
"Did you like the video?"
Yes.
It actually kinda looked cool because it looked like a game and stuff.
Funny at first, then it gets annoying.
I'm surprised my brain didn't go into a trauma.
It was kinda irritating, but funny that it was irritating.
I wanna see the amount of dislikes on the video so that I can join all those wonderful people.
[Fine Bros]
"And would you ever watch this again?"
No, it's....it's....it's nonsense to me.
No.
I don't think so.
Would I ever watch something that's totally crazy about a cat jumping up and down with a rainbow that makes no totally sense at all, that has music in the background?
No.
Yes.
Can you play it again?
Yes.
Play it again.
Thanks for watching.
See us next week in seven days.
Give the video a thumbs up in you liked it.
Let me know what videos you want me to watch next.
I'm gonna miss you okay, just don't forget me.
Goodbye!
We are asked, what is the value of the 100th term in this sequence?
And the first term is 15, then 9, then 3, then negative 3.
So let's write it like this, in a table.
So if we have the term, just so we have things straight, and then we have the value. and then we have the value of the term.
So our first term we saw is 15.
Our second term is 9.
Our third term is 3.
I'm just really copying this down, but I'm making sure we associate it with the right term.
And then our fourth term is negative 3.
And they want us to figure out what the 100th term of this sequence is going to be.
So let's see what's happening here, if we can discern some type of pattern.
So when we went from the first term to the second term, what happened?
15 to 9.
Looks like we went down by 6. It's always good to think about just how much the numbers changed by.
That's always the simplest type of pattern.
So we went down by 6, we subtracted 6.
Then to go from 9 to 3, well, we subtracted 6 again.
We subtracted 6 again.
And then to go from 3 to negative 3, well, we subtracted 6 again.
We subtracted 6 again.
So it looks like, every term, you subtract 6.
So the second term is going to be 6 less than the first term.
The third term is going to be 12 from the first term, or negative 6 subtracted twice.
So in the third term, you subtract negative 6 twice.
In the fourth term, you subtract negative 6 three times.
So whatever term you're looking at, you subtract negative 6 one less than that many times.
Let me write this down just so-- Notice when your first term, you have 15, and you don't subtract negative 6 at all.
So you can say this is 15 minus negative 6 times-- or
let me write it better this way --minus 0 times negative 6.
That's what that first term is right there.
What's the second term?
This is 15.
We just subtracted negative 6 once, or you could say, minus 1 times 6.
Either way, we're subtracting the 6 once.
Now what's happening here?
This is 15 minus 2 times negative 6-- or, sorry
--minus 2 times 6.
We're subtracting a 6 twice.
What's the fourth term? This is 15 minus-- We're subtracting the 6 three times from the 15, so minus 3 times 6.
So, if you see the pattern here, when we have our fourth term, we have the term minus 1 right there.
The fourth term, we have a 3.
The third term, we have a 2.
The second term, we have a 1.
So if we had the nth term, if we just had the nth term here, what's this going to be?
It's going to be 15 minus-- You see it's going to be n minus 1 right here.
Right?
When n is 4, n minus 1 is 3.
When n is 3, n minus 1 is 2.
When n is 2, n minus 1 is 1.
When n is 1, n minus 1 is 0.
So we're going to have this term right here is n minus 1.
So minus n minus 1 times 6.
So if you want to figure out the 100th term of this sequence, I didn't even have to write it in this general term, you can just look at this pattern.
It's going to be-- and I'll do it in pink --the 100th term in our sequence-- I'll continue our table down
--is going to be what?
It's going to be 15 minus 100 minus 1, which is 99, times 6. right?
I just follow the pattern. 1, you had a 0 here. 2, you had a 1 here.
So let's just calculate what this is.
What's 99 times 6?
So 99 times 6-- Actually you can do this in your head.
You could say that's going to be 6 less than 100 times 6, which is 600, and 6 less is 594.
But if you didn't want to do it that way, you just do it the old-fashioned way.
6 times 9 is 54.
Carry the 5. 9 times 6, or 6 times 9 is 54. 54 plus 5 is 594.
So this right here is 594.
And then to figure out what 15-- So we want to figure out what 15 minus 594 is.
And this can sometimes be confusing, but the way I always process this in my head is, I say that this is the exact same thing as the negative of 594 minus 15.
And if you don't believe me, distribute out this negative sign.
Negative 1 times 594 is negative 594.
Negative 1 times negative 15 is positive 15.
So these two statements are equivalent.
So what's 594 minus 15?
We can do this in our heads. 594 minus 14 would be 580, and then 580 minus 1 more would be 579.
So that right there is 579, and then we have this negative sign sitting out there.
So the 100th term in our sequence will be negative 579.
Let's get started with some problems. Let's see. First problem: what is fifteen percent of forty?
Put a zero there. And then one times zero is zero. one times four is four. And you get six zero zero.
No decimals up there, so you go one, two and you put the decimal there. So 15% of 40 is equal to 0.15 times 40, which equals 6.00. Well, that's just the same thing as six.
Well, this is pretty straightforward. seven times two is fourteen. And how many total numbers do we have or how many total digits do we have behind the decimal point? Let's see.
So a lot of people's reflex might just be, oh, let me take twenty percent. It becomes 0.20. And multiply it times four.
And this problem says that twenty percent of x is equal to four. I think now it's in a form that you might recognize. So how do we write twenty percent as a decimal?
And this is easy. two goes into forty how many times?
Well, two goes into four two times and then two goes into zero, zero times. You could've done that in your head. two into forty is twenty times. So 4 divided by 0.2 is 20.
I'm picking numbers randomly. Let's say three is nine percent of what?
Once again, let's let x equal the number that three is nine percent of. You didn't have to write all that. Well, in that case we know that 0.09x-- 0.09, that's the same thing as nine percent of x-- is equal to three.
And obviously, on tests and things you need to be precise as well.
The important thing for these type of problems is pay attention to how the problem is written. If it says find ten percent of one hundred. That's easy.
I'll now show you how to convert a fraction into a decimal.
And if we have time, maybe we'll learn how to do a decimal into a fraction.
So let's start with, what I would say, is a fairly straightforward example.
Let's start with the fraction 1/2.
And I want to convert that into a decimal.
So the method I'm going to show you will always work.
What you do is you take the denominator and you divide it into the numerator.
Let's see how that works.
So we take the denominator-- is 2-- and we're going to divide that into the numerator, 1.
And you're probably saying, well, how do I divide 2 into 1?
Well, if you remember from the dividing decimals module, we can just add a decimal point here and add some trailing 0's.
We haven't actually changed the value of the number, but we're just getting some precision here.
We put the decimal point here.
Does 2 go into 1?
No.
2 goes into 10, so we go 2 goes into 10 five times.
5 times 2 is 10.
Remainder of 0.
We're done.
So 1/2 is equal to 0.5.
Let's do a slightly harder one.
Let's figure out 1/3.
Well, once again, we take the denominator, 3, and we divide it into the numerator.
And I'm just going to add a bunch of trailing 0's here.
3 goes into-- well, 3 doesn't go into 1.
3 goes into 10 three times.
3 times 3 is 9.
Let's subtract, get a 1, bring down the 0.
3 goes into 10 three times.
Actually, this decimal point is right here.
3 times 3 is 9.
Do you see a pattern here?
We keep getting the same thing.
As you see it's actually 0.3333.
It goes on forever.
And a way to actually represent this, obviously you can't write an infinite number of 3's. Is you could just write 0.-- well, you could write 0.33 repeating, which means that the 0.33 will go on forever.
Or you can actually even say 0.3 repeating.
Although I tend to see this more often.
Maybe I'm just mistaken.
But in general, this line on top of the decimal means that this number pattern repeats indefinitely.
So 1/3 is equal to 0.33333 and it goes on forever.
Another way of writing that is 0.33 repeating.
Let's do a couple of, maybe a little bit harder, but they all follow the same pattern.
Let me pick some weird numbers.
Let me actually do an improper fraction.
Let me say 17/9.
So here, it's interesting.
The numerator is bigger than the denominator.
So actually we're going to get a number larger than 1.
But let's work it out.
So we take 9 and we divide it into 17.
And let's add some trailing 0's for the decimal point here.
So 9 goes into 17 one time.
1 times 9 is 9.
17 minus 9 is 8.
Bring down a 0.
9 goes into 80-- well, we know that 9 times 9 is 81, so it has to go into it only eight times because it can't go into it nine times.
8 times 9 is 72.
80 minus 72 is 8.
Bring down another 0.
I think we see a pattern forming again.
9 goes into 80 eight times.
8 times 9 is 72.
And clearly, I could keep doing this forever and we'd keep getting 8's.
So we see 17 divided by 9 is equal to 1.88 where the 0.88 actually repeats forever.
Or, if we actually wanted to round this we could say that that is also equal to 1.-- depending where we wanted to round it, what place.
We could say roughly 1.89.
Or we could round in a different place.
I rounded in the 100's place.
But this is actually the exact answer.
17/9 is equal to 1.88.
I actually might do a separate module, but how would we write this as a mixed number?
Well actually, I'm going to do that in a separate.
I don't want to confuse you for now.
Let's do a couple more problems.
Let me do a real weird one.
Let me do 17/93.
What does that equal as a decimal?
Well, we do the same thing.
93 goes into-- I make a really long line up here because I don't know how many decimal places we'll do.
And remember, it's always the denominator being divided into the numerator.
This used to confuse me a lot of times because you're often dividing a larger number into a smaller number.
So 93 goes into 17 zero times.
There's a decimal.
93 goes into 170?
Goes into it one time.
1 times 93 is 93.
170 minus 93 is 77.
Bring down the 0.
93 goes into 770?
Let's see.
It will go into it, I think, roughly eight times.
8 times 3 is 24.
8 times 9 is 72.
Plus 2 is 74.
And then we subtract.
10 and 6.
It's equal to 26.
Then we bring down another 0.
93 goes into 26-- about two times.
2 times 3 is 6.
18.
This is 74.
0.
So we could keep going.
We could keep figuring out the decimal points.
You could do this indefinitely.
But if you wanted to at least get an approximation, you would say 17 goes into 93 0.-- or 17/93 is equal to 0.182 and then the decimals will keep going.
And you can keep doing it if you want.
If you actually saw this on exam they'd probably tell you to stop at some point.
You know, round it to the nearest hundredths or thousandths place.
And just so you know, let's try to convert it the other way, from decimals to fractions.
Actually, this is, I think, you'll find a much easier thing to do.
If I were to ask you what 0.035 is as a fraction?
Well, all you do is you say, well, 0.035, we could write it this way-- we could write that's the same thing as 03-- well, I shouldn't write 035.
That's the same thing as 35/1,000.
And you're probably saying, Sal, how did you know it's 35/1000?
Well because we went to 3-- this is the 10's place. Tenths not 10's.
This is hundreths.
This is the thousandths place.
So we went to 3 decimals of significance.
So this is 35 thousandths.
If the decimal was let's say, if it was 0.030.
There's a couple of ways we could say this.
Well, we could say, oh well we got to 3-- we went to the thousandths Place.
So this is the same thing as 30/1,000. or.
We could have also said, well, 0.030 is the same thing as 0.03 because this 0 really doesn't add any value.
If we have 0.03 then we're only going to the hundredths place.
So this is the same thing as 3/100.
So let me ask you, are these two the same?
Well, yeah.
Sure they are.
If we divide both the numerator and the denominator of both of these expressions by 10 we get 3/100.
Let's go back to this case.
Are we done with this?
Is 35/1,000-- I mean, it's right. That is a fraction.
35/1,000.
But if we wanted to simplify it even more looks like we could divide both the numerator and the denominator by 5.
And then, just to get it into simplest form, that equals 7/200.
And if we wanted to convert 7/200 into a decimal using the technique we just did, so we would do 200 goes into 7 and figure it out.
We should get 0.035.
I'll leave that up to you as an exercise.
Hopefully now you get at least an initial understanding of how to convert a fraction into a decimal and maybe vice versa.
And if you don't, just do some of the practices.
And I will also try to record another module on this or another presentation.
Have fun with the exercises.
♪ (Betty Who, "Somebody Loves You") ♪
- People are dancing in a Home Depot.
- Ah, a flash mob?
- It's like an awesome flash mob. - ♪ ...when you can't be strong ♪
- This is like my cheer dance thing.
- Is that his family?
- Grandparents?
- Why is that a boy right there?
And why are they dancing?
- I should be in that video. - ♪ ...lay me down ♪
- Wait... wait a second.
- Okay, so there's a guy getting proposed to so...
- He does have a nice suit, I have to say that.
- If somebody proposes to me, that's what I want to happen.
- How do they get Home Depot to approve this though?
- Is he a business man? (giggles)
- ♪ Somebody misses you when you're away ♪ - That's cool.
- Okay, so they're gay.
But it's okay. - ♪ Ooh, somebody loves you ♪
- Good friends.
- (gasps) Is he going to propose?
- (whispering) That's so cute.
- (Spencer) Dustin, I love you more than anything in this entire world.
- A guy proposing to a guy?!
- Are they gay?
- (Spencer) Will you marry me?
- Marry who?
You mean a boy marrying a boy?
- That's nice.
(in video: cheering)
- Congratulations!
- This is crazy!
(giggles)
- How does a guy marry a guy?!
- So they're gay?
- (Finebros) Mm-hm.
Oh.
- That was so cute and it doesn't matter if they're gay or anything.
- That was just so cute!
I c-- I can't even.
Okay. ♪ (jubilant brassy music) ♪
- Is it another marriage proposal?
- A girl marrying a girl?
- Hi!
(in video: woman laughs in disbelief)
- Is that a girl? ♪ (The Lumineers, "Ho Hey") ♪
- That's a little dangerous, standing on a bus.
- What if she just fell off?
- "A little over six years ago..."
- "I met a girl..."
- No crying.
- "Who stole my heart..."
- I feel like I know what kind of topic this is.
- It's like the first thing you do, try to pinch yourself. - ♪ I belong with you ♪
- (singing along) ♪ You belong with me You're my sweetheart ♪
- (singing along) ♪ I belong with you You belong with me ♪ ♪ You're my sweet-- ♪ (giggles)
I love this song.
(in video: laughter and cheering)
- (falsetto voice) Will you marry me?
- How does a girl propose to a girl and how does a guy propose to a guy?
- Are they gay too?
- And there it comes.
- (excited) Yay!
- Now say, "Yes."
- (laughing) "Vote bot?"
- Awww.
- Guessing that's a "yes".
(in video: cheering) (shy giggle)
- That was so adorable!
- I love all these videos.
They're just too cute.
- Well, this is new!
- That's what I want to see a lot.
Gay and lesbian people shouldn't be hiding.
- Wait, what was that about? ♪ (theme music) ♪
- (Finebros) What did both those videos have happen in them?
- Justin Bieber married a guy.
- (Finebros) That wasn't Justin Bieber!
- Two marriage proposals, both with songs.
- I was really in awe of them.
- A boy and a boy together, and a girl and a girl.
- There was a guy proposing to a guy.
THAT'S JUST CRAZY!
Then there was a girl proposing to a girl.
THAT'S JUST CRAZY!
- (Finebros) How did the videos make you feel?
- Good.
- They made me feel good.
- It was really cool.
- Oh, I was so moved by that.
- I'm sad.
Gay is bad for you.
- (Finebros) Why do you think that is bad?
I don't know.
- (Finebros) What do you think people's reactions were when they watched these videos?
- Um, it depends for certain people.
- A lot of people were happy.
- Really good, positive things.
- Yeah, I hope not negative things.
- Some people must have been like, "Rock on!"
And some people were like, "Ew."
Some people are so anti-gay.
- You don't see that everyday.
It's okay though. A boy can like a boy or a girl can like a girl.
- Most people would probably have a reaction like, "It's not natural!"
It's normal now.
- (Finebros) A lot of people were upset at these marriage proposals
BECAUSE it was a man proposing to a man and a woman proposing to a woman.
- I don't get why anybody would be mad!
- That's just wrong.
Anyone should be able to marry anyone.
- You should feel happy that they're getting married.
- People that do not like gay-- I mean, they are good.
- That makes me mad.
- You can't tell another person who to marry!
What if you're a girl and your boyfriend proposes to you?
That's not different from a girl proposing to a girl.
- If you want to marry the same sex that's okay.
It's just like Macklemore said:
"I can't change you, even if I tried."
- (Finebros laughs) - ♪ Even if I wanted to ♪ ♪ My love, my love, my love ♪
- (Finebros) Do you know what being gay means?
- No.
- A boy likes a boy and a girl likes a girl.
- (Finebros) It means that they like someone of the same gender.
- Does that mean they're a gate?
- (Finebros) No, not a gate.
- Or a Golden Gay Bridge?
I just don't know where the name comes from.
- (Finebros) The word actually comes from the word that means happy.
- If I got a box of microscopes, would I be gay?
- (Finebros) Well, because you're happy?
- (Finebros) Why is it that some people like the opposite gender while some people like the same gender?
- Hmm.
I don't know.
- I don't know.
- Well, it's the same.
My best friend's a boy, not a girl.
- You're hanging out with a guy for the rest of your life.
All you're gonna know is guy things.
If you go to a fancy restaurant, you're just gonna be burping the whole time.
- People that like the same gender are depicted as abnormal, but they were born that way.
- Born that way.
- Just how they were born.
- I wasn't born that way.
- (Finebros) Well, do you think that people are born that way?
- (Finebros) Some people say that people choose to be gay and that it's something that can be corrected or fixed.
- Yeah, it could be possible actually.
But if you really like that person, you should be with that person.
- That kind of stuff makes me sick.
You like what you like!
- You can't be all bossy to people.
Like, "(bossily) You can't do that!
You can't do that!
You need to do this.
No! No! No!"
It's okay for school and stuff like that-- vocabulary, spelling, and everything, but when it's yourself don't let people tell you what to do.
- (Finebros) What do you think about gay marriage?
- I don't care.
- I'm just new to the concept.
- The first time I ever heard about it I was like, "Okay, that's kind of weird but... well, people should be together if they like each other a lot.
- If one person should be able to do something, then everybody else should be able to do it.
- That's awesome.
Some of our really good friends are gay and lesbian.
- You shouldn't have to be any different than regular marriage, even though in our society it is.
- My friends talk about it all the time.
They use the word "gay" as something else.
You don't just say, "(cruelly) Hey, you're gay.
Ha.
Ha."
That's dumb.
Why would you be that mean to someone?
- (Finebros) So in the United States, only 14 states are you allowed to get married if you are gay-- only 14.
- That is just insane.
- Out of 50.
That's outrageous.
- (sternly) I need to talk to Mr. President.
- You know what?
I feel bad for the people that live in that state and like the same gender.
Mmm, it's not right.
- It kinda takes away from whole freedom thing.
- Love's a freedom and they're totally taking that away.
- It used to be illegal for a black person to marry a white person.
I don't get why all this stuff has to be illegal.
- Slavery wasn't abolished until Abraham Lincoln.
Then women weren't even allowed to vote.
We've progressed a lot, and there was bumps in the road, but now we're at another bump.
- I think that you have to find a boy and a girl.
I mean, you can get married like that.
But gay? You can't get married.
- (Finebros) But do you know why you don't like it?
- I don't know.
- Some people want to live in one state and they want to get married.
They just ought to move to the other state.
But I'm afraid there's tornadoes.
I don't want to go there, but I have to because I want to marry someone I like!
And that's not right.
- (Finebros) Well, in some places in the world you can even be put in jail if you're gay.
- (put off) Wow!
- (Finebros) And even worse, in some places you even could be sentenced to death just because you love the same gender.
(frustrated scream)
- I'm not going wherever that is.
- You can't just kill someone for what they like.
- I'm kind of ashamed that I live in this world!
Why can't I live on that moon that supposedly has jellyfish on it?
- (Finebros) Why does it matter so much to other people who you love and who you marry?
- Because gay is bad for you.
- I don't know.
For crazy, dumb, selfish stuff.
- I'm not really sure what's in their mind, what they're thinking.
Well, I guess people consider it "not normal".
- Maybe their religion doesn't want that?
- Nobody really has a reason to hate gays.
It's not like-- there's no completely valid reason.
- (Finebros) A lot of people who are gay are afraid to admit it and afraid to come out.
They're worried about their family rejecting them or losing their friends.
Why does something like that happen so often?
- Because they know people are mean about it and they don't want to be bullied.
- 'Cause they're scared of what might happen.
- Some people, I guess, would think they're trying to hit on them.
That totally changes the perspective.
The thought might cross your mind of, "Oh my god. What if they have a crush on me?"
It's the same thing if a guy says he has a crush on me.
And you say, "Oh, well, you know, I don't really like you in that way but we can still be friends."
I mean, you don't just have to completely cast him out of your life.
You can't read minds, you can't tell if someone likes you or not so... yeah, just deal with it.
Deal with it.
(everyone laughs)
- (Finebros) So if someone was your friend and they turned out to be gay would you still be their friend?
- No.
- I would still be their friend but I would just ask them a few questions.
- Well, I would have a different look on it, but I think I'd still be friends with them.
- If it's your friend, then it's your friend.
- I'd love them more for being honest with me.
- They don't turn different.
They just turn out to love a boy.
- My best friend is gay, and so he came out last year.
And I mean, seriously, we've been best friends since third grade.
- I would keep being your friend.
Even if you think it's weird, it doesn't really affect on how they act.
If you don't think about it, they sound like a perfectly normal kid.
- (Finebros) So now let's go over some of the reasons people say they are against gay marriage.
- (wearily) Oh god.
- (Finebros) Some have said they're against it because they say it's not natural, because a man and a woman, they can have children.
Is that a valid reason to be against gay marriage?
- No!
- Nope.
- Adopt!
- People are mean to each other sometimes.
Maybe that's just their opinion.
- That's no reason at all.
Some people want to have kids.
Some people don't want to have kids.
So it doesn't really affect on it.
- If it's happening and it's not a chemical, it is natural.
(laughs) - (Finebros) Another major reason that it's very controversial is that every major religion has something in their books that could be interpreted as being against people who are gay.
What are your thoughts about people who are against it for religious beliefs?
- I mean, I'm a Christian and I don't think it's wrong.
- It's, like, the 21st century.
- Things have changed.
- If they said that, like, "God told me blah, blah, blah,"
I'd be like, "(mumbling) Um, that's nice.
I'm gonna leave you now."
- Religion shouldn't be something that determines who you're friends with.
- A lot of people have that logic.
My religion says so, so I have to do it.
When you're saying that someone's gay and that's wrong, you're using your religion against someone else.
That would be so wrong.
- (Finebros) Some states don't let you get married but they'll give gay couples the same rights as someone who is married.
Is that enough?
I feel like they should be able to get married if they want to but it's better than nothing.
- It's not good because it's like, "Oh, you can have every single right.
You just can't get married."
That's the one thing they want.
- I sort of get what they're saying about, "Oh. What are they complaining about?
They still have the same rights."
But they're still deprived of one thing which is sort of a major milestone in somebody's life.
- You could have your friend that's not gay.
He'll be married.
But then you'll be with your partner, but you won't be married.
It doesn't make sense.
- Before Martin Luther King stood up, it's like white people were like kings and queens!
Then black people were like tiny, little servants.
They're treating-- the people who get married like, "We're the people who own a mansion."
And then the other people... people in small cottages.
If a person wants to do something and they can't, that means something in your life is impossible,
like you have a brick wall all around you.
And you want to go to that tree, and you can't pass over that wall.
Would you want to move out?
Yeah.
But you can't.
It's like you're trapped.
- (Finebros) And what would you want to say to the people out there that believe gay marriage shouldn't be allowed?
- Get a hobby.
- Cry me a river, build me a bridge, and get over it.
- Just get a whole new idea about it because it's fine.
There's nothing wrong with it.
- If only gay people could marry, you'd be really sad.
So why shouldn't they be able to marry?
- It's not okay to hate gay people.
You can feel that way.
Don't bring it into the law.
- Think of God.
He loves everybody and he can't hate anything.
- You guys are basic and nobody likes you. No, I'm kidding.
If they've never been around gay people and they're just doing what the Bible says or what their parents say, you're judging that person without actually meeting them.
- You need to realize you're just a little speck.
No one cares what you think.
- I wouldn't exactly say, "You suck.
Get out of my life.," but I'd say that in the nicest words possible.
- (Finebros) And what about people who might be watching that are either in a bad situation and they are openly gay or they've not come out and are too afraid to come out?
- All right.
I think this is a quote.
"Never think about what someone says about you.
Only think about what you think of yourself."
- If someone doesn't accept you, then they obviously aren't your friends.
- I'm totally supporting you guys.
You guys are awesome.
- I'm your friend!
- (Finebros laughs) - Air hug!
- There are people who are supportive of your sexual orientation.
It does get better.
- You always hear, "Your real self shines through."
Maybe eventually someday the whole thing will be over and a nice gay couple can be together.
Maybe someday people won't have to worry about it and you might feel like you've done an actual good thing.
- (Finebros) Do you think that by the time you have grown up that gay marriage will be legal everywhere?
- Yes.
- I hope. - It should be.
- No!
No!
No!
- I'm not sure.
People are selfish.
I think the world everywhere-- like all planets-- just legalize it.
- (Finebros) Why is equal rights, as a concept for all people, something so important?
- Because human beings are human beings and they should all be treated the same.
- So it's fair for everyone and people don't get upset or sad.
- Remember that time where there were bathrooms for black people and bathrooms for white people?
This is the same thing.
No one has a greater power than you except, you know, the bureaucracy and everything. (laughs)
- It's so funny how people who, let's say, are racist.
And then you say to them, "We should be different because my eyes are blue and your eyes are brown."
They'd probably be like, "Oh what?
No, that's absurd!"
It's the same thing!
I mean, unless you guys want to hear me go on and on about this,
I suggest you just cut it right now.
- This is a really big situation of what people think and what people are hating.
Even though that's not my problem, I will still fight for it if I can. (silence)
A line has a slop of negatave 3/4ths, and goes through the point (0,8).
What is the equation of this line in slope-intercept form?
So any line can be represented in slope-intercept form as y=mx+b.
Where this 'm' right over here, that is the slope of the line, and this
'b' over here, this is the y-intercept of the line.
Let me draw a quick line here just so that we can visualize that a little bit.
So that is my y-axis, and then that is my x-axis.
And let me draw a line, and since our line here has a negative slope, I'll draw a downwards sloping line.
So let's say our line looks something like that.
So, hopefully we're a little familiar with the slope already, the slope essentially tells us, look start at some point on the line, and go to some other point on the line, measure how much you have to move in the x-direction, that is your run, and measure how much you have to move in the y-direction, that is your rise, and our slope is equal to rise over run.
And you go see over here, it will be downward sloping, because if you move in the positive x-direction, we have to go down.
If our run is positive, our rise here is negative.
So this will be a negative over positive, and will get a negative number
Which makes sense, because we're downward sloping.
The more we go down in this situation, for every step we move to the right, the more downward sloping we'll be; the more negative of a slope we'll have. so that's slope.
That's slope right over here.
The y-intercept just tells us where we intercept the y-axis.
So the y-intercept, this point right over here, this is where the line intersects with the y-axis.
This will be the point (0,b).
And this actually just falls straight out of this equation.
Let's evaluate this when x=0. y=m*0+b, well anything times zero is zero, so y=0+b or y=b, when x=0, so this is the point (0,b)
Now, they tell us what the slope of this line is.
They tell us a line has a slope of -3/4 so we know that our slope is -3/4
And they tell us that the line goes through the point (0,8)
They tell us we go through the, let me just do this in a new color
I've already used orange, let's use this green color.
They tell us that we go through the point (0,8) notice x is 0, so we're on the y-axis when x is zero, we're on the y-axis, so this is our y-interecept so b, we could say, we could do a couple of-- our y-intercept is the point (0,8), or we could say b, remember, it's also (0,b) we could say b=8
So we know m=-3/4, and b is equal to 8, so we can write the equation of this line. in slope-intercept form.
It's y=-3/4 times x, plus b, plus 8.
And we are done, we are done.
We're told that Jared is twice the age of his brother, Peter.
So, Jared is twice the age of his brother, Peter.
Peter is four years old.
Peter is four years old, and Jared is twice the age of his brother, Peter.
So, Jared is twice Peter's age of four.
And then they tell us Talia's age is 3 times Jared's age.
How old are Talia and Jared?
So Talia's age is 3 times Jared's age.
So let's write this down.
We have Peter is four years old.
So Peter- Peter's age- Peter's age,he's four years old.
Jared is twice the age of his brother, Peter.
So Jared-Let me do that in yellow-So Jared- That's not yellow.
Jared- Jared is twice the age of his brother.
So twice- twice is the same thing as two times, two times the age of his brother.
We could-though- You could say Jared is twice the age of his brother.
Or Jared is two times the age of his brother.
Well, his brother is four;they told us that right over there.
So Jared is going to be two times four years old.
Two times four years old and if you know your multiplication tables,
You know that's the same thing as eight.
Two times four is eight.
Four times two is eight or you know this is the same thing as Peter's age twice.
Which is the same thing as four plus four.
That would also get you eight.
So this would give you- so Jared's age is equal to eight.
And then finally they say Talia's age- let me write Talia's- Talia right over here. Talia's age and they say it- they tell it to us right over here.
It's three times Jared's age.
So Talia's age is three times Jared's age.
Well we were able to figure out Jared's age. it is eight.
It is three times Jared's age.
If you know your multiplication tables this should maybe jump out at you.
And your multiplication tables really are one of those things in mathmatics
That you should just, just really just know back and forth,
Just because it will make the rest of your life very, very, very simple,
But or you could do three times eight as literally eight three times.
So it's eight plus eight plus eight.
Eight plus eight is sixteen.
Sixteen plus eight is twenty-four.
So three times eight is twenty-four.
So Peter is four, Jared is eight, and Talia is twenty-four.
We are asked to simplify a log base 5 of 25 to the "x" power over "y"
So I will give you some logarithm properties and I do agree that this does require some simplification over here
So the first thing that we realize is that this is one of our logarithm properties
So logarithm for a given base so lets say that the base is "x" of a/b
That is equal to log base "x" of a minus log base "x" of b
Now here we have 25 to the "x" over y
So we can simplify
Log base 5 twenty five to the "x" over "y" to this property means that its the same thing as log base 5 to the twenty five to the "x" power minus log base 5 of "y"
It seems like the relevant logarithm property here is if I have log base "x" of a to the "p" power
That's the same thing as b times log base "x" of a
This exponent over here can go outfront, which is what we did right over there
So this part right over here can be written as "x" times the logarithm of base 5 of 25 and then of course we have minus log base 5 of "y"
This part right here is asking us what power do I have to raise 5 to to get to 25
So we have to raise 5 to the 2nd power to get 25.
So we are left with, this is equal to 2 times "x" minus log base 5 of "y"
There's something going on with you, isn't there?
You're not sleeping?
Don't even think about lying to me.
There's nothing going on.
I want to live here with dad, you and san. what...?
Why?
And what about Young Master JunPyo,school and everything?
Didn't I say it before?
I have nothing to do with Goo JunPyo
Also, after putting up with so much humiliation, you still regret it? Oh, gee!
So in this small rural town, selling fish, crabs and webfoot octopus, smelling like fish, that's how you want to live?
What's wrong with that?
Oh my gosh...
We're done for !
We're finished !
What hope do we have to live for now ?
Mom..
Forget it!
Yi Jung sunbae....
There's still no news from JanDi?
No. I don't know what she's thinking.
She hasn't called.
She just said she went to a fishing village but never said where it is.
She must be doing ok. It's Geum Jandi we're talking about.
You seem to know my friends better than I do.
Like I said before,
I have some knowledge when it comes to girls
How is JunPyo sunbae doing?
He's a mess.
GaEul...
Don't you think it's time we start talking about us?
GaEul
I...
I'll go first.
You don't have to feel burdened because of me. I already know how you feel.
So, from now on, I won't look for you anymore.
GaEul!
EunJae teacher said before, that because she did everything that was within her power, that she has no regrets.
Thank you.
For giving me the chance to do everything I could
If I hear from Jandi, I will inform you.
Bye.
What can we do?
Mister, I am so afraid that our Jun-Pyo might really become broken.
I'm really afraid.
Miss.. you can't be like this also..
No.
This time...
I have a really bad feeling about this.
Miss?
Dad....
Dad...
DAD!!!!
How could you do this?
Can't you see it's already hard without you screaming about it?
Mom.... no, I don't even want to call you mom anymore. how..how could a person.. how could a person do something like that?!?
What exactly are you talking about??
How could you say that dad was dead when he's still alive?!
- You...
- How did I know?
You're wondering about that at a time like this?
I'm asking you.
Leaving Dad buried like that, did you intend to deceive me forever?!
Why did you do that?!
WHY?!
This is what your father would have wanted
W... W... What?
I said I will take care of everything, but your dad suddenly collapsed.
He isn't different from a living corpse.
The head of the famous ShinHwa Group, I couldn't allow the last memories of him to become like that.
My pride wouldn't allow it.
Pride...
Now... Are you saying that you lied to the world and even to your children that my living father was dead because of your pride?
It was for your dad.
What is this about?
JunPyo....
I'll explain everything.
I...
I'm asking what does it mean?
When dad is not around what you have to do?
I have to take care of mother, sister, and Shinhwa group!
Goo Junpyo, can you promise me that as a man to man?
Yes, sir!
Your father tried his hardest till the very end for this group, which you can throw away any minute. Are you thinking of abandoning him as well? I'm sorry, young master. i am really sorry.
I haven't once forgotten that I have come to the fish market today. Everyone look at the fresh fish here.
- Look at this octopus.<Br>- $10!
- It seems this is the season for octopus. - $10!
Sure! It's drop-dead delicious! I'll give it to you for cheap, so buy some.
You hear that?
Why don't you set today's dinner table with this webfoot octopus in season?
This is the Saeuh island. I'm reporter Joh Boram.
I'm going to see dad.
Will you go with me?
I'm not going.
Junpyo...
Junpyo
Come talk with Mom.
Mom ?
Do you really think that you were even once my mom?
Why don't you quit with the act of being a mother when it doesn't suit you, Chairwoman Kang. i have no interest.
What? If you're going to go, go by yourself.
Goo Junpyo
JunPyo, are you serious?
Don't be like this. Go and see her once.
I said I'm not interested!
I'll ask you one more time.
Are you sure?
If you miss her so much, you should go.
Then I'm going first.
Whether you go or not, you do whatever you want.
When times are like this, don't you need Geum Jan Di the most?
What can I do by bringing her back here?
There is nothing that I can promise her....promising her that I'd always make her laugh, ...that I'd always make her happy so just trust in me I've lost the confidence to keep those kinds of promises.
Jun Pyo.
The fact that I am the son of that kind of person... ...the fact that I am a member of that kind of family... ...even I hate it so much...how do you think she feels?
With all that she's had to endure already, I'm sure she really hates it.
It's Geum JanDi, so the situation can be different.
That's even more reason not to.
Because it's the woman that I love.
That's why it's not going to happen even more now.
It would have been nice if we sold the rest of that
Mom, I'm hungry!
Oh, I'm sorry, San. I will have it ready soon.
What's going on?
What's going on? That's what we want to ask you. There's a limit to your thinking what dumb country folk we are!
This lady is the heiress to a group much bigger than ShinHwa! The fact that they were going to get married was even on the news! That's old news.
Oh... that... that... master is...
That money.... ...I'll repay it. What should we do? Did you see that, see that?
How can this happen?
How can a person do such a thing?
I...have received so much from you, Sunbae...
But you have given me more...
How is Grandpa doing?
The usual...attending to work...probably will continue until he collapses again...
That is so like him....
Grandpa gave me this.
It was what my Grandma gave my mother.
Sunbae.
I don't know when I started to feel like this. but...
I cannot live without you.
I cannot accept this.
Jandi...
I told myself I can forget it....
I thought I had forgotten it all.
However
However...
I can't seem to be able to throw this away.
I just can't seem to let it go....
I can't separate Goo JunPyo from me.
I'm sorry.
I'm sorry sunbae.
It's ok.
It's ok.
Jandi...I can't give her up.
Even though I always make things hard for her.
I've sometimes thought it might be better to let her go to you. no
If I had to give Jandi to another guy
I don't even want to think about it, but if I have to,
I thought you should the one.
It can't be anyone else but you, Jihoo
I've thought about that.
I won't die alone.
I will see to ShinHwa's end!
I won't go down alone.
NO!
Jun Pyo.
JunPyo! JunPyo!
JunPyo!
Yah, Goo JunPyo.
Wake up.
Goo JunPyo! The assailant who was caught at the scene said he was done wrong by ShinHwa Group and did it as an act of revenge on hostile takeover.
This isn't your fault.
This isn't your fault.
Goo JunPyo!
Wake up!
Hello? My friend is dying.
I said my friend is dying! JunPyo... Jun Pyo!
Don't worry...
Goo JunPyo
He's gonna be okay. JunPyo... JunPyo..
He especially likes eating fish cakes from street vendors...
He can eat 20 at one sitting.
Move on. I don't know when I started to feel this way. But...
Wake up. wake up Goo junPyo
Goo JunPyo Hubby.. Oh, Honey!
If you hit him, I thought you would be hurt more, emotionally.
That's why I stopped you .
How long did you wait outside?
Why are your hands so cold?
Let me see the one that's cold is your heart.
You don't have to pretend to be strong in front of me.
I'm not pretending to be strong.
It's because you're here.
You being here gives me strength.
I'll go make tea.
Abracadabra,Gu JunPyo, remember Geum JanDi.
I remember.
The thing I forgot is... you, right?
It's all over now.
That in this ridiculous way... ...you guys are ending....
I can't go along with it.
That girl's facial expression...I can't seem to erase...
In the end...
Geum JanDi and Goo JunPyo... ...only amounted to this...
This is all it amounted to..
We have gathered you all here to announce something special.
Goo JunPyo and Jang Yumi, we have decided to go study in the US next month.
 There's been a lot of talk very recently, or definitely over the last several years, about the idea of intelligent design and how it compares to evolution.
And my goal in this video isn't to enter into that discussion, or it's actually turned into an argument in most circles, but really to make my best attempt to kind of reconcile the notions.
So the idea behind intelligent design is really that there are some things that we see in our world that are just so amazing that it seems hard to believe that it could be the product of a set of random processes.
And the example that tends to be given is the human eye, which truly is an awe-inspiring device.
You can call it an organ or a machine.
Whatever you want to call it, it does all of these amazing things. It can focus at different lengths. It brings the light into focus at just the right spot, and then you have your retinal nerves and you have two eyes so can see in stereoscopic vision.
You can see in colors, and then you can adjust to light and dark, so the human eye truly is awe inspiring.
And the argument tends to go that, look, how can this be created from random processes? And the goal of this isn't to trace the evolution of the eye, but I'll do a little side note here that evolution is-- and natural selection, and I like the word natural selection more because it's not talking about an active process. Natural selection is acting over eons and eons of time, and we do see evidence in our world of a progression of different types of eyes.
We know that quadrilateral ABCD over here is a parallelogram.
And what I want to discuss in this video is a general way of finding the area of a parallelogram.
In the last video we talked about a particular way of finding a area of a rhombus.
You can take half the product of it's diagonals. And a rhombus is a parallelogram, but you can't just generally take the product of the half the product of the diagonals of any parallelogram
It has to be a rhombus.
So now were just going to talk about the parallelograms.
So what do we know about parallelograms?
Well we know the opposite sides are parallel. That side is parallel to that side and this side is parallel to this side. And we also know that opposite sides are congruent.
A, C We can split our parallelogram into two triangles.
We can look, obviously A,D is equal to B,C. We have D,C is equal to A,B. And then both of these triangles share this third side right over here.
So we can say triangle ADC is congruent to triangle, so we want to get this right.
So CBA, triangle CBA. And this is by Side Side Side (SSS) congruency.
All three sides, they have three corresponding sides that are congruent to each other.
So the triangles are congruent to each other.
And what that tells us is that the areas of these two triangles are going to be the same. So if I want to find the area, the area of ABCD, the whole parallelogram. It's going to be equal to the area of triangle ADC plus the area of CBA.
The area of triangles is literally just one half times base times height. So it's one half times base times height of this triangle. And we are given the base of ADC.
But if you want to find out the area of any parallelogram and if you can figure out the height it is literally, you just take one of the bases because opposite sides are equal times the height. So thats one way you could of found the area.
So if I were to rotate it like that. Stand it on this side, so this would be point A This would be point D.
Or you could say it's equal to AD times I'll call this altitude right here h2. Maybe I'll call this h1.
Remix.
To combine or edit existing materials to produce something new
The term remix originally applied to music.
It rose to prominence late last century during the heyday of hip-hop, the first musical form to incorporate sampling from existing recordings.
Early example: the Sugarhill Gang samples the bass riff from Chic's "Good Times" in the 1979 hit "Rapper's Delight".
Since then that same bassline has been sampled dozens of times.
Skip ahead to the present and anybody can remix anything — music, video, photos, whatever — and distribute it globally pretty much instantly.
You don't need expensive tools, you don't need a distributor, you don't even need skills.
Remixing is a folk art — anybody can do it.
Yet these techniques — collecting material, combining it, transforming it — are the same ones used at any level of creation.
You could even say that everything is a remix.
To explain, let's start in England in 1968.
Part One:
The Song Remains the Same
Jimmy Page recruits John Paul Jones, Robert Plant, and John Bonham to form Led Zeppelin.
They play extremely loud blues music that soon will be known as—
Wait, let's start in Paris in 1961.
William Burroughs coins the term "heavy metal" in the novel "The Soft Machine," a book composed using the cut-up technique, taking existing writing and literally chopping it up and rearranging it.
So in 1961 William Burroughs not only invents the term "heavy metal," the brand of music Zeppelin and a few other groups would pioneer, he also produces an early remix.
Back to Zeppelin.
By the mid-1970s Led Zeppelin are the biggest touring rock band in America, yet many critics and peers label them as rip-offs.
The case goes like this.
The opening and closing sections of "Bring it on Home" are lifted from a tune by Willie Dixon entitled — not coincidentally — "Bring it on Home."
Performed by Sonny Boy Williamson
"The Lemon Song" lifts numerous lyrics from Howlin" Wolf's "Killing Floor."
"Black Mountain Side" lifts its melody from "Blackwaterside," a traditional arranged by Bert Jansch.
(Traditional, Arranged Jansch)
"Dazed and Confused" features different lyrics but is clearly an uncredited cover of the same-titled song by Jake Holmes.
Oddly enough, Holmes files suit over forty years later in 2010.
And the big one, "Stairway to Heaven" pulls its opening from Spirit's "Taurus."
Zeppelin toured with Spirit in 1968, three years before "Stairway" was released.
Zeppelin clearly copied a lot of other people's material, but that alone, isn't unusual.
Only two things distinguished Zeppelin from their peers.
Firstly, when Zeppelin used someone else's material, they didn't attribute songwriting to the original artist.
Most British blues groups were recording lots of covers, but unlike Zeppelin, they didn't claim to have written them.
Secondly, Led Zeppelin didn't modify their versions enough to claim they were original.
Many bands knock-off acts that came before them, but they tend to emulate the general sound rather than specific lyrics or melodies.
Zeppelin copied without making fundamental changes.
So, these two things.
Covers: performances of other people's material And knock-offs: copies that stay within legal boundaries
These are long-standing examples of legal remixing.
This stuff accounts for almost everything the entertainment industry produces, and that's where we're headed in part two.
Written and Mixed by Kirby Ferguson
Follow this project on Twitter:
Twitter.com/RemixEverything
Full sources, references, and purchase links at EverythingisaRemix.info
Wait, one last thing.
In the wake of their enormous success,
Led Zeppelin went from the copier to the copied.
First in the 70s with groups like Aerosmith, Heart and Boston, then during the eighties heavy metal craze, and on into the era of sampling.
Here's the beats from "When the Levee Breaks" getting sampled and remixed.
In Zeppelin's defense, they never sued anybody.
Hi, I'm Kirby, I made the video you just watched, Everything is a Remix.
If you enjoyed the video please head over to EverythingisaRemix.info and donate a little money.
Anything you can muster would be greatly appreciated and will help me dedicate time to completing the remaining three episodes - it's going to be a four part series.
The site has plenty of complimentary information that I think you might find interesting as well.
You can also find links to songs and videos and stuff from the video.
If you happen to like them you can go there and purchase them.
It's also a good way to keep up with the latest with what's going on with the series.
I think that's it.
Okay, thank you for watching and I'll see you next time.
THE ADVENTURES OF SHERLOCK HOLMES by
SlR ARTHUR CONAN DOYLE
ADVENTURE I.
A SCANDAL IN BOHEMlA
I.
To Sherlock Holmes she is always THE woman.
I have seldom heard him mention her under any other name.
In his eyes she eclipses and predominates the whole of her sex.
It was not that he felt any emotion akin to love for Irene Adler.
All emotions, and that one particularly, were abhorrent to his cold, precise but admirably balanced mind.
He was, I take it, the most perfect reasoning and observing machine that the world has seen, but as a lover he would have placed himself in a false position.
He never spoke of the softer passions, save with a gibe and a sneer.
They were admirable things for the observer--excellent for drawing the veil from men's motives and actions.
But for the trained reasoner to admit such intrusions into his own delicate and finely adjusted temperament was to introduce a distracting factor which might throw a doubt upon all his mental results.
Grit in a sensitive instrument, or a crack in one of his own high-power lenses, would not be more disturbing than a strong emotion in a nature such as his.
And yet there was but one woman to him, and that woman was the late Irene Adler, of dubious and questionable memory.
I had seen little of Holmes lately. My marriage had drifted us away from each other.
My own complete happiness, and the home- centred interests which rise up around the man who first finds himself master of his own establishment, were sufficient to absorb all my attention, while Holmes, who
loathed every form of society with his whole Bohemian soul, remained in our lodgings in Baker Street, buried among his old books, and alternating from week to week between cocaine and ambition, the drowsiness of the drug, and the fierce energy of his own keen nature.
He was still, as ever, deeply attracted by the study of crime, and occupied his immense faculties and extraordinary powers of observation in following out those clues, and clearing up those mysteries which had been abandoned as hopeless by the official police.
From time to time I heard some vague account of his doings: of his summons to
Odessa in the case of the Trepoff murder, of his clearing up of the singular tragedy of the Atkinson brothers at Trincomalee, and finally of the mission which he had accomplished so delicately and successfully for the reigning family of Holland.
Beyond these signs of his activity, however, which I merely shared with all the readers of the daily press, I knew little of my former friend and companion.
One night--it was on the twentieth of
March, 1888--I was returning from a journey to a patient (for I had now returned to civil practice), when my way led me through
Baker Street.
As I passed the well-remembered door, which must always be associated in my mind with my wooing, and with the dark incidents of the Study in Scarlet, I was seized with a keen desire to see Holmes again, and to know how he was employing his extraordinary powers.
His rooms were brilliantly lit, and, even as I looked up, I saw his tall, spare figure pass twice in a dark silhouette against the blind.
He was pacing the room swiftly, eagerly, with his head sunk upon his chest and his hands clasped behind him.
To me, who knew his every mood and habit, his attitude and manner told their own story.
He was at work again.
He had risen out of his drug-created dreams and was hot upon the scent of some new problem.
I rang the bell and was shown up to the chamber which had formerly been in part my own.
His manner was not effusive.
It seldom was; but he was glad, I think, to see me.
With hardly a word spoken, but with a kindly eye, he waved me to an armchair, threw across his case of cigars, and indicated a spirit case and a gasogene in the corner.
Then he stood before the fire and looked me over in his singular introspective fashion.
"Wedlock suits you," he remarked.
"I think, Watson, that you have put on seven and a half pounds since I saw you."
"Seven!"
I answered.
"Indeed, I should have thought a little more.
Just a trifle more, I fancy, Watson.
And in practice again, I observe.
You did not tell me that you intended to go into harness."
"Then, how do you know?"
"I see it, I deduce it.
How do I know that you have been getting yourself very wet lately, and that you have a most clumsy and careless servant girl?"
"My dear Holmes," said I, "this is too much.
You would certainly have been burned, had you lived a few centuries ago.
It is true that I had a country walk on
Thursday and came home in a dreadful mess, but as I have changed my clothes I can't imagine how you deduce it.
As to Mary Jane, she is incorrigible, and my wife has given her notice, but there, again, I fail to see how you work it out."
He chuckled to himself and rubbed his long, nervous hands together.
"It is simplicity itself," said he; "my eyes tell me that on the inside of your left shoe, just where the firelight strikes it, the leather is scored by six almost parallel cuts.
Obviously they have been caused by someone who has very carelessly scraped round the edges of the sole in order to remove crusted mud from it.
Hence, you see, my double deduction that you had been out in vile weather, and that you had a particularly malignant boot- slitting specimen of the London slavey.
As to your practice, if a gentleman walks into my rooms smelling of iodoform, with a black mark of nitrate of silver upon his right forefinger, and a bulge on the right side of his top-hat to show where he has secreted his stethoscope, I must be dull, indeed, if I do not pronounce him to be an active member of the medical profession."
I could not help laughing at the ease with which he explained his process of deduction.
"When I hear you give your reasons," I remarked, "the thing always appears to me to be so ridiculously simple that I could easily do it myself, though at each successive instance of your reasoning I am baffled until you explain your process.
And yet I believe that my eyes are as good as yours."
"Quite so," he answered, lighting a cigarette, and throwing himself down into an armchair.
"You see, but you do not observe.
The distinction is clear.
For example, you have frequently seen the steps which lead up from the hall to this room."
"Frequently."
"How often?"
"Well, some hundreds of times."
"Then how many are there?"
"How many?
I don't know."
"Quite so!
You have not observed.
And yet you have seen.
That is just my point.
Now, I know that there are seventeen steps, because I have both seen and observed.
By-the-way, since you are interested in these little problems, and since you are good enough to chronicle one or two of my trifling experiences, you may be interested in this."
He threw over a sheet of thick, pink-tinted note-paper which had been lying open upon the table.
"It came by the last post," said he.
"Read it aloud."
The note was undated, and without either signature or address.
"There will call upon you to-night, at a quarter to eight o'clock," it said, "a gentleman who desires to consult you upon a matter of the very deepest moment.
Your recent services to one of the royal houses of Europe have shown that you are one who may safely be trusted with matters which are of an importance which can hardly be exaggerated.
This account of you we have from all quarters received.
Be in your chamber then at that hour, and do not take it amiss if your visitor wear a mask."
"This is indeed a mystery," I remarked.
"What do you imagine that it means?"
"I have no data yet.
It is a capital mistake to theorize before one has data.
Insensibly one begins to twist facts to suit theories, instead of theories to suit facts.
But the note itself.
What do you deduce from it?"
I carefully examined the writing, and the paper upon which it was written.
"The man who wrote it was presumably well to do," I remarked, endeavouring to imitate my companion's processes.
"Such paper could not be bought under half a crown a packet.
It is peculiarly strong and stiff."
"Peculiar--that is the very word," said
Holmes.
"It is not an English paper at all.
Hold it up to the light."
I did so, and saw a large "E" with a small
"g," a "P," and a large "G" with a small
"t" woven into the texture of the paper.
"What do you make of that?" asked Holmes.
"The name of the maker, no doubt; or his monogram, rather."
"Not at all.
The 'G' with the small 't' stands for
'Gesellschaft,' which is the German for
'Company.'
It is a customary contraction like our
'Co.'
'P,' of course, stands for 'Papier.'
Now for the 'Eg.'
Let us glance at our Continental
Gazetteer."
He took down a heavy brown volume from his shelves.
"Eglow, Eglonitz--here we are, Egria.
It is in a German-speaking country--in
Bohemia, not far from Carlsbad.
'Remarkable as being the scene of the death of Wallenstein, and for its numerous glass- factories and paper-mills.'
Ha, ha, my boy, what do you make of that?"
His eyes sparkled, and he sent up a great blue triumphant cloud from his cigarette.
"The paper was made in Bohemia," I said.
"Precisely.
And the man who wrote the note is a German.
Do you note the peculiar construction of the sentence--'This account of you we have from all quarters received.'
A Frenchman or Russian could not have written that.
It is the German who is so uncourteous to his verbs.
It only remains, therefore, to discover what is wanted by this German who writes upon Bohemian paper and prefers wearing a mask to showing his face.
And here he comes, if I am not mistaken, to resolve all our doubts."
As he spoke there was the sharp sound of horses' hoofs and grating wheels against the curb, followed by a sharp pull at the bell.
Holmes whistled.
"A pair, by the sound," said he.
"Yes," he continued, glancing out of the window.
"A nice little brougham and a pair of beauties.
A hundred and fifty guineas apiece.
There's money in this case, Watson, if there is nothing else."
"I think that I had better go, Holmes."
"Not a bit, Doctor.
Stay where you are.
I am lost without my Boswell.
And this promises to be interesting.
It would be a pity to miss it."
"But your client--"
"Never mind him.
I may want your help, and so may he.
Here he comes.
Sit down in that armchair, Doctor, and give us your best attention."
A slow and heavy step, which had been heard upon the stairs and in the passage, paused immediately outside the door.
Then there was a loud and authoritative tap.
"Come in!" said Holmes.
A man entered who could hardly have been less than six feet six inches in height, with the chest and limbs of a Hercules. His dress was rich with a richness which would, in England, be looked upon as akin to bad taste.
Heavy bands of astrakhan were slashed across the sleeves and fronts of his double-breasted coat, while the deep blue cloak which was thrown over his shoulders was lined with flame-coloured silk and secured at the neck with a brooch which consisted of a single flaming beryl.
Boots which extended halfway up his calves, and which were trimmed at the tops with rich brown fur, completed the impression of barbaric opulence which was suggested by his whole appearance.
He carried a broad-brimmed hat in his hand, while he wore across the upper part of his face, extending down past the cheekbones, a black vizard mask, which he had apparently adjusted that very moment, for his hand was still raised to it as he entered.
From the lower part of the face he appeared to be a man of strong character, with a thick, hanging lip, and a long, straight chin suggestive of resolution pushed to the length of obstinacy.
"You had my note?" he asked with a deep harsh voice and a strongly marked German accent.
"I told you that I would call."
He looked from one to the other of us, as if uncertain which to address.
"Pray take a seat," said Holmes.
"This is my friend and colleague, Dr.
Watson, who is occasionally good enough to help me in my cases.
Whom have I the honour to address?"
"You may address me as the Count Von Kramm, a Bohemian nobleman.
I understand that this gentleman, your friend, is a man of honour and discretion, whom I may trust with a matter of the most extreme importance.
If not, I should much prefer to communicate with you alone."
I rose to go, but Holmes caught me by the wrist and pushed me back into my chair.
"It is both, or none," said he.
"You may say before this gentleman anything which you may say to me."
The Count shrugged his broad shoulders.
"Then I must begin," said he, "by binding you both to absolute secrecy for two years; at the end of that time the matter will be of no importance.
At present it is not too much to say that it is of such weight it may have an influence upon European history."
"I promise," said Holmes.
"And I."
"You will excuse this mask," continued our strange visitor.
"The august person who employs me wishes his agent to be unknown to you, and I may confess at once that the title by which I have just called myself is not exactly my own."
"I was aware of it," said Holmes dryly.
"The circumstances are of great delicacy, and every precaution has to be taken to quench what might grow to be an immense scandal and seriously compromise one of the reigning families of Europe.
To speak plainly, the matter implicates the great House of Ormstein, hereditary kings of Bohemia."
"I was also aware of that," murmured
Holmes, settling himself down in his armchair and closing his eyes.
Our visitor glanced with some apparent surprise at the languid, lounging figure of the man who had been no doubt depicted to him as the most incisive reasoner and most energetic agent in Europe.
Holmes slowly reopened his eyes and looked impatiently at his gigantic client.
"If your Majesty would condescend to state your case," he remarked, "I should be better able to advise you."
The man sprang from his chair and paced up and down the room in uncontrollable agitation.
Then, with a gesture of desperation, he tore the mask from his face and hurled it upon the ground.
"You are right," he cried; "I am the King.
Why should I attempt to conceal it?"
"Why, indeed?" murmured Holmes.
"Your Majesty had not spoken before I was aware that I was addressing Wilhelm
Gottsreich Sigismond von Ormstein, Grand
Duke of Cassel-Felstein, and hereditary
King of Bohemia."
"But you can understand," said our strange visitor, sitting down once more and passing his hand over his high white forehead, "you can understand that I am not accustomed to doing such business in my own person.
Yet the matter was so delicate that I could not confide it to an agent without putting myself in his power.
I have come incognito from Prague for the purpose of consulting you."
"Then, pray consult," said Holmes, shutting his eyes once more.
"The facts are briefly these:
Some five years ago, during a lengthy visit to
Warsaw, I made the acquaintance of the well-known adventuress, Irene Adler.
The name is no doubt familiar to you."
"Kindly look her up in my index, Doctor," murmured Holmes without opening his eyes.
For many years he had adopted a system of docketing all paragraphs concerning men and things, so that it was difficult to name a subject or a person on which he could not at once furnish information.
In this case I found her biography sandwiched in between that of a Hebrew rabbi and that of a staff-commander who had written a monograph upon the deep-sea fishes.
"Let me see!" said Holmes.
"Hum!
Born in New Jersey in the year 1858.
Contralto--hum!
La Scala, hum!
Prima donna Imperial Opera of Warsaw--yes!
Retired from operatic stage--ha!
Living in London--quite so!
Your Majesty, as I understand, became entangled with this young person, wrote her some compromising letters, and is now desirous of getting those letters back."
"Precisely so.
But how--"
"Was there a secret marriage?"
"None."
"No legal papers or certificates?"
"None."
"Then I fail to follow your Majesty.
If this young person should produce her letters for blackmailing or other purposes, how is she to prove their authenticity?"
"There is the writing."
"Pooh, pooh!
Forgery."
"My private note-paper."
"Stolen."
"My own seal."
"Imitated."
"My photograph."
"Bought."
"We were both in the photograph."
"Oh, dear!
That is very bad!
Your Majesty has indeed committed an indiscretion."
"I was mad--insane."
"You have compromised yourself seriously."
"I was only Crown Prince then.
I was young.
I am but thirty now."
"It must be recovered."
"We have tried and failed."
"Your Majesty must pay.
It must be bought."
"She will not sell."
"Stolen, then."
"Five attempts have been made.
Twice burglars in my pay ransacked her house.
Once we diverted her luggage when she travelled.
Twice she has been waylaid.
There has been no result."
"No sign of it?"
"Absolutely none."
Holmes laughed.
"It is quite a pretty little problem," said he.
"But a very serious one to me," returned the King reproachfully.
"Very, indeed.
And what does she propose to do with the photograph?"
"To ruin me."
"But how?"
"I am about to be married."
"So I have heard."
"To Clotilde Lothman von Saxe-Meningen, second daughter of the King of Scandinavia.
You may know the strict principles of her family.
She is herself the very soul of delicacy.
A shadow of a doubt as to my conduct would bring the matter to an end."
"And Irene Adler?"
"Threatens to send them the photograph.
And she will do it.
I know that she will do it.
You do not know her, but she has a soul of steel.
She has the face of the most beautiful of women, and the mind of the most resolute of men.
Rather than I should marry another woman, there are no lengths to which she would not go--none."
"You are sure that she has not sent it yet?"
"I am sure."
"And why?"
"Because she has said that she would send it on the day when the betrothal was publicly proclaimed.
That will be next Monday."
"Oh, then we have three days yet," said
Holmes with a yawn.
"That is very fortunate, as I have one or two matters of importance to look into just at present.
Your Majesty will, of course, stay in
London for the present?"
"Certainly.
You will find me at the Langham under the name of the Count Von Kramm."
"Then I shall drop you a line to let you know how we progress."
"Pray do so.
I shall be all anxiety."
"Then, as to money?"
"You have carte blanche."
"Absolutely?"
"I tell you that I would give one of the provinces of my kingdom to have that photograph."
"And for present expenses?"
The King took a heavy chamois leather bag from under his cloak and laid it on the table.
"There are three hundred pounds in gold and seven hundred in notes," he said.
Holmes scribbled a receipt upon a sheet of his note-book and handed it to him.
"And Mademoiselle's address?" he asked.
"Is Briony Lodge, Serpentine Avenue, St.
John's Wood."
Holmes took a note of it.
"One other question," said he.
"Was the photograph a cabinet?"
"It was."
"Then, good-night, your Majesty, and I trust that we shall soon have some good news for you.
And good-night, Watson," he added, as the wheels of the royal brougham rolled down the street.
"If you will be good enough to call to- morrow afternoon at three o'clock I should like to chat this little matter over with you."
Il.
At three o'clock precisely I was at Baker
Street, but Holmes had not yet returned.
The landlady informed me that he had left the house shortly after eight o'clock in the morning.
I sat down beside the fire, however, with the intention of awaiting him, however long he might be.
I was already deeply interested in his inquiry, for, though it was surrounded by none of the grim and strange features which were associated with the two crimes which I have already recorded, still, the nature of the case and the exalted station of his client gave it a character of its own.
Indeed, apart from the nature of the investigation which my friend had on hand, there was something in his masterly grasp of a situation, and his keen, incisive reasoning, which made it a pleasure to me to study his system of work, and to follow the quick, subtle methods by which he disentangled the most inextricable mysteries.
So accustomed was I to his invariable success that the very possibility of his failing had ceased to enter into my head.
It was close upon four before the door opened, and a drunken-looking groom, ill- kempt and side-whiskered, with an inflamed face and disreputable clothes, walked into the room.
Accustomed as I was to my friend's amazing powers in the use of disguises, I had to look three times before I was certain that it was indeed he.
With a nod he vanished into the bedroom, whence he emerged in five minutes tweed- suited and respectable, as of old.
Putting his hands into his pockets, he stretched out his legs in front of the fire and laughed heartily for some minutes.
"Well, really!" he cried, and then he choked and laughed again until he was obliged to lie back, limp and helpless, in the chair.
"What is it?"
"It's quite too funny.
I am sure you could never guess how I employed my morning, or what I ended by doing."
"I can't imagine.
I suppose that you have been watching the habits, and perhaps the house, of Miss
Irene Adler."
"Quite so; but the sequel was rather unusual.
I will tell you, however.
I left the house a little after eight o'clock this morning in the character of a groom out of work.
There is a wonderful sympathy and freemasonry among horsey men.
Be one of them, and you will know all that there is to know.
I soon found Briony Lodge.
It is a bijou villa, with a garden at the back, but built out in front right up to the road, two stories.
Chubb lock to the door.
Large sitting-room on the right side, well furnished, with long windows almost to the floor, and those preposterous English window fasteners which a child could open.
Behind there was nothing remarkable, save that the passage window could be reached from the top of the coach-house.
I walked round it and examined it closely from every point of view, but without noting anything else of interest.
"I then lounged down the street and found, as I expected, that there was a mews in a lane which runs down by one wall of the garden.
I lent the ostlers a hand in rubbing down their horses, and received in exchange twopence, a glass of half and half, two fills of shag tobacco, and as much information as I could desire about Miss
Adler, to say nothing of half a dozen other people in the neighbourhood in whom I was not in the least interested, but whose biographies I was compelled to listen to."
"And what of Irene Adler?"
I asked.
"Oh, she has turned all the men's heads down in that part.
She is the daintiest thing under a bonnet on this planet.
So say the Serpentine-mews, to a man.
She lives quietly, sings at concerts, drives out at five every day, and returns at seven sharp for dinner.
Seldom goes out at other times, except when she sings.
Has only one male visitor, but a good deal of him.
He is dark, handsome, and dashing, never calls less than once a day, and often twice.
He is a Mr. Godfrey Norton, of the Inner
Temple.
See the advantages of a cabman as a confidant.
They had driven him home a dozen times from
Serpentine-mews, and knew all about him.
When I had listened to all they had to tell, I began to walk up and down near
Briony Lodge once more, and to think over my plan of campaign.
"This Godfrey Norton was evidently an important factor in the matter.
He was a lawyer.
That sounded ominous.
What was the relation between them, and what the object of his repeated visits?
Was she his client, his friend, or his mistress?
If the former, she had probably transferred the photograph to his keeping.
If the latter, it was less likely.
On the issue of this question depended whether I should continue my work at Briony
Lodge, or turn my attention to the gentleman's chambers in the Temple.
It was a delicate point, and it widened the field of my inquiry.
I fear that I bore you with these details, but I have to let you see my little difficulties, if you are to understand the situation."
"I am following you closely," I answered.
"I was still balancing the matter in my mind when a hansom cab drove up to Briony
Lodge, and a gentleman sprang out.
He was a remarkably handsome man, dark, aquiline, and moustached--evidently the man of whom I had heard.
He appeared to be in a great hurry, shouted to the cabman to wait, and brushed past the maid who opened the door with the air of a man who was thoroughly at home.
"He was in the house about half an hour, and I could catch glimpses of him in the windows of the sitting-room, pacing up and down, talking excitedly, and waving his arms.
Of her I could see nothing.
Presently he emerged, looking even more flurried than before.
As he stepped up to the cab, he pulled a gold watch from his pocket and looked at it earnestly, 'Drive like the devil,' he shouted, 'first to Gross & Hankey's in
Regent Street, and then to the Church of
St. Monica in the Edgeware Road.
Half a guinea if you do it in twenty minutes!'
"Away they went, and I was just wondering whether I should not do well to follow them when up the lane came a neat little landau, the coachman with his coat only half- buttoned, and his tie under his ear, while all the tags of his harness were sticking out of the buckles.
It hadn't pulled up before she shot out of the hall door and into it.
I only caught a glimpse of her at the moment, but she was a lovely woman, with a face that a man might die for. "'The Church of St. Monica, John,' she cried, 'and half a sovereign if you reach it in twenty minutes.'
"This was quite too good to lose, Watson.
I was just balancing whether I should run for it, or whether I should perch behind her landau when a cab came through the street.
The driver looked twice at such a shabby fare, but I jumped in before he could object.
'The Church of St. Monica,' said I, 'and half a sovereign if you reach it in twenty minutes.'
It was twenty-five minutes to twelve, and of course it was clear enough what was in the wind.
"My cabby drove fast.
I don't think I ever drove faster, but the others were there before us.
The cab and the landau with their steaming horses were in front of the door when I arrived.
I paid the man and hurried into the church.
There was not a soul there save the two whom I had followed and a surpliced clergyman, who seemed to be expostulating with them.
They were all three standing in a knot in front of the altar.
I lounged up the side aisle like any other idler who has dropped into a church.
Suddenly, to my surprise, the three at the altar faced round to me, and Godfrey Norton came running as hard as he could towards me. "'Thank God,' he cried.
'You'll do.
Come!
Come!' "'What then?'
I asked. "'Come, man, come, only three minutes, or it won't be legal.'
"I was half-dragged up to the altar, and before I knew where I was I found myself mumbling responses which were whispered in my ear, and vouching for things of which I knew nothing, and generally assisting in the secure tying up of Irene Adler, spinster, to Godfrey Norton, bachelor.
It was all done in an instant, and there was the gentleman thanking me on the one side and the lady on the other, while the clergyman beamed on me in front.
It was the most preposterous position in which I ever found myself in my life, and it was the thought of it that started me laughing just now.
It seems that there had been some informality about their license, that the clergyman absolutely refused to marry them without a witness of some sort, and that my lucky appearance saved the bridegroom from having to sally out into the streets in search of a best man. The bride gave me a sovereign, and I mean to wear it on my watch-chain in memory of the occasion."
"This is a very unexpected turn of affairs," said I; "and what then?"
"Well, I found my plans very seriously menaced.
It looked as if the pair might take an immediate departure, and so necessitate very prompt and energetic measures on my part.
At the church door, however, they separated, he driving back to the Temple, and she to her own house.
'I shall drive out in the park at five as usual,' she said as she left him.
I heard no more.
They drove away in different directions, and I went off to make my own arrangements."
"Which are?"
"Some cold beef and a glass of beer," he answered, ringing the bell.
"I have been too busy to think of food, and
I am likely to be busier still this evening.
By the way, Doctor, I shall want your co- operation."
"I shall be delighted."
"You don't mind breaking the law?"
"Not in the least."
"Nor running a chance of arrest?"
"Not in a good cause."
"Oh, the cause is excellent!"
"Then I am your man."
"I was sure that I might rely on you."
"But what is it you wish?"
"When Mrs. Turner has brought in the tray I will make it clear to you.
Now," he said as he turned hungrily on the simple fare that our landlady had provided,
"I must discuss it while I eat, for I have not much time.
It is nearly five now.
In two hours we must be on the scene of action.
Miss Irene, or Madame, rather, returns from her drive at seven.
We must be at Briony Lodge to meet her."
"And what then?"
"You must leave that to me.
I have already arranged what is to occur.
There is only one point on which I must insist.
You must not interfere, come what may.
You understand?"
"I am to be neutral?"
"To do nothing whatever.
There will probably be some small unpleasantness.
Do not join in it.
It will end in my being conveyed into the house.
Four or five minutes afterwards the sitting-room window will open.
You are to station yourself close to that open window."
"Yes."
"You are to watch me, for I will be visible to you."
"Yes."
"And when I raise my hand--so--you will throw into the room what I give you to throw, and will, at the same time, raise the cry of fire.
You quite follow me?"
"Entirely."
"It is nothing very formidable," he said, taking a long cigar-shaped roll from his pocket.
"It is an ordinary plumber's smoke-rocket, fitted with a cap at either end to make it self-lighting.
Your task is confined to that.
When you raise your cry of fire, it will be taken up by quite a number of people.
You may then walk to the end of the street, and I will rejoin you in ten minutes.
I hope that I have made myself clear?"
"I am to remain neutral, to get near the window, to watch you, and at the signal to throw in this object, then to raise the cry of fire, and to wait you at the corner of the street."
"Precisely."
"Then you may entirely rely on me."
"That is excellent.
I think, perhaps, it is almost time that I prepare for the new role I have to play."
He disappeared into his bedroom and returned in a few minutes in the character of an amiable and simple-minded
Nonconformist clergyman.
His broad black hat, his baggy trousers, his white tie, his sympathetic smile, and general look of peering and benevolent curiosity were such as Mr. John Hare alone could have equalled.
It was not merely that Holmes changed his costume.
His expression, his manner, his very soul seemed to vary with every fresh part that he assumed.
The stage lost a fine actor, even as science lost an acute reasoner, when he became a specialist in crime.
It was a quarter past six when we left
Baker Street, and it still wanted ten minutes to the hour when we found ourselves in Serpentine Avenue.
It was already dusk, and the lamps were just being lighted as we paced up and down in front of Briony Lodge, waiting for the coming of its occupant.
The house was just such as I had pictured it from Sherlock Holmes' succinct description, but the locality appeared to be less private than I expected.
On the contrary, for a small street in a quiet neighbourhood, it was remarkably animated.
There was a group of shabbily dressed men smoking and laughing in a corner, a scissors-grinder with his wheel, two guardsmen who were flirting with a nurse- girl, and several well-dressed young men who were lounging up and down with cigars in their mouths.
"You see," remarked Holmes, as we paced to and fro in front of the house, "this marriage rather simplifies matters.
The photograph becomes a double-edged weapon now.
The chances are that she would be as averse to its being seen by Mr. Godfrey Norton, as our client is to its coming to the eyes of his princess.
Now the question is, Where are we to find the photograph?"
"Where, indeed?"
"It is most unlikely that she carries it about with her.
It is cabinet size.
Too large for easy concealment about a woman's dress.
She knows that the King is capable of having her waylaid and searched.
Two attempts of the sort have already been made.
We may take it, then, that she does not carry it about with her."
"Where, then?"
"Her banker or her lawyer.
There is that double possibility.
But I am inclined to think neither.
Women are naturally secretive, and they like to do their own secreting.
Why should she hand it over to anyone else?
She could trust her own guardianship, but she could not tell what indirect or political influence might be brought to bear upon a business man.
Besides, remember that she had resolved to use it within a few days.
It must be where she can lay her hands upon it.
It must be in her own house."
"But it has twice been burgled."
"Pshaw!
They did not know how to look."
"But how will you look?"
"I will not look."
"What then?"
"I will get her to show me."
"But she will refuse."
"She will not be able to.
But I hear the rumble of wheels.
It is her carriage.
Now carry out my orders to the letter."
As he spoke the gleam of the side-lights of a carriage came round the curve of the avenue.
It was a smart little landau which rattled up to the door of Briony Lodge.
As it pulled up, one of the loafing men at the corner dashed forward to open the door in the hope of earning a copper, but was elbowed away by another loafer, who had rushed up with the same intention.
A fierce quarrel broke out, which was increased by the two guardsmen, who took sides with one of the loungers, and by the scissors-grinder, who was equally hot upon the other side.
A blow was struck, and in an instant the lady, who had stepped from her carriage, was the centre of a little knot of flushed and struggling men, who struck savagely at each other with their fists and sticks.
Holmes dashed into the crowd to protect the lady; but just as he reached her he gave a cry and dropped to the ground, with the blood running freely down his face.
At his fall the guardsmen took to their heels in one direction and the loungers in the other, while a number of better-dressed people, who had watched the scuffle without taking part in it, crowded in to help the lady and to attend to the injured man.
Irene Adler, as I will still call her, had hurried up the steps; but she stood at the top with her superb figure outlined against the lights of the hall, looking back into the street.
"Is the poor gentleman much hurt?" she asked.
"He is dead," cried several voices.
"No, no, there's life in him!" shouted another.
"But he'll be gone before you can get him to hospital."
"He's a brave fellow," said a woman.
"They would have had the lady's purse and watch if it hadn't been for him.
They were a gang, and a rough one, too.
Ah, he's breathing now."
"He can't lie in the street.
May we bring him in, marm?"
"Surely.
Bring him into the sitting-room.
There is a comfortable sofa.
This way, please!"
Slowly and solemnly he was borne into
Briony Lodge and laid out in the principal room, while I still observed the proceedings from my post by the window.
The lamps had been lit, but the blinds had not been drawn, so that I could see Holmes as he lay upon the couch.
I do not know whether he was seized with compunction at that moment for the part he was playing, but I know that I never felt more heartily ashamed of myself in my life than when I saw the beautiful creature against whom I was conspiring, or the grace and kindliness with which she waited upon the injured man.
And yet it would be the blackest treachery to Holmes to draw back now from the part which he had intrusted to me.
I hardened my heart, and took the smoke- rocket from under my ulster.
After all, I thought, we are not injuring her.
We are but preventing her from injuring another.
Holmes had sat up upon the couch, and I saw him motion like a man who is in need of air.
A maid rushed across and threw open the window.
At the same instant I saw him raise his hand and at the signal I tossed my rocket into the room with a cry of "Fire!"
The word was no sooner out of my mouth than the whole crowd of spectators, well dressed and ill--gentlemen, ostlers, and servant- maids--joined in a general shriek of
"Fire!" Thick clouds of smoke curled through the room and out at the open window.
I caught a glimpse of rushing figures, and a moment later the voice of Holmes from within assuring them that it was a false alarm.
Slipping through the shouting crowd I made my way to the corner of the street, and in ten minutes was rejoiced to find my friend's arm in mine, and to get away from the scene of uproar.
He walked swiftly and in silence for some few minutes until we had turned down one of the quiet streets which lead towards the
Edgeware Road.
"You did it very nicely, Doctor," he remarked.
"Nothing could have been better.
It is all right."
"You have the photograph?"
"I know where it is."
"And how did you find out?"
"She showed me, as I told you she would."
"I am still in the dark."
"I do not wish to make a mystery," said he, laughing.
"The matter was perfectly simple.
You, of course, saw that everyone in the street was an accomplice.
They were all engaged for the evening."
"I guessed as much."
"Then, when the row broke out, I had a little moist red paint in the palm of my hand.
I rushed forward, fell down, clapped my hand to my face, and became a piteous spectacle.
It is an old trick."
"That also I could fathom."
"Then they carried me in.
She was bound to have me in.
What else could she do?
And into her sitting-room, which was the very room which I suspected.
It lay between that and her bedroom, and I was determined to see which.
They laid me on a couch, I motioned for air, they were compelled to open the window, and you had your chance."
"How did that help you?"
"It was all-important.
When a woman thinks that her house is on fire, her instinct is at once to rush to the thing which she values most.
It is a perfectly overpowering impulse, and
I have more than once taken advantage of it.
In the case of the Darlington substitution scandal it was of use to me, and also in the Arnsworth Castle business.
A married woman grabs at her baby; an unmarried one reaches for her jewel-box.
Now it was clear to me that our lady of to- day had nothing in the house more precious to her than what we are in quest of.
She would rush to secure it.
The alarm of fire was admirably done.
The smoke and shouting were enough to shake nerves of steel.
She responded beautifully.
The photograph is in a recess behind a sliding panel just above the right bell- pull.
She was there in an instant, and I caught a glimpse of it as she half-drew it out.
When I cried out that it was a false alarm, she replaced it, glanced at the rocket, rushed from the room, and I have not seen her since.
I rose, and, making my excuses, escaped from the house.
I hesitated whether to attempt to secure the photograph at once; but the coachman had come in, and as he was watching me narrowly it seemed safer to wait.
A little over-precipitance may ruin all."
"And now?"
I asked.
"Our quest is practically finished.
I shall call with the King to-morrow, and with you, if you care to come with us.
We will be shown into the sitting-room to wait for the lady, but it is probable that when she comes she may find neither us nor the photograph.
It might be a satisfaction to his Majesty to regain it with his own hands."
"And when will you call?"
"At eight in the morning.
She will not be up, so that we shall have a clear field.
Besides, we must be prompt, for this marriage may mean a complete change in her life and habits.
I must wire to the King without delay."
We had reached Baker Street and had stopped at the door.
He was searching his pockets for the key when someone passing said:
"Good-night, Mister Sherlock Holmes."
There were several people on the pavement at the time, but the greeting appeared to come from a slim youth in an ulster who had hurried by.
"I've heard that voice before," said
Holmes, staring down the dimly lit street.
"Now, I wonder who the deuce that could have been."
IIl.
I slept at Baker Street that night, and we were engaged upon our toast and coffee in the morning when the King of Bohemia rushed into the room.
"You have really got it!" he cried, grasping Sherlock Holmes by either shoulder and looking eagerly into his face.
"Not yet."
"But you have hopes?"
"I have hopes."
"Then, come.
I am all impatience to be gone."
"We must have a cab."
"No, my brougham is waiting."
"Then that will simplify matters."
We descended and started off once more for
Briony Lodge.
"Irene Adler is married," remarked Holmes.
"Married!
When?"
"Yesterday."
"But to whom?"
"To an English lawyer named Norton."
"But she could not love him."
"I am in hopes that she does."
"And why in hopes?"
"Because it would spare your Majesty all fear of future annoyance.
If the lady loves her husband, she does not love your Majesty.
If she does not love your Majesty, there is no reason why she should interfere with your Majesty's plan."
"It is true.
And yet--Well!
I wish she had been of my own station!
What a queen she would have made!"
He relapsed into a moody silence, which was not broken until we drew up in Serpentine
Avenue.
The door of Briony Lodge was open, and an elderly woman stood upon the steps.
She watched us with a sardonic eye as we stepped from the brougham.
"Mr. Sherlock Holmes, I believe?" said she.
"I am Mr. Holmes," answered my companion, looking at her with a questioning and rather startled gaze.
"Indeed! My mistress told me that you were likely to call.
She left this morning with her husband by the 5:15 train from Charing Cross for the
Continent."
"What!"
Sherlock Holmes staggered back, white with chagrin and surprise.
"Do you mean that she has left England?"
"Never to return."
"And the papers?" asked the King hoarsely.
"All is lost."
"We shall see."
He pushed past the servant and rushed into the drawing-room, followed by the King and myself. The furniture was scattered about in every direction, with dismantled shelves and open drawers, as if the lady had hurriedly ransacked them before her flight.
Holmes rushed at the bell-pull, tore back a small sliding shutter, and, plunging in his hand, pulled out a photograph and a letter.
The photograph was of Irene Adler herself in evening dress, the letter was superscribed to "Sherlock Holmes, Esq.
To be left till called for."
My friend tore it open and we all three read it together.
It was dated at midnight of the preceding night and ran in this way:
"MY DEAR MR. SHERLOCK HOLMES,--You really did it very well.
You took me in completely.
Until after the alarm of fire, I had not a suspicion.
But then, when I found how I had betrayed myself, I began to think.
I had been warned against you months ago.
I had been told that if the King employed an agent it would certainly be you.
And your address had been given me.
Yet, with all this, you made me reveal what you wanted to know.
Even after I became suspicious, I found it hard to think evil of such a dear, kind old clergyman.
But, you know, I have been trained as an actress myself.
Male costume is nothing new to me.
I often take advantage of the freedom which it gives.
I sent John, the coachman, to watch you, ran up stairs, got into my walking-clothes, as I call them, and came down just as you departed.
"Well, I followed you to your door, and so made sure that I was really an object of interest to the celebrated Mr. Sherlock
Holmes.
Then I, rather imprudently, wished you good-night, and started for the Temple to see my husband.
"We both thought the best resource was flight, when pursued by so formidable an antagonist; so you will find the nest empty when you call to-morrow.
As to the photograph, your client may rest in peace.
I love and am loved by a better man than he.
The King may do what he will without hindrance from one whom he has cruelly wronged.
I keep it only to safeguard myself, and to preserve a weapon which will always secure me from any steps which he might take in the future.
I leave a photograph which he might care to possess; and I remain, dear Mr. Sherlock
Holmes,
"Very truly yours, "IRENE NORTON, née
ADLER."
"What a woman--oh, what a woman!" cried the
King of Bohemia, when we had all three read this epistle.
"Did I not tell you how quick and resolute she was?
Would she not have made an admirable queen?
Is it not a pity that she was not on my level?"
"From what I have seen of the lady she seems indeed to be on a very different level to your Majesty," said Holmes coldly.
"I am sorry that I have not been able to bring your Majesty's business to a more successful conclusion."
"On the contrary, my dear sir," cried the
King; "nothing could be more successful.
I know that her word is inviolate.
The photograph is now as safe as if it were in the fire."
"I am glad to hear your Majesty say so."
"I am immensely indebted to you.
Pray tell me in what way I can reward you.
This ring--" He slipped an emerald snake ring from his finger and held it out upon the palm of his hand.
"Your Majesty has something which I should value even more highly," said Holmes.
"You have but to name it."
"This photograph!"
The King stared at him in amazement.
"Irene's photograph!" he cried.
"Certainly, if you wish it."
"I thank your Majesty.
Then there is no more to be done in the matter.
I have the honour to wish you a very good- morning."
He bowed, and, turning away without observing the hand which the King had stretched out to him, he set off in my company for his chambers.
And that was how a great scandal threatened to affect the kingdom of Bohemia, and how the best plans of Mr. Sherlock Holmes were beaten by a woman's wit.
He used to make merry over the cleverness of women, but I have not heard him do it of late.
And when he speaks of Irene Adler, or when he refers to her photograph, it is always under the honourable title of the woman.
<i> Brought to you by the PKer team @ www.viki.com</i>
Episode 1
Oh Ha Ni?
Oh Ha Ni?!
Yes?
What are you thinking about so early in the morning?
Children, studying is tough, isn't it?
Yeah...
Is it tough?!
Yes!
I know, what it means to be living as a senior in South Korea.
How lonely and hard it is...
Stop digging through your bag!
Erase those fake eyes!
However, even if you guys complain about how difficult it is... Could it compare to the stress third year teachers have to endure?!
Do you know the bitter taste of the teaching organization!!
Seems our grades are out, right?
That's right.
We're probably placed last again.
It's not the first time. I don't understand why she gets so upset every time.
Your house construction is done right?
You're not going to have a house-warming party?
I haven't been able to unpack and organize any of my things.
My dad comes home late every day and so do I.
Have Bong Joon Gu do it for you.
Earlier, he was staring at you like this.
No!!
If it's no, then what else is it?
He even joined the art club because of you.
Don't you ever get tired of it?
What...this?
Hey, if the daughter of a pork hock restaurant gets tired of them, then who else would come and eat it?
Ha Ni, are you tired of eating noodles?
I mean does the daughter of a noodle restaurant get tired of eating noodles?
I don't get tired of my dad's noodles.
Your restaurant's noodles are really tasty!
I approve, I approve!
Agree!
Hi!
Hi!
Heya?
Did she just greet us like that?
Huh?
What is this?
Why isn't it coming out?
Thank you.
Thank you...?
The senior mid-term exams, Baek Seung Jo Oppa got first place again
Is first place a big deal? A perfect score! He got 500/500.
What?
Baek Seung Jo got 100% again?
Is he human?
I said he wasn't human.
He's a spirit. "Spirit of the Forest".
So, I was following this white horse and then...
It disappeared and suddenly it reappeared!
Seriously... How should I say this?
It's the kind of beauty you want to take a bite out of!
Take a bite?!
That's when I realized what a vampire must feel like.
Maybe in the beginning vampires were like that too.
The neck of the girl he loved was so very white and so very beautiful...
He had no choice but to bite her!
Really Ha Ni, just take a bite of this pig foot.
Hey! I'm not making this up!
Okay, so just eat this.
Bite this, here, here!
Seung Jo oppa...
You can have this, I just bought it.
My mom told me to tell your mom that she says hi.
I'm Jang Mi.
Hong Jang Mi.
My mom and your mom are close.
Oh my!
It's not working again.
Ha Ni sunbae!
It's not coming out!
That sunbae helped me get this.
Ha Ni Sunbae, hurry up!
Here you go, Oppa.
Oppa, you got a perfect score this time too, right?
Wow! You're the best!
Ha Ni!
Oh Ha Ni!
Oh Ha Ni!!
OH!
HA!
Nl!
That's why you should just confess.
Confess?
We're going to be graduating soon.
How long are you going to be like this?
Oh! It's because I haven't confessed.
Since he doesn't know how I feel, that's why he can't express himself towards me.
Because he's shy.
What are you looking up?
I'm looking up the word "shy".
Alright, I got it.
I'll confess in a wonderful way.
But, how should I do it?
I want it to be very impressive.
How about this? "My precious Seung Jo, I love you."
Oh...that's not bad!
Not bad!?
What the heck!
What are you looking up?
I'm looking up the words "not bad."
Don't you have any good ideas?
You read a lot of books.
When animals confess, they dance.
Dance?
Fish, birds, and penguins, too, and even drosophila. They all the dance...the "Courtship Dance."
Courtship dance?
Aish.
Oh my!
We meet again.
Yep.
We're examining a real life model today, right?
As a senior, shouldn't you be studying?
Yeah!
We don't do stuff like studying.
Is your throat okay?
It seemed like your throat was going to rip back there.
Hey!
Don't.
However, won't it be hard? Um?
What is?
Nothing.
Oh.
Seung Jo... ...likes girls with big breasts too?
Of course.
Isn't Seung Jo Oppa a man too?
But why is Joon Gu Oppa not here yet?
He knows he is going to model for us today, right? <i>Brought to you by the PKer team @ www.viikii.net</i>
What's that?
What what what's that?
Move it!
What's this?
It's a chiacken.
Chiacken?
What's chiacken?
Chicken, a chicken.
Oh!
It's Samgyetang!
(Korean chicken soup)
This is Samgye...
This is for you.
Why are you giving it to me?
Look at you! You are so thin.
Joon Gu Oppa!
Hurry up and get ready, we don't have time to waste.
Alright, alright!
You eat it all!
Lower your waist a little bit more.
And arm higher...
Raise your leg a little.
Huh?
A little bit more...
Like this?
No, a little bit more.
This?!
Stop!
Okay, today's concept is capturing movement.
Okay then... Let's start. <i>Ahh my joints are in pain! <i>I feel like I'm gonna die, <i>but look!
Ha Ni is looking at me right now. <i>Ha Ni is drawing me. <i>This kind of pain <i>is nothing! <i>doesn't know how to give up!
[Confess... Courtship dance... Gollum..?? ♡]
What kind of bastard...
Goodness...
Can you still laugh when looking at this, Ms. Song Gang Yi?
Mr. Song Ji Ho's class has a lot of white stickers over here...
And where there are a lot of blue stickers... ...represents your students, Ms. Song Gang Yi.
It's so very blue, isn't it?!
You're right. It's like an ocean.
Teacher Song!!
Yes?
Ah...not Mr. Song, but Ms. Song.
(same family name)
Teacher Song Gang Yi, your class is bringing
These kids right here!
Oh Ha Ni, Dok Go Mi Na, Jung Ju Ri, and Bong Jun Gu!
Do something with at least these four rascals.
Might as well not allow them to take the test!
They are such an embarrassment!
Embarrassment!
That such an intelligent student like Baek Seung Jo was able to attend our school...
I am truly grateful.
Now, for the finishing touches.
You know that if you add some details to the muscles it will look more realistic, right?
Joon Gu Oppa, you can come down now.
Oh, okay.
Ouch!
Ahhh!
My leg, my leg!
I feel like I'm going to die.
Oh, right there!
That's good, good!
Ha Ni Sunbae!
Yes?
Why?
What?
What's going on?
Huh?!
What's this?
Do I look like this?
[So Pal Bok Guksoo] (Korean noodles)
Ha Ni! Check!
Oh, okay.
Check, please.
Yes.
We can let them dry all night and take them down tomorrow.
I just can't tell.
I've seen you do this since I was a baby.
Ah, when you were little, the roof was open.
But nowadays people don't like it aired outside, because the air is bad.
When I was a baby, we used to air it outside.
Right?
Huh?
Did you just say that?
Dad?
I guess so...
Dad...
Yes?
Dad, how did you show your love to Mom?
Show my love?
I mean confess!
Huh??
I mean...
Dad, you know my friend Ju Ri, right?
Yes.
Well, she's come to like someone, and she's wondering how to confess to him.
You see, back then my car was a complete piece of crap!
I took your mom in that car... ...and we sped all around the city!
It felt like the car was going to flip over and the tires were about to fall out.
Your mom asked, "are you crazy?"
She screamed, telling me to let her out.
And then?
So as I drove that car, I yelled right back at her.
"Do you want to kiss me or do you want to date me?"
"Do you want to date me or do you want to live with me?"
"Want to live with me?" "Or do you want to just die with me?!"
And then...
She said she was going to live with you?
No.
She asked, "do you wanna die?"
"Don't joke around."
What is this?
Ha Ni, but she later told me,
Really?
Hey Baek Seung Jo.
Do you want to kiss me or do you want to date me?
Надтай болзох уу эсвэл хамт амьдрах уу?
Do you want to live with me or right over there...
Bam!
You want to be buried?
Surely...when you're confessing... a thought out letter works best.
Letter?
Yeah.
Something like a love letter.
Dad!
See you at home later!
Unnie! Good work!
Ha Ni!
Clean your room!
Oh... no...
I'm sorry.
It's okay.
Aigoo.
Did she find a crush? <i>I want to marry you, accept my heart.<i> <i>Playful Kiss~
[Baek Seung Jo]
Still no reply?
You wrote your name?
Yeah.
And your phone number?
Yeah.
But I don't think he will call.
Well, you never know.
There's always texting.
Maybe he didn't see it yet.
Oh!
He's coming this way!
What do I do?
Did he see you?
He might be here for you.
Maybe he didn't read the letter?
Maybe he didn't see Ha Ni?
Right?
Ha Ni!!!
Oh Ha Ni!
Oh Ha Ni!
OH HA Nl!!!
Oh Ha...
What should I do?
Ha Ni!!!
Oh Ha Ni!!!
Oh...
Ha...
He's just leaving?
Ha Ni!
Oh Ha Ni!
OH HA Nl!
Leave it.
Stop.
Oh Ha Ni?
Are you Oh Ha Ni?
He's coming, he's coming, he's coming!
Ah Oppa!
Where is he?
Where is he?
I wasn't expecting a reply.
Thanks.
Should I read it now?
Right here?
Hey, Hong Jang Mi.
- Hey, Hong Jang Mi, you better give that back!
- What is this?
Is this a love letter to Seung Jo oppa?
- Aren't you going to stop that?!
- But what is this?!
Oh my! He fixed her grammar mistakes!
It's not a love letter.
It's an exam paper! An exam!
Score D-!
"Truthfully, I don't call you Seung Jo."
"I call you the 'Spirit of the Forest.'"
Oh my God, she called him a Spirit of the Forest!
- "If you ask why..." - What the hell are you doing?!
I shouldn't really have gone to such an extent... but...
But?
But what?
I absolutely hate stupid girls.
Where are you going!?!
Apologize!
You're laughing?
Is this funny to you?
Do you mind moving?
Чи дүлий юм уу. Уучлалт гуй?
What do I have to apologize for?
For correcting her mistakes?
This little bastard...
Hey hey hey!!!
Do you only see mistakes in this?
You should be looking at the substance of it, not the words.
The feelings she put into it!
Ah, you punk, you're going to keep on doing that, huh?
Let's do this.
Don't just stand there, come at me!
Did you see that?
What? Scared? Are you scared!?
- Hey, come. Come! Bring it!
- Come? Come? Come for what?!
Bong Joon Gu, you! Come into my office right now!
- But Vice Principal, that isn't it.
Please listen to me. - Listen.
Listen to what?
Seung Jo, don't worry about this.
Go and study.
Don't hang around with this fool.
The top 4% is in red.
Orange is the top 11%.
Yellow has been the same for four years.
Green is just there to make the other students look better.
You guys are violet. You are the embarrassment of the school.
That's what the Vice Principal said.
There are 50 spots for study hall this month.
They're just numbers.
But I'm sure you realize that those numbers signify the highest ranked students, right?
I don't know how you can sit there laughing, writing such useless things when that list is right here.
Are you stupid or just thick skinned?
Regretably, I despise girls that are stupid whether or not they're thick skinned... ...they disgust me. <i>[Baek Seung Jo]</i> <i>[Oh Ha Ni]</i>
Stop running!
Will you stop running already?!
Hey, what are you doing?
You're already on your 34th lap.
Two more.
Two more laps.
What is this? Is she training for a marathon or something?
Why is she running so much?
Let her be.
Ha Ni likes running.
I suppose. If you could go to university by running long distances, Oh Ha Ni would be in the lead.
You're right. My specialty is doing anything... for a long period of time.
Even if I have to crawl, I'll get there.
Me too.
Let's go!
Last lap, let's go!
It's her, it's her!
The one who confessed to Baek Seung Jo and got rejected!
I heard she was humiliated and she wasn't even pretty. <i> I don't understand women like her... <i>I know!
Seung Jo Oppa is ours though.
- Hey, Oh Ha Ni, Oh Ha Ni...
- What?!
Oh Ha Ni.
What?
Auntie, it's too much.
You have to eat a lot to gain strength.
How else are you going to live?
Still she's very optimistic.
If it were me, I don't think I would be able to come to school.
You say so?
She's a senior yet she still doesn't know how to write Korean.
Aigoo, how frustrating.
Ha Ni! The two story house is really nice!!
Where did the scissors go?
Ummm... should be...
It's here.
Ha Ni!
Do you know how old this table is?
Grandma gave it to you when you opened the noodle shop; it's older than me.
That's right! The table is 21 years old!
There's not even a scratch! It's really sturdy!
When you were little...you played in here...
Jjan~! (Surprise!)
Ha Ni.
It's a two story house.
You sang a song about two story houses, so how do you like it?
I like it.
What's going on?
You didn't do well?
What do you mean?
Aah... that... let...
Nothing.
Aigooo~
This was here!
Here, look at this!
It's super cute right?
You were this small when you were a year old. You've grown up so much. But you are like this, rebellious now!
I am not!
My hand is similar to Mom's hand.
Right?
Huh?
Yes.
Dad.
Ha Ni~
We're here!
I'm here too!
Hurry up! I'm so hungry that I might die!
Wow, it's to die for!
Wow! This is just great!
Wow, is this your room?
It's so close! Right?! Right?!
Where? Where? Where?
Wow, this is great!
It's so great here.
Ha Ni, your house is awesome! Two story house!
For me, I like this the best!
Ha Ni! Is this your foot?
Yes.
It's so cute.
Hey!! Stop that! Bong Joon Gu!
- Why?
- Come on, kids! Ha Ni, get that.
- Yes. - I will get that.
I will get it.
It smells great!
Wow, it looks so good.
Aigoo.
There wasn't much time so I didn't prepare much food.
When did you prepare all this? This is a lot!
This is a feast!
Is that right?
We're having guests from Busan today so the main menu is Busan's Mil-myun (Busan's local noodles).
How did you know? It's my favorite.
Wah. Thank you, dad!
- I'll eat well! - I'll eat well!!
Father!
Hmm?
It's to die for.
To die for?
Yes, I ate Busan's Mil-myun for a long time!
But this is the best.
The noodles are soft yet so chewy!
It seems like you know something.
Yes, Father.
You can't tell, but my tongue is very sensitive.
At last year's festival, Joon Gu made and sold Dduk Bok Gi.
It was really good.
He's different than he looks.
Well, appearance-wise your face looks like a bear's feet...
Beer feet?
What? You didn't know?
Eat up...
But why is the store named So Pal Bok Noodles?
Ha Ni's grandma is So Pal Bok, so that's why we used it.
You mean you carried on the family business?
That's right!
My mother-in-law for 40 years and me for 20 years.
Ohhhh~
No wonder.
A deep taste like this can't come from an amateur.
True! I learned while being hit.
I wish my Ha Ni could carry on this business.
She doesn't seem to have the talent for cooking though.
Don't worry, Father! Ha Ni and I... will together...do our very best!
Hey! What's wrong with you?
What? A store that's been around for more than 60 years can't end just like that, right?
Yeah, but it's not a bad idea to donate everything back to society either.
Father! Now I see you're the kind of person who spits with a smile on your face.
Ha Ni!
Oh, Ha Ni!
What's this?
Hey, Bong Joon Gu, why are you trying to destroy someone else's home?
What are you on about?! This house is very stable.
What is this?!
Isn't it an earthquake?
Earthquake?
Dad, what are we gonna do?!
It's okay.
This is a new house.
It's stable... Very safe...
Ha Ni!
Get out! Father! Quickly!
Hurry hurry come on! Ha Ni, are you alright?
Wait a minute! Is everyone alright!? Yes!
How could this happen!?
Oh my!
That's right!
That... that...
That!
What?
That... that...just wait!
Dad!
No, you can't!
Don't!
I'll be back quickly!
Don't worry!
Dad...
Da... Dad!
At 5:30 this afternoon, there was a mild earthquake of 2.0 magnitude in Seoul.
It was a tremor that slightly shook windows, however... one house in this area, Yeonhee-dong, has collapsed, as you can see, to the point that it's unrecognizable.
He's still in there! My dad is still in there... <i>As far as we know there is still a person trapped within the collapsed house. <i>The 2.0 magnitude YeonHee-dong earthquake collapse site.
The rescue team is... <i>...now in the process of clearing a path and rescuing the person. <i>Yes, I believe they're looking to see if anyone is there!!</i> <i>Yes!
We can see someone's coming out from under a table in the living room!
Dad!
Dad!
What do you think this is, Dad!?
Aigoo, I lived!
- I'm alive!
I'm alive!
- Daddy! <i>Of course, there doesn't seem to be any fatal injuries. <i>The police suspect the collapse was caused by poor construction and are investigating the exact cause.</i>
Huh!?
Oh Gi Dong? -<i> Thank you. - Goodbye.
Aigoo!
Here... Huh?
What is this?
Was our house the only one... ...that collapsed?
Oh, really?
Hehe... let's go.
It's her, her, her.
Gee... What!
But, are you staying at a hotel again today?
- Yeah. - That must be really expensive.
No, for now we decided to stay at my dad's friend's house. At least until the house is rebuilt or we find another one.
We were contacted because of the newscast.
Oh really?
That's really great!
Oh, is it her?
What!? What the heck?
Even pictures now...
You're a total celebrity now.
I'm sorry.
Because of this unlucky friend, you guys are suffering a lot.
Let's go. <i>Please show your power of love.</i> <i>Thank you for your help.
What are they doing?
Of course you guys know about what happened on the news...
Our friend, Oh Ha Ni, lost her house overnight due to a sudden earthquake. <i>Let's all help Ha Ni.
What the heck is that?
What is Bong Joon Gu doing?
"Love's Fundraising?"
That idiot! Hey, let's just go this way.
Come on, follow me. <i>Oh!
Thank you. <i>Thank you, let's help Ha Ni.
We're all friends aren't we?
Show us the power of love!
Thank you!
Oh, Ha Ni, Oh Ha Ni!
Ha Ni, Ha Ni, move it, move it, move it!
Hey, everyone, everyone, everyone!
Please greet her with thunderous applause.
Even after going through such a horrible experience yesterday, she came to school all determined and ready!
Here is Oh Ha Ni!
Applause!
Ha Ni, Ha Ni!
What. What, what? <i> Now I'm really screwed.<i>
Hey! Hey, you!
Show some love, Baek Seung Jo.
Didn't you see the news yesterday?
Don't you have a TV at home?
Whose fault do you think it is that Ha Ni is going through such a difficult time?
Wasn't it because of a mild earthquake of 2.0 magnitude?
Oh...
Right, right...
However... Because of that small earthquake... ...the newly built house collapsed.
What do you think about that?
Are you saying that I caused the earthquake?
Then what?
Who can cause a bigger earthquake than you?
You're capable of causing such a great amount of pain to someone's heart, so capable of causing that.
Alright, all I need to do is give you money?
Right...
Put your wallet away!
Did anyone say they'd take your money?
Even if I were homeless, I would never take your money even if you offered.
Really?
Fine, I'll respect that.
Hey, Baek Seung Jo!
Who made you so mighty that you can ignore people like this?
To you, all the kids here look like idiots, don't they?
You think that acting superior and ignoring everyone makes you look cool, right?
Are you just that much better?
Why?
Because your IQ is higher? Because you're good at studying, you have a handsome face, and you're tall...
Is everything just dandy if you're better than others?
Hey! We can all study and be smart, who can't?
I just don't study, that's why my grades aren't great.
Do you think that my grades are bad because I can't study?
Really? Yeah! Then show me.
What?
Show you?
Ok fine, I'll show you.
During the next examining period.
How much?
How much? <i>There are 50 spots for study hall this month.<i> <i> I don't know how you can sit there laughing, writing such useless things. <i> <i> Don't you have any brains? <i> Or just thick skinned?
Right!
The study hall.
Study hall?
This month's study hall?
Yeah!
That high and mighty Special Study Hall.
Next month, I will get in there.
Are you making fun of me again?
If I do it?
And if I do it?
What will you do if I do it?
If you do it?
Yeah!
If you do it, I'll carry you on my back and walk around the school. <i>You'll give me a piggyback ride? <i>No, that's not it!
Fine. You better look forward to it.
Are you really that close?
Ah!
Of course!
From the day we were born until we finished junior high, we lived together like one family.
Then we moved up to Seoul and we lost touch.
Even when I'm asleep, I feel like bursting with anger because of our house was destroyed.
However, thanks to that... ...finding my friend again is really nice.
Oh why this thing!?
This thing!
Daddy is like an idiot right?
Thanks. <i> Every day with you, <i> Being held in the night's arms. <i> Every day with you, <i> I'm hungry to fall asleep.
Stop!
It's here. House number 142, right?
Oh, you're right.
Just wait here.
Baek Su Chang, it's right.
He must be really rich, your friend.
Yeah... It seems like it. <i>Who is it?
I...
Hello.
I'm Su Chang's friend, Oh Gi Dong. <i>Oh yes, come on in! <i>Honey! <i>- You've arrived!?</i> - Yes.
Come on over here, hurry!
Baek(white) Piggy!
How did you!
Aigoo.
You must have suffered a lot.
Aigoo! It's really great to see you!
Wow!
- Ah my wife.
-Hi there!
Oh my, welcome to our home.
Yes... I really am here.
It's really great that you're here.
You're completely welcome here!
Hi there.
Hello.
Oh, you must be Gi Dong's daughter.
Yes.
You're more beautiful in person. Excuse me?
Oh... In all honesty...
I couldn't wait until tonight.
I just stopped by in the morning.
Oh that...
That was me.
Well... We should unload all your stuff.
No, no, we don't have much stuff. Our Ha Ni can do it all by herself.
Yeah!
There isn't much.
Oh, don't worry, our child needs to help.
No, I said it's alright.
Son!
Come here and use your muscles!
Dad, here, here.
I'll do it
Aigoo, just go close the door. Alright.
Teddy~
From now on, I think our luck will be good.
Don't you think?
Let's go.
Should I help you?
No, it's alright. <i> Is this a dream?
You...you! <i>Brought to you by the PKer team @ www.viikii.net</i> <i>I can't believe it...
It's Seung Jo.
Excuse me!?
Hey!
Give me that!
I have a proposition.
Hey, Oh Ha Ni, what is "x" here?
Alphabet.
I feel like I'm going to explode. You as a child~
Hey!
Hello~ Camera!
Don't spread rumors.
I... I closed my feelings for you.
My feelings for you...aren't even this much.
Really?
Where I left off, we were just essentially chugging through this fairly hairy derivative-- this definite integral-- this antiderivative.
It takes my brain a little while to come up with the next term.
So we evaluated at 2 and now we have to subtract this evaluated at 1. So minus 16 pi minus 4 pi over 3-- oh, sorry. Plus.
Oh no, sorry.
That is a minus.
That's a minus. Plus 4 pi.
Right?
Because x is 1.
Minus pi over 2.
And now we can simplify it.
Let's see what we can do.
This is really a hairy problem. The 16 pi minus 8 pi, that equals 8 pi.
And then that's a plus.
The 32 plus 8 pi.
32 pi plus 8 pi, that equals 40 pi.
So let's see, I've simplified it to 40 pi, and what's minus 8 times 4 is 32 pi over 3.
And then all of that, let's see if I can simplify this.
Let's see, 16 pi plus 4 pi, that's 20 pi.
And then, let's see. Minus 4 pi over 3 minus pi over 2.
So let's get a common denominator for this part right here.
So if I put everything over 6-- 20 pi over 6 is the same thing is 120 pi over 6, and then minus-- 4 pi over 3, if I put it over 6 it becomes 8 pi over 6, right?
And then pi over 2, if I put it over 6 it becomes 3 pi over 6.
So minus 3 pi.
So this whole term that we're going to have to subtract from this term is equal to 120 minus 11, right?
So that's 109 pi over 6.
This equals 1-- is that right? Yeah, 109 pi over 6.
See what happens when you make up problems on the fly?
You get ugly numbers.
109 pi over 6.
And what does that top part translate?
So this is what we're going to subtract.
This is when we evaluated the antiderivative at 1.
And let's simplify this one.
So that one, if we put 3 common denominator, that's 120 pi over 3 minus 32 pi over 3.
120 minus 32, let's see, we get 90-- 88?
Right.
88 pi over 3.
So that equals 88 pi over 3, and remember, that's just the top part.
And then-- this is more of a review of fractions than anything else-- and then if I want to put it over 6, I just double it.
So I think we're almost done.
Let me switch colors.
So if you go over a denominator of 6-- 88 pi over 3-- let's see.
If I double that, I get 160-- 176, right?
176 pi minus this. Minus 109 pi.
I'm sure I made a careless mistake.
These are my least favorite type of things to do.
Hairy fractions. So 176 minus 109.
That's the same thing as 76 minus 9.
And that is 65.
So our final answer is 65 pi over 6.
Which isn't as hairy as it seemed when we started the problem.
But that's pretty neat.
This is kind of a strange shape.
It's kind of a wide ring that has-- the upper part of the ring and the inner part of the ring are hard edges.
But then it's curved on the outside.
And we were able to figure out the volume of that.
Especially-- and what was weird about this, is when it was rotated around the line y is equal to minus 2.
Hopefully I didn't confuse you.
These are about as difficult as these volume of revolution problems get.
If you want more, just let me know.
I will see you in the next video.
From Migrant Worker to Activist
[Talking on the phone]:
It was caused by over contract. The contract expired.
When coming home, it would be a problem if she doesn't get her rights.
She should come home bringing what she's entitled to, like her salary and others.
Hety was a migrant worker who faced abuses from her boss. She had returned home and is now actively giving counseling and education to potential migrant workers in the village she resides.
She works in the Middle East and now she is asking for the help from SBMC (Migrant Workers Solidarity in Cianjur).
We asked her to write the chronology of her case.
After that we can meet up in the City of Cianjur.
If there is problem, such as her salary not being given, we will call the boss, to ask for her to be sent home.
Aside being sent home, she should also be entitled to her rights, like her salary.
If she comes home without bringing her salary, it would not be good.
Right?
They have been working for three years.
In Saudi Arabia.
Both husband and wife.
She's coming home tomorrow.
She flew out yesterday at 4 pm.
The first time it was only two months, and then she left again.
It has been three years now and she doesn't want to come home.
It might also be because her husband had passed away.
So she extended her contract for another two months.
Thank God, she becomes a successful migrant worker.
Once or twice a week, her father comes to clean the house.
Ah, she's already in Jakarta this afternoon.
That means she will be here tonight.
Ah, early morning tomorrow.
Those two houses belong to sisters.
That one belongs to the older sister whose husband passed away.
The one below is the younger sister's.
Both are migrant workers.
And thank God she is also a successful migrant worker.
So she could afford a house and send her kids to school.
But too bad her husband passed away.
They could not enjoy the result of their work together.
This is Mrs. Aad, and her daughter, Lusni.
(Lusni) was a migrant worker from 2004 to 2007.
Then she went again in 2009 and came back in 2011.
Come and talk to us.
Ah, we're on camera.
Yes.
Thank God, she didn't have any problem when working as a migrant worker.
She brought home money and her salary was fully paid.
I work at home now.
I want to work if there is any job for me.
But there is no job.
I was married once, but it was short-lived.
Now, I am not married.
Everything is interconnected.
As a Shinnecock Indian, I was raised to know this.
We are a small fishing tribe situated on the southeastern tip of Long Island near the town of Southampton in New York.
When I was a little girl, my grandfather took me to sit outside in the sun on a hot summer day.
There were no clouds in the sky.
And after a while I began to perspire.
And he pointed up to the sky, and he said,
"Look, do you see that?
That's part of you up there.
That's your water that helps to make the cloud that becomes the rain that feeds the plants that feeds the animals."
In my continued exploration of subjects in nature that have the ability to illustrate the interconnection of all life, I started storm chasing in 2008 after my daughter said, "Mom, you should do that."
And so three days later, driving very fast,
I found myself stalking a single type of giant cloud called the super cell, capable of producing grapefruit-size hail and spectacular tornadoes, although only two percent actually do.
These clouds can grow so big, up to 50 miles wide and reach up to 65,000 feet into the atmosphere.
They can grow so big, blocking all daylight, making it very dark and ominous standing under them.
Storm chasing is a very tactile experience.
There's a warm, moist wind blowing at your back and the smell of the earth, the wheat, the grass, the charged particles.
And then there are the colors in the clouds of hail forming, the greens and the turquoise blues.
I've learned to respect the lightning.
My hair used to be straight.
(Laughter)
I'm just kidding.
(Laughter)
What really excites me about these storms is their movement, the way they swirl and spin and undulate, with their lava lamp-like mammatus clouds.
They become lovely monsters.
When I'm photographing them, I cannot help but remember my grandfather's lesson.
As I stand under them, I see not just a cloud, but understand that what I have the privilege to witness is the same forces, the same process in a small-scale version that helped to create our galaxy, our solar system, our sun and even this very planet.
All my relations.
Thank you.
(Applause)
Many people -- 20 years for Somalia -- [were] fighting.
So there was no job, no food.
Children, most of them, became very malnourished, like this.
Deqo Mohamed:
So as you know, always in a civil war, the ones affected most [are] the women and children.
So our patients are women and children.
And they are in our backyard.
It's our home. We welcome them.
That's the camp that we have in now 90,000 people, where 75 percent of them are women and children.
Pat Mitchell: We are doing C-sections and different operations because people need some help.
HA:
There is no government to protect them.
Every morning we have about 400 patients, maybe more or less.
But sometimes we are only five doctors and 16 nurses, and we are physically getting exhausted to see all of them.
But we take the severe ones, and we reschedule the other ones the next day.
It is very tough.
And as you can see, it's the women who are carrying the children; it's the women who come into the hospitals; it's the women [are] building the houses.
That's their house.
And we have a school. This is our bright -- we opened [in the] last two years [an] elementary school where we have 850 children, and the majority are women and girls.
(Applause)
PM:
And the doctors have some very big rules about who can get treated at the clinic.
Would you explain the rules for admission?
The people who are coming to us, we are welcoming.
We are sharing with them whatever we have.
But there are only two rules.
First rule: there is no clan distinguished and political division in Somali society.
[Whomever] makes those things we throw out.
The second: no man can beat his wife.
If he beat, we will put [him] in jail, and we will call the eldest people.
Until they identify this case, we'll never release him.
That's our two rules.
(Applause)
The other thing that I have realized, that the woman is the most strong person all over the world.
Because the last 20 years, the Somali woman has stood up.
They were the leaders, and we are the leaders of our community and the hope of our future generations.
We are not just the helpless and the victims of the civil war.
We can reconcile.
We can do everything.
(Applause)
As my mother said, we are the future hope, and the men are only killing in Somalia.
So we came up with these two rules.
In a camp with 90,000 people, you have to come up with some rules or there is going to be some fights.
So there is no clan division, and no man can beat his wife.
And we have a little storage room where we converted a jail.
So if you beat your wife, you're going to be there.
(Applause) So empowering the women and giving the opportunity -- we are there for them. They are not alone for this.
PM:
You're running a medical clinic.
It brought much, much needed medical care to people who wouldn't get it.
You're also running a civil society.
You've created your own rules, in which women and children are getting a different sense of security.
Talk to me about your decision, Dr. Abdi, and your decision, Dr. Mohamed, to work together -- for you to become a doctor and to work with your mother in these circumstances.
HA:
My age -- because I was born in 1947 -- we were having, at that time, government, law and order.
But one day, I went to the hospital -- my mother was sick -- and I saw the hospital, how they [were] treating the doctors, how they [are] committed to help the sick people.
I admired them, and I decided to become a doctor.
My mother died, unfortunately, when I was 12 years [old].
Then my father allowed me to proceed [with] my hope.
My mother died in [a] gynecology complication, so I decided to become a gynecology specialist.
That's why I became a doctor.
So Dr. Deqo has to explain.
For me, my mother was preparing [me] when I was a child to become a doctor, but I really didn't want to.
Maybe I should become an historian, or maybe a reporter.
I loved it, but it didn't work.
When the war broke out -- civil war --
I saw how my mother was helping and how she really needed the help, and how the care is essential to the woman to be a woman doctor in Somalia and help the women and children.
And I thought, maybe I can be a reporter and doctor gynecologist.
(Laughter)
So I went to Russia, and my mother also, [during the] time of [the] Soviet Union.
So some of our character, maybe we will come with a strong Soviet background of training.
So that's how I decided [to do] the same.
My sister was different.
She's here.
She's also a doctor.
She graduated in Russia also.
(Applause)
And to go back and to work with our mother is just what we saw in the civil war -- when I was 16, and my sister was 11, when the civil war broke out.
So it was the need and the people we saw in the early '90s -- that's what made us go back and work for them.
PM:
So what is the biggest challenge working, mother and daughter, in such dangerous and sometimes scary situations?
Yes, I was working in a tough situation, very dangerous.
And when I saw the people who needed me,
I was staying with them to help, because I [could] do something for them.
Most people fled abroad.
But I remained with those people, and I was trying to do something -- [any] little thing I [could] do.
I succeeded in my place.
Now my place is 90,000 people who are respecting each other, who are not fighting.
But we try to stand on our feet, to do something, little things, we can for our people.
And I'm thankful for my daughters.
When they come to me, they help me to treat the people, to help.
They do everything for them.
They have done what I desire to do for them.
PM:
What's the best part of working with your mother, and the most challenging part for you?
DM:
She's very tough; it's most challenging.
She always expects us to do more.
And really when you think [you] cannot do it, she will push you, and I can do it.
That's the best part.
She shows us, trains us how to do and how to be better [people] and how to do long hours in surgery -- 300 patients per day, 10, 20 surgeries, and still you have to manage the camp -- that's how she trains us.
It is not like beautiful offices here, 20 patients, you're tired.
You see 300 patients, 20 surgeries and 90,000 people to manage.
PM:
But you do it for good reasons.
(Applause)
Wait.
Wait.
HA:
Thank you.
DM:
Thank you.
(Applause)
HA:
Thank you very much. DM:
Thank you very much.
CHAPTER 12 Brute Neighbors
Sometimes I had a companion in my fishing, who came through the village to my house from the other side of the town, and the catching of the dinner was as much a social exercise as the eating of it.
Hermit.
I wonder what the world is doing now.
I have not heard so much as a locust over the sweet-fern these three hours.
The pigeons are all asleep upon their roosts--no flutter from them.
Was that a farmer's noon horn which sounded from beyond the woods just now?
The hands are coming in to boiled salt beef and cider and Indian bread.
Why will men worry themselves so?
He that does not eat need not work.
I wonder how much they have reaped.
Who would live there where a body can never think for the barking of Bose?
And oh, the housekeeping! to keep bright the devil's door-knobs, and scour his tubs this bright day!
Better not keep a house.
Say, some hollow tree; and then for morning calls and dinner-parties!
Only a woodpecker tapping.
Oh, they swarm; the sun is too warm there; they are born too far into life for me.
I have water from the spring, and a loaf of brown bread on the shelf.--Hark!
I hear a rustling of the leaves.
Is it some ill-fed village hound yielding to the instinct of the chase? or the lost pig which is said to be in these woods, whose tracks I saw after the rain?
It comes on apace; my sumachs and sweetbriers tremble.--Eh, Mr. Poet, is it you?
How do you like the world to-day?
Poet.
See those clouds; how they hang! That's the greatest thing I have seen to- day.
There's nothing like it in old paintings, nothing like it in foreign lands--unless when we were off the coast of Spain.
That's a true Mediterranean sky.
I thought, as I have my living to get, and have not eaten to-day, that I might go a- fishing.
That's the true industry for poets.
It is the only trade I have learned.
Come, let's along.
Hermit.
I cannot resist.
My brown bread will soon be gone.
I will go with you gladly soon, but I am just concluding a serious meditation.
I think that I am near the end of it.
Leave me alone, then, for a while.
But that we may not be delayed, you shall be digging the bait meanwhile.
Angleworms are rarely to be met with in these parts, where the soil was never fattened with manure; the race is nearly extinct.
The sport of digging the bait is nearly equal to that of catching the fish, when one's appetite is not too keen; and this you may have all to yourself today.
I would advise you to set in the spade down yonder among the ground-nuts, where you see the johnswort waving.
I think that I may warrant you one worm to every three sods you turn up, if you look well in among the roots of the grass, as if you were weeding.
Or, if you choose to go farther, it will not be unwise, for I have found the increase of fair bait to be very nearly as the squares of the distances.
Hermit alone.
Let me see; where was I?
Methinks I was nearly in this frame of mind; the world lay about at this angle.
Shall I go to heaven or a-fishing?
If I should soon bring this meditation to an end, would another so sweet occasion be likely to offer?
I was as near being resolved into the essence of things as ever I was in my life.
I fear my thoughts will not come back to me.
If it would do any good, I would whistle for them.
When they make us an offer, is it wise to say, We will think of it?
My thoughts have left no track, and I cannot find the path again.
What was it that I was thinking of?
It was a very hazy day.
I will just try these three sentences of
Confut-see; they may fetch that state about again.
There never is but one opportunity of a kind.
Mem.
Poet.
How now, Hermit, is it too soon?
I have got just thirteen whole ones, beside several which are imperfect or undersized; but they will do for the smaller fry; they do not cover up the hook so much.
Those village worms are quite too large; a shiner may make a meal off one without finding the skewer.
Hermit.
Well, then, let's be off.
There's good sport there if the water be not too high.
Why do precisely these objects which we behold make a world?
Why has man just these species of animals for his neighbors; as if nothing but a mouse could have filled this crevice?
I suspect that Pilpay & Co. have put animals to their best use, for they are all beasts of burden, in a sense, made to carry some portion of our thoughts.
The mice which haunted my house were not the common ones, which are said to have been introduced into the country, but a wild native kind not found in the village.
I sent one to a distinguished naturalist, and it interested him much.
When I was building, one of these had its nest underneath the house, and before I had laid the second floor, and swept out the shavings, would come out regularly at lunch time and pick up the crumbs at my feet.
It probably had never seen a man before; and it soon became quite familiar, and would run over my shoes and up my clothes.
It could readily ascend the sides of the room by short impulses, like a squirrel, which it resembled in its motions.
At length, as I leaned with my elbow on the bench one day, it ran up my clothes, and along my sleeve, and round and round the paper which held my dinner, while I kept the latter close, and dodged and played at bopeep with it; and when at last I held still a piece of cheese between my thumb and finger, it came and nibbled it, sitting in my hand, and afterward cleaned its face and paws, like a fly, and walked away.
A phoebe soon built in my shed, and a robin for protection in a pine which grew against the house.
In June the partridge (Tetrao umbellus), which is so shy a bird, led her brood past my windows, from the woods in the rear to the front of my house, clucking and calling to them like a hen, and in all her behavior proving herself the hen of the woods.
The young suddenly disperse on your approach, at a signal from the mother, as if a whirlwind had swept them away, and they so exactly resemble the dried leaves and twigs that many a traveler has placed his foot in the midst of a brood, and heard the whir of the old bird as she flew off, and her anxious calls and mewing, or seen her trail her wings to attract his attention, without suspecting their neighborhood.
The parent will sometimes roll and spin round before you in such a dishabille, that you cannot, for a few moments, detect what kind of creature it is.
The young squat still and flat, often running their heads under a leaf, and mind only their mother's directions given from a distance, nor will your approach make them run again and betray themselves.
You may even tread on them, or have your eyes on them for a minute, without discovering them.
I have held them in my open hand at such a time, and still their only care, obedient to their mother and their instinct, was to squat there without fear or trembling.
So perfect is this instinct, that once, when I had laid them on the leaves again, and one accidentally fell on its side, it was found with the rest in exactly the same position ten minutes afterward.
They are not callow like the young of most birds, but more perfectly developed and precocious even than chickens.
The remarkably adult yet innocent expression of their open and serene eyes is very memorable.
All intelligence seems reflected in them.
They suggest not merely the purity of infancy, but a wisdom clarified by experience.
Such an eye was not born when the bird was, but is coeval with the sky it reflects.
The traveller does not often look into such a limpid well.
The ignorant or reckless sportsman often shoots the parent at such a time, and leaves these innocents to fall a prey to some prowling beast or bird, or gradually mingle with the decaying leaves which they so much resemble.
It is said that when hatched by a hen they will directly disperse on some alarm, and so are lost, for they never hear the mother's call which gathers them again.
These were my hens and chickens.
It is remarkable how many creatures live wild and free though secret in the woods, and still sustain themselves in the neighborhood of towns, suspected by hunters only.
How retired the otter manages to live here!
He grows to be four feet long, as big as a small boy, perhaps without any human being getting a glimpse of him.
I formerly saw the raccoon in the woods behind where my house is built, and probably still heard their whinnering at night.
Commonly I rested an hour or two in the shade at noon, after planting, and ate my lunch, and read a little by a spring which was the source of a swamp and of a brook, oozing from under Brister's Hill, half a mile from my field.
The approach to this was through a succession of descending grassy hollows, full of young pitch pines, into a larger wood about the swamp.
There, in a very secluded and shaded spot, under a spreading white pine, there was yet a clean, firm sward to sit on.
I had dug out the spring and made a well of clear gray water, where I could dip up a pailful without roiling it, and thither I went for this purpose almost every day in midsummer, when the pond was warmest.
Thither, too, the woodcock led her brood, to probe the mud for worms, flying but a foot above them down the bank, while they ran in a troop beneath; but at last, spying me, she would leave her young and circle round and round me, nearer and nearer till within four or five feet, pretending broken wings and legs, to attract my attention, and get off her young, who would already have taken up their march, with faint, wiry peep, single file through the swamp, as she directed.
Or I heard the peep of the young when I could not see the parent bird.
There too the turtle doves sat over the spring, or fluttered from bough to bough of the soft white pines over my head; or the red squirrel, coursing down the nearest bough, was particularly familiar and inquisitive.
You only need sit still long enough in some attractive spot in the woods that all its inhabitants may exhibit themselves to you by turns.
I was witness to events of a less peaceful character.
One day when I went out to my wood-pile, or rather my pile of stumps, I observed two large ants, the one red, the other much larger, nearly half an inch long, and black, fiercely contending with one another.
Having once got hold they never let go, but struggled and wrestled and rolled on the chips incessantly.
Looking farther, I was surprised to find that the chips were covered with such combatants, that it was not a duellum, but a bellum, a war between two races of ants, the red always pitted against the black, and frequently two red ones to one black.
The legions of these Myrmidons covered all the hills and vales in my wood-yard, and the ground was already strewn with the dead and dying, both red and black.
It was the only battle which I have ever witnessed, the only battle-field I ever trod while the battle was raging; internecine war; the red republicans on the one hand, and the black imperialists on the other.
On every side they were engaged in deadly combat, yet without any noise that I could hear, and human soldiers never fought so resolutely.
I watched a couple that were fast locked in each other's embraces, in a little sunny valley amid the chips, now at noonday prepared to fight till the sun went down, or life went out.
The smaller red champion had fastened himself like a vice to his adversary's front, and through all the tumblings on that field never for an instant ceased to gnaw at one of his feelers near the root, having already caused the other to go by the board; while the stronger black one dashed him from side to side, and, as I saw on looking nearer, had already divested him of several of his members.
They fought with more pertinacity than bulldogs.
Neither manifested the least disposition to retreat.
It was evident that their battle-cry was "Conquer or die."
In the meanwhile there came along a single red ant on the hillside of this valley, evidently full of excitement, who either had despatched his foe, or had not yet taken part in the battle; probably the latter, for he had lost none of his limbs; whose mother had charged him to return with his shield or upon it.
Or perchance he was some Achilles, who had nourished his wrath apart, and had now come to avenge or rescue his Patroclus.
He saw this unequal combat from afar--for the blacks were nearly twice the size of the red--he drew near with rapid pace till he stood on his guard within half an inch of the combatants; then, watching his opportunity, he sprang upon the black warrior, and commenced his operations near the root of his right fore leg, leaving the foe to select among his own members; and so there were three united for life, as if a new kind of attraction had been invented which put all other locks and cements to shame.
I should not have wondered by this time to find that they had their respective musical bands stationed on some eminent chip, and playing their national airs the while, to excite the slow and cheer the dying combatants.
I was myself excited somewhat even as if they had been men.
The more you think of it, the less the difference.
And certainly there is not the fight recorded in Concord history, at least, if in the history of America, that will bear a moment's comparison with this, whether for the numbers engaged in it, or for the patriotism and heroism displayed.
For numbers and for carnage it was an Austerlitz or Dresden.
Concord Fight!
Two killed on the patriots' side, and Luther Blanchard wounded!
Why here every ant was a Buttrick--"Fire! for God's sake fire!"--and thousands shared the fate of Davis and Hosmer.
There was not one hireling there.
I have no doubt that it was a principle they fought for, as much as our ancestors, and not to avoid a three-penny tax on their tea; and the results of this battle will be as important and memorable to those whom it concerns as those of the battle of Bunker Hill, at least.
I took up the chip on which the three I have particularly described were struggling, carried it into my house, and placed it under a tumbler on my window- sill, in order to see the issue.
Holding a microscope to the first-mentioned red ant, I saw that, though he was assiduously gnawing at the near fore leg of his enemy, having severed his remaining feeler, his own breast was all torn away, exposing what vitals he had there to the jaws of the black warrior, whose breastplate was apparently too thick for him to pierce; and the dark carbuncles of the sufferer's eyes shone with ferocity such as war only could excite.
They struggled half an hour longer under the tumbler, and when I looked again the black soldier had severed the heads of his foes from their bodies, and the still
living heads were hanging on either side of him like ghastly trophies at his saddle- bow, still apparently as firmly fastened as ever, and he was endeavoring with feeble struggles, being without feelers and with only the remnant of a leg, and I know not how many other wounds, to divest himself of them; which at length, after half an hour more, he accomplished.
I raised the glass, and he went off over the window-sill in that crippled state.
Whether he finally survived that combat, and spent the remainder of his days in some
Hotel des Invalides, I do not know; but I thought that his industry would not be worth much thereafter.
I never learned which party was victorious, nor the cause of the war; but I felt for the rest of that day as if I had had my feelings excited and harrowed by witnessing the struggle, the ferocity and carnage, of a human battle before my door.
Kirby and Spence tell us that the battles of ants have long been celebrated and the date of them recorded, though they say that Huber is the only modern author who appears to have witnessed them.
"Aeneas Sylvius," say they, "after giving a very circumstantial account of one contested with great obstinacy by a great and small species on the trunk of a pear tree," adds that "this action was fought in the pontificate of Eugenius the Fourth, in the presence of Nicholas Pistoriensis, an eminent lawyer, who related the whole history of the battle with the greatest fidelity."
A similar engagement between great and small ants is recorded by Olaus Magnus, in which the small ones, being victorious, are said to have buried the bodies of their own soldiers, but left those of their giant enemies a prey to the birds.
This event happened previous to the expulsion of the tyrant Christiern the
Second from Sweden.
The battle which I witnessed took place in the Presidency of Polk, five years before the passage of Webster's Fugitive-Slave Bill.
Many a village Bose, fit only to course a mud-turtle in a victualling cellar, sported his heavy quarters in the woods, without the knowledge of his master, and ineffectually smelled at old fox burrows and woodchucks' holes; led perchance by some slight cur which nimbly threaded the wood, and might still inspire a natural terror in its denizens;--now far behind his guide, barking like a canine bull toward some small squirrel which had treed itself for scrutiny, then, cantering off, bending the bushes with his weight, imagining that he is on the track of some stray member of the jerbilla family.
Once I was surprised to see a cat walking along the stony shore of the pond, for they rarely wander so far from home.
The surprise was mutual.
Nevertheless the most domestic cat, which has lain on a rug all her days, appears quite at home in the woods, and, by her sly and stealthy behavior, proves herself more native there than the regular inhabitants.
Once, when berrying, I met with a cat with young kittens in the woods, quite wild, and they all, like their mother, had their backs up and were fiercely spitting at me.
A few years before I lived in the woods there was what was called a "winged cat" in one of the farm-houses in Lincoln nearest the pond, Mr. Gilian Baker's.
When I called to see her in June, 1842, she was gone a-hunting in the woods, as was her wont (I am not sure whether it was a male or female, and so use the more common pronoun), but her mistress told me that she came into the neighborhood a little more than a year before, in April, and was finally taken into their house; that she was of a dark brownish-gray color, with a white spot on her throat, and white feet, and had a large bushy tail like a fox; that in the winter the fur grew thick and flatted out along her sides, forming stripes ten or twelve inches long by two and a half wide, and under her chin like a muff, the upper side loose, the under matted like felt, and in the spring these appendages dropped off.
They gave me a pair of her "wings," which I keep still.
There is no appearance of a membrane about them.
Some thought it was part flying squirrel or some other wild animal, which is not impossible, for, according to naturalists, prolific hybrids have been produced by the union of the marten and domestic cat.
This would have been the right kind of cat for me to keep, if I had kept any; for why should not a poet's cat be winged as well as his horse?
In the fall the loon (Colymbus glacialis) came, as usual, to moult and bathe in the pond, making the woods ring with his wild laughter before I had risen.
At rumor of his arrival all the Mill-dam sportsmen are on the alert, in gigs and on foot, two by two and three by three, with patent rifles and conical balls and spy- glasses.
They come rustling through the woods like autumn leaves, at least ten men to one
loon.
Some station themselves on this side of the pond, some on that, for the poor bird cannot be omnipresent; if he dive here he must come up there.
But now the kind October wind rises, rustling the leaves and rippling the surface of the water, so that no loon can be heard or seen, though his foes sweep the pond with spy-glasses, and make the woods resound with their discharges.
The waves generously rise and dash angrily, taking sides with all water-fowl, and our sportsmen must beat a retreat to town and shop and unfinished jobs.
But they were too often successful.
When I went to get a pail of water early in the morning I frequently saw this stately bird sailing out of my cove within a few rods.
If I endeavored to overtake him in a boat, in order to see how he would manoeuvre, he would dive and be completely lost, so that I did not discover him again, sometimes, till the latter part of the day.
But I was more than a match for him on the surface.
He commonly went off in a rain.
As I was paddling along the north shore one very calm October afternoon, for such days especially they settle on to the lakes, like the milkweed down, having looked in vain over the pond for a loon, suddenly one, sailing out from the shore toward the middle a few rods in front of me, set up his wild laugh and betrayed himself.
I pursued with a paddle and he dived, but when he came up I was nearer than before.
He dived again, but I miscalculated the direction he would take, and we were fifty rods apart when he came to the surface this time, for I had helped to widen the interval; and again he laughed long and loud, and with more reason than before.
He manoeuvred so cunningly that I could not get within half a dozen rods of him.
Each time, when he came to the surface, turning his head this way and that, he cooly surveyed the water and the land, and apparently chose his course so that he might come up where there was the widest expanse of water and at the greatest distance from the boat.
It was surprising how quickly he made up his mind and put his resolve into execution.
He led me at once to the widest part of the pond, and could not be driven from it.
While he was thinking one thing in his brain, I was endeavoring to divine his thought in mine.
It was a pretty game, played on the smooth surface of the pond, a man against a loon.
Suddenly your adversary's checker disappears beneath the board, and the problem is to place yours nearest to where his will appear again.
Sometimes he would come up unexpectedly on the opposite side of me, having apparently passed directly under the boat.
So long-winded was he and so unweariable, that when he had swum farthest he would immediately plunge again, nevertheless; and then no wit could divine where in the deep pond, beneath the smooth surface, he might be speeding his way like a fish, for he had time and ability to visit the bottom of the pond in its deepest part.
It is said that loons have been caught in the New York lakes eighty feet beneath the surface, with hooks set for trout--though Walden is deeper than that.
How surprised must the fishes be to see this ungainly visitor from another sphere speeding his way amid their schools!
Yet he appeared to know his course as surely under water as on the surface, and swam much faster there.
Once or twice I saw a ripple where he approached the surface, just put his head out to reconnoitre, and instantly dived again.
I found that it was as well for me to rest on my oars and wait his reappearing as to endeavor to calculate where he would rise; for again and again, when I was straining my eyes over the surface one way, I would suddenly be startled by his unearthly laugh behind me.
But why, after displaying so much cunning, did he invariably betray himself the moment he came up by that loud laugh?
Did not his white breast enough betray him?
He was indeed a silly loon, I thought.
I could commonly hear the splash of the water when he came up, and so also detected him.
But after an hour he seemed as fresh as ever, dived as willingly, and swam yet farther than at first.
It was surprising to see how serenely he sailed off with unruffled breast when he came to the surface, doing all the work with his webbed feet beneath.
His usual note was this demoniac laughter, yet somewhat like that of a water-fowl; but occasionally, when he had balked me most successfully and come up a long way off, he uttered a long-drawn unearthly howl, probably more like that of a wolf than any bird; as when a beast puts his muzzle to the ground and deliberately howls.
This was his looning--perhaps the wildest sound that is ever heard here, making the woods ring far and wide.
I concluded that he laughed in derision of my efforts, confident of his own resources.
Though the sky was by this time overcast, the pond was so smooth that I could see where he broke the surface when I did not hear him.
His white breast, the stillness of the air, and the smoothness of the water were all against him.
At length having come up fifty rods off, he uttered one of those prolonged howls, as if calling on the god of loons to aid him, and immediately there came a wind from the east and rippled the surface, and filled the whole air with misty rain, and I was impressed as if it were the prayer of the
loon answered, and his god was angry with me; and so I left him disappearing far away on the tumultuous surface.
For hours, in fall days, I watched the ducks cunningly tack and veer and hold the middle of the pond, far from the sportsman; tricks which they will have less need to practise in Louisiana bayous.
When compelled to rise they would sometimes circle round and round and over the pond at a considerable height, from which they could easily see to other ponds and the river, like black motes in the sky; and, when I thought they had gone off thither long since, they would settle down by a slanting flight of a quarter of a mile on to a distant part which was left free; but what beside safety they got by sailing in the middle of Walden I do not know, unless they love its water for the same reason that I do. >
CHAPTER 13 House-Warming
In October I went a-graping to the river meadows, and loaded myself with clusters more precious for their beauty and fragrance than for food.
There, too, I admired, though I did not gather, the cranberries, small waxen gems, pendants of the meadow grass, pearly and red, which the farmer plucks with an ugly rake, leaving the smooth meadow in a snarl, heedlessly measuring them by the bushel and the dollar only, and sells the spoils of the meads to Boston and New York; destined to be jammed, to satisfy the tastes of
So butchers rake the tongues of bison out of the prairie grass, regardless of the torn and drooping plant.
The barberry's brilliant fruit was likewise food for my eyes merely; but I collected a small store of wild apples for coddling, which the proprietor and travellers had overlooked.
When chestnuts were ripe I laid up half a bushel for winter.
It was very exciting at that season to roam the then boundless chestnut woods of
Lincoln--they now sleep their long sleep under the railroad--with a bag on my shoulder, and a stick to open burs with in my hand, for I did not always wait for the frost, amid the rustling of leaves and the loud reproofs of the red squirrels and the jays, whose half-consumed nuts I sometimes stole, for the burs which they had selected were sure to contain sound ones.
Occasionally I climbed and shook the trees.
They grew also behind my house, and one large tree, which almost overshadowed it, was, when in flower, a bouquet which scented the whole neighborhood, but the squirrels and the jays got most of its fruit; the last coming in flocks early in the morning and picking the nuts out of the burs before they fell, I relinquished these trees to them and visited the more distant woods composed wholly of chestnut.
These nuts, as far as they went, were a good substitute for bread.
Many other substitutes might, perhaps, be found.
Digging one day for fishworms, I discovered the ground-nut (Apios tuberosa) on its string, the potato of the aborigines, a sort of fabulous fruit, which I had begun to doubt if I had ever dug and eaten in childhood, as I had told, and had not dreamed it.
I had often since seen its crumpled red velvety blossom supported by the stems of other plants without knowing it to be the same.
Cultivation has well-nigh exterminated it.
It has a sweetish taste, much like that of a frost-bitten potato, and I found it better boiled than roasted.
This tuber seemed like a faint promise of Nature to rear her own children and feed them simply here at some future period.
In these days of fatted cattle and waving grain-fields this humble root, which was once the totem of an Indian tribe, is quite forgotten, or known only by its flowering vine; but let wild Nature reign here once more, and the tender and luxurious English grains will probably disappear before a myriad of foes, and without the care of man the crow may carry back even the last seed of corn to the great cornfield of the
Indian's God in the southwest, whence he is said to have brought it; but the now almost exterminated ground-nut will perhaps revive and flourish in spite of frosts and wildness, prove itself indigenous, and resume its ancient importance and dignity as the diet of the hunter tribe.
Some Indian Ceres or Minerva must have been the inventor and bestower of it; and when the reign of poetry commences here, its leaves and string of nuts may be represented on our works of art.
Already, by the first of September, I had seen two or three small maples turned scarlet across the pond, beneath where the white stems of three aspens diverged, at the point of a promontory, next the water.
Ah, many a tale their color told!
And gradually from week to week the character of each tree came out, and it admired itself reflected in the smooth mirror of the lake.
Each morning the manager of this gallery substituted some new picture, distinguished by more brilliant or harmonious coloring, for the old upon the walls.
The wasps came by thousands to my lodge in October, as to winter quarters, and settled on my windows within and on the walls overhead, sometimes deterring visitors from entering.
Each morning, when they were numbed with cold, I swept some of them out, but I did not trouble myself much to get rid of them; I even felt complimented by their regarding my house as a desirable shelter.
They never molested me seriously, though they bedded with me; and they gradually disappeared, into what crevices I do not know, avoiding winter and unspeakable cold.
Like the wasps, before I finally went into winter quarters in November, I used to resort to the northeast side of Walden, which the sun, reflected from the pitch pine woods and the stony shore, made the fireside of the pond; it is so much pleasanter and wholesomer to be warmed by the sun while you can be, than by an artificial fire.
I thus warmed myself by the still glowing embers which the summer, like a departed hunter, had left.
When I came to build my chimney I studied masonry.
My bricks, being second-hand ones, required to be cleaned with a trowel, so that I learned more than usual of the qualities of bricks and trowels.
The mortar on them was fifty years old, and was said to be still growing harder; but this is one of those sayings which men love to repeat whether they are true or not.
Such sayings themselves grow harder and adhere more firmly with age, and it would take many blows with a trowel to clean an old wiseacre of them.
Many of the villages of Mesopotamia are built of second-hand bricks of a very good quality, obtained from the ruins of Babylon, and the cement on them is older and probably harder still.
However that may be, I was struck by the peculiar toughness of the steel which bore so many violent blows without being worn out.
As my bricks had been in a chimney before, though I did not read the name of
Nebuchadnezzar on them, I picked out as many fireplace bricks as I could find, to save work and waste, and I filled the spaces between the bricks about the fireplace with stones from the pond shore, and also made my mortar with the white sand from the same place.
I lingered most about the fireplace, as the most vital part of the house.
Indeed, I worked so deliberately, that though I commenced at the ground in the morning, a course of bricks raised a few inches above the floor served for my pillow at night; yet I did not get a stiff neck for it that I remember; my stiff neck is of older date.
I took a poet to board for a fortnight about those times, which caused me to be put to it for room.
He brought his own knife, though I had two, and we used to scour them by thrusting them into the earth.
He shared with me the labors of cooking.
I was pleased to see my work rising so square and solid by degrees, and reflected, that, if it proceeded slowly, it was calculated to endure a long time.
The chimney is to some extent an independent structure, standing on the ground, and rising through the house to the heavens; even after the house is burned it still stands sometimes, and its importance and independence are apparent.
This was toward the end of summer.
It was now November.
The north wind had already begun to cool the pond, though it took many weeks of steady blowing to accomplish it, it is so deep.
When I began to have a fire at evening, before I plastered my house, the chimney carried smoke particularly well, because of the numerous chinks between the boards.
Yet I passed some cheerful evenings in that cool and airy apartment, surrounded by the rough brown boards full of knots, and rafters with the bark on high overhead.
My house never pleased my eye so much after it was plastered, though I was obliged to confess that it was more comfortable.
Should not every apartment in which man dwells be lofty enough to create some obscurity overhead, where flickering shadows may play at evening about the rafters?
These forms are more agreeable to the fancy and imagination than fresco paintings or other the most expensive furniture.
I now first began to inhabit my house, I may say, when I began to use it for warmth as well as shelter.
I had got a couple of old fire-dogs to keep the wood from the hearth, and it did me good to see the soot form on the back of the chimney which I had built, and I poked the fire with more right and more satisfaction than usual.
My dwelling was small, and I could hardly entertain an echo in it; but it seemed
larger for being a single apartment and remote from neighbors.
All the attractions of a house were concentrated in one room; it was kitchen, chamber, parlor, and keeping-room; and whatever satisfaction parent or child, master or servant, derive from living in a house, I enjoyed it all.
Cato says, the master of a family (patremfamilias) must have in his rustic villa "cellam oleariam, vinariam, dolia multa, uti lubeat caritatem expectare, et rei, et virtuti, et gloriae erit," that is,
"an oil and wine cellar, many casks, so that it may be pleasant to expect hard times; it will be for his advantage, and virtue, and glory."
I had in my cellar a firkin of potatoes, about two quarts of peas with the weevil in them, and on my shelf a little rice, a jug of molasses, and of rye and Indian meal a peck each.
I sometimes dream of a larger and more populous house, standing in a golden age, of enduring materials, and without gingerbread work, which shall still consist of only one room, a vast, rude, substantial, primitive hall, without ceiling or plastering, with bare rafters and purlins supporting a sort of lower heaven over one's head--useful to keep off rain and snow, where the king and queen posts stand out to receive your homage, when you have done reverence to the prostrate Saturn of an older dynasty on stepping over the sill; a cavernous house, wherein you must reach up a torch upon a pole to see the roof; where some may live in the fireplace, some in the recess of a window, and some on settles, some at one end of the hall, some at another, and some aloft on rafters with the spiders, if they choose; a house which you have got into when you have opened the outside door, and the ceremony is over; where the weary traveller may wash, and eat, and converse, and sleep, without further journey; such a shelter as you would be glad to reach in a tempestuous night, containing all the essentials of a house, and nothing for house-keeping; where you can see all the treasures of the house at one view, and everything hangs upon its peg, that a man should use; at once kitchen, pantry, parlor, chamber, storehouse, and garret; where you can see so necessary a thing, as a barrel or a ladder, so convenient a thing as a cupboard, and hear the pot boil, and pay your respects to the fire that cooks your dinner, and the oven that bakes your bread, and the necessary furniture and utensils are the chief ornaments; where the washing is not put out, nor the fire, nor the mistress, and perhaps you are sometimes requested to move from off the trap-door, when the cook would descend into the cellar, and so learn whether the ground is solid or hollow beneath you without stamping.
A house whose inside is as open and manifest as a bird's nest, and you cannot go in at the front door and out at the back without seeing some of its inhabitants; where to be a guest is to be presented with the freedom of the house, and not to be carefully excluded from seven eighths of it, shut up in a particular cell, and told to make yourself at home there--in solitary confinement.
Nowadays the host does not admit you to his hearth, but has got the mason to build one for yourself somewhere in his alley, and hospitality is the art of keeping you at the greatest distance.
There is as much secrecy about the cooking as if he had a design to poison you.
I am aware that I have been on many a man's premises, and might have been legally ordered off, but I am not aware that I have been in many men's houses.
I might visit in my old clothes a king and queen who lived simply in such a house as I have described, if I were going their way; but backing out of a modern palace will be all that I shall desire to learn, if ever I am caught in one.
It would seem as if the very language of our parlors would lose all its nerve and degenerate into palaver wholly, our lives pass at such remoteness from its symbols, and its metaphors and tropes are necessarily so far fetched, through slides and dumb-waiters, as it were; in other words, the parlor is so far from the kitchen and workshop.
The dinner even is only the parable of a dinner, commonly.
As if only the savage dwelt near enough to Nature and Truth to borrow a trope from them.
How can the scholar, who dwells away in the North West Territory or the Isle of Man, tell what is parliamentary in the kitchen?
However, only one or two of my guests were ever bold enough to stay and eat a hasty- pudding with me; but when they saw that crisis approaching they beat a hasty retreat rather, as if it would shake the house to its foundations.
Nevertheless, it stood through a great many hasty-puddings.
I did not plaster till it was freezing weather.
I brought over some whiter and cleaner sand for this purpose from the opposite shore of the pond in a boat, a sort of conveyance which would have tempted me to go much farther if necessary.
My house had in the meanwhile been shingled down to the ground on every side.
In lathing I was pleased to be able to send home each nail with a single blow of the hammer, and it was my ambition to transfer the plaster from the board to the wall neatly and rapidly.
I remembered the story of a conceited fellow, who, in fine clothes, was wont to
lounge about the village once, giving advice to workmen.
Venturing one day to substitute deeds for words, he turned up his cuffs, seized a plasterer's board, and having loaded his trowel without mishap, with a complacent look toward the lathing overhead, made a bold gesture thitherward; and straightway, to his complete discomfiture, received the whole contents in his ruffled bosom.
I admired anew the economy and convenience of plastering, which so effectually shuts out the cold and takes a handsome finish, and I learned the various casualties to which the plasterer is liable.
I was surprised to see how thirsty the bricks were which drank up all the moisture in my plaster before I had smoothed it, and how many pailfuls of water it takes to christen a new hearth.
I had the previous winter made a small quantity of lime by burning the shells of the Unio fluviatilis, which our river affords, for the sake of the experiment; so that I knew where my materials came from.
I might have got good limestone within a mile or two and burned it myself, if I had cared to do so.
The pond had in the meanwhile skimmed over in the shadiest and shallowest coves, some days or even weeks before the general freezing.
The first ice is especially interesting and perfect, being hard, dark, and transparent, and affords the best opportunity that ever offers for examining the bottom where it is shallow; for you can lie at your length on ice only an inch thick, like a skater insect on the surface of the water, and study the bottom at your leisure, only two or three inches distant, like a picture behind a glass, and the water is necessarily always smooth then.
There are many furrows in the sand where some creature has travelled about and doubled on its tracks; and, for wrecks, it is strewn with the cases of caddis-worms made of minute grains of white quartz.
Perhaps these have creased it, for you find some of their cases in the furrows, though they are deep and broad for them to make.
But the ice itself is the object of most interest, though you must improve the earliest opportunity to study it.
If you examine it closely the morning after it freezes, you find that the greater part of the bubbles, which at first appeared to be within it, are against its under surface, and that more are continually rising from the bottom; while the ice is as yet comparatively solid and dark, that is, you see the water through it.
These bubbles are from an eightieth to an eighth of an inch in diameter, very clear and beautiful, and you see your face reflected in them through the ice.
There may be thirty or forty of them to a square inch.
There are also already within the ice narrow oblong perpendicular bubbles about half an inch long, sharp cones with the apex upward; or oftener, if the ice is quite fresh, minute spherical bubbles one directly above another, like a string of beads.
But these within the ice are not so numerous nor obvious as those beneath.
I sometimes used to cast on stones to try the strength of the ice, and those which broke through carried in air with them, which formed very large and conspicuous white bubbles beneath.
One day when I came to the same place forty-eight hours afterward, I found that those large bubbles were still perfect, though an inch more of ice had formed, as I could see distinctly by the seam in the edge of a cake.
But as the last two days had been very warm, like an Indian summer, the ice was not now transparent, showing the dark green color of the water, and the bottom, but opaque and whitish or gray, and though twice as thick was hardly stronger than before, for the air bubbles had greatly expanded under this heat and run together, and lost their regularity; they were no
longer one directly over another, but often like silvery coins poured from a bag, one overlapping another, or in thin flakes, as if occupying slight cleavages.
The beauty of the ice was gone, and it was too late to study the bottom.
Being curious to know what position my great bubbles occupied with regard to the new ice, I broke out a cake containing a middling sized one, and turned it bottom upward.
The new ice had formed around and under the bubble, so that it was included between the two ices.
It was wholly in the lower ice, but close against the upper, and was flattish, or perhaps slightly lenticular, with a rounded edge, a quarter of an inch deep by four inches in diameter; and I was surprised to find that directly under the bubble the ice was melted with great regularity in the form of a saucer reversed, to the height of five eighths of an inch in the middle, leaving a thin partition there between the water and the bubble, hardly an eighth of an inch thick; and in many places the small bubbles in this partition had burst out downward, and probably there was no ice at all under the largest bubbles, which were a foot in diameter.
I inferred that the infinite number of minute bubbles which I had first seen against the under surface of the ice were now frozen in likewise, and that each, in its degree, had operated like a burning- glass on the ice beneath to melt and rot it.
These are the little air-guns which contribute to make the ice crack and whoop.
At length the winter set in good earnest, just as I had finished plastering, and the wind began to howl around the house as if it had not had permission to do so till then.
Night after night the geese came lumbering in the dark with a clangor and a whistling of wings, even after the ground was covered with snow, some to alight in Walden, and some flying low over the woods toward Fair Haven, bound for Mexico.
Several times, when returning from the village at ten or eleven o'clock at night,
I heard the tread of a flock of geese, or else ducks, on the dry leaves in the woods by a pond-hole behind my dwelling, where they had come up to feed, and the faint honk or quack of their leader as they hurried off.
In 1845 Walden froze entirely over for the first time on the night of the 22d of
December, Flint's and other shallower ponds and the river having been frozen ten days or more; in '46, the 16th; in '49, about the 31st; and in '50, about the 27th of December; in '52, the 5th of January; in
'53, the 31st of December.
The snow had already covered the ground since the 25th of November, and surrounded me suddenly with the scenery of winter.
I withdrew yet farther into my shell, and endeavored to keep a bright fire both within my house and within my breast.
My employment out of doors now was to collect the dead wood in the forest, bringing it in my hands or on my shoulders, or sometimes trailing a dead pine tree under each arm to my shed.
An old forest fence which had seen its best days was a great haul for me.
I sacrificed it to Vulcan, for it was past serving the god Terminus.
How much more interesting an event is that man's supper who has just been forth in the snow to hunt, nay, you might say, steal, the fuel to cook it with!
His bread and meat are sweet.
There are enough fagots and waste wood of all kinds in the forests of most of our towns to support many fires, but which at present warm none, and, some think, hinder the growth of the young wood.
There was also the driftwood of the pond.
In the course of the summer I had discovered a raft of pitch pine logs with the bark on, pinned together by the Irish when the railroad was built.
This I hauled up partly on the shore.
After soaking two years and then lying high six months it was perfectly sound, though waterlogged past drying.
I amused myself one winter day with sliding this piecemeal across the pond, nearly half a mile, skating behind with one end of a log fifteen feet long on my shoulder, and the other on the ice; or I tied several
logs together with a birch withe, and then, with a longer birch or alder which had a hook at the end, dragged them across.
Though completely waterlogged and almost as heavy as lead, they not only burned long, but made a very hot fire; nay, I thought that they burned better for the soaking, as if the pitch, being confined by the water, burned longer, as in a lamp.
Gilpin, in his account of the forest borderers of England, says that "the encroachments of trespassers, and the houses and fences thus raised on the borders of the forest," were "considered as great nuisances by the old forest law, and were severely punished under the name of purprestures, as tending ad terrorem ferarum--ad nocumentum forestae, etc.," to the frightening of the game and the detriment of the forest.
But I was interested in the preservation of the venison and the vert more than the hunters or woodchoppers, and as much as though I had been the Lord Warden himself; and if any part was burned, though I burned it myself by accident, I grieved with a grief that lasted longer and was more inconsolable than that of the proprietors; nay, I grieved when it was cut down by the proprietors themselves.
I would that our farmers when they cut down a forest felt some of that awe which the old Romans did when they came to thin, or let in the light to, a consecrated grove (lucum conlucare), that is, would believe that it is sacred to some god.
The Roman made an expiatory offering, and prayed, Whatever god or goddess thou art to whom this grove is sacred, be propitious to me, my family, and children, etc.
It is remarkable what a value is still put upon wood even in this age and in this new country, a value more permanent and universal than that of gold.
After all our discoveries and inventions no man will go by a pile of wood.
It is as precious to us as it was to our Saxon and Norman ancestors.
If they made their bows of it, we make our gun-stocks of it.
Michaux, more than thirty years ago, says that the price of wood for fuel in New York and Philadelphia "nearly equals, and sometimes exceeds, that of the best wood in
Paris, though this immense capital annually requires more than three hundred thousand cords, and is surrounded to the distance of three hundred miles by cultivated plains."
In this town the price of wood rises almost steadily, and the only question is, how much higher it is to be this year than it was the last.
Mechanics and tradesmen who come in person to the forest on no other errand, are sure to attend the wood auction, and even pay a high price for the privilege of gleaning after the woodchopper.
It is now many years that men have resorted to the forest for fuel and the materials of the arts: the New Englander and the New Hollander, the Parisian and the Celt, the farmer and Robin Hood, Goody Blake and
Harry Gill; in most parts of the world the prince and the peasant, the scholar and the savage, equally require still a few sticks from the forest to warm them and cook their food.
Neither could I do without them.
Every man looks at his wood-pile with a kind of affection.
I love to have mine before my window, and the more chips the better to remind me of my pleasing work.
I had an old axe which nobody claimed, with which by spells in winter days, on the sunny side of the house, I played about the stumps which I had got out of my bean- field.
As my driver prophesied when I was plowing, they warmed me twice--once while I was splitting them, and again when they were on the fire, so that no fuel could give out more heat.
As for the axe, I was advised to get the village blacksmith to "jump" it; but I jumped him, and, putting a hickory helve from the woods into it, made it do.
If it was dull, it was at least hung true.
A few pieces of fat pine were a great treasure.
It is interesting to remember how much of this food for fire is still concealed in the bowels of the earth.
In previous years I had often gone prospecting over some bare hillside, where a pitch pine wood had formerly stood, and got out the fat pine roots.
They are almost indestructible.
Stumps thirty or forty years old, at least, will still be sound at the core, though the sapwood has all become vegetable mould, as appears by the scales of the thick bark forming a ring level with the earth four or five inches distant from the heart.
With axe and shovel you explore this mine, and follow the marrowy store, yellow as beef tallow, or as if you had struck on a vein of gold, deep into the earth.
But commonly I kindled my fire with the dry leaves of the forest, which I had stored up in my shed before the snow came.
Green hickory finely split makes the woodchopper's kindlings, when he has a camp in the woods.
Once in a while I got a little of this.
When the villagers were lighting their fires beyond the horizon, I too gave notice to the various wild inhabitants of Walden vale, by a smoky streamer from my chimney, that I was awake.--
Light-winged Smoke, Icarian bird, Melting thy pinions in thy upward flight,
Lark without song, and messenger of dawn, Circling above the hamlets as thy nest;
Or else, departing dream, and shadowy form Of midnight vision, gathering up thy skirts; By night star-veiling, and by day
Darkening the light and blotting out the sun;
Go thou my incense upward from this hearth, And ask the gods to pardon this clear flame.
Hard green wood just cut, though I used but little of that, answered my purpose better than any other.
I sometimes left a good fire when I went to take a walk in a winter afternoon; and when
I returned, three or four hours afterward, it would be still alive and glowing.
My house was not empty though I was gone.
It was as if I had left a cheerful housekeeper behind.
It was I and Fire that lived there; and commonly my housekeeper proved trustworthy.
One day, however, as I was splitting wood, I thought that I would just look in at the window and see if the house was not on fire; it was the only time I remember to have been particularly anxious on this score; so I looked and saw that a spark had caught my bed, and I went in and extinguished it when it had burned a place as big as my hand.
But my house occupied so sunny and sheltered a position, and its roof was so low, that I could afford to let the fire go out in the middle of almost any winter day.
The moles nested in my cellar, nibbling every third potato, and making a snug bed even there of some hair left after plastering and of brown paper; for even the wildest animals love comfort and warmth as well as man, and they survive the winter only because they are so careful to secure them.
Some of my friends spoke as if I was coming to the woods on purpose to freeze myself.
The animal merely makes a bed, which he warms with his body, in a sheltered place; but man, having discovered fire, boxes up some air in a spacious apartment, and warms that, instead of robbing himself, makes that his bed, in which he can move about divested of more cumbrous clothing, maintain a kind of summer in the midst of winter, and by means of windows even admit the light, and with a lamp lengthen out the day.
Thus he goes a step or two beyond instinct, and saves a little time for the fine arts.
Though, when I had been exposed to the rudest blasts a long time, my whole body began to grow torpid, when I reached the genial atmosphere of my house I soon recovered my faculties and prolonged my life.
But the most luxuriously housed has little to boast of in this respect, nor need we trouble ourselves to speculate how the human race may be at last destroyed.
It would be easy to cut their threads any time with a little sharper blast from the north.
We go on dating from Cold Fridays and Great Snows; but a little colder Friday, or greater snow would put a period to man's existence on the globe.
The next winter I used a small cooking- stove for economy, since I did not own the forest; but it did not keep fire so well as the open fireplace.
Cooking was then, for the most part, no longer a poetic, but merely a chemic process.
It will soon be forgotten, in these days of stoves, that we used to roast potatoes in the ashes, after the Indian fashion.
The stove not only took up room and scented the house, but it concealed the fire, and I felt as if I had lost a companion.
You can always see a face in the fire.
The laborer, looking into it at evening, purifies his thoughts of the dross and earthiness which they have accumulated during the day.
But I could no longer sit and look into the fire, and the pertinent words of a poet recurred to me with new force.--
"Never, bright flame, may be denied to me Thy dear, life imaging, close sympathy.
What but my hopes shot upward e'er so bright?
What but my fortunes sunk so low in night?
Why art thou banished from our hearth and hall,
Thou who art welcomed and beloved by all?
Was thy existence then too fanciful For our life's common light, who are so dull?
Did thy bright gleam mysterious converse hold
With our congenial souls? secrets too bold?
Well, we are safe and strong, for now we sit
Beside a hearth where no dim shadows flit,
Where nothing cheers nor saddens, but a fire
Warms feet and hands nor does to more aspire;
By whose compact utilitarian heap The present may sit down and go to sleep,
Nor fear the ghosts who from the dim past walked,
And with us by the unequal light of the old wood fire talked." >
CHAPTER 14 Former Inhabitants and Winter Visitors
I weathered some merry snow-storms, and spent some cheerful winter evenings by my fireside, while the snow whirled wildly without, and even the hooting of the owl was hushed.
For many weeks I met no one in my walks but those who came occasionally to cut wood and sled it to the village.
The elements, however, abetted me in making a path through the deepest snow in the woods, for when I had once gone through the wind blew the oak leaves into my tracks, where they lodged, and by absorbing the rays of the sun melted the snow, and so not only made a my bed for my feet, but in the night their dark line was my guide.
For human society I was obliged to conjure up the former occupants of these woods.
Within the memory of many of my townsmen the road near which my house stands resounded with the laugh and gossip of inhabitants, and the woods which border it were notched and dotted here and there with their little gardens and dwellings, though it was then much more shut in by the forest than now.
In some places, within my own remembrance, the pines would scrape both sides of a chaise at once, and women and children who were compelled to go this way to Lincoln alone and on foot did it with fear, and often ran a good part of the distance.
Though mainly but a humble route to neighboring villages, or for the woodman's team, it once amused the traveller more than now by its variety, and lingered
longer in his memory.
Where now firm open fields stretch from the village to the woods, it then ran through a maple swamp on a foundation of logs, the remnants of which, doubtless, still underlie the present dusty highway, from the Stratton, now the Alms-House Farm, to Brister's Hill.
East of my bean-field, across the road, lived Cato Ingraham, slave of Duncan
Ingraham, Esquire, gentleman, of Concord village, who built his slave a house, and gave him permission to live in Walden
Woods;--Cato, not Uticensis, but Concordiensis.
Some say that he was a Guinea Negro.
There are a few who remember his little patch among the walnuts, which he let grow up till he should be old and need them; but a younger and whiter speculator got them at
last.
He too, however, occupies an equally narrow house at present.
Cato's half-obliterated cellar-hole still remains, though known to few, being concealed from the traveller by a fringe of pines.
It is now filled with the smooth sumach (Rhus glabra), and one of the earliest species of goldenrod (Solidago stricta) grows there luxuriantly.
Here, by the very corner of my field, still nearer to town, Zilpha, a colored woman, had her little house, where she spun linen for the townsfolk, making the Walden Woods ring with her shrill singing, for she had a loud and notable voice.
At length, in the war of 1812, her dwelling was set on fire by English soldiers, prisoners on parole, when she was away, and her cat and dog and hens were all burned up together.
She led a hard life, and somewhat inhumane.
One old frequenter of these woods remembers, that as he passed her house one noon he heard her muttering to herself over her gurgling pot--"Ye are all bones, bones!"
I have seen bricks amid the oak copse there.
Down the road, on the right hand, on Brister's Hill, lived Brister Freeman, "a handy Negro," slave of Squire Cummings once--there where grow still the apple trees which Brister planted and tended; large old trees now, but their fruit still wild and ciderish to my taste.
Not long since I read his epitaph in the old Lincoln burying-ground, a little on one side, near the unmarked graves of some British grenadiers who fell in the retreat from Concord--where he is styled "Sippio
Brister"--Scipio Africanus he had some title to be called--"a man of color," as if he were discolored.
It also told me, with staring emphasis, when he died; which was but an indirect way of informing me that he ever lived.
With him dwelt Fenda, his hospitable wife, who told fortunes, yet pleasantly--large, round, and black, blacker than any of the children of night, such a dusky orb as never rose on Concord before or since.
Farther down the hill, on the left, on the old road in the woods, are marks of some homestead of the Stratton family; whose orchard once covered all the slope of
Brister's Hill, but was long since killed out by pitch pines, excepting a few stumps, whose old roots furnish still the wild stocks of many a thrifty village tree.
Nearer yet to town, you come to Breed's location, on the other side of the way, just on the edge of the wood; ground famous for the pranks of a demon not distinctly named in old mythology, who has acted a prominent and astounding part in our New England life, and deserves, as much as any mythological character, to have his biography written one day; who first comes in the guise of a friend or hired man, and then robs and murders the whole family-- New-England Rum.
But history must not yet tell the tragedies enacted here; let time intervene in some measure to assuage and lend an azure tint to them.
Here the most indistinct and dubious tradition says that once a tavern stood; the well the same, which tempered the traveller's beverage and refreshed his steed.
Here then men saluted one another, and heard and told the news, and went their ways again.
Breed's hut was standing only a dozen years ago, though it had long been unoccupied.
It was about the size of mine.
It was set on fire by mischievous boys, one
Election night, if I do not mistake.
I lived on the edge of the village then, and had just lost myself over Davenant's
"Gondibert," that winter that I labored with a lethargy--which, by the way, I never knew whether to regard as a family complaint, having an uncle who goes to sleep shaving himself, and is obliged to sprout potatoes in a cellar Sundays, in order to keep awake and keep the Sabbath, or as the consequence of my attempt to read
Chalmers' collection of English poetry without skipping.
It fairly overcame my Nervii.
I had just sunk my head on this when the bells rung fire, and in hot haste the engines rolled that way, led by a straggling troop of men and boys, and I among the foremost, for I had leaped the brook.
We thought it was far south over the woods- -we who had run to fires before--barn, shop, or dwelling-house, or all together.
"It's Baker's barn," cried one.
"It is the Codman place," affirmed another.
And then fresh sparks went up above the wood, as if the roof fell in, and we all shouted "Concord to the rescue!"
Wagons shot past with furious speed and crushing loads, bearing, perchance, among the rest, the agent of the Insurance Company, who was bound to go however far; and ever and anon the engine bell tinkled behind, more slow and sure; and rearmost of all, as it was afterward whispered, came they who set the fire and gave the alarm.
Thus we kept on like true idealists, rejecting the evidence of our senses, until at a turn in the road we heard the crackling and actually felt the heat of the fire from over the wall, and realized, alas! that we were there.
The very nearness of the fire but cooled our ardor.
At first we thought to throw a frog-pond on to it; but concluded to let it burn, it was so far gone and so worthless.
So we stood round our engine, jostled one another, expressed our sentiments through speaking-trumpets, or in lower tone referred to the great conflagrations which the world has witnessed, including Bascom's shop, and, between ourselves, we thought that, were we there in season with our
"tub," and a full frog-pond by, we could turn that threatened last and universal one into another flood.
We finally retreated without doing any mischief--returned to sleep and
"Gondibert."
But as for "Gondibert," I would except that passage in the preface about wit being the soul's powder--"but most of mankind are strangers to wit, as Indians are to powder."
It chanced that I walked that way across the fields the following night, about the same hour, and hearing a low moaning at this spot, I drew near in the dark, and discovered the only survivor of the family that I know, the heir of both its virtues and its vices, who alone was interested in this burning, lying on his stomach and looking over the cellar wall at the still smouldering cinders beneath, muttering to himself, as is his wont.
He had been working far off in the river meadows all day, and had improved the first moments that he could call his own to visit the home of his fathers and his youth.
He gazed into the cellar from all sides and points of view by turns, always lying down to it, as if there was some treasure, which he remembered, concealed between the stones, where there was absolutely nothing but a heap of bricks and ashes.
The house being gone, he looked at what there was left.
He was soothed by the sympathy which my mere presence implied, and showed me, as well as the darkness permitted, where the well was covered up; which, thank Heaven, could never be burned; and he groped long about the wall to find the well-sweep which his father had cut and mounted, feeling for the iron hook or staple by which a burden had been fastened to the heavy end--all that he could now cling to--to convince me that it was no common "rider."
I felt it, and still remark it almost daily in my walks, for by it hangs the history of a family.
Once more, on the left, where are seen the well and lilac bushes by the wall, in the now open field, lived Nutting and Le Grosse.
But to return toward Lincoln.
Farther in the woods than any of these, where the road approaches nearest to the pond, Wyman the potter squatted, and furnished his townsmen with earthenware, and left descendants to succeed him.
Neither were they rich in worldly goods, holding the land by sufferance while they lived; and there often the sheriff came in vain to collect the taxes, and "attached a chip," for form's sake, as I have read in his accounts, there being nothing else that he could lay his hands on.
One day in midsummer, when I was hoeing, a man who was carrying a load of pottery to market stopped his horse against my field and inquired concerning Wyman the younger.
He had long ago bought a potter's wheel of him, and wished to know what had become of him.
I had read of the potter's clay and wheel in Scripture, but it had never occurred to me that the pots we use were not such as had come down unbroken from those days, or grown on trees like gourds somewhere, and I was pleased to hear that so fictile an art was ever practiced in my neighborhood.
The last inhabitant of these woods before me was an Irishman, Hugh Quoil (if I have spelt his name with coil enough), who occupied Wyman's tenement--Col.
Quoil, he was called.
Rumor said that he had been a soldier at Waterloo.
If he had lived I should have made him fight his battles over again.
His trade here was that of a ditcher.
Napoleon went to St. Helena; Quoil came to Walden Woods.
All I know of him is tragic.
He was a man of manners, like one who had seen the world, and was capable of more civil speech than you could well attend to.
He wore a greatcoat in midsummer, being affected with the trembling delirium, and his face was the color of carmine.
He died in the road at the foot of Brister's Hill shortly after I came to the woods, so that I have not remembered him as a neighbor.
Before his house was pulled down, when his comrades avoided it as "an unlucky castle,"
I visited it.
There lay his old clothes curled up by use, as if they were himself, upon his raised plank bed.
His pipe lay broken on the hearth, instead of a bowl broken at the fountain.
The last could never have been the symbol of his death, for he confessed to me that, though he had heard of Brister's Spring, he had never seen it; and soiled cards, kings of diamonds, spades, and hearts, were scattered over the floor.
One black chicken which the administrator could not catch, black as night and as silent, not even croaking, awaiting Reynard, still went to roost in the next apartment.
In the rear there was the dim outline of a garden, which had been planted but had never received its first hoeing, owing to those terrible shaking fits, though it was now harvest time.
It was overrun with Roman wormwood and beggar-ticks, which last stuck to my clothes for all fruit. The skin of a woodchuck was freshly stretched upon the back of the house, a trophy of his last Waterloo; but no warm cap or mittens would he want more.
Now only a dent in the earth marks the site of these dwellings, with buried cellar stones, and strawberries, raspberries, thimble-berries, hazel-bushes, and sumachs growing in the sunny sward there; some pitch pine or gnarled oak occupies what was the chimney nook, and a sweet-scented black birch, perhaps, waves where the door-stone was.
Sometimes the well dent is visible, where once a spring oozed; now dry and tearless grass; or it was covered deep--not to be discovered till some late day--with a flat stone under the sod, when the last of the race departed.
What a sorrowful act must that be--the covering up of wells! coincident with the opening of wells of tears.
These cellar dents, like deserted fox burrows, old holes, are all that is left where once were the stir and bustle of human life, and "fate, free will, foreknowledge absolute," in some form and dialect or other were by turns discussed.
But all I can learn of their conclusions amounts to just this, that "Cato and
Brister pulled wool"; which is about as edifying as the history of more famous schools of philosophy.
Still grows the vivacious lilac a generation after the door and lintel and the sill are gone, unfolding its sweet- scented flowers each spring, to be plucked by the musing traveller; planted and tended once by children's hands, in front-yard plots--now standing by wallsides in retired pastures, and giving place to new-rising forests;--the last of that stirp, sole survivor of that family.
Little did the dusky children think that the puny slip with its two eyes only, which they stuck in the ground in the shadow of the house and daily watered, would root itself so, and outlive them, and house itself in the rear that shaded it, and grown man's garden and orchard, and tell their story faintly to the lone wanderer a half-century after they had grown up and died--blossoming as fair, and smelling as sweet, as in that first spring.
I mark its still tender, civil, cheerful lilac colors.
But this small village, germ of something more, why did it fail while Concord keeps its ground?
Were there no natural advantages--no water privileges, forsooth?
Ay, the deep Walden Pond and cool Brister's Spring--privilege to drink long and healthy draughts at these, all unimproved by these men but to dilute their glass.
They were universally a thirsty race.
Might not the basket, stable-broom, mat- making, corn-parching, linen-spinning, and pottery business have thrived here, making the wilderness to blossom like the rose, and a numerous posterity have inherited the land of their fathers?
The sterile soil would at least have been proof against a low-land degeneracy.
Alas! how little does the memory of these human inhabitants enhance the beauty of the
landscape!
Again, perhaps, Nature will try, with me for a first settler, and my house raised last spring to be the oldest in the hamlet.
I am not aware that any man has ever built on the spot which I occupy.
Deliver me from a city built on the site of a more ancient city, whose materials are ruins, whose gardens cemeteries.
The soil is blanched and accursed there, and before that becomes necessary the earth itself will be destroyed.
With such reminiscences I repeopled the woods and lulled myself asleep.
At this season I seldom had a visitor.
When the snow lay deepest no wanderer ventured near my house for a week or fortnight at a time, but there I lived as snug as a meadow mouse, or as cattle and poultry which are said to have survived for a long time buried in drifts, even without food; or like that early settler's family in the town of Sutton, in this State, whose cottage was completely covered by the great snow of 1717 when he was absent, and an
Indian found it only by the hole which the chimney's breath made in the drift, and so relieved the family.
But no friendly Indian concerned himself about me; nor needed he, for the master of the house was at home.
The Great Snow!
How cheerful it is to hear of!
When the farmers could not get to the woods and swamps with their teams, and were obliged to cut down the shade trees before their houses, and, when the crust was harder, cut off the trees in the swamps, ten feet from the ground, as it appeared the next spring.
In the deepest snows, the path which I used from the highway to my house, about half a mile long, might have been represented by a meandering dotted line, with wide intervals between the dots.
For a week of even weather I took exactly the same number of steps, and of the same length, coming and going, stepping deliberately and with the precision of a pair of dividers in my own deep tracks--to such routine the winter reduces us--yet often they were filled with heaven's own blue.
But no weather interfered fatally with my walks, or rather my going abroad, for I frequently tramped eight or ten miles through the deepest snow to keep an appointment with a beech tree, or a yellow birch, or an old acquaintance among the pines; when the ice and snow causing their limbs to droop, and so sharpening their tops, had changed the pines into fir trees; wading to the tops of the highest hills when the show was nearly two feet deep on a level, and shaking down another snow-storm on my head at every step; or sometimes creeping and floundering thither on my hands and knees, when the hunters had gone into winter quarters.
One afternoon I amused myself by watching a barred owl (Strix nebulosa) sitting on one of the lower dead limbs of a white pine, close to the trunk, in broad daylight, I standing within a rod of him.
He could hear me when I moved and cronched the snow with my feet, but could not plainly see me.
When I made most noise he would stretch out his neck, and erect his neck feathers, and open his eyes wide; but their lids soon fell again, and he began to nod.
I too felt a slumberous influence after watching him half an hour, as he sat thus with his eyes half open, like a cat, winged brother of the cat.
There was only a narrow slit left between their lids, by which he preserved a peninsular relation to me; thus, with half- shut eyes, looking out from the land of dreams, and endeavoring to realize me, vague object or mote that interrupted his visions.
At length, on some louder noise or my nearer approach, he would grow uneasy and sluggishly turn about on his perch, as if impatient at having his dreams disturbed; and when he launched himself off and flapped through the pines, spreading his wings to unexpected breadth, I could not hear the slightest sound from them.
Thus, guided amid the pine boughs rather by a delicate sense of their neighborhood than by sight, feeling his twilight way, as it were, with his sensitive pinions, he found a new perch, where he might in peace await the dawning of his day.
As I walked over the long causeway made for the railroad through the meadows, I encountered many a blustering and nipping wind, for nowhere has it freer play; and when the frost had smitten me on one cheek, heathen as I was, I turned to it the other also.
Nor was it much better by the carriage road from Brister's Hill.
For I came to town still, like a friendly Indian, when the contents of the broad open fields were all piled up between the walls of the Walden road, and half an hour sufficed to obliterate the tracks of the last traveller.
And when I returned new drifts would have formed, through which I floundered, where the busy northwest wind had been depositing the powdery snow round a sharp angle in the road, and not a rabbit's track, nor even the fine print, the small type, of a meadow mouse was to be seen.
Yet I rarely failed to find, even in midwinter, some warm and springly swamp where the grass and the skunk-cabbage still put forth with perennial verdure, and some hardier bird occasionally awaited the return of spring.
Sometimes, notwithstanding the snow, when I returned from my walk at evening I crossed the deep tracks of a woodchopper leading from my door, and found his pile of whittlings on the hearth, and my house filled with the odor of his pipe.
Or on a Sunday afternoon, if I chanced to be at home, I heard the cronching of the snow made by the step of a long-headed farmer, who from far through the woods sought my house, to have a social "crack"; one of the few of his vocation who are "men on their farms"; who donned a frock instead of a professor's gown, and is as ready to extract the moral out of church or state as to haul a load of manure from his barn- yard.
We talked of rude and simple times, when men sat about large fires in cold, bracing weather, with clear heads; and when other dessert failed, we tried our teeth on many a nut which wise squirrels have long since abandoned, for those which have the thickest shells are commonly empty.
The one who came from farthest to my lodge, through deepest snows and most dismal tempests, was a poet.
A farmer, a hunter, a soldier, a reporter, even a philosopher, may be daunted; but nothing can deter a poet, for he is actuated by pure love.
Who can predict his comings and goings?
His business calls him out at all hours, even when doctors sleep.
We made that small house ring with boisterous mirth and resound with the murmur of much sober talk, making amends then to Walden vale for the long silences.
Broadway was still and deserted in comparison.
At suitable intervals there were regular salutes of laughter, which might have been referred indifferently to the last-uttered or the forth-coming jest.
We made many a "bran new" theory of life over a thin dish of gruel, which combined the advantages of conviviality with the clear-headedness which philosophy requires.
I should not forget that during my last winter at the pond there was another welcome visitor, who at one time came through the village, through snow and rain and darkness, till he saw my lamp through the trees, and shared with me some long winter evenings.
One of the last of the philosophers-- Connecticut gave him to the world--he peddled first her wares, afterwards, as he declares, his brains.
These he peddles still, prompting God and disgracing man, bearing for fruit his brain only, like the nut its kernel.
I think that he must be the man of the most faith of any alive.
His words and attitude always suppose a better state of things than other men are acquainted with, and he will be the last man to be disappointed as the ages revolve.
He has no venture in the present.
But though comparatively disregarded now, when his day comes, laws unsuspected by most will take effect, and masters of families and rulers will come to him for advice.
"How blind that cannot see serenity!" A true friend of man; almost the only friend of human progress.
An Old Mortality, say rather an Immortality, with unwearied patience and faith making plain the image engraven in men's bodies, the God of whom they are but defaced and leaning monuments.
With his hospitable intellect he embraces children, beggars, insane, and scholars, and entertains the thought of all, adding to it commonly some breadth and elegance.
I think that he should keep a caravansary on the world's highway, where philosophers of all nations might put up, and on his sign should be printed, "Entertainment for man, but not for his beast.
Enter ye that have leisure and a quiet mind, who earnestly seek the right road."
He is perhaps the sanest man and has the fewest crotchets of any I chance to know; the same yesterday and tomorrow.
Of yore we had sauntered and talked, and effectually put the world behind us; for he was pledged to no institution in it, freeborn, ingenuus.
Whichever way we turned, it seemed that the heavens and the earth had met together, since he enhanced the beauty of the landscape.
A blue-robed man, whose fittest roof is the overarching sky which reflects his serenity.
I do not see how he can ever die; Nature cannot spare him.
Having each some shingles of thought well dried, we sat and whittled them, trying our knives, and admiring the clear yellowish grain of the pumpkin pine.
We waded so gently and reverently, or we pulled together so smoothly, that the fishes of thought were not scared from the stream, nor feared any angler on the bank, but came and went grandly, like the clouds which float through the western sky, and the mother-o'-pearl flocks which sometimes form and dissolve there.
There we worked, revising mythology, rounding a fable here and there, and building castles in the air for which earth offered no worthy foundation.
Great Looker!
Great Expecter! to converse with whom was a New England Night's Entertainment.
Ah! such discourse we had, hermit and philosopher, and the old settler I have spoken of--we three--it expanded and racked my little house; I should not dare to say how many pounds' weight there was above the atmospheric pressure on every circular inch; it opened its seams so that they had to be calked with much dulness thereafter to stop the consequent leak;--but I had enough of that kind of oakum already picked.
There was one other with whom I had "solid seasons," long to be remembered, at his house in the village, and who looked in upon me from time to time; but I had no more for society there.
There too, as everywhere, I sometimes expected the Visitor who never comes.
The Vishnu Purana says, "The house-holder is to remain at eventide in his courtyard as long as it takes to milk a cow, or longer if he pleases, to await the arrival of a guest."
I often performed this duty of hospitality, waited long enough to milk a whole herd of cows, but did not see the man approaching from the town. >
CHAPTER 15 Winter Animals
When the ponds were firmly frozen, they afforded not only new and shorter routes to many points, but new views from their surfaces of the familiar landscape around them.
When I crossed Flint's Pond, after it was covered with snow, though I had often paddled about and skated over it, it was so unexpectedly wide and so strange that I could think of nothing but Baffin's Bay.
The Lincoln hills rose up around me at the extremity of a snowy plain, in which I did not remember to have stood before; and the fishermen, at an indeterminable distance over the ice, moving slowly about with their wolfish dogs, passed for sealers, or Esquimaux, or in misty weather loomed like fabulous creatures, and I did not know whether they were giants or pygmies.
I took this course when I went to lecture in Lincoln in the evening, travelling in no road and passing no house between my own hut and the lecture room.
In Goose Pond, which lay in my way, a colony of muskrats dwelt, and raised their cabins high above the ice, though none could be seen abroad when I crossed it.
Walden, being like the rest usually bare of snow, or with only shallow and interrupted drifts on it, was my yard where I could walk freely when the snow was nearly two feet deep on a level elsewhere and the villagers were confined to their streets.
There, far from the village street, and except at very long intervals, from the jingle of sleigh-bells, I slid and skated, as in a vast moose-yard well trodden, overhung by oak woods and solemn pines bent down with snow or bristling with icicles.
For sounds in winter nights, and often in winter days, I heard the forlorn but melodious note of a hooting owl indefinitely far; such a sound as the frozen earth would yield if struck with a suitable plectrum, the very lingua vernacula of Walden Wood, and quite familiar to me at last, though I never saw the bird while it was making it.
I seldom opened my door in a winter evening without hearing it; Hoo hoo hoo, hoorer, hoo, sounded sonorously, and the first three syilables accented somewhat like how der do; or sometimes hoo, hoo only.
One night in the beginning of winter, before the pond froze over, about nine o'clock, I was startled by the loud honking of a goose, and, stepping to the door, heard the sound of their wings like a tempest in the woods as they flew low over my house.
They passed over the pond toward Fair Haven, seemingly deterred from settling by my light, their commodore honking all the while with a regular beat.
Suddenly an unmistakable cat-owl from very near me, with the most harsh and tremendous voice I ever heard from any inhabitant of the woods, responded at regular intervals to the goose, as if determined to expose and disgrace this intruder from Hudson's Bay by exhibiting a greater compass and volume of voice in a native, and boo-hoo him out of Concord horizon.
What do you mean by alarming the citadel at this time of night consecrated to me?
Do you think I am ever caught napping at such an hour, and that I have not got lungs and a larynx as well as yourself?
It was one of the most thrilling discords I ever heard.
And yet, if you had a discriminating ear, there were in it the elements of a concord such as these plains never saw nor heard.
I also heard the whooping of the ice in the pond, my great bed-fellow in that part of
Concord, as if it were restless in its bed and would fain turn over, were troubled with flatulency and had dreams; or I was waked by the cracking of the ground by the frost, as if some one had driven a team against my door, and in the morning would find a crack in the earth a quarter of a mile long and a third of an inch wide.
Sometimes I heard the foxes as they ranged over the snow-crust, in moonlight nights, in search of a partridge or other game, barking raggedly and demoniacally like forest dogs, as if laboring with some anxiety, or seeking expression, struggling for light and to be dogs outright and run freely in the streets; for if we take the ages into our account, may there not be a civilization going on among brutes as well as men?
They seemed to me to be rudimental, burrowing men, still standing on their defence, awaiting their transformation.
Sometimes one came near to my window, attracted by my light, barked a vulpine curse at me, and then retreated.
Usually the red squirrel (Sciurus Hudsonius) waked me in the dawn, coursing over the roof and up and down the sides of the house, as if sent out of the woods for this purpose.
In the course of the winter I threw out half a bushel of ears of sweet corn, which had not got ripe, on to the snow-crust by my door, and was amused by watching the motions of the various animals which were baited by it.
In the twilight and the night the rabbits came regularly and made a hearty meal.
All day long the red squirrels came and went, and afforded me much entertainment by their manoeuvres.
One would approach at first warily through the shrub oaks, running over the snow-crust by fits and starts like a leaf blown by the wind, now a few paces this way, with wonderful speed and waste of energy, making inconceivable haste with his "trotters," as if it were for a wager, and now as many paces that way, but never getting on more than half a rod at a time; and then suddenly pausing with a ludicrous expression and a gratuitous somerset, as if all the eyes in the universe were eyed on him--for all the motions of a squirrel, even in the most solitary recesses of the forest, imply spectators as much as those of a dancing girl--wasting more time in delay and circumspection than would have sufficed to walk the whole distance--I never saw one walk--and then suddenly, before you could say Jack Robinson, he would be in the top of a young pitch pine, winding up his clock and chiding all imaginary spectators, soliloquizing and talking to all the universe at the same time--for no reason that I could ever detect, or he himself was aware of, I suspect.
At length he would reach the corn, and selecting a suitable ear, frisk about in the same uncertain trigonometrical way to the topmost stick of my wood-pile, before my window, where he looked me in the face, and there sit for hours, supplying himself with a new ear from time to time, nibbling at first voraciously and throwing the half- naked cobs about; till at length he grew more dainty still and played with his food, tasting only the inside of the kernel, and the ear, which was held balanced over the stick by one paw, slipped from his careless grasp and fell to the ground, when he would
look over at it with a ludicrous expression of uncertainty, as if suspecting that it had life, with a mind not made up whether to get it again, or a new one, or be off; now thinking of corn, then listening to hear what was in the wind.
So the little impudent fellow would waste many an ear in a forenoon; till at last, seizing some longer and plumper one, considerably bigger than himself, and skilfully balancing it, he would set out with it to the woods, like a tiger with a buffalo, by the same zig-zag course and frequent pauses, scratching along with it as if it were too heavy for him and falling all the while, making its fall a diagonal between a perpendicular and horizontal, being determined to put it through at any rate;--a singularly frivolous and whimsical fellow;--and so he would get off with it to where he lived, perhaps carry it to the top of a pine tree forty or fifty rods distant, and I would afterwards find the cobs strewn about the woods in various directions.
At length the jays arrive, whose discordant screams were heard long before, as they were warily making their approach an eighth of a mile off, and in a stealthy and sneaking manner they flit from tree to tree, nearer and nearer, and pick up the kernels which the squirrels have dropped.
Then, sitting on a pitch pine bough, they attempt to swallow in their haste a kernel which is too big for their throats and chokes them; and after great labor they disgorge it, and spend an hour in the endeavor to crack it by repeated blows with their bills.
They were manifestly thieves, and I had not much respect for them; but the squirrels, though at first shy, went to work as if they were taking what was their own.
Meanwhile also came the chickadees in flocks, which, picking up the crumbs the squirrels had dropped, flew to the nearest twig and, placing them under their claws, hammered away at them with their little bills, as if it were an insect in the bark, till they were sufficiently reduced for their slender throats.
A little flock of these titmice came daily to pick a dinner out of my woodpile, or the crumbs at my door, with faint flitting lisping notes, like the tinkling of icicles in the grass, or else with sprightly day day day, or more rarely, in spring-like days, a wiry summery phe-be from the woodside.
They were so familiar that at length one alighted on an armful of wood which I was carrying in, and pecked at the sticks without fear.
I once had a sparrow alight upon my shoulder for a moment while I was hoeing in a village garden, and I felt that I was more distinguished by that circumstance than I should have been by any epaulet I could have worn.
The squirrels also grew at last to be quite familiar, and occasionally stepped upon my shoe, when that was the nearest way.
When the ground was not yet quite covered, and again near the end of winter, when the snow was melted on my south hillside and about my wood-pile, the partridges came out of the woods morning and evening to feed there.
Whichever side you walk in the woods the partridge bursts away on whirring wings, jarring the snow from the dry leaves and twigs on high, which comes sifting down in the sunbeams like golden dust, for this brave bird is not to be scared by winter.
It is frequently covered up by drifts, and, it is said, "sometimes plunges from on wing into the soft snow, where it remains concealed for a day or two."
I used to start them in the open land also, where they had come out of the woods at sunset to "bud" the wild apple trees.
They will come regularly every evening to particular trees, where the cunning sportsman lies in wait for them, and the distant orchards next the woods suffer thus not a little.
I am glad that the partridge gets fed, at any rate.
It is Nature's own bird which lives on buds and diet drink.
In dark winter mornings, or in short winter afternoons, I sometimes heard a pack of hounds threading all the woods with hounding cry and yelp, unable to resist the instinct of the chase, and the note of the hunting-horn at intervals, proving that man was in the rear.
The woods ring again, and yet no fox bursts forth on to the open level of the pond, nor following pack pursuing their Actaeon.
And perhaps at evening I see the hunters returning with a single brush trailing from their sleigh for a trophy, seeking their inn.
They tell me that if the fox would remain in the bosom of the frozen earth he would be safe, or if he would run in a straight line away no foxhound could overtake him; but, having left his pursuers far behind, he stops to rest and listen till they come up, and when he runs he circles round to his old haunts, where the hunters await him.
Sometimes, however, he will run upon a wall many rods, and then leap off far to one side, and he appears to know that water will not retain his scent.
A hunter told me that he once saw a fox pursued by hounds burst out on to Walden when the ice was covered with shallow puddles, run part way across, and then return to the same shore.
Ere long the hounds arrived, but here they lost the scent.
Sometimes a pack hunting by themselves would pass my door, and circle round my house, and yelp and hound without regarding me, as if afflicted by a species of madness, so that nothing could divert them from the pursuit.
Thus they circle until they fall upon the recent trail of a fox, for a wise hound will forsake everything else for this.
One day a man came to my hut from Lexington to inquire after his hound that made a large track, and had been hunting for a week by himself.
But I fear that he was not the wiser for all I told him, for every time I attempted to answer his questions he interrupted me by asking, "What do you do here?"
He had lost a dog, but found a man.
One old hunter who has a dry tongue, who used to come to bathe in Walden once every year when the water was warmest, and at such times looked in upon me, told me that many years ago he took his gun one afternoon and went out for a cruise in Walden Wood; and as he walked the Wayland road he heard the cry of hounds approaching, and ere long a fox leaped the wall into the road, and as quick as thought leaped the other wall out of the road, and his swift bullet had not touched him.
Some way behind came an old hound and her three pups in full pursuit, hunting on their own account, and disappeared again in the woods.
Late in the afternoon, as he was resting in the thick woods south of Walden, he heard the voice of the hounds far over toward Fair Haven still pursuing the fox; and on they came, their hounding cry which made all the woods ring sounding nearer and nearer, now from Well Meadow, now from the
Baker Farm.
For a long time he stood still and listened to their music, so sweet to a hunter's ear, when suddenly the fox appeared, threading the solemn aisles with an easy coursing pace, whose sound was concealed by a sympathetic rustle of the leaves, swift and still, keeping the round, leaving his pursuers far behind; and, leaping upon a rock amid the woods, he sat erect and listening, with his back to the hunter.
For a moment compassion restrained the latter's arm; but that was a short-lived mood, and as quick as thought can follow thought his piece was levelled, and whang!-
-the fox, rolling over the rock, lay dead on the ground.
The hunter still kept his place and listened to the hounds.
Still on they came, and now the near woods resounded through all their aisles with their demoniac cry.
At length the old hound burst into view with muzzle to the ground, and snapping the air as if possessed, and ran directly to the rock; but, spying the dead fox, she suddenly ceased her hounding as if struck dumb with amazement, and walked round and round him in silence; and one by one her pups arrived, and, like their mother, were sobered into silence by the mystery.
Then the hunter came forward and stood in their midst, and the mystery was solved.
They waited in silence while he skinned the fox, then followed the brush a while, and at length turned off into the woods again.
That evening a Weston squire came to the Concord hunter's cottage to inquire for his hounds, and told how for a week they had been hunting on their own account from
Weston woods.
The Concord hunter told him what he knew and offered him the skin; but the other declined it and departed.
He did not find his hounds that night, but the next day learned that they had crossed the river and put up at a farmhouse for the night, whence, having been well fed, they took their departure early in the morning.
The hunter who told me this could remember one Sam Nutting, who used to hunt bears on
Fair Haven Ledges, and exchange their skins for rum in Concord village; who told him, even, that he had seen a moose there.
Nutting had a famous foxhound named Burgoyne--he pronounced it Bugine--which my informant used to borrow.
In the "Wast Book" of an old trader of this town, who was also a captain, town-clerk, and representative, I find the following entry.
Jan.
18th, 1742-3, "John Melven Cr. by 1 Grey Fox 0--2--3"; they are not now found here; and in his ledger, Feb, 7th, 1743, Hezekiah Stratton has credit "by 1/2 a Catt skin 0-- 1--4-1/2"; of course, a wild-cat, for
Stratton was a sergeant in the old French war, and would not have got credit for hunting less noble game.
Credit is given for deerskins also, and they were daily sold.
One man still preserves the horns of the last deer that was killed in this vicinity, and another has told me the particulars of the hunt in which his uncle was engaged.
The hunters were formerly a numerous and merry crew here.
I remember well one gaunt Nimrod who would catch up a leaf by the roadside and play a strain on it wilder and more melodious, if my memory serves me, than any hunting-horn.
At midnight, when there was a moon, I sometimes met with hounds in my path prowling about the woods, which would skulk out of my way, as if afraid, and stand silent amid the bushes till I had passed.
Squirrels and wild mice disputed for my store of nuts.
There were scores of pitch pines around my house, from one to four inches in diameter, which had been gnawed by mice the previous winter--a Norwegian winter for them, for the snow lay long and deep, and they were obliged to mix a large proportion of pine bark with their other diet.
These trees were alive and apparently flourishing at midsummer, and many of them had grown a foot, though completely girdled; but after another winter such were without exception dead.
It is remarkable that a single mouse should thus be allowed a whole pine tree for its dinner, gnawing round instead of up and down it; but perhaps it is necessary in order to thin these trees, which are wont to grow up densely.
The hares (Lepus Americanus) were very familiar.
One had her form under my house all winter, separated from me only by the flooring, and she startled me each morning by her hasty departure when I began to stir--thump, thump, thump, striking her head against the floor timbers in her hurry.
They used to come round my door at dusk to nibble the potato parings which I had thrown out, and were so nearly the color of the ground that they could hardly be distinguished when still.
Sometimes in the twilight I alternately lost and recovered sight of one sitting motionless under my window.
When I opened my door in the evening, off they would go with a squeak and a bounce.
Near at hand they only excited my pity.
One evening one sat by my door two paces from me, at first trembling with fear, yet unwilling to move; a poor wee thing, lean and bony, with ragged ears and sharp nose, scant tail and slender paws.
It looked as if Nature no longer contained the breed of nobler bloods, but stood on her last toes.
Its large eyes appeared young and unhealthy, almost dropsical.
I took a step, and lo, away it scud with an elastic spring over the snow-crust, straightening its body and its limbs into graceful length, and soon put the forest between me and itself--the wild free venison, asserting its vigor and the dignity of Nature.
Not without reason was its slenderness.
Such then was its nature.
(Lepus, levipes, light-foot, some think.) What is a country without rabbits and partridges?
They are among the most simple and indigenous animal products; ancient and venerable families known to antiquity as to modern times; of the very hue and substance of Nature, nearest allied to leaves and to the ground--and to one another; it is either winged or it is legged.
It is hardly as if you had seen a wild creature when a rabbit or a partridge bursts away, only a natural one, as much to be expected as rustling leaves.
The partridge and the rabbit are still sure to thrive, like true natives of the soil, whatever revolutions occur.
If the forest is cut off, the sprouts and bushes which spring up afford them concealment, and they become more numerous than ever.
That must be a poor country indeed that does not support a hare.
Our woods teem with them both, and around every swamp may be seen the partridge or rabbit walk, beset with twiggy fences and horse-hair snares, which some cow-boy tends. >
Right, what I have right in front of me is the Khan Academy measuring angles, measuring angles exercise.
I have a small part of it in this screen right over here.
And it's a pretty cool exercise cause it has this little virtual protracter that we can use to actually measure angles. And I wanna give credit to the, the person who built this protracter, cause I think it's pretty neat.
Omar Rizwan, who's actually a high school interim made this, made this pretty neat module.
I said the vertex of the angle at the center of the protracter, and then, what you wanna do is, either rotate the angle or rotate the protractor in this case you are going to rotate the protractor you wanna rotate the protracor so that the zero angle are look at the zero mark is at one of the sides of the angle and the other side of the angle is within the protractor so lets,try to do that so if may be ,if you wanna do that this zero side it should be at this side of the angle so lets,rotate it
lets rotate it that way, its keep rotating it i can keep it press thats better alright ,thats looks about right so, one side, is that zero mark and then my angle my other side are if there is a way points 2 looks like pretty cause to the 20˚ mark so i would type the range of the screen you are seeing that and that is the right answer and we can get the other angle so lets,try the measure this one right over here so,once again place the center of the protractor at the center at the vertex of an angle we can place the zero degree the base of the protractor at this side of the angle so we should rotate it a little bit we want to do one more time that , looks about right and the angle is now opening up this is the other side of point to 110 degrees is this larger than 90 degree its also an obtuse angle. the last one is an acute angle,this is obtuse angle 110 degrees more than 90 degrees,we typed in i got the right answer just do couple of more than these so,once again put the center the protractor at the vertex of an angle now i want to rotate it ,there we go, and this looks liking roughly an 80 degree angle but,if i am really precise 81 or 82 degrees and 80 is my best guess
lets do one more of these.
Vertex of my angle at the center of my protractor.and I want to put one side of my angle at 0 degrees. here are two ways to do this, you could do just this, this is not too helpful as the angle is outside the protractor.
So lets keep rotating it, so our other side points to 70 degrees, so it is an acute angle.
I will leave you with that.
We're asked to look at the table below.
From the information given, is there a functional relationship between each person and his or her height? So a good place to start is just think about what a functional relationship means.
Now, there's definitely a relationship.
They say, hey, if you're Joelle, you're 5-6.
If you're Nathan, you're 4-11.
If you're Stewart, you're 5-11.
That is a relationship.
Now, in order for it to be a functional relationship, for every instance or every example of the independent variable, you can only have one example of the value of the function for it.
So if you say if this is a height function, in order for this to be a functional relationship, no matter whose name you put inside of the height function, you need to only be able to get one value.
If there were two values associated with one person's name, it would not be a functional relationship.
So if I were to ask you what is the height of Nathan?
Well, you'd look at the table and say, well, Nathan's height is 4 foot 11.
There are not two heights for Nathan.
There is only one height.
And for any one of these people that we can input into the function, there's only one height associated with them, so it is a functional relationship.
We can even see that on a graph.
Let's see, the highest height here is 6 foot 1.
So if we start off with one foot, two feet, three feet, four feet, five feet, and six feet.
And then if I were to plot the different names, the different people that I could put into our height function, we have--
We have Joelle, we have Nathan, we have Stewart, we have LJ, and then we have Tariq right there.
So lets plot them.
So you have Joelle, Joelle's height is 5-6, so 5-6 is right about there.
Then you have Nathan.
Nathan's height is 4-11.
We will plot to him right over there.
Stewart's height is 5-11.
So Stewart's height-- I made him like six feet; let me make it a little lower-- is 5-11.
LJ's height is 5-6.
So you have two people with a height of 5-6, but that's OK, as long as for each person you only have one height.
And then finally, Tariq is 6 foot 1.
He's the tallest guy here.
So notice, for any one of the inputs into our function, we only have one value, so this is a functional relationship.
If I gave you the situation, if I also wrote here-- let's say the table was like this and I also wrote that Stewart is 5 foot 3 inches.
If this was our table, then we would no longer have a functional relationship because for the input of Stewart, we would have two different values.
If we were to graph this, we have Stewart here at 5-11, and then all of a sudden, we would also have Stewart at 5-3.
So for Stewart, you would have two values, and so this wouldn't be a valid functional relationship because you wouldn't know what value to give if you were to take the height of Stewart.
In order for this to be a function, there can only be one value for this.
You don't know in this situation when I add this, whether it's 5-3 or 5-11.
Now, this wasn't the case, so that isn't there and so we know that the height of Stewart is 5-11 and this is a functional relationship.
I think to some level, it might be confusing, because it's such a simple idea.
Each of these values can only have one height associated with it.
That's what makes it a function.
If you had more than one height associated with it, it would not be a function.
Round 24,259 to the nearest hundred.
You're going to find that doing these problems are pretty straightforward, but what I want to do is just think about what it means to round to the nearest hundred.
So what I'm going to do is I'm going to draw a number line.
Let me draw a number line here, and I'm just going to mark off the hundreds on the number line.
So maybe we have 24,100, and then we go to 24,200, then we go to 24,300, and then we go to 24,400.
I think you see what I mean when I'm only marking off the hundreds.
I'm going up by increments of 100.
Now, on this number line, where is 24,259?
So if we look at the number line, it's more than 24,200 and it's less than 24,300.
And it's 259, so if this distance right here is 100, 59 is right about there, so that is where our number is.
That is 24,259.
So when someone asks you to round to the nearest hundred, they're literally saying round to one of these increments of 100 or round to whichever increment of 100 that it is closest to.
And if you look at it right like this, if you just eyeball it, you'll actually see that it is closer to 24,300 than it is to 24,200.
So when you round it, you round to 24,300.
So if you round to the nearest hundred, the answer literally is 24,300.
Now that's kind of the conceptual understanding of why it's even called the nearest hundred.
The nearest hundred is 24,300.
But every time you do a problem like this, you don't have to draw a number line and go through this whole process, although you might want to think about it.
An easier process, or maybe a more mechanical process, is you literally look at the number 24,259.
We want to round to the nearest hundred, so you look at the hundreds place.
This is the hundreds place right here, and when we round, that means we don't want any digits.
We only want zeroes after the hundreds place.
So what you do is you look at the place one less than the place you're rounding to.
This is the hundreds place so you look at the 5 right there, and if this number is 5 or greater, if it's 5, 6, 7, 8, or 9, you round up.
So 5 or greater, you round up.
And so rounding up in this situation, it is 5.
It is 5 or greater, so rounding up means that we go to 24,000, and since we're rounding up, we make the 2 into a 3.
We increment it by one, so rounding up, so 24,300.
That's what we mean by rounding up.
And just as kind of a counterexample, if I had 24,249 and I wanted to round to the nearest hundred, I would say, OK, I want to round to the nearest hundred.
Let me look at the tens place, this place one level to the right.
It is not 5 or greater, so I will round down.
And when you round down, be careful.
It doesn't mean you decreases this 2.
It literally means you just only have the 2. Just get rid of everything after it.
So it becomes 24,200.
That's the process where you round down.
If you round up, it becomes 24,300.
And it makes sense. 24,249 is going to be sitting right over here someplace, so it's going to be closer to 24,200.
24,200 would be the nearest hundred when we round down in this case.
For the case of the problem, 24,259, the nearest hundred is 24,300.
We round up.
The main mast of a fishing boat is supported by a sturdy rope that extends from the top of the mast to the deck.
If the mast is 20 feet tall and the rope attaches to the deck 15 feet away from the base of the mast, how long is the rope?
So let's draw ourselves a boat and make sure we understand what the deck and the mast and all of that is.
So let me draw a boat. I'll start with yellow.
So let's say that this is my boat.
That is the deck of the boat.
And the boat might look something like this.
It's a sailing boat.
This is the water down here.
And then the mast is the thing that holds up the sail.
So let me draw ourselves a mast.
And they say the mast is 20 feet tall. So this distance right here is 20 feet.
That is what is holding up the sail.
I can draw it as a pole so it's a little bit clearer. Even shade it in if we like.
And then they say a rope attaches to the deck 15 feet away from the base of the mast.
So this is the base of the mast. This is the deck right here.
The rope attaches 15 feet away from the base of the mast.
So if this is the base of the mast, we go 15 feet, might be about that distance right there.
Let me mark that.
Distance right there is 15 feet. And the rope attaches right here, from the top of the mast all the way that base. So the rope goes like that.
So there's a few things you might realize. We're dealing with a triangle here.
And it's not any triangle.
We're assuming that the mast goes straight up and that the deck is straight left and right.
So this is a right triangle. This is a 90 degree angle right here.
And we know that, if we know two sides of a right triangle, we can always figure out the third side of a right triangle using the Pythagorean theorem.
And all that tells us is it the sum of the squares of the shorter sides of the triangle are going to be equal to the square of the longer side.
And that longer side is call the hypotenuse.
And in all cases, the hypotenuse is the side opposite the 90 degree angle.
It is always going to be the longest side of our right triangle.
So we need to figure out the hypotenuse here.
We know the lengths of the two shorter sides.
So we can see that if we take 15 squared, that's one of the short sides, I'm squaring it.
And then add that to the square of the other shorter side, to 20 feet squared. And when I say the shorter side, I mean relative to the hypotenuse. The hypotenuse will always be the longest side.
Let's say the hypotenuse is in green just so we get our color coding nice.
That is going to be equal to the rope squared. Or the length of the rope.
Let's call this distance right here r. r for rope.
So 15 squared plus 20 squared is going to be equal to r squared.
And what's 15 squared?
It's 225.
20 squared is 400.
And that's going to be equal to r squared.
Now 225 plus 400 is 625.
625 is equal to r squared.
And then we can take the principal root of both sides of this equation. Because we're talking about distances, we want the positive square root.
So you take the positive square root, or the principal root, of both sides of this equation.
And you are left with r is equal to the square root of 625.
You can play with it a little bit if you like.
But if you've ever played with numbers around 25, you'll see that this is 25 squared.
So r is equal to the square root of 625, which is 25.
So this distance right here, the length of the rope, is equal to 25 feet.
Google Search is incredibly powerful.
You can search for text across the Internet most of human knowledge, images, books, videos.
But, we realized there was an important part of the Search experience that we'd overlooked.
Our task as designers is to get our users the information they're looking for as quickly and as beautifully as possible.
But, until now, we couldn't always give users what they're looking for
Because, sometimes, they're not looking at all.
My wife and I have a puppy with so much energy that we walk her 5 times a day, and she sniffs around every nook and cranny.
This is how she gets information about her world.
Photo-auditory-olfactory sensory convergence is a phenomenon that's been promised in science fiction for decades.
-We're excited to announce Google NoseBeta our flagship olfactory knowledge feature enabling users to search for smells.
Our mobile aroma indexing program has been able to amass a 15 million scentibite database of smells from around the world.
-With an elegant integration into our existing knowledge panels, the Google Nose Beta Smell button seamlessly connects scent to search.
By intersecting photons with infrasound waves,
Google Nose Beta temporarily aligns molecules to emulate a particular scent.
Google Nose Beta works on nearly all desktops, laptops, and quite a few mobile devices.
In the fast paced world that we live in, we don't always have time to stop and smell the roses.
Now, with Google Nose Beta, the roses are just a click away.
-If you have a question like
"what does a new car smell like?", who knows the answer?
Google Nose.
-What does a ghost smell like?
Google Nose.
What does the inside of an Egyptian tomb smell like?
Google Nose.
Google Nose.
Google Nose...Beta.
நமக்குக் கொடுக்கப்பட்ட சமன்பாட்டுல தனி மதிப்பைக் கண்டுபிடிக்கப்போறோம். மூணு எக்ஸ் கழித்தல் 9 இன் முழு மதிப்பு பூஜ்ஜியத்துக்குச் சமம். இதுக்கு எண் கோட்டின் வழியாத் தீர்வு காணலாம். முழுமதிப்புச் சமன்பாட்டை மறுபடியும் எழுதிக்கலாம். மூன்று எக்ஸ் கழித்தல் 9 இன் முழு மதிப்பு பூஜ்ஜியத்துக்குச் சமம். இது தான் நமக்குக் கொடுத்திருக்கு. ஏதோ ஒன்றின் முழு மதிப்பு அப்பிடின்னு சொல்றப்போ இந்த எடத்துல ஏதோ ஒன்றுன்றது மூன்று எக்ஸ் கழித்தல் 9 பூஜ்ஜியத்துக்கு சமமா இருக்கு. நமக்கு ஏதோ ஒன்னோட முழு மதிப்பு பூஜ்ஜியம்ன்னு கொடுத்திருந்தா அதோட மதிப்பு பூஜ்ஜியத்திற்கு அப்பால் மிகச் சரியாக பூஜ்ஜியம்ன்னு சொல்லலாம். அல்லது எண் கோட்டுக்கு அப்பால் பூஜ்ஜியம்ன்னு சொல்லலாம். அப்படின்னா அந்த ஏதோ ஒன்னு அப்படிங்க எண் பூஜ்ஜியமாத்தான் இருக்கணும். நமக்கு எக்ஸின் முழு மதிப்பு பூஜ்ஜியத்துக்கு சமம்ன்னு சொல்லியிருந்தா எக்ஸோட மதிப்பு பூஜ்ஜியத்துக்கு சமம் ஆகும்ன்னு நமக்குத் தெரியும். ஏன்னா பூஜ்ஜியத்தோட முழு மதிப்பு தான் இங்கே இருக்கிற ஒரே மதிப்பு. மூன்று எக்ஸ் கழித்தல் ஒன்பதின் மதிப்பு பூஜ்ஜியம்ன்னு சொல்லியிருந்தா மூன்று எக்ஸ் கழித்தல் 9 பூஜ்ஜியத்துக்குச் சமம் ஆகும்ன்றதை தெரிஞ்சிருப்போம். பூஜ்ஜியம் அதற்குரிய தனித்துவமான எண். அந்த எண்ணுக்கு மட்டுமே பூஜ்ஜியத்தின் முழுமதிப்பை அடையிற தனித்துவம் இருக்கு. இங்கே நமக்கு எண் 1 சொல்லப்பட்டிருந்தா அது 1 ஆக ஆகும்ன்னோ அல்லது எதிர் 1 ஆக ஆகும்ன்னோ நம்மலால சொல்ல முடியும். இங்கே நமக்குப் பூஜ்ஜியம் கொடுக்கப்பட்டிருப்பதால, இது பூஜ்ஜியமா மட்டுமே இருக்க முடியும். அதனால இந்த சமன்பாட்டை நாம நேரடியாவே தீர்க்கலாம். நாம் 3 எக்ஸை தனிமைப்படுத்தினா எதிர்ம 9 இன் இடது பக்க சேர்க்கை கிடைக்கும். அப்போ சமன்பாட்டின் இரண்டு பக்கமும் 9 ஐச் சேர்க்கணும். இந்த 9 கள் அடிபட்டுப் போகும். இதோட மொத்த அம்சமும் இதுதான். இடது பக்கம் நமக்கு வெறும் 3 x மட்டுமே இருக்கு. வலது பக்கம் நமக்கு ஒன்பது இருக்கு. இப்போ நாம x க்குத் தீர்வு பார்க்கணும். நம்மட்ட மூன்று பெருக்கல் எக்ஸ் இருக்கு. இத மூன்றால வகுப்போம். ஏன்னா மூன்று பெருக்கல் எக்ஸை மூன்றால வகுத்தா கிடைக்கிறது எக்ஸ் தான். நாம இடது பக்கத்தை மூன்றால வகுக்குறதா இருந்தால் வலது பக்கமும் மூன்றால வகுக்கணும். இந்த இரண்டு மூன்றுகளையும் அடித்து விடலாம். அப்போ எக்ஸானது 9 இன் கீழ் மூன்று அப்பிடின்னா கிடைக்கிறது மூன்று. ஆக இதுதான் நம்முடைய தீர்வு. இதை முயற்சித்துப் பார்த்து இந்தத் தீர்வு சரியா இருக்குமான்னு உறுதிப்படுத்திக்குவோம். மீண்டும் நமக்குக் கொடுக்கப்பட்ட சமன்பாட்டுக்கு கூடுதலா அதை வைச்சுக்குவோம். ஆக நம்மட்ட இருக்கிறது மூன்று பெருக்கல் எக்ஸோட முழுமை மதிப்பு இதுல எக்ஸுக்குப் பதிலா நமக்குக் கிடைச்ச விடைய இங்க எழுதிக்கலாம். மூன்று பெருக்கல் மூன்று கழித்தல் ஒன்பது என்றால் நமக்குக் கிடைப்பது பூஜ்ஜியத்துக்குச் சமமாத் தான் இருக்கும். இதுக்குச் சமமாக என்ன கிடைக்கும்..? மூன்று பெருக்கல் மூன்று ஒன்பது. இது தான் ஒன்பது கழித்தல் ஒன்பதின் முழுமதிப்பு. பூஜ்ஜியத்தின் முழு மதிப்பு உண்மையில் பூஜ்ஜியம் தான். அது பூஜ்ஜியத்திற்கு நிகரான மதிப்பையே நமக்கு அளிக்கிறது. கணக்கு நிறைவுற்றது.
Complete the square on the general quadratic equation.
We have ax squared plus bx plus c is equal to 0.
So whenever I complete the square, actually whenever I deal with any of these types of quadratic equations, I always like to not have an a, or a non 1 coefficient, on the x squared terms.
So let's make it into a 1 coefficient.
And the easiest way to do that is just divide everything by a.
So we divide every term on the left side by a, and of course we have to divide the right side by a as well.
And so the left side will become x squared plus b over ax.
And then I'll write c over a over here.
So we have some room to add and subtract things so we can really complete the square.
So plus c over a is equal to 0 divided by a, which is just going to be equal to 0.
Now when we complete the square, we've seen this multiple times before, what we want to do is take the coefficient on the x term right here, it's b over a, take half of it.
This right here is two times b over 2a.
Right?
The 2's cancel out.
This is just 2 times b over 2a.
So you take half of it, half of b over a is b over 2a.
You take half of it, and then you square it, and you add it right here.
So plus b squared-- Let me write it this way. b over 2a squared.
And of course I can't just add something to one side of the equation, that would change the equation.
I also either have to add it to the other side, or just subtract it from the same side that I'm adding it to.
So I'll also subtract the b over 2a squared just like that.
Now, the whole point of doing this is so these first three terms right here are a perfect square trinomial.
That's what completing the square is all about.
And we've seen the pattern multiple times.
If I have, let's say, m plus n squared-- and I'm using m and n so we don't get confused with the a's and b's and x's over here.
But if I have m plus n squared, we've seen multiple times, that's going to be equal to m squared plus 2mn plus n squared.
And here we have that pattern now.
That's the whole point behind completing the square.
That's the whole point behind taking half of b over a-- that's b over 2a-- and then squaring it and adding it right here.
We now fit that pattern. m is x. n is b over 2a.
And 2mn, if I take an x times a b over 2a, and multiply that by 2, I get b over ax.
So this expression, right here, this trinomial, the first three terms, it is a perfect square trinomial, and we can write it as x plus b over 2a squared.
And then of course we have all this other business right here.
And then of course we have all of this other stuff right here.
Which is negative b over, and let me just actually square it for you.
So b over 2a squared is negative b squared over 4a squared.
And then I have this plus c over a.
But let's write it with the same denominator here.
So I could have c over a, or I could multiply the numerator and the denominator by 4a.
So if I multiply the numerator by 4a, I get 4ac.
If I multiply the denominator by 4a, I get 4a squared.
And the whole reason why I multiplied the numerator and the denominator by 4a was so that we have the same denominator right here.
And, of course, that is going to be equal to 0.
And we could simplify it a little bit more, or actually, well yeah we'll just simplify it next in the next step.
We don't want to skip too many steps here.
So you have x plus b over 2a squared.
And then we could say, plus-- we could put the 4ac first, so we could say-- actually let's just say, plus negative b squared, plus 4ac, all of that over 4a squared is equal to 0.
I didn't put the 4ac first, I just put the negative b squared there.
Now let's isolate this squared binomial on the left hand side.
And the easiest way we can do that is to subtract this thing from both sides of the equation.
So let's do that.
So you can imagine if we add b-- let me do this in a different color.
If we were to add positive b squared minus 4ac over 4a squared on the left hand side, those will cancel out and we're also going to add it on the right hand side.
Positive b squared minus 4ac over 4a squared.
Anything I do the left I have to do the right.
What do we end up with?
We end up with, on the left hand side, these two guys cancel out.
We have the same denomenator, when you add the numerators, that cancels with that.
The 4ac cancels with the negative 4ac, these just completely cancel out.
And on the left hand side, you just have x plus b over 2a squared.
And on the right hand side, you have that being equal to b squared minus-- let me do that in a blue color. b squared minus 4ac, all of that over 4a squared.
Now the next thing we probably want to do, if we want to really solve for x, is to take the square root of both sides of this equation.
So let's do that.
Let's take the square root of both sides of this equation.
And if, when we do that-- We don't want to only take the positive square root because x plus b be over 2a could be a negative number, or it could be a positive number.
So we want to take the positive and negative square root.
So we could say that the square root, we could put the positive or negative here or, since we're taking the square root of both sides, we could put the positive or negative there.
If you put the positive or negative on both sides, it's really just telling you the same thing. It really is all the different combinations.
If the negative square root over here equals the negative square root over here, then it's just another combination of the different positives and negatives.
So you could just write it as, this square root is equal to the plus or minus square root of b squared minus 4ac over 4a squared.
Now what does this simplify to?
Well, the left hand side just becomes x plus b over 2a is equal to-- and now it gets interesting.
And you might even start recognizing parts of it.
So let's take the plus or minus square root of the top.
What is that going to be?
And you could just take the plus or minus only of the top because, once again, the same principles apply.
There's no reason why you have to do a plus or minus over a plus and minus and a plus or minus on the left hand side.
There's only one combination here, where there's only one plus or minus on the numerator.
I apologize if that confuses you.
So let's write this as the plus or minus square root of b squared minus 4ac over-- What's the square root of 4a a squared?
Well, it's just going to be 2a.
Right?
The square root of 4 is 2.
The square root of a squared is a.
And we're almost there.
To solve for x, we just have to subtract b over 2a from both sides.
We just have to subtract b over 2a from both sides of this equation.
The left hand side, we just end up with our x.
And then the right hand side, we have a negative b over 2a plus or minus the square root of b squared minus 4ac-- all of that over 2a.
Since we have the same denominator, we can write this as negative b plus or minus the square root of b squared minus 4ac-- all of that over 2a.
And we're done.
We've solved for the x's and you see there's actually two solutions here.
There's one where you take the positive square root, and there's another solution where you take the negative square root.
If this square root exists, and if the positive and negative-- and if it's not 0, you're going to have two solutions.
And this, right here, this result we have is-- Look, you give me any quadratic equation, you give me the a, the b, and the c, we could now substitute it into this formula essentially we just derived right here, and I'll give you the roots, I'll give you the x's for that quadratic equation-- the x's that satisfy that quadratic equation.
And this formula, right here, for solving any quadratic equation is called the quadratic formula.
And you could see it just comes straight out of completing the square.
There's no mystery, magic here.
But it's easily one of the most useful formulas in mathematics.
And I'm usually not a huge proponent of memorizing things.
But it probably will benefit you in life if you did.
Hope you enjoyed that.
Batu Caves, preparations are underway for the grandest Hindu Festival of the year.
Thaipusam is about faith, penance and endurance.
More than a million Hindu devotees are expected to congregate here, over the next few days. 5 days before Thaipusam, we follow a group of 50 devotees from the Sri Muniswarar Temple in Puchong as they make their climb up the 272 steps, to reach the top of the hill where the temple is located.
High priest Vasantha, aged 50 is leading a group of devotees to fulfil their vows, and to seek forgiveness for their sins from Lord Murugan.
She has been doing this for the past 20 years, only this year, it is a bit different.
To avoid the heavy traffic, due to a long stretch of public holidays, she is starting early.
And for many devotees , it is never too early to perform this pilgrimage
Every year in April we can see something unusual in the streets of the Netherlands: twelve-year-old kids on their bikes in numbered high visibility jackets.
They are taking a test.
About two hundred thousand children each year take a "verkeersexamen" or traffic exam.
In the next school year these children will start secondary school.
And to reach that school most will ride their bicycles.
Which is clear from this school's bicycle parking lot.
Up to 15 kilometers one way is no exception.
So they were taught the rules of conduct in traffic.
The tests are long tradition in the Netherlands.
These children were taking the test in 1935.
Children are being taught about traffic from an early age.
For very young children traffic is included in their plays.
In primary school real traffic education starts.
One year before the final test many students get to practice in a scaled version of traffic reality in so-called traffic gardens.
This one in Utrecht has been in use since 1963.
The final test has two parts: written exercises and a practical test, which is a ride through traffic.
The test route has to include ordinary traffic situations that the children will encounter on their ride to school.
It takes the children to residential streets, separate bicycle paths, as counter flow in a one way street, to traffic lights controlled junctions, and roundabouts.
Oh, and passed this unplanned building site.
The conduct of every child is monitored, and many will pass the test.
This year, the very first diploma's were handed out by her royal highness princess Máxima of the Netherlands.
Each year fifteen children are killed as a cyclist or as a pedestrian in traffic in the Netherlands.
It is hoped that besides good infrastructure and education of drivers
Children's education will also help to get that figure further down.
I think we've all heard of the word, bacteria.
Bacteria.
And we normally associate it with negative things.
You say bacteria, those are germs. So we normally associate those with germs, and they indeed are germs, and they cause a whole set of negative things.
Or at least from the standard point of view, people believe that they cause a whole bunch of negative things.
So let's just list them all just to make sure we know about them, we're all on the same page.
So the bad things they do, they cause a lot of diseases: tuberculosis, Lyme disease.
I mean, I could go on and on. You know, pretty much any time-- well, I'll be careful here.
It can also be caused by a virus.
An infection is, in general, anything entering you and taking advantage of your body to kind of replicate itself, and in the process, making you sick.
But bacterial infections, let me write that down.
And this whole perception of bacteria being a bad thing is probably a good reason why almost any soap you see now will say antibacterial on it.
Because the makers of the soap know that in conventional thinking, bacteria are viewed as a negative thing.
And you're like, OK, Sal, I know where you're going with this.
Bacteria isn't all bad.
There are some good traits of bacteria.
For example, I could stick some yogurt in some-- or I could stick some bacteria in some milk and it'll help produce some yogurt, sometimes spelled yoghurt.
And that's obviously a good thing. It's a delicious thing to eat.
You say, well, I know I have bacteria in my gut. It helps me digest food.
And these are all true, but you're like, look, you know, on balance, I still think bacteria is a bad thing.
I'm not going to take sides on that debate, as I tend to avoid taking sides on debates in these science videos.
Maybe I'll do a whole playlist where I do nothing but take sides on debates, but here I won't take any sides on that. But I'll just point out that you are to a large degree made up of bacteria.
It's not just your gut. It's not just the gut or the yogurt you might eat or the plaque on your teeth, which is caused by bacteria.
It's this kind of film that's created by bacteria that eventually causes cavities and whatever else.
And it's not just the pimples on your face.
Bacteria actually represents a majority of the cells on your body.
So for every-- and this is kind of an astounding fact.
For every one cell on the human body, every one human cell-- so these are all cells that all have your DNA in them and they'll have nucleuses, and I'll talk about that in a second-- you have 20 bacteria.
Now, your response there is to say, OK, that's fair enough, but these bacteria must be much smaller than the human cell, so it must be a very small fraction of my mass.
And you're right.
It's not like we're mostly bacteria by mass, although we are mostly bacteria by actual cells.
But even if you were to take out all of the water in your body, then by mass, bacteria is going to be roughly 10% of your mass.
So I weigh about 150 pounds, I've got 15 pounds of bacteria walking around with me.
So we always kind of think of ourselves as like the bacteria is riding on us, but to a large degree, we're kind of in symbiosis.
We're kind of two creatures, or not just two creatures, two types of creatures living together, because I don't have just one type of bacteria on me. I have thousands of types of bacteria on me.
There's a huge amount of diversity, and we're just scratching the surface in terms of the number and types and diversity of bacteria that exist.
So I've talked a lot about bacteria, and hopefully, this fact right here will make you realize that they're super important to just our everyday existence.
Just to make sure we understand the magnitude of this, in a previous video, and I looked this up again, we have on the order of 10 to a 100 trillion cells, human cells.
So for every one of these we have 20 bacteria, we're talking about having on the order of 200 to 2,000 trillion bacteria on us at any time.
And I'm a hygienic person.
I take showers daily, and that's even me.
It's not like you can somehow eliminate them. And even more, it's not like you even want to eliminate them.
But that's fair enough.
You're probably asking, OK, Sal, I'm convinced that bacteria are important.
What do they actually look like?
And they're these small unicellular organisms.
That's my bacteria right there.
And they're different from the cells that make up us.
When I say us, I'll throw in all plants, animals and funguses, fungi.
And the big difference, or the one that people noticed first, is that all of the Eukarya, which includes plants, animals and fungi, all of their DNA is inside of a nucleus, a cellular nucleus.
So that's the nucleus right there.
And all of our DNA, it's normally in its chromatin form.
It's all just spread around something like that.
In bacteria, which are what people originally just classify it on whether or not you have a nucleus, in bacteria, there is no membrane surrounding the DNA.
So what they have is just a big bundle of DNA.
They just have this big bundle of DNA.
It's sometimes in a loop all in one circle called a nucleoid.
Now, whenever we look at something, and we say, oh, we have this thing; it doesn't; there's this assumption that somehow we're superior or we're more advanced beings.
But the reality is that bacteria have infiltrated far more ecosystems in every part of the planet than Eukarya have, and there's far more diversity in bacteria than there is in Eukarya.
So when you really think about it, these are the more successful organisms. If a comet were to hit the Earth--
God forbid-- the organisms more likely to survive are going to be the bacteria than the Eukarya, than the ones with the larger-- not always larger, but the organisms that do have this nucleus and have membrane-bound organelles like mitochondria and all that.
We'll talk more about it in the future.
Bacteria, for the most part, are just big bags of cytoplasm.
They have their DNA there.
They do have ribosomes because they have to code for proteins just like the rest of us do.
Some of those proteins, they'll make some from-- bacteria, they'll make these flagella, which are tails that allow them to move around.
They also have these things called pili.
Pili is plural for pilus or pee-lus, so these pili.
And we'll see in a second that the pili are kind of how the bacteria are able to do one form of introducing genetic variation into their populations.
Actually, I'll take a little side note here. I'm pointing out bacteria as not having a cell wall.
There's actually another class that used to be categorized as type of a bacteria, and they're called Archaea.
I should give them a little bit of justice. They're always kind of the stepchild.
They used to be called Archaea bacteria, but now people realize, they've actually looked at the DNA, because when they originally looked at these, they said, OK, these guys also have no nucleus and a bunch of DNA running around. These must be a form of bacteria.
But now that we've actually been able to look into the DNA of the things, we've seen that they're actually quite different.
But all of these, both bacteria and Archaea, are considered prokaryotes.
And this just means no nucleus.
No nucleus, and more generally, this is what most people refer to, but more generally, they don't have these membrane-bound organelles that our cells have.
Now, the next question you might say is, well, how do these bacteria reproduce?
And for the most part, they do something not completely different from mitosis, although I want to call it mitosis.
We call it binary fission.
I'm not going to go into the deep mechanism here, but the idea is fairly simple.
I have a bacteria right here.
It replicates its DNA, so it'll have two of these nucleoids here, and then the cytoplasm essentially splits, or it's kind of a form of cleavage right there.
It splits and then you have two of them.
You have two of them then.
And then each of them, they can code for the proteins necessary to produce all of their extra appendages, the flagellum, which is this long tail-like thing that can help it move.
And it's actually fascinating because it's operating at such a small scale, but you can still kind of get this motor movement going on.
Even at this very, very small scale, using very primitive-- I won't say primitive, because that's making a value judgment on these things, but using-- you know, these flagellum are on the order of several nanometers, on the order of tens of nanometers wide.
So you don't have a lot of atoms to deal with, but you're still able to get this kind of wave-like motion that can move the bacteria around.
Now, you're saying, hey, Sal, in that first video on evolution, you told me that we see evolution every day and bacteria is one example.
When we use antibiotics, we think it'll help eliminate bacteria, but that one bacteria that has some type of resistance, it'll survive, so it is more fit.
How did these guys get variation?
Well, the one way, and this is the way everything can get variation, is they can get mutations.
And bacteria replicate so quickly, they reproduce so quickly that even if you have a mutation that's one in every thousand times, by the time you have a million bacteria, you'll have a thousand mutations.
So they have mutations, but they also have this form.
I don't want to call it sexual reproduction, because it's not sexual reproduction. They don't form gametes and the gametes don't fertilize each other and then produces a zygote.
But two bacteria can get near each other and then one of their piluses-- I'll do that right here.
So the piluses are these little structures on the side of the bacteria.
They're these little tubes, really.
One of the piluses can connect from one bacteria to another, and then essentially you have a mixing of what's inside one bacteria with another.
So let me draw their nucleoids.
And then they have these other pieces of just DNA that hangs out called plasmids.
These are just circular pieces of DNA.
Maybe this guy has got this extra neat plasmid. He got it from someplace, and it's making him able to do things that this guy couldn't do.
Maybe this is the R plasmid, which is known for making a bacteria resistant to a lot of antibiotics.
And what happens is, that bacteria-- and actually, there's mechanisms where the bacteria know that, hey, this guy doesn't have the R plasmid.
And we're just beginning to understand how it actually works, but this will actually replicate itself and give this guy a version of the R plasmid.
You could also have these things, transposons, and I should make a whole video on this because we have transposons, too.
But there's parts of DNA that can jump from one part of a fragment of DNA to another, and these can also end up in the other one.
So what you have is kind of-- it's not formal sexual reproduction, but what you essentially have is a connection, and these bacteria are just constantly swapping DNA with each other and DNA is jumping back and forth, so you can imagine all sorts of combinations of DNA happen even within what you used to call one bacterial species and very quickly can turn to multiple species and become resistant to different things.
If this makes it resistant to an antibiotic, then it can kind of spread the information to produce those resistant proteins or whatever to the other bacteria.
So this is kind of a form of introducing variation.
And so when you transfer stuff via this pilus, or the plural is pili, this is called conjugation, bacterial conjugation.
Now, the last thing I want to talk about, because it's something that you've heard a lot about, are antibiotics.
A lot of people, they get sick.
The first thing they want to get is an antibiotic.
And an antibiotic is just a whole class of chemicals and compounds, some of them naturally derived, some of them not, that kill bacteria.
So now if someone is undergoing a surgery and they get a cut, instead of them having to worry about getting an infection, they'll take some antibiotics to prevent the bacteria from growing on them.
But the question is how was this discovered or where does it come from?
It actually came from Alexander Fleming.
Let me write him down.
Very important, because the discovery of antibiotics is, in my opinion, the most important discovery in medicine so far.
So, Alexander Fleming.
He was studying-- I think it was Staphylococcus.
I forget which bacteria it was, but it was in a Petri dish.
He was using a Petri dish.
Let me draw a Petri dish.
There's a little circle.
There's some nutrients that the bacteria can grow on.
So let's say the bacteria, you know, it's growing on this Petri dish.
And he went out, and he came back into the room, and he saw that some mold, some fungus had grown on this, kind of a bluish-greenish fungus had grown on the center of his Petri dish.
And the bacteria, there was kind of this space around it, and the bacteria couldn't get close to it.
And this mold, this fungus was called Penicillium, the Penicillium fungus.
He was able to figure that out. He took a sample of this and then he cultured it, which means letting it grow and then seeing what it is. This was Penicillium.
And he figured out that, gee, this fungus must have something, some chemical that it's emitting that's essentially killing the bacteria around it, that's not allowing the bacteria to get near it.
And so that led to the discovery of penicillin.
This was in the late 20s, 1920s.
By the time World War II came around, now people had gunshot wounds and they had to get things amputated, whatnot, but for the first time, they could actually give people antibiotics and not worry about-- or they probably still worried about it, but didn't have to worry about this thing as much as they did before.
And now, you know, if you have bacteria, if you have tuberculosis or Lyme disease or anything, the treatment all involves taking antibiotics.
And there are many, many more types of antibiotics now coming from many, many more different sources, but the general idea is the same.
You want to kill bacteria.
Although you don't want to kill all bacteria, because some of it's good.
In fact, we are made up a whole lot of bacteria.
I don't know if I even mentioned this earlier in the video.
There's bacteria in our skin that helps take up oil and moisturizes and make our skin nice and supple.
So, you know, the way you think about it, you could view them as negative or you could view them as positive or you could view them as something in between, but the really amazing thing, at least in my mind, is that we're living in symbiosis with them.
I remember I saw a Star Trek episode once where you had these people. You had these people, and they were some alien race.
Jean-Luc Picard had-- they ran into them.
They looked very humanoid like that.
But it turns out-- let me draw this human-- that they had these little bugs in their brain stem.
So they had these big insects in their brain stem and these insects started infecting the crew of the Enterprise, and they were controlling their brains and making them act weird and whatever not, and this seemed like a very bizarre alien concept of some creepy-crawlie living in us and affecting our brains and affecting us in some ways.
But if you really think about it, we are doing this, and it's not just with one little bug, it's on the order of trillions.
Hundreds of trillions of bugs are with us every day and they make us us.
I mean, I'm here recording videos along with-- or maybe I should even say the bacteria is recording videos or it's maybe partially responsible for controlling bacteria.
And it's known that the bacteria can even affect our mental state.
There's a whole bunch of research now that certain types of bacteria can cause schizophrenia. Actually, syphilis does.
Bacteria can cause depression.
Lyme disease, it's known that when you go into later phases of Lyme disease, it can affect the mental condition of the person who has the infection, so it affects every part of who we are.
I mean, it would be hard to even talk of being a human being without the 10% of our mass or the 2,000 trillion cells or 2,000 trillion bacteria that really make us us.
Determine the number of solutions to the quadratic equation, x squared plus 14x plus 49 is equal to 0. There's a bunch of ways we could do it. We could factor it and just figure out the values of x that satisfy it and just count them.
So the quadratic formula tells us that if we have an equation of the form ax squared plus bx plus c is equal to 0, that the solutions are going to be-- or the solution if it exists is going to be-- negative b plus or minus the square root of b squared minus 4ac. All of that over 2a. Now the reason why this can be 2 solutions is that we have a plus or minus here.
Put a 0. 1 times 14 is 14. It is 6, 9, 1.
So 49 times 4. 4 times 9 is 36. 4 times 4 is 16 plus 3 is 190-- or is 19, so you get 196.
Negative b is negative 14 over 2 times a. a is just 1 over 2. So it's equal to negative 7. That's the only solution to this equation.
you ever feel like it's backpedaling even though your following the rules? you work long hours tolerated your boss You get and annual raise and you try to save money and budget where ever you can and clearly you're working with no system for financial success but something is very wrong the rules are not working the system is broken down you're barely making ends meet let alone getting ahead and retirement forget it your living day by day
You want to build financial security and wealth but it's just not happening
So where exactly has playing by the rules Gotten You?
So if you can change your outlook
Change some of your values and change your rules
You find that there is a whole set of rules out there
That are more Conducive for those who want to be rich
Conducive for those who want to be rich one of the image financial experts, Educator successful investor and best-selling author Robert Kiyosaki is about to give you the information You need to implement realistic achievable plan of building and growing Wealth
Kiyoski is the new york times selling author of among other
Books Rich Dad Poor Day to date this series has sold twenty million plus copies had worldwide
Today Kiyosaki shares his revolutionary wisdom with You just like his rich dad shared it with him it information that can take you from working for Money to your money working for you information that can set you free
The story of Rich Dad Poor Dad is really a story of two different fathers with two different sets of values and completely different sets of advice 0:01:49.490,0:01:53.000 so i don't mean to insult anybody or damage your values really that was the difference for example Poor Dad
Always said go to school get good grades get a high paying job work hard live below your means save money get out of get out of debt have a good retire plan
That was my Poor Dads Values my rich dad said you probably won't get rich doing that because very few people get rich following that plan
But you thought Saving Money Made You Money?
You take a look at this forty year run on the Dollar
The Dollar is designed economically to lose money every single year so why would you save something that loses money every year and what this means was somebody on retirement plans is that after you retire The value of your dollar goes down and the cost of living keeps going up to my Rich Dad that was bad advice and made no sense again he has different values this goes against everything you've heard it's very important that Diagram my Rich Dad showed me as a little boy was a diagram known as a cashflow quadrant and the quadrant is made up of the four different people who make up the world of business so my rich dad said in the world of business there's are E's and E's stand for employees and employees that you can always tell who will be our by their core values and what the 0:03:19.139,0:03:22.870 employee whether the president or the janitor of the company will always say the same words the words are i'm looking for safe secure job with benefits that's what makes a them an employees 'cause our core values are security the other other one of Four is the S or the small business owner of the self-employed and again their core values will cause them to use the same words which are if you want it done right do it by yourself the S also means are usually Solo
Generally one person act that tend operate by themselves on the right side of the quadrant are the B's and rich dad said to be stood for was big business or like Bill Gates Forbe's defines big business as five hundred employees are more and their words are different the will say
I'm looking for a good system good network and the smartest people I know to help run my business and their unlike the S they don't want to run the company by themselves they want smart people to run the companies for them and then the fourth of quadrant is the I 0:04:19.750,0:04:25.169 and I stands for investor these are people who have money work hard for them these people are people that people work hard for them and these were people that work hard for the rich here so early on in my life it was my my poor dad who all is said to me you know Robert go to school and get a high paying job and so my Poor Dad Poor values was to be an employee he wanted job security promotions a steady paycheck and all this and so it was my Rich Dad who said to me so Robert if you really want to be Rich
learn to build businesses it made more sense to him to work hard to build a business something you owned and something that passed on from generation to generation to your kids whereas my poor dad said work hard but by Rich Dad Said why would you work hard for something you'll never own and you can get fired from right away again that was a difference in values so Rich Dad suggested I learned how to be a business owner and learn how to be an investor and that's one of the big differences on this side of the quadrant these people here were for security they work for money also on the side of the here they're key value that they want is they want Freedom they don't want to have to work at a job anymore that i want to have to work for the rest of their lives so the beauty of building a Business and learning how to invest is very simply that this is passive income you work hard for a few years but possibly for the rest your life in income keeps flowing to you
Of All the businesses out there which type do you choose? one of the reasons i consider Direct Selling Business a perfect businesses are simply because the company will work with you to get the business skills that make you rich always remember that is not money that makes you rich it's business skills and that's why it's a perfect business they'll work take as long as you like 0:06:20.360,0:06:22.479 to get the skills to make the money and that's a lifetime skill thing the part about it is too low start-up costs and where else can you get in for under five hundred dollars and get these skills for people who want to make the shift over to the B Quadratnt which is what i recommend for people one of the beauties of the network marketing company is that you can do that for a very low price and that's why i talk to people about considering network marketing if you're to build a microsoft it would take you few hundreds of millions of dollars but a network marketing company allows you to start at a very rate will be patient within you they'll take their time to transition over here and the reason why that time is so important to most people is it takes time to change those values and the most important thing is once you take the time let's say it takes one year or two years five years whatever time the text once you see the value for the core values of this side and this side your unstoppable today i would never go back and get a job why should i i'd rather just stay on this side build companies pay less taxes make for money but the key as a person needs to change to values from my Poor Dad to the values of my Rich Dad and that's when the values of network marketing companies they allow you the time and and very low cost they'll work with you to make a transitional over there the number one asset a person can build is build a business that is the smartest thing you can do you've been told to corporate ladder is the surest route To your Success
Years ago I decided not to follow the Corporate Ladder simple because again it was values you know my poor dad always said go to school and get it high paying job with the government a big corporation but my rich dad said why would you worked so hard at something you'll never own you can't sell your job you can't pass it on to your kids so to me and never made any sense it made more sense to build my own business and hire other people the other reason is that you really don't have much control if you're in the corporate ladder world for example you can get fired at any time or today we were we have whats Called M&A
Stands for mergers and acquisitions it's when one of the company buys anther company so you could be a great employees but the company that buys your accomplishes just fires You wait a minute this sounds too good to be true
Like one of those Get Rich Quick Schemes
It's not get-rich-quick formula you don't just do it overnight it takes time
I still remember the first time I made that transition was back in nineteen seventy eight when i fully quit my job and i had to depend upon my company that i was building to support me so I understand the fear the beauty the most important thing to remember is this 0:09:09.900,0:09:12.470 there's two kinds of people in the world there are the types that will say you'll never make it and I had a lot of friends and family saying that
You're stupid don't do it and the second type where the people that said go for it you can do it don't worry about it will cover you so the most important thing is support of friends and family
One of the beauties direct selling company is that they provide that personal support to you for as long as it takes you to make the journey from the left side to my Rich Dad's
Side
You alway thought being self-employed was living the American dream one the challenges of being self-employed is that your your own boss here Your the solo act
Like in the S Quadrant your the individual you do it on your own whereas in the B Quadrant you're a team player you have to depend upon your team and count on your team
So the problem with being an S let's say you where in a traffic accident there goes our income and let's say you get older and you haven't set enough money aside to retire on that means you probably have to work for the rest of your life because you don't have anybody else to fall back on not a team to count on so one of the problems with the S although most people say is most satisfying of all work
It is a Solo Act and your totally on your own personally i'd rather be a member of the team
So they can count on me and I can count on them
It Sounds like a smart move but change
It's So
Difficult
We all know the world has changed but sometimes the hardest thing to change
Is Ourselves and being an old guys the older I get sometimes get more set in my ways and i think that's one of the things that a direct selling business offers people why is the perfect business they allow you to take your time to make the mental emotional and physical changes required to move from the left side to the Rich Dad side
I think that's a big thing it's a very gracious It's a very elegant way it's a patient way of supporting you in making the changes of your life so please remember change always creates upset but sometimes we all know we have to make those changes and if you know it's time for you to make that change than the perfect business may be a direct selling business for you direct selling it is quite possibly the perfect business for you for more information contact the person who gave you this video http://robertgallenariix.com
The game of poker--is this partially observable, stochastic, continuous, or adversarial?
Please check any or all of those that apply.
what number can you add to x squared minus 6x to complete the perfect square trinomial so trinomial is just a polynonial with 3 terms so right now we have 2 terms so they are essentialy saying can we add a term here essentially a number constant so this comes a perfect square the expression once becomes a trinomial becomes a perfect square so let me just write it here x squared minus 6x so we are going to add something right here so that the expression can be a perfect square a perfect square of a binomial and to think about that lets think about what a perfect square would look like so let's immagine if we had x plus a squared what would that look like if we were to expand it out let me do this in another color to show you it is a side note so I'll do it in blue so if I had x plus some constant a squared well this is the same thing as x plus a times x plus a and this is the same thing as you might remember this pattern well just multiply it out well just multiply x by everything here so x timesx is x squared then x times a is a x then a times x is a x then we have a times a which is a squared that all just comes out of doing the distubutiver property twice or you could think of it as foil if you find that a little bit easier and this gives you x squared plus 2ax plus a squared so if you have a trinomial in this form it is a perfect square and it can be factored out into x plus a squared and we see the pattern here in both cases its a coefficient on the x squared term is 1 and then we see whatever the coefficient here is on the first degree term on the x what ever half that number is and we square it and make that the constant then this will be a perfect square for example 1/2 of 2a is a and we are squaring a right over here and that makes it a perfect square so let's do the same thing with our binomial soon to be a trinomial lets look at the first degree coefficient it is a -6 you can view this right over here as our 2a and so what is half of this or in others words 2a is equal to -6 if we just pattern match right over here so what would a be? a would equal to -3 and so if we added a squared to this expression it would be a perfect square so we literally just took half of this which is -3 and then we are going to square it so -3 squared is positive 9 so this over here is just a squared notice
I called this 2a and took half of it to figure out what a is and I squared it to get this nine here so
I just took -6 divided by 2 is -3 squared it and got 9 and if you wanted to factor this out we have x squared minus 6x plus 9 so what 2 numbers when you take their product you get 9 and when you add them together you get -6 well -3 and -3 so this is going to be x-3 times x-3 or you could think of it as x-3 squared so it is a perfect square trinomial
Some 17 years ago, I became allergic to Delhi's air.
My doctors told me that my lung capacity had gone down to 70 percent, and it was killing me.
With the help of IlT,
TERl, and learnings from NASA, we discovered that there are three basic green plants, common green plants, with which we can grow all the fresh air we need indoors to keep us healthy.
We've also found that you can reduce the fresh air requirements into the building, while maintaining industry indoor air-quality standards.
The three plants are Areca palm, Mother-in-Law's Tongue and money plant.
The botanical names are in front of you.
Areca palm is a plant which removes CO2 and converts it into oxygen.
We need four shoulder-high plants per person, and in terms of plant care, we need to wipe the leaves every day in Delhi, and perhaps once a week in cleaner-air cities.
We had to grow them in vermi manure, which is sterile, or hydroponics, and take them outdoors every three to four months.
The second plant is Mother-in-law's Tongue, which is again a very common plant, and we call it a bedroom plant, because it converts CO2 into oxygen at night.
And we need six to eight waist-high plants per person.
The third plant is money plant, and this is again a very common plant; preferably grows in hydroponics.
And this particular plant removes formaldehydes and other volatile chemicals.
With these three plants, you can grow all the fresh air you need.
In fact, you could be in a bottle with a cap on top, and you would not die at all, and you would not need any fresh air.
We have tried these plants at our own building in Delhi, which is a 50,000-square-feet, 20-year-old building.
And it has close to 1,200 such plants for 300 occupants.
Our studies have found that there is a 42 percent probability of one's blood oxygen going up by one percent if one stays indoors in this building for 10 hours.
The government of India has discovered or published a study to show that this is the healthiest building in New Delhi.
And the study showed that, compared to other buildings, there is a reduced incidence of eye irritation by 52 percent, respiratory systems by 34 percent, headaches by 24 percent, lung impairment by 12 percent and asthma by nine percent.
And this study has been published on September 8, 2008, and it's available on the government of India website.
Our experience points to an amazing increase in human productivity by over 20 percent by using these plants.
And also a reduction in energy requirements in buildings by an outstanding 15 percent, because you need less fresh air.
We are now replicating this in a 1.75-million-square-feet building, which will have 60,000 indoor plants.
Why is this important?
It is also important for the environment, because the world's energy requirements are expected to grow by 30 percent in the next decade.
40 percent of the world's energy is taken up by buildings currently, and 60 percent of the world's population will be living in buildings in cities with a population of over one million in the next 15 years.
And there is a growing preference for living and working in air-conditioned places.
"Be the change you want to see in the world," said Mahatma Gandhi.
And thank you for listening.
(Applause)
Paulo wants to earn $1500 by mowing lawns.
He will charge $35 for each lawn he mows.
What is the minimum number of lawns the Paulo needs to mow to reach his goal of $1500?
So we need to figure out the minimum number of lawns that Paulo needs to mow.
Now, whatever that number is, that number times $35, because that's how much he's going to get per lawn.
So the number that he has to mow times $35 needs to be greater than 1,500.
So to figure out that number, let's just divide 1,500 divided by 35.
Maybe it goes evenly, and that'll be the number of lawn he needs to mow.
So we're going to take 1,500 and divide it by 35 because that's how much he gets paid per lawn.
Now 35 does not go into 1, so we have to add another digit.
35 does not go into 15.
35 goes into 150.
Well, 30 goes into 150 five times.
35 is bigger so it won't go into it five times.
Let's try out 4.
Let's see if it goes into it four times.
4 times 5 is 20.
Let's regroup the 2, or carry the 2.
Four times 3 is 12.
12 plus 2 is 14.
Now we subtract.
0 minus 0 is 0.
5 minus 4 is 1.
The ones cancel out, and then we bring down this zero right here.
35 goes into 100.
Well, 35 times 2 is 70, and if you add another-- 35 times 3 is 105, so that's too big, so it goes into it two times.
2 times 5 is 10.
Let's carry the 1.
2 times 3 is 6 plus 1 is 7, or 35 times 2 is 70.
You subtract.
0 minus 0 is 0.
0 minus 7, you can't do it.
You could already view it as 10 minus 7, or if you want to go in the traditional way, this 0 can take or borrow 1 from this 1, so that becomes a 0.
This becomes a 10.
10 minus 7 is 30.
And so there's nothing left to bring down. so we now know that 35 goes into 1,500 forty-two times, but there's a remainder of 30.
If he mowed 42 lawns, he'd be 30 short of 1,500.
35 times 42 is 30 less than 1,500.
What would it be?
1,470.
So in order to make 1,500, he's going to have to go over it, so he's going to have to do one more lawn than this.
So just to remind ourselves, if we just divide-- let me write it here.
1,500 divided by 35 is equal to 42, remainder 30, so 42 won't be enough lawns.
We're going to have more to-- we have 30 more bucks to earn, so he's going to have to mow one more lawn to get another $35, so he's going to have $5 left over after he makes up this 30.
So he's going to have to mow 43 lawns if he really wants to cross this threshold of $1500.
If he does mow the 43 lawns, he'll have more than $1500.
He'll actually have $5 more than $1500.
Rewrite the expression below applying the commutative and associative properties of addition, and then show that both expressions yield the same result.
So, one, we could just evaluate the expression the way that it is written, then we could mess around with it using the commutative and associative properties of addition.
So lets first add 17.5 plus 3 so that's going to give us 20.5, so this is going to be 20.5.
And to then to that we're going to add negative 7.5.
Now adding -7.5 is the exact same thing as subtracting 7.5. so this is going to be equal to - the .5s cancel out - and then 20 minus 7 is 13.
So that's our first way of getting the answer and we kind of adhere to the parentheses.
Now let's use the commuatative property.
The commutative property tells us that the order doesn't matter; we can commute these numbers around, they can move (commute).
It's like you're going to work. They can move around. So lets just move the numbers around.
Let's make it, let's make it, actually we could do all sorts of crazy things.
We could make it, one we could just change the order here.
We could make this -7.5 plus 17.5 plus 3.
We could keep the parentheses, just like that, so we would have essentially just changed the order of this expression, but let's use the commutative and the associaive property.
So now we've commuted everything around, and now we can reassociate everything.
So instead of putting the parentheses like that, we could put the parentheses like that.
So that's what the associate property tells us.
Let me write this down.
So associative property of addition tells us that (a+b)+c where you do a+b first is the same as a+(b+c) where you do b+c first.
The commutative property tells us that a + b = b + a that you can move these guys around.
So let's evaluate this one.
We actually got here using both the commutative and the associative property, so we get -7.5 + 17.5.
This is the exact same thing as 17.5 -7.5.
It might be easier for you to realize,
"Okay, I'm adding two numbers of different signs, so what I could do is take the difference between the two, and since the larger number is positive,
Or you could just do this as 17.5 - 7.5."
So 17.5 - 7.5, the .5s cancel out. 17 - 7 is 10.
So this part right here becomes 10.
And we still have the plus three there and that once again that is going to be equal to 13.
And we could keep commuting this around and keep reassociating it and no matter how we do it, we are going to get 13.
I wrote a letter last week talking about the work of the foundation, sharing some of the problems.
And Warren Buffet had recommended I do that -- being honest about what was going well, what wasn't, and making it kind of an annual thing.
A goal I had there was to draw more people in to work on those problems, because I think there are some very important problems that don't get worked on naturally.
That is, the market does not drive the scientists, the communicators, the thinkers, the governments to do the right things.
And only by paying attention to these things and having brilliant people who care and draw other people in can we make as much progress as we need to.
So this morning I'm going to share two of these problems and talk about where they stand.
But before I dive into those I want to admit that I am an optimist.
Any tough problem, I think it can be solved.
And part of the reason I feel that way is looking at the past.
Over the past century, average lifespan has more than doubled.
Another statistic, perhaps my favorite, is to look at childhood deaths.
As recently as 1960, 110 million children were born, and 20 million of those died before the age of five.
Five years ago, 135 million children were born -- so, more -- and less than 10 million of them died before the age of five.
So that's a factor of two reduction of the childhood death rate.
It's a phenomenal thing.
Each one of those lives matters a lot.
And the key reason we were able to it was not only rising incomes but also a few key breakthroughs: vaccines that were used more widely.
For example, measles was four million of the deaths back as recently as 1990 and now is under 400,000.
So we really can make changes.
The next breakthrough is to cut that 10 million in half again.
And I think that's doable in well under 20 years.
Why? Well there's only a few diseases that account for the vast majority of those deaths: diarrhea, pneumonia and malaria.
So that brings us to the first problem that I'll raise this morning, which is how do we stop a deadly disease that's spread by mosquitos?
Well, what's the history of this disease?
It's been a severe disease for thousands of years.
In fact, if we look at the genetic code, it's the only disease we can see that people who lived in Africa actually evolved several things to avoid malarial deaths.
Deaths actually peaked at a bit over five million in the 1930s.
So it was absolutely gigantic.
And the disease was all over the world.
A terrible disease.
It was in the United States.
It was in Europe.
People didn't know what caused it until the early 1900s, when a British military man figured out that it was mosquitos.
So it was everywhere.
And two tools helped bring the death rate down.
One was killing the mosquitos with DDT.
The other was treating the patients with quinine, or quinine derivatives.
And so that's why the death rate did come down.
Now, ironically, what happened was it was eliminated from all the temperate zones, which is where the rich countries are.
So we can see: 1900, it's everywhere.
1945, it's still most places.
1970, the U.S. and most of Europe have gotten rid of it.
1990, you've gotten most of the northern areas.
And more recently you can see it's just around the equator.
And so this leads to the paradox that because the disease is only in the poorer countries, it doesn't get much investment.
For example, there's more money put into baldness drugs than are put into malaria.
Now, baldness, it's a terrible thing.
(Laughter)
And rich men are afflicted.
And so that's why that priority has been set.
But, malaria -- even the million deaths a year caused by malaria greatly understate its impact.
Over 200 million people at any one time are suffering from it.
It means that you can't get the economies in these areas going because it just holds things back so much.
Now, malaria is of course transmitted by mosquitos.
I brought some here, just so you could experience this.
We'll let those roam around the auditorium a little bit. (Laughter)
There's no reason only poor people should have the experience.
(Laughter) (Applause)
Those mosquitos are not infected.
So we've come up with a few new things.
We've got bed nets.
And bed nets are a great tool.
What it means is the mother and child stay under the bed net at night, so the mosquitos that bite late at night can't get at them.
And when you use indoor spraying with DDT and those nets you can cut deaths by over 50 percent.
And that's happened now in a number of countries.
It's great to see.
But we have to be careful because malaria -- the parasite evolves and the mosquito evolves.
So every tool that we've ever had in the past has eventually become ineffective.
And so you end up with two choices.
If you go into a country with the right tools and the right way, you do it vigorously, you can actually get a local eradication.
And that's where we saw the malaria map shrinking.
Or, if you go in kind of half-heartedly, for a period of time you'll reduce the disease burden, but eventually those tools will become ineffective, and the death rate will soar back up again.
And the world has gone through this where it paid attention and then didn't pay attention.
Now we're on the upswing.
Bed net funding is up.
There's new drug discovery going on.
Our foundation has backed a vaccine that's going into phase three trial that starts in a couple months.
And that should save over two thirds of the lives if it's effective.
So we're going to have these new tools.
But that alone doesn't give us the road map.
Because the road map to get rid of this disease involves many things.
It involves communicators to keep the funding high, to keep the visibility high, to tell the success stories.
It involves social scientists, so we know how to get not just 70 percent of the people to use the bed nets, but 90 percent.
We need mathematicians to come in and simulate this, to do Monte Carlo things to understand how these tools combine and work together.
Of course we need drug companies to give us their expertise.
We need rich-world governments to be very generous in providing aid for these things.
And so as these elements come together, I'm quite optimistic that we will be able to eradicate malaria.
Now let me turn to a second question, a fairly different question, but I'd say equally important.
And this is:
How do you make a teacher great?
It seems like the kind of question that people would spend a lot of time on, and we'd understand very well.
And the answer is, really, that we don't.
Let's start with why this is important.
Well, all of us here, I'll bet, had some great teachers.
We all had a wonderful education.
That's part of the reason we're here today, part of the reason we're successful.
I can say that, even though I'm a college drop-out. I had great teachers.
In fact, in the United States, the teaching system has worked fairly well.
There are fairly effective teachers in a narrow set of places.
So the top 20 percent of students have gotten a good education.
And those top 20 percent have been the best in the world, if you measure them against the other top 20 percent.
And they've gone on to create the revolutions in software and biotechnology and keep the U.S. at the forefront.
Now, the strength for those top 20 percent is starting to fade on a relative basis, but even more concerning is the education that the balance of people are getting.
Not only has that been weak. it's getting weaker.
And if you look at the economy, it really is only providing opportunities now to people with a better education.
And we have to change this.
We have to change it so that people have equal opportunity.
We have to change it so that the country is strong and stays at the forefront of things that are driven by advanced education, like science and mathematics.
When I first learned the statistics, I was pretty stunned at how bad things are.
Over 30 percent of kids never finish high school.
And that had been covered up for a long time because they always took the dropout rate as the number who started in senior year and compared it to the number who finished senior year.
Because they weren't tracking where the kids were before that.
But most of the dropouts had taken place before that.
They had to raise the stated dropout rate as soon as that tracking was done to over 30 percent.
For minority kids, it's over 50 percent.
And even if you graduate from high school, if you're low-income, you have less than a 25 percent chance of ever completing a college degree.
If you're low-income in the United States, you have a higher chance of going to jail than you do of getting a four-year degree.
And that doesn't seem entirely fair.
So, how do you make education better?
Now, our foundation, for the last nine years, has invested in this.
There's many people working on it.
We've worked on small schools, we've funded scholarships, we've done things in libraries.
A lot of these things had a good effect.
But the more we looked at it, the more we realized that having great teachers was the very key thing.
And we hooked up with some people studying how much variation is there between teachers, between, say, the top quartile -- the very best -- and the bottom quartile.
How much variation is there within a school or between schools?
And the answer is that these variations are absolutely unbelievable.
A top quartile teacher will increase the performance of their class -- based on test scores -- by over 10 percent in a single year.
What does that mean?
That means that if the entire U.S., for two years, had top quartile teachers, the entire difference between us and Asia would go away.
Within four years we would be blowing everyone in the world away.
So, it's simple.
All you need are those top quartile teachers.
And so you'd say, "Wow, we should reward those people.
We should retain those people.
We should find out what they're doing and transfer that skill to other people."
But I can tell you that absolutely is not happening today.
What are the characteristics of this top quartile?
What do they look like?
You might think these must be very senior teachers.
And the answer is no.
Once somebody has taught for three years their teaching quality does not change thereafter.
The variation is very, very small.
You might think these are people with master's degrees.
They've gone back and they've gotten their Master's of Education.
This chart takes four different factors and says how much do they explain teaching quality.
That bottom thing, which says there's no effect at all, is a master's degree.
Now, the way the pay system works is there's two things that are rewarded.
One is seniority.
Because your pay goes up and you vest into your pension.
The second is giving extra money to people who get their master's degree.
But it in no way is associated with being a better teacher.
Teach for America: slight effect.
For math teachers majoring in math there's a measurable effect.
But, overwhelmingly, it's your past performance.
There are some people who are very good at this.
And we've done almost nothing to study what that is and to draw it in and to replicate it, to raise the average capability -- or to encourage the people with it to stay in the system.
You might say, "Do the good teachers stay and the bad teacher's leave?"
The answer is, on average, the slightly better teachers leave the system.
And it's a system with very high turnover.
Now, there are a few places -- very few -- where great teachers are being made.
A good example of one is a set of charter schools called KlPP.
KlPP means Knowledge Is Power.
It's an unbelievable thing.
They have 66 schools -- mostly middle schools, some high schools -- and what goes on is great teaching.
They take the poorest kids, and over 96 percent of their high school graduates go to four-year colleges.
And the whole spirit and attitude in those schools is very different than in the normal public schools.
They're team teaching. They're constantly improving their teachers.
They're taking data, the test scores, and saying to a teacher, "Hey, you caused this amount of increase."
They're deeply engaged in making teaching better.
When you actually go and sit in one of these classrooms, at first it's very bizarre.
I sat down and I thought, "What is going on?"
The teacher was running around, and the energy level was high.
I thought, "I'm in the sports rally or something.
What's going on?"
And the teacher was constantly scanning to see which kids weren't paying attention, which kids were bored, and calling kids rapidly, putting things up on the board.
It was a very dynamic environment, because particularly in those middle school years -- fifth through eighth grade -- keeping people engaged and setting the tone that everybody in the classroom needs to pay attention, nobody gets to make fun of it or have the position of the kid who doesn't want to be there.
Everybody needs to be involved.
And so KlPP is doing it.
How does that compare to a normal school?
Well, in a normal school, teachers aren't told how good they are.
The data isn't gathered.
In the teacher's contract, it will limit the number of times the principal can come into the classroom -- sometimes to once per year.
And they need advanced notice to do that.
So imagine running a factory where you've got these workers, some of them just making crap and the management is told, "Hey, you can only come down here once a year, but you need to let us know, because we might actually fool you, and try and do a good job in that one brief moment."
Even a teacher who wants to improve doesn't have the tools to do it.
They don't have the test scores, and there's a whole thing of trying to block the data.
For example, New York passed a law that said that the teacher improvement data could not be made available and used in the tenure decision for the teachers.
And so that's sort of working in the opposite direction.
But I'm optimistic about this,
I think there are some clear things we can do.
First of all, there's a lot more testing going on, and that's given us the picture of where we are.
And that allows us to understand who's doing it well, and call them out, and find out what those techniques are.
Of course, digital video is cheap now.
Putting a few cameras in the classroom and saying that things are being recorded on an ongoing basis is very practical in all public schools.
And so every few weeks teachers could sit down and say, "OK, here's a little clip of something I thought I did well.
Here's a little clip of something I think I did poorly.
Advise me -- when this kid acted up, how should I have dealt with that?"
And they could all sit and work together on those problems.
You can take the very best teachers and kind of annotate it, have it so everyone sees who is the very best at teaching this stuff.
You can take those great courses and make them available so that a kid could go out and watch the physics course, learn from that.
If you have a kid who's behind, you would know you could assign them that video to watch and review the concept.
And in fact, these free courses could not only be available just on the Internet, but you could make it so that DVDs were always available, and so anybody who has access to a DVD player can have the very best teachers.
And so by thinking of this as a personnel system, we can do it much better.
Now there's a book actually, about KlPP -- the place that this is going on -- that Jay Matthews, a news reporter, wrote -- called, "Work Hard, Be Nice."
And I thought it was so fantastic.
It gave you a sense of what a good teacher does.
I'm going to send everyone here a free copy of this book.
(Applause)
Now, we put a lot of money into education, and I really think that education is the most important thing to get right for the country to have as strong a future as it should have.
In fact we have in the stimulus bill -- it's interesting -- the House version actually had money in it for these data systems, and it was taken out in the Senate because there are people who are threatened by these things.
But I -- I'm optimistic.
I think people are beginning to recognize how important this is, and it really can make a difference for millions of lives, if we get it right.
I only had time to frame those two problems.
There's a lot more problems like that --
AlDS, pneumonia -- I can just see you're getting excited, just at the very name of these things.
And the skill sets required to tackle these things are very broad.
You know, the system doesn't naturally make it happen.
Governments don't naturally pick these things in the right way.
The private sector doesn't naturally put its resources into these things.
So it's going to take brilliant people like you to study these things, get other people involved -- and you're helping to come up with solutions.
And with that, I think there's some great things that will come out of it.
Thank you.
(Applause)
Subtitles are available in several languages
Sixty-nine year-old Palestinian Leila Khaled, once a medical student, became a resistance fighter for the PFLP movement (the Popular Front for the Liberation of Palestine) and with others hijacked an aeroplane in 1969.
She was convicted and later released in an exchange deal.
Forced to flee her home in Haifa in the 1948 Catastrophe, she famously demanded the pilot of hijacked flight TWA840 to fly over Haifa so she could see her hometown, inaccessible to her after the creation of Israel.
Leila continues to be a symbol of Palestinian armed resistance, while to Israel she is a convicted and unrepentant terrorist.
She now lives with her husband and 2 sons in Jordan; I met her during her recent visit to Gaza in a PFLP office.
Looking at what happened recently in Gaza with Israel's Operation Pillar of Cloud, the nature of the resistance force against the state of Israel during this time, I think surprised a lot of people, even maybe Gazans.
And it seemed that there was an ability to repel Israel to some extent.
So my question is in today's context, is resistance strategically or symbolically useful?
It's always strategic.
Because when there's occupation, there is always resistance.
And this is a fundamental equation.
History taught us that freedom and liberation cannot be achieved without facing reactionary violence (except by revolutionary resistance).
And this is guaranteed by the international law.
The eighth item of the United Nations Charter says people under oppression and occupation have the right to resist, including armed struggle.
So we are defending ourselves and as you said, Israel was the first one to be shocked by the resistance itself.
Our people, our factions learnt from [the] last war in 2008, that they have to prepare themselves for another attack because the war did not end.
This is a battle now and we are proud of the resistance and our people.
The main thing [is] that resistance united the people in spite of the division. While
Negotiations divided people.
And this is one of the main achievements.
This means that the leaderships of Hamas and Fatah should abide by the attitude of our people, whether inside Gaza, in the West Bank, in all [of] Palestine, in [the] All our masses were [in] the streets in different countries where they are, even in foreign countries, saying one thing: we are with the resistance.
Do you expect our people to go, throw roses on the planes which killed our children?
No.
Resistance is something human.
What about the French revolution?
This is from Europe.
Now you're asking about the people in Europe.
But let them think of what the Nazis did in Europe.
Destroyed Europe.
Fifty million casualties.
That was in Europe.
And the people resisted [Nazism] and it was defeated.
Are we waiting for...?
Nazism, yes?
Yes.
They defeated Nazism.
Are we waiting for the Zionists to launch a third World War?
I think it's important to think of that.
And think that fascists and Nazis and the Zionists cannot be defeated except by resistance, with all its means, including armed struggle.
What does the resistance (the Palestinian armed resistance) have to do with Islam?
Is there any relation with Islam?
It called for resistance of injustice, whoever inflict[s] atrocities upon our people.
Looking at the successful UN bid, I personally see this as a consolidation of the two-state resolution to the injustice.
So you famously asked the pilot to fly over Haifa to see your homeland.
So my question is to you, what of the one-state solution?
Do you support it?
If so, why?
And if so, how?
How?
Well, we in [the] PFLP, in our programme. There is a transitional period to achieve the strategic goal of our struggle.
And the programme that all factions [that] were united in [the] PLO — [the] right [of] return, right of self-determination, [the] building our own state with Jerusalem [as] its capital. These are the goals of our struggle as a transitional period to establish democratic Palestine.
And I think that this is realistic also.
But we can never, and we don't, accept the solution of the Americans, who are the supporters of our occupants.
That two-state solution means that we give up seventy-eight percent of our land. And how?
The core issues of the whole thing (of the Palestinian cause) lies in two: the land (to be sovereign over [it]) and the return of the refugees.
Any solution that doesn't deal with [these] two issues, I think that it [wouldn't] last long.
[The] Oslo Accords proved that it's a failure for both sides who signed and who accepted this signature.
But at the same time we believe in our people, we believe in the will of our people to practice their rights, the rights that were recognised also by the international community in the United Nations.
So thinking of [a] two-state solution means that we have twelve percent of the land.
This is not Palestine.
Palestine is the historical Palestine.
I'm from Haifa.
That one from Akka.
That one from Jaffa.
Those people have the right to go back to their homelands.
And it's guaranteed also by international law.
Thank you very much, indeed.
Most welcome.
Thank you.
You're from Britain?
Yup.
It's nice to meet you.
When you go there, ask them: if anybody attacks their homes would they smile in front of their occupants?
I don't think so.
This video's production was made possible by Gaza Report's funders
Visit GazaReport.com for more insight into the situation afflicting Gaza
English subtitles by Harry Fear
A popular R&B band recently returned from a successful three-city tour where they played to at least 120,000 people.
My brain immediately says that's greater than or equal to 120,000.
If they had an audience of 45,000 in Mesa and another 33,000 in Denver, how many people attended their show in Las Vegas?
So let's say Las Vegas, I'll just use I for Las Vegas.
So the number of people who attended their show in Las
Vegas plus the number that attended their show in Mesa, which is 45,000, plus the number of people that attended their show in Denver, which is 33,000-- those are three cities right there, Las Vegas, Mesa, and Denver-- that has to be at least 120,000 people.
Or another way of interpreting that is greater than or equal to 120,000.
So to figure out how many people attended their show in Las Vegas, we just solve for I on this inequalty.
So if we simplify this left-hand side, we get the number of people in Las Vegas plus-- what's 45,000 plus 33,000, that is 78,000-- 78,000 is going to be greater than or equal to 120,000.
Now to isolate the I on the left-hand side of the inequality, we can subtract 78,000 from both sides.
So minus 78,000, minus 78,000 on the left-hand side, these cancel out.
And we're just left with the number of people who attended the show in Las Vegas is going to be greater than or equal to 120,000 minus 78,000.
So 120,000 minus 80,000 is 40,000, and it's going to be another 2,000.
So the number of people who attended Las Vegas is going to be greater than or equal to 42,000 people.
And we're done, that's it
In the last video we went over the multiplication tables for one through nine and I ran out of time, and actually, it was a good thing because one through nine are kind of the core multiplication tables.
And you'll see that if you know all your multiplication tables from one to nine, so you know any number between one and nine times any other number between one and nine, you can actually do any multiplication problem out there.
But what I want to do now is I want to complete the multiplication tables for ten, eleven, and twelve.
So what is ten times-- let's just start with zero. Ten times zero.
Anything times zero is zero. Ten zeros are zero. Zero plus zero plus zero ten times is still zero.
What's ten times one?
Ten times one.
Well that's just ten one time.
Or one plus itself ten times. That's ten.
I think this is second nature to you at this point.
What's ten times two?
Ten times two.
I meant to switch colors, but I didn't. Ten times two?
That's ten plus ten, which is twenty. Fair enough.
And notice, we went up by ten the first time.
We went up by ten again to get to twenty.
What's ten times three?
Well, that's ten plus ten plus ten, or we could view it as ten times two plus another ten, which is equal to thirty.
What's ten times four?
I think you start to see a pattern. Ten times four is equal to forty.
Notice, ten times four is equal to forty.
If I were to ask you what is ten times-- let me do another color-- five?
Well that's equal to fifty. Ten times anything is that anything with a zero behind it.
So the ten times tables, you almost don't have to remember it.
So let's just keep going.
What's ten times six?
It's equal to sixty. Six zero.
What's ten times seven?
Seventy. Ten times eight?
This is almost ridiculous. Ten times eight is eighty. Ten times nine?
Ninety. Ten times ten?
Now this is interesting. Ten times ten, so it'll be a ten-- let's see me write this.
Let me do it in this orange color. Ten times ten.
So it'll be ten tens or a ten with a zero behind it.
There you go. Notice, whatever number times ten, I just add a zero, then I get the next number.
So it's one hundred.
And I think you understand why that is.
I added ten to itself ten times.
That each ten-- you go from ten, twenty, thirty. Thirty is just three tens or ten times three. Ninety is just nine tens or nine times ten.
Let's keep going.
So ten times eleven is equal to eleven with a zero behind it. One hundred and ten.
Finally, ten times twelve is equal to one hundred and twenty.
Now, just for fun, these are kind of your ten times tables.
But now that you know the pattern you can do anything.
If I asked you what five thousand seven hundred thirty-two times ten is, what's it going to be?
It's going to be this number with just one more zero.
So it's going to be-- I won't read it out yet. Five seven three two with a zero behind it.
And just so you know, this little comma that I wrote in the number there, that's just to make it easier for me to read that number.
So, you put the comma-- you start over here and every third number you put the comma.
So here I'm going to put the comma right here.
I'm going to put the comma right there.
So now I can read this.
The comma doesn't really add or take anything away from the number, it just helps me read it.
Now five thousand seven hundred thirty-two times ten is fifty-seven thousand three hundred twenty.
I just had to add a zero there, but that was a pretty straightforward multiplication.
And notice, we had five thousand times ten and we got to fifty-something thousand when we multiplied them.
So that's similar to five times ten is equal to fifty.
But instead of five I had a five thousand, and so I got a fifty thousand and something and all this other stuff.
We're going to learn more about how to do problems like this in the future.
But I thought I would introduce you to the idea that just from this little pattern of adding a zero, you already know your tens times tables.
Now let's do our elevens. Our elevens, Elevens get a little bit-- Well, they start off easy, and then they get a little more difficult as we get into high numbers.
So, eleven times zero.
This is easy, this is zero! Eleven times one.
This is also easy!
It's eleven! Eleven times two.
We're going to start seeing a pattern here.
It's eleven plus eleven or we could've added two to itself eleven times, but that is equal to twenty-two.
If we do eleven times three, it is equal to thirty-three. Eleven times four is equal to forty-four.
I think this is becoming obvious to you.
What's eleven times five?
Eleven times five is fifty-five!
Notice I put the five twice.
What's eleven times six?
It's sixty-six! Eleven times seven is eighty-four-- no!
I'm kidding!
I didn't want to mess with you like that. But no.
Of course, it's seventy-seven! Seventy-seven.
You just repeat the number twice. Seventy-seven.
Let me switch colors. Eleven times eight is equal to eighty-eight. Eleven times nine is equal to ninety-nine!
Now what's eleven times twelve?
Eleven times twelve.
Oh sorry, I skipped ten. Eleven times ten.
You might want to say it's "tenty-ten!"
No!
That's wrong!
It's not "tenty-ten!"
So that little pattern that we had where you just repeat the number, that only works for one digit numbers.
So it only works for one through nine. Eleven times ten-- well, we could think about it a couple of ways.
We can add eleven to ninety-nine. So we can say it's ninety-nine plus eleven.
And what's that?
That's equal to one hundred and ten.
And I'm going to show you how to do-- well, hopefully you've already watched the video on how to add two-digit numbers like this, but that's one hundred and ten.
Or you could just use the property from the tens times tables that we learned.
Where if you just take eleven times ten, you add a zero to the eleven, you get one hundred ten.
That's the eleven right there.
Finally, let's do eleven times twelve. Eleven times twelve.
No easy way to remember this, you just kind of should remember it.
Or you could say look, it's going to be eleven more than eleven times-- sorry.
I keep skipping things.
We should do eleven times eleven first.
Let me make sure this is clear.
We're doing eleven times eleven before we go to eleven times twelve.
So eleven times eleven is going to be eleven more than eleven times ten.
So we add eleven to this. Eleven plus one hundred ten is one hundred twenty-one.
And actually, as you'll see, there actually is an order as we get to higher multiples of eleven, but I'll leave that to a future video.
And then finally, we're at eleven times twelve. Eleven times twelve.
And we could add eleven to itself twelve times.
We could add twelve to itself eleven times.
Or we could just say, hey, it's going to be eleven more than eleven times eleven.
So that is what?
You add eleven to this.
What do you get?
You get one hundred thirty-two.
I just added one hundred twenty-one plus eleven and then got one hundred thirty-two.
Now the other way you could have said it is, well, what's ten times twelve?
Ten times twelve, we already knew that.
That was one hundred twenty.
So eleven times twelve, because we're multiplying twelve by one more should be twelve more than that.
So that should be one hundred thirty-two.
So two ways to get the exact same answer.
All right! Now let's do our twelve times tables.
Twelve times tables.
And once you know this you are ready to tackle any type of multiplication problem.
But we'll do that in future videos.
So twelve times zero.
Super easy! Zero.
Twelve times one.
Also super easy! Is twelve.
Now it gets interesting.
We're going to increase by twelve every time. Twelve times two is equal to twenty-four. Twelve plus twelve is twenty-four, right?
Twelve times-- not twenty-two.
Let me rewrite that. Twelve times three is going to be twelve plus twelve plus twelve.
Or we could write that as twelve times two.
I see my brain is doing the wrong things.
We could rewrite that as twelve times two plus twelve.
Or we could rewrite that as twenty-four plus twelve.
Either way, all of these get us to thirty-six.
And notice, that's just that plus twelve. Twelve times four. Twelve times four is equal to forty-eight.
There's a lot of ways you could think about it.
You could say eleven times four is forty-four.
Right?
Eleven times four is equal to forty-four.
And you go up by one more four, so you get to twelve times four.
Or you could say twelve times three is thirty-six and you can add one twelve to it to get to forty-eight.
Either way works, and that's because you can multiply in either direction.
Let's keep going. Twelve times five is equal to sixty. Ten times five is fifty, eleven times five is fifty-five, so twelve times five is sixty!
It's going to be twelve more than this.
It's going to be equal to seventy-two. Twelve times seven. Twelve more than this again.
And I'm serious, you know, I'm probably a lot older than you are, and I still, in my head to confirm,
I go to some twelve times tables that I remember as definitely right.
Like oh, twelve times five-- and sometimes in my head I say, oh, let me add another twelve.
Oh yeah, definitely, my memory was correct. Twelve times six is seventy-two.
All right.
Then you go to twelve times eight.
Add twelve to the twelve times seven. Ninety-six. Twelve times nine.
Well you add twelve to this, so it's one hundred eight. One hundred eight.
And then twelve times ten.
This is an easy one!
Right?
We just add a zero to the twelve to get one hundred twenty.
Or we could've added twelve to one hundred eight.
Either way. Twelve times eleven.
We just did this.
You add twelve to this to get one hundred thirty-two.
And then twelve times twelve, is equal to one hundred forty-four.
And this actually shows us--
If I had a dozen of a dozen eggs-- a dozen is twelve.
Or if I had a-- I think a gross is actually twelve dozens.
So that's one hundred forty-four eggs.
So you'll actually end up seeing this number a lot.
More than you would expect in life.
But anyway, we've now completed all of our multiplication tables.
And I really encourage you to take the time now to go and memorize them.
Make some flash cards.
Use the little software thing that I wrote on my website.
You could try that out.
As of September Two Thousand Nine, it's working.
I haven't touched it in a while, but I'm actually probably going to rebuild it soon.
So if you're watching this video in the year Two Thousand Two Hundred--
Well, I would probably not exist anymore.
But hopefully you'll get a better version of the software app.
But you should practice it.
You should get your parents to quiz you.
You should get notes cards.
You should just be mumbling to yourself as you walk to school--
What is twelve times nine?
What is eleven times eleven?
And you should quiz each other, because it'll pay huge rewards to you later on in life.
See you in the next video!
I remember Heaven and Hell had a lot of unwritten rules in those days and match making for the living was still a bit of a wild west.
But I guess that's where Death comes into the story... and the guy before me had pushed her too far.
It's not smart to toy with Death, but there was something hypnotic about her... and I wasn't the only one who thought so.
Speak of the Devil, that was me.
It was my first day on the job, and I was ready for... just about anything... except maybe this guy.
They say love is blind.
But Cupid was over a thousand years and it didn't stop him from flirting with Death.
Now, I could tell he was playing with fate that day.
But little did I know what fate had in store for me.
Up there Death was Judge, Jury and Executioner to all lovers, living or otherwise.
But despite his behavior, Death had a soft spot for him and loved watching him work.
While Cupid was matching up lovers all over the world, I was tasked with breaking them up.
Not exactly what I had in mind.
My demon instincts faced constant temptation but I wanted so much more than that.
She hid it well, but Death was facing her own demons that day.
I needed to figure out how to impress her.
Huh, turned out to be easier than I thought... but it's not every day I put the moves on an Overlord of the Afterlife!
It was my first time and nerves were all over the place.
My instincts were on fire, but not in a good way.
That wasn't my best move.
While Death's guard was down, Cupid saw an opportunity to take fate into his own hands.
My story didn't turn out quite the way I'd imagined.
Hey, somebody had to do Cupid's work, and the job had its perks.
This is another problem that Kortaggio sent me, and I like these problems a lot because they seem fairly simple on the surface, and actually the solutions are pretty simple. But just the nature of the lack of information they give, it becomes kind of hard to even get started with these problems. And I'll be frank, this problem, I kind of stumbled around with it for a couple of minutes until I finally realized what they were asking for or how to solve for it.
So in this problem, we have Bev, and she takes a train home at 4 o'clock.
She arrives at the station at 6 o'clock.
Every day, driving at the same rate, her husband meets her at the station.
Fair enough.
One day, she takes the train an hour early and arrives at 5:00.
Her husband leaves home to meet her at the same usual time.
Husband leaves home to meet her at the usual time.
So maybe an interesting thing is to think about when does the husband normally leave?
So let's say that this is a normal scenario.
I'll do that in green.
At 6 o'clock, she arrives.
We got there.
She arrives at the station at 6 o'clock.
I don't know if this 4 o'clock is useful yet. And the husband, he gets there right when she gets there.
So he traveled-- he gets there, and I don't know if I'm-- maybe I should draw a more-- well, let me just draw it this way.
I think this is how my brain kind of handles it.
So he gets there.
And when did he have to leave?
What was his time?
So let's say it takes him t minutes to get there, whatever t is given in.
So if he gets there at 6 o'clock, that means he left at 6 o'clock minus t.
If t is 30 minutes, it would be 5:30.
If t is one hour, it would be 5 o'clock.
So leaves at 6 o'clock minus t. And t, whatever units t happens to be.
Then he picks her up, and what does he do?
He goes back home, right?
He goes back home.
Let me do that with a-- I'll do that with a skinnier line.
He goes back home, same distance.
We assume that the car just turns around immediately, and that there's no time devoted to picking her up.
She just kind of jumps on the car as he spins around.
So it should take him the same amount of time, right, t.
So when does he arrive back at home?
So if it took him-- he left t minutes before 6 o'clock and got there, so when does he get back?
Well, it's going to take him t minutes to get back, so he's going to arrive at 6 o'clock plus t.
And this is almost superficially easy.
Well, if you-- 6 o'clock plus t minus 6 o'clock minus t, the difference in time is just 2t.
He traveled a distance of-- or a total time of 2t minutes, and that's almost obvious.
If it takes him t minutes to go and t minutes to come back, he traveled t minutes.
Fair enough.
Now, what happened on this day?
It says that he leaves-- her husband leaves home to meet her at the usual time.
So once again, he is going to leave-- he leaves--
I'll do this in red.
He leaves at 6 o'clock minus t, right? And then, she arrived early.
So she's going to be walking back.
So there's going to be some smaller time than it takes him to reach her.
So let's just leave that unlabeled right now.
So if I have a line here-- so he's going to travel a shorter distance, and, of course, it's going to take him less time because she started walking.
That's what the problem tells us, right?
Today she arrives at 5 o'clock, and she begins to walk home.
So she's going to make some distance up so he's not going to have to travel quite as far.
And then whatever time that was, he goes back the other way.
It's going to be the same amount of time.
It's the same amount of time.
And what does it tell us?
He meets her on the way, and then they arrive home 20 minutes early.
So normally, they arrive at 6 o'clock plus t, right?
That's normal.
So today, they're going to arrive 20 minutes early.
So they're going to arrive at, you could say, 6 o'clock plus t-- that's just that-- minus 20 minutes, right?
They're going to arrive 20 minutes early.
So what's the total amount of time that he would have traveled on that day?
The total amount of time?
Well, he essentially travels 20 minutes less than he does on a normal day, right?
He leaves at the same time and he gets there 20 minutes early. And if you take the difference between 6+t-20 and 6-t, you're going to get 2t-20. And that's almost--
I probably didn't even have to draw all of this.
You could just say, well, you know, on a regular day, it takes them two-- if t is the amount of time, it normally takes him to go to the station, on a normal day, he travels 2t minutes.
Today, he leaves at the same time, gets 20 minutes early, so he travels 2t minus 20 minutes.
Fair enough.
Now, what does that tell us?
Well, how long did it take him to get to her?
How long did this take her?
Well, to go to pick her up takes the same amount of time as to come back, so he must have taken half of this time to go and half of this time to come back.
So it must have been t minus 10 to go, and then t minus 10 to come back.
So it took him 10 minutes less to reach her this time.
So what time does he pick her up? And this is the key.
So normally, when it takes him t minutes, he gets there at 6 o'clock.
This time she started walking because she got there early, and he gets there 10 minutes-- he reaches her 10 minutes earlier than he normally would have reached her, right? t minus 10.
Normally, he reaches her at 6 o'clock.
Today he reaches her 10 minutes earlier.
So he reaches her at 5:50.
Now, the question is, how many minutes did Bev walk?
How many minutes did Bev walk?
Remember, she arrived an hour early and arrives at 5 o'clock, and then she starts walking.
She arrives at 5:00, 5 o'clock, and just starts walking. And when does he pick her up?
He picks her up at 5:50.
So she walked for 50 minutes.
That's a neat problem.
Because on some level, it's very easy, but on a lot of other levels, they give you all of this other information that's not necessary.
For example, you don't have to know that she leaves at 4 o'clock. That's actually probably the most unnecessary piece of information.
But everything else is kind of left abstract.
But even though you can-- they're not giving a lot of details.
You can actually figure out how far she walked without knowing how fast she walks, or how fast her husband drives, or how far they are from the train station, or how far the house is from the train station, or any of that.
You're still able to figure out how far she walked.
Anyway, neat problem.
Thanks again to Kortaggio.
Use the commutative law of multiplication to write 2 times 34 in a different way.
Simplify both expressions to show that they have identical results.
So once again, this commutative law just means that order doesn't matter.
It sounds very fancy.
Commutative law of multiplication.
But all that says is that it doesn't matter whether we do 2 times 34 or whether we do 34 times 2.
The order does not matter.
We can commute the two terms.
Both of these are going to get you the same exact answer.
So let's try it out.
What is 2 times 34?
And we could write it like this, literally.
You'll almost never see it written like this, but it is literally 2 times 34.
Almost always people write the larger digit on top, or the digit with more digits, or the number with more digits on top.
But let's do it this way.
4 times 2 is 8, and then we'll put a 0.
3 times 2 is 6, or you can view it as 30 times 2 is 60.
Add them together.
8 plus 0 is 8.
6, bring it down.
It's not being added to anything.
You get 68.
So 2 times 34 is 68.
Now, if you do 34 times 2, 2 times 4 is 8, 2 times 3 is 6.
That's why it's always nicer to write the number with more digits on top.
It also is equal to 68.
So it doesn't matter whether you have two groups of 34 or thirty-four groups of 2, in either case, you're going to have 68.
So we talked about inhaling and exhaling.
And I mentioned that the key first step for both of them is kind of the change in volume: going up in volume and going down in volume.
But I didn't really talk about how that happens exactly.
So, I'll kind of jump into that now.
And let me begin by telling you that in the middle of your chess, you have this enormous kind of bone that goes down.
I'm drawing it out of proportion just to make it very clear where the bone is being.
Go ahead and feel on your own body this bone which we called either the breast bone or the more technical name is sternum.
Write that down here.
The sternum is this middle bone and all the ribs on both sides attached there.
So, you've got a total of 14 ribs and 7 pairs of them.
Actually, I should say 14 pairs of ribs.
I don't want you to think there're 14 in total.
There are actually 14 in total and 7 pairs of the ribs.
So 14 ribs actually attached directly to this bone, the sternum bone.
So in white, these are the ribs.
And between the ribs, you actually have muscles.
So I'm gonna draw some of these muscles between the ribs.
And these muscles are all going to have their own nerve that allows them to contract.
So, these muscles are controlled by your body or your brain.
And their name, let me just jot down here on the side, is "intercostal muscle".
And "inter" just means "between".
So, this is the name of the muscle.
And "costal" refers to the ribs.
So, when you see that word "costal", you'll know we're talking about the ribs.
So what's between the ribs is these muscles: intercostal muscles.
And they're gonna start moving outwards when your brain says, "hey I want to take a deep breath!"
So, these muscles are going to contract and the ribs are gonna move outwards.
So these go out. And you also have...
Let me just make a little bit of space on this xxx.
You also have another muscle that kind of right down here.
And it has kind of a an upside down U shape to it.
So I'm drawing it kind of like a dome. You can think of it as a dome.
And this dome is the floor.
If you remember, we talked about the floor of the thorax.
So this is of course, our diaphram muscle.
So, you've got a diaphragm muscle.
And this one when it contracts, it's gonna go... instead of going out, it's gonna go down.
So it's gonna kind of flatten out.
And I can actually draw this if you just stick with me for a moment.
I'm gonna erase this dome-like shape.
And I'm gonna draw it when it looks like as it's contract.
So when it contracts, this is actually going to be more flat.
And this flat diaphragm, as you can see, is now further down that it used to be.
And as it goes down, all of the structures that are inside the space, so the two lungs, and of course, I didn't draw the heart here, but the heart would be this kind of this cardiac notch.
If you want me to, I can even draw that heart here.
This is our heart here.
They're all going to kind of physically moved down.
So this is our heart and our lungs.
They are physically gonna be kind of drawn downwards and out.
They're gonna also move out as the intercostal muscles move out.
So you have expansion of these lungs, that's basically the idea.
And if you kind of zoom in on this, to kind of see exactly what this expansion looks like, when I say, you know, you have more volume, the lungs, really what I should be saying, if I want to be more exact, is that all the alveoli, if these are the alveoli, let's say this is another branch, this is another alveolar right here; all these alveoli, they are actually expanding.
And you have about 500 million alveoli.
You can just kind of fathom how big a number that it is.
It's an enormous number of alveoli.
If I was actually drawing them here... drawing forever, right?
It'll take forever to kind of write out this many different alveoli.
But basically what happens is that, when the ribs go out, the diaphragm moves down.
These alveoli are actually being pulled out. They are actually pulled outwards.
So they are actually gonna be getting larger in size.
They literally look like they've grown in size.
And, this is what they look like.
And actually, if you take even a closer look, you'll see that these alveoli have around them, a bunch of protein.
The cells around them have a bunch of protein.
And this protein is called "elastin".
And you can guess what elastin might do.
It has kind of a similar sound to the word "elastic".
Elastin is basically kind of like a rubber band.
So you kind of thinking of elastin as a rubber band.
And, when the muscles move down and out, and the alveoli pulled open, let me actually kind of scroll up, because you can kind of go back to the idea of inhaling.
What is happening? Well, we have a couple things happening.
One, you have muscles contracting. Muscles contract.
And when I say "muscles", you know I'm talking about all those intercostal muscles in your diaphragm.
And as a result of the muscles contracting, you have now the alveoli, alveoli are streched open.
So those rubber bands are elastin, protein, are literally physically being stretched open.
So the alveoli are stretched open.
And keep that in mind, because what's gonna happen then is, when the muscles relax, which is what happens when you exhale, when the muscles relax, what do you think is going to happen to that elastin?
Well, it's like a rubber band, if that's what I'm saying, it's gonna be like, then the alveoli are going to recoil. They are gonna recoil.
And that's actually the driving force for why the volume goes back down.
So if you have a bunch of rubber bands that you're stretching out...
Let me actually bring up the picture so you'll see really clearly.
If you're physically kind of using your muscles to help pull this stuff open, then the moment that you start pulling open, the moment that you, you know, stop contracting those muscles, now you have a nice big volume.
What's gonna happen?
All these elastin molecules are gonna snap back.
We'll do it with a different color.
I'll do it with this color.
They are gonna snap back like this.
All that protein are gonna snap back into kind of the original size.
And when they do, this thing gets smaller.
So my alveoli kind of goes back to its original size, which is much smaller than this.
Let me actually show you that even though contraction is what opens up things it's the recoil that kind of brings things back down to their normal size.
Let me erase this to make it kind of neater drawing.
So you can see it now, inhaling, the way that we actually increase the volume, is by pulling things open through contraction.
And this actually requires energy, right?
Remember, you can't contract a muscle without spending chemical energy.
So this takes chemical energy.
And we usually think of this molecule ATP as the specific type of chemical energy we're gonna use.
And to exhale, when you reduce the volume, it's gonna be driven by this elastic recoil.
So that's a type of elastic potential energy.
So, this process of kind of inhaling and exhaling is really a little different from each other.
On the one hand, you're using ATP; you're actually burning through these molecules.
And when you exhale, you're actually not using chemical energy anymore.
You're just using that elastic potential energy, kind of the same sort of energy that you can imagine you would have if you snap a rubber band.
So, let's stop there.
We'll pick up the next video.
We are asked to approximate the principle root, or the positive square root 45, to the hundredths place, and I'm assuming they don't want us to use a calculator because that would be too easy.
So let's see if we can approximate this, just with our pen and paper right over here.
45 is not a, 45 is not a perfect square. It's definitely not a perfect square.
But, we know, let's see what are the perfect squares around it? We know that it is going to be less than, the next perfect square above 45 is going to be. Let's see it's going to be 49, because that is 7 times 7.
And if we look at it, it's only 4 away from 49 and it's 9 away, it's 9 away from 36. So it looks like, so the difference between 36 and 49 is.
It's 13, so it's a total 13 gap between the, 6 squared and 7 squared and this is, this is 9 of the way through it.
So just as a kind of an approximation, maybe and it's not going to work out perfectly because we're squaring it, this isn't a linear relationship, but it's going to be closer to, 7 than it's going to be to 6 and it, at least the square or the. 45 is 9 13th of the way.
So we could try, we could try, lets see, it looks like a, that's about, that's about two thirds of the way, so lets try 6.7, lets try 6.7 as a guess. Just based on, 0.7 it's about two thirds, it looks like about the same.
And actually we could calculate this right here if we want, actually let's do that just for fun.
So, 9 13th as a decimal is going to be what.
It's going to be 13 into 9 we are going to put some decimal places right over here, 13 doesn't go into 9, 13 does go into 90 and it goes into 90 as let's see it does go into 7 times It goes into it 6 times.
So went into it almost exactly 7 times, so this value right here, almost 0.7.
So you get, it's about .69, so 6, so 6.7 point would be a pretty good guess. This is .69 of the way between 36 and 49. So lets go roughly .69 of the way between 6 and 7.
Let's try 6.7 and the really way to try it is to square 6.7. So 6.7, 6.7 times 6 point, maybe I'll write the multiplication symbol there. 6.7 times 6.7.
7 times 6 is 42, plus 4, is 46, so the 0 now, cause we're now in, we're now moved up, to, we've moved a space to the left, so now we have 6 times 7 is 42, Carry the 4.
And so 9 plus 0 is 9, 6 plus 2 is 8, 4 plus 0 is 4, and then we have a 4 right over here.
And we have two total numbers behind the decimal point, one, two.
So this gives us 44.89.
So 6.7 gets us pretty close, but we're still not, we're still not probably right to the hundreds, well, it's definitely not to the hundreds place since we've only gone To the tenth place right over here.
So if we want to get to 45, the, the 6.7 squared is still less than, the square root, or I should say, 6.7 squared is still less than 45. Or 6.7 is still less than the square root of 45.
So, let's try 6.71. So let's try 6 point, let me do this in a new color. I'll do 6.71 in pink.
So once again, we have to do some arithmetic by hand.
We are assuming that they don't want us to use a calculator here.
And we have 1, 2, 3, 4 numbers behind the decimal point.
So when we squared 6.71, 6.71 is equal to 45.02. 41, so 6.71 is a little bit greater.
We know that, 6.7 is less than the square root of 45, and we know that, that is less than 6.71 cause when we square this we get something a little bit over the square root of 45.
But he key here is, is when we square this, so 6.7 squared, so let's, 6.7 squared guys. 44.89 which is eleven hundredths, eleven hundredths away from 45. So, this is and then if we look at 6.71 squared, we're only 2.400ths above 45, so this right here is closer to the square root of 45.
Rewrite the expression five times 9 minus 4-- that's in parentheses-- using the distributive law of multiplication over subtraction.
Then simplify.
So let me just rewrite it.
This is going to be 5 times 9 minus 4, just like that.
Now, if we want to use the distributive property, well, you don't have to.
You could just evaluate 9 minus 4 and then multiply that times 5.
But if you want to use the distributive property, you distribute the 5.
You multiply the 5 times the 9 and the 4, so you end up with 5 times 9 minus 5 times 4.
Notice, we distributed the 5. We multiplied it times both the 9 and the 4.
In the first distributive property video, we gave you an idea of why you have to distribute the 5, why it makes sense, why you don't just multiply it by the 9.
And we're going to verify that it gives us the same answer as if we just evaluated the 9 minus 4 first. But anyway, what are these things?
So 5 times 9, that is 45.
So we have 45 minus-- what's 5 times 4? Well, that's 20.
45 minus 20, and that is equal to 25, so this is using the distributive property right here.
If we didn't want to use the distributive property, if we just wanted to evaluate what's in the parentheses first, we would have gotten-- let's go in this direction-- 5 times-- what's 9 minus 4?
5 times 9 minus 4. So it's 5 times 5.
5 times 5 is just 25, so we get the same answer either way.
This is using the distributive law of multiplication over subtraction, usually just referred to as the distributive property.
This is evaluating the inside of the parentheses first and then multiplying by 5.
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los angeles police department we have air force chief of police being debated to preface our program he paid good evening ladies and gentlemen sometimes the most dramatic work on the part of the peace officer goes unnoticed by the rank and file of the city's people simply because network has not been blaze moon headlines sometimes an important case is broken but the story behind it never breaks for the average peace officer does not want publicity he does not needed he does his duty as he sees it and does not look for praise the vast majority of criminal cases were investigated and cold without them there such as our story tonight because person still living might be heard by the broadcasters certain facts surrounding our story we have purposely change both local and personnel it is our desire to present our problems without harm to anyone but to bring out most certainly but crime of any sort is an unprofitable enterprise actual reserve additional facts or the end of the problem interfaces home in one of the land of the most expensive resident of this bindle father and his son engage in heated argument well i cannot tell plane but mighty like a they sang and matt thinking it is standing there shouting and that isn't going to get your anywhere and thinking i thought then doing day and night thinking think if that medication wouldn't be talking like an idiot i might need it because the whole animal out you did a thing thing the left at the opposition and resentment he went right ahead married mother in spite of every time not offering any opposition i'm not holding any resentment you can marry anyone you peace and good luck to you about not now paddle wheels the op that i said i'll pay you when you refuse to give me a logical reason we won't go into that again my reason for that many of them a is sufficiently logic and a satisfying the even that's a big help business how relevant the marion on tell you have a logical reason why we shouldn't get married she'll probably appreciate that showed up with have great respect for the you care about bob dole out somewhere and cool off and come back and talk to me like a sensible person it's my turn to stand on my own p i can see where it's going to be necessary for me to take whatever action i think that rebuttable what do you mean they'll find out and only a money order you any good i'm going to get what i want in this case understand that no matter how i get it multan uh... this is uh... jim rather or u of i'm just wondering i thought the people's interval consolidated pipe short junk hedged didn't go up until about two months before the market closed for him to him on the morning to cover and you dig up two hundred thousand over the weekend chant but perhaps your garlic kick sold out out west it would mean a supposed quote well never mind uh... the funds almost learn data telephone consignment you can see it rumors loving theory is that i have something to do i'll call you as soon as it's done marshall him are you doing here coupons a told me to bring you some coffee maternity lots of its not when you wanna come in my room yes expert i have enough trouble without the seven spying on me up a copy dot i got here okay yesterday coming soon at high speed that is that rat kiley come out of that highest hammering i don't think i should say since a wifi sam matter with you with was that was good master collison a very bad humus us how many entertainment was generous shall i wait until you finish waking that met is all you heard me kind of a canary once at m no raceway the detailed by the one of the money consolidated iacocca seemingly kid i'm naked with your wireless at bank you're one of the meanness and carry this argument has stopped we won't have you come to your troubles in my severance i haven't been telling my published he also you can you have been cooking up something it's like a scare at whatever time i mention your name i wouldn't put up with a sentence in a business and i've been trying to write whatever that my home that all you have to say no also category because because i think that you're married a fresh petticoat essential i started you can't say that i think i a what's best for you and i'm going to allow it to
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like their security at it over my work and where antiseptic event there is a favor you could do for me return and return it may be persuaded to lend you the money and or doctor lovell programs and i won't do it on the other hand like andrew favor or forgetting to mention a few things you would want to hear him you'll you'll try that sooner or later when i got to where i want to mr richards come up with you but your best bet is that a couple took china october november what u door to quiet welcome at western coming here doubts but i would require you can take care of myself get tied up here uh... each witness male is letter grades turned places on the steps and harry i'll go to a couple months they're going to probably what got role would go to deliver to real puffy and it's a red herring i believe i told you believe i am not through with mr ritter i think that the caller we get to they've all week
lookup one hundred earlier kachigian accordion with water hain and public admit that across passed out colored optimistic but i'll get a lot of myself number one the water curled from under water and uh... further investigation shows qwestoffice dot was due to cyanide poisoning but how would that have gone with the minister of my home was still a mystery open water the homeless on the table sign the consent of ryan to investigate something wrong in this whiskey the sandy something we will look kinda about that when i'm in the end of one of my dreams i noticed that the papers this morning for michael new or heart failure dead that's fine long as they felt that way we'll have time to work it's when they start yelling murder without anything to go on that i get worried when i still can't see how men can die from cyanide poisoning and was he dubbed himself or somebody gave it to him yeah that's on this for grogram but obviously needed big according to the stories we've gotten so far the reform in in that room none of the mcveigh touching anything none of them so anything you cannot go yet suddenly one of the public over dead from simon and could have been suicide i don't think so evidently westcott was telling them all ready to go to he seemed entirely in command of the situation nine think he would be the last one of the group that everything for suicide when a person who are overlooked something important meantime the guy the dishes out cyanide in small doses a school that's right and want to boys to go over that whispered pleas from some of the wreckage and bring west that's popular young westcott and that ritter bird back here any particular reason for going in the back please and nominated comic that was lying in wait for sprint or news not that went on the job done very good sanderson trying to put one over on the press item lying in wait begins will play a run when he was doing a suicide case you see around i told you we'd get into an argument was was or or start getting sandy what's the idea so that's what i guess they were sent to you that talia one of the story of your papers dan ronan was about heart failure or don't you read the papers no prior item did you see if i told her i think this is a murder case i'd say you're not see sandy antwort and looks sunny let's get together but it was infected on the street would be a his memoir couple private detective agency the stadium the place across the street i wouldn't be surprised even the survey shows all the struggling here any minute now what's coming up around one comment from where i sit this looks like a perfect crime you've got a suicide it's neither one there's no such thing as a perfect crime and west cabin killing self post-game said to reproduce some copied rather than the proto women how do you happen to know about this quarter from a sort of quarters christian blueprint to the house i'm not mistaken roads into the kitchen are good doesn't sunday let's eat anybody that he entered into this house is really not rise to longer tourism for coming in the bike way sammy frustration of the rebel you all banks powell yet in the second place anymore crimson activity is coming and in the papers and that is to move into the process treatment serious they said that i don't want the officer on the door on the way here rowell yet how do you happen to be around back to them who will mean that you rail line was just trying to find out what was not committed suicide dr you remember that time calyx tomake shot himself a new insisted it was murdered why don't you give up this is murdered let's say you prove it quiet
library just russell that's where western diamond uh... somewhere three-point line there senior people i guess i was wrong animosity was cut was here by the desk writing there must have been about there on the sofa butler probably came from the same direction we didn't some said he was upstairs handedly air too that will be selected from a border there just about the size of a pinhead you know if that's what i think it is we've got the answer to one of our questions right there so i'm i'm coming take a look at that warm sunny open darien hundred and we look for that when we came in remembering the time it was the same problem a house to received and opened itself underscores this morning i saw it looks like whoever open that did it recently that sleep looks cool posted again which would crack and somebody away from that job moment extant and somebody who hasn't had time to get this league somebody coming to replied at the moment review m whisker so i heard isn't getting complicated i think we ought to come out new i've got a better plan occurred hipsters macroscopic so i'm not i suppose exactly what do you expect the planet stick around reporter you find out you know what protection just now may have been a ball he's had time to dispose of anything you might have taken from a safe users who may be the one who that well why don't you could get school up here on republicans hope that say devlin at times you amaze me that probably a couple of dozen prints on that too and you expect to find the murder of i'd check in the room suggestion seems to be a convention here tonight that's more of a little there will involve a lot more we sent for you the lord burghley remarkable typical the per worker young at the workbook or wearing you or your library or find out about this rick burke and this room here really grown almost missed this is beginning to smack of up m twenty that a melodrama orbit where what and under a minute into the latter you are just a minute in in manner remember oredi look like they were going to sleep organisms used temperament want him wieland used to hear both of you and find out what happens here i'm gonna exteriors podobnik warning to conclude who came to make it happen repair work work work with the idea of a sudden we're forever i didn't employed i didn't belinda body right there with him the is that it will be the poll if you're here did get a call ritter water broke around the world hildegun overdue removal of the library where i don't know your mind at that report no member of the promoter nevermind have a good note here on the old ones of you right now read allot don't worry i can find something that will be necessary to go undertaken that was probably a good on my interest in the order you to worry about iran record breaking or at the young man privately but this all about i haven't done anything europe if you go to outside where share come on you to project we were talking about after he's gone and return it sanderson police department the program experts a reporter but he's harmless also u colombo sunday talk about the funny stuff and get to the point but he's been mister west governments will tell you that your suspected of murdering her father for you crazy every why should i wanna kill my own father that's what we want to know ritter and on this i don't even know what you're talking about or with indonesia show but what the law does involve the father sometime or other andrew they also threatened to kill her father still has a lot and predicament reinstatement was a bit was the culmination here for the sake i don't know you didn't does porcelain unsafe open up like you ladies and im but it could be supposed to explain america get that's a problem i'm not talking anymore do whatever you want to who beat me up like you cop always do i'm not talking want me to do it sunday uh... recreation you've been seeing too many gangster pictures are reading reporters yarns about police we're gonna be chopra do anything else to we just want the truth ring a bell you gotta get outta me others bottles and i get in your room pot your edmy colonel anything about it i never saw a couple of course not how to get that i don't know i will tell you a pain ok sam come along maybe if you didn't sell it in your mind was ryan in-room forty-seven program ritter
let's go down there are you going to tell me that ridiculed allman western maybe most well if you ask me i don't think you too of planning how are you found out nothing waiting for you i'm a thriller or worldwide ridable bringing the number of them
levels of models little where mister of some kind of the things take a little longer closing we expect there appeared in the winning return such as you're needing two hundred thousand dollars seven mag nearby mister west cuts house tomorrow tomorrow removal of the school bring with them and that's true we found out also that you met your obligation monday morning what's true true i might have been looking for where did you get that much money i'm not at liberty to survivors are mature aware of the two hundred thousand dollar disappeared for mister west would save between the time he died saturday night in the time you graded up monday morning we're going on about glenn referred you have already arrived young was go further go to that while you are not sure at the way home anymore you going to cues about crime menacing implicated in it we can't find the money young was definitely didn't they did the natural inferences that you draw working together into a permanent give it to you i think i'll about the possibility of an these that's where we ask you to come down and program over or another with them uh... but have you given any thought to the question of why there were two hundred thousand dollars on a comparatively unimportant concern and that you know what works best business that's correct because there because he won't be available in book in new york coming to borrow money truck went into the wonderfully on certain conditions so he was treated with levels are going to philip pigeon threatened to kill it if i didn't i meant to
loretta it's a good story but will have to hold it about so on what's our as an accomplice in the murder of what's got and what you're talking to a way out of things thinkable good what about why you bought a large quantity of cyanide much intended to england with to logical suspect in custody police still don't feel entirely sure that the murderer was talking about apprehended certain that a crime had been committed cameramen ryan returned was problem pleading with the mood among some outcrop i want you to show me again just where you are standing when your father rather than with their just inside the door and you've got across here to this desperate for a collapsed well not quite you see mister read it was close to the dead that i was in the economy seat belt and uh... who else was here anomaly though that is nobody but him he does come in from the rear hallway over your father doing when he first showed signs of this error attack read just finished writing a letter he still didn't get it in the mail was made me when you came in and did he come in later by ability came in later yet adam emery has detected wrong and in the letter was already going hidden came in mapping summer yes i remember that couldn't find a stamp firstam when he found one right there on the body somebody's copies of what all we did would you do that but we had a reason knowledge going back to that night whose job isn't to keep this desk in order building quayle's that paper pens and so forth player didn't know it instead he has a special bundy uses the bus applies with stamps and things like that he'd buy stamps dancing and jim paper on pins and all the things like that don't know when they happen to buy supplies last april mel with you'll find a book and his room where he keeps all his accounts alerted man with a book is mention of the always keeping his desk in his room
let's go take a look it's the first room at the right just back to the states others did move in with your family ko model no
like as long as i can remember make good money idea so i never inquired we're doing it for the core of our time i'd rather not talk about it might help a lot is the room where she now we went to the marker is going to the cemetery later
listed this cuban program mesmo plattsburgh ny never has been before that i know of know where there's a key melva fuck you what the book let's break it open after all of those drugs okay youporn under a lot of pride cup go andrea dot is the book next year june tenth one pound package a paper two dozen envelopes twenty five two cent stamps twenty-five ones one bottle back from penang or they're the stamps right back at that page funny didn't put him in the desk in the library very funny your twenty four two cent stamps and twenty-five ones kill answers here
lonely without you risk of residents ast op uh... we've been when detective again sex when the issue you written a word came from auction ex-cop catapult or kill having procure she could see it is the voice recorder nicaragua as krueger's apartment leave a message for him before nevermind going in and hello is mister mitterand uh... will will you tell them to come over to mister west cups all right away when it comes in about coming shoes capitalist sunday night repute like yours are not one but work known was that was taken by the board room while someone run again started out to continue their investigation parked in the start of the morning revealed himself in the car watching the worst problem quiet couple would you come
let's talk brought me don't you ever sleep problema homicide squad is trying to make a mother out of a suicidal talks about the suspect hold good anytime always wanted to see one craft very comes we would get under way into whose him you'll find out reporter owner cold eat the starter sound record returning let me ask me and since my mission to buns worries european cagey incase when well if you don't at this moment going located in the form of brighton openings as you know rd this is the parliament like adding that the movement that is that there is one why that's the man who murdered old westbury new hope and no alone stopped we one-line waldman weren't mobile communication center pretty good place for barrington you could have been put on to much to open pretty quiet around here who goes on it looks like he's got a show russian winston big one coming you go around on the right and you take the left side i'm getting from the front here you would move and handy dot and b quiet watching tricky ally were you who's just hopped over the last well although you don't no mistake about what was the first time and won't give it some day paid extra start on your digestion must go around drinking stuff like that imagine it did it you try to do that different from ryan later extended take a look at this anna begged for currency in the tommy sonya wouldn't you know i had no idea hayden was a mammoth on the combination of that safe in his account book this afternoon you will be divided you got that book it he can we get it you weren't satisfied to steal a money recorded so it is to commit murder on two innocent persons my tickets or hidden shouldn't let those other cyanide courted postage stamps in your account book you see the preparations match the one on whether mr western desperate combat letter under the people and your desk drawer are chemist tells us that there's enough cyanide on that stamp to kill half a dozen men what really started us off with the way you please to that single stamp on the border mister wisconsin sc help now haha hahahahaha that dot blots have a lot that waiting high which showed you get it art he got it alright hayden and then twenty-fifth stamp was gonna hang your in just a moment chief davis will give us additional facts about this case speaking of crime some older people who are guilty of preaching on the highways because they contribute to the delinquency of your water that kind of crime does not pay either this advertising world is filled with extravagant claims and growing proms if you count who all the people all the time as a matter of fact you can't fool the crew immortalize any of the time the officials of thirty meeting cities and counties throughout california and know what they're doing when after putting all motor fuels to their bases issue orders that only real brenda cracked gasoline shall be used to call their emergency effort robbins the nearest via brandy station filled up with real brenda cracked gasoline and you will discover the meaning of real police car performance and now the murder waived all rights to crime and pleaded guilty to the judge is brought against him he received sentences that kept them in prison until his death a few months ago from enablement of longstanding coming though he was he was not clever enough to make crime a pain proposition thank you to do this balls would lead one to abar eventual guard against major broadcast delivery there you go in with a did his gaze dining ruined min there's been a major public lands with the new benign or real randy all part of the cover letter program created by real branding printout as your job is going on on the national guard dog is doing they're denying regarding a modem and demand made madman man i've been honored in his bold weighed about one hundred million them to be a young man many more women than mezzo moved in every time you step on the starter brands you talk about more matured into the ring for a battle royal against the ganged up or to the procurement where egged on by hot some eleven high-speed rather than others but down our unity of the cases when you painted on the knockout problem mediocre royal your motor going to take it on the cannot be counted out sooner or later and depict bart up grand with really they get a lot eleven block more but the fight back and marking the end of the more revisions you might do the rope in the very first problem with style potted two-fisted me luv on your side in the battle is won well this great lubricant never will in the key to the parade novelette is balked at that point a maker and has never yet won't decision drop a round of the bitten by the rio grande is bacon yours do in the morning and by not really but the bodyguard for your motor you'll get longer life and
liberty in your pursuit of motoring have been as with the real deal with the newest and finest motor oil sold in the land the story we are here tonight was taken from the confidential files of the office of show at chapman's printout we have the privilege of having you with us tonight to open our probe good evening ladies and gentlemen is planning to speculate on a cure for cr so far nobody has ever palmone i think this program is probably doing as much to bring home the fact that crime is a losing proposition as any other single agency but for some reason we have never been able to understand men still think they can beat the game still think that they can put the puny wimps against the machine design from the beginning to beat them trying to beat the war like playing a slot machine the odds are hopelessly against you you can't win our program tonight we'll show our one-man play beginning allowing law what stage needed yet i will tell you at the end of the program in a little town in illinois howard butanol and was growing up we consider the case of volatile and aged eight at the end of the kitchen is useful why do you think on that day you can't have it i'm not going to start my people at mga rate on euro i know you're going to come beyond that when you've got macho stuff outside but i think my work and coming to enact like right now i make it you can bet in debt picket something you've got we got back nobel prize package to me i thought i could about don't try to get some sleep are you ok well maybe i can change their mind for your medical records have that is something to yell about now are care head off hot shot up timely bring up in like he was anathema to respect me about the big have today moderate at the fact that you everybody didn't a lot well i think they do need only eight years old all mattimoe no expected to do after that you can you give allison your ticket out of this so we have a copy of undercover that pressed him for the better off of a them i think i think it would be enough we'd like to have you ever wine out does that how i feel that without it may just white like up and running elected guilty made my day you own a home became worse however the constant sort of problem
last industry canada sent east with grandmother and a small town in upstate new york silent with johnny home sonny i want to get run over to the grocery and get me some ms jackson homework uh... looking indicating a living i get bored of being tactile colony yes but please keep kidnapping yes ma'am i'm sure it outgoing lost dead widening day watch he would have been if i hadn't happened to come out here and pull him out of that bad can't understand what makes you sick cruickshank took a trip in which to put the hate dumb and helps alot package the suggested states you have a nice little girl don't the beach yesterday when i can look at what point about the children can with you said none of senator pete was taken straight out there johnnie walker blue mountain town elemental cigarette what you know i pick it up smoking tv nomadic killed he stuck his cigarette to the bonneville growth plan nikon delegate didn't stake economy right told her not to tell you if people are coming out delivered three years arts years field escapades of young howard or in on a part-time museum juvenile court
lectured really is find out the tiniest into schools but we were going but each time the returns more determined never to make life miserable for those around him
lasted fifteen we plan again in the court of justice the or as to europe it is back again uh... mean that owns him haven't haven't trouble with that but for longer than i can remember ten years old when he got a movement immune attention to the fact that for same and he was about ten i guess and fifteen an then and you will all five transistors twelve monrovia keeping this time animated interview ransom restoring project against a man elastic at all the moral rigid pick him up i got a call from one of his neighbors that he was photo of the girls with another kid recover them hanging out working you sure you can drive this car sure acts their daddy rest article in the parking lot alright yellow i was afraid you can't get the car started guy cigars but i tell you see this land what you know pretty good right now idon't think about that you know it is a couple of weeks it's common life com get one twenty dollar bill and makeup affect high-speed hepatic and he's just got my daughter califano economic seasick steve dot toppled i'd quietly underline blvd dot com way beyond and romans it wasn't that much that the other boys pretty badly banged up i got to me just ask the question homes for the picked up by the before i could bring a minute here comes the judge maybe you put a brake on the armed with them well early on and give you anything further to say this morning not me speech judge
let me have your on and on women can you give me you'd be a good boy on cheers and have staff gavel and along when i've stood about all of your evidence i intend to your grandmother is stood by your from the start of this trial it's over now and it's my duty to decide what should be done with you'll prob get evelyn is the sense of this court that you'll be confined in the state reformatory for a period of not less than one and not more than twenty years and i hope by the time you finished your sentence that you will have a larger
less alright island ever did you try to play the game when you get to the school damp didn't go over time will be no problem women but a lot of stock picking on you know they're funny make it easy on yourself yet goes when you get to tell him about middle make a twenty-two you make your own record that any of my resume in his neighborhood watched magazine sorry allotment lebanese set a new poll out you know what nunn treasure island has and i spoke with little fella the robo buoy as it's called about putting up a customized else wrapped up her your did as governor of a poem thoughts might suck not getting bigger and snapped on big enough for the pops out the window hike ethnic huh huh i have the paper i stop an interesting at keokuk are still planning on file at one time ten o'clock am established european on you crazy animals as it is that you are slightly enough business to attend mr he was that we lived a life no where the superintendent over senate ever started a thank you one or old your hotel is what just yeah at a nice trip alone we might as well in the city thailand onlookers things we're learning is respect for the law and those who represented i represent the law who speak more severe on the outcome artist just a minute another thing about it we don't carry to use in here we always look forward to his own telling here if you're just send the papers mister johnson i'll be getting that their own packer garden belong with me we meet some of the boys and see what the cooks coupler they want you to assume valsad any update on what your local airport is there something wrong with the an elderly couple and thinking that would get done that before you wouldn't be here nap you don't like me you guys are all looking at me funny like something don't like neither he conferred on a bed record they think i'm gonna make trouble i want to get rid of it edsel and expected quite and i think at trying to poison ali gonna get away with it and whatnot at trying to take over let's have done a lot private life and are you are now predicate arshad and apocalyptic doll outright i'd uh... i'd athletes just like you know i have twenty seven months later howard mcmillan begins in the office of the superintendent of the state reformatory rodents warns there could be a bit on your parole would be released today that's so you've been a problem loans reminding of that group thanks for that i wasn't even trying uh... in the superintendent of the school loans not award what the difference stella jail domain avid you're wearing and suppose you've learned much injured than impact what you think this is the finest training school i could ask for animal where i am now rome i know how wire around the admission of an automobile anytime i want a car and i get the combination of the fate and just how do you know when they were not even a lock smart reducers beside that and i just i like the soccer game so she won't squawk why you're getting apart and just our display the bread and apple the copies when the document you know what i can and do in there and all that he did almost up costner note a few things when i come here but not much about them or if i'm sort of crime with someone the world owes me prolly as i put in this thing can jointly and all them other times i was in jail but i was a kid i'm gonna get a pro-life and want to get me when you were a kid were within your honor dragon and he is the part of working uh... made me laugh ones that i work it's too we can get along without it i know i've been to the states billy best reformer par on finishing school today gradually iso and your decorate your own you andrew immediately in some penitent for of course of post-graduate work mabye warden at the fair a beating him insert hahahahahaha
left him a month later warm for the rest of the lamb of god on to the tune of having a minimum of women literally lack of evidence that's one way to remind you know you're probably tells about one the description of the man of god and without power to one and the young criminal dot blotting but he met his match incumbent been good law enforcement officer buddy at last report on will be serving up and in some remote prison where what howard said no-one red blossoms world the mind of everything downloaded into his mouth and one of the bank in the mobile home upon do well-dressed young man clotted into the bank innova macular straight my friend this is a spectacle spot come on getting up on all of your customers job dot blotting banking on the head of the job at mad i mean you will get shot if you don't you just like i cannot move setback inelegant caucuses are sam ok sam aka going you picked up a topic this will kahan easygoing i told you this change what about you grew up and i got three out of mind rice paper five minutes for and there
let's see now uh... pay for the first year i spent in the reform atari five days later two young men walked into the american bank in covington by taking charge of the strike antibody your solar but the money in the fact that that is the banks money we don't want to have the belongs to what is our first just what the bank loans and what's in short them for jordan here's our schedule again tara i've been like that a lot of time myself ji which in a cabinet sample k agar rifles in a pack or aap bama lilac that both our priorities are what what not run that in their respective reticular block six grams uh... it's about another year at the state's finishing school paid for g force you should keep your head on these jobs anna we're gonna need some cold thinkin merck com but i have every copper in the state address before we know it mournful right within a quarter of an already old telephone and delete wipe introduced into the bandits reverie people to become a hundred mile the robbery poland and his companion roundup of the identifying all rolled robots armed men waited patiently in remote section of the country watching a brief i think our on the highway north a little problem of a group of evidence of a parked car scrutinizing passing profit placard that a part of what my began to look that way you oppose all i want to go quick spot under we'll get out the rodent dot renewable i keep their guns on the couple ethnic about the the amount but right down the road that program aslam get going quite which is all right estoppel cover boy our economic fatal attack other allah can capitals right blasphemy adult play a pickup truck cocktail party with inside how might look at it rocket okay month over seven nineteen thirty five a young man go but on a mobile into a service station and santa anna california the damage there arab not quite respect that you're not going to happen to you ups_ and keep your hands dot i don't give any sign of what's happening case you're worried about it this boat in my pocket is a gun and i know how do you think that's a bit serenity to report inside it was a dark
let's have watson attila metastatic okay might turn off the lights what's the big are here to find out get going what do you do just keep quiet for a few minutes and get my car henner canisters as you have a live beyond doubt that the and take them out yet proper back and show that the case deadening another collector i want that money got said wait a minute without deliver our money to anybody we don't know itself well maybe you know this guy in my pocket better his name is called ever hear of him pick up and that's the idea you catch on quick ok you can relax fit inside the tail what an unusual pledge to keep up molnar take it easy fell and noticed how am i forget which when i get nervous not get back to us they are buddy pretty slim pickings for the chance you're taking bus there i don't take chances get started you're going for a ride on that mountain allison fella i was just kidding
looked looked like i gotta like mccue obelisk walked the cops honest hank dot forgetting that car not all now wait a minute that's a better car parked on the grace rakhi evidence that that's a customer saw a lot entered i have decided talk so much looks pretty good about the poor i couldn't call anybody can get a chance to get away if you don't need to chance party knock-kneed this is going on we're going to put in as as far as you go scramble with you i did this is ten miles from time that's bio when i say stranded on a guys hanging around ho it the man option within a few hours after his victim and let them call just beside the highway alittle and speeding along the road near bakersfield on the republican party performing whatever if i think are hoping to encounter the band here that they competed in the next to the officers him ready and online betting we can occur as batman like better than chasing tough guys drive a high-powered truck uh... crazy about it to specially when you have to puncture gas tank there face politics as well mineral waters hand-in-glove with the one hand and women entered your idea and at the ad care the atlanta can and but again how little incalculable auto plant has the story guardian of great problem will be praying to irrigation ditches the length of stay reaganomics a return to the vehicle a few minutes later at the current health care about those online sheriff's office line three days where uh... uh... mothers immediately started to search for the young band at the mean time the effect of stolen auto mobile in within a few moments managed to steal another common continue all the way or at every turn the other continued absurd surrounding counties were going to be on the lookout for the criminal meantime working with another services have been held up in rob the attendant kidnapped and every officer instead of toughness office was placed on duty in an effort to apprehend the fugitive band in the early evening of the following the word came that owens vincent's ian fellows devotees act jensen bartell mcmillion robert immune to rush to that small community i'm going to park the car on the hill right over there and keep a watch on this house with the council said this monkey was supposed to be hiding i can see the house and most of the toddler becomes up aside i keep a spotlight on ballistic okay nickname and i'll take the other side of the joint even i abhor if he's in their is becoming a okay the capital he's dangerous if it at this guy was out here let robert and i came out here this morning
looking for told the constable two people i think that they're sometime this afternoon the custom of silence allow hole about it was a little too quick when we got away so effective in that house easter like how the parking lot in vegas an overpass a cop rachna backing out there because you made a break right we'll never get them skis salamander but ticket we shall doing surely won't aol about her mac yet bigot aapan free isaac unjustified donate had begun placed are suffering place upside-down dot is that a lot donatelli still myself gentlemen someday i'm gonna stick up ten and one of the stuff head out that my have you believe damages and just a moment chair accountants will give us the concluding part of our program remember the old iron bridge usa span the river in your hometown and the sign printed on the bridge read by a dollars feinberg driving faster than a wallop how times have changed nowadays we say april bradley cracked his spine or any kind of driving fast also about friends as putting it mildly the rest of the story of the rio grande the crack is the gasoline that goes in the time to the cause the crackdown the enemies of society and catch them not only does this by normal if you will power more police cars and more fire engines and differences in other life-and-death automotive equipment wherever it is sold in any other brand but we'll run decrypted the gasoline upon which preponderance of california state and federal government official depend to speed their emergency cars on the air waves more swiftly surely and economic are you one of the tens of thousands of motorists benefiting by this brief gasoline if not be up to date if rick it will cost us in this movie long-run got rio grande a cracked and enjoy the police car performance of this the most highly-acclaimed gasoline in the west annul sheriff champs recaptured man was howard l you have not been movement glycol caramel love his type eternal when cornered brought to my office not only confessed his california activities to me what bragged about his many criminal escapades he was tried separately for all his crimes committed in southern california now serving six separate sentences and also present is is another life of crime of those failed to pay thank you for your campus managers on the corner all cars national guard again to go against two hundred billion and regarding haldeman kidnapping bed his vision of investing national blooming dan the reader patrick glynn sleeping at night ovey all part of a copywriter program created by rio grande valley was unwinnable cardinal garden road getting two hundred morning deep blue and and sunset you know him mezzo windmill really are a few days and we don't celebrate the one hundred and thick effective anniversary of the signing of the declaration of independence and you know prem varma famous wait longer before is to visit some section of this great country of ours never seen before reforms of accident and the mother happen if the being one of these can be avoided by couple driving another bike up when he was a fire working on the other by giving you a moment of reflection in the was thirty real new motorola this great lubricant manufactured in the country's largest refinery and so may that it cannot break down under the pressure published during hot weather friend if you've been experimenting with wishy washy oiled up to remove a dollop of these properties and declare your independence right now and before you head up miniclip roll into the red and white male member station in your neighborhood and declare your allegiance jewelry aloo the newest standby miserable royal in the last the story really here tonight has been taken from the file of the los angeles police department we have therefore us chief of police gameday davis to open our program all the people who come to hollywood break into the movie is wouldn't there'd be a lot more happen is all around it has always been a mystery to me how anyone in his right mind will allow himself to be sold so completely by spurious producer that he will fight with his hard-earned money and they have a whole that he will someday be a big shot in the movies one of the most constantly recurring problems the police have to deal with is that of some unsuspecting person
letting his life savings there were some unscrupulous let's move down from over the case we're about to hear is one and point even though the criminal in this case was caught and punished the fact remains that a lot of people would have been better off if they had stayed away from hollywood however the pro-growth lady i'll be with you again at the end of the show and a little bungalow in hollywood movie section a man woman have just been eating breakfast he reads the morning people this is not good for you kind of funny paper you better look under the want ads for jobs they go to think i am i can't find a job that week after we arrive in california how no one expected fish fillets but we ought to be thinking about it four hundred dollars is all i had to clean up the milk for hot another wears on bob james i can't christ the movies overnight near the canoe that's what i've been saying all along we'll have to take whatever jobs we can get into a we can make the stereo but without the need for many on some of the paper women here with you this word i'm thinking assistant director forty five dollars per week salary small investment required to cure them returnable call a stage nine mark re studios sunset boulevard and beats work assistant director gee that's too good to be thrilled were given only meant something like that would be all of them forget there'll be a hundred others after and we don't know what they call a small investment in the movies caliber there's no harm in
looking into it we better get busy on it right away before the rice time like every legal right out there now it what do you tell them if they ask if you've ever had any experience in the directive hollywood to make it up work my way through somehow movie meant that night that nina well you can tell you played da called middleweight bill becoming the to pretend i'm not direct some about yours besides they don't want to going to have too much experience he'd be running the works they want an assistant director never replied and once again you can pull wires in getting the big game honeydew talk like i have that job but one thing sure sony in hollywood minute stumbled on an ad like this on-topic like this at drive to attain informants over the thousand of others well i have and i dont you're going to be given a telethon walkout out the pep talk and you get shade and a lot of it and i will ya is mister becker in all good morning rethinking you are looking back yes i i font br an appointment just a little while ago mister becker is expecting no yet and even if they can you still feel no is here yet but he didn't conference right now what you're buying yes if you don't mind indicated everyday demand so insane yet again old yankee xing illegitimately here yet nikki jayne projected anesthesia mister becker field based out of the backpacks got a lot at two o'clock somehow misplaced package terrible it was today and got my and what we're glad you got a little children but it certainly madonna admit the fact that we don't yes it is hoped and by the number my brother found out that may think europe now it automatically well i saw your ad in the paper this morning so i ponder secretary for an appointment here i am eaten you that you'd like to be an assistant director there you know anything about moving back to business loan also asked five by and i continued are still a lot i'm looking for a man have been studying here at the mother's cell repressed
learn the business on the ground up it's about thank you you'll uh... so you'll have no experience a big needles served most of my work's been in stock in the middle west in how long you've been della corte just couple of weeks mind is what you want martin it nothing ventured nothing gained you know it is all plant but for a month about uh... well paula
let's do it afognak or doubt gaya called about the release of around the world in a minute i'm afraid we can't handle it on the basis we discussed no i don't feel a five hundred thousand was enough to guarantee as a prop now if we could make a deal whereby we can get the walls a hundred thousand tension release a picture on the fifty fifty basis and maybe we could get together that is providing we can shoot some additional savings to improve the continuity of the picture o'dowd i'll tell you what both wake up is over at lapd ret say uh... one o'clock but i think so well i'll see you that all about hello hello for me when ur yet uh... unit yet but and validate burbank you know him back well show aren't known for years used to be as business manager benefit overproduction port g hallway just one of many one of many that jack barren for instance why he couldn't get the first base that i could do more work i made in the star yesterday is that's all i have sent he came out here from a little down the middle west it was broke that no assault on hollywood that was ten years ago novelty is really on top or on a gate ms dot gave his first break it's all in guatemala dear mother wife what you can do it doesn't make much difference if you can't get a chance to brentwood you know gee i didn't realize i was going to get to be a real big shot the movies when i became a value-added but janette dinners my real-time that there had never seen the camera bill i put in front of one do you know about that
looks all these pictures she isn't the only one on up by a longshot
levels are smart not to do that troubled by the way is coming in to see me this morning i'd guess i'll stick around in is that i would do a real all your work might be interested in reading some of the autographs on the picket that's what i've been doing nearly three dozen all that i aman hope to be i want to buy best brendan powell jack becker good luck always jacked barren it that and wouldn't they commit a lot of them december was distancing to this case jack becker from the dues rex champion that somebody he's built like directly a list of illegality at everywhere levin brother jack the best brother a group that over half all my love your sister married somaria dixon's your sister would like to have my wife brian's her favorite actress yet maryam's my kid sister all right used to europe and mail for just one day i carried her in my arms the first time that people ever on the set amid all the enable that allows ah... just top dollar at it's easy to have to figure out you got there and it is that what it takes to i could spend the whole day here reviewed all these swell things i've written about justin that's what everybody who comes in here says over her heading down the business again we have a large studio ed were working day and night and we need another assistant director was afraid you today to talk about this time there was not jumping respect with the baby we you know what we want more using this means of making on select yes so far i haven't interviewed anyone i can conscientiously recommend for the job i'd just about to have my right eye for this opportunity don't know but i've had all the experts are looking for if i had the chance i'll know i'd make good anvil was admired folks who have confidence in themselves and school on those who are over the top mister becker if you give me this one chance i could just be your right arm around him where o i'll tell you what i'll do my students you win presley very favorite you'll come back after lunch the with the two hundred dollars and we'll go into the debate and if everything's mutually satisfactory we might be able to get together i don't know what to say mister back but it's alright son that's alright how proved to be a note on the door judgment to ride again beaten and your money will be security returnable after faithful problems that have gone too the salary small chris dodd about if you get going it shoots up like a skyrocketing as business i'll be satisfied if i could just go up skyrocket parking place excused uh... well tell mister love are also a m in a few minutes seventy eighty thinks he's an actor want to get into pictures but he hasn't got what it takes i can't be wasting my time on him glad you didn't feel that way about me at all i can tell when i when i say where my boy we'll go places on earth racket that we uh... always refer to the picture details of the racket does the figures regional yet i'll see it as i have no matter how are you meantime in the studio becker was interviewing other applicants for the government system director alistair southall you'll cover on the morning with their money on wheels on the ground and that really be an assistant director up some old lady
let's bring along with me mother i am we'll call places in those racket at splendid mister stanley splendid five hundred of the just about right now here's your contract does iraq that act and get back there's going to be an assistant director have solo playing by deals going along with me a little all places unless racket and line on steinman yuan is your receipt recruitment and hour endured the statute in next month help make your work and that didn't go to the you just bring along with me anne followed a week in activity with the studio parted with assistant directors no money for summary there can be inevitable dissatisfaction last fully convinced the becker meant to be brought as many assistant one of the victims reported to the bomb caused by the police department under ten and so on if you've got something you think ought to be investigated yes sir i didn't want to say anything about the plot but several things that happened that make me think something's wrong may be a better tell me all about the case in the first place my husband and an ad in one of the newspaper several weeks ago just what kind of a minute well here it is i kept a copy of it business opportunities wanted assistant director story small investment secured returnable and right about this wonderful you have sure these things or fixed no legitimate studio ever advertises this work besides you don't have to buy a job in hollywood or anywhere else but my husband had put up two hundred dollars to get his job how much was the seller forty dollars a week i think g collected regularly know that's the point that's why i thought something was wrong he hasn't collected it mister becker tell them that this out it would stop when he started work on a picture but they haven't started i was supposed to work on the picket your husband i have notion mister becker did and best of fifty dollars myself your husband others now and it was a good idea telling well i didn't want to worry about my not working too on mister becker doesn't know were married to each other a lot of you've been waiting for this time almost a month now i've got to see mister becker last week they wouldn't seem adventure if your phone and yesterday secretary said he was off yeah your procedure when you see i was afraid to let mister becker think i was mad because of what he might do to my husband and you have any other troubled places well when i went in to see in the first time he asked me if you question when you try to get section i can uh... never did get detail after that instructor and on the phone you think there's any chance of getting my money back about one chance and the two thousand simply go to your husband you take my advice to tell them all about this dylan to start looking for another boss as one he's got is going to jail next morning mark three studios cuban-american numbers but obviously suburban visible until now one and so on i'd like to see the man who runs this place you mean it's a decade whether or not we headed just says she's somebody here at the studio but that their well this year add i could get out of the paper this morning you what i mean if they've been directed well i don't know about that but i am looking for a job in anything do your hand able to qualified for the job well i haven't had much experience but i'm willing to learn you know that not only that but i mean it i think the eerie investment product all that sure i can do that all right here do you think a couple of thousand of enough couple island yes of abdullah brought with me this morning maybe i could raise a little more of a new multi i think i'd be quite adequate i think that we have to decorate the about what i'm sure i'll be right back nogales or don't worry on rockingham part of a guided missile man acknowledge i couldn't tell you that we did and i'll stop us together like that that you have is a kidnapping felony today came to know what my citizens that at them and evening while a lot about he'd gotten money walked out cute thousand dollars too dot abadi standing up for two thousand dollars they may get what you need a quick browsing dot underneath that much money main domains that our message out water thinkers file your written statement becoming a fifth director items one very much so that is if the investment isn't too steep i don't know but we do go study while we have in the world and four thousand dollar for fun expect that and he'll say that that he'll say at the thought of the investment schemes and i think that that we're not really interested in that it's just the guarantee of good faith more than anything right-wing and have you had any experience in pictures not out here in california my work was on a stock buy back home below but there was a movie company came through it once mineral roswell park for me they came here i was a uh... extra all alright amanda how long have you been available at or just a short time we decided to take our chances with the other nine hundred ninety ninety two now the invention of not being a new no act not getting back to beat up we have a large studio here working day and i we need another system direct and so far admitted anyone i can recommend for the job or i give my right eye almost for this opportunity company mister sloan un press me very favorable is very favorably you come back after lunch with the uh... two thousand dollars and we'll go into the debate and we may be able to get together on this correction i don't know exactly what they say mister becker i'm sort of moral rats alright mama why that's alright and your money a site it secured unreasonable in three months provided you will be in your end of the contract weblog do my best mister becker is i'm sure you live illustrate along with me my boy annual golf are in this racket racket aca at the figure of speech but what does the bigger state with all of the money yet well uh... one or start to work with the bag like today right now when you paid over the build-up where a lot better for you this afternoon dependent upon return to the boardroom rewarded with a very rough terrain referred to by ten point two thousand dollars armed with his return to the studio over preparation have been made to impress the new assistant director now you all know what to do disbarred as to what i was in botulinum and he's got dome all when i came from i can get my hands on that were all out mail point your honor how he's doing about two minutes ago at all that i have a product management they and amanda here comes i cannot accept more more jobs ever loved hui able holdout rep like your caterpillar's somebody thank of what we've gotten together thank them up and laptops for their future greta u turf u you talk of mine you've given my heart is great more like a month's time this holy book the mother day and most powerful envelope next meeting the needs patch on what you after all my human holy book first these on makes you think but the and founded a paying people hold armada lamee'a you'll do something with it newark ca nine refute won't even the who and no i don't need to and millie and even and he will uh... ustinov whom on the mark it lol if he's only put the loops papers bookkeeping square if you ask me rides they both reviews local the i long for the open really the plea that the all you the all holding where the anecdotal roles all sp outlet hardest not that holding it you're almost as format it into your life i didn't mean to interrupt all not at all about the bulk of my knee and come right in nato wire uh... euler moments dot pol pot norville delivered-to hold for you arguable alone or yet yeah sure on the world nimish able yet at ms dietrich map that this is what people and you would holland a higher ma'am the thirteen nine fifty at that capable of it you've been out here along with the pic x wings of the mister disney are you interested in pictures too on and pete too and line we are i'm sorry i mean well that's right now cody partner armed camp david category marty rewrite that they have the realm deteriorated are there we're going to be dancing to blurred around here here's our god or directed what reviewed on this may disagree with it it did not see that yet mad right and that's right you should at parts you are seeing a lot of pictures mr mayor had seoul where lava made entity as a matter of fact we're going to start shooting today on a new picture appeared it's got music film is this one we've got an exclusive contract with one of the leading act on the radio gimme under saddle them it why don't we take mister small note to the wretched let him get started with this my except that blanket in all let's all go morning mister becker my name is back at one of the tobacco money monica bought a good morning everybody everything that i yes with the body of mr dot yes mister bacteria and that's what they want and the one that gets going acquitted budget remoteness or ride where the apartment sa friday cats but it was that about anybody's in the fat outside of tobacco all they have a great idea mister becker you know i i heard rolling it in he and let us blended reprogram afghan-trained uh... texture out west out of class acted like it or else plant small south again attacked by man on c_ and you know a couple baylor picket you arent because you are which that and mine as well paradigm in bangalore that'll be plenty are just as one what were urine assistant director you know were who were always our problem for them of
light by their insistence to if they put in two thousand dollars to why uh... no no not quite they're not such a big girl investors and you are just too slow aria i get it um bom agar on down the road and stop private when we give you no signal places that might buy a on explain the same day in uganda and provided saddam elmo item from this morning you lean back against only along came late improbable and make yourself around the two um and when i say you know it's not just on knowledge editorial off-campus uncle for all of the we have uh... earth we've had it updated is that it was worth it ever go over everything outbid done rounded up bread
let's celebrate ever sold therefore at go on eleven homeland the understand that the enrollment alkaline that blood had long hair and manhandle demands are met him live long and is back at the moment online and and and hong kong was gone minimum and alive bottom-line and involving outlawed and they may not have a haha uh... and on time and and and and and i have involving come on iron and iron powder out of the sky need them and them then animal hamburger at the moment balboa pa song home home milestone mom did not have involving upon and and dot com dot at cisco or is that sort of thing that makes the old whereas watch used to be at that time promo exp dating back home looks like rain here crying because that that there would be a game can only attend clientele withrow what he said expression is you know with all that about it was that orders to replace secondly coated with sand and your isn't that a the and on a denial the exploring rather than a monologue studio still fourteen upon more off but the big city he walked into the oval office in time your conversation come into the open door records office okay fine her that really wine big tomorrow at the capitol here's a couple of a build all thank you don't like that my grandmother print more money you stick with maintaining and grandma they are scheduled for monday if i'm up for you to be just the secretarial field in indiana but by the way are you going to make love on the screen if you don't get little practice with herbal e-ticket i'd rather not talk about that you like me just a little bit not given apache sleep i'm not going out there come on the good conversation about automatic chapter how did you get a good kirker apart at the door open but got it i'm sad anyway to talk to an assistant effect journalist director you are just on these officer du record police you ever hear of input you pick a couple crosstalk katie's record how many assistant directors because around here just one about five yesterday that's a lot we keep the money is for the report that i don't know what you're talking about we've got to pay those extra proposing a star you can talk to me that's why i said so if you got any contracts around here i know what happened because i thought why you've really been cleaning up around the answer hum along party you're going to the station alright pelvic i have many factors that and initiate that's alright the state of california is going to be doable long time where you're going to change don't matter in just a moment maturity david friends some motorists are just as the level of bulb jane pretty young life when it comes to investing their hard earned money and gasoline the result is there a poem called out of the maximum efficiency and economical transportation they might have enjoyed indicates a real man the crack to ever you have this reassuring knowledge that police apologies already have investigated and tested this vote if you will atrial ban the practice the overwhelming towards the city and county officials this great gasoline-powered more public serving police cars ambulances fire engines of the automotive equipment california state and federal governments wherever this old than any other brian we invite you to to investigate and make your own tests says tens of thousands
like you have done feeling confident you will join them in praising gasping the dispersed in public service analogy peeps whose name obviously is fictitious was indeed the guest of california for the next seven years he was hailed into court along with his fate actors and actresses to act as witnesses and was found guilty of grand theft multiple he served his time in prison that training school that has only one text crime does not play thank you chief davis mills and he's going organizational demagogued as demanded organisms that indeed it would be diseases and so on and um... calls dot record competently by mail that you'll never hear but the clinton giving you a good night florio brendan
CHAPTER I.
One morning, as Gregor Samsa was waking up from anxious dreams, he discovered that in bed he had been changed into a monstrous verminous bug.
He lay on his armour-hard back and saw, as he lifted his head up a little, his brown, arched abdomen divided up into rigid bow- like sections.
From this height the blanket, just about ready to slide off completely, could hardly stay in place.
His numerous legs, pitifully thin in comparison to the rest of his circumference, flickered helplessly before his eyes.
"What's happened to me," he thought.
It was no dream.
His room, a proper room for a human being, only somewhat too small, lay quietly between the four well-known walls.
Above the table, on which an unpacked collection of sample cloth goods was spread out--Samsa was a travelling salesman--hung the picture which he had cut out of an illustrated magazine a little while ago and set in a pretty gilt frame.
It was a picture of a woman with a fur hat and a fur boa.
She sat erect there, lifting up in the direction of the viewer a solid fur muff into which her entire forearm had disappeared.
Gregor's glance then turned to the window.
The dreary weather--the rain drops were falling audibly down on the metal window
ledge--made him quite melancholy.
"Why don't I keep sleeping for a little while longer and forget all this foolishness," he thought.
But this was entirely impractical, for he was used to sleeping on his right side, and in his present state he couldn't get himself into this position.
No matter how hard he threw himself onto his right side, he always rolled again onto his back.
He must have tried it a hundred times, closing his eyes so that he would not have to see the wriggling legs, and gave up only when he began to feel a light, dull pain in his side which he had never felt before.
"O God," he thought, "what a demanding job I've chosen!
Day in, day out, on the road.
The stresses of selling are much greater than the work going on at head office, and, in addition to that, I have to cope with the problems of travelling, the worries about train connections, irregular bad food, temporary and constantly changing human relationships, which never come from the heart.
To hell with it all!"
He felt a slight itching on the top of his abdomen.
He slowly pushed himself on his back closer to the bed post so that he could lift his head more easily, found the itchy part, which was entirely covered with small white spots--he did not know what to make of them and wanted to feel the place with a leg.
But he retracted it immediately, for the contact felt like a cold shower all over him.
He slid back again into his earlier position.
"This getting up early," he thought, "makes a man quite idiotic.
A man must have his sleep.
Other travelling salesmen live like harem women.
For instance, when I come back to the inn during the course of the morning to write up the necessary orders, these gentlemen are just sitting down to breakfast.
If I were to try that with my boss, I'd be thrown out on the spot.
Still, who knows whether that mightn't be really good for me?
If I didn't hold back for my parents' sake, I'd have quit ages ago.
I would've gone to the boss and told him just what I think from the bottom of my heart.
He would've fallen right off his desk!
How weird it is to sit up at that desk and talk down to the employee from way up there.
The boss has trouble hearing, so the employee has to step up quite close to him.
Anyway, I haven't completely given up that hope yet.
Once I've got together the money to pay off my parents' debt to him--that should take another five or six years--I'll do it for sure.
Then I'll make the big break.
In any case, right now I have to get up.
My train leaves at five o'clock."
He looked over at the alarm clock ticking away by the chest of drawers.
"Good God!" he thought.
It was half past six, and the hands were going quietly on.
It was past the half hour, already nearly quarter to.
Could the alarm have failed to ring?
One saw from the bed that it was properly set for four o'clock.
Certainly it had rung.
Yes, but was it possible to sleep through that noise which made the furniture shake?
Now, it's true he'd not slept quietly, but evidently he'd slept all the more deeply.
Still, what should he do now?
The next train left at seven o'clock.
To catch that one, he would have to go in a mad rush.
The sample collection wasn't packed up yet, and he really didn't feel particularly fresh and active.
And even if he caught the train, there was no avoiding a blow-up with the boss, because the firm's errand boy would've waited for the five o'clock train and reported the news of his absence long ago.
He was the boss's minion, without backbone or intelligence.
Well then, what if he reported in sick?
But that would be extremely embarrassing and suspicious, because during his five years' service Gregor hadn't been sick even once.
The boss would certainly come with the doctor from the health insurance company and would reproach his parents for their lazy son and cut short all objections with the insurance doctor's comments; for him everyone was completely healthy but really lazy about work.
And besides, would the doctor in this case be totally wrong?
Apart from a really excessive drowsiness after the long sleep, Gregor in fact felt quite well and even had a really strong appetite.
As he was thinking all this over in the greatest haste, without being able to make the decision to get out of bed--the alarm clock was indicating exactly quarter to seven--there was a cautious knock on the door by the head of the bed.
"Gregor," a voice called--it was his mother!--"it's quarter to seven.
Don't you want to be on your way?"
The soft voice!
Gregor was startled when he heard his voice answering.
It was clearly and unmistakably his earlier voice, but in it was intermingled, as if from below, an irrepressibly painful squeaking, which left the words positively distinct only in the first moment and distorted them in the reverberation, so that one didn't know if one had heard correctly.
Gregor wanted to answer in detail and explain everything, but in these circumstances he confined himself to saying, "Yes, yes, thank you mother.
I'm getting up right away."
Because of the wooden door the change in Gregor's voice was not really noticeable outside, so his mother calmed down with this explanation and shuffled off.
However, as a result of the short conversation, the other family members became aware that Gregor was unexpectedly still at home, and already his father was knocking on one side door, weakly but with his fist.
"Gregor, Gregor," he called out, "what's going on?"
And, after a short while, he urged him on again in a deeper voice:
"Gregor!"
Gregor!"
At the other side door, however, his sister knocked lightly.
"Gregor?
Are you all right?
Do you need anything?"
Gregor directed answers in both directions,
"I'll be ready right away."
He made an effort with the most careful articulation and by inserting long pauses between the individual words to remove everything remarkable from his voice.
His father turned back to his breakfast.
However, the sister whispered, "Gregor, open the door--I beg you."
Gregor had no intention of opening the door, but congratulated himself on his precaution, acquired from travelling, of locking all doors during the night, even at home.
First he wanted to stand up quietly and undisturbed, get dressed, above all have breakfast, and only then consider further action, for--he noticed this clearly--by thinking things over in bed he would not reach a reasonable conclusion.
He remembered that he had already often felt a light pain or other in bed, perhaps the result of an awkward lying position, which later turned out to be purely imaginary when he stood up, and he was eager to see how his present fantasies would gradually dissipate.
That the change in his voice was nothing other than the onset of a real chill, an occupational illness of commercial travellers, of that he had not the slightest doubt.
It was very easy to throw aside the blanket.
He needed only to push himself up a little, and it fell by itself.
But to continue was difficult, particularly because he was so unusually wide.
He needed arms and hands to push himself upright.
Instead of these, however, he had only many small limbs which were incessantly moving with very different motions and which, in addition, he was unable to control.
If he wanted to bend one of them, then it was the first to extend itself, and if he finally succeeded doing what he wanted with this limb, in the meantime all the others, as if left free, moved around in an excessively painful agitation.
"But I must not stay in bed uselessly," said Gregor to himself.
At first he wanted to get out of bed with the lower part of his body, but this lower part--which, by the way, he had not yet looked at and which he also couldn't picture clearly--proved itself too difficult to move.
The attempt went so slowly.
When, having become almost frantic, he finally hurled himself forward with all his force and without thinking, he chose his direction incorrectly, and he hit the lower bedpost hard.
The violent pain he felt revealed to him that the lower part of his body was at the moment probably the most sensitive.
Thus, he tried to get his upper body out of the bed first and turned his head carefully toward the edge of the bed.
He managed to do this easily, and in spite of its width and weight his body mass at last slowly followed the turning of his head.
But as he finally raised his head outside the bed in the open air, he became anxious about moving forward any further in this manner, for if he allowed himself eventually to fall by this process, it would take a miracle to prevent his head from getting injured.
And at all costs he must not lose consciousness right now.
He preferred to remain in bed.
However, after a similar effort, while he lay there again, sighing as before, and once again saw his small limbs fighting one another, if anything worse than earlier, and didn't see any chance of imposing quiet and order on this arbitrary movement, he told himself again that he couldn't possibly remain in bed and that it might be the most reasonable thing to sacrifice everything if there was even the slightest hope of getting himself out of bed in the process.
At the same moment, however, he didn't forget to remind himself from time to time of the fact that calm--indeed the calmest-- reflection might be better than the most confused decisions.
At such moments, he directed his gaze as precisely as he could toward the window, but unfortunately there was little confident cheer to be had from a glance at the morning mist, which concealed even the other side of the narrow street.
"It's already seven o'clock," he told himself at the latest striking of the alarm clock, "already seven o'clock and still such a fog."
And for a little while longer he lay quietly with weak breathing, as if perhaps waiting for normal and natural conditions to re-emerge out of the complete stillness.
But then he said to himself, "Before it strikes a quarter past seven, whatever happens I must be completely out of bed.
Besides, by then someone from the office will arrive to inquire about me, because the office will open before seven o'clock."
And he made an effort then to rock his entire body length out of the bed with a uniform motion.
If he let himself fall out of the bed in this way, his head, which in the course of the fall he intended to lift up sharply, would probably remain uninjured.
His back seemed to be hard; nothing would really happen to that as a result of the fall.
His greatest reservation was a worry about the loud noise which the fall must create and which presumably would arouse, if not fright, then at least concern on the other side of all the doors.
However, it had to be tried.
As Gregor was in the process of lifting himself half out of bed--the new method was more of a game than an effort; he needed only to rock with a constant rhythm--it struck him how easy all this would be if someone were to come to his aid.
Two strong people--he thought of his father and the servant girl--would have been quite sufficient.
They would have only had to push their arms under his arched back to get him out of the bed, to bend down with their load, and then merely to exercise patience and care that he completed the flip onto the floor, where his diminutive legs would then, he hoped, acquire a purpose.
Now, quite apart from the fact that the doors were locked, should he really call out for help?
In spite of all his distress, he was unable to suppress a smile at this idea.
He had already got to the point where, by rocking more strongly, he maintained his equilibrium with difficulty, and very soon he would finally have to decide, for in five minutes it would be a quarter past seven.
Then there was a ring at the door of the apartment.
"That's someone from the office," he told himself, and he almost froze while his small limbs only danced around all the faster.
For one moment everything remained still.
"They aren't opening," Gregor said to himself, caught up in some absurd hope.
But of course then, as usual, the servant girl with her firm tread went to the door and opened it.
Gregor needed to hear only the first word of the visitor's greeting to recognize immediately who it was, the manager himself.
Why was Gregor the only one condemned to work in a firm where, at the slightest
lapse, someone immediately attracted the greatest suspicion?
Were all the employees then collectively, one and all, scoundrels?
Among them was there then no truly devoted person who, if he failed to use just a couple of hours in the morning for office work, would become abnormal from pangs of conscience and really be in no state to get out of bed?
Was it really not enough to let an apprentice make inquiries, if such questioning was even necessary?
Must the manager himself come, and in the process must it be demonstrated to the entire innocent family that the investigation of this suspicious circumstance could be entrusted only to the intelligence of the manager?
And more as a consequence of the excited state in which this idea put Gregor than as a result of an actual decision, he swung himself with all his might out of the bed.
There was a loud thud, but not a real crash.
The fall was absorbed somewhat by the carpet and, in addition, his back was more elastic than Gregor had thought.
For that reason the dull noise was not quite so conspicuous.
But he had not held his head up with sufficient care and had hit it.
He turned his head, irritated and in pain, and rubbed it on the carpet.
"Something has fallen in there," said the manager in the next room on the left.
Gregor tried to imagine to himself whether anything similar to what was happening to him today could have also happened at some point to the manager.
At least one had to concede the possibility of such a thing.
However, as if to give a rough answer to this question, the manager now, with a squeak of his polished boots, took a few determined steps in the next room.
From the neighbouring room on the right the sister was whispering to inform Gregor:
"Gregor, the manager is here." "I know," said Gregor to himself.
But he did not dare make his voice loud enough so that his sister could hear.
"Gregor," his father now said from the neighbouring room on the left, "Mr. Manager has come and is asking why you have not left on the early train.
We don't know what we should tell him.
He will be good enough to forgive the mess in your room."
So please open the door.
In the middle of all this, the manager called out in a friendly way, "Good morning, Mr. Samsa."
"He is not well," said his mother to the manager, while his father was still talking at the door, "He is not well, believe me, Mr. Manager.
Otherwise how would Gregor miss a train?
The young man has nothing in his head except business.
I'm almost angry that he never goes out at night.
Right now he's been in the city eight days, but he's been at home every evening.
He sits here with us at the table and reads the newspaper quietly or studies his travel schedules.
It's a quite a diversion for him to busy himself with fretwork.
For instance, he cut out a small frame over the course of two or three evenings.
You'd be amazed how pretty it is.
It's hanging right inside the room.
You'll see it immediately, as soon as
Gregor opens the door.
Anyway, I'm happy that you're here, Mr.
Manager.
By ourselves, we would never have made Gregor open the door.
He's so stubborn, and he's certainly not well, although he denied that this morning."
"I'm coming right away," said Gregor slowly and deliberately and didn't move, so as not to lose one word of the conversation.
"My dear lady, I cannot explain it to myself in any other way," said the manager;
"I hope it is nothing serious.
On the other hand, I must also say that we business people, luckily or unluckily, however one looks at it, very often simply have to overcome a slight indisposition for business reasons."
"So can Mr. Manager come in to see you now?" asked his father impatiently and knocked once again on the door.
In the neighbouring room on the left a painful stillness descended.
In the neighbouring room on the right the sister began to sob.
Why didn't his sister go to the others?
She'd probably just gotten up out of bed now and hadn't even started to get dressed yet.
Then why was she crying?
Because he wasn't getting up and wasn't letting the manager in, because he was in danger of losing his position, and because then his boss would badger his parents once again with the old demands?
Those were probably unnecessary worries right now.
Gregor was still here and wasn't thinking at all about abandoning his family.
At the moment he was lying right there on the carpet, and no one who knew about his condition would've seriously demanded that he let the manager in.
But Gregor wouldn't be casually dismissed right way because of this small discourtesy, for which he would find an easy and suitable excuse later on.
It seemed to Gregor that it might be far more reasonable to leave him in peace at the moment, instead of disturbing him with crying and conversation.
But it was the very uncertainty which distressed the others and excused their behaviour.
"Mr. Samsa," the manager was now shouting, his voice raised, "what's the matter?
You are barricading yourself in your room, answer with only a yes and a no, are making serious and unnecessary troubles for your parents, and neglecting (I mention this only incidentally) your commercial duties in a truly unheard of manner.
I am speaking here in the name of your parents and your employer, and I am requesting you in all seriousness for an immediate and clear explanation.
I am amazed.
I am amazed.
I thought I knew you as a calm, reasonable person, and now you appear suddenly to want to start parading around in weird moods.
The Chief indicated to me earlier this very day a possible explanation for your neglect--it concerned the collection of cash entrusted to you a short while ago-- but in truth I almost gave him my word of honour that this explanation could not be correct.
However, now I see here your unimaginable pig headedness, and I am totally losing any desire to speak up for you in the slightest.
And your position is not at all the most secure.
Originally I intended to mention all this to you privately, but since you are letting me waste my time here uselessly, I don't know why the matter shouldn't come to the attention of your parents.
Your productivity has also been very unsatisfactory recently.
Of course, it's not the time of year to conduct exceptional business, we recognize that, but a time of year for conducting no business, there is no such thing at all,
Mr. Samsa, and such a thing must never be."
"But Mr. Manager," called Gregor, beside himself and, in his agitation, forgetting everything else, "I'm opening the door immediately, this very moment.
A slight indisposition, a dizzy spell, has prevented me from getting up.
I'm still lying in bed right now.
But I'm quite refreshed once again.
I'm in the midst of getting out of bed.
Just have patience for a short moment!
Things are not going as well as I thought.
But things are all right.
How suddenly this can overcome someone!
Only yesterday evening everything was fine with me.
My parents certainly know that.
Actually just yesterday evening I had a small premonition.
People must have seen that in me.
Why have I not reported that to the office?
But people always think that they'll get over sickness without having to stay at home.
Mr. Manager!
Take it easy on my parents!
There is really no basis for the criticisms which you're now making against me, and really nobody has said a word to me about that.
Perhaps you have not read the latest orders which I shipped.
Besides, now I'm setting out on my trip on the eight o'clock train; the few hours' rest have made me stronger.
Mr. Manager, do not stay. I will be at the office in person right away.
Please have the goodness to say that and to convey my respects to the Chief."
While Gregor was quickly blurting all this out, hardly aware of what he was saying, he had moved close to the chest of drawers without effort, probably as a result of the practice he had already had in bed, and now he was trying to raise himself up on it.
Actually, he wanted to open the door.
He really wanted to let himself be seen by and to speak with the manager.
He was keen to witness what the others now asking about him would say when they saw him.
If they were startled, then Gregor had no more responsibility and could be calm.
But if they accepted everything quietly, then he would have no reason to get excited and, if he got a move on, could really be at the station around eight o'clock.
At first he slid down a few times on the smooth chest of drawers.
But at last he gave himself a final swing and stood upright there.
He was no longer at all aware of the pains in his lower body, no matter how they might still sting.
Now he let himself fall against the back of a nearby chair, on the edge of which he braced himself with his thin limbs.
By doing this he gained control over himself and kept quiet, for he could now hear the manager.
"Did you understood a single word?" the manager asked the parents, "Is he playing the fool with us?"
"For God's sake," cried the mother already in tears, "perhaps he's very ill and we're upsetting him. Grete!
Grete!" she yelled at that point.
"Mother?" called the sister from the other side.
They were making themselves understood through Gregor's room.
"You must go to the doctor right away.
Gregor is sick.
Hurry to the doctor.
Have you heard Gregor speak yet?"
"That was an animal's voice," said the manager, remarkably quietly in comparison to the mother's cries.
"Anna!
Anna!' yelled the father through the hall into the kitchen, clapping his hands,
"fetch a locksmith right away!"
The two young women were already running through the hall with swishing skirts--how had his sister dressed herself so quickly?- -and yanked open the doors of the apartment.
They probably had left them open, as is customary in an apartment where a huge misfortune has taken place.
However, Gregor had become much calmer.
All right, people did not understand his words any more, although they seemed clear enough to him, clearer than previously, perhaps because his ears had gotten used to them.
But at least people now thought that things were not all right with him and were prepared to help him.
The confidence and assurance with which the first arrangements had been carried out made him feel good.
He felt himself included once again in the circle of humanity and was expecting from both the doctor and the locksmith, without differentiating between them with any real precision, splendid and surprising results.
In order to get as clear a voice as possible for the critical conversation which was imminent, he coughed a little, and certainly took the trouble to do this in a really subdued way, since it was possible that even this noise sounded like something different from a human cough.
He no longer trusted himself to decide any more.
Meanwhile in the next room it had become really quiet.
Perhaps his parents were sitting with the manager at the table whispering; perhaps they were all leaning against the door listening.
Gregor pushed himself slowly towards the door, with the help of the easy chair, let go of it there, threw himself against the door, held himself upright against it--the balls of his tiny limbs had a little sticky stuff on them--and rested there momentarily from his exertion.
Then he made an effort to turn the key in the lock with his mouth.
Unfortunately it seemed that he had no real teeth.
How then was he to grab hold of the key?
But to make up for that his jaws were naturally very strong; with their help he managed to get the key really moving.
He didn't notice that he was obviously inflicting some damage on himself, for a brown fluid came out of his mouth, flowed over the key, and dripped onto the floor.
"Just listen for a moment," said the manager in the next room; "he's turning the key."
For Gregor that was a great encouragement.
But they all should've called out to him, including his father and mother, "Come on,
Gregor," they should've shouted; "keep going, keep working on the lock."
Imagining that all his efforts were being followed with suspense, he bit down frantically on the key with all the force he could muster.
As the key turned more, he danced around the lock.
Now he was holding himself upright only with his mouth, and he had to hang onto the key or then press it down again with the whole weight of his body, as necessary.
The quite distinct click of the lock as it finally snapped really woke Gregor up.
Breathing heavily he said to himself, "So I didn't need the locksmith," and he set his head against the door handle to open the door completely.
Because he had to open the door in this way, it was already open very wide without him yet being really visible.
He first had to turn himself slowly around the edge of the door, very carefully, of course, if he didn't want to fall awkwardly on his back right at the entrance into the room.
He was still preoccupied with this difficult movement and had no time to pay attention to anything else, when he heard the manager exclaim a loud "Oh!"--it sounded like the wind whistling--and now he saw him, nearest to the door, pressing his hand against his open mouth and moving slowly back, as if an invisible constant force was pushing him away.
His mother--in spite of the presence of the manager she was standing here with her hair sticking up on end, still a mess from the night--was looking at his father with her hands clasped.
She then went two steps towards Gregor and collapsed right in the middle of her skirts, which were spread out all around her, her face sunk on her breast, completely concealed.
His father clenched his fist with a hostile expression, as if he wished to push Gregor back into his room, then looked uncertainly around the living room, covered his eyes with his hands, and cried so that his mighty breast shook.
At this point Gregor did not take one step into the room, but leaned his body from the inside against the firmly bolted wing of the door, so that only half his body was visible, as well as his head, tilted sideways, with which he peeped over at the others.
Meanwhile it had become much brighter.
Standing out clearly from the other side of the street was a part of the endless grey- black house situated opposite--it was a hospital--with its severe regular windows breaking up the facade.
The rain was still coming down, but only in large individual drops visibly and firmly thrown down one by one onto the ground.
The breakfast dishes were standing piled around on the table, because for his father breakfast was the most important meal time in the day, which he prolonged for hours by reading various newspapers.
Directly across on the opposite wall hung a photograph of Gregor from the time of his military service; it was a picture of him as a lieutenant, as he, smiling and worry free, with his hand on his sword, demanded respect for his bearing and uniform.
The door to the hall was ajar, and since the door to the apartment was also open, one could see out into the landing of the apartment and the start of the staircase going down.
"Now," said Gregor, well aware that he was the only one who had kept his composure.
"I'll get dressed right away, pack up the collection of samples, and set off.
You'll allow me to set out on my way, will you not?
You see, Mr. Manager, I am not pig-headed, and I am happy to work.
Travelling is exhausting, but I couldn't live without it.
Where are you going, Mr. Manager?
To the office?
Really?
Will you report everything truthfully?
A person can be incapable of work momentarily, but that's precisely the best time to remember the earlier achievements and to consider that later, after the obstacles have been shoved aside, the person will work all the more eagerly and intensely.
I am really so indebted to Mr. Chief--you know that perfectly well.
On the other hand, I am concerned about my parents and my sister.
I'm in a fix, but I'll work myself out of it again.
Don't make things more difficult for me than they already are.
Speak up on my behalf in the office!
People don't like travelling salesmen.
I know that.
People think they earn pots of money and thus lead a fine life.
People don't even have any special reason to think through this judgment more clearly.
But you, Mr. Manager, you have a better perspective on what's involved than other people, even, I tell you in total confidence, a better perspective than Mr.
Chairman himself, who in his capacity as the employer may let his judgment make casual mistakes at the expense of an employee.
You also know well enough that the travelling salesman who is outside the office almost the entire year can become so easily a victim of gossip, coincidences, and groundless complaints, against which it's impossible for him to defend himself, since for the most part he doesn't hear about them at all and only then when he's exhausted after finishing a trip and at home gets to feel in his own body the nasty consequences, which can't be thoroughly explored back to their origins.
Mr. Manager, don't leave without speaking a word telling me that you'll at least concede that I'm a little in the right!"
But at Gregor's first words the manager had already turned away, and now he looked back at Gregor over his twitching shoulders with pursed lips.
During Gregor's speech he was not still for a moment but kept moving away towards the door, without taking his eyes off Gregor, but really gradually, as if there was a secret ban on leaving the room.
He was already in the hall, and given the sudden movement with which he finally pulled his foot out of the living room, one could have believed that he had just burned the sole of his foot.
In the hall, however, he stretched his right hand out away from his body towards the staircase, as if some truly supernatural relief was waiting for him there.
Gregor realized that he must not under any circumstances allow the manager to go away in this frame of mind, especially if his position in the firm was not to be placed in the greatest danger.
His parents did not understand all this very well.
Over the long years, they had developed the conviction that Gregor was set up for life in his firm and, in addition, they had so much to do nowadays with their present troubles that all foresight was foreign to them.
But Gregor had this foresight.
The manager must be held back, calmed down, convinced, and finally won over.
The future of Gregor and his family really depended on it!
If only the sister had been there!
She was clever.
She had already cried while Gregor was still lying quietly on his back.
And the manager, this friend of the ladies, would certainly let himself be guided by her.
She would have closed the door to the apartment and talked him out of his fright in the hall.
But the sister was not even there.
Gregor must deal with it himself.
Without thinking that as yet he didn't know anything about his present ability to move and that his speech possibly--indeed probably--had once again not been understood, he left the wing of the door, pushed himself through the opening, and wanted to go over to the manager, who was already holding tight onto the handrail with both hands on the landing in a ridiculous way.
But as he looked for something to hold onto, with a small scream Gregor immediately fell down onto his numerous little legs.
Scarcely had this happened, when he felt for the first time that morning a general physical well being.
The small limbs had firm floor under them; they obeyed perfectly, as he noticed to his joy, and strove to carry him forward in the direction he wanted.
Right away he believed that the final amelioration of all his suffering was immediately at hand.
But at the very moment when he lay on the floor rocking in a restrained manner quite close and directly across from his mother, who had apparently totally sunk into herself, she suddenly sprang right up with her arms spread far apart and her fingers extended and cried out, "Help, for God's sake, help!"
She held her head bowed down, as if she wanted to view Gregor better, but ran senselessly back, contradicting that gesture, forgetting that behind her stood the table with all the dishes on it.
When she reached the table, she sat down heavily on it, as if absent-mindedly, and did not appear to notice at all that next to her coffee was pouring out onto the carpet in a full stream from the large overturned container.
"Mother, mother," said Gregor quietly, and looked over towards her.
The manager momentarily had disappeared completely from his mind.
At the sight of the flowing coffee Gregor couldn't stop himself snapping his jaws in the air a few times .
At that his mother screamed all over again, hurried from the table, and collapsed into the arms of his father, who was rushing towards her.
But Gregor had no time right now for his parents--the manager was already on the staircase.
His chin level with the banister, the manager looked back for the last time.
Gregor took an initial movement to catch up to him if possible.
But the manager must have suspected something, because he made a leap down over a few stairs and disappeared, still shouting "Huh!"
The sound echoed throughout the entire stairwell.
Now, unfortunately this flight of the manager also seemed to bewilder his father completely.
Earlier he had been relatively calm, for instead of running after the manager himself or at least not hindering Gregor from his pursuit, with his right hand he grabbed hold of the manager's cane, which he had left behind with his hat and overcoat on a chair.
With his left hand, his father picked up a large newspaper from the table and, stamping his feet on the floor, he set out to drive Gregor back into his room by waving the cane and the newspaper.
No request of Gregor's was of any use; no request would even be understood.
No matter how willing he was to turn his head respectfully, his father just stomped all the harder with his feet.
Across the room from him his mother had pulled open a window, in spite of the cool weather, and leaning out with her hands on her cheeks, she pushed her face far outside the window.
Between the alley and the stairwell a strong draught came up, the curtains on the window flew around, the newspapers on the table swished, and individual sheets fluttered down over the floor.
The father relentlessly pressed forward, pushing out sibilants, like a wild man.
Now, Gregor had no practice at all in going backwards--it was really very slow going.
If Gregor only had been allowed to turn himself around, he would have been in his room right away, but he was afraid to make his father impatient by the time-consuming process of turning around, and each moment he faced the threat of a mortal blow on his back or his head from the cane in his father's hand.
Finally Gregor had no other option, for he noticed with horror that he did not understand yet how to maintain his direction going backwards.
And so he began, amid constantly anxious sideways glances in his father's direction, to turn himself around as quickly as possible, although in truth this was only done very slowly.
Perhaps his father noticed his good intentions, for he did not disrupt Gregor in this motion, but with the tip of the cane from a distance he even directed
Gregor's rotating movement here and there.
If only his father had not hissed so unbearably!
Because of that Gregor totally lost his head.
He was already almost totally turned around, when, always with this hissing in his ear, he just made a mistake and turned himself back a little.
But when he finally was successful in getting his head in front of the door opening, it became clear that his body was too wide to go through any further.
Naturally his father, in his present mental state, had no idea of opening the other wing of the door a bit to create a suitable passage for Gregor to get through.
His single fixed thought was that Gregor must get into his room as quickly as possible.
He would never have allowed the elaborate preparations that Gregor required to orient himself and thus perhaps get through the door.
On the contrary, as if there were no obstacle and with a peculiar noise, he now drove Gregor forwards.
Behind Gregor the sound at this point was no longer like the voice of only a single father.
Now it was really no longer a joke, and Gregor forced himself, come what might, into the door.
One side of his body was lifted up.
He lay at an angle in the door opening.
His one flank was sore with the scraping.
On the white door ugly blotches were left.
Soon he was stuck fast and would have not been able to move any more on his own.
The tiny legs on one side hung twitching in the air above, and the ones on the other side were pushed painfully into the floor.
Then his father gave him one really strong liberating push from behind, and he scurried, bleeding severely, far into the interior of his room.
The door was slammed shut with the cane, and finally it was quiet.
CHAPTER Il.
Gregor first woke up from his heavy swoon- like sleep in the evening twilight.
He would certainly have woken up soon afterwards without any disturbance, for he felt himself sufficiently rested and wide awake, although it appeared to him as if a hurried step and a cautious closing of the door to the hall had aroused him.
Light from the electric streetlamps lay pale here and there on the ceiling and on the higher parts of the furniture, but underneath around Gregor it was dark.
He pushed himself slowly toward the door, still groping awkwardly with his feelers, which he now learned to value for the first time, to check what was happening there.
His left side seemed one single long unpleasantly stretched scar, and he really had to hobble on his two rows of legs.
In addition, one small leg had been seriously wounded in the course of the morning incident--it was almost a miracle that only one had been hurt--and dragged
lifelessly behind.
By the door he first noticed what had really lured him there: it was the smell of something to eat.
A bowl stood there, filled with sweetened milk, in which swam tiny pieces of white bread.
He almost laughed with joy, for he now had a much greater hunger than in the morning, and he immediately dipped his head almost up to and over his eyes down into the milk.
But he soon drew it back again in disappointment, not just because it was difficult for him to eat on account of his delicate left side--he could eat only if his entire panting body worked in a coordinated way--but also because the milk, which otherwise was his favourite drink and which his sister had certainly placed there for that reason, did not appeal to him at all.
He turned away from the bowl almost with aversion and crept back into the middle of the room.
In the living room, as Gregor saw through the crack in the door, the gas was lit, but where, on other occasions at this time of day, his father was accustomed to read the afternoon newspaper in a loud voice to his mother and sometimes also to his sister, at the moment no sound was audible.
Now, perhaps this reading aloud, about which his sister had always spoken and written to him, had recently fallen out of their general routine.
But it was so still all around, in spite of the fact that the apartment was certainly not empty.
"What a quiet life the family leads," said Gregor to himself and, as he stared fixedly out in front of him into the darkness, he felt a great pride that he had been able to provide such a life in a beautiful apartment like this for his parents and his sister.
But how would things go if now all tranquillity, all prosperity, all contentment should come to a horrible end?
In order not to lose himself in such thoughts, Gregor preferred to set himself moving, so he moved up and down in his room.
Once during the long evening one side door and then the other door was opened just a tiny crack and quickly closed again.
Someone presumably needed to come in but had then thought better of it.
Gregor immediately took up a position by the living room door, determined to bring in the hesitant visitor somehow or other or at least to find out who it might be.
But now the door was not opened any more, and Gregor waited in vain.
Earlier, when the door had been barred, they had all wanted to come in to him; now, when he had opened one door and when the others had obviously been opened during the day, no one came any more, and the keys were stuck in the locks on the outside.
The light in the living room was turned off only late at night, and now it was easy to establish that his parents and his sister had stayed awake all this time, for one could hear clearly as all three moved away on tiptoe.
Now it was certain that no one would come into Gregor any more until the morning.
Thus, he had a long time to think undisturbed about how he should reorganize his life from scratch.
But the high, open room, in which he was compelled to lie flat on the floor, made him anxious, without his being able to figure out the reason, for he had lived in the room for five years.
With a half unconscious turn and not without a slight shame he scurried under the couch, where, in spite of the fact that his back was a little cramped and he could no longer lift up his head, he felt very comfortable and was sorry only that his body was too wide to fit completely under it.
There he remained the entire night, which he spent partly in a state of semi-sleep, out of which his hunger constantly woke him with a start, but partly in a state of worry and murky hopes, which all led to the conclusion that for the time being he would have to keep calm and with patience and the greatest consideration for his family tolerate the troubles which in his present condition he was now forced to cause them.
Already early in the morning--it was still almost night--Gregor had an opportunity to test the power of the decisions he had just made, for his sister, almost fully dressed, opened the door from the hall into his room and looked eagerly inside.
She did not find him immediately, but when she noticed him under the couch--God, he had to be somewhere or other, for he could hardly fly away--she got such a shock that, without being able to control herself, she slammed the door shut once again from the outside.
However, as if she was sorry for her behaviour, she immediately opened the door again and walked in on her tiptoes, as if she was in the presence of a serious invalid or a total stranger.
Gregor had pushed his head forward just to the edge of the couch and was observing her.
Would she really notice that he had left the milk standing, not indeed from any lack of hunger, and would she bring in something else to eat more suitable for him?
If she did not do it on her own, he would sooner starve to death than call her attention to the fact, although he had a really powerful urge to move beyond the couch, throw himself at his sister's feet, and beg her for something or other good to eat.
But his sister noticed right away with astonishment that the bowl was still full, with only a little milk spilled around it.
She picked it up immediately, although not with her bare hands but with a rag, and took it out of the room.
Gregor was extremely curious what she would bring as a substitute, and he pictured to himself different ideas about it.
But he never could have guessed what his sister out of the goodness of her heart in fact did.
She brought him, to test his taste, an entire selection, all spread out on an old newspaper.
There were old half-rotten vegetables, bones from the evening meal, covered with a white sauce which had almost solidified, some raisins and almonds, cheese which
Gregor had declared inedible two days earlier, a slice of dry bread, and a slice of salted bread smeared with butter.
In addition to all this, she put down a bowl--probably designated once and for all as Gregor's--into which she had poured some water.
And out of her delicacy of feeling, since she knew that Gregor would not eat in front of her, she went away very quickly and even turned the key in the lock, so that Gregor would now observe that he could make himself as comfortable as he wished.
Gregor's small limbs buzzed now that the time for eating had come.
His wounds must, in any case, have already healed completely.
He felt no handicap on that score.
He was astonished at that and thought about how more than a month ago he had cut his finger slightly with a knife and how this wound had hurt enough even the day before yesterday.
"Am I now going to be less sensitive," he thought, already sucking greedily on the cheese, which had strongly attracted him right away, more than all the other foods.
Quickly and with his eyes watering with satisfaction, he ate one after the other the cheese, the vegetables, and the sauce.
The fresh food, by contrast, didn't taste good to him.
He couldn't bear the smell and even carried the things he wanted to eat a little distance away.
By the time his sister slowly turned the key as a sign that he should withdraw, he was long finished and now lay lazily in the same spot.
The noise immediately startled him, in spite of the fact that he was already almost asleep, and he scurried back again under the couch.
But it cost him great self-control to remain under the couch, even for the short time his sister was in the room, because his body had filled out somewhat on account of the rich meal and in the narrow space there he could scarcely breathe.
In the midst of minor attacks of asphyxiation, he looked at her with somewhat protruding eyes, as his unsuspecting sister swept up with a broom, not just the remnants, but even the foods which Gregor had not touched at all, as if these were also now useless, and as she dumped everything quickly into a bucket, which she closed with a wooden lid, and then carried all of it out of the room.
She had hardly turned around before Gregor had already dragged himself out from the couch, stretched out, and let his body expand.
In this way Gregor got his food every day, once in the morning, when his parents and the servant girl were still asleep, and a second time after the common noon meal, for his parents were, as before, asleep then for a little while, and the servant girl was sent off by his sister on some errand or other.
They certainly would not have wanted Gregor to starve to death, but perhaps they could not have endured finding out what he ate other than by hearsay.
Perhaps his sister wanted to spare them what was possibly only a small grief, for they were really suffering quite enough already.
What sorts of excuses people had used on that first morning to get the doctor and the locksmith out of the house Gregor was completely unable to ascertain.
Since they could not understand him, no one, not even his sister, thought that he might be able to understand others, and thus, when his sister was in her room, he had to be content with listening now and then to her sighs and invocations to the saints.
Only later, when she had grown somewhat accustomed to everything--naturally there could never be any talk of her growing completely accustomed to it--Gregor sometimes caught a comment which was intended to be friendly or could be interpreted as such. "Well, today it tasted good to him," she said, if Gregor had really cleaned up what he had to eat; whereas, in the reverse situation, which gradually repeated itself more and more frequently, she used to say sadly, "Now everything has stopped again."
But while Gregor could get no new information directly, he did hear a good deal from the room next door, and as soon as he heard voices, he scurried right away to the appropriate door and pressed his entire body against it.
In the early days especially, there was no conversation which was not concerned with him in some way or other, even if only in secret.
For two days at all meal times discussions on that subject could be heard on how people should now behave; but they also talked about the same subject in the times between meals, for there were always at least two family members at home, since no one really wanted to remain in the house alone and people could not under any circumstances leave the apartment completely empty.
In addition, on the very first day the servant girl--it was not completely clear what and how much she knew about what had happened--on her knees had begged his mother to let her go immediately, and when she said good bye about fifteen minutes later, she thanked them for the dismissal with tears in her eyes, as if she was receiving the greatest favour which people had shown her there, and, without anyone demanding it from her, she swore a fearful oath not to betray anyone, not even the slightest bit.
Now his sister had to team up with his mother to do the cooking, although that didn't create much trouble because people were eating almost nothing.
Again and again Gregor listened as one of them vainly invited another one to eat and received no answer other than "Thank you.
I've had enough" or something like that.
And perhaps they had stopped having anything to drink, too.
His sister often asked his father whether he wanted to have a beer and gladly offered to fetch it herself, and when his father was silent, she said, in order to remove any reservations he might have, that she could send the caretaker's wife to get it.
But then his father finally said a resounding "No," and nothing more would be spoken about it.
Already during the first day his father laid out all the financial circumstances and prospects to his mother and to his sister as well.
From time to time he stood up from the table and pulled out of the small lockbox salvaged from his business, which had collapsed five years previously, some document or other or some notebook.
The sound was audible as he opened up the complicated lock and, after removing what he was looking for, locked it up again.
These explanations by his father were, in part, the first enjoyable thing that Gregor had the chance to listen to since his imprisonment.
He had thought that nothing at all was left over for his father from that business; at least his father had told him nothing to contradict that view, and Gregor in any case hadn't asked him about it.
At the time Gregor's only concern had been to use everything he had in order to allow his family to forget as quickly as possible the business misfortune which had brought them all into a state of complete hopelessness.
And so at that point he'd started to work with a special intensity and from an assistant had become, almost overnight, a travelling salesman, who naturally had entirely different possibilities for earning money and whose successes at work were converted immediately into the form of cash commissions, which could be set out on the table at home in front of his astonished and delighted family.
Those had been beautiful days, and they had never come back afterwards, at least not with the same splendour, in spite of the fact that Gregor later earned so much money that he was in a position to bear the expenses of the entire family, costs which he, in fact, did bear.
They had become quite accustomed to it, both the family and Gregor as well.
They took the money with thanks, and he happily surrendered it, but the special warmth was no longer present.
Only the sister had remained still close to Gregor, and it was his secret plan to send her next year to the conservatory, regardless of the great expense which that necessarily involved and which would be made up in other ways.
In contrast to Gregor she loved music very much and knew how to play the violin charmingly.
Now and then during Gregor's short stays in the city the conservatory was mentioned in conversations with his sister, but always only as a beautiful dream, whose realization was unimaginable, and their parents never listened to these innocent expectations with pleasure.
But Gregor thought about them with scrupulous consideration and intended to explain the matter ceremoniously on Christmas Eve.
In his present situation, such futile ideas went through his head, while he pushed himself right up against the door and listened.
Sometimes in his general exhaustion he couldn't listen any more and let his head bang listlessly against the door, but he immediately pulled himself together, for even the small sound which he made by this motion was heard near by and silenced everyone.
"There he goes on again," said his father after a while, clearly turning towards the door, and only then would the interrupted conversation gradually be resumed again.
Gregor found out clearly enough--for his father tended to repeat himself often in his explanations, partly because he had not personally concerned himself with these matters for a long time now, and partly also because his mother did not understand everything right away the first time--that, in spite all bad luck, a fortune, although a very small one, was available from the old times, which the interest, which had not been touched, had in the intervening time gradually allowed to increase a little.
Furthermore, in addition to this, the money which Gregor had brought home every month-- he had kept only a few florins for himself- -had not been completely spent and had grown into a small capital amount.
Gregor, behind his door, nodded eagerly, rejoicing over this unanticipated foresight and frugality.
True, with this excess money, he could have paid off more of his father's debt to his employer and the day on which he could be rid of this position would have been a lot closer, but now things were doubtless better the way his father had arranged them.
At the moment, however, this money was not nearly sufficient to permit the family to live on the interest payments.
Perhaps it would be enough to maintain the family for one or at most two years, that's all.
Thus, it only added up to an amount which one should not really draw upon and which must be set aside for an emergency.
But the money to live on had to be earned.
Now, although his father was old, he was a healthy man who had not worked at all for five years and thus could not be counted on for very much.
He had in these five years, the first holidays of his trouble-filled but unsuccessful life, put on a good deal of fat and thus had become really heavy.
And should his old mother now perhaps work for money, a woman who suffered from asthma, for whom wandering through the apartment even now was a great strain and who spent every second day on the sofa by the open window labouring for breath?
Should his sister earn money, a girl who was still a seventeen-year-old child whose earlier life style had been so very delightful that it had consisted of dressing herself nicely, sleeping in late, helping around the house, taking part in a few modest enjoyments and, above all, playing the violin?
When it came to talking about this need to earn money, at first Gregor went away from the door and threw himself on the cool leather sofa beside the door, for he was quite hot from shame and sorrow.
Often he lay there all night long.
He didn't sleep a moment and just scratched on the leather for hours at a time.
He undertook the very difficult task of shoving a chair over to the window.
Then he crept up on the window sill and, braced in the chair, leaned against the window to look out, obviously with some memory or other of the satisfaction which that used to bring him in earlier times.
Actually, from day to day he perceived things with less and less clarity, even those a short distance away: the hospital across the street, the all-too-frequent sight of which he had previously cursed, was not visible at all any more, and if he had not been precisely aware that he lived in the quiet but completely urban Charlotte Street, he could have believed that from his window he was peering out at a featureless wasteland, in which the grey heaven and the grey earth had merged and were indistinguishable.
His attentive sister must have observed a couple of times that the chair stood by the window; then, after cleaning up the room, each time she pushed the chair back right against the window and from now on she even left the inner casement open.
If Gregor had only been able to speak to his sister and thank her for everything that she had to do for him, he would have tolerated her service more easily.
As it was, he suffered under it.
The sister admittedly sought to cover up the awkwardness of everything as much as possible, and, as time went by, she naturally got more successful at it.
But with the passing of time Gregor also came to understand everything more precisely.
Even her entrance was terrible for him.
As soon as she entered, she ran straight to the window, without taking the time to shut the door, in spite of the fact that she was otherwise very considerate in sparing anyone the sight of Gregor's room, and yanked the window open with eager hands, as if she was almost suffocating, and remained for a while by the window breathing deeply, even when it was still so cold.
With this running and noise she frightened Gregor twice every day.
The entire time he trembled under the couch, and yet he knew very well that she would certainly have spared him gladly if it had only been possible to remain with the window closed in a room where Gregor lived.
On one occasion--about one month had already gone by since Gregor's transformation, and there was now no particular reason any more for his sister to be startled at Gregor's appearance--she arrived a little earlier than usual and came upon Gregor as he was still looking out the window, immobile and well positioned to frighten someone.
It would not have come as a surprise to Gregor if she had not come in, since his position was preventing her from opening the window immediately.
But she not only did not step inside; she even retreated and shut the door.
A stranger really might have concluded from this that Gregor had been lying in wait for her and wanted to bite her.
Of course, Gregor immediately concealed himself under the couch, but he had to wait until the noon meal before his sister returned, and she seemed much less calm than usual.
From this he realized that his appearance was still constantly intolerable to her and must remain intolerable in future, and that she really had to exert a lot of self- control not to run away from a glimpse of only the small part of his body which stuck out from under the couch.
In order to spare her even this sight, one day he dragged the sheet on his back and onto the couch--this task took him four hours--and arranged it in such a way that he was now completely concealed and his sister, even if she bent down, could not see him.
If this sheet was not necessary as far as she was concerned, then she could remove it, for it was clear enough that Gregor could not derive any pleasure from isolating himself away so completely.
But she left the sheet just as it was, and Gregor believed he even caught a look of gratitude when, on one occasion, he carefully lifted up the sheet a little with his head to check, as his sister took stock of the new arrangement.
In the first two weeks his parents could not bring themselves to visit him, and he often heard how they fully acknowledged his sister's present work; whereas, earlier they had often got annoyed at his sister because she had seemed to them a somewhat useless young woman.
However, now both his father and his mother often waited in front of Gregor's door while his sister cleaned up inside, and as soon as she came out, she had to explain in detail how things looked in the room, what
Gregor had eaten, how he had behaved this time, and whether perhaps a slight improvement was perceptible.
In any event, his mother comparatively soon wanted to visit Gregor, but his father and his sister restrained her, at first with reasons which Gregor listened to very attentively and which he completely endorsed.
Later, however, they had to hold her back forcefully, and when she then cried "Let me go to Gregor.
Don't you understand that I have to go to him?"
Gregor then thought that perhaps it would be a good thing if his mother came in, not every day, of course, but maybe once a week.
She understood everything much better than his sister, who, in spite of all her courage, was still a child and, in the last analysis, had perhaps undertaken such a difficult task only out of childish recklessness.
Gregor's wish to see his mother was soon realized.
While during the day Gregor, out of consideration for his parents, did not want to show himself by the window, he couldn't crawl around very much on the few square metres of the floor.
He found it difficult to bear lying quietly during the night, and soon eating no longer gave him the slightest pleasure.
So for diversion he acquired the habit of crawling back and forth across the walls and ceiling.
He was especially fond of hanging from the ceiling.
The experience was quite different from lying on the floor.
It was easier to breathe, a slight vibration went through his body, and in the midst of the almost happy amusement which Gregor found up there, it could happen that, to his own surprise, he let go and hit the floor.
However, now he naturally controlled his body quite differently, and he did not injure himself in such a great fall.
His sister noticed immediately the new amusement which Gregor had found for himself--for as he crept around he left behind here and there traces of his sticky stuff--and so she got the idea of making
Gregor's creeping around as easy as possible and thus of removing the furniture which got in the way, especially the chest of drawers and the writing desk.
But she was in no position to do this by herself.
She did not dare to ask her father to help, and the servant girl would certainly not have assisted her, for although this girl, about sixteen years old, had courageously remained since the dismissal of the previous cook, she had begged for the privilege of being allowed to stay permanently confined to the kitchen and of having to open the door only in answer to a special summons.
Thus, his sister had no other choice but to involve his mother while his father was absent.
His mother approached Gregor's room with cries of excited joy, but she fell silent at the door.
Of course, his sister first checked whether everything in the room was in order.
Only then did she let his mother walk in.
In great haste Gregor had drawn the sheet down even further and wrinkled it more.
The whole thing really looked just like a coverlet thrown carelessly over the couch.
On this occasion, Gregor held back from spying out from under the sheet.
Thus, he refrained from looking at his mother this time and was just happy that she had come.
"Come on; he's not visible," said his sister, and evidently led his mother by the hand.
Now Gregor listened as these two weak women shifted the still heavy old chest of drawers from its position, and as his sister constantly took on herself the greater part of the work, without listening to the warnings of his mother, who was afraid that she would strain herself.
The work lasted a long time.
After about a quarter of an hour had already gone by, his mother said it would be better if they left the chest of drawers where it was, because, in the first place, it was too heavy: they would not be finished before his father's arrival, and leaving the chest of drawers in the middle of the room would block all Gregor's pathways, but, in the second place, they could not be certain that Gregor would be pleased with the removal of the furniture.
To her the reverse seemed to be true; the sight of the empty walls pierced her right to the heart, and why should Gregor not feel the same, since he had been accustomed to the room furnishings for a long time and in an empty room would feel himself abandoned?
"And is it not the case," his mother concluded very quietly, almost whispering as if she wished to prevent Gregor, whose exact location she really didn't know, from hearing even the sound of her voice--for she was convinced that he did not understand her words--"and isn't it a fact that by removing the furniture we're showing that we're giving up all hope of an improvement and are leaving him to his own resources without any consideration?
I think it would be best if we tried to keep the room exactly in the condition it was in before, so that, when Gregor returns to us, he finds everything unchanged and can forget the intervening time all the more easily."
As he heard his mother's words Gregor realized that the lack of all immediate human contact, together with the monotonous life surrounded by the family over the course of these two months, must have confused his understanding, because otherwise he couldn't explain to himself how he, in all seriousness, could have been so keen to have his room emptied.
Was he really eager to let the warm room, comfortably furnished with pieces he had inherited, be turned into a cavern in which he would, of course, then be able to crawl about in all directions without disturbance, but at the same time with a quick and complete forgetting of his human past as well?
Was he then at this point already on the verge of forgetting and was it only the voice of his mother, which he had not heard for a long time, that had aroused him?
Nothing was to be removed--everything must remain.
In his condition he could not function without the beneficial influences of his furniture.
And if the furniture prevented him from carrying out his senseless crawling about all over the place, then there was no harm in that, but rather a great benefit.
But his sister unfortunately thought otherwise.
She had grown accustomed, certainly not without justification, so far as the discussion of matters concerning Gregor was concerned, to act as an special expert with respect to their parents, and so now the mother's advice was for his sister sufficient reason to insist on the removal, not only of the chest of drawers and the writing desk, which were the only items she had thought about at first, but also of all the furniture, with the exception of the indispensable couch.
Of course, it was not only childish defiance and her recent very unexpected and hard won self-confidence which led her to this demand.
She had also actually observed that Gregor needed a great deal of room to creep about; the furniture, on the other hand, as far as one could see, was not of the slightest use.
But perhaps the enthusiastic sensibility of young women of her age also played a role.
This feeling sought release at every opportunity, and with it Grete now felt tempted to want to make Gregor's situation even more terrifying, so that then she would be able to do even more for him than now.
For surely no one except Grete would ever trust themselves to enter a room in which
Gregor ruled the empty walls all by himself.
And so she did not let herself be dissuaded from her decision by her mother, who in this room seemed uncertain of herself in her sheer agitation and soon kept quiet, helping his sister with all her energy to get the chest of drawers out of the room.
Now, Gregor could still do without the chest of drawers if need be, but the writing desk really had to stay.
And scarcely had the women left the room with the chest of drawers, groaning as they pushed it, when Gregor stuck his head out from under the sofa to take a look how he could intervene cautiously and with as much consideration as possible.
But unfortunately it was his mother who came back into the room first, while Grete had her arms wrapped around the chest of drawers in the next room and was rocking it back and forth by herself, without moving it from its position.
His mother was not used to the sight of Gregor; he could have made her ill, and so, frightened, Gregor scurried backwards right to the other end of the sofa, but he could no longer prevent the sheet from moving forward a little.
That was enough to catch his mother's attention.
She came to a halt, stood still for a moment, and then went back to Grete.
Although Gregor kept repeating to himself over and over that really nothing unusual was going on, that only a few pieces of furniture were being rearranged, he soon had to admit to himself that the movements of the women to and fro, their quiet conversations, and the scratching of the furniture on the floor affected him like a great swollen commotion on all sides, and, so firmly was he pulling in his head and legs and pressing his body into the floor, he had to tell himself unequivocally that he wouldn't be able to endure all this much longer.
They were cleaning out his room, taking away from him everything he cherished; they had already dragged out the chest of drawers in which the fret saw and other tools were kept, and they were now loosening the writing desk which was fixed tight to the floor, the desk on which he, as a business student, a school student, indeed even as an elementary school student, had written out his assignments.
At that moment he really didn't have any more time to check the good intentions of the two women, whose existence he had in any case almost forgotten, because in their exhaustion they were working really silently, and the heavy stumbling of their feet was the only sound to be heard.
And so he scuttled out--the women were just propping themselves up on the writing desk in the next room in order to take a breather--changing the direction of his path four times.
He really didn't know what he should rescue first.
Then he saw hanging conspicuously on the wall, which was otherwise already empty, the picture of the woman dressed in nothing but fur.
He quickly scurried up over it and pressed himself against the glass which held it in place and which made his hot abdomen feel good.
At least this picture, which Gregor at the moment completely concealed, surely no one would now take away.
He twisted his head towards the door of the living room to observe the women as they came back in.
They had not allowed themselves very much rest and were coming back right away.
Grete had placed her arm around her mother and held her tightly.
"So what shall we take now?" said Grete and looked around her.
Then her glance met Gregor's from the wall.
She kept her composure only because her mother was there.
She bent her face towards her mother in order to prevent her from looking around, and said, although in a trembling voice and too quickly, "Come, wouldn't it be better to go back to the living room for just another moment?"
Grete's purpose was clear to Gregor: she wanted to bring his mother to a safe place and then chase him down from the wall.
Well, let her just try!
He squatted on his picture and did not hand it over.
He would sooner spring into Grete's face.
But Grete's words had immediately made the mother very uneasy.
She walked to the side, caught sight of the enormous brown splotch on the flowered wallpaper, and, before she became truly aware that what she was looking at was
Gregor, screamed out in a high pitched raw voice "Oh God, oh God" and fell with outstretched arms, as if she was surrendering everything, down onto the couch and lay there motionless.
"Gregor, you. . ." cried out his sister with a raised fist and an urgent glare.
Since his transformation these were the first words which she had directed right at him.
She ran into the room next door to bring some spirits or other with which she could revive her mother from her fainting spell.
Gregor wanted to help as well--there was time enough to save the picture--but he was stuck fast on the glass and had to tear himself loose forcefully.
Then he also scurried into the next room, as if he could give his sister some advice, as in earlier times, but then he had to stand there idly behind her, while she rummaged about among various small bottles.
Still, she was frightened when she turned around.
A bottle fell onto the floor and shattered.
A splinter of glass wounded Gregor in the face, some corrosive medicine or other dripped over him.
Now, without lingering any longer, Grete took as many small bottles as she could hold and ran with them into her mother.
She slammed the door shut with her foot.
Gregor was now shut off from his mother, who was perhaps near death, thanks to him.
He could not open the door, and he did not want to chase away his sister who had to remain with her mother.
At this point he had nothing to do but wait, and overwhelmed with self-reproach and worry, he began to creep and crawl over everything: walls, furniture, and ceiling.
Finally, in his despair, as the entire room started to spin around him, he fell onto the middle of the large table.
A short time elapsed.
Gregor lay there limply.
All around was still.
Perhaps that was a good sign.
Then there was ring at the door.
The servant girl was naturally shut up in her kitchen, and therefore Grete had to go to open the door.
The father had arrived.
"What's happened?" were his first words.
Grete's appearance had told him everything.
Grete replied with a dull voice; evidently she was pressing her face into her father's chest:
"Mother fainted, but she's getting better now.
Gregor has broken loose." "Yes, I have expected that," said his father, "I always told you that, but you women don't want to listen."
It was clear to Gregor that his father had badly misunderstood Grete's short message and was assuming that Gregor had committed some violent crime or other.
Thus, Gregor now had to find his father to calm him down, for he had neither the time nor the ability to explain things to him.
And so he rushed away to the door of his room and pushed himself against it, so that his father could see right away as he entered from the hall that Gregor fully intended to return at once to his room, that it was not necessary to drive him back, but that one only needed to open the door, and he would disappear immediately.
But his father was not in the mood to observe such niceties.
"Ah," he yelled as soon as he entered, with a tone as if he were all at once angry and pleased.
Gregor pulled his head back from the door and raised it in the direction of his father.
He had not really pictured his father as he now stood there.
Of course, what with his new style of creeping all around, he had in the past while neglected to pay attention to what was going on in the rest of the apartment, as he had done before, and really should have grasped the fact that he would encounter different conditions.
Nevertheless, nevertheless, was that still his father?
Was that the same man who had lain exhausted and buried in bed in earlier days when Gregor was setting out on a business trip, who had received him on the evenings of his return in a sleeping gown and arm chair, totally incapable of standing up, who had only lifted his arm as a sign of happiness, and who in their rare strolls together a few Sundays a year and on the important holidays made his way slowly forwards between Gregor and his mother--who themselves moved slowly--always a bit more slowly than them, bundled up in his old coat, all the time setting down his walking stick carefully, and who, when he had wanted to say something, almost always stood still and gathered his entourage around him?
But now he was standing up really straight, dressed in a tight-fitting blue uniform with gold buttons, like the ones servants wear in a banking company.
Above the high stiff collar of his jacket his firm double chin stuck out prominently, beneath his bushy eyebrows the glance of his black eyes was freshly penetrating and alert, his otherwise dishevelled white hair was combed down into a carefully exact shining part.
He threw his cap, on which a gold monogram, apparently the symbol of the bank, was affixed, in an arc across the entire room onto the sofa and moved, throwing back the edge of the long coat of his uniform, with his hands in his trouser pockets and a grim face, right up to Gregor.
He really didn't know what he had in mind, but he raised his foot uncommonly high anyway, and Gregor was astonished at the gigantic size of the sole of his boot.
However, he did not linger on that point.
For he knew from the first day of his new life that, as far as he was concerned, his father considered the greatest force the only appropriate response.
And so he scurried away from his father, stopped when his father remained standing, and scampered forward again when his father merely stirred.
In this way they made their way around the room repeatedly, without anything decisive taking place.
In fact, because of the slow pace, it didn't look like a chase.
Gregor remained on the floor for the time being, especially since he was afraid that his father could take a flight up onto the wall or the ceiling as an act of real malice.
At any event, Gregor had to tell himself that he couldn't keep up this running around for a long time, because whenever his father took a single step, he had to go through an enormous number of movements.
Already he was starting to suffer from a shortage of breath, just as in his earlier days when his lungs had been quite unreliable.
As he now staggered around in this way in order to gather all his energies for running, hardly keeping his eyes open and feeling so listless that he had no notion at all of any escape other than by running and had almost already forgotten that the walls were available to him, although they were obstructed by carefully carved furniture full of sharp points and spikes, at that moment something or other thrown casually flew down close by and rolled in front of him.
It was an apple.
Immediately a second one flew after it.
Gregor stood still in fright.
Further running away was useless, for his father had decided to bombard him.
From the fruit bowl on the sideboard his father had filled his pockets.
And now, without for the moment taking accurate aim, he was throwing apple after apple.
These small red apples rolled around on the floor, as if electrified, and collided with each other.
A weakly thrown apple grazed Gregor's back but skidded off harmlessly.
However, another thrown immediately after that one drove into Gregor's back really hard.
Gregor wanted to drag himself off, as if the unexpected and incredible pain would go away if he changed his position.
But he felt as if he was nailed in place and lay stretched out completely confused in all his senses.
Only with his final glance did he notice how the door of his room was pulled open and how, right in front of his sister--who was yelling--his mother ran out in her undergarments, for his sister had undressed her in order to give her some freedom to breathe in her fainting spell, and how his mother then ran up to his father, on the way her tied up skirts slipped toward the floor one after the other, and how, tripping over her skirts, she hurled herself onto his father and, throwing her arms around him, in complete union with him--but at this moment Gregor's powers of sight gave way--as her hands reached to the back of his father's head and she begged him to spare Gregor's life.
CHAPTER ill.
Gregor's serious wound, from which he suffered for over a month--since no one ventured to remove the apple, it remained in his flesh as a visible reminder--seemed by itself to have reminded the father that, in spite of his present unhappy and hateful appearance, Gregor was a member of the family, something one should not treat as an enemy, and that it was, on the contrary, a requirement of family duty to suppress one's aversion and to endure--nothing else, just endure.
And if through his wound Gregor had now apparently lost for good his ability to move and for the time being needed many, many minutes to crawl across his room, like an aged invalid--so far as creeping up high was concerned, that was unimaginable-- nevertheless for this worsening of his condition, in his opinion, he did get completely satisfactory compensation, because every day towards evening the door to the living room, which he was in the habit of keeping a sharp eye on even one or two hours beforehand, was opened, so that he, lying down in the darkness of his room, invisible from the living room, could see the entire family at the illuminated table and listen to their conversation, to a certain extent with their common permission, a situation quite different from what had happened before.
Of course, it was no longer the animated social interaction of former times, which
Gregor in small hotel rooms had always thought about with a certain longing, when, tired out, he had had to throw himself into the damp bedclothes.
For the most part what went on now was very quiet.
After the evening meal, the father fell asleep quickly in his arm chair.
The mother and sister talked guardedly to each other in the stillness.
Bent far over, the mother sewed fine undergarments for a fashion shop.
The sister, who had taken on a job as a salesgirl, in the evening studied stenography and French, so as perhaps later to obtain a better position.
Sometimes the father woke up and, as if he was quite ignorant that he had been asleep, said to the mother "How long you have been sewing today?" and went right back to sleep, while the mother and the sister smiled tiredly to each other.
With a sort of stubbornness the father refused to take off his servant's uniform even at home, and while his sleeping gown hung unused on the coat hook, the father dozed completely dressed in his place, as if he was always ready for his responsibility and even here was waiting for the voice of his superior.
As a result, in spite of all the care of the mother and sister, his uniform, which even at the start was not new, grew dirty, and Gregor looked, often for the entire evening, at this clothing, with stains all over it and with its gold buttons always polished, in which the old man, although very uncomfortable, slept peacefully nonetheless.
As soon as the clock struck ten, the mother tried gently encouraging the father to wake up and then persuading him to go to bed, on the ground that he couldn't get a proper sleep here and that the father, who had to report for service at six o'clock, really needed a good sleep.
But in his stubbornness, which had gripped him since he had become a servant, he insisted always on staying even longer by the table, although he regularly fell asleep and then could only be prevailed upon with the greatest difficulty to trade his chair for the bed.
No matter how much the mother and sister might at that point work on him with small admonitions, for a quarter of an hour he would remain shaking his head slowly, his eyes closed, without standing up.
The mother would pull him by the sleeve and speak flattering words into his ear; the sister would leave her work to help her mother, but that would not have the desired effect on the father.
He would settle himself even more deeply in his arm chair.
Only when the two women grabbed him under the armpits would he throw his eyes open, look back and forth at the mother and sister, and habitually say "This is a life.
This is the peace and quiet of my old age."
And propped up by both women, he would heave himself up elaborately, as if for him it was the greatest trouble, allow himself to be led to the door by the women, wave them away there, and proceed on his own from there, while the mother quickly threw down her sewing implements and the sister her pen in order to run after the father and help him some more.
In this overworked and exhausted family who had time to worry any longer about Gregor more than was absolutely necessary?
The household was constantly getting smaller.
The servant girl was now let go.
A huge bony cleaning woman with white hair flying all over her head came in the morning and evening to do the heaviest work.
The mother took care of everything else in addition to her considerable sewing work.
It even happened that various pieces of family jewellery, which previously the mother and sister had been overjoyed to wear on social and festive occasions, were sold, as Gregor found out in the evening from the general discussion of the prices they had fetched.
But the greatest complaint was always that they could not leave this apartment, which was too big for their present means, since it was impossible to imagine how Gregor might be moved.
But Gregor fully recognized that it was not just consideration for him which was preventing a move, for he could have been transported easily in a suitable box with a few air holes.
The main thing holding the family back from a change in living quarters was far more their complete hopelessness and the idea that they had been struck by a misfortune like no one else in their entire circle of relatives and acquaintances.
What the world demands of poor people they now carried out to an extreme degree.
The father bought breakfast to the petty officials at the bank, the mother sacrificed herself for the undergarments of strangers, the sister behind her desk was at the beck and call of customers, but the family's energies did not extend any further.
And the wound in his back began to pain Gregor all over again, when now mother and sister, after they had escorted the father to bed, came back, let their work lie, moved close together, and sat cheek to cheek and when his mother would now say, pointing to Gregor's room, "Close the door,
Grete," and when Gregor was again in the darkness, while close by the women mingled their tears or, quite dry eyed, stared at the table.
Gregor spent his nights and days with hardly any sleep.
Sometimes he thought that the next time the door opened he would take over the family arrangements just as he had earlier.
In his imagination appeared again, after a long time, his employer and supervisor and the apprentices, the excessively spineless custodian, two or three friends from other businesses, a chambermaid from a hotel in the provinces, a loving fleeting memory, a female cashier from a hat shop, whom he had seriously but too slowly courted--they all appeared mixed in with strangers or people he had already forgotten, but instead of helping him and his family, they were all unapproachable, and he was happy to see them disappear.
But then he was in no mood to worry about his family.
He was filled with sheer anger over the wretched care he was getting, even though he couldn't imagine anything which he might have an appetite for.
Still, he made plans about how he could take from the larder what he at all account deserved, even if he wasn't hungry.
Without thinking any more about how they might be able to give Gregor special pleasure, the sister now kicked some food or other very quickly into his room in the morning and at noon, before she ran off to her shop, and in the evening, quite indifferent to whether the food had perhaps only been tasted or, what happened most frequently, remained entirely undisturbed, she whisked it out with one sweep of her broom.
The task of cleaning his room, which she now always carried out in the evening, could not be done any more quickly.
Streaks of dirt ran along the walls; here and there lay tangles of dust and garbage.
At first, when his sister arrived, Gregor positioned himself in a particularly filthy corner in order with this posture to make something of a protest.
But he could have well stayed there for weeks without his sister's changing her ways.
In fact, she perceived the dirt as much as he did, but she had decided just to let it stay.
In this business, with a touchiness which was quite new to her and which had generally taken over the entire family, she kept watch to see that the cleaning of
Gregor's room remained reserved for her.
Once his mother had undertaken a major cleaning of Gregor's room, which she had only completed successfully after using a few buckets of water.
But the extensive dampness made Gregor sick and he lay supine, embittered and immobile on the couch.
However, the mother's punishment was not delayed for long.
For in the evening the sister had hardly observed the change in Gregor's room before she ran into the living room mightily offended and, in spite of her mother's hand lifted high in entreaty, broke out in a fit of crying.
Her parents--the father had, of course, woken up with a start in his arm chair--at first looked at her astonished and helpless, until they started to get agitated.
Turning to his right, the father heaped reproaches on the mother that she was not to take over the cleaning of Gregor's room from the sister and, turning to his left, he shouted at the sister that she would no
longer be allowed to clean Gregor's room ever again, while the mother tried to pull the father, beside himself in his excitement, into the bed room.
The sister, shaken by her crying fit, pounded on the table with her tiny fists, and Gregor hissed at all this, angry that no one thought about shutting the door and sparing him the sight of this commotion.
But even when the sister, exhausted from her daily work, had grown tired of caring for Gregor as she had before, even then the mother did not have to come at all on her behalf.
And Gregor did not have to be neglected.
For now the cleaning woman was there.
This old widow, who in her long life must have managed to survive the worst with the help of her bony frame, had no real horror of Gregor.
Without being in the least curious, she had once by chance opened Gregor's door.
At the sight of Gregor, who, totally surprised, began to scamper here and there, although no one was chasing him, she remained standing with her hands folded across her stomach staring at him.
Since then she did not fail to open the door furtively a little every morning and evening to look in on Gregor.
At first, she also called him to her with words which she presumably thought were friendly, like "Come here for a bit, old dung beetle!" or "Hey, look at the old dung beetle!"
Addressed in such a manner, Gregor answered nothing, but remained motionless in his place, as if the door had not been opened at all.
If only, instead of allowing this cleaning woman to disturb him uselessly whenever she felt like it, they had given her orders to clean up his room every day!
One day in the early morning--a hard downpour, perhaps already a sign of the coming spring, struck the window panes-- when the cleaning woman started up once again with her usual conversation, Gregor was so bitter that he turned towards her, as if for an attack, although slowly and weakly.
But instead of being afraid of him, the cleaning woman merely lifted up a chair standing close by the door and, as she stood there with her mouth wide open, her intention was clear: she would close her mouth only when the chair in her hand had been thrown down on Gregor's back.
"This goes no further, all right?" she asked, as Gregor turned himself around again, and she placed the chair calmly back in the corner.
Gregor ate hardly anything any more.
Only when he chanced to move past the food which had been prepared did he, as a game, take a bit into his mouth, hold it there for hours, and generally spit it out again.
At first he thought it might be his sadness over the condition of his room which kept him from eating, but he very soon became reconciled to the alterations in his room.
People had grown accustomed to put into storage in his room things which they couldn't put anywhere else, and at this point there were many such things, now that they had rented one room of the apartment to three lodgers.
These solemn gentlemen--all three had full beards, as Gregor once found out through a crack in the door--were meticulously intent on tidiness, not only in their own room but, since they had now rented a room here, in the entire household, and particularly in the kitchen.
They simply did not tolerate any useless or shoddy stuff.
Moreover, for the most part they had brought with them their own pieces of furniture.
Thus, many items had become superfluous, and these were not really things one could sell or things people wanted to throw out.
All these items ended up in Gregor's room, even the box of ashes and the garbage pail from the kitchen.
The cleaning woman, always in a hurry, simply flung anything that was momentarily useless into Gregor's room.
Fortunately Gregor generally saw only the relevant object and the hand which held it.
The cleaning woman perhaps was intending, when time and opportunity allowed, to take the stuff out again or to throw everything out all at once, but in fact the things remained lying there, wherever they had ended up at the first throw, unless Gregor squirmed his way through the accumulation of junk and moved it.
At first he was forced to do this because otherwise there was no room for him to creep around, but later he did it with a growing pleasure, although after such movements, tired to death and feeling wretched, he didn't budge for hours.
Because the lodgers sometimes also took their evening meal at home in the common living room, the door to the living room stayed shut on many evenings.
But Gregor had no trouble at all going without the open door.
Already on many evenings when it was open he had not availed himself of it, but, without the family noticing, was stretched out in the darkest corner of his room.
However, once the cleaning woman had left the door to the living room slightly ajar, and it remained open even when the lodgers came in in the evening and the lights were put on.
They sat down at the head of the table, where in earlier days the mother, the father, and Gregor had eaten, unfolded their serviettes, and picked up their knives and forks.
The mother immediately appeared in the door with a dish of meat and right behind her the sister with a dish piled high with potatoes.
The food gave off a lot of steam.
The gentlemen lodgers bent over the plate set before them, as if they wanted to check it before eating, and in fact the one who sat in the middle--for the other two he seemed to serve as the authority--cut off a piece of meat still on the plate obviously to establish whether it was sufficiently tender and whether or not something should be shipped back to the kitchen.
He was satisfied, and mother and sister, who had looked on in suspense, began to breathe easily and to smile.
The family itself ate in the kitchen.
In spite of that, before the father went into the kitchen, he came into the room and with a single bow, cap in hand, made a tour of the table.
The lodgers rose up collectively and murmured something in their beards.
Then, when they were alone, they ate almost in complete silence.
It seemed odd to Gregor that, out of all the many different sorts of sounds of eating, what was always audible was their chewing teeth, as if by that Gregor should be shown that people needed their teeth to eat and that nothing could be done even with the most handsome toothless jawbone.
"I really do have an appetite," Gregor said to himself sorrowfully, "but not for these things.
How these lodgers stuff themselves, and I am dying."
On this very evening the violin sounded from the kitchen.
Gregor didn't remember hearing it all through this period.
The lodgers had already ended their night meal, the middle one had pulled out a newspaper and had given each of the other two a page, and they were now leaning back, reading and smoking.
When the violin started playing, they became attentive, got up, and went on tiptoe to the hall door, at which they remained standing pressed up against one another.
They must have been audible from the kitchen, because the father called out
"Perhaps the gentlemen don't like the playing?
It can be stopped at once."
"On the contrary," stated the lodger in the middle, "might the young woman not come into us and play in the room here, where it is really much more comfortable and cheerful?"
"Oh, thank you," cried out the father, as if he were the one playing the violin.
The men stepped back into the room and waited.
Soon the father came with the music stand, the mother with the sheet music, and the sister with the violin.
The sister calmly prepared everything for the recital.
The parents, who had never previously rented a room and therefore exaggerated their politeness to the lodgers, dared not sit on their own chairs.
The father leaned against the door, his right hand stuck between two buttons of his buttoned-up uniform.
The mother, however, accepted a chair offered by one lodger.
Since she left the chair sit where the gentleman had chanced to put it, she sat to one side in a corner.
The sister began to play.
The father and mother, one on each side, followed attentively the movements of her hands.
Attracted by the playing, Gregor had ventured to advance a little further forward and his head was already in the living room.
He scarcely wondered about the fact that recently he had had so little consideration for the others.
Earlier this consideration had been something he was proud of.
And for that very reason he would have had at this moment more reason to hide away, because as a result of the dust which lay all over his room and flew around with the slightest movement, he was totally covered in dirt.
On his back and his sides he carted around with him dust, threads, hair, and remnants of food.
His indifference to everything was much too great for him to lie on his back and scour himself on the carpet, as he often had done earlier during the day.
In spite of his condition he had no timidity about inching forward a bit on the spotless floor of the living room.
In any case, no one paid him any attention.
The family was all caught up in the violin playing.
The lodgers, by contrast, who for the moment had placed themselves, hands in their trouser pockets, behind the music stand much too close to the sister, so that they could all see the sheet music, something that must certainly bother the sister, soon drew back to the window conversing in low voices with bowed heads, where they then remained, worriedly observed by the father.
It now seemed really clear that, having assumed they were to hear a beautiful or entertaining violin recital, they were disappointed and were allowing their peace and quiet to be disturbed only out of politeness.
The way in which they all blew the smoke from their cigars out of their noses and mouths in particular led one to conclude that they were very irritated.
And yet his sister was playing so beautifully.
Her face was turned to the side, her gaze followed the score intently and sadly.
Gregor crept forward still a little further, keeping his head close against the floor in order to be able to catch her gaze if possible.
Was he an animal that music so captivated him?
For him it was as if the way to the unknown nourishment he craved was revealing itself.
He was determined to press forward right to his sister, to tug at her dress, and to indicate to her in this way that she might still come with her violin into his room, because here no one valued the recital as he wanted to value it.
He did not wish to let her go from his room any more, at least not as long as he lived.
His frightening appearance would for the first time become useful for him.
He wanted to be at all the doors of his room simultaneously and snarl back at the attackers.
However, his sister should not be compelled but would remain with him voluntarily.
She would sit next to him on the sofa, bend down her ear to him, and he would then confide in her that he firmly intended to send her to the conservatory and that, if his misfortune had not arrived in the interim, he would have declared all this last Christmas--had Christmas really already come and gone?--and would have brooked no argument.
After this explanation his sister would break out in tears of emotion, and Gregor would lift himself up to her armpit and kiss her throat, which she, from the time she started going to work, had left exposed without a band or a collar.
"Mr. Samsa," called out the middle lodger to the father and, without uttering a further word, pointed his index finger at Gregor as he was moving slowly forward.
The violin fell silent.
The middle lodger smiled, first shaking his head once at his friends, and then looked down at Gregor once more.
Rather than driving Gregor back again, the father seemed to consider it of prime importance to calm down the lodgers, although they were not at all upset and
Gregor seemed to entertain them more than the violin recital.
The father hurried over to them and with outstretched arms tried to push them into their own room and simultaneously to block their view of Gregor with his own body.
At this point they became really somewhat irritated, although one no longer knew whether that was because of the father's behaviour or because of knowledge they had just acquired that they had, without knowing it, a neighbour like Gregor.
They demanded explanations from his father, raised their arms to make their points, tugged agitatedly at their beards, and moved back towards their room quite slowly.
In the meantime, the isolation which had suddenly fallen upon his sister after the sudden breaking off of the recital had overwhelmed her.
She had held onto the violin and bow in her limp hands for a little while and had continued to look at the sheet music as if she was still playing.
All at once she pulled herself together, placed the instrument in her mother's lap-- the mother was still sitting in her chair having trouble breathing for her lungs were labouring--and had run into the next room, which the lodgers, pressured by the father, were already approaching more rapidly.
One could observe how under the sister's practiced hands the sheets and pillows on the beds were thrown on high and arranged.
Even before the lodgers had reached the room, she was finished fixing the beds and was slipping out.
The father seemed so gripped once again with his stubbornness that he forgot about the respect which he always owed to his renters.
He pressed on and on, until at the door of the room the middle gentleman stamped loudly with his foot and thus brought the father to a standstill.
"I hereby declare," the middle lodger said, raising his hand and casting his glance both on the mother and the sister, "that considering the disgraceful conditions prevailing in this apartment and family"-- with this he spat decisively on the floor-- "I immediately cancel my room.
I will, of course, pay nothing at all for the days which I have lived here; on the contrary I shall think about whether or not I will initiate some sort of action against you, something which--believe me--will be very easy to establish."
He fell silent and looked directly in front of him, as if he was waiting for something.
In fact, his two friends immediately joined in with their opinions, "We also give immediate notice."
At that he seized the door handle, banged the door shut, and locked it.
The father groped his way tottering to his chair and let himself fall in it.
It looked as if he was stretching out for his usual evening snooze, but the heavy nodding of his head, which looked as if it was without support, showed that he was not sleeping at all.
Gregor had lain motionless the entire time in the spot where the lodgers had caught him.
Disappointment with the collapse of his plan and perhaps also weakness brought on by his severe hunger made it impossible for him to move.
He was certainly afraid that a general disaster would break over him at any moment, and he waited.
He was not even startled when the violin fell from the mother's lap, out from under her trembling fingers, and gave off a reverberating tone.
"My dear parents," said the sister banging her hand on the table by way of an introduction, "things cannot go on any longer in this way.
Maybe if you don't understand that, well, I do.
I will not utter my brother's name in front of this monster, and thus I say only that we must try to get rid of it.
We have tried what is humanly possible to take care of it and to be patient.
I believe that no one can criticize us in the slightest."
"She is right in a thousand ways," said the father to himself.
The mother, who was still incapable of breathing properly, began to cough numbly with her hand held up over her mouth and a manic expression in her eyes.
The sister hurried over to her mother and held her forehead.
The sister's words seemed to have led the father to certain reflections.
He sat upright, played with his uniform hat among the plates, which still lay on the table from the lodgers' evening meal, and looked now and then at the motionless
Gregor.
"We must try to get rid of it," the sister now said decisively to the father, for the mother, in her coughing fit, was not listening to anything.
"It is killing you both.
I see it coming.
When people have to work as hard as we all do, they cannot also tolerate this endless torment at home.
I just can't go on any more."
And she broke out into such a crying fit that her tears flowed out down onto her mother's face.
She wiped them off her mother with mechanical motions of her hands.
"Child," said the father sympathetically and with obvious appreciation, "then what should we do?"
The sister only shrugged her shoulders as a sign of the perplexity which, in contrast to her previous confidence, had come over her while she was crying.
"If only he understood us," said the father in a semi-questioning tone.
The sister, in the midst of her sobbing, shook her hand energetically as a sign that there was no point thinking of that.
"If he only understood us," repeated the father and by shutting his eyes he absorbed the sister's conviction of the impossibility of this point, "then perhaps some compromise would be possible with him.
But as it is. . ." "It must be gotten rid of," cried the sister.
"That is the only way, father.
You must try to get rid of the idea that this is Gregor.
The fact that we have believed for so long, that is truly our real misfortune.
But how can it be Gregor?
If it were Gregor, he would have long ago realized that a communal life among human beings is not possible with such an animal and would have gone away voluntarily.
Then we would not have a brother, but we could go on living and honour his memory.
But this animal plagues us.
It drives away the lodgers, will obviously take over the entire apartment, and leave us to spend the night in the alley.
Just look, father," she suddenly cried out,
"he's already starting up again."
With a fright which was totally incomprehensible to Gregor, the sister even left the mother, pushed herself away from her chair, as if she would sooner sacrifice her mother than remain in Gregor's vicinity, and rushed behind her father who, excited merely by her behaviour, also stood up and half raised his arms in front of the sister as though to protect her.
But Gregor did not have any notion of wishing to create problems for anyone and certainly not for his sister.
He had just started to turn himself around in order to creep back into his room, quite a startling sight, since, as a result of his suffering condition, he had to guide himself through the difficulty of turning around with his head, in this process lifting and banging it against the floor several times.
He paused and looked around.
His good intentions seem to have been recognized.
Now they looked at him in silence and sorrow.
His mother lay in her chair, with her legs stretched out and pressed together; her eyes were almost shut from weariness.
The father and sister sat next to one another.
The sister had set her hands around the father's neck.
"Now perhaps I can actually turn myself around," thought Gregor and began the task again.
He couldn't stop puffing at the effort and had to rest now and then.
Besides, no one was urging him on.
It was all left to him on his own.
When he had completed turning around, he immediately began to wander straight back.
He was astonished at the great distance which separated him from his room and did not understand in the least how in his weakness he had covered the same distance a short time before, almost without noticing it.
Constantly intent only on creeping along quickly, he hardly paid any attention to the fact that no word or cry from his family interrupted him.
Only when he was already in the door did he turn his head, not completely, because he felt his neck growing stiff.
At any rate he still saw that behind him nothing had changed.
Only the sister was standing up.
His last glimpse brushed over the mother who was now completely asleep.
Hardly was he inside his room when the door was pushed shut very quickly, bolted fast, and barred.
Gregor was startled by the sudden commotion behind him, so much so that his little It was his sister who had been in such a hurry.
She had stood up right away, had waited, and had then sprung forward nimbly.
Gregor had not heard anything of her approach.
She cried out "Finally!" to her parents, as she turned the key in the lock.
Gregor asked himself and looked around him in the darkness.
He soon made the discovery that he could no longer move at all.
He was not surprised at that.
On the contrary, it struck him as unnatural that up to this point he had really been able up to move around with these thin little legs.
Besides he felt relatively content.
True, he had pains throughout his entire body, but it seemed to him that they were gradually becoming weaker and weaker and would finally go away completely.
The rotten apple in his back and the inflamed surrounding area, entirely covered with white dust, he hardly noticed. He remembered his family with deep feelings of love.
In this business, his own thought that he had to disappear was, if possible, even more decisive than his sister's.
He remained in this state of empty and peaceful reflection until the tower clock struck three o'clock in the morning.
From the window he witnessed the beginning of the general dawning outside.
Then without willing it, his head sank all the way down, and from his nostrils flowed out weakly his last breath.
Early in the morning the cleaning woman came.
In her sheer energy and haste she banged all the doors--in precisely the way people had already asked her to avoid--so much so that once she arrived a quiet sleep was no longer possible anywhere in the entire apartment.
In her customarily brief visit to Gregor she at first found nothing special.
She thought he lay so immobile there because he wanted to play the offended party.
She gave him credit for as complete an understanding as possible.
Since she happened to be holding the long broom in her hand, she tried to tickle
Gregor with it from the door.
When that was quite unsuccessful, she became irritated and poked Gregor a little, and only when she had shoved him from his place without any resistance did she become attentive.
When she quickly realized the true state of affairs, her eyes grew large, she whistled to herself.
However, she didn't restrain herself for long.
She pulled open the door of the bedroom and yelled in a loud voice into the darkness,
"Come and look.
It's kicked the bucket.
It's lying there, totally snuffed!"
The Samsa married couple sat upright in their marriage bed and had to get over their fright at the cleaning woman before they managed to grasp her message.
But then Mr. and Mrs. Samsa climbed very quickly out of bed, one on either side.
Mr. Samsa threw the bedspread over his shoulders, Mrs. Samsa came out only in her night-shirt, and like this they stepped into Gregor's room.
Meanwhile, the door of the living room, in which Grete had slept since the lodgers had arrived on the scene, had also opened.
She was fully clothed, as if she had not slept at all; her white face also seem to indicate that.
"Dead?" said Mrs. Samsa and looked questioningly at the cleaning woman, although she could check everything on her own and even understand without a check.
"I should say so," said the cleaning woman and, by way of proof, poked Gregor's body with the broom a considerable distance more to the side.
Mrs. Samsa made a movement as if she wished to restrain the broom, but didn't do it.
"Well," said Mr. Samsa, "now we can give thanks to God."
He crossed himself, and the three women followed his example.
Grete, who did not take her eyes off the corpse, said, "Look how thin he was.
He had eaten nothing for such a long time.
The meals which came in here came out again exactly the same."
In fact, Gregor's body was completely flat and dry.
That was apparent really for the first time, now that he was no longer raised on his small limbs and nothing else distracted one's gaze.
"Grete, come into us for a moment," said Mrs. Samsa with a melancholy smile, and
Grete went, not without looking back at the corpse, behind her parents into the bed room.
The cleaning woman shut the door and opened the window wide.
In spite of the early morning, the fresh air was partly tinged with warmth.
It was already the end of March.
The three lodgers stepped out of their room and looked around for their breakfast, astonished that they had been forgotten.
"Where is the breakfast?" asked the middle one of the gentlemen grumpily to the cleaning woman.
However, she laid her finger to her lips and then quickly and silently indicated to the lodgers that they could come into Gregor's room.
So they came and stood in the room, which was already quite bright, around Gregor's corpse, their hands in the pockets of their somewhat worn jackets.
Then the door of the bed room opened, and Mr. Samsa appeared in his uniform, with his wife on one arm and his daughter on the other.
All were a little tear stained.
Now and then Grete pressed her face onto her father's arm.
"Get out of my apartment immediately," said Mr. Samsa and pulled open the door, without
letting go of the women.
"What do you mean?" said the middle lodger, somewhat dismayed and with a sugary smile.
The two others kept their hands behind them and constantly rubbed them against each other, as if in joyful anticipation of a great squabble which must end up in their favour.
"I mean exactly what I say," replied Mr. Samsa and went directly with his two female companions up to the lodger.
The latter at first stood there motionless and looked at the floor, as if matters were arranging themselves in a new way in his head.
"All right, then we'll go," he said and looked up at Mr. Samsa as if, suddenly overcome by humility, he was asking fresh permission for this decision.
Mr. Samsa merely nodded to him repeatedly with his eyes open wide.
Following that, the lodger actually went with long strides immediately out into the hall.
His two friends had already been listening for a while with their hands quite still, and now they hopped smartly after him, as if afraid that Mr. Samsa could step into the hall ahead of them and disturb their reunion with their leader.
In the hall all three of them took their hats from the coat rack, pulled their canes from the cane holder, bowed silently, and left the apartment.
In what turned out to be an entirely groundless mistrust, Mr. Samsa stepped with the two women out onto the landing, leaned against the railing, and looked over as the three lodgers slowly but steadily made their way down the long staircase, disappeared on each floor in a certain turn of the stairwell, and in a few seconds came out again.
The deeper they proceeded, the more the Samsa family lost interest in them, and when a butcher with a tray on his head come to meet them and then with a proud bearing ascended the stairs high above them, Mr.
Samsa., together with the women, left the banister, and they all returned, as if relieved, back into their apartment.
They decided to pass that day resting and going for a stroll.
Not only had they earned this break from work, but there was no question that they really needed it.
And so they sat down at the table and wrote three letters of apology:
During the writing the cleaning woman came in to say that she was going off, for her morning work was finished.
The three people writing at first merely nodded, without glancing up.
Only when the cleaning woman was still unwilling to depart, did they look up angrily.
"Well?" asked Mr. Samsa.
The cleaning woman stood smiling in the doorway, as if she had a great stroke of luck to report to the family but would only do it if she was asked directly.
The almost upright small ostrich feather in her hat, which had irritated Mr. Samsa during her entire service, swayed lightly in all directions.
"All right then, what do you really want?" asked Mrs. Samsa, whom the cleaning lady still usually respected.
"Well," answered the cleaning woman, smiling so happily she couldn't go on speaking right away, "about how that rubbish from the next room should be thrown out, you mustn't worry about it.
It's all taken care of."
letters, as though they wanted to go on writing. Mr. Samsa, who noticed that the cleaning woman wanted to start describing everything in detail, decisively prevented her with an outstretched hand.
But since she was not allowed to explain, she remembered the great hurry she was in, and called out, clearly insulted, "Bye bye, everyone," turned around furiously and left the apartment with a fearful slamming of the door.
"This evening she'll be let go," said Mr. Samsa, but he got no answer from either his wife or from his daughter, because the cleaning woman seemed to have upset once again the tranquillity they had just attained.
They got up, went to the window, and remained there, with their arms about each other.
Mr. Samsa turned around in his chair in their direction and observed them quietly for a while.
Then he called out, "All right, come here then.
Let's finally get rid of old things.
And have a little consideration for me."
The women attended to him at once. They rushed to him, caressed him, and quickly ended their letters.
Then all three left the apartment together, something they had not done for months now, and took the electric tram into the open air outside the city.
The car in which they were sitting by themselves was totally engulfed by the warm sun.
Leaning back comfortably in their seats, they talked to each other about future prospects, and they discovered that on closer observation these were not at all bad, for the three of them had employment, about which they had not really questioned each other at all, which was extremely favourable and with especially promising prospects.
The greatest improvement in their situation at this moment, of course, had to come from a change of dwelling.
Now they wanted to rent an apartment smaller and cheaper but better situated and generally more practical than the present one, which Gregor had found.
While they amused themselves in this way, it struck Mr. and Mrs. Samsa, almost at the same moment, how their daughter, who was getting more animated all the time, had blossomed recently, in spite of all the troubles which had made her cheeks pale, into a beautiful and voluptuous young woman.
Growing more silent and almost unconsciously understanding each other in their glances, they thought that the time was now at hand to seek out a good honest man for her.
And it was something of a confirmation of their new dreams and good intentions when at the end of their journey their daughter got up first and stretched her young body.
What I want to do in this video is to prove one of the more useful results in geometry, and that's that an inscribed angle is just an angle whose vertex sits on the circumference of the circle.
So that is our inscribed angle.
I'll denote it by psi -- I'll use the psi for inscribed angle and angles in this video.
That psi, the inscribed angle, is going to be exactly 1/2 of the central angle that subtends the same arc.
So I just used a lot a fancy words, but I think you'll get what I'm saying.
So this is psi.
It is an inscribed angle.
It sits, its vertex sits on the circumference.
And if you draw out the two rays that come out from this angle or the two cords that define this angle, it intersects the circle at the other end.
And if you look at the part of the circumference of the circle that's inside of it, that is the arc that is subtended by psi.
It's all very fancy words, but I think the idea is pretty straightforward.
This right here is the arc subtended by psi, where psi is that inscribed angle right over there, the vertex sitting on the circumference.
Now, a central angle is an angle where the vertex is sitting at the center of the circle.
So let's say that this right here -- I'll try to eyeball it -- that right there is the center of the circle.
So let me draw a central angle that subtends this same arc.
So that looks like a central angle subtending that same arc.
Just like that.
Let's call this theta.
So this angle is psi, this angle right here is theta.
What I'm going to prove in this video is that psi is always going to be equal to 1/2 of theta.
So if I were to tell you that psi is equal to, I don't know, 25 degrees, then you would immediately know that theta must be equal to 50 degrees.
Or if I told you that theta was 80 degrees, then you would immediately know that psi was 40 degrees.
So let's actually proved this.
So let me clear this.
So a good place to start, or the place I'm going to start, is a special case.
I'm going to draw an inscribed angle, but one of the chords that define it is going to be the diameter of the circle.
So this isn't going to be the general case, this is going to be a special case.
So let me see, this is the center right here of my circle.
I'm trying to eyeball it.
Center looks like that.
So let me draw a diameter.
So the diameter looks like that.
Then let me define my inscribed angle.
This diameter is one side of it.
And then the other side maybe is just like that.
So let me call this right here psi.
If that's psi, this length right here is a radius -- that's our radius of our circle.
Then this length right here is also going to be the radius of our circle going from the center to the circumference.
Your circumference is defined by all of the points that are exactly a radius away from the center.
So that's also a radius.
Now, this triangle right here is an isosceles triangle.
It has two sides that are equal. Two sides that are definitely equal.
We know that when we have two sides being equal, their base angles are also equal.
So this will also be equal to psi.
You might not recognize it because it's tilted up like that.
But I think many of us when we see a triangle that looks like this, if I told you this is r and that is r, that these two sides are equal, and if this is psi, then you would also know that this angle is also going to be psi.
Base angles are equivalent on an isosceles triangle.
So this is psi, that is also psi.
Now, let me look at the central angle.
This is the central angle subtending the same arc.
Let's highlight the arc that they're both subtending.
This right here is the arc that they're both going to subtend.
So this is my central angle right there, theta.
Now if this angle is theta, what's this angle going to be?
This angle right here.
Well, this angle is supplementary to theta, so it's 180 minus theta.
When you add these two angles together you go 180 degrees around or they kind of form a line.
They're supplementary to each other.
Now we also know that these three angles are sitting inside of the same triangle.
So they must add up to 180 degrees.
So we get psi -- this psi plus that psi plus psi plus this angle, which is 180 minus theta plus 180 minus theta. These three angles must add up to 180 degrees.
They're the three angles of a triangle.
Now we could subtract 180 from both sides. psi plus psi is 2 psi minus theta is equal to 0.
Add theta to both sides.
You get 2 psi is equal to theta.
Multiply both sides by 1/2 or divide both sides by 2.
You get psi is equal to 1/2 of theta.
So we just proved what we set out to prove for the special case where our inscribed angle is defined, where one of the rays, if you want to view these lines as rays, where one of the rays that defines this inscribed angle is along the diameter.
The diameter forms part of that ray.
So this is a special case where one edge is sitting on the diameter.
So already we could generalize this.
So now that we know that if this is 50 that this is going to be 100 degrees and likewise, right?
Whatever psi is or whatever theta is, psi's going to be 1/2 of that, or whatever psi is, theta is going to be 2 times that.
And now this will apply for any time.
We could use this notion any time that -- so just using that result we just got, we can now generalize it a little bit, although this won't apply to all inscribed angles.
Let's have an inscribed angle that looks like this.
So this situation, the center, you can kind of view it as it's inside of the angle.
That's my inscribed angle.
And I want to find a relationship between this inscribed angle and the central angle that's subtending to same arc.
So that's my central angle subtending the same arc.
Well, you might say, hey, gee, none of these ends or these chords that define this angle, neither of these are diameters, but what we can do is we can draw a diameter.
If the center is within these two chords we can draw a diameter.
We can draw a diameter just like that.
If we draw a diameter just like that, if we define this angle as psi 1, that angle as psi 2.
Clearly psi is the sum of those two angles.
And we call this angle theta 1, and this angle theta 2.
We immediately you know that, just using the result I just got, since we have one side of our angles in both cases being a diameter now, we know that psi 1 is going to be equal to 1/2 theta 1.
And we know that psi 2 is going to be 1/2 theta 2.
Psi 2 is going to be 1/2 theta 2.
So psi, which is psi 1 plus psi 2, so psi 1 plus psi 2 is going to be equal to these two things. 1/2 theta 1 plus 1/2 theta 2. psi 1 plus psi 2, this is equal to the first inscribed angle that we want to deal with, just regular psi.
That's psi.
And this right here, this is equal to 1/2 times theta 1 plus theta 2.
What's theta 1 plus theta 2?
Well that's just our original theta that we were dealing with.
So now we see that psi is equal to 1/2 theta.
So now we've proved it for a slightly more general case where our center is inside of the two rays that define that angle.
Now, we still haven't addressed a slightly harder situation or a more general situation where if this is the center of our circle and I have an inscribed angle where the center isn't sitting inside of the two chords.
Let me draw that.
So that's going to be my vertex, and I'll switch colors, so let's say that is one of the chords that defines the angle, just like that.
And let's say that is the other chord that defines the angle just like that.
So how do we find the relationship between, let's call, this angle right here, let's call it psi 1.
How do we find the relationship between psi 1 and the central angle that subtends this same arc?
So when I talk about the same arc, that's that right there.
So the central angle that subtends the same arc will look like this.
Let's call that theta 1.
What we can do is use what we just learned when one side of our inscribed angle is a diameter.
So let's construct that.
So let me draw a diameter here.
The result we want still is that this should be 1/2 of this, but let's prove it.
Let's draw a diameter just like that.
Let me call this angle right here, let me call that psi 2.
And it is subtending this arc right there -- let me do that in a darker color.
It is subtending this arc right there.
So the central angle that subtends that same arc, let me call that theta 2.
Now, we know from the earlier part of this video that psi 2 is going to be equal to 1/2 theta 2, right?
They share -- the diameter is right there.
The diameter is one of the chords that forms the angle.
So psi 2 is going to be equal to 1/2 theta 2.
This is exactly what we've been doing in the last video, right?
This is an inscribed angle.
One of the chords that define is sitting on the diameter.
So this is going to be 1/2 of this angle, of the central angle that subtends the same arc.
Now, let's look at this larger angle.
This larger angle right here.
Psi 1 plus psi 2.
Right, that larger angle is psi 1 plus psi 2.
Once again, this subtends this entire arc right here, and it has a diameter as one of the chords that defines this huge angle.
So this is going to be 1/2 of the central angle that subtends the same arc.
We're just using what we've already shown in this video.
So this is going to be equal to 1/2 of this huge central angle of theta 1 plus theta 2.
So far we've just used everything that we've learned earlier in this video.
Now, we already know that psi 2 is equal to 1/2 theta 2.
So let me make that substitution.
This is equal to that.
So we can say that si 1 plus -- instead of si 2 I'll write 1/2 theta 2 is equal to 1/2 theta 1 plus 1/2 theta 2.
We can subtract 1/2 theta 2 from both sides, and we get our result.
Si 1 is equal to 1/2 theta one.
And now we're done.
We have proven the situation that the inscribed angle is always 1/2 of the central angle that subtends the same arc, regardless of whether the center of the circle is inside of the angle, outside of the angle, whether we have a diameter on one side.
So any other angle can be constructed as a sum of any or all of these that we've already done.
So hopefully you found this useful and now we can actually build on this result to do some more interesting geometry proofs.
We're on problem 15.
It asks us, if triangle ABC and triangle XYZ are two triangles such that-- OK, let me draw these two triangle.
Triangle ABC, maybe it looks something like that, and then we have triangle XYZ, and we want to prove that they are similar.
Similar means that they look the same.
They have a similar shape, but could be of different sizes.
So essentially all of their angles are the same or all the ratios of their sides of the same.
So XYZ might just be a smaller version.
Maybe I should have drawn a bigger one.
It looks like they want us to prove the triangles are similar.
They tell us that the ratio of AB to XY-- let me color that.
They say the ratio of AB to XY is equal to the ratio of BC to YZ.
So there's a couple of times when you know that a triangle is similar, is if the ratio of all the sides are equal.
Well, after the last video, hopefully, we're a little familiar with how you add matrices.
So now let's learn how to multiply matrices.
And keep in mind, these are human-created definitions for matrix multiplication.
We could have come up with completely different ways to multiply it.
But I encourage you to learn this way because it'll help you in math class.
And we will see later that there's actually a lot of applications that come out of this type of matrix multiplication.
So let me think of two matrices.
I will do two 2 by 2 matrices, and let's multiply them.
Let's say-- let me pick some random numbers:
2, minus 3, 7, and 5.
And I'm going to multiply that matrix, or that table of numbers, times 10, minus 8-- let me pick a good number here-- 12, and then minus 2.
So now there might be a strong temptation-- and you know in some ways it's not even an illegitimate temptation-- to do the same thing with multiplication that we did with addition, to just multiply the corresponding terms.
So you might be tempted to say, well, the first term right here, the 1, 1 term, or in the first row and first column, is going to be 2 times 10.
And this term is going to be minus 3 times minus 8 and so forth.
And that's how we added matrices so maybe it's a natural extension to multiply matrices the same way.
And that is legitimate.
One could define it that way, but that's not the way it is in the real world.
And the way in the real world, unfortunately, is more complex.
But if you look at a bunch of examples I think you'll get it.
And you'll learn that it's actually fairly straightforward.
So how do we do it?
So this first term that's in the first row and its first column, is equal to essentially this first row's vector-- no, this first row vector-- times this column vector.
Now what do I mean by that, right?
So it's getting it's row information from the first matrix's row, and it's getting it's column information from the second matrix's column.
So how do I do that?
If you're familiar with dot product, it's essentially the dot product of these two matrices.
Or without saying it that fancy, it's just this: it's 2 times 10, so 2-- I'm going to write small-- times 10, plus minus 3 times 12.
I'm going to run out of space.
And so what's this second term over here? Well, we're still on the first row of the product vector but now we're on the second column.
We get our column information from here.
So let's pick a good color-- this is a slightly different shade of purple.
So now this is going to be-- I'll do that in another color-- 2 times minus 8-- let me just write out the number-- 2 times minus 8 is minus 16, plus minus 3 times minus 2-- what's minus 3 times minus 2?
That is plus 6, right?
So that's in row 1 column 2.
It's minus 16 plus 6.
And then let's come down here.
So now we're in the second row.
So now we're going to use-- we're getting our row information from the first matrix-- I know this is confusing and I feel bad for you right now, but we're going to a bunch of examples and I think it'll make sense.
So this term-- the bottom left term-- is going to be this row times this column.
So it's going to be 7 times 10, so 70, plus 7 times 10 plus 5 times 12, plus 60.
And then the bottom right term is going to be 7 times minus 8, which is minus 56 plus 5 times minus 2.
So that's minus 10.
So the final product is going to be 2 times 10 is 20, minus 36, so that's minus 16 plus 6, that's 10.
90-- was that what I said?
No, it was-- 70, plus 60, that's 130.
And then minus 56 minus 10, so minus 66.
So there you have it.
We just multiplied this matrix times this matrix.
Let me do another example.
And I think I'll actually squeeze it on this side so that we can write this side out a little bit more neatly.
So let's take the matrix and now 1, 2, 3, 4, times the matrix 5, 6, 7, 8.
Now we have much more space to work with so this should come out neater.
OK, but I'm going to do the same thing, so to get this term right here-- the top left term-- we're going to take-- or the one that has row 1 column 1-- we're going to take the row 1 information from here, and the column 1 information from here.
So you can view it as this row vector times this column vector.
So it results, 1 times 5 plus 2 times 7.
There you go.
And so this term, it'll be this row vector times this column vector-- let me do that in a different color-- will be 1 times 6 plus 2 times 8.
Let me write that down.
So it's 1 times 6 plus 2 times 8.
And we get our row information from the first vector-- let me circle it with this color-- and it is 3 times 5 plus 4 times 7.
So we get our row information from here and our column information from here.
So it's 3 times 6 plus 4 times 8.
Well actually, let me just remind you where all the numbers came from.
So we have that green color, right?
This 1 and this 2, that's this 1 and this 2, this 1 and this 2.
Right?
And notice, these were in the first row and they're in the first row here.
And this 5 and this 7?
Well, that's this 5 and this 7, and this 5 and this 7.
So, interesting.
This was in column 1 of the second matrix and this is in column 1 in the product matrix.
And similarly, the 6 and the 8.
That's this 6, this 8, and then it's used here, this 6 and this 8.
And then finally this 3 and the 4 in the brown, so that's this 3, this 4, and this 3 and this 4.
And we could of course simplify all of it.
This was 1 times 5 plus 2 times 7, so that's 5 plus 14, so this is 19.
This is 1 times 6 plus 2 times 8, so it's 6 plus 16, so that's 22.
This is 3 times 5 plus 4 times 7.
So 15 plus 28, 38, 43-- if my math is correct-- and then we have 3 times 6 plus 4 times 8.
So that's 18 plus 32, that's 50.
So now let me ask you-- just so you know that the product matrix-- just write it neatly-- is 19, 22, 43, and 50.
So now let me ask you a question.
When we did matrix addition we learned that if I had two matrices-- it didn't matter what order we added them in.
So if we said, A plus B-- and these are matrices; that's why
I'm making them all bold-- we said this is the same thing as
B plus A, based on how we define matrix addition, B plus A.
So now let me ask you a question.
Is multiplying two matrices, is AB-- that's just means we're multiplying A and B-- is that the same thing as BA?
Does the order of the matrix multiplication matter?
And so, I'll tell you right now, it actually matters a tremendous amount.
And actually there are certain matrices that you can add in one direction that you can't add in the other-- oh, that you can multiply in one way but you can't multiply in the other order.
And well, I'll show you that in an example-- but just to show that this isn't even equal for most matrices, I encourage you to multiply these two matrices in the other order.
Actually let me do that.
Let me do that really fast just to prove the point to you.
So let me delete all this top part.
Let me delete all of it, and actually I can delete to this.
So hopefully, you know that when I multiply this matrix times this matrix, I got this.
So let me switch the order-- and I'll do it fairly fast just so as to not bore you-- so let me switch the order of the matrix multiplication.
This is good as this is another example-- so I'm going to multiply this matrix:
5, 6, 7, 8, times this matrix-- and
I just switched the order; and we're testing to see whether order matters-- 1, 2, 3, 4.
Let's do it-- and I won't do all the colors and everything,
I'll just do it systematically.
I think you just have to see a lot of examples here-- So this first term gets its row information from the first matrix, column information from the second matrix.
So it's 5 times 1 plus 6 times 3, so it's 5 times 1--
Let me just write, actually edit.
I'm going to skip a step here-- OK so it's 5 times 1 plus 6 times 3, plus 18.
What's the second term here?
It's going to be 5 times 2 plus 6 times 4.
So 5 times 2 is 10, plus 6 times 4 is 24.
Right, now we just took this row times this column right here.
OK now we're down here for the set-- so then we're doing this row, this element right here at the bottom left is going to use this row, and this column.
So it's 7 times 1 plus 8 times 3.
8 times 3 is 24.
And then finally, to get this element we're essentially multiplying this row times this column, so it's 7 times 2 is 14, plus 8 times 4, plus 32.
So this is equal to 5 plus 18 is 23, 34.
What's 7 plus 24?
That's 31, 46.
So notice, if we called this matrix A and this is matrix B, right?
In the last example, we showed that A times B is equal to 19, 22, 43, 50.
And we just showed that, well, if you reverse the order, B times A is actually this completely different matrix.
So the order in which you multiply matrices completely matters.
So I'm actually running out of time.
In the next video I going talk a little bit more about the types of matrix-- well, one, we know that order matters-- and in the next video I'll show that what type of matrices can be multiplied by each other.
When we added or subtracted matrices, we just said, well they have to have the same dimensions because you're adding or subtracting corresponding terms.
But you'll see with multiplication it's a little bit different.
And we'll do that in the next video.
See you soon.
Greetings, Long live Tamil Language, Develop Tamil School
My name is Nagarajan.
My daughter is studying in Year 4 in this school
Both my boys have studied in this school
My wife is a teacher in this school
This school has been in operation for 60 years now
However, the school cannot be in full operation because lack of basic amenities
Currently there are 212 students in this school
The students are studying in a crowded and non conclusive environment
The school land belongs to a Chinese.
Lately, the owner wishes to have the land back
The assembly hall is situated close to the road
Sand lorries often passes by the sharp bend of the road where is school is situated
The location of this school is dangerous to the students and staff here
We take initiative to avoid any unwanted occurrence to the students and staff
We have asked the government to assist us but we have not received any forms of resolutions
Our PTA president Mr Morgan has worked hard to get assistance to the school
The enrollment of new students to this school is increasing
The situation is sad and dampens our enthusiasm
We hope the government will be able to allocate a land where a new school could be build
Thank you
What you see here is a new road barrier build
The old barrier had been damaged by a lorry, and that time this wall was not been build
To avoid such incidents to occur, we had to build this wall
However, we cannot be sure whether this wall will be able to avoid any unforeseen circumstances
This is the assembly ground
Previously this ground had many holes and after rain there will be pools of water
Students will be unable to assembly during those times
This is a classroom.
Before we fixed a shutter, we used a cupboard as a barrier
It seems this place is called a field
But for me this is not a field.
This place is used for teachers to park their cars
This place is used by 212 students for their physical education activities
That is not the only problem, the field is also not protected.
The fence on this side is spoiled and sometimes students runaway from the school to the road.
This has happened before
The public has frequently trespass this place to park their car
As such the security of the students are at stake
Annual school sport has never been organized by this school.
Only a telematch can be held in a space like this
We can only organize activities such as throwing ball and etc
This is our school laundry system
I have never seen such a Laundry System in this century
Laundry system during the Yap Ah Loy is still in existence in this school
The problem now, when it rains the sewage from the students toilet overflows
In this situation, students are unable to use the toilet and nature calls will have to be put on hold
Here is a conduit pipe from the septic tank to prevent tank overflow.
Water from this conduit will flow to the drainage beside the classroom and foul smell disrupt the students concentration in learning
The backyard of the school is filled with bushes
There are all types of poisonous animals and insect there, eg snake and centipede that would enter the classroom during the rainy season
After every school holidays, student will complain that snake has coiled in the classrooms
This is the fence that protects the school ground
But, lately robbers has entered the school through this fence
Nutritious food such as bread and multi vitamin has been stolen
We got to know that that roof is in a bad condition as well
Because the beams were all eaten by white ants and can cause the roof to fall
Below this beam, we have a functional ceiling fan, so we took initiative to add a ceiling below this roof
But this is a short term plan.
If the roof roots, the ceiling will fall on the students
Because the quality of the ceiling is bad and not a long lasting one
My name is Muniswara Rao
Both my sons are studying in this school
But i got to know the basic amenities is lacking in this school
At the moment many parents are sending their children to different school because of the lack of basic amenities
If the situation persist, then the Tamil Language and Tamil School will be obsolete in this country
I have seen such plans been executed by certain quaters
We have to stop such violation immediately
If we want our language and culture to progress, we have to improvise this school
For that reason we have to fight
The duty of the federal and state government is to assist us
We have organize this press conference, is to send a message to the KPM and Tan Sri Muhyiddin Yassin
This is our main focus
The slogan 1 Student 1 Sport which is propagated by the government, seems to be untrue
What can we do to the place that is so called the school field?
Recognizing Prime Numbers
Determine whether the following numbers are prime, composite, or neither.
Just as a bit of a review, a prime number is a natural number, so one of the counting numbers 1, 2, 3, 4, 5, 6, and so on, that has exactly two factors.
Its factors are 1 and itself.
So an example of a prime number is 3.
There's only two natural numbers that are divisible into 3:
1 and 3.
Another way to think about it is the only way to get 3 as a product of other natural numbers is 1 × 3.
So it only has 1 and itself.
A composite number is a natural number that has more than just 1 and itself as factors and we'll see examples of that.
And neither, we'll see an interesting case of that in this problem.
First let's think about 24.
Let's think about all of the natural numbers, or the whole numbers, although 0 is also included in the whole numbers
Let's think of all of the natural counting numbers that we can actually divide into 24 without having any remainder.
We'd consider those the factors.
Clearly, it is divisible by 1 and 24; in fact, 1 × 24 = 24.
But it's also divisible by 2.
2 × 12 = 24, so it's also divisible by 12.
It is also divisible by 3; 3 × 8 = 24.
And at this point, we don't actually have to find all of the factors to realize that it's not prime.
It clearly has more factors than just 1 and itself.
So then it is clearly going to be composite.
This is going to be composite.
Let's just finish factoring it since we started it.
It's also divisible by 4, and 4 × 6 = 24.
So these are all of the factors of 24, clearly more than just 1 and 24.
Now let's think about 2.
The non-zero whole numbers that are divisible into 2 1 × 2 definitely works, 1 and 2, but there really aren't any others that are divisible into 2.
So it has only 2 factors, 1 and itself.
That's a definition of a prime number.
So 2 is prime.
2 is prime.
2 is interesting, because it is the only even prime number.
Only even prime number. And that might be common sense to you, because by definition, an even number is divisible by 2.
So 2 is clearly divisible by 2, that's what makes it even
But it's only divisible by 2 and 1, that's what makes it prime.
But anything that's even is going to be divisible by 1, itself, and 2.
Any other number that is even is going to be divisible by 1, itself, and 2.
So by definition it's going to have 1 and itself and something else, so it's going to be composite. So 2 is prime; every other even number other than 2 is composite.
Here is an interesting case:
1. 1 is only divisible by 1.
1 is only divisible by 1.
So it is not prime, technically, because it only has 1 as a factor; it does not have two factors.
1 is itself, but it order to be prime, you have to have exactly two factors.
1 has only one factor.
In order to be composite you have to have more than two factors: 1, yourself, and some other things.
So it's not composite.
1 is neither prime nor composite. 1 is neither.
And finally we get to 17.
17 is divisible by 1 and 17.
It's not divisible by 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, or 16.
It has exactly two factors, 1 and itself, so 17 is prime.
I collaborate with bacteria.
And I'm about to show you some stop-motion footage that I made recently where you'll see bacteria accumulating minerals from their environment over the period of an hour.
So what you're seeing here is the bacteria metabolizing, and as they do so they create an electrical charge.
And this attracts metals from their local environment.
And these metals accumulate as minerals on the surface of the bacteria.
One of the most pervasive problems in the world today for people is inadequate access to clean drinking water.
And the desalination process is one where we take out salts.
We can use it for drinking and agriculture.
Removing the salts from water -- particularly seawater -- through reverse osmosis is a critical technique for countries who do not have access to clean drinking water around the globe.
So seawater reverse osmosis is a membrane-filtration technology.
We take the water from the sea and we apply pressure.
And this pressure forces the seawater through a membrane.
This takes energy, producing clean water.
But we're also left with a concentrated salt solution, or brine.
But the process is very expensive and it's cost-prohibitive for many countries around the globe.
And also, the brine that's produced is oftentimes just pumped back out into the sea.
And this is detrimental to the local ecology of the sea area that it's pumped back out into.
So I work in Singapore at the moment, and this is a place that's really a leading place for desalination technology.
And Singapore proposes by 2060 to produce [900] million liters per day of desalinated water.
But this will produce an equally massive amount of desalination brine.
And this is where my collaboration with bacteria comes into play.
So what we're doing at the moment is we're accumulating metals like calcium, potassium and magnesium from out of desalination brine.
And this, in terms of magnesium and the amount of water that I just mentioned, equates to a $4.5 billion mining industry for Singapore -- a place that doesn't have any natural resources.
So I'd like you to image a mining industry in a way that one hasn't existed before; imagine a mining industry that doesn't mean defiling the Earth; imagine bacteria helping us do this by accumulating and precipitating and sedimenting minerals out of desalination brine.
And what you can see here is the beginning of an industry in a test tube, a mining industry that is in harmony with nature.
Thank you.
(Applause)
We've got a scale here, and as you see, the scale is balanced.
And we have a question to answer.
We have this mystery mass over here.
It's a big question mark on this blue mass.
And we also have a bunch of 1 kilogram masses.
These are all each a 1kg mass.
And my question to you is:
What could we do to either side of this scale in order to figure out what the mystery mass is?
Or maybe we can't figure it out at all?
Is there something that we can do either removing or adding these things, so that we can figure out what this mystery mass is?
I will give you a couple of seconds to think about it.
To figure out what this mystery mass is, we essentially just want this on one side of this scale
But that by itself is not enough.
We could just remove these three, but that won't do the job, because if we just remove these three, then the left side of this scale is clearly going to have less mass, and it will go up, and the right side will go down.
And that will not give us much information.
It would just tell us that this blue thing has a lower mass than what is over here.
So just removing this will not help us much.
I won't let us know that this is equal to that.
What we have to do if we want to keep the scale balanced, is that we have to remove the same amount of mass from both sides of the scale.
So, if we want to remove 3 things here, (let me try my best to remove 3 things here) (I will just erase it)
If we want to remove 3 things there, If we did this by itself, just removed these 3 things, the two sides would not have an equal mass anymore. this side would have a lower mass.
So we have to remove 3 from both sides.
If we want to make sure our scale is balanced, we have to remove 3 from both sides.
If we started off with the scales balanced, and then we removed 3 from both sides, the scale will still be balanced and then we would have a clear idea of what the mass of this object actually is.
Now, with 3 removed from both sides, the scale will still be balanced, and we know that this mass is equal to whatever is left over here.
It is equal to 1, 2, 3, 4, 5, 6, 7 - and if we're assuming they are kilograms - we'll know that the question mark mass question mark is equal to 7 kilograms.
So this is a seven kilogram mass.
In this video, we will look at a few examples that will let us practice inductive reasoning.
Now remember, inductive reasoning is any time you are making conclusions based on observations of patterns.
So inductive reasoning has a lot to do with patterns.
In Example A, it says a dot pattern is shown below.
The first question:
How many dots would there be in the bottom row of the fourth figure?
So if we look, we see we have a first figure, second figure, third figure.
Now, when you are working on patterns, its often helpful to just start by extending the pattern yourself, so that you sort of get a feel for it.
So I notice in the first figure there is just one circle.
In the second figure there is one circle and then two circles under it.
And then in the third, there is one and then two and then three.
So I would guess in the fourth, there would be one, and then two under that, and then three under that, and then another row with four under it.
So it looks like basically the number of circles in the bottom row always corresponds to the figure number.
So the third figure had three circles in the bottom row.
And the answer to this question, in the fourth figure there would be four dots in the bottom row.
Next question:
What would the total number of dots be in the sixth figure?
So now we are trying to look at the total number of dots.
Well as we already talked about, if we look at a specific figure, so say the third figure, the way that figure is created is there is one circle on the top, two underneath that, and then three underneath that.
And it keeps going until you reach that term number.
So if you are in the fourth figure, you are at one, two, three, and then four all together.
So there is one circle, two more, three more, four more.
So by the time you get to the sixth figure, it's going to start with one circle on top, and then two under that, and three under that, etc., until you get to six.
So the total number of dots would be one plus two plus three plus four plus five plus six, which would be 21 dots.
Now lets go on to Example B, which says how many triangles would be in the tenth figure.
So lets again just sort of look at the pattern and try to get a feel for it.
And I want to start by actually counting how many triangles are in each one.
So I noticed in this first figure, there are four triangles; one, two, three, four.
In this second figure, there are one, two, three, four, five, six triangles.
In the third figure there is one, two, three, four, five, six, seven, eight triangles.
And just by looking at these I notice each time we are going up by two.
So one way to come up with the answer to this would just be to keep going and write out all the way to like the tenth figure.
And then just keep track of how many triangles there would have to be if you keep adding by twos.
So in the fourth figure there would have to be ten triangles.
In the fifth figure there would be twelve, then fourteen, then sixteen, then eighteen, then twenty, and then twenty-two.
So I know that the answer would have to be 22 triangles if it keeps going up by two triangles each time.
You could also try to come up with a rule that would help you figure that out more quickly, as opposed to having to count all the way up to ten figures.
Because if the question had been about figure 100, it would be annoying to have to go all the way out to figure 100.
So if you want to think about that, the fact that you are adding by two every time means that all of the numbers of triangles, all of these numbers, are all multiples of two.
And they're a specific multiple of two.
It is the original figure number, plus one, times two.
So one plus one is two; two times two is four.
Two plus one is three; three times two is six.
Three plus one is four; four times two is eight.
So basically, if you add one to your figure number, and then times by two, you will get the number of triangles.
So, just remember both of these examples were inductive reasoning where you are looking at some patterns, trying to generalize, to come up with conclusions just based on those patterns.
A few years ago, I felt like I was stuck in a rut, so I decided to follow in the footsteps of the great American philosopher, Morgan Spurlock, and try something new for 30 days.
The idea is actually pretty simple.
Think about something you've always wanted to add to your life and try it for the next 30 days.
It turns out 30 days is just about the right amount of time to add a new habit or subtract a habit -- like watching the news -- from your life.
There's a few things I learned while doing these 30-day challenges.
The first was, instead of the months flying by, forgotten, the time was much more memorable.
This was part of a challenge I did to take a picture every day for a month. And I remember exactly where I was and what I was doing that day.
I also noticed that as I started to do more and harder 30-day challenges, my self-confidence grew.
I went from desk-dwelling computer nerd to the kind of guy who bikes to work. For fun! (Laughter)
Even last year, I ended up hiking up Mt. Kilimanjaro, the highest mountain in Africa.
I would never have been that adventurous before I started my 30-day challenges.
I also figured out that if you really want something badly enough, you can do anything for 30 days.
Have you ever wanted to write a novel?
Every November, tens of thousands of people try to write their own 50,000-word novel, from scratch, in 30 days.
It turns out, all you have to do is write 1,667 words a day for a month.
So I did.
By the way, the secret is not to go to sleep until you've written your words for the day.
You might be sleep-deprived, but you'll finish your novel.
Now is my book the next great American novel?
No. I wrote it in a month.
It's awful. (Laughter)
But for the rest of my life, if I meet John Hodgman at a TED party,
I don't have to say,
"I'm a computer scientist."
No, no, if I want to, I can say, "I'm a novelist."
(Laughter)
So here's one last thing I'd like to mention.
I learned that when I made small, sustainable changes, things I could keep doing, they were more likely to stick.
There's nothing wrong with big, crazy challenges.
In fact, they're a ton of fun.
But they're less likely to stick.
When I gave up sugar for 30 days, day 31 looked like this.
(Laughter)
So here's my question to you:
What are you waiting for?
I guarantee you the next 30 days are going to pass whether you like it or not, so why not think about something you have always wanted to try and give it a shot! For the next 30 days.
Thanks. (Applause)
CHAPTER I THERE IS NO ONE LEFT
When Mary Lennox was sent to Misselthwaite Manor to live with her uncle everybody said she was the most disagreeable-looking child ever seen.
It was true, too.
She had a little thin face and a little thin body, thin light hair and a sour expression.
Her hair was yellow, and her face was yellow because she had been born in India and had always been ill in one way or another.
Her father had held a position under the English Government and had always been busy and ill himself, and her mother had been a great beauty who cared only to go to parties and amuse herself with gay people.
She had not wanted a little girl at all, and when Mary was born she handed her over to the care of an Ayah, who was made to understand that if she wished to please the
Mem Sahib she must keep the child out of sight as much as possible.
So when she was a sickly, fretful, ugly little baby she was kept out of the way, and when she became a sickly, fretful, toddling thing she was kept out of the way also.
She never remembered seeing familiarly anything but the dark faces of her Ayah and the other native servants, and as they always obeyed her and gave her her own way in everything, because the Mem Sahib would be angry if she was disturbed by her crying, by the time she was six years old she was as tyrannical and selfish a little pig as ever lived.
The young English governess who came to teach her to read and write disliked her so much that she gave up her place in three months, and when other governesses came to try to fill it they always went away in a shorter time than the first one.
So if Mary had not chosen to really want to know how to read books she would never have learned her letters at all.
One frightfully hot morning, when she was about nine years old, she awakened feeling very cross, and she became crosser still when she saw that the servant who stood by her bedside was not her Ayah.
"Why did you come?" she said to the strange woman.
"I will not let you stay.
Send my Ayah to me."
The woman looked frightened, but she only stammered that the Ayah could not come and when Mary threw herself into a passion and beat and kicked her, she looked only more frightened and repeated that it was not possible for the Ayah to come to Missie Sahib.
There was something mysterious in the air that morning.
Nothing was done in its regular order and several of the native servants seemed missing, while those whom Mary saw slunk or hurried about with ashy and scared faces.
But no one would tell her anything and her Ayah did not come.
She was actually left alone as the morning went on, and at last she wandered out into the garden and began to play by herself under a tree near the veranda.
She pretended that she was making a flower- bed, and she stuck big scarlet hibiscus blossoms into little heaps of earth, all the time growing more and more angry and muttering to herself the things she would say and the names she would call Saidie when she returned.
Daughter of Pigs!" she said, because to call a native a pig is the worst insult of all.
Pig!
She was grinding her teeth and saying this over and over again when she heard her mother come out on the veranda with some one.
She was with a fair young man and they stood talking together in low strange voices.
Mary knew the fair young man who looked like a boy.
She had heard that he was a very young officer who had just come from England.
The child stared at him, but she stared most at her mother.
She always did this when she had a chance to see her, because the Mem Sahib--Mary used to call her that oftener than anything else--was such a tall, slim, pretty person and wore such lovely clothes.
Her hair was like curly silk and she had a delicate little nose which seemed to be disdaining things, and she had large laughing eyes.
All her clothes were thin and floating, and Mary said they were "full of lace."
They looked fuller of lace than ever this morning, but her eyes were not laughing at all.
They were large and scared and lifted imploringly to the fair boy officer's face.
"Is it so very bad?
Oh, is it?"
Mary heard her say.
You ought to have gone to the hills two weeks ago."
"Awfully, Mrs. Lennox.
The Mem Sahib wrung her hands.
"Oh, I know I ought!" she cried.
"I only stayed to go to that silly dinner party.
What a fool I was!"
At that very moment such a loud sound of wailing broke out from the servants' quarters that she clutched the young man's arm, and Mary stood shivering from head to foot.
The wailing grew wilder and wilder.
"What is it?
What is it?"
Mrs. Lennox gasped.
"Some one has died," answered the boy officer. Come with me!" and she turned and ran into the house.
"I did not know!" the Mem Sahib cried.
"Come with me!
After that, appalling things happened, and the mysteriousness of the morning was explained to Mary.
The cholera had broken out in its most fatal form and people were dying like flies.
The Ayah had been taken ill in the night, and it was because she had just died that the servants had wailed in the huts.
Before the next day three other servants were dead and others had run away in terror.
There was panic on every side, and dying people in all the bungalows.
During the confusion and bewilderment of the second day Mary hid herself in the nursery and was forgotten by everyone.
Nobody thought of her, nobody wanted her, and strange things happened of which she knew nothing.
Mary alternately cried and slept through the hours.
She only knew that people were ill and that she heard mysterious and frightening sounds.
Once she crept into the dining-room and found it empty, though a partly finished meal was on the table and chairs and plates looked as if they had been hastily pushed back when the diners rose suddenly for some reason.
The child ate some fruit and biscuits, and being thirsty she drank a glass of wine which stood nearly filled.
It was sweet, and she did not know how strong it was.
Very soon it made her intensely drowsy, and she went back to her nursery and shut herself in again, frightened by cries she heard in the huts and by the hurrying sound of feet.
The wine made her so sleepy that she could scarcely keep her eyes open and she lay down on her bed and knew nothing more for a long time.
Many things happened during the hours in which she slept so heavily, but she was not disturbed by the wails and the sound of things being carried in and out of the bungalow.
She had never known it to be so silent before.
The house was perfectly still.
She heard neither voices nor footsteps, and wondered if everybody had got well of the cholera and all the trouble was over.
She wondered also who would take care of her now her Ayah was dead.
There would be a new Ayah, and perhaps she would know some new stories.
Mary had been rather tired of the old ones.
She did not cry because her nurse had died.
She was not an affectionate child and had never cared much for any one.
The noise and hurrying about and wailing over the cholera had frightened her, and she had been angry because no one seemed to remember that she was alive.
Everyone was too panic-stricken to think of a little girl no one was fond of.
When people had the cholera it seemed that they remembered nothing but themselves.
But if everyone had got well again, surely some one would remember and come to look for her.
But no one came, and as she lay waiting the house seemed to grow more and more silent.
She heard something rustling on the matting and when she looked down she saw a little snake gliding along and watching her with eyes like jewels.
She was not frightened, because he was a harmless little thing who would not hurt her and he seemed in a hurry to get out of the room.
He slipped under the door as she watched him.
"How queer and quiet it is," she said.
"It sounds as if there were no one in the bungalow but me and the snake."
Almost the next minute she heard footsteps in the compound, and then on the veranda.
They were men's footsteps, and the men entered the bungalow and talked in low voices.
No one went to meet or speak to them and they seemed to open doors and look into rooms.
"What desolation!" she heard one voice say.
I heard there was a child, though no one ever saw her."
I suppose the child, too.
Mary was standing in the middle of the nursery when they opened the door a few minutes later.
She looked an ugly, cross little thing and was frowning because she was beginning to be hungry and feel disgracefully neglected.
The first man who came in was a large officer she had once seen talking to her father.
He looked tired and troubled, but when he saw her he was so startled that he almost jumped back.
"Barney!" he cried out.
"There is a child here!
A child alone!
In a place like this!
Mercy on us, who is she!" "I am Mary Lennox," the little girl said, drawing herself up stiffly.
She thought the man was very rude to call her father's bungalow "A place like this!"
"I fell asleep when everyone had the cholera and I have only just wakened up.
Why does nobody come?"
"It is the child no one ever saw!" exclaimed the man, turning to his companions.
"She has actually been forgotten!"
"Why was I forgotten?"
Mary said, stamping her foot.
"Why does nobody come?"
The young man whose name was Barney looked at her very sadly.
Mary even thought she saw him wink his eyes as if to wink tears away.
"Poor little kid!" he said.
"There is nobody left to come."
It was in that strange and sudden way that Mary found out that she had neither father nor mother left; that they had died and been carried away in the night, and that the few native servants who had not died also had left the house as quickly as they could get out of it, none of them even remembering that there was a Missie Sahib.
That was why the place was so quiet.
It was true that there was no one in the bungalow but herself and the little rustling snake. >
CHAPTER II MlSTRESS MARY QUlTE CONTRARY
Mary had liked to look at her mother from a distance and she had thought her very pretty, but as she knew very little of her she could scarcely have been expected to love her or to miss her very much when she was gone.
She did not miss her at all, in fact, and as she was a self-absorbed child she gave her entire thought to herself, as she had always done.
If she had been older she would no doubt have been very anxious at being left alone in the world, but she was very young, and as she had always been taken care of, she supposed she always would be.
What she thought was that she would like to know if she was going to nice people, who would be polite to her and give her her own way as her Ayah and the other native servants had done.
She knew that she was not going to stay at the English clergyman's house where she was taken at first.
She did not want to stay.
The English clergyman was poor and he had five children nearly all the same age and they wore shabby clothes and were always quarreling and snatching toys from each other.
Mary hated their untidy bungalow and was so disagreeable to them that after the first day or two nobody would play with her.
By the second day they had given her a nickname which made her furious.
It was Basil who thought of it first.
Basil was a little boy with impudent blue eyes and a turned-up nose, and Mary hated him.
She was playing by herself under a tree, just as she had been playing the day the cholera broke out.
She was making heaps of earth and paths for a garden and Basil came and stood near to watch her.
Presently he got rather interested and suddenly made a suggestion.
"Why don't you put a heap of stones there and pretend it is a rockery?" he said.
"There in the middle," and he leaned over her to point.
"Go away!" cried Mary.
"I don't want boys.
Go away!"
For a moment Basil looked angry, and then he began to tease.
He was always teasing his sisters.
He danced round and round her and made faces and sang and laughed.
"Mistress Mary, quite contrary, How does your garden grow?
With silver bells, and cockle shells, And marigolds all in a row."
He sang it until the other children heard and laughed, too; and the crosser Mary got, the more they sang "Mistress Mary, quite contrary"; and after that as long as she stayed with them they called her "Mistress
Mary Quite Contrary" when they spoke of her to each other, and often when they spoke to her.
"You are going to be sent home," Basil said to her, "at the end of the week.
And we're glad of it." "I am glad of it, too," answered Mary.
"Where is home?" "She doesn't know where home is!" said
Basil, with seven-year-old scorn.
"It's England, of course.
Our grandmama lives there and our sister
Mabel was sent to her last year.
You are not going to your grandmama.
You have none.
You are going to your uncle.
His name is Mr. Archibald Craven."
"I don't know anything about him," snapped Mary.
"I know you don't," Basil answered.
"You don't know anything.
Girls never do.
I heard father and mother talking about him.
He lives in a great, big, desolate old house in the country and no one goes near him.
He's so cross he won't let them, and they wouldn't come if he would let them.
He's a hunchback, and he's horrid." "I don't believe you," said Mary; and she turned her back and stuck her fingers in her ears, because she would not listen any more.
But she thought over it a great deal afterward; and when Mrs. Crawford told her that night that she was going to sail away to England in a few days and go to her uncle, Mr. Archibald Craven, who lived at
Misselthwaite Manor, she looked so stony and stubbornly uninterested that they did not know what to think about her.
They tried to be kind to her, but she only turned her face away when Mrs. Crawford attempted to kiss her, and held herself stiffly when Mr. Crawford patted her shoulder.
"She is such a plain child," Mrs. Crawford said pityingly, afterward.
"And her mother was such a pretty creature.
She had a very pretty manner, too, and Mary has the most unattractive ways I ever saw in a child.
The children call her 'Mistress Mary Quite Contrary,' and though it's naughty of them, one can't help understanding it."
"Perhaps if her mother had carried her pretty face and her pretty manners oftener into the nursery Mary might have learned some pretty ways too.
It is very sad, now the poor beautiful thing is gone, to remember that many people never even knew that she had a child at all."
"I believe she scarcely ever looked at her," sighed Mrs. Crawford.
"When her Ayah was dead there was no one to give a thought to the little thing.
Think of the servants running away and leaving her all alone in that deserted bungalow.
Colonel McGrew said he nearly jumped out of his skin when he opened the door and found her standing by herself in the middle of the room."
Mary made the long voyage to England under the care of an officer's wife, who was taking her children to leave them in a boarding-school.
She was very much absorbed in her own little boy and girl, and was rather glad to hand the child over to the woman Mr. Archibald Craven sent to meet her, in
London.
The woman was his housekeeper at Misselthwaite Manor, and her name was Mrs.
She was a stout woman, with very red cheeks and sharp black eyes.
She wore a very purple dress, a black silk mantle with jet fringe on it and a black bonnet with purple velvet flowers which stuck up and trembled when she moved her head.
Mary did not like her at all, but as she very seldom liked people there was nothing remarkable in that; besides which it was very evident Mrs. Medlock did not think much of her.
"My word! she's a plain little piece of goods!" she said.
"And we'd heard that her mother was a beauty.
She hasn't handed much of it down, has she, ma'am?"
"Perhaps she will improve as she grows older," the officer's wife said good- naturedly.
"If she were not so sallow and had a nicer expression, her features are rather good.
Children alter so much." "She'll have to alter a good deal," answered Mrs. Medlock.
"And, there's nothing likely to improve children at Misselthwaite--if you ask me!"
They thought Mary was not listening because she was standing a little apart from them at the window of the private hotel they had gone to.
She was watching the passing buses and cabs and people, but she heard quite well and was made very curious about her uncle and the place he lived in.
What sort of a place was it, and what would he be like?
What was a hunchback?
She had never seen one.
Perhaps there were none in India.
Since she had been living in other people's houses and had had no Ayah, she had begun to feel lonely and to think queer thoughts which were new to her.
She had begun to wonder why she had never seemed to belong to anyone even when her father and mother had been alive.
Other children seemed to belong to their fathers and mothers, but she had never seemed to really be anyone's little girl.
She had had servants, and food and clothes, but no one had taken any notice of her.
She did not know that this was because she was a disagreeable child; but then, of course, she did not know she was disagreeable.
She often thought that other people were, but she did not know that she was so herself.
She thought Mrs. Medlock the most disagreeable person she had ever seen, with her common, highly colored face and her common fine bonnet.
When the next day they set out on their journey to Yorkshire, she walked through the station to the railway carriage with her head up and trying to keep as far away from her as she could, because she did not want to seem to belong to her.
It would have made her angry to think people imagined she was her little girl.
But Mrs. Medlock was not in the least disturbed by her and her thoughts.
She was the kind of woman who would "stand no nonsense from young ones."
At least, that is what she would have said if she had been asked.
She had not wanted to go to London just when her sister Maria's daughter was going to be married, but she had a comfortable, well paid place as housekeeper at
Misselthwaite Manor and the only way in which she could keep it was to do at once what Mr. Archibald Craven told her to do.
She never dared even to ask a question.
"Captain Lennox and his wife died of the cholera," Mr. Craven had said in his short, cold way.
So she packed her small trunk and made the journey.
The child is to be brought here.
You must go to London and bring her yourself."
Mary sat in her corner of the railway carriage and looked plain and fretful.
She had nothing to read or to look at, and she had folded her thin little black-gloved hands in her lap.
Her black dress made her look yellower than ever, and her limp light hair straggled from under her black crepe hat.
"A more marred-looking young one I never saw in my life," Mrs. Medlock thought.
(Marred is a Yorkshire word and means spoiled and pettish.)
She had never seen a child who sat so still without doing anything; and at last she got tired of watching her and began to talk in a brisk, hard voice.
"I suppose I may as well tell you something about where you are going to," she said.
"Do you know anything about your uncle?" "No," said Mary.
"Never heard your father and mother talk about him?"
"No," said Mary frowning.
She frowned because she remembered that her father and mother had never talked to her about anything in particular.
Certainly they had never told her things.
"Humph," muttered Mrs. Medlock, staring at her queer, unresponsive little face.
She did not say any more for a few moments and then she began again.
"I suppose you might as well be told something--to prepare you.
You are going to a queer place."
Mary said nothing at all, and Mrs. Medlock looked rather discomfited by her apparent indifference, but, after taking a breath, she went on.
"Not but that it's a grand big place in a gloomy way, and Mr. Craven's proud of it in his way--and that's gloomy enough, too.
The house is six hundred years old and it's on the edge of the moor, and there's near a hundred rooms in it, though most of them's shut up and locked.
And there's pictures and fine old furniture and things that's been there for ages, and there's a big park round it and gardens and trees with branches trailing to the ground-
-some of them."
She paused and took another breath.
Mary had begun to listen in spite of herself.
It all sounded so unlike India, and anything new rather attracted her.
But she did not intend to look as if she were interested.
That was one of her unhappy, disagreeable ways.
So she sat still.
"Well," said Mrs. Medlock.
"What do you think of it?"
"Nothing," she answered.
"I know nothing about such places."
That made Mrs. Medlock laugh a short sort of laugh.
"Eh!" she said, "but you are like an old woman.
"It doesn't matter" said Mary, "whether I care or not."
"You are right enough there," said Mrs. Medlock.
"It doesn't.
What you're to be kept at Misselthwaite Manor for I don't know, unless because it's the easiest way.
He's not going to trouble himself about you, that's sure and certain.
He never troubles himself about no one."
She stopped herself as if she had just remembered something in time.
"He's got a crooked back," she said.
"That set him wrong.
He was a sour young man and got no good of all his money and big place till he was married." Mary's eyes turned toward her in spite of her intention not to seem to care.
She had never thought of the hunchback's being married and she was a trifle surprised.
Mrs. Medlock saw this, and as she was a talkative woman she continued with more interest.
This was one way of passing some of the time, at any rate.
"She was a sweet, pretty thing and he'd have walked the world over to get her a blade o' grass she wanted.
Nobody thought she'd marry him, but she did, and people said she married him for his money.
But she didn't--she didn't," positively.
"When she died--"
Mary gave a little involuntary jump.
"Oh! did she die!" she exclaimed, quite without meaning to.
She had just remembered a French fairy story she had once read called "Riquet a la
Houppe."
It had been about a poor hunchback and a beautiful princess and it had made her suddenly sorry for Mr. Archibald Craven.
"Yes, she died," Mrs. Medlock answered.
"And it made him queerer than ever.
He cares about nobody.
He won't see people.
Most of the time he goes away, and when he is at Misselthwaite he shuts himself up in the West Wing and won't let any one but Pitcher see him.
Pitcher's an old fellow, but he took care of him when he was a child and he knows his ways."
It sounded like something in a book and it did not make Mary feel cheerful. A house with a hundred rooms, nearly all shut up and with their doors locked--a house on the edge of a moor--whatsoever a moor was--sounded dreary.
A man with a crooked back who shut himself up also!
She stared out of the window with her lips pinched together, and it seemed quite natural that the rain should have begun to pour down in gray slanting lines and splash and stream down the window-panes.
If the pretty wife had been alive she might have made things cheerful by being something like her own mother and by running in and out and going to parties as she had done in frocks "full of lace."
But she was not there any more.
"You needn't expect to see him, because ten to one you won't," said Mrs. Medlock.
"And you mustn't expect that there will be people to talk to you.
You'll have to play about and look after yourself.
You'll be told what rooms you can go into and what rooms you're to keep out of.
There's gardens enough.
But when you're in the house don't go wandering and poking about.
Mr. Craven won't have it."
"I shall not want to go poking about," said sour little Mary and just as suddenly as she had begun to be rather sorry for Mr. Archibald Craven she began to cease to be sorry and to think he was unpleasant enough to deserve all that had happened to him.
And she turned her face toward the streaming panes of the window of the railway carriage and gazed out at the gray rain-storm which looked as if it would go on forever and ever.
She watched it so long and steadily that the grayness grew heavier and heavier before her eyes and she fell asleep. >
CHAPTER ill ACROSS THE MOOR
She slept a long time, and when she awakened Mrs. Medlock had bought a
lunchbasket at one of the stations and they had some chicken and cold beef and bread and butter and some hot tea.
The rain seemed to be streaming down more heavily than ever and everybody in the station wore wet and glistening waterproofs.
The guard lighted the lamps in the carriage, and Mrs. Medlock cheered up very much over her tea and chicken and beef.
She ate a great deal and afterward fell asleep herself, and Mary sat and stared at her and watched her fine bonnet slip on one side until she herself fell asleep once more in the corner of the carriage, lulled by the splashing of the rain against the windows.
It was quite dark when she awakened again.
The train had stopped at a station and Mrs.
Medlock was shaking her.
"You have had a sleep!" she said.
"It's time to open your eyes!
We're at Thwaite Station and we've got a long drive before us."
Mary stood up and tried to keep her eyes open while Mrs. Medlock collected her parcels.
The little girl did not offer to help her, because in India native servants always picked up or carried things and it seemed quite proper that other people should wait on one.
The station was a small one and nobody but themselves seemed to be getting out of the train.
The station-master spoke to Mrs. Medlock in a rough, good-natured way, pronouncing his words in a queer broad fashion which Mary found out afterward was Yorkshire.
"I see tha's got back," he said. "An' tha's browt th' young 'un with thee." "Aye, that's her," answered Mrs. Medlock, speaking with a Yorkshire accent herself and jerking her head over her shoulder toward Mary.
"How's thy Missus?" "Well enow.
Th' carriage is waitin' outside for thee."
A brougham stood on the road before the little outside platform.
Mary saw that it was a smart carriage and that it was a smart footman who helped her in.
His long waterproof coat and the waterproof covering of his hat were shining and dripping with rain as everything was, the burly station-master included.
When he shut the door, mounted the box with the coachman, and they drove off, the little girl found herself seated in a comfortably cushioned corner, but she was not inclined to go to sleep again.
She sat and looked out of the window, curious to see something of the road over which she was being driven to the queer place Mrs. Medlock had spoken of.
She was not at all a timid child and she was not exactly frightened, but she felt that there was no knowing what might happen in a house with a hundred rooms nearly all shut up--a house standing on the edge of a moor.
"What is a moor?" she said suddenly to Mrs. Medlock.
"Look out of the window in about ten minutes and you'll see," the woman answered.
"We've got to drive five miles across
Missel Moor before we get to the Manor.
You won't see much because it's a dark night, but you can see something."
Mary asked no more questions but waited in the darkness of her corner, keeping her eyes on the window.
The carriage lamps cast rays of light a little distance ahead of them and she caught glimpses of the things they passed.
After they had left the station they had driven through a tiny village and she had seen whitewashed cottages and the lights of a public house.
Then they had passed a church and a vicarage and a little shop-window or so in a cottage with toys and sweets and odd things set out for sale.
Then they were on the highroad and she saw hedges and trees.
After that there seemed nothing different for a long time--or at least it seemed a long time to her.
At last the horses began to go more slowly, as if they were climbing up-hill, and presently there seemed to be no more hedges and no more trees.
She could see nothing, in fact, but a dense darkness on either side.
She leaned forward and pressed her face against the window just as the carriage gave a big jolt.
"Eh!
We're on the moor now sure enough," said Mrs. Medlock.
The carriage lamps shed a yellow light on a rough-looking road which seemed to be cut through bushes and low-growing things which ended in the great expanse of dark apparently spread out before and around them.
A wind was rising and making a singular, wild, low, rushing sound.
"It's--it's not the sea, is it?" said Mary, looking round at her companion.
"No, not it," answered Mrs. Medlock.
"Nor it isn't fields nor mountains, it's just miles and miles and miles of wild land that nothing grows on but heather and gorse and broom, and nothing lives on but wild ponies and sheep."
"I feel as if it might be the sea, if there were water on it," said Mary.
"It sounds like the sea just now." "That's the wind blowing through the bushes," Mrs. Medlock said.
"It's a wild, dreary enough place to my mind, though there's plenty that likes it-- particularly when the heather's in bloom."
On and on they drove through the darkness, and though the rain stopped, the wind rushed by and whistled and made strange sounds.
The road went up and down, and several times the carriage passed over a little bridge beneath which water rushed very fast with a great deal of noise.
Mary felt as if the drive would never come to an end and that the wide, bleak moor was a wide expanse of black ocean through which she was passing on a strip of dry land.
"I don't like it," she said to herself.
"I don't like it," and she pinched her thin lips more tightly together.
The horses were climbing up a hilly piece of road when she first caught sight of a light.
Mrs. Medlock saw it as soon as she did and drew a long sigh of relief.
"Eh, I am glad to see that bit o' light twinkling," she exclaimed.
"It's the light in the lodge window.
We shall get a good cup of tea after a bit, at all events."
It was "after a bit," as she said, for when the carriage passed through the park gates there was still two miles of avenue to drive through and the trees (which nearly met overhead) made it seem as if they were driving through a long dark vault.
They drove out of the vault into a clear space and stopped before an immensely long but low-built house which seemed to ramble round a stone court.
At first Mary thought that there were no lights at all in the windows, but as she got out of the carriage she saw that one room in a corner upstairs showed a dull glow.
The entrance door was a huge one made of massive, curiously shaped panels of oak studded with big iron nails and bound with great iron bars.
It opened into an enormous hall, which was so dimly lighted that the faces in the portraits on the walls and the figures in the suits of armor made Mary feel that she did not want to look at them.
As she stood on the stone floor she looked a very small, odd little black figure, and she felt as small and lost and odd as she looked.
A neat, thin old man stood near the manservant who opened the door for them.
"You are to take her to her room," he said in a husky voice.
"He doesn't want to see her.
He's going to London in the morning." "So long as I know what's expected of me, I can manage."
"What's expected of you, Mrs. Medlock," Mr. Pitcher said, "is that you make sure that he's not disturbed and that he doesn't see what he doesn't want to see."
And then Mary Lennox was led up a broad staircase and down a long corridor and up a short flight of steps and through another corridor and another, until a door opened in a wall and she found herself in a room with a fire in it and a supper on a table.
Mrs. Medlock said unceremoniously:
"Well, here you are!
This room and the next are where you'll live--and you must keep to them.
Don't you forget that!"
It was in this way Mistress Mary arrived at Misselthwaite Manor and she had perhaps never felt quite so contrary in all her life. >
CHAPTER IV MARTHA
When she opened her eyes in the morning it was because a young housemaid had come into her room to light the fire and was kneeling on the hearth-rug raking out the cinders noisily.
Mary lay and watched her for a few moments and then began to look about the room.
She had never seen a room at all like it and thought it curious and gloomy.
The walls were covered with tapestry with a forest scene embroidered on it.
There were fantastically dressed people under the trees and in the distance there was a glimpse of the turrets of a castle.
There were hunters and horses and dogs and ladies.
Mary felt as if she were in the forest with them.
Out of a deep window she could see a great climbing stretch of land which seemed to have no trees on it, and to look rather like an endless, dull, purplish sea.
"What is that?" she said, pointing out of the window.
Martha, the young housemaid, who had just risen to her feet, looked and pointed also.
"That there?" she said.
"Yes." "That's th' moor," with a good-natured grin. "Does tha' like it?"
"No," answered Mary.
"I hate it." "That's because tha'rt not used to it,"
Martha said, going back to her hearth.
"Tha' thinks it's too big an' bare now.
But tha' will like it."
"Do you?" inquired Mary.
"Aye, that I do," answered Martha, cheerfully polishing away at the grate.
"I just love it.
It's none bare.
It's covered wi' growin' things as smells sweet.
It's fair lovely in spring an' summer when th' gorse an' broom an' heather's in flower.
It smells o' honey an' there's such a lot o' fresh air--an' th' sky looks so high an' th' bees an' skylarks makes such a nice noise hummin' an' singin'.
Eh!
I wouldn't live away from th' moor for anythin'."
Mary listened to her with a grave, puzzled expression.
The native servants she had been used to in India were not in the least like this.
They were obsequious and servile and did not presume to talk to their masters as if they were their equals.
They made salaams and called them "protector of the poor" and names of that sort.
Indian servants were commanded to do things, not asked.
It was not the custom to say "please" and "thank you" and Mary had always slapped her
Ayah in the face when she was angry.
She wondered a little what this girl would do if one slapped her in the face.
She was a round, rosy, good-natured-looking creature, but she had a sturdy way which made Mistress Mary wonder if she might not even slap back--if the person who slapped her was only a little girl.
"You are a strange servant," she said from her pillows, rather haughtily.
Martha sat up on her heels, with her blacking-brush in her hand, and laughed, without seeming the least out of temper.
"Eh!
I know that," she said.
"If there was a grand Missus at
Misselthwaite I should never have been even one of th' under house-maids.
I might have been let to be scullerymaid but I'd never have been let upstairs.
I'm too common an' I talk too much Yorkshire.
But this is a funny house for all it's so grand.
Seems like there's neither Master nor Mistress except Mr. Pitcher an' Mrs.
Medlock.
Mr. Craven, he won't be troubled about anythin' when he's here, an' he's nearly always away.
Mrs. Medlock gave me th' place out o' kindness.
She told me she could never have done it if Misselthwaite had been like other big houses." "Are you going to be my servant?"
Mary asked, still in her imperious little Indian way.
Martha began to rub her grate again.
"I'm Mrs. Medlock's servant," she said stoutly.
"An' she's Mr. Craven's--but I'm to do the housemaid's work up here an' wait on you a bit. But you won't need much waitin' on."
"Who is going to dress me?" demanded Mary.
Martha sat up on her heels again and stared.
She spoke in broad Yorkshire in her amazement.
"Canna' tha' dress thysen!" she said.
"What do you mean?
I don't understand your language," said
Mary.
"Eh!
I forgot," Martha said.
"Mrs. Medlock told me I'd have to be careful or you wouldn't know what I was sayin'. I mean can't you put on your own clothes?"
"No," answered Mary, quite indignantly.
"I never did in my life.
My Ayah dressed me, of course."
"Well," said Martha, evidently not in the least aware that she was impudent, "it's time tha' should learn.
Tha' cannot begin younger.
It'll do thee good to wait on thysen a bit.
My mother always said she couldn't see why grand people's children didn't turn out fair fools--what with nurses an' bein' washed an' dressed an' took out to walk as if they was puppies!"
"It is different in India," said Mistress Mary disdainfully.
She could scarcely stand this.
But Martha was not at all crushed.
"Eh!
I can see it's different," she answered almost sympathetically.
"I dare say it's because there's such a lot o' blacks there instead o' respectable white people.
When I heard you was comin' from India I thought you was a black too."
Mary sat up in bed furious.
"What!" she said.
"What!
You thought I was a native.
You--you daughter of a pig!"
Martha stared and looked hot.
"Who are you callin' names?" she said.
"You needn't be so vexed.
That's not th' way for a young lady to talk. When you read about 'em in tracts they're always very religious.
You always read as a black's a man an' a brother.
I've never seen a black an' I was fair pleased to think I was goin' to see one close.
When I come in to light your fire this mornin' I crep' up to your bed an' pulled th' cover back careful to look at you.
An' there you was," disappointedly, "no more black than me--for all you're so yeller."
Mary did not even try to control her rage and humiliation.
"You thought I was a native!
You dared!
You don't know anything about natives!
They are not people--they're servants who must salaam to you.
You know nothing about India.
You know nothing about anything!"
She was in such a rage and felt so helpless before the girl's simple stare, and somehow she suddenly felt so horribly lonely and far away from everything she understood and which understood her, that she threw herself face downward on the pillows and burst into passionate sobbing.
She sobbed so unrestrainedly that good- natured Yorkshire Martha was a little frightened and quite sorry for her.
She went to the bed and bent over her.
"Eh! you mustn't cry like that there!" she begged. "You mustn't for sure.
I didn't know you'd be vexed.
I don't know anythin' about anythin'--just like you said.
I beg your pardon, Miss.
Do stop cryin'."
There was something comforting and really friendly in her queer Yorkshire speech and sturdy way which had a good effect on Mary.
She gradually ceased crying and became quiet.
Martha looked relieved.
"It's time for thee to get up now," she said.
"Mrs. Medlock said I was to carry tha' breakfast an' tea an' dinner into th' room next to this.
I'll help thee on with thy clothes if tha'll get out o' bed.
If th' buttons are at th' back tha' cannot button them up tha'self."
When Mary at last decided to get up, the clothes Martha took from the wardrobe were not the ones she had worn when she arrived the night before with Mrs. Medlock.
"Those are not mine," she said.
"Mine are black." She looked the thick white wool coat and dress over, and added with cool approval:
"Those are nicer than mine."
"These are th' ones tha' must put on," Martha answered.
"Mr. Craven ordered Mrs. Medlock to get 'em in London.
He said 'I won't have a child dressed in black wanderin' about like a lost soul,' he said.
'It'd make the place sadder than it is.
Put color on her.'
Mother she said she knew what he meant.
Mother always knows what a body means.
She doesn't hold with black hersel'." "I hate black things," said Mary.
The dressing process was one which taught them both something.
Martha had "buttoned up" her little sisters and brothers but she had never seen a child who stood still and waited for another person to do things for her as if she had neither hands nor feet of her own.
"Why doesn't tha' put on tha' own shoes?" she said when Mary quietly held out her foot.
"My Ayah did it," answered Mary, staring.
"It was the custom."
She said that very often--"It was the custom."
The native servants were always saying it.
If one told them to do a thing their ancestors had not done for a thousand years they gazed at one mildly and said, "It is not the custom" and one knew that was the end of the matter.
It had not been the custom that Mistress Mary should do anything but stand and allow herself to be dressed like a doll, but before she was ready for breakfast she began to suspect that her life at
Misselthwaite Manor would end by teaching her a number of things quite new to her-- things such as putting on her own shoes and stockings, and picking up things she let fall.
If Martha had been a well-trained fine young lady's maid she would have been more subservient and respectful and would have known that it was her business to brush hair, and button boots, and pick things up and lay them away.
She was, however, only an untrained Yorkshire rustic who had been brought up in a moorland cottage with a swarm of little brothers and sisters who had never dreamed of doing anything but waiting on themselves and on the younger ones who were either babies in arms or just learning to totter about and tumble over things.
If Mary Lennox had been a child who was ready to be amused she would perhaps have laughed at Martha's readiness to talk, but Mary only listened to her coldly and wondered at her freedom of manner.
At first she was not at all interested, but gradually, as the girl rattled on in her good-tempered, homely way, Mary began to notice what she was saying.
"Eh! you should see 'em all," she said.
"There's twelve of us an' my father only gets sixteen shilling a week.
I can tell you my mother's put to it to get porridge for 'em all.
They tumble about on th' moor an' play there all day an' mother says th' air of th' moor fattens 'em.
She says she believes they eat th' grass same as th' wild ponies do.
Our Dickon, he's twelve years old and he's got a young pony he calls his own."
"Where did he get it?" asked Mary.
"He found it on th' moor with its mother when it was a little one an' he began to make friends with it an' give it bits o' bread an' pluck young grass for it.
And it got to like him so it follows him about an' it lets him get on its back.
Dickon's a kind lad an' animals likes him."
Mary had never possessed an animal pet of her own and had always thought she should like one.
So she began to feel a slight interest in Dickon, and as she had never before been interested in any one but herself, it was the dawning of a healthy sentiment.
When she went into the room which had been made into a nursery for her, she found that it was rather like the one she had slept in.
It was not a child's room, but a grown-up person's room, with gloomy old pictures on the walls and heavy old oak chairs.
A table in the center was set with a good substantial breakfast.
But she had always had a very small appetite, and she looked with something more than indifference at the first plate Martha set before her.
"I don't want it," she said.
"Tha' doesn't want thy porridge!" Martha exclaimed incredulously.
"No." "Tha' doesn't know how good it is.
Put a bit o' treacle on it or a bit o' sugar."
"I don't want it," repeated Mary.
"Eh!" said Martha.
"I can't abide to see good victuals go to waste.
If our children was at this table they'd clean it bare in five minutes."
"Why?" said Mary coldly.
"Why!" echoed Martha.
"Because they scarce ever had their stomachs full in their lives.
They're as hungry as young hawks an' foxes."
"I don't know what it is to be hungry," said Mary, with the indifference of ignorance.
Martha looked indignant.
"Well, it would do thee good to try it.
I can see that plain enough," she said outspokenly.
"I've no patience with folk as sits an' just stares at good bread an' meat.
My word! don't I wish Dickon and Phil an' Jane an' th' rest of 'em had what's here under their pinafores." "Why don't you take it to them?" suggested
Mary.
"It's not mine," answered Martha stoutly.
"An' this isn't my day out.
I get my day out once a month same as th' rest.
Then I go home an' clean up for mother an' give her a day's rest."
Mary drank some tea and ate a little toast and some marmalade.
"You wrap up warm an' run out an' play you," said Martha.
"It'll do you good and give you some stomach for your meat."
Mary went to the window.
There were gardens and paths and big trees, but everything looked dull and wintry.
"Out?
Why should I go out on a day like this?"
"Well, if tha' doesn't go out tha'It have to stay in, an' what has tha' got to do?"
Mary glanced about her.
There was nothing to do.
When Mrs. Medlock had prepared the nursery she had not thought of amusement.
Perhaps it would be better to go and see what the gardens were like.
"Who will go with me?" she inquired.
Martha stared.
"You'll go by yourself," she answered.
"You'll have to learn to play like other children does when they haven't got sisters and brothers.
Our Dickon goes off on th' moor by himself an' plays for hours.
That's how he made friends with th' pony.
He's got sheep on th' moor that knows him, an' birds as comes an' eats out of his hand.
However little there is to eat, he always saves a bit o' his bread to coax his pets."
It was really this mention of Dickon which made Mary decide to go out, though she was not aware of it.
There would be, birds outside though there would not be ponies or sheep.
They would be different from the birds in India and it might amuse her to look at them.
Martha found her coat and hat for her and a pair of stout little boots and she showed her her way downstairs.
"If tha' goes round that way tha'll come to th' gardens," she said, pointing to a gate in a wall of shrubbery.
"There's lots o' flowers in summer-time, but there's nothin' bloomin' now."
She seemed to hesitate a second before she added, "One of th' gardens is locked up.
No one has been in it for ten years."
"Why?" asked Mary in spite of herself.
Here was another locked door added to the hundred in the strange house.
"Mr. Craven had it shut when his wife died so sudden.
He won't let no one go inside.
It was her garden.
He locked th' door an' dug a hole and buried th' key.
There's Mrs. Medlock's bell ringing--I must run."
After she was gone Mary turned down the walk which led to the door in the shrubbery.
She could not help thinking about the garden which no one had been into for ten years.
She wondered what it would look like and whether there were any flowers still alive in it.
When she had passed through the shrubbery gate she found herself in great gardens, with wide lawns and winding walks with clipped borders.
There were trees, and flower-beds, and evergreens clipped into strange shapes, and a large pool with an old gray fountain in its midst.
But the flower-beds were bare and wintry and the fountain was not playing.
This was not the garden which was shut up.
How could a garden be shut up?
You could always walk into a garden.
She was just thinking this when she saw that, at the end of the path she was following, there seemed to be a long wall, with ivy growing over it.
She was not familiar enough with England to know that she was coming upon the kitchen- gardens where the vegetables and fruit were growing.
She went toward the wall and found that there was a green door in the ivy, and that it stood open.
This was not the closed garden, evidently, and she could go into it.
She went through the door and found that it was a garden with walls all round it and that it was only one of several walled gardens which seemed to open into one another.
She saw another open green door, revealing bushes and pathways between beds containing winter vegetables.
Fruit-trees were trained flat against the wall, and over some of the beds there were glass frames.
The place was bare and ugly enough, Mary thought, as she stood and stared about her.
It might be nicer in summer when things were green, but there was nothing pretty about it now.
Presently an old man with a spade over his shoulder walked through the door leading from the second garden.
He looked startled when he saw Mary, and then touched his cap.
He had a surly old face, and did not seem at all pleased to see her--but then she was displeased with his garden and wore her "quite contrary" expression, and certainly did not seem at all pleased to see him.
"What is this place?" she asked.
"One o' th' kitchen-gardens," he answered.
"What is that?" said Mary, pointing through the other green door.
"Another of 'em," shortly.
"There's another on t'other side o' th' wall an' there's th' orchard t'other side o' that."
"Can I go in them?" asked Mary.
"If tha' likes.
But there's nowt to see."
Mary made no response.
She went down the path and through the second green door.
There, she found more walls and winter vegetables and glass frames, but in the second wall there was another green door and it was not open.
Perhaps it led into the garden which no one had seen for ten years.
As she was not at all a timid child and always did what she wanted to do, Mary went to the green door and turned the handle.
She hoped the door would not open because she wanted to be sure she had found the mysterious garden--but it did open quite easily and she walked through it and found herself in an orchard.
There were walls all round it also and trees trained against them, and there were bare fruit-trees growing in the winter- browned grass--but there was no green door to be seen anywhere.
Mary looked for it, and yet when she had entered the upper end of the garden she had noticed that the wall did not seem to end with the orchard but to extend beyond it as if it enclosed a place at the other side.
She could see the tops of trees above the wall, and when she stood still she saw a bird with a bright red breast sitting on the topmost branch of one of them, and suddenly he burst into his winter song-- almost as if he had caught sight of her and was calling to her.
She stopped and listened to him and somehow his cheerful, friendly little whistle gave her a pleased feeling--even a disagreeable little girl may be lonely, and the big closed house and big bare moor and big bare gardens had made this one feel as if there was no one left in the world but herself.
If she had been an affectionate child, who had been used to being loved, she would have broken her heart, but even though she was "Mistress Mary Quite Contrary" she was desolate, and the bright-breasted little bird brought a look into her sour little face which was almost a smile.
She listened to him until he flew away.
He was not like an Indian bird and she liked him and wondered if she should ever see him again.
Perhaps he lived in the mysterious garden and knew all about it.
Perhaps it was because she had nothing whatever to do that she thought so much of the deserted garden. She was curious about it and wanted to see what it was like.
Why had Mr. Archibald Craven buried the key?
If he had liked his wife so much why did he hate her garden?
She wondered if she should ever see him, but she knew that if she did she should not like him, and he would not like her, and that she should only stand and stare at him and say nothing, though she should be wanting dreadfully to ask him why he had done such a queer thing.
"People never like me and I never like people," she thought.
"And I never can talk as the Crawford children could.
They were always talking and laughing and making noises."
She thought of the robin and of the way he seemed to sing his song at her, and as she remembered the tree-top he perched on she stopped rather suddenly on the path.
"I believe that tree was in the secret garden--I feel sure it was," she said.
"There was a wall round the place and there was no door."
She walked back into the first kitchen- garden she had entered and found the old man digging there.
She went and stood beside him and watched him a few moments in her cold little way.
He took no notice of her and so at last she spoke to him.
"I have been into the other gardens," she said.
"There was nothin' to prevent thee," he answered crustily.
"I went into the orchard." "There was no dog at th' door to bite thee," he answered.
"There was no door there into the other garden," said Mary.
"What garden?" he said in a rough voice, stopping his digging for a moment.
"The one on the other side of the wall," answered Mistress Mary.
"There are trees there--I saw the tops of them.
A bird with a red breast was sitting on one of them and he sang."
To her surprise the surly old weather- beaten face actually changed its expression.
A slow smile spread over it and the gardener looked quite different.
It made her think that it was curious how much nicer a person looked when he smiled.
She had not thought of it before.
He turned about to the orchard side of his garden and began to whistle--a low soft whistle.
She could not understand how such a surly man could make such a coaxing sound.
Almost the next moment a wonderful thing happened.
She heard a soft little rushing flight through the air--and it was the bird with the red breast flying to them, and he actually alighted on the big clod of earth quite near to the gardener's foot.
"Here he is," chuckled the old man, and then he spoke to the bird as if he were speaking to a child.
"Where has tha' been, tha' cheeky little beggar?" he said.
"I've not seen thee before today.
Has tha, begun tha' courtin' this early in th' season?
Tha'rt too forrad."
The bird put his tiny head on one side and looked up at him with his soft bright eye which was like a black dewdrop.
He seemed quite familiar and not the least afraid.
He hopped about and pecked the earth briskly, looking for seeds and insects.
It actually gave Mary a queer feeling in her heart, because he was so pretty and cheerful and seemed so like a person.
He had a tiny plump body and a delicate beak, and slender delicate legs.
"Will he always come when you call him?" she asked almost in a whisper.
"Aye, that he will.
I've knowed him ever since he was a fledgling.
He come out of th' nest in th' other garden an' when first he flew over th' wall he was too weak to fly back for a few days an' we got friendly.
When he went over th' wall again th' rest of th' brood was gone an' he was lonely an' he come back to me." "What kind of a bird is he?"
Mary asked.
"Doesn't tha' know?
He's a robin redbreast an' they're th' friendliest, curiousest birds alive.
They're almost as friendly as dogs--if you know how to get on with 'em.
Watch him peckin' about there an' lookin' round at us now an' again.
He knows we're talkin' about him."
It was the queerest thing in the world to see the old fellow.
He looked at the plump little scarlet- waistcoated bird as if he were both proud and fond of him.
"He's a conceited one," he chuckled.
"He likes to hear folk talk about him.
An' curious--bless me, there never was his like for curiosity an' meddlin'.
He's always comin' to see what I'm plantin'.
He knows all th' things Mester Craven never troubles hissel' to find out.
He's th' head gardener, he is."
The robin hopped about busily pecking the soil and now and then stopped and looked at them a little.
Mary thought his black dewdrop eyes gazed at her with great curiosity.
It really seemed as if he were finding out all about her.
The queer feeling in her heart increased. "Where did the rest of the brood fly to?" she asked.
"There's no knowin'.
The old ones turn 'em out o' their nest an' make 'em fly an' they're scattered before you know it.
This one was a knowin' one an' he knew he was lonely."
Mistress Mary went a step nearer to the robin and looked at him very hard.
"I'm lonely," she said.
She had not known before that this was one of the things which made her feel sour and cross.
She seemed to find it out when the robin looked at her and she looked at the robin.
The old gardener pushed his cap back on his bald head and stared at her a minute.
"Art tha' th' little wench from India?" he asked.
Tha'It be lonlier before tha's done," he said.
"Then no wonder tha'rt lonely.
He began to dig again, driving his spade deep into the rich black garden soil while the robin hopped about very busily employed.
"What is your name?"
Mary inquired.
He stood up to answer her.
"Ben Weatherstaff," he answered, and then he added with a surly chuckle, "I'm lonely mysel' except when he's with me," and he jerked his thumb toward the robin.
"He's th' only friend I've got."
"I have no friends at all," said Mary.
"I never had.
My Ayah didn't like me and I never played with any one."
It is a Yorkshire habit to say what you think with blunt frankness, and old Ben
"Tha' an' me are a good bit alike," he said.
"We was wove out of th' same cloth.
We're neither of us good lookin' an' we're both of us as sour as we look. We've got the same nasty tempers, both of us, I'll warrant."
This was plain speaking, and Mary Lennox had never heard the truth about herself in her life.
Native servants always salaamed and submitted to you, whatever you did.
She had never thought much about her looks, but she wondered if she was as unattractive as Ben Weatherstaff and she also wondered if she looked as sour as he had looked before the robin came.
She actually began to wonder also if she was "nasty tempered."
She felt uncomfortable.
Suddenly a clear rippling little sound broke out near her and she turned round.
She was standing a few feet from a young apple-tree and the robin had flown on to one of its branches and had burst out into a scrap of a song.
Ben Weatherstaff laughed outright.
"What did he do that for?" asked Mary.
"He's made up his mind to make friends with thee," replied Ben.
"Dang me if he hasn't took a fancy to thee."
"To me?" said Mary, and she moved toward the little tree softly and looked up.
"Would you make friends with me?" she said to the robin just as if she was speaking to a person.
"Would you?"
And she did not say it either in her hard little voice or in her imperious Indian voice, but in a tone so soft and eager and coaxing that Ben Weatherstaff was as surprised as she had been when she heard him whistle.
"Why," he cried out, "tha' said that as nice an' human as if tha' was a real child instead of a sharp old woman.
Tha' said it almost like Dickon talks to his wild things on th' moor."
Mary asked, turning round rather in a hurry.
"Everybody knows him.
Dickon's wanderin' about everywhere.
Th' very blackberries an' heather-bells knows him.
I warrant th' foxes shows him where their cubs lies an' th' skylarks doesn't hide their nests from him."
Mary would have liked to ask some more questions.
She was almost as curious about Dickon as she was about the deserted garden.
But just that moment the robin, who had ended his song, gave a little shake of his wings, spread them and flew away.
He had made his visit and had other things to do.
"He has flown over the wall!" Mary cried out, watching him.
"He has flown into the orchard--he has flown across the other wall--into the garden where there is no door!" "He lives there," said old Ben.
"He came out o' th' egg there.
If he's courtin', he's makin' up to some young madam of a robin that lives among th' old rose-trees there."
"Rose-trees," said Mary.
"Are there rose-trees?"
Ben Weatherstaff took up his spade again and began to dig.
"There was ten year' ago," he mumbled.
"I should like to see them," said Mary.
"Where is the green door?
There must be a door somewhere."
Ben drove his spade deep and looked as uncompanionable as he had looked when she first saw him.
"There was ten year' ago, but there isn't now," he said.
"No door!" cried Mary.
"There must be."
"None as any one can find, an' none as is any one's business.
Don't you be a meddlesome wench an' poke your nose where it's no cause to go.
Here, I must go on with my work.
Get you gone an' play you.
I've no more time."
And he actually stopped digging, threw his spade over his shoulder and walked off, without even glancing at her or saying good-by. >
CHAPTER V THE CRY IN THE CORRlDOR
At first each day which passed by for Mary Lennox was exactly like the others.
Every morning she awoke in her tapestried room and found Martha kneeling upon the hearth building her fire; every morning she ate her breakfast in the nursery which had nothing amusing in it; and after each breakfast she gazed out of the window across to the huge moor which seemed to spread out on all sides and climb up to the sky, and after she had stared for a while she realized that if she did not go out she would have to stay in and do nothing--and so she went out.
She did not know that this was the best thing she could have done, and she did not know that, when she began to walk quickly or even run along the paths and down the avenue, she was stirring her slow blood and making herself stronger by fighting with the wind which swept down from the moor.
She ran only to make herself warm, and she hated the wind which rushed at her face and roared and held her back as if it were some giant she could not see.
But the big breaths of rough fresh air blown over the heather filled her lungs with something which was good for her whole thin body and whipped some red color into her cheeks and brightened her dull eyes when she did not know anything about it.
But after a few days spent almost entirely out of doors she wakened one morning knowing what it was to be hungry, and when she sat down to her breakfast she did not glance disdainfully at her porridge and push it away, but took up her spoon and began to eat it and went on eating it until her bowl was empty.
"Tha' got on well enough with that this mornin', didn't tha'?" said Martha.
"It tastes nice today," said Mary, feeling a little surprised her self.
"It's th' air of th' moor that's givin' thee stomach for tha' victuals," answered
Martha.
"It's lucky for thee that tha's got victuals as well as appetite.
There's been twelve in our cottage as had th' stomach an' nothin' to put in it.
You go on playin' you out o' doors every day an' you'll get some flesh on your bones an' you won't be so yeller."
"I don't play," said Mary.
"I have nothing to play with."
"Nothin' to play with!" exclaimed Martha.
"Our children plays with sticks and stones.
They just runs about an' shouts an' looks at things."
Mary did not shout, but she looked at things.
There was nothing else to do.
She walked round and round the gardens and wandered about the paths in the park.
Sometimes she looked for Ben Weatherstaff, but though several times she saw him at work he was too busy to look at her or was too surly.
Once when she was walking toward him he picked up his spade and turned away as if he did it on purpose.
One place she went to oftener than to any other.
It was the long walk outside the gardens with the walls round them.
There were bare flower-beds on either side of it and against the walls ivy grew thickly.
There was one part of the wall where the creeping dark green leaves were more bushy than elsewhere.
It seemed as if for a long time that part had been neglected.
The rest of it had been clipped and made to look neat, but at this lower end of the walk it had not been trimmed at all.
A few days after she had talked to Ben Weatherstaff, Mary stopped to notice this and wondered why it was so.
She had just paused and was looking up at a long spray of ivy swinging in the wind when she saw a gleam of scarlet and heard a brilliant chirp, and there, on the top of the wall, forward perched Ben
Weatherstaff's robin redbreast, tilting forward to look at her with his small head on one side.
"Oh!" she cried out, "is it you--is it you?"
And it did not seem at all queer to her that she spoke to him as if she were sure that he would understand and answer her.
He twittered and chirped and hopped along the wall as if he were telling her all sorts of things.
It seemed to Mistress Mary as if she understood him, too, though he was not speaking in words.
It was as if he said:
"Good morning!
Isn't the wind nice?
Isn't the sun nice?
Isn't everything nice?
Let us both chirp and hop and twitter.
Come on!
Come on!"
Mary began to laugh, and as he hopped and took little flights along the wall she ran after him.
Poor little thin, sallow, ugly Mary--she actually looked almost pretty for a moment.
"I like you!
I like you!" she cried out, pattering down the walk; and she chirped and tried to whistle, which last she did not know how to do in the least.
But the robin seemed to be quite satisfied and chirped and whistled back at her.
At last he spread his wings and made a darting flight to the top of a tree, where he perched and sang loudly.
That reminded Mary of the first time she had seen him.
He had been swinging on a tree-top then and she had been standing in the orchard.
Now she was on the other side of the orchard and standing in the path outside a wall--much lower down--and there was the same tree inside.
"It's in the garden no one can go into," she said to herself.
"It's the garden without a door.
He lives in there.
How I wish I could see what it is like!"
She ran up the walk to the green door she had entered the first morning.
Then she ran down the path through the other door and then into the orchard, and when she stood and looked up there was the tree on the other side of the wall, and there was the robin just finishing his song and, beginning to preen his feathers with his beak.
"It is the garden," she said.
"I am sure it is."
She walked round and looked closely at that side of the orchard wall, but she only found what she had found before--that there was no door in it.
Then she ran through the kitchen-gardens again and out into the walk outside the long ivy-covered wall, and she walked to the end of it and looked at it, but there was no door; and then she walked to the other end, looking again, but there was no door.
"It's very queer," she said.
"Ben Weatherstaff said there was no door and there is no door.
But there must have been one ten years ago, because Mr. Craven buried the key."
This gave her so much to think of that she began to be quite interested and feel that she was not sorry that she had come to Misselthwaite Manor.
In India she had always felt hot and too languid to care much about anything.
The fact was that the fresh wind from the moor had begun to blow the cobwebs out of her young brain and to waken her up a little.
She stayed out of doors nearly all day, and when she sat down to her supper at night she felt hungry and drowsy and comfortable.
She did not feel cross when Martha chattered away.
She felt as if she rather liked to hear her, and at last she thought she would ask her a question.
"Why did Mr. Craven hate the garden?" she said.
She had made Martha stay with her and Martha had not objected at all.
She was very young, and used to a crowded cottage full of brothers and sisters, and she found it dull in the great servants' hall downstairs where the footman and upper-housemaids made fun of her Yorkshire speech and looked upon her as a common little thing, and sat and whispered among themselves.
Martha liked to talk, and the strange child who had lived in India, and been waited upon by "blacks," was novelty enough to attract her.
She sat down on the hearth herself without waiting to be asked.
"Art tha' thinkin' about that garden yet?" she said.
"I knew tha' would.
That was just the way with me when I first heard about it."
"Why did he hate it?" Mary persisted.
Martha tucked her feet under her and made herself quite comfortable.
"Listen to th' wind wutherin' round the house," she said.
"You could bare stand up on the moor if you was out on it tonight."
Mary did not know what "wutherin'" meant until she listened, and then she understood.
It must mean that hollow shuddering sort of roar which rushed round and round the house as if the giant no one could see were buffeting it and beating at the walls and windows to try to break in.
But one knew he could not get in, and somehow it made one feel very safe and warm inside a room with a red coal fire.
"But why did he hate it so?" she asked, after she had listened.
She intended to know if Martha did.
Then Martha gave up her store of knowledge.
"Mind," she said, "Mrs. Medlock said it's not to be talked about.
There's lots o' things in this place that's not to be talked over.
His troubles are none servants' business, he says.
But for th' garden he wouldn't be like he is.
It was Mrs. Craven's garden that she had made when first they were married an' she just loved it, an' they used to 'tend the flowers themselves.
An' none o' th' gardeners was ever let to go in.
Him an' her used to go in an' shut th' door an' stay there hours an' hours, readin' and talkin'.
An' she was just a bit of a girl an' there was an old tree with a branch bent like a seat on it.
An' she made roses grow over it an' she used to sit there.
But one day when she was sittin' there th' branch broke an' she fell on th' ground an' was hurt so bad that next day she died. Th' doctors thought he'd go out o' his mind an' die, too.
That's why he hates it.
No one's never gone in since, an' he won't
let any one talk about it." Mary did not ask any more questions.
She looked at the red fire and listened to the wind "wutherin'."
It seemed to be "wutherin'" louder than ever.
At that moment a very good thing was happening to her.
Four good things had happened to her, in fact, since she came to Misselthwaite
Manor.
She had felt as if she had understood a robin and that he had understood her; she had run in the wind until her blood had grown warm; she had been healthily hungry for the first time in her life; and she had found out what it was to be sorry for some one.
But as she was listening to the wind she began to listen to something else.
She did not know what it was, because at first she could scarcely distinguish it from the wind itself.
It was a curious sound--it seemed almost as if a child were crying somewhere.
Sometimes the wind sounded rather like a child crying, but presently Mistress Mary felt quite sure this sound was inside the house, not outside it.
It was far away, but it was inside.
She turned round and looked at Martha.
"Do you hear any one crying?" she said.
Martha suddenly looked confused.
"No," she answered.
"It's th' wind.
Sometimes it sounds like as if some one was lost on th' moor an' wailin'.
It's got all sorts o' sounds." "But listen," said Mary.
"It's in the house--down one of those long corridors."
And at that very moment a door must have been opened somewhere downstairs; for a great rushing draft blew along the passage and the door of the room they sat in was blown open with a crash, and as they both jumped to their feet the light was blown out and the crying sound was swept down the far corridor so that it was to be heard more plainly than ever.
"There!" said Mary.
"I told you so!
It is some one crying--and it isn't a grown-up person."
Martha ran and shut the door and turned the key, but before she did it they both heard the sound of a door in some far passage shutting with a bang, and then everything was quiet, for even the wind ceased "wutherin'" for a few moments.
"It was th' wind," said Martha stubbornly. "An' if it wasn't, it was little Betty
Butterworth, th' scullery-maid.
She's had th' toothache all day."
But something troubled and awkward in her manner made Mistress Mary stare very hard at her.
She did not believe she was speaking the truth. >
CHAPTER VI "THERE WAS SOME ONE CRYlNG--THERE WAS!"
The next day the rain poured down in torrents again, and when Mary looked out of her window the moor was almost hidden by gray mist and cloud.
There could be no going out today.
"What do you do in your cottage when it rains like this?" she asked Martha.
"Try to keep from under each other's feet mostly," Martha answered.
"Eh! there does seem a lot of us then.
Mother's a good-tempered woman but she gets fair moithered.
The biggest ones goes out in th' cow-shed and plays there.
Dickon he doesn't mind th' wet.
He goes out just th' same as if th' sun was shinin'.
He says he sees things on rainy days as doesn't show when it's fair weather.
He once found a little fox cub half drowned in its hole and he brought it home in th' bosom of his shirt to keep it warm.
Its mother had been killed nearby an' th' hole was swum out an' th' rest o' th' litter was dead.
He's got it at home now.
He found a half-drowned young crow another time an' he brought it home, too, an' tamed it.
It's named Soot because it's so black, an' it hops an' flies about with him everywhere."
The time had come when Mary had forgotten to resent Martha's familiar talk.
She had even begun to find it interesting and to be sorry when she stopped or went away.
The stories she had been told by her Ayah when she lived in India had been quite unlike those Martha had to tell about the moorland cottage which held fourteen people who lived in four little rooms and never had quite enough to eat.
The children seemed to tumble about and amuse themselves like a litter of rough, good-natured collie puppies.
Mary was most attracted by the mother and Dickon.
When Martha told stories of what "mother" said or did they always sounded comfortable.
"If I had a raven or a fox cub I could play with it," said Mary.
"But I have nothing." Martha looked perplexed.
"Can tha' knit?" she asked.
"No," answered Mary.
"Can tha' sew?"
"No." "Can tha' read?"
"Yes."
"Then why doesn't tha, read somethin', or learn a bit o' spellin'?
Tha'st old enough to be learnin' thy book a good bit now."
"I haven't any books," said Mary.
"Those I had were left in India." "That's a pity," said Martha.
"If Mrs. Medlock'd let thee go into th' library, there's thousands o' books there."
Mary did not ask where the library was, because she was suddenly inspired by a new idea.
She made up her mind to go and find it herself.
She was not troubled about Mrs. Medlock.
Mrs. Medlock seemed always to be in her comfortable housekeeper's sitting-room downstairs.
In this queer place one scarcely ever saw any one at all.
In fact, there was no one to see but the servants, and when their master was away they lived a luxurious life below stairs, where there was a huge kitchen hung about with shining brass and pewter, and a large servants' hall where there were four or five abundant meals eaten every day, and where a great deal of lively romping went on when Mrs. Medlock was out of the way.
Mary's meals were served regularly, and Martha waited on her, but no one troubled themselves about her in the least.
Mrs. Medlock came and looked at her every day or two, but no one inquired what she did or told her what to do. She supposed that perhaps this was the
English way of treating children.
In India she had always been attended by her Ayah, who had followed her about and waited on her, hand and foot.
She had often been tired of her company.
Now she was followed by nobody and was learning to dress herself because Martha looked as though she thought she was silly and stupid when she wanted to have things handed to her and put on.
"Hasn't tha' got good sense?" she said once, when Mary had stood waiting for her to put on her gloves for her.
"Our Susan Ann is twice as sharp as thee an' she's only four year' old.
Sometimes tha' looks fair soft in th' head."
Mary had worn her contrary scowl for an hour after that, but it made her think several entirely new things.
She stood at the window for about ten minutes this morning after Martha had swept up the hearth for the last time and gone downstairs.
She was thinking over the new idea which had come to her when she heard of the library.
She did not care very much about the library itself, because she had read very few books; but to hear of it brought back to her mind the hundred rooms with closed doors.
She wondered if they were all really locked and what she would find if she could get into any of them.
Were there a hundred really?
Why shouldn't she go and see how many doors she could count?
It would be something to do on this morning when she could not go out.
She had never been taught to ask permission to do things, and she knew nothing at all about authority, so she would not have thought it necessary to ask Mrs. Medlock if she might walk about the house, even if she had seen her.
She opened the door of the room and went into the corridor, and then she began her wanderings.
It was a long corridor and it branched into other corridors and it led her up short flights of steps which mounted to others again.
There were doors and doors, and there were pictures on the walls.
Sometimes they were pictures of dark, curious landscapes, but oftenest they were portraits of men and women in queer, grand costumes made of satin and velvet.
She found herself in one long gallery whose walls were covered with these portraits.
She had never thought there could be so many in any house.
She walked slowly down this place and stared at the faces which also seemed to stare at her.
She felt as if they were wondering what a little girl from India was doing in their house.
Some were pictures of children--little girls in thick satin frocks which reached to their feet and stood out about them, and boys with puffed sleeves and lace collars and long hair, or with big ruffs around their necks.
She always stopped to look at the children, and wonder what their names were, and where they had gone, and why they wore such odd clothes.
There was a stiff, plain little girl rather like herself.
She wore a green brocade dress and held a green parrot on her finger.
Her eyes had a sharp, curious look.
"Where do you live now?" said Mary aloud to her.
"I wish you were here." Surely no other little girl ever spent such a queer morning.
It seemed as if there was no one in all the huge rambling house but her own small self, wandering about upstairs and down, through narrow passages and wide ones, where it seemed to her that no one but herself had ever walked.
Since so many rooms had been built, people must have lived in them, but it all seemed so empty that she could not quite believe it true.
It was not until she climbed to the second floor that she thought of turning the handle of a door.
All the doors were shut, as Mrs. Medlock had said they were, but at last she put her hand on the handle of one of them and turned it.
She was almost frightened for a moment when she felt that it turned without difficulty and that when she pushed upon the door itself it slowly and heavily opened.
It was a massive door and opened into a big bedroom.
There were embroidered hangings on the wall, and inlaid furniture such as she had seen in India stood about the room.
A broad window with leaded panes looked out upon the moor; and over the mantel was another portrait of the stiff, plain little girl who seemed to stare at her more curiously than ever.
"Perhaps she slept here once," said Mary.
"She stares at me so that she makes me feel queer."
After that she opened more doors and more.
She saw so many rooms that she became quite tired and began to think that there must be a hundred, though she had not counted them.
In all of them there were old pictures or old tapestries with strange scenes worked on them.
There were curious pieces of furniture and curious ornaments in nearly all of them.
In one room, which looked like a lady's sitting-room, the hangings were all embroidered velvet, and in a cabinet were about a hundred little elephants made of ivory.
They were of different sizes, and some had their mahouts or palanquins on their backs.
Some were much bigger than the others and some were so tiny that they seemed only babies.
Mary had seen carved ivory in India and she knew all about elephants.
She opened the door of the cabinet and stood on a footstool and played with these for quite a long time.
When she got tired she set the elephants in order and shut the door of the cabinet.
In all her wanderings through the long corridors and the empty rooms, she had seen nothing alive; but in this room she saw something.
Just after she had closed the cabinet door she heard a tiny rustling sound.
It made her jump and look around at the sofa by the fireplace, from which it seemed to come.
In the corner of the sofa there was a cushion, and in the velvet which covered it there was a hole, and out of the hole peeped a tiny head with a pair of frightened eyes in it.
Mary crept softly across the room to look.
The bright eyes belonged to a little gray mouse, and the mouse had eaten a hole into the cushion and made a comfortable nest there.
Six baby mice were cuddled up asleep near her.
If there was no one else alive in the hundred rooms there were seven mice who did not look lonely at all.
"If they wouldn't be so frightened I would take them back with me," said Mary.
She had wandered about long enough to feel too tired to wander any farther, and she turned back.
Two or three times she lost her way by turning down the wrong corridor and was obliged to ramble up and down until she found the right one; but at last she reached her own floor again, though she was some distance from her own room and did not know exactly where she was.
"I believe I have taken a wrong turning again," she said, standing still at what seemed the end of a short passage with tapestry on the wall.
"I don't know which way to go.
How still everything is!"
It was while she was standing here and just after she had said this that the stillness was broken by a sound.
It was another cry, but not quite like the one she had heard last night; it was only a short one, a fretful childish whine muffled by passing through walls.
"It's nearer than it was," said Mary, her heart beating rather faster.
"And it is crying."
She put her hand accidentally upon the tapestry near her, and then sprang back, feeling quite startled.
The tapestry was the covering of a door which fell open and showed her that there was another part of the corridor behind it, and Mrs. Medlock was coming up it with her bunch of keys in her hand and a very cross look on her face.
"What are you doing here?" she said, and she took Mary by the arm and pulled her away.
"What did I tell you?" "I turned round the wrong corner," explained Mary.
"I didn't know which way to go and I heard some one crying."
She quite hated Mrs. Medlock at the moment, but she hated her more the next.
"You didn't hear anything of the sort," said the housekeeper.
"You come along back to your own nursery or I'll box your ears."
And she took her by the arm and half pushed, half pulled her up one passage and down another until she pushed her in at the door of her own room.
"Now," she said, "you stay where you're told to stay or you'll find yourself locked up.
The master had better get you a governess, same as he said he would.
You're one that needs some one to look sharp after you.
I've got enough to do."
She went out of the room and slammed the door after her, and Mary went and sat on the hearth-rug, pale with rage.
She did not cry, but ground her teeth.
"There was some one crying--there was-- there was!" she said to herself.
She had heard it twice now, and sometime she would find out.
She had found out a great deal this morning.
She felt as if she had been on a long journey, and at any rate she had had something to amuse her all the time, and she had played with the ivory elephants and had seen the gray mouse and its babies in their nest in the velvet cushion. >
CHAPTER VII THE KEY TO THE GARDEN
Two days after this, when Mary opened her eyes she sat upright in bed immediately, and called to Martha.
"Look at the moor!
Look at the moor!"
The rainstorm had ended and the gray mist and clouds had been swept away in the night by the wind.
The wind itself had ceased and a brilliant, deep blue sky arched high over the moorland.
Never, never had Mary dreamed of a sky so blue.
In India skies were hot and blazing; this was of a deep cool blue which almost seemed to sparkle like the waters of some lovely bottomless lake, and here and there, high, high in the arched blueness floated small clouds of snow-white fleece.
The far-reaching world of the moor itself looked softly blue instead of gloomy purple-black or awful dreary gray.
"Aye," said Martha with a cheerful grin.
"Th' storm's over for a bit.
It does like this at this time o' th' year.
It goes off in a night like it was pretendin' it had never been here an' never meant to come again.
That's because th' springtime's on its way.
It's a long way off yet, but it's comin'."
"I thought perhaps it always rained or looked dark in England," Mary said.
"Eh! no!" said Martha, sitting up on her heels among her black lead brushes.
"Nowt o' th' soart!"
"What does that mean?" asked Mary seriously.
In India the natives spoke different dialects which only a few people understood, so she was not surprised when Martha used words she did not know.
Martha laughed as she had done the first morning.
"There now," she said.
"I've talked broad Yorkshire again like
Mrs. Medlock said I mustn't.
'Nowt o' th' soart' means 'nothin'-of-the- sort,'" slowly and carefully, "but it takes so long to say it.
Yorkshire's th' sunniest place on earth when it is sunny.
I told thee tha'd like th' moor after a bit.
Just you wait till you see th' gold-colored gorse blossoms an' th' blossoms o' th' broom, an' th' heather flowerin', all purple bells, an' hundreds o' butterflies flutterin' an' bees hummin' an' skylarks soarin' up an' singin'.
You'll want to get out on it as sunrise an' live out on it all day like Dickon does."
"Could I ever get there?" asked Mary wistfully, looking through her window at the far-off blue.
It was so new and big and wonderful and such a heavenly color.
"I don't know," answered Martha.
"Tha's never used tha' legs since tha' was born, it seems to me.
Tha' couldn't walk five mile.
It's five mile to our cottage."
"I should like to see your cottage." Martha stared at her a moment curiously before she took up her polishing brush and began to rub the grate again.
She was thinking that the small plain face did not look quite as sour at this moment as it had done the first morning she saw it.
It looked just a trifle like little Susan Ann's when she wanted something very much.
"I'll ask my mother about it," she said.
"She's one o' them that nearly always sees a way to do things.
It's my day out today an' I'm goin' home.
Eh!
I am glad.
Mrs. Medlock thinks a lot o' mother.
Perhaps she could talk to her."
"I like your mother," said Mary.
"I should think tha' did," agreed Martha, polishing away.
"I've never seen her," said Mary.
"No, tha' hasn't," replied Martha.
She sat up on her heels again and rubbed the end of her nose with the back of her hand as if puzzled for a moment, but she ended quite positively. "Well, she's that sensible an' hard workin' an' goodnatured an' clean that no one could help likin' her whether they'd seen her or not.
When I'm goin' home to her on my day out I just jump for joy when I'm crossin' the moor." "I like Dickon," added Mary.
"And I've never seen him."
"Well," said Martha stoutly, "I've told thee that th' very birds likes him an' th' rabbits an' wild sheep an' ponies, an' th' foxes themselves.
I wonder," staring at her reflectively, "what Dickon would think of thee?"
"He wouldn't like me," said Mary in her stiff, cold little way.
"No one does."
Martha looked reflective again.
"How does tha' like thysel'?" she inquired, really quite as if she were curious to know.
Mary hesitated a moment and thought it over.
"Not at all--really," she answered.
"But I never thought of that before."
Martha grinned a little as if at some homely recollection.
"Mother said that to me once," she said.
"She was at her wash-tub an' I was in a bad temper an' talkin' ill of folk, an' she turns round on me an' says: 'Tha' young vixen, tha'!
There tha' stands sayin' tha' doesn't like this one an' tha' doesn't like that one.
How does tha' like thysel'?' It made me laugh an' it brought me to my senses in a minute."
She went away in high spirits as soon as she had given Mary her breakfast.
She was going to walk five miles across the moor to the cottage, and she was going to help her mother with the washing and do the week's baking and enjoy herself thoroughly.
Mary felt lonelier than ever when she knew she was no longer in the house.
She went out into the garden as quickly as possible, and the first thing she did was to run round and round the fountain flower garden ten times.
She counted the times carefully and when she had finished she felt in better spirits.
The sunshine made the whole place look different.
The high, deep, blue sky arched over Misselthwaite as well as over the moor, and she kept lifting her face and looking up into it, trying to imagine what it would be like to lie down on one of the little snow- white clouds and float about.
She went into the first kitchen-garden and found Ben Weatherstaff working there with two other gardeners.
The change in the weather seemed to have done him good.
He spoke to her of his own accord.
"Springtime's comin,'" he said.
"Cannot tha' smell it?"
Mary sniffed and thought she could.
"I smell something nice and fresh and damp," she said.
"That's th' good rich earth," he answered, digging away.
"It's in a good humor makin' ready to grow things.
It's glad when plantin' time comes.
It's dull in th' winter when it's got nowt to do.
In th' flower gardens out there things will be stirrin' down below in th' dark.
Th' sun's warmin' 'em.
You'll see bits o' green spikes stickin' out o' th' black earth after a bit."
"What will they be?" asked Mary.
"Crocuses an' snowdrops an' daffydowndillys.
Has tha' never seen them?"
"No.
Everything is hot, and wet, and green after the rains in India," said Mary.
"And I think things grow up in a night." "These won't grow up in a night," said
Weatherstaff.
"Tha'll have to wait for 'em.
They'll poke up a bit higher here, an' push out a spike more there, an' uncurl a leaf this day an' another that.
You watch 'em."
"I am going to," answered Mary.
Very soon she heard the soft rustling flight of wings again and she knew at once that the robin had come again.
He was very pert and lively, and hopped about so close to her feet, and put his head on one side and looked at her so slyly that she asked Ben Weatherstaff a question.
"Do you think he remembers me?" she said.
"Remembers thee!" said Weatherstaff indignantly.
"He knows every cabbage stump in th' gardens, let alone th' people.
He's never seen a little wench here before, an' he's bent on findin' out all about thee.
Tha's no need to try to hide anything from him."
"Are things stirring down below in the dark in that garden where he lives?"
"What garden?" grunted Weatherstaff, becoming surly again.
"The one where the old rose-trees are." She could not help asking, because she wanted so much to know.
"Are all the flowers dead, or do some of them come again in the summer?
Are there ever any roses?" "Ask him," said Ben Weatherstaff, hunching his shoulders toward the robin.
"He's the only one as knows.
No one else has seen inside it for ten year'."
Ten years was a long time, Mary thought.
She had been born ten years ago.
She walked away, slowly thinking.
She had begun to like the garden just as she had begun to like the robin and Dickon and Martha's mother.
She was beginning to like Martha, too.
That seemed a good many people to like-- when you were not used to liking.
She thought of the robin as one of the people.
She went to her walk outside the long, ivy- covered wall over which she could see the tree-tops; and the second time she walked up and down the most interesting and exciting thing happened to her, and it was all through Ben Weatherstaff's robin.
She heard a chirp and a twitter, and when she looked at the bare flower-bed at her left side there he was hopping about and pretending to peck things out of the earth to persuade her that he had not followed her.
But she knew he had followed her and the surprise so filled her with delight that she almost trembled a little.
"You do remember me!" she cried out.
"You do!
You are prettier than anything else in the world!"
She chirped, and talked, and coaxed and he hopped, and flirted his tail and twittered.
It was as if he were talking.
His red waistcoat was like satin and he puffed his tiny breast out and was so fine and so grand and so pretty that it was really as if he were showing her how important and like a human person a robin could be.
Mistress Mary forgot that she had ever been contrary in her life when he allowed her to draw closer and closer to him, and bend down and talk and try to make something like robin sounds.
Oh! to think that he should actually let her come as near to him as that!
He knew nothing in the world would make her put out her hand toward him or startle him in the least tiniest way.
He knew it because he was a real person-- only nicer than any other person in the world.
She was so happy that she scarcely dared to breathe.
The flower-bed was not quite bare.
It was bare of flowers because the perennial plants had been cut down for their winter rest, but there were tall shrubs and low ones which grew together at the back of the bed, and as the robin hopped about under them she saw him hop over a small pile of freshly turned up earth.
He stopped on it to look for a worm.
The earth had been turned up because a dog had been trying to dig up a mole and he had scratched quite a deep hole.
Mary looked at it, not really knowing why the hole was there, and as she looked she saw something almost buried in the newly- turned soil.
It was something like a ring of rusty iron or brass and when the robin flew up into a tree nearby she put out her hand and picked the ring up.
It was more than a ring, however; it was an old key which looked as if it had been buried a long time.
Mistress Mary stood up and looked at it with an almost frightened face as it hung from her finger.
"Perhaps it has been buried for ten years," she said in a whisper.
"Perhaps it is the key to the garden!" >
CHAPTER Vill THE ROBlN WHO SHOWED THE WAY
She looked at the key quite a long time.
She turned it over and over, and thought about it.
As I have said before, she was not a child who had been trained to ask permission or consult her elders about things.
All she thought about the key was that if it was the key to the closed garden, and she could find out where the door was, she could perhaps open it and see what was inside the walls, and what had happened to the old rose-trees.
It was because it had been shut up so long that she wanted to see it.
It seemed as if it must be different from other places and that something strange must have happened to it during ten years.
Besides that, if she liked it she could go into it every day and shut the door behind her, and she could make up some play of her own and play it quite alone, because nobody would ever know where she was, but would think the door was still locked and the key buried in the earth.
The thought of that pleased her very much.
Living as it were, all by herself in a house with a hundred mysteriously closed rooms and having nothing whatever to do to amuse herself, had set her inactive brain to working and was actually awakening her imagination.
There is no doubt that the fresh, strong, pure air from the moor had a great deal to do with it.
Just as it had given her an appetite, and fighting with the wind had stirred her blood, so the same things had stirred her mind.
In India she had always been too hot and languid and weak to care much about anything, but in this place she was beginning to care and to want to do new things.
Already she felt less "contrary," though she did not know why.
She put the key in her pocket and walked up and down her walk.
No one but herself ever seemed to come there, so she could walk slowly and look at the wall, or, rather, at the ivy growing on it.
The ivy was the baffling thing.
Howsoever carefully she looked she could see nothing but thickly growing, glossy, dark green leaves.
She was very much disappointed.
Something of her contrariness came back to her as she paced the walk and looked over it at the tree-tops inside.
It seemed so silly, she said to herself, to be near it and not be able to get in.
She took the key in her pocket when she went back to the house, and she made up her mind that she would always carry it with her when she went out, so that if she ever should find the hidden door she would be ready.
Mrs. Medlock had allowed Martha to sleep all night at the cottage, but she was back at her work in the morning with cheeks redder than ever and in the best of spirits.
"I got up at four o'clock," she said.
"Eh! it was pretty on th' moor with th' birds gettin' up an' th' rabbits scamperin' about an' th' sun risin'.
I didn't walk all th' way.
A man gave me a ride in his cart an' I did enjoy myself."
She was full of stories of the delights of her day out.
Her mother had been glad to see her and they had got the baking and washing all out of the way.
She had even made each of the children a doughcake with a bit of brown sugar in it.
"I had 'em all pipin' hot when they came in from playin' on th' moor.
An' th' cottage all smelt o' nice, clean hot bakin' an' there was a good fire, an' they just shouted for joy.
Our Dickon he said our cottage was good enough for a king."
In the evening they had all sat round the fire, and Martha and her mother had sewed patches on torn clothes and mended stockings and Martha had told them about the little girl who had come from India and who had been waited on all her life by what Martha called "blacks" until she didn't know how to put on her own stockings.
"Eh! they did like to hear about you," said
Martha.
"They wanted to know all about th' blacks an' about th' ship you came in.
I couldn't tell 'em enough."
Mary reflected a little.
"I'll tell you a great deal more before your next day out," she said, "so that you will have more to talk about.
I dare say they would like to hear about riding on elephants and camels, and about the officers going to hunt tigers." "My word!" cried delighted Martha.
"It would set 'em clean off their heads.
It would be same as a wild beast show like we heard they had in York once."
"India is quite different from Yorkshire," Mary said slowly, as she thought the matter over.
"I never thought of that.
Did Dickon and your mother like to hear you talk about me?"
"Why, our Dickon's eyes nearly started out o' his head, they got that round," answered
Martha.
"But mother, she was put out about your seemin' to be all by yourself like.
She said, 'Hasn't Mr. Craven got no governess for her, nor no nurse?' and I said, 'No, he hasn't, though Mrs. Medlock says he will when he thinks of it, but she says he mayn't think of it for two or three years.'"
"I don't want a governess," said Mary sharply.
"But mother says you ought to be learnin' your book by this time an' you ought to have a woman to look after you, an' she says: 'Now, Martha, you just think how you'd feel yourself, in a big place like that, wanderin' about all alone, an' no mother.
You do your best to cheer her up,' she says, an' I said I would."
Mary gave her a long, steady look.
"You do cheer me up," she said.
"I like to hear you talk."
Presently Martha went out of the room and came back with something held in her hands under her apron.
"What does tha' think," she said, with a cheerful grin.
"I've brought thee a present." "A present!" exclaimed Mistress Mary.
How could a cottage full of fourteen hungry people give any one a present!
"A man was drivin' across the moor peddlin'," Martha explained. "An' he stopped his cart at our door.
He had pots an' pans an' odds an' ends, but mother had no money to buy anythin'.
Just as he was goin' away our 'Lizabeth Ellen called out, 'Mother, he's got skippin'-ropes with red an' blue handles.'
An' mother she calls out quite sudden, 'Here, stop, mister!
How much are they?'
An' he says 'Tuppence', an' mother she began fumblin' in her pocket an' she says to me, 'Martha, tha's brought me thy wages like a good lass, an' I've got four places to put every penny, but I'm just goin' to take tuppence out of it to buy that child a skippin'-rope,' an' she bought one an' here it is."
She brought it out from under her apron and exhibited it quite proudly.
It was a strong, slender rope with a striped red and blue handle at each end, but Mary Lennox had never seen a skipping- rope before.
She gazed at it with a mystified expression.
"What is it for?" she asked curiously.
"For!" cried out Martha.
"Does tha' mean that they've not got skippin'-ropes in India, for all they've got elephants and tigers and camels!
No wonder most of 'em's black.
This is what it's for; just watch me."
And she ran into the middle of the room and, taking a handle in each hand, began to skip, and skip, and skip, while Mary turned in her chair to stare at her, and the queer faces in the old portraits seemed to stare at her, too, and wonder what on earth this common little cottager had the impudence to be doing under their very noses.
But Martha did not even see them.
The interest and curiosity in Mistress Mary's face delighted her, and she went on skipping and counted as she skipped until she had reached a hundred.
"I could skip longer than that," she said when she stopped.
"I've skipped as much as five hundred when I was twelve, but I wasn't as fat then as I am now, an' I was in practice."
Mary got up from her chair beginning to feel excited herself.
"It looks nice," she said.
"Your mother is a kind woman.
Do you think I could ever skip like that?"
"You just try it," urged Martha, handing her the skipping-rope.
"You can't skip a hundred at first, but if you practice you'll mount up.
That's what mother said.
She says, 'Nothin' will do her more good than skippin' rope.
It's th' sensiblest toy a child can have.
Let her play out in th' fresh air skippin' an' it'll stretch her legs an' arms an' give her some strength in 'em.'"
It was plain that there was not a great deal of strength in Mistress Mary's arms and legs when she first began to skip.
She was not very clever at it, but she liked it so much that she did not want to stop.
"Put on tha' things and run an' skip out o' doors," said Martha.
"Mother said I must tell you to keep out o' doors as much as you could, even when it rains a bit, so as tha' wrap up warm."
Mary put on her coat and hat and took her skipping-rope over her arm.
She opened the door to go out, and then suddenly thought of something and turned back rather slowly.
"Martha," she said, "they were your wages.
It was your two-pence really.
Thank you."
She said it stiffly because she was not used to thanking people or noticing that they did things for her.
"Thank you," she said, and held out her hand because she did not know what else to do.
Martha gave her hand a clumsy little shake, as if she was not accustomed to this sort of thing either.
Then she laughed.
"Eh! th' art a queer, old-womanish thing," she said.
"If tha'd been our 'Lizabeth Ellen tha'd have given me a kiss."
Mary looked stiffer than ever.
"Do you want me to kiss you?" Martha laughed again.
"Nay, not me," she answered.
"If tha' was different, p'raps tha'd want to thysel'.
But tha' isn't.
Run off outside an' play with thy rope."
Mistress Mary felt a little awkward as she went out of the room.
Yorkshire people seemed strange, and Martha was always rather a puzzle to her.
At first she had disliked her very much, but now she did not.
The skipping-rope was a wonderful thing.
She counted and skipped, and skipped and counted, until her cheeks were quite red, and she was more interested than she had ever been since she was born.
The sun was shining and a little wind was blowing--not a rough wind, but one which came in delightful little gusts and brought a fresh scent of newly turned earth with it.
She skipped round the fountain garden, and up one walk and down another.
She skipped at last into the kitchen-garden and saw Ben Weatherstaff digging and talking to his robin, which was hopping about him.
She skipped down the walk toward him and he lifted his head and looked at her with a curious expression.
She had wondered if he would notice her.
She wanted him to see her skip.
"Well!" he exclaimed.
"Upon my word.
P'raps tha' art a young 'un, after all, an' p'raps tha's got child's blood in thy veins instead of sour buttermilk.
Tha's skipped red into thy cheeks as sure as my name's Ben Weatherstaff.
I wouldn't have believed tha' could do it." "I never skipped before," Mary said.
"I'm just beginning.
I can only go up to twenty." "Tha' keep on," said Ben.
"Tha' shapes well enough at it for a young 'un that's lived with heathen.
Just see how he's watchin' thee," jerking his head toward the robin.
"He followed after thee yesterday.
He'll be at it again today.
He'll be bound to find out what th' skippin'-rope is.
He's never seen one.
Eh!" shaking his head at the bird, "tha' curiosity will be th' death of thee sometime if tha' doesn't look sharp."
At length she went to her own special walk and made up her mind to try if she could skip the whole length of it.
It was a good long skip and she began slowly, but before she had gone half-way down the path she was so hot and breathless that she was obliged to stop.
She did not mind much, because she had already counted up to thirty.
She stopped with a little laugh of pleasure, and there, lo and behold, was the robin swaying on a long branch of ivy.
He had followed her and he greeted her with a chirp.
As Mary had skipped toward him she felt something heavy in her pocket strike against her at each jump, and when she saw the robin she laughed again.
"You showed me where the key was yesterday," she said.
"You ought to show me the door today; but I don't believe you know!"
The robin flew from his swinging spray of ivy on to the top of the wall and he opened his beak and sang a loud, lovely trill, merely to show off.
Nothing in the world is quite as adorably lovely as a robin when he shows off--and they are nearly always doing it.
Mary Lennox had heard a great deal about Magic in her Ayah's stories, and she always said that what happened almost at that moment was Magic.
One of the nice little gusts of wind rushed down the walk, and it was a stronger one than the rest.
It was strong enough to wave the branches of the trees, and it was more than strong enough to sway the trailing sprays of untrimmed ivy hanging from the wall.
Mary had stepped close to the robin, and suddenly the gust of wind swung aside some
loose ivy trails, and more suddenly still she jumped toward it and caught it in her hand.
This she did because she had seen something under it--a round knob which had been covered by the leaves hanging over it.
It was the knob of a door.
She put her hands under the leaves and began to pull and push them aside.
Thick as the ivy hung, it nearly all was a loose and swinging curtain, though some had crept over wood and iron.
Mary's heart began to thump and her hands to shake a little in her delight and excitement.
The robin kept singing and twittering away and tilting his head on one side, as if he were as excited as she was.
What was this under her hands which was square and made of iron and which her fingers found a hole in?
It was the lock of the door which had been closed ten years and she put her hand in her pocket, drew out the key and found it fitted the keyhole.
She put the key in and turned it.
It took two hands to do it, but it did turn.
And then she took a long breath and looked behind her up the long walk to see if any one was coming.
No one was coming.
No one ever did come, it seemed, and she took another long breath, because she could not help it, and she held back the swinging curtain of ivy and pushed back the door which opened slowly--slowly.
Then she slipped through it, and shut it behind her, and stood with her back against it, looking about her and breathing quite fast with excitement, and wonder, and delight.
She was standing inside the secret garden. >
CHAPTER IX THE STRANGEST HOUSE ANY ONE EVER LlVED IN
It was the sweetest, most mysterious- looking place any one could imagine.
The high walls which shut it in were covered with the leafless stems of climbing roses which were so thick that they were matted together.
Mary Lennox knew they were roses because she had seen a great many roses in India.
All the ground was covered with grass of a wintry brown and out of it grew clumps of bushes which were surely rosebushes if they were alive.
There were numbers of standard roses which had so spread their branches that they were
There were other trees in the garden, and one of the things which made the place look strangest and loveliest was that climbing roses had run all over them and swung down
long tendrils which made light swaying curtains, and here and there they had caught at each other or at a far-reaching branch and had crept from one tree to another and made lovely bridges of themselves.
There were neither leaves nor roses on them now and Mary did not know whether they were dead or alive, but their thin gray or brown branches and sprays looked like a sort of hazy mantle spreading over everything, walls, and trees, and even brown grass, where they had fallen from their fastenings and run along the ground.
It was this hazy tangle from tree to tree which made it all look so mysterious.
Mary had thought it must be different from other gardens which had not been left all by themselves so long; and indeed it was different from any other place she had ever seen in her life.
"How still it is!" she whispered.
"How still!"
Then she waited a moment and listened at the stillness.
The robin, who had flown to his treetop, was still as all the rest.
He did not even flutter his wings; he sat without stirring, and looked at Mary.
"No wonder it is still," she whispered again.
"I am the first person who has spoken in here for ten years."
She moved away from the door, stepping as softly as if she were afraid of awakening some one.
She was glad that there was grass under her feet and that her steps made no sounds.
She walked under one of the fairy-like gray arches between the trees and looked up at the sprays and tendrils which formed them.
"I wonder if they are all quite dead," she said.
"Is it all a quite dead garden?
I wish it wasn't."
If she had been Ben Weatherstaff she could have told whether the wood was alive by looking at it, but she could only see that there were only gray or brown sprays and branches and none showed any signs of even a tiny leaf-bud anywhere.
But she was inside the wonderful garden and she could come through the door under the ivy any time and she felt as if she had found a world all her own.
The sun was shining inside the four walls and the high arch of blue sky over this particular piece of Misselthwaite seemed even more brilliant and soft than it was over the moor.
The robin flew down from his tree-top and hopped about or flew after her from one bush to another.
He chirped a good deal and had a very busy air, as if he were showing her things.
Everything was strange and silent and she seemed to be hundreds of miles away from any one, but somehow she did not feel lonely at all.
All that troubled her was her wish that she knew whether all the roses were dead, or if perhaps some of them had lived and might put out leaves and buds as the weather got warmer.
She did not want it to be a quite dead garden.
If it were a quite alive garden, how wonderful it would be, and what thousands of roses would grow on every side!
Her skipping-rope had hung over her arm when she came in and after she had walked about for a while she thought she would skip round the whole garden, stopping when she wanted to look at things.
There seemed to have been grass paths here and there, and in one or two corners there were alcoves of evergreen with stone seats or tall moss-covered flower urns in them.
As she came near the second of these alcoves she stopped skipping.
There had once been a flowerbed in it, and she thought she saw something sticking out of the black earth--some sharp little pale green points.
She remembered what Ben Weatherstaff had said and she knelt down to look at them.
"Yes, they are tiny growing things and they might be crocuses or snowdrops or daffodils," she whispered.
She bent very close to them and sniffed the fresh scent of the damp earth.
She liked it very much.
"Perhaps there are some other ones coming up in other places," she said.
"I will go all over the garden and look." She did not skip, but walked.
She went slowly and kept her eyes on the ground.
She looked in the old border beds and among the grass, and after she had gone round, trying to miss nothing, she had found ever so many more sharp, pale green points, and she had become quite excited again.
"It isn't a quite dead garden," she cried out softly to herself.
"Even if the roses are dead, there are other things alive."
She did not know anything about gardening, but the grass seemed so thick in some of the places where the green points were pushing their way through that she thought they did not seem to have room enough to grow.
She searched about until she found a rather sharp piece of wood and knelt down and dug and weeded out the weeds and grass until she made nice little clear places around them.
"Now they look as if they could breathe," she said, after she had finished with the first ones.
"I am going to do ever so many more.
I'll do all I can see.
If I haven't time today I can come tomorrow."
She went from place to place, and dug and weeded, and enjoyed herself so immensely that she was led on from bed to bed and into the grass under the trees.
The exercise made her so warm that she first threw her coat off, and then her hat, and without knowing it she was smiling down on to the grass and the pale green points all the time.
The robin was tremendously busy.
He was very much pleased to see gardening begun on his own estate.
He had often wondered at Ben Weatherstaff.
Where gardening is done all sorts of delightful things to eat are turned up with the soil.
Now here was this new kind of creature who was not half Ben's size and yet had had the sense to come into his garden and begin at once.
Mistress Mary worked in her garden until it was time to go to her midday dinner.
In fact, she was rather late in remembering, and when she put on her coat and hat, and picked up her skipping-rope, she could not believe that she had been working two or three hours.
She had been actually happy all the time; and dozens and dozens of the tiny, pale green points were to be seen in cleared places, looking twice as cheerful as they had looked before when the grass and weeds had been smothering them.
"I shall come back this afternoon," she said, looking all round at her new kingdom, and speaking to the trees and the rose- bushes as if they heard her.
Then she ran lightly across the grass, pushed open the slow old door and slipped through it under the ivy.
She had such red cheeks and such bright eyes and ate such a dinner that Martha was delighted.
"Two pieces o' meat an' two helps o' rice puddin'!" she said.
"Eh! mother will be pleased when I tell her what th' skippin'-rope's done for thee."
In the course of her digging with her pointed stick Mistress Mary had found herself digging up a sort of white root rather like an onion.
She had put it back in its place and patted the earth carefully down on it and just now she wondered if Martha could tell her what it was.
"Martha," she said, "what are those white roots that look like onions?"
"They're bulbs," answered Martha.
"Lots o' spring flowers grow from 'em.
Th' very little ones are snowdrops an' crocuses an' th' big ones are narcissuses an' jonquils and daffydowndillys.
Th' biggest of all is lilies an' purple flags.
Eh! they are nice.
Dickon's got a whole lot of 'em planted in our bit o' garden." "Does Dickon know all about them?" asked
Mary, a new idea taking possession of her.
"Our Dickon can make a flower grow out of a brick walk.
Mother says he just whispers things out o' th' ground."
"Do bulbs live a long time?
Would they live years and years if no one helped them?" inquired Mary anxiously.
"They're things as helps themselves," said Martha.
"That's why poor folk can afford to have 'em.
If you don't trouble 'em, most of 'em'll work away underground for a lifetime an' spread out an' have little 'uns.
There's a place in th' park woods here where there's snowdrops by thousands.
They're the prettiest sight in Yorkshire when th' spring comes.
No one knows when they was first planted."
"I wish the spring was here now," said Mary.
"I want to see all the things that grow in England."
She had finished her dinner and gone to her favorite seat on the hearth-rug.
"I wish--I wish I had a little spade," she said.
"Whatever does tha' want a spade for?" asked Martha, laughing.
"Art tha' goin' to take to diggin'?
I must tell mother that, too."
Mary looked at the fire and pondered a little.
She must be careful if she meant to keep her secret kingdom.
She wasn't doing any harm, but if Mr. Craven found out about the open door he would be fearfully angry and get a new key and lock it up forevermore.
She really could not bear that.
"This is such a big lonely place," she said slowly, as if she were turning matters over in her mind.
"The house is lonely, and the park is lonely, and the gardens are lonely.
So many places seem shut up.
I never did many things in India, but there were more people to look at--natives and soldiers marching by--and sometimes bands playing, and my Ayah told me stories.
There is no one to talk to here except you and Ben Weatherstaff.
And you have to do your work and Ben Weatherstaff won't speak to me often.
I thought if I had a little spade I could dig somewhere as he does, and I might make a little garden if he would give me some seeds."
Martha's face quite lighted up.
"There now!" she exclaimed, "if that wasn't one of th' things mother said.
She says, 'There's such a lot o' room in that big place, why don't they give her a bit for herself, even if she doesn't plant nothin' but parsley an' radishes?
She'd dig an' rake away an' be right down happy over it.'
Them was the very words she said." "Were they?" said Mary.
"How many things she knows, doesn't she?"
"Eh!" said Martha.
"It's like she says:
'A woman as brings up twelve children learns something besides her A B C.
Children's as good as 'rithmetic to set you findin' out things.'"
"How much would a spade cost--a little one?"
Mary asked.
"Well," was Martha's reflective answer, "at Thwaite village there's a shop or so an' I saw little garden sets with a spade an' a rake an' a fork all tied together for two shillings.
An' they was stout enough to work with, too."
"I've got more than that in my purse," said Mary.
"Mrs. Morrison gave me five shillings and Mrs. Medlock gave me some money from Mr.
Craven." "Did he remember thee that much?" exclaimed
Martha.
"Mrs. Medlock said I was to have a shilling a week to spend.
She gives me one every Saturday.
I didn't know what to spend it on."
"My word! that's riches," said Martha.
"Tha' can buy anything in th' world tha' wants.
Th' rent of our cottage is only one an' threepence an' it's like pullin' eye-teeth to get it.
Now I've just thought of somethin'," putting her hands on her hips.
"What?" said Mary eagerly.
"In the shop at Thwaite they sell packages o' flower-seeds for a penny each, and our
Dickon he knows which is th' prettiest ones an' how to make 'em grow.
He walks over to Thwaite many a day just for th' fun of it.
Does tha' know how to print letters?" suddenly.
"I know how to write," Mary answered.
Martha shook her head.
"Our Dickon can only read printin'.
If tha' could print we could write a letter to him an' ask him to go an' buy th' garden tools an' th' seeds at th' same time."
"Oh! you're a good girl!"
Mary cried.
"You are, really!
I didn't know you were so nice.
I know I can print letters if I try.
Let's ask Mrs. Medlock for a pen and ink and some paper."
"I've got some of my own," said Martha.
"I bought 'em so I could print a bit of a letter to mother of a Sunday.
I'll go and get it."
She ran out of the room, and Mary stood by the fire and twisted her thin little hands together with sheer pleasure.
"If I have a spade," she whispered, "I can make the earth nice and soft and dig up weeds.
If I have seeds and can make flowers grow the garden won't be dead at all--it will come alive."
She did not go out again that afternoon because when Martha returned with her pen and ink and paper she was obliged to clear the table and carry the plates and dishes downstairs and when she got into the kitchen Mrs. Medlock was there and told her to do something, so Mary waited for what seemed to her a long time before she came back.
Then it was a serious piece of work to write to Dickon.
Mary had been taught very little because her governesses had disliked her too much to stay with her.
She could not spell particularly well but she found that she could print letters when she tried.
This was the letter Martha dictated to her:
"My Dear Dickon:
This comes hoping to find you well as it leaves me at present.
Miss Mary has plenty of money and will you go to Thwaite and buy her some flower seeds and a set of garden tools to make a flower- bed.
Pick the prettiest ones and easy to grow because she has never done it before and
lived in India which is different. Give my love to mother and every one of you.
Miss Mary is going to tell me a lot more so that on my next day out you can hear about elephants and camels and gentlemen going hunting lions and tigers.
"Your loving sister, Martha Phoebe Sowerby."
"We'll put the money in th' envelope an' I'll get th' butcher boy to take it in his cart.
He's a great friend o' Dickon's," said Martha.
"How shall I get the things when Dickon buys them?"
"He'll bring 'em to you himself.
He'll like to walk over this way."
I never thought I should see Dickon."
"Does tha' want to see him?" asked Martha suddenly, for Mary had looked so pleased.
"Yes, I do.
I never saw a boy foxes and crows loved.
I want to see him very much."
Martha gave a little start, as if she remembered something.
"Now to think," she broke out, "to think o' me forgettin' that there; an' I thought I was goin' to tell you first thing this mornin'.
I asked mother--and she said she'd ask Mrs. Medlock her own self."
"Do you mean--" Mary began.
"What I said Tuesday.
Ask her if you might be driven over to our cottage some day and have a bit o' mother's hot oat cake, an' butter, an' a glass o' milk."
It seemed as if all the interesting things were happening in one day.
To think of going over the moor in the daylight and when the sky was blue!
To think of going into the cottage which held twelve children!
"Does she think Mrs. Medlock would let me go?" she asked, quite anxiously.
"Aye, she thinks she would.
She knows what a tidy woman mother is and how clean she keeps the cottage."
"If I went I should see your mother as well as Dickon," said Mary, thinking it over and liking the idea very much.
"She doesn't seem to be like the mothers in India."
Her work in the garden and the excitement of the afternoon ended by making her feel quiet and thoughtful.
Martha stayed with her until tea-time, but they sat in comfortable quiet and talked very little.
But just before Martha went downstairs for the tea-tray, Mary asked a question.
"Martha," she said, "has the scullery-maid had the toothache again today?"
Martha certainly started slightly.
"What makes thee ask that?" she said.
"Because when I waited so long for you to come back I opened the door and walked down the corridor to see if you were coming.
And I heard that far-off crying again, just as we heard it the other night.
There isn't a wind today, so you see it couldn't have been the wind."
"Eh!" said Martha restlessly.
"Tha' mustn't go walkin' about in corridors an' listenin'.
Mr. Craven would be that there angry there's no knowin' what he'd do."
"I wasn't listening," said Mary. "I was just waiting for you--and I heard it.
That's three times." "My word!
There's Mrs. Medlock's bell," said Martha, and she almost ran out of the room.
"It's the strangest house any one ever lived in," said Mary drowsily, as she dropped her head on the cushioned seat of the armchair near her.
Fresh air, and digging, and skipping-rope had made her feel so comfortably tired that she fell asleep. >
CHAPTER X DlCKON
The sun shone down for nearly a week on the secret garden.
The Secret Garden was what Mary called it when she was thinking of it.
She liked the name, and she liked still more the feeling that when its beautiful old walls shut her in no one knew where she was.
It seemed almost like being shut out of the world in some fairy place.
The few books she had read and liked had been fairy-story books, and she had read of secret gardens in some of the stories.
Sometimes people went to sleep in them for a hundred years, which she had thought must be rather stupid.
She had no intention of going to sleep, and, in fact, she was becoming wider awake every day which passed at Misselthwaite.
She was beginning to like to be out of doors; she no longer hated the wind, but enjoyed it.
She could run faster, and longer, and she could skip up to a hundred.
The bulbs in the secret garden must have been much astonished.
Such nice clear places were made round them that they had all the breathing space they wanted, and really, if Mistress Mary had known it, they began to cheer up under the dark earth and work tremendously.
The sun could get at them and warm them, and when the rain came down it could reach them at once, so they began to feel very much alive.
Mary was an odd, determined little person, and now she had something interesting to be determined about, she was very much absorbed, indeed.
She worked and dug and pulled up weeds steadily, only becoming more pleased with her work every hour instead of tiring of it.
It seemed to her like a fascinating sort of play.
She found many more of the sprouting pale green points than she had ever hoped to find.
They seemed to be starting up everywhere and each day she was sure she found tiny new ones, some so tiny that they barely peeped above the earth.
There were so many that she remembered what Martha had said about the "snowdrops by the thousands," and about bulbs spreading and making new ones.
These had been left to themselves for ten years and perhaps they had spread, like the snowdrops, into thousands.
She wondered how long it would be before they showed that they were flowers.
Sometimes she stopped digging to look at the garden and try to imagine what it would be like when it was covered with thousands of lovely things in bloom.
During that week of sunshine, she became more intimate with Ben Weatherstaff.
She surprised him several times by seeming to start up beside him as if she sprang out of the earth.
The truth was that she was afraid that he would pick up his tools and go away if he saw her coming, so she always walked toward him as silently as possible.
But, in fact, he did not object to her as strongly as he had at first.
Perhaps he was secretly rather flattered by her evident desire for his elderly company.
Then, also, she was more civil than she had been.
He did not know that when she first saw him she spoke to him as she would have spoken to a native, and had not known that a cross, sturdy old Yorkshire man was not accustomed to salaam to his masters, and be merely commanded by them to do things.
"Tha'rt like th' robin," he said to her one morning when he lifted his head and saw her standing by him.
"I never knows when I shall see thee or which side tha'll come from."
"He's friends with me now," said Mary.
"That's like him," snapped Ben
Weatherstaff.
"Makin' up to th' women folk just for vanity an' flightiness.
There's nothin' he wouldn't do for th' sake o' showin' off an' flirtin' his tail- feathers.
He's as full o' pride as an egg's full o' meat."
He very seldom talked much and sometimes did not even answer Mary's questions except by a grunt, but this morning he said more than usual.
"How long has tha' been here?" he jerked out.
"I think it's about a month," she answered.
"Tha's beginnin' to do Misselthwaite credit," he said.
"Tha's a bit fatter than tha' was an' tha's not quite so yeller.
Tha' looked like a young plucked crow when tha' first came into this garden.
Thinks I to myself I never set eyes on an uglier, sourer faced young 'un."
Mary was not vain and as she had never thought much of her looks she was not greatly disturbed.
"I know I'm fatter," she said.
"My stockings are getting tighter.
They used to make wrinkles.
There's the robin, Ben Weatherstaff."
There, indeed, was the robin, and she thought he looked nicer than ever.
His red waistcoat was as glossy as satin and he flirted his wings and tail and tilted his head and hopped about with all sorts of lively graces.
He seemed determined to make Ben Weatherstaff admire him.
But Ben was sarcastic.
"Aye, there tha' art!" he said.
"Tha' can put up with me for a bit sometimes when tha's got no one better.
Tha's been reddenin' up thy waistcoat an' polishin' thy feathers this two weeks.
I know what tha's up to.
Tha's courtin' some bold young madam somewhere tellin' thy lies to her about bein' th' finest cock robin on Missel Moor an' ready to fight all th' rest of 'em."
"Oh! look at him!" exclaimed Mary.
The robin was evidently in a fascinating, bold mood.
He hopped closer and closer and looked at Ben Weatherstaff more and more engagingly.
He flew on to the nearest currant bush and tilted his head and sang a little song right at him.
"Tha' thinks tha'll get over me by doin' that," said Ben, wrinkling his face up in such a way that Mary felt sure he was trying not to look pleased.
"Tha' thinks no one can stand out against thee--that's what tha' thinks."
The robin spread his wings--Mary could scarcely believe her eyes.
He flew right up to the handle of Ben Weatherstaff's spade and alighted on the top of it.
Then the old man's face wrinkled itself slowly into a new expression.
He stood still as if he were afraid to breathe--as if he would not have stirred for the world, lest his robin should start away.
He spoke quite in a whisper.
"Well, I'm danged!" he said as softly as if he were saying something quite different.
"Tha' does know how to get at a chap--tha' does!
Tha's fair unearthly, tha's so knowin'."
And he stood without stirring--almost without drawing his breath--until the robin gave another flirt to his wings and flew away.
Then he stood looking at the handle of the spade as if there might be Magic in it, and then he began to dig again and said nothing for several minutes.
But because he kept breaking into a slow grin now and then, Mary was not afraid to talk to him.
"Have you a garden of your own?" she asked.
"No.
I'm bachelder an' lodge with Martin at th' gate."
"If you had one," said Mary, "what would you plant?"
"Cabbages an' 'taters an' onions."
"But if you wanted to make a flower garden," persisted Mary, "what would you plant?" "Bulbs an' sweet-smellin' things--but mostly roses."
Mary's face lighted up.
"Do you like roses?" she said.
Ben Weatherstaff rooted up a weed and threw it aside before he answered.
"Well, yes, I do.
I was learned that by a young lady I was gardener to.
She had a lot in a place she was fond of, an' she loved 'em like they was children-- or robins.
I've seen her bend over an' kiss 'em." He dragged out another weed and scowled at it.
"That were as much as ten year' ago."
"Where is she now?" asked Mary, much interested.
"Heaven," he answered, and drove his spade deep into the soil, "'cording to what parson says."
"What happened to the roses?"
"They was left to themselves."
Mary was becoming quite excited.
"Did they quite die?
Do roses quite die when they are left to themselves?" she ventured.
"Well, I'd got to like 'em--an' I liked her--an' she liked 'em," Ben Weatherstaff admitted reluctantly.
"Once or twice a year I'd go an' work at 'em a bit--prune 'em an' dig about th' roots.
They run wild, but they was in rich soil, so some of 'em lived."
"When they have no leaves and look gray and brown and dry, how can you tell whether they are dead or alive?" inquired Mary.
"Wait till th' spring gets at 'em--wait till th' sun shines on th' rain and th' rain falls on th' sunshine an' then tha'll find out."
"How--how?" cried Mary, forgetting to be careful.
"Look along th' twigs an' branches an' if tha' see a bit of a brown lump swelling here an' there, watch it after th' warm rain an' see what happens."
He stopped suddenly and looked curiously at her eager face.
"Why does tha' care so much about roses an' such, all of a sudden?" he demanded.
Mistress Mary felt her face grow red.
She was almost afraid to answer.
"I--I want to play that--that I have a garden of my own," she stammered.
"I--there is nothing for me to do.
I have nothing--and no one."
"Well," said Ben Weatherstaff slowly, as he watched her, "that's true.
Tha' hasn't."
He said it in such an odd way that Mary wondered if he was actually a little sorry for her.
She had never felt sorry for herself; she had only felt tired and cross, because she disliked people and things so much.
But now the world seemed to be changing and getting nicer.
If no one found out about the secret garden, she should enjoy herself always.
She stayed with him for ten or fifteen minutes longer and asked him as many questions as she dared.
He answered every one of them in his queer grunting way and he did not seem really cross and did not pick up his spade and leave her.
He said something about roses just as she was going away and it reminded her of the ones he had said he had been fond of.
My rheumatics has made me too stiff in th' joints."
"Not been this year.
He said it in his grumbling voice, and then quite suddenly he seemed to get angry with her, though she did not see why he should.
"Now look here!" he said sharply.
"Don't tha' ask so many questions.
Tha'rt th' worst wench for askin' questions I've ever come a cross.
Get thee gone an' play thee.
I've done talkin' for today."
And he said it so crossly that she knew there was not the least use in staying another minute.
She went skipping slowly down the outside walk, thinking him over and saying to herself that, queer as it was, here was another person whom she liked in spite of his crossness.
She liked old Ben Weatherstaff.
Yes, she did like him.
She always wanted to try to make him talk to her.
Also she began to believe that he knew everything in the world about flowers.
There was a laurel-hedged walk which curved round the secret garden and ended at a gate which opened into a wood, in the park.
She thought she would slip round this walk and look into the wood and see if there were any rabbits hopping about.
She enjoyed the skipping very much and when she reached the little gate she opened it and went through because she heard a low, peculiar whistling sound and wanted to find out what it was.
It was a very strange thing indeed.
She quite caught her breath as she stopped to look at it.
A boy was sitting under a tree, with his back against it, playing on a rough wooden pipe.
He was a funny looking boy about twelve.
He looked very clean and his nose turned up and his cheeks were as red as poppies and never had Mistress Mary seen such round and such blue eyes in any boy's face.
And on the trunk of the tree he leaned against, a brown squirrel was clinging and watching him, and from behind a bush nearby a cock pheasant was delicately stretching his neck to peep out, and quite near him were two rabbits sitting up and sniffing with tremulous noses--and actually it appeared as if they were all drawing near to watch him and listen to the strange low
When he saw Mary he held up his hand and spoke to her in a voice almost as low as and rather like his piping.
"Don't tha' move," he said.
"It'd flight 'em."
Mary remained motionless.
He stopped playing his pipe and began to rise from the ground.
He moved so slowly that it scarcely seemed as though he were moving at all, but at last he stood on his feet and then the squirrel scampered back up into the branches of his tree, the pheasant withdrew his head and the rabbits dropped on all fours and began to hop away, though not at all as if they were frightened.
"I'm Dickon," the boy said.
"I know tha'rt Miss Mary."
Then Mary realized that somehow she had known at first that he was Dickon.
Who else could have been charming rabbits and pheasants as the natives charm snakes in India?
He had a wide, red, curving mouth and his smile spread all over his face.
"I got up slow," he explained, "because if tha' makes a quick move it startles 'em.
A body 'as to move gentle an' speak low when wild things is about."
He did not speak to her as if they had never seen each other before but as if he knew her quite well.
Mary knew nothing about boys and she spoke to him a little stiffly because she felt rather shy.
"Did you get Martha's letter?" she asked.
He nodded his curly, rust-colored head.
"That's why I come." He stooped to pick up something which had been lying on the ground beside him when he piped.
"I've got th' garden tools.
There's a little spade an' rake an' a fork an' hoe.
Eh! they are good 'uns.
There's a trowel, too.
An' th' woman in th' shop threw in a packet o' white poppy an' one o' blue larkspur when I bought th' other seeds." "Will you show the seeds to me?"
Mary said.
She wished she could talk as he did.
His speech was so quick and easy.
It sounded as if he liked her and was not the least afraid she would not like him, though he was only a common moor boy, in patched clothes and with a funny face and a rough, rusty-red head.
As she came closer to him she noticed that there was a clean fresh scent of heather and grass and leaves about him, almost as if he were made of them.
She liked it very much and when she looked into his funny face with the red cheeks and round blue eyes she forgot that she had felt shy.
"Let us sit down on this log and look at them," she said.
They sat down and he took a clumsy little brown paper package out of his coat pocket.
He untied the string and inside there were ever so many neater and smaller packages with a picture of a flower on each one.
"There's a lot o' mignonette an' poppies," he said.
"Mignonette's th' sweetest smellin' thing as grows, an' it'll grow wherever you cast it, same as poppies will.
Them as'll come up an' bloom if you just whistle to 'em, them's th' nicest of all."
He stopped and turned his head quickly, his poppy-cheeked face lighting up.
"Where's that robin as is callin' us?" he said.
The chirp came from a thick holly bush, bright with scarlet berries, and Mary thought she knew whose it was.
"Is it really calling us?" she asked.
"Aye," said Dickon, as if it was the most natural thing in the world, "he's callin' some one he's friends with.
That's same as sayin' 'Here I am.
Look at me.
I wants a bit of a chat.'
There he is in the bush.
Whose is he?" "He's Ben Weatherstaff's, but I think he knows me a little," answered Mary.
"Aye, he knows thee," said Dickon in his low voice again.
"An' he likes thee.
He's took thee on.
He'll tell me all about thee in a minute."
He moved quite close to the bush with the slow movement Mary had noticed before, and then he made a sound almost like the robin's own twitter.
The robin listened a few seconds, intently, and then answered quite as if he were replying to a question.
"Aye, he's a friend o' yours," chuckled
Dickon.
"Do you think he is?" cried Mary eagerly.
She did so want to know.
"Do you think he really likes me?" "He wouldn't come near thee if he didn't," answered Dickon.
"Birds is rare choosers an' a robin can flout a body worse than a man.
See, he's making up to thee now.
'Cannot tha' see a chap?' he's sayin'."
And it really seemed as if it must be true.
He so sidled and twittered and tilted as he hopped on his bush.
"Do you understand everything birds say?" said Mary.
Dickon's grin spread until he seemed all wide, red, curving mouth, and he rubbed his rough head.
"I think I do, and they think I do," he said.
"I've lived on th' moor with 'em so long.
I've watched 'em break shell an' come out an' fledge an' learn to fly an' begin to sing, till I think I'm one of 'em.
Sometimes I think p'raps I'm a bird, or a fox, or a rabbit, or a squirrel, or even a beetle, an' I don't know it."
He laughed and came back to the log and began to talk about the flower seeds again.
He told her what they looked like when they were flowers; he told her how to plant them, and watch them, and feed and water them.
"See here," he said suddenly, turning round to look at her.
"I'll plant them for thee myself.
Where is tha' garden?"
Mary's thin hands clutched each other as they lay on her lap.
She did not know what to say, so for a whole minute she said nothing.
She had never thought of this.
She felt miserable.
And she felt as if she went red and then pale.
"Tha's got a bit o' garden, hasn't tha'?"
Dickon said.
It was true that she had turned red and then pale.
Dickon saw her do it, and as she still said nothing, he began to be puzzled.
"Wouldn't they give thee a bit?" he asked.
"Hasn't tha' got any yet?" "I don't know anything about boys," she said slowly.
I don't know what I should do if any one found it out.
It's a great secret.
I believe I should die!"
She said the last sentence quite fiercely.
Dickon looked more puzzled than ever and even rubbed his hand over his rough head again, but he answered quite good- humoredly.
"I'm keepin' secrets all th' time," he said.
"If I couldn't keep secrets from th' other lads, secrets about foxes' cubs, an' birds' nests, an' wild things' holes, there'd be naught safe on th' moor.
Aye, I can keep secrets."
Mistress Mary did not mean to put out her hand and clutch his sleeve but she did it.
"I've stolen a garden," she said very fast.
"It isn't mine.
It isn't anybody's.
Nobody wants it, nobody cares for it, nobody ever goes into it.
Perhaps everything is dead in it already.
I don't know."
She began to feel hot and as contrary as she had ever felt in her life.
"I don't care, I don't care!
Nobody has any right to take it from me when I care about it and they don't.
They're letting it die, all shut in by itself," she ended passionately, and she threw her arms over her face and burst out crying-poor little Mistress Mary.
Dickon's curious blue eyes grew rounder and rounder.
"Eh-h-h!" he said, drawing his exclamation out slowly, and the way he did it meant both wonder and sympathy.
"I've nothing to do," said Mary.
"Nothing belongs to me.
I found it myself and I got into it myself.
I was only just like the robin, and they wouldn't take it from the robin."
"Where is it?" asked Dickon in a dropped voice.
Mistress Mary got up from the log at once.
She knew she felt contrary again, and obstinate, and she did not care at all.
She was imperious and Indian, and at the same time hot and sorrowful.
"Come with me and I'll show you," she said.
She led him round the laurel path and to the walk where the ivy grew so thickly.
Dickon followed her with a queer, almost pitying, look on his face.
He felt as if he were being led to look at some strange bird's nest and must move softly.
When she stepped to the wall and lifted the hanging ivy he started.
There was a door and Mary pushed it slowly open and they passed in together, and then
Mary stood and waved her hand round defiantly.
"It's this," she said.
"It's a secret garden, and I'm the only one in the world who wants it to be alive."
Dickon looked round and round about it, and round and round again.
"Eh!" he almost whispered, "it is a queer, pretty place!
It's like as if a body was in a dream." >
We are asked to divide 99.061 or ninety nine and sixty one thousandths by 100.
And there is a few ways to do it but all I'm going to do in this video is focus on kind of a faster way to think about it.
And hopefully it will make sense to you.
And that is also the focus of it.
That it makes sense to you.
Let us just think about it a little bit.
So 99.061.
So if we were to divide this by 10, just to make the point clear, if we were to divide this by 10, what would we get?
Well, we would essentially move the decimal place one spot to the left.
And it should make sense because we have a little over 99.
If you took 99 divided by 10, you should have a little over 9.
So essentially you would move the decimal place one to the left when you divide by 10.
So this would be equal to 9.9061.
If you were to divide it by 100, which is actually the focus of this problem, so if we divide 99.061 divided by 100.
If we move the decimal place once to the left, we're dividing by 10.
To divide it by 100, we have to divide it by 10 again.
So we move it over twice.
So one, two times.
And so now the decimal place is out in front of that first leading 9.
Which also should make sense.
99 is almost 100.
Or a little bit less than 100.
So if you divide it by 100 we should be a little bit less than 1.
And so if you move the decimal place two places over to the left, because we're really dividing by 10 twice if you want to think of it that way, we will get the decimal in front of the 99. .99061, we should put a 0 out here, just sometimes it clarifies things.
So then we get this right over here.
Now one way to think about it, although I do want you to always imagine that when you move the decimal place over to the left, you really are dividing by 10 when you move it to the left.
When you move it to the right, you are multiplying by 10.
Sometimes people say, hey look, you could just count the number of zeros.
And if you are dividing, so over here you are dividing by 100, 100 has two zeros, so when we're dividing by it, so we can move our decimal two spaces to the left.
That's alright to do that, if you know especially if it's kind of a fast way to do it.
If this had 20 zeros, you would have needed to say, ok, let us move the decimal 20 spaces to the left.
But I really want you to think about why that's working.
Why that makes sense?
Why it's giving you a number that seems to be in the right kind of size number.
That this is why it makes sense that if you take something that's almost 100 and divide it by 100, you'll get something that's almost 1.
And that part, frankly, is just a really good reality check to make sure you're going in the right direction with the decimal.
Because if you were to try this five or ten years from now, maybe your memory of the rule or whatever you want to call it for doing it, you're like, hey, wait.
Do I move the decimal to the left or the right?
It's really good to do that reality check to say, ok, look.
If I'm dividing by 100, I should be getting a smaller value.
And that moving the decimal to the left gives me that smaller value.
If I was multiplying by 100, I should get a larger value.
And moving the decimal to the right would give you that larger value.
Find the mean, median, and mode of the following sets of numbers, and they give us the numbers right over here.
So if someone just says "the mean", they're really referring to what we typically, in everyday language, call "the average".
Sometimes it's called "the arithmetic mean" because you'll learn that there are actually other ways of calculating a mean.
But it's really, you just sum up all of the numbers and you divide by the numbers there are.
And so it's one way of measuring the central tendency or, you know, the average, I guess we could say.
So this is our mean.
We want to average 23 plus 29, or we want to sum 23 plus 29 plus 20 plus 32 plus 23 plus 21 plus 33 plus 25 and then divide that by the number of numbers.
So if [counting] 1, 2, 3, 4, 5, 6, 7, 8 numbers.
So you want to divide that by 8.
So let's figure out what that actually is.
Actually, I'll just get the calculator out for this part. I could do it by hand, but we'll save some time over here.
So we have 23 plus 29 plus 20 plus 20 plus 32 plus 23 plus 21 plus 33 plus 25.
So the sum of all the numbers is 206, and then we want to divide 206 by 8. So, if I say 206 divided by 8 gets us 25.75. So the mean is equal to 25.75.
So this is one way to kind of measure the center, the central tendency.
Another way is with the median. And this is to pick out the middle number.
The median.
And to figure out the median, what we want to do is order these numbers from least to greatest.
So it looks like the smallest number here is 20. Twenty.
Then the next one is 21. Twenty-one.
Then we go... there's no 22 here. There's uh, let's see here, there's two 23s... 23 and a 23. So twenty-three and a twenty-three.
So what's the middle number now that we've ordered it?
So we have [counting] 1, 2, 3, 4, 5, 6, 7, 8 numbers; we already knew that.
And so there's actually going to be two middles.
If you have two... if you have an even number, there's actually two numbers that kind of qualify for close to the middle, and to actually get the median we're going average them.
So, 23 will be one of them.
That by itself can't be the median, because there's three less than it, and there's four greater than it.
And 25 by itself can't be the median because there's three larger than it and four less than it.
So what we do is we take the mean of these two numbers and we pick that as the median.
So if you take 23 plus 25 divided by 2, that's 48 over 2 which is equal to 24. So even though 24 isn't one of these numbers, the median is 24. So this is the middle number.
So once again, this is one way of thinking about central tendency.
If you wanted a number that could somehow represent the middle, and I'm going to be clear, there's no one way of doing it. This is one way of measuring the middle, the middle, let me put that in quotes... the middle, if you had to represent this data with one number.
And this is another way of representing the middle.
Then finally, we can think about the mode.
And the mode is just the number that shows up the most in this data set.
And all of these numbers show up once except we have the 23 that shows up twice. And so twenty... since, since because 23 shows up the most, It shows up twice, every other number only shows up once, 23... 23 is our mode.
Today I'm going to show you how to make a mini indoor bow and arrow.
Start by taking a lolly pop stick, putting it in a bowl of water
And leaving it to soak for half an hour.
Next dry it off, then using a small pair of scissors or nail clippers
Cut two small grooves at each end of the stick.
It should look like this.
Next take a short length of dental floss
Wrap it around the grooves at one end of the stick, and tie it on.
Then we need to gently bend the stick into a bow shape
Wrap the floss around the grooves at the other end, tie it on with a knot
And cut the end off using scissors.
And there we have it, our completed bow.
If you want to customise your bow, use a ball point pen to draw a design on before you bend it into shape.
To make the arrows, we're going to use a cotton bud
And cut the end off using a pair of scissors.
Firing it takes a little bit of practice, but you soon pick it up, and its safe to use indoors.
If you want to make a flaming arrow, first you need to reinforce the cotton bud tube
With a shaved down cocktail stick.
Otherwise the plastic arrow melts and the cotton bud falls off.
Next roll the cotton in some Vaseline
Get it into position ready to fire, and light the arrow.
The arrow will stay alight long after its landed
So you should only do this outside, somewhere safe where nothing can catch fire
And keep some water on standby to put it out.
It you like this project, maybe you'd like to take a look at some of my other videos
By clicking on the links on the right hand side, or take a look at my youtube channel page.
Happy shooting, stay safe and as always, thanks for watching.
Use a number line to compare 11.5 and 11.7.
So let's draw a number line here.
And I am going to focus between 11 and 12 because that's where our two numbers are sitting.
They are 11 and then something else, some number of tenths.
So this right here is 11.
This right here would be 12.
And then let me draw the tenths.
So this would be, smack-dab in between, so that would be eleven and five tenths, or that would be 11.5.
Well, I've already done the first part.
I've figured out where 11.5 is.
It's smack-dab in between 11 and 12.
It's eleven and five tenths.
But let me find everything else.
Let me mark everything else on this number line.
So that's 1 tenth, 2 tenths, 3 tenths, 4 tenths, 5 tenths, 6 tenths, 7 tenths, 8 tenths, 9 tenths and then 10 tenths right on the 12.
It's not completely drawn to scale.
I'm hand-drawing it as good as I can.
So where is 11.7 going to be?
Well this is 11.5.
This is 11.6.
This is 11.7.
Eleven and seven tenths.
1 tenth, 2 tenths, 3 tenths, 4 tenths, 5 tenths, 6 tenths, 7 tenths.
This is 11.7.
And the way we've drawn our number line, we are increasing as we go to the right.
11.7 is to the right of 11.5.
It's clearly greater than 11.5.
11.7 > 11.5
And really, seriously, you didn't have to draw a number line to figure that out.
They're both 11 and something else. This is 11 and 5 tenths.
This is 11 and 7 tenths.
So, clearly, this one is going to be greater.
Both have 11, but this has 7 tenths as opposed to 5 tenths.
 In this video we're going to do a couple of examples that deal with parallel and perpendicular lines.
So you have parallel, you have perpendicular, and, of course, you have lines that are neither parallel nor perpendicular.
And just as a bit of review, if you've never seen this before, parallel lines, they never intersect.
So let me draw some axes.
So if those are my coordinate axes right there, that's my x-axis, that is my y-axis.
If this is a line that I'm drawing in magenta, a parallel line might look something like this.
It's not the exact same line, but they have the exact same slope.
If this moves a certain amount, if this change in y over change in x is a certain amount, this change in y over change in x is the same amount.
And that's why they never intersect.
So they have the same slope.
Parallel lines have the same slope.
Perpendicular lines, depending on how you want to view it, they're kind of the opposite.
Let's say that this is some line.
A line that is perpendicular to that will not only intersect the line, it will intersect it at a right angle, at a 90 degree angle. And I'm not going to prove it for you here.
I actually prove it in the linear algebra playlist. But a perpendicular line's slope-- so let's say that this one right here, let's say that yellow line has a slope of m.
Then this orange line, that's perpendicular to the yellow
line, is going to have a slope of negative 1 over m.
Their slopes are going to be the negative inverse of each other.
Now, given this information, let's look at a bunch of lines and figure out if they're parallel, if they're perpendicular, or if they are neither. And to do that, we just have to keep looking at the slopes.
So let's see, they say one line passes through the points, 4, negative 3, and negative 8, 0.
Another line passes through the points, negative 1, negative 1, and negative 2, 6.
So let's figure out the slopes of each of these lines.
So I'll first do this one in pink.
So this slope right here, so line 1, so I'll call it slope 1.
Slope 1 is, let's just say it is-- well, I'll take this as the finishing point. So negative 3 minus 0-- remember change in y-- negative 3 minus 0, over 4 minus negative 8.
So this is equal to negative 3 over-- this is the same thing as 4 plus 8-- negative 3 over 12, which is equal to negative 1/4.
Divide the numerator and the denominator by 3. That's this line.
That's the first line.
Now, what about the second line?
The slope for that second line is, well, let's take, here, negative 1 minus 6, over negative 1 minus negative 2 is equal to-- negative 1 minus 6 is negative 7, over negative 1 minus negative 2.
That's the same thing as negative 1 plus 2. Well, that's just 1.
So the slope here is negative 7.
So here, their slopes are neither equal-- so they're not parallel-- nor are they the negative inverse of each other.
So this is neither. This is neither parallel nor perpendicular.
So these two lines, they intersect, but they're not going to intersect at a 90 degree angle.
Let's do a couple more of these.
So I have here, once again, one line passing through these points, and then another line passing through these points.
So let's just look at their slopes.
So this one in the green, what's the slope?
The slope of the green one, I'll call that the first line. We could say, let's see, change in y. So we could do negative 2 minus 14, over-- I did negative 2 first, so I'll do 1 first-- over 1 minus negative 3.
So negative 2 minus 14 is negative 16.
1 minus negative 3 is the same things as 1 plus 3. That's over 4.
So this is negative 4.
Now, what's the slope of that second line right there? So we have the slope of that second line. Let's say 5 minus negative 3, that's our change in y, over negative 2 minus 0.
So this is equal to 5 minus negative 3.
That's the same thing as 5 plus 3.
That's 8.
And then negative 2 minus 0 is negative 2.
So this is also equal to negative 4.
So these two lines are parallel.
They have the exact same slope.
And I encourage you to find the equations of both of these lines and graph both of these lines, and verify for yourself that they are indeed parallel.
Let's do this one.
Once again, this is just an exercise in finding slope.
So this first line has those points.
Let's figure out its slope. The slope of this first line, one line passes through these points.
So let's see, 3 minus negative 3, that's our change in y, over 3 minus negative 6.
So this is the same thing as 3 plus 3, which is 6, over 3 plus 6, which is 9.
So this first line has a slope of 2/3. What is the second line's slope?
This was the second line there, that's the other line passing through these points.
So the other line's slope, let's see, we could say negative 8 minus 4, over 2 minus negative 6.
So what is this equal to? Negative 8 minus 4 is negative 12.
2 minus negative 6, that's the same thing as 2 plus 6. The negatives cancel out.
So it's negative 12 over 8, which is the same thing if we divide the numerator and the denominator by 4, that's negative 3/2.
Notice, these guys are the negative inverse of each other.
If I take negative 1 over 2/3, that is equal to negative 1 times 3/2, which is equal to negative 3/2.
These guys are the negative inverses of each other. You swap the numerator and the denominator, make them negative, and they become equal to each other.
So these two lines are perpendicular.
And I encourage you to find the equations-- I already got the slopes for you-- but find the equations of both of these lines, plot them, and verify for yourself that they are perpendicular.
Let's do one more.
Find the equation of a line perpendicular to this line that passes through the point 2 comma 8.
So this first piece of information, that it's perpendicular to that line right over there, what does that tell us?
Well, if it's perpendicular to this line, its slope has to be the negative inverse of 2/5.
So its slope, the negative inverse of 2/5, the inverse of 2/5 is-- let me do it in a better color, a nicer green. If this line's slope is negative 2/5, the equation of the line we have to figure out that's perpendicular, its slope is going to be the inverse.
So instead of 2/5, it's going to be 5/2. Instead of being a negative, it's going to be a positive.
So this is a negative inverse of negative 2/5. Right?
You take the negative sign and it becomes positive. You swap the 5 and the 2, you get 5/2.
So that is going to have to be our slope.
And we can actually use the point-slope form right here. It goes through this point right there.
So let's use point-slope form. y minus this y-value, which has to be on the line, is equal to our slope, 5/2 times x minus this x-value, the x-value when y is equal to 8.
And this is the equation of the line in point-slope form.
If you want to put it in slope-intercept form, you can just do a little bit of algebra, algebraic manipulation. y minus 8 is equal to-- let's distribute the 5/2-- so 5/2 x minus-- 5/2 times 2 is just-- 5.
And then add 8 to both sides. You get y is equal to 5/2x.
Add 8 to negative 5, so plus 3.
And we are done.
Everybody's really been looking forward to the new video from Lumpy and the Lumpettes
Even Lumpy!
Russell's a huge fan!
He can't wait to tell all his friends about it!
Hey, Russell!
You didn't create that video!
You just copied someone else's content.
Uploading someone else's content without permission could get you into a lot of trouble --
-- it may be copyright infringement.
Copyright is a form of protection for original works of authorship including literary, dramatic, musical, graphic, and audiovisual creations.
Copyright infringement occurs when a copyrighted work is reproduced, distributed, performed or publicly displayed without the permission of the copyright holder or the legal right to do so.
Even though YouTube is a free site, you can get in serious trouble for copyright infringement
You can be sued --
-- and found liable for monetary damages.
You could lose your booty!
Or worse, you could lose your YouTube account!
You only get a few chances.
If YouTube receives a valid notification of alleged copyright infringement from a copyright holder for one of your videos, the video will be removed in accordance with the law.
You'll be notified via email and in your account, and you'll get a strike.
If YouTube finds you're a repeat offender --
-- you'll get banned for life!
Here's an idea: why not make your own video?
You're making a video of Lumpy's live performance of his song, which is still protected by copyright.
You still may not be able to upload it without permission.
Oh, Russell.
Your reuse of Lumpy's content is clever, but did you get permission for it?
Mashups or remixes of content may also require permission from the original copyright owner, depending on whether or not the use is a "fair use."
In the United States, copyright law allows for the fair use of copyrighted material under certain limited circumstances without prior permission from the owner.
Under the law, determinations of fair use take into account the purpose and character of the use, the nature of the copyrighted work, the amount and substantiality of the work used in relation to the work as a whole, and the effect of the use upon the potential market for the copyrighted work.
Other jurisdictions may have similar copyright provisions protecting fair use or fair dealing.
If you are uncertain as to whether a specific use qualifies as a fair use, you should consult a qualified copyright attorney.
If someone copies your work after you've posted it, you have the right to take it down.
YouTube provides tools for rights holders to control the use of their content.
If someone takes down your video by mistake, or as the result of a misidentification of the material to be removed, there's a counter-notification process for that.
You can send YouTube a notice that there was an error.
But be careful...
If you misuse the process, you could end up in court.
And then you would get in a lot of trouble!
That's how the law works.
That's more like it!
By singing an original song, you're creating your own content.
When you make an original video, you're the owner of your own copyright, and... ...you have the right to post it to YouTube.
Original content is what makes YouTube interesting.
Start creating your own, and who knows?
Your video could explode!
[BOOM!]
If you're still unsure about copyright issues, YouTube has some resources as a starting point.
For more information, click the link for "Copyright" at the bottom of every page.
The Internet is one of the United States' most robust and growing industries.
It enables free and open communication among billions, and it's been the backbone for protests around the world.
But a new bill proposes to give the power to censor the Internet to the entertainment industry.
It's called PROTECT IP, and here's how it works.
Private corporations want the ability to shut down unauthorized sites where people download movies, TV shows, and music.
Since most of these sites are outside US jurisdiction,
PROTECT IP uses a couple different tactics within American borders.
Firstly, it gives the government the power to make US Internet providers block access to infringing domain names.
They can also sue US-based search engines, directories, or even blogs and forums, to have links to these sites removed.
Secondly, PROTECT IP gives corporations and the government the ability to cut off funds to infringing websites by having US-based advertisers and payment services cancel those accounts.
In a nutshell, that's what PROTECT IP will try to do.
But in all likelihood, it'll do something else altogether.
For starters, it won't stop downloaders.
You'll still be able to access a blocked site just by entering its IP address instead of its name.
What PROTECT IP will do is cripple new startups because it also lets companies sue any site they feel isn't doing their filtering well enough.
These lawsuits could easily bankrupt new search engines and social media sites.
And PROTECT IP's wording is ambiguous enough that important social media sites could become targets.
Lots of trailblazing websites could look like piracy heavens to the wrong judge.
Tumblr, SoundCloud, an early YouTube, wherever people express themselves, make art, broadcast news or organize protests, there's plenty of TV footage, movie clips, and copyrighted music mixed in.
And even if you trust the US government not to abuse their new power to censor the Net, what about the countries that follow in our path and pass similar laws?
People around the world will have very different
Internets, and unscrupulous governments will have powerful tools to hinder free expression.
But perhaps most dangerously, PROTECT IP will meddle with the inner workings of the Net.
Experts believe by fiddling with the web's registry of domain names, the result will be less security, and less stability.
In short, PROTECT IP won't stop piracy, but it will introduce vast potential for censorship and abuse, while making the web less safe and less reliable.
This is the Internet we're talking about!
It's a vital and vibrant medium.
And our government is tampering with its basic structure, so people will maybe buy more Hollywood movies.
But Hollywood movies don't get grassroots candidates elected.
They don't overthrow corrupt regimes, and the entire entertainment industry doesn't even contribute that much to our economy.
The Internet does all these, and more.
Corporations already have tools to fight piracy.
They have the power to take down specific content, to sue peer-to-peer software companies out of existence, and to sue journalists just for talking about how to copy a DVD.
They have a history of stretching and abusing their powers.
They tried to take a baby video off YouTube, just for the music playing in the background.
They've used legal penalties written for large-scale commercial piracy to go after families and children.
They even sued to ban the VCR and the first MP3 players.
So the question is, "How far will they take all this?"
The answer at this point, is obvious.
As far as we'll let them.
Determine the domain and range of the function f of x is equal to 3x squared plus 6x minus 2.
So, the domain of the function is: what is a set of all of the valid inputs, or all of the valid x values for this function?
And, I can take any real number, square it, multiply it by 3, then add 6 times that real number and then subtract 2 from it.
So essentially any number if we're talking about reals when we talk about any number.
So, the domain, the set of valid inputs, the set of inputs over which this function is defined, is all real numbers.
So, the domain here is all real numbers.
And, for those of you who might say, well, you know, aren't all numbers real?
You may or may not know that there is a class of numbers, that are a little bit bizarre when you first learn them, called imaginary numbers and complex numbers.
But, I won't go into that right now.
But, most of the traditional numbers that you know of, they are part of the set of real numbers.
It's pretty much everything but complex numbers.
So, you take any real number and you put it here, you can square it, multiply it by 3, then add 6 times it and subtract 2.
Now, the range, at least the way we've been thinking about it in this series of videos-- The range is set of possible, outputs of this function.
Or if we said y equals f of x on a graph, it's a set of all the possible y values. And, to get a flavor for this, I'm going to try to graph this function right over here.
And, if you're familiar with quadratics-- and that's what this function is right over here, it is a quadratic-- you might already know that it has a parabolic shape.
And, so its shape might look something like this.
And, actually this one will look like this, it's upward opening. But other parabolas have shapes like that.
And, you see when a parabola has a shape like this, it won't take on any values below its vertex when it's upward opening, and it won't take on any values above its vertex when it is downward opening.
So, let's see if we can graph this and maybe get a sense of its vertex.
There are ways to calculate the vertex exactly, but let's see how we can think about this problem.
So, I'm gonna try some x and y values. There's other ways to directly compute the vertex.
Negative b over 2a is the formula for it. It comes straight out of the quadratic formula, which you get from completing the square.
Lets try some x values and lets see what f of x is equal to.
So, let's try, well this the values we've been trying the last two videos.
What happens when x is equal to negative two?
Then f of x is 3 times negative 2 squared, which is 4, plus 6 times negative 2, which is 6 times negative 2, so it's minus 12 minus 2.
So, this is 12 minus 12 minus 2.
So, it's equal to negative 2.
Now, what happens when x is equal to negative 1? So, this is going to be 3 times negative 1 squared, which is just 1, minus, or I should say plus 6 times negative 1 which is minus 6 and then minus 2, and then minus 2.
So, this is 3 minus 6 is negative 3 minus 2 is equal negative 5, and that actually is the vertex.
And, you know the formula for the vertex, once again, is negative b over 2 a. So, negative b. That's the coefficient on this term right over here.
It's negative 6 over 2 times this one right over here, 2 times 3.
2 times 3, this is equal to negative 1.
So, that is the vertex, but let's just keep on going right over here.
So, what happens when x is equal to 0?
These first two terms are 0, you're just left with a negative 2.
When x is equal to positive 1.
And, this is where you can see that this is the vertex, and you start seeing the symmetry.
If you go one above the vertex, f of x is equal to negative 2.
If you go one x value below the vertex, or below the x value of the vertex, f of x is equal to negative 2 again. But, let's just keep going.
We could try, let's do one more point over here.
So, we have, we could try, x is equal to 1. When x is equal to 1, you have 3 times one squared which is 1. So, 3 times 1 plus 6 times 1, which is just 6, minus 2.
This is x is equal to negative 1, this is x is equal to, this is x is equal to 0 and then this is x is equal to 1 right over there and then when x is equal to, we go from negative 2 all the way to positive. Or, we should go from negative 5 all the way to positive 7. So, let's say this is negative 1,2,3,4,5.
I could keep going, this is in the y, and we're going to set y equal to whatever our output of the function is. Y is equal to f of x.
And this is one right here. So, lets plot the points. You have the point negative 2, negative 2.
Then, we have this point that we have this pink or purplish color.
Negative, when x is negative 1, f of x is negative 5. When x is negative 1, f of x is negative 5.
And, we already said that this is the vertex. And, you'll see the symmetry around it in a second. So, this is the point negative 1, negative 5.
0, negative when x is a 0, y is negative 2, for f' of x is negative 2 or f of 0 is negative 2, so this is the point 0, negative 2, and then finally when x is equal to 1 and f of 1 is 7, f of 1 is 7. So, that's right there it's a point 1, 7 and it gives us a scaffold for what this parabola, what this curve will look like. So, I'll try my best to draw it respectably.
But, I think you see the symmetry around the vertex. That if you were to. If you were to put a line right over here, the two sides are kind of the mirror images of each other.
But, since it's an upward opening parabola, where the vertex is going to be, the minimum point. This is the minimum value that the parabola will take on. So, going back to the original question, this is all for trying to figure out the range, the set of y values, the set of outputs that this function can generate.
So, the parabola can never give you values-- f of x is never going to be less than negative 5. So, our domain, but it can take on all the vaues. It can keep on increasing forever as x gets
So, our range, so we already said our domain is all real numbers. Our range, the possible y values is all real numbers greater than or equal to negative 5. It can take on the value of any real number greater than or equal to negative 5.
Nothing less than negative 5.
Solve for x.
And we have 5x plus 7 is greater than 3 times x plus 1.
So let's just try to isolate "x" on one side of this inequality.
But before we do that, let's just simplify this righthand side. so we get 5x plus 7 is greater than -
So 3 times x plus 1 is the same thing as 3 times x plus 3 times 1 so it's going to be 3x plus 3 times 1 is 3.
Now if we want to put our x's on the lefthand side, we can subtract 3x from both sides.
That will get rid of this 3x on the righthand side.
Let's subtract 3x from both sides, and we get on the lefthand side:
5x minus 3x is 2x plus 7 is greater than - 3x minus 3x - those cancel out.
That was the whole point behind subtracting 3x from both sides - is greater than 3.
Is greater than 3. No we can subtract 7 from both sides to get rid of this positive 7 right over here.
So, let's subtract, let's subtract 7 from both sides.
And we get on the lefthand side... 2x plus 7 minus 7 is just 2x. Is greater than 3 minus 7 which is negative 4.
And then let's see, we have 2x is greater than negative 4.
If we just want an x over here, we can just divide both sides by 2.
Since 2 is a positive number, we don't have to swap the inequality.
So let's just divide both sides by 2, and we get x is greater than negative 4 divide by 2 is negative 2.
So the solution will look like this.
Draw the number line.
I can draw a straighter number line than that. There we go.
Still not that great, but it will serve our purposes.
Let's say that's -3, -2, -1, 0, 1, 2, 3. X is greater than negative 2. It does not include negative 2.
It is not greater than or equal to negative 2, so we have to exclude negative 2.
And we exclude negative 2 by drawing an open circle at negative 2, but all the values greater than that are valid x's that would solve, that would satisfy this inequality.
So anything above it - anything above it will work.
And let's just try, let's try just try something that should work. and then let's try something that shouldn't work.
So 0 should work.
It is greater than negative 2.
It's right over here.
So, let's verify that.
5 times 0 plus 7 should be greater than 3 times 0 plus 1.
So this is 7 - 'cause this is just a 0 - 7 should be greater than 3.
Right.
3 times 1.
So 7 should be greater than 3, and it definitely is.
Now let's try something that should not work.
Let's try negative 3.
So 5 times negative 3... 5 times negative 3 plus 7, let's see if it is greater than 3 times negative 3 plus 1.
So this is negative 15 plus 7 is negative 8
That is negative 8.
Let's see if that is greater than negative 3 plus 1 is negative 2 times 3 is negative 6.
Negative 8 is not - is not greater than negative 6.
So, it is good that negative 3 didn't work 'cause we didn't include that in our solution set.
It's less than.
So we tried something that is in our solution set and it did work.
And something that is not, and it didn't work.
So we are feeling pretty good.
Let's say that I have five lemons so that's [counting to five] ... five lemons and I were to ask you: what do I have to multiply times five to get one? or in this case: what do I have to multiply times five lemons to get one lemon? and so, another question you might ask because really multiplication and division are two sides of the same coin is what do I have to divide five by to get to one lemon or yellow circle, or whatever I have drawn right over here
Well, if you have five things and you divide by five, you're gonna have five groups of one so if you divide by five, you're gonna have [counting to five] ... five groups
So you could say five divided by five is equal to one take five things and divide it into five groups then each group is going to have one in them or you could say five times one fifth is equal to one (and I use the dot for multiplication)
I could also say five times one fifth is equal to one these are all really saying the same thing
Maybe what's kind of interesting here (although it's not some huge learning) it's really just another way of writing what you already probably know, is this idea that if I have a number and I multiply times it's multiplicative inverse (and most of the time when people talk about inverses in mathematics they are talking about the multiplicative inverse) then I'm going to get one so five time one fifth is equal to one but that's just because five times one fifth is the same thing as five divided by five if you were to actually multiply this out you actually take five times one fifth this is equal to five-over-one times one-over-five you multiply the numerators: five times one is five multiply the denominators: one times five is five so you have five fifths, and five fifths is the exact same thing as one
So if someone where to ask you a question, they say "Hey, I have the number 217 and I want to multiply it by something, and I want to get one after multiplying it by that something"
Well then you say - Well look, If I took 217 and divided it by 217 that would get me to one and dividing by 217 is the exact same thing as multiplying by one-over-217 multiplying by its multiplicative inverse which is, once again, a word that is fancier than the actual concept you are just multiplying by the inverse of this number
Another way to think about it is if I have five things and I take one fifth of those things, how many things do I have?
Well, if I take one fifth of five things I have exactly one thing right over here
But the general idea is super-duper-duper simple if I have some crazy number ... 8,345 that's actually not so crazy, let's turn it to something in the millions ... and 271 ... so 8,345,271
And I say, what do I have to multiply by (and now I use this multiplication symbol right now) what do I have to multiply that by in order to get one?
I just have to multiply it by the inverse of this the multiplicative inverse of this so one-over-8,345,271
He was totally unexcited about starting businesses and making money. There is a profound sense of loss tonight in Highland Park, Aaron Swartz's hometown as loved ones say goodbye to one of the Internet's brightest light. Freedom, Open Access, and computer activists are mourning his loss.
The circle is arguably the most fundamental shape in our universe, whether you look at the shapes of orbits of planets, whether you look at wheels, whether you look at things on kind of a molecular level.
The circle just keeps showing up over and over and over again.
So it's probably worthwhile for us to understand some of the properties of the circle.
So the first thing when people kind of discovered the circle, and you just have a look at the moon to see a circle, but the first time they said well, what are the properties of any circle?
So the first one they might want to say is well, a circle is all of the points that are equal distant from the center of the circle.
All of these points along the edge are equal distant from that center right there.
So one of the first things someone might want to ask is what is that distance, that equal distance that everything is from the center?
Right there.
We call that the radius of the circle.
It's just the distance from the center out to the edge.
If that radius is 3 centimeters, then this radius is going to be 3 centimeters.
And this radius is going to be 3 centimeters.
It's never going to change.
By definition, a circle is all of the points that are equal distant from the center point.
And that distance is the radius.
Now the next most interesting thing about that, people might say well, how fat is the circle?
How wide is it along its widest point?
Or if you just want to cut it along its widest point, what is that distance right there?
And it doesn't have to be just right there, I could have just as easily cut it along its widest point right there.
I just wouldn't be cutting it like some place like that because that wouldn't be along its widest point.
There's multiple places where I could cut it along its widest point.
Well, we just saw the radius and we see that widest point goes through the center and just keeps going.
So it's essentially two radii.
You got one radius there and then you have another radius over there.
We call this distance along the widest point of the circle, the diameter.
So that is the diameter of the circle.
It has a very easy relationship with the radius.
The diameter is equal to two times the radius.
Now, the next most interesting thing that you might be wondering about a circle is how far is it around the circle?
So if you were to get your tape measure out and you were to measure around the circle like that, what's that distance?
We call that word the circumference of the circle.
Now, we know how the diameter and the radius relates, but how does the circumference relate to, say, the diameter.
And if you're not really used to the diameter, it's very easy to figure out how it relates to the radius.
Well, many thousands of years ago, people took their tape measures out and they keep measuring circumferences and radiuses.
And let's say when their tape measures weren't so good, let's say they measured the circumference of the circle and they would get well, it looks like it's about 3.
And then they measure the radius of the circle right here or the diameter of that circle, and they'd say oh, the diameter looks like it's about 1.
So they would say -- let me write this down.
So we're worried about the ratio -- let me write it like this.
The ratio of the circumference to the diameter.
So let's say that somebody had some circle over here -- let's say they had this circle, and the first time with not that good of a tape measure, they measured around the circle and they said hey, it's roughly equal to 3 meters when I go around it.
And when I measure the diameter of the circle, it's roughly equal to 1.
OK, that's interesting.
Maybe the ratio of the circumference of the diameter's 3.
So maybe the circumference is always three times the diameter.
Well that was just for this circle, but let's say they measured some other circle here.
It's like this -- I drew it smaller.
Let's say that on this circle they measured around it and they found out that the circumference is 6 centimeters, roughly -- we have a bad tape measure right then.
Then they find out that the diameter is roughly 2 centimeters.
And once again, the ratio of the circumference of the diameter was roughly 3.
OK, this is a neat property of circles.
Maybe the ratio of the circumference to the diameters always fixed for any circle.
So they said let me study this further.
So they got better tape measures.
When they got better tape measures, they measured hey, my diameter's definitely 1.
They say my diameter's definitely 1, but when I measure my circumference a little bit, I realize it's closer to 3.1.
And the same thing with this over here.
They notice that this ratio is closer to 3.1.
Then they kept measuring it better and better and better, and then they realized that they were getting this number, they just kept measuring it better and better and they were getting this number 3.14159.
And they just kept adding digits and it would never repeat.
It was a strange fascinating metaphysical number that kept showing up.
So since this number was so fundamental to our universe, because the circle is so fundamental to our universe, and it just showed up for every circle.
The ratio of the circumference of the diameter was this kind of magical number, they gave it a name.
They called it pi, or you could just give it the Latin or the Greek letter pi -- just like that.
That represents this number which is arguably the most fascinating number in our universe.
It first shows up as the ratio of the circumference to the diameter, but you're going to learn as you go through your mathematical journey, that it shows up everywhere.
It's one of these fundamental things about the universe that just makes you think that there's some order to it.
But anyway, how can we use this in I guess our basic mathematics?
So we know, or I'm telling you, that the ratio of the circumference to the diameter -- when I say the ratio,
literally I'm just saying if you divide the circumference by the diameter, you're going to get pi.
Pi is just this number.
I could write 3.14159 and just keep going on and on and on, but that would be a waste of space and it would just be hard to deal with, so people just write this Greek letter pi there.
So, how can we relate this?
We can multiply both sides of this by the diameter and we could say that the circumference is equal to pi times the diameter.
Or since the diameter is equal to 2 times the radius, we could say that the circumference is equal to pi times 2 times the radius.
Or the form that you're most likely to see it, it's equal to 2 pi r.
So let's see if we can apply that to some problems.
So let's say I have a circle just like that, and I were to tell you it has a radius -- it's radius right there is 3.
So, 3 -- let me write this down -- so the radius is equal to 3.
Maybe it's 3 meters -- put some units in there.
What is the circumference of the circle?
The circumference is equal to 2 times pi times the radius.
So it's going to be equal to 2 times pi times the radius, times 3 meters, which is equal to 6 meters times pi or 6 pi meters.
6 pi meters.
Now I could multiply this out.
Remember pi is just a number.
Pi is 3.14159 going on and on and on.
So if I multiply 6 times that, maybe I'll get 18 point something something something.
If you have your calculator you might want to do it, but for simplicity people just tend to leave our numbers in terms of pi.
Now I don't know what this is if you multiply 6 times 3.14159, I don't know if you get something close to 19 or 18, maybe it's approximately 18 point something something something.
I don't have my calculator in front of me.
But instead of writing that number, you just write 6 pi there.
Actually, I think it wouldn't quite cross the threshold to 19 yet.
Now, let's ask another question.
What is the diameter of the circle?
Well if this radius is 3, the diameter is just twice that.
So it's just going to be 3 times 2 or 3 plus 3, which is equal to 6 meters.
So the circumference is 6 pi meters, the diameter is 6 meters, the radius is 3 meters.
Now let's go the other way.
Let's say I have another circle.
Let's say I have another circle here.
And I were to tell you that its circumference is equal to 10 meters -- that's the circumference of the circle.
If you were to put a tape measure to go around it and someone were to ask you what is the diameter of the circle?
Well, we know that the diameter times pi, we know that pi times the diameter is equal to the circumference; is equal to 10 meters.
So to solve for this we would just divide both sides of this equation by pi.
The diameter would equal 10 meters over pi or 10 over pi meters.
And that is just a number.
If you have your calculator, you could actually divide 10 divided by 3.14159, you're going to get 3 point something something something meters.
I can't do it in my head.
But this is just a number.
But for simplicity we often just leave it that way.
Now what is the radius?
Well, the radius is equal to 1/2 the diameter.
So this whole distance right here is 10 over pi meters.
If we just 1/2 of that, if we just want the radius, we just multiply it times 1/2.
So you have 1/2 times 10 over pi, which is equal to 1/2 times 10, or you just divide the numerator and the denominator by 2.
You get 5 there, so you get 5 over pi.
So the radius over here is 5 over pi.
Nothing super fancy about this.
I think the thing that confuses people the most is to just realize that pi is a number.
Pi is just 3.14159 and it just keeps going on and on and on.
There's actually thousands of books written about pi, so it's not like -- I don't know if there's thousands, I'm exaggerating, but you could write books about this number.
But it's just a number.
It's a very special number, and if you wanted to write it in a way that you're used to writing numbers, you could literally just multiply this out.
But most the time people just realize they like leaving things in terms of pi.
Anyway, I'll leave you there.
In the next video we'll figure out the area of a circle.
From Migrant Worker to Activist
[Talking on the phone]:
It was caused by over contract. The contract expired.
When coming home, it would be a problem if she doesn't get her rights.
She should come home bringing what she's entitled to, like her salary and others.
Hety was a migrant worker who faced abuses from her boss. She had returned home and is now actively giving counseling and education to potential migrant workers in the village she resides.
She works in the Middle East and now she is asking for the help from SBMC (Migrant Workers Solidarity in Cianjur).
We asked her to write the chronology of her case.
After that we can meet up in the City of Cianjur.
If there is problem, such as her salary not being given, we will call the boss, to ask for her to be sent home.
Aside being sent home, she should also be entitled to her rights, like her salary.
If she comes home without bringing her salary, it would not be good.
Right?
They have been working for three years.
In Saudi Arabia.
Both husband and wife.
She's coming home tomorrow.
She flew out yesterday at 4 pm.
The first time it was only two months, and then she left again.
It has been three years now and she doesn't want to come home.
It might also be because her husband had passed away.
So she extended her contract for another two months.
Thank God, she becomes a successful migrant worker.
Once or twice a week, her father comes to clean the house.
Ah, she's already in Jakarta this afternoon.
That means she will be here tonight.
Ah, early morning tomorrow.
Those two houses belong to sisters.
That one belongs to the older sister whose husband passed away.
The one below is the younger sister's.
Both are migrant workers.
And thank God she is also a successful migrant worker.
So she could afford a house and send her kids to school.
But too bad her husband passed away.
They could not enjoy the result of their work together.
This is Mrs. Aad, and her daughter, Lusni.
(Lusni) was a migrant worker from 2004 to 2007.
Then she went again in 2009 and came back in 2011.
Come and talk to us.
Ah, we're on camera.
Yes.
Thank God, she didn't have any problem when working as a migrant worker.
She brought home money and her salary was fully paid.
I work at home now.
I want to work if there is any job for me.
But there is no job.
I was married once, but it was short-lived.
Now, I am not married.
Sarah has $48.
She wants to save 1/3 of her money for a trip.
How many dollars should she set aside?
So we essentially want to think about what 1/3 of 48 is.
Use 48 as the denominator and find an equivalent fraction to 1/3.
So what they want us to do in this problem is they want us to say, OK, we want 1/3 of her money, but we want to write this as an equivalent fraction where we have 48 in the denominator.
So this is equal to something, some blank up here.
This is equal to something over 48.
So how can we get it to that something over 48?
So let's think about what this means for a second.
So 1/3, if we were to draw 1/3, it looks like this.
You could imagine a box or a pie, I guess.
So let's say that this is my pie, and I have it split into three pieces.
So let me split it into three even pieces.
And 1/3 is one of those three pieces.
That is what 1/3 means.
Now, if we want express this as a fraction over 48, how can we do that?
Well, we're going to have to split this thing into 48 pieces.
How can we split something into 48?
Well, 3 times 16 is 48, so if we split each of these into 16 pieces-- and it's going to be hard to draw here, but you can imagine.
Let's see, you split it into two, now we've split it into four, now you split it into eight.
You're just going to end up with a bunch of lines here, but you can imagine, you can just split each of these.
If you split each of these into enough, you would have 16 pieces, so those would be 16 right there.
You would have 16 right there and you have 16 right there.
And I can just keep doing it.
Let me do it in the green over here.
So if we just kept splitting it up, we would get 48, because you have this first third would be 16 pieces, the second third would be 16, and then this third third would be 16 pieces.
Altogether, you would have 48 pieces.
Now, that 1/3, what does that represent?
Well, that represents 16 of the 48.
It represents these 16 right here.
It represents these 16 right there, so 1 over 3 is the exact same thing.
So 1 over 3 is the exact same thing as 16 over 48.
Now, we did it just by thinking about it kind of intuitively what 1/3 of 48 is, but one way to do it more-- I guess a process for doing it-- we would say, well, look, to get the denominator, the bottom number, from 3 to 48, we multiply by 16.
3 times 16 is 48.
And that's literally the process of going from 3 pieces to 48 pieces.
We have to multiply by 16.
We have to turn each of our pieces into 16 pieces.
That's what we did.
Now, you can't just multiply only the denominator by 16.
You have to multiply the numerator by the same number.
And so if each of my pieces now become 16 pieces, then that one piece will now become 16.
So one way to think about it, you just say, well, 3 times 16 is 48, so 1 times 16 will be my numerator, so it'll be 16.
So 1/3 is equal to 16/48.
And another way you could think about it, which you'll learn in more detail later on, is we want 1/3 of 48, right?
That's how much she wants to save. 1/3 of 48 is equal to 1/3 times 48.
And when you multiply-- let me write it like this-- 1/3 times 48, and you could rewrite 48 as a fraction 48/1.
It literally represents 48 wholes.
And when you multiply fractions, you can just multiply the numerators.
So this is equal to 48 over-- and then you just multiply the denominators.
48/3, 1 times 48 is 48.
We'll see this in more detail in the future.
Don't worry about it if it confuses you.
In the denominator, 3 times 1 is 3, and 48 divided by 3, or 48/3, is equal to 16.
So 1/3 of 48 is 16, or 16/48 is 1/3.
Hopefully, that make sense to you.
Most cells in the human body just go about their business on a daily basis in a fairly respectable way.
Let's say that I have some cell here.
This could be maybe a skin cell or really any cell in any tissue in the body.
As that tissue is growing or it's replacing dead cells the cells will experience mitosis and replicate themselves make perfect copies of each other.
And then those two maybe will experience mitosis and then if they realize that, gee, you know it's getting a little bit crowded.
They'll recognize that, and say, you know, I'm going to stop growing a little bit.
That's called contact inhibition.
And so they'll just start growing.
And then let's say one of them experiences a little defect, and he says, you know what, gee, something's a little bit wrong with me.
I, the cell, recognize this in myself, and the cells will actually kill themselves.
That's how good of cellular citizens they are.
They'll kind of make way for other healthy cells.
So this guy might even kill himself if he realizes that there's something wrong with him.
There's actually a cellular mechanism that does that called apoptosis.
And I want to make this very clear.
This isn't some type of outside influence on the cell.
The cell itself recognizes that it's somehow damaged and it just destroys itself, so apoptosis.
So that's the regular circumstance even when there is a mutation.
And just to give you an idea, even if mutations are relatively infrequent.
And I don't know the exact frequencies at which mutations occur.
I suspect it's of different frequencies in different types of tissues.
There are on the order of 100 billion.
Let me do it in a different color.
There are on the order of 100 billion new cells in the human body per day.
So even if a mutation only occurs one in a million times, you're still dealing with roughly 100,000 mutations, and maybe most of the mutations, maybe they're just some little random things that don't really do a lot.
But if the mutations are a little bit more severe, the cell will recognize it and destroy itself.
And I want to make a very clear point here.
I'm talking about the cells of the body or most of the body.
These could be cells in my eyes or the cells in my brain or the cells on my leg.
These aren't my germ cells.
So these mutations, even if the cell survives will not be passed on to my offspring.
That's an entirely different discussion when we talk about meiosis.
These are all my body cells and they're replicating, and we've gone over this with mitosis.
So any mutations here, they'll either do nothing, or the cells might malfunction a little bit, or the cells might hurt themselves or hurt me, but they're not going to affect my offspring.
And I want to make that point very clear.
Now, you're saying, hey, Sal, 100 billion new cells a day?
That must mean like every cell in my body has created, well that just gives you an idea of how many cells we have.
We actually have on the order of, and you know it's obviously not an exact number, but actually in the human body, there's on the order of 100 trillion cells.
And if you look at it that way, you say on average, one thousandth of your cells replicate each day, but the reality is some cells don't replicate that frequently at all and some cells replicate much more frequently.
Just to take a little side note here, this gives you an appreciation, I think, for the complexity of the human body.
I mean we think of our own world economy and world society as so complex, it's made up of 6 billion humans.
We're made up of 100 trillion cells.
Let me rewrite 100 trillion in billions.
100 trillion can be rewritten as 100,000 billion cells.
And each one of those 100,000 billion cells are these huge-- I know I shouldn't use the word huge-- but they're these complex ecosystems in and of themselves with their nucleuses.
And we'll talk about all the different organelles they have, and we talked about cellular replication, DNA replication and how the cell replicates.
So these things aren't jokes and they have all of these complex membranes that take things into them.
They are creatures to themselves, but they live in this complex environment or society that is each of us.
So that's just a side note just to appreciate how large and how complex we are.
But you can imagine, and this is how I got off on this tangent, if we're making on the order of 100 billion new cells every day, you're going to have a lot of mutations, and maybe some of the mutations, you know I said some of them don't do anything.
Some of them, the cell recognizes that the cell is just going to be kind of dead weight so the cell kind of eliminates itself.
But every now and then, you have mutations where the cell doesn't eliminate itself and it also deforms the cell.
So when you have that, let's say I have some cell here.
I have some cell and it's got some mutation.
I'll do that mutation with a little x right here.
That's in its DNA.
Maybe it's got a couple of mutations.
So one of the mutations keeps it from experiencing apoptosis, or destroying itself, and maybe one of the mutations makes it replicate a little bit faster than its neighbors.
So this cell, through mitosis, it makes a bunch of copies of itself or a ton of copies of itself.
And this kind of body of cells that essentially has a defect, they're all from one original cell that kept duplicating and then those duplicating, but all these are defective cells.
If you were to look at them compared to the tissue around it, it would look abnormal in some way.
Maybe it wouldn't function properly.
This is called a neoplasm.
Now, a lot of neoplasms, well they don't have to form a body like this.
Sometimes they might somehow circulate in the body, but most of the time they form this kind of big lump.
And if they get large enough, they're noticeable.
And that's when we call it a tumor.
So if this is actually a lump of kind of differentiated tissue that's definitely abnormal, that's what you call a tumor.
So the term neoplasm and tumor are often used interchangeably.
Tumor is the word we use more in our everyday vocabulary.
Now, if this lump just kind of grows to a certain size, it's just there, it doesn't really do anything dangerous, it's not replicating out of control.
I guess it's not replicating a lot faster than its neighboring cells and it's just hanging out, maybe growing a little bit, but not in any significant way harming our environment, we call that a benign tumor or a benign neoplasm.
And benign essentially means harmless.
Benign tumor.
That means that's good.
You want to hear that.
If you got a lump-- God forbid you have a lump either way-- but if you do and it's a benign tumor, that means that lump, it can kind of stick around, no damage done.
But if these DNA mutations, and maybe some of these are, it is benign, but maybe one of the benign ones has another mutation in it that starts making it grow like crazy.
And not only does it grow like crazy, but it becomes invasive.
And invasive means that it doesn't care what's going on around it. It just wants to infiltrate everything.
So let's say that guy grows like crazy.
Let me do it in a different color.
And he starts infiltrating other tissue, so he's invasive.
So super growth, he's invasive.
So he doesn't care what's going on.
He's all of a sudden turned into some type of a cellular psychopath.
And even worse, his descendants, it's not just one cell anymore.
He just keeps duplicating and passing on this kind of broken genetic information that makes it want to replicate.
And then maybe there could be more and more things that break down in its I guess offspring or the DNA that comes from its replications.
And actually, that's a good likelihood, because the same parts of its DNA that broke down, some of the DNA that broke down in this guy, some of the mutations might have actually hurt the DNA replication scheme, so that mutations become more frequent.
So more frequent mutations.
So as these replicate, more and more mutations appear, and then maybe eventually one of the mutations appears that allows these cells to break off and then travel to other parts of the body.
And then those parts of the body start to take over and start taking over all of the cells.
And this process is called the cell has-- this is one of the hardest words for me to say, something wrong with my brain-- but the cell has metastasized.
You might have heard the word metastasis, and that's just the notion of these run amok cells all of a sudden being able to travel to different parts of the body.
And I think you guys know what we call these cells.
These cells that aren't respecting their cellular neighborhood.
They're growing like crazy.
They don't experience that contact inhibition.
They're invasive.
They start crowding out other cells and hogging up the resources.
And they keep mutating really fast because they have all of these genetic abnormalities.
And eventually they might even break away and start infiltrating other parts of the body.
These are cancers or cancer cells.
And so you might have an appreciation for why this is so hard.
Cancer is such a hard disease to quote, unquote, cure.
Because it really isn't just one disease.
It's not like one type of bacteria or one type of virus that you can pinpoint and say let's attack this.
Cancer is a whole class of mutations where the cells start exhibiting this fast invasive growth and this metastasis.
So you might look at one type of cancer and be able to say, hey, let's target the mutation where the cells look like this and you're able to knock out some of them.
Let me do this in this color.
So maybe you're able to knock out that guy, that guy, that guy.
But because their DNA replication system might be broken in some way, they continue to mutate, so eventually you have one version that's able to not be knocked out by whatever method you get.
And so you have this kind of new form of cancer, and then that new form of cancer is even harder to kill.
So you can imagine that cancer is kind of a never ending fight.
And you kind of have to attack the general idea behind it.
Chemotherapy and radiation, all of these type of things. They try to attack things that are fast growing because that's the kind of one common theme behind all of the cancers.
And we could do a whole playlist on what cancer is and how people are attacking it, but I wanted to at least show you in this video that cancer really is just a byproduct of broken mitosis, or even more specifically, broken DNA replication.
That we have all of these cells replicating themselves every day on the order of 100 billion, and every now and then something breaks.
Usually when they break, either nothing happens or the cell kills itself.
But every now and then, the cells start replicating even though they're broken.
And sometimes they start replicating like crazy.
If they just replicate, but they're really not doing any harm, it's benign.
But if they start replicating like crazy, taking over resources and spreading through the body, you're dealing with a cancer.
So hopefully, you found that interesting.
You already know a good bit of the science that kind of deals with what is probably one of the worst ailments that we deal with as creatures.
I mean, obviously, we're not the only people who can experience cancers. Even plants have cancers.
So the correct answer is all of those-- finance, robotics, games, medicine, the Web, and many more applications.
So let me talk about them in some detail.
There is a huge number of applications of artificial intelligence in finance, very often in the shape of making trading decisions-- in which case, the agent is called a trading agent.
And the environment might be things like the stock market or the bond market or the commodities market.
And our trading agent can sense the course of certain things, like the stock or bonds or commodities.
It can also read the news online and follow certain events.
And its decisions are usually things like buy or sell decisions--trades.
There's a huge history of artificial intelligence finding methods to look at data over time and make predictions as to how courses develop over time-- and then put in trades behind those.
And very frequently, people using artificial intelligence trading agents have made a good amount of money with superior trading decisions.
There's also a long history of AI in Robotics.
Here is my depiction of a robot.
Of course, there are many different types of robots and they all interact with their environments through their sensors, which include things like cameras, microphones, tactile sensor or touch.
And the way they impact their environments is to move motors around, in particular, their wheels, their legs, their arms, their grippers.
They can also say things to people using voice. Now there's a huge history of using artificial intelligence in robotics.
Pretty much, every robot that does something interesting today uses Al.
In fact, often AI has been studied together with robotics, as one discipline.
But because robots are somewhat special in that they use physical actuators and deal with physical environments, they are a little bit different from just artificial intelligence, as a whole.
When the Web came out, the early Web crawlers were called robots and to block a robot from accessing your website, to the present day, there's a file called robot.txt, that allows you to deny any Web crawler to access and retrieve that information from your website.
So historically, robotics played a huge role in artificial intelligence and a good chunk of this class will be focusing on robotics.
AI has a huge history in games-- to make games smarter or feel more natural.
There are 2 ways in which AI has been used in games, as a game agent.
One is to play against you, as a human user.
So for example, if you play the game of Chess, then you are the environment to the game agent.
The game agent gets to observe your moves, and it generates its own moves with the purpose of defeating you in Chess.
So most adversarial games, where you play against an opponent and the opponent is a computer program, the game agent is built to play against you--against your own interests--and make you lose.
And of course, your objective is to win.
That's an AI games-type situation.
The second thing is that games agents in AI also are used to make games feel more natural.
So very often games have characters inside, and these characters act in some way.
And it's important for you, as the player, to feel that these characters are believable.
There's an entire sub-field of artificial intelligence to use AI to make characters in a game more believable--look smarter, so to speak-- so that you, as a player, think you're playing a better game.
Artificial intelligence has a long history in medicine as well.
The classic example is that of a diagnostic agent.
So here you are--and you might be sick, and you go to your doctor.
And your doctor wishes to understand what the reason for your symptoms and your sickness is.
The diagnostic agent will observe you through various measurements-- for example, blood pressure and heart signals, and so on-- and it'll come up with the hypothesis as to what you might be suffering from.
But rather than intervene directly, in most cases the diagnostic of your disease is communicated to the doctor, who then takes on the intervention.
This is called a diagnostic agent.
There are many other versions of AI in medicine.
AI is used in intensive care to understand whether there are situations that need immediate attention.
It's been used for life-long medicine to monitor signs over long periods of time.
And as medicine becomes more personal, the role of artificial intelligence will definitely increase.
We already mentioned AI on the Web.
The most generic version of AI is to crawl the Web and understand the Web, and assist you in answering questions.
So when you have this search box over here and it says "Search" on the left, and "I'm Feeling Lucky" on the right, and you type in the words, what AI does for you is it understands what words you typed in and finds the most relevant pages.
That is really co-artificial intelligence.
It's used by a number of companies, such as Microsoft and Google and Amazon, Yahoo, and many others.
And the way this works is that there's a crawling agent that can go to the World Wide Web and retrieve pages, through just a computer program.
It then sorts these pages into a big database inside the crawler and also analyzes developments of each page to any possible query.
When you then come and issue a query, the AI system is able to give you a response-- for example, a collection of 10 best Web links.
In short, every time you try to write a piece of software, that makes your computer software smart likely you will need artificial intelligence.
And in this class, Peter and I will teach you many of the basic tricks of the trade to make your software really smart.
Simplify 48/64 to lowest terms.
Let's see if we can visualize this.
So we have 64.
I guess 64 would be a whole, so let's draw a whole here.
So let's say that's a whole.
Maybe we're talking about a candy bar.
Let me draw the whole.
We're talking about a whole candy bar.
That would be 64 fourths.
It would be the whole candy bar right there.
And 48 of the 64, you could imagine splitting this up into 64 super-small pieces.
You wouldn't be able to see what I drew here, but if we had 48 of them, it would get us about that much of them, so that would be the 48 out of the 64.
So this whole blue area is 64. The 48 is this purple area right over here.
So let me write it over here.
48/64, and we want to write it in lowest terms, and we'll talk more about what lowest terms even means.
Now, is there a way to group these 48 or these 64 into groups of numbers that will maybe simplify them a little bit?
And to think about that, you'd have to think about what is the largest factor that is common to both 48 and 64?
Or you can think of it as what is their greatest common divisor?
Well, the largest number that I can think of that goes into 48-- you could do it either by just thinking about it or you could actually write out all of its factors.
But if you were to write all the factors for 48 and all the factors for 64, the one that pops out at me as the largest that goes into both is 16.
So you could say that 48 is equal to-- well, what is it?
It's 3 times 16, and 64 is 4 times 16.
Now this is interesting.
So this 48 that we drew in magenta right here, we could view this as three groups of 16.
So that's one, two-- let me make them a
little bit more even.
So one, two, three groups of 16, so that's 16, that's 16, and that is 16.
That would be 48.
I could draw 16 bars here so that we have 16 pieces, but that's a group of 16, a group of 16 and a group of 16.
That's what 48 is.
Now, 64 is four groups of 16.
So we could make, if you look at the 64, that is a 16, that is a 16, that is a 16, and then that is another 16.
These should all be the same length.
I drew it a little bit off.
So what is 48/64 in lowest terms?
We want to write this in as simple as possible fraction.
Well, if we make each of the pieces equal to 16 of our old pieces, if we make this into one piece, if we turn 16 into one, then we are talking about instead of 48/64, we're talking about three.
So this is one piece, two pieces, three pieces of a total of four.
So this is going to be equal to 3/4.
And hopefully, you see kind of a mathematical way of immediately thinking about it.
If you can factor this out and you can actually factor out its greatest common factor, so 48 is 3 times 16, 64 is 4 times 16, and then these cancel each other out. view This is equivalent to 3/4 times 16/16.
This is the same thing as that.
And 16/16 is 1, and you're just left with 3/4.
Now, if you didn't immediately recognize that 16 goes into both 48 and 64, you could do it step by step.
So let's say we started off with 48/64.
Now, the key thing to remember with any fraction, whatever you do to the numerator, you have to do to the denominator.
So let's say we divide the numerator by 2, we also have to divide the denominator by 2, so we could get 2.
We know that these are both divisible by 2. They're both even.
So that would get us to 24/32.
And we'll say, well, look, these two numbers, those are both divisible by 2.
Well, see if we can think of a larger number.
Well, actually, they're both divisible by 4, so maybe you don't realize that they're also both divisible by 8.
So let's say you did it with 4.
So now we divide the top by 4.
So we're going to divide by 4.
We get 6.
You have to do the same to the bottom, to the denominator.
Divide by 4, you get 8.
So 48/64 is the same thing as 24/32, which is the same thing as 6/8.
And these are both divisible by 2, so if you divide the numerator by 2, you get 3.
You divide that the denominator by 2, you get 4.
And so this is the simplest possible terms, because 3 and 4 share no common factors greater than 1, so we're in lowest possible terms.
So however you want to do it.
The easiest way or the fastest way is to say, hey, 16 is the biggest number that goes into both of these.
Divide both by 16.
You get 3/4.
And really when you're dividing the numerator and denominator by 16, you're turning groups of 16 into one piece or 16 super-small pieces of the pie into one bigger piece of the pie.
So this goes from 64 pieces to 4 pieces.
This goes from 48 pieces to 3 pieces.
It is almost midnight here at Morib Beach, 75kilometres from Kuala Lumpur.
More than a thousand people are eagerly waiting for the arrival of the Nine Emperor Gods to kick start this year's Vegetarian Festival.
The prayer altars are quickly being set up.
Devotees light candles, joss sticks and make food offerings to the Gods.
Mediums go into a trance to welcome the Gods,
it being low tide, they have to walk some 500 metres over soft sand to reach the sea.
In the meantime, devotees continue to pour onto the beach and while waiting for the Chariot to return, they start to make fire offerings to the Gods, many release hot air lanterns into the air.
The mediums and Chariots return having receive the Gods and are quickly transported back to the Temple in Petaling Jaya for the start of the Annual nine day Festival known locally as Nine Emperor Gods Festival.
 In this video, I want to cover several topics that are all related.
And on some level, they're really simple, but on a whole other level, they tend to confuse people a lot.
So hopefully we can make some headway.
So a good place to start-- let's just imagine that I have some type of container here.
Let's say that's my container and inside of that container, I have a bunch of water molecules.
It's just got a bunch of water molecules. They're all rubbing against each other.
It's in its liquid form, this is liquid water. and inside of the water molecules, I have some sugar molecules.
Maybe I'll do sugar in this pink color.
So I have a bunch of sugar molecules right here.
I have many, many more water molecules though.
I want to make that clear.
I have many, many more water molecules in this container that we are dealing with.
Now in this type of situation, we call, we call the thing that there's more of, the solvent.
So in this case, there's more water molecules and you can literally just view more as the number of molecules.
I'm not going to go into a whole discussion of moles and all of that because you may or may not have been exposed to that yet, but just imagine whatever there's more of, that's what we're going to call the solvent.
So in this case, water is the solvent.
And whatever there is less of, so the more water is the solvent and in that case, that is the in this case, that is the sugar-- that is considered the solute. this is the solute, so the sugar.
It doesn't have to be sugar.
It could be any molecule that there's less of, in the water, in this case,sugar. is the solute
And we say that the sugar has been dissolved into the water. sugar,has been dissolved, dissolved into, into the water
And this whole thing right here, the combination of the water and the sugar molecules, we call a solution.
We call this whole thing a solution.
And a solution has a solvent and the solute.
The solvent is water.
That's the thing doing the dissolving and the thing that is dissolved is the sugar.
That's the solute.
Now all of this may or may not be review for you, but I'm doing it for a reason-- because I want to talk about, I want to talk about the idea of diffusion, diffusion
And the,the idea is actually pretty straightforward.
If I have, let's say,let's same the same container.
Let me do it in a slightly different container here, just to talk about diffusion.
We'll go back to water and sugar-- especially back to water.
Let's say we have a container here and let's say it just has a bunch of-- let's say it just has some air particles in it.
It could be anything-- oxygen or carbon dioxide.
So let me just draw a couple of air molecules here.
So let's say that that is a gaseous-- just for the sake of argument-- gaseous oxygen.
So each of this is an O2-- each of those, right?
And let's say that this is the current configuration, that all of this is a vacuum here and that there's some temperatures.
So these water molecules, they have some type, some type of kinetic energy.
They're moving in some type of random directions right there.
So my question is, what is going to happen, what is goign to happen in this type of container?
Well, any of these guys are going to be randomly bumping into each other.
They're more likely to bump into things in this down-left direction than they are in the up-right direction.
So if this guy was happening to go in this down-left direction, he's going to bump into something and then ricochet into the up-right direction.
But in the up-right direction, there's nothing to bounce into.
So in general, everything is moving in random directions, but you're more likely to be able to move in the rightward direction.
When you go to the left, you're more likely to bump into each other, into something.
So it's almost common sense.
Over time, if you just let this system come to some type of equilibrium-- I'm not going to go into detail on what that means.
You can watch the thermodynamics videos if you'd like to see that.
You'll eventually see the container will look something like this.
I can't guarantee it.
There's some probability it would actually stay like this, but very likely that those five particles are going to get relatively spread out.
This is diffusion and so it's really just the spreading of particles or molecules from high concentration to low concentration areas, right?
In this case, the molecules are going to spread in that direction from a high concentration to a low concentration area.
Now you're saying, Sal, what is concentration?
And there's many ways to measure concentration and you can go into molarity and molality and all of that.
But the very simple idea is, how much of that particle do you have per unit space?
So here, you have a lot of those particles per unit space and here you have very few of those particles per unit space.
So this is a high concentration and that's a low concentration.
So you could imagine other experiments like this.
You could imagine a solution like-- let's do something like this. let me make
Let's say I have two containers. let's see two container.
Let's go back to the solution situation.
This was a gas, but I started off with that example so let's stay with that example.
So let's say that I have a door right there that's larger than either the water or the sugar molecules.
On either side, I have a bunch of water molecules.
I have a bunch of water molecules on either side, just like that on either side
So I have a lot of water molecules.
So if I just had water molecules here-- they're all bouncing around in random directions-- and so the odds of a water molecule going this way, equivalent to what odds of a water molecule going that way, assuming that both sides have the same level of water molecule, otherwise the pressures would be different.
But let's say, you know that the top of this is the same as the top of this.
So there's no more pressure going in one direction or another.
So you know if,it for whatever reason, a bunch of more water molecules were going in the rightward direction, then all of a sudden this would fill up with more water and we know that that isn't likely to occur.
So this is,you know, this is just a solution, with or , this is just two containers of waters of water.
Now let's put some solute in it.
Let's dissolve some solute in it and let's say we do all the dissolving on the left-hand side.
So we put some sugar molecules on the left-hand side.
And these are small enough to fit through this little pipe. right, that's just one assumption that I'm making.
So what's going to happen?
All of these things have some type of kinetic energy.
They're all bouncing , they're all bouncing around.
Well, over time,you know, the water's going back and forth.
This water molecule might go that way.
That water molecule might go that way, but they net out each other out, but over time one of these big sugar molecules will be going in just the right direction to go through--maybe you know maybe this guy's, instead of going that direction, he starts off going in that direction.
He goes just through this,throught this,uhm throught this tunnel connecting this two containers and he'll end up there, right?
And this guy will still be bouncing around.
There's some probability he goes back, but there's still more particles,more sugar particles here than there.
So there's still more probability that one of, so these guys will go to that side than one of these guys will go to that side, that one of these guys will go to that side,
So you can imagine if you're doing this with gazillions of particles-- I'm only doing it with four-- over time, the particles will have spread out so that their concentrations are roughly equal.
So that maybe you'll have two here over time.
But if, but when you're only dealing with three or four or five particles, there's some probability it doesn't happen, but when you're doing it with a gazillion and they're super small, it's a very, very, very high likelihood.
But anyway, this whole process-- we went from a container of high concentration to a container of low concentration and the particles would have spread from the low concentration container to the high concentration container.
So they diffused.
This is diffusion.
This is diffusion
And just so that we learn some other words that tend to be used with the idea of diffusion-- when we started off, this had a higher concentration.
The left-hand side container had higher concentration.
Higher concentration, higher concentration
It's all relative, right?
It's higher than this guy,higher concentration
And this right here had a lower concentration.
Lower concentrarion
And there are words for these things.
This solution with a high concentration is called a hypertonic solution.
Let me write that in yellow.
Hyoer, Hypertonic solution
Hyper, in general, meaning having a lot of something, having too much of something.
And this lower concentration is hypo, hypotonic
Hypotonic solution,lower concentration
You might have heard maybe one of your relatives, if they haven't had a meal in awhile say, I'm hypoglycemic.
That means that they have not-- they're feeling lightheaded.
There's not enough sugar in their bloodstream and they want to pass out so they want a meal.
If you just had a candy bar, maybe you're hyperglycemic-- or maybe you're just hyper in general.
But, so, you know, so these are just good prefixes to know, but hypertonic-- you have a lot of the solute.
You have a high concentration.
And then in hypotonic, not too much of the solute so you have a low concentration.
These are good words to know.
So in general, diffusion-- if there's no barriers to the diffusion like we had here, you will have the solute go from a high concentration or hypertonic solution if they can travel to a hypotonic solution, to a hypo, where the concentration is lower.
Now let's do an interesting experiment here.
We've talked about diffusion and so far we've been talking about the diffusion of the solute, right?
And in general-- and this is not always the case-- if you want to be as general as possible, the solute is whatever you have less of, the solvent is whatever you have more of.
And the most common solvent tends to be water, but it doesn't have to be water.
It could be some type of alcohol.
It could be a...you, know it could be mercury.
It could be a whole set of molecules, but water in most biological or chemical systems tends to be the most typical solvent.
It's what other things are dissolved into.
But what happens if we have a tunnel where the solute is too big to travel, but water is small enough to travel?
Let's think about that situation, let's think about the situation
In order to think about it, I'm going to do something interesting.
Let's say we have a container here,let's say
Actually, I won't even draw a container.
Let's just say we have an outside environment that has a bunch of water.
This is the outside environment and then you have some type of membrane. you have some type of membrane here, that's a membrane
Water can go in and out of this membrane.
So it's semi-permeable.
Well, it's permeable to water, but the solute cannot go through the membrane.
So let's say that the solute is sugar.
So we have water on the outside and also inside the membrane.
So these are little small water molecules.
This is a membrane right here.
And let's say that we have some sugar molecules again--
I'm just picking on sugar.
It could have been anything.
So we have some sugar molecules here that are just a little bit bigger-- or they could be a lot bigger.
Actually, they're a lot bigger than water molecules.
You have a bunch of-- and I only draw four, but you have a gazillion of them, right?
You have that much more water molecules.
I'm just trying to show you have more water molecules than sugar molecules.
And this membrane is semi-permeable.
Permeable means it allows things to pass.
Semi-permeables means it's not completely permeable.
So semi-permeable-- in this context, I'm saying I allow water to pass through the membrane.
So water can pass, but sugar cannot.
Sugar is too large.
So if we were to zoom in on the actual membrane itself-- maybe the membrane looks like this.
I'm going to zoom in on this membrane.
So it has little holes in the membrane, just like that.
And maybe the water molecules are about that size.
So they can go through those holes.
So the water molecules can go back and forth through the holes, but the sugar molecules are about that big.
So they cannot go through that hole.
They're too big for this opening right here to go back and forth between them.
Now what do you think is going to happen in this situation?
So first of all, let's use our terminology.
Remember, sugar is our solute.
Water is our solvent.
Semi-permeable membrane.
Which side of the membrane has a higher or lower concentration of solute?
Well, the inside does.
The inside is hypertonic.
The outside has a lower concentration so it's hypotonic.
Now, if these openings were big enough, based on what we just talked about-- these guys are bouncing around, water is travelling in either direction, and equal probability or-- actually I'm going to talk about that in a second.
If everything was wide open, it would be equal probability, but if it was wide open, these guys eventually would bounce their ways over to this side and you'd probably end up with equal concentrations eventually.
And so you would have your traditional diffusion, where high concentration of solute to low concentrations of solute.
But in this case, these guys-- they can't fit through the hole.
Only water can go back and forth.
If these guys were not here, water would have an equal likelihood of going in this direction as they would be going in that direction, a completely equal likelihood.
But because these guys are on the right-hand side of-- or in this case, on the inside of our membrane. This is our inside of our membrane zoomed up-- it's less
likely because these guys might be in the approach position of the holes-- that's slightly less likely for water to be in the approach position for the holes so it's actually more probable that water could enter than water exit.
And I want to make that very clear.
If these sugar molecules were not here, obviously it's equally likely for water to go in either direction.
Now that these sugar molecules are there, these sugar molecules might be on the right-hand side.
They might be blocking-- I guess the best way to think about it is blocking the approach to the hole.
They'll never be able to go through the hole themselves and might not even be blocking the hole, but they're going in some random direction.
So if a water molecule was approaching-- it's all probabilistic and we're dealing with gazillions of molecules-- it's that much more likely to be blocked to get outside.
But the water molecules from the outside-- there's nothing blocking them to get in so you're going to have a flow of water inside.
So in this situation, with a semi-permeable membrane, you're going to have water. You're going to have a net inward flow of water.
And so this is kind of interesting.
We have the solvent flowing from a hypotonic situation to a hypertonic solution, but it's only hypotonic in the solute.
But water-- if you flip it the other way-- if you've used sugar as the solvent, then you could say, we're going from a high concentration of water to a low concentration of water.
I don't want to confuse you too much.
This is what tends to confuse people, but just think about what's going to happen.
No matter in what situation, the solution is going to do what it can to try to equilibriate the concentration. To make the concentrations on both sides as close as possible.
And it's not just some magic.
It's not like the solution knows.
It's all based on probabilities and these things bumping around, but in this situation, water is more likely to flow into the container.
So it's actually going to go from the hypotonic side when we talk about low concentration of solute to the side that has high concentrations of solute, of sugar-- and actually, if this thing is stretchable, more water will keep flowing in and this membrane will stretch out.
I won't go to too much detail here, but this idea of water-- of the solvent-- if in this case, water is the solvent-- of water as a solvent diffusing through a semi-permeable membrane, this is called osmosis.
You've probably heard learning by osmosis-- if you put a book against your head, maybe it'll just seep into your brain.
Same idea.
That's where the word comes from.
This idea of water seeping through membranes to try to make concentrations more equal.
So if you say, well, I have high concentration here, low concentration here.
If there was no membrane here, these big molecules would exit, but because there's this semi-permeable membrane here, they can't.
So the system just probabilistically-- no magic here-- more water will enter to try to equilibriate concentration.
Eventually-- if maybe there's a few molecules out here-- not as high concentration here-- eventually if everything was allowed to happen fully, you'll get to the point where you have just as many-- you have just as high concentration on this side as you have on the right-hand side because this right-hand side is going to fill with water and also probably become a larger volume.
And then, once again, the probabilities of a water molecule going to the right and to the left will be the same and you'll get to some type of equilibrium.
But I want to make it very clear-- diffusion is the idea of any particle going from higher concentration and spreading into a region that has a lower concentration and just spreading out.
Osmosis is the diffusion of water.
And usually you're talking about the diffusion of water as a solvent and usually it's in the context of a semi-permeable membrane, where the actual solute cannot travel through the membrane.
Anyway, hopefully you've found that useful and not completely confusing.
I've noticed something interesting about society and culture.
Everything risky requires a license. So, learning to drive, owning a gun, getting married.
There's a certain -- (Laughter)
That's true in everything risky, except technology.
For some reason, there's no standard syilabus, there's no basic course.
They just sort of give you your computer and then kick you out of the nest.
You're supposed to learn this stuff -- how?
Just by osmosis.
Nobody ever sits down and tells you, "This is how it works."
So today I'm going to tell you ten things that you thought everybody knew, but it turns out they don't.
First of all, on the web, if you want to scroll down, don't pick up the mouse and use the scroll bar.
That's a terrible waste of time.
Do that only if you're paid by the hour.
Instead, hit the space bar.
The space bar scrolls down one page.
Hold down the Shift key to scroll back up again.
So, space bar to scroll down one page; works in every browser, in every kind of computer.
Also on the web, when you're filling in one of these forms like your addresses, I assume you know that you can hit the Tab key to jump from box to box to box.
But what about the pop-up menu where you put in your state?
Don't open the pop-up menu.
That's a terrible waste of calories.
Type the first letter of your state over and over and over.
So if you want Connecticut, go, C, C, C.
If you want Texas, go T, T, and you jump right to that thing without even opening the pop-up menu.
Also on the web, when the text is too small, what you do is hold down the Control key and hit plus, plus, plus.
You make the text larger with each tap.
Works on every computer, every web browser, or minus, minus, to get smaller again.
If you're on the Mac, it might be Command instead.
When you're typing on your Blackberry, Android, iPhone, don't bother switching layouts to the punctuation layout to hit the period and then a space, then try to capitalize the next letter.
Just hit the space bar twice.
The phone puts the period, the space, and the capital for you.
Go space, space.
It is totally amazing.
Also when it comes to cell phones, on all phones, if you want to redial somebody that you've dialed before, all you have to do is hit the call button, and it puts the last phone number into the box for you, and at that point you can hit call again to actually dial it.
No need to go to the recent calls list if you're trying to call somebody just hit the call button again.
Something that drives me crazy:
When I call you and leave a message on your voice mail, I hear you saying, "Leave a message," and then I get these 15 seconds of freaking instructions,
like we haven't had answering machines for 45 years!
(Laughter)
I'm not bitter. (Laughter)
So it turns out there's a keyboard shortcut that lets you jump directly to the beep like this.
At the tone, please... (Beep)
Unfortunately, the carriers didn't adopt the same keystroke, so it's different by carrier, so it devolves upon you to learn the keystroke for the person you're calling.
I didn't say these were going to be perfect.
So most of you think of Google as something that lets you look up a web page, but it is also a dictionary.
Type the word "define" and the word you want to know.
You don't even have to click anything.
There's the definition as you type.
It's also a complete FAA database.
Type the name of the airline and the flight.
It shows you where the flight is, the gate, the terminal, how long until it lands.
You don't need an app. It's also unit and currency conversion.
Again, you don't have to click one of the results.
Just type it into the box, and there's your answer.
While we're talking about text -- When you want to highlight -- this is just an example -- (Laughter)
When you want to highlight a word, please don't waste your life dragging across it with the mouse like a newbie.
Double click the word.
Watch "200" -- I go double-click, it neatly selects just that word.
Also, don't delete what you've highlighted.
You can just type over it.
This is in every program.
Also, you can go double-click, drag, to highlight in one-word increments as you drag.
Much more precise.
Again, don't bother deleting.
Just type over it.
(Laughter)
Shutter lag is the time between your pressing the shutter button and the moment the camera actually snaps.
It's extremely frustrating on any camera under $1,000.
(Camera click) (Laughter)
So, that's because the camera needs time to calculate the focus and exposure, but if you pre-focus with a half-press, leave your finger down -- no shutter lag!
You get it every time.
I've just turned your $50 camera into a $1,000 camera with that trick.
And finally, it often happens that you're giving a talk, and for some reason, the audience is looking at the slide instead of at you!
(Laughter)
So when that happens -- this works in Keynote, PowerPoint, it works in every program -- all you do is hit the letter B key,
B for blackout, to black out the slide, make everybody look at you, and then when you're ready to go on, you hit B again, and if you're really on a roll, you can hit the W key for "whiteout," and you white out the slide, and then you can hit W again to un-blank it.
So I know I went super fast.
If you missed anything, I'll be happy to send you the list of these tips.
In the meantime, congratulations.
You all get your California Technology License.
Have a great day.
(Applause)
I think you've been exposed to the idea of a function at some point in your mathematical career.
But what I want to do in this video is explain it a little bit more formerly than you might be used to, and then relate it to some of the concepts of vectors and linear algebra that we've seen so far.
A function really is just a relation between the members of one set and the members of the other set.
So let's have some set x, and for every member of that set x I'm going to relate that member, or associate that member, with another member of a set y.
So if I imagine that is my set x, and that this is my set y-- and y doesn't have to be smaller, that's just the way I drew it-- the function is just a relation.
That if I just take a member of my set x, let's see that's the member that I'm taking, we're visualizing it as a point.
This function will say, OK you gave me a member of x, then I will give you a member of y associated with that member of x.
So the function will say, you give me that, then I will map it to that member right there.
And that really just means relating it to, or associating with another member of y.
And if you'd give me some other point right here, I'll relate it to another member of y.
And so this notation just says this is a mapping from one set x, and I'm speaking in very general terms, to another set y.
And so you're probably saying, Hey Sal, this is very abstract, how does this relate to the functions that I've seen in the past?
Well let me just write down a function you've probably seen a lot in the past.
You've dealt with f of x is equal to x squared.
How would we write this in this notation?
Let me just write with the f, I was going to write it with the g of x, just so this doesn't always have to be an f, but I think you get that idea.
In this case f is a mapping from real numbers-- the real numbers are everything that I can put in here-- actually this is part of the function definition.
I could constrain this to just be integers, or just be even numbers, or just be even integers.
But this is part of the function definition, I'm defining the function to be a mapping from real numbers.
I'm saying you can put any real number here, and it's going to map to real numbers.
So in this case, if x is real numbers, it's going to map to itself, which is completely legitimate.
So if this is the real numbers-- and obviously the real numbers would go off in every direction forever-- but if this for real numbers, this function mapping is just taking every point in R and mapping it to another point in R.
It's taking every point and associating with it its perfect square.
But the mathematical definition I'm introducing here is more that I'm associating x with x squared.
This is another function notation of writing this exact same thing. These two statements right here, this statement and this statement are identical.
This statement you've probably never seen before, but I like it because it shows the mapping or the association more, while this association I think that you're putting an x into a little meat grinder or some machine that's going to ground up the x or square the x, or do whatever it needs to do to the x.
You give me an x, and I'm going to associate another number in real numbers called x squared.
So it's going to be just another point.
And just as a little bit of terminology, and I think you've seen this terminology before, the set that you are mapping from is called the domain and it's part of the function definition.
Now the set that I'm mapping to is called the codomain.
How does this codomain relate to range?
So the codomain is a set that you're mapping to, and in this example this is the codomain.
In this example, the real numbers are the domain and the codomain.
So the question is how does the range relate to this?
So the codomain is the set that can be possibly mapped to.
You're not necessarily mapping to every point in the codomain.
I'm just saying that this function is generally mapping from members of this set to that set.
The range is the subset -- let me write it this way.
It could be equal to the codomain.
A set is a subset of itself, every member of a set is also a member of itself, so it's a subset of itself.
So range is a subset of the codomain which the function actually maps to.
So let me give you an example.
Let's say I define the function g, and it is a mapping from the set of real numbers.
Let me say it's a mapping from R2 to R.
So I'm essentially taking 2-tuples and I'm mapping it to R.
And I will define g, I'll write it a couple of different ways.
So now I'm going to take g of two values, I could say xy or I could say x1, x2.
Let me do it that way. g of x1, x2 is always equal to 2.
It's a mapping from R2 to R, but this always equals 2.
And let me actually write the other notation just because you probably haven't seen this much.
g maps any points x1 and x2 to the point 2.
But just to get the notation right, what is our domain?
What's the real number?
That was part of my function definition, I said we're mapping from R2, so my domain is R2.
Now what is my codomain?
My codomain is the set that I'm potentially mapping to, and is part of the function definition.
This by definition is the codomain.
So my codomain is R.
Now what is the range of my function?
The range is the set of values that the function actually maps to.
In this case, we always map to the value 2, so the range is actually just the value 2.
And if we were to visualize this-- R2 is actually-- I wouldn't draw it as a blurb, I would draw it as the entire
That's R2.
If I really have to draw R, I'd draw it as some type of a number line.
But I could just draw R like that's R2, and I could just draw R as some straight line.
So this is the set R.
I could draw it like that as well, but let's just say this is set R.
And my function g essentially maps any point over here to exactly the point 2.
2 is just one little point in R.
My function g takes any point in R2, any coordinate, this is the point 3, minus 5, whatever it is.
It always maps it to the point 2 in R.
So g's codomain-- you could say it's all of the real numbers, but it's range is really just 2.
Let me do another example that might be interesting.
If I just write h is a function that goes from R2 to R3, and I'll be a little careful here, h goes from R2 to R3.
And I'll write here that h of x1, x2 is equal to -- so now
I'm mapping a higher dimension space, so I'm going to say that that is going to be equal to, let's say my first coordinate or my first component at R3 is x1 plus x2.
Let's say my second coordinate is x2 minus x1.
And let's say my third coordinate is x2 times x1.
Now what is my domain and my range and my codomain?
So my domain by definition is this right there.
My codomain by definition is R3.
But I can always associate some point with x1, x2 with some point in my R3 there.
A slightly trickier question here is, what is the range?
Can I always associate every point-- maybe this wasn't the best example because it's not simple enough -- but can I associate every point in R3-- so this is my codomain, my domain was R2, and my function goes from R2 to
Let me give you an example.
I could put some x1's and x2's here and figure it out.
Let's take our h of-- let me use my other notation-- let's say that I said h, and I wanted to find the mapping from the point in R2, let's say the point 2 comma 3.
And then my function tells me that this will map to the point in R3.
I add the two terms, the 2 plus 3, so it's 5.
I'd find the difference between x2 and x1-- so 3 minus 2 is 1-- and then I multiply the two, 6.
So clearly this will be in the range, this is a member of the range.
So for example the point 2, 3, which might be right there, will be mapped to the three dimensional point, it's kind of just drawn as a two dimensional blurb right there, but I think you get the idea, would be mapped to the three dimensional point 5, 1, 6.
So this is definitely a member of the range.
Now my question to you, if I have some point in R3, let's say that this is the point 5, 1, 0.
Is this point a member of the range?
It's definitely a member of the codomain, it's in R3.
But is this in our range?
5 has to be the sum of two numbers, the 1 has to be the difference of two numbers, and then the 0 would have to be the product of two numbers.
And clearly we know 5 is the sum, and 1 is the difference, we're dealing with 2 and 3, and there's no way you can get the product of those numbers to be equal to 0.
So this guy is not in the range.
So the range would be the subset of all of these points in R3, so there'd be a ton of points that aren't in the range, and there'll be a smaller subset of R3 that is in the range.
These functions up here, this function that mapped from points in R2 to R, so its codomain was R.
These functions that map to R are called scalar value or real value, depending on how you want to think about it.
But if they map to a one dimensional space, we call them a scalar valued function, or a real valued function.
Now the functions that map to spaces or subspaces that have more than one dimension-- so if you map to R or any subset of R, you have a real valued function, or a scalar valued function.
If you map to Rn, where n is greater than 1, so if you map to R2, R3, R4, R100, you're then dealing with a vector valued function.
So this last function that I defined over here, h is a vector valued function.
In this video we're going to think a little bit about parallel lines, and other lines that intersect the parallel lines, and we call those transversals.
So first let's think about what a parallel or what parallel lines are.
So one definition we could use, and I think that'll work well for the purposes of this video, are they're two lines that sit in the same plane.
And when I talk about a plane, I'm talking about a, you can imagine a flat two-dimensional surface like this screen -- this screen is a plane.
So two lines that sit in a plane that never intersect.
So this line -- I'll try my best to draw it -- and imagine the line just keeps going in that direction and that direction -- let me do another one in a different color -- and this line right here are parallel.
They will never intersect.
If you assume that I drew it straight enough and that they're going in the exact same direction, they will never intersect.
And so if you think about what types of lines are not parallel, well, this green line and this pink line are not parallel.
They clearly intersect at some point.
So these two guys are parallel right over here, and sometimes it's specified, sometimes people will draw an arrow going in the same direction to show that those two lines are parallel.
If there are multiple parallel lines, they might do two arrows and two arrows or whatever.
But you just have to say OK, these lines will never intersect.
What we want to think about is what happens when these parallel lines are intersected by a third line.
Let me draw the third line here.
So third line like this.
And we call that, right there, the third line that intersects the parallel lines we call a transversal line.
Because it tranverses the two parallel lines.
Now whenever you have a transversal crossing parallel lines, you have an interesting relationship between the angles form.
Now this shows up on a lot of standardized tests.
It's kind of a core type of a geometry problem.
So it's a good thing to really get clear in our heads.
So the first thing to realize is if these lines are parallel, we're going to assume these lines are parallel, then we have corresponding angles are going to be the same.
What I mean by corresponding angles are I guess you could think there are four angles that get formed when this purple line or this magenta line intersects this yellow line.
You have this angle up here that I've specified in green, you have -- let me do another one in orange -- you have this angle right here in orange, you have this angle right here in this other shade of green, and then you have this angle right here -- right there that I've made in that bluish-purplish color.
So those are the four angles.
So when we talk about corresponding angles, we're talking about, for example, this top right angle in green up here, that corresponds to this top right angle in, what I can draw it in that same green, right over here.
These two angles are corresponding.
These two are corresponding angles and they're going to be equal.
These are equal angles.
If this is -- I'll make up a number -- if this is 70 degrees, then this angle right here is also going to be 70 degrees.
And if you just think about it, or if you even play with toothpicks or something, and you keep changing the direction of this transversal line, you'll see that it actually looks like they should always be equal.
If I were to take -- let me draw two other parallel lines, let me show maybe a more extreme example.
So if I have two other parallel lines like that, and then let me make a transversal that forms a smaller -- it's even a smaller angle here -- you see that this angle right here looks the same as that angle.
Those are corresponding angles and they will be equivalent.
From this perspective it's kind of the top right angle and each intersection is the same.
Now the same is true of the other corresponding angles.
This angle right here in this example, it's the top left angle will be the same as the top left angle right over here.
This bottom left angle will be the same down here.
If this right here is 70 degrees, then this down here will also be 70 degrees.
And then finally, of course, this angle and this angle will also be the same.
So corresponding angles -- let me write these -- these are corresponding angles are congruent.
Corresponding angles are equal.
And that and that are corresponding, that and that, that and that, and that and that.
Now, the next set of equal angles to realize are sometimes they're called vertical angles, sometimes they're called opposite angles.
But if you take this angle right here, the angle that is vertical to it or is opposite as you go right across the point of intersection is this angle right here, and that is going to be the same thing.
So we could say opposite -- I like opposite because it's not always in the vertical direction, sometimes it's in the horizontal direction, but sometimes they're referred to as vertical angles.
Opposite or vertical angles are also equal.
So if that's 70 degrees, then this is also 70 degrees.
And if this is 70 degrees, then this right here is also 70 degrees.
So it's interesting, if that's 70 degrees and that's 70 degrees, and if this is 70 degrees and that is also 70 degrees, so no matter what this is, this will also be the same thing because this is the same as that, that is the same as that.
Now, the last one that you need to I guess kind of realize are the relationship between this orange angle and this green angle right there.
You can see that when you add up the angles, you go halfway around a circle, right?
If you start here you do the green angle, then you do the orange angle.
You go halfway around the circle, and that'll give you, it'll get you to 180 degrees.
So this green and orange angle have to add up to 180 degrees or they are supplementary.
And we've done other videos on supplementary, but you just have to realize they form the same line or a half circle.
So if this right here is 70 degrees, then this orange angle right here is 110 degrees, because they add up to 180.
Now, if this character right here is 110 degrees, what do we know about this character right here?
Well, this character is opposite or vertical to the 110 degrees so it's also 110 degrees.
We also know since this angle corresponds with this angle, this angle will also be 110 degrees.
Or we could have said that look, because this is 70 and this guy is supplementary, these guys have to add up to 180 so you could have gotten it that way.
And you could also figure out that since this is 110, this is a corresponding angle, it is also going to be 110.
Or you could have said this is opposite to that so they're equal.
Or you could have said that this is supplementary with that angle, so 70 plus 110 have to be 180.
Or you could have said 70 plus this angle are 180.
So there's a bunch of ways to come to figure out which angle is which.
In the next video I'm just going to do a bunch of examples just to show that if you know one of these angles, you can really figure out all of the angles.
Determine the domain and range for the relation described by the table and so, what they want us to say, what they want us to figure out, when they say the domain what are all the possible inputs that we could put into, this case, a relation and later we'll see a function and so over here, i guess one way to think about it the inputs that this relationship is defined for and so you can view the x as the input so when x is -1, y is 3 when x is 3, y is -2 when x is 3, again, y is 2 that's why we can't describe this as a function here because we have two y values for a given x value but it can be a relation when x is 4, y is 8 when x is 6, y is -1 so to answer the first part, when they ask us what is the domain of this relation they're really just saying what are all of the inputs, what are all of the x values for which this relation is defined? and they list the x values over here so it is a set, and that is what these curly brackets mean that i'm about to describe a set it is the set of the numbers -1, 3, 4, and 6 so all we're saying here if we saying the domain of this relation is these 4 numbers it says that this relation is defined for any of these four numbers if you give any of these numbers as an x value there is a y, at least one y value associated with it now, when they talk about the range of this relation and the idea also applies to functions, which are a more specific class of relations you can view them as a well behaved relation the range is all the possible output that this relation can give you given the inputs, what are all the possible values that this relation can take on? so here you'll take a look at all the possible y values that this relation can take on we can write them in order, or we don't have to write them in order, but i'll just write them in order actually let's just go straight this way a set does not imply some type of order, it just means a collection of things so the range here, well our y value can take on the value 3, it can take on the value 2, it can take on the value 8, and it can take on the value -1 and we're done! these are the x values for which this relation is defined then you can actually find an association or relationship and these are all the y values these are kind of all the outputs of the relation that it can take on we just look right over here to find them
I am going to ask you about the problem to learn about a loaded coin.
A loaded coin is a coin, that if you flip it, might have a non 0.5 chance of coming up heads or tails.
Fair coins always come up 50% heads or tails.
Loaded coins might come up, for example, 0.9 chance heads and 0.1 chance tails.
Your task will be to understand, from coin flips, whether a coin is loaded, and if so, at what probability.
I don't want you to solve the problem, but I want you to answer the following questions:
Is it partially observable?
Yes or no.
Is it stochastic?
Yes or no.
Is it continuous?
[Yes or no.]
And finally, is it adversarial?
Yes or no.
We're told that as part of an experiment about train speed, 4 different train conductors measured the distance that they covered over a certain amount of time during a recent journey. So these are the 4 trains.
This is how long it took them to go this many miles.
However, they all use different time intervals. Yeah, you see this guy, he did it over half an hour. This guy did it over 2 hours.
It is 55, and it is miles per hour. So his speed is 55 miles per hour. Now, this guy, this is pretty straightforward.
And I'll have to do a little bit of decimal long division to do this. So we have 1.5 goes into 82.5. Let's multiply both of these numbers by 10, essentially shift their decimals one over, so shift that decimal over here.
So 15 doesn't go into 8 at all. It goes into 82 five times. 5 times 5 is 25, carry the 2.
Let's do some compound inequality problems, and these are just inequality problems that have more than one set of constraints. You're going to see what I'm talking about in a second. So the first problem I have is negative 5 is less than or equal to x minus 4, which is also less than or equal to 13.
So we have two sets of constraints on the set of x's that satisfy these equations. x minus 4 has to be greater than or equal to negative 5 and x minus 4 has to be less than or equal to 13.
So we could rewrite this compound inequality as negative 5 has to be less than or equal to x minus 4, and x minus 4 needs to be less than or equal to 13.
And then we could solve each of these separately, and then we have to remember this "and" there to think about the solution set because it has to be things that satisfy this equation and this equation. So let's solve each of them individually. So this one over here, we can add 4 to both sides of the equation.
The left-hand side, negative 5 plus 4, is negative 1.
Negative 1 is less than or equal to x, right?
These 4's just cancel out here and you're just left with an x on this right-hand side. So the left, this part right here, simplifies to x needs to be greater than or equal to negative 1 or negative 1 is
less than or equal to x. So we can also write it like this.
X needs to be greater than or equal to negative 1. These are equivalent. I just swapped the sides.
Let's add 4 to both sides of this equation.
The left-hand side, we just get an x. And then the right-hand side, we get 13 plus 14, which is 17. So we get x is less than or equal to 17.
So our two conditions, x has to be greater than or equal to negative 1 and less than or equal to 17. So we could write this again as a compound inequality if we want. We can say that the solution set, that x has to be less than or equal to 17 and greater than or equal to negative 1.
It has to satisfy both of these conditions. So what would that look like on a number line? So let's put our number line right there.
Then we would have a negative 1 right there, maybe a negative 2.
So x is greater than or equal to negative 1, so we would start at negative 1. We're going to circle it in because we have a greater than or equal to. And then x is greater than that, but it has to be less than or equal to 17.
And if we wanted to write it in interval notation, it would be x is between negative 1 and 17, and it can also equal negative 1, so we put a bracket, and it can also equal 17. So this is the interval notation for this compound inequality right there. Let's do another one.
Let's say that we have negative 12. I'm going to change the problem a little bit from the one that I've found here.
Negative 12 is less than 2 minus 5x, which is less than or equal to 7. I want to do a problem that has just the less than and a less than or equal to.
left-hand side becomes negative 14, is less than-- these cancel out-- less than negative 5x. Now let's divide both sides by negative 5. And remember, when you multiply or divide by a negative number, the inequality swaps around.
So if you divide both sides by negative 5, you get a negative 14 over negative 5, and you have an x on the right-hand side, if you divide that by negative 5, and this swaps from a less than sign to a greater than sign. The negatives cancel out, so you get 14/5 is greater than x, or x is less than 14/5, which is-- what is this?
This is 2 and 4/5. x is less than 2 and 4/5.
I just wrote this improper fraction as a mixed number. Now let's do the other constraint over here in magenta. So let's subtract 2 from both sides of this equation, just
On the right-hand side, 5 divided by negative 5 is negative 1. And since we divided by a negative number, we swap the inequality. It goes from less than or equal to, to greater than or equal to.
So we have our two constraints. x has to be less than 2 and 4/5, and it has to be greater than or equal to negative 1.
So we could write it like this. x has to be greater than or equal to negative 1, so that would be the lower bound on our interval, and it has to be less than 2 and 4/5.
And notice, not less than or equal to. That's why I wanted to show you, you have the parentheses there because it can't be equal to 2 and 4/5. x has to be less than 2 and 4/5.
Or we could write this way. x has to be less than 2 and 4/5, that's just this inequality, swapping the sides, and it has to be greater than or equal to negative 1.
So these two statements are equivalent. And if I were to draw it on a number line, it would look like this. So you have a negative 1, you have 2 and 4/5 over here.
Maybe, you know, 0 sitting there. We have to be greater than or equal to negative 1, so we can be equal to negative 1. And we're going to be greater than negative 1, but we also have to be less than 2 and 4/5.
Now, let's do an "or" problem. So let's say I have these inequalities. Let's say I'm given-- let's say that 4x minus 1 needs to be greater than or equal to 7, or 9x over 2 needs to be less than 3.
In the last few videos or in the last few problems, we had to find x's that satisfied both of these equations. Here, this is much more lenient. We just have to satisfy one of these two.
Let's see, if we multiply both sides of this equation by 2/9, what do we get? If you multiply both sides by 2/9, it's a positive number, so we don't have to do anything to the inequality. These cancel out, and you get x is less than 3 times 2/9.
So that's our solution set. x needs to be greater than or equal to 2, or less than 2/3. So this is interesting. Let me plot the solution set on the number line.
So that is our number line. Maybe this is 0, this is 1, this is 2, 3, maybe that is negative 1. So x can be greater than or equal to 2.
We can start at 2 here and it would be greater than or equal to 2, so include everything greater than or equal to 2. That's that condition right there. Or x could be less than 2/3.
So 2/3 is going to be right around here, right?
That is 2/3. x could be less than 2/3. And this is interesting. Because if we pick one of these numbers, it's going to satisfy this inequality.
So the only way that there's any solution set here is because it's "or." You can satisfy one of the two inequalities. Anyway, hopefully you, found that fun.
You are a miracle
You are a blessing from above
You brought joy to my soul
And pleasure to my eyes
In my heart I can feel it
An unexplainable feeling
Being a father
The best thing that I could ever ask for
Just thinking of you, makes me smile
Holding you, looking in your eyes
I'm so grateful for having you
And everyday I pray
I pray that you'll find your way
You know I love you
I love you
My little girl, my little girl
I ask God to bless you, and protect you always
My little girl, my little girl
You're like a shining star
So beautiful you are
My baby girl
You light up my world
I pray that I'll get the chance
To be around and watch you grow
And witness your first steps
And the first time when you will call me dad
Just thinking of you, makes me smile
Holding you, looking in your eyes
I'm so grateful for having you
And everyday I pray
I pray that you'll find your way
You know I love you I love you
My little girl, my little girl
I ask God to bless you, and protect you always
My little girl, my little girl
I could spend hours watching you
You're so innocent, so lovely and so pure
Oh, God I can not express my gratitude
Ohh, but i'll raise her good, cause all I want is to please you
And now I pray, You'll guide her ways forever
You know I love you I love you
My little girl, my little girl
I ask God to bless you, and protect you always
My little girl, my little girl
Welcome to the presentation on finding the equation of a line.
Let's get started.
Say I had two points.
Let's say I have the point one comma two, and I have the point three comma four, and I want to figure out the equation of the line through these points.
So let's at least figure out what that line looks like.
So one comma two is here, and two, three; three, four. three comma four is here, and if I want to draw a line through them, it'll look something like that.
So what we want to do is figure out the equation of this line.
Well, we know the form of an equation of a line is y equals mx plus b, where m is the slope, and that tells you how steep the line is, and b is the y-intercept. And I don't know why people chose m and b.
We'll have to do some research on that. b is the y-intercept and the y-intercept is just where does it intersect the y-axis.
And this problem, you could actually look at it and figure it out, but let's do it mathematically.
So the equation for the slope m: it's rise over run.
Another way to view that is for any amount that you run along the x-axis, how much do you rise?
Well, let's do that numerically.
Rise is the same thing as change over y, and run is the same thing as change over x.
Delta, this triangle, means change, change in y.
Well, change in y, let's take the starting point to be three comma four.
Let's say we're going from three comma four to two comma one.
The change in y is four minus two.
We just took this four minus this two over three minus one.
My phone was ringing.
And that's just this three minus this one.
So if we just solve for it, we get four minus two is two, and three minus one is also two, so we get the slope is equal to one.
And that makes sense because when we move over one in x, we go up exactly one in y.
When we move to the left one in x, we move down exactly one in y.
So now we know the equation is y equals onex plus b because we solved the m equals one.
And this is, of course, the same thing as y equals x plus b.
Now, all we have left to do is solve for b.
Well, how do we do that because we have three variables here.
Well, we could actually substitute one of these pairs of points in for y and x, and that makes sense, because these points have to satisfy this equation.
So let's take this first pair. y is equal to two. two is equal to x, which is one plus b.
It's a pretty easy equation to solve.
We get b equals one, so that tells us that the equation of this line is y equals x plus one.
That's a pretty straightforward equation, and it makes sense.
The y-intercept is one, which is exactly here, zero comma one, and the slope is one, and that's pretty obvious.
For every amount that we move to the right, we move the same amount up, so the slope is one.
Let's do another problem.
Let's say I wanted to find the equation of the line between the points negative three comma five and two comma negative six.
Well, we do the same thing. m is equal to change in y over change in x.
So let's take this as the starting point.
So say negative six minus five.
So we just took negative six minus five over two minus negative three.
You've got to be real careful to get the signs right.
So it's two minus negative three.
Negative six minus five is minus eleven, and two minus negative three, well, that's the same thing as two plus plus three, so that's five.
So we have the slope is equal to negative eleven / five. And notice that if on the numerator we use negative six as the starting point, that in the denominator, we have to use two as the starting point.
We could have done it the other way around.
We could have said five minus negative six over negative three minus two, in which case we would have gotten-- this would have been eleven over negative five.
So as long as you-- if you use the negative six first, then you have to use the two first, or if you use the five first, then you have to use the negative three first.
I hope I'm not completely confusing you guys.
Well, anyway, we know the slope is negative eleven / five, so the equation of this line so far is y equals minus eleven / fivex plus b.
Now we can take one of these pairs on the top and substitute back and solve for b.
Let's take the first pair.
So five is y.
So we say five equals negative three, so it's negative eleven / five times negative three, right?
I just put the x in for x plus b.
So just simplifying that, I get five is equal to thirty-three / five plus b, or b is equal to five minus thirty-three / five, and this equals twenty-five minus thirty-three / five. twenty-five minus thirty-three is minus eight / five.
So the equation of this line, and this one wasn't as clean as the other one, obviously, is-- let me do it in another color for emphasis-- y equals minus eleven / fivex minus eight / five.
Hopefully, those two examples will give you enough of an idea to do the figuring out the equation of a line problems. And if you have problems with this, you might just want to try just the slope of the line problems or the y-intercept problems separately.
I hope you have fun.
Bye.
Huh...
Harlem Shake
Oh, I don't know what a Harlem Shake is...
Some odd guy is...
Oh, okay then...
What are they doing?!
There's always like a naked guy, just somewhere... hidden in there, there's a naked guy.
At least put some pants on, dude!
That's funny.
Again?!
I like his mask.
He has a horsey head...
A computer person, wearing a horse and dancing?!
(Sings) And do the Harlem Shake!
I thought these were business people...
Yeah, normal work day.
I love these videos, they're great.
How many are there?
Oh, this is the best one.
Attention, do the Harlem Shake.
What if this was real and they were actually doing this... on the battlefield?
What?
Aren't these people like in the army or something?
What the heck are those boys doing in that blanket?
(Laughs)
My side is hurting.
I just don't understand...
Shamu gonna come out of somewhere?
Oh yeah, I watched this one...
This is pretty funny.
All are pretty funny.
It's coming!
It's coming!
Oh my God, they even had a walrus!
This is horrifying!
What even is that?
Oh!
A seal!
What..?
What?
What? And why are they shirtless, some of them?
That's such a weird-looking walrus.
Ah!
(Chuckles)
Really?
Is that you, guys?
That's you!
There I am!
Right there!
Look, it's me right there!
This one really sucks, you can already tell.
What?!
What are you guys doing? I'm like... Right...
Determine whether 30/45 and 54/81 are equivalent fractions.
Well, the easiest way I can think of doing this is to put both of these fractions into lowest possible terms, and then if they're the same fraction, then they're equivalent.
So 30/45, what's the largest factor of both 30 and 45?
15 will go into 30.
It'll also go into 45.
So this is the same thing.
30 is 2 times 15 and 45 is 3 times 15.
So we can divide both the numerator and the denominator by 15.
So if we divide both the numerator and the denominator by 15, what happens?
Well, this 15 divided by 15, they cancel out, this 15 divided by 15 cancel out, and we'll just be left with 2/3.
So 30/45 is the same thing as 2/3.
It's equivalent to 2/3.
2/3 is in lowest possible terms, or simplified form, however you want to think about it.
Now, let's try to do 54/81.
Let's see, 9 is divisible into both of these.
We could write 54 as being 6 times 9, and 81 is the same thing as 9 times 9.
You can divide the numerator and the denominator by 9.
So we could divide both of them by 9.
9 divided by 9 is 1, 9 divided by 9 is 1, so we get this as being equal to 6/9.
6 is the same thing as 2 times 3.
9 is the same thing as 3 times 3.
We could just cancel these 3's out, or you could imagine this is the same thing as dividing both the numerator and the denominator by 3, or multiplying both the numerator and the denominator by 1/3.
These are all equivalent.
I could write divide by 3 or multiply by 1/3.
Actually, let me write divide by 3. Let me write divide by 3 for now.
I don't want to assume you know how to multiply fractions, because we're going to learn that in the future.
So we're going to divide by 3.
3 divided by 3 is just 1.
3 divided by 3 is 1, and you're left with 2/3.
So both of these fractions, when you simplify them, when you put them in simplified form, both end up being 2/3, so they are equivalent fractions.
Martin Luther King did not say,
"I have a nightmare," when he inspired the civil rights movements.
He said, "I have a dream."
And I have a dream.
I have a dream that we can stop thinking that the future will be a nightmare, and this is going to be a challenge, because, if you think of every major blockbusting film of recent times, nearly all of its visions for humanity are apocalyptic.
I think this film is one of the hardest watches of modern times, "The Road."
It's a beautiful piece of filmmaking, but everything is desolate, everything is dead.
And just a father and son trying to survive, walking along the road.
And I think the environmental movement of which I am a part of has been complicit in creating this vision of the future.
For too long, we have peddled a nightmarish vision of what's going to happen.
We have focused on the worst-case scenario.
We have focused on the problems.
And we have not thought enough about the solutions.
We've used fear, if you like, to grab people's attention.
And any psychologist will tell you that fear in the organism is linked to flight mechanism.
It's part of the fight and flight mechanism, that when an animal is frightened -- think of a deer.
A deer freezes very, very still, poised to run away.
And I think that's what we're doing when we're asking people to engage with our agenda around environmental degradation and climate change.
People are freezing and running away because we're using fear.
And I think the environmental movement has to grow up and start to think about what progress is.
What would it be like to be improving the human lot?
And one of the problems that we face, I think, is that the only people that have cornered the market in terms of progress is a financial definition of what progress is, an economic definition of what progress is -- that somehow, if we get the right numbers to go up, we're going to be better off, whether that's on the stock market, whether that's with GDP and economic growth, that somehow life is going to get better.
This is somehow appealing to human greed instead of fear -- that more is better.
Come on.
In the Western world, we have enough.
Maybe some parts of the world don't, but we have enough.
And we've know for a long time that this is not a good measure of the welfare of nations.
In fact, the architect of our national accounting system,
Simon Kuznets, in the 1930s, said that, "A nation's welfare can scarcely be inferred from their national income."
But we've created a national accounting system which is firmly based on production and producing stuff.
And indeed, this is probably historical, and it had its time.
In the second World War, we needed to produce a lot of stuff.
And indeed, we were so successful at producing certain types of stuff that we destroyed a lot of Europe, and we had to rebuild it afterwards.
And so our national accounting system became fixated on what we can produce.
But as early as 1968, this visionary man, Robert Kennedy, at the start of his ill-fated presidential campaign, gave the most eloquent deconstruction of gross national product that ever has been.
And he finished his talk with the phrase, that, "The gross national product measures everything except that which makes life worthwhile."
How crazy is that?
That our measure of progress, our dominant measure of progress in society, is measuring everything except that which makes life worthwhile?
I believe, if Kennedy was alive today, he would be asking statisticians such as myself to go out and find out what makes life worthwhile.
He'd be asking us to redesign our national accounting system to be based upon such important things as social justice, sustainability and people's well-being.
And actually, social scientists have already gone out and asked these questions around the world.
This is from a global survey.
It's asking people, what do they want.
And unsurprisingly, people all around the world say that what they want is happiness, for themselves, for their families, their children, their communities.
Okay, they think money is slightly important.
It's there, but it's not nearly as important as happiness, and it's not nearly as important as love.
We all need to love and be loved in life.
It's not nearly as important as health.
We want to be healthy and live a full life.
These seem to be natural human aspirations.
Why are statisticians not measuring these?
Why are we not thinking of the progress of nations in these terms, instead of just how much stuff we have?
And really, this is what I've done with my adult life -- is think about how do we measure happiness, how do we measure well-being, how can we do that within environmental limits.
And we created, at the organization that I work for, the New Economics Foundation, something we call the Happy Planet Index, because we think people should be happy and the planet should be happy.
Why don't we create a measure of progress that shows that?
And what we do, is we say that the ultimate outcome of a nation is how successful is it at creating happy and healthy lives for its citizens.
That should be the goal of every nation on the planet.
But we have to remember that there's a fundamental input to that, and that is how many of the planet's resources we use.
We all have one planet.
We all have to share it.
It is the ultimate scarce resource, the one planet that we share.
And economics is very interested in scarcity.
When it has a scarce resource that it wants to turn into a desirable outcome, it thinks in terms of efficiency.
It thinks in terms of how much bang do we get for our buck.
And this is a measure of how much well-being we get for our planetary resource use.
It is an efficiency measure.
And probably the easiest way to show you that, is to show you this graph.
Running horizontally along the graph, is "ecological footprint," which is a measure of how much resources we use and how much pressure we put on the planet.
More is bad.
Running vertically upwards, is a measure called "happy life years."
It's about the well-being of nations.
It's like a happiness adjusted life-expectancy.
It's like quality and quantity of life in nations.
And the yellow dot there you see, is the global average.
Now, there's a huge array of nations around that global average.
To the top right of the graph, are countries which are doing reasonably well and producing well-being, but they're using a lot of planet to get there.
They are the U.S.A., other Western countries going across in those triangles and a few Gulf states in there actually.
Conversely, at the bottom left of the graph, are countries that are not producing much well-being -- typically, sub-Saharan Africa.
In Hobbesian terms, life is short and brutish there.
The average life expectancy in many of these countries is only 40 years.
Malaria, HlV/AlDS are killing a lot of people in these regions of the world.
But now for the good news!
There are some countries up there, yellow triangles, that are doing better than global average, that are heading up towards the top left of the graph.
This is an aspirational graph. We want to be top left, where good lives don't cost the earth.
They're Latin American.
The country on its own up at the top is a place I haven't been to.
Maybe some of you have.
Costa Rica.
Costa Rica -- average life expectancy is 78-and-a-half years.
That is longer than in the USA.
They are, according to the latest Gallup world poll, the happiest nation on the planet -- than anybody; more than Switzerland and Denmark.
They are the happiest place.
They are doing that on a quarter of the resources that are used typically in [the]
Western world -- a quarter of the resources.
What's going on there?
What's happening in Costa Rica?
We can look at some of the data.
99 percent of their electricity comes from renewable resources.
Their government is one of the first to commit to be carbon neutral by 2021.
They abolished the army in 1949 -- 1949.
And they invested in social programs -- health and education.
They have one of the highest literacy rates in Latin America and in the world.
And they have that Latin vibe, don't they.
They have the social connectedness.
(Laughter)
The challenge is, that possibly -- and the thing we might have to think about -- is that the future might not be North American, might not be Western European.
It might be Latin American.
And the challenge, really, is to pull the global average up here.
That's what we need to do.
And if we're going to do that, we need to pull countries from the bottom, and we need to pull countries from the right of the graph.
And then we're starting to create a happy planet.
That's one way of looking at it.
Another way of looking at it is looking at time trends.
We don't have good data going back for every country in the world, but for some of the richest countries, the OECD group, we do.
And this is the trend in well-being over that time, a small increase, but this is the trend in ecological footprint.
And so in strict happy-planet methodology, we've become less efficient at turning our ultimate scarce resource into the outcome we want to.
And the point really is, is that I think, probably everybody in this room would like society to get to 2050 without an apocalyptic something happening.
It's actually not very long away.
It's half a human lifetime away.
A child entering school today will be my age in 2050.
This is not the very distant future.
This is what the U.K. government target on carbon and greenhouse emissions looks like.
And I put it to you, that is not business as usual.
That is changing our business.
That is changing the way we create our organizations, we do our government policy and we live our lives.
And the point is, we need to carry on increasing well-being.
No one can go to the polls and say that quality of life is going to reduce.
None of us, I think, want human progress to stop.
I think we want it to carry on.
I think we want the lot of humanity to keep on increasing.
And I think this is where climate change skeptics and deniers come in.
I think this is what they want. They want quality of life to keep increasing.
They want to hold on to what they've got.
And if we're going to engage them,
I think that's what we've got to do. And that means we have to really increase efficiency even more.
Now that's all very easy to draw graphs and things like that, but the point is we need to turn those curves.
And this is where I think we can take a leaf out of systems theory, systems engineers, where they create feedback loops, put the right information at the right point of time.
Human beings are very motivated by the "now."
You put a smart meter in your home, and you see how much electricity you're using right now, how much it's costing you, your kids go around and turn the lights off pretty quickly.
What would that look like for society?
Why is it, on the radio news every evening, I hear the FTSE 100, the Dow Jones, the dollar pound ratio --
I don't even know which way the dollar pound ratio should go to be good news.
And why do I hear that?
Why don't I hear how much energy Britain used yesterday, or American used yesterday?
Did we meet our three percent annual target on reducing carbon emissions?
That's how you create a collective goal.
You put it out there into the media and start thinking about it.
And we need positive feedback loops for increasing well-being
At a government level, they might create national accounts of well-being.
At a business level, you might look at the well-being of your employees, which we know is really linked to creativity, which is linked to innovation, and we're going to need a lot of innovation to deal with those environmental issues.
At a personal level, we need these nudges too.
Maybe we don't quite need the data, but we need reminders.
In the U.K., we have a strong public health message on five fruit and vegetables a day and how much exercise we should do -- never my best thing.
What are these for happiness?
What are the five things that you should do every day to be happier?
We did a project for the Government Office of Science a couple of years ago, a big program called the Foresight program --
lots and lots of people -- involved lots of experts -- everything evidence based -- a huge tome.
But a piece of work we did was on: what five positive actions can you do to improve well-being in your life?
And the point of these is they are, not quite, the secrets of happiness, but they are things that I think happiness will flow out the side from.
And the first of these is to connect, is that your social relationships are the most important cornerstones of your life.
Do you invest the time with your loved ones that you could do, and energy?
Keep building them.
The second one is be active.
The fastest way out of a bad mood: step outside, go for a walk, turn the radio on and dance.
Being active is great for our positive mood.
The third one is take notice.
How aware are you of things going on around the world, the seasons changing, people around you?
Do you notice what's bubbling up for you and trying to emerge?
Based on a lot of evidence for mindfulness, cognitive behavioral therapy, [very] strong for our well being.
The fourth is keep learning and keep is important --
learning throughout the whole life course.
Older people who keep learning and are curious, they have much better health outcomes than those who start to close down.
But it doesn't have to be formal learning; it's not knowledge based.
It's more curiosity. It can be learning to cook a new dish, picking up an instrument you forgot as a child.
Keep learning.
And the final one is that most anti-economic of activities, but give.
Our generosity, our altruism, our compassion, are all hardwired to the reward mechanism in our brain.
We feel good if we give.
You can do an experiment where you give two groups of people a hundred dollars in the morning.
You tell one of them to spend it on themselves and one on other people.
You measure their happiness at the end of the day, those that have gone and spent on other people are much happier that those that spent it on themselves.
And these five ways, which we put onto these handy postcards,
I would say, don't have to cost the earth.
They don't have any carbon content.
They don't need a lot of material goods to be satisfied.
And so I think it's really quite feasible that happiness does not cost the earth.
Now, Martin Luther King, on the eve of his death, gave an incredible speech.
He said, "I know there are challenges ahead, there may be trouble ahead, but I fear no one.
I don't care.
I have been to the mountain top, and I have seen the Promised Land."
Now, he was a preacher, but I believe the environmental movement and, in fact, the business community, government, needs to go to the top of the mountain top, and it needs to look out, and it needs to see the Promised Land, or the land of promise, and it needs to have a vision of a world that we all want.
And not only that, we need to create a Great Transition to get there, and we need to pave that great transition with good things.
Human beings want to be happy.
Pave them with the five ways.
And we need to have signposts gathering people together and pointing them -- something like the Happy Planet Index.
And then I believe that we can all create a world we all want, where happiness does not cost the earth.
(Applause)
<i>Brought to you by the PKer team @ www.viikii.net
Episode 8 <i>The shining era of high school has passed, and I have become a 20-year-old. <i>The reason that that time in high school was shining... <i>because of Baek Seung Jo.ا <i>I am going to have fun.
I am going to live happily. <i>Oh Ha Ni? <i>I'm asking you if you're Oh Ha Ni. <i>To put it simply, I hate stupid girls. <i> You, you!
Why did you come out from there? <i>Because it's my house. <i> I can't believe it!
To be having breakfast with Baek Seung Jo. <i>What to do? <i>Logx = log (2^30 * 10^-7), <i>logx = 30log2 - 7log10 logx=30*0.3-7 <i>For this problem we use f=ma. <i> Good luck. <i> This one. <i>Thank you. <i>What is this? <i>Oh Ha Ni! <i>Hey!
Oh Ha Ni! <i>Hey!
Hey! <i>Hey! <i> What I said about you being a pain, <i> Weren't just empty words.
Ever since I met you, I did not have one quiet day. <i> I told you to stop this.
How far do you intend to take this? <i>Please just knock it off! <i>Even though he's cold, I cannot stop my feelings towards him. <i>That's because I'm a persevering snail heading towards Seung Jo. <i> You're amazing, Oh Ha Ni. <i> You want to drink some water? <i>Come here. <i>Your girlfriend? <i>There's no way. <i> What does he mean "There is no way"? <i> You and Oh Ha Ni are very well suited. <i> Now, it's time I let go of my feelings. <i>Let's move out Ha Ni. <i>Good bye... <i>Baek Seung Jo.
What were you looking at?
The street down there.
People walking by and the alley... it's fun.
It's refreshing.
We'll stay here, and then we'll find a new house.
Even though it's uncomfortable, just bear with it for a little while.
I'm alright.
It's fine, and I really like this neighborhood.
Since it's an old neighborhood,and it's a little emotional.
That's right. it definitely seems homey.
Yup there is definitely
Let's go eat.
Yes.
Ha Ni, you came down?
Yeah...
Just wait a bit, I'll make it right away.
Here. I knew you would come back!
I didn't know that we would be together this soon though.
You rascal, what do you mean by being together, huh?
Hey, give me a plate.
Ha Ni this is called yeongbap.
Come on and try it.
Father, we eat and breathe together both upstairs and downstairs.
If it's not being together then what is it?
If you're going to keep drinking Kim Chi soup and make things chaotic then just leave!
Father, how could you say something so sad.
I...
Eat.
Should I open it for you?
Have a meal.
But I don't have any appetite.
Don't just stay at home, go outside, take some photos. And meet your friends.
Because you keep staying at home.
I don't even have anything I want to do.
Are you okay?
Isn't there anything wrong with you?
I'm great, very peaceful.
Peace?
What's the peace that you're talking about? Not having anything you don't expect? Being everything by yourself?
Isn't that why you were so quiet and suffocating in your own bubble?
Not going to DaeSun University and going to Parang University, didn't you do that because you hated the peace?
Please try this.
Our Ha Ni is so out of it right now that...
I'm a bit worried.
Don't you think I should cheer her up by giving her a call?
This late?
This rascal.
Ha Ni is the prettiest when she's smiling.
I'm just saying this because she's always sad now.
I'll make her return to a smiling face at once...
Couldn't you allow us to go on a night date?
You can make her return to a smiling face?
Ah, of course.
Will you allow it?
Then well...
Yes.
Ha Ni... <i>Not available to answer the call. After the beep....
Ah, why?
She didn't answer.
Really?
Aigoo...
For the time being, dad said to split up some of the house chores.
Really?
Hyung, you have the cleaning, dishwashing, and the cooking.
What?!
I'm doing it all?
Should a young kid like me have to do it?
Dad has to go to work... <i>You're going to take the test tomorrow, right? <i>You can do everything. <i>You have to use your brains to benefit people. <i>I think people who has a lot should share what he has.
Good luck on your test!
FlGHTlNG!!
I thought that you would always live in that house.
You're losing your advantage little by little.
It's fine, I don't need it now.
I really gave up Baek Seung Jo.
What?
Really?
You, the one that was so stubborn?
I'm a different person now than I was before. Because I realized that there's nothing more I can do.
I won't go chasing after Baek Seung Jo again.
Ha Ni.
I've talked about it with dad, and closed my heart against him.
Now, I will look for a really cool boyfriend.
Really? <i>Good-bye, Baek Seung Jo.
Hey!
Let's go have lunch.
I came out without the dean knowing.
I have to quickly eat and go back.
Right. I'm hungry.
I don't feel like it.
You guys go ahead.
Oh Ha Ni.
Because you're being like this, you don't seem like the Oh Ha Ni I know.
Is it because you're afraid that if you go to the cafeteria you might meet Baek Seung Jo?
If I see Seung Jo, my heart might waver again.
I really can't hold you back.
I wonder if you won't be able to meet another guy because you're like this.
Even so...
I'll eat later!
Hey Oh Ha Ni.
If you made your decision, then it's a good thing to run into him often.
That way you can build tolerance.
Do you think you won't run into him when you go to the same school?
That's right!
Dok Go Min Ah said something right.
It's actually good to meet him first.
Let's go.
I'm hungry!
Let's go quickly!
Let's go!
Let's go!
What do you want to have?
Huh?
Omo!
[Oh Ha Ni grew tired of Baek Seung Jo and broke up!]
It's now time for a lovely mood with Bong Joon Goo.
Did you see above?
Please spread the word.
Even if you see someone you don't know, tell them about it.
Next order!
- Gogi dub bap please <Br> - Gogi dup bap right here
Hey Bong Joon Gu, what are you doing?!
Ha Ni, you came.
What do you want to eat today?
The Gogi Dup Bap (meat on top of rice) is really good today.
Eat that.
Hey Bong Joon Gu!
I'm not in the mood to play around.
Hey Bong Joon Gu, you're causing an incident.
Hey Bong Joon Gu, what are you thinking?
If Baek Seung Jo sees this, what will Ha Ni become?
Baek Seung Jo?
He already saw it.
He's over there.
What?!
This is completely cheesy.
I'd probably get sick of it too.
You must get really tired, Baek Seung Jo.
Is this possibly a struggle to change Baek Seung Jo's interests?
Hey girl!
What did you just say?
No.
I forgot Seung Jo.
Baek Seung Jo has nothing to do with me anymore.
We don't live in one house anymore...
Just...
We're strangers now.
Our Ha Ni is speaking well!
Hey Baek Seung Jo, you heard right?
You heard correctly right?
Ha Ni ah!
You're not going to eat Gogi Dup Bap?
Hey Oh Ha Ni!
Why are you being so sluggish?
Hurry up and bring the balls.
I'm really tired.
Just a little...
What did you do that you're so tired?
Stop talking and bring the balls.
Hurry!
Sunbaenim.
That racket...
Could you put it down when you talk?
What?
It's nothing.
I heard you're still just picking up the balls.
Why... did you come?
Why would I have come?
I'm part of the staff here too.
No...
That's that. <i>I'm trying so hard to suppress my feelings.
I'm not even attending classes. <i>But if you just come like this, what am I supposed to do?
Ha Ni ah.
Ha Ni ah.
Seung Jo.
You're here, I have something to say to you.
Next Friday and Saturday, our Top Spin Club is going on an MT for two nights and three days.
Let's go together.
I don't want to.
Why?
I came on the condition where I could come only if I wanted to.
Seung Jo ah.
Since we're players, should we make a bet with a match?
If you win, you don't have to go.
And if I win, you go.
Let's go outside and have a game. What do you think about that ?
I don't care...
But will you really be okay?
Ah brat.
I know that you play well.
Let's just try it for fun.
Let's do a dual match.
That sounds fun.
You and Ha Ni on one team.
-Pardon?
-Pardon?
Then I... uh...
Should I play with Yoon Hae Ra?
Is your brother upstairs?
No.
He's not there.
Where did he go?
He said he didn't have class today, so he was going to stay home and read.
Earlier, he was holding a tennis bag and left.
Ahh, he went to the Tennis Club.
Have you been well?
Yeah I'm Seung Jo's mom.
I've gotten curious about something.
Do you know what club Ha Ni signed up for?
Oh my!
Really?!
Oh excuse me.
Where can I find the Tennis Club?
I came to meet a student named Oh Ha Ni.
You probably don't know Oh Ha Ni.
The club's name is Top Spin.
Ah Oh Ha Ni?
Oh my!
You know Oh Ha Ni?
Something about her breaking up with Baek Seung Jo... there was some commotion at the cafeteria.
Oh my, what?!
What kind of rumor is that?
That is all a lie!
Baek Seung Jo and Oh Ha Ni will never break up.
Those two people are doing fine!
You students tell the others too!
But then, who are you ma'am??
Who's that lady?
Excuse me.
Where should I go to find the Tennis Club?
Ah wait a min...
Possibly, Seung Jo's mother?
Ah I was right!
Hello.
Oh Joo Ri, Min Ah!
Nice to see you!
What's going on?
Wearing those kinds of clothes...
Oh, I was trying to disguise.
Does it show??
It's very obvious.
Did you come to watch Ha Ni play tennis?
When you watch the Wimbledon matches,
Sharapova wears those white tennis uniforms.
And she does the swishing!
Imagining Ha Ni do that, could I just sit at home?
Where are they playing?
Let's hurry up and go watch.
I think the practice is over now.
It's over?
Later tonight, Ha Ni and Seung Jo will be playing tennis on one team.
What's up with being on the same side as Seung Jo?
Yeah.
Ha Ni is desperately trying to forget Seung Jo.
Oh my.
What are you talking about?
Actually, I thought everything was going to be okay between Ha Ni and Seung Jo.
I thought that way too.
Think about it.
After graduation, they...
They even kissed.
What?!
KlSS!!!
That was on the night of graduation.
And, Baek Seung Jo did it first!
Awesome!
Seung Jo, really!
After doing that... why?!
I've made my decision.
I'm going to have Ha Ni back at our house.
Even if Seung Jo says something, it doesn't matter.
They even kissed. <i>Brought to you by the PKer team @ www.viikii.net
We're going to lose anyways.
So just tell them you're going to the MT.
You're saying to give up now?
Listen carefully.
You just run the opposite way from the ball.
Don't get in my way.
Understood?
Just pretend that I'm not here
Don't serve me any balls, okay?
I want to go with Seung Jo to the MT.
So I don't intend to go easy on you.
Show me what you've got.
PLAY.
I told you to not get in my way!
Sorry.
0 - 15
Ah, come on!
Hey!
Don't come, don't come.
Advantage.
Wang Kyung Su and Yoon Hae Ra.
This time, if we don't get the point.
It will be the game set.
Keep your mind on the game Oh Ha Ni.
Got it?
Then, this is the last one.
Game set.
Wang Kyung Soo and Yoon Hae Ra's win.
Yes!
We won, we won!
That punk!
Thank you Oh Ha Ni.
Thanks to you, ever since the day I was born, this is the first time I ever lost.
Feels very refreshing.
I'm sorry.
That's why, from the start...
Aigoo, Mr. Baek Seung Jo
Oh, your pride must have been hurt a lot.
Is this the first time you've lost?
I'd like to pay you back sometime.
Really?
I'm cool, whenever you want.
However, we'll stay teamed the same way we are now.
How about having it when we go on the MT?
Huh?
But the MT is next week.
Right, no matter how much of a genius you might be, 1 week is pushing it.... right?
Fine.
Let's try it out.
On the last day of the MT.
Call
Call!
We have only one week.
After one week, we'll win, for sure.
Do you understand?
Does that make any sense?
When did you ever know what makes sense or not?
When you asked me to raise you to the top 50 students,
Where'd that attitude go?
Now, spread your legs shoulder width apart.
A little more, Yeah.
Now lower your stance.
Follow me.
1 2
Put your foot forward.
3
Your right foot too.
3 You should hold the racquet
Like this...
And keep your hand like this.
3!
Like so, to the right side.
Again.
Try it again.
Like this.
1 2, 3 1, 2, 3
In every sport the fundamentals are important.
Every step should be at the same pace.
Keeping it steady.
Come on.
Hurry, hurry.
Hey!
Here.
Now harder.
Good.
Good.
She's really trying her best.
I mean Oh Ha Ni.
Even so, what can you do with only one week?!
Well, it's fun.
Oh Ha Ni has the joy of raising /teaching.
Joy of raising/ teaching?
She's amazing.
It's like if she puts her mind into something and works hard, she can achieve it.
Certainly,
That's because you're good at everything without having to make an effort, and having to work to death to accomplish something, you don't know anything about it.
You're like that too.
You're right.
Follow the ball until the end.
To the right, to the right.
Keep your eyes on it until the end.
No matter how hard I try I keep closing my eyes, so I can't see.
What can I do?!
I said No!
How many times do I need to tell you that.
Father,
Please think about it.
If they stay for 3 nights and 2 days, something's bound to happen, right?
If you let me have a break...
I can plan everything out.
Hey!
How long are you just going to chase her?
Don't just chase her.
Can't you make Ha Ni come to you?
You need to have respect.
Because you follow her around so crazily,
That's why she's not acknowledging you!
Hurry up and go finish what needs to be done in the kitchen.
HEY!
Change that hairstyle of yours!
That-little- thing- That's not Ha Ni's style!
What am I really?
Even though my resolution was firm... just thinking about spending 3 days and 2 nights with Baek Seung Jo... my heart is fluttering.
What to do?
This isn't right.
Ha Ni! Ah, Joon Gu.
You came early.
Here, take this with you.
What is it?
It's a lunch box.
Joon Gu.
You have to remember,
I am your home.
Home?
Right.
A home that will always be there for you no matter what.
It's still there after you've partied so much, and even after you've sobbed because things are so tough and then you come home.
The thing that always stays the same, your home.
Hurry up and go.
Be sure to come back safely.
Don't hurt yourself.
Thank you.
I'll eat it well.
Right.
Joon Gu!
Thank you.
Aish!
This really isn't my style.
It's really tough to earn respect.
Respect....
Ah, Sunbaenim!
You rascals... look at the way you're dressed.
The MT of our tennis club... is for us to reside on campus... and undergo special training.
It's a tradition.
Sunbaenim!
That's ridiculous!
Be quiet.
Starting now, I'll give you 5 minutes
Go back and drop your stuff at the clubroom.
And then meet here again.
Some people are not here yet,
Once everyone is here,
We'll do it.
What?
Who hasn't showed up yet?
Baek Seung Jo,Yoon Hae Ra and Oh Ha Ni.
Fine.
Baek Seung Jo and Yoon Hae Ra
Are special members so that's okay,
But Oh Ha Nl?
What's with that punk?
Omo!
Hello.
Yes.
It's a little idle right now.
Before the customers start coming for dinner...
Please take a seat.
Ah but... People like Ha Ni always ride these. It was so cute to me.
So I bought one, but it doesn't fit in my car.
I just brought it here.
Tell Ha Ni to ride it.
I'm not sure if it's okay to keep receiving things.
If you don't take it, then it's not okay.
And...
Your mail...
Ah thank you.
I haven't been able to change the address yet. I'm sorry.
Do you like it?
Just the two of you living together?
What?
Ah well.
I got a disease... depression.
It's pretty serious. I heard from Soo Chang.
Before Ha Ni came, at our house, the person who talked and made mistakes...
I was the only one.
Seung Jo and Eun Jo... they don't have that type of personality.
And my husband is busy.
If I don't laugh, our house turns into a depressing hole.
But when Ha Ni came, I liked it so much.
It felt like I was living.
I was happy.
Would it be okay to live together again?
You haven't changed your address yet.
I thought about it a lot.
Maybe I'm being too selfish.
That I'll be the only one that's happy.
She seemed like the perfect match for Seung Jo.
Maybe I'm being too greedy.
But...
I feel like Ha Ni will be sad alone too.
Actually I was waiting for that too.
But now they're all in college, and if Seung Jo gets a new girlfriend...
Rather than having a hard time moving after getting close to everyone...
I thought it might be better to hurt a little bit right now.
To Ha Ni...
We'll start tomorrow at 6:00AM.
In the morning we'll swing. In the afternoon we'll learn how to top spin.
To the people who think we're going on the MT to have fun, it's a good idea to reset that mindset.
Here here here.
It's time to rest.
We'll all rest and after an hour, let's meet at the front court.
Good work.
Yah Han Ni ah.<BR><BR>Come here.
You don't need to come to the evening training.
Why?
You're in charge of the dinner now.
By myself?
You were tardy this morning.
Think of it as a punishment and go make dinner.
It's better off this way.
You don't have to train.
Wait a second.
Then what about the match on the last day?
Oh that?
Of course we have to do that, since I promised.
How can you put her in charge of the food?
She needs to train more than the others.
That's your problem. She was tardy though.
Are you not letting her practice because you think you might lose?
Sunbae (Senior)
You have that low of confidence?
Ah.. that...
Hurry up with the food.
So we can train with the time leftover.
I told you...
The match after tomorrow, we have to win.
It'll probably be tiring... by yourself.
You're not saying that you'll help me.
I don't really like cooking.
I have something to say.
You might have already noticed, but I'm interested in Seung Jo.
So I'm going to tell Seung Jo this time.
It should be okay, right?
Why are you asking me?
I'm not sure.
I keep feeling like I'm taking candy from a baby.
What?
Ah, it's not that.
I'm fine.
Really?
I feel better then.
Then work hard.
There's no end to this peeling.
Ah hot.
Yah Oh Ha Ni
Do you still have a lot left?
If you keep going slow like that, there won't be any time to practice.
Seung Jo ah.
Baek Seung Jo.
Help me.
I need to hurry up and finish so I can practice.
Sesame oil.
Yes!
Yah Yah Yah!<BR><BR>Stop.
Ground red pepper.
Yes.
Put in a little bit.
I said just put in just a little.
Woah.
It looks so good.
Who made this?
It looks so good!
Please sit down.
Ha Ni, did you do this?
You're really great.
You can get married now.
What is all this?
It looks so delicious Ha Ni.
Woah it's really good, it's really good!
Try it, try it!
What is this?
This is quite good.
It's shrimp!
So good!
Try this.
It's really good.
Yah Baek Seung Jo.
What are you?
Give her some compliments.
Seung Jo, he's very picky.
Oh Ha Ni.
Let's go practice.
I wonder if the kids are doing okay.
It would be nice if they got closer so that she can come back.
We spent all that time together.
How can Seung Jo be so cold?
I didn't notice it when they were here.
But since Ha Ni is gone, the house seems empty and no fun.
You think that way too, don't you?
Honey,
Can we ask Ki Dong shi to come live with us again?
Should I meet Ki Dong once then?
Honey, thank you so much.
Even if we live together again,
I'm not going to give up my room.
Definitely not.
1, 2 3 1, 2
How many do you have left?
Keep your hips straight.
Keep your back straight
Keep your back straight
Keeps your hips straight. And your butt too.
Ah I can't do this.
Yah<BR><BR>Get up.
Get up.
Yah!
Get up.
Quickly.
I'm tired.
Mmh.
Tired is playing tennis.
Get up.
Swing.
To the outside.
Back hand.
One more time. <i>Brought to you by the PKer team @ www.viikii.net</i>
What are you doing?
Let's do it again. <i>Brought to you by the PKer team @ www.viikii.net
Baek Seung Jo!
You missed the afternoon training yesterday.
Without catching up first, don't do anything else.
Will it be okay?
You'll probably regret.
What?
Then maybe I should go buy some ramen.
Ha Ni ah.
What happened with this?
Even though it looks like that, the taste should be okay.
Really?
Jong Suk.
You eat one.
Yes?
Try one.
Where did the Dae Jang Geum from yesterday go?
I'm sorry.
-Actually, I didn't make it yesterday.
-Then who made it?
You were the only one who missed the evening training.
Ah!
Baek Seung Jo.
Huh?
Seung Jo?
Good job!
Doing a good job!
Ah, you came? <i>What are you doing Oh Ha Ni... <i>What are you going to do by following them? <i>No, I'm not following them.
What? Is there something you wanted to tell me?
I don't know what to say..this isn't my usual style.
I was second when I entered the school
I also applied to lower school than the ones that I could go.
There were some circumstances.
Is that so?
I like you.
And you?
How do you feel?
Hey.
What are you doing?
What are you doing? Watching them.
Possibly, do you like Hae Ra?
Sh!
From the looks of it, this seems fun.
However, I'm sorry but...
I'm going to borrow her since we have a match tomorrow.
Huh? Oh okay take her.
You're doing good. In a position that can't even serve.
That's not it.
Come! We're going to practice until you get it right.
Should I change my hairstyle?
It's the coolest style in my neighborhood though.
Oh Ha Ni is really working hard. Right?
You're alright?
Yes, I'm alright.
Good Job.
You succeeded.
The speed of your serve was pretty fast too.
It works if I do it like this?
Yeah...
You did well. <i>He smiled. <i>Baek Seung Jo looked at me and smiled. <i>To see that smiling face. <i>"Good Job." <i>To hear him say that...
Did you get hurt?
Huh?
No.
You are hurt.
Well, it isn't Oh Ha Ni to just fall (and not cause trouble).
What is it?
We'll forfeit the doubles we were going to do later.
Huh?
Injury.
No, we have to do it.
How can you do it like this?
You can't even get up.
But still.
You said we have to win...
I practiced really hard.
With your feet?
It's fine.
There's nothing we can do about it.
I'm sorry...
-Because of me...
-I wasn't even counting on winning anyways.
Get on.
Hey! Baek Seung Jo!
You have to play the match you promised.
How can you just go?
Do we have to do the game now?
Let's set up another one soon.
Today, as you can see...
Omo! You look so cool!
Huh? Woah.
Ah.
Who are you?
It's a little awkward.
You look like a different person.
Yeah totally! You should have done it sooner.
What happened to your hair?
I cut it. ohh
Who is that?
Is it Seung Jo?
What's going on? What's going on?
She got hurt?
Ha Ni!
Where? Where did you get hurt?
It seems she hurt her leg.
Sit down, sit down!
While training, she twisted her ankle.
It also seems to be weaker because of the accident from before.
Looks like you're going to have to put it in a cast again.
Try using an ankle brace
It'll be a good idea to keep it on for 6 weeks.
A half cast?
Alright.
You look different.
What are you talking about, environment?
Can you say something like that right now?
Bringing someone who was healthy home like this
That's not it.
It was my fault that I got hurt. So don't say that.
That's right.
I guess If you say so.
I get it.
I'll keep my mouth shut.
Ha Ni really didn't say anything about you changing your style?
That's because she was with Baek Seung Jo.
You're so pitiful!
Though, your hair looks great!
I think so too! You look like a totally different person. You should have done this sooner!
Hey, do you know?
Ha Ni really likes this style.
He said she didn't notice.
Ha Ni.
Here eat!
Eat this too.
It's a boiled egg.
What about the other people?
It's okay.
Thank you Joon Gu. I'll eat well.
Okay.
Ha Ni, I'm really doing my best.
Do you know? or from the movie Personal Taste you can sense... the first quote goes, "All things are not studio but location."
We take it from a realistic perspective.
So, location, sound, and art.
Without even knowing, I ended up coming here.
Since I already came,
How about I catch a little look of his face?
Seung Jo.
How about we go see a movie today?
There is a movie I really want to see.
What do you think? After watching it we can go . Okay, sounds good, I've been wanting to get out anyway.
Popcorn and two sodas.
It's 7000 won.
Let me pay. <i>I dreamed about going on a date together since freshman year of high school. <i>I would even have a fashion show the night before to pick out clothes to wear. <i>Watch a movie, and when it ends go window shopping together. <i>Then sit together at a coffee shop and chat. <i> All of that he's doing with Yoon Hae Ra.
I'm sorry.
Ha Ni! What are you doing here?
Sunbae!
You... You!
Sunbae you too.
Ha Ni.
You like Seung Jo, right? I know.
And that's right, I like Hae Ra.
But Hae Ra likes Seung Jo.
Don't you think that's wrong too?
That's why, you and I should collaborate.
Collaborate?
First, since we don't really have anything planned... we'll follow them...
When we get a chance, or if it gets dangerous we can leave.
That's a little...
What's a little?
Then did we come out just to watch them have fun together?
Anyways, does Seung Jo... does he have fast hands?
Huh? What are you talking about?
Ah touching. Skinship.
This kind of stuff.
I'm not sure.
I don't think it's like that.
He doesn't like doing those...
Not interested...?
That's because it's you.
I don't think it'll be easy for Seung Jo to hold it in with someone as sexy as Hae Ra. <i>I love you. <i>I love you. <i>This is me saying this. <i>So... <i>Like I said, these are my feelings. <i>It's not a dream or anything, but... <i>Please don't let anything happen in this dark place.
I heard those two were engaged in real life.
Aigoo.
Aigoo.
I'm so sorry.
You did well!
I'm sorry.
That brat... where is he puttng that hand?
Thanks.
-Ah really.
-Thanks. <i>What am I doing? <i>Sneaking around on someone else's date, planning to intrude. <i>I just got to see them get along in the end.
Ha Ni, they're going that way.
Let's go quickly.
What is it?
I'm thinking about stopping.
What are you talking about?
I can't watch anymore.
It's too difficult.
Ah, what's wrong all of a sudden?
We have to go, what if they make a move?
If they like each other, there's nothing we can do.
I've realized that now.
Then, are you saying that you're going to acknowledge them doing that?
I don't wan't to be made a fool of anymore.
Aish!
I'm so sorry!
How am I supposed to get rid of it?
I have to go meet my girlfriend right now!
Do you know how much this is?
I'll give you the money for dry cleaning.
Yes, the money for dry cleaning.
Dry cleaning money?
Yes. How much...?
Ah, she's my hoobae.
I'll give it to you.
Right here. 10,000 won.($10)
Are you playing around right now?
Huh?
100,000 won ($100)?
Oh. Why are you being like this?
You're playing around with me right now, aren't you?
Huh?
This is worth 2,000,000 won ($2000)!
Then you should at least pay half.
1,000,000 won ($1000)?
Sir!
I'm only 21.
Where do I have that kind of money? Please forgive us.
Do you want to get beat up or do you want to quietly figure it out here?
Ah please let this go and talk.
Why are you being like this?
Ha Ni!
Are you okay?
Boss.
What's going on here?
Seung Jo.
Do you have 1,000,000 won? You're from a rich family.
Sunbae!
Yes?
I will, you know...
Ah!
One, two, three.
-Hurry!
-Get them!
Get them!! <i>Brought to you by the PKer team @ www.viikii.net
Let's move, Ha Ni.
Bye, Baek Seung Jo.
I forgot Seung Jo.
Baek Seung Jo has nothing to do with me anymore.
What is it that you wanted to tell me?
I like you.
You?
Find all of the factors of 120.
Or another way to think about it, find all of the whole numbers that 120 is divisible by.
So the first one, that's maybe obvious. All whole numbers are divisible by 1.
So we could write 120 is equal to is to 1 times 120.
So let's write a factors list over here.
So we just found two factors.
We said, well, is it divisible by 1?
Well, every whole number is divisible by 1.
This is a whole number, so 1 is a factor at the low end.
1 is a factor.
That's its actual smallest factor, and its largest factor is 120.
You can't have something larger than 120 dividing evenly into 120.
121 will not go into 120.
So the largest factor on our factors list is going to be 120.
Now let's think about others.
Let's think about whether is 2 divisible into 120? So there's 120 equals 2 times something?
Well, when you look here, maybe you immediately recognize that 120 is an even number.
It's ones place is a 0.
As as long as its ones place is a 0, 2, 4, 6 or 8, as long as it's an even number, the whole number is even and the whole number is divisible by 2.
And to figure out what you have to multiply by 2 to get 120, well, you can think of 120 as 12 times 10, or another way to think about it, it's 2 times 6 times 10, or 2 times 60.
You could divide it out if you want.
You could say, OK, 2 goes into 120.
2 goes into 1 no times.
2 goes into 12 six times.
6 times 2 is 12.
Subtract.
You get 0.
Bring down the 0.
2 goes into 0 zero times.
0 times 2 is 0, and you get no remainder there, so it goes sixty times.
So we have two more factors right here.
So we have the factors.
So we've established the next lowest one is 2, and the next highest factor, if we're starting from the large end, is going to be 60.
Now let's think about three. Is 120 equal to 3 times something?
Well, we could just try to test and divide it from the get go, but hopefully, you already know the divisibility rule.
To figure out if something is divisible by 3, you add up its digits, and if the sum is divisible by 3, we're in business.
So if you take 120-- let me do it over here.
1 plus 2 plus 0, well, that's equal to 1 plus 2 is 3 plus 0 is 3, and 3 is definitely divisible by 3.
So 120 is going to be divisible by 3.
To figure what that number that you have to multiply by 3 is, you could do it in your head.
You could say, well, 3 goes into 12 four times, and then you-- well, let me just do it out, just in case, just for those of you who want to see it worked out.
3 goes into 12 four times.
4 times 3 is 12.
You subtract.
You're left with nothing here.
You bring down this 0.
3 goes into 0 zero times.
0 times 3 is 0.
Nothing left over.
So it goes into it forty times.
And the way to think of it in your head is this is the same thing as 12 times 10.
12 divided by 3 is 4, but this is going to be 4 times 10, because you have that 10 left over.
Whatever works for you.
Or you can just ignore the 0, divide by 3, you get a 4, and then put the 0 back there.
Whatever works.
So we have two more factors.
At the low end, we have 3, and at the high end, we have a 40.
Now, let's see if 4 divisible into 120.
Now we saw the divisibility rule for 4 is you ignore everything beyond the tens places and you just look at the last two digits.
So if we're going to to think about whether 4 is divisible, you just look at the last two digits.
The last two digits are 20.
20 is definitely divisible by 4, so 120 will be divisible by 4.
4 is going to be a factor.
And to figure out what we have to multiply 4 by to get 120, you could do it in your head.
You could say 12 divided by 4 is 3, so 120 divided by 4 is 30.
So we have two more factors:
4 and 30.
And you could work this out in long division if you want to make sure that this works out, so let's keep going.
And then we have 120 is equal to-- is 5 a factor?
Is 5 times something equal to 120?
Well, you can't do that simple-- well, first of all, we could just test is it divisible?
And 120 ends with a 0.
If you end with a 0 or a 5, you are divisible by 5.
So 5 definitely goes into it.
Let's figure out how many times.
So 5 goes into 120.
It doesn't go into 1.
It goes into 12 two times.
2 times 5 is 10.
Subtract.
You get 2. Bring down the 0.
5 goes into 20 four times.
4 times 5 is 20, and then you subtract, and you have no left over, as we expect, because it should go in evenly.
This number ends with a 0 or a 5.
Let me delete all of this so we can have our scratch space to work with later on.
So 5 times 24 is also equal to 120, we have two more factors:
5 and 24.
Let me clear up some space here because I think we're going to be dealing with a lot of factors.
So let me move this right here.
Let me cut it and then let me paste it and move this over here so we have more space for our factors.
So we have 5 and 24.
Let's move on to 6.
So 120 is equal to 6 times what?
Now, to be divisible by 6, you have to be divisible by 2 and 3.
Now, we know that we're already divisible by 2 and 3, so we're definitely going to be divisible by 6, and you should hopefully be able to do this one in your head.
5 was a little bit harder to do in your head. but 120, you could say, well, 12 divided by 6 is 2, and then you have that 0 there, so 120 divided by 6 would be 20.
And you could work it out in long division if you like.
So 6 times 20 are two more factors.
Now let's think about 7.
Let's think about 7 here.
7 is a very bizarre number, and just to test it, you could think of other ways to do it.
Let's just try to divide 7 into 120.
7 doesn't go into 1.
It goes into 12 one time.
1 times 7 is 7.
You subtract.
12 minus 7 is 5.
Bring down the 0.
7 times 7 is 49, so it goes into it seven times. 7 times 7 is 49.
Subtract.
You have a remainder, so it does not divide evenly.
So 7 does not work.
Let's think about whether 8 works.
Let's think about 8.
I'll do the same process.
Let's take 8 into 120.
Let's just work it out.
And just as a little bit of a hint-- well, I'll just work it out.
8 goes into 12-- it doesn't go into 1, so it goes into 12 one time.
1 times 8 is 8.
Subtract there.
12 minus 8 is 4.
Bring down the 0.
8 goes into 40 five times.
5 times 8 is 40, and you're left with no remainder, so it goes evenly.
So 120-- let me get rid of that.
120 is equal to 8 times 15, so let's add that to our factor
list. We now have an 8 and now we have a 15.
Now, is it divisible by 9?
Is 120 divisible by 9?
To test that out, you just add up the digits.
1 plus 2 plus 0 is equal to 3.
Well, that'll satisfy our 3 divisibility rule, but 3 is not divisible by 9, so our number will not be divisible by 9.
So 9 will not work out.
9 does not work out.
So let's move on to 10.
Well, this is pretty straightforward.
It ends in 0, so we will be divisible by 10.
So let me write that down.
120 is equal to 10 times-- and this is pretty straightforward-- 10 times 12.
This is exactly what 120 is.
It's 10 times 12, so let's write those factors down.
10 and 12.
And then we have one number left.
We have 11.
We don't have to go above 11, because we already went through 12, and we know that there aren't any factors above that, because we were going in descending order, so we've really filled in all the gaps.
You could try 11.
We could try it by hand, if you like.
11 goes into 120-- now you know, if with you know your multiplication tables through 11, that this won't work, but I'll just show you.
11 goes into 12 one time.
1 times 11 is 11.
Subtract.
1, bring down the 0.
11 goes into 10 zero times.
0 times 11 is 0. you're left with a remainder of 10.
So 11 goes into 20 ten times with a remainder of 10.
It definitely does not go in evenly.
So we have all of our factors here:
1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60 and 120.
And we're done!
Express 0.0000000003457 in scientific notation
So let's just remind ourselves what it means to be in scientific notation
Scientific notation will be some number times some power of 10
Where this number right here is going to be
Let me write it this way
It's going to be greater than or equal to 1, and it's going to be less than 10
So over here, what we want to put here is that leading number is going to be
And in general you're going to look for the first non-zero digit
And this is the number that you're going to want to start off with
This is the only number you're going to want to put ahead of - or I guess to the left of - Of the decimal point
And it's going to be multiplied by 10 to something
Now let's think about what we're going to have to multiply it by
To go from 3.457 to this very, very small number
I mean we have had to move the decimal from 3.457 to get to this
You have to move the decimal to the left a bunch
You have to add a bunch of 0's to the left of the 3
You have to keep moving the decimal over to the left
To do that, we're essentially making the number much, much, much smaller
So we are not going to multiply it with a positive exponent of 10
We are going to multiply it times a negative exponent of 10 that the equivalent is you kind of dividing by a positive exponent of 10 the best way to think about it
When you move your exponent one to the left
You dividing by 10 which is equivalent to multiply by 10 to the negative 1 power
Let me give you an example here
So if I have 1 times 10 is clearly just equal to 10 1 times 10 to the negative 1
That's equal to 1 times 1/10 which is equal to 1/10 1 times---which is equal to 0--I skip the step right there
Let me add 1 times 10 to the 0
So we have something natural
So this is 1 times to the first 1 times to the 0 is equal to 1 times 1 which is equal to 1 1 times 10 to the negative 1 is equal to 1/10 which is equal to 0.1
If I do 1 times 10 to the negative 2 10 to the negative 2 is 1/10 squared or 1/100 so this is going to be 1/100 which is 0.01
What happened here?
When I read it to the negative power
I read it to the negative 1 power
I essentially move the decimal from the right of the one to the left of the one
I move from there to there
When I get to -2, I move the 2 over the left
So how many times we are going to move it over to the left to get this number right over here
So we essentially, so let's think about how many zeros we have
So we have to move it 1 times to get in front of the 3 and then we have to move it that means more times to get all of the zeros in there so we have to move it 1 time to get the 3
So we start here
We are going to move 1,2,3,4,5,6,7,8,9,10..10 times
So this is going to be 3.457 times 10 to the negative 10 power
Let me just rewrite it
So 3.457 times 10 to the negative 10 power
So in general, what you want to do is you want to find the first non zero number here
Remember, you want a number here that between 1 and 10 and it could be equal to 1 but it has to be less than 10 3.457 definitely fits that bill
It's between 1 and 10 And then you just want to count the leading zero between the decimal of that number and and include the number because that tells you how many times you have to shift the decimal over to actually get this number up here
So we have to shift this decimal 10 times to the left to get this thing up here
Determine whether 394 is greater than or less than 397.
Then write the expression that shows this using either this symbol or that symbol, and this is actually the less than symbol.
We'll think a little bit more about how to remember that.
That is the less than symbol and this is the greater than symbol.
So first of all, let's just look at the two numbers:
394 and 397.
So let me write them down.
394 and the other number is 397.
Now, they both have 3 hundreds, so their hundreds place is equivalent.
They both have 90 with that 9 there, but this is 300 plus 90 plus 4 and this is 300 plus 90 plus 7.
And we know that 4 is less than 7.
If you look on a number line, 4 comes before 7.
If you're counting the 7, you're going to pass up 4, so 394 is less than 397.
And the way that we write that, we would just write 394 is less than 397.
And the way I remember that this means less than is that the smaller number is on the side that has kind of a smaller side.
You can imagine this side is much smaller than this side over here.
We could also write it the other way.
We could write 397 is greater than 394.
And once again, the bigger number is the side that this little thing is opening onto or the side that has the bigger side of this symbol right here.
This point is the smaller side.
This out here is the bigger side.
That's where you put the larger number.
Greater than, less than.
The decorative use of wire in southern Africa dates back hundreds of years.
But modernization actually brought communication and a whole new material, in the form of telephone wire.
Rural to urban migration meant that newfound industrial materials started to replace hard-to-come-by natural grasses.
So, here you can see the change from use -- starting to use contemporary materials.
These pieces date back from the '40s to the late '50s.
In the '90s, my interest and passion for transitional art forms led me to a new form, which came from a squatter camp outside Durban.
And I got the opportunity to start working with this community at that point, and started developing, really, and mentoring them in terms of scale, in terms of the design. And the project soon grew from five to 50 weavers in about a year.
Soon we had outgrown the scrap yards, what they could provide, so we coerced a wire manufacturer to help us, and not only to supply the materials on bobbins, but to produce to our color specifications.
At the same time, I was thinking, well, there's lots of possibility here to produce contemporary products, away from the ethnic, a little bit more contemporary.
So I developed a whole range around -- mass-produced range -- that obviously fitted into a much higher-end decor market that could be exported and also service our local market.
We started experimenting, as you can see, in terms of shapes, forms.
The scale became very important, and it's become our pet project.
It's successful, it's been running for 12 years.
And we supply the Conran shops, and Donna Karan, and so it's kind of great.
This is our group, our main group of weavers.
They come on a weekly basis to Durban.
They all have bank accounts.
They've all moved back to the rural area where they came from.
It's a weekly turnaround of production.
This is the community that I originally showed you the slide of.
And that's also modernized today, and it's supporting work for 300 weavers.
And the rest says it all.
Thank you very much.
(Applause)
What I wanna do in this video is See if we can identify similar triangles here
And prove to ourselves that they really are similar
Using some of the postulates that we've set up
So over here I have triangle B, D, C it's inside of triangle A, E, C
They both share this angle right over there
So that gives us one angle
We need two to angle -angle which gives us similarity
And we know that these two lines are parallel
And we know if two lines are parallel we have transversal
That corresponding angles are gonna be congruent
So that angle is gonna correspond to that angle right over there
And we're done
We have one angle and triangle A, E, C that is congruent to another angle in B, D, C and then we have this angle that is obviously congruent to itself, That's in both triangles
So both triangles have a pair of corresponding angles that are congruent, So they must be similar So we can write triangle A, C, E
A, C, E is gonna be similar triangle
We wanna get the letters in the right order
So where the blue angle is here, the blue angle there is vertex B
We're gonna go to the white angles C and then we go to the unlabeled angle right over there B, C, D
B, C, D
So we did that first one
Now let's do this one right over here
This is kinda similar but at least it looks just superficial looking at it
YZ is definitely not parallel to ST
So we won't be able to do this corresponding angle argument
Alright, especially cuz I didn't even labelled this parallel And so you wanna, you don't wanna look at things just by the way they look
You definitely want to say what am I given and what am I not given
These weren't labelled parallel, we wouldn't be able to make this statement Even though if they look parallel
One thing we do have is that we have this angle right here,
This common to the inner triangle and to the outer triangle
And then given us a bunch of sides
So maybe we could use SAS for similarity
Meaning if we can show the ratio of the sides on either sides of this angle, And they have the same ratio from the smaller triangle to the larger triangle
Then we can show similarity
So let's go, we have to go on either side of this angle right over here
Let's look at shorter side on on either side of this angle
So the shorter is 2, and let's look at the shorter side on other side of the angle for the larger triangle
Well then the shorter side is on the right hand side
And that's gonna have, that's gonna be xt
So we wanna compare is the ratio between, right this way,
We wanna see is xy/ xt, over xt is that equal to the ratio of the longer side Or if we're looking relative to this angle, the longer of the two
I'm sorry the longest of the triangle, though it looks like that as well
Is that equal to the ratio of xz, xz over the longer of the two sides,
When you're looking at this angle right here on either side of that angle for the larger triangle over xs, over xs
And it's a little confusing cuz we've kinda flip with side
But I'm just thinking about the shorter side on either side of this angle and between, and then the longer side of either side of this angle
So these are the shorter side for the smaller triangle and the larger triangle
These are the longer sides for the smaller triangle and the larger triangle
And we see xy this is 2
Xt is 3 +1 is 4, xz is 3, xz is 3 and xs is 6
So you have 2/4 which is ? which is the same thing as 3/6
So the ration between the shorter sides on either side of the angle
And the longer side on either sides of the angle for both triangles
The ratio is the same, so by SAS we know, so by SAS we know that the 2 triangles are congruent
But we have to be careful on how we state the triangles
We wanna make sure we get the corresponding sides
So we could say that triangle, and I'm running out of space here
Let me write it write above here
We can write the triangle xyz, xyz is similar, is similar to triangle
So we started up at x which is the vertex of the angle
And we went to the shorter side first
So now we want to start at x and go to shorter side of large triangle
So x, so you go to xts, xts Xyz is similar to xts
Now let's look at this over here, so in our larger triangle we have a right angle here
But we really know nothing, we really know nothing about What's going on with any of these smaller triangles in terms of their actual angles
You know this looks like a right angle
We cannot assume it
And it shares, if we look at this smaller triangle right over here
It shares one side with the larger triangle,
Well that's not enough to do anything
And then this triangle over here also shares another side,
But that also doesn't do anything
So we really can't make any statement here
About any kind of similarities
So there's no similarity going on here
If they, if they gave us, if they gave us,
And well there are some, there are some shared angles
This guy they both share that angle the larger triangles, small triangle
So there could be a statement of similarity we can make
If we knew that this definitely was a right angle
Then we can make some interesting statement about similarity
But right now we can't really do, we can't do anything as is
Let's try this one out or this pair right over here
So this the first ones that we've actually separated out the triangles
So they've given us the 3 sides of both triangles,
So let's just figure out the ratios between corresponding sides are a constant
So let's start with the short side
So the short side here is 3, shorter side is here is 9,
So we have, wanna see whether this the ratio of 3 to 9 is equal to The next longest side over here is 3, is equal to 3 over the next longest side over here which is 27, which is 27
And then if that's gonna be equal to, if that's gonna be equal to the ratio of the longest side So the longest side here is 6, 6 and then the longest side over here is 18, 18
So this is going to give us, let's see this is 3 This is 8, let me do this in a neutral color
So 3, we could this becomes 1/3
This becomes which seems like a different number
But we wanna be careful here
And this right over here this becomes, this is a if you divide the numerator and denominator by 6 this becomes a 1 and this becomes 3
So you get 1 , 1/3 is to be equal to 1, needs to be equal of /9 which needs to be equal to 1/3
At first they don't look equal
But we can actually rationalize this denominator right over here
We show that 1/ 3 if you multiply it by a /,
This actually gives you a numerator of / 9 is 3 times 3 is 9
So these actually are all the same
This is actually saying this is 1/ 3 root 3 which is the same thing as Which is this right over here which is the same thing as 1 /
So actually these are similar triangles
So we actually say it and I'll make sure I get the order right
So let's start with E which is between the blue and the magenta side
So that's between the blue and the magenta side that is H, right over here
So triangle E, I'll do it like this, triangle E and then I'll go along the blue side F
Then I go over along, along the blue side over here side
Let me do it this way
Actually let me just write it this way
E triangle E, F, G we know is similar to triangle
So E is between the blue and magenta side, blue and magenta side that is H
And then we go along the blue side to F Go along the blue side to I
And then we're go along the orange side to G
Then you go along the orange to J
So triangle E,F,J is, E,F,G is similar to triangle H,I,J by side, side, side similarity
They're not congruent sides
They all have just the same ratio or the same scaling factor
Now let's do this last one right over here
So we have, let's see, we have an angle that's congruent to another angle right over here
And we have 2 sides, and so it might be attempting to use side angle side
Because we have side angle side here
And even the ratio's looks kind of tempting
Because 4 times 2 is 8, 5 times 2 is 10,
But it's tricky here because they aren't the same corresponding sides
In order to use side angle side, the 2 sides that have the same corresponding ratios
That could be on either side of the angle
So in this case they are aren't on either of the angle
In this case the 4's on one side of the angle but the 5 is not, the 5 is not
So because if this 5 was over here, if it was over here then we could make it an argument for similarity
But this 5 not being on the other side of the angle is not sandwiching the angle with the 4
We can't use side angle side and frankly there's nothing that we can do over here
So we can't make some strong statement about similarity for this last one
I think we're all reasonably familiar with the three states of matter in our everyday world. At very high temperatures you get a fourth. But the three ones that we normally deal with are, things could be a solid, a liquid, or it could be a gas.
So let's think a little bit about what, at least in the case of water, and the analogy will extend to other types of molecules. But what is it about water that makes it solid, and when it's colder, what allows it to be liquid. And I'll be frank, liquids are kind of fascinating because you can never nail them down, I guess is the best way to view them.
Or a gas. So let's just draw a water molecule.
So you have oxygen there. You have some bonds to hydrogen. And then you have two extra pairs of valence electrons in the oxygen.
Now, if these molecules have very little kinetic energy, they're not moving around a whole lot, then the positive sides of the hydrogens are very attracted to the negative sides of oxygen in other molecules. Let me draw some more molecules. When we talk about the whole state of the whole matter, we actually think about how the molecules are interacting with each other.
If I was a cartoonist, they way you'd draw a vibration is to put quotation marks there. That's not very scientific. But they would vibrate around, they would buzz around a
So now all of a sudden, the molecule will start shifting. But they're still attracted. Maybe this side is moving here, that's moving there.
I think that makes intuitive sense if you just think about what a gas is. For example, it's hard to see a gas. Why is it hard to see a gas?
So they're not acting on the light in the way that a liquid or a solid would. And if we keep making that extended further, a solid-- well, I probably shouldn't use the example with ice. Because ice or water is one of the few situations where the solid is less dense than the liquid.
That's another reason why you can see through it a little bit better. Or it's not diffracting-- well I won't go into that too much, than maybe even a solid. But the gas is the most obvious.
The liquid form is definitely more dense than the gas form. In the gas form, the molecules are going to jump around, not touch each other. And because of that, more light can get through the substance.
It sounds like empathy, but it's quite a different concept. At least, as far as my neural connections could make it. But enthalpy is closely related to heat.
For our purposes, when you hear someone say change in enthalpy, you should really just be thinking of change in heat. I think this word was really just introduced to confuse chemistry students and introduce a non-intuitive word into their vocabulary. The best way to think about it is heat content.
Now let's say at low temperatures I'm here and as I add heat my temperature will go up. Temperature is average kinetic energy. Let's say I'm in the solid state here.
No I already was using purple. I'll use magenta. So as I add heat, my temperature will go up.
All solids aren't ice.
Although, you could think of a rock as solid magma. Because that's what it is.
I could take that analogy a bunch of different ways.
But the interesting thing that happens at zero degrees.
Depending on what direction you're going, either the freezing point of water or the melting point of ice, something interesting happens. As I add more heat, the temperature does not to go up. As I add more heat, the temperature does not go up for a little period.
For a little period, the temperature stays constant. And then while the temperature is constant, it stays a solid. We're still a solid.
Let's say right there. So we added a certain amount of heat and it just stayed a solid. But it got us to the point that the ice turned into a liquid.
Now, we get to, what temperature becomes interesting again for water? Well, obviously 100 degrees Celsius or 373 degrees Kelvin. I'll do it in Celsius because that's what we're familiar with.
And actually, it's a good amount at this point. Where the water is turning into vapor, but it's not getting any hotter.
So we have to keep adding heat, but notice that the temperature didn't go up. We'll talk about it in a second what was happening then. And then finally, after that point, we're completely vaporized, or we're completely steam.
When you put me in a plane you have put me in a higher energy state. I have a lot more potential energy. I have the potential to fall towards the earth.
Because it's the same amount of heat regardless how much direction we go in. When we go from solid to liquid, you view it as the heat of melting. It's the head that you need to put in to melt the ice into liquid.
To pull the molecules apart, to give them more potential energy. If you pull me apart from the earth, you're giving me potential energy. Because gravity wants to pull me back to the earth.
And then, once you are fully a liquid, then you just become a warmer and warmer liquid. Now the heat is, once again, being used for kinetic energy. You're making the water molecules move past each other faster, and faster, and faster.
And the same idea is happening. Before we were sliding next to each other, now we're pulling apart altogether. So they could definitely fall closer together.
Now, if President Obama invited me to be the next Czar of Mathematics, then I would have a suggestion for him that I think would vastly improve the mathematics education in this country.
And it would be easy to implement and inexpensive.
The mathematics curriculum that we have is based on a foundation of arithmetic and algebra.
And everything we learn after that is building up towards one subject.
And at top of that pyramid, it's calculus.
And I'm here to say that I think that that is the wrong summit of the pyramid ... that the correct summit -- that all of our students, every high school graduate should know -- should be statistics: probability and statistics.
(Applause)
I mean, don't get me wrong.
Calculus is an important subject.
It's one of the great products of the human mind.
The laws of nature are written in the language of calculus.
And every student who studies math, science, engineering, economics, they should definitely learn calculus by the end of their freshman year of college.
But I'm here to say, as a professor of mathematics, that very few people actually use calculus in a conscious, meaningful way, in their day-to-day lives.
On the other hand, statistics -- that's a subject that you could, and should, use on daily basis. Right?
It's risk.
It's reward.
It's randomness.
It's understanding data.
I think if our students, if our high school students -- if all of the American citizens -- knew about probability and statistics, we wouldn't be in the economic mess that we're in today. (Laughter) (Applause)
Not only -- thank you -- not only that ... but if it's taught properly, it can be a lot of fun.
I mean, probability and statistics, it's the mathematics of games and gambling.
It's analyzing trends.
It's predicting the future.
Look, the world has changed from analog to digital.
And it's time for our mathematics curriculum to change from analog to digital, from the more classical, continuous mathematics, to the more modern, discrete mathematics -- the mathematics of uncertainty, of randomness, of data -- that being probability and statistics.
In summary, instead of our students learning about the techniques of calculus, I think it would be far more significant if all of them knew what two standard deviations from the mean means.
And I mean it.
Thank you very much.
(Applause)
We're asked to shade 20% of the square below.
Before doing that, let's just even think about what percent means.
Let me just rewrite it.
20% is equal to-- I'm just writing it out as a word-- 20 percent, which literally means 20 per cent.
And if you're familiar with the word century, you might already know that cent comes from the Latin for the word hundred.
This literally means you can take cent, and that literally means 100.
So this is the same thing as 20 per 100.
20% means you're really going to meet
That means if you want to shade 20%, if you break up the square into 100 pieces, we want to shade 20 of them.
20 per 100.
So how many squares have they drawn here?
So if we go horizontally right here, we have 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 squares.
If we go vertically, we have 1, 2, 3, 4, 5, 6, 7, 8, 9, 10.
So this is a 10 by 10 square.
So it has 100 squares here.
Another way to say it is that this larger square-- I guess that's the square that they're talking about. This larger square is a broken up into 100 smaller squares, so it's already broken up into the 100.
So if we want to shade 20% of that, we need to shade 20 of every 100 squares that it is broken into.
So with this, we'll just literally shade in 20 squares.
So let me just do one.
So if I just do one square, just like that, I have just shaded 1 per 100 of the squares.
100 out of 100 would be the whole.
I've shaded one of them.
That one square by itself would be 1% of the entire square.
If I were to shade another one, if I were to shade that and that, then those two combined, that's 2% of the entire square.
It's literally 2 per 100, where 100 would be the entire square.
If we wanted to do 20, we do one, two, three, four-- if we shade this entire row, that will be 10%, right?
One, two, three, four, five, six, seven, eight, nine, ten.
And we want to do 20, so that'll be one more row.
So I can shade in this whole other row right here.
And then I would have shaded in 20 of the 100 squares.
Or another way of thinking about it, if you take this larger square, divide it into 100 equal pieces, I've shaded in 20 per 100, or 20%, of the entire larger square.
Hopefully, that makes sense.
When we compare triangle ABC to triangle XYZ, it's pretty clear they aren't congruent, that they have a very different lengths of their sides
But, there does to be seem something interesting about the relationship between this two triangles
One, all of their corresponding angles are the same
So, the angle right here, angle BAC is congruent to XYZ
Angle BCA is congruent to YZX,
And angle ABC is congruent to XYZ
So all of their angles, the corresponding angles are the same And we also see, we also see that the sides are just scaled up versions of each other
So the goal from the length of XZ to AC, we can, we can multiply by 3, we multiplied by 3 there, to go from, to go from XY, the length of XY to the length of AB which is of course the corresponding side
We are multiplying by 3, we have to multiply by 3 And then, to go from the length of YZ to the length of BC, we also, we also, multiplied We also multiplied by 3
So essentially, triangle ABC is just a scaled up version of triangle XYZ If they were the same scale, they would be the exact same triangles but, one is just a bigger, a blown up version of the other one or, this is miniaturize version of that one over there
If you just multiply all of the sides by 3, you get to this triangle
And so, we can't call them congruent but they're, there does seem to be a bit of a special relationship
So we call this special relationship "similarity"
So we can write that triangle, triangle ABC is similar, similar to triangle, and we wanna make sure we get the corresponding sides right,
ABC is gonna be similar to XYZ To XYZ
And so, based on what we just saw, there's actually kind of 3 ideas here, and they're all equivalent ways of thinking about similarities
One way to think about it is that, one is a scaled up version of the other
So scaled, scaled up or down of the other Down versions
When we talk about congruency, they have to be exactly the same
You could rotate, you could shift it, you could flip it, but when you do all those things, they would have to be essentially identical With similarity, you can rotate it, you can shift it, you can flip it, and you can also scale it up and down in order for something to be similar
So for example, if you say, if something is congruent, if, if, let me say triangle, let's say triangle CDE, if we know that triangle CDE is congruent to triangle FGH, then we definitely know that they're similar
They're scaled up by factor of one
Then, we know for a fact that CDE Is also similar to triangle FGH, but we can't say the other way around
If, if trianlge ABC is similar to XYZ, we can't say that it's necessarily congruent, and we see for this particular example, they definitely are not congruent
So this is one way to think about similarity
The other way to think about similarity is that, all the corresponding angles will be equal
So, if something is similar, then all of the corresponding angles are going to be congruent Corresponding, corresponding angle Always having trouble spelling this
It is two R's, one S Corresponding, corresponding angles, corresponding angles are congruent Are congruent
So, if we say that triangle ABC is, triangle ABC is similar to triangle XYZ, that is equivalent to saying that angle, angle ABC, angle ABC is congruent, or we can say their measures are equal to angle XYZ, to angle XYZ, that angle, that angle BAC,
BAC is going to be congruent to angle YXZ, to angle YXZ And then finally, angle ACB, ACB is going to be congruent to angle, to angle XZY
XZY Angle XZY
So if you have two triangles, all of their angles are the same, then you could say that they are similar Or if you find two triangles, and you are told they are similar triangles then you know that all of their corresponding angles are the same
And the last, I guess the way to think about it is that, all the sides are just scaled up versions of each other
So the sides, so sides, scaled by the same factor, scaled by same, same factor
And the example we did here, the scaling factor was 3, it doesn't have to be 3 It just to be the same scaling factor for every side
If this side, if we scaled this side up by 3, and we only scaled this side up by 2 then, we would not be dealing with a similar triangle
But, if we scaled all of these sides up by 7, then that's still similar
As long as you have all of them scaled up by, or scaled down by the exact same factor So one way to think about it is, and I wanna, wanna keep having, well, I wanna still visualize those triangles
Let me, let me re-draw em' right over here, a little bit simpler
So I'm now talkig in, now in general terms, not even for that specific case
So, if we say that this is A B and C, and this right over here is, X, XYZ
I just re-drew em' so I can refer to them when we write down here
If we're saying that this two things right over here are similar, that means that corresponding sides are scaled up versions of each other
So we could say that the length of AB, we could say that the length of AB,
AB, is equal to some scaling factor, and this thing could be less than one, some scaling factor times the length of XY, the corresponding sides
And I know that AB corresponds to XY because of the order in which I wrote this similarity statement
So some scaling factor times XY, we know that BC, the length of BC we know that the length of BC needs to be that same scaling factor
The same scaling factor times the length of YZ, times the length of YZ, so that same scaling factor
And then, we know the length of AC, the length of AC, is going to be equal to that same scaling factor times XZ
So that's XZ and this could be a scaling factor
So if AB is larger than, if ABC is larger than XYZ, than this K's will be larger than one, if they're the exact same size, if they are essentially congruent triangles, than this K's will be one
And if XYZ is bigger than ABC, than this scaling factors will be less than one
But another way to write the same, all I'm saying is corresponding sides are scaled up versions of each other
This first statement right here if you divide both sides by XY, you get AB over XY, is equal to, our scaling factor
And then the second statement right over here, if you divide both sides by YZ, you get B, let me do that same colour
You get BC divided by YZ is equal to that scaling factor, is equal to that scaling factor
Whatever, the example we just showed that scaling factor was, scaling factor was 3 but, now we're saying in a more general term, similarities, as long as you have same scaling factor And then finally, if you divide both sides here by the length between X,XZ , or segment XZ's length, you get AC over XZ is equal to K as well Is equal to K as well
Or another way to think about it is, the ratio between corresponding sides, notice this is the ratio between AB and XY
AB and XY The ratio between BC and YZ, BC and YZ The ratio between AC and XZ, AC and XZ
That the ratio between corresponding sides all gives us the same constant
Or you can rewrite this as, AB over XY is equal to BC over YZ, is equal to, is equal to AC over XZ, which would be equal to some scaling factor, which is equal to K
So if you have similar triangles, let me draw an arrow right over here, similar triangles means that they're scaled up versions and, you can also flip and rotate, do all the stuff with congruency, and you can scale them up or down, which means, all of the corresponding angles are congruent, which also means that the ratio between corresponding sides is going to be the same concept for all the corresponding sides, or the ratio between the corresponding sides is constant
Let's say we had to figure out how many times 16 goes into 1,388. And what I want to do is first think about how we traditionally solve a problem like this, and then introduce another method that allows for a little bit more approximation. So traditionally you would say, well sixteen does not go into one any times, so then you move over one spot, and then how many times does it go into 13?
Well, 16 times 5, I know, is 80, so 16 times 50, I have multiplied by 10, is 800. And then I just subtract.
8-0 is 8, and then you can say 13-5 is 588. Now we ask ourselves, how many times does 16 go into 588? How close can we get to that.
8-0 is 8, 8-2 is 6 and then 5-3 is 2. Now I'm left with 268 and we say, how many times does 16 go into 268. Let's see, 800 is too big, even 320 is now too big.
We are left with how many times does 16 go into 108. And we can go back to..., we know 16 times 5 is 80. So let's just try out 5.
8-0 is 8, 10-8 is 2, so we are left with 28. Now it is pretty simple. How many times does 16 go into 28?
Hopefully you found that kind of interesting.
We're asked to solve the equation 2x squared plus 3 = 75.
So in this situation looks like we might be able to isolate the x squared pretty simply. 'Cause there's only one term that involves an x here. It's the only x squared term.
So let me just rewrite it.
So 2x squared + 3 = 75.
I'm going to try to isolate this x squared over here.
The best way to do that or at least the first step, would be the subtract 3 from both sides of this equation.
So lets subtract 3 from both sides.
The left hand side we're just left with 2x squared.
That was the whole point of subtracting 3 from both sides.
And on the right hand side 75 minus 3 is 72.
Now I wanna isolate this x squared, I have a 2x squared here.
So I could have just have an x squared here if I divide this side or really both sides by 2. Anything that I do on 1 side,
I have to do the other side. If I want them to mantain the quality.
So the left side just becomes x squared.
And the right hand side, the 72 divided by 2 is 36.
So we're up with x squared is equal to 36.
And then to solve for x we can take the positive plus or minus squared root of both sides.
So we can say the plus or
let me right it this way.
If we take the squared root of both sides, we would get x is equal to the plus or minus square root of 36. Which is equal to plus or minus 6. let me just write it on another line.
So x is equal to plus or minus 6.
And remember here!
If something squared is equal to 36, that something could be the negative version, or the positive version.
It could be the principle root, or it could be the negative root.
Both negative 6 squared is 36 and positive 6 squared is 36.
So both of these work.
And you can put them back into the original equation, to varify it.
Let's do that.
If you say 2 times 6 squared plus 3, that's 2 times 36 which is 72 plus 3 is 75.
So that works.
If you put negative 6 in there, you're going to get the exact same result.
Cause negative 6 squared is also 36, 2 times 36 is 72, plus 3 is 75.
The Khan Academy is most known for its collection of videos, so before I go any further, let me show you a little bit of a montage. (Video) Salman Khan:
Welcome to the presentation on multiplying decimals. Let's get started. So I think you'll find out that multiplying decimals is not a lot more difficult than just multiplying regular numbers.
Clearly you can tell I'm doing this on the fly. Seventy-five point one eight times zero point nine seven. So first you look at this problem and you're like, oh boy that's tough.
These decimals-- I don't even know how to approach it. Well this is what you do. You ignore the decimals when you start the problem and you pretend like it's just a regular multiplication problem.
Two down here. Carry the one. Seven times five is thirty-five.
Put the six here. Carry the three. And then seven times seven is forty-nine.
So just like normal multiplication we just took the ones place right here, the seven.
So it's actually not the ones, but we're ignoring the decimals so if there were no decimals this would be the ones place.
And we're multiplying it by the top number. Seven times seven thousand five hundred eighteen is equal to fifty-two thousand six hundred twenty-six. And just like regular multiplication, we do the tens place.
And this isn't really the tens place, but if you ignore the decimals it would be.
And let's cross all this stuff out since we're not using it. Nine times eight is seventy-two. Carry the seven.
This is good practice for me, too.
I haven't done my multiplication tables in a long time. Nine times five is forty-five. Plus one is forty-six.
And your I think you're going to be shocked by how straightforward this is. What I do is I go back to the original problem and now I actually pay attention to the decimals. And I say, how many total numbers are behind the decimal point?
Well, it only would have been if you actually used the zero in the multiplication.
Maybe that confuses you.
What I would recommend, if you have any trailing zeros with a decimal like this, you should actually just ignore those zeros, and then do the problem just the way I did it. And remember, that's only for trailing zeros. If this was the bottom number then that zero would matter because it's not a trailing zero, its actually part of the number.
So let's say I had five-- and I'm going to do a simpler example arithmetically.
I think it'll help you with some principles. If I said five point one zero times one point zero nine.
So there's two things we could do. We could just multiply it the way it is. Actually let's do it both ways.
So in the first case let's not ignore the zero. Let's use that zero, even though that trailing zero in the decimal-- five point one zero is the same thing as five point one.
But let's use it. Nine times zero is zero. Nine times one is nine.
So the decimal will go here.
So we got five point five five nine zero as the answer. Now what if we did like I was recommending, we actually ignored the zero? So I say, And I can actually rewrite it as one point zero nine times five point one.
Two times three is the same thing as three times two. So one point zero nine times five point one is the same thing as five point one times one point zero nine. So let's just multiply this out.
Put a zero here. Five times nine is forty-five. Carry the four.
Now I'm at the point that I can actually pay attention to the decimal points. How many numbers are behind the decimals?
Well, there's one, two, three. So I go one, two, three, and put the decimal point right here. Notice I got the same exact answer.
If you were a computer programmer or a statistician of some kind, this could be an important number.
But ignore what I just said. But for your purposes, these trailing zeros mean nothing. Same way a leading zero actually would mean nothing.
Let me do-- well, let me see how much time I have. I have two more minutes. Let me do one more problem just to maybe hit the point home.
And at the end you just have to count the numbers behind the decimal point. So five times five is twenty-five.
Whoops. Twenty-five.
I'm already getting messy. Carry the two. Fve times seven is thirty-five.
I'm sorry for being so messy. And then you put a zero. One times five is five.
Ignore that. Now we add. We say five plus zero is five.
See what I just did? We had to have five numbers behind the decimal point. And we only had four numbers in the answer.
Hopefully in the future I can give you a seminar on actually why this method of counting the numbers behind the decimal points actually works.
But I think you are ready to try some problems on multiplying decimals. Have fun!
Produced by Lee Choon-yeon Executive producer Park Mu-seung Associate producer Lee Mi-young
Producer Im Hye-won
Original screenplay Byun Won-mi & Song Min-ho
Screenplay revised by Gwak Jae-yong
Director of photography Kim Byung-il
Lighting director Lee Kang-san
Location sound Ahn Sang-ho
Set design Art Service Production designer Lee Jung-woo
Edited by Gyung Min-ho
Music by Jung Jae-hyung
Starring Lee Byung-hun
Lee Mee-yeon
Lee Eul
Park Sun-young
Directed by Park Young-hoon
You scared me.
I can't concentrate because of you.
It's not the first time you've heard this.
My eardrums are gonna pop!
Doesn't this sound great?
After your military service, I thought you'd grow up.
Anyway, you can't car race.
It's too dangerous.
Hey, Dae-jin.
Look for other work while helping me out like old times.
Your work is just as dangerous.
You always cut your hand.
Over 10,000 people die a year from car accidents.
But I haven't seen anyone die from a car race yet.
Ho-jin.
Step aside.
You worry too much.
I can't die that easily.
Be careful.
Mr. Choi, check the singers' MR tape.
Okay.
Mr. Jun, check the moving lights.
Take a look.
OK!
Mr. Choi, check the monitor speaker.
- Please hurry.
Over here.
- Yes.
Go inside the dome instead of Hyun-woo.
Yes.
It has to be checked properly.
It has to open during the concert.
Why not?
It'll be fun.
Sure.
Getting trapped instead would be fun, huh?
- It won't open!
- Open it up!
I didn't do it.
Don't turn on the master so fast.
Thanks.
Hello?
Yes.
Really?
From the 16th to the 18th?
Yes.
But the exhibition will last for only three days.
Yes.
I'd like it to be for a week though.
Yes.
Then please ask around again.
Thank you.
Bye.
How'd you time it perfectly?
It's pouring.
- Hungry, huh?
- Yes.
This song.
Don't you remember it?
It's my favorite song.
It's nice hearing it in the rain.
Here.
It's a present.
What's with you today?
Thank you.
That's all?
I love you.
What's this?
What's gotten into you today?
You made all this?
Of course.
But it's not my birthday, and yours is much later than mine.
Hey, Eun-soo.
It's our anniversary, dummy.
My goodness, you're right.
I totally forgot.
I'm sorry, Ho-jin.
There's one more thing.
It's the most valuable thing to you, but the chain was always a problem.
Eun-soo, I love you.
Honey.
It's like as if my dad sent you to me.
Why?
Whatever my dad makes, it becomes precious no matter how trifling it is.
Even this necklace, he made it out of peach flower seeds when I was a kid.
I know.
That's why you deserve this much.
There's only one like this in the world, huh?
But I'm sorry I didn't prepare anything.
Then how about I steam you up tonight?
Really?
Tonight?
Sure.
Bastard.
What perfect timing.
He's too big to live with us, huh?
Shall we get him married?
Shall we?
Yeah.
But right after I said it, it really didn't open.
No way.
I must have some telekinetic power.
Do it.
Do what?
Do it.
Okay, I'll give it a try.
Look straight into my eyes.
Yawn.
Should I do it on Dae-jin, too?
Hiccups.
Sorry, I guess I can't.
He did it.
I really had to.
- It switched.
- Stop joking around.
No, it was real.
Don't joke with...
Come on.
No, mine was real, too.
It was real?
Yeah.
I'll go drink some water.
Come here.
No, I have to go drink some water.
Stop joking around.
I'm serious.
Dae-jin, don't you want a girlfriend?
The best times are at your age.
I like it now.
Like what?
Fiddling with your car in the garage?
I'm curious as to what's in that mind of yours.
I'm going to bed so you two drink up.
- Good night.
- You, too.
I'll be in soon.
Dae-jin.
Make sure you block your ears tonight.
- Good night.
- You, too.
I've never seen you neat freak who can't close a lid right.
Thanks a lot for today.
It's nothing.
I'm so happy.
You still have the hiccups?
No, I'm okay.
You still have them.
There's no use tonight.
Let's just go to bed.
It stopped.
It stopped?
It did.
Really?
You're doing it again.
Just go to sleep.
Ho-jin.
Yeah.
You're supposed to put it all the way on.
That's because it's used up.
I'll buy it later.
I think a lot of reporters are coming to my exhibition.
Dae-jin.
Act like a reporter and ask me questions.
So I can practice.
Come on, that's dumb.
Just this once.
Mr. Hwang Ho-jin, please explain your work.
Yes.
From the furniture we commonly see, I felt like I twisted them a little.
Similar to Marcel Duchamp's toilet, I recreated what we commonly see.
Furniture...
Ho-jin.
You practiced a lot, huh?
Does it show?
Of course.
Be a little artsy and inarticulate.
As if it just came to you, and say 'and' a lot.
Also, smiling and lifting your eyes is better.
You're right.
Do it again.
Mr. Hwang Ho-jin, please describe your work.
Yes.
From the furniture... we commonly see...
How can I put it?
I twisted them a little.
That is...
Ho-jin.
Just do it like before.
Bastard.
You did well.
Oh, hi.
What are you doing?
They say pollacks can look far with their big eyes, and can eat a lot with their big mouths.
Then how could they get caught then?
You're right.
If I get hungry while driving, I'm gonna eat it.
Do as you please.
Whether you cook or fry it,
I'll put it here for your sake, so be careful.
Thanks, Ho-jin.
Ho-jin.
It's your favorite dish.
Hey.
Is Dae-jin still in the garage?
Wait.
Wait.
What are you doing?
I don't have the hiccups today.
So what?
What if Dae-jin comes?
He's leaving soon.
Wait.
Is it bothering you?
Do something with the table.
Okay, just a sec.
Aren't you going to fast?
I can handle it.
He's taking it too hard from the beginning.
I told him to pace himself and go slow.
Would a drug addict listen if you said to inject slowly?
What's he doing?
I don't know.
Might be engine trouble.
You exhausted the engine.
The race isn't far away, so don't blow the engine.
Don't use too much RPM.
I didn't overdo it.
It'll be fine.
Your record's improving, so I'll let it pass.
But racing isn't all about luck.
Take caution.
I got it.
Hey, the car's in great shape.
Damn it.
I should've been born a car.
Good job everyone.
A coin that brought you pleasure?
Eun-soo.
Huh?
You got another love letter today?
You're so lucky.
For what?
You've been married for three years, but you still exchange love letters?
You're so lucky, Eun-soo.
I wish I could meet a guy like that.
It won't be too easy.
Can't there be a guy like Ho-jin?
What?
Ho-jin.
But the letter's not finished.
That's okay.
- Sleep well?
- Oh, yes.
You must've came in late last night.
Yeah, I had a drink with Yae-joo.
I'm out of lotion, so I came for Ho-jin's.
- It's on the dresser.
- Okay.
That's our business, Dae-jin.
It was just here, but I wasn't looking at it.
If you're done, then please leave.
We live in the same house, but you two are unfair.
So hurry and get married.
Okay.
Ho-jin.
Look at this.
Hello.
Hello.
You're here early, Yae-joo.
Of course.
It's an important day for Dae-jin.
You're the only one who thinks of him.
Ho-jin, this came off.
I'll fix it later.
The more I see it, the prettier it is.
There's only one like this in the world.
I'm so jealous.
- Stay for a while.
- Okay.
You and Dae-jin seem to hit it off.
I wish.
It was better when he took pictures.
I feel like I'm left in the cold now.
He always worries me when he car races.
You should change his mind.
Think he will if I tell him?
Hey, am I invisible now?
- What's up?
- Hey.
Ho-jin, I'm leaving now.
- You're going now?
- Yeah.
Going to the race, right?
Of course.
Tell him good luck for me.
I will.
I'll see you later.
Be careful driving.
See you later.
- Have a nice day.
- Okay.
Oh no.
Drivers please come to the record room for tests.
Five minutes left until the race begins.
Did Ho-jin say he'll come?
Yeah, he did.
He doesn't like me racing, so he might not.
Then why are you if your brother opposes it?
Because I like it.
Drivers please report to the waiting area.
Hey, good luck!
Welcome.
To Yongin Speedway please.
I'm very late.
I have to be there by one.
Wow, you're really late.
I'll go fast.
It's the third Korea Motor Championship.
1st place in the GT Class, Indigo's Kim Yi-soo.
He took pole position in the last match.
3rd place was the wild horse, Bak Joon-woo of Oilbank.
Fourth was Hwang Dae-jin.
Feeling good, huh?
- And don't pass up the in course.
- Okay.
Remember, you're buying tonight.
I know.
Three minutes left until the race.
The gates are closing.
Please clear away from the grid.
The sign board is up.
Start your engines.
I screwed up on corner three.
What's my time?
Present lap time is 1:08:07.
You're doing alright.
Aren't you going too fast?
I thought you were late.
Right.
Don't worry.
I've been accident free for 10 years.
Even as a speed taxi.
It's the 7th head pin, so slow it down.
He wants to kill himself!
He's scaring me!
The steering wheel is strange.
I'm going in.
Hurry up!
What happened?
The steering wheel shakes too much.
Check the tires fast.
Check the tires!
Dae-jin, please be careful.
How much am I behind?
0.3 seconds behind in lap time.
Run the course instead of placing.
No, I have to place.
You still have more to go, so it's okay.
Be careful.
The traffic lights aren't cooperating today.
Dae-jin, there's trouble on the course.
Slow down!
Dae-jin!
What?
What did you say?
I can't hear you well.
His pulse rate and brain waves are improving, but he still can't wake up.
It's too bad.
Dr. Lee, what happened to this patient?
Didn't I tell you?
Both brothers got into a car accident.
His older brother got hit by a truck while in a taxi.
So he's pretty much dead.
I guess so.
But the younger one was in a car race accident.
What a strange world.
But is there any hope for this patient?
I don't know.
Are you okay?
Jung-woo, match the steps.
You're falling back.
You're supposed to turn there.
Young-eun!
Are you checking the distance?
They're off.
Mr. Kim, please check the lights.
There are shadows on the models' faces.
Hello?
Oh, hello.
What?
Please rest for now.
It's really fortunate that you at least have come back.
Are you okay?
Get up.
Go rest in your room.
Hey, Dae-jin!
Thanks for being alive.
You were lying there like a corpse, and I was helpless, thinking you'd leave forever.
I'm just really happy that you're alive.
You were a heavy smoker before.
While you were in bed, know how stupid I acted?
I went all the way to the junkyard.
I wanted to see your car get totally demolished.
When I went to see it, I laughed a lot.
You were in bed like that, and I was jealous of that car.
I was acting overboard.
But now
I'm just really thankful that you've come back.
Yae-joo.
Hi, Eun-soo.
Is Dae-jin really alright?
Dae-jin.
What are you doing?
Have a seat.
Did you buy that flower?
No. I thought you bought it.
Was Dae-jin always a good cook?
The way he cuts vegetables is amazing.
Sit.
Yae-joo, too.
Hurry and eat.
Dae-jin.
Right now, this is all that I can do for you.
Now eat.
Dae-jin.
Dae-jin...
Mr. Hwang Dae-jin.
- After you woke up...
- My name is Hwang Ho-jin.
Any other symptoms besides headaches?
Sometimes my ears ring.
I'm cold.
And I keep getting sleepy.
But doctor, I'm Hwang Ho-jin.
What happened to me?
From a psychologist's perspective, his depression and hysteria have sprung up in a peculiar way after his trauma.
On the surface, he believes he's Hwang Ho-jin.
But the problem is that his consciousness firmly believes that he's possessed.
Possessed?
If I explain it simply, the body is taken over by someone else's spirit.
The best way to know is to find proof of his believe from his unconscious.
Doctor.
How can this be possible?
Oh my goodness.
Oh my goodness.
Your hand.
Oh no.
Eun-soo, he cut his hand.
He kept saying he's Ho-jin.
Wait.
My hands aren't listening to me.
I don't know how this happened.
Dae-jin, hurry and go inside first.
Yeah, let's hurry, Dae-jin.
I'm not Dae-jin.
I don't know.
I don't know why I'm like this.
Hey.
Pull yourself together.
You're Hwang Dae-jin.
You're the Hwang Dae-jin.
I've always liked!
Eun-soo, I'm sorry.
I'm really sorry.
Yae-joo.
Dae-jin is still sick.
He's doing this because he's still mentally unstable.
When time passes, he'll be better.
That bastard.
He's trying to suck me dry forever.
I'll be back after I give this to him.
The gift your father gave you.
I've finally fixed it.
- Can you hear my voice?
- Yes.
Tell me your name.
Hwang Ho-jin.
Good.
You're falling into a calmer and deeper sleep.
Imagine a cloud.
A soft wind is blowing.
The cloud is moving slowly.
Very slowly.
Now look slowly below the cloud.
What do you see?
A road.
What's on top of this road?
A taxi.
Taxi.
Are you riding in this taxi?
I don't know.
You're moving forward.
Slowly.
What do you see in front of you?
What do you see?
Calm down.
Put your mind at ease.
Common symptoms for possessed patients are a drop in their temperature and feeling very cold.
They keep sleeping, and even their ears ring.
But doctor how could my husband's soul...
Even modern psychology can't prove whether possession exists or not.
By simply acknowledging it and nursing him is better.
Take your medicine.
How I'm acting now...
I'm not sick, Eun-soo.
I understand.
But you have to take this medicine.
Eun-soo.
Eun-soo, open the door.
Eun-soo, open the door.
I'm not going to do anything.
Eun-soo.
I'm sorry.
I didn't want to do this.
But being alone in that room is too hard for me.
Don't go.
I'm scared, Eun-soo.
If I sleep in that room alone, I feel like I'll never wake up.
I'm very frightened.
Being with Dae-jin is too hard on me.
I feel like I'm unconsciously looking for Ho-jin in him.
No. Honestly, I saw him.
I'm so confused.
I feel like I know what you're going through.
Eun-soo.
I finished my thesis, so I have a lot of time now.
If it's okay that I spend time with him, he'll get better.
When you were in the marines, you said it was hell, but you felt peaceful.
If we work our butt off at my family's ranch, that mildew in your head will wash away.
Yae-joo.
Where can I go?
I'm not going anywhere.
This is my place.
Eun-soo agreed with me.
Eun-soo did?
Yes, your sister-in-law.
If I just stay here like this, everything will turn back to normal.
Hey, how long will you keep this up?
Are you planning to drive us crazy?
Eun-soo is having it hard enough taking care of Ho-jin.
Seeing him in a coma for over a year is hell enough.
What did you just say?
Look.
Look very carefully.
That's Hwang Dae-jin's face.
Know do you get it?
Do you?
If it's that hard on you, I'll become Dae-jin.
I'll live like Dae-jin.
Scared, huh?
Cutting grass, chasing and milking cows.
You'll probably pass out.
But don't worry.
I'll help you.
Ho-jin.
It's Eun-soo.
I see that my Ho-jin is still sleeping.
I thought you hated being lazy.
So how could you sleep this long?
I've changed a lot lately.
I get angry with people a lot, and I don't laugh easily.
If you saw me, you'd be surprised.
I can't remember your voice.
The harder I try, the more I can't remember.
I wish you'd call me just once.
Eun-soo.
Hey, Eun-soo.
Without you, I can't do anything.
Go!
Hey.
You're working up a real sweat.
Trying hard to make my family rich?
Dae-jin.
Leave me alone if you want to make me into Dae-jin.
Since you're not complaining and whining, you're no fun at all.
Fine.
I guess I'll just be a one-woman band forever.
I'll play drums with you sometimes.
Bang, bang.
Hey.
Like you, if I could become someone else, then I wish I had never met you.
Then I could've made about 100 guys like me.
Hey.
Look.
When you do this, you're totally Dae-jin.
Now you laugh for me?
I tried so hard to see it just once.
Hey.
I don't care who you are.
You're simply someone who I love.
Also, I'm going to hold on to that love.
Until I die.
I'm sorry.
I had no choice but to come back.
For Eskimos, when someone they love dies, they gather and talk about that person for five days.
While they talk, they erase their memories of that person.
Afterwards, they never talk about that person again.
If they do, then that person's soul can't rest in peace.
Let's talk about Ho-jin.
About everything you and I know.
Eun-soo.
And then never talk about him again.
After you left to serve,
I begged Ho-jin to go over his place.
Stop it, Eun-soo.
It was about the end of June.
It rained the whole day.
When I got there, his place was flooded in.
While we poured water out all day, Ho-jin said,
Feels like the world has flooded, and we're the only two left.
To raise money for your tuition, did you know that he worked in a factory for two months?
I was worried so I went to him, and saw him limping while carrying bricks.
I wanted to take him out of there, but I couldn't.
I thought he'd be more upset if he knew I came, so I couldn't.
No one knows.
No one can know.
How we met.
How we loved.
No one knows.
It was exactly on June 28th.
And it started raining from the afternoon.
While pouring out the water, you said, I wish the world swept away, and we were the only two left.
I couldn't bare watching you, and told you to stop, but you silently scooped the water.
A man can never leave a woman, who overcame an obstacle with him.
I worked at the factory for one and a half months.
It was a Saturday.
You suddenly...
You came right before lunch.
After getting yelled at, I turned around, and saw a girl with a yellow shirt walking away.
I also saw you that day.
I wanted to call you, I wanted to grab you,
But I couldn't.
Seeing me like that, I thought make you upset.
I knew how you'd feel, so I couldn't call you.
Stop it.
Eun-soo.
Whenever you laughed or became upset, I was always with you.
So that's why we're the same inside. You know better.
Stop it.
Stop.
Look.
Look at me, Eun-soo.
It's me.
Can't you see?
I should've died then, but I couldn't.
I should've died, and be gone forever, but I couldn't.
Because of you.
No one can love you as much as me.
That's why I returned.
Remember this, right?
How could you not?
All the memories that are hidden in our home are proof that we've loved each other until now.
Ho-jin.
Ho-jin.
Eun-soo.
You're all that I have.
Let's buy bananas.
I don't want to.
Why?
I don't like bananas.
But it's for our baby.
You're out of lotion, right?
Should we buy it?
I brought your lunch.
Is it going well?
Yep.
I'm going to have an exhibition.
I feel a lot better now.
That's great.
Don't overwork yourself.
Okay.
What's wrong?
Because you're pretty.
Why do you keep laughing?
Because you're pretty.
It's good to see you a lot happier now.
Does it show?
Yae-joo.
I'm okay.
Anyway, it feels strange.
I tried so hard to bring Dae-jin back, but suddenly, I thought what difference would it make.
Since Dae-jin thought of me only as a friend.
I'm sorry, Yae-joo.
I didn't want to...
But Yae-joo, he's really Ho-jin.
I always felt my father was with me after he died.
Even though I can't see him, it feels the same with Ho-jin.
He's really Ho-jin.
I know.
That Dae-jin isn't someone I can love.
He's someone else now.
And it's not like we can share the same person.
It's a complicated fate.
But I'm glad to see Dae-jin happy before I leave.
You two have to live happily.
Mine and Dae-jin's worth.
I'll go say bye to Dae-jin...
I mean Ho-jin before I leave.
Had it hard because of me, huh?
Because of who?
Dae-jin or Ho-jin?
So you're studying abroad?
Yeah.
When will you come back?
If I do?
Will you become Dae-jin then?
Can I think of you as Dae-jin and say something?
You're a rotten bastard.
Have a good life.
Hey.
Whether you're Dae-jin or Ho-jin, give me a hug.
You really must not be Dae-jin.
Dae-jin never gave me a warm hug like this before.
One sec.
Hello?
Oh, hi.
Yes, it's Hwang Ho-jin.
You remembered.
Yes...
So I'll be ready for the exhibition in about a week I think.
I'd like about two days in advance to set it up.
Yes.
I see.
Wouldn't just one banner out in front be good enough?
Yes.
And for the opening and closing ceremonies,
I'd like a sufficient.
It's because of traffic, and I'd like to focus a lot on the opening party.
Yes.
Thank you.
Bye.
To be honest, he's been brain dead for too long.
And some of his body parts are rotten.
I'm sorry to tell you this, but for the patient's sake,
I think it's good to send him away.
The latest test results show a lost of corneal reflexes.
Reflexes in the spinal cord have been lost.
Even after the latest test, the patient's brain waves were flat for 30 minutes.
With the test results as proof, we confirm Hwang Ho-jin as brain dead.
Hwang Ho-jin is now deceased.
Yes, I'll see you in a bit.
Okay.
- Please look around.
- Thank you.
Ho-jin, I'll go home and come back tonight.
Why?
Not feeling well?
Your face looks bad.
I just feel a bit dizzy.
Go get some rest then.
Eun-soo.
Why'd you come out?
I wanted to see you leave.
Can you drive?
Of course.
Come here.
I don't want you to leave.
I'll go rest a little and come back.
When you go home... call me.
Okay.
Boy, he scared me.
Go back in.
Go.
Who is it?
I have a package for you.
A package for you.
Please sign here.
Thank you.
I thought you might need the original so I'm returning it.
Even when I'm lying dead in my coffin,
I still won't be able to understand your sick love.
Before then, I hope I forget you.
Wouldn't just one banner out in front be good enough?
Yes.
And for the opening and closing ceremonies,
I'd like a sufficient amount of time.
It's because of traffic, and I'd like to focus a lot on the opening party.
Yes.
Thank you.
Bye.
Like what Marcel Duchamp intended to do with the toilet,
I wanted to make things common to us closer to real life.
So there are a lot of images, like flowers and butterflies.
Eun-soo's Dandelions I saw a girl today.
She was like the sunshine of September.
The moment I caught all the sadness within me disappeared.
I don't know how to explain this strong feeling.
What are you so nervous about?
No, I'm not.
For someone who's clueless about women,
I'm very curious as to who she is.
I met my brother's woman.
- Sorry I'm late.
- It's okay.
Dae-jin, right?
Dae-jin say hello to Han Eun-soo.
- The world...
- Hi. abandoned me.
Even the skies.
Today is the happiest day of my brother's life.
After today, his life will be even happier.
Since Eun-soo will be with him.
I'm also a happy person.
I'll be able to see Eun-soo forever.
From behind.
Ho-jin told me everything about his times with Eun-soo.
Ho-jin doesn't know women.
So I told him how to write love letters.
And through his letters, Eun-soo became happier.
Ho-jin said he's lucky to have a brother like me.
I'm a luckier guy.
Seeing that I haven't gone insane yet, living under the same roof with them.
To give a pure and fairy-tail like feeling, and to make it pleasurable, was my intention.
Furniture is something that people are very familiar with.
But they easily forget its actual existence.
Dae-jin, don't you want a girlfriend?
The best times are at your age.
I like it now.
Like what?
Fiddling with that car of yours in the garage?
Of course.
Just with that I'm happy enough.
Sometimes I want to just throw it all away, but I can't.
I can't think of anything else, and I don't want to.
I think I'll be like this until I die.
Since it's next to me,
I like it.
I can always see it, and feel it.
I like this a lot.
You're here.
Did everything go well?
So are you okay now?
This piece.
To make this, you stayed up for three days, huh?
Are you really okay?
Yes.
This is the door to heaven.
If I were to explain it, I made it thinking that death isn't a scary thing after all.
Think it gives off a pretty and warm feeling?
Yeah.
And this?
This is Alice in Wonderland.
I made it to be fun and cute, while thinking of our baby.
There's a mirror inside, too.
That'll look better at our doorway.
Sounds good.
Since it's blue, it'll feel fresh.
And we can put the CDs on it.
You haven't seen this, huh?
Yes.
Oh yeah, you saw this while I was working on it.
I saw.
My brother...
My kind brother...
You lived while sacrificing your life for me.
But did you know this?
That I loved Eun-soo first?
I loved her enough to abandon myself.
But Eun-soo never knew.
All she thought of was you.
Yes, my brother.
I'm not in this world anymore.
I'm the one who really died.
I'm going to become you and love Eun-soo now.
Eun-soo will think of you when she's with me, while loving only you.
Ho-jin.
Ho-jin.
You can never forgive me, right?
Don't forgive me.
Never.
Don't ever forgive me.
Ho-jin, I'm sorry.
A single postage stamp costs $0.44.
How much would a roll of 1000 stamps cost?
And there is really a couple of ways to do it, and I'll do it both ways just to show you they both work.
One is a kind of a faster way, but I want to make sure you understand why it works.
And then we'll verify that it actually gives us the right answer using maybe the more traditional way of multiplying decimals.
So, we're starting at $0.44.
I'll just write a 0.44.
Well, that's one stamp, so this is one stamp.
I'll write it like this, 1 stamp.
How much would 10 stamps cost?
Well, if 1 stamp is $0.44, then 10 stamps, we could move the decimal to the right one place, and so it would be, and now this leading zero is not that useful, so it would now be $4.4.
Or if you want to make it clear, it would be $4.40.
Now, what happens if you want to have a hundred stamps?
100 stamps.
Well, the same idea is going to happen.
We're now taking 10 times more so we're going to move to the decimal to the right once.
So, a hundred stamps are going to cost, are going to cost $44.00.
And this should make sense for you.
If one stamp is 44 hundreths of a dollar, then a hundred stamps are going to be 44 hundreths of a hundred dollars, or $44.
Or you could view it as we've just moved the decimal over one place.
So if we want a thousand stamps, if we want 1000 stamps, we would move the decimal to the right one more time.
Moving the decimal to the right is equivalent to multiplying by ten.
So then it would be $440.
Now, we could put, add another trailing zero just to make it clear that there is no cents over here.
So if you want to do it really quickly, you could've started with $0.44.
And you say, look, I'm not multiplying by ten.
I'm not multiplying by a hundred.
I'm multiplying by a thousand.
You're going to have to put another trailing zero over here.
And you would move the decimals from over here to over here.
You've essentially multiplied this times ten times ten times ten, which is a thousand.
So then this would become $440.
So let's verify that this works the exactly the same if we multiply the traditional way the way we multiply decimals.
So if you have 1000 times $0.44.
So you start over here.
4 times 0 is 0, 4 times 0 is 0, 4 times 0 is 0, 4 times 1 is 4.
Or you could just say, hey, this was 4 times a thousand.
Then we're going to go one place over so we're going to add a zero.
And we, once again, we're going to have 4 times 0 is 0, 4 times 0 is 0, 4 times 0 is 0, 4 times 1 is 4.
Or we just did 4 times a thousand.
So that is 4000, if you don't include this zero that we added here ahead of time because we're going one place to the left.
And then we have nothing left.
I haven't at all thought about the decimals right now.
So far I've really just viewed it as a thousand times 44.
I've been ignoring the decimal.
So if it was a thousand times 44, we would get 0 plus 0 is 0, 0 plus 0 is 0, 0 plus 0 is 0, 4 plus 0 is 4, 4 plus nothing is 4.
And if you ignore the decimal, that makes a lot of sense.
Because a thousand times 4 is 4000 and a thousand times 40 would be 40 000.
So you would get 44 000.
But this of course is not a 44.
This is a 44 hundreths.
We have, between the two numbers, two numbers behind the decimal point.
So we need to have two numbers behind or to the right of the decimal point in our answer.
So one, two.
Right over there.
So, once again, we get $440.00 for the thousand stamps.
So let's do another problem.
So I'll show you-- I showed you that 1, you could define a function as just kind of a standard algebraic expression, you could also do it a kind of if number is odd, this is what you do, if a number is this, is what you do.
Let's say-- let me draw a graph, and I'll use the line tool so it's a reasonably neat graph-- that's the x-axis there.
And let's draw the f of x-axis, or you might be used to calling that the y-axis, but-- OK.
Let me draw a-- let's say that-- let me draw this function.
This is 1, 2, 3, 4, 5, this is negative 5, this is 5, this is 5, this is negative 5.
And this is x-axis, and this is-- we'll call this the f of x-axis.
Now that might not seem obvious to you at first, but all this is saying is let's say when x is equal to negative 5, this function-- I'm creating a function definition-- let's say it equals 2, that's negative 1, that stays the same, that stays the same, then it goes to here, and then it goes to here, to here, and then-- let's see.
This tells you whenever I input an x, at least for the x's that we can see on the graph, this graph tell me what f of x equals.
So if x is equal to negative 5, f of x would equal plus 2.
And we could draw a couple of examples. f of 0, well we go to 0 on the x-axis, and we say f of 0 is equal to 0. f of 1 is equal to-- well, we go to x equal to 1, and we just see where the chart is, well, it equals negative 1.
This isn't too difficult, but this is a function definition.
So we've defined this graph right here as f of x.
So if that graph-- that's the graph of f of x, and let's say that we define g of x is equal to f of x-- let's say it's equal to f of x squared minus f of x.
And let's say that h of x is equal to 3 minus x.
So what if I were to ask you, what is h of g of negative 1?
So just like we did in the previous problems, first we'll say, well, let's try to figure out what g of negative 1 is, and then we can substitute that into h of x.
So g of negative 1 is equal to-- and this is how I do it.
Wherever you see the x, you just substitute it with the number that you're saying is now the value for x.
So you say, well, that's equal to f of negative 1 squared minus f of negative 1.
All I did is at g of negative 1, I just substituted it wherever I saw an x.
Well what's f of negative 1?
Well, when x is equal to negative 1, f of x is equal to 1.
So f of negative 1-- let's write that, f of negative 1 is equal to 1.
So g of negative 1 is equal to-- well, that's just 1 squared minus 1, well that equals 0.
Because f of negative 1 is 1, so it's 1 squared minus 1 that equals 1 minus 1.
0.
So g of negative 1 is 0, so this is the same thing as h of 0.
Because g of negative 1, we just figured out is 0. h of 0, we just take that 0 and substitute it here, so it's 3 minus 0, so that just equals 3.
Let's do another example, and I don't want to erase my graph since I took four minutes to actually draw it, let me erase what we just did here.
I'm going to create another definition for g of x this time.
Let's say that g of x-- oh whoops, I was trying to write in black-- let's say that g of x is equal to f of x squared plus f of x plus 2.
So now, in this case, what is g of-- let's pick a random number-- what is g of minus-- no, let's pick a, let's say-- what is g of minus 2?
After we try and pick a number that we could find an actual solution for. Well g of minus 2, wherever we see the x, x is not going to be minus 2.
That is equal to f of minus 2 squared plus f of minus 2 plus 2.
All we did is wherever we saw an x, we substituted it, minus 2 there.
Well, f of minus 2 squared, we know what minus 2 squared is, that's the same thing as f of 4, plus f of minus 2 plus 2.
That's 0.
Plus f of 0.
And now we just figure out what f of 4 and f of 0 is.
Well, f of 4, we go where x equals r, it's right here, and when x equals 4, f of 4 is equal to 2.
So this is equal to 2 plus f of 0.
And just as a reminder, this is the definition of f.
We didn't define it in terms of an algebraic expression, we defined in terms of an actual visual graph.
So what's f of 0? f of 0 is 0.
When x is equal to 0-- f of 0 is 0 so that's 2 plus 0-- so g of negative 2 is equal to 2.
I think maybe we'll do that in the future modules to kind of play with functions and actually to try graph the functions and see how they turn out.
I want to do as many examples on the functions as I can with you, because I think as you keep watching and watching the function problems and seeing more and more variations on functions, you'll see both how general of a concept this is, and hopefully you'll get an idea of how the functions actually work.
Well, I'll see you in the next lecture. Have fun.
When I was studying ancient Rome one of the most difficult things for me to understand is how all of these ancient ruins fit together, but luckily we have Dr. Bernard Frischer who has built an extraordinary video simulation that allows us to move through this space.
The difficulty is always two-fold.
First of all, that ancient cities are now in ruins so the one problem we have is how do you go from ruins to the way it did look in antiquity.
So even if you can visualize what the Pantheon looks like or the Colosseum, they are a mile apart in the city .
What was everything else? Most of it is missing. So the visualization is trying to put the whole city together
Okay.
It's a good place to start because you know, the Tibre does divide Rome into two parts.
And I see in the distance a very large temple.
Jupiter, the best and the greatest, which was the main temple of the Roman state cult.
And it's on top of the Capitoline Hill which because of this temple and some others, was considered the center of the state cult and the state religion.
So what moment in Rome's history have you chosen?
CHAPTER XVII The Freeman's Defence
There was a gentle bustle at the Quaker house, as the afternoon drew to a close.
Rachel Halliday moved quietly to and fro, collecting from her household stores such needments as could be arranged in the smallest compass, for the wanderers who were to go forth that night.
The afternoon shadows stretched eastward, and the round red sun stood thoughtfully on the horizon, and his beams shone yellow and calm into the little bed-room where George and his wife were sitting.
He was sitting with his child on his knee, and his wife's hand in his.
Both looked thoughtful and serious and traces of tears were on their cheeks.
"Yes, Eliza," said George, "I know all you say is true.
You are a good child,--a great deal better than I am; and I will try to do as you say.
I'll try to act worthy of a free man.
I'll try to feel like a Christian.
God Almighty knows that I've meant to do well,--tried hard to do well,--when everything has been against me; and now I'll forget all the past, and put away every hard and bitter feeling, and read my Bible, and learn to be a good man."
"And when we get to Canada," said Eliza, "I can help you.
I can do dress-making very well; and I understand fine washing and ironing; and between us we can find something to live on."
"Yes, Eliza, so long as we have each other and our boy.
Eliza, if these people only knew what a blessing it is for a man to feel that his wife and child belong to him!
I've often wondered to see men that could call their wives and children their own fretting and worrying about anything else.
Why, I feel rich and strong, though we have nothing but our bare hands.
I feel as if I could scarcely ask God for any more.
Yes, though I've worked hard every day, till I am twenty-five years old, and have not a cent of money, nor a roof to cover me, nor a spot of land to call my own, yet, if they will only let me alone now, I will be satisfied,--thankful; I will work, and send back the money for you and my boy.
As to my old master, he has been paid five times over for all he ever spent for me.
I don't owe him anything."
"But yet we are not quite out of danger," said Eliza; "we are not yet in Canada."
"True," said George, "but it seems as if I smelt the free air, and it makes me strong."
At this moment, voices were heard in the outer apartment, in earnest conversation, and very soon a rap was heard on the door.
Eliza started and opened it.
Simeon Halliday was there, and with him a Quaker brother, whom he introduced as
Phineas Fletcher.
Phineas was tall and lathy, red-haired, with an expression of great acuteness and shrewdness in his face.
He had not the placid, quiet, unworldly air of Simeon Halliday; on the contrary, a particularly wide-awake and au fait appearance, like a man who rather prides himself on knowing what he is about, and keeping a bright lookout ahead; peculiarities which sorted rather oddly with his broad brim and formal phraseology.
"Our friend Phineas hath discovered something of importance to the interests of thee and thy party, George," said Simeon; "it were well for thee to hear it."
"That I have," said Phineas, "and it shows the use of a man's always sleeping with one ear open, in certain places, as I've always said.
Last night I stopped at a little lone tavern, back on the road.
Thee remembers the place, Simeon, where we sold some apples, last year, to that fat woman, with the great ear-rings.
Well, I was tired with hard driving; and, after my supper I stretched myself down on a pile of bags in the corner, and pulled a buffalo over me, to wait till my bed was ready; and what does I do, but get fast asleep."
"With one ear open, Phineas?" said Simeon, quietly.
"No; I slept, ears and all, for an hour or two, for I was pretty well tired; but when
I came to myself a little, I found that there were some men in the room, sitting round a table, drinking and talking; and I thought, before I made much muster, I'd just see what they were up to, especially as I heard them say something about the Quakers.
'So,' says one, 'they are up in the Quaker settlement, no doubt,' says he.
Then I listened with both ears, and I found that they were talking about this very party.
So I lay and heard them lay off all their plans.
This young man, they said, was to be sent back to Kentucky, to his master, who was going to make an example of him, to keep all niggers from running away; and his wife two of them were going to run down to New
Orleans to sell, on their own account, and they calculated to get sixteen or eighteen hundred dollars for her; and the child, they said, was going to a trader, who had bought him; and then there was the boy,
Jim, and his mother, they were to go back to their masters in Kentucky.
They said that there were two constables, in a town a little piece ahead, who would go in with 'em to get 'em taken up, and the young woman was to be taken before a judge; and one of the fellows, who is small and smooth-spoken, was to swear to her for his property, and get her delivered over to him to take south.
They've got a right notion of the track we are going tonight; and they'll be down after us, six or eight strong.
So now, what's to be done?"
The group that stood in various attitudes, after this communication, were worthy of a painter.
Rachel Halliday, who had taken her hands out of a batch of biscuit, to hear the news, stood with them upraised and floury, and with a face of the deepest concern.
Simeon looked profoundly thoughtful; Eliza had thrown her arms around her husband, and was looking up to him.
George stood with clenched hands and glowing eyes, and looking as any other man might look, whose wife was to be sold at auction, and son sent to a trader, all under the shelter of a Christian nation's laws.
"What shall we do, George?" said Eliza faintly.
"I know what I shall do," said George, as he stepped into the little room, and began examining pistols.
"Ay, ay," said Phineas, nodding his head to Simeon; "thou seest, Simeon, how it will work." "I see," said Simeon, sighing; "I pray it come not to that."
"I don't want to involve any one with or for me," said George.
"If you will lend me your vehicle and direct me, I will drive alone to the next stand.
Jim is a giant in strength, and brave as death and despair, and so am I."
"Ah, well, friend," said Phineas, "but thee'll need a driver, for all that.
Thee's quite welcome to do all the fighting, thee knows; but I know a thing or two about the road, that thee doesn't." "But I don't want to involve you," said
George.
"Involve," said Phineas, with a curious and keen expression of face, "When thee does involve me, please to let me know." "Phineas is a wise and skilful man," said
Simeon.
"Thee does well, George, to abide by his judgment; and," he added, laying his hand kindly on George's shoulder, and pointing to the pistols, "be not over hasty with these,--young blood is hot."
"I will attack no man," said George.
"All I ask of this country is to be let alone, and I will go out peaceably; but,"-- he paused, and his brow darkened and his face worked,--"I've had a sister sold in that New Orleans market.
I know what they are sold for; and am I going to stand by and see them take my wife and sell her, when God has given me a pair of strong arms to defend her?
No; God help me!
I'll fight to the last breath, before they shall take my wife and son.
Can you blame me?" "Mortal man cannot blame thee, George.
Flesh and blood could not do otherwise," said Simeon.
"Woe unto the world because of offences, but woe unto them through whom the offence cometh."
"Would not even you, sir, do the same, in my place?"
"I pray that I be not tried," said Simeon; "the flesh is weak."
"I think my flesh would be pretty tolerable strong, in such a case," said Phineas, stretching out a pair of arms like the sails of a windmill.
"I an't sure, friend George, that I shouldn't hold a fellow for thee, if thee had any accounts to settle with him."
"If man should ever resist evil," said Simeon, "then George should feel free to do it now: but the leaders of our people taught a more excellent way; for the wrath of man worketh not the righteousness of
God; but it goes sorely against the corrupt will of man, and none can receive it save they to whom it is given.
Let us pray the Lord that we be not tempted."
"And so I do," said Phineas; "but if we are tempted too much--why, let them look out, that's all." "It's quite plain thee wasn't born a
Friend," said Simeon, smiling.
"The old nature hath its way in thee pretty strong as yet."
To tell the truth, Phineas had been a hearty, two-fisted backwoodsman, a vigorous hunter, and a dead shot at a buck; but, having wooed a pretty Quakeress, had been moved by the power of her charms to join the society in his neighborhood; and though he was an honest, sober, and efficient member, and nothing particular could be alleged against him, yet the more spiritual among them could not but discern an exceeding lack of savor in his developments.
"Friend Phineas will ever have ways of his own," said Rachel Halliday, smiling; "but we all think that his heart is in the right place, after all."
"Well," said George, "isn't it best that we hasten our flight?"
"I got up at four o'clock, and came on with all speed, full two or three hours ahead of them, if they start at the time they planned.
It isn't safe to start till dark, at any rate; for there are some evil persons in the villages ahead, that might be disposed to meddle with us, if they saw our wagon, and that would delay us more than the waiting; but in two hours I think we may venture.
I will go over to Michael Cross, and engage him to come behind on his swift nag, and keep a bright lookout on the road, and warn us if any company of men come on.
Michael keeps a horse that can soon get ahead of most other horses; and he could shoot ahead and let us know, if there were any danger.
I am going out now to warn Jim and the old woman to be in readiness, and to see about the horse.
We have a pretty fair start, and stand a good chance to get to the stand before they can come up with us.
So, have good courage, friend George; this isn't the first ugly scrape that I've been in with thy people," said Phineas, as he closed the door.
"Phineas is pretty shrewd," said Simeon.
"He will do the best that can be done for thee, George."
"All I am sorry for," said George, "is the risk to you."
"Thee'll much oblige us, friend George, to say no more about that.
What we do we are conscience bound to do; we can do no other way.
And now, mother," said he, turning to Rachel, "hurry thy preparations for these friends, for we must not send them away fasting."
And while Rachel and her children were busy making corn-cake, and cooking ham and chicken, and hurrying on the et ceteras of the evening meal, George and his wife sat in their little room, with their arms folded about each other, in such talk as husband and wife have when they know that a few hours may part them forever.
"Eliza," said George, "people that have friends, and houses, and lands, and money, and all those things can't love as we do, who have nothing but each other.
Till I knew you, Eliza, no creature had loved me, but my poor, heart-broken mother and sister.
I saw poor Emily that morning the trader carried her off.
She came to the corner where I was lying asleep, and said, 'Poor George, your last friend is going.
What will become of you, poor boy?'
And I got up and threw my arms round her, and cried and sobbed, and she cried too; and those were the last kind words I got for ten long years; and my heart all withered up, and felt as dry as ashes, till I met you.
And your loving me,--why, it was almost like raising one from the dead!
I've been a new man ever since!
And now, Eliza, I'll give my last drop of blood, but they shall not take you from me.
Whoever gets you must walk over my dead body."
"O, Lord, have mercy!" said Eliza, sobbing.
"If he will only let us get out of this country together, that is all we ask."
"Is God on their side?" said George, speaking less to his wife than pouring out his own bitter thoughts.
"Does he see all they do?
Why does he let such things happen?
And they tell us that the Bible is on their side; certainly all the power is.
They are rich, and healthy, and happy; they are members of churches, expecting to go to heaven; and they get along so easy in the world, and have it all their own way; and poor, honest, faithful Christians,--
Christians as good or better than they,-- are lying in the very dust under their feet.
They buy 'em and sell 'em, and make trade of their heart's blood, and groans and tears,--and God lets them."
"Friend George," said Simeon, from the kitchen, "listen to this Psalm; it may do thee good."
George drew his seat near the door, and Eliza, wiping her tears, came forward also to listen, while Simeon read as follows:
"But as for me, my feet were almost gone; my steps had well-nigh slipped.
For I was envious of the foolish, when I saw the prosperity of the wicked.
They are not in trouble like other men, neither are they plagued like other men.
Therefore, pride compasseth them as a chain; violence covereth them as a garment.
Their eyes stand out with fatness; they have more than heart could wish.
They are corrupt, and speak wickedly concerning oppression; they speak loftily.
Therefore his people return, and the waters of a full cup are wrung out to them, and they say, How doth God know? and is there knowledge in the Most High?"
"Is not that the way thee feels, George?"
"It is so indeed," said George,--"as well as I could have written it myself."
"Then, hear," said Simeon:
"When I thought to know this, it was too painful for me until I went unto the sanctuary of God.
Then understood I their end.
Surely thou didst set them in slippery places, thou castedst them down to destruction.
As a dream when one awaketh, so, oh Lord, when thou awakest, thou shalt despise their image.
Nevertheless I am continually with thee; thou hast holden me by my right hand.
Thou shalt guide me by thy counsel, and afterwards receive me to glory.
It is good for me to draw near unto God.
I have put my trust in the Lord God." (NOTE: Ps.
The words of holy trust, breathed by the friendly old man, stole like sacred music over the harassed and chafed spirit of George; and after he ceased, he sat with a gentle and subdued expression on his fine features.
"If this world were all, George," said Simeon, "thee might, indeed, ask where is the Lord?
But it is often those who have least of all in this life whom he chooseth for the kingdom.
Put thy trust in him and, no matter what befalls thee here, he will make all right hereafter."
If these words had been spoken by some easy, self-indulgent exhorter, from whose mouth they might have come merely as pious and rhetorical flourish, proper to be used to people in distress, perhaps they might not have had much effect; but coming from one who daily and calmly risked fine and imprisonment for the cause of God and man, they had a weight that could not but be felt, and both the poor, desolate fugitives found calmness and strength breathing into them from it.
And now Rachel took Eliza's hand kindly, and led the way to the supper-table.
As they were sitting down, a light tap sounded at the door, and Ruth entered.
"I just ran in," she said, "with these little stockings for the boy,--three pair, nice, warm woollen ones.
It will be so cold, thee knows, in Canada.
Does thee keep up good courage, Eliza?" she added, tripping round to Eliza's side of the table, and shaking her warmly by the hand, and slipping a seed-cake into Harry's hand.
"I brought a little parcel of these for him," she said, tugging at her pocket to get out the package.
"Children, thee knows, will always be eating."
"O, thank you; you are too kind," said Eliza.
"Come, Ruth, sit down to supper," said Rachel.
"I couldn't, any way.
I left John with the baby, and some biscuits in the oven; and I can't stay a moment, else John will burn up all the biscuits, and give the baby all the sugar in the bowl.
That's the way he does," said the little Quakeress, laughing.
"So, good-by, Eliza; good-by, George; the Lord grant thee a safe journey;" and, with a few tripping steps, Ruth was out of the apartment.
A little while after supper, a large covered-wagon drew up before the door; the night was clear starlight; and Phineas jumped briskly down from his seat to arrange his passengers.
George walked out of the door, with his child on one arm and his wife on the other.
His step was firm, his face settled and resolute.
Rachel and Simeon came out after them.
"You get out, a moment," said Phineas to those inside, "and let me fix the back of the wagon, there, for the women-folks and the boy."
"Here are the two buffaloes," said Rachel.
"Make the seats as comfortable as may be; it's hard riding all night."
Jim came out first, and carefully assisted out his old mother, who clung to his arm, and looked anxiously about, as if she expected the pursuer every moment.
"Jim, are your pistols all in order?" said George, in a low, firm voice.
"And you've no doubt what you shall do, if they come?"
"I rather think I haven't," said Jim, throwing open his broad chest, and taking a deep breath.
"Do you think I'll let them get mother again?"
During this brief colloquy, Eliza had been taking her leave of her kind friend,
Rachel, and was handed into the carriage by Simeon, and, creeping into the back part with her boy, sat down among the buffalo- skins.
The old woman was next handed in and seated and George and Jim placed on a rough board seat front of them, and Phineas mounted in front.
"Farewell, my friends," said Simeon, from without.
"God bless you!" answered all from within.
And the wagon drove off, rattling and jolting over the frozen road.
There was no opportunity for conversation, on account of the roughness of the way and the noise of the wheels.
The vehicle, therefore, rumbled on, through long, dark stretches of woodland,--over wide dreary plains,--up hills, and down valleys,--and on, on, on they jogged, hour after hour.
The child soon fell asleep, and lay heavily in his mother's lap.
The poor, frightened old woman at last forgot her fears; and, even Eliza, as the night waned, found all her anxieties insufficient to keep her eyes from closing.
Phineas seemed, on the whole, the briskest of the company, and beguiled his long drive with whistling certain very unquaker-like songs, as he went on.
But about three o'clock George's ear caught the hasty and decided click of a horse's hoof coming behind them at some distance and jogged Phineas by the elbow.
Phineas pulled up his horses, and listened.
"That must be Michael," he said; "I think I know the sound of his gallop;" and he rose up and stretched his head anxiously back over the road.
A man riding in hot haste was now dimly descried at the top of a distant hill.
"There he is, I do believe!" said Phineas.
George and Jim both sprang out of the wagon before they knew what they were doing.
All stood intensely silent, with their faces turned towards the expected messenger.
On he came.
Now he went down into a valley, where they could not see him; but they heard the sharp, hasty tramp, rising nearer and nearer; at last they saw him emerge on the top of an eminence, within hail.
"Yes, that's Michael!" said Phineas; and, raising his voice, "Halloa, there,
Michael!" "Phineas! is that thee?"
"Yes; what news--they coming?"
"Right on behind, eight or ten of them, hot with brandy, swearing and foaming like so many wolves."
And, just as he spoke, a breeze brought the faint sound of galloping horsemen towards them.
"In with you,--quick, boys, in!" said
Phineas.
"If you must fight, wait till I get you a piece ahead."
And, with the word, both jumped in, and Phineas lashed the horses to a run, the horseman keeping close beside them.
The wagon rattled, jumped, almost flew, over the frozen ground; but plainer, and still plainer, came the noise of pursuing horsemen behind.
The women heard it, and, looking anxiously out, saw, far in the rear, on the brow of a distant hill, a party of men looming up against the red-streaked sky of early dawn.
Another hill, and their pursuers had evidently caught sight of their wagon, whose white cloth-covered top made it conspicuous at some distance, and a loud yell of brutal triumph came forward on the wind.
Eliza sickened, and strained her child closer to her bosom; the old woman prayed and groaned, and George and Jim clenched their pistols with the grasp of despair.
The pursuers gained on them fast; the carriage made a sudden turn, and brought them near a ledge of a steep overhanging rock, that rose in an isolated ridge or clump in a large lot, which was, all around it, quite clear and smooth.
This isolated pile, or range of rocks, rose up black and heavy against the brightening sky, and seemed to promise shelter and concealment.
It was a place well known to Phineas, who had been familiar with the spot in his hunting days; and it was to gain this point he had been racing his horses.
"Now for it!" said he, suddenly checking his horses, and springing from his seat to the ground.
"Out with you, in a twinkling, every one, and up into these rocks with me.
Michael, thee tie thy horse to the wagon, and drive ahead to Amariah's and get him and his boys to come back and talk to these fellows."
In a twinkling they were all out of the carriage.
"There," said Phineas, catching up Harry, "you, each of you, see to the women; and run, now if you ever did run!"
They needed no exhortation.
Quicker than we can say it, the whole party were over the fence, making with all speed for the rocks, while Michael, throwing himself from his horse, and fastening the bridle to the wagon, began driving it rapidly away.
"Come ahead," said Phineas, as they reached the rocks, and saw in the mingled starlight and dawn, the traces of a rude but plainly marked foot-path leading up among them;
"this is one of our old hunting-dens.
Come up!"
Phineas went before, springing up the rocks like a goat, with the boy in his arms.
Jim came second, bearing his trembling old mother over his shoulder, and George and
Eliza brought up the rear.
The party of horsemen came up to the fence, and, with mingled shouts and oaths, were dismounting, to prepare to follow them.
A few moments' scrambling brought them to the top of the ledge; the path then passed between a narrow defile, where only one could walk at a time, till suddenly they came to a rift or chasm more than a yard in breadth, and beyond which lay a pile of rocks, separate from the rest of the ledge, standing full thirty feet high, with its sides steep and perpendicular as those of a castle.
Phineas easily leaped the chasm, and sat down the boy on a smooth, flat platform of crisp white moss, that covered the top of the rock.
"Over with you!" he called; "spring, now, once, for your lives!" said he, as one after another sprang across.
Several fragments of loose stone formed a kind of breast-work, which sheltered their position from the observation of those below. "Well, here we all are," said Phineas, peeping over the stone breast-work to watch the assailants, who were coming tumultuously up under the rocks.
"Let 'em get us, if they can.
Whoever comes here has to walk single file between those two rocks, in fair range of your pistols, boys, d'ye see?"
"I do see," said George! "and now, as this matter is ours, let us take all the risk, and do all the fighting."
"Thee's quite welcome to do the fighting, George," said Phineas, chewing some checkerberry-leaves as he spoke; "but I may have the fun of looking on, I suppose.
But see, these fellows are kinder debating down there, and looking up, like hens when they are going to fly up on to the roost.
Hadn't thee better give 'em a word of advice, before they come up, just to tell
'em handsomely they'll be shot if they do?"
The party beneath, now more apparent in the light of the dawn, consisted of our old acquaintances, Tom Loker and Marks, with two constables, and a posse consisting of such rowdies at the last tavern as could be engaged by a little brandy to go and help the fun of trapping a set of niggers.
"Well, Tom, yer coons are farly treed," said one.
"Yes, I see 'em go up right here," said Tom; "and here's a path.
I'm for going right up.
They can't jump down in a hurry, and it won't take long to ferret 'em out."
"But, Tom, they might fire at us from behind the rocks," said Marks.
"That would be ugly, you know." "Ugh!" said Tom, with a sneer.
"Always for saving your skin, Marks!
No danger! niggers are too plaguy scared!" "I don't know why I shouldn't save my skin," said Marks.
"It's the best I've got; and niggers do fight like the devil, sometimes."
At this moment, George appeared on the top of a rock above them, and, speaking in a calm, clear voice, said, "Gentlemen, who are you, down there, and what do you want?"
"We want a party of runaway niggers," said Tom Loker.
"One George Harris, and Eliza Harris, and their son, and Jim Selden, and an old woman.
We've got the officers, here, and a warrant to take 'em; and we're going to have 'em, too. D'ye hear?
An't you George Harris, that belongs to Mr. Harris, of Shelby county, Kentucky?"
"I am George Harris. A Mr. Harris, of Kentucky, did call me his property.
But now I'm a free man, standing on God's free soil; and my wife and my child I claim as mine.
Jim and his mother are here.
We have arms to defend ourselves, and we mean to do it.
You can come up, if you like; but the first one of you that comes within the range of our bullets is a dead man, and the next, and the next; and so on till the last."
"O, come! come!" said a short, puffy man, stepping forward, and blowing his nose as he did so.
"Young man, this an't no kind of talk at all for you.
You see, we're officers of justice.
We've got the law on our side, and the power, and so forth; so you'd better give up peaceably, you see; for you'll certainly have to give up, at last."
"I know very well that you've got the law on your side, and the power," said George, bitterly.
"You mean to take my wife to sell in New Orleans, and put my boy like a calf in a trader's pen, and send Jim's old mother to the brute that whipped and abused her before, because he couldn't abuse her son.
You want to send Jim and me back to be whipped and tortured, and ground down under the heels of them that you call masters; and your laws will bear you out in it,-- more shame for you and them!
But you haven't got us.
We don't own your laws; we don't own your country; we stand here as free, under God's sky, as you are; and, by the great God that made us, we'll fight for our liberty till we die."
George stood out in fair sight, on the top of the rock, as he made his declaration of independence; the glow of dawn gave a flush to his swarthy cheek, and bitter indignation and despair gave fire to his dark eye; and, as if appealing from man to the justice of God, he raised his hand to heaven as he spoke.
If it had been only a Hungarian youth, now bravely defending in some mountain fastness the retreat of fugitives escaping from Austria into America, this would have been sublime heroism; but as it was a youth of
African descent, defending the retreat of fugitives through America into Canada, of course we are too well instructed and patriotic to see any heroism in it; and if any of our readers do, they must do it on their own private responsibility.
When despairing Hungarian fugitives make their way, against all the search-warrants and authorities of their lawful government, to America, press and political cabinet ring with applause and welcome.
When despairing African fugitives do the same thing,--it is--what is it?
Be it as it may, it is certain that the attitude, eye, voice, manner, of the speaker for a moment struck the party below to silence.
There is something in boldness and determination that for a time hushes even the rudest nature.
Marks was the only one who remained wholly untouched.
He was deliberately cocking his pistol, and, in the momentary silence that followed
George's speech, he fired at him.
"Ye see ye get jist as much for him dead as alive in Kentucky," he said coolly, as he wiped his pistol on his coat-sleeve.
George sprang backward,--Eliza uttered a shriek,--the ball had passed close to his hair, had nearly grazed the cheek of his wife, and struck in the tree above.
"It's nothing, Eliza," said George, quickly.
"Thee'd better keep out of sight, with thy speechifying," said Phineas; "they're mean scamps."
"Now, Jim," said George, "look that your pistols are all right, and watch that pass with me.
The first man that shows himself I fire at; you take the second, and so on.
It won't do, you know, to waste two shots on one."
"But what if you don't hit?" "I shall hit," said George, coolly.
"Good! now, there's stuff in that fellow," muttered Phineas, between his teeth.
The party below, after Marks had fired, stood, for a moment, rather undecided.
"I think you must have hit some on 'em," said one of the men.
"I heard a squeal!" "I'm going right up for one," said Tom.
"I never was afraid of niggers, and I an't going to be now.
Who goes after?" he said, springing up the rocks.
George heard the words distinctly.
He drew up his pistol, examined it, pointed it towards that point in the defile where the first man would appear.
One of the most courageous of the party followed Tom, and, the way being thus made, the whole party began pushing up the rock,- -the hindermost pushing the front ones faster than they would have gone of themselves.
On they came, and in a moment the burly form of Tom appeared in sight, almost at the verge of the chasm.
George fired,--the shot entered his side,-- but, though wounded, he would not retreat, but, with a yell like that of a mad bull, he was leaping right across the chasm into the party.
"Friend," said Phineas, suddenly stepping to the front, and meeting him with a push from his long arms, "thee isn't wanted here."
Down he fell into the chasm, crackling down among trees, bushes, logs, loose stones, till he lay bruised and groaning thirty feet below.
The fall might have killed him, had it not been broken and moderated by his clothes catching in the branches of a large tree; but he came down with some force, however,-
-more than was at all agreeable or convenient.
"Lord help us, they are perfect devils!" said Marks, heading the retreat down the rocks with much more of a will than he had joined the ascent, while all the party came tumbling precipitately after him,--the fat constable, in particular, blowing and puffing in a very energetic manner.
"I say, fellers," said Marks, "you jist go round and pick up Tom, there, while I run and get on to my horse to go back for help,--that's you;" and, without minding the hootings and jeers of his company,
Marks was as good as his word, and was soon seen galloping away.
"Was ever such a sneaking varmint?" said one of the men; "to come on his business, and he clear out and leave us this yer way!"
"Well, we must pick up that feller," said another.
"Cuss me if I much care whether he is dead or alive."
The men, led by the groans of Tom, scrambled and crackled through stumps, logs and bushes, to where that hero lay groaning and swearing with alternate vehemence.
"Ye keep it agoing pretty loud, Tom," said one.
"Ye much hurt?" "Don't know.
Get me up, can't ye?
Blast that infernal Quaker!
If it hadn't been for him, I'd a pitched some on 'em down here, to see how they liked it."
With much labor and groaning, the fallen hero was assisted to rise; and, with one holding him up under each shoulder, they got him as far as the horses.
"If you could only get me a mile back to that ar tavern.
Give me a handkerchief or something, to stuff into this place, and stop this infernal bleeding."
George looked over the rocks, and saw them trying to lift the burly form of Tom into the saddle.
After two or three ineffectual attempts, he reeled, and fell heavily to the ground.
"O, I hope he isn't killed!" said Eliza, who, with all the party, stood watching the proceeding.
"Why not?" said Phineas; "serves him right."
"Because after death comes the judgment," said Eliza.
"Yes," said the old woman, who had been groaning and praying, in her Methodist fashion, during all the encounter, "it's an awful case for the poor crittur's soul."
"On my word, they're leaving him, I do believe," said Phineas.
It was true; for after some appearance of irresolution and consultation, the whole party got on their horses and rode away.
When they were quite out of sight, Phineas began to bestir himself.
"Well, we must go down and walk a piece," he said.
"I told Michael to go forward and bring help, and be along back here with the wagon; but we shall have to walk a piece along the road, I reckon, to meet them.
The Lord grant he be along soon!
It's early in the day; there won't be much travel afoot yet a while; we an't much more than two miles from our stopping-place.
If the road hadn't been so rough last night, we could have outrun 'em entirely."
As the party neared the fence, they discovered in the distance, along the road, their own wagon coming back, accompanied by some men on horseback.
"Well, now, there's Michael, and Stephen and Amariah," exclaimed Phineas, joyfully.
"Now we are made--as safe as if we'd got there."
"Well, do stop, then," said Eliza, "and do something for that poor man; he's groaning dreadfully."
"It would be no more than Christian," said George; "let's take him up and carry him on." "And doctor him up among the Quakers!" said
Phineas; "pretty well, that! Well, I don't care if we do.
Here, let's have a look at him;" and Phineas, who in the course of his hunting and backwoods life had acquired some rude experience of surgery, kneeled down by the wounded man, and began a careful examination of his condition.
"Marks," said Tom, feebly, "is that you, Marks?"
"No; I reckon 'tan't friend," said Phineas.
"Much Marks cares for thee, if his own skin's safe.
He's off, long ago." "I believe I'm done for," said Tom.
"The cussed sneaking dog, to leave me to die alone!
My poor old mother always told me 't would be so."
"La sakes! jist hear the poor crittur.
He's got a mammy, now," said the old negress.
"I can't help kinder pityin' on him."
"Softly, softly; don't thee snap and snarl, friend," said Phineas, as Tom winced and pushed his hand away.
"Thee has no chance, unless I stop the bleeding."
And Phineas busied himself with making some off-hand surgical arrangements with his own pocket-handkerchief, and such as could be mustered in the company.
"You pushed me down there," said Tom, faintly.
"Well if I hadn't thee would have pushed us down, thee sees," said Phineas, as he stooped to apply his bandage.
"There, there,--let me fix this bandage.
We mean well to thee; we bear no malice.
Thee shall be taken to a house where they'll nurse thee first rate, well as thy own mother could."
Tom groaned, and shut his eyes.
In men of his class, vigor and resolution are entirely a physical matter, and ooze out with the flowing of the blood; and the gigantic fellow really looked piteous in his helplessness.
The other party now came up.
The seats were taken out of the wagon.
The buffalo-skins, doubled in fours, were spread all along one side, and four men, with great difficulty, lifted the heavy form of Tom into it.
Before he was gotten in, he fainted entirely.
The old negress, in the abundance of her compassion, sat down on the bottom, and took his head in her lap.
Eliza, George and Jim, bestowed themselves, as well as they could, in the remaining space and the whole party set forward.
"What do you think of him?" said George, who sat by Phineas in front.
"Well it's only a pretty deep flesh-wound; but, then, tumbling and scratching down that place didn't help him much.
It has bled pretty freely,--pretty much drained him out, courage and all,--but he'll get over it, and may be learn a thing or two by it."
"I'm glad to hear you say so," said George.
"It would always be a heavy thought to me, if I'd caused his death, even in a just cause."
"Yes," said Phineas, "killing is an ugly operation, any way they'll fix it,--man or beast.
I've seen a buck that was shot down and a dying, look that way on a feller with his eye, that it reely most made a feller feel wicked for killing on him; and human creatures is a more serious consideration yet, bein', as thy wife says, that the judgment comes to 'em after death.
So I don't know as our people's notions on these matters is too strict; and, considerin' how I was raised, I fell in with them pretty considerably."
"What shall you do with this poor fellow?" said George.
"O, carry him along to Amariah's.
There's old Grandmam Stephens there,-- Dorcas, they call her,--she's most an amazin' nurse.
She takes to nursing real natural, and an't never better suited than when she gets a sick body to tend.
We may reckon on turning him over to her for a fortnight or so."
A ride of about an hour more brought the party to a neat farmhouse, where the weary travellers were received to an abundant breakfast.
Tom Loker was soon carefully deposited in a much cleaner and softer bed than he had ever been in the habit of occupying.
His wound was carefully dressed and bandaged, and he lay languidly opening and shutting his eyes on the white window- curtains and gently-gliding figures of his sick room, like a weary child.
And here, for the present, we shall take our leave of one party.
In the last video, we had a word problem where we had-- we essentially had to figure out the sides of a triangle, but instead of, you know, just being able to do the Pythagorean theorem and because it was a right triangle, it was just kind of a normal triangle. It wasn't a right triangle.
I want to show you, once you know the law of cosines, so you can then apply it to a problem, like we did in the past, and you'll do it faster.
So let's go and let's see what this law of cosines is all about.
And let's called this side-- I don't know, a. No, let's call this side b.
Let's call that b and let's call this c, and let's call this side a. So if this is a right triangle, then we could have used the Pythagorean theorem somehow, but now we can't. So what do we do?
So I can drop a line like that. So I have two right angles. And then once I have right triangles, then now I can start to use trig functions and the Pythagorean theorem, et cetera, et cetera.
So what is this side here? What is the length of that side, that purple side? Well, that purple side is just, you know, we use SOHCAHTOA.
So this purple side is adjacent to theta, and then this blue or mauve side b is the hypotenuse of this right triangle. So we know that-- I'm just going to stick to one color because it'll take me forever if I keep switching colors. We know that cosine of theta-- let's call this side, let's call this kind of subside-- I don't know, let's call this d, side d.
Well, e is this whole c side-- c side, oh, that's interesting-- this whole c side minus this d side, right? So e is equal to c minus d. We just solved for d, so side e is equal to c minus b cosine of theta.
Well, what's this magenta side going to be?
Well, m is opposite to theta.
We've solved for c as well, but we know b, and b is simple. So what relationship gives us m over b, or involves the opposite and the hypotenuse? Well, that's sine: opposite over hypotenuse.
Let me switch to another color just to be arbitrary. a squared is equal to m squared. m is b sine of theta. So it's b sine of theta squared plus e squared. Well, e we figure out is this.
Well, if we take this term and this term, we get-- those two terms are b squared sine squared of theta plus b squared cosine-- this should be squared there, right, because we squared it. b squared cosine squared of theta, and then we have plus c squared minus 2bc cosine theta. Well, what does this simplify to? Well, this is the same thing as b squared times the sine squared theta plus cosine squared of theta.
Solve for a and check your solution. And, we have a plus 5 is equal to 54.
Now, all this is saying is that we have some number, some variable a, and if I add 5 to it, I will get 54. And you might be able to do this in your head, but we're going to do it a little bit more systematically, 'cause that'll be helpful when you have more complicated problems.
So, in general, whenever you have an equation like this we want the variable, we want this a, all by itself on one side of the equation.
We want to isolate it.
It's already on the left hand side, so let's try to get rid of everything else on the left hand side.
Well, the only other thing on the left hand side is this positive 5.
Well, the best way to get rid of a plus 5, or of a positive 5, is to subtract 5.
So, let's subtract 5, but remember this says "a plus 5 is equal to 54".
If we want the equality to still hold, anything we do to the left hand side of this equation we have to do to the right side of the equation.
So we also have to subtract 54 [sic] from the right.
So, we have a plus 5 minus 5, well that's just going to be "a plus 0", cause you add 5 and subtract 5, they cancel out.
So a + 0 is just a. And then, 54 minus 5 that is 49, and we're done.
We have solved for a. a is equal to 49. And now we can check it.
And we can check it by just substituting 49 back for a in our original equation.
So instead of writing a plus 5 is equal to 54, let's see if 49 plus 5 is equal to 54.
So, we're just substituting it back in.
49 plus, let me do that in that same shade of green, 49 + 5 is equal to 54, we're trying to check this, 49 + 5 is 54, and that indeed is equal to 54, so it all checks out.
We all need a lot of information to get through our day.
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I've done a bunch of videos already on respiration.
I think even before those videos, you had a sense that we need oxygen and that we release CO2.
And if you watched the videos on respiration, you know that we need the oxygen in order to metabolize our food, in order to turn our food into ATPs that can then drive other types of cellular functions-- or anything that we have to do; move, or breathe, or think, or everything that we have to do.
And that through the process of respiration, we break down those sugars and we release carbon dioxide.
So in this video, what I want to do is take a big step back and think about how we actually get our oxygen into our body and how we release it back out into the atmosphere.
Another way to think about it is how we ventilate ourselves.
How do we get the oxygen in, and how do we get the carbon dioxide out?
And I think any of us could at least start off this video.
It starts off in either our nose or our mouth.
I always have a clogged sinus so I often have to deal with my mouth.
I sleep with my mouth often.
But it always starts in our nose or our mouths.
Let me draw someone with a nose and a mouth.
So let's say that this is my person.
Maybe his mouth will be open so that he can breathe.
His eyes aren't important, but just so you know it's a person.
So this is my test subject or the person I'm going to use to diagram.
That's his ear.
Maybe he has a bit of a-- let's give him some hair.
All of that is irrelevant, but this is our guy.
This is the guy that's going to show us how we take air in and how we take air out of the body.
So let's go inside of this guy.
I can draw his outside first. Let me see how well I can do this.
So this is outside the guy.
That doesn't look right.
Let's say the guy looks something like this and he's got-- this is his shoulders.
That's our guy.
All right.
So in our mouth, we have our oral cavity right there, which is just the space that our mouth creates.
We have our oral cavity.
I could draw our tongue and all of that and maybe I will.
Maybe I'll draw the tongue.
But you have this space inside of the mouth-- call that the oral cavity.
And then also you have your nostrils and they open up into a nasal cavity.
So that's another big space just like this.
And we know that they connect at the back of our nose or the back of our mouth.
And this passage right here where they connect is called the pharynx.
When your air goes through your nose-- they say breathing through your nose is better, probably because it gets filtered by your nose hairs and it gets warmed up and and what not, but you can breathe through either side.
The air goes in through either your nasal cavity or your oral cavity and then comes back through your pharynx and then the pharynx splits into two pipes.
One for-- well, one, air can go down either one, but the other one is for food.
So your pharynx gets split.
In the back you have your esophagus-- and we'll talk more about the esophagus in a future video.
In the back you have your esophagus and in the front--
let me draw a little dividing line there.
In the front, maybe this-- let me make it connect like that.
I was using yellow.
I'm going to use yellow to continue and I'm going to use green for the air.
So it divides just like that.
So behind your air pipe, you have your esophagus.
Let me make that another color.
And then right here is your larynx.
And I'm going to concern ourselves with the larynx.
Esophagus is where your food goes down.
We know that we eat food with our mouth as well.
So this is where we want our food to go-- down the esophagus.
But the focus of this video is our ventilation.
What do we do with our air?
So I'm going to focus as the air goes through our larynx.
And the larynx is also our voicebox.
So as you hear me talking right now, there are these little things right about here that are vibrating at just the right frequencies and I'm able to shape the sound with my mouth to make this video.
So that's also your voicebox, but I won't focus on that right now.
It's called a voicebox because of this whole anatomical structure that looks something like that.
But then after the air passes through the larynx-- this is on the way in-- it goes to the trachea, which is essentially just the pipe for air.
The esophagus is the pipe for food.
Let me write this down.
And then from the trachea-- and the trachea is actually a reasonably rigid structure.
It has cartilage around it and it makes sense that it has cartilage.
You don't want-- you can imagine a hose-- if it bent a lot, you wouldn't be able to get a lot of water through it, or a lot of air through it.
So you don't want this thing to bend a lot.
So that's why it needs to have some rigidity-- so that's why it has cartilage around it.
And then it splits into two tubes-- and I think you know where these two tubes are going to.
And I'm not drawing this in super detail.
I just want you to get the idea of them, but these two tubes are the bronchi-- or each one is a bronchus.
And they also have cartilage, so they're fairly rigid, but the bronchi keep splitting.
They keep splitting into smaller and smaller tubes just like that and at some point, they stop having cartilage.
They stop being reasonably rigid, but they keep splitting off.
So I'll just draw them as these little lines.
At some point they become such thin things.
They just keep splitting off.
So the air just keeps splitting off and spread and goes down the different paths.
And when the bronchi no longer have cartilage around them, they're no longer rigid.
The first of those are called-- or actually all the tubes after that point are called bronchioles.
These are bronchioles.
So for example, that we could call a bronchiole.
And there's nothing fancy here.
It's just a pipe that just gets thinner and thinner and thinner.
We've labeled the different parts of the pipes different things, but the idea is, let's take it through our mouth or our nose and we just keep dividing and keep dividing this main division into two different paths that takes us into each of our lungs.
Let me draw this guy's lungs here.
And these bronchi-- or the bronchi split into the lungs-- the bronchioles are in the lungs and eventually the bronchioles terminate.
And this is where it gets interesting.
They keep dividing smaller and smaller, thinner and thinner and thinner, into these little air sacs, just like that.
At the end of every super small bronchiole are these
little air sacs-- super small air sacs-- and I'm going to talk about these air sacs in a second.
And these are called alveoli.
So I've used a lot of fancy words, but the general idea is simple.
Air comes in through a pipe.
The pipe gets thinner and thinner and thinner and they end up at these little air sacs.
And you're saying, well, how does that get the oxygen into my system?
Well, the key here is that these air sacs are super small and have very, very, very thin walls-- or I guess thin membranes.
So let me zoom in.
So if I were to zoom in on one of these alveoli-- and just to give you an idea, these are super duper duper small.
I've drawn them fairly large here, but each alveoli-- let me draw a little bit bigger.
Let me draw these air sacs.
So you have these air sacs like this.
And then you have a bronchiole that's terminating in that air sac.
Maybe a bronchiole is terminating in another air sac just like that-- another set of air sacs just like that.
Each of these are only 200 to 300 microns in diameter.
So that distance right there-- let me switch colors-- that distance right there is 200 to 300 microns.
And in case you don't know what a micron is, a micron is a millionth of a meter-- or you can view it as a thousandth of a millimeter.
So this is 200 thousandths of a millimeter.
Or you can think of them as-- and this is actually a very easy way to visualize it-- this is about one fifth of a millimeter.
So if I actually try to draw it on the screen-- if you made this full screen, a millimeter is about that far.
Maybe a little farther than that.
Maybe about that far.
So imagine a fifth of that and that's what we're talking about the diameter of one of these things.
And just to put it in the whole scheme relative to cells, the average cell in the human body is about 10 microns.
So this is only about 20 or 30 cells in diameter or relative to the average cell in the human body.
So these have a super thin membrane.
If you view them as balloons, the balloon is very thin-- pretty much one cell thick and they're connected to the bloodflow-- or actually, a better way to think about is that our circulatory system passes right next to each of these things.
So you have blood vessels that come from the heart and they want to be oxygenated.
In general, the blood vessels that don't have oxygen-- and
I'm going to do this in a lot more detail when I make the videos about the heart and our circulation system-- the blood vessels that don't have oxygen-- de-oxygenated blood is a little bit darker.
It looks a little bit purplish.
So I'll draw it as blue.
So these are vessels that are coming from the heart.
So this blood right here has no oxygen in it or it's been de-oxygenated or it has very little oxygen in it.
And the word for the blood vessels that comes from the heart are arteries.
Let me write that down.
I'll review that again when we cover it in the heart.
So arteries are blood vessels from the heart.
And you've probably heard of arteries.
Vessels that go to the heart are called veins.
This is really important to keep in mind because later on, you're going to see that arteries don't always carry oxygen or they're always not de-oxygenated and veins always aren't one way or the other.
We're going to go into a lot more detail when we actually cover the heart and the circulatory system, but just remember, arteries go away.
Veins go to the heart.
So here, these are arteries going away from the heart to the lungs, to the alveoli because they want the blood that's traveling in them to get oxygen.
So what's going to happen is that the air is flowing through the bronchioles and circulating around the alveoli, filling the alveoli-- and as they fill the alveoli, the little molecules of oxygen are allowed to cross the membrane of the alveoli and essentially be absorbed into the blood.
I'll do a lot more on that when we talk about hemoglobin and red blood cells, but you just have to realize that there's just a lot of capillaries.
Capillaries are just super small blood vessels that allow air to pass-- essentially oxygen and carbon dioxide molecules to pass between them.
These have a lot of capillaries on them that allow the exchange of gases.
So the oxygen can go into this blood and so once the oxygen-- so this is the vessel that's coming from the heart and then it's just a tube.
So then once it gets the oxygen, it's going to go back to the heart.
And so essentially this is the point where this vessel, this pipe, part of our circulatory system, goes from being an artery-- because it's coming from the heart-- to a vein because it's going back to the heart.
And there's a special word for these arteries and veins.
They're called pulmonary arteries and veins.
So going away from the heart to the lungs, to the alveoli, these are the pulmonary arteries.
And going back to the heart are the pulmonary veins.
Now you're saying, Sal, what does pulmonary mean?
Well, pulmo comes from the Latin for the lungs.
It literally means the arteries that are of the lungs or that go to the lungs and the veins that come from the lungs.
So anytime people talk about pulmonary anything, they're talking about our lungs-- or maybe something related to how we breathe.
So it's a good word to know.
So anyway, you have your oxygen coming in through your mouth or your nose, through the pharynx-- it could fill your stomach.
We can blow up our stomach like a balloon, but that doesn't help us actually get oxygen to our blood stream.
But the oxygen will come through our larynx, into our trachea, through the bronchi, eventually in bronchioles, ending up in alveoli and being able to be absorbed into what where the arteries, but then we're going to go back and then essentially oxygenate the blood.
The red blood cells become red once the hemoglobin becomes very red or scarlet once it actually has the oxygen and then we go back.
But at the same time, this isn't just about getting oxygen into our arteries or onto the hemoglobin.
It's also about releasing carbon dioxide.
So these blue arteries coming from the lungs are also going to release carbon dioxide into the alveoli.
And these will be exhaled.
So we have oxygen coming in.
Other things will be coming in, but the O2 is what gets absorbed in the alveoli.
And then when we breathe out, we're going to have carbon dioxide that was in our blood, but then it gets absorbed into the alveoli and they get squeezed out.
I'm going to tell you in a second how it gets squeezed.
It's actually that squeezing out that actually-- when the air goes back out, it can vibrate my vocal cords and it'll allow me to talk, but I'm not going to go into too much detail about that.
So the last thing to consider about this whole pulmonary system or about our lungs is, how does it force the air in and how does it force the air out?
And the way it's done is really kind of like a-- you could imagine it's kind of a pump or a balloon-- is that we have this huge layer of flat muscles.
Let me pick a good color here.
Right below the lungs-- and this is called a thoracic diaphragm.
And so when it's relaxed, it kind of has this arch shape, and so the lungs are kind of squeezed in.
They don't have a lot of volume.
But when I essentially breathe in, what's happening is this thoracic diaphragm is contracted and when it's contracted, it gets shorter, but more importantly, it opens up the space where my lungs are.
So my lungs can fill up that space.
So what it does is, it essentially-- it's like pulling a balloon larger, making the volume of my lungs larger.
And when you make the volume of something larger-- so the
lungs will become larger as my thoracic diaphragm is contracted and it kind of arches down, creates more space-- and as the volume of something becomes larger, the pressure inside of them goes down.
If you remember from physics, the pressure times volume is a constant.
So when we breathe in, our brain is essentially telling our diaphragm to contract.
We have more space around our lungs.
Our lungs expand to fill the space.
We have less pressure here than we have outside-- or you can view it as negative pressure.
So air always wants to go from high pressure to low pressure and so air is going to flow into our lungs.
And hopefully there'll be some oxygen there that can then essentially go into our alveoli and end up in our arteries and then go back in the veins as oxygen attached to hemoglobin.
I'll talk more about that in detail.
And then when we stop contracting the diaphragm, it goes back to this arched position.
It contracts.
It's kind of like a rubber band.
It contracts back the lungs and it essentially expels the air back and now that air's going to have a lot more carbon dioxide.
And just to get a sense of-- I can look at my lungs-- I can't look at them, but they don't seem too large.
How do I get enough oxygen in them-- and the key is, is that because of this branching process and the alveoli, the inside surface area of the lungs are actually much larger than you can imagine-- or actually than I could have imagined had someone not told me.
So it actually turns out-- I looked it up-- the internal surface area of your alveoli-- so the total surface area where the oxygen can be absorbed in or the carbon dioxide can be absorbed out from the blood-- it's actually 75 square meters.
That's meters, not feet.
If you think about it, that's like a-- imagine some type of a tarp or a field.
That's almost nine by nine meters.
That's almost 27 by 27 square feet.
That's the size of some people's backyards.
That's how much surface air you have inside of your lungs.
It's all folded up.
That's how it gets jammed into what look like relatively small lungs.
But that's what gives us enough surface area for enough of the air, enough of the oxygen, to cross the alveoli membrane into our blood system and enough of the carbon dioxide to go back in.
And just to have a sense of how many alveoli we had-- I told you that they're very small-- we actually have 300 million in each lung.
In each lung, we have 300 million alveoli.
So anyway, hopefully that gives you a decent sense of how we at least get oxygen into our blood system and carbon dioxide out of it.
In the next video, I'll talk more about our actual circulatory system and how we get the oxygen from the lungs to the rest of the body and how do we get the carbon dioxide from the rest of the body into the lungs?
I'm five years old, and I am very proud.
My father has just built the best outhouse in our little village in Ukraine.
Inside, it's a smelly, gaping hole in the ground, but outside, it's pearly white formica and it literally gleams in the sun.
This makes me feel so proud, so important, that I appoint myself the leader of my little group of friends and I devise missions for us.
So we prowl from house to house looking for flies captured in spider webs and we set them free.
Four years earlier, when I was one, after the Chernobyl accident, the rain came down black, and my sister's hair fell out in clumps, and I spent nine months in the hospital.
There were no visitors allowed, so my mother bribed a hospital worker.
She acquired a nurse's uniform, and she snuck in every night to sit by my side.
Five years later, an unexpected silver lining.
Thanks to Chernobyl, we get asylum in the U.S.
I am six years old, and I don't cry when we leave home and we come to America, because I expect it to be a place filled with rare and wonderful things like bananas and chocolate and Bazooka bubble gum, Bazooka bubble gum with the little cartoon wrappers inside,
Bazooka that we'd get once a year in Ukraine and we'd have to chew one piece for an entire week.
So the first day we get to New York, my grandmother and I find a penny in the floor of the homeless shelter that my family's staying in.
Only, we don't know that it's a homeless shelter.
We think that it's a hotel, a hotel with lots of rats.
So we find this penny kind of fossilized in the floor, and we think that a very wealthy man must have left it there because regular people don't just lose money.
And I hold this penny in the palm of my hand, and it's sticky and rusty, but it feels like I'm holding a fortune.
I decide that I'm going to get my very own piece of Bazooka bubble gum.
And in that moment, I feel like a millionaire.
About a year later, I get to feel that way again when we find a bag full of stuffed animals in the trash, and suddenly I have more toys than I've ever had in my whole life.
And again, I get that feeling when we get a knock on the door of our apartment in Brooklyn, and my sister and I find a deliveryman with a box of pizza that we didn't order.
So we take the pizza, our very first pizza, and we devour slice after slice as the deliveryman stands there and stares at us from the doorway.
And he tells us to pay, but we don't speak English.
My mother comes out, and he asks her for money, but she doesn't have enough.
She walks 50 blocks to and from work every day just to avoid spending money on bus fare.
Then our neighbor pops her head in, and she turns red with rage when she realizes that those immigrants from downstairs have somehow gotten their hands on her pizza.
Everyone's upset.
But the pizza is delicious.
It doesn't hit me until years later just how little we had.
On our 10 year anniversary of being in the U.S., we decided to celebrate by reserving a room at the hotel that we first stayed in when we got to the U.S.
The man at the front desk laughs, and he says,
"You can't reserve a room here. This is a homeless shelter."
And we were shocked.
My husband Brian was also homeless as a kid.
His family lost everything, and at age 11, he had to live in motels with his dad, motels that would round up all of their food and keep it hostage until they were able to pay the bill.
And one time, when he finally got his box of Frosted Flakes back, it was crawling with roaches.
But he did have one thing.
He had this shoebox that he carried with him everywhere containing nine comic books, two G.I. Joes painted to look like Spider-Man and five Gobots.
And this was his treasure.
This was his own assembly of heroes that kept him from drugs and gangs and from giving up on his dreams.
I'm going to tell you about one more formerly homeless member of our family.
This is Scarlett.
Once upon a time, Scarlet was used as bait in dog fights.
She was tied up and thrown into the ring for other dogs to attack so they'd get more aggressive before the fight.
And now, these days, she eats organic food and she sleeps on an orthopedic bed with her name on it, but when we pour water for her in her bowl, she still looks up and she wags her tail in gratitude.
Sometimes Brian and I walk through the park with Scarlett, and she rolls through the grass, and we just look at her and then we look at each other and we feel gratitude.
We forget about all of our new middle-class frustrations and disappointments, and we feel like millionaires.
Thank you.
(Applause)
Indian Story:
Hindus and Muslims
In Tamil Nadu we live in peace without the barrier of race, culture and language
Hindu and Christian brothers will attend and participate in a Muslim wedding as though it's their own family function
We can see the happiness in their eyes
That's the spirit of unity and brotherhood that we have there
In my hometown Rameshwaram, my friend's sister got married...
They printed my name as their brother in the Hindu wedding invitation
We've gone over the general idea behind mitosis and meiosis.
It's a good idea in this video to go a little bit more in detail.
I've already done a video on mitosis, and in this one, we'll go into the details of meiosis.
Just as a review, mitosis, you start with a diploid cell, and you end up with two diploid cells.
Essentially, it just duplicates itself.
And formally, mitosis is really the process of the duplication of the nucleus, but it normally ends up with two entire cells.
Cytokinesis takes place.
So this is mitosis.
We have a video on it where we go into the phases of it: prophase, metaphase, anaphase and telophase.
Mitosis occurs in pretty much all of our somatic cells as our skin cells replicate, and our hair cells and all the tissue in our body as it duplicates itself, it goes through mitosis.
Meiosis occurs in the germ cells and it's used essentially to produce gametes to facilitate sexual reproduction.
So if I start off with a diploid cell, and that's my diploid cell right there, this would be a germ cell.
It's not just any cell in the body.
It's a germ cell.
It could undergo mitosis to produce more germ cells, but we'll talk about how it produces the gametes.
It actually goes under two rounds.
They're combined, called meiosis, but the first round you could call it meiosis 1, so I'll call that M1.
I'm not talking about the money supply here.
And in the first round of meiosis, this diploid cell essentially splits into two haploid cells.
So if you started off with 43 chromosomes, formally have 23 chromosomes in each one, or you can almost view it if you have 23 pairs here, each have two chromosomes, those pairs get split into this stage.
And then in meiosis 2, these things get split in a mechanism very similar to mitosis.
We'll see that when we actually go through the phases.
In fact, the prophase, metaphase, anaphase, telophase also exist in each of these phases of meiosis.
So let me just draw the end product.
The end product is you have four cells and each of them are haploid.
And you could already see, this process right here, you essentially split up your chromosomes, because you end up with half in each one, but here, you start with N and you end up with two chromosomes that each have N, so it's very similar to this.
You preserve the number of chromosomes.
So let's delve into the details of how it all happens.
So all cells spend most of their time in interphase.
Interphase is just a time when the cell is living and transcribing and doing what it needs to do.
But just like in mitosis, one key thing does happen during the interphase, and actually, it happens during the same thing, the S phase of the interphase.
So if that's my cell, that's my nucleus right here.
And I'm going to draw it as chromosomes, but you have to remember that when we're outside of mitosis or meiosis formally, the chromosomes are all unwound, and they exist as chromatin, which we've talked about before.
It's kind of the unwound state of the DNA.
But I'm going to draw them wound up because I need to show you that they replicate.
Now, I'm going to be a little careful here.
In the mitosis video, I just had two chromosomes.
They replicated and then they split apart.
When we talk about meiosis, we have to be careful to show the homologous pairs.
So let's say that I have two homologous pairs.
So let's say I have-- let me do it in appropriate colors.
So this is the one I got from my dad.
This is the one I got from my mom.
They're homologous.
And let's say that I have another one that I got from my dad.
Let me do it in blue.
Actually, maybe I should do all the ones from my dad in this color.
Maybe it's a little bit longer.
You get the idea.
And then a homologous one for my mom that's also a little bit longer.
Now, during the S phase of the interphase-- and this is just like what happens in mitosis, so you can almost view it as it always happens during interphase.
It doesn't happen in either meiosis or mitosis.
You have replication of your DNA.
So each of these from the homologous pair-- and remember, homologous pairs mean that they're not identical chromosomes, but they do code for the same genes.
They might have different versions or different alleles for a gene or for a certain trait, but they code essentially for the same kind of stuff.
Now, replication of these, so each of these chromosomes in this pair replicate.
So that one from my dad replicates like this, it replicates and it's connected by a centromere, and the one from my mom replicates like that, and it's connected by a centromere like that, and then the other one does as well.
That's the shorter one.
Oh, that's the longer one, actually.
That's the longer one.
I should be a little bit more explicit in which one's shorter and longer.
The one from my mom does the same thing.
This is in the S phase of interphase.
We haven't entered the actual cell division yet.
And the same thing is true-- and this is kind of a little bit of a sideshow-- of the centrosomes.
And we saw in the mitosis video that these are involved in kind of eventually creating the microtubule structure in pulling everything apart, but you'll have one centrosome that's hanging out here, and then it facilitates its own replication, so then you have two centrosomes.
So this is all occurring in the interphase, and particularly in the S part of the interphase, not the growth part.
But once that's happens, we're ready-- in fact, we're ready for either mitosis or meiosis, but we're going to do meiosis now.
This is a germ cell.
So what happens is we enter into prophase I.
So if you remember, in my-- let me write this down because I think it's important.
In mitosis you have prophase, metaphase, anaphase and telophase.
I won't keep writing phase down.
PMAT.
In meiosis, you experience these in each stage, so you have to prophase I, followed by metaphase I, followed by anaphase I, followed by telophase I.
Then after you've done meiosis 1, then it all happens again.
You have prophase Il, followed by metaphase Il, followed by anaphase Il, followed by telophase.
So if you really just want to memorize the names, which you unfortunately have to do in this, especially if you're going to get tested on it, although it's not that important to kind of understand the concept of what's happening, you just have to remember prophase, metaphase, anaphase, telophase, and it'll really cover everything.
You just after memorize in meiosis, it's happening twice.
And what's happening is a little bit different, and that's what I really want to focus on here.
So let's enter prophase I of meiosis I.
So let me call this prophase I.
So what's going to happen?
So just like in prophase and mitosis, a couple of things start happening.
Your nuclear envelope starts disappearing.
The centromeres-- sorry, not centromeres.
I'm getting confused now.
The centrosomes.
The centromeres are these things connecting these sister chromatids.
The centrosomes start facilitating the development of the spindles, and they start pushing apart a little bit from the spindles.
They start pushing apart and going to opposite sides of the chromosomes.
And this is the really important thing in prophase I.
And actually, I'll make this point.
Remember, in interface, even though I drew it this way, they don't exist in this state, the actual chromosomes.
They exist more in a chromatin state.
So if I were to really draw it, it would look like this.
The chromosomes, it would all be all over the place, and it actually would be very difficult to actually see it in a microscope.
It would just be a big mess of proteins and of histones, which are proteins, and the actual DNA.
And that's what's actually referred to as the chromatin.
Now, in prophase, that starts to form into the chromosomes.
It starts to have a little bit of structure, and this is completely analogous to what happens in prophase in mitosis.
Now, the one interesting thing that happens is that the homologous pairs line up.
And actually, I drew it like that over here and maybe I should just cut and paste it.
Let me just do that.
If I just cut and paste that, although I said that the nucleus is disappearing, so let me get rid of the nucleus.
I already said that.
The nucleus is slowly disassembling.
The proteins are coming apart during this prophase I.
I won't draw the whole cell, because what's interesting here is happening at the nuclear, or what once was the nucleus level.
So the interesting thing here that's different from mitosis is that the homologous pairs line up next to each other.
Not only do they line up, but they can actually share-- they can actually have genetic recombination.
So you have these points where analogous-- or I guess you could say homologous-- points on two of these chromosomes will cross over each other.
So let me draw that in detail.
So let me just focus on maybe these two right here.
So I have one chromosome from my dad, and it's made up of two chromatids, so it's already replicated, but we only consider it one chromosome, and then I have one from my mom in green.
I'm going to draw it like that.
One from my mom in green, and it also has two chromatids.
Sometimes this is called a tetrad because it has four chromatids in it, but it's in a pair of homologous chromosomes.
These are the centromeres, of course.
What happens is you have crossing over, and it's a surprisingly organized process.
When I say organized, it crosses over at a homologous point.
It crosses over at a point where, for the most part, you're exchanging similar genes.
It's not like one is getting two versions of a gene and the other is getting two versions of another gene.
You're changing in a way that both chromosomes are still coding for the different genes, but they're getting different versions of those genes or different alleles, which are just versions of those genes.
So once this is done, the ones from my father are now not completely from my father, so it might look something like this.
Let me see, it'll look like this.
The one from my father now has this little bit from my mother, and the one from my-- oh, no, my mother's chromosome is green-- a little bit from my mother, and the one from my mother has a little bit from my father.
And this is really amazing because it shows you that this is so favorable for creating variation in a population that it has really become a formal part of the meiosis process.
It happens so frequently.
This isn't just some random fluke, and it happens in a reasonably organized way.
It actually happens at a point where it doesn't kind of create junk genes.
Because you can imagine, this cut-off point, which is called a chiasma, it could have happened in the middle of some gene, and it could have created some random noise, and it could have broken down some protein development in the future or who knows what.
But it doesn't happen that way.
It happens in a reasonably organized way, which kind of speaks to the idea that it's part of the process.
So prophase in I, you also have this happening.
So once that happens you could have this guy's got a little bit of that chromatid and then this guy's got a little bit of that chromatid.
So all of this stuff happens in prophase I.
You have this crossing over.
The nuclear envelope starts to disassemble, and then all of these guys align and the chromatin starts forming into these more tightly wound structures of chromosomes.
And really, that's all-- when we talk about even mitosis, that's where a lot of the action really took place.
Once that happens, then we're ready to enter into the metaphase I, so let's go down to metaphase I.
In metaphase I-- let me just copy and paste what I've already done-- the nuclear envelope is now gone.
The centrosomes have gone to opposite sides of the cell itself.
Maybe I should draw the entire cell now that there's no nucleus.
Let me erase the nucleus a little bit better than I've done.
Let me erase all of that.
And, of course, we have the spindles fibers that have been generated by now with the help of the centrosomes.
And some of them, as we learned, this is exactly what happened in mitosis.
They attach to the kinetochores, which are attached to the centromeres of these chromosomes.
Now, what's interesting here is that they each attach-- so this guy's going to attach to-- and actually, let me do something interesting here.
Instead of doing it this way, because I want to show that all my dad's chromosomes don't go to one side and all my mom's chromosomes don't go to the other side.
So instead of drawing these two guys like this, let me see if I can flip them.
Let me see.
Let me just flip them the other way.
Whether or not which direction they're flipped is completely random, and that's what adds to the variation.
As we said before, sexual reproduction is key to introducing variation into a population.
So that's the mom's and that's the dad's.
They don't have to.
All of the ones from my dad might have ended up on one side and all of them from my mom might end up on one side, although when you're talking about 23 pairs, the probability becomes a lot, lot lower.
So this is one from my dad.
Of course, it has some centromeres.
Let me draw that there.
And so these microspindles, some of them attach to kinetochores, which are these protein structures on the centromeres.
And this is just like metaphase.
It's very similar to metaphase in mitosis.
This is called metaphase I, and everything aligns.
Now we're going to enter anaphase I.
Now, anaphase I is interesting, because remember, in mitosis in anaphase, the actual chromatids, the sister chromatids separated from each other.
That's not the case in anaphase I here in meiosis.
So when we enter anaphase I, you have just the homologous pairs separate, so the chromatids stay with their sister chromatids.
So on this side, you'll have these to go there.
While I have the green out, let me see if I can draw this respectably.
I have the purple.
It's a little bit shorter version here.
He's got a little bit of a stub of green there.
This guy's got little stub of purple there.
And then they have this longer purple chromosome here.
This is anaphase I.
They're being pulled apart, but they're being pulled apart-- the homologous pair is being pulled apart, not the actual chromosomes, not the chromatids.
So let me just draw this.
So then you have your microtubules.
Some are connected to these kinetochores.
You have your centromeres.
Of course, all of this is occurring within the cell and these are getting pulled apart.
So it's analogous to anaphase in mitosis, but the key difference is you're pulling apart homologous pairs. You're not actually splitting the chromosomes into their constituent chromatids, and that's key.
And if you forget that, you can review the mitosis video.
So this is anaphase I.
And then as you could imagine, telophase I is essentially once these guys are at their respective ends of the cell-- it's getting tiring redrawing all of these, but I guess it gives you time to let it all sink in.
So these guys are now at the left end of the cell and these guys are now at the right end of the cell.
Now, the microtubules start to disassemble.
So maybe they're there a little bit, but they're disassembling.
You still have your centromeres here and they're at opposite poles.
And to some degree, in the early part of telophase, they're still pushing the cell apart, and at the same time, you have cytokinesis happening.
So by the end of telophase I, you have the actual cytoplasm splitting during telophase right there, and the nuclear envelope is forming.
You can almost view it as the opposite of prophase.
The nuclear envelope is forming, and by the end of telophase I, it will have completely divided.
So this is telophase I.
Now, notice: we started off with a diploid cell, right?
It had two pairs of homologous chromosome, but it had four chromosomes.
Now, each cell only has two chromosomes.
Essentially, each cell got one of the pair of each of those homologous pairs, but it was done randomly, and that's where a lot of the variation is introduced.
Now, once we're at this stage, each of these cells now undergo meiosis Il, which is actually very similar to mitosis.
And sometimes, there's actually an in-between stage called interphase Il, where the cell kind of rests and whatever else, and actually the centromeres now have to duplicate again.
So these two cells-- I've drawn them separately-- let's see what happens next.
So let's say that the centromere-- actually, I shouldn't have drawn the centromere inside the nucleus like that.
The centromere's going to be outside the nucleus, outside of the newly formed nucleus there and there.
And then it'll actually replicate itself at this point as well.
So now we have two cells.
Let me just cut and paste what I have. I have this one, this chromosome right here.
It's got this little green stub there and then I have this longer fully green chromosome there.
Now, this guy, he's got this little purple stub here.
Let me draw this whole purple chromosome there.
Then this guy has one chromatid like that and one chromatid like that.
Now, when we enter prophase Il, what do you think is going to happen?
Well, just like before, you have your nuclear envelope that formed in telophase I.
It's kind of a temporary thing.
It starts to disintegrate again.
And then you have your centromeres.
They start pushing apart so now I had two centromeres.
They replicated, and now they start pushing apart while they generate their little spindles.
They push apart in opposite directions.
Now, this is happening in two cells, of course.
They go in opposite directions while they generate their spindle fibers.
And let me make it very clear that this is two cells we're talking about.
That's one of them and that's the second of them.
Now it's going to enter metaphase Il, which is analogous to metaphase I, or metaphase in mitosis, where the chromosomes get lined up.
Let me draw it this way.
So now the centromeres, they've migrated to the two poles of the cell.
So those are my centromeres.
I have all of my spindles fibers.
Oh, sorry, did I call those centromeres?
The centrosomes.
I don't know how long I've been calling them centromeres.
These are centrosomes, and my brain keeps confusing them.
The centromeres, and maybe this'll help you not do what I just did, the centromeres are the things that are connecting the two sister chromatids.
Those are centromeres.
Centrosomes are the things that are pushing back the-- that generate the spindle fibers.
The chromosomes line up during metaphase.
Metaphase always involves the lining up of chromosomes so that one-- let me just draw it.
So I have that and that.
This one's got a purple guy, too.
This guy's got a purple guy, a long purple guy, and then there's a little stub for the other guy.
This guy's got a long green guy and this guy's got a little green stub, and then this is the short green guy right there.
And, of course, they're being aligned.
Some of these spindle fibers have been attached to the centromeres or the kinetochores that are on the centromeres that connect these two chromatids, these sister chromatids.
And, of course, we don't have a nuclear membrane anymore, and these are, of course, two separate cells.
And then you can guess what happens in anaphase Il.
It's just like anaphase in mitosis.
These things get pulled apart by the kinetochore microtubules, while the other microtubules keep growing and push and these two things further apart.
So let me show that.
And they the key here: this is the difference between anaphase II and anaphase I.
Anaphase I, the homologous pairs were broken up, but the chromosomes themselves were not.
Now, in anaphase Il, we don't have homologous pairs. We just have chromatid pairs, sister chromatids.
Now, those are separated, which is very similar to anaphase in mitosis.
So now, this guy gets pulled in that direction so it look something like this.
The drawing here is the hardest part of this video.
So that guy gets pulled there.
That guy's getting pulled in that direction.
He's got that little green stub on him.
And then you have one green guy getting pulled in that direction with the longer chromosome.
And then one of the other longer is getting pulled in that direction, and it's all by these microtubules connected at the kinetochore structures by a centrosome as kind of the coordinating body.
It's all being pulled apart.
Anaphase has always involved the pulling apart of the chromosomes or pulling apart of something.
Let me put it that way.
And it's happening on this side of the cell as well.
Of course, this is all one cell.
And just like in mitosis, as soon as the sister chromatids are split apart, they are now referred to as chromosomes, or sister chromosomes.
And, of course, this is happening twice.
This is also happening in the other cell.
The other cell's a little bit cleaner.
It didn't have that crossover occur.
So you have the longer purple one.
He gets split up into two chromatids, which we are now calling chromosomes, or sister chromosomes.
And then this guy up here, he gets split up into this short green, and then there's a-- let me do it this way-- this short green, and he's got a little purple stub on it right there.
And, of course, it's all being pulled away by the same idea, by the centrosomes.
I want to make sure I get that word right.
I'm afraid whether I used centromeres for the whole first part of the video, but hopefully, my confusion will help you from getting confused because you'll realize that it's a pitfall to fall into.
So that's anaphase.
Everything is getting pulled apart.
And then you can imagine what telophase II is.
In fact, I won't even redraw it.
Telophase Il, these things get pulled apart even more, so this is telophase Il.
They get pulled apart even more.
The cell elongates.
You start having this cleavage occur right here.
So at the same time that in telophase II these get pulled part, you have the cytokinesis.
The tubules start disintegrating and then you have a nucleus that forms around these.
So what is the end result of all of these?
Well, that guy's going to turn into a nucleus that has this purple dude with a little green stub, and then a long green guy, and then he's got his nuclear membrane.
And, of course, there's the entire cytoplasm in the rest of the cell.
The other person that was his kind of partner in this meiosis Il, he's going to have a short purple and a long green.
He has a nuclear membrane, and, of course, it has cytoplasm around it.
And then on this side, you have something similar happening.
You see this first guy, this first one right here has two long purple ones.
They get separated.
So let me see, you have one long purple in that cell and you have another long purple in this cell.
In that top one, you have a short green one, and in this bottom, you have a short green one that had got a little bit of one of my dad's-- a homologous part of one of my dad's chromosomes on it.
And, of course, these also have nuclear membranes, nuclear membranes, and, of course, it has a cytoplasm in the rest of the cell, which we'll learn more about all those other things.
So what we see here is that we went from a diploid starting way-- where did we start?
We started up here with a diploid germ cell, and we went through two stages of division.
The first stage split up homologous pairs, but it started over with that crossing over, that genetic combination, which is a key feature of meiosis, which adds a lot a variation to a species or to a gene pool.
And then the second phase separated the sister chromatids, just like what happens in mitosis.
And we end up with four haploid cells because they have half the contingency of chromosomes, and these are called gametes.
Write the prime factorization of 75.
Write your answer using exponential notation.
So we have a couple of interesting things here.
Prime factorization, and they say exponential notation.
We'll worry about the exponential notation later.
So the first thing we have to worry about is what is even a prime number?
And just as a refresher, a prime number is a number that's only divisible by itself and one, so examples of prime numbers-- let me write some numbers down.
Prime, not prime. Not prime.
So 2 is a prime number.
It's only divisible by 1 and 2.
3 is another prime number.
Now, 4 is not prime, because this is divisible by 1, 2 and 4.
We could keep going.
5, well, 5 is only divisible by 1 and 5, so 5 is prime.
6 is not prime, because it's divisible by 2 and 3.
I think you get the general idea.
You move to 7, 7 is prime.
It's only divisible by 1 and 7.
8 is not prime.
9 you might be tempted to say is prime, but remember, it's also divisible by 3, so 9 is not prime.
Prime is not the same thing as odd numbers.
Then if you move to 10, 10 is also not prime, divisible by 2 and 5.
11, it's only divisible by 1 and 11, so 11 is then a prime number.
And we could keep going on like this.
People have written computer programs looking for the highest prime and all of that.
So now that we know what a prime is, a prime factorization is breaking up a number, like 75, into a product of prime numbers.
So let's try to do that.
So we're going to start with 75, and I'm going to do it using what we call a factorization tree.
So we first try to find just the smallest prime number that will go into 75.
Now, the smallest prime number is 2.
Does 2 go into 75?
Well, 75 is an odd number, or the number in the ones place, this 5, is an odd number.
5 is not divisible by 2, so 2 will not go into 75.
So then we could try 3.
Does 3 go into 75?
Well, 7 plus 5 is 12.
12 is divisible by 3, so 3 will go into it.
So 75 is 3 times something else.
And if you've ever dealt with change, you know that if you have three quarters, you have 75 cents, or if you have 3 times 25, you have 75.
So this is 3 times 25.
And you can multiply this out if you don't believe me.
Multiple out 3 times 25.
Now, is 25 divisible by-- you can give up on 2.
If 75 wasn't divisible by 2, 25's not going to be divisible by 2 either.
But maybe 25 is divisible by 3 again.
So if you take the digits 2 plus 5, you get 7.
7 is not divisible by 3, so 25 will not be divisible by 3.
So we keep moving up: 5. Is 25 divisible by 5?
Well, sure.
It's 5 times 5.
So 25 is 5 times 5.
And we're done with our prime factorization because now we have all prime numbers here.
So we can write that 75 is 3 times 5 times 5.
So 75 is equal to 3 times 5 times 5.
We can say it's 3 times 25.
25 is 5 times 5.
3 times 25, 25 is 5 times 5.
So this is a prime factorization, but they want us to write our answer using exponential notation.
So that just means, if we have repeated primes, we can write those as an exponent.
So what is 5 times 5?
5 times 5 is 5 multiplied by itself two times.
This is the same thing as 5 to the second power.
So if we want to write our answer using exponential notation, we could say this is equal to 3 times 5 to the second power, which is the same thing as 5 times 5.
Space - there's only so much.
And when you run out...
That's it.
Or is it?
What if you could do more with the space you have?
What if there was a smarter way to use space?
There is.
Let's imagine a room everyone uses.
24 hours a day.
It's a living room.
It's a playroom.
We'd better make it easy to clean up.
And if we use this space up here, it can also be a bedroom.
Smart.
Stackable stools, drawers on wheels, a bed up in the air.
Small ideas can transform a small space into a generous space-
-that works for everyone.
It's about maximising space - being a little creative with how you use it.
So, what if we get a little creative with a space like this.
Does a living room really need a sofa?
What if we tried something different?
There, we just created a whole wall for storage.
And a cosy little nest for two.
Now everyone can do what they want.
At the same time.
Together.
And being together is a good thing, right?
So, let's try something completely different.
Here are six friends.
And this is where they live.
Together.
Why not? With bunk beds, curtains for privacy-
-and a big communal table to gather around.
It can work.
To make the most of the space you've got all you need is an open mind.
And a few smart, small ideas.
It's about finding and using hidden spaces-
-and choosing furniture that does more than one thing.
And it works.
No matter how much or how little space you have.
It's not about giving up your dreams.
It's about shrinking them, just a little bit.
It's about making space do more.
Even more than you could imagine.
And it's not about waiting.
It's about doing it today.
A dream home doesn't need to be big...
Just smart.
And it's kind of funny when you think about it.
The space you've been looking for-
-it's been right there.
Welcome to the second presentation on functions. So let's take off where we left off before. I still apologize -- in retrospect that that whole Sal food example.
Let's do some more problems.
Let's start off with an example, not too different than what we saw before. Let's say that g of x is equal to 1 if x is even, and it equals 0 if x is odd. And let's say f of x is equal to x plus 3 times g of x.
We just literally took this 5 and replace it everywhere where we see an x.
If instead of a 5, I had like a dog here, it would be f of dog would equal dog plus 3 times g of dog. Not that that would necessarily make any sense, but you get the idea. So f of 5 equals 5 plus 3 times g of 5.
So the 5 stays the same, plus 3 times -- well what's g of 5? Well, if we put 5 here, if 5 is even we do 1, if five is odd we do 0. Well 5 is odd so it's a 0.
At first you might say wow, this is crazy, Sal, I don't know how to even start here. But you just take it step-by-step. What can we figure out?
So it's 2 times 3, so that's 6, plus f of -- what, we'll just replace the x again. 3 minus 3, right? So this g of 3 is equal to 6 plus f of what?
3 minus 3 is 0. Now we have to figure out f of 0 is. We have a definition here for f, so we just figure it out. f of 0 is equal to -- well, you replace the 0 here.
I have a definition of what the function g does when it's given an x, or in this case, was given a 3. And that's what we did. We figured out what g of 3 was first.
You can sit and think a little bit about what we just did while I erase.
So let's do another problem. What is f of h of 10?
Well, first we want to figure out what h of 10 is, right? Well, we could do it in a different way as we'll see later. But we can figure out what h of 10 is pretty easily.
And then f of 50 is, I think pretty straightforward at this point. You just take that 50 and replace it back here. Well, it's 50 squared plus 1.
That equals 2,501. What is g of h of 1? Well, we take h of 1, h of 1 is 5, so this is equal to g of 5.
Well, 2 squared plus 1 is 5, right? f of 2 is 5
-- 2 squared plus 1. So that equals 10 plus 5 which equals 15. If you're still confused, don't worry.
We need to divide 0.25 into 1.03075.
Now the first thing you want to do when your divisor, the number that you're dividing into the other number, is a decimal, is to multiply it by 10 enough times so that it becomes a whole number so you can shift the decimal to the right.
So every time you multiply something by 10, you're shifting the decimal over to the right once.
So in this case, we want to switch it over the right once and twice.
So 0.25 times 10 twice is the same thing as 0.25 times 100, and we'll turn the 0.25 into 25.
Now if you do that with the divisor, you also have to do that with the dividend, the number that you're dividing into.
So we also have to multiply this by 10 twice, or another way of doing it is shift the decimal over to the right twice.
So we shift it over once, twice.
It will sit right over here.
And to see why that makes sense, you just have to realize that this expression right here, this division problem, is the exact same thing as having 1.03075 divided by 0.25.
And so we're multiplying the 0.25 by 10 twice.
We're essentially multiplying it by 100.
Let me do that in a different color.
We're multiplying it by 100 in the denominator.
This is the divisor.
We're multiplying it by 100, so we also have to do the same thing to the numerator, if we don't want to change this expression, if we don't want to change the number.
So we also have to multiply that by 100.
And when you do that, this becomes 25, and this becomes 103.075.
Now let me just rewrite this.
Sometimes if you're doing this in a workbook or something, you don't have to rewrite it as long as you remember where the decimal is.
But I'm going to rewrite it, just so it's a little bit neater.
So we multiplied both the divisor and the dividend by 100.
This problem becomes 25 divided into 103.075.
These are going to result in the exact same quotient.
They're the exact same fraction, if you want to view it that way.
We've just multiplied both the numerator and the denominator by 100 to shift the decimal over to the right twice.
Now that we've done that, we're ready to divide.
So the first thing, we have 25 here, and there's always a little bit of an art to dividing something by a multiple-digit number, so we'll see how well we can do.
So 25 does not go into 1.
25 does not go into 10.
25 does go into 103.
We know that 4 times 25 is 100, so 25 goes into 100 four times.
4 times 5 is 20.
4 times 2 is 8, plus 2 is 100.
We knew that.
Four quarters is $1.00.
It's 100 cents.
And now we subtract.
103 minus 100 is going to be 3, and now we can bring down this 0.
So we bring down that 0 there.
25 goes into 30 one time.
And if we want, we could immediately put this decimal here.
We don't have to wait until the end of the problem.
This decimal sits right in that place, so we could always have that decimal sitting right there in our quotient or in our answer.
So we were at 25 goes into 30 one time.
1 times 25 is 25, and then we can subtract.
30 minus 25, well, that's just 5.
I mean, we can do all this borrowing business, or regrouping.
This can become a 10.
This becomes a 2.
10 minus 5 is 5.
2 minus 2 is nothing.
But anyway, 30 minus 25 is 5.
Now we can bring down this 7.
25 goes into 57 two times, right?
25 times 2 is 50.
25 goes into 57 two times.
2 times 25 is 50.
And now we subtract again.
57 minus 50 is 7.
And now we're almost done.
We bring down that 5 right over there.
25 goes into 75 three times.
3 times 25 is 75.
3 times 5 is 15.
Regroup the 1.
We can ignore that.
That was from before.
3 times 2 is 6, plus 1 is 7.
So you can see that.
And then we subtract, and then we have no remainder.
So 25 goes into 103.075 exactly 4.123 times, which makes sense, because 25 goes into 100 about four times.
This is a little bit larger than 100, so it's going to be a little bit more than four times.
And that's going to be the exact same answer as the number of times that 0.25 goes into 1.03075.
This will also be 4.123.
So this fraction, or this expression, is the exact same thing as 4.123.
And we're done!
J.T. loves burgers and loves to subscribes to a cell phone texting plan with three other members of his family.
Within any given month, they cannot send more than 500 text messages total.
So they cannot send more than 500 text messages total.
At the end of this month, J.T. had sent 25 more texts than his older sister.
Let me highlight.
Let me do this in different colors.
So at the end of the month, J.T. had sent 25 more texts than his older sister, 50 fewer texts than his younger sister, and 125 more texts than his mother.
How may texts could J.T. have sent if they did not go over the 500-text limit?
So let's just define some variables over here. Well, let's say o.s. o dot s is, well let's just say o, o is for older sister.
So this is number of texts by older sister.
Let's say that y is equal to number of texts by his younger sister.
And then we'll use m is equal to the number of texts by his mother.
And we'll use j for a number of texts by J.T.
So the total number of texts that everyone sent cannot be more than 500.
So if we take the sum of J.T.'s texts, plus his older sister's texts, plus his younger sister's texts, plus his mother's texts, they all have to be less than or equal to 500 total texts.
Right, it can't be more than 500, so the sum has to be less than or equal to 500.
Now, how can we express each of these in terms of the number of texts J.T. sent?
Well, they give us some information here.
This first statement, J.T. had sent 24 more texts than his older sister.
So j is equal to 25 plus the number of texts of his older sister, which we say is o. It's not a 0, that's an o for older sister.
And they also tell us that J.T. sent 50 fewer texts than his younger sister, so j is also equal to the younger sister minus 50, right?
50 fewer texts than his younger sister. And then finally, they say 125 more texts than his mother, so j is equal to mother plus 125.
Now, I want this equation all in terms of j's, because we want to say how many texts could J.T. have sent.
So I want all of these expressed in j, so let's just solve each of these for o in terms of j, solve for y in terms of j, solve for m in terms of j, and then we can substitute back over here. So if j is equal to 25 plus o, if we subtract 25 from both sides of this equation, we get j minus 25 is equal to o.
These are the same thing.
If you just take this and subtract 25 from both sides, you get that right there.
Now here, if you add 50 to both sides of this equation, if you add to 50 to both sides of this equation, j plus 50 is equal to the number of texts that his younger sister sent.
I just added 50 to both sides.
And then over here, if you subtract 125 from both sides of this equation-- scroll over a little bit-- if you subtract 125 from both sides, you get j minus 125 is equal to the number of texts sent by his mother.
And we could have gone straight here.
This first statement, J.T. has sent 25 more texts than is older sister.
So if you take the number of texts J.T. sent, subtracted 25, you'd get the number of texts by his older sister.
That is an o, it is not a 0. o for older.
Likewise, he sent 50 fewer texts than his younger sister, so if you took the number of texts he sent, add 50 to it, you're going to get how many his younger sister had sent.
And then finally, he sent 125 more than his mother, so if you took J.T.'s texts, you take out 125, then that's how many his mother sent.
So now that we have this, we can substitute for each of these variables into the original equation.
So you have J.T.'s texts, plus his older sister's texts.
But we know that o is the same thing as J.T.'s texts minus 25, so we write J.T.'s texts minus 25.
And then you have plus his younger sister's texts, but we know that's J.T.'s texts plus 50.
And then you have his mother's texts, but his mother's texts are just J.T.'s texts minus 125, so plus j minus 125.
And all of that has to be less than or equal to 500. So let's add the j's.
We have 1, 2, 3, 4 j's, so you have 4 j's.
And let's add the constants.
You have a negative 25 plus a 50, which is 25.
And then you have 25 minus 125, so 25 minus 125 is negative 100.
So 4j minus 100-- I just added all the constant terms-- has to be less than or equal to 500.
And now this is a pretty straightforward inequality. Add 100 to both sides and we get 4j-- these cancel out-- we get 4j is less than or equal to 600.
Divide both sides by 4-- don't have to worry about the inequality since 4 is a positive number-- and we get j is less than or equal to 150.
So J.T. had to send less than or equal, he had to send 150 or fewer texts in that month in order for all the constraints to match up and for the family as a combined unit to send less than 500.
They call me here, Mr Singh, or Big Teacher
My name is Dino, I'm 24 years old
Hi I'm Danusha Cheraya, I'm Malaysian, and I'm 25 years old
Welcome to the presentation on adding and subtracting negative numbers.
So let's get started.
So what is a negative number, first of all?
Well, let me draw a number line.
Well it's not much of a line, but I think you'll get the picture.
So we're used to the positive numbers, so if that's 0 you have one, you have 2, you have 3, you have 4 and you keep going.
And if I were to say what's 2+2 you'd start at 2, and then you'd add 2 you'd get to 4.
I mean most of us it's second nature.
But if you actually drew it on a number line, you'd say 2+2=4
And if I asked you what's 2-1 or let's say what's 3-2
If you start at 3 and you subtracted 2 you would end up at 1
That's 2+2=4, and 3-2=1
And this is a joke for you.
Now what if I were to say what is 1-3?
Huh.
Well, it's the same thing.
You start at 1 and we're going to go 1-- well, now we're going to go below 0 what happens below 0?
Well then you start going to the negative numbers.
-1, -2, -3, and so on.
So if I start at 1 right here, so 1-3 so I go 1,2,3, I end up at -2
So 1-3=-2
This is something that you're probably already doing in your everyday life
If I were to tell you that boy, it's very cold today, it's one degree, but tomorrow it's going to be three degrees colder, you might already know intuitively, well then we're going to be at a temperature of negative two degrees.
So that's all a negative number means.
And just remember when a negative number is big, so like -50, that's actually colder than -20, right?
So a -50 is actually even a smaller number than -20 because it's even further to the left of -20
That's just something you'll get an intuitive feel for.
Sometimes when you start you feel like oh, 50 is a bigger number than 20 but it's a -50 as opposed to a 50
So let's do some problems, and I'm going to keep using the number line because I think it's useful
So let's do the problem 5-12
I think you already might have an intuition of what this equals.
But let me draw a line, 5-12
So let me start with -10, -9, -8--
I think I'm going to run out of space-- -7, -6, -5
I should have this pre-drawn -- -4, -3, -2, -1 0,1,2,3,4, and I'll put 5 right here.
I'm gonna push this arrow out a little bit.
Okay.
5-12
So if we start at 5-- let me use a different color-- we start at 5 right here and we're going to go to the left 12 because we're subtracting 12
So then we go 1,2,3...
Negative 7
That's pretty interesting.
Because it also happens to be that 12 - 5 = +7
So, I want you to think a little bit about why that is.
Why the difference between 12 and 5 is 7, and the difference between -- well, I guess it's either way.
In this situation we're also saying that the difference between 5 and 12 is -7, but the numbers are that far apart, but now we're starting with the lower number.
I think that last sentence just completely confused you, but we'll keep moving forward.
We just said 5-12=-7
Let's do another one.
What's -3+5?
Well, let's use the same number line.
Let's go to -3 plus 5
So we're going to go to the right 5
One, two, three, four, five.
It's a two.
It equals two.
So -3 + 5 = 2
That's interesting because 5 - 3 is also equal to 2
Well, it turns out that 5 - 3 is the same thing, it's just another way of writing 5 plus -3 or -3 plus 5
A general, easy way to always do negative numbers is it's just like regular addition and subtraction, but now when we subtract we can go to the left below zero
Let's do another one.
So what happens when you get let's say, 2 minus -3?
Well, if you think about how it should work out, I think this will make sense.
But it turns out that the negative number, the negative signs actually cancel out.
So this is the same thing as 2 plus +3 and that just equals 5
Another way you could say is-- let's do another one-- what is -7 minus -2?
Well that's the same thing as -7 + 2
And remember, so we're doing to start at -7 and we're going to move 2 to the right.
So if we move 1 to the right we go to -6 and then we move 2 to the right we get -5
That makes sense because -7 + 2 that's the same thing as 2 - 7
If it's two degrees and it gets seven degrees colder, it's -5
Let's do a bunch of these.
I think the more you do, the more practice you have, and the modules explain it pretty well.
Probably better than I do.
So let's just do a ton of problems.
So if I said -7 - 3
Well, now we're going to go 3 to the left of -7
We're going to get 3 less than -7 so that's -10, right?
That makes sense, because if we had 7 + 3 we're at 7 to the right of 0 and we're going to go 3 more to the right of 0 and we get positive 10
So for 7 to the left of 0 and go 3 more to the left, we're going to get -10
Let's do a bunch more.
I know I'm probably confusing you, but practice is what's going to really help us.
So let's say 3 minus -3 well, these negatives cancel out, so that just equals 6
What's 3-3?
Well, 3-3, that's easy.
That's just 0
What's -3 nimus 3?
Well now we're going to get 3 less than -3 well that's -6
What's -3 minus -3
Interesting.
Well, the minuses cancel out, so you get -3 plus 3
Well, if we start 3 to the left of 0 and we move 3 to the right, we end up at 0 again.
So that makes sense, right?
Let me do that again.
-3 minus -3
Anything minus itself should equal 0, right?
That's why that equals 0
And that's why it makes sense that those two negatives cancel out and that's the same thing as this.
Let's do a bunch more.
Let's do 12 - 13
That's pretty easy.
Well, 12 - 12 = 0, so12 - 13 = -1 because we're going to go 1 the left of 0
Let's do 8 - 5
Well, this one is just a normal problem, that's 3
What's 5 - 8?
Well, we're going to go all the way to 0 and then 3 more to the left of 0, so it's -3
I could draw a number line here.
If this is 0, this is 5 and now we're going to go to left 8, then we end up at -3
You could do that for all of these.
That actually might be a good exercise.
I think this will give you good introduction and I recommend that you just do the modules, because the modules actually especially if you do the hints it has a pretty nice graphic that's a lot nicer than anything I could draw on this chalkboard.
So, try that out and I'm going to try to record some more modules that hopefully won't confuse you as badly.
You could also attend the seminar on adding and subtracting negative numbers.
I hope you have fun!
Bye.
I'm now going to do a bunch more examples using the chain rule.
So let's see.
Once again.
If I had f of x is equal to, let's see, I don't like this tool that I'm using now, let's have one of these. f of x is equal to, say, x to the third plus 2x squared minus, let's say, minus x to the negative 2.
We haven't put any negative exponents in yet, but I think you'll see that the same patterns apply.
And all of that to, let's say, the minus seven.
We want to figure out what f prime of x, what the derivative of f of x is.
So this might seem very complicated and daunting to you, and obviously to take this entire polynomial to the negative seventh power would take you forever.
But using the chain rule, we can do it quite quickly.
So the first thing we want to do, is we want to take the derivative of the inner function, I guess you could call it.
We want to take the derivative of this.
And what's the derivative of x to the third plus 2x squared minus x to the negative 2?
Well, we know how to do that.
That was the first type of derivatives we learned how to do.
It's 3x squared and 2 times 2, plus 4x to the first, or just 4x, and then here, with a negative exponent, we do the exact same thing.
We say negative 2 times negative 1, right, there's a 1 here, we don't write it down.
So negative 2 times negative 1 is plus 2 x to the, and then we decrease the exponent by 1, so it's x to the negative 3, right?
So we figured out what the derivative of the inside is, and then we just multiply that, that whole thing, times the derivative of kind of the entire expression.
So then that'll be, we take the minus 7, let me do a different color.
So this is the entire thing.
So then we take minus 7, so it's times minus 7, this whole expression, I'm going to run out of space. x to the third plus 2x squared minus x to the minus 2. That's minus x to the minus 2. And all of that, we just decrease this exponent by 1, to the minus 8.
So let me write it all down a little bit neater now.
So we get f prime of x as the derivative of f of x is equal to 3x squared plus 4x plus 2x to the minus third power, I don't know why did that. That's minus 3. Times minus seven times x to the third plus 2x squared minus x to the minus two, all of that to the negative eight power.
Maybe we could just multiply this minus 7, times, we could distribute it across this expression.
So we'd say, that equals minus 7, so this equals minus 21 x squared, minus 28 x minus 14x to the negative 3. All of that times x to the third plus 2 x squared minus x to the minus 2 to the minus 8.
So there we did it.
We took this, what I would say is a very complicated function, and using the chain rule and just the basic rules we had introduced a couple of presentations ago, we were able to find the derivative of it. And now, if we wanted to, for whatever application, we could find the slope of this function at any point x by just substituting that point into this equation, and we'll get the slope at that point.
We're on problem 31.
A sewing club is making a quilt consisting of 25 squares, with each side of the square measuring 30 centimeters.
OK, and there's going to be 25 of these.
And they're going to be 30 by 30.
If the quilt has 5 rows and 5 columns, what is the perimeter of the quilt?
OK, so let me draw that out.
So it has 5 rows and 5 columns and they're all squares.
So the quilt itself is going to be a square.
It has 4 rows, one two, three, four, and then five.
And then one, two, three, four.
So that's a 5 by 5.
And each of these squares, their sides are 30 centimeters.
So how long is one side of this quilt going to be?
It's going to be 30 times 5.
So it's going to be 150 centimeters.
Same argument, that's going to be 150 centimeters.
And that's going to be 150 centimeters. 30 times 5.
And this is going to be 150 centimeters.
So the perimeter is 150 plus 150 plus 150 plus 150 and that's 600.
So that's choice C. 32. The four sides of this figure will be folded up and taped to make a box.
Fair enough.
What will be the volume of the box?
OK, so if we cut this out right now and we folded it along where I'm drawing these green lines, we'll get a box.
And they want to say, what's the volume?
Well, volume is just the base times the height times the depth.
So if I were to fold up this box is going to look something like this.
You're going to have the base, which is this base right here.
And this is one, one, two, three, four, five by one, two, three, four, five.
So it's 5 by 5 base.
And then each of the sides are going to be 2 high if I fold this up, it's going to be 2 high like that.
It's going to look like that if I folded that side up.
This side, when I fold it up, is going to look like this. One, two, three, four, five.
That's side when I fold it is going to look like that.
And this side when I fold it up is going to look like that. One, two, three, four, five.
The big picture, the width is 5, the depth is 5, and the height is 2.
So the volume is 5 times 5 is 25 times 2. Which is equal to 50.
And that's choice A.
Problem 33.
Where's 33, I think it's on the next page.
OK, let me copy and paste it.
I should just copy and paste the whole test.
OK, it says a classroom globe has a diameter of 18 inches.
If I were to go from the center to the side, it's 18 inches.
Which of the following is the approximate surface area.
Oh no, sorry, I just drew the radius.
It has a diameter of 18 inches.
This is 18.
Which of the following is an approximate surface area in square inches of the globe?
And surface area, they give us the equation, they give it in terms of the radius.
So if the diameter is 18, what's the radius?
The radius is half of the diameter.
So the radius is equal to 9.
And we just plug that into here.
So the surface area is equal to 4 pi times the radius squared, times 9 squared.
That equals 4 times 81 times pi.
So it's 324 pi.
And they actually multiplied it out.
So let's see.
Let's see, 324 pi.
And if I were to guess this, I mean, look at all the choices.
Pi is more than 3.
So this value is going to be more than 3 times 324.
So it's going to be around 1,000 or a little bit more than 1,000.
And the only one that's even close to that is D.
But if you wanted to confirm that, you could multiply 324 times 3.14 and that is equal to 1,017.4.
All right, next problem.
Problem 34.
I'll copy and paste 34 and 35 at the same time.
There you go.
I put this there.
All right, ready to do it.
The rectangle shown below has a length of 20 meters and width of 10.
So this is 10 and this is 20.
I just picked that because this looks longer than that.
That's a 10 I drew.
I know it doesn't look like a 10.
If the four triangles are removed from the rectangle as shown, what will be the area of the remaining figure?
So what's the are before I remove them?
It's 20 times 10.
That's the area of the whole rectangle.
So it's 200.
And then how much area am I removing?
So each of these triangles, what's its area?
It's base times height times 1/2.
That's the area of a triangle.
Because if you just did base times height, you'd be figuring out the area of this little rectangle there.
So the area of this is 4 times 4 is 16 times 1/2, which is 8.
This is going to be 8, going to be 8, going to be 8.
So we're removing four 8's from this area.
So we're removing 32.
So minus 32.
And that's 168.
So that's choice C.
Problem 35.
If RSTW is a rhombus, so rhombus tells us that all the sides are equal and they're parallel.
What is the area of WXT.
So this right here.
OK, so this is something that you may or may not have learned about a rhombus already. But its diagonals actually intersect at a perpendicular line.
And let me see what else we can see.
This is 60 degrees, so this is 30 degrees.
Let's see what we can get from this.
This is 12.
Then this is 12.
OK, I see where they're going with this.
So if this is 90 degrees, this is 90 degrees.
This is a rhombus, so all the sides are the same.
If this is 60, this is 90, this has to be 30 degrees.
And then you could actually make a very strong argument that these are similar triangles.
Whatever length this is, that's the same length, because this is a parallelogram and the diagonals bisect each other.
This side is equal to that side.
That side is equal to this side.
So these are congruent triangles.
So this is also going to be 60 degrees.
This is going to be 30.
But if you have a 60, let me do it in another color, if you have a 60, 60, 60 triangle, all of the angles are 60 degrees, you're dealing with an equilateral triangle.
So that tells you that all the sides are the same.
So if this side is 12, that side is 12, this side right here also has to be 12.
If that whole side is 12, what's this length?
We already know that in a parallelogram the diagonals bisect each other.
So this length is 6. And this length is 6.
Fair enough.
And let's see, if each of these lengths are 6, can we figure out what this height is equal to?
Because if we know the base and the height, we're ready to figure out the area of a triangle.
So let's see if we can use the Pythagorean Theorem.
If we called this x, we could say x squared plus 6 squared plus 36 is equal to 12 squared, is equal to 144.
And we you could say that x squared is equal to, what's 144 minus 36, that's 108.
Let's see, 108. x squared is equal to 108. x is equal to the square root of 108.
And I can simplify that more because 9 goes into 108 12 times.
Let me do that.
So x is equal to the square root of 9 times 12, that's 108.
So that's equal to the square root of 9 times the square root of 12.
That's equal to 3 times the square root of 12.
Square root of 12 is the same thing as the square root of 3 times the square root of 4.
Square root of 4 is 2.
So that's 2 times 3 is 6 square root of 3.
This is 36 times 3.
We could have said this is equal to the square root of 36 times the square root of 3.
All right, so 6 square roots of 3.
That's this side.
So what's the area of this triangle right there?
It's 1/2 times this base times 6 times 6 square roots of 3.
So that's 1/2 times 6 is 3, times, 6 square roots of 3 is 18 square roots of 3.
Now that's just this triangle.
This triangle is congruent to this triangle, so it will have the same area.
And you can make the same argument that all of these triangles are congruent.
So the area of this entire rhombus is going to be 4 times this.
Is that what they wanted?
Oh no, they wanted of the area of WXD.
That's what we just figured out.
They didn't want the area of the whole rhombus.
They want just the area of this triangle right there, which we just figured out, which is 18 square roots of 3.
I'm trying to think if there's a simpler way of doing this.
There might be some formula for the equation for the area of a rhombus that I've forgotten in my memory.
But we were able to re-prove it.
And that's always better, to come from basic principles.
Anyway, I'll see you in the next video.
How many ounces are in 6 pounds?
So we have 6 pounds and we need to convert them to ounces.
And if you don't know it already, you'll know it now, that there are 16 ounces per pound.
So what we want to do is we want to have pounds in the denominator.
It's in the numerator right now.
So we want to divide by pounds and multiply by ounces.
Maybe I'll write it out.
And I just told you that there are 16 ounces for every 1 pound.
So if we multiplied these two expressions, this pounds will cancel with that pounds, and we'll just be left with the unit of ounces, which is what we want, and we just multiply 6 times 16.
So it works out unit-wise, and it makes sense as well.
If we have 16 ounces per pound, and we have 6 pounds, we just have to multiply 6 times 16.
That'll be the total number of ounces we have.
So this is going to be equal to-- what's 6 times 16?
So if you take 16 times 6, 6 times 6 is 36. Carry the 3. 6 times 1 is 6, plus 3 is 9.
So 6 times 16 is 96.
You have this divided by 1 here, but that's not going to change anything.
And then all we're left with in the dimensions are the ounces.
So 6 pounds are 96 ounces.
Halt...
Open up.
Just a minute sir.
This man's in a hurry.
Who's he?
Where's he going?
Got to catch the Valley Express.
I'm already late.
If you'd hurry...
Open the boot.
It's not locked.
Hope there's no bomb in the boot.
You'll find bombs 30 kilometers ahead.
Move on!
Will we reach the station?
If the Lord wishes.
Has the Barrack Valley Express left?
Has the Barrack Valley Express left?
It's running late.
How late?
- 8 hours late.
It's terribly cold!
I'll freeze in this cold!
There's not a soul around.
Station master!
You'll have to cremate me!
Where are you running to?
Matches!
Brother!
Hey there!
Uncle!
Do you have a match?
Never mind, if you don't have it.
Glad to know you're alive.
What do you think?
Will the train arrive?
If it does come, will it also leave?
I hope the bridges are strong enough.
Not built by a dishonest contractor.
Because if a bridge collapses, we'll be in deep trouble.
You're the limit!
Forgive me.
Taking you for a man, I asked you for a match.
But you're a girl and a beautiful one at that.
Forgive me.
Do you have a match stick?
Don't you ever smile?
I mean, it's good to laugh.
Don't tell me your name.
My name is Amarkant Varma.
Only tell me where you were born.
Or a relative's name... tell me your mother's name.
Maybe you have a dog at home?
No dog?
Say something...
Tell me to shut up.
Can I do something for you?
I mean, get you the stars or the moon?
Conquer a fort?
But no match stick!
You're all alone.
Can I get you something?
A cup of hot tea.
Don't go away.
I'll just get it.
There's a bomb in my suitcase.
If you move it will...!
Uncle.
Make us some special tea.
Closed for the day.
No, my future depends on this.
Here's the money.
Make a nice cup.
With cream.
I'll take some biscuits as well.
The station master said the train is running 8 hours late.
That's another train.
Hope she's not taking it.
What did you say?
Nothing.
You make the tea.
I'll add the sugar.
This must be the shortest love story.
What's your name?
Where's the boss?
The vegetable market.
You're all cheats!
Not one paise extra!
Am I new to these parts?
Are you from All India Radio?
Yes, but after this fight.
Cheats!
Do you have change for 50 bucks?
Give me 20 bucks.
What?
Yes...
No, it's not fair.
It's absolutely fair.
Put this away...
I owe you 20 bucks.
Couldn't talk to you while arguing, or I'd forget the abuses.
I knew it would be you.
Don't throw the cigarette.
India can't bear any kind of wastage.
What do you think of the last 50 years of India's independence?
What progress have we made?
What freedom?
We have no freedom.
Village leaders got only more powerful and started fleecing us.
Has free India made any progress?
No.
The central government threatens us and keeps us cowed down.
Atrocities are inflicted on the poor and innocent.
And you say we are free!
Is this what freedom means?
Louder.
No progress at all.
We have progressed.
No way!
Do you feel India has progressed?
Yes.
India is the best.
Have you ever met these terrorists or their leaders?
I have two children.
Don't want to see me happy?
I'm going to meet them.
Are you crazy?
Why?
For an interview.
You won't return alive.
I already told him that.
We work for the radio, not for the newspapers.
We don't have to sensationalise news.
They are dangerous people.
It's my job to find out after 50 years of independence... ...what is the average Indian's mindset?
For that you need to get into the jungles and meet with them?
They are citizens of our country.
And are upset.
We must find out why, and what they think.
It's impossible.
You won't find them.
We've spoken to them.
The jeep is on its way.
Didn't you tell her?
Yes.
Have you made all these arrangements?
Actually, last night, he saw some trees...
Since then he's been screaming to see either trees or...
You don't find trees in Delhi.
I have to give you something.
A cup of piping hot tea.
Will you have it here or prefer to go to a restaurant?
Or there's a good joint...
Move out of my way.
Maybe you haven't recognised me.
We met at the railway station.
I asked you for a match.
Match?
You were covered in a dark shawl.
No.
Look, I don't know you.
You are mistaken.
You must have seen somebody else.
Wasn't that you?
Not to you.
Can you see anything?
I see the gong of death!
Don't be afraid.
Listen.
What is it?
Brother.
Yes?
Sounds like a female.
What's your name?
I wanted to ask if... you...
What's your age?
And since when are you doing this?
Sister.
I've 2 wives and 8 kids.
I'm fed up.
Why do you do this?
Yes.
Come soon.
We are.
Let me drink the tea.
Don't pester me.
Don't be angry now.
This is for the radio.
You won't speak in my tongue.
But I must speak in your language?
First of all I wanted to ask, you look just like us.
Absolutely normal.
What did you think?
What's your aim?
Independence.
From whom?
Your government.
India.
Why?
Why?
I mean why?
India became free 50 years ago.
Many promises were made to us.
Not one was kept.
We have been oppressed.
Yet the nation is yours.
No.
You feel Delhi is India.
The states in the far flung area have no meaning for you.
Because they are small, not big.
Delhi cares about places that have vote banks.
Terrorism...
We are not terrorists.
Where do you get weapons from?
Where did you get this courage?
Where do you get weapons?
Anywhere.
So China and Pakistan help you?
These weapons come here and you...
I can't tell you any more.
You've given guns to little kids.
Made them terrorists only for your selfish motives...
That is too much!
He can join us.
The same courage and dedication.
If you lose your job at the radio station, you can come and join us.
It is night at the station...
He was waiting... ...for the train, but the rains came.
Playing like a child.
Piercing through the sky.
The trees were swaying as if they had lost their senses.
The tin-roofs danced in gay abandon with each other.
Such was the fury of the sky.
As if it would drown the world!
In the midst of this, he saw somebody on the dark platform.
Brother, do you have a match?
A gust of wind blew the cloth off the stranger's head...
A girl.
Dark black, but little eyes.
High cheek bones.
A flat nose as if somebody had pasted it on in a rush.
One look and he decided to save her from the villains and carry her away.
But he had neither horses nor were there any villains.
Forgive me.
I thought you were a man and asked you for a match.
Her answer.
Nothing.
Her eyes... full of magic.
Not even a smile.
Why doesn't she ask something?
All of a sudden...
As if pearls are falling...
She says... tea.
Today is going to be different.
Meaning?
Amar is looking after everything today.
He gets hot tea in a floral glass.
He runs hard.
So as not to spill any.
But a train that would be offended to halt at this little station...
I looked at the train.
I didn't know whether it was mine or hers.
The guard showed the red along with the green flag.
I ran towards the train.
The train left.
She too left.
Here.
Is a rupee stamp sufficient?
I'm standing here.
Just a minute.
Can I talk to him?
No local calls.
I know.
The meter is not working.
Will this do?
Make the call only if you have the change.
All right.
Twenty rupees.
Full rate.
Join politics.
This is wrong.
You've met me twice and yet, refuse to recognise me.
Stop following me.
No.
You will have to.
Why?
I don't like it.
I don't believe it.
I...
What's the problem?
Is it your parents, caste, community... religion?
Or the two gangsters in the train?
I can even talk to them.
Even if I have to use my fists...
It's not that.
I don't like it.
Leave me alone.
You don't like me?
Hope you won't follow me now.
It's done!
Did you talk?
Yes.
Have you eaten?
Yes.
Who is it?
Now where are you going?
I'll be back.
Go anywhere.
As if I care.
Go away!
Will you come with me?
I'm not what you think I am.
How do you know what I think?
I've found you with great difficulty.
How can I let you go so easily?
Either you tell your family.
Or I'll talk to them.
Think it over and tell me.
What do you know about me?
Nothing except that I love you.
With all my heart.
Surprised?
Worried?
Angry?
I don't believe in one-sided love.
There must be something between us.
The only difference being you're not willing to accept the truth.
And I do.
What's the matter?
No courage?
The truth...
Leave me alone!
Answer a question of mine.
Then I won't bother you.
You don't know anything.
I've come to find out.
You are very wrong.
Why don't you understand?
You don't tell me anything.
How can I understand?
I am married.
Now you won't follow me?
To whom?
The man with you in the train?
Yes.
One moment.
Nothing.
How can I love a married girl?
Infatuation, not love.
Get in.
Your books must be on the table in 5 minutes.
What do I do?
Forget her.
There's no shortage of girls.
I don't mean that.
I must apologise to her.
Then do so.
It's necessary.
I must apologise to her.
She's come.
Is she the one?
Why has she brought this gang?
You wanted to apologise to the girl.
So why are the men coming here?
Her husband.
Two husbands?
You have 2 wives.
There's a lot of difference between a husband and a wife.
Listen, we want to talk to you.
Pardon me?
We want to talk.
Yes?
In privacy.
Talk here.
There's no need to worry.
Come on.
Go ahead.
I'll tell madam you'll be late.
Why don't you go?
I must tell you some things clearly.
I'm a government servant.
If anything happens to me, the matter goes to the police.
And also to the government.
I also have quite a few terrorist friends.
I know the leader very well.
Don't listen to him.
I was a bo xing champ at college.
I can throw a bottle in the air and break it with another.
Don't say I didn't warn you.
What do we do with him?
What do you mean?
So you're a policeman?
I'm not a policeman.
I work for the radio.
Look like a policeman!
What do you do?
Why are you talking to him?
Drag him out!
Let us talk.
What are you doing here?
Why are you asking me so many questions?
Want to get a girl married?
Pull him out!
Don't touch me.
Just talk.
And you behave yourself.
Explain to him.
We live in the hills.
We have some rules and customs.
It will be better if you leave the girl alone.
What if I don't?
I told you not to touch me!
I didn't know she knows you!
I told you not to touch me!
I didn't know she was married!
In any case, your women have 5 husbands.
Our sisters don't marry outside.
Is she your sister?
And yours?
She's my cousin.
Is she married?
Did you see him?
Yes, there.
The rascals threw him here.
Stop!
Back.
Where?
There!
Got beaten black and blue for her!
Now do you intend to work or not?
What?
Says no.
You won't forget that girl.
Yes?
Her...
What's he saying?
Marriage...
She's not married.
She's not married?
She's not married!
She says they've left.
They'd come for 2 months.
Where have they gone?
I don't know.
When did they leave?
Some time ago.
Are you the girl's grandmother?
She says the girl was lovely.
I wish I was her grandma.
From where had they come?
From where had they come?
From the city.
Doesn't she know where they've gone?
Don't know.
She knows nothing.
What's she saying?
The girl was good, boys useless.
Don't know what they always talked about.
Only the girl would run around.
Attend to the phone.
Why can't you?
Amar?
Mother, it's brother on the line.
How are you?
Talk to grandma.
Give me the line.
Ask him why he hasn't written!
I'm growing even more old!
Grandma is growing older!
When is he returning?
Come back soon.
Give me the line!
We are very worried!
The newspapers publish some terrible news everyday.
Take care of yourself.
Let me also talk!
Your Dad's friend from the army, Mr Nair... ...is bringing his daughter here.
When should he come?
After 5 years.
When are you coming?
May you live long.
One minute.
Bring something for me.
It's not a local call.
Give it to me!
That girl doesn't come these days.
Do you know the number the girl would dial from here?
I have a record of all the numbers dialled from here.
Can you tell me?
Why not?
But Why?
I had a fight with her.
I wanted to talk to her.
I don't give out numbers like this.
It's a government office.
What office?
Keep this.
No!
Yes?
What code is this?
Yes, it's almost over.
I'll assume I'd lost my head for a few days.
But don't tell anyone.
Pay up!
Move aside.
The army shot a running man.
I'm from All India Radio.
I want to know what happened.
Hurry up.
Isn't this a violation against human rights?
Human rights!
Ask him...
He was blowing up school kids with RDX!
Recognize me?
Your husband is not to be seen.
Sent him to thrash somebody?
I don't have a husband.
Are you looking for one?
Who are you?
Why have you come here?
Come to cover the festival?
And you?
I'm with him.
His wife?
Whose kids are these?
Are you my wife?
She's my wife.
We've been married for 25 years!
Wife!
Let me knew if somebody is to be thrashed.
Give me a hand.
Help the kids.
Mother this way.
Where are these people going?
To Kargill.
How long will it take?
2 days.
The route is long.
Let's walk.
Throw carefully!
I'm talking to you.
Stop!
What do you want?
Some answers.
I've been betrayed.
I was beaten up and dumped in an isolated spot.
And today I am your husband?
Don't you think I'd have some questions for you to answer?
By what name do I address you?
Real or false?
Who were those men?
My brothers.
Just as Rajiv Gandhi is mine?
Why did you lie that you were married?
If I hadn't, would you have left me?
No.
That is why.
Don't try to act innocent.
I know you're not as innocent as you look.
Will I dance to your tunes all my life?
Your game is exposed!
You love to tease boys.
Know what we call girls like you?
We call them fast.
You really hate me.
Yes; with all my heart.
Look into my eyes and say that.
Here, take some water.
Haven't you ever seen a girl?
Where are you going?
Call back your husband, too.
Let's go back.
A storm is raging.
There's some innocence still left in you.
Everyone has gone to a cave nearby.
Sometimes, somebody is ahead at others they follow behind.
What's the matter?
What's wrong?
Tell me what happened!
You are in tears.
What is it?
Can't you speak?
Has this happened before?
Has this happened before?
The more you try to hide it, the more it will torment you.
Don't hold your feelings back!
Please move aside.
Come with me.
One minute.
Do you follow Hindi?
Yes, a bit.
I want to marry her.
When?
Right now.
Excuse me, he's mad.
What have I said that's crazy?
Just because I want to marry you?
Will anybody say something stupid in such a holy place?
But you never asked me.
Then I'll ask you now.
Will you marry me?
No.
I don't have the time.
Don't have the time?
Suppose we do get married.
Not now.
Now we don't have time.
Suppose we get married.
What do you think...
Will we be happy together?
Lots of love and happiness?
Then we'll fight.
Break heads.
But let me make one thing clear.
I won't accept defeat.
You'll have to make the first move to make up.
You won't?
Meaning, I'll have to apologise to you?
But once the kids come, no fights.
No, they will be involved, too.
Really?
How many kids will we have?
One?
Two?
Three?
Four?
Eight?
But they have to resemble me.
Look like me.
Then you keep them!
If not me, should they look like you?
This flat nose!
This flat nose?
Didn't anyone ever tell you only your smile is all right?
Do you know what it means to hit like this?
You like me very much.
Hitting like this... ...means you love me very much.
This means you can't live without me!
I'll die.
Really?
Just like this.
Who is asking you to die?
Say you love me.
I've no time.
Don't desert the old lady.
Why didn't they take them along?
Left them with us for nothing!
They understand Hindi.
And the language of the heart?
If they don't leave us alone, when will we romance?
What's wrong?
Not sleepy?
I am, but I won't sleep.
Why?
Are you scared of me?
My family taught me the one who sleeps in a strange land loses all.
You are scared.
No.
Do you have any idea what fear is?
Now we won't argue or fight.
We'll just talk.
What do you like the best?
Answer quickly.
I'll count to 3
- 1, 2...
Mother's hands.
Mother's hands.
Second?
The pigeons of the village temple.
Third?
Poetry.
A local song?
What do you dislike the most?
I don't like you getting close.
That's a lie Your laughter and mischief.
The zest in you.
Wrong.
Actually you envy me.
Yes.
You tell me what you like.
First I'll tell you what I don't like.
I hate this distance between us.
All that is hidden within you.
And I hate your eyes the most.
However hard I try, I can't read anything in them.
Now I'll tell you what I like.
I like your eyes the most.
Because however hard I try, I read nothing in them.
There's so much hidden in you.
I like that very much.
And I like this distance the best.
Because if not for this distance, I would have no excuse to get closer.
Go to sleep.
Just sleep?
With your mouth shut.
Some people are like names written in the sand.
Just one gust of wind blows them away.
Go!
Go away!
This aim of our revolutionis the freedom for our country.
This aim of our revolution is the freedom for our country.
For this, we will sacrifice our bodies and our lives.
We also accept... ...our commander and his aim.h
We will sacrifice ourselves for the attainment of these goals.
We do solemnly swear.
The time draws near.
The passport is ready.
The entry passes have been arranged.
The dress rehearsal is on 23rd.
Friday.
What about the car passes, etc?
Don't use them.
I'll play you a song...
Any song of your choice.
My choice?
Has my stuff arrived?
It's on the table.
Take it.
Okay.
This song is for Dinu and his friends and... that's all.
Have you fixed up the house?
Plan out what you need.
Be careful.
You've come?
Amar has been waiting impatiently.
Kids!
May I say something before you do?
Can I talk informally?
Whatever...
There was a boy I loved.
He too loved me.
In college.
One spoonful of sugar?
He found a job in Dubai.
And when the question arose; Dubai or me...
Is that his name?
No, he is.
That means an idiot, an ass.
I'm telling you this because our families want us married.
And I don't want you to...
Don't worry about that.
By the way, even I went through this.
Love or lost?s
Both.
Did the girl ditch you?
Yes.
Didn't you feel like slapping her hard?
I felt like wringing her neck.
And killing her!
Shake!
They feel the promises made to them were not kept.
The bigger states have grabbed their rights.
The cause for this are the politicians
Who feel they are not important.
These rumours have been spread by nations across the border.
We've invested money in the north east area without expecting returns.
Then where does the money go?
Businessmen or middlemen grab it?
They are all hand in glove!
Is this for the radio?
Yes.
All India.
Food.
I don't know.
One last question.
Who is responsible?
Politics or the politician?
How can we celebrate 50 years of independence...
When there are so many problems in the border states...?
I mean, did you just love that girl quietly or...
Did something ever happen?
I don't want an answer.
I just wanted to see if you get shocked.
If I ask you the same question?s
Sure.
But what do you think?
I feel you talk too much.
And also at this moment, there's lettuce on your nose...
But 80%% of the girls of today...
Before marriage...
So you're from the remaining 20%%
What else?
I didn't have the guts.
Tell you something?i
Looks like you're from the 20%% too
Thinking about that girl?
No.
Is that true or a lie?g
Lie.
Forget that lie.
Tell me a lie about me.o
What lies can I tell about you?
That I'm very beautiful.
I'm wonderful, and so on.
You're very beautiful, wonderful, and so on.
You do lie beautifully.
At home, everybody must be waiting for us.
To see if we say yes or no.
So if you don't like me, you can say so.
So will I.
But a yes...
I want to talk to you.
Stay there.
I want to talk to you.
Stop!
I want to talk to you!
Please forgive me.
Hope you're not hurt.
What's the matter?d
Where are you running off to?
Strip and check him.w
What is this?s
He's swallowed it!
Take it out!
Forget about her.
She's just a dream
I thought you loved a girl.e
But you were chasing a man.
Are you a normal man?
Hope you're not...s
I thought might as well ask.
No harm
This way.
Your purse.
Kim was caught in Connaught Place.
God knows how.s
The police even found his cyanide.
And he swallowed it.w
They have come!
What are kids doing here?
Go up.
So what have you thought?
We had lunch and were returning in a bus, Dad.
When a man started running.
Amar ran after him.
I ran after him and in this running, we couldn't talk.
We only want to know yes or no.
How can we say anything so soon...?
We've just met...
I accept.
But ask her once.
What do we assume?
Say yes!
Answer her!
Say yes!
I won't say anything.
Please.
No!
She accepted!o
Look at his body.
Blood red.
His eyes have turned blue.
His tongue and lips are the same.
There will be deposits of potassium cyanide in his stomach.
Could he have survived?
He may have died in 10 minutes.
There was a 40%% chance if a malnitrate was administered.
Have you seen this?
Looks like some notation.
Find out.
Look up the yellow pages.
Check every music shop in the vicinity
God knows what the police must have got out of him.
I'm sure he won't divulge anything.
He won't say a word.
Stop crying.
He was like her brother.
There are no brothers or sisters here.
We haven't come here to cry!
He wouldn't like your tears!
He was a soldier who was martyred in the battle!
He didn't die as somebody's brother.
Now what will we stay here and do?
We'll do something.
Getting engaged?
Then you'll get married.
And you'll have children too.
Then they too will get married.
They too will have kids!
One day you'll become an old granny!
And you'll have to see the same man's face every morning!
She's here!
Where are you going?
Will you let me go only after I tell you?
Yes!
I'm going to meet the groom.u
No!
Not allowed!
Do you know what I'm called at home?
No.
Hitler!s
I'm going to come here after marriage.
If you don't keep me happy...
Where are you going?
To meet the bridegroom.
No mischief before marriage.
I was going to tell him just that.
What is it?
I saw nothing!
What's the matter?
Something urgent.
Go on.
I forgot.
I remember.
What is it?
You'll be stuck after marriage.
If you want to change your mind...e
Think about it.i
Come soon.
Guests have come.t
Sure, I'm coming.
Must I come in the nude?
Don't bother him.
Who has come?
Have I come at the wrong time?
Why have you made them stand outside the house.
Bring them in, I say.
Come in, child.
We've been thrown out of our rented accommodation.
We have no place to stay.
We can't even go back to the village.
Sister's calling you.
Go away.
I can't understand where to go.
Congratulations.h
Can I get a job?
Any kind of job.l
I can do a bit of recording.
I've also worked for radio.
I'll do any job in All India Radio.
Even a temporary one.
Preeti asks where's the groom; Has he got cold feet?
My son get scared?
Mother, this is Meghna.
She'll stay upstairs.
Have her luggage sent there.
Where do you work?
The wedding is on our heads and you're inviting strangers...
I listened to you and got ready for marriage.
They're my friends.
So what?
She's coming!
My grandson is getting married!
Congratulations to you too.g
Who is that girl?
The one in red.
She's working with me in all India radio...
I just asked.
Forget it.
This is your room.
Come in.
I'll take it.
This is...
My Papa.
This was his room.
Is he in the army?
Was.
He's no more.
May I leave?
Wait for me.
I'm coming!
Edit it and show it to me.
I'll come back in a minute.
The certificates you'd asked for.
And my bio-data.
The photocopy is with me.
You desperately want this job.
Then answer my questions.
Why should I get you this job?
Why did you leave me?
And why have you returned now?
Will I get the job only if I answer these questions?
Forget it.
Come back here.o
What's the point in wanting something not in your fate?
There's no sympathy in your heart.
Don't you love me?
I can't answer this...
I've spoken to the ST.
You'll get a temporary job.
Go out to the second room on the left.
Go on.
And listen... wipe your tears.
It's a casual job.
Temporary broadcasts.
Got the parade duty?
I'll get it.
Does Amar suspect anything?
No.
He's very innocent.
There's no suspicion in him.
What else is in him?
And you?
What's in you?
Anger.o
And?
Ideals.
And?
My future.
And?
Courage.
Have you forgotten why you came here?
Do you remember what our people have been through?
I remember everything.
Love is into xicating.
It's not made for us.
Why don't you sing?
You look so pretty when you smile.
Or you're glum.
When I was 8, my smile left me.
What's hidden in you?
Nothing.
Just unhappiness.
Goodness me!
Not good to be so sad!
Like Preeti, find yourseld a good boy.
We'll get you married too.
What can I do if it's not fated?
What fate?
We carve our own fate!
Welcome.
Go and call Amar.
He must be upstairs.
Call him.g
Suppose we get married.
What do you think?
Mummy is calling you.
Coming.
But no fights after the kids are born.
They too will be involved in our fights.
Coming!
One?
Two?
Three?
More.
Eight?
Had it!
But the kids will be like me.
Eyes like mine.
Then keep them to yourself!
Will they look like you?
This flat nose!
This flat nose?
Didn't anyone ever tell you only your smile is decent?
Know what hitting like this means?
You like me a lot.
Hitting like this means...
You love me a lot.l
This also means that you can't live without me.
Say yes just once.
We'll go far away from here.
Say yes just once.
They are calling you downstairs.
Look at this.
It's beautiful.
I've called Amar.
Come here, child.
I'll call Preeti.
Who knows where she must be.
Try it on.
How will we know otherwise?
Bring the mirror.
She looks just like a bride.
Tell us if you have a groom in mind, we'll get you married!
How are they?
It's a marching tune on the tuba.
Did anyone buy a tuba from you very recently?
Yes.
Who wants to know?
Who was he?
An old man.
He came a few days ago.
Here's his address.
Near Jama Masjid.
Quick!d
To the back lane!
Search every house.
Sir, they've escaped.
No!
There's a call for you.
May I come in?
Yes.
I am frightened.
I'm getting married.
So far, I was happy.
But as the day draws close I feel...
Will I be trapped?
Everything will be fine.
Really?
Yes.
Amar and you...
You'll be happy.
Are you sure?
You are responsible.
If anything goes wrong, I'll question you.
Be informal.
Stay with me till the wedding.
Sensible girl.
Tied you to her apron and slipped away.
What about the recording?
How is your leg?
And did you find the dog?
The recording?
In a while.
Kids wait for so long?
I'll just arrange it.
Need a wheelchair?
Definitely not!
Watch where you go.
It will be done in half an hour.
In half an hour.
How come you dropped by suddenly?
My second wife's mother has passed away.
I fought and got myself transferred.
I brought my 2 wives, kids and the leftover mother-in-law and came here.
Heard you're getting married.
Checked everything?
Now you'll understand my problem.
Good day.
Good day.
Send this with the tape to Bangalore?a
How did she come here?
No, it's not so.
It's not what you think it is.
Getting married but keep your beloved in your arms.
You're also giving her a job!
And she stays in our out house.
What?
In your house?
May you go to hell!
You...
If you've spoken your bit, may I speak?
Yes.
I don't know why she left me.
I don't even know why she returned.
But I know it's not for me.
I want to find out why.
Now may I speak?
Yes.
Throw her out immediately!
I can't do it.
I can't do it.
Why not?
Because I can't do it!
Then do one thing.
Leave either one of them.
Don't ride 2 boats or you'll drown!
Learn from my experience!
Think it over and tell one of them.
What will happen to them?
Because of us, they will be ruined.
They are not bad people.
What wrong have they done?
Their lives will be ruined!
They trusted us.o
Gave us shelter.
Is what we're doing right?
The innocent will be killed.
Don't you ever doubt yourself?
There is one aim to our revolution.
There is one aim to our revolution.
Independence for our country.
We'll sacrifice everything for it.
We sacrifice our bodies for it.
Our dreams.
Our souls.
And impartially accept... ...our commander...
And every command of his.
For the progress of our revolution.
We'll sacrifice ourselves.
We hereby swear.
How many were they?
About 3 men and 2 women.
How were they?
What do you mean?
From where were they?
Bengal, Assam?
That I don't know.
What's this picture of an army vehicle doing in your studio?
A customer asked me to make a copy.
Why?
That's his business.
I won't give it!
It's mine!
She's talking to a man!
You're quietly listening!
If grandma hears...?
She's talking to her boyfriend!r
They have to meet at night.
Please be seated.
Yes?
I've seen this man.
This was published some days ago.
I saw him just yesterday.
Him?
No, the one who was chasing him.
You know him?
I broke my leg thanks to him!
My dog almost died!
My father always said...
Who is this man?
I don't know.
What's his name?
I don't know.
Don't lie.
The lie detector is connected.
Who are you?,
Who are you?
And in what capacity are you asking me this?
How many others in your group?
I don't belong to any group.
I told you I work for All India Radio.
I know nothing else.
You can't leave this room.
Please don't threaten me.
I'm also a government servant.
My father was in the Indian army.
And my grandfather fought in the freedom struggle in IN A.
And I too am worried for India.
Who is he?
Where does he live?
Where has he come from?
Why does he stay here?
I know nothing.
Then why were you chasing him?
Because if somebody abuses, beats you and then runs away...
Won't you follow him?
Why did he abuse you?
I don't know.
Go and ask him.
He abused me!
Hit me!
And you don't say anything to him instead catch me!
I am extremely sorry.
I had called you to talk about your station director.
It's our job.
We have to do it.
I don't need to wait...?
Definitely not.
See him out.
Did you see Meghna?
The new fair girl with small eyes.
Who stays with me?
She came, smiled a bit.
Shukla took her with him.
Parade rehearsal?
Of course.
Drive faster.
Take another cab if you're in such a rush.
I have this pass.
Drive on.
They will still create a scene.
They do it everyday.
You'll have to drive around.
Come on.
Didn't I tell you?
I know!
Where are you taking the car?
I know sir.
Can I go from ahead?
Yes, that way.
They always do their work well.
And trouble the citizens.
Turn right.
I hope you're not a terrorist.
Drive fast!
This is wonderful!
I've left in a rush.
I thought you...
Where are you going?
Come here.
Who are you?
Who are you and why have you come here?
Don't tell me any more lies!
I'm fed up of your lies!
Why did that boy run away on seeing me?
Was it a co-incidence that I saw him?
Tell me the truth.
He is dead
You came home and didn't ask for any job.
Why did you ask for a job in All India radio?
I chased you like a madman.
And you used me!
Why did you do this?
Why are you doing this?
So much of hatred?
Such bestiality!
Would your parents approve?
You talked of difficulty.
You talked of your mother's palms in the temple.
And what do you do?
Make bombs!
Kill people!n
The kind of life I've lived... ...you haven't seen what I have.
You sit in Delhi and play songs on the radio.
What do you know of our difficulties for the past 50 years?
We're being deceived for 50 years!
When we ask questions, we are silenced.
You know nothing!
What do you know?
You feel the revolution has grown but you're not to be blamed!
Lives are being taken and you have no hand in it?
The way we live...
We have no other alternative.
Dad!
Dad!
Death at every footstep.
Day and night.
Every moment.
They kept killing us!
We kept shedding our blood!
There was blood everywhere!
Screams of people still echo in my ears!
Stop it!
Sister!
Do you know it?
Sister!
Leave her!
Run away!
Little one run away!
Leave her!
Have you ever smelt death?
We pledge our bodies and souls...
With impartiality...
Every child has the same story to tell.
Maybe worse than mine.
I'll give up everything.
My family, job... everything.
Come with me.
Forget all this ever happened to you.
We'll go away from here.
We'll run away.
Won't you do this?
I can't do it.
So terrorism...
Now what do you want to do?
How many do you want to slay?
Come, I'll accompany you.
We'll kill people together!
You still don't understand.
I can understand what must have happened.
But I can't understand what is going to happen.
How many will you kill?
- 20, 30, 50?
Will this ease the suffering of your state?
Will happiness return?
I know what you went through was wrong.
But because of the mistakes of some... ...you can't take it out on the whole country.
A few peoples' mistakes?
What are these mistakes?
Killing innocent people?
Or setting entire villages aflame?
Raping a 12 year old child!
If you can't answer our struggle...
If you can't give us justice...
Is it a crime to ask for justice?
Little kids wield guns and their parents don't stop them...
Why?
Because it makes no difference even if they die!
There's no other way of survival.
Your army is your protection.
Quiet!
I know the army well!
You would have fought each other to death!
Each little village fighting against the other!
Had it not been for the army, this nation would be torn to shreds!
You think the army helps us?
Who else will save you?
Your terrorists?
Will you protect your nation with terrorism?
Your nation not mine.
What will you do?
Will you kill people or blow the country with a bomb?
You will celebrate the joy of 50 years of independence.
And the world will watch how we've been oppressed.
- 50 years...?
What are you going to do?
What are you going to do?
You used me...
Yes!
What do you mean to me?
Nothing!
What your heart says, what you think your marriage, family, children...
They hold no meaning for me!
Tell me what you're going to do!
What?
What will you do?
What is this?
Don't touch me!
Leave me!
What are you wearing?
What are you wearing?
Tell me what this is!
Let me go!
Teasing a girl!
Rascal!
You may go, madam.
Sit inside.
I'll show you!
Three men and two women.
They seem to be using old trucks.
We have found the chassis and engine number of the trucks.
To remove suspicion from that spot they used 555 timer... ...along with RDX.
What does all this mean?
Sir, January 26...
Hang on!
Amar here.
You called at the right time.
I was bathing, I'm wet...
Listen to me.
No, you listen!
I'm wearing only a bathrobe!
Listen, this is very urgent!
Of love or...
Don't talk nonsense!
Meeta and Meghna who are staying with us...
If they return don't let them leave.
This boy is our brother.
If you suppress this matter...
He hit a constable!
I know.
But everything is in your hands.
No!
It concerns a woman!
Yes, I'm fine.
I'll explain when I return.
Let me talk...
Bail paid.
Now if you slap a policeman I'll lock you up!
Go away!
Somebody teach him manners.
Sit quietly.
Keep it away.
We want to search your house... talk to your son.
Your information is wrong.
This is impossible.
We have enough proof.
My son is an army officer's son!
Some people were staying here.
Where are they now?
They were Meghna and Meeta, friends of Amar.
Where are they?
They were around.
And Amar?
There's a wedding in 4 days.
There are hundreds of jobs.
Clothes, jewellery, food...
Must be doing something.
Why did Meghna and Meeta leave?
If you have any letter or newspaper or anything at all...
Or any phone call that they made or received over here.
Give me anything of theirs that you have or remember.
It would be a service to the nation.
If I find out my son is a terrorist I'll call you myself to arrest him!
What's going on?
Where are they taking her?
Take care of everyone.
Keep walking quietly.
One word and you'll drop dead!
You can't get away...
The CBI knows everything.
They must be behind right now.
Where are you taking me?
Come to the police station.
I'll show you.
Imbecile!
My sweet...
Flirting with a girl!
Impressing a girl!
You...!
I won't leave him!
I'll lock you up!
Move behind!
Hit me, will you!
Hit me?
Now hit me!
Let go!
Who is it?
Muster up courage and come to me.
Are you hurt?
I am not dead.
And I won't die...
Till I find you.
Please come to me.
Where are you?
You can't come here.
You're my life.
Try to understand.
Don't you feel our love is more important than terrorism?
I'm too far gone... it's too late.
I won't let you go.
I won't let you go.
It's not too late.
What are you doing?
Don't shoot!
I need permission sir.
All the army cars used in the parade are to be checked.
What are you saying?
I even want to check the tanks.
That will salute the President.
This is not a fair demand.
Sir listen to me.
We've already lost a Prime Minister because of the body guards.
Security never harmed anyone.
This parade has been going on for years.
What do you think of yourself!
All the security units be revamped.
This remain secret till the morning of January 26, nobody must know...
Who is in charge of which gate...
Can this be done, General?
Yes, sir.
It will be done.
What happened to you?
I have to find Meghna.
I have to stop this.
Why don't you understand?
It is beyond us.
The CBI considers you a terrorist.
They've taken mother for inquiry.
Mother...?
Please give this up.
I have to find Meghna.
I have to stop her before morning.
You can't forget her, isn't it?
She will listen to me.
She won't do anything if she sees me.
I can stop her.
Then why have you come here?
You should've gone to Sundernagar!
What do I do about these wedding cards?
Should I write Meghna's name next to yours?
What about Sundernagar?
Why should I tell you?
I don't know there's some place behind the bus stand!
So?
Who told you about this?
The children and I overheard on the phone.
Happy?
Now answer my question.
What do I do about these?
Search him!
Who are you?
What are you doing?
He's not a terrorist!
What will happen tomorrow?
I'm not one of them.
I don't know if they make bombs.
Where are the explosives?
I'm not one of them!
You gave them shelter.
Did you keep her in your house?
Yes or no?
Yes, she had no place to stay.
Did you get her a job?
Yes I did!
Because I love her!
We accept that.
Now listen to what I say!
Did you meet terrorists in north-east?
Yes, I did.
But that's my job!
Interviewing them is your job?
Hold him.
I'm telling you, sir!
What are you doing?
All will be well in 24 hours.
You'll sleep for 24 hours.
I don't have 24 hours!
And we'll get the truth out of you!
What is going to happen?
How many people do they have?
What is their plan?
Keep shaking him awake and ask questions every half an hour.
Call me up on the wireless as soon as you get an answer.
- 2 men in the corridor and 2 men in the room.
Yes, sir.
Where has he gone?
You search here.
I'll take a look down there.
- 7 tomorrow morning...
The military van will be in place.
- 7.
15...
Jeep in position with remote.
I'll be at the block security post by 8.45.
- 9.
15...
I'll enter with the dancers by the security gate block.
Here's my security card.
If Meghna makes a mistake I'll be prepared.
- 9.30?
I'll be ready.
- 9.45...
Everyone will be in position.
The President will take his position at 9.58.
The parade will begin at 10
At 10.40...?
The dancers pass before the stage.
- 10.42...?
The wires of the sound system will be snapped.
In this confusion, I'll reach the stage with my all India radio pass.
I'll be before the television camera.
Independence of our state.
Don't fall asleep!
Stop!
Stay awake!
Get up!
Don't fall asleep...
What are you watching?
My last morning.
Are you frightened?
Not since last night.
You're looking beautiful.
Do you know why?
Because nobody is more beautiful than a martyr.
It's not essential that you take birth in a better society.
But it's essential that you give others a better society.
Who are you?
What are you doing in this van?
Where is Meghna?
Where is Meghna?
Where is she?
Don't come forward.
Why?
Don't come close to me.
I once said, I'd never leave you.
I have come.
This is the truth.
Don't touch me!
Don't come with me if you don't want to.
Take me with you.
Take me along.
Take me along.
Take me too along.
You love me.
Just once say that you love me.
Just once say that you love me.
Say it just once!
We're on problem 61.
It says the point minus 3, 2 lies on a circle whose equation is x plus 3 squared plus y plus 1 squared is equal to r squared. Which of the following must be the radius of the circle? So the way to think about it is, is that this point satisfies this equation.
Any point on the equation will satisfy both sides of this equality sign. So all we have to do is substitute the x and the y here and see what r squared has to be equal to. So let's do that.
You get minus 3, I just substituted for the x. Plus 3 squared plus, now y, y is 2. 2 plus 1 squared is equal to r squared.
Minus 3 plus 3, that's just 0. 0 squared is 0. And then 2 plus 1 squared.
And that means SOH is sine is equal to to opposite over hypotenuse. Cosine is equal to adjacent over hypotenuse. And I'll tell you what these mean in a second.
So if I took the sine of this angle. That means the opposite side of this angle over the hypotenuse is equal to the sine of this angle.
Let's call this the opposite. This is the hypotenuse. This is the adjacent side.
And they tell us that that is equal to 5/13. So opposite over hypotenuse is equal to 5/13. Now we know that that's just the ratio between the two.
So if the opposite soon. is 5 and the hypotenuse is 13, what would the adjacent be equal to? We could use the Pythagorean theorem. So we could say the adjacent squared.
A squared plus the opposite squared. So plus 5 squared, plus 25. Is equal to 13 squared.
A is equal to 12. We don't know that a is definitely equal to 12. But we know that the ratio of the opposite to adjacent is 5 to 12.
SOHCAHTOA. Cosine of x is equal to the adjacent over the hypotenuse. The adjacent is 12.
TOA, opposite over adjacent. So opposite is 4, adjacent is 12. Equal to 5/12.
In the figure below, sine of A is equal to 0.7.
They say what is the length of AC? So we want to know that. Let's call that x.
SOH tells us that sine of some angle, let's call that theta, is equal to the opposite over the hypotenuse. So sine of A, in this example, is going to be equal to the opposite, 21, over the hypotenuse, over x.
So now we can just solve this equation for x and we're done. Let's see. So if you multiply x times both sides, you get 21 is equal to 0.7x.
Well that's tangent.
TOA. Tangent of any angle is equal to the opposite over the adjacnet. In this case, tangent of 40 degrees is going to be equal to the opposite, the opposite is h, that's what we're trying to solve for, over the adjacent.
The adjacent is 20 feet.
Tangent of 40 degrees is 0.84. So we get 0.84 is equal to h/20. So we can multiply both sides of that by 20 and we get h is equal to 20 times 0.84.
Problem 65. Right triangle ABC is pictured below. Which equation gives the correct value for BC?
This is BC right there. OK, let's read them.
OK, so they're saying that the sine of 32 degrees is equal to
BC over 8.2. Is that right? Sine is opposite over hypotenuse.
BC is definitely the opposite. 8.2 is not the hypotenuse, 10.6 is the hypotenuse. So they're doing, this is the adjacent.
So this should be a tangent. Tangent of 32 is equal to BC over 8.2. This is the adjacent side, adjacent to 32 degrees.
Consider the numbers one third, seven, and negative fifteen.
To which sets of numbers, listed below does each of these numbers belong?
So let's think about the sets first and then that'll make it pretty straightforward to think about what sets these guys are members of.
So natural numbers - you can kind of view these as the counting numbers. This is one, two, three, four, five, six. Or another way to think about it - it's the whole numbers except for zero.
So zero is not in the natural numbers. It starts at one. One, two, three, four, so on and so forth.
Whole numbers, is the natural numbers, plus zero - plus zero.
Integers are the whole numbers plus the negative versions of the natural numbers.
Then rational numbers - these are any number that can be represented by a fraction.
Irrational numbers cannot be represented by a fraction.
And then real numbers are essentially all of these.
Let's think about the numbers that they gave us.
So let's first think about one third.
One third is not a counting number.
It's not a whole number - it's a fraction.
It's not an integer (it's a fraction.)
It is a rational number - it can clearly be represented as a fraction.
So I'll write it over here.
One third is a rational number. It's not an irrational number.
There's nothing that's part of both the rational and irrational.
You have to pick between one of those two.
But it's clearly a real number.
So one third is rational and it is real.
So let's do seven here.
So seven is a natural number.
When you count things, you can count up to seven. it's definately a whole number.
In fact anything that's a natural number is also going to be a whole number.
And anything that's a natural number or a whole number is also going to be an integer.
Anything that is a natural number, a whole number or integer is also going to be a rational number.
Cuz you can represent this as seven over one. Seven is equal to seven over one. And you can do this with any integer.
You can just say it's the same thing as that over one.
So you can represent it as a fraction.
So it's clearly not irrational.
But it's going to be real.
It's going to be real.
And then finally you might be saying "Hey, why do we even care about real numbers?"
In the future we'll be introduced to things called imaginary and complex numbers. And those aren't real.
But most of the numbers that you've dealt with so far, they're going to be real numbers.
So let's just finish up with negative fifteen over here.
Negative fifteen is not a counting number, it's not a natural number - it's not one two three and so on and so forth.
It's not a whole number, because that would just be zero plus one two three four five.
It is an integer though. It is an integer - so it is negative fifteen is right over here.
You can view natural numbers as all positive integers. You can view whole numbers as all non negative integers. And of course integers will include negative and nonnegative integers.
Negative fifteen can be represented as a rational number. It can be negative fifteen over one.
So we're going to put negative fifteen over here.
If it's rational it can't be irrational, and it's gonna be a real number.
And we are done.
Time flies.
It's actually almost 20 years ago when I wanted to reframe the way we use information, the way we work together:
I invented the World Wide Web.
Now, 20 years on, at TED,
I want to ask your help in a new reframing.
So going back to 1989,
I wrote a memo suggesting the global hypertext system.
Nobody really did anything with it, pretty much.
But 18 months later -- this is how innovation happens -- 18 months later, my boss said I could do it on the side, as a sort of a play project, kick the tires of a new computer we'd got.
And so he gave me the time to code it up.
So I basically roughed out what HTML should look like: hypertext protocol, HTTP; the idea of URLs, these names for things which started with HTTP.
I wrote the code and put it out there.
Why did I do it?
Well, it was basically frustration.
I was frustrated -- I was working as a software engineer in this huge, very exciting lab, lots of people coming from all over the world.
They brought all sorts of different computers with them.
They had all sorts of different data formats, all sorts, all kinds of documentation systems.
So that, in all that diversity, if I wanted to figure out how to build something out of a bit of this and a bit of this, everything I looked into, I had to connect to some new machine,
I had to learn to run some new program, I would find the information I wanted in some new data format. And these were all incompatible.
It was just very frustrating.
The frustration was all this unlocked potential.
In fact, on all these discs there were documents.
So if you just imagined them all being part of some big, virtual documentation system in the sky, say on the Internet, then life would be so much easier.
Well, once you've had an idea like that it kind of gets under your skin and even if people don't read your memo -- actually he did, it was found after he died, his copy.
He had written, "Vague, but exciting," in pencil, in the corner.
(Laughter)
But in general it was difficult -- it was really difficult to explain what the web was like.
It's difficult to explain to people now that it was difficult then.
But then -- OK, when TED started, there was no web so things like "click" didn't have the same meaning.
I can show somebody a piece of hypertext, a page which has got links, and we click on the link and bing -- there'll be another hypertext page.
Not impressive.
You know, we've seen that -- we've got things on hypertext on CD-ROMs.
What was difficult was to get them to imagine: so, imagine that that link could have gone to virtually any document you could imagine.
Alright, that is the leap that was very difficult for people to make.
Well, some people did.
So yeah, it was difficult to explain, but there was a grassroots movement.
And that is what has made it most fun.
That has been the most exciting thing, not the technology, not the things people have done with it, but actually the community, the spirit of all these people getting together, sending the emails.
That's what it was like then.
Do you know what? It's funny, but right now it's kind of like that again.
I asked everybody, more or less, to put their documents --
I said, "Could you put your documents on this web thing?"
And you did.
Thanks.
It's been a blast, hasn't it?
I mean, it has been quite interesting because we've found out that the things that happen with the web really sort of blow us away.
They're much more than we'd originally imagined when we put together the little, initial website that we started off with.
Now, I want you to put your data on the web.
Turns out that there is still huge unlocked potential.
There is still a huge frustration that people have because we haven't got data on the web as data.
What do you mean, "data"? What's the difference -- documents, data?
Well, documents you read, OK?
More or less, you read them, you can follow links from them, and that's it.
Data -- you can do all kinds of stuff with a computer.
Who was here or has otherwise seen Hans Rosling's talk?
One of the great -- yes a lot of people have seen it -- one of the great TED Talks.
Hans put up this presentation in which he showed, for various different countries, in various different colors -- he showed income levels on one axis and he showed infant mortality, and he shot this thing animated through time.
So, he'd taken this data and made a presentation which just shattered a lot of myths that people had about the economics in the developing world.
He put up a slide a little bit like this.
It had underground all the data
OK, data is brown and boxy and boring, and that's how we think of it, isn't it?
Because data you can't naturally use by itself
But in fact, data drives a huge amount of what happens in our lives and it happens because somebody takes that data and does something with it.
In this case, Hans had put the data together he had found from all kinds of United Nations websites and things.
He had put it together, combined it into something more interesting than the original pieces and then he'd put it into this software, which I think his son developed, originally, and produces this wonderful presentation.
And Hans made a point of saying, "Look, it's really important to have a lot of data."
And I was happy to see that at the party last night that he was still saying, very forcibly, "It's really important to have a lot of data."
So I want us now to think about not just two pieces of data being connected, or six like he did, but I want to think about a world where everybody has put data on the web and so virtually everything you can imagine is on the web and then calling that linked data.
The technology is linked data, and it's extremely simple.
If you want to put something on the web there are three rules: first thing is that those HTTP names -- those things that start with "http:" -- we're using them not just for documents now, we're using them for things that the documents are about.
All kinds of conceptual things, they have names now that start with HTTP.
Second rule, if I take one of these HTTP names and I look it up and I do the web thing with it and I fetch the data using the HTTP protocol from the web,
I will get back some data in a standard format which is kind of useful data that somebody might like to know about that thing, about that event.
Who's at the event?
Whatever it is about that person, where they were born, things like that.
So the second rule is I get important information back.
Third rule is that when I get back that information it's not just got somebody's height and weight and when they were born, it's got relationships.
Data is relationships.
Interestingly, data is relationships.
This person was born in Berlin; Berlin is in Germany.
And when it has relationships, whenever it expresses a relationship then the other thing that it's related to is given one of those names that starts HTTP.
So, I can go ahead and look that thing up.
So I look up a person -- I can look up then the city where they were born; then
I can look up the region it's in, and the town it's in, and the population of it, and so on.
So I can browse this stuff.
So that's it, really.
That is linked data.
I wrote an article entitled "Linked Data" a couple of years ago and soon after that, things started to happen.
The idea of linked data is that we get lots and lots and lots of these boxes that Hans had, and we get lots and lots and lots of things sprouting.
It's not just a whole lot of other plants.
It's not just a root supplying a plant, but for each of those plants, whatever it is -- a presentation, an analysis, somebody's looking for patterns in the data -- they get to look at all the data and they get it connected together, and the really important thing about data is the more things you have to connect together, the more powerful it is.
So, linked data.
The meme went out there.
And, pretty soon Chris Bizer at the Freie Universitat in Berlin who was one of the first people to put interesting things up, he noticed that Wikipedia -- you know Wikipedia, the online encyclopedia with lots and lots of interesting documents in it.
Well, in those documents, there are little squares, little boxes.
And in most information boxes, there's data.
So he wrote a program to take the data, extract it from Wikipedia, and put it into a blob of linked data on the web, which he called dbpedia.
Dbpedia is represented by the blue blob in the middle of this slide and if you actually go and look up Berlin, you'll find that there are other blobs of data which also have stuff about Berlin, and they're linked together.
So if you pull the data from dbpedia about Berlin, you'll end up pulling up these other things as well.
And the exciting thing is it's starting to grow.
This is just the grassroots stuff again, OK?
Let's think about data for a bit.
Data comes in fact in lots and lots of different forms.
Think of the diversity of the web.
It's a really important thing that the web allows you to put all kinds of data up there.
So it is with data.
I could talk about all kinds of data.
We could talk about government data, enterprise data is really important, there's scientific data, there's personal data, there's weather data, there's data about events, there's data about talks, and there's news and there's all kinds of stuff.
I'm just going to mention a few of them so that you get the idea of the diversity of it, so that you also see how much unlocked potential.
Let's start with government data.
Barack Obama said in a speech, that he -- American government data would be available on the Internet in accessible formats.
And I hope that they will put it up as linked data.
That's important.
Why is it important?
Not just for transparency, yeah transparency in government is important, but that data -- this is the data from all the government departments
Think about how much of that data is about how life is lived in America.
It's actual useful.
It's got value.
I can use it in my company.
I could use it as a kid to do my homework.
So we're talking about making the place, making the world run better by making this data available.
In fact if you're responsible -- if you know about some data in a government department, often you find that these people, they're very tempted to keep it --
Hans calls it database hugging.
You hug your database, you don't want to let it go until you've made a beautiful website for it.
Well, I'd like to suggest that rather -- yes, make a beautiful website, who am I to say don't make a beautiful website?
Make a beautiful website, but first give us the unadulterated data, we want the data.
We want unadulterated data.
OK, we have to ask for raw data now.
And I'm going to ask you to practice that, OK?
Can you say "raw"?
Audience:
Raw.
Tim Berners-Lee:
Can you say "data"?
Audience:
Data.
TBL:
Can you say "now"?
Audience:
Now!
TBL:
Alright, "raw data now"!
Audience:
Raw data now!
Practice that.
It's important because you have no idea the number of excuses people come up with to hang onto their data and not give it to you, even though you've paid for it as a taxpayer.
And it's not just America. It's all over the world.
And it's not just governments, of course -- it's enterprises as well.
So I'm just going to mention a few other thoughts on data.
Here we are at TED, and all the time we are very conscious of the huge challenges that human society has right now -- curing cancer, understanding the brain for Alzheimer's, understanding the economy to make it a little bit more stable, understanding how the world works.
The people who are going to solve those -- the scientists -- they have half-formed ideas in their head, they try to communicate those over the web.
But a lot of the state of knowledge of the human race at the moment is on databases, often sitting in their computers, and actually, currently not shared.
In fact, I'll just go into one area -- if you're looking at Alzheimer's, for example, drug discovery -- there is a whole lot of linked data which is just coming out because scientists in that field realize this is a great way of getting out of those silos, because they had their genomics data in one database in one building, and they had their protein data in another.
Now, they are sticking it onto -- linked data -- and now they can ask the sort of question, that you probably wouldn't ask, I wouldn't ask -- they would.
What proteins are involved in signal transduction and also related to pyramidal neurons?
Well, you take that mouthful and you put it into Google.
Of course, there's no page on the web which has answered that question because nobody has asked that question before.
You get 223,000 hits -- no results you can use.
You ask the linked data -- which they've now put together -- 32 hits, each of which is a protein which has those properties and you can look at.
The power of being able to ask those questions, as a scientist -- questions which actually bridge across different disciplines -- is really a complete sea change.
It's very very important.
Scientists are totally stymied at the moment -- the power of the data that other scientists have collected is locked up and we need to get it unlocked so we can tackle those huge problems.
Now if I go on like this, you'll think that all the data comes from huge institutions and has nothing to do with you.
But, that's not true.
In fact, data is about our lives.
You just -- you log on to your social networking site, your favorite one, you say, "This is my friend."
Bing!
Relationship.
Data.
You say, "This photograph, it's about -- it depicts this person. "
Bing!
That's data.
Data, data, data.
Every time you do things on the social networking site, the social networking site is taking data and using it -- re-purposing it -- and using it to make other people's lives more interesting on the site.
But, when you go to another linked data site -- and let's say this is one about travel, and you say, "I want to send this photo to all the people in that group," you can't get over the walls.
The Economist wrote an article about it, and lots of people have blogged about it -- tremendous frustration.
The way to break down the silos is to get inter-operability between social networking sites.
We need to do that with linked data.
One last type of data I'll talk about, maybe it's the most exciting.
Before I came down here, I looked it up on OpenStreetMap
The OpenStreetMap's a map, but it's also a Wiki.
Zoom in and that square thing is a theater -- which we're in right now --
The Terrace Theater.
It didn't have a name on it.
So I could go into edit mode, I could select the theater,
I could add down at the bottom the name, and I could save it back.
And now if you go back to the OpenStreetMap. org, and you find this place, you will find that The Terrace Theater has got a name.
I did that.
Me!
I did that to the map. I just did that!
I put that up on there.
Hey, you know what?
If I -- that street map is all about everybody doing their bit and it creates an incredible resource because everybody else does theirs.
And that is what linked data is all about.
It's about people doing their bit to produce a little bit, and it all connecting.
That's how linked data works.
You do your bit.
Everybody else does theirs.
You may not have lots of data which you have yourself to put on there but you know to demand it.
And we've practiced that.
So, linked data -- it's huge.
I've only told you a very small number of things
There are data in every aspect of our lives, every aspect of work and pleasure, and it's not just about the number of places where data comes, it's about connecting it together.
And when you connect data together, you get power in a way that doesn't happen just with the web, with documents. You get this really huge power out of it.
So, we're at the stage now where we have to do this -- the people who think it's a great idea.
And all the people -- and I think there's a lot of people at TED who do things because -- even though there's not an immediate return on the investment because it will only really pay off when everybody else has done it -- they'll do it because they're the sort of person who just does things which would be good if everybody else did them.
OK, so it's called linked data.
I want you to make it.
I want you to demand it.
And I think it's an idea worth spreading.
Thanks.
(Applause)
This story is about taking imagination seriously.
Fourteen years ago, I first encountered this ordinary material, fishnet, used the same way for centuries.
Today, I'm using it to create permanent, billowing, voluptuous forms the scale of hard-edged buildings in cities around the world.
I was an unlikely person to be doing this.
I never studied sculpture, engineering or architecture.
In fact, after college I applied to seven art schools and was rejected by all seven.
I went off on my own to become an artist, and I painted for 10 years, when I was offered a Fulbright to India.
Promising to give exhibitions of paintings, I shipped my paints and arrived in Mahabalipuram.
The deadline for the show arrived -- my paints didn't.
I had to do something.
This fishing village was famous for sculpture.
So I tried bronze casting.
But to make large forms was too heavy and expensive.
I went for a walk on the beach, watching the fishermen bundle their nets into mounds on the sand.
I'd seen it every day, but this time I saw it differently -- a new approach to sculpture, a way to make volumetric form without heavy solid materials.
My first satisfying sculpture was made in collaboration with these fishermen.
It's a self-portrait titled "Wide Hips."
(Laughter)
We hoisted them on poles to photograph.
I discovered their soft surfaces revealed every ripple of wind in constantly changing patterns.
I was mesmerized.
I continued studying craft traditions and collaborating with artisans, next in Lithuania with lace makers.
I liked the fine detail it gave my work, but I wanted to make them larger -- to shift from being an object you look at to something you could get lost in.
Returning to India to work with those fishermen, we made a net of a million and a half hand-tied knots -- installed briefly in Madrid.
Thousands of people saw it, and one of them was the urbanist
Manual Sola-Morales who was redesigning the waterfront in Porto, Portugal.
He asked if I could build this as a permanent piece for the city.
I didn't know if I could do that and preserve my art.
Durable, engineered, permanent -- those are in opposition to idiosyncratic, delicate and ephemeral.
For two years, I searched for a fiber that could survive ultraviolet rays, salt, air, pollution, and at the same time remain soft enough to move fluidly in the wind.
We needed something to hold the net up out there in the middle of the traffic circle.
So we raised this 45,000-pound steel ring.
We had to engineer it to move gracefully in an average breeze and survive in hurricane winds.
But there was no engineering software to model something porous and moving.
I found a brilliant aeronautical engineer who designs sails for America's Cup racing yachts named Peter Heppel.
He helped me tackle the twin challenges of precise shape and gentle movement.
I couldn't build this the way I knew because hand-tied knots weren't going to withstand a hurricane.
So I developed a relationship with an industrial fishnet factory, learned the variables of their machines, and figured out a way to make lace with them.
There was no language to translate this ancient, idiosyncratic handcraft into something machine operators could produce.
So we had to create one.
Three years and two children later, we raised this 50,000-square-foot lace net.
It was hard to believe that what I had imagined was now built, permanent and had lost nothing in translation.
(Applause)
This intersection had been bland and anonymous.
Now it had a sense of place.
I walked underneath it for the first time.
As I watched the wind's choreography unfold, I felt sheltered and, at the same time, connected to limitless sky.
My life was not going to be the same.
I want to create these oases of sculpture in spaces of cities around the world.
I'm going to share two directions that are new in my work.
Historic Philadelphia City Hall: its plaza, I felt, needed a material for sculpture that was lighter than netting.
So we experimented with tiny atomized water particles to create a dry mist that is shaped by the wind and in testing, discovered that it can be shaped by people who can interact and move through it without getting wet.
I'm using this sculpture material to trace the paths of subway trains above ground in real time -- like an X-ray of the city's circulatory system unfolding.
Next challenge, the Biennial of the Americas in Denver asked, could I represent the 35 nations of the Western hemisphere and their interconnectedness in a sculpture?
(Laughter)
I didn't know where to begin, but I said yes.
I read about the recent earthquake in Chile and the tsunami that rippled across the entire Pacific Ocean.
It shifted the Earth's tectonic plates, sped up the planet's rotation and literally shortened the length of the day.
So I contacted NOAA, and I asked if they'd share their data on the tsunami, and translated it into this.
Its title:
"1.26" refers to the number of microseconds that the Earth's day was shortened.
I couldn't build this with a steel ring, the way I knew.
Its shape was too complex now.
So I replaced the metal armature with a soft, fine mesh of a fiber 15 times stronger than steel.
The sculpture could now be entirely soft, which made it so light it could tie in to existing buildings -- literally becoming part of the fabric of the city.
There was no software that could extrude these complex net forms and model them with gravity.
So we had to create it.
Then I got a call from New York City asking if I could adapt these concepts to Times Square or the High Line.
This new soft structural method enables me to model these and build these sculptures at the scale of skyscrapers.
They don't have funding yet, but I dream now of bringing these to cities around the world where they're most needed.
Fourteen years ago, I searched for beauty in the traditional things, in craft forms.
Now I combine them with hi-tech materials and engineering to create voluptuous, billowing forms the scale of buildings.
My artistic horizons continue to grow.
I'll leave you with this story.
I got a call from a friend in Phoenix.
An attorney in the office who'd never been interested in art, never visited the local art museum, dragged everyone she could from the building and got them outside to lie down underneath the sculpture.
There they were in their business suits, laying in the grass, noticing the changing patterns of wind beside people they didn't know, sharing the rediscovery of wonder.
Thank you.
(Applause)
Thank you.
Thank you.
Thank you.
Thank you.
Thank you.
(Applause)
In the last video we did some examples were we had one digit repeating on and on forever and we were able to convert those into fractions. In this video, we want to tackle something a little bit more interesting which is multiple digits repeating on and on forever.
So let's say I had 0.36 repeating, which is the same thing as -- since the bar is over the three and the six, both of those repeat: 3 6, 3 6, 3 6... and it just keeps going on and on like that forever.
Now the key to doing this type of problem is instead of multiplying --
like we did in the last video: we said "this is equal to x".
Instead of just multiplying it by 10, ten would only shift it one over
We want to shift it over enough so that we can kind of... so that when we line them up, the decimal parts will still line up with each other.
And to do that, we want to actually shift the decimal space 2 to the right.
And to shift it 2 to the right, we have to multiply it by 100, or 10^2.
So, 100x is going to be equal to what?
We are shifting this two to the right:
One... two...
So 100x is going to be equal to...
The decimal is going to be there now, so, its going to be 36.36...36...36... and on and on forever.
And then let me rewrite x over here, we are going to subtract that from the 100x. X is equal to 0.363636... repeating on and on forever.
And notice when we multiply it by 100, the 3's and the 6's still line up with each other.
When we align the decimals, you want to make sure that the decimals line up appropriately.
And the reason why this is valuable is that now, when we subtract x from 100x, the repeating parts will cancel out.
So, let's subtract. Let us subtract these two things.
On the left-hand side we have 100x - x, so that gives us 99x.
And then on the right-hand side, this part cancels out with that part, and we are just left with 36.
We can divide both sides by 99, and we are left with x = 36 / 99 and both the numerator and the denominator is divisible by 9, so we can reduce this.
If we divide the numerator by 9 we get 4, and the denominator by 9, we get 11.
So 0.363636 forever and forever repeating is four elevenths.
Now let's do another interesting one. Let's say we have... - and I will just set it equal to x -
let's say we have the number the number 0.714, and the 14 is repeating. so this the same thing, so notice the 714 isn't going to repeat, just the 14 is going to repeat.
So this is 0.714, 14, 14... on and on and on.
So lets set this equal to X. Now you might be tempted to multiply this by 1000, to get the decimal all the way clear of 714.
So again in this situation, even though we have 3 numbers behind the decimal point, because only two of them are repeating we only want to multiply it by 10^2.
So once again, you want to multiply it by 100.
So you get 100x = ...
One..., two...
So, it's going to be 71.414141 and on and on. And then let me rewrite x below this. we have x = 0.1714, 14, 14 ... And notice: now, the 14, 14, 14's are lined up right below each other. so it is going to work out when we subtract.
So, let's subtract these things:
100x - x = 99x, and this is going to be equal to... these 14, 14's are going to cancel those 14, 14's and we have 71.4 - .7 we can do this in our head or we can borrow if you like: this could be fourteen, this is a zero, so you have 14 - 7 = 7 and then 70 minus 0.
So, you have 99x = 70.7. And then we can divide both sides by 99; you could see that also something strange is happening because we still have a decimal, but we can fix that up in the end.
So, lets divide both sides by ninety-nine: You get x = 70.7 / 99. Now, obviously, we have not converted this into a pure fraction yet.
But that is pretty easy to fix: you just have to multiply the numerator and the denominator by ten to get rid of this decimal. So lets multiply the numerator by ten and the denominator by ten. and so we get 707 / 990. Let's do one more example.
Let's say we have something like 3.257 repeating, and we want to covert this into a fraction. so once again, we set this equal to X, and notice: this is going to be 3.257, 257, 257...
The 257 is going to repeat on and on and on. Since we have three digits that are repeating, we want to think about a thousand x, 10 to the 3rd power times x and that will let us shift it just right so that the repeating parts can cancel out. so 1,000x is going to be equal to what?
We're going to shift the decimal to the right, 1, 2, 3... so it' s going to be 3,257 point... and then the 257 keeps repeating: 257, 257, 257 keeps going on and on forever. And then we are going to subtract X from that. so here is x; x is equal to 3.
- You want to make sure you have your decimals lined up - 3.257 257 257 . . . keeps going on forever.
Notice when we multiply it by 1,000 it allowed us to line up the 257's so that when we subtract, the repeating part cancels out.
So let's do that subtraction. On the left-hand side a thousand of something minus One of that something, You are left with 999 of that something. is equal to
So you have 999x = 3,254.
And then you can divide both sides of this by 999.
And you are left with x = 3,254 / 999.
Obviously this is improper fraction the numerator is larger than the denominator.
You could convert this to a proper fraction if you like, You could just try to figure out what the 0,257 repeating forever part is equal to and have 3 being the whole number part of the mixed fraction, or you can just divide 999 into 3254.
999 goes into 3254... it will go into it 3 times, we know that because this is originally 3.257 so we are just going to find out the remainder. So, 3 x 9 = 27, we add the 2's, so we have 29 3 x 9 = 27, we add the 2's, so we have 29 so we are left with, if we subtract, if we re-group, or borrow, however we want to call it, this could be 14, this could be a 4, (I'll use a new color) this would be a 4, and then the 4 is still smaller than this 9, so we need to re-group again so this could be 14 and this could be 1, but this is still smaller then this 9 right over here, so we re-group it again, this would be 11 and then this is a 2, 14 - 7 = 7, 14 - 9 = 5, 11 - 9 = 2, so we are left with did I do that right? - Yep so this is going to be equal to 3 and 257 over 999.
For years I've been feeling frustrated, because as a religious historian,
I've become acutely aware of the centrality of compassion in all the major world faiths.
Every single one of them has evolved their own version of what's been called the Golden Rule.
Sometimes it comes in a positive version --
"Always treat all others as you'd like to be treated yourself."
And equally important is the negative version --
"Don't do to others what you would not like them to do to you."
Look into your own heart, discover what it is that gives you pain and then refuse, under any circumstance whatsoever, to inflict that pain on anybody else.
And people have emphasized the importance of compassion, not just because it sounds good, but because it works.
People have found that when they have implemented the Golden Rule as Confucius said, "all day and every day," not just a question of doing your good deed for the day and then returning to a life of greed and egotism, but to do it all day and every day, you dethrone yourself from the center of your world, put another there, and you transcend yourself.
And it brings you into the presence of what's been called God, Nirvana, Rama, Tao.
Something that goes beyond what we know in our ego-bound existence.
But you know you'd never know it a lot of the time, that this was so central to the religious life.
Because with a few wonderful exceptions, very often when religious people come together, religious leaders come together, they're arguing about abstruse doctrines or uttering a council of hatred or inveighing against homosexuality or something of that sort.
Often people don't really want to be compassionate.
I sometimes see when I'm speaking to a congregation of religious people a sort of mutinous expression crossing their faces because people often want to be right instead.
And that of course defeats the object of the exercise.
Now why was I so grateful to TED?
Because they took me very gently from my book-lined study and brought me into the 21st century, enabling me to speak to a much, much wider audience than I could have ever conceived.
Because I feel an urgency about this.
If we don't manage to implement the Golden Rule globally, so that we treat all peoples, wherever and whoever they may be, as though they were as important as ourselves,
I doubt that we'll have a viable world to hand on to the next generation.
The task of our time, one of the great tasks of our time, is to build a global society, as I said, where people can live together in peace.
And the religions that should be making a major contribution are instead seen as part of the problem.
And of course it's not just religious people who believe in the Golden Rule.
This is the source of all morality, this imaginative act of empathy, putting yourself in the place of another.
And so we have a choice, it seems to me.
We can either go on bringing out or emphasizing the dogmatic and intolerant aspects of our faith, or we can go back to the rabbis. Rabbi Hillel, the older contemporary of Jesus, who, when asked by a pagan to sum up the whole of Jewish teaching while he stood on one leg, said, "That which is hateful to you, do not do to your neighbor.
That is the Torah and everything else is only commentary."
And the rabbis and the early fathers of the church who said that any interpretation of scripture that bred hatred and disdain was illegitimate.
And we need to revive that spirit.
And it's not just going to happen because a spirit of love wafts us down.
We have to make this happen, and we can do it with the modern communications that TED has introduced.
Already I've been tremendously heartened at the response of all our partners.
In Singapore, we have a group going to use the Charter to heal divisions recently that have sprung up in Singaporean society, and some members of the parliament want to implement it politically.
In Malaysia, there is going to be an art exhibition in which leading artists are going to be taking people, young people, and showing them that compassion also lies at the root of all art.
Throughout Europe, the Muslim communities are holding events and discussions, are discussing the centrality of compassion in Islam and in all faiths.
But it can't stop there.
It can't stop with the launch.
Religious teaching, this is where we've gone so wrong, concentrating solely on believing abstruse doctrines.
Religious teaching must always lead to action.
And I intend to work on this till my dying day.
And I want to continue with our partners to do two things -- educate and stimulate compassionate thinking.
Education because we've so dropped out of compassion.
People often think it simply means feeling sorry for somebody.
But of course you don't understand compassion if you're just going to think about it.
You also have to do it.
I want them to get the media involved because the media are crucial in helping to dissolve some of the stereotypical views we have of other people, which are dividing us from one another.
The same applies to educators.
I'd like youth to get a sense of the dynamism, the dynamic and challenge of a compassionate lifestyle.
And also see that it demands acute intelligence, not just a gooey feeling.
I'd like to call upon scholars to explore the compassionate theme in their own and in other people's traditions.
And perhaps above all, to encourage a sensitivity about uncompassionate speaking, so that because people have this Charter, whatever their beliefs or lack of them, they feel empowered to challenge uncompassionate speech, disdainful remarks from their religious leaders, their political leaders, from the captains of industry.
Because we can change the world, we have the ability.
I would never have thought of putting the Charter online.
I was still stuck in the old world of a whole bunch of boffins sitting together in a room and issuing yet another arcane statement.
And TED introduced me to a whole new way of thinking and presenting ideas.
Because that is what is so wonderful about TED.
In this room, all this expertise, if we joined it all together, we could change the world.
And of course the problems sometimes seem insuperable.
But I'd just like to quote, finish at the end with a reference to a British author, an Oxford author whom I don't quote very often,
C.S. Lewis.
But he wrote one thing that stuck in my mind ever since I read it when I was a schoolgirl.
It's in his book "The Four Loves."
He said that he distinguished between erotic love, when two people gaze, spellbound, into each other's eyes.
And then he compared that to friendship, when two people stand side by side, as it were, shoulder to shoulder, with their eyes fixed on a common goal.
We don't have to fall in love with each other, but we can become friends.
And I am convinced.
I felt it very strongly during our little deliberations at Vevey, that when people of all different persuasions come together, working side by side for a common goal, differences melt away.
And we learn amity.
And we learn to live together and to get to know one another.
Thank you very much.
(Applause)
<i> Flnal Episode
Abracadabra...Goo Jun Pyo, remember Geum Jan Di, remember Geum Jan Di...
Abracadabra, abracadabra..!!
Ohhh!! You scared mee!
You little brat!!
What the hell are you doing here?? i also think that,I think you've been under a lot of stress lately.
You're getting a zit on that good-looking face of yours.
What is this?
Can't you see, it's a lunchbox.
Lunchbox?
Is it good??
This...
- You made this? <BR>- What??
Yeah...if it's good, I'll bring it again next time.!
You must be thirsty.
Do you want me to go get you some water?
I remember.!
The person that I forgot.. is you, right?
Here you go.
Thank you.
Come back again. Welco ...
- One order of abalone porridge.
- And one order of pumpkin porridge.
Sunbae...
What brings you guys here?
Can't you see?
We came to eat porridge.
- Ahh, I'm so full. <BR>- Me too.
Now tell us, is there something wrong?
For Geum JanDi who can't even take care of her boyfriend because of her job...we brought some news.
Huh?
JunPyo finally got discharged.
R..Really?
How can you guys say something so important after you're done eating?
Hurry up and go.
I'll be back.
Sunbae, you're not going?
No. I came here because of you.
They look happy...the pottery that's in there.
Instead of suffering from the heat, they rather look happy.
Why?
Because if they endure it, once they come out, they will be loved...they hold that hope.
That's so like Gaeul.
You can tell me now.
I'm ready.
You have something to say, right?
Would you like the bad news first again?
I'm ... ....leaving.
If you think about it, that might not be such bad news for you.
Where to?
Sweden.
When....no - or how long? - Soon
Probably about four to five years.
That's great.
You'll be an even greater potter.
If you think about it, this can also be good news...so what's the other news?
When I come back.... ....you'll be the first one I look for.
Sunbae...
I mean, that's only if by that time, you still haven't found your soulmate.
Put more firewood! The pottery has to be 1300 degrees C!
Goo JunPyo, congrats on your discharge..... Oh, it's JanDi Unnie.
Hi, JanDi Unnie!
Oh, hi. Yumi, you're here, too.
What are you doing here?
JiHoo is not here.
I heard that you were discharged. Just wanted to say congrats.
How nosy you are!
Why don't you just take care of your own boyfriend.
Does JiHoo know that you're going around like this?
- Hey, watch what you say.
- What?
JiHoo Sunbae has no reason to hear such things from you.
Then why don't you behave so it's not so embarrassing.
Fine.
I shouldn't have come.
You just take care of youself.
What's wrong with you, Oppa.
You're so mean.
Unnie, don't go.
Tea's coming.
Oppa's tea is really good.
Have some tea.
Tea is ready.
Bring it here, please.
Unnie, come sit over here.
Oh, it looks so good.
Ah!
I'll do it myself
Is it good?
I spilled it all over.
You should try it.
Mmmm, tastes good.
I'm leaving
You... don't come back again.
Whenever I see you, my mood turns sour.
You get on my nerves.
I get it. I'm sorry.
I won't come back again!
Unni!
The person that JunPyo oppa has to remember, is that you, by any chance?
I'm right.
But as you can see, seeing you isn't good for him.
Whenever he sees you, his condition worsens.
So, from the moment on, it's best if you don't come here anymore.
But don't worry.
Every chance I get, I'll work really hard to try and get him to remember you.
Take care, then.
- Make me that. <BR>- What?
- That lunchbox that you made last time.<BR>- Lunchbox?
The rolled eggs that you made for me at the hospital.
Make that for me again.
Ahhh, that.
Okay, oppa.
But there are so many more tasty foods to eat here.
Why do you want to eat that?
I'm sorry.
-Sunbae? <BR> -Don't escape.
- Let me go. <BR>- No!
You can't back off now.
Jandi!
It's all over now.
It's useless now
You see, I believed that even though he lost his memory, even if we had to start all over again, that he'd recognize me.
But, the fact is I was wrong.
-That's not it. <BR> -No.
I may be upset and feel cheated, but I have to accept it.
The Goo Joonpyo that I liked, the Goo Joonpyo who loved me, doesn't exist anymore.
I told you, you can't become like the little mermaid
I refuse to accept that you, two will break up over something as nonsensical as this. i can't accept it
It's not because of Yumi.
Ultimately, Goo Joonpyo and Geum Jandi...
It's the end for us
Eat it all
What's wrong?
Does it taste bad?
-This isn't it. <BR>-Huh?
This isn't the same flavor as before.
Did you really make that other one?
Uh, of course.
Of course I made it.
Who else would have?
It's just that each time you make it, it tastes a little different.
Next time, I'll make it just right.
Is there something making you feel bad?
That girl...
Jandi or Japcho ("lawn" or "weed"), that girl's expression...
I can't erase it from my mind.
You're too much.
How could you?
From the time you were in the hospital until now, I was the one who has been at your side.
But that un-nee who pops up every now and then to irritate you, she gets stuck in your mind?
Your friends treat me like crap and always take that un-nee's side.
And that un-nee's boyfriend treats me as though I have some disease, completely ignoring me.
But, for you...because I was worried about you, I put up with it all...
But, if you act like this too, then what am I supposed to do?
Hey!
What's the matter? <i>Invitation: "Surprise pool party thrown by Goo Joonpyo and Chang Yumi"
Un-nee, you came!
- Have you been well?<BR>- I'm glad you came, I have something to report to you.
Report....?
Oppa still can't remember you.
- Is that so?<BR>- And one other thing...
I'm sorry for you, but I like Joonpyo oppa.
What?
It's not that I did it on purpose; it just happened.
I like him so much that I can't part from him.
Oppa feels the same way as I do. Sorry.
I know you'll understand, right?
A person's heart can't be controlled the way we want...
Oh, look at the time...
I need to tell everyone the reason for this party.
Reason?
Un-nee, come over in a little bit.
Don't collapse now.
Let's go hear what they have to say.
We invited you all here because we have a special announcement to make.
Goo Joonpyo and Jang Yumi, we have decided to study in America next month.
What?
What is that girl talking about?
Study abroad?
I'm going to continue my studies and oppa will carry on with his business.
Don't feel too sad while we're gone, and be happy until we meet again.
That girl is something else.
It's a shock to get hit in the back of the head like this.
Let's go.
I'll get you a glass of warm water.
Goo JoonPyo!
Do you remember this?
What is it?
You don't remember the names on this?
JJ
How would I know something like this?
I'll return it.
Take it back.
Why would I take something like this?
If you want to get rid of it, throw it away yourself.
Yeah.
Goo JoonPyo.
I'll ask just once more, just one more question.
What now?
Do you know how to swim?
Swim?
I don't swim.
Don't swim or can't swim?
Because of a bad experience when I was a kid, I don't swim.
I've never done it.
No.
You do know how to swim
What are you?
Who do you think you are to blab off about me.
You don't fear anything in the world, but you're so scared of bugs, you shake.
You the idiot who would rather his ribs all bust apart than see one finger on his woman hurt.
You're the idiot who doesn't know the difference between "privacy" and "pride" who insists that the 38th parallel are train tracks.
You freak out when it comes to kids, but... you want to be a devoted father... who will go out and look at the stars with his son.
You're a lonely but loving guy.
Who do you think you are?
That's who you are, Goo Joonpyo.
I'm asking who you are?
You call it out.
My name.
Geum JanDi.
JanDi yah!!
Geum JanDi...wake up!
JanDi....Geum JanDi!!
Are you all right?
Do you remember now?
Geum JanDi...you scare me like that one more time and you're dead!
You remember....
I'm sorry...
I'm sorry...
Say it again....my name.
Jan Di...
It seems like just yesterday that our Jandi started high school, yet it's already graduation.
I'm sorry mom that I can't get a job or go to college like others do.
Noona, you don't have to take a test to go to Shinhwa University, isn't it the same for medical school?
If I want to get a scholarship, I have to take the test.
No, your life has been full of obstacles, now, I want you to do what you want to do.
And by the way, what are you wearing to the graduation?
I'm not going...
Why would I....
Aren't you a graduate of ShinHwa?
Why wouldn't you go?
Please don't concern yourself. Come out to the front of your house.
Congratulations on your graduation.
Thanks!
Do you really need to go to medical school?
Why?
What are you about to say?
There's no guarantee that studying for another year is going to help.
And?
If any, think about it...a doctor like you?
You'd probably cut them up.
What?
Even without a scalpel (surgical knife) you cut people up.
You...didn't really come to congratulate me on my graduation, did you?
You came to make fun of me, right?
Ah, hey!
Hey, Geum Jandi, tomorrow, you...
Got it?
If you're late again this time, you're dead!
Go on in and sleep.
It's F4!! Grandpa!
I'll throw the garbage out and then get your tea
Oh, okay.
That little rascal...
Came already!
Geum Jandi!
Why did you come this late?
Oh, well, I...
You weren't planning to just skip this last event, were you?
We're not even high schoolers, so why do you think we're here?
Huh?
The great F4 have been waiting all day to dance with Geum Jandi.
Miss Jandi, would you do me the great honor of dancing with me?
- With me? <BR>- Let's go.
No, just a minute...
Woobin sunbae, who was the backbone and support of F4...
I know that you are always one step behind, offering your heart in support...
I know that now.
Although you act cold and mean... in reality, you are warmer and more pure than others.
Thanks to you, I think that Gaeul has experienced a beautiful love.
Don't you think it's time to give others a turn?
Rascal...
What can I do since my clothes are like this? <BR> It's perfect.
Don't you think it's the perfect outfit for Geum Jandi to finish her high school life?
As if having falling into a wonderland like Alice....
It will go to the emergency bell, the possibility which it will meet you there is a fact. .<br/> Do you knowhow comforting it is...
You're like someone sent from the heaven to me like bonus....
I'll never be able to forget you...
My soulmate...JiHoo Sunbae....
Thank you.
What happened to JunPyo??
His phone is off.
Do you think something's happened?
You....tomorrow.....
All right?
Saturday.
4 pm.
Front of NamSan Tower.
I...have to...leave first....
You're crazy until the end.
Geum JanDi!
Didn't I say that if you were late, you'd be dead?
You're even late on a day like this...
You always just do whatever you want.
It's not some kind of magic. This kind of thing... It's easy ..
Compared to grassland management
Come here
It's a coffee that costs $36.3.
Drink it up!
Let's go.
It's been a long time since we've been here huh?
Is it open??
Why don't I see anyone here??
I rented it.
What?
I basically bought it until the morning.
And I also have something to show you.
Come here.
I told you there's something I want to show you!
What's wrong with you...there's something I want to show you...
You...do you already know?
You...do you intend to make it so that I can't get married?
You just need to marry me.
Who were you going to marry???
Move.
Just move aside. Goo Jun Pyo loves Geum Jan Di <br/> Our first night together!!! <3
It's still here!!
Now you can not get married.
Geum Jan Di.
Listen carefully to what I have to say...
So ominous... W-...W-...What is it now???
Us......
Let's get married...
Married?
Yes, married.
Why are you suddenly joking around like that??
I'm not joking
I've just barely graduated from high school.
I.... ...have to go to the U.S.
U.S?
This time, it's not because of my mom..... ...and not because of the business...
It was my decision.
Killing off a living dad...forcing an offspring to marry... or having to lobby all the time.
I don't want that kind of corporation.
I'm.... ...going to try my best.
So...if I can save the corporation then that's great... but if I can't... then I'll shut it down with my own hands.
How long will it take? ......4 years.
At least it will be 4 years...
For that long??...
So.....come with me then.
I can't..
What???
Why can't you??
When you went to Macau..... ....I made a decision, too..
About my dreams and my futuree..
What is it that I want and what is it that I want to do.
Like you..... ...the thing that I want to try my best at ,and do my best...is right here...
So???
Have a good trip....
Whatt??
I said, "Have a good trip."
4 years later, if you come back as a great man, I will think about it again then..
Geum Jan Di.
Are you serious
You are going to regret for letting me go
Hey, you are the one who is going to regret it!
Alright, you win
I already know... that I would regret until I die for letting you go
Goo Joon Pyo
You might not be as stupid as you look
You wanna die?
4 years later <i>Shinhwa group's managing Director, Goo JunPyo covers 3 international economic magazines.
Thank you for coming on our show.
Hello.
I heard not too long ago that you are the first Korean to be on the cover of 3 international economic magazines.
Congratulations.
-Thank you.
We'll change the topic a little bit now.
The viewers, especially the women in Korea, would like to hear some personal information.
Of course, you're managing an international company, but you're also in the prime of your 20s
So I'm sure you're lonely sometimes.
How do you overcome that?
Dating or love.
It seems like you're curious about these aspects of my life.
You certainly have a faster understanding of things than others.
Yes.
Well, to say I wasn't lonely or had it hard is probably a lie.
But because of a promise I made with someone, I was able to rely on that and endure it.
It shows that you have someone special in your heart. yes...well
A lover?
Lately, there's been a lot of rumors about your marriage.
Since you're already here.
How about you tell us a little about who she is?
Is that a grape?
-Yes
You're still putting too much pressure in your hands.
YiJung Sunbae...
Hi
Who is he?
Is he teacher's boyfriend?
Mister did you just come back from another country ?
Oh, how did you know?
Then, did you just come back from Sweden?
Little miss, you're really amazing.
Then you're him!
Our teacher said her boyfriend was there.
You can't tell him that!
Hey wait!
Wait!
Wait!
Thank you!
Hey, third repeater.
Are you late even on a day like today?
Not a day goes by that you don't cause trouble..
I'm sorry, Sunbae-nim.
I'm sorry.
Do you think it'll end like that?
Sunbae!
Hey, Geum JanDi!
-Yes.
Can't you do this properly?
What is this?
I'm sorry.
Do it again. Hurry!
-I'm sorry Sunbae-nim..
You came?
By the look on your face, looks like you made another mistake.
Sunbae, since you entered on time, you're already in the graduating class...
When am I, a third-year ever going to finish and in what millennium will I become a doctor?
The future sure looks dark.
You're not worried about flunking?
Sunbae!
It's because of you that I've lasted this long as an outcast.
When I think about what I'm going to do when you go to the hospital, it looks dark..
Then, should I repeat too?
Aigoo, that's all right.
That's scarier than a flunking joke.
It's not a joke.
Sunbae, you have to hurry and become a doctor so you can reopen your grandfather's clinic..
That's why you went back and studied.. That wasn't the only reason.
What?
Doctor prince, my throat hurts.
Doctor prince?
SaeByul is going to grow up and marry Doctor Prince later in the future.
We'll get married next time.
Right now, say "ah'.
Commoner, can you hear me?
Geum JanDi respond.
Are you there Geum JanDi?
If you're there, come meet me on the beach. Goo JoonPyo?.
Goo Joon Pyo?
You took 5 minutes!
Can't you walk faster?!
Goo JoonPyo.
What's going on?
What do you mean?
Goo JoonPyo has come back for Geum JanDi.
Seeing you wearing this white gown, I guess ugly ducklings can become swans after all.
It's Goo JoonPyo.
You're really Goo JoonPyo.
I missed you.
Enough to die.
I'm not going to let you go again.
You promised, didn't you?
When I returned, you'd take responsibility for me.
Look here, Mr. Goo JoonPyo with a bad memory.
I said when you returned in four years, I would think about it.
I never said I would take responsibility.
Your memory is bad too, but you remember that well.
In my memory, there was another condition.
What?
The one about if you come back as a really amazing man.
Can you really say that in front of the great Goo JunPyo?
Geum JanDi...
Please marry this great Goo JunPyo.
I object to that proposal!
I also object!
Me too!
You guys can't do that so easily without our permission.
Welcome back.
So let's figure out the equation for the volume of a sphere.
So what's the equation?
It's x squared plus y squared is equal to r squared.
And let's just write y as a function of x, just so we can do it the way we did that last problem.
So you get y squared is equal to r squared minus x squared. y is equal to the square root of r squared minus x squared. And let's draw it.
So if this is my y-axis, this is my x-axis, and the equation-- draw it straight-- that's my x-axis, and then I actually have a circle tool, let me see if I can use it effectively-- well, close enough.
So y equals the square root of r squared minus x squared.
That's just going to be the upper half of the circle.
So it will be the positive x quadrant-- and then actually,
I should have drawn the whole hemisphere.
So this, that's the y-axis, that's my x-axis, and then this-- the square root is, since it's a function, it can only have one value, so we assume it's defined as the positive square root.
So if we were to graph that, it would look like this.
Something like that, where this would be minus r and that's r.
So if we want to find the volume of a sphere with radius r, we just have to rotate this function around the x-axis.
This is the x-axis, that's the y-axis.
So let's see what we can do.
So let me make a disk.
So let's say that that's the side of one of the disks again, and as we know, the depth of the disk is just going to be dx.
And its radius at any point is f of x, and in this case, it's y is equal to square root of r squared minus x squared.
So what's the surface area of each disk?
What's this?
The surface area of each of the disks.
So area is equal to pi r squared, the radius at any point is equal to this, radius is equal to y which is equal to square root-- and remember, this is not this r.
This is the radius of this disk.
I know it might be a little confusing. y is equal to the square root of r squared minus x squared.
So the area is going to equal pi times this squared.
So if you square this quantity, you just get rid of the square root sign, right?
So pi r squared minus x squared, and that's the area, and so what's the volume of that disk?
Well just like we've done in every video up to this point, the volume of that disk is just that, so the volume of that disk is just this pi r squared minus x squared times dx.
And so if we want to figure out the volume of all these disks,
I have a disk here, a disk here, going around and around and around and around and around and they get smaller and smaller until we have a sphere.
We just take the integral, the upper bound is positive r, the lower bound is minus r, and we take the integral of this expression. pi-- let me distribute it, because that's going to make it easier-- pi r squared, which is just a constant term, minus pi x squared, all of that dx.
So what's the antiderivative of that expression?
The antiderivative within the parentheses.
Well, this is just a constant term. pi r squared, that's just a number, because we're just taking the integral with respect to x.
So the antiderivative of pi r squared is just pi r squared x, the derivative of pi r squared x is just pi r squared, minus-- and we did this in the last video.
Actually, well now, it's the antiderivative x squared, which is x to the third over 3, and the pi is just a constant, so pi x to the third over 3, and we're going to evaluate that at r and minus r.
So let's evaluate it at r.
So this is pi r squared, and then for x, we'll substitute the positive r times r minus pi x cubed, but now we have this r here, so r cubed over 3 minus pi r squared, and then we have a minus r here, because we're evaluating the antiderivative at minus r, times minus r, minus pi minus r cubed.
So what's minus r cubed?
It's r cubed, but we'll keep the minus sign. r cubed, and at that minus sign, let's just make that-- that'll turn that into a plus-- over 3.
So that first term is pi r cubed, r squared times r, minus essentially 1/3pi r cubed.
And then, what is this?
This is pi r cubed, but then we have a minus sign up.
This is minus pi r cubed, and then we have a minus sign up here, so this becomes plus pi r cubed, and then minus-- because we have a plus here and a minus out here, so distribute it-- so minus 1/3pi r cubed.
And let's see, what do we have?
We have essentially 1.
If we just distribute out the pi r cubes, we have pi r cubed times 1 minus 1/3 plus 1 minus 1/3.
Well that's 2 minus 2/3, or another way, let's see, is 2 minus 2/3-- this is turning into a fractions problem-- and what's-- well, that's 6/3 minus 2/3, it equals 4/3.
So this is equal to 4/3.
So the volume of the sphere is equal to 4/3 pi r cubed, which is the equation for the volume of a sphere.
It's going to be a cube of the radius, pi is involved.
Area is pi r squared, and then all of a sudden you get a 4/3 here, so it is something for you to think about.
I'll see you in the next video.
Let's say I have an angle ABC, and it looks somethings like this, so its vertex is going to be at 'B', Maybe 'A' sits right over here, and 'C' sits right over there.
And then also let's say we have another angle called DAB, actually let me call it DBA,
I want to have the vertex once again at 'B'.
So let's say it looks like this, so this right over here is our point 'D'.
And let's say we know the measure of angle DBA, let's say we know that that's equal to 40 degrees.
So this angle right over here, its measure is equal to 40 degrees,
And let's say we know that the measure of angle ABC is equal to 50 degrees.
Right, so there's a bunch of interesting things happening over here, the first interesting thing that you might realize is that both of these angles share a side, if you view these as rays, they could be lines,
line segments or rays, but if you view them as rays, then they both share the ray BA, and when you have two angles like this that share the same side, these are called adjacent angles because the word adjacent literally means 'next to'.
Adjacent, these are adjacent angles.
Now there's something else you might notice that's interesting here, we know that the measure of angle DBA is 40 degreees and the measure of angle ABC is 50 degrees and you might be able to guess what the measure of angle DBC is, the measure of angle DBC, if we drew a protractor over here
I'm not going to draw it, it will make my drawing all messy, but if we, well I'll draw it really fast,
So, if we had a protractor over here, clearly this is opening up to 50 degrees, and this is going another 40 degrees, so if you wanted to say what the measure of angle DBC is, it would be, it would essentially be the the sum of 40 degrees and 50 degrees.
And let me delete all this stuff right here, to keep things clean,
So the measure of angle DBC would be equal to 90 degrees and we already know that 90 degrees is a special angle, this is a right angle, this is a right angle.
There's also a word for two angles whose sum add to 90 degrees, and that is complementary.
So we can also say that angle DBA and angles ABC are complementary.
And that is because their measures add up to 90 degrees,
So the measure of angle DBA plus the measure of angle ABC, is equal to 90 degrees, they form a right angle when you add them up.
And just as another point of terminology, that's kind of related to right angles, when you form, when a right angle is formed, the two rays that form the right angle, or the two lines that form that right angle, or the two line segments, are called perpendicular.
So because we know the measure of angle DBC is 90 degrees, or that angle DBC is a right angle, this tells us
that DB, if I call them, maybe the line segment DB is perpendicular, is perpendicular to line segment BC, or we could even say that ray BD, is instead of using the word perpendicular there is sometimes this symbol right here, which just shows two perpendicular lines,
DB is perpendicular to BC
So all of these are true statements here, and these come out of the fact that the angle formed between DB and BC that is a 90 degree angle.
Now we have other words when our two angles add up to other things, so let's say for example I have one angle over here, that is, I'll just make up, let's just call this angle, let me just put some letters here to specify, 'X', 'Y' and 'Z'.
Let's say that the measure of angle XYZ is equal to 60 degrees, and let's say you have another angle, that looks like this, and I'll call this, maybe 'M', 'N', 'O', and let's say that the measure of angle MNO is 120 degrees.
So if you were to add the two measures of these, so let me write this down, the measure of angle MNO plus the measure of angle XYZ, is equal to, this is going to be equal to 120 degrees plus 60 degrees.
Which is equal to 180 degrees, so if you add these two things up, you're essentially able to go halfway around the circle.
Or throughout the entire half circle, or a semi-circle for a protractor.
And when you have two angles that add up to 180 degrees, we call them supplementary angles
I know it's a little hard to remember sometimes, 90 degrees is complementary, there are two angles complementing each other, and then if you add up to 180 degrees, you have supplementary angles, and if you have two supplementary angles that are adjacent, so they share a common side, so let me draw that over here,
So let's say you have one angle that looks like this,
And that you have another angle, so so let me put some letters here again, and I'll start re-using letters, so this is 'A', 'B', 'C', and you have another angle that looks like this, that looks like this, I already used 'C', that looks like this notice and let's say once again that this is 50 degrees, and this right over here is 130 degrees, clearly angle DBA plus angle ABC, if you add them together, you get 180 degrees.
So they are supplementary, let me write that down,
Angle DBA and angle ABC are supplementary, they add up to 180 degrees, but they are also adjacent angles, they are also adjacent, and because they are supplementary and they're adjacent, if you look at the broader angle, the angle formed from the sides they don't have in common, if you look at angle DBC, this is going to be essentially a straight line, which we can call a straight angle.
So I've introduced you to a bunch of words here and now I think we have all of the tools we need to start doing some interesting proofs, and just to review here we talked about adjacent angles, and I guess any angles that add up to 90 degrees are considered to be complementary, this is adding up to 90 degrees.
If they happen to be adjacent then the two outside sides will form a right angle, when you have a right angle the two sides of a right angle are considered to be perpendicular.
And then if you have two angles that add up 180 degrees, they are considered supplementary, and then if they happen to be adjacent, they will form a straight angle.
Or another way of saying itis that if you have a straight angle, and you have one of the angles, the other angle is going to be supplementary to it, they're going to add up to 180 degrees.
So I'll leave you there.
Ladies and gentlemen, at TED we talk a lot about leadership and how to make a movement.
So let's watch a movement happen, start to finish, in under three minutes and dissect some lessons from it.
First, of course you know, a leader needs the guts to stand out and be ridiculed.
What he's doing is so easy to follow.
Here's his first follower with a crucial role; he's going to show everyone else how to follow.
Now, notice that the leader embraces him as an equal.
Now it's not about the leader anymore; it's about them, plural.
Now, there he is calling to his friends.
Now, if you notice that the first follower is actually an underestimated form of leadership in itself.
It takes guts to stand out like that.
The first follower is what transforms a lone nut into a leader.
(Laughter) (Applause)
And here comes a second follower.
Now it's not a lone nut, it's not two nuts -- three is a crowd, and a crowd is news.
So a movement must be public.
It's important to show not just the leader, but the followers, because you find that new followers emulate the followers, not the leader.
Now, here come two more people, and immediately after, three more people.
Now we've got momentum.
This is the tipping point.
Now we've got a movement. (Laughter)
So, notice that, as more people join in, it's less risky.
So those that were sitting on the fence before now have no reason not to.
They won't stand out, they won't be ridiculed, but they will be part of the in-crowd if they hurry.
(Laughter)
So, over the next minute, you'll see all of those that prefer to stick with the crowd because eventually they would be ridiculed for not joining in. And that's how you make a movement.
But let's recap some lessons from this.
So first, if you are the type, like the shirtless dancing guy that is standing alone, remember the importance of nurturing your first few followers as equals so it's clearly about the movement, not you. (Laughter)
Okay, but we might have missed the real lesson here.
The biggest lesson, if you noticed -- did you catch it? -- is that leadership is over-glorified. Yes, it was the shirtless guy who was first, and he'll get all the credit, but it was really the first follower that transformed the lone nut into a leader.
So, as we're told that we should all be leaders, that would be really ineffective.
If you really care about starting a movement, have the courage to follow and show others how to follow.
And when you find a lone nut doing something great, have the guts to be the first one to stand up and join in.
And what a perfect place to do that, at TED.
Thanks.
(Applause)
"Richard Nixon President of the United States "
"In the 1970s, the US declared war on drugs.
Drug consumption was defined as a crime punishable by jail. "
"Ronald Reagan President of the United States "
"But has a drug free world ever existed?"
"40,000,000 B.C. The Drunken Monkey Hypothesis"
BREAKlNG THE TABOO DVDRip - MP3- NandOlocal
"2700 B.C. China - Cannabis"
"1300 B. C Assyria - Cannabis
"1000 B.C. Egypt - Opium"
"500 B.C. Greece - Wine"
"1492 Columbus brings cannabis seeds to the Americas"
"1600 Arabis - Hashish"
"1800 China - Opium War"
"1885 Freud - Morphine"
"1914- 1918 World War I - Medicinal Cocaine"
"1920 US Alcohol Prohibition"
"1965 Vietnam War"
"1960s Counterculture"
"1971 Richard Nixon declares War on Drugs"
"1960s Bob Marley"
"1970s Eric Clapton"
"Synthetic Drugs"
The Latin American Commission on Drugs and Democracy met today in Rio de Janeiro to discuss new ways to fight drug trafficking and narcotics consumption.
"2008 The Latin American Commission on Drugs and Democracy"
It is not easy to talk about drugs.
But we must since democracy is at stake.
Drugs lead to violence, undermine the rule of law and contribute to illegal repression.
They also facilitate corruption.
All this erodes credibility of the institutions.
Any questions?
Would the legalization of marijuana reduce the power of traffickers?
Bolivia is leading a campaign to take out the coca leaf from this list of drugs, bad drugs. So what is your opinion on this issue?
Since repression has not worked, do you think the right approach is decriminalization and liberalization?
What legal changes do you think should be made?
Is the state prepared to treat addicts instead of putting them in jail?
Won't we be making life easier for the traffickers?
Rational people change their minds when confronted with new evidence.
"Fernando Henrique Cardoso, sociologist President of Brazil "
Back then, I was not aware of the seriousness of the issue.
People ask me why I didn't do anything as President.
I did not have the right information.
I was not directly involved.
The general consensus was that police repression was the solution.
The repressive policy was a failure.
I did not see this. I was wrong.
There are risks involved.
One could ask why am I meddling with the drug issue when I should be at home looking after my great-grandchildren?
I remember a favela in the outskirts of Săo Paulo.
A lady approached me and asked:
"Is it true that you are going to put marijuana in children's snacks?"
So I understand how risky this issue is.
Getting it wrong could be devastating.
Early on this debate I read in a local newspaper that the active ingredient of marijuana was not THC but FHC.
They were mocking me.
"Favela Vigario Geral, Rio de Janeiro"
"Afroreggae Waly Salomao Cultural Center"
When I turned 13, my only option was drug trafficking.
You end up believing that this is the right option.
"Vitor Onofre Afroreggae coordinator"
The only path.
It's the only reality you face each day.
Guns, drugs and violence.
"Favela Santa Marta, Rio de Janeiro"
Sixty years ago, our guns were. 22 and. 32 caliber.
Forty years ago,.38 specials, pistols and 12 gauges arrived.
"Former drug trafficker"
Then came assault rifles, machine guns and AK-47s.
So there is a link between the introduction of new weapons
- and shifts in trafficking?
- Yes.
Every time a new gun showed up, there was a new trafficker behind it.
And did this increase the power of the drug market?
No.
But it increased crime.
- Crime?
Killing?
- More bloodshed.
"Firearms seized by Rio's police - 2009"
We have around 150,000 firearms here.
"Allan Turnowski Former Civil Police Director"
War weapons seized in Rio.
This one was made in Switzerland.
- This one's global.
- It is the AK-47.
Born in Russia and spread worldwide.
"Carlos Oliveira Former Deputy Director of the Civil Police"
Guns made in countries such as Austria or Germany...
"In 2011, Carlos Oliveira was arrested for diverting weapons seized from drug traffickers.
He was released a few months later.
An investigation was opened up to review the Federal Police's poor record in combating arms trafficking.
Carlos claims to have been a victim of a political witchhunt.
To date, this case has not been decided on. "
I was surprised by the way we got to the favela.
We arrived in a strange way:
By helicopter.
The chopper has to dodge because the traffickers may shoot at it.
I live in a community where rival factions are at war.
One night I went to a party with my girlfriend.
That was when it happened.
I was hit by a stray bullet.
I woke up at the hospital, and realized what had happened.
So I ended up like this.
I was 18 or 19 years old.
When the police raid a favela, traffickers shoot at residents to force the police to stop and help the injured.
"Stray bullet victim - 19 years old"
Innocent people always pay the highest price.
I had nothing to do with trafficking and then this happened.
It makes me angry.
"Cracolandia - Sao Paulo, Brazil"
The crack situation in Brazil is the best example of the failed war on drugs.
Crack arrived to Brazil during the 1990s.
It came from the US, where it's long been used.
We had no educational campaigns.
Kids started using crack believing that it was like any other drug you smoke, like marijuana or cigarettes, just a little stronger.
But it's a hugely addictive drug.
So what is the situation today?
We waged war on crack and what happened?
It spread nationwide, becoming an epidemic.
"Brazilian Anti-Drug Commercial"
Drug trafficking finances violence.
And you fund the trade.
If you are going to buy drugs, remember the cost.
"Denis R. Marijuana User - Sao Paulo, Brazil"
It's not my fault if I finance trafficking.
Because the only way I can smoke a joint is by getting some weed from the traffickers at the favela, and they are usually armed.
If I'm caught by the cops, they'll beat me up.
Once I was picking up marijuana and two police cars showed up.
I heard gunshots.
I don't feel safe, but in my case, there's no alternative.
So I'd rather take the risk then end up empty-handed.
My mother is terrified that I'm in contact with traffickers.
She thinks I'm going to super dangerous places where everyone's armed.
But the truth is that all drug users are also dealers.
Users buy drugs from someone, then consume them.
He gives some to his friends.
Since drugs are criminalized, it's a crime to have drugs on you.
Why would ten people go uphill to buy drugs, when only one can go buy some for everyone?
And the kid understands that if he sells it for a bit more, his stash is free.
"Washington D.C., USA"
We have to look at what is happening in the US because of its power to influence repressive drug policies across Latin America and the world.
And also because of its crucial role in the UN.
UN Conventions require all countries to enforce total drug prohibition without considering alternatives.
"Bill Clinton President of the United States "
"Georgetown High School"
Where should I sit?
"Ranking of drugs according to harm The Lancet Medical Journal "
"1.
Heroine; 2.
Cocaine; 5.
Alcohol; 9.
Tobacco; 11.
Cannabis"
"Ethan Nadelmann Director, Drug Policy Alliance"
"Jimmy Carter President of the United States "
"Mexico City"
"Ernesto Zedillo President of Mexico "
Organized crime would not have had the power it has in Mexico and other countries without the huge amounts of funds from illegal trafficking.
Part of this money is used to buy guns, most of which are legally purchased in the US and handed over to the Mexican cartels.
Once the drugs cross the US border, we lose track of who buys
"Carlos Fuentes Mexican novelist" and consumes them or who profits from the trade or how banks launder the money.
We haven't a clue.
All the blame is directed to the supply side and never on the demand.
Mexico is currently sending its citizens into exile.
"Gael Garcia Bernal Mexican actor"
you falling cop copyrighted program and pride and edited into the program not primed moan and all non and gone and and and and them and and and and and weighed one hundred and my mom there on the mainland
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let the public is willing to end does spend the money necessary in this division of law enforcement will result in handicapping essential police work not only that but it will give the criminal an advantage over the authorities the chattering results to society naal the true story all the batman here the golden or flight you're pretty young to be in a place like this never mind the horatio alger step and then we don't tolerate an attitude like yours in this institution you will obey the rules of the people and school and conduct yourself in such a manner will make your stay in as brief as possible every year to do all right out to a year according to your commitment you were found guilty of petty theft and impersonating an officer realize that you're starting the wrong way don't you so i have to stay in the eighteenth and i think he's talking to you yet one might expect i'm not in didn't which uh... thank god taking up landlord iraq stop shopping we've got to do something about the flight kit now i think i'm not practically everything you ship money economic apply work up at the national guard when the kids are having breakfast implied that was recipe a picture which is getting all the attention he's doctoral actually i'd recommend stomach now now that the contract and principles and that at comment on and we get rid of him to do we expect the line beginning particulate federal penitentiary in leavenworth kansas two years later william edward at age twenty one served one year for petty theft impersonation liquor abuser and that that invite you think indexing specter we'll do that you've been personally a federal officer again so what so we'll be with us for three years at your story look good we might as well on the stand each other now i don't think smart talk from prisoners were don't know why dont to make up your mind behave yourself when you're here if certain rules are not particularly hard but we insist upon the main update uh... you can do to flee hugo they didn't get along with us or you can follow the same court you'll definitely been in the habit of doing in that case we have our old method of dealing with lot method well if you're interested it's easy enough to find out to maybe only with wouldn't tap into your flight ok captain st as is the third week in solitary for fraud captain pretty good well expressed personally i don't think it will be what we call good how much longer to get to go six-month my coworker with the land antenna ended void in court the virus olympus and now they have an exhibition is now let's get
'em out here opioids get it out the atheist that i said get off your texas into the young men wanting this prison doesnt tolerate dozens of population ever but you put it up mugs in this place but they stay in line around our house what try getting out of line and you'll soon find out that this joining sub-type that remains to be seen knocked up if you are not just in case you decide to start something reminder of the discipline is on specialty we're not interested in what you did before you came here why you're here you i'll give you a chance we enough interested chances are your opinion about methods it would be rules or suffer the consequences in moscow thanks paddle exterior getting rid of you today freud and get pretending need just said we're getting rid of your ideal you don't feel uh... wouldn't good riddance of bedrock issues that we had to pay make it above i suppose i should ask what you're going to do now i'd suppose you should do which i would be quiet too many of business but your way remember though next time we'll be priya preview you won't come back here you've got out the transaction take it was hoping to stay out of my sight thanks wouldn't immediate didn't trying word earnings a large gap and this time you're an architect that's what it says donut serial ata baghdad and don't start the usual line about rules and regulations state interested me how you treat prisoners along i gotta stay here and what or saint occurred right around it everybody going on tranny rest up and we're going to have this alive but don't worry about me would not do exactly site gender built incentive that too according to your education they haven't gotten back so late may dot obc in you know what you know that's what i'm afraid of gin and tonic though floyd will react and naal ok and don't get tough about it just making and recession well save you know those at six weeks to go rather presentation words that i was played pretend and i was an army officer right now have a lot like pipe down it makes him here conduct going in so what unisom houston in san diego still select yourselves communique became to let you know mom consider season a week from monday which is to make it we can't make it we've got this name in one of them see that you can't see you won't lose nothing by okay sapir and just go to the old record clinton st and strong women room floor it didn't turn out so tupac from which you conclude i've learned a lesson and then maybe is right and congratulate yourself warden just not interested in this joint already breaking my heart take it easy wouldn't maybe back into the lord forbid ella tell me how you wouldn't welcome florida do you ever come back to alcatraz images when they could be a man to spend the rest of your life by yourself ever come back here it'll be solitary from then on double or a capital they won't be back i wish i could be sure that take my word for it i won't be back just outside the city of walla walla a motorist give the young man a lift it an hardware and yet walking yet acute world word dad on large ideal i'll tell you what i tried decided right we'd want to go beers services radio on everything at bc what we can get it and meanwhile about visible but but but but the police alters citizens i want to be on the top of that but i come back to that
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longer mileage greater reserve power and maximum speed which the driver the police problems in other words you can get by always coming up with real bandit cracked company because they demand all of the potential qualities the officials of thirty meetings cities and counties identify real than the fact that the gasoline used exclusively to father emergency public service call would be a good bargain give your car the best governing that his work with drop in at the red ant bites taken a view of that may be a bandit either tomorrow morning and give you a call the means of delivering police comparable almonds by taking a border kind one of the old man the cotton level highly recommended deafening in the west it here tonight we again take pleasure in presenting teeth james e david's of the los angeles police department keep dates good evening friends there seems to be a general there are only a study of that so-called society crooks part of a higher title criminal this is not true it is of course foregone conclusion that any person is going to fail at any game outside the law he may get by for months or even years but eventually is going to wind up behind bars that is certain but they are not many criminals who will admit this only fifty percent of the society cooks intake source for transportation and hotel bills he was keep on the move continuously and uh... the usual rounds of the night clubs and parties political quiz poses a big shot show me a man who spent a lifetime outside the law that i'll show you a man who died a pauper i'm not moralizing in making this statement it is a fact a story that you will your tonight definitely shows that crime does not pay in the hotel in downtown multi-mode a man or woman are dancing were very good dancer her journey i've been around they're not that gets out
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living advice it yet year former reagan circles in my etc night leading the having records over your marks of aboard young womanhood movement embassy lapping at the start i do i think the weather's mine maybe these apparent i've noticed unity among removes whom i don't think that this came to town within our product you are not the case here very probably if you let the dcm i'll consider it katie i think that about the contact now goodnight well see you safely tucked in aware of it species door at that ensign armenia bapak doctor has talked about how do nothing but for all of your shoe will however you have academic candy just is what caused moderate w us companies chemical hours later the bruised and battered you're recovering bodies leveling with the stereo issued by the way to the telephone some of the hotel manager and not qualified official called the police and effective date you models of the robberies one working alone responded to the call uh... there's going to try to cut yourself tell me what happened and looked at me and i don't give them accompanied by the clinton the lobbying you don't deal with it i didn't think anything up but at the time probably delivered everywhere in had a drink at the blind if they do that on the floor of the dimensional or before seven ido impacted ltd well we came up in the elevator the gathering he picked up a about document with any other proposition one hundred negative attitude ability in defensive
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lives a rather than walking around in the history of the remaining houston removed at least or no removed two but none of my business under the covers room duck pond and of adopting at this point i think that these trees wiping let a little over the number of mine a game motherhood to clean the place and where i want to leave the game opening up in a painted out so it's uh... living in the plot to blow up but israeli upto remotely when he and i think that the temple important numbers written on the wall made america but not really restricted you know a thorough going to be sure that you know that they can you bring your liver you know anything about the fellowship in not never paid attention to biggest coming when they're going to get ready nobody ran around them you get people into a dozen yet independently ronningen you know anything about his girlfriend neff militant union were you know anything about any phone call each other and he made system that part of what you placed don't know that the other i don't the you know that i just returned here why don't you and i can find no hempstead almost one delivering them to bother with about the roar of approval i didn't know the problem you wouldn't mind that when the barber somewhere in that room with a will be working for the overlook the up but the the return of the balcony time recruitment but then one day almost a week every birthday made the final who the uh... the again i'd like to that were worded with and invented crazy though with that and have a group of women room right landing
look i think you have blamed if you wanna you know what i like about you
lose your spirit of cooperation yet lengthened to help them well-intentioned letting the will lead to it the then isn't bad but in the there rather than martin with a reporter for the feel like there's a lot of income randomly mondale woman written that'd be the the but alot of the beaver them too record number the ran or for mine but the problem i've got mr shared her write what i wanted but they've had ordered by detective mark employees not private plan for the cap finally began calling the number six nine four five within every possible alternative in uh... mister schaffer then remember mom at work out which should read uh... what are lower i want charlie shavers action uh... really are operable about battle upon them with all the more they are it but not normal them in desperation market the number and also the album federal investigators bob either through the telephone company other than the militant phone number i've tried everything that was an does not want to be a long distance calls within one hour that number is you haven't done anything about their montana than then another million to one them on the trip is called problem but you want to know six months of luck with the gain surround the parliament get out of the report where we're going to with with the problem with that they will not or go far enough admitted that the pure worker work as long as you're wonderful on quitting that what no with a look at that wellman their demand six nine four five medford oregon to seven or template working outside i think i can right through the content of charlie shape uh... people believe liberal these are the two two seven org and please where people charles b shoot meant one of the rather than a lot and included notify more rabbit forty five minutes later the late maybe at different that uh... limit that that given by you that that position paul remembered buildup of the most armed with with the but that isn't what bobby caper in net but are looking into the lead and one day at the railway station in that book right annual market collected by the name paper uh... that it will return habitat bird back for trial but what if something happens that you'll be able to defend itself would do anything to keep that get tough rajitha nanum yes but you've already spent two days in the hospital were not well enough to be a no plaza without the day the perspective of the of the or k_ hair coating understandable it had along to your incomplete but doesn't that mean that in my life while at the mild line like into cattle uh... what we know and back in the butt of panic button on top of a political beliefs at allied attorney excitement market oh off but not meant you realize that this might be next or every one of the right now that handcuff and not a completely lawful a replica lip often there helpless other major remove mahal bookclub bookclub notifier happily places in the public by the credit from top companies article could be pardoned field that might get landed eat the scene at the battle reflects paper prize pickup
little by little didn't include that upholding prison about his hand up we cautiously hypothetical about his ankle difficult kind of a pledge to the end of the kingsport and on and off then no big deal fingers of dawn pushed back the curtain at the white knight thing they would open up the grade popping island at the carter he predicted with the president opened the front door tv dead and that can help our political upon the brief thing begin elmwood wiped out the fugitive takes bargains around out being shipped salt of the office of the sort of a printout highway patrolman william snail report for duty uh... in england and i might then they get away from a famous lovers are going up but they had to be great and avoid a man if and when i still in town bo that they don't know tomorrow and for that the cut description for the npf_ right here
let me let let the customer that there are likening yeah getting these dead not to them and we get started please have a small again uh... because i have a credit card with an eleventh-hour mailing regular epidemic resident determined that the other thing that did the lead normal lives have been on the web and moving in the mid level in the living room the job rather than by the road and that is going to do that in there that that word we're going on at that time online require held up a little while ago dr point com visit my aunt world events but they wouldn't find a mile a little ave you can get ok it
laying around worker lead right now well again i thought i know that when we get over that i had that way ear yet but in the telephone offices elected last but people adam a command and i think that it let me get if you have to be that way wallet was stolen cousin suspects if they like it was just up with that that that was that way camping at the license number that uh... cut job yeah right here dot check on that about this paper the description and at that nobody can occur again in a manner their there erythromycin may be contacted bakit located so i can became a description of that but never got a little more five eleven well i think we've got you waiting to take me back or bedtime get compiler let that get you back with the atlanta difficulty of it but found that uh... you know copper uh... though well i think
level by the description define what that we got it man and that the coroner yet rambo was sentiment is happily some brands of what you might call fair weather friend but we'll ban the practice of kind of friend up never lets you down no matter how hard the growing after the other demands of unforeseen emergencies regardless of weather conditions rio grande iquest gives you more than the maximum performance of with his people the drivers of your emergency public serving cause discovered that backed by testing all brands of motor fuel then they rolled up fifty five million miles of the hottest fastest kind of driving over california highway using real democrat exclusively if you want that kind of a friend giving your more than more efficient operation and save you money in the bargain
left a man of the red and white rio grande decision in two days riding tomorrow morning fill up with real round the clock gasoline that and that the police car performance of your neighbors cost that police caught efficiency in your own with real vanderkloet a favorite gasoline of those who died below and those who think the most of their proper now again we hear he faced desperation of the manchester and his determination to escape punishment for his crime caused him to pay the supreme penalty for is the no stigma attached to be the detective morris who lost the fugitive lecture rentals who's gonna chairperson actually is ever to gain freedom in most cases the sadness the attack penitent help us to defend himself at all events shavers crime failed at that thank you keep davis bd little legal adviser told by the end of radio broadcast to deny would manage a window werner and the the but a the
letter subject lindley reading of the night coriolan calling all part of the copyrighted programs created by real branding networking returns on the bottom of the religion card will get to argue that we're going to bed button needed in atlanta with world no wound off a third of the law conduct many of the with investigating but it is no speed record for what it takes from their own brings them back but maximum be safety an economy every one of the difficult knows but this time but it was real bandit back got believed that there will be on the wall three cards and into the fire engine and other public service called wherever he told than any other brand yes most of the private limited are newsreel bambi practical blueprint but they are not the only one all the problems of motrin although not with government is really superior governing stockport delivers who the recovery and more miles with great arether power and speak unique envy your neighbor if you want police proper format for your call although that may bring to the nearest red and white rio grande dayton tomorrow morning and getting take on the paint will be open to crack and you will understand private minor mode if you will of the most highly recommended governing in the west or pull measure more complete motoring later dot rio grande decrypted kapiti and but do it is our pleasure to present a method on the telephone bamberger legal copy allocate thank you doctor in peru evening ladies and humbled today's so are planned parenthood writers telephone there's not a single outpost of the law work out of the lee the envelope today that i'm going to be no sheriff's office which i have the honor to be the head is in common with every other law enforcement office in the city equipped in a minute beneath the best of the worst in criminal element crimes today are of course the thing that they were years ago where there is still there but no longer that the share of helpful head of a prostitute second man through the practice that's it that scientific method to imply to bring the criminal to death better there and patients an intelligent deduction coupled with expert analysis contributed to the solution of the case we are about to get asia product that it at that wilder a coupla get right on top of all pop records by contemporary little while ago that are bad light back at the back the butcher dot both the
line for twelve hope have tried chicas just a few hours ago all clout heartbreak that great but the quiet fell back already about no i'm not for a couple of months norvasc dorm data it right but what about date he's arava right or that the off about the crime of accounting almost after five p m hire a state of new york that update under the command offered over historic alcohol the top overturned a woman had been the bob talked into the purple san fernando valley pops picturesque pictorial beeping defied the meandering mojave and out into a dusty road that leads to langford twelve megan right over probably or wait a minute to go to vote
looks like the man was killed here on the road and ride over their yet at the field made those marks near the big batch of blood
looks like the killer as to the while here bennett fairly small man how do you know well i looked at the body this morning in the following bright they can sell well anyway we know the two men going to carry the body after than just one man and i would uh... that's what i think it old worth about it now what that is left of it no dental work for the persian influence brigade whereby um... certified by a wouldn't do them just about cannot go about bringing everywhere
let me have always been the written about over historical out about a hundred yards and on the senate that part you've got a ride on the list of these clothes and things follow-up i go ahead there is a suit knitted sweater ananth i gotta like it ochoa notepad concept and two any labels on the quote allah uh... or there habit a man was killed my comment dragged over here blood whether in fact the game planning a puppet nothing their retirement and for the last part the civil that looks like this to britain on the other side looks like there she'd off of a memo pad yes uh... that's just what it is oracle's if they don't know if it were reflect the and notes and some figures on that uh... i can't make 'em out though i'd like you know we'll see the them it so that they could back whatever little bit magnifying glass yes that's the best now let's get busy and their this fella a lot of taken in march after them
losing any other identification that might be here all realizing that what the month that way in the dark but people to come over one thousand one set up a independent board whatever the identity of the victim but by the on the part of a blueprint for repair uh... paper well that's not a lot of figures i can't believe that seems to be a complete set right there on the back website eighty seven seventeen that might mean anything that's right them to the bank memo i figure they meant that much money moats and natural assumption head of the total opening a resolution of the case and we were before and i'm not so sure about that blaming and going up to a demonstrate what i can find out in the security state that at in building about a recognized this memo she maybe not but that i got my my gems this is the only clearly have grammatical ekata and no i'm not going to pass it up uh... which a lot that banks and even iam things when i'm gone good morning they are helping rarely has a i'm looking for the president of this that played out here right now we're going to lunch probably will be back burner to also maybe i could help me will maybe animal overstate shipments and then have been accounted on a couple of tornado chip i'm george dot cashier the bank well maybe you can help me of that you see we have a little killing down our neck of the woods sometime back found out about it just after christmas well we have in got hide nor hair others a clue as to who committed the murder anything we found that this little piece of paper uh... with that but faceted ever see a piece of paper like that here and uh... yes of course at one of our memos we keep them right here on the counter for the customer to use actually kept the same kind of that so that means i a man was originally a dozen of the damage in the best we got the less chip into these beds but you've ever the first time that we do this particular time as a set of figures on the back right here eighty seven and seven m act no analyst at standard life but is there a possibility that those figures mean anything to you the city at
lead i don't know about the other writing but mister stevens the bank president of the world grows bigger down to one of the customers and i've got to know which customer figures look familiar let me think
lol it would be the one c right judge i do remember something about that seems to me i remember transaction involving that amount uh... right around the holiday
lemme think as he there was christmas with what i was thanksgiving and back close armistice day right around the early part of the web a do you remember the customer was well he wasn't exactly a customer you see this man came in and mister stevens creek area i recall the at a bank account becky somewhere and the weather transfers funds out here image of passing through here said he'd become strand there's a telegraphic transfer if i remember rightly do you happen to remember the name the laptop and but i could check up on it but it was built recall telegraph office and asked them to go through their piled up a couple months ago and maybe we can get a double check up it kurdish state bank today speaking ox and at that just you will please is that the name all right x heading out x and let them know all right thanks a lot and a man's name rupert hate cv should have received for the money in this trial right here anna's anderson the him it is will today received a security state bank of the new till eighty seven dollars and seventy nine cents in telegraphic transfer of funds at request of peoples state bank detroit michigan happen to remember what this fellow looked like little yes uh... you see this business with a lot of the ordinary and i noticed the man rather closely had reddish brown hair as i recall it but the way the around eleven thirty a hundred forty rather slight at long taping fingers seemed rather refined and i'm a blizzard should i believe say what his business was yes i uh... i believe he said he was a printer going west look for a job that sounds like the man we found our life you're a member of the was alone or i don't think so it seems there was another fellow within i didn't have any conversation that you have been though so president they particularly tensions are seems like he was smooth shaven seem sort of quiet and reserved i noticed that needed to be pretty close attention with a major some british war bonds yield you don't happen to know where they lived well he was here they are really gave us the address the grand hotel volume i talked to japan he might have a line item well thank you i'm water straightens and ended in california and checking up on a couple of bars again to hear about the first and last month domain adm_ another bombing walks the levity at at at at the moment the dayton and that they were in that that few weeks indicate uh... epip irritant any brennan bout thirty but but but but one weapons with them the dramatic i was broken down headed out of roses verizon whitehead theater at the record and characters their pinnacle new york it and checking up on the cat named in one of the named well a member of the double booking so that that would be it for
look them up but the panic roaming isn't the right there november ninth state for uh... the un and part of the mca if it is the money to buy food for work and baby is a good don't have any record of a woman in this case the one twenty th at work that he did it makes the from wyoming let him have biven started on the or what kind of car was it more than through and go whatever that was the germany getting a bit too because the recall how this man walks look with uh... there was five nine attendances song nifty way around hundred inflicted on bomb minimal as muslim yet legal led a duck dot it bracket athletic build a slight burst out of that and i think i'll start looking for that young man therapy return to resolve a dumbarton you know of any of the compact adaption of effective edward baca of the poet asking here that the clinton breaking the movement of the day in law all with thirteen point big time me one phone at the bottom information and then do business with them intimidate noting about in their kids a big deal we receive them unless you have to and felt quite a large quantity of wall bond in some time ago you know here for about twenty dollars that often got the money from the barnesandnoble savings account according to our records you talked about a hundred dollars another counter
left for california anything more about america that yeah actually i think that several programs about his accountant finally transfer the balance of eighty seven seventy nine too often with your records show he lived well it was the vendors to give us respecting sixty-eight ferries g the thing going over there as they were the landlady might know uh... you with a buddy yet they are looking for information in a cat named heba i haven't been that he think that like me
like even talked about filter what sort of public yun quiet dot boy english nine eaten info to do in the warrant thank you how long did it moving evening about the fact that you live in you need to know that that would be an active sometime around the middle of the report card september donna d'amico walked in with a one night in told me he'd be gaining new robot it did what they any of the remote control i got the impression that the plot barnwell i didn't see him it any eighty-eight embankment there and uh... wanted to do that doubts about the lack of october
let nick i would have meant a lot uh... avenue apartment adeptly e and v are taking all yet day the hope the at world well america that with that the public that they according i've got an idea about this case anywhere developer that right bank it would have done it from quote by the bank frontier and but for the telegraph of wealthy ready replete dot with randu telegram we think might have been sent from here on november the twenty ninth last year you see if you've got a record of it complete right for them we're going to come from if not move upon them for peoples state bank detroit michigan sent by a fellow named pain we are transfer of power and accountant birthday activity seven adult laughlin frankness that helps a lot that name they didn't have to have said elected sold on december fifth one of our customers into the the mister fadely opened an account for transferring some funds from a bank in detroit that's the one how much money what the standardized wrote judge it was rejected one of the students from london one minimum wage when would be in the last uh... a nineteen no i don't know the nine hundred dollar withdrawal of the family that the last time for a political nicely uh... and all is detected on the twelfth through the date of december night endorsed by a manicure others not here well that would indicate that they would eleven december ninth emma systems i don't believe it nevertheless about even out there for at least amount that we found that will discuss ruin a good for you minimal white at W watch sent us a statewide san what that this what's on the flight five-feet nine of ten digit tong way to get around a hundred and sixty two sixty five pounds lieutenant reflective around please other athletic building well i think i'll go over to that leaking state address bubble jobs back on the late in the best now the dome of the information that a man for the name of what might be a better but it left sometime in december bubble viable dot lovely lama being about directing that mail a deadly we probably won't like involving but that doesn't mean that that the best for the blind repeated on the theory that the fed over brothers indicated that the really did made by hand wake up ever
lots of other and there were no right thinking here yes there's estimate the square the murder complete set a date works for the murder of a perfect similar to the chief of police and book what has been particularly at that the other one at the bank at the front of a police investigating their report and i asked them to uh... to the post office anything out yes delaware up to the motor vehicle apartment aspen the check up on that overall length of the other state registration but i got a letter of the character of the president to asking to find out my thoughts on the support others about that check tickets for the and their promise to stardom and communication accomplishing at about a beloved by that giving a complete description of what's from the mouth all the places up another coach pat within the special supplied to san francisco there just to put a well i guess that are keeping busy for a while pad it hundreds of cooperative at the pump in earnest detective sergeant carmarthen richard on account takeout for making the rounds for help elaine sunblock one day they confirm whether there was a kind of making a big mcdonald in every window when for if he already you transcript it one left hectare settle
legal turkey okay what's the idea that i would let alone whether individual in making a big mistake mister ever never been in san bernardino well maybe not repudiate what waiting to happen in san bernardino but we are gone mob will return the family nobody and legal machinery began to turn covering the trial although he admitted his name and that he knew well today slightly he's got the main thing to them on april ten people talking trial district attorney george johnson cabinet available parade of witnesses kilometers fellas escort challenger an expert devoting handwriting m actually assembled and ready to defend and walked to the victim over today i would like to have you examined the uh... and what your butt eleven running the man at the same as that but on the hotel register log on the telegram sent them on there's no way some of the better watch is the handwriting you walked into that part of the check marked exhibit being kept in corona california on december ninth the signature objects i'd in san francisco reading the navy added autocrat is that the signage or whoever they i was not as identical with the handwriting at jake's watch at all this is all the way facilitator you're employed by the western union to let government yes and i live in seven muhammed you'll recognize the defendant what yet here's a man who sent a telegram detroit band beckett at all but the government your may expect a graphic in microscopic tests and taken the scene where the body rupert he was found and did you make similar analysis of centered in the clothing of the defendant walked i didn't end with a similar they were identical thank you that they had a will you tell the court and jury does what happened in relation to the defendant now on trial on the evening of november twenty four blasts well i was on the way the law's biggest look at the money property i have a prayer a car broke down on the road but when team up with the biggest eyes dot blot silver lake friend of mine that that runs a garage took care of his garage for that night did you see the depended on that night issit added that he walked into the garage into the woods other jessa lee sold on the roadways alot for the way down the road with the vienna companion in the government yes it so man in the car that had to be description the officers gave this mandate that will say anything about this man really fit i'm riding with the dead if any reason for this remark note for george sure at the defendant was in the copy of a man who went to date description on the night of november twenty fourth i thought this was a symbolic gesture thank you another loss assaults is the kind of jayesh what's really to do you he's my brother if you would anytime introduce your brother to any official of the bank of italy in los angeles but some of my brother came to los angeles said he was driving drunk on or the capsule that some of them seconds produced some of the bank guaranteed a signature what needed to use it opened it up use google pretty what reason did he give for using that name incident at some probably used much couple on the use of the bombing but what's what is your address at this time some crippled and what is the reason for you being there i was convicted los angeles grand lux connection with my brother spectacle regular stores that as well attache euro altercation per cent of the democratic ab if you see the body of the man identified as we are pretty i'd have upon what you'll be cured identification of this bit by a comparison of the handwriting on the sheet of memorandum people from the victim's body with special needs of the normally what other meats comparison of the victims description furnished by witnesses of your with that of the dead man then you can say project that the man whose body was part of the desert near langford well wildblue pretty like that at all side of the people case really generated by the defendant baking parts guilty of murder in the russian during the uh... always secure the standards of the book people anything you'd like to say at the built on the crack is not a special privilege gasoline is the specified choice of the officials of thirty leading cities and counties throughout california and he used exclusively to power other emergency call there seems to want to cut government but what we're reporters in california the same final copy will the sped police cars and other public service department over fifty five million miles of california highway through all the hardships and weather changes of a single year as bangalore opium patronage of thousands of people i feel confident that real grandpa will win your approval to when you get to the trial saying we open the plane prep you see swatches police and fire department chair of the red ant bites rio grande a station in your neighborhood with the same we'll go into cracked up to mean you will to power emergency public service call that's fine you two will begin getting squeezed compliments for your call when you bring them tomorrow morning and i the family we are going to be there for a pamphlet we'll run the crap the government prepared by officials for emergency call the governing prepared by a great army of workers all emergency october fifteenth two years after his crime batteries fuel to the state's highest courts
lofts walked up the steps of the download san quentin sent there by a lot of cheated memorandum people without an apparent on launched the truck the brutal murder we'll prepare with event today this case is referred to as an outstanding one covering the most circumstantial evidence and managers on the long haul garlands on hard again they did not get into the
lemon benign and and money and and and negligently was in indonesia and lynn's old movies with the a this is an elevator fabric lends me hiding you good night rearmament guide
Let's say we have some function, f, and it's a mapping from the set X to Y.
So if I were to draw the set X right there, that's my set X. If I were to draw the set Y, just like that.
We know, and I've done this several videos ago, that a function just associates any member of our set X-- so I have some member of my set X there-- if I apply the function to it, or if we're dealing with vectors, we can imagine instead of using the word function, we would use the word transformation.
But it's the same thing.
We would associate with this element, or this member of X, a member of Y.
So that's why we call it a mapping.
When I apply this function-- I'll do it in a different color-- this little member of X is associated with this member of Y.
If this is right here, this is a capital X.
Let's say we call this a, and let's call that b.
We would say that the function where a is a member of X and b is a member of Y, we would say that f of a is equal to b.
This is all a review of everything that we've learned already about functions.
Now I'm going to define a couple of interesting functions.
The first one-- I guess it's really just one function, I said it's a couple-- but I'll call it the identity function.
I'll just call it a big capital I.
This identity function operates on some set.
So let's say this is the identity function on set X, and it's a mapping from X to X.
What's interesting about the identity function is that if you give it some a that is a member of X-- so lets say you give it that a-- the identity function applied to that member of X, the identity function of a, is going to be equal to a.
So it literally just maps things back to itself.
So the identity function, if I were draw it on this diagram right here, would look like this.
It would look like-- we pick a nice suitable color-- it would look like this. It would just kind of be a circle.
It associates all points with themselves.
That's the identity function on X, especially as it applies to the point a.
If you apply it to some other point in X, it would just refer back to itself.
That's the identity function on X.
You could also have an identity function on Y.
So let's say that b is a member of Y.
So I drew b right there.
Then the Y identity function-- so this would be that identity function on Y applied to b-- would just refer back to itself.
This is the identity function on Y.
They're actually at least a useful notation to use as we progress through our explorations of linear algebra.
But I'm going to make a new definition.
I'm going to say that a function-- let me pick a nice color, pink-- I'm going to say that a function, let me say f since we already established it right over here.
I'm going to say that f is invertible, introducing some new terminology. f is invertible if and only if the following is true.
I could either write it with these two-way arrows like that, or I could write it as iff with two f's.
That means that if this is true, then this is true, and only if this is true.
So this implies that, and that implies this.
So f is invertible-- I'm kind of making a definition right here-- if and only if there exists a function, I'll call it nothing just yet.
I'll write it as this f with this negative 1 superscript on it.
So f is invertible if and only if there exists a function f inverse-- well I guess I just called it something.
Remember f is just a mapping from X to Y.
So this function, f inverse, is going to be a mapping from Y to X.
So I'm saying that f is invertible if there exists a function, f inverse, that's a mapping from Y to X such that if I take the composition of f inverse with f, this is equal to the identity function over X.
So let's think about what's happening.
This is true, this has to be true, and the composition of f with the inverse function has to be equal to the identity function over Y.
There's some function-- I'll call it right now, this called the inverse of f-- and it's a mapping from Y to X.
So f is a mapping from X to Y.
This is the mapping of f right there.
We're saying there has be some other function, f inverse, that's a mapping from Y to X.
So let's write it here.
So f inverse is a mapping from Y to X. f inverse, if you give me some value in set Y, I go to set X.
It's saying that the composition of f inverse with f, has to be equal to the identity matrix.
So essentially it's saying if I apply f to some value in X-- right, if you think about what's this composition doing-- this guy's going from X to Y.
This guy goes from Y to X.
So let's think about what's happening here. f is going from X to Y.
Then f inverse is going from Y to X.
So this composition is going to be a mapping from X to X, which the identity function needs to do.
It needs to go from X to X.
They're saying this equals the identity function.
So that means when you apply f on some value in our domain, so you go here, and then you apply f inverse to that point over there, you go back to this original point.
So another way of saying this is that f-- let me do it in another color-- the composition of f inverse with f of some member of the set X is equal to the identity function applied on that item.
These two statements are equivalent.
So by definition, this thing is going to be your original thing.
Or another way of writing this is that f inverse applied to f of a is going to be equal to a.
That's what this first statement tells us.
That is f of a.
Then if you apply this f inverse-- and it doesn't always exist-- but if you apply that f inverse to this function, it needs to go back to this.
Now that's what this statement is telling us right here.
The second statement is saying look, if I apply f to f inverse, I'm getting the identity function on Y.
So if I start at some point in Y right there, and I apply f inverse first, maybe I go right here.
Then if I were to apply f to that-- I know this chart is getting very confusing-- if I apply f to this right here, I need to go right back to my original Y.
So when I apply f to f inverse of Y this has to be equivalent of just doing the identity function on y.
So that's what the second statement is saying.
Or another way to write it is that f of f inverse of y, where y is a member of the set capital Y, it has to be equal to Y.
You've been exposed to the idea of an inverse before.
We're just doing it a little bit more precisely because we're going to start dealing with these notions with transformations and matrices in the very near future.
Now the first thing you might ask is let's say that I have a function f, and there does exist a function f inverse that satisfies these two requirements.
So f is invertible.
The obvious question, or maybe it's not an obvious question is, is f inverse unique?
Actually probably the obvious question is how do you know when something's invertible.
We're going to talk a lot about that in the very near future.
But let's say we know that f is invertible.
How do we know, or do we know whether f inverse is unique?
To answer that question, let's assume it's not unique.
So if it's not unique, let's say that there's two functions that satisfy our two constraints that can act as inverse functions of f.
Let's say that g is one of them.
So let's say g is a mapping.
Remember f is a mapping from X to Y.
Let's say that g is a mapping from Y to X such that if I apply f to something and then apply g to it-- so this gets me from X to Y.
Then when I do the composition with g, that gets me back into X.
This is equivalent to the identity function.
This was part of the definition of what it means to be an inverse.
I'm assuming that g is an inverse of f.
This assumption implies these two things.
Now let's say that h is another inverse of f.
It has to be a mapping from Y to X.
Then if I take the composition of h with f, I have to get the identity matrix on the set X.
Now that wasn't just part of the definition.
It implies even more than that.
If something is an inverse, it has to satisfy both of these.
The composition of the inverse with the function has to become the identity matrix on x.
Then the composition of the function with the inverse has to be the identity function on Y.
So g is an inverse of f.
It implies this.
It also implies-- I'll do it in yellow-- that the composition of f with g is equal to the identity function on y.
Then if we do it with h, the fact that h is an inverse of f implies that the composition of f with h is equal to the identity function on y as well.
So if this is a set X right here-- let me do it in a different color-- let's say this right here is the set Y.
We know that f is a mapping X to Y.
So any inverse, so we're saying that g is a situation that if you take the composition of g with f, you get the identity matrix.
If you could take g you're going to go back to the same point.
So it's equivalent.
So taking the composition of g with f-- that means doing f first then g-- this is the equivalent of just taking the identity function in X, so just taking an X and going back to an X.
It's equivalent to that.
So this is g right here.
The same thing is true with h. h should also be.
If I start with some element in X and go into Y, and then apply h, it should also be equivalent to the identity transformation.
That's what this statement and this statement are saying.
Now this statement is saying that if I start with some entry in Y here and I apply g, which is the inverse of f, I'm going to go here.
So g will take me there.
When I apply f then to that, I'm going to go back to that same element of Y.
That's equivalent to just doing the identity function on Y.
That's the same thing as the identity function of Y.
I could do the same thing here with h.
I just take a point here, apply h, then apply f back.
I should just go back to that point.
So let's go back to the question of whether g is unique.
Can we have two different inverse functions g and h?
So let's start with g.
Remember g is just a mapping from Y to X.
So this is going to be equal to, this is the same thing as the composition of the identity function over x with g.
let's say this is x and this is y. Remember g is a mapping from y to x.
So g will take us there.
There's a mapping from y to x. I'm saying that this g is equivalent to the identity mapping, or the identity function in composition with this.
So these are equivalent.
But what is another way of writing the identity mapping on x?
Well by definition, if h is another inverse of f, this is true.
So I can replace this in this expression with a composition of h with f.
So this is going to be equal to the composition of h with f, and the composition of that with g.
But I showed you a couple of videos ago that the composition of functions, or of transformations, is associative.
But we know that composition is associative.
So this is equal to the composition of h with the composition of f and g.
Now what is this equal to, the composition of f and g?
Well it's equal to, by definition, it's equal to the identity transformation over y.
So this is equal to h composed with, or the composition of h with, the identity function over y with this right here.
Now what is this going to be?
Remember h is a mapping from y to x.
Let me redraw it.
So that's my x and that is my y. h could take some element in y and gives me some element in x.
If I take the composition of the identity in y-- so that's essentially I take some element, let me do it this way-- I take some element in y, I apply the identity function, which essentially just gives me that element again, and then I apply h to that.
So just going through this little exercise we've shown, even though we started off saying I have these two different inverses, we've just shown that g must be equal to h.
So any function has a unique inverse.
You can't set up two different inverses.
If you do you'll find that they're always going to be equal to each other. So far we know what an inverse is.
Hello everyone, my name is Rui Hui, I'm 30 years old, and I'm still single.
The purpose of me shooting this video, is to find two girls from my past, two girls.
First, let's talk about our first encounter, the first and only encounter, that was when we were in high school, which named S.M.K Bo Gui.
That year was my Form 3 in High School.
As usual Dad used to fetch me to school around 7 in the morning.
I remember that day, he was rushing off to Penang, so I had to go to school early..
And then...
Boy, we're here.
Boy, get up.
We're here.
Boy, wake up.
Hey!
Dad, can we not be this early next time?
I'm not awake yet...
Then go continue sleeping in class!
It's so early, there's no one there...
That's good!
No one will disturb you...
Kid, here so early?
Dating?
Can you handle it?
Stop annoying me!
Excuse me, can you please accompany us to get something from the classroom?
It's too dark, we dare not go...
It's all your fault for not bringing it out!Now we have to go back to get it!
Oh...
Where is your classroom?
What is it that you're trying to get?
Why not wait till when class starts?
She needs it now...
Aiya, girl stuff, you won't understand!
Oh, girl stuff?
Just started using, can't predict it correctly, it's normal!
Don't be nervous, these things, I usually......
Use it?!
Impossible... Usually, I see my mom buy them in the supermarket..
My mom's one can fly..
How about you guys?
Fly?
It can fly if it has wings!
We're here.
Which floor is your classroom at?
At the top floor...
Which is your classroom?
The last one...
It's really dark...
Now what?
We're here now... Just get it fast so we can leave fast!
You lead the way.
Stay close to me.
We...
We...
We're here.
It's so dark, turn on the lights...
The switches are inside.
What are you waiting for?
Why don't we go in together...
Are you scared?
But you're a guy...
I'm not scared, it's just that, I'm worried that if I leave the two of you out here, and then... suddenly...
Stop talking, we'll go in together...
What's that noise?
Who's flicking pages?
Where are the switches?
Hey, where are the switches?
Behind you!
Oh Thanks!
Everything after that, doesn't ring a bell to me...
Then, I never saw them again.
So, with this video, I hope I can find them again.
Because I really want to know...
Where exactly............ were the switches?
If you have any news about these two girls, or if you are them...
Please call this number.
Thank you...
I haven't even posted it...
Kid, here so early?
Dating?
That day, everyone was busy with the general election.
So no one could hear her scream.
I was not, of course, the first to discover her.
A security guard found the drowned corpse.
Meanwhile, I was half-awake,
Waiting quietly for the arrival of dawn.
Chen Xiao Hui?
What are you doing here?
Why are you crying?
I don't know.
Do you want to come in?
Hold on a sec.
Hello?
Teacher Lim?
Chen Xiao Hui?
That's impossible.
She's with me right now.
Teacher Lim called to tell me that
Chen Xiao Hui from my school is dead.
In fact, she was already dead for many days.
Her face...
Her face...
Ever since I started writing this
I often dream of her drowned corpse.
But I can't see her face.
What are you doing?
You're so sweaty!
How was school?
I played hide-and-seek
Hide-and-seek?
You weren't studying?
I was!
Hey, look who's here?
Uncle Wai Loon.
You're early today.
Teng, go watch TV, okay?
Okay.
You still write everything by hand?
I'm retro.
I know.
Look at this place.
You're writing about that incident?
I have to give readers what they want.
It's still fiction, I dramatized many things.
Besides, it's already been so many years. No one will remember.
Can you even remember our high school lives?
Of course I do.
You were the fiercest school prefect around.
Always yelling at us to keep quiet.
Answer your phone, school prefect.
It's my wife.
Keep quiet eh?
Hi, honey.
What's up?
Yeah, I'm outside now.
Meeting a client.
Tonight?
I can't.
How about tomorrow?
All right, see you later.
You don't need to work that hard.
I can look after you and Teng.
Besides, most people in our country don't read much anymore.
They're so uncultured.
Grains of sand, glittering like crystal, have lodged themselves between her lips.
Accompanying her in death.
This was the last time I met Xiao Hui.
Do you know?
If you look at the sun from underneath the water
It is as if the sun if floating.
It's a lovely sight.
But sad at the same time.
This was what Xiao Hui saw.
And then...
Was she your friend?
The dead girl.
Ever since I found her,
I came here everyday all the time.
Sometimes, it was real.
Sometimes, it was a dream.
It's not day or night.
But it is always this river.
That morning when we met
She was crying.
I really wanted to know why.
I still see the girl, you know?
At this place.
Where?
Come with me.
Teng!
Where are you?
Teng!
Are you hiding?
This isn't funny anymore.
I don't want to be alone.
You can't leave me too.
Teng!
Oh my god, where did you go?
Papa!
Papa!
It's okay.
Hey lady, is anything wrong?
Mama.
Shh... don't be afraid.
Hey, wait a minute.
Aren't you Fiona Wong?
It's me, Wai Loon!
Wow!
I haven't seen you since high school!
We were in the same class, remember?
Mommy!
Mommy!
Open the door, mommy.
Open the door, mommy.
Open the door, mommy.
Teng...
Teng!
I'm sorry, Teng.
I'm so sorry.
Good girl.
Tell papa that lunch is ready.
Papa, lunchtime!
Lunch is ready, papa!
Okay!
Let's go!
Teng, eat more, okay?
Where did you buy this?
It's delicious!
I cooked them myself.
But don't you have to buy them before you cook them?
We went grocery shopping together, remember?
You have improved.
Way better than when we first met
You paid for my cooking classes.
Glad you know.
It's already been 8 years. Now the marriage is worth it!
You said you'll always love me, Wai Loon.
Teng.
Let's go home with mommy, okay?
Mommy will buy you a doll.
Teng.
Why are you ignoring me?
I'm not dead!
If I look like this again...
Will you still love me?
Chen Xiao Hui.
You're the only one I have now.
Don't worry. it's quite common we encounter such incidents in our work.
Have you called the company?
What are you waiting for?
Ah Tuck, I....
Give me!
Tuck, we've got some problem.
Our actress Candy was possesesed during filming.
You just contact Master Wong to meet us when we reach the office.
It'll take us about an hour to reach the office.
Rush, rush, rush...
Haven't even checked the location properly and they start filming...
Now we're in deep shit.
Fuck!
I thought we still have some scenes to complete... ...where are we going?
Candy, are you alright?
What happened?
Nothing happened...
We wrapped early tonight!
So we're heading back to the office.
If you don't feel well, just take a nap.
When we reache we'll wake you up.
Shit, her make up is scary enough.
Don't worry, everything will be alright.
Go pick her up.
Pick her up.
What are you afraid of?
We can't just let her lie on the floor...
Be quick, don't waste time!
What are you waiting for?
What a noob!
You go behind, I'll hold her up.
Quick!
Candy, you okay?
Are you hurt?
You stay here, and hold her.
Strange... I though we have passed this road just now.
Sorry, I thought I saw something!
But you're doing good!
Keep it up.
Stay away!
Amen!
Amen!
Stay away!
Fuck!
Ah Kit...
Xiao Wen, what is it?
Have you guys reached the office?
Where are you guys?
What are you doing here?
Don't look, stay back.
Up...up...
What?
Huh?
Up there!
What is it?
Hey, it's their van!
Where are they?
Let's search around.
Hey, I found Candy!
Where?
Here!
Come give me a hand.
We are on problem 56.
Scott is constructing a line perpendicular to line
L from point P.
Fair enough.
Which of the following should be his first step?
So he wants to draw a line that looks something like this.
He want to draw it going straight up through the point P. And so how do you do that? Obviously, if you just use a ruler, maybe by accident, you draw it at a slight angle or something like that, right?
So he wants to have an exact line.
Let's see, I don't even know what he's doing in this first one.
He's drawing these x's.
I don't know how he's determining where those x's go.
So that A doesn't look right.
Step B, it looks like he kind of picked two points and is drawing and using his compass to pivot off of those to kind of draw arcs there.
But that's still not clear how it could help.
If he knew that he could do some math and try to figure out that these are equidistant from P.
But still, what he wants to do is find a point right around there, right below P, where if he draws a line between P and that point, it'll be perpendicular.
So that doesn't seem to be of much help.
Here, he picked a point and he's drawing an arc, but that arc doesn't really tell me much information.
Let me see, D.
This looks interesting.
So it looks like he took the pivot of his compass and he drew a circle around with a constant radius.
Obviously, that's what makes it a circle.
And then what do he could do now is he could take his pivot.
He could you could mark each of these points, right?
If he marked each of those points and just pivoted around them and drew a circle, he would actually-- so let's say that around that point, he were to pivot and the circles looks something like-- I don't know.
And he would want to change the radius a little bit, so let's say it looks something like that.
I'm going to try my best to draw it.
Let's say it looks something like that.
And then around that point, he does the same thing.
He pivots around it.
I guess the two would have to be big enough to intersect with each other.
I know I'm drawing it really horrible.
The point at which they do intersect would be equidistant between those two points.
Another way to think about it, it would be another point that's equidistant between the two points, because when you do it first with P and you draw that circle, you're saying both of these points are going to be equidistant from P.
Just by definition, right?
This is a circle and that's a constant radius.
And then if you were to take each of those points and draw circles or draw arcs-- so let's say from that on you draw an arc like that and from that one you draw an arc like that-- you'd say, wow, this point is also going to be of a constant distance from both of them.
So if I were to draw a line between both of these points using a straight edge, that line will be perpendicular to line L.
So if I were to just do that, then it would be perpendicular, so I think D is the first step.
All right, problem 57:
Which triangle can be constructed using the following steps?
OK, this is interesting.
A lot of compass work here.
Put the tip of the compass on point A.
Open the compass so that the pencil tip is on point B.
Draw arc above AB.
So then they drew this arc right here.
That's this thing that I'm trying to color in.
Fair enough.
Without changing the opening, put the metal tip on points B, so now you put the pivot there, and draw an arc interesting the first point at C.
So now they want us to draw that second-- let me do it in another color.
They're going to draw that second arc.
OK, now draw AC and BC.
Now what have we drawn?
So when you draw this first arc-- what they drew is really a semicircle-- the radius is constant.
So if the radius is constant, you know that this distance right here is going to be equal to this distance.
They're just both radiuses of this semicircle or of this arc.
They're just radiuses.
They're equal to the length of the opening of our compass.
So that's going to be equal to that.
And then when you put the pivot here and you keep that distance the same, so now the pencil edge goes here, the distance is still there.
And now when you do this arc, you now know that this length is equal to this length, because now they're both radiuses of this second arc.
So now, you know all three sides are equal, so this is an equilateral triangle.
Equilateral, D.
OK, the diagram shows triangle ABC.
Fair enough.
Which statement would prove that ABC is a right triangle?
This is clearly not a right angle.
This is probably the right angle for the right triangle.
And this is something that maybe you learned in algebra class, and if you didn't, you're about to learn it right now.
And I'm looking at the choices.
They talk a lot about slope.
If I just have a line let's say here, and it has slope M, and I want to say what is the slope on a line that is perpendicular to this line right here?
Well then, it would look like that.
It would be perpendicular.
It would have a 90-degree angle, and its slope would be the negative inverse.
The negative inverse of this first slope.
So if the slope from A to B is a negative inverse of the slope for B to C, then we're in business.
These are definitely perpendicular, at least line segments, and this would be a 90-degree angle.
Let's see.
So what did I say? Slope AB, or we could say slope BC, should be equal to the negative inverse of the slope of A to B.
See, if you multiply both sides of that times the slope
AB, you get slope AB times slope BC is equal to negative 1.
I just multiplied both sides times slope of AB.
And if we could go here, choice B is exactly what we wrote right there. Next problem, 59:
Figure ABC, oh!
It's a parallelogram.
Fair enough.
That's parallel to that.
That's parallel to that.
What are they asking us?
What are the coordinates of the point of intersection of the diagonals?
So what are these coordinates?
And we've mentioned it before, but the big kind of crux of this problem or what you need to know is that for any parallelogram, the diagonals bisect each other.
So that means that the distance from here to here, from O to the intersection point is equal to the intersection point to B.
And so this intersection point is the midpoint.
It is bisected by line AC.
And similarly, you can make the argument that this line segment right here is equal to-- is congruent to that line segment.
If this is really the midpoint between O and B, then we just have to find the midpoint of their coordinates.
And the way to find the midpoint of two coordinates is actually very intuitive.
You just average the coordinates.
So if I were to average the x's-- so the x-coordinate here is going to be-- the x-coordinate of point B, which is A plus C, plus the x-coordinate of the origin which is 0 over 2, because I had two points that I'm averaging.
So that's going to be the x-coordinate.
And then y-coordinate is going to be the y-coordinate coordinate of B plus the y-coordinate of the origin.
I'm just averaging them.
The y-coordinate of the origin is 0 divided by 2.
This will give me the coordinate of the midpoint between origin and B. So that equals A plus C over 2 and then B over 2, so this is
A plus C over 2.
That makes sense because A plus C is going to be here someplace, and we just took the average of the two between zero and that, and you got the midpoint.
And then the y-coordinate is going to be B over 2, which makes sense because that up there is B and we're just halfway between B and zero.
So it's A plus C over 2, B over 2.
And is that one of the choices?
A plus C over 2, I'm assuming that they want us to do choice
C and they just forgot to type the B in there.
This is supposed to be a B.
Because this is definitely not right.
That's not right.
And we know that this is right, but it's not A plus something over on this side.
It's just B over 2 on the y-coordinate.
So that's not right.
All right, problem 60.
I tried to squeeze it in.
I don't know if you can see the whole problem.
But it says what type of triangle is formed by the points A is 4 comma 2, B is 6 comma negative 1, and C is negative 1 comma 3?
So I think the best thing is to just try to graph it and at least start getting an intuition, and then we can see the distances between the points, and hopefully, figure out what type of triangle it is.
So let's see, some of the points get a little bit negative.
I'll have to draw some of the negative quadrants.
So if I were to draw it like that.
OK, let's see.
So 4 comma 2.
That's right there.
That's point A.
And then I have 6 comma negative 1.
That's point B.
I don't know if you can see it down there.
And C is negative 1 comma 3.
So it's out here.
Now let me connect the dots.
That's one side, that's another side, and that's the other side.
So off the bat, I just know this isn't going to be a right triangle.
It's not an equilateral triangle.
And the only way it's going to be an isosceles triangle is if this length is equal to that length, so let's just try it.
Let's just test it out.
So what is the distance from A to C?
The distance squared from A to C is equal to the differences in their x's.
So 4 minus negative 1, so there's a difference of 5, right?
So there's a difference in their x's squared plus a difference in their y's.
So 2 and 3.
You could just say 2 minus 3 or 3 minus is 2.
It doesn't matter.
We just care about the difference. Plus one squared.
So the distance squared is equal to 25 plus 1 is equal to 26.
So this distance is the square root of 26.
And the distance between A and B, same logic.
Let's see, when you go from the distance squared, the difference is in there x's.
Between 6 and 4, you have a distance of 2, so it's 2 squared plus the difference in their y's. 2 and negative 1 are 3 apart, right? Plus 3 squared.
OK, and this number down here, you can figure it out, but it's going to be bigger than both of them, right?
You can just look at it and say that.
So this is definitely a scalene triangle.
All of the sides are different. Anyway, see you in the next video.
THE ADVENTURES OF SHERLOCK HOLMES by SlR ARTHUR CONAN DOYLE
ADVENTURE I. A SCANDAL IN BOHEMlA
I. To Sherlock Holmes she is always THE woman.
I have seldom heard him mention her under any other name.
In his eyes she eclipses and predominates the whole of her sex.
It was not that he felt any emotion akin to love for Irene Adler.
All emotions, and that one particularly, were abhorrent to his cold, precise but admirably balanced mind.
He was, I take it, the most perfect reasoning and observing machine that the world has seen, but as a lover he would have placed himself in a false position.
He never spoke of the softer passions, save with a gibe and a sneer.
They were admirable things for the observer--excellent for drawing the veil from men's motives and actions.
But for the trained reasoner to admit such intrusions into his own delicate and finely adjusted temperament was to introduce a distracting factor which might throw a doubt upon all his mental results.
Grit in a sensitive instrument, or a crack in one of his own high-power lenses, would not be more disturbing than a strong emotion in a nature such as his.
And yet there was but one woman to him, and that woman was the late Irene Adler, of dubious and questionable memory.
I had seen little of Holmes lately.
My marriage had drifted us away from each other.
My own complete happiness, and the home- centred interests which rise up around the man who first finds himself master of his own establishment, were sufficient to absorb all my attention, while Holmes, who loathed every form of society with his whole Bohemian soul, remained in our lodgings in Baker Street, buried among his old books, and alternating from week to week between cocaine and ambition, the drowsiness of the drug, and the fierce energy of his own keen nature.
He was still, as ever, deeply attracted by the study of crime, and occupied his immense faculties and extraordinary powers of observation in following out those clues, and clearing up those mysteries which had been abandoned as hopeless by the official police.
From time to time I heard some vague account of his doings: of his summons to
Odessa in the case of the Trepoff murder, of his clearing up of the singular tragedy of the Atkinson brothers at Trincomalee, and finally of the mission which he had accomplished so delicately and successfully for the reigning family of Holland.
Beyond these signs of his activity, however, which I merely shared with all the readers of the daily press, I knew little of my former friend and companion.
One night--it was on the twentieth of March, 1888--I was returning from a journey to a patient (for I had now returned to civil practice), when my way led me through
Baker Street.
As I passed the well-remembered door, which must always be associated in my mind with my wooing, and with the dark incidents of the Study in Scarlet, I was seized with a keen desire to see Holmes again, and to know how he was employing his extraordinary powers.
His rooms were brilliantly lit, and, even as I looked up, I saw his tall, spare figure pass twice in a dark silhouette against the blind.
He was pacing the room swiftly, eagerly, with his head sunk upon his chest and his hands clasped behind him.
To me, who knew his every mood and habit, his attitude and manner told their own story.
He was at work again.
He had risen out of his drug-created dreams and was hot upon the scent of some new problem.
I rang the bell and was shown up to the chamber which had formerly been in part my own.
His manner was not effusive.
It seldom was; but he was glad, I think, to see me.
With hardly a word spoken, but with a kindly eye, he waved me to an armchair, threw across his case of cigars, and indicated a spirit case and a gasogene in the corner.
Then he stood before the fire and looked me over in his singular introspective fashion.
"Wedlock suits you," he remarked.
"I think, Watson, that you have put on seven and a half pounds since I saw you."
"Seven!" I answered.
"Indeed, I should have thought a little more.
Just a trifle more, I fancy, Watson.
You did not tell me that you intended to go into harness."
"Then, how do you know?"
"I see it, I deduce it.
How do I know that you have been getting yourself very wet lately, and that you have a most clumsy and careless servant girl?" "My dear Holmes," said I, "this is too much.
You would certainly have been burned, had you lived a few centuries ago.
It is true that I had a country walk on Thursday and came home in a dreadful mess, but as I have changed my clothes I can't imagine how you deduce it.
As to Mary Jane, she is incorrigible, and my wife has given her notice, but there, again, I fail to see how you work it out."
He chuckled to himself and rubbed his long, nervous hands together.
"It is simplicity itself," said he; "my eyes tell me that on the inside of your left shoe, just where the firelight strikes it, the leather is scored by six almost parallel cuts.
Obviously they have been caused by someone who has very carelessly scraped round the edges of the sole in order to remove crusted mud from it.
Hence, you see, my double deduction that you had been out in vile weather, and that you had a particularly malignant boot- slitting specimen of the London slavey.
As to your practice, if a gentleman walks into my rooms smelling of iodoform, with a black mark of nitrate of silver upon his right forefinger, and a bulge on the right side of his top-hat to show where he has secreted his stethoscope, I must be dull, indeed, if I do not pronounce him to be an active member of the medical profession."
I could not help laughing at the ease with which he explained his process of deduction.
"When I hear you give your reasons," I remarked, "the thing always appears to me to be so ridiculously simple that I could easily do it myself, though at each successive instance of your reasoning I am baffled until you explain your process.
And yet I believe that my eyes are as good as yours."
"Quite so," he answered, lighting a cigarette, and throwing himself down into an armchair.
"You see, but you do not observe.
The distinction is clear.
For example, you have frequently seen the steps which lead up from the hall to this room." "Frequently."
"How often?"
"Well, some hundreds of times." "Then how many are there?"
"How many?
I don't know."
"Quite so!
You have not observed.
And yet you have seen.
That is just my point.
Now, I know that there are seventeen steps, because I have both seen and observed.
By-the-way, since you are interested in these little problems, and since you are good enough to chronicle one or two of my trifling experiences, you may be interested in this."
He threw over a sheet of thick, pink-tinted note-paper which had been lying open upon the table.
"It came by the last post," said he.
"Read it aloud."
The note was undated, and without either signature or address.
"There will call upon you to-night, at a quarter to eight o'clock," it said, "a gentleman who desires to consult you upon a matter of the very deepest moment.
Your recent services to one of the royal houses of Europe have shown that you are one who may safely be trusted with matters which are of an importance which can hardly be exaggerated.
This account of you we have from all quarters received.
Be in your chamber then at that hour, and do not take it amiss if your visitor wear a mask."
"This is indeed a mystery," I remarked.
"What do you imagine that it means?"
It is a capital mistake to theorize before one has data.
Insensibly one begins to twist facts to suit theories, instead of theories to suit facts.
But the note itself.
What do you deduce from it?"
I carefully examined the writing, and the paper upon which it was written.
"The man who wrote it was presumably well to do," I remarked, endeavouring to imitate my companion's processes.
"Such paper could not be bought under half a crown a packet.
It is peculiarly strong and stiff." "Peculiar--that is the very word," said
Holmes.
"It is not an English paper at all.
Hold it up to the light."
I did so, and saw a large "E" with a small "g," a "P," and a large "G" with a small
"t" woven into the texture of the paper.
"What do you make of that?" asked Holmes.
"The name of the maker, no doubt; or his monogram, rather." "Not at all.
The 'G' with the small 't' stands for 'Gesellschaft,' which is the German for
'Company.' It is a customary contraction like our
'Co.'
'P,' of course, stands for 'Papier.' Now for the 'Eg.'
Let us glance at our Continental Gazetteer."
He took down a heavy brown volume from his shelves.
"Eglow, Eglonitz--here we are, Egria.
It is in a German-speaking country--in
Bohemia, not far from Carlsbad.
'Remarkable as being the scene of the death of Wallenstein, and for its numerous glass- factories and paper-mills.'
Ha, ha, my boy, what do you make of that?"
His eyes sparkled, and he sent up a great blue triumphant cloud from his cigarette.
"The paper was made in Bohemia," I said.
"Precisely.
And the man who wrote the note is a German.
Do you note the peculiar construction of the sentence--'This account of you we have from all quarters received.'
A Frenchman or Russian could not have written that.
It is the German who is so uncourteous to his verbs.
It only remains, therefore, to discover what is wanted by this German who writes upon Bohemian paper and prefers wearing a mask to showing his face.
And here he comes, if I am not mistaken, to resolve all our doubts."
As he spoke there was the sharp sound of horses' hoofs and grating wheels against the curb, followed by a sharp pull at the bell.
Holmes whistled.
"A pair, by the sound," said he.
"Yes," he continued, glancing out of the window.
"A nice little brougham and a pair of beauties.
There's money in this case, Watson, if there is nothing else."
"I think that I had better go, Holmes."
"Not a bit, Doctor.
Stay where you are.
I am lost without my Boswell.
And this promises to be interesting.
It would be a pity to miss it."
"But your client--"
"Never mind him.
I may want your help, and so may he.
Here he comes.
Sit down in that armchair, Doctor, and give us your best attention."
Then there was a loud and authoritative tap.
"Come in!" said Holmes.
A man entered who could hardly have been less than six feet six inches in height, with the chest and limbs of a Hercules.
His dress was rich with a richness which would, in England, be looked upon as akin to bad taste.
Heavy bands of astrakhan were slashed across the sleeves and fronts of his double-breasted coat, while the deep blue cloak which was thrown over his shoulders was lined with flame-coloured silk and secured at the neck with a brooch which consisted of a single flaming beryl.
Boots which extended halfway up his calves, and which were trimmed at the tops with rich brown fur, completed the impression of barbaric opulence which was suggested by his whole appearance.
He carried a broad-brimmed hat in his hand, while he wore across the upper part of his face, extending down past the cheekbones, a black vizard mask, which he had apparently adjusted that very moment, for his hand was still raised to it as he entered.
From the lower part of the face he appeared to be a man of strong character, with a thick, hanging lip, and a long, straight chin suggestive of resolution pushed to the length of obstinacy.
"You had my note?" he asked with a deep harsh voice and a strongly marked German accent.
"I told you that I would call."
He looked from one to the other of us, as if uncertain which to address.
"Pray take a seat," said Holmes.
"This is my friend and colleague, Dr. Watson, who is occasionally good enough to help me in my cases.
Whom have I the honour to address?"
"You may address me as the Count Von Kramm, a Bohemian nobleman.
I understand that this gentleman, your friend, is a man of honour and discretion, whom I may trust with a matter of the most extreme importance.
If not, I should much prefer to communicate with you alone."
I rose to go, but Holmes caught me by the wrist and pushed me back into my chair.
"It is both, or none," said he.
"You may say before this gentleman anything which you may say to me."
The Count shrugged his broad shoulders.
"Then I must begin," said he, "by binding you both to absolute secrecy for two years; at the end of that time the matter will be of no importance.
At present it is not too much to say that it is of such weight it may have an influence upon European history." "I promise," said Holmes.
"And I."
"You will excuse this mask," continued our strange visitor.
"The august person who employs me wishes his agent to be unknown to you, and I may confess at once that the title by which I have just called myself is not exactly my own."
"I was aware of it," said Holmes dryly.
"The circumstances are of great delicacy, and every precaution has to be taken to quench what might grow to be an immense scandal and seriously compromise one of the reigning families of Europe.
To speak plainly, the matter implicates the great House of Ormstein, hereditary kings of Bohemia."
"I was also aware of that," murmured Holmes, settling himself down in his armchair and closing his eyes.
Our visitor glanced with some apparent surprise at the languid, lounging figure of the man who had been no doubt depicted to him as the most incisive reasoner and most energetic agent in Europe.
Holmes slowly reopened his eyes and looked impatiently at his gigantic client.
"If your Majesty would condescend to state your case," he remarked, "I should be better able to advise you."
The man sprang from his chair and paced up and down the room in uncontrollable agitation.
Then, with a gesture of desperation, he tore the mask from his face and hurled it upon the ground.
"You are right," he cried; "I am the King.
Why should I attempt to conceal it?"
"Why, indeed?" murmured Holmes.
"Your Majesty had not spoken before I was aware that I was addressing Wilhelm
Gottsreich Sigismond von Ormstein, Grand Duke of Cassel-Felstein, and hereditary
King of Bohemia."
"But you can understand," said our strange visitor, sitting down once more and passing his hand over his high white forehead, "you can understand that I am not accustomed to doing such business in my own person.
Yet the matter was so delicate that I could not confide it to an agent without putting myself in his power.
I have come incognito from Prague for the purpose of consulting you."
"Then, pray consult," said Holmes, shutting his eyes once more.
"The facts are briefly these:
Some five years ago, during a lengthy visit to
Warsaw, I made the acquaintance of the well-known adventuress, Irene Adler.
The name is no doubt familiar to you."
"Kindly look her up in my index, Doctor," murmured Holmes without opening his eyes.
For many years he had adopted a system of docketing all paragraphs concerning men and things, so that it was difficult to name a subject or a person on which he could not at once furnish information.
In this case I found her biography sandwiched in between that of a Hebrew rabbi and that of a staff-commander who had written a monograph upon the deep-sea fishes.
"Let me see!" said Holmes.
"Hum!
Born in New Jersey in the year 1858.
Contralto--hum!
La Scala, hum!
Prima donna Imperial Opera of Warsaw--yes!
Retired from operatic stage--ha!
Living in London--quite so!
Your Majesty, as I understand, became entangled with this young person, wrote her some compromising letters, and is now desirous of getting those letters back."
"Precisely so.
But how--" "Was there a secret marriage?"
"None." "No legal papers or certificates?"
"None."
"Then I fail to follow your Majesty.
If this young person should produce her letters for blackmailing or other purposes, how is she to prove their authenticity?"
"There is the writing."
"Pooh, pooh!
Forgery."
"My private note-paper." "Stolen."
"My own seal."
"Imitated." "My photograph."
"Bought." "We were both in the photograph."
Your Majesty has indeed committed an indiscretion."
"You have compromised yourself seriously."
"I was only Crown Prince then.
I was young.
I am but thirty now." "It must be recovered."
"We have tried and failed."
"Your Majesty must pay. It must be bought."
"She will not sell." "Stolen, then."
"Five attempts have been made.
Twice burglars in my pay ransacked her house.
Once we diverted her luggage when she travelled.
Twice she has been waylaid.
There has been no result." "No sign of it?"
"Absolutely none." Holmes laughed.
"It is quite a pretty little problem," said he.
"But a very serious one to me," returned the King reproachfully.
"Very, indeed.
And what does she propose to do with the photograph?"
"To ruin me." "But how?"
"I am about to be married."
"So I have heard." You may know the strict principles of her family.
She is herself the very soul of delicacy.
A shadow of a doubt as to my conduct would bring the matter to an end." "And Irene Adler?"
"Threatens to send them the photograph.
And she will do it.
I know that she will do it.
You do not know her, but she has a soul of steel.
She has the face of the most beautiful of women, and the mind of the most resolute of men.
Rather than I should marry another woman, there are no lengths to which she would not go--none."
"You are sure that she has not sent it yet?"
"I am sure." "And why?"
"Because she has said that she would send it on the day when the betrothal was publicly proclaimed.
That will be next Monday." "Oh, then we have three days yet," said
Holmes with a yawn.
"That is very fortunate, as I have one or two matters of importance to look into just at present.
Your Majesty will, of course, stay in
London for the present?"
"Certainly.
You will find me at the Langham under the name of the Count Von Kramm." "Then I shall drop you a line to let you know how we progress."
"Pray do so.
I shall be all anxiety."
"Then, as to money?" "You have carte blanche."
"Absolutely?"
"I tell you that I would give one of the provinces of my kingdom to have that photograph." "And for present expenses?"
The King took a heavy chamois leather bag from under his cloak and laid it on the table.
"There are three hundred pounds in gold and seven hundred in notes," he said.
Holmes scribbled a receipt upon a sheet of his note-book and handed it to him.
"And Mademoiselle's address?" he asked.
"Is Briony Lodge, Serpentine Avenue, St.
John's Wood."
Holmes took a note of it.
"One other question," said he.
"Was the photograph a cabinet?" "It was."
"Then, good-night, your Majesty, and I trust that we shall soon have some good news for you.
And good-night, Watson," he added, as the wheels of the royal brougham rolled down the street.
"If you will be good enough to call to- morrow afternoon at three o'clock I should like to chat this little matter over with you."
Il.
At three o'clock precisely I was at Baker
Street, but Holmes had not yet returned.
The landlady informed me that he had left the house shortly after eight o'clock in the morning.
I sat down beside the fire, however, with the intention of awaiting him, however long he might be.
I was already deeply interested in his inquiry, for, though it was surrounded by none of the grim and strange features which were associated with the two crimes which I have already recorded, still, the nature of the case and the exalted station of his client gave it a character of its own.
Indeed, apart from the nature of the investigation which my friend had on hand, there was something in his masterly grasp of a situation, and his keen, incisive reasoning, which made it a pleasure to me to study his system of work, and to follow the quick, subtle methods by which he disentangled the most inextricable mysteries.
So accustomed was I to his invariable success that the very possibility of his failing had ceased to enter into my head.
It was close upon four before the door opened, and a drunken-looking groom, ill- kempt and side-whiskered, with an inflamed face and disreputable clothes, walked into the room.
Accustomed as I was to my friend's amazing powers in the use of disguises, I had to look three times before I was certain that it was indeed he.
With a nod he vanished into the bedroom, whence he emerged in five minutes tweed- suited and respectable, as of old.
Putting his hands into his pockets, he stretched out his legs in front of the fire and laughed heartily for some minutes.
"Well, really!" he cried, and then he choked and laughed again until he was obliged to lie back, limp and helpless, in the chair.
"What is it?"
"It's quite too funny.
I am sure you could never guess how I employed my morning, or what I ended by doing."
"I can't imagine.
I suppose that you have been watching the habits, and perhaps the house, of Miss
"Quite so; but the sequel was rather unusual.
I will tell you, however.
I left the house a little after eight o'clock this morning in the character of a groom out of work.
There is a wonderful sympathy and freemasonry among horsey men.
Be one of them, and you will know all that there is to know.
I soon found Briony Lodge.
It is a bijou villa, with a garden at the back, but built out in front right up to the road, two stories.
Chubb lock to the door.
Large sitting-room on the right side, well furnished, with long windows almost to the floor, and those preposterous English window fasteners which a child could open.
Behind there was nothing remarkable, save that the passage window could be reached from the top of the coach-house.
I walked round it and examined it closely from every point of view, but without noting anything else of interest.
"I then lounged down the street and found, as I expected, that there was a mews in a
lane which runs down by one wall of the garden.
I lent the ostlers a hand in rubbing down their horses, and received in exchange twopence, a glass of half and half, two fills of shag tobacco, and as much information as I could desire about Miss
Adler, to say nothing of half a dozen other people in the neighbourhood in whom I was not in the least interested, but whose biographies I was compelled to listen to."
"And what of Irene Adler?"
I asked.
"Oh, she has turned all the men's heads down in that part.
She is the daintiest thing under a bonnet on this planet.
So say the Serpentine-mews, to a man.
She lives quietly, sings at concerts, drives out at five every day, and returns at seven sharp for dinner.
Seldom goes out at other times, except when she sings.
Has only one male visitor, but a good deal of him.
He is dark, handsome, and dashing, never calls less than once a day, and often twice.
He is a Mr. Godfrey Norton, of the Inner
Temple.
See the advantages of a cabman as a confidant.
They had driven him home a dozen times from Serpentine-mews, and knew all about him.
When I had listened to all they had to tell, I began to walk up and down near
Briony Lodge once more, and to think over my plan of campaign.
"This Godfrey Norton was evidently an important factor in the matter.
He was a lawyer.
That sounded ominous.
What was the relation between them, and what the object of his repeated visits?
Was she his client, his friend, or his mistress?
If the former, she had probably transferred the photograph to his keeping.
If the latter, it was less likely.
On the issue of this question depended whether I should continue my work at Briony
Lodge, or turn my attention to the gentleman's chambers in the Temple.
It was a delicate point, and it widened the field of my inquiry.
I fear that I bore you with these details, but I have to let you see my little difficulties, if you are to understand the situation."
"I am following you closely," I answered.
"I was still balancing the matter in my mind when a hansom cab drove up to Briony
Lodge, and a gentleman sprang out.
He was a remarkably handsome man, dark, aquiline, and moustached--evidently the man of whom I had heard.
He appeared to be in a great hurry, shouted to the cabman to wait, and brushed past the maid who opened the door with the air of a man who was thoroughly at home.
"He was in the house about half an hour, and I could catch glimpses of him in the windows of the sitting-room, pacing up and down, talking excitedly, and waving his arms.
Of her I could see nothing.
Presently he emerged, looking even more flurried than before.
As he stepped up to the cab, he pulled a gold watch from his pocket and looked at it earnestly, 'Drive like the devil,' he shouted, 'first to Gross & Hankey's in
Regent Street, and then to the Church of St. Monica in the Edgeware Road.
Half a guinea if you do it in twenty minutes!'
"Away they went, and I was just wondering whether I should not do well to follow them when up the lane came a neat little landau, the coachman with his coat only half- buttoned, and his tie under his ear, while all the tags of his harness were sticking out of the buckles.
It hadn't pulled up before she shot out of the hall door and into it.
I only caught a glimpse of her at the moment, but she was a lovely woman, with a face that a man might die for. "'The Church of St. Monica, John,' she cried, 'and half a sovereign if you reach it in twenty minutes.'
I was just balancing whether I should run for it, or whether I should perch behind her landau when a cab came through the street.
The driver looked twice at such a shabby fare, but I jumped in before he could object.
'The Church of St. Monica,' said I, 'and half a sovereign if you reach it in twenty minutes.'
It was twenty-five minutes to twelve, and of course it was clear enough what was in the wind.
"My cabby drove fast.
I don't think I ever drove faster, but the others were there before us.
The cab and the landau with their steaming horses were in front of the door when I arrived.
I paid the man and hurried into the church.
There was not a soul there save the two whom I had followed and a surpliced clergyman, who seemed to be expostulating with them.
They were all three standing in a knot in front of the altar.
I lounged up the side aisle like any other idler who has dropped into a church.
Suddenly, to my surprise, the three at the altar faced round to me, and Godfrey Norton came running as hard as he could towards me. "'Thank God,' he cried.
'You'll do.
Come!
Come!' "'What then?'
I asked. "'Come, man, come, only three minutes, or it won't be legal.'
"I was half-dragged up to the altar, and before I knew where I was I found myself mumbling responses which were whispered in my ear, and vouching for things of which I knew nothing, and generally assisting in the secure tying up of Irene Adler, spinster, to Godfrey Norton, bachelor.
It was all done in an instant, and there was the gentleman thanking me on the one side and the lady on the other, while the clergyman beamed on me in front.
It was the most preposterous position in which I ever found myself in my life, and it was the thought of it that started me laughing just now.
It seems that there had been some informality about their license, that the clergyman absolutely refused to marry them without a witness of some sort, and that my lucky appearance saved the bridegroom from having to sally out into the streets in search of a best man.
The bride gave me a sovereign, and I mean to wear it on my watch-chain in memory of the occasion."
"This is a very unexpected turn of affairs," said I; "and what then?"
"Well, I found my plans very seriously menaced.
It looked as if the pair might take an immediate departure, and so necessitate very prompt and energetic measures on my part.
At the church door, however, they separated, he driving back to the Temple, and she to her own house.
'I shall drive out in the park at five as usual,' she said as she left him.
I heard no more.
They drove away in different directions, and I went off to make my own arrangements."
"Which are?"
"Some cold beef and a glass of beer," he answered, ringing the bell.
"I have been too busy to think of food, and I am likely to be busier still this evening.
By the way, Doctor, I shall want your co- operation."
"I shall be delighted." "You don't mind breaking the law?"
"Not in the least."
"Nor running a chance of arrest?" "Not in a good cause."
"Oh, the cause is excellent!" "Then I am your man."
"I was sure that I might rely on you."
"But what is it you wish?" "When Mrs. Turner has brought in the tray I will make it clear to you.
Now," he said as he turned hungrily on the simple fare that our landlady had provided,
"I must discuss it while I eat, for I have not much time.
It is nearly five now.
In two hours we must be on the scene of action.
Miss Irene, or Madame, rather, returns from her drive at seven.
We must be at Briony Lodge to meet her."
"And what then?" "You must leave that to me.
I have already arranged what is to occur.
There is only one point on which I must insist.
You must not interfere, come what may.
You understand?"
"I am to be neutral?" "To do nothing whatever.
There will probably be some small unpleasantness.
It will end in my being conveyed into the house.
Four or five minutes afterwards the sitting-room window will open.
You are to station yourself close to that open window."
"Yes."
"You are to watch me, for I will be visible to you."
"Yes."
"And when I raise my hand--so--you will throw into the room what I give you to throw, and will, at the same time, raise the cry of fire.
You quite follow me?"
"Entirely." "It is nothing very formidable," he said, taking a long cigar-shaped roll from his pocket.
"It is an ordinary plumber's smoke-rocket, fitted with a cap at either end to make it self-lighting.
Your task is confined to that.
When you raise your cry of fire, it will be taken up by quite a number of people.
You may then walk to the end of the street, and I will rejoin you in ten minutes.
I hope that I have made myself clear?"
"I am to remain neutral, to get near the window, to watch you, and at the signal to throw in this object, then to raise the cry of fire, and to wait you at the corner of the street."
"Precisely." "Then you may entirely rely on me."
I think, perhaps, it is almost time that I prepare for the new role I have to play."
He disappeared into his bedroom and returned in a few minutes in the character of an amiable and simple-minded Nonconformist clergyman.
His broad black hat, his baggy trousers, his white tie, his sympathetic smile, and general look of peering and benevolent curiosity were such as Mr. John Hare alone could have equalled.
It was not merely that Holmes changed his costume.
His expression, his manner, his very soul seemed to vary with every fresh part that he assumed.
The stage lost a fine actor, even as science lost an acute reasoner, when he became a specialist in crime.
It was a quarter past six when we left Baker Street, and it still wanted ten minutes to the hour when we found ourselves in Serpentine Avenue.
It was already dusk, and the lamps were just being lighted as we paced up and down in front of Briony Lodge, waiting for the coming of its occupant.
The house was just such as I had pictured it from Sherlock Holmes' succinct description, but the locality appeared to be less private than I expected.
On the contrary, for a small street in a quiet neighbourhood, it was remarkably animated.
There was a group of shabbily dressed men smoking and laughing in a corner, a scissors-grinder with his wheel, two guardsmen who were flirting with a nurse- girl, and several well-dressed young men who were lounging up and down with cigars in their mouths.
"You see," remarked Holmes, as we paced to and fro in front of the house, "this marriage rather simplifies matters.
The photograph becomes a double-edged weapon now.
The chances are that she would be as averse to its being seen by Mr. Godfrey Norton, as our client is to its coming to the eyes of his princess.
Now the question is, Where are we to find the photograph?"
"Where, indeed?" "It is most unlikely that she carries it about with her.
It is cabinet size.
Too large for easy concealment about a woman's dress.
She knows that the King is capable of having her waylaid and searched.
Two attempts of the sort have already been made.
We may take it, then, that she does not carry it about with her."
"Where, then?"
"Her banker or her lawyer.
There is that double possibility.
But I am inclined to think neither.
Women are naturally secretive, and they like to do their own secreting.
Why should she hand it over to anyone else?
She could trust her own guardianship, but she could not tell what indirect or political influence might be brought to bear upon a business man.
Besides, remember that she had resolved to use it within a few days.
It must be where she can lay her hands upon it.
It must be in her own house."
"But it has twice been burgled." "Pshaw!
They did not know how to look." "But how will you look?"
"I will not look."
"What then?" "I will get her to show me."
"But she will refuse." "She will not be able to.
But I hear the rumble of wheels.
It is her carriage.
Now carry out my orders to the letter."
As he spoke the gleam of the side-lights of a carriage came round the curve of the avenue.
It was a smart little landau which rattled up to the door of Briony Lodge.
As it pulled up, one of the loafing men at the corner dashed forward to open the door in the hope of earning a copper, but was elbowed away by another loafer, who had rushed up with the same intention.
A fierce quarrel broke out, which was increased by the two guardsmen, who took sides with one of the loungers, and by the scissors-grinder, who was equally hot upon the other side.
A blow was struck, and in an instant the lady, who had stepped from her carriage, was the centre of a little knot of flushed and struggling men, who struck savagely at each other with their fists and sticks.
Holmes dashed into the crowd to protect the lady; but just as he reached her he gave a cry and dropped to the ground, with the blood running freely down his face.
At his fall the guardsmen took to their heels in one direction and the loungers in the other, while a number of better-dressed people, who had watched the scuffle without taking part in it, crowded in to help the lady and to attend to the injured man.
Irene Adler, as I will still call her, had hurried up the steps; but she stood at the top with her superb figure outlined against the lights of the hall, looking back into the street.
"Is the poor gentleman much hurt?" she asked.
"He is dead," cried several voices.
"No, no, there's life in him!" shouted another.
"But he'll be gone before you can get him to hospital."
"He's a brave fellow," said a woman.
"They would have had the lady's purse and watch if it hadn't been for him.
They were a gang, and a rough one, too.
Ah, he's breathing now."
"He can't lie in the street.
May we bring him in, marm?"
"Surely.
Bring him into the sitting-room.
There is a comfortable sofa.
This way, please!"
Slowly and solemnly he was borne into Briony Lodge and laid out in the principal room, while I still observed the proceedings from my post by the window.
The lamps had been lit, but the blinds had not been drawn, so that I could see Holmes as he lay upon the couch.
I do not know whether he was seized with compunction at that moment for the part he was playing, but I know that I never felt more heartily ashamed of myself in my life than when I saw the beautiful creature against whom I was conspiring, or the grace and kindliness with which she waited upon the injured man.
And yet it would be the blackest treachery to Holmes to draw back now from the part which he had intrusted to me.
I hardened my heart, and took the smoke- rocket from under my ulster.
After all, I thought, we are not injuring her.
We are but preventing her from injuring another.
Holmes had sat up upon the couch, and I saw him motion like a man who is in need of air.
A maid rushed across and threw open the window.
At the same instant I saw him raise his hand and at the signal I tossed my rocket into the room with a cry of "Fire!"
The word was no sooner out of my mouth than the whole crowd of spectators, well dressed and ill--gentlemen, ostlers, and servant- maids--joined in a general shriek of
"Fire!"
Thick clouds of smoke curled through the room and out at the open window.
I caught a glimpse of rushing figures, and a moment later the voice of Holmes from within assuring them that it was a false alarm.
Slipping through the shouting crowd I made my way to the corner of the street, and in ten minutes was rejoiced to find my friend's arm in mine, and to get away from the scene of uproar.
He walked swiftly and in silence for some few minutes until we had turned down one of the quiet streets which lead towards the Edgeware Road.
"You did it very nicely, Doctor," he remarked.
"Nothing could have been better.
It is all right."
"You have the photograph?"
"I know where it is." "And how did you find out?"
"She showed me, as I told you she would." "I am still in the dark."
"I do not wish to make a mystery," said he, laughing.
"The matter was perfectly simple.
You, of course, saw that everyone in the street was an accomplice.
They were all engaged for the evening." "I guessed as much."
"Then, when the row broke out, I had a little moist red paint in the palm of my hand.
I rushed forward, fell down, clapped my hand to my face, and became a piteous spectacle.
It is an old trick."
"That also I could fathom."
"Then they carried me in.
She was bound to have me in.
What else could she do?
And into her sitting-room, which was the very room which I suspected.
It lay between that and her bedroom, and I was determined to see which.
They laid me on a couch, I motioned for air, they were compelled to open the window, and you had your chance."
"How did that help you?" "It was all-important.
When a woman thinks that her house is on fire, her instinct is at once to rush to the thing which she values most.
It is a perfectly overpowering impulse, and I have more than once taken advantage of it.
In the case of the Darlington substitution scandal it was of use to me, and also in the Arnsworth Castle business.
A married woman grabs at her baby; an unmarried one reaches for her jewel-box.
Now it was clear to me that our lady of to- day had nothing in the house more precious to her than what we are in quest of.
She would rush to secure it.
The alarm of fire was admirably done.
The smoke and shouting were enough to shake nerves of steel.
She responded beautifully.
The photograph is in a recess behind a sliding panel just above the right bell- pull.
She was there in an instant, and I caught a glimpse of it as she half-drew it out.
When I cried out that it was a false alarm, she replaced it, glanced at the rocket, rushed from the room, and I have not seen her since.
I rose, and, making my excuses, escaped from the house.
I hesitated whether to attempt to secure the photograph at once; but the coachman had come in, and as he was watching me narrowly it seemed safer to wait.
A little over-precipitance may ruin all."
"And now?" I asked.
"Our quest is practically finished.
I shall call with the King to-morrow, and with you, if you care to come with us.
We will be shown into the sitting-room to wait for the lady, but it is probable that when she comes she may find neither us nor the photograph.
It might be a satisfaction to his Majesty to regain it with his own hands."
"And when will you call?" "At eight in the morning.
She will not be up, so that we shall have a clear field.
Besides, we must be prompt, for this marriage may mean a complete change in her life and habits.
I must wire to the King without delay."
We had reached Baker Street and had stopped at the door.
He was searching his pockets for the key when someone passing said:
"Good-night, Mister Sherlock Holmes." There were several people on the pavement at the time, but the greeting appeared to come from a slim youth in an ulster who had hurried by.
"I've heard that voice before," said Holmes, staring down the dimly lit street.
"Now, I wonder who the deuce that could have been."
IIl. I slept at Baker Street that night, and we were engaged upon our toast and coffee in the morning when the King of Bohemia rushed into the room.
"You have really got it!" he cried, grasping Sherlock Holmes by either shoulder and looking eagerly into his face.
"Not yet."
"But you have hopes?"
"I have hopes." "Then, come.
I am all impatience to be gone." "We must have a cab."
"No, my brougham is waiting."
"Then that will simplify matters." We descended and started off once more for
Briony Lodge.
"Irene Adler is married," remarked Holmes.
"Married!
When?" "Yesterday."
"But to whom?" "To an English lawyer named Norton."
"But she could not love him."
"I am in hopes that she does." "And why in hopes?"
"Because it would spare your Majesty all fear of future annoyance.
If the lady loves her husband, she does not love your Majesty.
If she does not love your Majesty, there is no reason why she should interfere with your Majesty's plan."
"It is true.
And yet--Well!
I wish she had been of my own station!
What a queen she would have made!"
He relapsed into a moody silence, which was not broken until we drew up in Serpentine
The door of Briony Lodge was open, and an elderly woman stood upon the steps.
She watched us with a sardonic eye as we stepped from the brougham.
"Mr. Sherlock Holmes, I believe?" said she.
"I am Mr. Holmes," answered my companion, looking at her with a questioning and rather startled gaze.
"Indeed!
My mistress told me that you were likely to call.
She left this morning with her husband by the 5:15 train from Charing Cross for the
Continent."
"What!" Sherlock Holmes staggered back, white with chagrin and surprise.
"Do you mean that she has left England?"
"Never to return."
"And the papers?" asked the King hoarsely.
"All is lost."
"We shall see."
He pushed past the servant and rushed into the drawing-room, followed by the King and myself.
The furniture was scattered about in every direction, with dismantled shelves and open drawers, as if the lady had hurriedly ransacked them before her flight.
Holmes rushed at the bell-pull, tore back a small sliding shutter, and, plunging in his hand, pulled out a photograph and a letter.
The photograph was of Irene Adler herself in evening dress, the letter was superscribed to "Sherlock Holmes, Esq.
To be left till called for."
My friend tore it open and we all three read it together.
It was dated at midnight of the preceding night and ran in this way:
"MY DEAR MR. SHERLOCK HOLMES,--You really did it very well.
You took me in completely.
Until after the alarm of fire, I had not a suspicion.
But then, when I found how I had betrayed myself, I began to think.
I had been warned against you months ago. I had been told that if the King employed an agent it would certainly be you.
And your address had been given me. Yet, with all this, you made me reveal what you wanted to know.
Even after I became suspicious, I found it hard to think evil of such a dear, kind old clergyman.
But, you know, I have been trained as an actress myself.
I often take advantage of the freedom which it gives.
I sent John, the coachman, to watch you, ran up stairs, got into my walking-clothes, as I call them, and came down just as you departed.
"Well, I followed you to your door, and so made sure that I was really an object of interest to the celebrated Mr. Sherlock Holmes.
Then I, rather imprudently, wished you good-night, and started for the Temple to see my husband.
"We both thought the best resource was flight, when pursued by so formidable an antagonist; so you will find the nest empty when you call to-morrow.
As to the photograph, your client may rest in peace.
I love and am loved by a better man than he.
The King may do what he will without hindrance from one whom he has cruelly wronged.
I keep it only to safeguard myself, and to preserve a weapon which will always secure me from any steps which he might take in the future.
I leave a photograph which he might care to possess; and I remain, dear Mr. Sherlock
Holmes, "Very truly yours, "IRENE NORTON, née
ADLER."
"What a woman--oh, what a woman!" cried the King of Bohemia, when we had all three read this epistle.
"Did I not tell you how quick and resolute she was?
"From what I have seen of the lady she seems indeed to be on a very different level to your Majesty," said Holmes coldly.
"I am sorry that I have not been able to bring your Majesty's business to a more successful conclusion." "On the contrary, my dear sir," cried the
King; "nothing could be more successful.
The photograph is now as safe as if it were in the fire."
"I am glad to hear your Majesty say so."
"I am immensely indebted to you.
Pray tell me in what way I can reward you.
This ring--" He slipped an emerald snake ring from his finger and held it out upon the palm of his hand.
"Your Majesty has something which I should value even more highly," said Holmes.
"You have but to name it." "This photograph!"
The King stared at him in amazement.
"Irene's photograph!" he cried.
"Certainly, if you wish it."
"I thank your Majesty.
Then there is no more to be done in the matter.
I have the honour to wish you a very good- morning."
He bowed, and, turning away without observing the hand which the King had stretched out to him, he set off in my company for his chambers.
And that was how a great scandal threatened to affect the kingdom of Bohemia, and how the best plans of Mr. Sherlock Holmes were beaten by a woman's wit.
He used to make merry over the cleverness of women, but I have not heard him do it of
late.
And when he speaks of Irene Adler, or when he refers to her photograph, it is always under the honourable title of the woman. >
THE ADVENTURES OF SHERLOCK HOLMES by SlR ARTHUR CONAN DOYLE
ADVENTURE Il.
THE RED-HEADED LEAGUE
I had called upon my friend, Mr. Sherlock Holmes, one day in the autumn of last year and found him in deep conversation with a very stout, florid-faced, elderly gentleman with fiery red hair.
With an apology for my intrusion, I was about to withdraw when Holmes pulled me abruptly into the room and closed the door behind me.
"You could not possibly have come at a better time, my dear Watson," he said cordially.
"I was afraid that you were engaged."
"So I am.
Very much so." "Then I can wait in the next room."
"Not at all.
This gentleman, Mr. Wilson, has been my partner and helper in many of my most successful cases, and I have no doubt that he will be of the utmost use to me in yours also."
The stout gentleman half rose from his chair and gave a bob of greeting, with a quick little questioning glance from his small fat-encircled eyes.
"Try the settee," said Holmes, relapsing into his armchair and putting his fingertips together, as was his custom when in judicial moods.
"I know, my dear Watson, that you share my love of all that is bizarre and outside the conventions and humdrum routine of everyday life.
You have shown your relish for it by the enthusiasm which has prompted you to chronicle, and, if you will excuse my saying so, somewhat to embellish so many of my own little adventures."
"Your cases have indeed been of the greatest interest to me," I observed.
"You will remember that I remarked the other day, just before we went into the very simple problem presented by Miss Mary Sutherland, that for strange effects and extraordinary combinations we must go to life itself, which is always far more daring than any effort of the imagination."
"A proposition which I took the liberty of doubting."
"You did, Doctor, but none the less you must come round to my view, for otherwise I shall keep on piling fact upon fact on you until your reason breaks down under them and acknowledges me to be right.
Now, Mr. Jabez Wilson here has been good enough to call upon me this morning, and to begin a narrative which promises to be one of the most singular which I have listened to for some time.
You have heard me remark that the strangest and most unique things are very often connected not with the larger but with the smaller crimes, and occasionally, indeed, where there is room for doubt whether any positive crime has been committed.
As far as I have heard it is impossible for me to say whether the present case is an instance of crime or not, but the course of events is certainly among the most singular that I have ever listened to.
Perhaps, Mr. Wilson, you would have the great kindness to recommence your narrative.
I ask you not merely because my friend Dr. Watson has not heard the opening part but also because the peculiar nature of the story makes me anxious to have every possible detail from your lips.
As a rule, when I have heard some slight indication of the course of events, I am able to guide myself by the thousands of other similar cases which occur to my memory.
In the present instance I am forced to admit that the facts are, to the best of my belief, unique."
The portly client puffed out his chest with an appearance of some little pride and pulled a dirty and wrinkled newspaper from the inside pocket of his greatcoat.
As he glanced down the advertisement column, with his head thrust forward and the paper flattened out upon his knee, I took a good look at the man and endeavoured, after the fashion of my companion, to read the indications which might be presented by his dress or appearance.
I did not gain very much, however, by my inspection.
Our visitor bore every mark of being an average commonplace British tradesman, obese, pompous, and slow.
He wore rather baggy grey shepherd's check trousers, a not over-clean black frock- coat, unbuttoned in the front, and a drab waistcoat with a heavy brassy Albert chain, and a square pierced bit of metal dangling down as an ornament.
A frayed top-hat and a faded brown overcoat with a wrinkled velvet collar lay upon a chair beside him.
Altogether, look as I would, there was nothing remarkable about the man save his blazing red head, and the expression of extreme chagrin and discontent upon his features.
Sherlock Holmes' quick eye took in my occupation, and he shook his head with a smile as he noticed my questioning glances.
"Beyond the obvious facts that he has at some time done manual labour, that he takes snuff, that he is a Freemason, that he has been in China, and that he has done a considerable amount of writing lately, I can deduce nothing else."
Mr. Jabez Wilson started up in his chair, with his forefinger upon the paper, but his eyes upon my companion.
"How, in the name of good-fortune, did you know all that, Mr. Holmes?" he asked.
"How did you know, for example, that I did manual labour.
It's as true as gospel, for I began as a ship's carpenter."
"Your hands, my dear sir.
Your right hand is quite a size larger than your left.
You have worked with it, and the muscles are more developed."
"Well, the snuff, then, and the Freemasonry?"
"I won't insult your intelligence by telling you how I read that, especially as, rather against the strict rules of your order, you use an arc-and-compass breastpin."
"Ah, of course, I forgot that.
But the writing?"
"What else can be indicated by that right cuff so very shiny for five inches, and the left one with the smooth patch near the elbow where you rest it upon the desk?"
"Well, but China?"
"The fish that you have tattooed immediately above your right wrist could only have been done in China.
I have made a small study of tattoo marks and have even contributed to the literature of the subject.
That trick of staining the fishes' scales of a delicate pink is quite peculiar to
China.
When, in addition, I see a Chinese coin hanging from your watch-chain, the matter becomes even more simple." Mr. Jabez Wilson laughed heavily.
"Well, I never!" said he.
"I thought at first that you had done something clever, but I see that there was nothing in it, after all." "I begin to think, Watson," said Holmes,
"that I make a mistake in explaining.
'Omne ignotum pro magnifico,' you know, and my poor little reputation, such as it is, will suffer shipwreck if I am so candid. Can you not find the advertisement, Mr.
Wilson?"
"Yes, I have got it now," he answered with his thick red finger planted halfway down the column.
"Here it is.
This is what began it all.
You just read it for yourself, sir."
I took the paper from him and read as follows:
"TO THE RED-HEADED LEAGUE: On account of the bequest of the late Ezekiah Hopkins, of
Lebanon, Pennsylvania, U. S. A., there is now another vacancy open which entitles a member of the League to a salary of 4 pounds a week for purely nominal services.
All red-headed men who are sound in body and mind and above the age of twenty-one years, are eligible.
Apply in person on Monday, at eleven o'clock, to Duncan Ross, at the offices of the League, 7 Pope's Court, Fleet Street."
I ejaculated after I had twice read over the extraordinary announcement.
Holmes chuckled and wriggled in his chair, as was his habit when in high spirits.
"It is a little off the beaten track, isn't it?" said he.
"And now, Mr. Wilson, off you go at scratch and tell us all about yourself, your household, and the effect which this advertisement had upon your fortunes.
You will first make a note, Doctor, of the paper and the date."
"It is The Morning Chronicle of April 27, 1890.
Just two months ago."
"Very good.
Now, Mr. Wilson?"
"Well, it is just as I have been telling you, Mr. Sherlock Holmes," said Jabez
Wilson, mopping his forehead; "I have a small pawnbroker's business at Coburg
Square, near the City.
It's not a very large affair, and of late years it has not done more than just give me a living.
I used to be able to keep two assistants, but now I only keep one; and I would have a job to pay him but that he is willing to come for half wages so as to learn the business."
"What is the name of this obliging youth?" asked Sherlock Holmes.
"His name is Vincent Spaulding, and he's not such a youth, either.
It's hard to say his age.
I should not wish a smarter assistant, Mr. Holmes; and I know very well that he could better himself and earn twice what I am able to give him.
But, after all, if he is satisfied, why should I put ideas in his head?"
"Why, indeed?
You seem most fortunate in having an employé who comes under the full market price.
It is not a common experience among employers in this age.
I don't know that your assistant is not as remarkable as your advertisement."
"Oh, he has his faults, too," said Mr. Wilson.
"Never was such a fellow for photography.
Snapping away with a camera when he ought to be improving his mind, and then diving down into the cellar like a rabbit into its hole to develop his pictures.
That is his main fault, but on the whole he's a good worker.
There's no vice in him." "He is still with you, I presume?"
"Yes, sir.
He and a girl of fourteen, who does a bit of simple cooking and keeps the place clean--that's all I have in the house, for I am a widower and never had any family.
We live very quietly, sir, the three of us; and we keep a roof over our heads and pay our debts, if we do nothing more. "The first thing that put us out was that advertisement.
Spaulding, he came down into the office just this day eight weeks, with this very paper in his hand, and he says: "'I wish to the Lord, Mr. Wilson, that I was a red-headed man.' "'Why that?'
I asks. "'Why,' says he, 'here's another vacancy on the League of the Red-headed Men.
It's worth quite a little fortune to any man who gets it, and I understand that there are more vacancies than there are men, so that the trustees are at their wits' end what to do with the money.
If my hair would only change colour, here's a nice little crib all ready for me to step into.' "'Why, what is it, then?'
I asked.
You see, Mr. Holmes, I am a very stay-at- home man, and as my business came to me instead of my having to go to it, I was often weeks on end without putting my foot over the door-mat.
In that way I didn't know much of what was going on outside, and I was always glad of a bit of news. "'Have you never heard of the League of the Red-headed Men?' he asked with his eyes open. "'Never.' "'Why, I wonder at that, for you are eligible yourself for one of the vacancies.' "'And what are they worth?'
I asked. "'Oh, merely a couple of hundred a year, but the work is slight, and it need not interfere very much with one's other occupations.'
"Well, you can easily think that that made me prick up my ears, for the business has not been over-good for some years, and an extra couple of hundred would have been very handy. "'Tell me all about it,' said I.
"'Well,' said he, showing me the advertisement, 'you can see for yourself that the League has a vacancy, and there is the address where you should apply for particulars.
As far as I can make out, the League was founded by an American millionaire, Ezekiah
Hopkins, who was very peculiar in his ways.
He was himself red-headed, and he had a great sympathy for all red-headed men; so when he died it was found that he had left his enormous fortune in the hands of trustees, with instructions to apply the interest to the providing of easy berths to men whose hair is of that colour.
From all I hear it is splendid pay and very little to do.' "'But,' said I, 'there would be millions of red-headed men who would apply.' "'Not so many as you might think,' he answered.
'You see it is really confined to Londoners, and to grown men.
This American had started from London when he was young, and he wanted to do the old town a good turn.
Then, again, I have heard it is no use your applying if your hair is light red, or dark red, or anything but real bright, blazing, fiery red.
Now, if you cared to apply, Mr. Wilson, you would just walk in; but perhaps it would hardly be worth your while to put yourself out of the way for the sake of a few hundred pounds.'
"Now, it is a fact, gentlemen, as you may see for yourselves, that my hair is of a very full and rich tint, so that it seemed to me that if there was to be any competition in the matter I stood as good a chance as any man that I had ever met.
Vincent Spaulding seemed to know so much about it that I thought he might prove useful, so I just ordered him to put up the shutters for the day and to come right away with me.
He was very willing to have a holiday, so we shut the business up and started off for the address that was given us in the advertisement.
"I never hope to see such a sight as that again, Mr. Holmes.
From north, south, east, and west every man who had a shade of red in his hair had tramped into the city to answer the advertisement.
Fleet Street was choked with red-headed folk, and Pope's Court looked like a coster's orange barrow.
I should not have thought there were so many in the whole country as were brought together by that single advertisement.
Every shade of colour they were--straw, lemon, orange, brick, Irish-setter, liver, clay; but, as Spaulding said, there were not many who had the real vivid flame- coloured tint.
When I saw how many were waiting, I would have given it up in despair; but Spaulding would not hear of it.
How he did it I could not imagine, but he pushed and pulled and butted until he got me through the crowd, and right up to the steps which led to the office.
There was a double stream upon the stair, some going up in hope, and some coming back dejected; but we wedged in as well as we could and soon found ourselves in the office."
"Your experience has been a most entertaining one," remarked Holmes as his client paused and refreshed his memory with a huge pinch of snuff.
"Pray continue your very interesting statement."
"There was nothing in the office but a couple of wooden chairs and a deal table, behind which sat a small man with a head that was even redder than mine.
He said a few words to each candidate as he came up, and then he always managed to find some fault in them which would disqualify them.
Getting a vacancy did not seem to be such a very easy matter, after all.
However, when our turn came the little man was much more favourable to me than to any of the others, and he closed the door as we entered, so that he might have a private word with us. "'This is Mr. Jabez Wilson,' said my assistant, 'and he is willing to fill a vacancy in the League.' "'And he is admirably suited for it,' the other answered.
I cannot recall when I have seen anything so fine.'
He took a step backward, cocked his head on one side, and gazed at my hair until I felt quite bashful.
Then suddenly he plunged forward, wrung my hand, and congratulated me warmly on my success. "'It would be injustice to hesitate,' said he.
'You will, however, I am sure, excuse me for taking an obvious precaution.'
With that he seized my hair in both his hands, and tugged until I yelled with the pain.
'There is water in your eyes,' said he as he released me.
'I perceive that all is as it should be.
But we have to be careful, for we have twice been deceived by wigs and once by paint.
I could tell you tales of cobbler's wax which would disgust you with human nature.'
He stepped over to the window and shouted through it at the top of his voice that the vacancy was filled.
A groan of disappointment came up from below, and the folk all trooped away in different directions until there was not a red-head to be seen except my own and that of the manager. "'My name,' said he, 'is Mr. Duncan Ross, and I am myself one of the pensioners upon the fund left by our noble benefactor.
Are you a married man, Mr. Wilson?
Have you a family?'
"I answered that I had not.
"His face fell immediately. "'Dear me!' he said gravely, 'that is very serious indeed!
I am sorry to hear you say that.
The fund was, of course, for the propagation and spread of the red-heads as well as for their maintenance.
It is exceedingly unfortunate that you should be a bachelor.'
"My face lengthened at this, Mr. Holmes, for I thought that I was not to have the vacancy after all; but after thinking it over for a few minutes he said that it would be all right. "'In the case of another,' said he, 'the objection might be fatal, but we must stretch a point in favour of a man with such a head of hair as yours.
When shall you be able to enter upon your new duties?' "'Well, it is a little awkward, for I have a business already,' said I.
'I should be able to look after that for you.' "'What would be the hours?'
I asked. "'Ten to two.'
"Now a pawnbroker's business is mostly done of an evening, Mr. Holmes, especially
Thursday and Friday evening, which is just before pay-day; so it would suit me very well to earn a little in the mornings.
Besides, I knew that my assistant was a good man, and that he would see to anything that turned up. "'That would suit me very well,' said I.
'And the pay?' "'Is 4 pounds a week.' "'And the work?' "'Is purely nominal.' "'What do you call purely nominal?' "'Well, you have to be in the office, or at least in the building, the whole time.
If you leave, you forfeit your whole position forever.
The will is very clear upon that point.
You don't comply with the conditions if you budge from the office during that time.' "'It's only four hours a day, and I should not think of leaving,' said I.
"'No excuse will avail,' said Mr. Duncan Ross; 'neither sickness nor business nor anything else.
There you must stay, or you lose your billet.' "'And the work?' "'Is to copy out the "Encyclopaedia
There is the first volume of it in that press.
You must find your own ink, pens, and blotting-paper, but we provide this table and chair.
Will you be ready to-morrow?' "'Certainly,' I answered. "'Then, good-bye, Mr. Jabez Wilson, and let me congratulate you once more on the important position which you have been fortunate enough to gain.'
He bowed me out of the room and I went home with my assistant, hardly knowing what to say or do, I was so pleased at my own good fortune.
"Well, I thought over the matter all day, and by evening I was in low spirits again; for I had quite persuaded myself that the whole affair must be some great hoax or fraud, though what its object might be I could not imagine.
It seemed altogether past belief that anyone could make such a will, or that they would pay such a sum for doing anything so simple as copying out the 'Encyclopaedia
Britannica.'
Vincent Spaulding did what he could to cheer me up, but by bedtime I had reasoned myself out of the whole thing.
However, in the morning I determined to have a look at it anyhow, so I bought a penny bottle of ink, and with a quill-pen, and seven sheets of foolscap paper, I started off for Pope's Court.
"Well, to my surprise and delight, everything was as right as possible.
The table was set out ready for me, and Mr. Duncan Ross was there to see that I got fairly to work.
He started me off upon the letter A, and then he left me; but he would drop in from time to time to see that all was right with me.
At two o'clock he bade me good-day, complimented me upon the amount that I had written, and locked the door of the office after me.
"This went on day after day, Mr. Holmes, and on Saturday the manager came in and planked down four golden sovereigns for my week's work.
It was the same next week, and the same the week after.
Every morning I was there at ten, and every afternoon I left at two.
By degrees Mr. Duncan Ross took to coming in only once of a morning, and then, after a time, he did not come in at all.
Still, of course, I never dared to leave the room for an instant, for I was not sure when he might come, and the billet was such a good one, and suited me so well, that I would not risk the loss of it.
"Eight weeks passed away like this, and I had written about Abbots and Archery and
Armour and Architecture and Attica, and hoped with diligence that I might get on to the B's before very long.
It cost me something in foolscap, and I had pretty nearly filled a shelf with my writings.
And then suddenly the whole business came to an end."
"To an end?" "Yes, sir.
And no later than this morning.
I went to my work as usual at ten o'clock, but the door was shut and locked, with a little square of cardboard hammered on to the middle of the panel with a tack.
Here it is, and you can read for yourself."
He held up a piece of white cardboard about the size of a sheet of note-paper.
It read in this fashion:
THE RED-HEADED LEAGUE
IS
DlSSOLVED.
October 9, 1890.
Sherlock Holmes and I surveyed this curt announcement and the rueful face behind it, until the comical side of the affair so completely overtopped every other consideration that we both burst out into a roar of laughter.
"I cannot see that there is anything very funny," cried our client, flushing up to the roots of his flaming head.
"If you can do nothing better than laugh at me, I can go elsewhere."
"No, no," cried Holmes, shoving him back into the chair from which he had half risen.
"I really wouldn't miss your case for the world.
It is most refreshingly unusual.
But there is, if you will excuse my saying so, something just a little funny about it.
Pray what steps did you take when you found the card upon the door?"
"I was staggered, sir.
I did not know what to do.
Then I called at the offices round, but none of them seemed to know anything about it.
Finally, I went to the landlord, who is an accountant living on the ground-floor, and
I asked him if he could tell me what had become of the Red-headed League.
He said that he had never heard of any such body.
Then I asked him who Mr. Duncan Ross was.
He was a solicitor and was using my room as a temporary convenience until his new premises were ready.
He moved out yesterday.' "'Where could I find him?' "'Oh, at his new offices.
He did tell me the address.
Yes, 17 King Edward Street, near St. Paul's.'
"I started off, Mr. Holmes, but when I got to that address it was a manufactory of artificial knee-caps, and no one in it had ever heard of either Mr. William Morris or
Mr. Duncan Ross."
"And what did you do then?" asked Holmes.
"I went home to Saxe-Coburg Square, and I took the advice of my assistant.
But he could not help me in any way.
He could only say that if I waited I should hear by post.
But that was not quite good enough, Mr. Holmes.
I did not wish to lose such a place without a struggle, so, as I had heard that you were good enough to give advice to poor folk who were in need of it, I came right away to you."
"And you did very wisely," said Holmes.
"Your case is an exceedingly remarkable one, and I shall be happy to look into it.
From what you have told me I think that it is possible that graver issues hang from it than might at first sight appear." "Grave enough!" said Mr. Jabez Wilson.
"Why, I have lost four pound a week."
"As far as you are personally concerned," remarked Holmes, "I do not see that you have any grievance against this extraordinary league.
On the contrary, you are, as I understand, richer by some 30 pounds, to say nothing of the minute knowledge which you have gained on every subject which comes under the letter A.
You have lost nothing by them." "No, sir.
But I want to find out about them, and who they are, and what their object was in playing this prank--if it was a prank--upon me.
It was a pretty expensive joke for them, for it cost them two and thirty pounds."
"We shall endeavour to clear up these points for you.
And, first, one or two questions, Mr. Wilson.
This assistant of yours who first called your attention to the advertisement--how
long had he been with you?"
"About a month then." "How did he come?"
"In answer to an advertisement." "Was he the only applicant?"
"No, I had a dozen."
"Why did you pick him?" "Because he was handy and would come cheap." "At half-wages, in fact."
"Yes."
"What is he like, this Vincent Spaulding?" "Small, stout-built, very quick in his ways, no hair on his face, though he's not short of thirty.
Has a white splash of acid upon his forehead."
Holmes sat up in his chair in considerable excitement.
"I thought as much," said he.
"Have you ever observed that his ears are pierced for earrings?"
He told me that a gipsy had done it for him when he was a lad."
"Hum!" said Holmes, sinking back in deep thought.
"He is still with you?" "Oh, yes, sir; I have only just left him."
"And has your business been attended to in your absence?"
"Nothing to complain of, sir. There's never very much to do of a morning."
"That will do, Mr. Wilson. I shall be happy to give you an opinion upon the subject in the course of a day or two.
To-day is Saturday, and I hope that by Monday we may come to a conclusion."
"Well, Watson," said Holmes when our visitor had left us, "what do you make of it all?"
"I make nothing of it," I answered frankly.
"It is a most mysterious business."
"As a rule," said Holmes, "the more bizarre a thing is the less mysterious it proves to be.
It is your commonplace, featureless crimes which are really puzzling, just as a commonplace face is the most difficult to identify.
But I must be prompt over this matter."
"What are you going to do, then?" I asked.
"To smoke," he answered.
"It is quite a three pipe problem, and I beg that you won't speak to me for fifty minutes."
He curled himself up in his chair, with his thin knees drawn up to his hawk-like nose, and there he sat with his eyes closed and his black clay pipe thrusting out like the bill of some strange bird.
I had come to the conclusion that he had dropped asleep, and indeed was nodding myself, when he suddenly sprang out of his chair with the gesture of a man who has made up his mind and put his pipe down upon the mantelpiece.
"Sarasate plays at the St. James's Hall this afternoon," he remarked.
"What do you think, Watson?
Could your patients spare you for a few hours?"
"I have nothing to do to-day.
My practice is never very absorbing."
"Then put on your hat and come.
I am going through the City first, and we can have some lunch on the way.
I observe that there is a good deal of German music on the programme, which is rather more to my taste than Italian or French.
It is introspective, and I want to introspect.
Come along!"
We travelled by the Underground as far as Aldersgate; and a short walk took us to
Saxe-Coburg Square, the scene of the singular story which we had listened to in the morning.
It was a poky, little, shabby-genteel place, where four lines of dingy two- storied brick houses looked out into a small railed-in enclosure, where a lawn of weedy grass and a few clumps of faded
laurel-bushes made a hard fight against a smoke-laden and uncongenial atmosphere.
Three gilt balls and a brown board with "JABEZ WlLSON" in white letters, upon a corner house, announced the place where our red-headed client carried on his business.
Sherlock Holmes stopped in front of it with his head on one side and looked it all over, with his eyes shining brightly between puckered lids.
Then he walked slowly up the street, and then down again to the corner, still looking keenly at the houses.
Finally he returned to the pawnbroker's, and, having thumped vigorously upon the pavement with his stick two or three times, he went up to the door and knocked.
It was instantly opened by a bright- looking, clean-shaven young fellow, who asked him to step in.
"Thank you," said Holmes, "I only wished to ask you how you would go from here to the
Strand." "Third right, fourth left," answered the assistant promptly, closing the door.
"Smart fellow, that," observed Holmes as we walked away.
"He is, in my judgment, the fourth smartest man in London, and for daring I am not sure that he has not a claim to be third.
I have known something of him before."
"Evidently," said I, "Mr. Wilson's assistant counts for a good deal in this mystery of the Red-headed League.
I am sure that you inquired your way merely in order that you might see him."
"Not him." "What then?"
"The knees of his trousers."
"And what did you see?" "What I expected to see."
"Why did you beat the pavement?" "My dear doctor, this is a time for observation, not for talk.
We are spies in an enemy's country.
We know something of Saxe-Coburg Square.
Let us now explore the parts which lie behind it."
The road in which we found ourselves as we turned round the corner from the retired
Saxe-Coburg Square presented as great a contrast to it as the front of a picture does to the back.
It was one of the main arteries which conveyed the traffic of the City to the north and west.
The roadway was blocked with the immense stream of commerce flowing in a double tide inward and outward, while the footpaths were black with the hurrying swarm of pedestrians.
It was difficult to realise as we looked at the line of fine shops and stately business premises that they really abutted on the other side upon the faded and stagnant square which we had just quitted.
"Let me see," said Holmes, standing at the corner and glancing along the line, "I should like just to remember the order of the houses here.
It is a hobby of mine to have an exact knowledge of London.
There is Mortimer's, the tobacconist, the little newspaper shop, the Coburg branch of the City and Suburban Bank, the Vegetarian Restaurant, and McFarlane's carriage- building depot.
That carries us right on to the other block.
And now, Doctor, we've done our work, so it's time we had some play.
A sandwich and a cup of coffee, and then off to violin-land, where all is sweetness and delicacy and harmony, and there are no red-headed clients to vex us with their conundrums."
My friend was an enthusiastic musician, being himself not only a very capable performer but a composer of no ordinary merit.
All the afternoon he sat in the stalls wrapped in the most perfect happiness, gently waving his long, thin fingers in time to the music, while his gently smiling face and his languid, dreamy eyes were as unlike those of Holmes the sleuth-hound, Holmes the relentless, keen-witted, ready- handed criminal agent, as it was possible to conceive.
In his singular character the dual nature alternately asserted itself, and his extreme exactness and astuteness represented, as I have often thought, the reaction against the poetic and contemplative mood which occasionally predominated in him.
The swing of his nature took him from extreme languor to devouring energy; and, as I knew well, he was never so truly formidable as when, for days on end, he had been lounging in his armchair amid his improvisations and his black-letter editions.
Then it was that the lust of the chase would suddenly come upon him, and that his brilliant reasoning power would rise to the level of intuition, until those who were unacquainted with his methods would look askance at him as on a man whose knowledge was not that of other mortals.
When I saw him that afternoon so enwrapped in the music at St. James's Hall I felt that an evil time might be coming upon those whom he had set himself to hunt down.
"You want to go home, no doubt, Doctor," he remarked as we emerged.
"And I have some business to do which will take some hours.
This business at Coburg Square is serious." "Why serious?"
"A considerable crime is in contemplation.
I have every reason to believe that we shall be in time to stop it.
But to-day being Saturday rather complicates matters.
I shall want your help to-night." "At what time?"
"Ten will be early enough."
"I shall be at Baker Street at ten." "Very well.
And, I say, Doctor, there may be some little danger, so kindly put your army revolver in your pocket."
He waved his hand, turned on his heel, and disappeared in an instant among the crowd.
I trust that I am not more dense than my neighbours, but I was always oppressed with a sense of my own stupidity in my dealings with Sherlock Holmes.
Here I had heard what he had heard, I had seen what he had seen, and yet from his words it was evident that he saw clearly not only what had happened but what was about to happen, while to me the whole business was still confused and grotesque.
As I drove home to my house in Kensington I thought over it all, from the extraordinary story of the red-headed copier of the "Encyclopaedia" down to the visit to Saxe-
Coburg Square, and the ominous words with which he had parted from me.
What was this nocturnal expedition, and why should I go armed?
Where were we going, and what were we to do?
I had the hint from Holmes that this smooth-faced pawnbroker's assistant was a formidable man--a man who might play a deep game.
I tried to puzzle it out, but gave it up in despair and set the matter aside until night should bring an explanation.
It was a quarter-past nine when I started from home and made my way across the Park, and so through Oxford Street to Baker Street.
Two hansoms were standing at the door, and as I entered the passage I heard the sound of voices from above.
On entering his room I found Holmes in animated conversation with two men, one of whom I recognised as Peter Jones, the official police agent, while the other was a long, thin, sad-faced man, with a very shiny hat and oppressively respectable frock-coat.
"Ha!
Our party is complete," said Holmes, buttoning up his pea-jacket and taking his heavy hunting crop from the rack.
"Watson, I think you know Mr. Jones, of
Scotland Yard?
Let me introduce you to Mr. Merryweather, who is to be our companion in to-night's adventure."
"We're hunting in couples again, Doctor, you see," said Jones in his consequential way.
"Our friend here is a wonderful man for starting a chase.
All he wants is an old dog to help him to do the running down."
"I hope a wild goose may not prove to be the end of our chase," observed Mr.
Merryweather gloomily.
"You may place considerable confidence in Mr. Holmes, sir," said the police agent loftily.
"He has his own little methods, which are, if he won't mind my saying so, just a little too theoretical and fantastic, but he has the makings of a detective in him.
It is not too much to say that once or twice, as in that business of the Sholto murder and the Agra treasure, he has been more nearly correct than the official force."
"Oh, if you say so, Mr. Jones, it is all right," said the stranger with deference.
"Still, I confess that I miss my rubber.
It is the first Saturday night for seven- and-twenty years that I have not had my rubber."
"I think you will find," said Sherlock Holmes, "that you will play for a higher stake to-night than you have ever done yet, and that the play will be more exciting.
For you, Mr. Merryweather, the stake will be some 30,000 pounds; and for you, Jones, it will be the man upon whom you wish to lay your hands."
"John Clay, the murderer, thief, smasher, and forger.
He's a young man, Mr. Merryweather, but he is at the head of his profession, and I would rather have my bracelets on him than on any criminal in London.
He's a remarkable man, is young John Clay.
His grandfather was a royal duke, and he himself has been to Eton and Oxford.
His brain is as cunning as his fingers, and though we meet signs of him at every turn, we never know where to find the man himself.
He'll crack a crib in Scotland one week, and be raising money to build an orphanage in Cornwall the next.
I've been on his track for years and have never set eyes on him yet."
"I hope that I may have the pleasure of introducing you to-night.
I've had one or two little turns also with Mr. John Clay, and I agree with you that he is at the head of his profession.
It is past ten, however, and quite time that we started.
If you two will take the first hansom, Watson and I will follow in the second."
Sherlock Holmes was not very communicative during the long drive and lay back in the cab humming the tunes which he had heard in the afternoon.
We rattled through an endless labyrinth of gas-lit streets until we emerged into
Farrington Street. I thought it as well to have Jones with us also.
"This fellow Merryweather is a bank director, and personally interested in the matter.
He is not a bad fellow, though an absolute imbecile in his profession.
He has one positive virtue.
He is as brave as a bulldog and as tenacious as a lobster if he gets his claws upon anyone.
Here we are, and they are waiting for us."
We had reached the same crowded thoroughfare in which we had found ourselves in the morning.
Our cabs were dismissed, and, following the guidance of Mr. Merryweather, we passed down a narrow passage and through a side door, which he opened for us.
Within there was a small corridor, which ended in a very massive iron gate.
This also was opened, and led down a flight of winding stone steps, which terminated at another formidable gate.
Mr. Merryweather stopped to light a lantern, and then conducted us down a dark, earth-smelling passage, and so, after opening a third door, into a huge vault or cellar, which was piled all round with crates and massive boxes.
"You are not very vulnerable from above," Holmes remarked as he held up the lantern and gazed about him.
"Nor from below," said Mr. Merryweather, striking his stick upon the flags which lined the floor.
"Why, dear me, it sounds quite hollow!" he remarked, looking up in surprise.
"I must really ask you to be a little more quiet!" said Holmes severely.
"You have already imperilled the whole success of our expedition.
Might I beg that you would have the goodness to sit down upon one of those boxes, and not to interfere?"
The solemn Mr. Merryweather perched himself upon a crate, with a very injured expression upon his face, while Holmes fell upon his knees upon the floor and, with the lantern and a magnifying lens, began to examine minutely the cracks between the stones.
A few seconds sufficed to satisfy him, for he sprang to his feet again and put his glass in his pocket.
"We have at least an hour before us," he remarked, "for they can hardly take any steps until the good pawnbroker is safely in bed.
Then they will not lose a minute, for the sooner they do their work the longer time they will have for their escape.
We are at present, Doctor--as no doubt you have divined--in the cellar of the City branch of one of the principal London banks.
Mr. Merryweather is the chairman of directors, and he will explain to you that there are reasons why the more daring criminals of London should take a considerable interest in this cellar at present."
"It is our French gold," whispered the director.
"We have had several warnings that an attempt might be made upon it."
We had occasion some months ago to strengthen our resources and borrowed for that purpose 30,000 napoleons from the Bank of France.
"Yes.
It has become known that we have never had occasion to unpack the money, and that it is still lying in our cellar.
The crate upon which I sit contains 2,000 napoleons packed between layers of lead foil.
Our reserve of bullion is much larger at present than is usually kept in a single branch office, and the directors have had misgivings upon the subject."
"Which were very well justified," observed Holmes.
"And now it is time that we arranged our little plans.
I expect that within an hour matters will come to a head.
In the meantime Mr. Merryweather, we must put the screen over that dark lantern."
"And sit in the dark?"
"I am afraid so.
I had brought a pack of cards in my pocket, and I thought that, as we were a partie carrée, you might have your rubber after all.
But I see that the enemy's preparations have gone so far that we cannot risk the presence of a light. And, first of all, we must choose our positions.
These are daring men, and though we shall take them at a disadvantage, they may do us some harm unless we are careful.
I shall stand behind this crate, and do you conceal yourselves behind those.
Then, when I flash a light upon them, close in swiftly.
If they fire, Watson, have no compunction about shooting them down."
I placed my revolver, cocked, upon the top of the wooden case behind which I crouched.
Holmes shot the slide across the front of his lantern and left us in pitch darkness-- such an absolute darkness as I have never before experienced.
The smell of hot metal remained to assure us that the light was still there, ready to flash out at a moment's notice.
To me, with my nerves worked up to a pitch of expectancy, there was something depressing and subduing in the sudden gloom, and in the cold dank air of the vault.
"They have but one retreat," whispered Holmes.
"That is back through the house into Saxe- Coburg Square.
I hope that you have done what I asked you, Jones?"
"I have an inspector and two officers waiting at the front door."
"Then we have stopped all the holes.
And now we must be silent and wait."
What a time it seemed!
From comparing notes afterwards it was but an hour and a quarter, yet it appeared to me that the night must have almost gone and the dawn be breaking above us.
My limbs were weary and stiff, for I feared to change my position; yet my nerves were worked up to the highest pitch of tension, and my hearing was so acute that I could not only hear the gentle breathing of my companions, but I could distinguish the deeper, heavier in-breath of the bulky
Jones from the thin, sighing note of the bank director.
From my position I could look over the case in the direction of the floor.
Suddenly my eyes caught the glint of a light.
At first it was but a lurid spark upon the stone pavement.
Then it lengthened out until it became a yellow line, and then, without any warning or sound, a gash seemed to open and a hand appeared, a white, almost womanly hand, which felt about in the centre of the little area of light.
For a minute or more the hand, with its writhing fingers, protruded out of the floor.
Then it was withdrawn as suddenly as it appeared, and all was dark again save the single lurid spark which marked a chink between the stones.
Its disappearance, however, was but momentary.
With a rending, tearing sound, one of the broad, white stones turned over upon its side and left a square, gaping hole, through which streamed the light of a lantern.
Over the edge there peeped a clean-cut, boyish face, which looked keenly about it, and then, with a hand on either side of the aperture, drew itself shoulder-high and waist-high, until one knee rested upon the edge.
In another instant he stood at the side of the hole and was hauling after him a companion, lithe and small like himself, with a pale face and a shock of very red hair.
"It's all clear," he whispered.
"Have you the chisel and the bags?
Great Scott!
Jump, Archie, jump, and I'll swing for it!"
Sherlock Holmes had sprung out and seized the intruder by the collar.
The other dived down the hole, and I heard the sound of rending cloth as Jones clutched at his skirts.
The light flashed upon the barrel of a revolver, but Holmes' hunting crop came down on the man's wrist, and the pistol clinked upon the stone floor.
"It's no use, John Clay," said Holmes blandly.
"You have no chance at all." "So I see," the other answered with the utmost coolness.
"I fancy that my pal is all right, though I see you have got his coat-tails."
"There are three men waiting for him at the door," said Holmes.
"Oh, indeed!
You seem to have done the thing very completely.
I must compliment you." "And I you," Holmes answered.
"Your red-headed idea was very new and effective."
"You'll see your pal again presently," said Jones.
"He's quicker at climbing down holes than I am.
Just hold out while I fix the derbies."
"I beg that you will not touch me with your filthy hands," remarked our prisoner as the handcuffs clattered upon his wrists.
"You may not be aware that I have royal blood in my veins.
Have the goodness, also, when you address me always to say 'sir' and 'please.'"
"All right," said Jones with a stare and a snigger.
"Well, would you please, sir, march upstairs, where we can get a cab to carry your Highness to the police-station?" "That is better," said John Clay serenely.
He made a sweeping bow to the three of us and walked quietly off in the custody of the detective.
"Really, Mr. Holmes," said Mr. Merryweather as we followed them from the cellar, "I do not know how the bank can thank you or repay you.
There is no doubt that you have detected and defeated in the most complete manner one of the most determined attempts at bank robbery that have ever come within my experience."
"I have had one or two little scores of my own to settle with Mr. John Clay," said
Holmes.
"I have been at some small expense over this matter, which I shall expect the bank to refund, but beyond that I am amply repaid by having had an experience which is in many ways unique, and by hearing the very remarkable narrative of the Red-headed League."
"You see, Watson," he explained in the early hours of the morning as we sat over a glass of whisky and soda in Baker Street, "it was perfectly obvious from the first that the only possible object of this rather fantastic business of the advertisement of the League, and the copying of the 'Encyclopaedia,' must be to get this not over-bright pawnbroker out of the way for a number of hours every day.
It was a curious way of managing it, but, really, it would be difficult to suggest a better.
The method was no doubt suggested to Clay's ingenious mind by the colour of his accomplice's hair.
The 4 pounds a week was a lure which must draw him, and what was it to them, who were playing for thousands?
They put in the advertisement, one rogue has the temporary office, the other rogue incites the man to apply for it, and together they manage to secure his absence every morning in the week.
From the time that I heard of the assistant having come for half wages, it was obvious to me that he had some strong motive for securing the situation."
"But how could you guess what the motive was?"
"Had there been women in the house, I should have suspected a mere vulgar intrigue.
That, however, was out of the question.
The man's business was a small one, and there was nothing in his house which could account for such elaborate preparations, and such an expenditure as they were at.
It must, then, be something out of the house.
What could it be?
I thought of the assistant's fondness for photography, and his trick of vanishing into the cellar.
The cellar!
There was the end of this tangled clue.
Then I made inquiries as to this mysterious assistant and found that I had to deal with one of the coolest and most daring criminals in London.
He was doing something in the cellar-- something which took many hours a day for months on end.
What could it be, once more?
I could think of nothing save that he was running a tunnel to some other building.
"So far I had got when we went to visit the scene of action.
I surprised you by beating upon the pavement with my stick.
I was ascertaining whether the cellar stretched out in front or behind.
It was not in front.
Then I rang the bell, and, as I hoped, the assistant answered it.
We have had some skirmishes, but we had never set eyes upon each other before.
I hardly looked at his face.
His knees were what I wished to see.
You must yourself have remarked how worn, wrinkled, and stained they were.
They spoke of those hours of burrowing.
The only remaining point was what they were burrowing for.
I walked round the corner, saw the City and Suburban Bank abutted on our friend's premises, and felt that I had solved my problem.
When you drove home after the concert I called upon Scotland Yard and upon the chairman of the bank directors, with the result that you have seen."
"And how could you tell that they would make their attempt to-night?"
I asked.
"Well, when they closed their League offices that was a sign that they cared no
longer about Mr. Jabez Wilson's presence-- in other words, that they had completed their tunnel.
But it was essential that they should use it soon, as it might be discovered, or the bullion might be removed.
Saturday would suit them better than any other day, as it would give them two days for their escape.
For all these reasons I expected them to come to-night."
"You reasoned it out beautifully," I exclaimed in unfeigned admiration.
"It is so long a chain, and yet every link rings true."
"It saved me from ennui," he answered, yawning.
"Alas!
I already feel it closing in upon me.
My life is spent in one long effort to escape from the commonplaces of existence.
"And you are a benefactor of the race," said I.
He shrugged his shoulders.
"Well, perhaps, after all, it is of some
little use," he remarked. "'L'homme c'est rien--I'oeuvre c'est tout,' as Gustave Flaubert wrote to George Sand." >
Hello.
Welcome to internet history, technology and security.
I'm Charles
Severance.
And I'll be your instructor for this course.
So let's start right away.
Like, who do I think should take this course?
And the course the answer is you,
You should take this course.
Because everyone should take this course.
The network that we touch and use is with us pretty much all the time.
Obviously, if you're watching this lecture. You're watching it over the internet.
How does all this stuff work?
Who made it?
You know this didn't just grow on trees.
People built this, right?
And we're gonna talk about a highly technical thing.
Perhaps the most complex engineering task humanity's ever undertaken, maybe.
But we're not gonna talk from a math perspective, and we're not gonna talk from a programming perspective.
I mean, really, were not going to, we're not gonna push you on that stuff. We gonna talk about really cool technical things, we're gonna meet some really cool people, but it's not a technical course. It's a course about
listening and understanding and thinking critically about the people who made the internet what it is. So it's, we are going to explain some things and ask you to reflect a bit.
So.
This is going to include a bunch of oral history.
Oral history that I've gathered. And my co-host on my television show, Richard Wiggins gathered. Starting in the.
Through the, present day I continue to gather this.
And continue to keep asking people who've done amazing things on the internet.
Like, what did it take?
How did it work?
What were you thinking?
What was innovative.
What, what went wrong?
Real history's a bit messy.
Real history is not. As simple as a 30 minute PBS special would like it to be sometimes.
Those are actually sort of fun television.
We are actually going to hear from people listen to them a little bit longer.
We aren't going to try to collapse everything into two minute segments.
We are gonna listen to these people .
Then we're gonna ask some critical questions about what do we think about the way folks talk about these innovations.
And then the second half of the class we'll really dig into to how the Internet works.
Still avoiding any programming or any technology or anything complicated.
We are just gonna sort of from a. A simple set of metaphors as we can possibly come up with understand the architecture of the internet and you'll be fine. You'll be surprised at just how much you understand.
So, I always
like to start the first lecture talking a little about me, so you get to know me. I am a professor at the University of Michigan School of Information.
School of
Information studies a lot of things.
It studies social science like things. Data and information and technology so we like to say School of Information studies connecting people information and technology in more interesting ways. And I as a faculty member have written several books.
And I am on the web and you can follow me on Twitter and I do a lot of traveling.
Who knows maybe. Maybe during this class I'll end up in your country or in your town, and, and who knows, we can do something.
So, if you want, feel free to stalk me on Twitter.
I'm, I'm always on
Twitter.
A big feature of this class is. Videos, particularly the first half where we're talking about the history.
And I was really fortunate in 1995.
Really most people would say that the, the internet and web took off in the, outside the academic sector in like 1994.
And in 1995, I had a television show.
It was sponsored by, TCI CableVision, which is a cable company that no longer exists because it, because it got eaten by I think AT&T ultimately.
But through 1995, from 1995 through 1999 my, me and my co-host Richard Wiggans We would run around with cameras, and go to conferences and do whatever.
Now back in the mid 90's, the internet wasn't nearly as fancy and as important as it is now, so it was really easy to find these people and they were always happy to talk.
So, we got in their own words, the kind of innovation.
So, the people on this slide...
On one side here, we have Tim Berners-Lee. Tim
Berners-Lee is the inventor of the world wide web and we'll meet him later in the history lecture.
Right now, we're gonna take a look at a fellow named James Wells.
He was one of the founders of the real audio.
And just to kind of give you a sense of the kinds of things that led me. >> It really inspired me by some of the people doing some really kind of amazing thinking in this internet was just, first getting started, so here's, here's James Wells of RealAudio. >> We have sort of over 700 thousand people who have downloaded the player in a last six months at a rate of 250,000 per month, so if we just do the arithmetic you will imagine that over the next six months, there would be many millions of people listening and tens of thousands of people producing.
Write 14,897 in expanded form.
Let me just rewrite the number, and I'll color code it, and that way, we can keep track of our digits.
So we have 14,000.
I don't have to write it-- well, let me write it that big. 14,000, 800, and 97-- I already used the blue; maybe I should use yellow-- in expanded form.
So let's think about what place each of these digits are in.
This right here, the 7, is in the ones place.
The 9 is in the tens place.
This literally represents 9 tens, and we're going to see this in a second.
This literally represents 7 ones.
The 8 is in the hundreds place.
The 4 is in the thousands place. It literally represents 4,000.
And then the 1 is in the ten-thousands place.
And you see, every time you move to the left, you move one place to the left, you're multiplying by 10.
Ones place, tens place, hundreds place, thousands place, ten-thousands place.
Now let's think about what that really means.
If this 1 is in the ten-thousands place, that means that it literally represents-- I want to do this in a way that my arrows don't get mixed up.
Actually, let me start at the other end.
Let me start with what the 7 represents.
The 7 literally represents 7 ones.
Or another way to think about it, you could say it represents 7 times 1.
All of these are equivalent. They represent 7 ones.
Now let's think about the 9.
That's why I'm doing it from the right, so that the arrows don't have to cross each other.
So what does the 9 represent?
It represents 9 tens.
You could literally imagine you have 9 actual tens.
You could have a 10, plus a 10, plus a 10.
Do that nine times.
That's literally what it represents: 9 actual tens.
9 tens, or you could say it's the same thing as 9 times 10, or 90, either way you want to think about it.
So let me write all the different ways to think about it.
It represents all of these things:
9 tens, or 9 times 10, or 90.
So then we have our 8. Our 8 represents-- we see it's in the hundreds place.
It represents 8 hundreds.
Or you could view that as being equivalent to 8 times 100-- a hundred, not a thousand-- 8 times 100, or 800.
That 8 literally represents 8 hundreds, 800.
And then the 4. I think you get the idea here.
This represents the thousands place.
It represents 4 thousands, which is the same thing as 4 times 1,000, which is the same thing as 4,000.
4,000 is the same thing as 4 thousands.
Add it up.
And then finally, we have this 1, which is sitting in the ten-thousands place, so it literally represents 1 ten-thousand.
You can imagine if these were chips, kind of poker chips, that would represent one of the blue poker chips and each blue poker chip represents 10,000.
I don't know if that helps you or not.
And 1 ten-thousand is the same thing as 1 times 10,000 which is the same thing as 10,000.
So when they ask us to write it in expanded form, we could write 14,897 literally as the sum of these numbers, of its components, or we could write it as the sum of these numbers.
Actually, let me write this.
This top 7 times 1 is just equal to 7.
So 14,897 is the same thing as 10,000 plus 4,000 plus 800 plus 90 plus 7.
So you could consider this expanded form, or you could use this version of it, or you could say this the same thing as 1 times 10,000, depending on what people consider to be expanded form-- plus 4 times 1,000 plus 8 times 100 plus 9 times 10 plus 7 times 1.
I'll scroll to the right a little bit.
So either of these could be considered expanded form.
DARUS (Abandoned Widowers)
I had a small business before.
Making bread, sponge cakes and donuts.
I had people who sold my products.
I also had some employees.
Aside from that, I also worked as an administrative staff at SMP (Junior High School) 2, which now has become SMP 2 Balongan.
Tempted with the offer of being granted a visa, right away I went to Al-Masjid al-Ḥarām (The Grand Mosque).
I had imagined what Al-Masjid al-Ḥarām looks like.
I finally signed up by paying a lump sum from selling my land and rice field.
I also left my job at the school.
I signed up in Jakarta and was going back and forth for almost a year.
It cost me a lot of money.
But then the sponsor (agent) ran away.
During that year I was going back and forth between Jakarta and Indramayu.
But the sponsor (agent) disappeared and I was deserted in the (migrant workers) compound with 3-4 other people.
In that uncertain situation with the sponsor disappearing, we all went back home.
Back to the village.
When I got home, I was deeply in debt.
I sold my rice field and borrowed money.
My wife and I discussed about it.
Half-heartedly, my wife had to go abroad (to become a migrant worker) to pay off our debt, that I used to sign up (to go to the Al-Masjid al-Ḥarām).
Also to pay off our previous debts, we pawned off our rice field, borrowed money for my business, borrowed money for our daily needs and for our children's school tuition.
So that they could stay in school.
I failed twice.
First, the plan to go to Al-Masjid al-Ḥarām, and second, to Malaysia.
When I got back home, I had so much burden in my mind.
Then I thought of forming a Depok (traditional cultural) group.
I gathered friends who were left by their wives abroad.
I named it DARUS, which stands for "Duda nggak ada yang ngurus" (Abandoned Widowers).
That's the group's name.
To gather friends who felt left behind (by their wives), we practiced every afternoon.
That was the beginning.
When it started to go well, I changed the name into Putra Millenium.
Thank God for every performance we could get even though I don't have much capital to start the business.
But I can create job opportunities for friends, even if it's only seasonal.
Usually during harvest time.
How many personnel I can bring depends on the request.
Some clients ask for 30 people, some ask for 40 people to perform.
It's dangdut music with someone wearing a large lion costume and 4 people carrying it.
The daughter of the person who hold the celebration sits on top of the lion.
They would go round and round.
One lion needs four men to carry, so if there are four lions, it means we need 16 men.
Not to mention we need men to push the carriage and the singer on the stage.
This is what we call Depok Lion, with the kids of those who hold the celebration, or the neighbors or family members sit on top.
One lion needs four men to carry, so five lions needs 20 men.
The lions would be carried around the neighborhood.
The singer and musicians are on the carriage as well.
Being pushed by some men.
The sound system is put in here.
Around 15 people are on the carriage. We need at least 4-5 men to push the carriage.
This man is one of the managers. The 25 personnel includes the musicians who are in the carriage.
We go around the neighborhood and stop right before the afternoon prayer time.
We stop at the celebration venue around 12 pm, and start again at 1 pm.
But at 1 pm we don't go around anymore, we perform at the venue.
We play different kind of songs, Javanese songs, and also dangdut songs. Many people come and watch. (The fee) depends on how far the location is.
If it is far, in Indramayu for instance, it could be around 2,5 - 3 million Rupiah ($250 - $300).
But if it is only around here, we charge around 2 million Rupiah ($200).
It can provide job opportunity to friends to earn more money.
At least each person get 25 - 30 thousand Rupiah ($2,5 - $3).
If get saweran (donation) from people who watch, then we get more money.
The audience gives money.
Sometimes we can get around 700 thousand - 1 million Rupiah ($70 - $100), and we divide the money equally between all personnel.
Most of the singers are also former migrant workers.
And the personnel are mostly men whose wives have left abroad to be migrant workers.
Find the probability of getting exactly two heads when flipping three coins.
So let's think about the sample space, here.
So I can get all heads.
So, on flip #1, I get a head. Flip #2, I get a head.
Flip #3, I get a head.
I could get 2 heads and then a tail.
I could get heads, tail, heads. Or I can get heads, tails, tails. I could get tails, heads, heads.
Or I could get tails, tails, and tails.
These are all the different ways that I could flip three coins.
And you could maybe say that this is the first flip, the second flip, and the third flip. Now, so this right over here is the sample space.
There's eight possible outcomes.
Let me write this.
The probability of exactly two heads, exactly... exactly two heads... two, I'll say h's there for short, the probability of exactly two heads.
Well, what is the size of our sample space?
I have eight possible outcomes.
So, eight... this is possible outcomes, or the size of our sample space... possible outcomes.
And how many of those possible outcomes are associated with this event?
You could call this a compound event because there's more than one outcome that's associated with this.
Well, so let's think about exactly... exactly two heads... This is three heads, so it's not exactly two heads.
This is exactly two heads right over here.
This is exactly two heads right over here.
There's only one head.
This is exactly two heads.
This is only one head, only one head, no heads.
So you have [counting] 1, 2, 3 of the possible outcomes are associated with this event.
So you have three possible outcomes.
Three outcomes associated with the event.
Three outcomes.
Outcomes.
Satisfy... satisfy this event, or are associated, with this event.
So the probability of getting exactly two heads, when flipping three coins is three outcomes satisfying this event over eight possible outcomes.
So it is three-eighths.
At this point I think you know a little bit about what multiplication is.
Or "multi"-plication.
What we're going to do in this video is to give you just a ton of more practice, and start you on your memorization of the multiplication tables.
And if you watch enough Khan Academy videos, and hopefully you will in the future, you'll realize that I'm normally not a big fan of memorization.
But the one thing about multiplication is if you memorize your multiplication tables that we'll start to do in this video, it'll pay huge benefits the rest of your life.
So I promise you, do it now, you'll never forget it, and the rest of your life everything will be-- well, I don't want to make false promises to you, but they'll be better than if you didn't memorize your multiplication tables.
So what are the multiplication tables?
Well that's all of the different numbers times each other.
So let's actually do a little bit of review.
So if I say, what is two times one?
That is equal to two plus itself one time.
So this is equal to just two.
That's two plus itself one time.
I don't have to say plus anything because there's only one two there.
I could also write this as one plus itself two times.
So that's also one plus one.
Well that also equals two. Fair enough.
So two times one is two.
And if you watched the last video, what's two times zero?
Well that's zero.
So you don't have to memorize your zero multiplication tables because everything times zero is zero, or zero times anything is zero.
So let's see.
What's two times two?
Two times two.
Well, this is equal to-- we're going to add two to itself two times.
So that's two plus two.
And there's only a way to do that.
I could say take this two and add it to itself two times, but it's the same thing.
And what's two plus two?
That's equal to four.
What's two times three?
Two times three is equal to two plus two plus two.
It can also be equal to three plus three.
We learned in a previous video this statement can be written either of these ways.
And in either case, what's it equal to?
Well three plus three is the same thing as two plus two plus two, and that's equal to six.
All right.
Now what is two times four?
Two times four.
Well that's equal to two plus two plus two plus two.
And notice, it's exactly what two times three was. Two times three was that.
I have that here, but now I'm just adding another two to it.
So if we're too lazy to sit here and add two plus two is four. Four plus two is six.
Instead of doing that, we could say, hey look, we already know that this thing over here, this was six.
We figured it out in the previous line right there.
We figured out this is six, so we could just say, oh, two times four is going to be two more than that, which is equal to eight.
And you should hopefully see that pattern.
As we go from two times one, to two times two, to two times three, what's happening?
How much are we going up by?
From two to four we're going plus two.
From four to six we're going plus two.
And then from six to eight we're going plus two.
So you could figure out what two times five is, even without doing the addition. Two times five is equal to two plus two plus two plus two plus two.
It could also be written as five plus five. Two times four could've been written as four plus four as well.
And what's that equal to?
We could add all of these up or we could add these two up.
Or we could just say it's going to be two more than two times four.
So it's going to be ten.
I'll finish the two times tables.
And I think you see all of the patterns that emerge from it.
So two times six.
That's going to be two plus itself six times.
Let's see.
One, two, three, four, five, six, which should also be equal to six plus itself two times.
This could be interpreted either way.
And that's going to be equal to twelve.
Once again, two more than two times five because we're adding two to itself one more time.
So it's going to be two more.
Let's keep going.
So two times seven. Two times seven is equal to-- well, I could write two plus two plus two plus two-- this is getting tiring-- plus two plus two.
Is that seven?
One, two, three, four, five, six, seven.
And that's the same thing as seven plus seven, which you may or may not know is equal to fourteen.
You could just say hey, that's going to be two more than twelve.
So twelve plus one plus two is-- twelve plus one is thirteen. Twelve plus two is fourteen.
All right, let's just keep going. Two times eight.
I could do all of this business here where I add the twos or I could say, look, it's just going to be two more than two times seven.
So I could say it's going to be fourteen plus two.
I'm just adding two to that one.
So I could say it's sixteen.
Or I could also say that's eight plus eight.
That's also sixteen.
I could have done all the twos out, but if you like you could do that for your own benefit and learning.
We're almost-- well, we could go forever because there is no largest number.
I can keep going. Two times nine times ten times one hundred times one thousand times one million.
But I'm going to stop at twelve because that tends to be what people need to memorize.
But if you really want to be a "mathelete" you want to go up to twenty.
But let's go to two times nine.
That's going to be two more than two times eight.
It's going to be eighteen.
Or that's nine plus nine.
Also eighteen.
What's two times ten?
And ten times tables are interesting.
And we're going to see a pattern there in a second when we try to complete an entire times tables.
So two times ten?
Two more than two times nine.
It's twenty.
Or we could also say that's ten plus ten. Ten plus itself two times.
Now what's interesting about this?
This looks just like a two with a zero added.
And you're going to see that with anything times ten, you just put a zero on the right.
And you can think about why that is.
You can view this as two tens is twenty.
That's what twenty is.
We're almost done.
Let's do two times eleven. Two times eleven is going to be two more than this right here.
It's going to be twenty-two.
Another interesting pattern.
I have the number repeated twice-- a two and a two.
Interesting.
Something to watch out for as we look at other multiplication tables.
And then finally-- and it's not finally, we could keep going-- Two times-- that's too dark of a color. Two times twelve.
That's twenty-four.
We could have also written that as twelve plus twelve.
Or we could've said two plus two plus two plus two plus two... twelve times.
It all gets you to twenty-four.
So that's the two times tables and I think you see the pattern.
Every time you multiply it by one higher number you just add two to that number.
So now that we see that pattern, let's see if we can complete a multiplication table.
So what I want to do, I'm going to write all the numbers.
Let's see.
I hope I have space for this. One, two, three, four, five, six, seven, eight, nine.
Actually, I'll just do it till nine.
I'll just keep going. Nine.
Actually I won't have space to do that because I want you to see the entire table.
So I'm just going up till nine here, but I encourage you after this video to complete it on your own.
Maybe if we have time I'll complete it here as well.
So these are the first numbers that I'm going to multiply.
And I'm going to multiply it times one, two, three, four, five, six, seven, eight, and nine.
What I'm going to do is, I'm going to--
So first of all--
Actually I should have written this one under-- well, what's one times one?
So this is the way I'm going to view it.
Whatever is one times one I'm going to write here.
Well that's one.
What's one times two?
That's two.
What's one times three?
That's three. One times anything is that number, so I can just write four, five, six, seven, eight, nine. One times nine is nine.
Fair enough.
Now let's do the two times tables.
I'll do that in a blue.
Actually, let me do one in that color and now in maybe a darker blue I'll do the two times tables.
What's two times one?
That's two.
It's the same thing as one times two.
Notice, these two numbers are the same thing.
What's two times two?
That's four. Two times three is six.
We just did this.
Every time you increment or you multiply by a higher number, you just add by two. Two times four is eight.
Same thing as four times two. Two times five is ten. Two times six is twelve.
I'm just adding two every time.
Up here I added one from every step, here I'm adding two. Two times seven, fourteen. Two times eight, sixteen.
All right, let's do our three times tables.
I'll do it in yellow.
Yellow. Three times one is three.
Notice, three times one is three. One times three is three.
These are the same values. Three times two is the same thing as two times three. Three times two should be the same thing as two times three.
So it's six.
And that makes sense. Three plus three is six or two plus two plus two is six.
So every time here we're going to increase by three.
You see the pattern. Three times three is nine. Three plus three plus three.
So we went from three to six to nine.
So three times four is going to be twelve.
I'm just adding three every time. Twelve plus three is fifteen. Fifteen plus three is eighteen.
So three times nine is twenty-seven. Three times eight is twenty-four.
So if you were to say eight plus eight plus eight, it would be twenty-four.
Let's see if I can--
So now I'm going to speed it up a little bit, now that we see the pattern.
And you should do this on your own and you really should memorize everything we're doing.
You should actually go all the way up to twelve in both directions.
So let's see. Four times one is four.
I'm just going to go up by increments of four.
So four plus four is eight. Eight plus four is twelve. Twelve plus four is sixteen.
I'm just going up by four. Thirty-two and thirty-six.
All right, five times one. Five times one is going to be five.
Actually, we know that anything that-- well, I want us to keep changing colors, so I'll just do it in rows like this. Five times one is five. Five times two is ten.
I'm just going to increase by five.
Five times tables are very fun as well because every number you're going to add-- if we multiply five times-- well, we'll learn about even and odd in the future.
But every other number in its times tables is going to end with a five, and then every other one's going to end with a zero.
Because if you add five to fifteen you get twenty.
You get twenty-five, thirty, thirty-five, forty, forty-five.
Fair enough.
Six times tables, let me do it in green. Six times one is six.
That's easy.
You add six to that, you get twelve.
You add six to that, you get eighteen.
You add six to that, you get twenty-four.
You add six to that, you get thirty.
Then you go six more, thirty-six, forty-two, forty-eight. Forty-eight plus six is fifty-four.
So six times nine is fifty-four.
All right, we're almost there. Seven times one, that's seven. Seven times one is seven.
Let's see, if you add two you get to thirty.
Then you add five, it's thirty-five. Seven times six, forty-two. Seven times seven, forty-nine.
I always used to get confused between seven times eight being fifty-six and six times nine being fifty-four.
So now that I pointed out to you that I always got confused between those two, it's your job not to be confused by those two. Seven times eight you could say has the six in it. Six times nine doesn't have the six in it.
That's the way I think of it.
Anyway, seven times nine.
We're going to add another seven here.
It's going to be sixty-three.
I'll do it in the same color.
All right, we're at our eight times tables. Eight times one is eight. Eight times two is sixteen.
And if we go to three times eight we should also see the twenty-four.
Yep, it's there.
These values are the same.
So we're actually doing things twice.
We're doing it when you do eight times three and we're doing it when we did three times eight.
Let's see, eight times four, you're going to add eight to it-- thirty-two. Forty.
Add another eight, forty-eight.
Notice, eight times six, forty-eight. Six times eight, forty-eight.
All right, eight times seven.
Well, we already pointed that one out, that was fifty-six. Eight times eight, sixty-four. Eight times nine, add eight to this, is seventy-two.
Now we're at the nine times tables.
I'm running out of colors.
Maybe I'll reuse a color or two.
I'll use the blue again. Nine times one is nine. Nine times two, eighteen nine times three-- we actually know all of these.
We could look it up in the rest of the table because nine times three is the same thing as three times nine.
It's twenty-seven.
Add nine to that. Twenty-seven plus nine is thirty-six. Thirty-six plus nine is forty-five.
Notice, every time you add nine, you go almost up by ten, but one less than that.
So up by ten would be forty-six, and then one less than that is forty-five.
But anyway, notice, the ones-- well, I'll talk more about it in the future.
But we go from a nine, eight, seven, six, five on this digit, on the second digit.
And on this digit here you go one, two, three, four.
So it's an interesting pattern.
Another interesting pattern is the digits will add up to nine. Three plus six is nine, two plus seven is nine.
We'll talk more about that in the future and maybe prove that to you. Nine times six, fifty-four.
That was this one as well. Nine times seven, sixty-three. Nine times eight, seventy-two.
I don't know if you can see that. Eighty-one.
There you go.
Now, I could keep going.
Actually, I should keep going.
Well, I realize this video is already pretty long.
I want you to memorize this right now because this is going to get you pretty far.
In the next video I'm going to do the times tables past nine.
See you soon!
We're told that the total cost of filling up your car with gas varies directly with the number of gallons of gasoline you are purchasing.
So this first statement tells us that if x is equal to the number of gallons purchased, and y is equal to the cost of filling up the car, this first statement tells us that y varies directly with the number of gallons, with x.
So that means that y is equal to some constant, we'll just call that k, times x.
This is what it means to vary directly.
If x goes up, y will go up.
We don't know what the rate is. k tells us the rate.
If x goes down, y will be down.
Now, they give us more information, and this will help us figure out what k is.
If a gallon of gas costs $2.25, how many gallons could you purchase for $18?
So if x is equal to 1-- this statement up here, a gallon of gas-- that tells us if we get 1 gallon, if x is equal to 1, then y is $2.25, right? y is what it costs.
They tell us 1 gallon costs $2.25, so you could write it right here, $2.25 is equal to k times x, times 1.
Well, I didn't even have to write the times 1 there.
It's essentially telling us exactly what the rate is, what k is.
We don't even have to write that 1 there. k is equal to 2.25.
That's what this told us right there.
So the equation, how y varies with x, is y is equal to 2.25x, where x is the number of gallons we purchase. y is the cost of that purchase, so it's $2.25 a gallon.
And then they ask us, how many gallons could you purchase for $18?
So $18 is going to be our total cost.
It is y cost of filling the car.
So 18 is going to be equal to 2.25x.
Now if we want to solve for x, we can divide both sides by 2.25, so let's do that.
You divide 18 by 2.25, divide 2.25x by 2.25, and what do we get?
Let me scroll down a little bit.
The right-hand side, the 2.25's cancel out, you get x.
And then what is 18 divided by 2.25?
So let me write this down.
So first of all, I just like to think of it as a fraction.
2.25 is the same thing-- let me write over here-- 2.25 is equal to 2 and 1/4, which is the same thing as 9 over 4.
So 18 divided by 2.25 is equal to 18 divided by 9 over 4, which is equal to 18 times 4 over 9, or 18 over 1 times 4 over 9.
And let's see, 18 divided by 9 is 2, 9 divided by 9 is 1.
That simplifies pretty nicely into 8.
So 18 divided by 2.25 is 8, so we can buy 8 gallons for $18.
A carpet measures 7 feet long and has a diagonal measurement of square root of 74 feet.
Find the width of the carpet.
So let's draw ourselves a carpet here.
So let's draw a carpet.
It has a length of 7 feet, so let's say that that is 7 feet, right there.
And it's going to be a rectangle of some kind.
So let's say that we're looking down on the carpet like that.
That's our carpet.
And then it has a diagonal measurement of square root of 74 feet.
So that means that this distance, right here-- draw it a little bit neater than that --this distance right here, the diagonal of the carpet, is the square root of 74 feet.
And what they want to know is the width of the carpet.
Find the width of the carpet.
So let's say that this is the width of the carpet.
That is w, right there.
Now, you might already realize that what I have drawn here is a right triangle.
Let me make sure you realize it.
This is a 90 degree angle here.
And since that is a triangle that has a 90 degree angle, it's a right triangle.
The side opposite the right angle, or the 90 degrees, is a hypotenuse, or the longest side.
It is the square root of 74.
And the shorter sides are w and 7.
And the Pythagorean Theorem tells us that the sum of the squares of the shorter side will be equal to the square of the hypotenuse, so the square of the longer side.
So we get w squared, this side squared. plus 7 squared, this other side squared, is going to be equal to the hypotenuse squared, square root of 74 squared.
And then we get w squared plus 49 is equal to the square root of 74 squared.
Well, that's just going to be 74.
It is equal to 74.
We can subtract 49 from both sides of this equation.
So we have just a w squared on the left-hand side.
Subtract 49 from both sides.
The left side-- these guys are going to cancel out, we're just going to be left with a w squared --is equal to-- What's 74 minus 49?
74 minus 49, well, we can do a little bit of regrouping or borrowing here, if we don't want to do it in our head.
We can make this a 14.
This becomes a 6.
14 minus 9 is 5.
6 minus 4 is 2.
And we have w squared is equal to 25.
So w is going to be equal to the square root of 25, the positive square root.
So let's take the square root of both sides, the positive square root, and we will get w is equal to 5.
Because we obviously we don't want it to be negative 5.
That wouldn't be a realistic distance.
So the width of the carpet is 5.
And we're done.
We saw in the last video that when you multiply or you divide numbers, or (I guess I should say when you multiply or divide measurements) your result can only have as many significant digits as the thing with the smallest significant digits you ended up multiplying and dividing.
So just as a quick example, if I have 2.00 times (I don't know) 3.5 my answer over here can only have 2 significant digits
This has 2 significant digits, this has 3. 2 times 3.5 is 7, and we can get to 1 zero to the right of the decimal.
Because we can have 2 significant digits.
This was 3, this is 2.
We only limited it to 2, because that was the smallest number of significant digits we had in all of the things that we were taking the product of.
When we do addition and subtraction, it's a little bit different.
And I'll do an example first.
I just do a kind of a numerical example first, and then I'll think of a little bit more of a real world example.
And obviously even my real world examples aren't really real world.
In my last video, I talked about laying down carpet and someone rightfully pointed out,"Hey, if you are laying down carpet, you always want to round up.
Just because you don't wanna it's easier to cut carpet away, then somehow glue carpet there.
But that's particular to carpet.
I was just saying a general way to think about precision in significant figures.
That was only particular to carpets or tiles.
But when you add, when you add, or subtract, now these significant digits or these significant figures don't matter as much as the actual precision of the things that you are adding.
How many decimal places do you go?
For example, if I were to add 1.26, and I were to add it to - let's say - to 2.3.
If you just add these two numbers up, and let's say these are measurements, so when you make it (these are clearly 3 significant digits) we're able to measure to the nearest hundreth.
Here this is two significant digits so three significant digits this is two significant digits, we are able to measure to the nearest tenth.
Let me label this.
This is the hundredth and this is the tenth.
When you add or subtract numbers, your answer, so if you just do this, if we just add these two numbers, I get - what?
- 3.56.
The sum, or the difference whatever you take, you don't count significant figures
You don't say,"Hey, this can only have two significant figures."
What you can say is, "This can only be as precise as the least precise thing that I had over here.
The least precise thing I had over here is 2.3.
It only went to the tenths place, so in our answer we can only go to the tenths place.
So we need to round this guy up.
Cause we have a six right here, so we round up so if you care about significant figures, this is going to become a 3.7.
And I want to be clear.
This time it worked out, cause this also has 2 significant figures, this also has two significant figures.
But this could have been... (let me do another situation) you could have 1.26 plus 102.3, and you would get obviously 103.56.
Then, in this situation - this obviously over here has 4 significant figures, this over here has 3 significant figures.
But in our answer we don't want to have 3 significant figures.
We wanna have the... only as precise as the least precise thing that we added up.
The least precise thing we only go one digit behind the decimal over here, so we can only go to the tenth, only one digit over the decimal there.
So once again, we round it up to 103.6.
And to see why that makes sense, let's do a little bit of an example here with actually measuring something.
So let's say we have a block here, let's say that I have a block, we draw that block a little bit neater, and let's say we have a pretty good meter stick, and we're able to measure to the nearest centimeter, we get, it is 2.09 meters.
Let's say we have another block, and this is the other block right over there.
We have a, let's say we have an even more precise meter stick, which can measure to the nearest millimeter.
And we get this to be 1.901 meters.
So measuring to the nearest millimeter.
And let's say those measurements were done a long time ago, and we don't have access to measure them any more, but someone says 'How tall is it if I were stack the blue block on the top of the red block - or the orange block, or whatever that color that is?"
So how high would this height be?
Well, if you didn't care about significant figures or precision, you would just add them up.
You'd add the 1.901 plus the 2.09.
So let me add those up: so if you take 1.901 and add that to 2.09, you get 1 plus nothing is 1, 0 plus 9 is 9, 9 plus 0 is 9, you get the decimal point, 1 plus 2 is 3.
So you get 3.991.
And the problem with this, the reason why this is a little bit... it's kind of misrepresenting how precise you measurement is.
You don't know, if I told you that the tower is 3.991 meters tall,
I'm implying that I somehow was able to measure the entire tower to the nearest millimeter.
The reality is that I was only be able to measure the part of the tower to the millimeter.
This part of the tower I was able to measure to the nearest centimeter.
So to make it clear the our measurement is only good to the nearest centimeter, because there is more error here, then... it might overwhelm or whatever the precision we had on the millimeters there.
To make that clear, we have to make this only as precise as the least precise thing that we are adding up.
So over here, the least precise thing was, we went to the hundredths, so over here we have to round to the hundredths.
So, since 1 is less then 5, we are going to round down, and so we can only legitimately say, if we want to represent what we did properly that the tower is 3.99 meters.
And I also want to make it clear that this doesn't just apply to when there is a decimal point.
If I were tell you that... Let's say that I were to measure...
I want to measure a building.
I was only able to measure the building to the nearest 10 feet.
So I tell you that that building is 350 feet tall.
So this is the building.
This is a building.
And let's say there is a manufacturer of radio antennas, so... or radio towers.
And the manufacturers has measured their tower to the nearest foot.
And they say, their tower is 8 feet tall.
So notice: here they measure to the nearest 10 feet, here they measure to the nearest foot.
And actually to make it clear, because once again, as I said, this is ambiguous, it's not 100% clear how many significant figures there are.
Maybe it was exactly 350 feet or maybe they just rounded it to the nearest 10 feet.
So a better way to represent this, they... would be to say instead of writing it 350, a better way to write it would be 3.5 times 10 to the second feet tall.
And when you are writing in scientific notation, that makes it very clear that there is only 2 significant digits here, you are only measuring to the nearest 10 feet.
Other way to represent it: you could write 350 this notation has done less, but sometimes the last significant digit has a line on the top of it, or the last significant digit has a line below it.
Either of those are ways to specify it, this is probably the least ambiguous, but assuming that they only make measure to the nearest 10 feet,
If someone were ask you: "How tall is the building plus the tower?"
Well, your first reaction were, let's just add the 350 plus 8, you get 358.
You'd get 358 feet.
So this is the building plus the tower.
358 feet.
For once again, we are misrepresenting it.
We are making it look like we were able to measure the combination to the nearest foot.
But we were able to measure only the tower to the nearest foot.
So in order to represent our measurement at the level of precision at we really did, we really have to round this to the nearest 10 feet.
Because that was our least precise measurement.
So we would really have to round this up to, 8 is greater-than-or-equal to 5, so we round this up to 360 feet.
So once again, whatever is...
Just to make it clear, even this ambiguous, maybe we put a line over to show, that is our level of precision, that we have 2 significant digits.
Or we could write this as 3.6 times 10 to the second.
Which is times 100.
3.6 times 10 to the second feet in scientific notation.
And this makes it very clear that we only have 2 significant digits here.
It's a game
That they play شتموه لما جهلوه (They insulted him when they didn't know who he was) تبعوه لما عرفوا هداه (They became his followers when they truly knew his way)
What a shame
What they say شتموه لما جهلوه (They insulted him when they didn't know who he was) تبعوه لما عرفوا هداه (They became his followers when they truly knew his way)
Where are you in my dreams?
You feel so close but so far
When All I want is to see
Your face in front of me
You make me chase around
Shadows in the moonlight
Only for the sunrise
To open my eyes
Makes me jump to my feet
Walk around the city streets
Hoping that I'll find you
By my side
Then I feel your sunlight
Beautiful and so bright
Feeling I'm in your arms
For a while
Hours pass like a breeze
Moving through the palm trees
Hand in hand you and me
With your smile شتموه لما جهلوه (They insulted him when they didn't know who he was) تبعوه لما عرفوا هداه (They became his followers when they truly knew his way)
What a shame
What they say شتموه لما جهلوه (They insulted him when they didn't know who he was) تبعوه لما عرفوا هداه (They became his followers when they truly knew his way)
Sen benim nazli yarimsin (You, my delicate beloved)
Sen benim gozbebegimsin (You, the light of my eye)
Sana gonulden baglanmisim ben (Tied to you, at the heart)
Sen en sevdigim sevdicegimsin (You are my deepest love, my beloved)
Ben seni bir gul gibi koklar¦m (Inhaling your scent, just like smelling a rose)
Ask¦nla tutusur ask¦nla yanarim (Burning inside, with the fire of your love)
Hep seni arar seni sorarim (I always look for, and ask of you)
Sana varmak icin hayal kurar¦m (Always dream of reaching you) تیرا تصور میرا ہی سکوں ھے (The very mention of you becomes my tranquility) تیرا نام لینا میرا ھے جنوں (To take your name, it becomes my sanity) وہ میٹھی باتیں تیری ھی سنوں میں (Those sweet conversations of yours I would listen to) دنیا برا مانے تو میں کیا کروں؟ (If the world deems them offensive, what do I care?) شتموه لما جهلوه (They insulted him when they didn't know who he was) تبعوه لما عرفوا هداه (They became his followers when they truly knew his way)
What a shame
What they say شتموه لما جهلوه (They insulted him when they didn't know who he was) تبعوه لما عرفوا هداه (They became his followers when they truly knew his way)
I need you in my life
Like the air with which I breathe
Salutations upon my beloved
So let them say what they want to say
Salutations upon my beloved
It's the same game they always play
Salutations upon my beloved
I'll turn my ears the other way
Salutations upon my beloved
It makes no difference either way
Salutations upon my beloved
It's a game they're always going to play
Let them say what they want to say
Salutations upon my beloved
It's a game
It's a game
It's a game
It's a game
It's a game
It's a game
They're always going to
Play Play
Play
Play
Play
Play
Welcome back.
On the last video we came to the conclusion that we could figure out the volume when we rotate a function about the x-axis, so let's apply that to an actual exercise.
So let me draw the axes again.
That's my y-axis.
That's my x-axis.
And so since our first example was y equals square root of x, let's stick with that.
OK, so that's y equals square root of x, it's just f of x this time, I've defined it.
This is the x-axis.
That's the y-axis.
And I'm going to rotate this around the x-axis again.
And let's say I want to figure out the volume of that cup between the points 0-- and to make it simple, let's just say the points 0 and 1.
So essentially we're just going to get a cup, a sideways cup, it's going to look something like this.
So the cup's going to look like that, so the bottom part of the cup's going to look like this.
And it's solid, so we want the volume of the whole thing.
In future videos I'm going to show you actually how to figure out the surface area of the cup, which I find in some ways more interesting.
So how do we think about that again?
Let's just rederive it, but this time we'll use a specific equation.
So we just have to figure out what is the volume of one disk and then sum up all the disks.
So let's say this disk right here-- actually let's just take this disk at the end point right here that I've already drawn something for.
The radius of that disk is f of x at that point. Well f of x at that point is just square root of x.
Radius is equal to square root of x.
And so the area of that disk is going to equal pi r squared.
Well the radius is square root of x, so it equals pi times square root of x squared.
So it equals pi times x.
That's the area of each disk.
And then if we want the volume, you just have to multiply the area of that surface times the depth of the disk.
We saw in the last video that depth, that's just a very small change in x, because we want each disk to be infinitesimally thin.
So the width is just dx at any point.
So the volume of each disk is equal to the area, which we just figured out was pi x times the depth, times dx.
That's the volume of each disk.
So the total volume is going to be equal to the sum of all of these.
That was one disk I drew, then you're going to have another one here, you're going to have another one here, another one here.
You're going to have infinitely many, and you want them to be super, super, super thin so that you get an accurate measure of the exact volume of this curve.
So it will be the integral from.
And my original boundaries were 0 to 1.
The disk we used as an example, this is probably you know the last disk, so this one will actually have a radius of the square root of 1, which is 1.
So what will be the integral?
Well we're going to go from 0 to 1, and we're going to sum up a bunch of these disks, which we've already defined, so it's pi x dx.
This is looking to be a fairly straightforward integral.
So what's the integral of that?
It's x squared over 2.
So we get x squared, we get pi times x squared over 2.
And then we have to evaluate it at 1 and then subtract it and evaluate it at 0.
And so what do we have.
We get 1/2 pi, so we get pi over 2 minus 0 pi, minus 0.
So it equals pi over 2.
We just figured out the volume of this cup from 0 to 1.
Let's see if we can do that again to figure out the-- just to give you another example, just hit the point home-- to see if we can figure out the volume of a sphere, the equation for the volume of a sphere.
So what's the equation for a circle?
It's x squared plus y squared is equal to r squared. And let's write that in terms of y is a function of x, just so we have something that we can work with the way we learned it.
So we get y squared is equal to r squared minus x squared, and then we get y is equal to the square root of r squared minus x squared.
But in the next video I will do slightly more complicated without going to this one, because I probably don't have time for it I just realized.
Anyway I'll see you in the next video.
Assalamualaikum warehmatullahI wabarakatuhu
Dua
I'm going to tell you tonight About my journey From why once was I a former Christian Youth Minister
There are a lot of bumps on the road You know, it seems pretty clear Yeah, you were a minister
And now you're Muslim There's a little more to it, inshaAllah So just bear with me
I was born and raised in South Carolina repeatI was born and raised in Greenville South Carolina.
And I was raised by my grandparents Because at a very early age my mother had stepped out And my father was working two jobs
They were very very conservative In their ideals and their ideologies In their ways
As you here about people Being set in their ways That was my grandparents
We were very religious in the sense that we went to church on sundays sunday evenings We went to church wensday And in Christianity that is considered very religious
This as a kid is what they had to do because the church was two houses down from our house there were two houses and then there was the church
It wasn’t hard for them to drag me every sunday
I hated church as kid because of the simple reason that we were bought up as United Methodist And methodist is,for any of you who know is very traditional Its not like you think about screaming and shouting in church and all that you listen to the preacher stand up and you sing you sit back down you listen to the preacher you stand up and sing you sit back down and listen to the preacher and that is it that’s all that happens
Sunday school was from what I got my enjoyment from Because I went to Sunday school You are painting pictures
And it was a big deal for me to ride to school with a senior Especially since he had a brand new....a. a... I don’t know if it was brand new
It’s probably the most conservative College I have ever Seen
You didn't party You didn’t drink There was none of this to happen
And he started going There And his major was textual criticism
And textual criticism is probably Doesn’t ring a bell with anyone And to explain it in detail
Textual critic takes the ancient manuscripts Of the bible The pieces of parchment that were found all over the world
let’s say you have Mathew chapter 1 from the bible there might be 5000 variant different readings of Mathew chapter 1 in 6 languages and he has to take all these and sift through them try to find out why there are so many variations in the readings and then determine which one is the original um and that’s not as easy a task as it seems which one is the oldest is probably the more original which is not the case since there are no originals you might have one parchment which is the oldest parchment of the group but it might be a copy of the copy of the copy of a copy of a copy of a copy. which is laden with mistakes and then you might have the newest parchment in the series that might be once over copied from the original or twice over of a second copy of the original therefore making the newer parchment making more original than the older one so it’s not a very easy field to go into and he started studying textual criticism and being that I was his best friend
I also started studying textual criticism whenever he was doing his homework his research papers I was right there with him whenever he did his homework he would always let me read it when he finished his papers he would give them to me he would pass down all those papers to me every textbook when he was done with it he would give it to me
I started to learn a little bit of Greek little bit of Hebrew um so I became a laymen textual critic and I applied to Bob Jones university in my sophomore year because there was a 3 year waiting process for Bob Jones and when I turned sixteen almost 17
My friend came to me one day and he asked me a question that I had never even really pondered upon he asked me and said have you read the bible? and I said uh no, in church, we have all read the bible in church you know your parents make you open it up and look at it and for bible studies I went to young men to Christ we did have bible studies and we read a few passages and talked for 2 hrs about those few passages but he is like
No have you ever read it you know like you read a book beginning to end
I said No, I don’t know anybody, and nobody that I know may have ever read it beginning Genesis 1:1 to the end he said so this is the inerrant word of God as we are taught but he said that this our instruction on earth why haven’t we read it? you know why we haven’t read this book
And I said you know that is a very good question and he gave me a challenge basically the challenge was for us both he said
let us start with genesis 1:1 and let’s read the bible and let’s see what God says to us because this is the the inerrant word of God inspired to men for instructions for us so let us see what God says to us if God can talk to the preacher through this book why can’t he talk to me?
I said your right
I said that is very good I had a lot of time on my hand wasn’t really allowed to do much anyway So after school I said why not the bible read
I was somewhat nerdy as for a 16yr old so we started to read the bible and we decide to go from genesis 1:1 and what we tried to do is this was the attempt that we made was to not think of anything that we had ever heard about Christianity but to open the bible...
let’s say I just found this book in the desert and really see what it says to me
let it talk to us so we started from genesis 1:1 and we started reading though the bible we did some of it together most of it I did it by my self because I’m a very very quick reader so I sat and read a lot on my own and as I was reading through the bible um
I started to notice the story that I had heard in Sunday school u know u started reading genesis and we read about Adam and eve you know we all know that story we started to read about Deuteronomy, exodus you know stories of Moses story of Noah the story of Lot and Abraham and all these stories that I know but I was surprisingly and astonish shocked by some of the stories that I read about the same people that I learned about in Sunday school just for instance and this is a big testament to why Allah kept send us prophets and why was Islam sent as a completed perfected
Deen with the Quran if you read about Noah in the bible there is the story of Noah saving the humanity from the flood with an ark and all of that there is this in the bible there is another aspect to this story of Noah that many people know about and not many people take the actual time to open the bible this story will not be taught from any pulpit anywhere is that the bible says that
Noah was an alcoholic this is the bibles portrayal of Noah or Nuh alayhis salaam that he was an alcoholic that he was a drunkard this the word used in the bible that he was the man given to alcohol and I’m a Psychology major and my my my field of specialty is mental illnesses and alcoholism is one of those mental illness and I know from seeing alcoholism’s effect on one of my close friend’'s parents
I know that someone who is truly addicted to alcohol and if Noah lived for so long addicted to alcohol he was seriously addicted to alcohol um it is hard for someone addicted to alcohol to hold down a 9-5 job at McDonalds flipping hamburgers much less construct an ark to save humanity from a flood that has never happened so that stopped me for a moment in my tracks and I said Noah was an alcoholic you know and it bothered me because I said things started to pop in my mind if Noah was a drunkard how did he know that God was talking to him? you know I’ve seen some people alcoholics
laughs
You were just asleep in my dog's food bowl the other night drooling and now you are telling me that you were talking to God last night to rationally that did not make sense to me that’s like an alcoholic
like on the street coming up to you and saying God’s talking to him you know this man has no validity with anyone
I didn’t pay it too much attention.
It caught me but I said you know what I’m going to keep going because there is one thing that you don’t do in Christianity and I will tell you what it is in a minute.....when I started doing it then I came across the story of lot or Lut alayhis salaam and we all know the story of Sodom and Gomorrha and these stories but there is another very twisted story in the bible about lot and his daughters there is a story of lot and his daughter in the bible that says that his daughters got him drunk one night and seduced him and committed incest with him audhubillah this is one of the bible portrayals of the prophets of God the person who saved his family from
Sodom and Gomorrha this is the story that is in the bible so I’m catching myself again like how it is becoming a really bad bad habit this is becoming a bad recurrence that I am seeing over and over again in this bible so after that I started speeding through the other mumbo jumbo to get more of these prophet stories and I got to the story there are others and there are some stories in the bible that are not PG rated period. they are not rated for talking anywhere you would need an 18+ id card to be able for me to even tell you these stories the one that intrigued me the most that caught my attention the most was of my most beloved story in the bible and that was of David and goliath that was my most intriguing story to me because not only did it say in the bible that David was a very small man, and goliath was a very big man and that was very appealing to me because I have always been very short as a kid I was really short so... you know I said this was a very beautiful story for me in its prose in its concept of overcoming so I started to read about David and there are very beautiful stories about David in the bible they are indeed (beautiful). but there is one story about David in the bible that shocked me to my core and it’s a story about 3 people in this drama david, Bathsheba and Uriah and it says that David saw this woman named Bathsheba and she was one of the most beautiful women of her time and she happened to be married to one of his commanders in the army , named Uriah but David on this day decided that he was not able to resist his temptation to be with this women Bathsheba so he did and he committed adultery with her and knowing that he did this the way he decided to cover up he sent a letter to the generals of his army saying that when the battle was fierce for everyone to pull back and abandon Uriah so that he would be killed and when he dies he could have Bathsheba no harm no foul
David went from being the slayer of goliath the hero of man to an adulterer a plotter and a murderer and so this is when I really caught myself and said hold on now something’s is wrong in here
I said because to me God’s prophet in my mind were people with examples people who I could follow as an example someone who was supposed to be the best of us so that we could follow them and emulate them and they are turning out to be some of the worst people that you see on Americas most wanted
David was somebody... If I only knew this about him from the bible I see him coming down the streets
I will go the other way and call 911 because he has to have a warrant out on him for something this is what I am thinking about in my mind this man an honourable man at all he he...ok he killed goliath but he killed this other guy named Uriah to be able to commit adultery with his wife so I committed sin in Christianity
I started asking questions this is one thing that you do not do in Christianity is that you don’t ask questions especially not about issues like this so I went to my pastor and I started asking questions what’s going on here?
Pastor there is this very bad recurring habit about these men in the bible what is the deal here?
and I remember he told me the same thing that I almost every pastor or every evangelist or anyone I talked to about... same answer they are almost like he was programmed they would put the hand on my shoulder and say brother Joshua don’t let a little bit of knowledge wreak your faith because you are not justified by knowledge you are justified by faith and they would quote me verses like “lean not on understanding you know Pauls way justified by faith in Jesus Christ this they would quote this whole line like it was already pre-programmed they like programmed the pastors when people ask you questions and here is the answer
laughs so I said to myself you know I don’t know pastor this seems kind of odd he said let me tell you something what you are reading is the old testament referring to the covenant of God with the children of Israel and they were a different people people who were very stubborn crazy people so why don’t you move on to the new testament in the new testament you will find the new covenant underwent with Jesus Christ and I promise you things will change and be better
I said ok perfect so I read all in one hit and finished then got to Malachi then started with the new testament so I opened the book and said here we go
let’s start of over again
But there were a few things that I had learnt from the old testament that I wanted to keep in mind when I started to read the new testament
I learned No.1 That God was one in a unique sense this is what I learned from the old testament that God was one in a singular unique sense this is over and over and over and over very clearly in the bible
God’s nature is one this is so clear through the old testament and that He was very jealous about His worship and every single time the children of Israel would turn to something else other than Him
He would punish them and restrict their lifestyles this is something that I learned and it kind off. similitude to me of how God dealt with the children of Israel
I hate to use this stark contrast but it’s almost as if one of us went out
God forbid audhubillah I hope not and let’s say we went out here and robbed the bank u rob a bank u go in jail for a long time and every dad when you wake up
Do you think that the jail is going to look like the Hilton at LAX
No I doubt it it’s probably dark, cold bad food orange jumpsuits not nice people the whole 9 yards and the reason why this is and I study psychology I know that this is supposed to be a stark reminder every single day this person wakes up that you are in jail this is supposed to remind them every single day you are in jail because you committed a crime and we run this not you this is the message that is being portrayed to the person in jail
So the children of Israel kept rebelling against God
He restricted their lifestyle
If you study Judaic law now it is one of the strictest religious law you can find all of the good things that we enjoy as Muslims even when it comes to dietary laws
like the good parts of the meat that we are allowed to ear they can’t have these things these are the things that are restricted from them Why? because God.
Allah wanted to remind them everyday That I am Allah I am your God and you will worship me
Not you and I understood this from reading the OT this is a concept that I have come across
So I started with the NT Mathew mark Luke and john and one other thing that I did when I started to read the bible was that if you go to Barnes and noble
let’s say you go to Barnes and nobles and you take a book of the shelf what is usually the first thing you look at? the title then the next thing, the author you want to know the title and the author what is the name of the book? and who wrote it and if you do this test with every single book of the bible you get a title and no author or author unknown or author is appears to be so and so or we derived this so and so has possibly written this you know like, just say like for exodus they say that Moses wrote the exodus which if you read some of exodus he couldn’t have written all of this because the last part of exodus is Moses's death burial and Joshua taking over the children of Israel and now unless Moses was a sure indeed prophet that was able to write things after he died then he did not write these things so when you go to Mathew mark Luke and john
I wanted to know Mathew who? mark who? Luke who? john who? because it’s called a gospel according to Mathew the bad thing is that no one know
No one knows because no one penned their name down to these things
No bible scholar in his right mind will tell you that "we know for sure that Mathew so and so wrote this mark so and so wrote this Luke so and so wrote this john so and so wrote this its factual information that we do not know who write these So I was intrigued
I am like why would somebody write this book that is? supposed to be passed down to generations and people are supposed to (believe) this is the inspired word of God to guide mankind and nobody decided to pin down who wrote it but anyway
I started to read it and I started to notice things about the teachings of Jesus
Christ and they were not what I had learned in Church when Jesus spoke he spoke of the nature of God and when he spoke of the nature of God it was the same nature of God that I found in the old testament
Jesus said many times that God is one? God is unique he would even quote from the
Hebrew scriptures hear o Israel the lord your God is but one when he was asked what is the greatest commandment? he said that the greatest commandment and every Muslim should understand these two concepts this should be nothing new to you the greatest commandment is to love your lord the God, with all your heart with all your might with all your strength and to love your neighbour as you love yourself he said the rest hang on these two in Islam we have rights of the creator and rights of the creation so this was the concept that he was teaching and he even said in first john 5 and 17 and this was clearer to me than anything else can be
This is life eternal that they may know you the only true God and Jesus Christ whom you have sent and when you look at that in the Greek and the Aramaic it is almost exactly like of la ilaha illalah muhamadur rasullalah (There is no God except Allah and Muhammad is his messenger)
Now that I know Arabic and I have understood it very same similar same statements yes indeed there were some implicit statements about ...that if you took them and separate everything else. you could derive that Jesus was trying to claim some divinity or something for himself but... but I also know from doing psychology and I did a little bit of Law implicit statement cannot overwrite an explicit statement an explicit statement always takes precedence so if Jesus said God is one and he may have allegoricaly alluded to God being more than one
Then the clear statement overwrites that each and every single time so this is what I found through the new testament and I also found that Jesus taught salvation but his salvation that he taught was obeying God and following the commandments this was his mode of salvation one man asked him good master tell me how can I inherit the eternal life he said follow the commandments follow the commandments (emphasis) so even Mathew was so sincere about this, he said that whosoever shall follow the least of these commandments and teach men to do so shall be called the greatest in the kingdom of heaven but whosever shall break the least of the commandments and teach men to do so called the least in the kingdom of heaven
So this I understood clearly that Jesus taught the same nature of God that was in the OT he taught that salvation lied in the worshipping God and following the commandments this I understood
Mathew mark Luke and john very clear about this you know there were other things the only begotten son but these things were not in red letter so I did not give them as much weight
like I did to the actual word that Jesus Christ was saying from his own mouth so I read Mathew mark Luke and john all of it was sounding the same to me but I was thinking to myself this is not what I was taught about Christianity you know you are taught that God is one and one in three 1+1+1 = 3 farther son holy spirit
Jesus died on the cross to forgive of your sins you know... and there was another thing that I noticed from the OT and then this is a beautiful lesson to Muslims because you are asked this all the time especially when it comes to dawah and I never put 2 and 2 together until I learned Islam and read the bible one more time is I wanted to know why did the Jews wanted to crucify Jesus so bad .why... so bad they could have just mobbed him anywhere and killed him on the street he is not like he had clans like the Arabs that they would have come in and back him up
I said why didn’t they just kill him you know why were they so strict and sincere to tell pointis Pilate that you gotta kill him and you need to sanction it we can do it but you need to sanction it to kill him and I now I understand it it was that
Jesus had a mission and..and that mission was to share God with the world and Paul even kind off tells on himself in his book of galatians as to why
Jesus was meant to be crucified why the Jews wanted to crucify him
Paul said that the crucifixion is the stumbling block for the Jew’s and he explained in Galatians that Jesus Christ this is how he tried to round about it explaining was cursed for us, to remove us from the curse of Allah by taking this curse upon us for it is Witten and he quoted the old testament everything that hangeth on a tree is cursed so I went back and studied the old testament in Judaic law and I realised that people who were crucified that was considered a curse upon them you had to do something pretty serious to get crucifixion cause it was considered a curse from God it was part of their law that someone is crucified, that person is cursed so wherever they buried these criminals
like in the graveyards in Israel in Jerusalem in Palestine where they buried these criminals that were crucified this was considered curse ground this was considered ground that you didn’t go on you did nothing here because these people are cursed by God so I started to put 2 and 2 together that it’s not that they wanted to kill Jesus because they could have just killed him they wanted to disprove who he was this was there point to disprove who this man was he said he is the messiah they wanted to disprove it and they knew if you can crucify Jesus , then he can’t be the messiah he cannot be our messiah if you can crucify him and even if he is... if we can still force our crucifixion on him then that will determent his message so they understood this and knew this and this is why they wanted to crucify him and this is exactly why Allah saved him from him from it because everyone is asking why Allah saved him from crucifixion because ... you cannot...that was part of his law that he came to fulfil that he could not be cursed according to this law he said I have come to fulfil the law to fulfil it therefore he couldn’t be cursed according to it and this why he went to the garden to get thimony and asks God to remove him from this because he knew how detrimental to his message of crucifixion so
I began to see all of these things and I started to read, I got to the book of acts and started to read the writing of
Paul the apostle and things went from this >action< to this >action<
I went from one way to another way it completely flipped turned around the entire teachings went from obeying God worshipping God, following God, obeying the law to... worshipping Jesus Christ and abolishing the law completely
Paul even wrote to the Galatians o you foolish Galatians why are you still following this cursed law?
Jesus Christ came as a curse to remove us from the affliction of this curse umm... so I said to myself but Jesus just said a few books before this that whosoever shall break these men the commandments and teach men to do so shall be the least in the kingdom of heaven and here you go, Paul teaching this gospel to abolish the law so I even asked what is going on here
So so I started asking my pastor and my pastor said Now you are getting into deep water
Now you are starting to question the new testament you really have some issues they even though I might even be possessed and all kind of things umm so
I had a very big conflict going on inside of me and my friend took me too his textual critic his textual critic teacher his professor and what this man told me probable wrecked my faith in Christianity but I always say I doubt he would be very happy me travelling around the world telling people that a Christian professor from
Bob Jones university wrecked my faith in Christianity but he did cause what I asked him was happened to all these contradictions
No in the old testament there are many contradictions if you study Hebrew language you will understand that when you read some of the old testament or the torah that there are some parts of the torah that you can see is the most beautiful Hebrew you can see just like when you read the Quran it’s very beautiful, Hebrew
And 2 chapters later you will see Hebrew that looks like a broken 3 year old who is trying to scribble some Hebrew down looks very dialectic you can tell it’s not the same person speaking
I went and asked him about all this stuff I saw and he told me, and he said what you have is a book written by men over centuries and centuries and eon and eons and he said that this book started as an original then it was copied and copied and copied and copied and then somebody added a mistake and somebody came behind him and corrected that mistake and added 2 of his own someone came and copied and skipped a line and added a line where it wasn’t supposed to be and someone else came and copied and took it to his country and in order for it to fit well in the doctrine that they were teaching he would cross out a dot here or cross out a word hear or change a word here so that it would fit the theological ideas of this part of the world and he said that after all these years you have a book now that has been compiled from all of this written by the hands of men that still have men’s fingerprints
left on it and that what you have you have an imperfect book that is only perfected through faith this is exactly what he told me this book is perfected through faith you cannot perfect it textually it not a textually perfect book those who believe in it, believe in it by faith and so I said here we go again with this faith thing you know I said that God gave me a brain for a reason and if he did not want me to use it he would have removed this reason and logic part out of my brain and replaced it with more faith >laughs< and I was of the opinion you know as the saying goes my grandmother didn’t raise a fool
I’m no fool you know I said I can’t believe in this this book I have been taught is the inerrant word of God and you are just telling me that it’s a book of errors that is only perfect through faith that is like me taking a 1982 car and I will say that if you BELlEVE it’s, really can be a Mercedes >Audience Laughs< if you believe you know that would make no sense you can’t take a car to the car dealer and say that
No if you really believe it if you look at it right it’s a Mercedes so I said no this is a a book full of errors and God’s religion is perfect if God has a religion it’s perfect if he has a book it has to be perfect because he is perfect so I left Christianity completely and I...um decided that
I had learned some concepts from the bible That God was one you couldn’t fool me of that
I had also concepted that there should be nobody standing between me and God because he created me without permission from anyone therefore I don’t need to be taking permission from someone to go to him if I had to be forgiven of something that should come from Him because on the day of judgment it’s going to be me and Him alone umm and I didn’t know about God’s prophets yet
I had my doubts and persuasions about that
So I decided to start searching other religions I went back to Judaism I studied Judaism
I studied Budhisim hinduism taoism confusicim winkin bushido everything I can get my hands on any type of ism or religon
I studied it but there was one litmus test that I used for every religion and whenever I met them or the people or whatever about this religion I asked them
I always asked them do you have a book? do you have a book because another thing
I had come to the conclusion is that if your religion is true you should tangibly hand me something and show me that this religion is true give me something that I can see
I don’t wanna hear any faith stuff anymore
I heard that all my life and look where it got me it got me thinking I am drving a mercedes running around in a 1982 car >audience laughs<
I said that no you will have to show me and so I read the bhagvad gita
I read the torah I read the scrolls of tao I read the code of the bushido
I read the winken book of spirits and spells and all the other magic stuff they had and I read all of these things and I found something very congruent with all of them was that they were very same philosophy and teachings and all of these major religion book they all talked about God and his nature most of them alluded to the fact that God is one and that God sends messengers and prophets to teach us but they were filled with a whole bunch of garbage to be honest with you
I couldn’t logically rationally believe so at about that age of 17 about 17 and a half I gave my search for a
God and I became kinda angry with God because here I am looking for you
I can’t find you and he doesn’t like to give me the help and I don’t know how many of you know but when 17yr old is frustrated with God in the world there is a lot of trouble he can get into there are a lot of things he can do to put himself in predicaments when he is frustrated with the world and he comes to the conception you know if there is a God that exists then he really doesn’t care about me you know that kind off a dangerous young man
So I started doing the whole partying thing going to parties drinking underage all of this stuff I started doing
I am a perfectionist at heart so I was a Christian
I tried to be the best one I could be if I was going to switch to being any other religion then I was going to that a 100% so you better believe that when I went after the dunya (worldy life)
I did it a 100% umm.. and I was a martial artist since I was 15 years old and even though it was only 2 yrs so I got into a lot of fights got kicked out of school had to go to another school got in one fight, got arrested for a fight there were a couple of incidents that stopped this downward spiral because
I believe if I were to continue that downward spiral I would probably end up hurting someone killing someone or them hurting and killing me and there were two incidents that bought that back to an abrupt stop
like pulling the emergency break and the first one was a car accident that I was in my friend and I were all the way back from university from a party and we were driving up pretty fast in south Carolina and we were both highly intoxicated
I decided...he was driving I decided to put my seat belt on for the only reason I kept falling over when I fell asleep without a seatbelt on because I didn’t really believe in the seat belt thing
I am gonna die you know that is the conception
I had come up with you know if its time for me to die its time for me to die so I put up my seat belt and I fell asleep and the next thing I remember waking up with the car shaking and I woke up to grab my friend because I thought maybe he had fallen asleep but when I woke up the only thing I saw was the tree line and then the pavement coming right up my face and the window smashing and the car flipping and the whole nine yards and us landing in a ditch and I remember getting out of the car that was the first thing I thought no.1 I couldn’t believe that you don’t really think about "Oh you are alive"... you know you just move
I jumped out of the car and realised that I had jumped out of the back of the car that wasn’t there anymore it was still on the median on the other side of the highway and the front part of the car was over I the ditch and I drew up my friend out who was not conscious and pulled him over to the side of the road
I had no injuries I looked up myself trying to find what’s missing and there was nothing but a piece of glass stuck in my arm that I pulled out and it just so happened that a state trooper was passing the other way because he turned around and came back and when he came back he he had asked what had happened the first thing he asked me was did you see what happened because there were other people pulling over so I guess he thought that I was a bystander coz I started to walk towards him he is like "did you see what happened
I said ya I really saw what happened
I was in the car and he was like you know as they say the color drained out of his face cause he was shocked no how were you in that car you knoe... and umm
Of course they took us to the hospital my friend got arrested but before he put us in the ambulance he was a man of God because he looked at men and he told me young man you should better realise that you are on this earth tonight for a purpose the only reason you are still alive is that God has a purpose for you if not you don’t live though things like that people without purpose if you didn’t have a purpose then this night would have been your night so you need to realise that
I said this old man is out of his mind >audience laughs< you know.. if God had been looking for me he had the opportunity to get me a long time ago so don’t tell me about that God stuff umm so I paid no attention and about a month later 3-4 weeks later my friend and I same too he is still on crutches, we decide to go to new york city we decided to just take off drive to NY city we didn’t tell our parents where we were going
I said I was sleeping (at his house ) and he said he was sleeping in my house for the weekend so we drove to NY and in NY I remember going to the ATM to get some money and in new york they have these
I don’t know if they had that here if any of you have been to NY now alhamdulilah you have to put your bank card in to go in there but in 97 it was not like this you went in and it was almost like the game mouse trap because you go in take out your money criminal comes right behind you there is nowhere for you to go because there is no where to run so I went in the ATM and I heard the door open behind me you know so I turned around
I thought someone was behind me and there was a man who put a gun to my face and he must have really realily really needed this money because he didn’t ask me anything he didn’t say a single word I just remember looking at the gun at my face and him pulling the trigger and it was a revolver and to this day I will never forget that image in my head of seeing that liitle spindle turn and hearing that very distinct click of a revolver it probably could have been a 32 stun nose gun like this>action< but when it was in my face it looked like one of the cannons that you see in the movie >audience laughs< and I remember when he pulled the trigger I didn’t think anything you don’t think anything you just blink you just go into this shock of blankness and then a couple of seconds later thankfully I had been doing martial arts that might have helped me overcome the fight of blank syndrome because I was like thinking Go!!
like myself kicking myself what are you doing Go!!
I rushed him we went flying he went flying and I took off and went to the hotel And didn't say anything to anybody and went back to south Carolina next day umm
I didn’t say anything because we were supposed to be near and my grandfather would have killed me if that guy didn’t kill me my grandfather would have taken care of me >laughs< so I didn’t say anything until about a month or two later
I kept having having nightmare of the same incident
I kept having night terrorists from this incident and so I told my grandmother about it and she told me the same thing the officer had told me she said you know you have to realise that God has a purpose for your life you are here for a reason people don’t go through the things that you have been through and still walking on this earth without a reason and you are pushing the limit
That is what she told me you are pushing the limits really
God has something for you and he wants you to get it but you are pushing it and she didn’t tell me to go back to Christianity and study my bible only one thing she told me was
God has not gone anywhere you haven’t just looked in the right place yet umm and so I decided to put myself back together you the car wreck the gun thing the getting arrested for fighting like all of that made me stop really quick and think that I need to get my my stuff together so I became an agnostic
I believed in God with no formal religion
I pray to God on the floor on my hands and knees this is how all the books of God this is how the bible the torah the new testament the bhagvad gita all of these scriptures that I read they said this is how the men of God pray and it was during this time that I did read one book about Islam in the public library because I had never heard of Islam ever but I remember I was looking in the religious section in the library at school and there was a book about Islam
And I remember I was in the public library and I remember it was some title like
"Why I am not a Muslim" or you know one of these titles that was against Islam but I had no idea so I just took the book and I just read it and I remember it said that Muslims
M-O-S-L-E-M-s and if anyone of you know Arabic you would know that that is a very derogatory term
A M-O-S-L-E-M is someone who oppresses someone else that was a very quick slight of the pen that was used in the past for a very real purpose umm it said that Muslims were people who worshipped a moon God named Allah who lived in a box in the desert in Saudi Arabia >audience laughs< and and they were oppressive to women I I remember there was a whole chapter of about how they could have 4 wives as many as they want Cause they can marry 2 and divorce one get 3 more
I remember that one thing that really caught my attention was the whole chapter on jihad where it said that Muslims were allowed to kill non Muslims non Muslims at any time at any place without discretion and it was an honourable act not only would they go to heaven before but they would get 70 virgins on the way >Audience laughs< you know I closed the book on Islam put it back on the shelf and marked of Islam on my little list of religions >audience laughs< and said thanks and no thanks but if I ever see a Muslim im out >audience laughs< and I pretty safe in south Carolina
I have never seen a Muslim ever so I said naaa I don’t have to worry about running from Muslims thank God so you know I started worshipping
I just tried to be a good person pray to God ask him for guidance try to be generally a good person umm and I remember the changes when I met a Muslim
I met a Muslim who I had a couple of times met at school we went to school together I knew him
I never knew that he was Muslim and there is couple of reasons why I never knew he wasn’t Muslim because he was african american and the book said that Muslims were Arabs and no.2 I though Muslims ran around marrying as many women as they wan’t and killing non Muslims I didn’t also know they could also be part time drug dealers >audience laughs hard< so I didn’t really know
so we were at his house one day and me and my other friend that I got in a some trouble with
I am trying to keep him out of trouble now uh we were at his house and we were debating something about religion I forgot even what the topic was two teenagers thinking that they know everything umm and I was trying to explain something to him about the bible and that guy came and was listening he said have you ever heard of Islam
I said I have heard ALLL(emphasis) about Islam. >audience laughs< he was like ok so what do you think of it
I said what do you mean what I think of it that is probably the worst religion I have ever seen on the planet he is like why and he is like
I am a Muslim
I was like man stop playing me>audience laughs< you know like you are an african american he goes like so the book said you guys were Arabs all the Muslims were Arabs he was like what else did you read in the book he told me like "Man what have you been reading >audience laughs< he is like you need to go to the mosque for jummah he is like he told me that I am not a good Muslim that is what he said to me
I am not a goold Muslim
I am not even try to say that I am a good Muslim he said but I can guide you to some people who can tell you some real truth about Islam he knew about my story of wanting to find a religion and he said that you need to go to the mosque for Jummah and I said what is Jummah? he said its just like church with no chiars >audience laughs hard<
I said I can do church with no chairs because in church the chairs were the worst part anyway >audience laughs< because they had these hard benches they are like this (action) that is good you sit on carpet? wow and I said that every church should be like that and I said where is the mosque he said its on [place] is said where on [place]
I live on wayhampton bolevard
I live right of wayhampton he said where de road intersects with ray hampton I said yeah I live on the other side of the intersection he said its right there
I said no its not there is nothing there is gas station and a church
He said you know the church the evangelical training facility
I used to take missionary classes there he said you know that building in the parking lot with the gold thing on top
I said yeah the gym? he said no that is the mosque cause I had always though it was the gym because it was in the same parking lot and it was rectangular with just two glass door
And you could literally walk in between the church and the masjid and touch them like this>action< anyone who doesn’t believe me
Go to south Carolina you can almost touch them just like this he said yes just rigth there
You know first I was shock I have been living across the street with all these crazy Muslims all my life >audience laughs<
I never knew and he told me to go to jummah and I asked him what time and he said he would meet me there at 1 o’clock in the afternoon on Friday
So I said ok
I went on Friday and im waiting outside for him im not going inside that not happening!! and I seeing all these people going in this time it was a predominently indo paki arab masjid anyone who went in was not american. period and I did not see one african american go in there and I did see one and he went in
I heard him talking in a dialect that I realised he was probably from africa and I said he is not american so im waiting and im standing outside sitting on the church step and the imam pulls the car in front of me and I had no idea he was the imam but he was the imama but he got out and he asked me that if I am waiting for someone and I explained to him he said oh ya we know this brother we don’t see him that much but we know who he os and he said im glad you came and he was a very nice gentle young man umm and he invited me into the mosque and I kinda wanted to wait for my friend but at the same time I didn’t want to tell this man I didn’t wanted to go in so I went in and they put me in the back and they gave me a chair anyway >audience laughs<
I said I came to sit on the floor they gave me the chair anyway and all of these people are piled up in front of me and there is no american here and I am starting to wonder you know if this is a setup because it started to smell like a setup to me >audience laughs< because in my mind im like you have been set up before this seems kind of like this and im starting thinking I my head you know scenarios
A young mind at play
I was thinking this guy my friend was in the same situiation like me and he probably made a deal with them that to get out as long as he brought other americans >audience laughs< to trick them to come to the mosque so they could do their jihad after jummuah and get their 70 virginss >audience laughs< so I am sitting here and there all these people in front of me and there is a curtain behind me with all these people making noise and I have no idea who is back here so I am stuck in the middle of this
I hear there are some women but I don’t know there is a curtain
I have no idea so im like there is something very odd about this what is going on right here
I am starting to look for the exit I am calculating how many people are there b/w me and the exit >audience laughs< u know I know some martial arts
I am gonna hit a couple of them and I am out and then the imam came
I just now realised he was the imam because he got up on the mimbar and they startted to call the adhan that man seemed genrally nice so got a little more comfort and then he got up after the adhan and he started his kutbha inal hamdulilah nahmaduhu
I said OOOOO OOO my God
I said I bet he is talking about me >audience laughs hard and he is being forcefull he was getting loud and banging on the mimbar and he is pointing in my direction >audience continues laughing< and I am like o man
I am going for the curtain >audience laughs< and then when he got done with his Arabic he started to explain it that verily all things belong to Allah alone
God alone and Him do we worship and Him do we seek help and assistance seek refuge from him with the evil and the like you know he explained what he said in Arabic and it sounded so beautiful to me and it was very very beautiful prose what he said and I wanted to know what he said from where did he got that because it was only about God and about the nature of ourselves all of that what is said in the beginning of the kuthbah and he qouted the 3 verses from the Quran o you who believe fear God as he should be feared and do not die in a sate of submission other than Islam he was a very wise man because he translated everything because it was as if he knew I was there translating everything for me and I remember to this day what the khutbah was baout and I don’t know if he did it because I was there or that was his already planned khutbha but it was almost as if it was meant for me the khutbah was that the title of it was the forgiveness of Allah open to anyone at anytime any place
No matter what unless they have comitted Shirk the prose of he kutbah was a very long hadith a very long hadith that some of you may know
And just to make it short it was a hadith where the prophet (pbuh) me angel gabriel the angel jibreel and angel jibreel was telling them to tell him that if the Muslims commit this sin to tell them that Allah would forgive them everytime he would tell the Muslims they would say and what about this sin and he would go back and meet with angel jibreel and he would go back and come back tell him that Allah will forgive him for that this ofcourse happened for many different sins and finally angel Jibreel (AS) said tell them that Allah has said nomatter what they do even if there sins are like the oceans from the east and the west as long as they have not associated partners with Allah tell them that Allah will forgive them
And I remember that he told me that the door of repentence to God is open as long as you have not seen the angel of death or the sun hasn't arisen from the west
I really didn’t understand the sun rising from the west at that time but he said
God’s forgiveness has to come from God alone and this was the whole premise of his kuthbah it was o frogivness and taubah and I was saying to myself these are all the same concepts that I had formulated through reading the religious scriptures my self and I am asking myself where did he get this stuff from where did he get all this from!! and you know he started using names like ebrahim musa he trasnslated to abrahahm and moses where is he getting...these are the names from the bible
I know these people so after the kuthbah they started lining up for the prayer and I got aprehensive because every one is getting up in front of me and blocking my exit from the door >audience laughs< so I guess one guy from the back saw me and I had to move back a liitle bit so he said to me we are about to pray and I said pray to who and he said to God and I said which one and he said the one that created the heavens and the earths the same one that is in the bible the only creator of the heavens and the earths the only God
I said yes
I know him >audience laughs< and so the imam started praying and when he recited the Quran
I knew it sounded very intruguing
I had no idea what it was but then when I saw Muslims bow and prostate on the floor verses and verses of every religous book that I had ever read started ringing in my head this was the way men of God prayed and the first thing that I could think of in my mind was this is worshp that was what I said to myself this is not prayer because prayers are for asking God for somethings these people are worshipping God
So I said to my self you have written this religion of way to easily
I though I was a much more open minded person than that and I was ashamed of myself that I had written it of because of one little book
I had put all this study in the other religion
I just read one thing about Islam and I was done so I went to the imam after jummah he talked to me and I would have to say that I was probably a little bit rude to him and I asked him to frogive I saw him a few years later I said to him that you have to forgive me for the first time you saw me because he started telling me
He had a very heavy accent he was an egyption brother he started telling me will you like to know more about Islam he started to give me some phamplets
I said "No....No...No" I don’t want any of this right here I said
Do you have a book this is waht I wanted to know do you have a book can you give ... he said yes we have a book he said its called the Quran
I said that can I read it is it in english can I read it? he said sure you can read it and then he tried to explain it to me a little bit how it came by
I said noo noo
I said just give me the book because the book should speak for itself so I took the Quran home and on Friday night I started to read it because it was a book I had never seen before and I was very interested so I went home and I opened this opened the Quran and I read the Fatiha it seemed to me kinda like a lords prayer
little similar to what I found in the bible but then I started to read suratul baqarah(chapter 2 of the Quran) I started to read surah ale imran(chapter 3) and I started to see names that I had seen before I started to see names like Abraham
Moses David Jesus
Yahya John the Baptist zacharaiya
Mary and I said I know all of these names but there was something different about these people in this book the prophets that I found in the bible were people that were deplorable of not a very good character these same men in the Quran were someone who were the highest echelon of moral character and moral fibre they were someone who's example is to be followed because they lived the message that they preached therefore they were able to be followed and emulated so
I read all of these chapters and I read the story of Jesus pbuh because when I saw the name of Jesus first that really intruiged me
I wanted to see what did this book had to say about Jesus and I read the story in ale imran and I read the story in surahtul maryam and it was more beautiful than anything that I had read in the NT it was more beautiful than that time x10
I remember that the only thing I could capture in my mind was the miracle of how ... because in the bible you never really figure out the conflict of how mary gets over with this finger pointing at her of having a baby when she is not married there is no real in to that there is no good defence for her from this in the NT but the Quran is so explicit and is so clear that Jesus's first miracle was to speak from the womb to speak as a baby to defend the honour of his mother something that you cannot deny something you cannot deny[emphasis] about her who mary was who had this baby speaking on her behalf so
I would say that I read the quran entirely in 3 days but that first night after I had made it through surahtul ale imran my heart was already given to this book
I didn’t know what it meant it to be a Muslim I didn’t know how to be a Muslim, I didn’t even know what that meant but I knew that whoever it was that followed this book
I wanted to be like the people I read about in this book these are people I could follow these were prophets this was a book of guidance and this is something that this book is calling appealing to me that you don’t believe in this book
I have never seen this in any other scripture the direct challenges that are in the Quran if you don’t believe this book is true put it to the test put it to the test and this was something that was so astounding to me that God is telling you over and over again that if you don’t believe if this is true test it bring something else like it test it put it to the test
I mean.. all the analogies about God everything was so logical so rational so reasonable in my mind it was
like 2 +2 =4 and that was it there was no 1 + 1+ 1=3 and yoke water there was none of that ; foolishness the Quran was very directly and very straight forward in its teachings so I gave my heart to Islam that night in my living room, reading the Quran and I cried and cried you know that I had been looking for the truth all this time had searched all this was and it was right across the street right across the street from my house and so I went back on Monday to accept Islam ask these Muslims where in the world have they been all this time and I go...ready to go in there and do my thing and I go and the masjid is locked!! >laughs< because they only came on Fridays and for Isha (night prayer) during that time I didn’t know so I said ok I guess I have to come back on Friday because every time I go past the masjid it is always locked so I came back on friday and I took my shahadah (testimony of faith) you know as they say the rest is history but..
I don’t travel around the world and this was in December 1998 I don’t travel around the country or the world telling my story just for the entertainment value even though o have been told that I does have some entertainment value I’m sure if that was the purpose the only reason then you could just get it off of YouTube and it was the same exact story
I am gonna finish with this and I hope you can give me 10 more mins inshaAllah to tell you why I go around telling my story
I tell my story to let everyone realise that there are millions of million of millions of millions people just like me just like me in 1998 searching for the truth can’t find a way out there are probably millions of people in california hundreds and thousands if not millions right here in orange county
los Angeles in the southern California area they want to know the truth they are tired of hearing the same garbage preached to them over and over again they are tired of this shaitaan box telling them the same thing over and over again tired of the world being in the condition that it is in tired of there life being in the condition that it is in and we as Muslims have the solution to every single one of there problems and guess what where we keep it at right here inside the masjid right here inside the masjid we have all of this truth we have the solution to every problem, in the world you wanna solve world hunger the problem of world hunger
Islam has the (solution) you wanna solve the problem of world poverty?
Islam has the solution
Islam has the answer you wanna fix the economic situation? of this country
Islam could fix it tomorrow and this was an op-ed piece in the Washington post in the Washington post there was an op-ed piece that the two markets that have fallen apart in the country are investments in housing and there are two people in this market this market is steadily climbing its not shooting over night getting rich over night
like people want to but it is continuously going up that is Islamic finance and Islamic housing market these two things are so steady and so strong that economist in Dc are trying to figure out how can they take some of these Islamic principles from these investing and housing firms and plug them in to this system to give it some stability because they realized that you wont get rich overnight in the Islamic system but it will be stable it will be something that will give stability so they are starting to find out that Islam had the answer in the solutions to their problems but we already knew this we already know this that we can solve every world problem with Islam we will put an end to it but the problem is we are hiding it from the people unfortunately willingly or unwillingly knowingly or unknowingly we are hiding this from the people and there is a statement in the Quran that Allah warns the Jews about what they did with there religion there is a statement that is left in the Quran for us that verily those who conceal the evidences and the clear proofs after we have made it clear to them in the book they are those who are cursed by Allah and cursed by those who curse unless they repent and reveal that which they have been concealing those I would accept there repentance because I am the one who accepts it the Most Mercifull we have become just the same way the Jew were hiding the truth of their reilgion when they saw the prophet Muhammad (pbuh) they knew the truth but they wanted to hide it people !! we know the truth about Islam and we are hiding ti we as Muslims are running around begging Allah for dignity and honour and help when he has already given it to us in this Deen every thing a Muslim could ever want has already been given to him in this Deen of Islam anything that you ask Allah for there is an account set up for you to go take it out you jsut gotta find it where it is at and anyone of you...im not want to go for too long but if you wanna know the solution to everyone of your problems in this world and the hereafter just go read suratul saf ayah 10 to 13 very very easy solution if I had the time
I will read it to you inshaAllah but we have the cure to every disease in the world and and we are not giving it to the people and I wanna use it to this parable
I really want this to get home with you
let say...>asks brother a question< what is your name brother
"Abdullah" Br.Joshua: mashaAllah
lets say me and Abdullah are are best friends we are brothers in Deen we are roommates and we have been roommates for years and years and years and lets say brother Abdullah had a, he contracts an illness ,a disease that is one of the most painful diseases that any human being can ever ever go through in his life its not something that is gonna kill him quickly
lets say this disease is gonna suffer ,infest Abdullah and make him not eat sleep.... he is just miserable all the time when I come home in the evening he is rolling around the floor in pain and I know him in this condition and lets say I one day come across the cure for his disease someone tells me that if you give this guy Abdullah or anyone like him, he will be instantly cured and he will never suffer again and lets say I take that(cure)and put it in my pocket and I don’t give it to Abdullah why? why wont will you give it to Abdullah?
No.1
I am way too busy I have two jobs going to school I have a long commute back and forth
I have to drive up and down everyday I don’t have time to give Abdullah his medicine if he wants the medicine he will get it himself
I don’t have time I am really busy
No.2 I am not a docter I should not be prescribing
Abdullah medicine and I am not knowledgable in medicine if he wants help he should go to a doctor I am not a doctor no.3
Abdullah please forgive me but he is kind off stubborn he doesn’t really listen very well he is probably kind of set in his way even if I tell him this medicine is good for him and it will cure him he probably wouldn’t take him anyway so why waste my time do any of these excuses sound familiar and lets say I don’t give this medicine to Abdullah and he dies and lets say he dies the most painfull death that you can ever imagine
I wann ask you a kind of a rhetorical question
do you think on the day of judgement that Allah is going to call me and Abdullah and ask him about this incident between me and him because I have oppressed him I have oppressed him I allowed him to suffer knowing that I could ease his suffering
I am sure Allah is going to ask us about this but you know the beauty about Islam is Abdullah was a good Muslim bore this disease patiently and died he dies as a shaheed (martyr) inshaAllah and on the day of judgement this is how beautfiul Islam is that he could very well come before
Allah and He will ask him and brother Abdullah says you know what
Allah I forgive him so you are forgiven this is the beauty of our religion
and Allah will forgive me but the disease I want to tell you about is a disease that every single non-Muslim walks around with every single day and they don’t even know it it has no real physical symptoms and that is the disease of shirk the disease of being jahl(ignorant) ignorant about Allah(swt)
Allah give them life and they worship someone else
Allah feeds them and they thank someone else
Allah fashioned them in the womb of their mothers and He knows them better than they know them selves and they have no idea who He is they don’t even know who He is(emphasis) if that does not pain your heart to see a person in this condition then for sure hearts have become hardened because when I see Non Muslims especially when I sit in place like airports
I see this disease I see it on them I see them walking around with it and there are so many of them passing
I think to myself that there is no way I can talk to all of them there is nothing I can do and this disease is something that not only is not going to show up as a physical symptom it is gonna leave them ignorant about Allah swt but on the day they die they will die the most physically painful death that anyone can ever suffer
Prophet(pbuh) said that when the angle of death comes to the disbeliever it doesn’t come kindly he yanks the soul through he nose as if his flesh is torn from his bones its as if they take brother Abdullah upside down and stuff him in an human paper shredder this sis the death that is waiting for those who do not know Allah swt and you knw the unfortunate thing that while you have been sitting here listening to me thousands of people have died thousands of people have
lost their life not knowing Allah while I am talking to you right now people in this city have lost there lives and there is nothing we can do about that they are gone its too late for them we can’t save them even if we want to and that is a deplorable...deplorable sad sad fact that we can’t save them but there are many many many who we can save and that all that takes us taing this light of Islam that we have and showing to the world there is a statement in the bible and I finish with this whether Jesus AS said this or not doesn’t matter because this statement is one of the most profound statements that has been some what of a focus from me in my mission of dawah it is said that no one would bring a candle into his home and place a bucket on top of it because then no one would benefit from the light if someone would bring the candle in their home and set it on the table in the middle of the room so that everyone can benefit from this light and unfortunately the Muslims of this generation we are a bunch of candles with buckets on top of them no one can see our light no one can see the beauty of Islam believe me if you don’t see it take it from someone who was once standing on the outside
looking through at window it is one the most beautiful things you can ever lay your eyes on it is a treasure to be found of treasures and everyone else can see this and they will se this if we show it to them if we allow Islam to be Islam if we start becoming
Muslims meaning that we the best form of dawah that you can do this world is very very simple its not complex its not a 10 hour workshop even though some of the details do if you wanna know the way the best way to do dawah is for Muslims to be Muslims that is it study our history study the history of Islam why was the world conquered by Islam not through military campaigns and wars but through Muslims being Muslims the most populated Muslim country Indonesia was because of Muslims being Muslims a few Muslims decided to go to another country and live their lives as Muslims not shaving of their Deen to be pleasing to those people but being Muslims and when the people asked them what is it about you backward Arabs that we have heard all these crazy things about now you come out of the desert with pristine morals and characters and you have better ethics and morals then we do what is this...what has happened to these people there answer was la ilaha illAllah muhamdur rasulAllah that we believe I Allah and he has sent us a man named Muhammad and we emulate his lifestyle that is why we are like this this is what conquered the world for Islam this is what conquered the people's hearts for Islam was the truth and the beauty of it in its simplicity in its message this is what the world needs with all of this foolishness going on in this world this is what it needs the simplicity of Islam whether they wanna hear it or not they know it in the bottom of their hearts when you show them the truth even if they turn away from it they know its the right and they know its the truth and on the DOJ stand before Allah having washed your hands and saying I did my job
I finished with this if you don’t believe that this is important if you don’t believe that this is one of the most important things you can do as a Muslim then the last statement of the prophet Muhammad pbuh to the Muslims as a whole he gave his farewell sermon and we know what his farewell sermon was summary or synopsis of what Islam is and its general principles and he knew that this was the last thing he was going to say to the Muslims as a whole and how did he end his sermon those who were here pass this on to those who are not here for verily it might be that the last one who hears my message may understand like who was right here amongst is he gave a command to those Muslims to pass it on and for those Muslims to pass it on for those Muslims to pass it on until there was no one left to hear this message this was a command he gave the last command he gave to the Muslims his Ummah as a whole and then what happened he pointed his finger to the heavens and said oh Allah bear witness that I have indeed conveyed the message and upon saying this what happened
Allah revealed the surah... this day I have perfected for you your Deen and completed my favour upon you and chose for you Islam as your religion and the last statement the prophet Muhammad(pbuh) gave to us before this was revealed was that we must pass this message on he gave us that duty he took that duty that was only reserved for prophets no one else ...if you don’t believe me go and read surahtul bayyinah about what was commanded of the other nations no other nation was given this opportunity and blessing to pass on this message this Deen except us because there are no more prophets coming so the job falls on our shoulders
Qurans are not gonna fall down the sky and and hit people when they are walking on the street this job has now become ours and just like if the prophet Muhammad pbuh had not done his mission he would have been accountable before Allah if we do not do our job of spreading this message that of Islam we will stand before Allah on the DOJ don’t be the person standing before Allah on the DOJ and your neighbour that you know your co worker that you have known for 15 10 years come and find you and telling you you knew this day was coming you knew this day was coming and what was gonna happen to me and you did not say anything to me and those people will complain to Allah about us they will complain to Allah about us because we have the truth right amongst us and we are not giving it to them we need to stop hiding it in our masjids in our homes in our hearts and we need to give it to the people its beautiful trust me just hand it to them just hand it to them
I promise you they will take it because its something so pure and pristine and forgive me for probably going above my time and if we have time
I wanna leave some time for questions and answers and I will be outside for taking any question and answers the only last thing that I want to announce and you brothers and sisters no is that one of my biggest dawah projects is a DVD project that I do and my goal is to put a DVD about Islam in the hands of every single person in the united states of America right now other brothers working on it in other places because people will watch a DVD
People will watch a DVD we did a study studies on this and people will watch media before reading a book before they will listen to an audio CD and alhamdulilah through these DVDs we have got
I would say an average of 2 Shahadas a month because my personal contact info is on the DVD and people watch them and they call me and I converse with them and usually most of them accept Islam
I just had a shahadah the day before yesterday from Irvine,Texas from someone who had bought the DVD a Muslim had bought the DVD and had given to his friend his friend hated it didn’t want it so he gave it to another person and that person gave it to a co worker who watched it and accepted Islam so this is one of my biggest projects and the way this project works is I make a 100 DVDs and I bought 2 of them with me ....the way this project works is that I make a 100 dvds and 75 go out to different dawah arenas and the other 25
I make available for Muslims to purchase for two reasons so that I can buy a another100 and so that you can share in this ajar along with me because when you purchase a DVD it makes another DVD or you give it to your friend then you share in this ajar with me if anyone knows .. that Dawah is the biggest pyramid system because a hadith of the prophet pbuh the one who calls to guidance to Islam gets the same reward who as the one who is guided without any loss of reward so I make these DVDs available to the Muslims so that you can put a little effort in dawah and make another 100 inshaAllah so I brought 2 today and they are outside one of them is called Islam in the bible which is basically what I just told you in a power point format so that you could see all these verses that I saw all these things that I read that allowed me to see the truth of Islam very clearly when I saw it and I coincide them with the Quran so that you could see them and there is another one the other one is called the true gospel of Jesus Christ where I go through the new testament well first part I think is an interview about me my story to Islam and there are some Q and A on the other DVDs about nature of God and all these different things its a power point presentation about the new testament and Jesus Christ and how you can prove to someone that Jesus Christ taught Islam from the new testament from there own book that they have to agree they either have to believe it or reject it and if you believe it then you will have to believe what I am saying is true about Islam if you reject it this your book not mine so I try to use these 2 teaching methods and they can also be given to non Muslims because they are in a power point format they are in a very educative format and they are available outside for sale for 10$ each if you could please take it back home so please come and get them if you have any questions my contact info is on there and everything if you have more questions for me on my website thank you for your time and if there has been anything that has been of benefit then know truly that all Good comes from Allah(swt) and if anything that I said is incorrect or hurtful or shameful that indeed it comes from my own lack of understanding
DUA as salaam alaikum warahmatullahI wabarakatuhu
Everyone is both a learner and a teacher.
This is me being inspired by my first tutor, my mom, and this is me teaching Introduction to Artificial Intelligence to 200 students at Stanford University.
Now the students and I enjoyed the class, but it occurred to me that while the subject matter of the class is advanced and modern, the teaching technology isn't.
In fact, I use basically the same technology as this 14th-century classroom.
Note the textbook, the sage on the stage, and the sleeping guy in the back. (Laughter)
Just like today.
So my co-teacher,
Sebastian Thrun, and I thought, there must be a better way.
We challenged ourselves to create an online class that would be equal or better in quality to our Stanford class, but to bring it to anyone in the world for free.
We announced the class on July 29th, and within two weeks, 50,000 people had signed up for it.
And that grew to 160,000 students from 209 countries.
We were thrilled to have that kind of audience, and just a bit terrified that we hadn't finished preparing the class yet.
(Laughter)
So we got to work.
We studied what others had done, what we could copy and what we could change.
Benjamin Bloom had showed that one-on-one tutoring works best, so that's what we tried to emulate, like with me and my mom, even though we knew it would be one-on-thousands.
Here, an overhead video camera is recording me as I'm talking and drawing on a piece of paper.
A student said, "This class felt like sitting in a bar with a really smart friend who's explaining something you haven't grasped, but are about to."
And that's exactly what we were aiming for.
Now, from Khan Academy, we saw that short 10-minute videos worked much better than trying to record an hour-long lecture and put it on the small-format screen.
We decided to go even shorter and more interactive.
Our typical video is two minutes, sometimes shorter, never more than six, and then we pause for a quiz question, to make it feel like one-on-one tutoring.
Here, I'm explaining how a computer uses the grammar of English to parse sentences, and here, there's a pause and the student has to reflect, understand what's going on and check the right boxes before they can continue.
Students learn best when they're actively practicing.
We wanted to engage them, to have them grapple with ambiguity and guide them to synthesize the key ideas themselves.
We mostly avoid questions like, "Here's a formula, now tell me the value of Y when X is equal to two."
We preferred open-ended questions.
One student wrote, "Now I'm seeing Bayes networks and examples of game theory everywhere I look." And I like that kind of response.
That's just what we were going for.
We didn't want students to memorize the formulas; we wanted to change the way they looked at the world.
And we succeeded.
Or, I should say, the students succeeded.
And it's a little bit ironic that we set about to disrupt traditional education, and in doing so, we ended up making our online class much more like a traditional college class than other online classes.
Most online classes, the videos are always available.
You can watch them any time you want.
But if you can do it any time, that means you can do it tomorrow, and if you can do it tomorrow, well, you may not ever get around to it. (Laughter)
So we brought back the innovation of having due dates.
(Laughter)
You could watch the videos any time you wanted during the week, but at the end of the week, you had to get the homework done.
This motivated the students to keep going, and it also meant that everybody was working on the same thing at the same time, so if you went into a discussion forum, you could get an answer from a peer within minutes.
Now, I'll show you some of the forums, most of which were self-organized by the students themselves.
From Daphne Koller and Andrew Ng, we learned the concept of "flipping" the classroom.
Students watched the videos on their own, and then they come together to discuss them.
From Eric Mazur, I learned about peer instruction, that peers can be the best teachers, because they're the ones that remember what it's like to not understand.
Sebastian and I have forgotten some of that.
Of course, we couldn't have a classroom discussion with tens of thousands of students, so we encouraged and nurtured these online forums.
And finally, from Teach For America, I learned that a class is not primarily about information.
More important is motivation and determination.
It was crucial that the students see that we're working hard for them and they're all supporting each other.
Now, the class ran 10 weeks, and in the end, about half of the 160,000 students watched at least one video each week, and over 20,000 finished all the homework, putting in 50 to 100 hours.
They got this statement of accomplishment.
So what have we learned?
Well, we tried some old ideas and some new and put them together, but there are more ideas to try.
Sebastian's teaching another class now.
I'll do one in the fall.
Stanford Coursera, Udacity, MlTx and others have more classes coming.
It's a really exciting time.
But to me, the most exciting part of it is the data that we're gathering.
We're gathering thousands of interactions per student per class, billions of interactions altogether, and now we can start analyzing that, and when we learn from that, do experimentations, that's when the real revolution will come.
And you'll be able to see the results from a new generation of amazing students.
(Applause)
Let’'s say that this is you. You’'re enjoying a nice sunny day and you decided to take a nice long deep breath of air.
And of course when I say air the part that you probably care the most about is just the oxygen, part of that air, that'’s the part that we as humans need to survive.
So you take a deep breath.
Let'’s say you take it through your mouth, you take a deep breath through your mouth.
And then let’s say you take one more deep breath, a second deep breath, and then you take that one through your nose.
And you might think, "Well, these are two totally different ways of getting in air."
That’'s certainly how it looks when you look at the mouth and nose.
They don'’t look like they have much in common.
But the truth is that actually if you follow the air, it almost follows an identical path.
The air is gonna go into the back of the throat really regardless of how you took it in.
So here we have air coming in from the nose, in here yet air coming in from the mouth and they meet up in the back of throat.
And then they go down down down, they go towards this thing that we call the Adam’'s apple.
I'’m gonna bring it up a little bit, you can see it more easily.
But basically you bring up this, you see this Adam’'s apple right there.
And actually you can go ahead and take a feel of you own Adam’'s apple.
It’'s a pretty cool structure in the middle of your throat and everybody has it, that'’s the first thing I want to tell you, that everybody has it, not just men, women have it too.
And the reason it’'s called an Adam’'s apple is because "Adam" is generally a boy'’s name.
And so it'’s to remind us that usually men or boys have larger Adam'’s apples than girls.
And if you’'re trying to find it, I also want to point that it'’s a notch here.
And you if you can feel the notch with your fingers, in that case you have a nice clue as to where it is located.
This is Adam’'s apple and what it does is, it helps you control your voice.
And actually there’'s another name for Adam’'s apple.
Another name for it, sometimes people call it the voice box. The voice box.
And of course air is passing through the voice box in this kind of the entry way into the trachea.
And so it actually allows me to make my voice very high or make my voice very low, depending on how you change the muscles around in that Adam'’s apple.
So that'’s actually kind of a first cool thing I want to point out to you, that you can actually control your voice.
I’'m sure you knew this already but what you’'re using is the Adam’'s apple, your voice box.
Now air keeps going, air is just gonna keeps making its journey down and specifically of course the part of air I said, you know, we care about is the oxygen.
It’'s gonna keep making its journey down into the lung areas, now the lung areas, it's gone down the trachea and it goes into the two lungs, the right and left lungs.
This is the left lung, I'’m gonna put L for left and this is the right lung, I'’il put R for right.
And immediately you’'il think, "Wait a second, aren'’t they switched?"
Now I want you to remember that this is from the perspective of the person who owns the lungs.
So that'’s why I put it in left where I put it, in right where I put it.
Now we should probably go ahead and start labelling some of these.
You can see that the lungs actually don'’t look identical, right?
They look slightly different, for example, this one has three lobes.
The right side has three lobes called the upper lobe, middle lobe and lower lobe.
And the left one only has two lobes, that'’s the first kind of a big difference.
And the other difference is that you actually have this thing in the middle that we call a cardiac notch.
This thing right here, this is called the cardiac notch.
And the reason we call it that is that it'’s a little spot that gets formed because the heart is literally kind of peeking out here.
And as a result it’'s kind of makes a notch in the lung where it develops.
So the heart takes a little space here, this is the heart.
And as a result, it takes or makes that notch.
So this is our heart space there.
So on the other side you'’ve got of course your two lobes, your upper and lower lobes.
And these are exclusive, you see a lung that's kind of sitting by itself.
And you want to figure out whether it’'s the left lung or the right lung, you can look for the lobes, the number of lobes, or you can look for that cardiac notch.
Now around here, around these lungs, you'’ve got ribs.
You’'ve got ribs here and between the ribs you'’ve got rib muscles and of course on both sides.
And below the lungs and below the heart, you’'ve got a muscle, a big muscle.
Actually it'’s gonna come through here, I'’m just gonna kind of go through the word “heart”, and it basically becomes the floor.
So the heart and the two lungs sit on this floor that made up of this muscle and this muscle is the diaphragm muscle.
So this diaphragm muscle makes up the floor; the ribs make up the walls.
So what do we have?
We have basically a room, we have a giant room with walls and the floor.
And this entire room we actually call the thorax.
So within this room then you have your two lungs and your heart.
So, so far so good, but I haven'’t done a very nice job of actually showing you where the air goes.
I just kind of pointed that it goes to the two lungs, we don’'t have to get to see where it goes after that.
So let me actually, I’'m gonna erase a lot of these.
I'm gonna reveal to you what it would look like.
If you could slip on some X-ray glasses and look into your two lungs, this is kind of what it would look like.
You’'ve got all these interesting architecture and the easiest way to kind of think about this, probably the simplest way to think about this, is to imagine a tree, to imagine a tree, and that tree has been flipped upside down, so you'’ve got all these branches of that tree and they are branching and branching.
And if you flip this tree upside down, you start seeing that it looks a lot like what we have in our lungs.
Our lungs basically look like a flipped up or a flipped upside down tree and we even call that, we even call this entire structure, we call it a bronchial tree.
So when you look at the lungs and they look kind of messier and complicated.
Just think of them as an upside down bronchial tree and all of a sudden it’'il look much simpler with basically in the middle you’'ve got this nice trunk, this is our trunk, and then it'’s kind of branching from there.
So air goes down this main trunk, this trachea, and they kind of start splitting up.
And each of this kind of colored regions, the green region and the purple region serve a different lobe.
So this green region serves the lower lobe down here, the purple serves the upper lobe.
And on this side, you've got an upper, a middle and a lower lobe.
Now I know it looks a little bit strange because you've got some green branches in what should be the middle lobe like right here; you’'ve got some orange branches in what looks like the upper lobe like right there.
But what you have to remember, this is kind of tricky, just try to play it in you head, what you have to remember is that, what you have is basically a three dimensional lung.
So you have to imagine that we are literally looking at the front side, but of course that middle lobe does go back.
And if you went back then you'’d make perfect sense why the orange branches are where they are at.
Now let me continue the air journey because I wanna make sure we finish it off.
So let'’s say we take a little branch like that, we expand it.
We keep zooming into it, zooming into it, zooming into it, until it'’s microscopic, you can’t see it with your eyes any more; but you could see it under a microscope. It would look like this.
It would basically in a microscope, it would look like a bunch of little sacs like these.
And these sacs, we call these alveoli. Alveoli. And the air, it actually kind of runs into the alveoli.
It has a dead end and then it comes back around.
And then you breathe it out.
So that'’s how breathing works.
The air goes all the way from the mouth down to the alveoli, takes a U-turn and it goes back out.
But before it does that, before it leaves- Very close to the alveoli is blood.
Let’'s say blood is coming this way and going that way, and what will happen is that, actually out of the or into the blood, let'’s do that first.
We'’ve got oxygen, oxygen will actually go into the blood, and out of the blood will be waste.
So you'’il have some carbon dioxide waste that your cells have been making.
And that waste actually then gets thrown back into the alveoli.
So now you can see how oxygen gets from the outside world, gets breathed into the lungs when you inhale, gets down into the alveoli, exchanges with the blood; and then you exhale and let all that carbon dioxide out.
Which of the following names can be used to describe the geometric shape below?
So the first name in question is a quadrilateral, and a quadrilateral is literally any closed shape that has four sides, and this is definitely a closed shape that has four sides so it is definitely a quadrilateral.
Next we have to think about whether it is a parallelogram.
A parallelogram is a quadrilateral that has two pairs of parallel sides where in each pair they are opposite sides.
And in this case if you look at this side over here it forms a ninety degree angle with this line, and this side over here also forms a ninety degree angle with this line over here, so these two sides, these two sides, are parallel.
Hi.
I'm here to talk to you about the importance of praise, admiration and thank you, and having it be specific and genuine.
And the way I got interested in this was, I noticed in myself, when I was growing up, and until about a few years ago, that I would want to say thank you to someone, I would want to praise them,
And I asked myself, why?
I felt shy, I felt embarrassed.
And then my question became, am I the only one who does this?
So, I decided to investigate.
I'm fortunate enough to work in the rehab facility, so I get to see people who are facing life and death with addiction.
And sometimes it comes down to something as simple as, their core wound is their father died without ever saying he's proud of them.
But then, they hear from all the family and friends that the father told everybody else that he was proud of him, but he never told the son.
It's because he didn't know that his son needed to hear it.
So my question is, why don't we ask for the things that we need?
I know a gentleman, married for 25 years, who's longing to hear his wife say,
"Thank you for being the breadwinner, so I can stay home with the kids," but won't ask.
I know a woman who's good at this.
She, once a week, meets with her husband and says,
"I'd really like you to thank me for all these things I did in the house and with the kids."
And he goes, "Oh, this is great, this is great."
And praise really does have to be genuine, but she takes responsibility for that.
And a friend of mine, April, who I've had since kindergarten, she thanks her children for doing their chores.
And she said, "Why wouldn't I thank it, even though they're supposed to do it?"
So, the question is, why was I blocking it?
Why were other people blocking it?
Why can I say, "I'll take my steak medium rare,
I need size six shoes," but I won't say,
"Would you praise me this way?"
And it's because I'm giving you critical data about me.
I'm telling you where I'm insecure.
I'm telling you where I need your help.
And I'm treating you, my inner circle, like you're the enemy.
Because what can you do with that data?
You could neglect me.
You could abuse it.
Or you could actually meet my need.
And I took my bike into the bike store-- I love this -- same bike, and they'd do something called "truing" the wheels.
The guy said, "You know, when you true the wheels, it's going to make the bike so much better."
I get the same bike back, and they've taken all the little warps out of those same wheels I've had for two and a half years, and my bike is like new.
So, I'm going to challenge all of you.
I want you to true your wheels: be honest about the praise that you need to hear.
What do you need to hear?
Go home to your wife -- go ask her, what does she need?
Go home to your husband -- what does he need?
Go home and ask those questions, and then help the people around you.
And it's simple.
And why should we care about this?
We talk about world peace.
How can we have world peace with different cultures, different languages?
I think it starts household by household, under the same roof.
So, let's make it right in our own backyard.
And I want to thank all of you in the audience for being great husbands, great mothers, friends, daughters, sons.
And maybe somebody's never said that to you, but you've done a really, really good job.
And thank you for being here, just showing up and changing the world with your ideas.
Thank you.
(Applause)
In an age of global strife and climate change,
I'm here to answer the all important question:
Why is sex so damn good?
If you're laughing, you know what I mean.
Now, before we get to that answer, let me tell you about Chris Hosmer.
Chris is a great friend of mine from my university days, but secretly, I hate him.
Here's why.
Here's my clock.
It uses something called the dwarf sunflower, which grows to about 12 inches in height.
Now, as you know, sunflowers track the sun during the course of the day.
So in the morning, you see which direction the sunflower is facing, and you mark it on the blank area in the base.
At noon, you mark the changed position of the sunflower, and in the evening again, and that's your clock.
Now, I know my clock doesn't tell you the exact time, but it does give you a general idea using a flower.
So, in my completely unbiased, subjective opinion, it's brilliant.
However, here's Chris's clock. It's five magnifying glasses with a shot glass under each one.
In each shot glass is a different scented oil.
In the morning, the sunlight will shine down on the first magnifying glass, focusing a beam of light on the shot glass underneath.
This will warm up the scented oil inside, and a particular smell will be emitted.
A couple of hours later, the sun will shine on the next magnifying glass, and a different smell will be emitted.
So during the course of the day, five different smells are dispersed throughout that environment.
Anyone living in that house can tell the time just by the smell.
You can see why I hate Chris.
I thought my idea was pretty good, but his idea is genius, and at the time, I knew his idea was better than mine, but I just couldn't explain why.
One thing you have to know about me is I hate to lose.
This problem's been bugging me for well over a decade.
All right, let's get back to the question of why sex is so good.
Many years after the solar powered clocks project, a young lady I knew suggested maybe sex is so good because of the five senses.
And when she said this, I had an epiphany.
So I decided to evaluate different experiences I had in my life from the point of view of the five senses.
To do this, I devised something called the five senses graph.
Along the y-axis, you have a scale from zero to 10, and along the x-axis, you have, of course, the five senses.
Anytime I had a memorable experience in my life, I would record it on this graph like a five senses diary.
Here's a quick video to show you how it works.
(Video) Jinsop Lee:
Hey, my name's Jinsop, and today, I'm going to show you what riding motorbikes is like from the point of view of the five senses.
Bike designer: This is [unclear], custom bike designer.
(Motorcyle revving)
[Sound]
[Touch]
[Sight]
[Smell]
[Taste]
JL:
And that's how the five senses graph works.
Now, for a period of three years, I gathered data, not just me but also some of my friends, and I used to teach in university, so I forced my --
I mean, I asked my students to do this as well.
So here are some other results.
The first is for instant noodles.
Now obviously, taste and smell are quite high, but notice sound is at three.
Many people told me a big part of the noodle-eating experience is the slurping noise.
You know.
(Slurps)
Needless to say, I no longer dine with these people.
OK, next, clubbing.
OK, here what I found interesting was that taste is at four, and many respondents told me it's because of the taste of drinks, but also, in some cases, kissing is a big part of the clubbing experience.
These people I still do hang out with.
All right, and smoking.
Here I found touch is at [six], and one of the reasons is that smokers told me the sensation of holding a cigarette and bringing it up to your lips is a big part of the smoking experience, which shows, it's kind of scary to think how well cigarettes are designed by the manufacturers.
OK. Now, what would the perfect experience look like on the five senses graph?
It would, of course, be a horizontal line along the top.
Now you can see, not even as intense an experience as riding a motorbike comes close.
In fact, in the years that I gathered data, only one experience came close to being the perfect one.
That is, of course, sex.
Great sex.
Respondents said that great sex hits all of the five senses at an extreme level.
Here I'll quote one of my students who said,
"Sex is so good, it's good even when it's bad."
So the five senses theory does help explain why sex is so good.
Now in the middle of all this five senses work, I suddenly remembered the solar-powered clocks project from my youth.
And I realized this theory also explains why Chris's clock is so much better than mine.
You see, my clock only focuses on sight, and a little bit of touch.
Here's Chris's clock.
It's the first clock ever that uses smell to tell the time.
In fact, in terms of the five senses, Chris's clock is a revolution.
And that's what this theory taught me about my field.
You see, up till now, us designers, we've mainly focused on making things look very pretty, and a little bit of touch, which means we've ignored the other three senses.
Chris's clock shows us that even raising just one of those other senses can make for a brilliant product.
So what if we started using the five senses theory in all of our designs?
Here's three quick ideas I came up with.
This is an iron, you know, for your clothes, to which I added a spraying mechanism, so you fill up the vial with your favorite scent, and your clothes will smell nicer, but hopefully it should also make the ironing experience more enjoyable.
We could call this "the perfumator."
All right, next.
So I brush my teeth twice a day, and what if we had a toothbrush that tastes like candy, and when the taste of candy ran out, you'd know it's time to change your toothbrush?
Finally, I have a thing for the keys on a flute or a clarinet.
It's not just the way they look, but I love the way they feel when you press down on them.
Now, I don't play the flute or the clarinet, so I decided to combine these keys with an instrument I do play: the television remote control.
Now, when we look at these three ideas together, you'll notice that the five senses theory doesn't only change the way we use these products but also the way they look.
So in conclusion, I've found the five senses theory to be a very useful tool in evaluating different experiences in my life, and then taking those best experiences and hopefully incorporating them into my designs.
Now, I realize the five senses isn't the only thing that makes life interesting.
There's also the six emotions and that elusive x-factor.
Maybe that could be the topic of my next talk.
Until then, please have fun using the five senses in your own lives and your own designs.
Oh, one last thing before I leave.
Here's the experience you all had while listening to the TED Talks.
However, it would be better if we could boost up a couple of the other senses like smell and taste.
And the best way to do that is with free candy.
You guys ready?
All right.
(Applause)
So congratulations, you just finished unit 1.
You just finished unit 1 of this class, where I told you about key applications of artificial intelligence,
I told you about the definition of an intelligent agent,
I gave you 4 key attributes of intelligent agents (partial observability, stochasticity, continuous spaces, and adversarial natures),
I discussed sources and management of uncertainty, and I briefly mentioned the mathematical concept of rationality.
Obviously, I only touched any of these issues superficially, but as this class goes on you're going to dive into any of those and learn much more about what it takes to make a truly intelligent AI system.
Thank you.
We are losing our listening.
We spend roughly 60 percent of our communication time listening, but we're not very good at it.
We retain just 25 percent of what we hear.
Now not you, not this talk, but that is generally true.
Let's define listening as making meaning from sound.
It's a mental process, and it's a process of extraction.
We use some pretty cool techniques to do this.
One of them is pattern recognition.
(Crowd Noise) So in a cocktail party like this, if I say, "David, Sara, pay attention," some of you just sat up.
We recognize patterns to distinguish noise from signal, and especially our name.
Differencing is another technique we use.
If I left this pink noise on for more than a couple of minutes, you would literally cease to hear it.
We listen to differences, we discount sounds that remain the same.
And then there is a whole range of filters.
These filters take us from all sound down to what we pay attention to.
Most people are entirely unconscious of these filters.
But they actually create our reality in a way, because they tell us what we're paying attention to right now.
Give you one example of that:
Intention is very important in sound, in listening.
When I married my wife, I promised her that I would listen to her every day as if for the first time.
Now that's something I fall short of on a daily basis.
(Laughter)
But it's a great intention to have in a relationship.
But that's not all.
Sound places us in space and in time.
If you close your eyes right now in this room, you're aware of the size of the room from the reverberation and the bouncing of the sound off the surfaces.
And you're aware of how many people are around you because of the micro-noises you're receiving.
And sound places us in time as well, because sound always has time embedded in it.
In fact, I would suggest that our listening is the main way that we experience the flow of time from past to future.
So, "Sonority is time and meaning" -- a great quote.
I said at the beginning, we're losing our listening.
Why did I say that?
Well there are a lot of reasons for this.
First of all, we invented ways of recording -- first writing, then audio recording and now video recording as well.
The premium on accurate and careful listening has simply disappeared.
Secondly, the world is now so noisy, (Noise) with this cacophony going on visually and auditorily, it's just hard to listen; it's tiring to listen.
Many people take refuge in headphones, but they turn big, public spaces like this, shared soundscapes, into millions of tiny, little personal sound bubbles.
In this scenario, nobody's listening to anybody.
We're becoming impatient.
We don't want oratory anymore, we want sound bites.
And the art of conversation is being replaced -- dangerously, I think -- by personal broadcasting.
I don't know how much listening there is in this conversation, which is sadly very common, especially in the U.K.
We're becoming desensitized.
Our media have to scream at us with these kinds of headlines in order to get our attention.
And that means it's harder for us to pay attention to the quiet, the subtle, the understated.
This is a serious problem that we're losing our listening.
This is not trivial.
Because listening is our access to understanding.
Conscious listening always creates understanding.
And only without conscious listening can these things happen -- a world where we don't listen to each other at all, is a very scary place indeed.
So I'd like to share with you five simple exercises, tools you can take away with you, to improve your own conscious listening.
Would you like that?
(Audience:
Yes.) Good.
The first one is silence.
Just three minutes a day of silence is a wonderful exercise to reset your ears and to recalibrate so that you can hear the quiet again.
If you can't get absolute silence, go for quiet, that's absolutely fine.
Second, I call this the mixer.
(Noise) So even if you're in a noisy environment like this -- and we all spend a lot of time in places like this -- listen in the coffee bar to how many channels of sound can I hear?
How many individual channels in that mix am I listening to?
You can do it in a beautiful place as well, like in a lake.
How many birds am I hearing?
Where are they?
Where are those ripples?
It's a great exercise for improving the quality of your listening.
Third, this exercise I call savoring, and this is a beautiful exercise.
It's about enjoying mundane sounds.
This, for example, is my tumble dryer.
(Dryer) It's a waltz.
One, two, three.
One, two, three.
One, two, three.
I love it.
Or just try this one on for size.
(Coffee grinder)
Wow!
So mundane sounds can be really interesting if you pay attention.
I call that the hidden choir.
It's around us all the time.
The next exercise is probably the most important of all of these, if you just take one thing away.
This is listening positions -- the idea that you can move your listening position to what's appropriate to what you're listening to.
This is playing with those filters.
Do you remember, I gave you those filters at the beginning.
It's starting to play with them as levers, to get conscious about them and to move to different places.
These are just some of the listening positions, or scales of listening positions, that you can use.
There are many.
Have fun with that.
It's very exciting.
And finally, an acronym.
You can use this in listening, in communication.
If you're in any one of those roles -- and I think that probably is everybody who's listening to this talk -- the acronym is RASA, which is the Sanskrit word for juice or essence.
And RASA stands for Receive, which means pay attention to the person;
Appreciate, making little noises
like "hmm," "oh," "okay";
Summarize, the word "so" is very important in communication; and Ask, ask questions afterward.
Now sound is my passion, it's my life.
I wrote a whole book about it.
So I live to listen.
That's too much to ask from most people.
But I believe that every human being needs to listen consciously in order to live fully -- connected in space and in time to the physical world around us, connected in understanding to each other, not to mention spiritually connected, because every spiritual path I know of has listening and contemplation at its heart.
That's why we need to teach listening in our schools as a skill.
Why is it not taught?
It's crazy.
And if we can teach listening in our schools, we can take our listening off that slippery slope to that dangerous, scary world that I talked about and move it to a place where everybody is consciously listening all the time -- or at least capable of doing it.
Now I don't know how to do that, but this is TED, and I think the TED community is capable of anything.
So I invite you to connect with me, connect with each other, take this mission out and let's get listening taught in schools, and transform the world in one generation to a conscious listening world -- a world of connection, a world of understanding and a world of peace.
Thank you for listening to me today.
(Applause)
Let's say I go to the fruit store today and they have a sale on guavas.
Everything is thirty percent off.
This is for guavas.
And it's only today.
So I go and I buy six guavas.
And it ends up, when I go to the register, and we're assuming no tax, it's a grocery and I live in a state where they don't tax groceries.
So for the six guavas, they charge me, I get the thirty percent off.
They charge me $12.60. $12.60.
So this is the thirty percent off sale price on six guavas.
I go home, and then my wife tells me, you know, Sal, can you go get two more guavas tomorrow?
So the next day I go and I want to buy two more guavas.
So, two guavas.
But now the sale is off.
There's no more thirty percent.
That was only that first day that I bought the six.
So how much are those two guavas going to cost me?
How much are those two guavas going to cost at full price?
At full price?
This is the sale price, right here?
How much would those have cost me at full price?
So let's do a little bit of algebra here.
So, let's say that x is equal to the cost of six guarvas. six guavas, at full price.
So, essentially, if we take thirty percent off of this, we should get $12.60.
So if we have the full price of six guavas, we're going to take thirty percent off of that.
So that's the same thing as 0.30.
I could ignore that zero if I like.
Actually, let me write it like this.
So that's the full price of 6 guavas minus 0.30 times the full price of guavas.
Some I'm just taking thirty percent off of the full price, off of the full price.
This is going to be equal to that $12.60 right there.
I just took thirty percent off of the full price.
And now we just do algebra.
We could imagine there's a one in front -- you know, x is the same thing as onex.
So 1x minus 0.3x is going to be equal to 0.7x.
Point, or 0.7x, is equal to 12.60.
And once you get used to these problems, you might just skip straight to this step right here.
Where you say, seventy percent of the full price is equal to my sale price, right?
I took thirty percent off.
This is seventy percent of the full price.
And now we just have to solve for x.
Divide both sides by 0.7, so you get x is equal to 12.60 divided by 0.7.
We could use a calculator, but it's always good to get a little bit of practice dividing decimals.
So we get 0.7 goes into 12.60.
Let's multiply both of these numbers by ten, which is what we do when we move both of their decimals one to the right.
So the 0.7 becomes a 7.
The 12.60 becomes 126, put the decimal right there.
Decimal right there.
So seven goes into twelve one time. one times seven is seven. twelve minus seven is five.
Bring down the six. seven goes into fifty-six eight times. eight times seven is fifty-six.
And then we have no remainder.
So it's eighteen, and there's nothing behind the decimal point. So it;s eighteen, in our case, $eighteen. So x is equal to $eighteen.
Remember what x was? x was the full price of six guavas. x was the full price of six. x is the full price of six guavas.
Well, this is full price of six.
So you immediately could figure out what's the full price of one guava.
You divide eighteen by six.
So eighteen divided by six is $three. That's $three per guava at full price.
And they're asking us, we want two guavas.
So two guavas is going to be two times $three, so this is going to be $six. $six.
Another way you could have done it, you could have just said, hey, six at full price are going to cost me $eighteen. two is one / three of six.
So one / three of $eighteen is $six.
So, just to give a quick review what we did.
We said the sale price on six guavas, $12.60.
That's thirty percent off the full price.
Or you could say this is seventy percent of the full price. seventy percent of the full price.
And so you could say, thirty percent -- so if you say x is the full price of six guavas, you could say the full price of six guavas minus 30% of the full price of 6 guavas is equal to 12.60, and that's equivalent to saying, 70% of the full price is 12.60.
Divide both sides by 0.7, and then we got x, the full price of six guavas, is $eighteen, or that's $three per guava or $six for two.
Anyway, hopefully you found that helpful.
I thought I would do some more example problems involving triangles.
And so in this first one it says the measure of the largest angle in a triangle is four times the measure of the second largest angle.
The smallest angle is ten degrees. What are the measures of all the angles?
Well we know one of them, we know it's ten degrees.
Let's draw an arbitrary triangle right over here. now let's say that is our triangle.
We know the the smallest angle is going to be ten degrees and I'll just say let's just assume that this right over here is the measure of the smallest angle.
It's ten degrees.
Now let's call the second largest angle, let's call that x. So this is going to be x.
And then the first sentence, they say the measure of the largest angle in the triangle is four times, four times the measure of the second largest angle.
So if the second largest angle is x, four times that measure is going to be 4x.
And so, the one thing we know about the measures of the angles inside a triangle is they add up to 180 degrees.
So we know that 4x + x + 10 degrees is going to be equal to 180 degrees.
And 4x + x, that just gives us 5x.
And then we have 5x + 10 is equal to 180 degrees.
Subtract 10 from both sides, you get 5x = 170.
And so, x = 170 / 5.
Let's see, it will go into it 34 times? Let me verify this.
So 5 goes into, yeah, it should be 34 times. It's going to go into it twice as many times as 10 would go into it.
10 would go into 170 17 times, 5 would go into 170 34 times.
So we can verify it.
3 times 5 is 15.
Subtract, we get 2.
Bring down the 0.
5 goes into 20 four times. And then you can have the remainder.
4 times 5 is 20.
No remainder. So it's 34 times. X is equal to 34.
So the second largest angle has the measure of 34 degrees.
This angle up here is going to be 4 times that.
So 4 times 34, it's gonna be 120 degrees plus 16 degrees.
This is going to be... 136 degrees.
Is that right?
4 times 4 is 16. 4 times 30 is 120.
16 plus 120 is 136 degrees.
So we're done.
The three measures or the sizes of the three angles are 10 degrees, 34 degrees and 136 degrees.
Let's do another one.
So let's see. We have a little bit of a drawing here.
And what I want to do is, and we could think about different things.
We could say, let's solve for x.
I'm assuming that 4x is the measure of this angle.
2x is the measure of that angle right over there.
We can solve for x and if we know x we can figure out what the actual measures of these angles are. Assuming that we can figure out x.
And the other thing that they tell us is that this line over here is parallel to this line over here.
And it's craftily drawn because it's parallel but one stops here and one sparks up there.
So the first thing I want to do, if they're telling us these two lines are parallel, it's probably going to be something involving transversals or something.
It might be something involving, the other option is something involving triangles.
And at first you might say, wait, is this angle and that angle vertical angle?
But we have to be very careful.
They are not.
These are not the same lines.
This line is parallel to that line.
This line it's bending right over there.
So we can't make any attempt of assumption like that.
So the interesting thing, and I'm not sure if this will lead us in the right direction, is to just make it clear that these two are part of parallel lines.
So I could continue this line down like this.
And I can continue this line up like that.
And then that starts to look a little bit more like we're used to when we're dealing with parallel lines.
And then this line segment BC or we could even say line BC if we were to continue it on, if we were to continue it on and on even pass D.
Then this is clearly a transversal of those two parallel lines. This is clearly a trasnversal.
And so if this angle right over here, if this angle right over here is 4x, it has a corresponding angle.
Half of the..or maybe most of the work on all these is to try to see the parallel lines and see the transversal and see the things that might be useful for you.
So that right there is the transversal.
These are the parallel lines, that's one parallel line, that's the other parallel line. You can almost try to zone out all the other stuff in the diagram.
And so if this angle right over here is 4x, it has a corresponding angle where the transversal intersects the other parallel line.
This right here is its corresponding angle.
So let me draw it in the same yellow.
So this right here is the corresponding angle.
So this will also be, this will also be 4x.
And we see that this angle and this angle, this angle has a measure of 4x, this angle has a measure of 2x.
We can see that they're supplementary.
They're adjacent to each other.
The outer sides form a straight angle.
So they're supplementary which means that their measure add up to 180 degrees.
They go all the way around like that, if you add the two adjacent angles together.
So we know that 4x plus 2x needs to be equal to 180 degrees.
Or we get 6x is equal to 180 degrees.
Divide both sides by 6, you get x is equal to 30.
And this angle right over here is 2 times x, so it's going to be 60 degrees.
So this angle right over here is going to be 60 degrees.
And this angle right over here is 4 times x.
So it is 120 degrees.
And we're done.
We're asked to represent the inequality y is greater than 5 on a number line and on the coordinate plane.
Let's do the number line first.
Let me just draw out a number line.
That's my number line, all the possible values of y.
Let's make that 0 on the number line.
We could obviously go into negative numbers, but we're going to be greater than 5, so I'll focus on the positive side.
So let's say that's 1, 2, 3, 4, 5, and then 6, 7, so forth and so on.
This number line represents y, and y is going to be greater than 5, not greater than or equal to.
So we're not going to be including 5 in the numbers that can be y.
So we're not going to include 5, so we're going to do an open circle around 5, and all of the other values greater than 5 will be included.
So if there was a greater than or equal to sign, we would have filled it in, but since it's just greater than, we're not including the 5.
So we've represented it on the number line.
Let's do the same thing on the coordinate plane.
Let me draw a coordinate plane here.
I'm just using the standard convention.
That is my y-axis right there.
And then the horizontal axis, I'll just assume is my x-axis.
1, 2, 3, 4, 5.
That is 5 right there, and you go 6, 7, you can just keep going into larger and larger numbers.
And we want y to be greater than 5, so it's not going to be greater than or equal to.
So we're not going to include 5.
So at 5, at y is equal to 5, we will draw a dotted line.
That shows that we're not including y is equal to 5, but we want include all of the other values greater than 5.
So that we will shade in.
So here we have shaded in all of the values greater than 5.
If it was greater than or equal to 5, we would have drawn a bold line over here.
So no matter what x is, no matter what x we pick, y is going to be greater than 5.
In this video, we're going to learn how to take the distance between any two points in our x, y coordinate plane, and we're going to see, it's really just an application of the Pythagorean theorem. So let's start with an example. Let's say I have the point, I'll do it in a darker color so we can see it on the graph paper.
I don't see a triangle there!
Let me draw this triangle right there, just like that.
So there is our triangle. And you might immediately recognize this is a right triangle. This is a right angle right there.
And then we have the side on the right, the side that goes straight up and down. And then we have our base. Now, how do we figure out-- let's call this d for distance.
6 minus 3. That's this distance right here, which is equal to 3. So we figured out the base.
And over here, you're at y is equal to negative 4. So change in y is equal to 0 minus negative 4.
I'm just taking the larger y-value minus the smaller y-value, the larger x-value minus the smaller x-value. But you're going to see we're going to square it in a second, so even if you did it the other way around, you'd get a negative number, but you'd still get the same answer, so this is equal to 4. So this side is equal to 4.
Sometimes people will call this the distance formula. It's just the Pythagorean theorem. This side squared plus that side squared is equal to hypotenuse squared, because this is a right triangle.
And just so you're exposed to all of the ways that you'll see the distance formula, sometimes people will say, oh, if I have two points, if I have one point, let's call it x1 and y1, so that's just a particular point. And let's say I have another point that is x2 comma y2. Sometimes, you'll see this formula, that the distance-- you'll see it in different ways.
looks as though there's this really complicated formula, but I want you to see that this is really just the Pythagorean theorem. You see that the distance is equal to x2 minus x1 minus x1 squared plus y2 minus y1 squared.
And it's a complete waste of your time to memorize it because it's really just the Pythagorean theorem. This is your change in x. And it really doesn't matter which x you pick to be first or second, because even if you get the negative of this value, when you square it, the negative disappears.
And let's say I want to find the distance between that and 1 comma 1, 2, 3, 4, 5, 6, 7, and the point 1 comma 7, so I want to find this distance right here. So it's the exact same idea. We just use the Pythagorean theorem.
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Welcome to the presentation on functions.
Functions are something that when I first learned it, it was kind of like I had a combination of I was, one, confused, and at the same time I was like, well what's even the point of, of learning this.
So, hopefully at least in this introduction lecture we can get at least a very general sense of, of what a function is, and why it might be useful.
So let's just start off with just the overall concept of a function.
A function is something that you can give it an input, and we'll start with just one input, but actually you can give it multiple inputs.
You give a function an input, let's call that input x, right?
And you could view a function as, I guess a bunch of different ways you can view it, I don't know if you're familiar with the concept of a black box.
A black box is kind of a box you don't know what's inside of it, but if you put something into like this x. And let's call that box, let's say the function is called f, then it'll output what we call f of x.
Now I know this, this terminology might seem a little confusing at first, but let's make some I guess let's define what's inside the box in different ways.
Let's say that the function was let's say that f of x is equal to x squared plus 1.
Then, if I were to say what is f of, let's say what's f of 2.
Right?
Well that means we're taking two, and we're going to put it into the box. Right? And I wanna know what comes out of the box when I put two into it.
Well, inside the box we know, we do this to the input.
We take the x, we square it and we add one. So f(2) is 2 squared which is 4, + 1. Which is equal to 5.
Probably like, well, Sal, this just seems like a very convoluted way of substituting x into an equation and just finding out the result.
And, and I agree with you right now.
But as you'll see, a function can become kind of a more general thing than just an equation.
For example, let me say, let me, actually, let me not erase this.
Let me, let me define a function as this: f(x) is equal to x squared plus 1 if x is even and equals x squared minus 1 if x is odd.
I noticed that this would have been this is something that we've never really seen before.
This isn't just what I would call an analytic expression.
This isn't just, you know, x plus something squared.
We're actually saying depending on what type of x you put in we're going to do a different thing to that x.
So, let me ask you a question.
What's f(2) in this example?
Well, if we put 2 here, it's as if x was even you do this one.
If x is odd you do this one.
Well, 2 is even so we do this top one.
So, we say 2 squared plus 1, well that equals 5. But then, what's f(3)?
Well, if we put the 3 in here, we'd use this case cuz 3 is odd.
So we'd do 3 squared minus 1, f(3) is equal to 8.
So notice this was a little bit more I guess, you could even say abstract or unusual than this case.
And I'm gonna keep doing examples of functions. And I'm gonna show you how general this idea can be.
And if you get confused, I'm gonna show you that the actual function of problems you're gonna encounter are actually not that hard to do.
I, I just wanna make sure that you at least get exposed to kind of the general idea of what a function is.
You, you could view almost anything in the world as, as a function.
Let's say that there is a, a function called Sal. In case you don't know, that's my name.
I'm a function.
Let's say that you were to if you were to, let me think.
If you were to give me food, what do I produce. Right.
So what is Sal, a food, right?
So, if you input food into Sal, what will Sal produce?
Well, I won't go into some of the things that I would produce, but I would produce, I would produce videos.
I would produce math videos if you gave me food.
Math videos. Right?
I, I'm just a function.
You give me food, and, and maybe actually, maybe have multiple inputs.
Maybe you give me food and a computer. And I would produce math videos for you, right?
And maybe you are a function.
I don't know your name.
I, I would like to, but I don't know your name.
And let's say if I were to input math videos into you, then you will produce let's see, what would you produce?
If I gave you math videos, you would produce A's on test.
A's on your math test, hopefully, you are not taking someone else's math test, right.
That's interesting.
If you gave, let's, let's, let's take the computer away.
Let's say that all Sal needs is food which is kind of true.
So if you put food into Sal, Sal of food he produces math videos. Right?
And then if I were to put math videos into you, then you produce A's on your math test, right?
So let's, let's think of an interesting problem.
What is you of Sal of food.
[BLANK_AUDlO] I know this seems very ridiculous, but I actually think we, we, we might be going someplace. So [LAUGH] we might be getting somewhere with this idea.
Well, first we would try to figure out what is Sal, a food?
Well, we've already figured out if you put food into Sal, Sal of food is equal to math videos.
So this is the same thing as you of. Oh sorry, you, that's Y-O-U, I'm trying to confuse you.
And I already determined, we already said, well, if you put math videos into the function called you, or, you know, whatever your name might be then it produces A's on your math tests.
So that you of math videos equals A's on your math test.
So you of Sal of food will produce A's on your math test.
And notice, I mean, we just said what happens when you put food into Sal.
You know, it, it, this would be a very different outcome if you put, like, if, you replace food with let's say poison.
Right, cuz if you put poison into Sal, Sal of poison, not that I would recommend that you did this.
Sal of poison would equal, would equal would equal death.
No, no, I shouldn't say something so, no, no, no, no.
I well, you, you, you get the idea.
There, there wouldn't, there wouldn't be math videos anyway.
Let, let me move on.
So with that kind of I'm not so clear whether that would be useful example of the food with the math videos.
Let, let's do some actual problems using functions.
So if I were to tall you that I had one function, called f of x is equal to x plus 2.
And had another function that said g of x is equal to, let's say, x squared minus 1.
If I were to ask you what g (f (3)) is, well, the first thing we want to do is evaluate what f (3) is, right?
So if you, if you, the 3 would replace the x. So, f (3), so f (3) is equal to 3 plus 2, which equals 5, right? So g (f (3)) is the same thing as g of, of 5, right?
Cuz f (3) is equal to 5. Sorry for the little bit of messiness, right?
So then, what's g (5)?
Well then, we take this 5. And we put it in, in place of this x, right? So, g(5) = 5 squared, 25, minus 1, which equals 24.
So, g(f(3)) = 24.
Hopefully that gives you a taste of what a function is all about, and I really apologize if I have either confused or scared you with the Sal food, poison math video example.
But in the next set of presentations, I'm gonna do a lot more of these examples and I think you'll get the idea of at least how to do these problems that, that you might see on your, on your math test and maybe get a sense of what functions are all about.
See you in the next video.
I think we're just about ready to learn how to subtract pretty much any number from any other number.
So let's just review a little bit of what we know already.
So if I were to ask you what 16 - 4 is, I could draw 16 apples and then take away 4 of the apples.
Or I could actually draw a number line, and actually let me do it here just to start off the video to get warmed up.
I could draw the number line and maybe that's 16 maybe that's 17.
It's 15, 14, 13, 12, let me go down all the way to 11.
I could keep going but I've run out of space.
Now, if I don't know in my head what 16 - 4 is, and it's a pretty good one to eventually know in your head, you could start in your number line or you could imagine the number line in your brain and you could go down by 4s.
16 - 1 is 15, minus 2 is 14, minus 3 is 13, minus 4 is 12.
And you would have the answer.
16 - 4 is 12.
Now an even easier way to do this problem is just to focus on the places of the digits.
Now let me be clear what I mean when I say that.
Let me re-write it.
16 - 4, and I've gone over this a little bit in the addition videos.
This is the ones place.
The 6 is in the ones place.
The 4 is in the ones place.
The 1, right here, this right here, or there was something down here, this column, that is the tens place.
Now what do we mean by that?
Well 16 is the same thing as 10 + 6.
So when we write it, this 1 literally means one 10.
If you think of it in money it means one $10 bill.
If I had a 2 there, if I had 26, that means two $10 bills.
Two $10 bills would mean $20.
So that's two $10 bills and then six $1 bills.
You can view this as a $1 bill place, that's the $10 bill place.
If I had 357, you could view this as three $100 bills, five $10 bills, and seven $1 bills, and that's why this is called the 100s, that's the 100s place, this is the tens place, and this is the ones place.
And we'll dig a little bit deeper into this as we explore borrowing and regrouping more in this video and in others.
But I wanted to label these places because what I want to show you is you don't even have to think about 16 - 4.
You can actually just look at just the ones place and think about 6 - 4, and say 6 - 4 well you could draw a number line or you could even use your fingers if you have to, but you probably have that memorized.
You could probably visualize it in your head, 6 - 4 is 2. And then 1, then we go to the tens place, 1 minus nothing -- there's nothing over here.
So 1 minus nothing is 1, and you get 12.
Same answer, we were able to simplify a little bit.
Let's try another problem like that.
If I were to ask you what 78 - 37 is.
So we start off in the ones place and we say 8 - 7 that's 8 ones minus 7 ones, or just 8 - 7.
8 - 7 is equal to 1.
Then we go to the 10s place.
7 - 3 -- now remember, this is seven 10s, or seven $10 bills, minus three $10 bills. If I had seven $10 bills and I give away three of those $10 bills, then I'll have four $10 bills, or 7 - 3 is equal to 4.
And just like that we were able to figure out that 78 - 37 is 41.
This would have been really hard to do, it would take me forever to draw 78 apples and to cross out 37 of them.
Or to draw a number line all the way up to 78 then go back 37 spaces.
That would have given you the answer, but it would have taken you forever to solve it that way. Just by focusing on just each column, you're able to get the right answer.
Well, you might say, hey Sal, but what happens if I can't -- well, let me give you an example where this will start to become difficult doing it this way.
I'll do one more example like this.
So let's say I had 95 - 31.
Just like that, 5 - 1 is 4.
9 - 3 is 6.
95 - 31 is 64.
You're probably saying, Sal, subtraction is easy. I can just look at each place, the ones place and subtract, tens places and subtract.
But I'm about to show you that it's not always at least that easy.
With a little bit of practice hopefully you'll realize that it's also not too bad.
So what if I were to ask you what 22 - 17 is. Now once again, I could draw 22 oranges or apples and take away 17 of them and you could count what's left and you would get the right answer, but that would take you forever.
Is there any way I could do that maybe just on the paper right here?
Now your reaction might say let me just do what you just did before.
But if you look here, if I try to subtract 7 from 2, if I have two things, at least for the mathematics that we know right now,
I can't give away 7.
I only have 2 to give away. This would give me something smaller than 0 which we don't know about.
That's a negative number.
As far as we know right now, we can't subtract 7 from 2.
But we know that 17 is smaller than 22. So what can we do here to actually do this subtraction problem?
So what we do here, and you might call it borrowing, you might call it regrouping.
This 2 right here, this 22 is the same thing as 20 + 2.
That's the 22 right there.
It's 20 + 2.
The 17 is 10 + 7.
That's just another way to write 17.
Now we have a 2 here.
We want something larger than a 7 to subtract from. So what we can do is we can borrow from this 2 or from this 20, they're the same thing.
Let me do that in another color.
This 2 right here is the same thing as that 20.
A 2 in the tens place means two $10 bills.
Two $10 bills is the same thing as $20.
That's what that 2 represents. So if I want to make this 2 into something larger, why don't I take a $10 bill from here.
If I take a $10 bill from here and I turn it into one's
I go to the cashier and say give me a bunch of ones. So if I take a $10 bill from here, then this will become $10.
And then I cash into a bunch of ones and put it here.
So then this will become $12. If we look over here, what it looks like I did is
I took a 1 from this 2, so this 2 will now become a 1, right? We went from two $10s to one $10 and it became just one $10 bill.
Then I gave that 1 to this 2.
This 2 then becomes a 12.
And now we can actually subtract.
12 - 7 is 5.
12 - 7 -- I'm just doing the same problem -- just written slightly different on this right hand side -- is also 5.
Then we have 1 - 1 is 0.
I could write this as 05, but that's just the same thing as 5.
And here I'd have 10 - 10. Well, 10 -10 is just 0.
So it's just 05.
So 22 - 17 is 5.
Let's try to extend this to an even harder problem.
Hopefully you'll get the hang of how this borrowing or regrouping, depending on how you want to view it, actually works.
So let's say that we have 703 - 67. So if I tried the technique that we learned earlier in this video,
I immediately hit a roadblock. I say 3 - 7 -- well if I have 3 apples,
I can't take away 7 from there.
So I'm at an impasse.
I don't know what to do next.
And you say well, maybe I can borrow. But I look to the left, well gee, there's a 0 there, how can I borrow from a 0?
Then well, there's a 7 there, but then how do I borrow from the 7, all of that.
And the best way to think about it and the more practice you do the better, remember this 703 is seven $100 bills plus zero $10 bills plus three $1 bills.
And 67 is six $10 bills or $60 plus 7.
So if we can't borrow from here because I have no $10 bills, what we want to do is break one of the $100 bills.
So what I do is I take $100 bill from here, so now I'm left with $600.
So this 7 becomes a 6, right?
It's a 6 in 100s place and it represents six 100's, six $100 bills.
So, remember, I took out a $100 bill. And then what I can do is I can split that $100 bill, I can give $10 to this guy
-- or sorry, I can give $90 to this guy right here, and then I can give $1 to this guy
-- sorry, I could give $99. sorry --
I could give $90 to this guy and then I can give $10 to that guy right there.
I have $100 to work with, right?
So what happens?
If I do that, if I take that $100 bill that I took out from here, went to the cash register, I got nine 10s or $90.
So now I have nine 10s here.
And then I have ten 1s here, so I add 10 + 3, it becomes 13.
And just like that, all my numbers in each column, if I were to draw columns like this, divide them up. Everything on top is bigger than everything on the bottom so now I can subtract.
So 13 - 7 is 6.
9 - 6 is 3.
6 minus nothing is 6.
So 703 - 67 is 636.
Now you might be saying, OK Sal, I kind of get what you did, you took 100 from here, you put 90 here, so that became a 9, you gave 10 here.
But how did you know to do that or what's a more systematic way of doing it.
This kind of is a conceptual way, which is, in my mind, the most important way to understand it.
But let me show you kind of a mechanical way to do that.
So let's say we have 700
-- I'll do the same problem over again 703 - 67.
I look at all of the numbers on the top and I say are they all larger than the numbers on the bottom?
I said well, 3 -- well, 7 is larger than 3, that's not good.
6 is larger than 0, that's not good.
So I need to do something.
So what I do is I start with this 3 right here, and I say well, can I borrow from this number to the left? And I look to the number to the left and I can not borrow from 0.
So then I look to the two numbers to the left and say can I borrow from 70?
I say well gee, I can definitely borrow from 70 we know this is actually 700.
So if I borrow from 70 what happens?
If I borrow one 10 from 70, 70 becomes 69, right?
If I borrow 1 from 70, it becomes 69.
And I take that 1 and it's essentially a 10, right?
So that 10 + 3 is now 13.
And now these are my columns.
Just just like that.
You have 13 - 7 is 6, 9 - 6 is 3.
And then 6 right down here.
Now, another way you can think about it,
I'll do the exact same problem.
703 - 67.
You could start at the left.
You could say look, 7 is, well, it's larger than what's below it.
Nothing is below it, so I'm cool there.
And then you go 1 right to the right of it.
And you say well, 0
-- well, 0 is not bigger than what's below it. it's not bigger than the 6 below it.
So I'm going to need to borrow.
So what I can do is I can borrow 1 from the 7
I'm essentially borrowing 100, right?
So if I borrow -- this is 700, let me make it 600. Now if I take 100 away and I turn it to tens, that's 10 tens.
It looks like we took a 1 away and we just put the 1 in front of 0, but we essentially added 10 ten's to it.
But if it helps your mind, we took a 1 away from this, put it right in front of the 0 just like that.
This is the same 0 as that 0 right there.
And this 1 we took from this guy.
He became 6 and we have a 1 there. And then we say OK, 10 is definitely greater than 6, we're cool there.
But all of a sudden here on the 3 we're still not good.
3 is smaller than 7.
Still not cool.
I won't be able to subtract, so let me borrow again.
Now I have something to borrow from. Remember we went from the left to right this time instead of from the right to left.
All of these are valid ways of doing it.
So we say let me borrow 1 from the 10.
So 10 - 1 is 9, and let me give that 1 to the 3 to go 13.
Remember, it's not a 1.
I added 10 to it. If I take 1 from the ten's place, that's like adding 10 to the ones place.
Don't want to confuse you.
Hopefully you see the system here.
I want you to be able to do the problems before you have to get the real deep understanding of what's going on.
So 13 - 7 is 6, 9 - 6 is 3, 6 - 0 is 6.
636. Let's do a couple more problems, because the subtraction sometimes with the borrowing can become a little bit confusing on what to do next.
Let's say 953 - 754. Maybe we'll do it in all of the different ways that you can actually do this type of problem.
First, one of the ways I talked about is to start at the right.
Let's see, is 3 larger than 4?
No, it's not.
So we're going to have to make it larger than 4.
So let's borrow from this 5 over here.
-- So you'll say...let me do it right here -- So if I borrow from the 5, the 5 will become a 4, and I'd borrowed 1, the 3 becomes a 13.
Remember, if I borrow 1 from the tens place, that's actually a 10.
This is 5 tens. I took one of the 10s away, so I'm left with four 10s, and I added that 10 to the 3, so I have 13.
So this looks good.
13 - 4, I'll be able to subtract there.
But here I have a problem.
4 is less than 5.
It was cool before but now all of a sudden it's messed up.
So I'm going to have to borrow again. I'm going to say well, let me take a 1 from the 100s place, so that will become an 8.
And let me give that 100 to my tens place.
100 is 10 tens.
So I'm going to add a 10 here, so it's going to become 14.
I took the 1 from there and I borrowed it, or I rearranged that 100. I could re-write that 100 as one 10, and so that's what got us to that from 9 to 8
-- or sorry, 100.
I took away 100 from the 900 to get 800. And when I re-wrote the 100 in the tens place, it's ten 10s.
So that's why I added a 10 to the 4 that I had before. I could have just scratched it out and put the 14 like that to show that I had to re-write the 4.
But now all of a sudden I'm cool.
13 - 4 is 9.
14 - 5 is 9.
8 - 7 is 1.
953 - 754 is 199. Now let's do it the left to right way.
953 -- let me use a different color -- minus 754.
Now this is will be a little bit different than I did last time.
I say well 9 is definitely larger than 7. 5 is definitely larger -- well, at least it's equal to 5, so if I subtract maybe I'll get a 0 there.
And 3 is less than 4.
So maybe I'll just have to borrow here. If I borrow here than this is going to become a 4 and
I'm going to have to borrow from there and give me 14. It'll essentially boil down to what we did on this left hand side right here.
Instead, one thing you can do is say OK, 9 is larger than 7.
That's cool.
Or even better you could say 953 is larger than 754.
You know that.
You know that this is going to be a positive number.
That this number is larger than that.
Then you shift over one to the left.
Is 53 larger than 54?
Well no, 53 is not larger than 54.
And because 53 is not larger than 54, let's borrow.
Let's borrow from the the 100s place.
So this will become an 8.
And we have 100 to work with.
So maybe we'll just throw that 100 right here. So if we throw the 100 into the ten's place, it's ten 10s.
So the 5 becomes 15.
We're going from left to right.
So now we say 8 is larger than 7.
Well, 8 is definitely larger than 7, 15 is definitely larger than 5.
And then here, once again, we see 3 is less than 4.
But now we can borrow from the 15. So if we borrow from the 15, the 15 becomes a 14, and then the 3 becomes a 13.
Because you take 1 away from the tens place, one $10 bill is equal to 10 ones.
So that's why you added 10 to the 3 and you got 13. And notice, we ended up really with the same thing no matter how we did this problem.
So just like that you get 13 - 4 is 9.
14 - 5 is 9.
8 - 7 is 1.
Hopefully you found that pretty straightforward.
These are, frankly, as hard as the borrowing problems get. The ones where you don't have something to borrow from or when you do borrow from it, all of a sudden you get a number that
-- then you need to borrow from something else. If you ever get really confused about it, you should always go back to this.
You should always go back to this notion of regrouping. This notion of OK, if these things are all too small, let me take $100 bill over here, so I have six $100 bills left.
And let me regroup that $100 bills into the other spaces. In this case, we took the $100 bill and we put 90 here or nine 10s, nine $10 bills, and then $10 of it right there to make everything in the numerator
larger than everything in the denominator.
A club of nine people wants to choose a board of three officers, President, Vice President, and Secretary.
Assuming the officers are chosen at random, what is the probability that the officers are Marcia for president,
Sabita for Vice President, and Robert for Secretary?
So to think about the probability of Marcia-- so let me write this-- President is equal to Marcia, or Vice
President is equal to Sabita, and
This, right here, is one possible outcome, one specific outcome.
So it's one outcome out of the total number of outcomes, over the total number of possibilities.
Now what is the total number of possibilities?
Well to think about that, let's just think about the three positions.
You have President, you have Vice President, and you have Secretary.
Now let's just assume that we're going to fill the slot of President first. We don't have to do President first, but we're just going to pick here.
So if we're just picking President first, we haven't assigned anyone to any officers just yet, so we have nine people to choose from.
So there are nine possibilities here.
Now, when we go to selecting our Vice President, we would have already assigned one person to the President.
So we only have eight people to pick from.
And when we assign our Secretary, we would've already assigned our President and Vice President, so we're only going to have seven people to pick from.
So the total permutations here or the total number of possibilities, or the total number of ways, to pick President, Vice President, and Secretary from nine people, is going to be 9 times 8 times 7.
Which is, let's see, 9 times 8 is 72.
72 times 7, 2 times 7 is 14, 7 times 7 is 49 plus 1 is 50.
So there's 504 possibilities.
So to answer the question, the probability of Marcia being
President, Sabita being Vice President, and Robert being Secretary is 1 over the total number of possibilities, which is 1 over 504.
That's the probability.
We're asked to solve the quadratic equation, negative 3x squared, plus 10x, minus 3 is equal to 0.
And it's already written in standard form.
And there's many ways to solve this, but in particular I'll solve it using the quadratic formula.
So let me just rewrite it.
We have negative 3x squared Plus 10x, minus 3 is equal to 0, and actually solved it twice using the quadratic formula, to show you that, as
long as we manipulated this, in the valid way, the quadratic formula will give us the exact same roots, or the exact same solution to this equation.
So, in this form right over here, what are a, b, c?
Let's just remind ourselves what the quadratic formula even is, actually, that's a good place to start.
The quadratic formula tells us that if we have a quadratic equation, in the form ax squared, plus bx, plus c is equal to 0, so in standard form.
Then the roots of this are x are equal to negative b, plus or minus, the square root of b squared minus 4ac, all of that over 2a, all of that over 2a.
And this is derived from completing the square, in a general way.
So, it's no magic here, and I've derived it, in other videos.
But this is the quadratic formula, this is actually giving you two solutions, cause you have the plu, the positive squared here, and the negative square root.
So let's apply it here, in the case where, in this case a is equal to negative 3, a is equal to negative 3. B is equal to 10. B is equal to 10.
So applying the quadratic formula right here we get our solutions to be x is equal to negative b. b is 10.
So negative b is 10.
Negative 10.
Plus or minus the square root of b squared. b is 10 so b squared is 100 minus 4 times a times c.
So minus 4 times negative 3 times negative 3.
Let me just write it down.
Minus 4 times negative 3 times negative 3.
All of that's under the radical sign.
And then all of that is over 2a.
So 2 times a is negative 6.
So this is going to be equal to negative 10, plus or minus the square root of 100 minus 3 times, negative 3 times negative 3 is positive 9. Positive 9 times 4 is positive 36.
We have a minus sign out here.
So minus 36 all of that over negative 6.
This is equal to, 100 minus 36 is 64.
So negative 10 plus or minus the square root of 64.
All of that over negative 6.
The principle score of 64 is 8.
Voting the positive and negative square roots.
So this is negative 10 plus or minus 8 over negative 6.
So if we take the positive version, we say x could be equal to negative 10 plus 8, is negative 2 over negative 6.
So that was taking the plus version.
That's this right over here.
And negative 2 over negative 6 is equal to 1 3rd.
If we take the negative square root, negative 10 minus 8, so let's take negative 10 minus 8, that would be x is equal to negative 10 minus 8 is negative 18, and that's going to be over negative 6.
Negative 18 divided by negative 6 is positive 3.
So the two roots for this quadratic equation are positive.
1 3rd and positive 3.
And I want to show you that we'll get the same answer even if we manipulate this.
Some people might not like the fact that our first coefficient here is a negative 3.
So, to get rid of that negative 3, they can multiply both sides of this equation times negative 1.
And then if you did that you would get 3x squared minus 10x plus 3 is equal to 0 times negative 1, which is still equal to 0.
So in this case a is equal to 3, b is equal to negative 10, and c is equal to 3 again.
And we can apply the quadratic formula, we get X is equal to negative b. B is negative 10.
So negative negative 10 is positive 10, plus or minus the square root of b squared, which is negative 10 squared, which is 100.
A times c is 9, times 4 is 36.
So minus 36 all of that over 2 times a, all of that over 6.
So this is equal to 10 plus or minus the squared root of 64 or really that's just going to be 8, all of that over 6.
If we add 8 here, we get 10 plus 8 is 18 over 6, we get x could be equal to 3 or, if we take the negative, the negative squared, of the negative 8 here, 10 minus 8 is 2, 2 over 6 is.
1 3rd, so once again, you get the exact same solution.
It will be good to introduce some basic terminology that is commonly used in artificial intelligence to distinguish different types of problems.
The very first word I will teach you is fully versus partially observable.
An environment is called fully observable if what your agent can sense at any point in time is completely sufficient to make the optimal decision.
So, for example, in many card games, when all the cards are on the table, the momentary site of all those cards is really sufficient to make the optimal choice.
That is in contrast to some other environments where you need memory on the side of the agent to make the best possible decision.
For example, in the game of poker, the cards aren't openly on the table, and memorizing past moves will help you make a better decision.
To fully understand the difference, consider the interaction of an agent with the environment to its sensors and its actuators, and this interaction takes place over many cycles, often called the perception-action cycle.
For many environments, it's convenient to assume that the environment has some sort of internal state.
For example, in a card game where the cards are not openly on the table, the state might pertain to the cards in your hand.
An environment is fully observable if the sensors can always see the entire state of the environment.
It's partially observable if the sensors can only see a fraction of the state, yet memorizing past measurements gives us additional information of the state that is not readily observable right now.
So any game, for example, where past moves have information about what might be in a person's hand, those games are partially observable, and they require different treatment.
Very often agents that deal with partially observable environments need to acquire internal memory to understand what the state of the environment is, and we'll talk extensively when we talk about hidden Markov models about how this structure has such internal memory.
A second terminology for environments pertains to whether the environment is deterministic or stochastic.
Deterministic environment is one where your agent's actions uniquely determine the outcome.
So, for example, in chess, there's really no randomness when you move a piece.
The effect of moving a piece is completely predetermined, and no matter where I'm going to move the same piece, the outcome is the same.
That we call deterministic.
Games with dice, for example, like backgammon, are stochastic.
While you can still deterministically move your pieces, the outcome of an action also involves throwing of the dice, and you can't predict those.
There's a certain amount of randomness involved for the outcome of dice, and therefore, we call this stochastic.
Let me talk about discrete versus continuous.
A discrete environment is one where you have finitely many action choices, and finitely many things you can sense.
So, for example, in chess, again, there's finitely many board positions, and finitely many things you can do.
That is different from a continuous environment where the space of possible actions or things you could sense may be infinite.
So, for example, if you throw darts, there's infinitely many ways to angle the darts and to accelerate them.
Finally, we distinguish benign versus adversarial environments.
In benign environments, the environment might be random.
It might be stochastic, but it has no objective on its own that would contradict the own objective.
So, for example, weather is benign.
It might be random.
It might affect the outcome of your actions.
But it isn't really out there to get you.
Contrast this with adversarial environments, such as many games, like chess, where your opponent is really out there to get you.
It turns out it's much harder to find good actions in adversarial environments where the opponent actively observes you and counteracts what you're trying to achieve relative to benign environment, where the environment might merely be stochastic but isn't really interested in making your life worse.
So, let's see to what extent these expressions make sense to you by going to our next quiz.
So here are the 4 concepts again: partially observable versus fully, stochastic versus deterministic, continuous versus discrete, adversarial versus benign.
And let me ask you about the game of checkers.
Check one or all of those attributes that apply.
So, if you think checkers is partially observable, check this one.
Otherwise, just don't check it.
If you think it's stochastic, check this one, continuous, check this one, adversarial, check this one.
If you don't know about checkers, you can check the Web and Google it to find a little more information about checkers.
Let's start with a warm up ratio problem.
So I have the ratio 13/6 is equal to 5/x.
I don't like having this x in the denominator, so let's multiply both sides of this equation by x.
So if I multiply both sides by x, what's going to happen?
On the right hand side, this x cancels out with that x.
And then the left hand side going to become 13 over 6x is equal to-- you're just going to have a 5 there.
And then to solve for x, you just multiply both sides by the inverse of 13/6. 6/13.
These, obviously, cancel out.
That's why I multiplied it by the inverse.
And you get x is equal to 5 times 6, which is 30/13.
Now one way that you might see this done-- it's kind of skipping a step-- is called cross multiplying.
You look at a ratio like this, and you immediately say the numerator on this side times the denominator on that side is equal to the numerator on this side times the denominator on that side.
Let me write that out.
So you might sometimes see people immediately go to-- let me just rewrite the problem actually-- So that original problem was 13/6 is equal to 5/x.
You might sometimes immediately see someone go to 13 times x is equal to 5 times 6.
And it might look like magic.
How does that work out? Why does that make sense?
And really, all they're doing to get to this point is they are simultaneously multiplying both sides of the equation by both denominators.
Let me show you what I mean.
If I multiply both sides of this equation by 6 and an x, what's going to happen? If I multiply it by 6x times both sides of this equation--
And where did I get the 6?
From here.
Where did I get the x?
From there.
Both denominators. What's going to happen?
On this side of the equation, the 6 is going to cancel out with this denominator.
And on the right hand side of the equation, the x is going to cancel with this denominator.
So you're going to be left with 13 times x is equal to 5 times 6.
So nothing fancy there.
You're just multiplying by the denominators of both sides of the equation.
And it looks like you're cross multiplying.
13x is equal to 5 times 6.
And then from here, of course, you divide both sides by 13.
You get x is equal to 30/13.
Now that we're all warmed up, let's tackle some actual word problems.
So we have the highest mountain in Canada is Mount Yukon.
It is 298/67 the size of then Ben Nevis.
Let's Y for Yukon is equal to 298/67 the size of-- let's say N for Nevis.
That's what this in green tells us. The highest peak in Scotland.
Mount Elbert in Colorado is the highest peak in the Rocky Mountains.
Mount Elbert-- so we have this other information here-- Mount Elbert is 220/67 the height of Ben Nevis.
So let's say, E for Elbert.
E is equal to 22/67 times Nevis.
Times the same Ben Nevis, right there.
And they're telling us more.
And, it is 44/48 the size of Mont Blanc.
So Elbert is equal to 44/48 the size of Mont Blanc.
Let's write B for Mount Blanc.
They also tell us Mont Blanc is 4,800 meters high.
Mont Blanc is 4,800. meters high.
So B is equal to 4,800.
And they ask us, how high is Mount Yukon?
So we have to figure out Y.
So let's see if we can work backwards, and figure out all the variables in between.
So let's start with this information here.
B is equal to 4,800.
E is equal to 44/48 times B.
So E-- so Elbert-- is equal to 44/48 times Mont Blanc, which is 4,800 meters.
Now if you divide that by 48-- 4,800 divided by 48 is 100.
So Elbert is 44 times 100 meters high.
So it's equal to 4,400 meters.
Fair enough. Now we can use this information and substitute it over here.
We get Elbert, which is 4,400 meters high, is equal to 220/67 times Ben Nevis.
N for Nevis.
To solve for Nevis, we multiply both sides by the inverse of this coefficient right here. So we multiply both sides by 67/220.
So times 67/220.
The 67 cancels with that 67.
That 220 cancels with that 220.
And then you get-- let's see, if I take 4,400 divided by 220-- 440 divided by 220 is 2.
So this is going to be 20.
So 4,400 divided by 220 is just 20. So you get Nevis is equal to-- I'll swap sides.
So Ben Nevis is equal to 67 times 20 meters.
And now that's what?
1,340 meters.
Is that is right?
Well, lets just leave it like that, because we could-- actually it looks like that's 67-- I'm going to leave Nevis as 67 times 20 meters. And substitute it right there.
So Yukon-- I'll just go down here, because I have more real estate there-- Yukon is equal to 298 over 67 times the height of Nevis.
Nevis is 67 times 20.
So times 67 times 20.
Well I can divide 67 by 67, and I get Yukon is 298 times 20 meters.
So Yukon is equal to 298 times 20.
And what is that equal to?
That is equal to-- Let's see that's 2 times 298 is going to be 396.
Oh sorry, it's going to be 596.
This is almost 300, so it should be close to 600.
This is 2 less than 300, so this should be 4 less than 300.
And then, I have a 0 here.
So it's going to be 5,960 meters.
And we are done.
Let's do one more of these word problems. All right.
At a large high school, it is estimated that 2 out of every 3 students have a cell phone.
And 1 in 5 of all students have a cellphone that is one year old or less.
All right. So let's think about it.
Let's say that x is equal to the total number of students. ...
This first line, 2 out of 3 students have a cell phone, so we could say that 2/3 x have cell phone. ...
That's what that green statement tells us.
And then that purple statement-- 1 in 5 of all students have a cellphone that is one year old or less.
So 1/5 x have less than 1/5 year cell phone. ...
So they want to know, out of the students who own a cell phone-- so it's out of this-- that's our denominator.
So let me write that down.
That is our denominator.
So out of the students who have a cellphone-- that's right there-- they want to know what proportion owns a phone that is more than one year old.
So how many students have a cell phone that is more than one year old?
Well, we could take the total number that have a cellphone, which is 2/3 x.
2/3 of all the students have a cell phone. We can subtract out all of the students that have a new cellphone-- a cell phone that is less than one year. Remember they're saying more than one year here.
So we want to subtract out all the students with the new cellphone, minus 1/5x, and you will then have the proportion of students who have this right here.
This is, have greater than 1/5 year cell phone.
They have a phone, but it's more than 1/5 years old.
This is all of them that have a cellphone.
We subtract out the new ones.
So this is, essentially, all of the people who have an older than one-year old cell phone.
So to solve this, we just subtract the fractions.
So this is just going to be, let's see, 2/3 is the same thing as 10/15.
That's 2/3 minus 1/5. The same thing as 3/15 x.
Which is equal to 10 minus 3 is 7/15 x.
Is the total proportion of students-- that's this orange-- what proportion owns a phone that is more than one year old?
It's 7/15 x. That's an actual number.
So if you want to know, out of the students who own a cell phone-- so out of the students who own a cell phone, right there-- 2/3x, what proportion owns a phone that it is more than one year old?
This is the number that own a cellphone that is more than one year old.
And this whole value is the proportion out of the students who have a cell phone.
Lucky for us, the x's cancel out. And we are left with this is equal to 7/15 times the inverse of the denominator.
You divide by 2/3. That's the same thing as multiplying by 3/2.
And what does this equal to?
Divide by 3. ...
We are left with 7/10.
So of the students who own a cell phone, 7 out of 10 of the students who own a cell phone, own a cell phone that is more than one year old.
And we are done.
Welcome back.
We're almost done learning all the rules or laws of angles that we need to start playing the angle game.
So let's just teach you a couple of more.
So let's say I have two parallel lines, and you may not know what a parallel line is and I will explain it to you now.
So I have one line like this -- you probably have an intuition what a parallel line means.
That's one of my parallel lines, and let me make the green one the other parallel line.
So parallel lines, and I'm just drawing part of them.
We assume that they keep on going forever because these are abstract notions -- this light blue line keeps going and going on and on and on off the screen and same for this green line.
And parallel lines are two lines in the same plane.
And a plane is just kind of you can kind of use like a flat surface is a plane.
We won't go into three-dimensional space in geometry class.
But they're on the same plane and you can view this plane as the screen of your computer right now or the piece of paper you're working on that never intersect each other and they're two separate lines.
Obviously if they were drawn on top of each other then they intersect each other everywhere.
So it's really just two lines on a plane that never intersect each other.
That's a parallel line.
If you've already learned your algebra and you're familiar with slope, parallel lines are two lines that have the same slope, right?
They kind of increase or decrease at the same rate.
But they have different y intercepts.
If you don't know what I'm talking about, don't worry about it.
I think you know what a parallel line means.
You've seen this -- parallel parking, what's parallel parking is when you park a car right next to another car without having the two cars intersect, because if the cars did intersect you would have to call your insurance company.
But anyway, so those are parallel lines.
The blue and the green lines are parallel.
And I will introduce you to a new complicated geometry term called a transversal.
All a transversal is is another line that actually intersects those two lines.
That's a transversal.
Fancy word for something very simple, transversal.
Let me write it down just to write something down.
Transversal. 54 00:02:18,69 --> 00:02:23,51 It crosses the other two lines.
I was thinking of pneumonics for transversals, but I probably was thinking of things inappropriate. 58 00:02:31,71 --> 00:02:33,81 Going on with the geometry.
So we have a transversal that intersects the two parallel lines.
What we're going to do is think of a bunch of -- and actually if it intersects one of them it's going to intersect the other.
I'll let you think about that.
There's no way that I can draw something that intersects one parallel line that doesn't intersect the other, as long as this line keeps going forever.
I think that that might be pretty obvious to you.
But what I want to do is explore the angles of a transversal.
So the first thing I'm going to do is explore the corresponding angles.
So let's say corresponding angles are kind of the same angle at each of the parallel lines.
corresponding angles.
They kind of play the same role where the transversal intersects each of the lines.
As you can imagine, and as it looks from my amazingly neat drawing -- I'm normally not this good -- that these are going to be equal to each other.
So if this is x, this is also going to be x.
If we know that then we could use, actually the rules that we just learned to figure out everything else about all of these lines.
Because if this is x then what is this going to be right here?
What is this angle going to be in magenta?
90 00:03:58,97 --> 00:04:00,99 Well, these are opposite angles, right?
They're on opposite side of crossing lines so this is also x. 94 00:04:06,94 --> 00:04:08,41 And similar we can do the same thing here.
This is the opposite angle of this angle, so this is also x. 97 00:04:18,58 --> 00:04:21,01 Let me pick a good color.
What is yellow?
What is this angle going to be?
Well, just like we were doing before.
Look, we have this huge angle here, right?
This angle, this whole angle is 180 degrees.
So x and this yellow angle are supplementary, so we could call
Well, if this angle is y, then this angle is opposite to y.
So this angle is also y. Fascinating.
And similarly, if we have x up here and x is supplementary to this angle as well, right?
So this is equal to 180 minus x where it also equals y.
And then opposite angles, this is also equal to y.
So there's all sorts of geometry words and rules that fall out of this, and I'll review them real fast but it's really nothing fancy.
All I did is I started off with the notion of corresponding angles.
I said well, this x is equal to this x.
I said, oh well, if those are equal to each other, well not even if -- I mean if this is x and this is also x because they're opposite, and the same thing for this.
Then, well, if this is x and this is x and those equal each other, as they should because those are also corresponding angles.
These two magenta angles are playing the same role.
They're both kind of the bottom left angle.
That's how I think about it.
We went around, we used supplementary angles to kind of derive well, these y angles are also the same.
This y angle is equal to this y angle because it's corresponding.
So corresponding angles are equal to each other.
It makes sense, they're kind of playing the same role.
The bottom right, if you look at the bottom right angle.
So corresponding angles are equal. 139 00:06:22,87 --> 00:06:25,13 That's my shorthand notation.
And we've really just derived everything already.
That's all you really have to know.
But if you wanted to kind of skip a step, you also know the alternate interior angles are equal.
So what do I mean by alternate interior angles?
Well, the interior angles are kind of the angles that are closer to each other in the two parallel lines, but they're on opposite side of the transversal.
That's a very complicated way of saying this orange angle and this magenta angle right here.
These are alternate interior angles, and we've already proved if this is x then that is x.
So these are alternate interior angles. This x and then that x are alternate interior.
And actually this y and this y are also alternate interior, and we already proved that they equal each other.
Then the last term that you'll see in geometry is alternate --
I'm not going to write the whole thing -- alternate exterior angle.
Alternate exterior angles are also equal.
That's the angles on the kind of further away from each other on the parallel lines, but they're still alternate.
So an example of that is this x up here and this x down here, right, because they're on the outsides of the two parallel
of the transversal.
These are just fancy words, but I think hopefully you have the intuition.
Corresponding a angles make the most sense to me.
Then everything else proves out just through opposite angles and supplementary angles.
But alternate exterior is that angle and that angle.
Then the other alternate exterior is this y and this y.
Those are also equal.
So if you know these, you know pretty much everything you need to know about parallel lines.
The last thing I'm going to teach you in order to play the geometry game with full force is just that the angles in a triangle add up to 180 degrees. 181 00:08:41,77 --> 00:08:45,58 So let me just draw a triangle, a kind of
random looking triangle.
That's my random looking triangle.
And if this is x, this is y, and this is z.
We know that the angles of a triangle -- x degrees plus y degrees plus z degrees are equal to 180 degrees.
So if I said that this is equal to, I don't know, 30 degrees, this is equal to, I don't know, 70 degrees.
Then what does z equal?
Well, we would say 30 plus 70 plus z is equal to 180, or 100 plus z is equal to 180.
Subtract 100 from both sides. z would be equal to 80 degrees.
We'll see variations of this where you get two of the angles and you can use this property to figure out the third.
With everything we've now learned, I think we're ready to kind of ease into the angle game.
I'll see you in the next video.
What is the cost of 14.6 gallons of gasoline at $2.70 per gallon?
So we have 14.6 gallons, and each gallon's going to cost $2.70.
Or we can even view $2.70 as 2.7 dollars.
Let's just multiply times 2.7.
It makes things a little bit simpler.
I think you'll appreciate $2.70 is the same thing as 2.7 dollars per gallon.
So let's multiply this out.
So first we have, and just as a reminder, when you multiply decimals, you just have to treat the numbers like whole numbers and then worry about the decimals later.
So right now, we can just view this as 146 times 27, and then we'll worry about the decimals.
So first we have a 7 times a 6.
7 times 6 is 42.
Regroup the 4.
7 times 4 is 28, plus 4 is 32.
Regroup the 3.
7 times 1 is 7, plus 3 is 10.
So we get 7 times 146 is 1,022.
Now we're going to deal with this 2.
But this 2, at least before we consider the decimal, is really a 20.
So we're going to put a 0 here.
We're doing it exactly the same way we do a traditional multiplication problem.
We're ignoring the decimals for now.
2 times 6 is 12.
Carry the 1, or regroup the 1.
We can ignore these guys right now.
2 times 4 is 8, plus 1 is 9.
2 times 1 is 2, and now we can add.
2 plus 2 is 4.
0 plus 9 is 9.
1 plus 2 is 3.
Now we've figured out what 146 times 27 is.
It's 3,942.
But this wasn't 146 times 27.
It was 14.6 times 2.7.
So now we have to worry about the decimals.
We just count how many numbers are sitting behind decimals.
We have one right there and a second one right there.
So our product has to have two numbers to the right of the decimal.
So one, two, stick it right over there.
So for 14.6 gallons of gas at $2.70 per gallon, it's going to cost $39.42.
Imagine a big explosion as you climb through 3,000 ft.
Imagine a plane full of smoke.
Imagine an engine going clack, clack, clack.
It sounds scary.
Well, I had a unique seat that day.
I was sitting in 1D.
I was the only one who could talk to the flight attendants.
So I looked at them right away, and they said, "No problem.
We probably hit some birds." The pilot had already turned the plane around, and we weren't that far.
You could see Manhattan.
Two minutes later, three things happened at the same time.
The pilot lines up the plane with the Hudson River.
That's usually not the route.
(Laughter)
He turns off the engines.
Now, imagine being in a plane with no sound.
And then he says three words. The most unemotional three words I've ever heard.
He says, "Brace for impact."
I didn't have to talk to the flight attendant anymore.
(Laughter)
I could see in her eyes, it was terror.
Life was over.
Now I want to share with you three things I learned about myself that day.
I learned that it all changes in an instant.
We have this bucket list, we have these things we want to do in life, and I thought about all the people I wanted to reach out to that I didn't, all the fences I wanted to mend, all the experiences I wanted to have and I never did.
As I thought about that later on, I came up with a saying, which is, "I collect bad wines."
Because if the wine is ready and the person is there, I'm opening it.
I no longer want to postpone anything in life. And that urgency, that purpose, has really changed my life.
The second thing I learned that day -- and this is as we clear the George Washington Bridge, which was by not a lot -- (Laughter)
I thought about, wow, I really feel one real regret.
I've lived a good life.
In my own humanity and mistakes,
I've tried to get better at everything I tried.
But in my humanity, I also allow my ego to get in.
And I regretted the time I wasted on things that did not matter with people that matter.
And I thought about my relationship with my wife, with my friends, with people.
And after, as I reflected on that,
I decided to eliminate negative energy from my life.
It's not perfect, but it's a lot better.
I've not had a fight with my wife in two years.
It feels great. I no longer try to be right;
I choose to be happy.
The third thing I learned -- and this is as your mental clock starts going, "15, 14, 13."
You can see the water coming.
I'm saying, "Please blow up."
I don't want this thing to break in 20 pieces like you've seen in those documentaries.
And as we're coming down,
I had a sense of, wow, dying is not scary.
It's almost like we've been preparing for it our whole lives.
But it was very sad.
I didn't want to go; I love my life.
And that sadness really framed in one thought, which is, I only wish for one thing.
I only wish I could see my kids grow up.
About a month later, I was at a performance by my daughter -- first-grader, not much artistic talent -- (Laughter)
Yet! (Laughter) And I'm bawling, I'm crying, like a little kid.
And it made all the sense in the world to me.
I realized at that point, by connecting those two dots, that the only thing that matters in my life is being a great dad.
Above all, above all, the only goal I have in life is to be a good dad.
I was given the gift of a miracle, of not dying that day.
I was given another gift, which was to be able to see into the future and come back and live differently.
I challenge you guys that are flying today, imagine the same thing happens on your plane -- and please don't -- but imagine, and how would you change?
What would you get done that you're waiting to get done because you think you'll be here forever?
How would you change your relationships and the negative energy in them?
And more than anything, are you being the best parent you can?
Thank you.
(Applause)
A club of nine people wants to choose a board of three officers: a President, a Vice President, and a Secretary.
How many ways are there to choose the board from the nine people?
Now, we're going to assume that one person can't hold more than one office.
That if I'm picked for President, then I'm no longer a valid person for Vice President or Secretary.
So let's just think about the three different positions.
So you have the President, you have the Vice President, VP, and then you have the Secretary.
Now, let's say that we go for the President first.
It actually doesn't matter.
Let's say we were picking the President slot first and we haven't appointed any other slots yet.
How many possibilities are there for President?
Well, the club has nine people, so there's nine possibilities for President.
There's going to be nine possibilities for President.
Now, we're going to pick one of those nine.
We're going to kind of take them out of the running for the other two offices.
Right?
Because someone's going to be President, so one of the nine is going to be President.
There's nine possibilities, but one of the nine is going to be President.
So you take that person aside.
He or she is now the President.
How many people are left to be Vice President?
Well, now there's only eight possible candidates for Vice President?
Eight possibilities.
Now he or she also goes aside.
Now how many people are left for Secretary?
Well, now there's only seven possibilities for Secretary.
So if you want to think about all of the different ways there are to choose a board from the nine people, there's the 9 for President times the 8 for Vice President times the 7 for Secretary.
You didn't have to do it this way.
It could've been-- you could've picked Secretary first.
Then there would've been nine choices.
And then you could've picked Vice President, and there would've still been eight choices.
And then you could've picked President last, and there would've only been seven choices.
But either way you would've got 9 times 8 times 7.
And that is, let's see, 9 times 8 is 72 times 7 is-- 2 times 7 is 14, 7 times 7 is 49 plus 1 is 50.
So 504 possible ways to pick your board out of a club of only nine people.
This brain teaser is a bit of a classic, and I'm sure a bunch of you have heard it before.
But I wanted to include this in the brain teaser playlist that I'm making right now.
Because this one is actually a good build up, and a bit of a nice warm up session for a slightly harder brain teaser that deals with people telling the truth and lying.
So this one, we could call it the truth teller and the liar.
So we're on some type of adventure quest, and we get to a fork in a road, right?
So let's say that there's two doors.
That's even better.
So there's two doors.
And I've gotten to the end of my adventure quest.
And I know that my treasure is behind one of these two doors.
Unfortunately, behind the other door is slow and painful death, and all of the misery in the world.
So I want to pick the door carefully.
And beside these doors, there are two people sitting there.
There's one guy that looks like this.
And then there's another guy that looks like this.
And I know for a fact - the gods of brain teasers have come and told me - that both of these guys know which door has the treasure, and both of these guys know which door has the unbelievable despair that would ensue if I opened that door.
So both of these guys know which door I should be opening.
And I also know, and both of them know, that one of them always tells the truth.
One is always honest.
And then one of them always lies.
And the problem is I don't know who's who.
And I only have one chance.
Obviously I can't just open a door and close it.
If I open the wrong door, the despair will come out and kill.
And you know, all of the pain will happen.
And I can only ask one question of one of them to decide which door to open.
So remember, they both know the correct answer.
But one of them always lies.
One of them always tells the truth.
And I only have one question to ask of one of them.
So the brain teaser is:
What question do you ask?
Who do you ask it to?
Do you ask it to the green guy or to the brown guy?
And then what do you do based on what they tell you?
So that is the problem description.
And I will now give you the solution.
So if you don't want the solution, and I encourage you not to.
I think if you think about this one for maybe 20 or 30 minutes, or at most a day.
Sometimes when you sleep on a brain teaser it might come to you.
So I encourage you to do that.
So pause it, stop it, whatever.
Don't listen anymore.
Because here is the solution.
So what you do is-- I mean, you don't know who's who.
So it's not like there's a correct answer on who you ask a question of.
But what you do is you ask you either of the people, what would the other guy say is the correct door to open?
So let's think about this.
So I could ask this guy, I'm asking the green guy, what would this guy say is the correct door to open?
Now what happens if this guy tells the truth?
If this guy tells the truth, then this guy's the liar, right?
And so he will actually tell me what this guy would tell me to do.
So this guy, if you were to tell him the correct door to open, he would tell you the incorrect door to open.
Right?
So when you ask this guy what would that guy say, he'll be honest about what this guy would say.
And since he's a liar, he would tell you the incorrect door.
So the answer to this question, you would get the incorrect door.
Incorrect door would be the answer to that question if this guy's the truth teller and this guy's the liar.
Now what happens if it's the other way around?
What if I ask this guy and he happens to be the liar?
So this guy's the liar, this guy's the truth teller.
So the liar, he can't help himself. He will lie.
So he knows that this other guy is the truth teller there, right?
There's only two of them there.
He knows this guy's the truth teller.
And he knows that this guy when asked will say the correct door to open.
So if you happened to be lucky and you ask this guy the correct door, he would tell it to you.
This guy will lie.
Let's say that this is the correct door, door number two is the correct door.
So let's say that door number two is the correct door.
If you ask this guy directly, he'll say oh yeah, door number two.
You'll find all your happiness behind door number two.
Now if this guy's a liar, he knows that the truth teller will say door number two.
But he's a liar, so he'll tell you door number one.
So once again, if I ask the same question of the liar, i still get the incorrect door.
Right?
So no matter who I ask this question to, their answer will be the wrong door, the incorrect door, or the door that I get all of the pain from.
So what you do is you ask this question, what would the other guy say is the correct door to open?
And no matter who you ask that to, they're going to answer the incorrect door.
And so you do the opposite.
So I ask this guy, mister green guy, what would mister brown guy say is the correct door to open?
And green guy will say brown guy will tell you to open door number one.
Well green guy says that brown guy will tell me to open door number one, then I should open up door number two.
And likewise, if green guy says brown guy will say to open door number two, then I should open door number one.
Anyway that's a nice warm up brain teaser for the next one I'm going to give you.
Let's do a couple more rotational volume problems, and
I'm going to make these a little bit more difficult.
And hopefully after these if you've understood everything we've done up to now and the ones I'm about to do, I think you're pretty set for most of what you should face in most math classes.
And definitely I think you'll be set for the AP exam, and either ab or bc on this concept.
So let's do another example.
OK.
So let's say that I want to-- actually, let me do something different.
Let me draw here.
So that's my y-axis.
This is my x-axis.
Now let me draw the function y is equal to x squared.
And we know that that could be written as y is equal to x squared, or we could write that as x is equal to square root of y, depending on what we want to be a function of what.
This is the y-axis.
This is the x-axis.
Let's say I also have the line y equals 2.
Goes over what I just wrote. y equals 2.
Now this problem is going to be slightly different then what we've done so far.
I'm going to take a rotation, but instead of taking a rotation around the y or the x-axis, I'm going to take a rotation around another line.
So let's say I want to take a rotation between x is equal to 0.
Actually let me do something arbitrary.
Let me say between x is equal to 1, so that's that point, and x is equal to 2.
That's where they intersect.
This is the point right here, this is 2,2.
I'm sorry, no, 2,4.
Because y is equal to x squared.
So this is 2,4. This is the point 4.
So what point is this.
This is the point 1, right?
So our y values go from 4 to 1, our x values go from 1 to 2.
And that makes sense, because y is x squared.
And so if we were to kind of take the area that we're going to rotate, and I haven't told you what we're going to rotate it around yet, and this might prove to be shocking to you.
So this is the area we're going to rotate.
Instead of rotating it around the y-axis, I want to rotate it around the line y is equal to minus 2.
So if that's 2, y equals minus 2 should be roughly here.
So I'm going to rotate this area around this line.
So what's it going to look like?
It's going to be a fairly big ring.
Like if I were to try to draw it-- let me see if I can even make an attempt.
Once again this is always the hardest part, just drawing what I'm trying to rotate.
I'll try to do it from an upward perspective.
So that's kind of the inner loop, and then there will be an outer loop.
The top is flat right, because it's defined by y is equal to 4, so that's the top.
And the inside is also going to be a hard edge.
But then the outside is going to curve inward.
I don't know if you see what I'm saying, because this is the outside, it's curving inward.
So it's going to be a big ring.
So if I were to draw the axis, this would be the y-axis access coming in-- no, no, sorry.
Whoops. The y-axis is actually going to be closer to this hand side. The y-axis is going to be in the middle of kind of-- so this is going to be the y-axis coming up here.
And then the x-axis is going to come below that.
I'm drawing everything at an angle as best as I can.
The x-axis is going to come a below that.
And then this line we're rotating it around, that's going to be someplace over here.
That's going to be something like that.
It's going to go behind there and come back over there.
Hopefully that makes sense.
We're just getting a big ring.
So how are we going to do this?
Well actually there's a couple of things we can do.
First we could just use the shell method, using the x value.
So how do we do that?
The important thing is to always visualize the shell or the disk.
So the shell method we're going to take slivers like this, where the width of that sliver is dx. I could draw it really big.
So that's our direct angle, is going to be dx.
What's the height going to be of the sliver? Well it's going to be the top function minus the bottom function. It's going to be y equals 4 minus x squared.
So this is going to be 4 minus x squared, the height at any point right here.
And then if I were to do the shell just like we did before-- let me see if I can draw a decent shell. I think I'm getting better at this. This is one edge of the shell, that's the other shell.
And then what's the radius going to be?
What's the radius of that shell going to be?
Well, is it going to be just x? Is it just going to be x value?
No, the x value will tell you the distance from the y-axis to that shell, and it's going to be from minus 2 to the e value.
So it's going to be essentially 2 plus x. That's going to be the radius at any point.
And this is where we diverge from what we've done before. Before the radius was just x, but now it's 2 plus x. So what's the circumference of each shell going to be?
So it's 2 pi times 2 plus x, which equals 4 pi plus 4 pi plus 2 pi x.
That's the circumference.
And then what's the surface area of this?
Well it's going to be the circumference times the height.
So surface area is equal to that.
The circumference 4 pi plus 2 pi x, all of that times the height-- times 4 minus x squared.
And let's see if we can foil this out or distribute this out.
So 4 pi times 4 is 16 pi.
4 pi minus x squared minus 4 pi x squared.
2 pi x times 4 plus 8 pi x, and then 2 pi x times minus x squared, so that's minus 2 pi x to the third.
So that's the surface area of each ring.
And then if we want the volume of each shell, essentially we multiply it times the width, the dx.
So that's the volume of each shell, and if we want the volume of all the shells, we sum them up.
So we take the integral, that's an integral sign, and I'm running out of space like I always do.
And where did I take the integral from?
I take the integral from x is equal to 1 to x is equal to 2.
From 1 to 2.
That's probably too small for you to read.
So let's see if we can take the antiderivative of this.
Let me make some space free just so I don't have to write so small.
So I'll keep this down here, because that's the set up of the problem.
I think I can get rid of a lot of this.
I think that is pretty good.
OK.
And let me switch to another color.
And we're going to take the antiderivative.
So what's the antiderivative of this?
So the antiderivative of 16 pi is 16 pi x.
And then what's the antiderivative of 4 pi x squared?
It's going to be x to the third over 3, so it'll be minus 4 pi over 3-- sorry-- 4 pi over 3 x to the third.
Well this will be x squared over 2, so it'll be plus 4 pi x squared.
And then minus, this will be x to the fourth over 4, so minus pi over 2.
Just divided by 4. x to the fourth.
I'm going to evaluate that.
This is a much hairrier problem then what we've been doing.
So what is it evaluated at 2?
It is 32 pi minus 4 pi over 3 times 8 plus 4 pi times 4 plus 16 pi minus 2 to the fourth is 16 divided by 2 minus 8 pi.
And then I just realized I'm running out time, so I will continue this in the next video.
All right. We're on problem 26. For the quadrilateral shown below, a quadrilateral has four sides, measure of angle A plus the measure of angle C is equal to what?
Like the angles in a triangle are equal to 180. And I'll show you no, you don't have to memorize that. Because if you imagine any quadrilateral, let me draw a quadrilateral for you.
So let's say this is some quadrilateral. You don't have to memorize that the sum of the angles is equal to 360. Although it might be useful for a quadrilateral.
So now hopefully, if I gave you a 20 sided polygon, you can figure out how many times can I fit triangles into it. And you'll know how many angles there are. And the sum of all of them.
Let's see, 95 plus 32 is 127. Plus 127 is equal to 360.
A plus C is equal to 360 minus 127. And what is that? That is 233.
If you have a parallelogram, the opposite sides are parallel, then their diagonals are actually bisecting each other.
So if this is 6, this is also going to be 6. And this diagonal splits BD in two. So if this is 5, then this is also 5.
What is the lateral area of the cone? Good, they gave us a definition. Lateral area of a cone is equal to pi times r times l, where I is the slant height.
And so, I is equal to the square root of 89.
So I is equal to the square root of 89. And they give us the formula for the lateral area of a cone as pi r l. So pi r I is equal to pi times r, the radius of the base, which is 5.
Problem 29. OK.
OK, figure ABCD is a kite. And it looks like a kite. What is the area of figure ABCD in square centimeters.
The area of a triangle is equal to 1/2 base times height. So what's the area of this triangle? Well, actually, this is symmetric.
So the area of this one is 6 times 8 is 48. 48 times 1/2 is 24. This one is also going to be 24 by the same argument.
Now, this triangle, 8 times 15 times 1/2. That's 4 times 15, which is equal to 60.
60. We don't even have to multiply by 1/2, because we're going to multiply by 2 eventually. Or add it to each other again.
Anyway, if a cylindrical barrel measures 22 inches in diameter, how many inches will it roll in 8 revolutions along a smooth surface? So we could imagine a wheel. It's a tire of some kind.
That distance right there is 22. And what they say is, this thing is going to roll 8 revolutions on a smooth surface. It's going to go around 8 times.
So if you think about it, it's going to cover its circumference 8 times. If this point is starting touching the ground, after it moves a circumference of distance, that point will be touching the ground again. An easy way to think about it is, as this thing moves to the right, as it rolls, when it moves 1 foot, 1 foot along of circumference will then be touching the ground.
Then 2 inches along its circumference will be touching the ground. So it's going to go 8 circumferences in 8 revolutions. So what's the circumference of this?
Circumference is equal to pi times the diameter. The diameter they already gave us is 22.
So the circumference is equal to 22 pi. So it's going to move 8 circumferences in 8 revolutions. So 22 pi times 8 is 176 pi.
[Teacher]
My name?
Good!
Yours?
Yeah!
Anne, Anne, good!
My name?
[Girl signing] Miriam.
[Teacher]
Good!
Good, good.
Yours?
Your name?
Uh uh, you are not Anne.
My name? Hmm.
Yours, yours, yours.
[Boy]
Yours, yours, yours.
[Teacher]
Hmm.
What is her name?
[Girl signing] "Beautiful"
[Teacher]
Yeah, beautiful.
She's very good in taking in the sign language.
It's very important to have because she can now be communicating to other people.
While she was at home there was no sign language being taught there.
Are you happy, happy, happy, happy, happy?
[Teacher]
Yeah, happy, happy, happy, happy. [Child signing]
I'm happy to be at school.
[Teacher speaking and child signing]
True.
Everyday... you... come... school.
Yes.
[Signing and interpretation]
These six year olds are so happy to finally be able to express themselves and communicate with others.
It is only by learning sign language that deaf children can fully communicate.
Today, deaf children and young people worldwide are too often denied their right to education.
This is because of a lack of teachers well-trained in sign language and a lack of awareness by parents that their children can and have a right to go to school.
Sign language is mandatory if these deaf people are going to learn.
Without it they cannot.
So it is a mother language that helps them to communicate with others.
So without this it means the communication will be at zero.
And without communication then you cannot impart skills.
Here we shall learn about the Europeans who came to East Africa... why the Europeans came to Kenya.
Lucy?
[Signing]
To get land.
[Teacher]
Ok, you can say to get land.
Another one?
[Signing]
They came to trade. [Teacher]
They came to trade.
That's right.
Uh huh.
Another one?
[Signing]
Economic reasons.
The economic reason is similar to the trades... whereby they came to trade.
Ok?
Understand well.
It's possible for the deaf to learn anything, but what should happen is that they should have people who can communicate to them very well.
People who can use sign language.
People who understand the way they react.
You look at their face, how they are communicating, their body.
The teachers come here and they teach very well and I understand.
[Elizabeth Gituku]
It is very important that we have learning opportunities so that they also join the other citizens in careers that will make them stand on their own, make them independent and also support their own families.
I wish to become a teacher teaching small children in primary schools.
[Signing and interpretation]
I would like to become a pharmacist.
[Signing and interpretation]
I would wish to become a doctor or a lawyer.
Majority of the colleges, over ninety percent, they actually have no support for the deaf people.
[Signing and interpretation]
For example, myself, I struggled very hard to get accounting.
I had passed well in the mathematics, but there was no college which was accepting me.
[Signing and interpretation]
So if I go to the university and I find that there is no interpreter,
I will look for a person who can help me to interpret because it is hard for me to follow something which is happening without an interpreter or that... if the teacher is not using sign language.
[Signing and interpretation]
In class, we don't have an interpreter but I learn together with others.
So I sit with a person and when the lecturer is writing something or is teaching
I always copy from my friend.
If I have a question, I write it down and pass it to this person who is hearing and will ask the lecturer to explain.
[Speaking softly]
We are set back because we [our] disability [?] only affects the ear, not the mind.
The mind of deaf children is as well as someone who's hearing.
[Clapping and murmuring]
Being denied the human right to education in sign language has long-term consequences.
If deaf children do not develop the ability to communicate, they are unable to learn and get jobs and are isolated within their communities.
[Signing]
I love to learn sign language.
Let's see if we can use our example to understand the 3 types of income statements and hopefully understanding those income statements will also help us understand this example.
So I'm gonna start of, we're gonna focus on month 2 and what I've done is I've rewritten some of this accrual income statement down here so it really looks like a statement so this right here is the income statement for month 2 on an accrual basis.
And that month, we said we had $400 of revenue, $200 of expense, $400 minus $200 gives us $200 of income.
And income statement tells us what happened over a period of time, what was the activity?
How much revenue, how much expenses, and other things this is just a super simplified one, without taxes without interest, without other types of expenses over here.
I also have drawn the balance sheet at the end of month 1 and the balance sheet at the end of month 2.
Or you could also view this balance sheet here as the balance sheet at the beginning of month 2.
And the main thing to realize is the income statement tells you what happens over a time period, while balance sheets are snapshots, or they're pictures at a given moment.
Snapshots.
So this tells us essentially, what did I have?
The assets are the things that can give me future benefits. So what do I have, and the liabilities are things that I have to give future benefit to, or things that I owe so this is what I have, this is what I owe, and then the equity is really what I have to my name if I net out the liabilities from the assets.
So the beginning of month 2, which is the end of month 1,
I had $100 of cash, no accounts receiveables,
I didn't owe anyone anything,
I didn't owe them money, I didn't owe them services
So $100 minus 0, means I had $100, that's kind of what the owners of the company can say they have of value at the beginning of the month.
You fast forward, now at the end of the month 2
I now owe the bank $100,
So I just put this as negative $100 here, it normally wouldn't be accounted that way on an actual company's balance sheet, but just to simplify it,
But I have an accounts receivable of $400, so my total assets now are $300 of assets, remember, accounts receivables aren't assets, because someone owes me something, someone owes me cash in the future.
I still have no liabilities
So you take all of your assets, minus all of your liabilities, and now I have $300 in equity.
So you can see the snapshot at the beginning of the month: $100 in equity snapshot at the end of the month: $300 in equity.
And so to go from one point to the other, to go from $100 to $300,
I must have grown in equity by $200,
I must have gotten $200 worth of value from someplace and that's what the income statement describes.
It describes it right over here the change in equity, sometime the change in retained earnings, or just change in equity, that is going to be the $200 in net income that the company got over that time period.
Now there's one thing that you're probably confused by right now well you know, how do we reconcile everything with the cash we know that over this period we got $200 in income on an accrual basis.
But when you look at the cash, we went from $100 positive cash, to negative $100 in cash. It looks like we lost $200.
So how can we reconcile the fact that we got $200 income?
How can we reconcile that with the fact that we lost $200 in cash?
And that reconciliation is going to be done on the cash flow statement, and I'll do that in the next video.
Now that we've got the basics of order of operations out of the way, let's try to tackle a really hairy and beastly problem.
So here, we have all sorts of parentheses and numbers flying around.
But in any of these order of operations problems, you really just have to take a deep breath and remember, we're going to do parentheses first.
Parentheses.
P for parentheses.
Then exponents.
Don't worry if you don't know what exponents are, because this has no exponents in them.
Then you're going to do multiplication and division.
They're at the same level.
Then you do addition and subtraction.
So some people remember PEMDAS.
But if you remember PEMDAS, remember multiplication, division, same level.
Addition and subtraction, also at the same level.
So let's figure what the order of operations say that this should evaluate to.
So the first thing we're going to do is our parentheses.
And we have a lot of parentheses here.
We have this expression in parentheses right there, and then even within that we have these parentheses.
So our order of operations say, look, do your parentheses first, but in order to evaluate this outer parentheses-- this orange thing-- we're going to have to evaluate this thing in yellow right there.
Well, if we look at just inside of it, the first thing we want to do is simplify the parentheses inside the parentheses.
So you see this 5 minus 2 right there?
We're going to do that first no matter what.
And so this simplifies to-- I'll do it step by step.
Once you get the hang of it, you can do multiple steps at once.
So this is going to be 7 plus 3 times the 5 minus 2, which is 3.
And all of those have parentheses around it.
I want to copy and paste that right there.
It would've been easier-- let me just rewrite it.
I'm having technical difficulties.
So divided by 4 times 2.
And on this side, you had that 7 times 2 plus this thing in orange parentheses there.
We always want to do parentheses first.
So we have to evaluate this thing first.
But in order to evaluate this thing, we have to look inside of it.
And when you look inside of it, you have 7 plus 3 times 3.
So if you just had 7 plus 3 times 3, how would you evaluate it?
Well, look back to your order of operations.
We're inside the parentheses here, so inside of it there are no longer any parentheses.
So the next thing we should do...
There are no exponents.
The next thing is multiplication.
So we do that before we do any addition or subtraction.
So we want to do the 3 times 3 before we add the 7.
7 plus 9.
That's going to be in the orange parentheses.
And then you have the 7 times 2 plus that, on the left hand side.
You have the divided by 4 times 2 on the right hand side.
And now this-- the thing in parentheses-- because we still want to do the parentheses first.
7 plus 9 is 16.
And so everything we have simplifies to 7 times 2 plus 16 divided by 4 times 2.
Now we don't have any parentheses left, so we don't have to worry about the P in PEMDAS.
We have no E, no exponents in this.
So then we go straight to multiplication and division.
We have a multiplication-- we have some multiplication going on there.
We have some division going on here, and a multiplication there.
So we should do these next, before we do this addition right there.
7 times 2 is 14.
And then here we have a 16 divided by 4 times 2.
That gets priority of the addition, so we're going to do that before we do the addition.
But how do we evaluate that?
Do we do the division first, or the multiplication first?
And remember, I told you in the last video, when you have 2-- when you have multiple operations of the same level-- in this case, division and multiplication-- they're at the same level.
You're safest going left to right.
So you do 16 divided by 4 is 4.
It simplifies to 4 times 2.
So this is going to simplify to-- because multiplication takes priority over addition-- this simplifies to 8.
And so you get 14-- this 14 right here-- plus 8.
And what's 14 plus 8?
That is 22.
That is equal to 22.
And we are done.
Solve for x and check your solution.
We have x divided by 3 is equal to 14.
So to solve for x, to figure out what the variable x must be equal to, we really just have to isolate it on the left hand side of this equation
It's already sitting there.
And we have x divided by 3 is equal to 14
We could also write this as 1/3 x =14.
Obviously x*1/3 is going to be x/3.
These are equivalent.
So how can we just end up with x on the left hand side of either of these equations?
These are really the same thing.
Or another way, how can we just have a 1 in front of the x
A 1x, which is really just saying x over here
Well, I'm dividing it by 3 right now
So if I were to multiply both sides of this equation by 3 that would isolate the x And the reason that would work is if I multiply this by 3 over here
I'm multiplying by 3 and dividing by 3 that's equivalent you would just, that's equivalent to multiplying or dividing by 1 these guys cancel out
But remember, if you do it to the left hand side you also have to do it to the right hand side And actually, I'll do both of these equations at the same time Cuz they're really the exact same equation
So what are we going to get over here on the left hand side?
3 times anything divided by 3 is going to be that anything we're just going to have an x left over on the left hand side
And on the right hand side what's 14*3 310 is 30, 34 is 12, so it's going to be 42
So we get x=42 And the same thing would happen here 3*1/3 is just 1
So you get 1x is equal to 14*3 which is 42 now let's just check our answer
let's substitute 42 into our original equation
So we have 42 in place for x in place for x over 3 is equal to 14
So what's 42 divided by 3 And we could do a little bit of
I guess we'd call it medium long division
It's not really long division. 3 into 4, 3 goes into 4 one time 1*3 is 3
You subtract:
4-3 is 1
Bring down the 2 3 goes into 12 four times
So 3 goes into 42 14 times
So this right over here simplifies to 14 And it all checks out
So we're done.
I think what is probably the most misunderstood concept in all of science and, as we all know, is now turning into one of the most contentious concepts - may be not in science, but in our popular culture - is the idea of evolution.
Evolution.
And whenever we hear this word - I mean: even if we don't hear in in the biological context -, we imagine that something is changing, it is evolving, and so when people use the word evolution in its everyday context, they think of this notion of change that, you know, - this is going to test my drawing ability - , but they, you know:
You see an ape, bent over, we've all seen this picture at the natural museum and he is walking hunchback like that, and his head's bent down, and
- well, I'm doing my best - that's the ape, and may be is also wearing a hat and then they show this picture where he slowly slowly becomes more and more upright and eventually he turns into some dude who is just walking on his way to work, also just as happy.
And now he is walking completely upright and - you know - there is some kind of implication that walking upright is better than not walking upright, and - oh he doesn't have a tail anymore.
Let me eliminate that.
This guy does have a tail.
And let me do it in a appropriate width.
You are gonna have to excuse my drawing skills.
But we've all seen this, if you have ever gone to a natural history museum.
They'll just make more and more upright apes and eventually you get to a human being.
And there is this idea that the apes somehow changed into a human being. and I've seen this in multiple contexts and even inside of biology classes and even in the scientific community they'll say: oh the ape evolved into the human or the ape evolved into the pre-human: the guy that almost stood upright, you know, the guy that was a little bit hunched back, he looked a little bit like an ape and a little bit like a human and so on and so forth.
And I want to be very clear here:
Even though this process did happen, that you did have creatures that over time accumulated changes, that maybe their ancestors might have looked more like this and eventually they looked more like this.
There was no active process going on, called evolution.
It was not like the ape said:
Gee, I would like my kids to look more like this dude.
So somehow I'm gonna get my DNA to get enough changes to look more like this.
It is not like the DNA knew.
The DNA didn't say:
Hey, it is better to be walking than to be kind of hunched back like an ape and you know therefore I'm going to try to somehow spontaneously change into this dude.
That is not what evolution is.
It is not like - you know - some people imagine that:
Maybe there was a tree.
There is a tree and on that tree there is a bunch of good fruit at the top of the tree.
There is a bunch of good fruit at the top of the tree.
Maybe they are apples.
And then maybe, you know, you have some type of cow-like creature, or maybe it is some type of horse-like creature.
It says:
Gee, I would like to get to those apples.
And that - you know - just because they want to get to those apples, may be the next generation.... they keep trying to raise their neck, and then after generation after generation, their necks get longer and longer and eventually they turn into giraffes.
That is not what evolution is and that is not what evolution implies, although sometimes the everyday notion of the word seems to make us think that way.
What evolution is, and actually this is the word that I prefer to use, it's natural selection.
Natural selection, let me write that word down.
Natural selection.
And literally what it means is that in any population of living organisms you're going to have some variation.
And this is an important key-word here.
Variation just means:
Look, there is just some change
If you look at the kids in your school, you'll see variations.
Some people are tall, some people are short, some people have blond hair, some people have black hair.
So on and so forth.
There is always variation. and what natural selection is, is this process that sometimes environmental factors will select for certain variations.
Some variation might not matter at all, but some variations matter a lot.
One example that is given in every biology book, but it really is interesting, is
I believe they are called the peppered moth, and this was in pre-industrial revolution England, that these moths, that some of the moths were - let me see if I can draw a moth to give you the idea, you know, let me draw a couple of them, let me draw a few peppered moths.
A couple of peppered moths there.
Let me draw one more.
So, most peppered moths there was just this variation, some of them were I guess we could call them more peppered than others.
So, some of them might look like this, you know.
No let me do another colour.
Let's do white.
So it has spots like that, some of them might have looked more like that.
And of course they also had some black spots on them.
And then some of them might have been, you know, almost - barely have any spots.
You just have this natural variation like you would see in any population of animals.
You'll see some variation in colours .
Now they were all happy, probably for thousands of years, just this natural variation.
Just this it was a non-important trait for these peppered moths but then all of a sudden the industrial revolution happens in England, and all of this soot gets released from all of these factories that are running these steam engines powered by coal, and so, all of a sudden all of these things that once were grey or white, for example maybe some tree trunks - let me draw some tree trunks - may there were some tree trunks that used to look like this, you know, may be it looked like a maybe it kept the, maybe some tree trunks looked something like this and a peppered moth would be pretty OK, maybe there were some tree trunks were pretty dark, but all of a sudden the industrial revolution happened, everything gets covered with soot from the coal being burned and then all of a sudden all the trees look like this:
They are completely pitch black or they are a lot darker than they were before.
Now all of a sudden you have had a major change to these moths' environment, and you have to think:
What is going to select for these moths?
Well, one thing that might get these moths are birds and the ability of these birds to see the moths.
So all of a sudden if the environment became a lot blacker than it was before you can guess what is going to happen:
The birds are gonna see this dude a lot easier than they are gonna see this dude, cause this dude on the black background is gonna be a lot harder to see.
And it is not like the birds won't catch this guy, they'll catch all of them, but they're gonna catch this guy a lot more frequently.
So you can imagine what happens if the birds start catching these guys before they can reproduce or may be while they are reproducing what's going to happen:
This guy, the darker dudes are going to reproduce a lot more often and all of a sudden you're gonna have a lot more moths that look like this.
You're gonna have a lot more of these dudes.
So what happened here?
Was there any design or was there any active change by any of the moths?
It looks like a really smart thing to do, to become black.
Your surroundings became black and you wait for a couple of generations of these moths and all of a sudden the moths are black and you say:
Wow, these moths are geniuses.
They all somehow decided to evolve into black moths in order to hide from the birds more easily.
But that is not what happened.
You had a lot of variation in your peppered moth population and what happened was that when everything turned darker and darker, these dudes right here, and dudettes, had a lot less success in reproducing.
These guys just reproduced more and more and more and these guys got eaten up before they were able to reproduce or may while they were reproducing so that they couldn't produce as many offspring and then this trait became dominant. and then the peppered moth became - you can kind of view it as a black moth.
Now you might say:
OK Sal, that is one example, but I need more.
This is natural selection, this is purported to apply to everything, it purports to explain why we evolved from basic bacteria or maybe from self replicating RNA which I will talk about more in the future.
You know, I need more evidence of this - you know - I need to see it in real time. and the best example of this is really the flu is really the flu.
And I'll do other videos in the future on what viruses are and how they replicate and viruses actually are fascinating, because it is not actually clear that they are alive, they're literally just little buckets of DNA and sometimes RNA which we'll learn is genetic information and they're just contained in these viral... these little protein containers that are these neat geometrical shapes and that's all they are, they really don't have - you know - they are not like regular living organisms, that actively move and that actively have metabolisms and all that.
What they do is they take that little DNA and then they inject it into other things that can process it and then they use that DNA to produce more viruses.
But anyway, I could, we could do a whole series of videos on viruses, but the flu is a virus and what happens every year is that you have a certain type of virus a certain type of virus and they have some variation and I'll just make the variation by how many dots they have. how many dots they have and they, in fact, - let's say it is a human flu, they infect humans - and slowly our immune systems, which we could make a whole set of videos on as well, start to recognize the virus and are able to attack them before they can do a lot of damage.
So now you can imagine what happens, if let's say this is the current flu, let me do all of them, they all have these little two dots and that's how and we'll talk in the future about what these dots are. and how they can be recognized, but let's say that's how our immune system recognizes them. they start realizing:
O, any time I get this little green dude with 2 dots on it, that is not a good thing to have around.
So I am going to attack it in some way and destroy it before he infects my immune system and DNA and all the rest.
And so you have a very strong natural selection once immune systems learn what this virus is and we'll talk more about what learning means for an immune system. that they'll start attacking these guys, right?
But flu , you can kind of think of them as being tricky, but they are not really tricky, they are not sentient objects.
But what they do do:
They constantly change. so what you have in any flu population, you're always having a little bit of change, so may be the great majority of them have those two dots, but may be every now and then one of them has one dot, one of them has 3 dots, and maybe that is just a random mutation, this just randomly happened, maybe one in every - I'll make up a number - one in every million of these viruses has this only one dot instead of two dots, but what's gonna happen as soon as the human immune system gets used to attacking the virus with the two red dots, well then this guy isn't gonna have to compete with the other virus capsules for infecting people he's going to have people's DNA all to himself.
He or she or what ever you want to call this virus, is then going to be more successful so by next year's flu season when people start sneezing and are able to spread it on door knobs and whatever else again, This guy is going to be the new flu virus.
So when you see this process of every year there is a new flu virus, that is evolution and natural selection in real time.
It is happening!
It isn't this thing that only happens over eons and eons of time.
Although most of the substantial things that we see in our lives or even in ourselves are based on these things that happened over eons and eons of time, but it happens on a yearly basis.
Another example is if you think about antibiotics and bacteria.
Bacteria are these little cells that move around and we'll talk more about them, they are definitely living, they have metabolisms and whatever else.
And so this is just a nice thing to know: When people talk about infections it could either be a viral infection which are these things that go and infect your DNA and then use your cell mechanisms to reproduce or it could be a bacterial infection which are literally little cells and they move around and they release toxins that make you sick and whatever else, so bacteria these are what antibiotics kill.
Anti-biotics.
Actually I don't think there is a hyphen:
Antibiotics.
They attack bacteria, they kill them.
Now you've probably, if you know a couple of doctors or whatever, and you say:
Hey I am sick, I think I have bacterial infection, give me some antibiotics, a responsible doctor says:
No I shouldn't give you antibiotics just willy nilly, because what happens is that the more antibiotics you use, you're more likely to create versions and I want to be very careful about the word create, because you are not actively creating them, but let's say
- and let me finish my sentence - you are very likely to help select for antibiotic-resistant bacteria.
Now how does that work?
Now let's say this is a green let's say that these are all bacteria and you have bazillions of them, right?
And every now and then, you get one that is slightly different.
Now in a random population of bacteria these all will make you equally sick and this is just some random difference in the bacteria may be on his DNA some slightly different changes happened, but whatever happened, these all are the kind of bacteria that you don't want to get a lot of them in your system.
If you get a lot of them they might kill you or make you sick or whatever else.
(Potter Puppet Pals theme opens) (ticking) What is that mysterious ticking noise?
Look over there... Hmm, kind of catchy (sings with ticking) Snape, Snape,
(All) Sing our song... ...all day long at... ...Hog-gg-ggwarr-rr-rts -I found the source of the ticking!
It's pipe bomb!
(Harry and Hermonie cheers) (explodes) Mwah-ha-ha-ha!
(Cane taps) Voldemort, Voldemort.
Oooh, Ahh Voldy, Voldy, Voldemort! (music "Wha, wha, whaaaa")
Consider the numbers 1/3 , 7 , -15
To which of these sets of numbers these numbers belong to.
Lets review each of these
Natural numbers are counting numbers not equal 0. it is 1,2,3,... so on and so forth
The whole numbers are natural numbers plus 0
Whole numbers are 0,1,2,3,4
The integers is the whole numbers plus opposite of it
It is whole numbers plus negative of natural numbers
like -4,-3,-2,-1 0, 1, 2, 3,4, ... so on and so forth rational numbers are numbers that can be expressed as a ratio of two integers.Rational number can be expressed as m/n where m and n are integers and n cannot be 0 as anything divided by 0 is not defined.
But m could be 0 as 0 can be expressed as 0/1 or 0/2 or 0/3 or 0/-537 these are all representations of 0
Irrational numbers are numbers that cannot be expressed as ratios of integers examples of irrational numbers are numbers that keeps repeating on and on and on π, √2 are examples of irrational numbers and then real numbers are really all of these combined if you are combining the rational numbers and irrational numbers you are talking about real numbers.every real number is either rational or irrational.
lets classify what we have 1/3 is not a natural number as it is not a counting number.
It is not a whole number it is not an integer.is it a rational number sure it is as 1 and 3 are integers. so 1/3 is a rational number.if something is rational it cannot be irrational and it is also a real number
lets try 7 number 7 is a natural number, whole number any natural is a whole number any natural and whole number si an integer so 7 is also a integer. any number that is natural, whole and integer is a rational number. we can write 7 as 7/1 we can write any integer as that number / 1 if it is rational it cannot be irrational. it is also going to be real we have -15. it is not a natural number natural number are positive integers only it is not a whole number it is an integer, it is the opposite of +15 it is rational as it can be written as -15/1 and because it is rational it cannot be irrational it is also real.
A line goes through the points (-1, 6) and (5, 4).
What is the equation of the line?
Let's just try to visualize this.
So that is my x axis.
And you don't have to draw it to do this problem but it always help to visualize
That is my y axis.
And the first point is (-1,6)
So (-1, 6).
So negative 1 coma, 1, 2, 3, 4 ,5 6.
So it's this point, rigth over there, it's (-1, 6).
And the other point is (5, -4).
So 1, 2, 3, 4, 5.
And we go down 4, So 1, 2, 3, 4
So it's rigth over there.
So the line connects them will looks something like this.
Line will draw a rough approximation.
I can draw a straighter than that.
I will draw a doted line maybe
Easier do doted line.
So the line will looks something like that.
So let's find its equation.
So good place to start is we can find its slope.
Remember, we want, we can find the equation y is equal to mx plus b.
This is the slope-intercept form where m is the slope and b is the y-intercept.
We can first try to solve for m.
We can find the slope of this line.
So m, or the slope is the change in y over the change in x.
Or, we can view it as the y value of our end point minus the y value of our starting point over the x-value of our end point minus the x-value of our starting point.
Let me make that clear.
So this is equal to change in y over change in x wich is the same thing as rise over run wich is the same thing as the y-value of your ending point minus the y-value of your starting point.
This is the same exact thing as change in y and that over the x value of your ending point minus the x-value of your starting point
This is the exact same thing as change in x.
And you just have to pick one of these as the starting point and one as the ending point.
So let's just make this over here our starting point and make that our ending point.
So what is our change in y?
So our change in y, to go we started at y is equal to six, we started at y is equal to 6.
And we go down all the way to y is equal to negative 4
So this is rigth here, that is our change in y
You can look at the graph and say, oh, if I start at 6 and I go to negative 4 I went down 10. or if you just want to use this formula here it will give you the same thing
We finished at negative 4, we finished at negative 4 and from that we want to subtract, we want to subtract 6.
This right here is y2, our ending y and this is our beginning y
This is y1.
So y2, negative 4 minus y1, 6. or negative 4 minus 6.
That is equal to negative 10.
And all it does is tell us the change in y you go from this point to that point
We have to go down, our rise is negative we have to go down 10.
That's where the negative 10 comes from.
Now we just have to find our change in x.
So we can look at this graph over here.
We started at x is equal to negative 1 and we go all the way to x is equal to 5.
So we started at x is equal to negative 1, and we go all the way to x is equal to 5.
So it takes us one to go to zero and then five more.
So are change in x is 6.
You can look at that visually there or you can use this formula same exact idea, our ending x-value, our ending x-value is 5 and our starting x-value is negative 1. 5 minus negative 1. 5 minus negative 1 is the same thing as 5 plus 1.
So our slope here is negative 10 over 6. wich is the exact same thing as negative 5 thirds. as negative 5 over 3 I devided the numerator and the denominator by 2.
So we now know our equation will be y is equal to negative 5 thirds, that's our slope, x plus b.
So we still need to solve for y-intercept to get our equation.
And to do that, we can use the information that we know in fact we have several points of information
We can use the fact that the line goes through the point (-1,6) you could use the other point as well.
We know that when is equal to negative 1,
So y is eqaul to 6.
So y is equal to six when x is equal to negative 1
So negative 5 thirds times x, when x is equal to negative 1 y is equal to 6.
So we literally just substitute this x and y value back into this and know we can solve for be.
So let's see, this negative 1 times negative 5 thirds.
So we have 6 is equal to positive five thirds plus b.
And now we can subtract 5 thirds from both sides of this equation. so we have subtracted the left hand side.
From the left handside and subtracted from the rigth handside
And then we get, what's 6 minus 5 thirds.
So that's going to be, let me do it over here
We take a common denominator.
So 6 is the same thing as
Let's do it over here.
So 6 minus 5 over 3 is the same thing as 6 is the same thing as 18 over 3 minus 5 over 3 6 is 18 over 3.
And this is just 13 over 3.
And this is just 13 over 3.
And then of course, these cancel out.
So we get b is equal to 13 thirds.
So we are done.
We know
We know the slope and we know the y-intercept.
The equation of our line is y is equal to negative 5 thirds x plus our y-intercept which is 13 which is 13 over 3.
And we can write these as mixte numbers. if it's easier to visualize.
13 over 3 is four and 1 thirds.
So this y-intercept right over here. this y-intercept right over here.
That's 0 coma 13 over 3 or 0 coma 4 and 1 thirds.
And even with my very roughly drawn diagram it those looks like this.
And the slope negative 5 thirds that's the same thing as negative 1 and 2 thirds.
You can see here the slope is downward because the slope is negative.
It's a little bit steeper than a slope of 1.
It's not quite a negative 2.
It's negative 1 and 2 thirds. if you write ithis as a mixt number.
So, hopefully, you found that entertaining.
In the beginning the web was simple, connected open, safe designed as a force for good it would become something far greater a living, breathing ecosystem in service of humanity a public resource for innovation and opportunity.
A place to build your dreams.
But in those early days, like any ecosystem, the web needed nurturing.
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Popups.
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Users began to ask... is this it? or could the web be something better?
A small group of people coders, designers, idealists believed it could.
They had an audacious idea.
That a tiny non-profit and a global community could build something better and force new ideas and innovation on to the Web.
They called it the Mozilla project.
They began by making a new kind of Web browser.
What we know today as Firefox. And they made it a non-profit, so it would always put the people who use the web first. more than software, it was a platform that anyone could use to build on their ideas.
The nuisances diminished.
The foundations of the Web we know today began to appear
Now the Web is a place where you can build almost anything you can imagine
Mozilla and Firefox exist to help people everywhere seize this opportunity and to stand up for users in a world where choice and control are too often at risk.
But what if Firefox was just the beginning?
What if it was part of something bigger?
From user privacy to Firefox Mobile, to apps and identity, we're pushing the boundaries of the web every day. And we are going beyond software.
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Let's do another states of matter phase change problem.
And we'll deal with water again.
But this one hopefully will stretch our neurons a little bit further.
So let's say I have 500 grams of water.
Of liquid water.
At 60 degrees Celsius.
Now my goal is to get it to zero degrees Celsius.
And the way I'm going to do it is, I'm going to put ice into this 500 grams of water.
And my ice machine at home makes ice that comes out of the machine at minus 10 degrees Celsius ice.
And my question is, exactly how much ice do I need?
So how much, or how many grams of ice? And I'm going to take the ice out of the freezer and just plop it into my liquid.
How much do I need to bring this liquid, this 500 grams of
liquid water, down to zero degrees?
So the idea, if we just imagine a cup here.
Let me draw a cup.
This is a cup. I have some 60 degree water in there.
I'm going to plunk a big chunk of ice in there.
And what's going to happen is that heat from the water is going to go into the ice.
So the ice is going to absorb heat from the water.
So in order for water to go from 60 degrees to zero degrees, I have to extract heat out of it.
And we're about to figure out just how much heat.
And so we have to say, whatever was extracted out of the water, essentially has to be contained by the ice.
And the ice can't get above zero degrees. Essentially, that amount of ice has to absorb all that heat to go from minus 10 to zero.
And then also, that energy will be used to melt it a bit.
But if we don't have enough ice, then the ice is going to go beyond that and then warm up even more. So let's see how we do this.
So how much energy do we have to take out of the 500 grams of liquid water?
Well, it's the same amount of energy that it would take to put into zero degrees liquid water and get it to 60 degrees.
So we're talking about a 50 degree change.
So the energy or the heat out of the water is going to be the specific heat of water, 4.178 joules per grams Kelvin.
And I have to multiply that times the number of grams of water I have to cool down, I have to take the heat out of.
And we know that's 500 grams.
And then I multiply that times the temperature differential that we care about.
And just a side note, I use this specific heat because we're dealing with liquid water.
So the final thing, I have to multiply it by the change in temperature.
The change in temperature is 60 degrees.
Times 60 degrees.
There's a little button on the side of my pen, when I press it by accident sometimes it does that weird thing.
So let's see what this is. So this is 4.178 times 500 times change of 60 degrees.
It could be a change of 60 degrees Kelvin or a change of 60 degrees Celsius.
It doesn't matter. The actual difference is the same, whether we're doing
Kelvin or Celsius.
And it's 125,340 joules.
So this is the amount of heat that you have to take out of 60 degree water in order to get it down to zero degrees.
Or the amount of heat you have to add to zero degree water to get it to 60 degrees.
So essentially, our ice has to absorb this much energy without going above zero degrees.
So how much energy can the ice absorb? Well let's set a variable. The question is how much ice.
So let's set our variable, maybe we'll call it I.
Let's do x. x is always the unknown variable.
So we're going to have x grams of ice.
OK, and it starts at minus 10 degrees.
So when this x grams of ice warms from minus 10 degrees to zero degrees Celsius, how much energy will it be absorbing?
So to go from minus 10 degrees Celsius to zero degrees
Celsius, the heat that's absorbed by the ice is equal to-- is equal to the specific heat of ice, ice water, 2.05 joules per gram Kelvin, times the amount of ice.
That's what we're solving for.
So times x.
Times the change in temperature.
So this is a 10 degree change in Celsius degrees, which is also a 10 degree change in Kelvin degrees.
We can just do 10 degrees. I could write Kelvin here, just because at least when I wrote the specific heat units, I have a Kelvin in the denominator.
It could have been a Celsius, but just to make them cancel out.
This is, of course, x grams. So the grams cancel out.
So that heat absorbed to go from minus 10 degree ice to zero degree ice is 2.05 times 10 is 20.5.
So it's 20.5 times x joules. This is to go from minus 10 degrees to zero degrees.
Now, once we're at zero degrees, the ice can even absorb more energy before increasing in temperature as it melts.
Remember, when I drew that phase change diagram.
The ice gains some energy and then it
levels out as it melts.
As the the bonds, the hydrogen bonds start sliding past each other, and the crystalline structure breaks down.
So this is the amount of energy the ice can also absorb.
Zero degree ice to zero-- I did it again-- to zero degree water.
Well the heat absorbed now is going to be the heat of fusion of ice.
Or the melting heat, either one. That's 333 joules per gram.
It's equal to 333.55 joules per gram times the number of grams we have.
They cancel out. So the ice will absorb 333.55 joules as it goes from zero degree ice to zero degree water.
Or 333.55x joules. Let me put the x there, that's key.
So the total amount of heat that the ice can absorb without going above zero degrees.
Because once it's at zero degree water, as you put more heat into it, it's going to start getting warmer again.
If the ice gets above zero degrees, there's no way it's going to bring the water down to zero degrees.
The water can't get above zero degrees. So how much total heat can our ice absorb? So heat absorbed is equal to the heat it can absorb when it goes from minus 10 to zero degrees ice.
And that's 20.5x.
Where x is the number of grams of ice we have.
Plus the amount of heat we can absorb as we go from zero degree ice to zero degree water.
And that's 333.55x.
And of course, all of this is joules.
So this is the total amount of heat that the ice can absorb without going above zero degrees.
Now, how much real energy does it have to absorb?
Well it has to absorb all of this 125,340 joules of energy out of the water.
Because that's the amount of energy we have to extract from the water to bring it down to zero degrees.
So the amount of energy the ice absorbs has to be this 125,340.
So that has to be equal to 125,340 joules.
We can do a little bit of algebra here.
Add these two things.
20.5x plus 333.55x is 354.05x.
Is that right? Yeah, 330 plus 30 is 350.
Then you have a 3 with a 0.5 there.
354.05x and that is equal to the amount of energy we take out of the water.
You divide both sides.
So x is equal to 125,340 divided by 354.05.
I'll take out the calculator for this.
The calculator tells me 125,340, the amount of energy that has to be absorbed by the ice, divided by 354.05 is equal to 354 grams.
So actually, just to be careful maybe I'll take 355 grams of ice.
Because I definitely want my water to be chilled.
So our answer is x is equal to 354.02 grams of ice. So this is interesting. I had 500 grams of liquid.
And you know, intuitively I said, well if I have to bring that down to zero degrees, I'd have to have a ton of ice.
But it turns out, I only need, what was the exact number?
Motor racing is a funny old business.
We make a new car every year, and then we spend the rest of the season trying to understand what it is we've built to make it better, to make it faster.
And then the next year, we start again.
Now, the car you see in front of you is quite complicated.
The chassis is made up of about 11,000 components, the engine another 6,000, the electronics about eight and a half thousand.
So there's about 25,000 things there that can go wrong.
So motor racing is very much about attention to detail.
The other thing about Formula 1 in particular is we're always changing the car.
We're always trying to make it faster.
So every two weeks, we will be making about 5,000 new components to fit to the car.
Five to 10 percent of the race car will be different every two weeks of the year.
So how do we do that?
Well, we start our life with the racing car.
We have a lot of sensors on the car to measure things.
On the race car in front of you here there are about 120 sensors when it goes into a race.
It's measuring all sorts of things around the car.
That data is logged.
We're logging about 500 different parameters within the data systems, about 13,000 health parameters and events to say when things are not working the way they should do, and we're sending that data back to the garage using telemetry at a rate of two to four megabits per second.
So during a two-hour race, each car will be sending 750 million numbers.
That's twice as many numbers as words that each of us speaks in a lifetime.
It's a huge amount of data.
But it's not enough just to have data and measure it.
You need to be able to do something with it.
So we've spent a lot of time and effort in turning the data into stories to be able to tell, what's the state of the engine, how are the tires degrading, what's the situation with fuel consumption?
So all of this is taking data and turning it into knowledge that we can act upon.
Okay, so let's have a look at a little bit of data.
Let's pick a bit of data from another three-month-old patient.
This is a child, and what you're seeing here is real data, and on the far right-hand side, where everything starts getting a little bit catastrophic, that is the patient going into cardiac arrest.
It was deemed to be an unpredictable event.
This was a heart attack that no one could see coming.
But when we look at the information there, we can see that things are starting to become a little fuzzy about five minutes or so before the cardiac arrest.
We can see small changes in things like the heart rate moving.
These were all undetected by normal thresholds which would be applied to data.
So the question is, why couldn't we see it?
Was this a predictable event?
Can we look more at the patterns in the data to be able to do things better?
So this is a child, about the same age as the racing car on stage, three months old.
It's a patient with a heart problem.
Now, when you look at some of the data on the screen above, things like heart rate, pulse, oxygen, respiration rates, they're all unusual for a normal child, but they're quite normal for the child there, and so one of the challenges you have in health care is, how can I look at the patient in front of me, have something which is specific for her, and be able to detect when things start to change, when things start to deteriorate?
Because like a racing car, any patient, when things start to go bad, you have a short time to make a difference.
So what we did is we took a data system which we run every two weeks of the year in Formula 1 and we installed it on the hospital computers at Birmingham Children's Hospital.
We streamed data from the bedside instruments in their pediatric intensive care so that we could both look at the data in real time and, more importantly, to store the data so that we could start to learn from it.
And then, we applied an application on top which would allow us to tease out the patterns in the data in real time so we could see what was happening, so we could determine when things started to change.
Now, in motor racing, we're all a little bit ambitious, audacious, a little bit arrogant sometimes, so we decided we would also look at the children as they were being transported to intensive care.
Why should we wait until they arrived in the hospital before we started to look?
And so we installed a real-time link between the ambulance and the hospital, just using normal 3G telephony to send that data so that the ambulance became an extra bed in intensive care.
And then we started looking at the data.
So the wiggly lines at the top, all the colors, this is the normal sort of data you would see on a monitor -- heart rate, pulse, oxygen within the blood, and respiration.
The lines on the bottom, the blue and the red, these are the interesting ones.
The red line is showing an automated version of the early warning score that Birmingham Children's Hospital were already running.
They'd been running that since 2008, and already have stopped cardiac arrests and distress within the hospital.
The blue line is an indication of when patterns start to change, and immediately, before we even started putting in clinical interpretation, we can see that the data is speaking to us.
It's telling us that something is going wrong.
The plot with the red and the green blobs, this is plotting different components of the data against each other.
The green is us learning what is normal for that child.
We call it the cloud of normality.
And when things start to change, when conditions start to deteriorate, we move into the red line.
There's no rocket science here.
It is displaying data that exists already in a different way, to amplify it, to provide cues to the doctors, to the nurses, so they can see what's happening.
In the same way that a good racing driver relies on cues to decide when to apply the brakes, when to turn into a corner, we need to help our physicians and our nurses to see when things are starting to go wrong.
So we have a very ambitious program.
We think that the race is on to do something differently.
We are thinking big.
It's the right thing to do.
We have an approach which, if it's successful, there's no reason why it should stay within a hospital.
It can go beyond the walls.
With wireless connectivity these days, there is no reason why patients, doctors and nurses always have to be in the same place at the same time.
And meanwhile, we'll take our little three-month-old baby, keep taking it to the track, keeping it safe, and making it faster and better.
Thank you very much.
(Applause)
We're asked to graph the function f(x)=5x-4 and we'll do it by really just sampling some points from the domain and seeing what value our function takes and then we'll just graph those points and then we'll just connect the dots and see what forms, and there's other ways to do this but this is kind of the most simple, or the most basic way.
So if you look at this function over here, it's actually defined for any real number that you stick there for x so, when we talk about sampling the domain, we can actually pick any real number for x
I'm actually going to pick real numbers that are fairly small in magnitude so that they're easy to graph, so you don't have to plot, you know, 8 billion on a number line over here.
So let's draw ourselves some simple graph paper,
let's call that the x-axis
let's call that the y-axis or actually I should call it the y=f(x) so whatever my x is, I input it into this function definition, it'll tell me what the function value is there, it'll tell me f(x), and we're going to say that y is equal to that.
So, let's say that this is x values and this is f(x) and I can even say that these are my y values which are going to be equal to f(x).
So let's start with, I'm going to try,
-2, -1, 0, 1, and 2.
So let's try -2 first.
If x is equal to -2, what is f(x)?
Well f(x) is going to 5 times -2 minus 4, so it's 5 times -2 minus 4 which is equal to -10 minus 4, which is -14
So let me plot that over here,
So let's say that this is -5, this is -10, and this is -15, and then this would be +5, and this would be +10.
So, when x is -2, f(x) is equal to -14 which is right about there, so that is -14 so that right over there is the point (-2, -14) which we got right from that
Now let's try another point. Let's try -1.
When x is -1, f(x) is 5 times -1 minus 4 5 times -1 is -5, minus 4 is -9.
So when x is -1, f(x) is -9.
So -9 is right about here.
So this is -9, so this is the point (-1, -9).
That is on the graph of f(x).
When x is 0, f(x) is going to be 5 times 0 minus 4
Well that's just 0 minus 4 which is equal to -4,
So when x is 0, f(x) is equal to -4.
That's -4 right over there and actually, our point is going to be sitting right over there, that is 0, -4, we're to the left of the point.
Let's keep going! Let's see what happens when x is equal to 1.
When x is equal to 1, f(x) is equal to 5 times 1 minus 4.
5 times 1 is 5, minus 4 is equal to 1.
So we get to the point (1,1), which is right about there so this is point (1,1). and then let's just try one more.
Let's see what happens when x is equal to 2. Then f(x) is 5 times 2 minus 4, which is 10 minus 4, which is equal to 6.
So, we have when x is equal to 2, f(x) is equal to 6.
That's 6 right there, so this is the point (2, 6).
So once again, these are just sample points from the domain, this isn't the entire domain, but it gives us enough points to see the general structure of the graph.
If we connect the dots, we see a line forming.
And I want to make it clear that we just sampled points from the domain, but we can take any point in the domain, which we already said is all real numbers, so if we took right over here, we said 1.5, you could see, and if you graph 1.5, f(1.5) should sit on that line right over there.
If you graph f(-.5), so this is -.5, if you graphed f(-.5), it should sit on the line right over there.
We have graphed the function f(x)=5x-4.
The height of a triangle is 4 inches less than the length of the base.
The area of the triangle is 30 in^2. Find the height and base.
Use the formula A=1/2 base times height for the area of a triangle.
Ok.
So let's think about it a little bit.
Let me draw a triangle here.
So this is our triangle and let's say the length of this bottom side, that's the base, lets call that 'b'.
And then this is the height, this is the height, right over here.
And then the area is equal to one-half base times height.
A = 1/2 b h .
Now this first sentence is telling us that height of a triangle is 4 inches less than the length of the base.
So the height is equal to the base minus 4.
That's what the first sentence tells us.
The area of the triangle is 30 inches^2.
So if we take one-half the base times height we will get 30 inches^2.
Or we can say that 30 inches^2 is equal to one-half times the base times the height.
Now instead of putting that 'h' in for height we know that the height is the same thing as 4 less than the base.
So let's just put that in there.
And then let's see what we get in here.
I'll put this in yellow.
We get 30 equals one half b/2 times b-4
Now let's distribute the b, so 30 is equal to b squared over 2- be careful. b/2 times b is just b squared over 2- and then b/2 times -4 is -2b now just to get rid of this fraction here, let's multiply both sides of the equation by two
So let's multiply that side by 2 and that side by two.
On the left hand side you get 60 on the right hand side, 2 times b^2/2 equals b squared, -2b times 2 is -4b
And now we have a quadratic here, and the best way to solve a quadratic is to get all of the terms on one side of the equation and have them equal 0.
So let's subtract 60 from both sides of the equation.
And we get 0 is equal to b squared minus 4 b minus 60.
So what we need to do is factor this thing right now, and then know that if we have the product of some things and that equals zero, that means that either one or both of those thing need to be equal to zero, so we need factor b squared minus 4b minus 60.
So what we want to find 2 numbers whose sum is -4 and whose product is -60.
Now given that the product is negative, we know that they will have different signs.
And this tells us that their absolute value will be four apart.
So let's look at the factors of 60: 1 and 60 are too far apart.
If you made one of them negative, you would get positive 59 or negative 59 as a sum.
2 and 30, still to far apart.
3 and 20, still to far apart.
If you made one of them negative, you would either get negative 17 or positive 17.
Then you could have 4 and 15- still to far apart.
If you made one of them negative, you would either get -11 or positive 11.
Then you have 5 and 12- still too far apart, you could either have positive 7 or negative 7.
Now you have 6 and 10: now this looks interesting.
They are 4 apart, and we want the larger number to be negative so that their sum is negative.
So if we make it 6 and negative 10, their sum will be negative 4, and their product is -60.
So you can say that this is equal to b+6 times b-10. Let me be careful. This b over here is different than the b that we are using in the equation.
I just used this b to say look, we are looking for 2 numbers that add up to this second term.
It's a different
'b.' I could have used x and y.
In fact let me do it that way. now x plus y = -4, and x times y is -60. so we have b + x times b + y. x is six and y is negative 10.
You could also solve this by grouping.
We know that either b + 6 is equal to zero, or b - 10 = 0.
If we subtract 6 from both side of the equation you get b = -6, and if you subtract be from both sides of this equation you get b = 10.
The other way to solve this is break up this -4b into its consitutents.
So you could have broken this up into 0 = b squared, and you could have broken if up into +6b -10b, and then factor is by grouping.
Group these first two terms, group these second two terms.
Just add them together. the first one you can factor out a b to you have b times b + 6, the second one you have factor out a negative 10, to -10 times b + 6 all of that is equal to zero, now factor out a b + 6.
Then you get 0 = b-10 times b+6.
We are just factoring out this out of the expression.
We have to think about whether this makes sense in the context of the actual problem.
We are talking about lengths of triangles, we cannot have a negative length.
So we can cross out -6 and we are left with 1 solution.
The only possible base is 10.
They say "find the height and the base." So the base is 10 and the height is 4 inches less, so the height is 6.
And then you can verify.
The area is 6 times 10 times 1/2, which is 30.
"The owner of a restaurant wants to find out more about where his patrons are coming from.
One day he decided to gather data about the distance in miles that people commuted to get to his restaurant.
People reported the following distances traveled."
This is our data right over here.
"He wants to create a graph that helps him understand the spread of the distances and the median distance that people travel.
What kind of a graph should he create?"
And you can plot this data in many different types of graphs, but they tend to depict things in different ways.
For example, a line graph shows a trend over time.
He's not interested in a trend over time, so a line graph doesn't make sense.
Or a line graph could be a trend of one variable with respect to another variable; it doesn't just have to be time.
But he doesn't want to see a trend here.
A bar graph is good when you're trying to bucket things, put things into buckets and see how those buckets are performing.
Once again, that's not exactly what he wants to see.
A pie graph, you want to see kind of how things make up a whole.
That's not what he wants to see right over here.
A stem and leaf plot does help with distributions a little bit, but it really doesn't tackle the median distance and the spread really, really well. So the one that does -- and especially when people talk about medians and spread -- is a box-and-whiskers plot.
I'll show you how to do it right now. Box-and-whiskers.
And what a box-and-whiskers plot literally does is it shows the spread of the data, it splits it into quartiles (I'll talk about that in a second), and it also shows you where the median of the data actually is.
And that's one of the things that the owner of the restaurant cares about. So whenever you're dealing with medians -- And box-and-whiskers plots deal with medians -- the first thing you want to do is order all the numbers.
'Cause a median is really the middle number when you order them all up. So let's order this; let's write it in order. So, first we have 1 (so get rid of that 1).
14. And we have a 15. (People must like this restaurant; they're traveling a good bit.)
And we have a 20, and then we have a 22.
So I've ordered all the numbers. Let me make sure I haven't skipped or gotten some duplicates. So 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17 people were surveyed, seventeen patrons of the restaurant.
Alright. It seems like I got all of them, and I've ordered them now.
Now the median is the middle number.
We just said that we had seventeen of these numbers. So we want the number -- And since it's an odd number of numbers, the median actually will be one of these numbers.
It's actually the middle number. It'll be the number where eight are larger and eight are smaller.
So 1, 2, 3, 4, 5, 6, 7, 8. It looks like this is our median. It will be the ninth number.
And then you have 1, 2, 3, 4, 5, 6, 7, 8 that are larger.
So eight are smaller than 6; eight are larger than 6.
So 6 is the middle number.
If we had an even number of numbers here, we had two middle numbers, then we would take the average of them.
But when you have an odd number of data points, then you can just take the middle one.
So this right over here is our median.
And then when you do a box plot, what you want to do is you want to find the median of the set of numbers that are smaller than the median.
And you also want want to find the median of the set of numbers that are larger than the median.
And these are called the first quartile and the second quartile. Because when you do that, you split your data into four sections, or quartiles.
"Quar-" you normally associate with four.
So let's look at this set that's smaller than 6.
So we have 1, 2, 3, 4, 5, 6, 7, 8 numbers.
So if you have eight data points, you're going to actually have two middle numbers. So, for example, you have these two right over here are the two middle numbers. Three less, three more.
So these are our two middle numbers.
So the median of this group right over here is 2.5.
I averaged these two middle numbers.
And then let's do it over here with this group. (I'll do it in blue.)
So once again we have eight numbers, we're going to have two middles, and so it's going to be the third and the fourth number, which is 11 and 14.
let's see 11+14 is 25, divided by 2 is 12.5.
So this essentially divides the data into four sections. You have everything up to this first quartile -- so you have this first section, or this first median of the lower half of the data is 2.5. Then you have everything between 2.5 and 6.
Then 6 to 12.5, and then everything more than 12.5.
And so a box-and-whiskers plot is essentially a graphical depiction of this over here.
So let's do that. I'm going to set up a number line. And let's say that this is 0.
25 would be right around there.
So first thing on the box and whiskers plot, you want to show the entire range of data.
So our smallest data point starts at 1. So 1 is right about here. (This is 2-1/2, so 1 is right about here.)
22 would sit right about there.
And I'll even label it, although you often won't see it labeled like that.
That's 1, and then that is 22.
And the middle half of the data we do in the box.
So the middle half is this quartile, and this quartile right over there.
So the second quartile starts at 2.5. So 2.5 is right there.
This is where we start our box, 2.5. And then our third quartile ends at 12.5.
12.5 is right over there. And then we can draw the box here.
So the box shows where the middle half of our data is. Now I can draw these two arrows.
So that's the box part. And then these two arrows are what you would call the whiskers, and that shows where all the other data is.
It's really showing the spread of the data.
And then the last thing we need to show is the actual median.
And the median (I'll do it in purple) we already figured out is 6.
So the median sits right about (so let's see, this is 5, this would be 7-1/2) 6 would be right over there.
So with this one diagram, we've actually depicted all of this information, in terms of where is the median?
The median is at 6; that is 6 right over there.
Where is the middle half of the data? Well, it's between 2-1/2 and 12-1/2. And all of the data, the entire spread, for all of the customers, sits between -- and this is what the whiskers do for us -- it sits between 1 and 22.
And if you wanted to color-code it a little bit better, we could do that just 'cause it's fun. We could make ---
So, this data right over here -- and really, if you think about it, it's kind of inluding this data too -- that's what this whisker is depicting.
This data right over here (I'll do that in a different color.) is kind of the first half of the box, then you have your median in magenta, then this data right over here is the second part of the box.
So that's all of this stuff, right over here. And then finally (let me pick a new color that I haven't used yet) this data is kind of represented by this part, by this whisker, right over here. Now there's one thing I want to leave you with.
Complete this statement using less than or greater than-- that's what those symbols are-- for this kind of brackets there.
So all they're asking is they have a 5 and they have a 2, and they want us to put either a less than sign for these brackets or a greater than sign.
So we just have a 5 and a 2, and we're just comparing the two.
Which number is greater?
Well, 5 is greater.
If you count to 5, you're going to pass up 2.
If you look at a number line here, if you started at 0, 1, 2, 3, 4, 5, you see that 2 comes before 5.
2 is less than 5.
If I have $2, that's less than $5, or $5 is greater than $2.
And so the symbol for greater than, the way you remember it-- this is probably the hardest part of how do you remember it-- is you want the larger side of the symbol facing the larger number.
So 5 is the larger number, so we want the bigger side of the symbol.
So we want it like this.
The way I think about is that this right here is the big side of the symbol, and this right here, this point, is the small side of the symbol, so 5 is greater than 2.
If it was the other way, we would write 2 is less than 5.
Once again, though, we always have the point pointing to the smaller number, and we have the wide-open part, the big part of the symbol, pointing to the larger number.
We already know that the sum of the interior angles of a triangle add up to 180 degrees
If the measure of this angle is A, the measure of this angle over here is B, and the measure of this angle is C, we know that A + B + C = 180 degrees
What happens when we have polygons with more than 3 sides?
a quadrilateral
probably applies to any quadrilateral with four sides, not just things that have right angles and parallel lines and all the rest
Actually, that looks a little too close to being parallel so let me draw it like this
The way you can think about it, with the 4-sided quadrilateral is, we already know about this: the measures of the interior angles of a triangle add up to 180 so maybe we can divide this into 2 triangles
From this point right over here, if we draw a line like this,
Then if measure of this angle is A, measure of this is B, measure of that is C
We know that A + B + C = 180 degrees
Then if we call this over here, X, this over here, Y and that, Z
Those are the measures of those angles
We know that X + Y + Z = 180 degrees
So, if we want the measure of the sum of all of the interior angles, all of the interior angles are going to be:
plus this angle, which is going to be A + X
A + X is that whole angle for the quadrilateral
Plus this whole angle, which is going to be C + Y
And where you know A + B + C is 180 degrees
And we know that Z + X + Y = 180 degrees
So plus 180 degrees which is equal to 360 degrees
I think you see the general idea here
We just have to figure out how many triangles we can divide something into
Then we just multiply it by 180 degrees, since each of those triangles will have 180 degrees
can we fit into that thing
Let me draw an irregular pentagon 1, 2, 3, 4, 5
Looks more like a bit of a side-ways house there
Once again, we can draw our triangles inside of this pentagon
That would be one triangle there
That would be another triangle
that perfectly cover this pentagon
This is one triangle, the other triangle and the other one
We know each of those have 180 degrees, if we take the sum of their angles
We also know the sum of all those interior angles are equal to the sum of the interior angles of the polygon as a whole
To see that, clearly this interior angle is one of the angles of the polygon
This is, as well
When you take the sum of this one and this one,
We take the sum of that one and that one, you get that entire one
Then when you take the sum of that one, plus that one, plus that one, you get that entire interior angle
So if you take the sum of all the interior angles of all of the interior angles of the polygon
In this case you have 1, 2, 3 triangles 3 times 180 degrees is equal to what?
300 +240 = 540 degrees
To generalize it,
we have up to use up four sides
We have to use up all the four sides of this quadrilateral
We had to use up four of the five sides right here in this pentagon 1, 2, and then 3, 4
So four sides give you two triangles
It seems like maybe every incremental side you have after that, you can get another triangle out of it
1, 2, 3, 4, 5, 6 sides and I can get one triangle out of these 2 sides 1, 2 sides of the actual hexagon
I can get another triangle out of these 2 sides of the actual hexagon And it looks like I can get another triangle out of each of the remaining sides
So one out of that one, and then, one out of that one right over there
S-sided polygon
or 6 sides
So we can assume that S is greater than 4 sides
I want to figure out how many non-overlapping triangles that perfectly cover that polygon
How many can I fit inside of it
Then I just have to multiply the number of triangles times 180 degrees to figure out what are the sum of the interior angles of that polygon as a function of the number of sides
Once again, four of the sides are going to be used to make two triangles and we have two sides right over there
I can have, I can draw one triangle what happens to the rest of the sides of the polygon
You can imagine putting a big black piece of construction paper
There might be other sides here
So out of these 2 sides I can draw one triangle just like that
Out of these two sides, I can draw another triangle right over there
So 4 sides used for two triangles
Then, no matter how many sides I have left over, if I have all sorts of craziness here
Let me draw a little bit neater than that
So I can have all sorts of craziness right over here
It looks like every other incremental side
I can get another triangle out of it
one triangle out of that side, one triangle out of that side and then one triangle out of this side
For example, this figure that I have drawn is a very irregular 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, is that right?
1, 2, 3, 4, 5, 6, 7 ,8 ,9 10 It is a decagon
In this decagon, four of the sides were used for two triangles
Then the other 6 sides I was able to get a triangle each
I have 1, 2, 3, 4, 5, 6, 7, 8, 9, 10
Did I count, am I just not seeing something?
Oh I see, I have to draw another line right over here
These are two different sides
I can get another triangle out of that right over there
There you have it
I have these two triangles out of 4 sides
Then out of the other 6 remaining sides I get a triangle each
Plus 6 triangles, I got a total of 8 triangles
So we can generally think about it
Let me write this down
Our number of triangles is going to be equal to 2,
The remaining sides, I get a triangle each
The remaining sides are going to be S minus 4
The number of triangles are going to be 2 plus S minus 4
So, if I have an S-sided polygon, I can get S minus two triangles that perfectly cover that polygon
Which tells us that an S-sided polygon if it has S minus 2 triangles, that the interior angles in it are going to be
S minus 2 times 180 degrees, which is a pretty cool result
So someone told you that they had a 102-sided polygon
So, S is equal to 102 sides
You can say, okay the number of interior angles are going to be
Which is equal to 180, with two more zeros behind it
of a 102-sided polygon
<music>
My name's Aleli Alcala and I'm here to represent Universal Subtitles We realized that video was fast becoming the most proliferate content on the internet It delivers content like education, politics, health and because of language barriers, or if someone was deaf or hard of hearing, they would be excluded from participating in the world they live in
For tens of thousands of years,
Homo sapiens lived throughout Africa, but only some of these people were our ancestors.
By 60,000 years ago, our ancestors were on the move, and their expansions started to have staying power,
we don't know how fast, or how far they traveled.
Today, hunter-gatherer groups move, on average, about 1 km a year, it's about half mile.
But it's not always consistent--what we do know is this, as their descendants moved into new environments, they became more isolated from one another, setting the stage for the high level of genetic diversity that we see in Africa today.
By 50,000 years ago, people started making more sophisticated tools, and creating a lot more art.
Did new language abilities spark this burst of innovation?
Maybe a genetic change in a population allowed some people to express more complex concepts through language, and so to out-compete those who couldn't, no one really knows.
Around 50,000 years ago, small groups of travelers crossed into Asia, possibly as few as a hundred people in all.
Everyone alive today who has any non-African ancestors is probably descended from these travelers.
Within a few thousand years, climatic conditions became drier, and the Sahara desert expanded, making it harder to turn back, the intrepid travelers and their descendants followed a coastal route, eastward in Asia, reaching present day Malaysia within a few millenium.
Did they meet Homo erectus along the way?
By 45,000 years ago, people were living in parts of Australia and making their mark.
In order to get there, they had to cross the 90 km--that's about 50 miles--of open water which separates Australia from the nearest islands of present-day Indonesia.
Just how this was done, no one knows.
It's amazing to think that people reached Australia and Europe at around the same time.
Traveling eastward and southward along the coast of Asia, people didn't experience big and hard environmental changes; but hitting northward, into Europe, they faced extremely harsh, cold climates and tough terrain.
As humans moved into Europe, they also ran into the Neanderthals, who'd been living there for hundreds of thousands of years.
The Neanderthals were stocky, and physically better adapted to the cold climates, but the newcomers proved to be very skilled at shaping natural materials into useful and attractive objects.
Though the Neanderthals may have acquired some of their neighbors' advanced technologies, they soon found it hard to keep up.
Humans' success might have meant the Neanderthals' downfall.
The two populations coexisted, even interbred, for a few millenium, but by 35,000 years ago, Neanderthals were confined to the southwest corner of Europe, and soon thereafter, they had disappeared, another unsolved mystery, yes, our story is full of them.
Homo sapiens outlasted their cousins, and expanded their reach across Africa, Eurasia, and Australia; but soon times got tough for everyone, how would our ancestors cope with the extreme temperatures of the ice age.
Calculate the area of a rectangular room that is 13 feet wide and 18 feet long.
So the room might look like this.
We're looking at a floor plan.
So it is 13 feet wide and it is 18 feet long.
So that dimension is 18 feet.
And when you're looking for the area of a rectangle, you literally just multiply the two dimensions.
You multiply the width times the length in this case.
So the area is going to be equal to 13 times 18 square feet.
So let's multiply that out.
13 times 18.
Now we're first going to worry about this 8 in the ones place, right?
18 is really 10 plus 8.
So when we take this 8 in the ones place, 8 times 3 is 24, the 4 in the ones places.
Regroup the 2, which is really a 20, or carry the 2.
8 times 1, now this 1 is really a 10, so 8 times 1 is 8, plus 2 is 10, and there's no other digits, so we can write the whole 10 down here.
So we now see that 8 times 13 is 104.
Now let's worry about the next digit.
Let us worry about this 1 right here in the tens place.
Now since it's in the tens place, we want to put a zero down here.
1 times 3 is 3.
1 times 1, we ignore this 2.
That was from the other digit so we ignore it.
1 times 1 is 1.
So you see that 8 times 13 is 104, 1 times 13, or we should say 10 times 13, because that 1 is in the tens place, is 130.
18 is the sum of 10 and 8, so 18 times 13 is going to be the sum of these two numbers.
So it's going to be 104 plus 130.
4 plus 0 is 4, 0 plus 3 is 3, 1 plus 1 is 2.
So the area of the room is 234 square feet, or you could call it feet squared, however you want to do it.
I'll write it like this: square feet.
And if you're actually draw a grid where you drew 18 lines in this direction, if you kept going, and 13 lines in this direction, if you were to count all the boxes, you would get 234.
I know what you're thinking.
You think I've lost my way, and somebody's going to come on the stage in a minute and guide me gently back to my seat.
(Applause)
I get that all the time in Dubai.
"Here on holiday are you, dear?"
(Laughter)
"Come to visit the children?
How long are you staying?"
Well actually, I hope for a while longer yet.
I have been living and teaching in the Gulf for over 30 years.
(Applause)
And in that time, I have seen a lot of changes.
Now that statistic is quite shocking.
And I want to talk to you today about language loss and the globalization of English.
I want to tell you about my friend who was teaching English to adults in Abu Dhabi.
And one fine day, she decided to take them into the garden to teach them some nature vocabulary.
But it was she who ended up learning all the Arabic words for the local plants, as well as their uses -- medicinal uses, cosmetics, cooking, herbal.
How did those students get all that knowledge?
Of course, from their grandparents and even their great-grandparents.
It's not necessary to tell you how important it is to be able to communicate across generations.
But sadly, today, languages are dying at an unprecedented rate.
A language dies every 14 days.
Now, at the same time, English is the undisputed global language.
Could there be a connection?
Well I don't know.
But I do know that I've seen a lot of changes.
When I first came out to the Gulf, I came to Kuwait in the days when it was still a hardship post.
Actually, not that long ago.
That is a little bit too early.
But nevertheless,
I was recruited by the British Council, along with about 25 other teachers.
And we were the first non-Muslims to teach in the state schools there in Kuwait.
We were brought to teach English because the government wanted to modernize the country and to empower the citizens through education.
And of course, the U.K. benefited from some of that lovely oil wealth.
Okay.
Now this is the major change that I've seen -- how teaching English has morphed from being a mutually beneficial practice to becoming a massive international business that it is today.
No longer just a foreign language on the school curriculum, and no longer the sole domain of mother England, it has become a bandwagon for every English-speaking nation on earth.
And why not?
After all, the best education -- according to the latest World University Rankings -- is to be found in the universities of the U.K. and the U.S.
So everybody wants to have an English education, naturally.
But if you're not a native speaker, you have to pass a test.
Now can it be right to reject a student on linguistic ability alone?
Perhaps you have a computer scientist who's a genius.
Would he need the same language as a lawyer, for example?
Well, I don't think so.
We English teachers reject them all the time.
We put a stop sign, and we stop them in their tracks.
They can't pursue their dream any longer, 'til they get English.
Now let me put it this way: if I met a monolingual Dutch speaker who had the cure for cancer, would I stop him from entering my British University?
I don't think so.
But indeed, that is exactly what we do.
We English teachers are the gatekeepers.
And you have to satisfy us first that your English is good enough.
Now it can be dangerous to give too much power to a narrow segment of society.
Maybe the barrier would be too universal.
Okay.
"But," I hear you say,
"what about the research?
It's all in English."
So the books are in English, the journals are done in English, but that is a self-fulfilling prophecy.
It feeds the English requirement.
And so it goes on.
I ask you, what happened to translation?
If you think about the Islamic Golden Age, there was lots of translation then.
They translated from Latin and Greek into Arabic, into Persian, and then it was translated on into the Germanic languages of Europe and the Romance languages.
And so light shone upon the Dark Ages of Europe.
Now don't get me wrong; I am not against teaching English, all you English teachers out there.
I love it that we have a global language.
We need one today more than ever.
But I am against using it as a barrier.
Do we really want to end up with 600 languages and the main one being English, or Chinese?
We need more than that.
Where do we draw the line?
This system equates intelligence with a knowledge of English, which is quite arbitrary.
(Applause)
And I want to remind you that the giants upon whose shoulders today's intelligentsia stand did not have to have English, they didn't have to pass an English test.
Case in point, Einstein.
He, by the way, was considered remedial at school because he was, in fact, dyslexic.
But fortunately for the world, he did not have to pass an English test. Because they didn't start until 1964 with TOEFL, the American test of English.
Now it's exploded.
There are lots and lots of tests of English.
And millions and millions of students take these tests every year.
Now you might think, you and me,
"Those fees aren't bad, they're okay," but they are prohibitive to so many millions of poor people.
So immediately, we're rejecting them.
(Applause)
It brings to mind a headline I saw recently:
"Education:
The Great Divide."
Now I get it, I understand why people would want to focus on English.
They want to give their children the best chance in life.
And to do that, they need a Western education.
Because, of course, the best jobs go to people out of the Western Universities, that I put on earlier.
It's a circular thing.
Okay.
Let me tell you a story about two scientists, two English scientists.
They were doing an experiment to do with genetics and the forelimbs and the hind limbs of animals.
But they couldn't get the results they wanted.
They really didn't know what to do, until along came a German scientist who realized that they were using two words for forelimb and hind limb, whereas genetics does not differentiate and neither does German.
So bingo, problem solved.
If you can't think a thought, you are stuck.
But if another language can think that thought, then, by cooperating, we can achieve and learn so much more.
My daughter came to England from Kuwait.
She had studied science and mathematics in Arabic.
It's an Arabic-medium school.
She had to translate it into English at her grammar school.
And she was the best in the class at those subjects.
Which tells us that when students come to us from abroad, we may not be giving them enough credit for what they know, and they know it in their own language.
When a language dies, we don't know what we lose with that language.
This is -- I don't know if you saw it on CNN recently -- they gave the Heroes Award to a young Kenyan shepherd boy who couldn't study at night in his village, like all the village children, because the kerosene lamp, it had smoke and it damaged his eyes.
And anyway, there was never enough kerosene, because what does a dollar a day buy for you?
So he invented a cost-free solar lamp.
And now the children in his village get the same grades at school as the children who have electricity at home.
(Applause)
When he received his award, he said these lovely words:
"The children can lead Africa from what it is today, a dark continent, to a light continent."
A simple idea, but it could have such far-reaching consequences.
People who have no light, whether it's physical or metaphorical, cannot pass our exams, and we can never know what they know.
Let us not keep them and ourselves in the dark.
Let us celebrate diversity.
Mind your language.
Use it to spread great ideas.
(Applause)
Thank you very much.
(Applause)
Round 423,275 to the nearest thousand.
So let me rewrite it:
423,275.
And so the thousands place is the 3 right here, and so if we were round it up to the nearest thousand, we would go to 420-- let me write it so we just focus on the 3-- we would go up to 424,000 if we wanted to round up, 424,000, and if we wanted to round down, we would go to 423,000.
We would get rid of the 275.
423,000.
So this is our choice. Round up to 424,000 or round down to 423,000.
And to figure it out, we just look at the digit one place to the right of the 3, so we look at the 2 right there.
If that digit is 5 or greater, you round up.
So if this is greater than or equal to 5, 5 or greater, you round up.
If it's less than 5, you round down.
2 is definitely less than 5, so we just round down, so it is 423,000.
Now just to visualize what this means to the nearest thousand, if I were to do a number line-- and you don't have to do this.
We've gotten the answer, but just to have a little bit better visualization of it, if I were to increment by thousands, you might have 422,000, 423,000. You have 424,000, and then maybe over here, you have 425,000, and you could keep going.
Now 423,275 is going to be someplace right around here.
And so when we round to the nearest thousand, we have to pick between that and that.
We see that it much closer to 423,000 than to 424,000, so we round it right there.
But you just use the rules we just came up with, and we rounded down to 423,000.
Greece and the crisis in the European Union has been in the news for some time now, so it's long past due that I did a video on it and just so we have a time context that you might be watching this video far in the future.
This video is being done in May, 2012.
So we really don't know how all this is going to play out, but I hope over the next few videos to lay out the potential scenarios and what might be the risks and drawbacks, uh, drawbacks of each of them. So this right over here, that is Greece. And so let's just think about it on a very high level, what the situation that they find themselves in.
Let's review a little bit of everything we learned so far and hopefully it'll make everything fit together a little bit better.
Then we'll do a bunch of calculations with real numbers and I think it'll really hit the point home.
So, first of all if we're dealing with a-- let me actually write down, let me make some columns.
So if we're dealing with-- let's see, we could call it the concept and then we'll call it whether we're dealing with a population or a sample.
So the first statistical concept we came up with was the notion of the mean or the central tendency and we learned of that was one way to measure the average or central tendency of a data set.
The other ways were the median and the mode.
But the mean tends to show up a lot more, especially when we start talking about variances and, as we'll do in this video, the standard deviation.
But the mean of a population we learned-- we use the greek letter Mu-- is equal to the sum of each of the data points in the population. That's an i.
So you're going to sum up each of those data points.
You're going to start with the first one and you're going to go to the nth one.
We're assuming that there are n data points in the population.
And then you divide by the total number that you have.
And this is like the average that you're used to taking before you learned any of the statistics stuff.
You add up all the data points and you divide by the number there are.
The sample is the same thing.
We just use a slightly different terminology.
The mean of a sample-- and I'll do it in a different color-- just write it as x with a line on top.
So each of the xi in the sample.
But we're serving the sample is something less than a population.
So you start with the first one still. And then you go to the lower case n where we assume that lowercase n is less than the big N.
If this was the same thing then we're actually taking the average or we're taking the mean of the entire population.
And then you divide by the number of data points you added. You get to n.
Then we said OK, how far-- this give us the central tendency.
It's one measure of the central tendency.
But what if we wanted to know how good of an indicator this is for the population or for the sample?
Or, on average, how far are the data points from this mean?
And that's where we came up with the concept of variance. And I'll arbitrarily switch colors again.
Variance.
And in a population the variable or the notation for variance is the sigma squared.
This means variance. And that is equal to-- you take each of the data points.
You find the difference between that and the mean that you calculate up there. You square it so you get the squared difference. And then you essentially take the average of all of these.
So that's-- so you take the sum from i is equal to 1 to n and you divide it by n.
That's the variance.
And then the variance of a sample mean-- and this was a little bit more interesting and we talked a little bit about it in the last video. You actually want to provide a-- you want to estimate the variance of the population when you're taking the variance of a sample.
And in order to provide an unbiased estimate you do something very similar to here but you end up dividing by n minus 1. So let me write that down.
So the variance of a population-- I'm sorry, the variance of a sample or samples variance or unbiased sample variance if that's why we're going to divide by n minus 1.
That's denoted by s squared.
What you do is you take the difference between each of the data points in the sample minus the sample mean.
We assume that we don't know the population mean. Maybe we did.
If we knew the population mean we actually wouldn't have to do the unbiased thing they were going to do here in the denominator.
But when you have a sample the only way to kind of figure out the population mean is to estimate it with sample mean.
So we assume that we only have the sample mean.
And you're going to square those and then you're going to sum them up from i is equal to 1 to i is equal to n because you have n data points.
And if you want an unbiased estimator you divide by n minus 1. And we talked a little bit before why you want this to be a n minus 1 instead of a n. And actually in a couple of videos I'll actually prove this to you.
The next thing we'll learn is something that you've probably heard a lot of, especially sometimes in class, teachers talk about the standard deviation of a test or-- it's actually probably one of the most use words in statistics.
I think a lot of people unfortunately maybe use it or maybe use it without fully appreciating everything that it involves. But the goal we'll eventually hopefully appreciate all that involves soon.
But the standard deviation-- and once you know variance it's actually quite straightforward. It's the square root of the variance.
So the standard deviation of a population is written as sigma which is equal to the square root of the variance.
And now I think you understand why a variance is written as sigma squared.
And that is equal to just the square root of all that. It's equal to the square root-- I'll probably run out of space-- of all of that. So the sum-- I won't write at the top or the bottom, that makes it messy-- if xi minus Mu squared, everything over n.
And then if you wanted the standard deviation of a sample-- and it actually gets a little bit interesting because the standard deviation of a sample, which is equal to the square root of the variance of a sample-- it actually turned out that this is not an unbiased estimator for this-- and I don't want to get to technical for it right now-- that this is actually a very good estimate of this.
The expected value of this is going to be this. And I'll go into more depth on expected values in the future.
But it turns out that this is not quite the same expected value as this. But you don't have to worry about it for now.
So why even talk about the standard deviation? Well, one, the units work out a little better.
If let's say all of our data points were measured in meters, right? If we were taking a bunch of measurements of length then the units of the variance would be meter squared. right?
Because we're taking meters minus meters.
Then you're squaring. You're getting meters squared.
And that's kind of a strange concept if you say you know the average dispersion from the center is in meter squares.
Well first, when you take the square root of it you get this-- you get something that's again in meters. So you're kind of saying, oh well the standard deviation is x or y meters. And then we'll learn a little bit it if you can actually model your data as a bell curve or if you assume that your data has a distribution of a bell curve then this tells you some interesting things about where all of the probability of finding someone within one or two standard deviations of the of the mean.
Let's just calculate a bunch.
Let's calculate.
Let's see, if I had numbers 1, 2, 3, 8, and 7.
And let's say that this is a population.
So what would its mean be? So I have 1 plus 2 plus 3. So it's 3 plus 3 is 6.
14 plus 7 is 21.
So the mean of this population-- you sum up all the data points. You get 21 divided by the total number of data points, 1, 2, 3, 4, 5. 21 divided by 5 which is equal to what?
Now we want to figure out the variance.
And we're assuming that this is the entire population.
So the variance of this population is going to be equal to the sum of the squared differences of each of these numbers from 4.2.
I'm going to have to get my calculator out.
So it's going to be 1 minus 4.2 squared plus 2 minus 4.2 squared plus 3 minus 4.2 squared plus 8 minus 4.2 squared plus 7 minus 4.2 squared.
And it's going to be all of that-- I know it looks a little bit funny-- divided by the number of data points we have-- divided by 5.
So let me take the calculator out. All right. Here we go.
So I want to take 1 minus 4.2 squared plus 2 minus 4.2 squared plus 3 minus 4.2 squared plus 8 minus 4.2 squared, where I'm just taking the sum of the squared distances from the mean squared, one more, plus 7 minus 4.2 squared. So that's the sum. The sum is 38.8.
So this is the sum of the squared distances, right? Each of these-- just so you can relate to the formula-- each of that is xi minus the mean squared.
And so if we take the sum of all of them-- this numerator is the sum of each of the xi minus the mean squared from i equals 1 to n. And that ended up to be 38.8. And I just calculated like that.
So the variance-- let me scroll down a little bit-- the variance is equal to 7.76. Now if this was a sample of a larger distribution, if this was a sample-- if the 1, 2, 3, 8, and 7, weren't the population-- if it was a sample from a larger population, instead of dividing by 5 we would have divided by 4. And we would have gotten the variance as 38.8 divided by n minus 1, which is divided by 4.
But once you have the variance, it's very easy to figure out the standard deviation.
You just take the square root of it. The square root of 7.76-- 2.78.
Let's say 2.79 is the standard deviation.
So this gives us some measure of, on average, how far the numbers are away from the mean which was 4.2. And it gives it in kind of the units of the original measurement. Anyway, I'm all out of time.
Or actually, let's figure out-- we said if this was a sample, if those numbers were sample and not the population, that we figured out that the sample variance was 9.7. And so then the sample standard deviation is just going to be the square root of that.
The square root of 9.7 seven which would be 3.1.
3.11.
Anyway, hopefully that makes it a little bit more concrete. We've been dealing with these sigma notation variables and all that so far.
So when you actually do it with numbers you see it's hopefully not that difficult.
Anyway, see you in the next video.
Our question asks us, what equation describes the growth pattern of this sequence of a block?
So we want to figure out, if I know that x is equal to 10, how many blocks am I going to have?
So let's just look at this pattern here. So our first term in our sequence, or our first object, or our first pattern of blocks right here, we just have 1 block right there. So let me write, the term-- write it up here --so I have the term and, then I'll have the number of blocks.
So in our first term, we had one block. And then our second term-- I'll just write this down, just so we have it --what happened here? So it looks just like our first term, but we added a column here of four blocks.
Well it just looks just like the second term, but we added another column of four blocks here. Right? We added this column right there.
And in every one of these columns, so this right here, x minus 1 is the number of columns, and then in each column we have four blocks. So it's the number of columns times 4, right? For each of these columns, we have one column.
4 times x is 4x, and then 4 times negative 1 is negative 4. So that's equal to the number of blocks.
And we could simplify this. We have a 1 and we have a minus 4, or I guess we're subtracting 4 from it, so this is going to be equal to 4x minus 3 is the number of blocks given our x term. So if we're on term 50, it's going to be 4 times 50, which is 200 minus 3, which is 197 blocks.
Now another way you could have done it is you could have just said, look, every time we're adding 4, this is a linear relationship, and you could essentially find the slope of the line that connects this, but assume that our line is only defined on integers. And that might be a little bit more complicated, but the way that you think about it is, every one, every time we added a block, we added-- or every time we added a term we added four blocks. So we could write it this way.
On the left-hand side, 1 minus 4 is negative 3, and that's equal to-- these 4's cancel out --and and that's equal to b. So another way to get the equation of a line, we have just solved that b is equal to negative 3. We said how much do the number of blocks change for a certain change in x, which is a change in the number blocks for a change in x, we saw it's always 4.
Hello!
I am very glad to see you!
Today I am going to draw a water drop.
And do not leave because at the end of the tutorial I am going to show you 2 paintings to give examples of how you can use a water drop in a work of art.
To start I sketch the shape of the drop and go over it.
In a transparent object, the light behaves in a particular way:
Lets say that the beams of light come from the top-left, then the darkest part would be precisely on this part, as the light would go through the drop and illuminate the bottom-right.
And here, if anything, will be a little reflexion.
Down here then, would be the most light.
I start shading the darkest part of the drop.
I"m using a slightly hard lead: an H
It would cast a shadow on this side, but in the middle of it, would be a light.
Then with a brush I smudge the graphite for a more even finish.
I reinforce the shadow in the vicinity of the drop, and then smudge it.
With a kneaded eraser I pull some reflexions.
And then with a white pencil, pastel like, I reinforce the lights.
It is dry. A sort of chalk.
I darken a little further.
This is not a drawing paper and is leaving me black spots.
Even after smudging you can still see them.
Therefore I sharpen my eraser like an ant eater [chuckles], and I pull the dots.
Then, if I left some white spots, I fill them in carefully with the lead.
It should be smooth and uniform, to look like a water drop.
I want to give it even more light!
The beauty of drawing on a toned paper, is that the lights really stand out.
Specially if they go with good shadows.
I will extend it further up, although this part is going to be flatter and without reflexions.
I hope you liked it.
That is finished!
And as promised, I will show you 2 paintings:
This is an oil on canvas called Freshness.
It is a pretty simple one.
While this... does not have a water drop... it has about 320 drops!
I would really like to know what do you think about it. You can write me in the comments section of the video.
And if you liked the tutorial, please give it a LlKE and subscribe to my channel.
You know where to follow me, and where are the links.
See you next Tuesday!
In this video, I'm going to show you a technique called completing the square.
And what's neat about this is that this will work for any quadratic equation, and it's actually the basis for the quadratic formula.
And in the next video or the video after that I'll prove the quadratic formula using completing the square.
But before we do that, we need to understand even what it's all about.
And it really just builds off of what we did in the last video, where we solved quadratics using perfect squares.
So let's say I have the quadratic equation x squared minus 4x is equal to 5.
And I put this big space here for a reason.
In the last video, we saw that these can be pretty straightforward to solve if the left-hand side is a perfect square.
You see, completing the square is all about making the quadratic equation into a perfect square, engineering it, adding and subtracting from both sides so it becomes a perfect square.
So how can we do that?
Well, in order for this left-hand side to be a perfect square, there has to be some number here.
There has to be some number here that if I have my number squared I get that number, and then if I have two times my number I get negative 4.
Remember that, and I think it'll become clear with a few examples.
I want x squared minus 4x plus something to be equal to x minus a squared.
We don't know what a is just yet, but we know a couple of things.
When I square things-- so this is going to be x squared minus 2a plus a squared.
So if you look at this pattern right here, that has to be-- sorry, x squared minus 2ax-- this right here has to be 2ax.
And this right here would have to be a squared. So this number, a is going to be half of negative 4, a has to be negative 2, right?
Because 2 times a is going to be negative 4. a is negative 2, and if a is negative 2, what is a squared? Well, then a squared is going to be positive 4.
And this might look all complicated to you right now, but I'm showing you the rationale.
You literally just look at this coefficient right here, and you say, OK, well what's half of that coefficient?
Well, half of that coefficient is negative 2.
So we could say a is equal to negative 2-- same idea there-- and then you square it. You square a, you get positive 4.
So we add positive 4 here. Add a 4.
Now, from the very first equation we ever did, you should know that you can never do something to just one side of the equation.
You can't add 4 to just one side of the equation.
If x squared minus 4x was equal to 5, then when I add 4 it's not going to be equal to 5 anymore.
It's going to be equal to 5 plus 4.
We added 4 on the left-hand side because we wanted this to be a perfect square.
But if you add something to the left-hand side, you've got to add it to the right-hand side.
And now, we've gotten ourselves to a problem that's just like the problems we did in the last video.
What is this left-hand side?
Let me rewrite the whole thing. We have x squared minus 4x plus 4 is equal to 9 now.
All we did is add 4 to both sides of the equation.
But we added 4 on purpose so that this left-hand side becomes a perfect square.
Now what is this?
What number when I multiply it by itself is equal to 4 and when I add it to itself I'm equal to negative 2?
Well, we already answered that question.
It's negative 2. So we get x minus 2 times x minus 2 is equal to 9.
Or we could have skipped this step and written x minus 2 squared is equal to 9.
And then you take the square root of both sides, you get x minus 2 is equal to plus or minus 3.
Add 2 to both sides, you get x is equal to 2 plus or minus 3. That tells us that x could be equal to 2 plus 3, which is 5.
Or x could be equal to 2 minus 3, which is negative 1.
And we are done.
Now I want to be very clear.
You could have done this without completing the square.
We could've started off with x squared minus 4x is equal to 5.
We could have subtracted 5 from both sides and gotten x squared minus 4x minus 5 is equal to 0.
And you could say, hey, if I have a negative 5 times a positive 1, then their product is negative 5 and their sum is negative 4.
So I could say this is x minus 5 times x plus 1 is equal to 0.
And then we would say that x is equal to 5 or x is equal to negative 1.
And in this case, this actually probably would have been a faster way to do the problem. But the neat thing about the completing the square is it will always work. It'll always work no matter what the coefficients are or no matter how crazy the problem is.
And let me prove it to you.
Let's do one that traditionally would have been a pretty painful problem if we just tried to do it by factoring, especially if we did it using grouping or something like that.
Let's say we had 10x squared minus 30x minus 8 is equal to 0.
Now, right from the get-go, you could say, hey look, we could maybe divide both sides by 2.
That does simplify a little bit.
Let's divide both sides by 2.
So if you divide everything by 2, what do you get?
We get 5x squared minus 15x minus 4 is equal to 0.
But once again, now we have this crazy 5 in front of this coefficent and we would have to solve it by grouping which is a reasonably painful process.
But we can now go straight to completing the square, and to do that I'm now going to divide by 5 to get a 1 leading coefficient here.
And you're going to see why this is different than what we've traditionally done.
So if I divide this whole thing by 5, I could have just divided by 10 from the get-go but I wanted to go to this the step first just to show you that this really didn't give us much.
Let's divide everything by 5.
So if you divide everything by 5, you get x squared minus 3x minus 4/5 is equal to 0.
So, you might say, hey, why did we ever do that factoring by grouping?
If we can just always divide by this leading coefficient, we can get rid of that.
We can always turn this into a 1 or a negative 1 if we divide by the right number.
But notice, by doing that we got this crazy 4/5 here. So this is super hard to do just using factoring.
You'd have to say, what two numbers when I take the product is equal to negative 4/5?
It's a fraction and when I take their sum, is equal to negative 3?
This is a hard problem with factoring.
This is hard using factoring.
So, the best thing to do is to use completing the square.
So let's think a little bit about how we can turn this into a perfect square.
What I like to do-- and you'll see this done some ways and
I'll show you both ways because you'll see teachers do it both ways-- I like to get the 4/5 on the other side.
So let's add 4/5 to both sides of this equation.
You don't have to do it this way, but I like to get the 4/5 out of the way.
And then what do we get if we add 4/5 to both sides of this equation?
The left-hand hand side of the equation just becomes x squared minus 3x, no 4/5 there.
I'm going to leave a little bit of space.
And that's going to be equal to 4/5.
Now, just like the last problem, we want to turn this left-hand side into the perfect square of a binomial.
How do we do that?
Well, we say, well, what number times 2 is equal to negative 3?
So some number times 2 is negative 3.
Or we essentially just take negative 3 and divide it by 2, which is negative 3/2.
And then we square negative 3/2.
So in the example, we'll say a is negative 3/2.
And if we square negative 3/2, what do we get?
We get positive 9/4.
I just took half of this coefficient, squared it, got positive 9/4.
The whole purpose of doing that is to turn this left-hand side into a perfect square.
Now, anything you do to one side of the equation, you've got to do to the other side.
So we added a 9/4 here, let's add a 9/4 over there.
And what does our equation become?
We get x squared minus 3x plus 9/4 is equal to-- let's see if we can get a common denominator.
So, 4/5 is the same thing as 16/20.
Just multiply the numerator and denominator by 4. Plus over 20. 9/4 is the same thing if you multiply the numerator by 5 as 45/20.
And so what is 16 plus 45?
You see, this is kind of getting kind of hairy, but that's the fun, I guess, of completing the square sometimes. 16 plus 45.
See that's 55, 61.
So this is equal to 61/20.
So let me just rewrite it. x squared minus 3x plus 9/4 is equal to 61/20.
Crazy number.
Now this, at least on the left hand side, is a perfect square.
This is the same thing as x minus 3/2 squared. And it was by design.
Negative 3/2 times negative 3/2 is positive 9/4.
Negative 3/2 plus negative 3/2 is equal to negative 3.
So this squared is equal to 61/20.
We can take the square root of both sides and we get x minus 3/2 is equal to the positive or the negative square root of 61/20.
And now, we can add 3/2 to both sides of this equation and you get x is equal to positive 3/2 plus or minus the square root of 61/20. And this is a crazy number and it's hopefully obvious you would not have been able to-- at least I would not have been able to-- get to this number just by factoring.
And if you want their actual values, you can get your calculator out.
And then let me clear all of this.
And 3/2-- let's do the plus version first.
So we want to do 3 divided by 2 plus the second square root.
We want to pick that little yellow square root. So the square root of 61 divided by 20, which is 3.24.
This crazy 3.2464, I'll just write 3.246.
So this is approximately equal to 3.246, and that was just the positive version.
Let's do the subtraction version.
So we can actually put our entry-- if you do second and then entry, that we want that little yellow entry, that's why I pressed the second button.
So I press enter, it puts in what we just put, we can just change the positive or the addition to a subtraction and you get negative 0.246.
So you get negative 0.246.
And you can actually verify that these satisfy our original equation.
Our original equation was up here.
Let me just verify for one of them.
So the second answer on your graphing calculator is the last answer you use.
So if you use a variable answer, that's this number right here.
So if I have my answer squared-- I'm using answer represents negative 0.24.
Answer squared minus 3 times answer minus 4/5-- 4 divided by 5-- it equals--.
And this just a little bit of explanation.
This doesn't store the entire number, it goes up to some level of precision.
It stores some number of digits.
So when it calculated it using this stored number right here, it got 1 times 10 to the negative 14.
So that is 0.0000.
So that's 13 zeroes and then a 1.
A decimal, then 13 zeroes and a 1.
So this is pretty much 0.
Or actually, if you got the exact answer right here, if you went through an infinite level of precision here, or maybe if you kept it in this radical form, you would get that it is indeed equal to 0.
So hopefully you found that helpful, this whole notion of completing the square.
Now we're going to extend it to the actual quadratic formula that we can use, we can essentially just plug things into to solve any quadratic equation.
The pictures are really fantastic, Deepak!
When the person in the picture is so lovely, the photo too will be lovely! But there's magic in your hands'
Rupali, I have something important to say to you' Yes?
I " ' I " '
You are being as bashful as a person declaring his love for the first time' It's true'
I love you'
You are a very nice person and a very good friend'
Please don't misunderstand me, but I have some constraints'
What are they?
You know me, Deepak' I hail from a middle class family' I have dreams aplenry' I have come to Mumbai from Pune to fullfil them' So that, after marriage, " '
My husband will be a millionaire!
He'll have a plush office, a magnificent car, a palatial bungalow!
Father has still not come, the circus will begin'
Rinku, he must be on his way'
It's Prem on the line' You still haven't come? - I have an urgent meeting'
What are you saying!
The children are ready, they'll be disappointed!
What to do, darling?
It's a very important meeting' lf I don't attend it, I'll incur a loss in millions'
But if you insist, then l can be there right away' No, it's okay' I'll explain to the children'
Mother, how naive she is! What about your meeting? - Which meeting?
ls a meeting more important than my children?
This means, you've suffered a loss?
Of course not! Your happiness is worth Rs'50 million' The smile of my children is worth 50 million'
And my mother's love is worth another 50 million' I have earned a profit of 150 million in just 5 seconds! You're right, son " ' It's getting late, let's go'
After showing the circus to the children, I'll show you one! Stop it!
Not even one of the models have it in them!
You'll ruin my agency! I won't even employ them as my maids! " ' When will you like her?! I'll like her very much after having 2 pegs, sir'
Sir, what rype of a model are you looking out for?
Someone who has hael eyes, around 5 feet 8 inch tall, " " " ' has a figure of 36-24-36' lf such a girl can be found, won't a man marry her and keep her at home?
My story begins in Zimbabwe with a brave park ranger named Orpheus and an injured buffalo.
And Orpheus looked at the buffalo on the ground, and he looked at me, and as our eyes met, there was an unspoken grief between the three of us.
She was a beautifully wild and innocent creature, and Orpheus lifted the muzzle of his rifle to her ear.
(Gunshot)
And at that moment, she started to give birth.
As life slipped from the premature calf, we examined the injuries.
Her back leg had been caught in an eight-strand wire snare.
She'd fought for freedom [for] so hard and so long that she'd ripped her pelvis in half.
Well, she was finally free.
Ladies and gentlemen, today I feel a great sense of responsibility in speaking to you on behalf of those that never could.
Their suffering is my grief, is my motivation.
Martin Luther King best summarises my call to arms here today.
He said, "There comes a time when one must take a position that's neither safe, nor politic, nor popular.
But he must take that position because his conscience tells him that it's right."
Because his conscience tells him it is right.
At the end of this talk I'm gonna ask you all a question.
That question is the only reason I traveled here today all the way from the African savanna. That question for me has cleansed my soul.
How you answer that question will always be yours.
I remember watching the movie The Wizard of Oz as a young kid, and I was never scared of the witch or the flying monkeys.
My greatest fear was that I'd grow up like the Lion, without courage.
And I grew up always asking myself if I thought I'd be brave?
Well, years after Dorothy had made her way back to Kansas, and the Lion had found his courage,
I walked into a tattoo parlor and had the words 'Seek and Destroy' tattooed across my chest.
And I thought that'd make me big and brave.
But it'd take me almost a decade to grow into those words.
By the age of 20 I'd become a clearance diver in the navy.
By 25, as a special operations sniper,
I knew exactly how many clicks of elevation I needed on the scope of my rifle to take a headshot on a moving target from 700m away.
I knew exactly how many grams of high explosives it takes to blast through a steel plate door from only a few meters away, without blowing myself, or my team, up behind me.
And I knew that Baghdad was a shitty place, and when things go bang, well, people die.
Now back then, I'd no idea what a conservationist did, other than hug trees and piss off large corporations.
(Laughter)
I knew they had dreadlocks.
I knew they smoked dope.
(Laughter)
I didn't really give a shit about the environment, and why should I?
I was the idiot that used to speed up in his car just trying to hit birds on the road.
My life was a world away from conservation.
I'd just spent nine years doing things in real life most people wouldn't dream of trying on a Playstation.
Well, after 12 tours to Iraq as a so-called 'mercenary', the skills I had were good for one thing:
I was programmed to destroy.
Looking back now, on everything I've done, and the places I've been, in my heart, I've only ever performed one true act of bravery. And that was a simple choice of deciding 'Yes' or deciding 'No'.
But it was that one act which defines me completely and ensures there'll never be separation between who I am, and what I do.
When I finally left Iraq behind me I was lost.
Yeah I felt - ahh - I just had no idea where I was going in life or where I was meant to be and I arrived in Africa at the beginning of 2009.
I was aged 29 at the time.
Somehow, I always knew I'd find a purpose amongst chaos, and that's exactly what happened.
I'd no idea though, I'd find it in a remote part of the Zimbabwe bush.
And we were patrolling along, and the vultures circled in the air and as we got closer the stench of death hung there, in the air like a thick, dark veil, and sucked the oxygen out of your lungs.
And as we got closer, there was a great bull elephant, resting on its side, with its face cut away.
And the world around me stopped.
I was consumed by a deep and overwhelming sadness.
Seeing innocent creatures killed like this hit me in a way like nothing before.
I'd actually poached as a teenager and they're memories I'll take to the grave.
Time had changed me though; something inside wasn't the same.
And it's never gonna be again.
I asked myself, "Does that elephant need its face more than some guy in Asia needs a tusk on his desk?"
Well of course it bloody does, that was irrelevant.
All that mattered there and then was:
Would I be brave enough to give up everything in my life to try and stop the suffering of animals?
This was the one true defining moment of my life:
Yes or no?
I contacted my family the next day and began selling all my houses.
These are assets a well-advised mercenary quickly acquires with the proceeds of war.
My life-savings have since been used to found and grow the International Anti-Poaching Foundation.
The IAPF is a direct-action, law enforcement organization.
From drone technology, to an international qualification for rangers, we're battling each and every day to bring military solutions to conservation's thin green line.
Now my story may be slightly unique, but I'm not going to use it to talk to you today about the organization I run -- in what probably could have been a pretty good fundraiser.
(Laughter) (Applause)
Remember, today is about the question I'm gonna ask you at the end.
Because it's impossible for me to get up here and talk about just saving wildlife when I know the problem of animal welfare is much broader throughout society.
A few years after I saw that elephant I woke up very early one morning.
I already knew the answer to the question I was about to ask myself, but it was the first time I'd put it into words:
Does a cow value its life more than I enjoy a barbecue?
See, I'd been guilty all this time of what's termed 'speciesism'.
Speciesism is very much the same as racism or sexism.
It involves the allocation of a different set of values, rights or special considerations to individuals, based solely on who or what they are.
The realisation of the flexible morality I'd used to suit my everyday conveniences made me sick in the stomach.
See, I'd loved blaming parts of Asia for their insatiable demand for ivory and rhino horn, and the way the region's booming economic growth is dramatically increasing the illegal wildlife trade.
When I woke up that morning though I realised, even though I'd dedicated my life to saving animals, in my mind I was no better than a poacher, or the guy in Asia with a tusk on his desk.
As this 'over-consumptive meat-eater' I'd referred to some animals as 'beasts'. When in reality I'd been the beast: destructively obedient, a slave to my habits, a cold shoulder to my conscience.
We've all had contact with pets or other animals in our lives.
We can't deny our understanding of the feelings that each animal has. The ability to suffer pain or loneliness. And to fear.
Like us also, each animal has the ability to express contentment, to build family structures, and want of satisfying basic instincts and desires.
For many of us though, that's as far as we allow our imagination to explore before the truth inconveniences our habits.
The disconnect that exists between consuming a product and the reality it takes to bring that product to market is a phenomenon to itself.
Animals are treated like commodities and referred to as property.
We call it 'murder' to kill a human being yet create legal and illegal industries out of what would be regarded as torture if humans were involved.
And we pay people to do things to animals that none of us would engage in personally.
Just because we don't see it up close does not mean we're not responsible.
Peter Singer, the man who popularised the term 'speciesism' wrote,
"Although there may be differences between animals and humans they each share the ability to suffer.
And we must give equal consideration to that suffering.
Any position that allows similar cases to be treated in a dissimilar fashion fails to qualify as an acceptable moral theory."
Around the world this year 65 billion animals will be killed in factory farms.
How many animals' lives is one human's life worth?
A meat-eater in this room will consume, on average, 8,000 animals in their lifetime.
Ocean pollution, global warming and deforestation are driving us towards the next great mass-extinction and the meat industry is the greatest negative factor in all of these phenomena.
The illegal traffic in wildlife now ranks as one of the largest criminal industries in the world -- it's up there with drugs, guns and human trafficking.
The ability to stop this devastation lies in the willingness of an international community to step in and preserve a dying global treasure.
Experimentation on animals -
If animals are so like us that we can substitute using them instead of humans then surely they have the very same attributes that mean they deserve to be protected from harm?
Whether we're talking about factory farming, live export, poaching, the fur trade, logically, it's all on the same playing field to me.
Suffering is suffering, and murder is murder.
And the more helpless the victim, the more horrific the crime.
Next time you think an animal lover is too emotional, too passionate, or even a little crazy, please remember we see things through a different lens.
So in a few days, my son's gonna be born.
I find myself wondering, "What kind of world is he entering?"
Are we gonna be the generation that defines our failure as a species?
I believe our generation will be judged by our moral courage to protect what's right.
And that every worthwhile action requires a level of sacrifice.
Well, I now offer myself, without reservation, to animals.
And when I strip away all the material belongings around me, I see that I too, am an animal.
We're family. Together on one planet.
And of the five million species on that planet, only one has the power to determine what level of suffering is acceptable for all other sentient beings to endure.
Whether it's eating less meat, contributing to the fight against poaching or speaking up for the voiceless, we all have choices.
And small changes in our lives mean big changes in others' [lives].
So now back to the beginning.
My reason for being here is my question for you: next time you have an opportunity to make a difference for animals, will you be brave enough?
Yes or no?
Thank you very much. (Applause)
I have the answer to a question that we've all asked.
The question is,
Why is it that the letter X represents the unknown?
Now I know we learned that in math class, but now it's everywhere in the culture --
The X prize, the X-Files,
Project X, TEDx.
Where'd that come from?
About six years ago I decided that I would learn Arabic, which turns out to be a supremely logical language.
To write a word or a phrase or a sentence in Arabic is like crafting an equation, because every part is extremely precise and carries a lot of information.
That's one of the reasons so much of what we've come to think of as Western science and mathematics and engineering was really worked out in the first few centuries of the Common Era by the Persians and the Arabs and the Turks.
This includes the little system in Arabic called al-jebra.
And al-jebr roughly translates to
"the system for reconciling disparate parts."
Al-jebr finally came into English as algebra.
One example among many.
The Arabic texts containing this mathematical wisdom finally made their way to Europe -- which is to say Spain -- in the 11th and 12th centuries.
And when they arrived there was tremendous interest in translating this wisdom into a European language. But there were problems.
One problem is there are some sounds in Arabic that just don't make it through a European voice box without lots of practice.
Trust me on that one.
Also, those very sounds tend not to be represented by the characters that are available in European languages.
Here's one of the culprits.
This is the letter SHeen, and it makes the sound we think of as SH -- "sh."
It's also the very first letter of the word shalan, which means "something" just like the the English word "something" -- some undefined, unknown thing.
Now in Arabic, we can make this definite by adding the definite article "al."
So this is al-shalan -- the unknown thing.
And this is a word that appears throughout early mathematics, such as this 10th century derivation of proofs.
The problem for the Medieval Spanish scholars who were tasked with translating this material is that the letter SHeen and the word shalan can't be rendered into Spanish because Spanish doesn't have that SH, that "sh" sound.
So by convention, they created a rule in which they borrowed the CK sound, "ck" sound, from the classical Greek in the form of the letter Kai.
Later when this material was translated into a common European language, which is to say Latin, they simply replaced the Greek Kai with the Latin X.
And once that happened, once this material was in Latin, it formed the basis for mathematics textbooks for almost 600 years.
But now we have the answer to our question.
Why is it that X is the unknown?
X is the unknown because you can't say "sh" in Spanish.
(Laughter)
And I thought that was worth sharing.
(Applause)
อัสสสาลามุอาลัยกุม อยากให้คุณแนะนำตัว และบอกที่อาศัยด้วยครับ วาอาลัยกุมมุสสาลาม ผมชื่อนายไฟซอล
่้เดเกด า่่้ดเ้ด ้เัเี ี้เ้ด ้เ้เดัด ้เดั เเเเเเเ ีรร่าทืา กหำพกเ้ นนยยย
In this video I want to talk about how we can convert repeating decimals into fractions.
So let's say I had the repeating decimal zero point seven and sometimes it'll be written like that.
[bar above the seven]
Which just means that the 7 keeps on repeating.
So this is the same thing as zero point seven seven seven seven And I could just keep going on and on and on, forever with those sevens.
So the trick to converting these things into fractions is to essentially set this equal to a variable.
And we will sort of do it step by step.
So let set this equal to a variable, let me call this x.
So x is equal to zero point seven and the seven repeats on an on for ever.
Now what would ten x be?
Well let's think about this, ten x would just be ten times this so it would be, we can even think of it right over here. it would be, if we multiplied this by ten.
We would be moving the decimal one to the right it would be seven point seven seven seven, on and on and on forever.
Or we could say it is seven point seven repeating.
So we know what x is, it is point seven seven repeating forever.
Ten x is this. And it is another repeating thing.
Now the way we can get rid of the repeating decimals is if we subtracting x from ten x, right?
Because x has all these repeating point seven seven seven.
If you subtract that from seven point seven seven seven, you are just going to be left with seven.
So let's do that.
Let me rewrite it here.
Ten, ten x is equal to seven point seven repeating. Which is equal to seven point seven seven seven on and on forever.
As we established earlier that x is equal to zero point seven repeating; which is equal to seven point seven seven seven on and on and on forever.
Now what happens when you subtract x from ten x.
Well ten of something minus one of something is just going to be nine of that something.
And then that is going to be equal to:
What's seven point seven seven repeating, minus point seven seven, going on and on, forever repeating?
Well it is just going to be seven.
These parts are going to cancel out, you are just left with seven or we could say, these two parts cancel out and you are left with seven.
To solve for x you just divide both sides nine.
Well I could do all three sides, although these are all saying the same thing and you get x is equal to seven ninths. [7/9]
Let's do another one.
I will leave this one here so you can refer to it.
So let's say I have the number one point two repeating.
So this is the same as one point two two two and on and on.
So just like we did over here, lets set this equal to x.
And let's say ten x -- let's multiply this by ten.
So ten x is equal to twelve point two repeating.
Which is the same thing as twelve point two two two on and on and on.
Then we can subtract x from ten x.
So we have x is equal to one point two repeating.
And if we subtract x from ten x what do we get.
On the left hand side we get x minus, ten x minus x is equal to to nine x and this is going to be equal to: Well the two repeating parts cancel out.
This cancels with that.
If two repeating minus two repeating that's just a bunch of zeros.
Twelve minus one is eleven.
You have nine x is equal to eleven.
Divide both sides by nine, and you get left with x is equal to eleven over nine.
 Welcome back. I'm now going to do a series of videos on the trigonometric identities.
So sine over cosine theta, I think we learned that already. That's just the tangent of theta. And in case you actually haven't learned that already, think about it this way.
I'm a designer and an educator.
I'm a multitasking person, and I push my students to fly through a very creative, multitasking design process.
But how efficient is, really, this multitasking?
Let's consider for a while the option of monotasking.
A couple of examples.
Look at that.
This is my multitasking activity result.
(Laughter)
So trying to cook, answering the phone, writing SMS, and maybe uploading some pictures about this awesome barbecue.
So someone tells us the story about supertaskers, so this two percent of people who are able to control multitasking environment.
But what about ourselves, and what about our reality?
When's the last time you really enjoyed just the voice of your friend?
So this is a project I'm working on, and this is a series of front covers to downgrade our super, hyper — (Laughter) (Applause) to downgrade our super, hyper-mobile phones into the essence of their function.
Another example:
Have you ever been to Venice?
How beautiful it is to lose ourselves in these little streets on the island.
But our multitasking reality is pretty different, and full of tons of information.
So what about something like that to rediscover our sense of adventure?
I know that it could sound pretty weird to speak about mono when the number of possibilities is so huge, but I push you to consider the option of focusing on just one task, or maybe turning your digital senses totally off.
So nowadays, everyone could produce his mono product.
Why not?
So find your monotask spot within the multitasking world.
Thank you.
(Applause)
The whole process of natural selection is to some degree dependent on the idea of variation, that within any population of a species, you have some genetic variation. So, for example, let's say I have a bunch of-- well, this is a circle species, and one guy is that color, and then I got a bunch more, maybe some are that color-- oh, that's the same color-- that one, and that one, and that one. And for whatever reason, sometimes there are no environmental factors that will predispose one of these guys to be able to survive and reproduce over the other, but every now and then, there might be some environmental factor, and it makes maybe, all of a sudden, this guy more fit to reproduce.
And so for whatever reason, this guy is able to reproduce more frequently and these guys less frequently. And some of them get killed, or whatever, or eaten by birds, or whatever, or they're just not able to reproduce for whatever reason, and then maybe these guys are something in between. So over time, the frequency of the different traits you see in this population will change.
In a population what leads to this-- in fact, even in our population, what leads to one person having dirty blonde hair, one person having brown hair, one person having black hair, and we have the spectrum of skin complexions and heights is pretty much infinite. What causes that? And then one thing that I kind of point to, we talked about this a little bit in the DNA video, is this notion of mutations.
DNA, we learned, is just a sequence of these bases. So adenine, guanine, let's say I've got some thymine going. I have some more adenine, some cytosine.
And when I mean sexual reproduction, it's this notion that you have, and pretty much if you look at all organisms that have nucleuses-- and we call those eukaroytes. Maybe I'll do a whole video on eukaryotes versus prokaryotes, but it's the notion that if you look universally all the way from plants-- not universally, but if you look at cells that have nucleuses, they almost universally have this phenomenon that you have males and you have females. In some organisms, an organism can be both a male and a female, but the common idea here is that all organisms kind of produce versions of their genetic material that mix with other organisms' version of their genetic material.
But that would, as we already talked about, most of the time, we would have very little change, very little variation, and whatever variation does occur because of any kind of noise being introduced into this kind of budding process where I just replicate myself identically, most of the time it'll be negative. Most of the time, it'll break the organism. Now, when you have sexual reproduction, what happens?
Well, you keep mixing and matching every possible combination of DNA in a kind of species pool of DNA. So let me make this a little bit more concrete for you. So let me erase this horrible drawing I just did.
I'll throw another one here that looks a little bit different. I'll throw one here that looks like a Y, and we'll talk more about the X's and the Y chromosomes. Then I have 23 chromosomes from my mother.
It's a densely wrapped version of-- well, it's a long string of DNA, and when it's normally drawn like this, which is not always the way it is, and we'll talk more about that, they draw it as densely packed like that. So let's say that's from my mother and that's from my father. Now, let's call this chromosome 3.
But most of my cells have a complete collection of these, and what I want to give you the idea is that for every trait, I essentially have two versions: one from my mother and one from my father.
What that means is every time you see this prefix homologous or if you see like Homo sapiens or even the word homosexual or homogeneous, it means same, right? You see that all the time. So homologous means that they're almost the same.
So the possible combinations that just one couple can produce, and I'm using my life as an example, but this applies to everything. This applies to every species that experiences sexual reproduction. So if I can give 2 to twenty-third combinations of
So there's a huge amount of variation that even one couple can produce. And if you thought that even that isn't enough, it turns out that amongst these homologous pairs, and we'll talk about when this happens in meiosis, you can actually have DNA recombination. And all that means is when these homologous pairs during meiosis line up near each other, you can have this thing called crossover, where all of this DNA here crosses over and touches over here, and all this DNA crosses over and touches over there.
So all of this goes there and all of this goes there. What you end up with after the crossover is that one DNA, the one that came from my mom, or that I thought came from my mom, now has a chunk that came from my dad, and the chunk that came from my dad, now has a chunk that came from my mom. Let me do that in the right color.
Compute twenty-five hundred times 80, or 2,500 times 80.
Now, we could just do this multiplication problem like a traditional one, but when you have these numbers with a lot of zeroes there, and it actually sometimes helps you do it in your head, is to kind of think about the zeroes later.
And the reason why we can do that-- let's rewrite this multiplication problem.
2,500 times 80.
This is equivalent to-- 2,500 is what?
It's 25 times 100.
This is equivalent to 25 times 100.
That's what 2,500 is.
2,500 is 25 times 100 times 80.
And what's 80?
80 is 8 times 10.
And in multiplication, you can rearrange it any way you like.
You can change the order when it's all a bunch of numbers being multiplied.
So this is the same thing, this is the equivalent to 25 times 8 times 100 times 10.
And in the future, you're going to be able to do this in your head, but I really want to show you why you can do this in your head, why you can just multiply 25 times 8, and then worry about the zeroes.
So what's this going to be equal to?
So this is going to be equal to 25 times 8.
And what's 100 times 10?
Well, 100 times 10 is 1,000.
You can maybe do that in your head.
And whenever you multiply powers of ten, the way you can think about it is you just literally add the zeroes.
You had two zeroes here.
You have one zero here.
When you take their product, you're going to get something with three zeroes.
100 times 10 is 1,000.
And when we multiply this times whatever this is, we'll literally just add three zeroes to the product, so that's why this is useful.
We can now think about this as being-- this is the same thing as 25 times 8, and then whatever 25 times 8 is, we can then add three zeroes to it.
Hopefully, this explained a little bit about why.
Let's figure out what 25 times 8 is.
25 times 8.
5 times 8 is 40.
Put the zero down.
Carry the 4.
8 times 2 is 16 plus 4 is 20.
So it's an even 200, which makes sense. 4 times 24 is 100, or four quarters make a $1.00, so eight quarters would make $2.00, so that all makes sense.
So this part right here is 200, so we're going to multiply 200 times 1,000.
The easiest way to think about it is you just add the zeroes when you're multiplying times a power of ten.
So this is going to be-- we're going to have a 200, or you could just imagine you have 2, 0, 0, and then you add the three zeroes there.
One, two, three, and you are left with 200,000.
So 2,500 times 80:
200,000.
You could've multiplied it out in the traditional sense, but it's good to see this-- I guess you could call it a trick or a way to do it in your head a little bit.
And you'll see that more and more, the more practice you get.
I think we've had some pretty good exposure to the quadratic formula, but just in case you haven't memorized it yet, let me write it down again. So let's say we have a quadratic equation of the form, ax squared plus bx, plus c is equal to 0.
The quadratic formula, which we proved in the last video, says that the solutions to this equation are x is equal to negative b plus or minus the square root of b squared, minus 4ac, all of that over 2a.
Now, in this video, rather than just giving a bunch of examples of substituting in the a's, the b's, and the c's, I want to talk a little bit about this part of the quadratic formula, this part right there. The b squared minus 4ac.
The square root of some positive number that's non-zero, there's going to be a positive and negative version of it-- we're always going to have a b over 2a or negative b over 2a-- so you're going to have negative b plus that positive square root, and a negative b minus that positive square root, all over 2a. So if the discriminant is greater 0, then that tells us that we have two solutions.
And all that is referring to is this part of the quadratic formula.
That right there-- let me do it in a different color-- this right here is the discriminant of the quadratic equation right here.
And you just have to remember, it's the part that's under the radical sign of the quadratic formula. And that's why it matters, because if this is greater than 0, you're having a positive square root, and you'll have the positive and negative version of it, you'll have two solutions. Now, what happens if b squared minus 4ac is equal to 0?
And that solution is actually going to be the vertex, or the x-coordinate of the vertex, because you're going to have a parabola that just touches the x-axis like that, just touches there, or just touches like that, just touches at exactly one point, when b squared minus 4ac is equal to 0.
Then over here, you're going to get a negative number under the radical. And we saw an example of that in the last video. If we're dealing with real numbers, we can't take a square root of a negative number, so this means that we have no real solutions.
If we do have a positive discriminant, if b squared minus 4ac is positive, we can think about whether the solutions are going to be rational or not. If this is 2, then we're going to have the square root of 2 in our answer, it's going to be an irrational answer, or our solutions are going to be irrational. If b squared minus 4ac is 16, we know that's a perfect square, you take the square root of a perfect square, we're going to have a rational answer.
So let's say I have the equation negative x squared plus 3x, minus 6 is equal to 0. And all I'm concerned about is I just want to know a little bit about what kinds of solutions this has. I don't want to necessarily even solve for x.
Let's say I have-- I'll do this one in pink-- let's say I have the equation, 5x squared is equal to 6x. Well, let's put this in the form that we're used to. So let's subtract 6x from both sides, and we get 5x squared minus 6x is equal to 0.
There's no c. So in this situation, c is equal to 0. There is no c in that equation.
Negative 6 squared is positive 36. The discriminant is positive. You'd have a positive 36 under the radical right there, so not only is it positive, it's also a perfect square.
And not only are they're going to be real, but I also know they're going to be rational, because I have the square root of 36. The square root of 36 is positive or negative 6. I don't end up with an irrational number here, so two real solutions that are also rational.
This is this scenario right there.
Let's do a couple more, just to get really warmed. Let's say I have 41x squared minus 31x, minus 52 is equal to 0. Once again, I just want to think about what type of solution I might be dealing with.
Negative the 31 squared minus 4, times a, times 41, times c-- times negative 52.
So what do I have here? This is going to be a positive 31 squared. The negative times the negative, these are both positive.
And we could think about whether this is some type of perfect square. I don't know. I'm not going to do it here.
This is equal to 64 minus 64, which is equal to 0. So we only have one solution, and by definition it's going to be rational. I mean, you could actually look at it right here.
look there, if this is a 0, all you're left with is negative b over 2a, which is definitely going to be rational, assuming you have a, b, and c are, of course, rational numbers. Anyway, hopefully you found that useful. It's a quick way.
We're asked to simplify 12 plus, and then in parentheses, 5 minus 1 times 3 to the second power, or 3 squared, minus 8 divided by the square root, or really the principal root, of 4.
Now, whenever you see something like this, you really just want to put your brain into order of operations mode.
And just to remind ourselves, the top priority goes to parentheses, so I'll just draw some parentheses there.
Then after that, we do exponents.
And in exponents, we also consider square roots to be an exponent.
So after parentheses, we then worry about things that look like a to the b power or things that look like they have a radical on them.
You'll learn in the future that the square root is really raising something to the 1/2 power.
That's why it's the same thing as an exponent.
And then we do multiplication and division.
So let's apply that to this over here.
So we have one set of parentheses right there.
You have that parentheses, and inside you have 5 minus 1, so we want evaluate that first of all.
So 5 minus 1 is 4.
So our problem becomes 12-- plus the 5 minus 1 is 4-- times 3 squared minus 8 divided by the positive square root of 4, the principal root of 4.
Now, we got all our parentheses out of the way.
Do we see any exponents here?
We're at this stage now.
Well, I have this 3 to the second power, 3 squared, and I also have the square root of 4, so let's evaluate those next.
3 to the second power is 9.
That's the same thing as 3 times 3.
So let me write that down just as a review.
3 to the second power is equal to 3 times 3, which is equal to 9.
It is NOT equal to 3 times 2.
It's 3 times 3.
So 3 squared is 9, so we'll put that 9 there.
And the square root of 4, so the square root of 4, I'll do it down here.
The square root of 4, what times itself or what positive number, or non-negative number, I should say, times itself is equal to 4?
Well, it's 2, right?
This is the same thing as the square root of 2 times 2, which is equal to 2.
So the principal root of 4 is 2, and then we have everything else there.
We have the 12 plus this 4 times this 9 minus 8 divided by that 2 right there.
Now, what's next?
Well, we're done with the parentheses and exponents.
Now we go to the multiplication and division.
Is that going on anywhere?
Well, sure.
We have this multiplication right over there, and then we have this division right over there, so lets evaluate those next.
So 4 times 9 is 36 and 8 divided by 2 is 4, so we are left with 12 plus 36 minus 8 divided by 2, which is 4.
And now we're finally at this stage of our order of operation, so we can just evaluate left to right.
What is 12 plus 36?
12 plus 36-- I'll do this right here-- is 48.
So we have 48 minus 4.
When you evaluate that, 48 minus 4 is just 44.
And we're all done!
I just received this drug calculation problem from a nursing student, and I think it's essential that the nursing students out there are able to do this, just in case I'm the patient receiving the drug.
So let's do it.
And I think it's an interesting unit conversion problem for pretty much anyone who wants practice with unit conversion.
So the question is that we have a doctor. The doctor orders drug x.
And this is the dosage that the doctor's requesting. They're saying five milligrams per pound of patient weight-- I'll just write per pound of patient weight-- every twelve hours. This is what we're supposed to do.
But our supply of the drug-- it isn't just, you know, not just nuggets and milligrams. It's a solution.
There's a certain amount of grams for every milliliter that we have of the solution. It's dissolved in some water. So this is our supply of drug x.
We have 0.9-- I'll write a 0 in front.
We have 0.9 grams per milliliter of solution. So if I were to take one milliliter out of my solution and give it to someone, I'm essentially giving them 0.9 grams of this drug. And the final piece of information we're given is that the patient-- they weigh-- and maybe we should say they mass, because kilograms is mass, but we get the idea.
The patient is 72.7 kilograms.
So there's a couple interesting things here.
We have to figure out the dosage in terms of milliliters. We have to-- oh, actually, I didn't even tell you the question. The question is, how many milliliters of solution do we have to give to the patient per dose?
So let's do five-- I'll write it down here in magenta-- five milligrams per pound. And then we want to convert this to per kilogram. So we can multiply this times the number of pounds per kilogram-- I'll do it in yellow-- times this information up here.
Notice, I wrote 2.2 pounds per kilogram. 2.2 pounds per 1 kilogram. And you know this'll work out, because you have a pound in the numerator and you have a pound in the denominator.
This is equal to-- let's see. five times two is ten. 5 times 0.2 is 1. So this is equal to eleven.
So now we have everything in terms of grams, but we want it in terms of milliliters. The question is, how many milliliters of solution per dose?
So let me go down here on this line right here. So we had this result. We have eleven / one thousand-- I won't do the division just yet-- grams of drug x per kilogram.
So in our solution, how many grams are there per milliliter? Well, they told us. There are 0.9 grams per milliliter.
Notice, I just took the inverse of that. Because we want a milliliter in the numerator, grams in the denominator, so that these two cancel out. And let's do this multiplication now.
And then we multiply it out. 11/1,000 times 1 over 0.9. So I'll just keep-- let me just write it like this.
So there's going to be 11/1,000 times 0.9 milliliters of our solution per kilogram. So we've gotten this far. So this is per kilogram of patient body weight.
We'll have milliliters per patient-- milliliters of solution per patient-- which is exactly what we want. We want milliliters of solution per dose per patient. But everything we've assumed so far has been per dose.
We'd multiply it by four. But that twelve hours was extra information in this problem. But anyway, hopefully this is useful, and it'll ensure that any nurses serving me in the future are giving me my proper dosage.
Compute 23 times 44.
And maybe the hardest part of this problem, or maybe the first hard part, is to recognize that that dot even means multiplication.
This could have also been written as 23 times 44, or they could have written it as 23 in parentheses times 44, so you just put the two parentheses next to each other.
That also implies multiplication.
So now that we know we're multiplying, let's actually do the problem.
So we're going to multiply 23-- I'll write it bigger.
We're going to multiply 23 by 44.
I'll write the traditional multiplication sign there, just so that we know we're multiplying.
When you write it vertically like this, you very seldom put a dot there.
So let's do some multiplication.
Let's start off multiplying this 4 in the ones place times 23.
So you have 3 times 4 is 12.
We can write 2 in the ones place, but then we want to carry the 1, or we want to regroup that 1 in the tens place.
So it's 12, so you put the 1 over here.
And now you have 4 times 2 is 8 plus 1 is 9.
So you can think about it as 4, this 4 right here, times 23 is 92.
That's what we just solved for.
Now, we want to figure out what this 4 times 23 is.
Now what we do here is, when you just do it mechanically, when you just learn the process, you stick a 0 here.
But the whole reason why you're putting a 0 here is because you're now dealing with a 4 in the tens place.
If you had another-- I don't know, a 3 or a 4 or whatever digit, and you're dealing with the hundreds place, you'd put more zeroes here, because we're going to find out 4 times 23 is 92.
We just figured that out.
If we just multiplied this 4 times 23 again, we would get 92 again.
But this 4 is actually a 40, so it actually should be 920, and that's why we're putting that 0.
Now you're going to see it in a second.
So we have-- so let me put this in a different color.
So this 4 now we're multiplying. 4 times 3 is 12.
Let's put the 2 right here.
It should be in the tens place because this is really a 40 times the 3.
Just think about it, or you could just think of the process.
It's the next space that's free.
4 times 3 is 12.
Carry the 1.
This blue 1 is from last time.
You ignore it now.
You don't want to make that mess it up.
That's when we multiplied this 4.
So now we have 4 times 2 is 8 plus 1 is 9.
So what we figured out so far is 4 times 23 is 92, and this green 4 times 23 is 920, and that's because this green 4 actually represents 40.
It's in the tens place.
So when you multiply 44 times 23, it's going to be 4 times 23, which is 92, plus 40 times 23, which is 920.
I just want to make sure we understand what we're doing here.
And so we can take their sum now.
Let's add them up.
2 plus 0 is 2.
9 plus 2 is 11.
Carry the 1.
1 plus 9 is 10.
Put a comma here, just so it's easy to read, every third digit.
So 23 times 44 is 1,012.
Sociolab Concursos is a platform for entrepreneurship and social inovation that brings together the public sector, private sector, students and the most vulnerable families in society.
The objective is to develop products, services and business models which provide effective solutions to the problems faced by people who are socially excluded due to either lack of resources or lack of opportunities. How can you join in?
This process starts with a challenge:
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In the first stage "ideation", the users share their ideas with the community.
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We're told that A B C D E F is a regular hexagon And this regular part hexagon obviously tells us That we're dealing with six sides and you could just count that
With the hexagon, what you can think about is if we If we take this point right over here and let's call this point G Now let's say it's the center of the hexagon
I'm talking about a point it can't be equidistant
From everything over here coz this isn't a circle [1:08 7]
But we could say it's equidistant from all of the vertices So GD is the same thing as GC is the same thing as GB, Which is the same thing as GA, which is the same thing as GF, which is the same thing as GE
If we go all the way around the circle like that, We've gone 360 degrees And we know that these triangles, these triangles are all going to be congruent to each other and there's multiple ways if we could show it;
X is equal to 60 degrees
X is equal to 60 degrees All of these are equal to 60 degrees Now there's something interesting
We know that all of the angles of a triangle are 60 degrees And we're dealing with an equilateral triangle！ Which means that all the sides have the same length
To figure out the area of any one of these triangles And then we can just multiply it by six So let's focus on let me focus on this triangle right over here
We can drop an altitude over here
And then we if we drop an altitude, we know that this is we know that this is an equilateral triangle And we can show very easily That these two triangles are symmetric
DH is going to be the square root of three And we are or hopefully we already recognized this is a 30-60-90 triangle Let me draw it over here
So the area of this little sub slice is just one half times our base; Just the base over here Actually let's take a step back
Show how homes are destroyed (inaudible) The cries of the young people (inaudible) they are experiencing
Where is the freedom for the poor.
The government system is rotten.
More rotten than rats.
Government is worthless!
Government is worthless!
Many homes destroyed... (inaudible) the priority given to foreigners... always disappointing... justice and freedom
Sadness and anger put to the streets
Change fear into bravery
Government is worthless!
Government is worthless!
Government is worthless!
Don't make the mistake of invading our community.
(inaudible) ... leaders of the country... who hold the country in our hands ... poverty gets worse... The corruption of our leaders instead of focusing on poverty, they focus on strengthening themselves...
You're all worthless!
You keep promising...
But because of you our dreams disappear like bubbles.
You're the ones that have education but we're the ones serving you!
You have eyes and ears but you don't use them!
You have eyes but do not righteous doing just hearing while you swim...
The Government is worthless!
The Government is worthless!
The government is worthless!
So today we are here
Because the Government is worthless!
The government is worthless!
Yo, the government is worthless!
So today we're here today even though it's hot
Where we left off after the meiosis videos is that we had two gametes. We had a sperm and an egg.
Let me draw the sperm.
So you had the sperm and then you had an egg.
Maybe I'll do the egg in a different color.
That's the egg, and we all know how this story goes.
The sperm fertilizes the egg.
And a whole cascade of events start occurring.
The walls of the egg then become impervious to other sperm so that only one sperm can get in, but that's not the focus of this video.
The focus of this video is how this fertilized egg develops once it has become a zygote.
So after it's fertilized, you remember from the meiosis videos that each of these were haploid, or that they had-- oh, I added an extra i there-- that they had half the contingency of the DNA. haploid
As soon as the sperm fertilizes this egg, now, all of a sudden, you have a diploid zygote.
Let me do that.
So now let me pick a nice color.
So now you're going to have a diploid zygote that's going to have a 2N complement of the DNA material or kind of the full complement of what a normal cell in our human body would have.
So this is diploid, and it's a zygote, which is just a fancy way of saying the fertilized egg.
And it's now ready to essentially turn into an organism.
So immediately after fertilization, this zygote starts experiencing cleavage.
It's experiencing mitosis, that's the mechanism, but it doesn't increase a lot in size.
So this one right here will then turn into-- it'll just split up via mitosis into two like that.
And, of course, these are each 2N, and then those are going to split into four like that.
And each of these have the same exact genetic complement as that first zygote, and it keeps splitting.
And this mass of cells, we can start calling it, this right here, this is referred to as the morula.
And actually, it comes from the word for mulberry because it looks like a mulberry.
So actually, let me just kind of simplify things a little bit because we don't have to start here.
So we start with a zygote.
This is a fertilized egg.
It just starts duplicating via mitosis, and you end up with a ball of cells.
It's often going to be a power of two, because these cells, at least in the initial stages are all duplicating all at once, and then you have this morula.
Now, once the morula gets to about 16 cells or so-- and we're talking about four or five days.
This isn't an exact process-- they started differentiating a little bit, where the outer cells-- and this kind of turns into a sphere.
Let me make it a little bit more sphere like.
So it starts differentiating between-- let me make some outer cells.
This would be a cross-section of it.
It's really going to look more like a sphere.
That's the outer cells and then you have your inner cells on the inside.
These outer cells are called the trophoblasts.
Let me do it in a different color.
Let me scroll over.
I don't want to go there.
And then the inner cells, and this is kind of the crux of what this video is all about-- let me scroll down a little bit.
The inner cells-- pick a suitable color.
The inner cells right there are called the embryoblast.
And then what's going to happen is some fluid's going to start filling in some of this gap between the embryoblast and the trophoblast, so you're going to start having some fluid that comes in there, and so the morula will eventually look like this, where the trophoblast, or the outer membrane, is kind of this huge sphere of cells.
And this is all happening as they keep replicating.
Mitosis is the mechanism, so now my trophoblast is going to
look like that, and then my embryoblast is going to look like this.
Sometimes the embryoblast-- so this is the embryoblast.
Sometimes it's also called the inner cell mass, so let me write that.
And this is what's going to turn into the organism.
And so, just so you know a couple of the labels that are involved here, if we're dealing with a mammalian organism, and we are mammals, we call this thing that the morula turned into is a zygote, then a morula, then the cells of the morula started to differentiate into the trophoblast, or kind of the outside cells, and then the embryoblast.
And then you have this space that forms here, and this is just fluid, and it's called the blastocoel.
A very non-intuitive spelling of the coel part of blastocoel.
But once this is formed, this is called a blastocyst.
That's the entire thing right here.
Let me scroll down a little bit.
This whole thing is called the blastocyst, and this is the case in humans.
Now, it can be a very confusing topic, because a lot of times in a lot of books on biology, you'll say, hey, you go from the morula to the blastula or the blastosphere stage.
Let me write those words down.
So sometimes you'll say morula, and you go to blastula.
Sometimes it's called the blastosphere.
And I want to make it very clear that these are essentially the same stages in development.
These are just for-- you know, in a lot of books, they'll start talking about frogs or tadpoles or things like that, and this applies to them.
While we're talking about mammals, especially the ones that are closely related to us, the stage is the blastocyst stage, and the real differentiator is when people talk about just blastula and blastospheres.
There isn't necessarily this differentiation between these outermost cells and these embryonic, or this embryoblast, or this inner cell mass here.
But since the focus of this video is humans, and really that's where I wanted to start from, because that's what we are and that's what's interesting, we're going to focus on the blastocyst.
Now, everything I've talked about in this video, it was really to get to this point, because what we have here, these little green cells that I drew right here in the blastocysts, this inner cell mass, this is what will turn into the organism.
And you say, OK, Sal, if that's the organism, what's all of these purple cells out here?
This trophoblast out there?
That is going to turn into the placenta, and I'll do a future video where in a human, it'll turn into a placenta.
So let me write that down.
It'll turn into the placenta.
And I'll do a whole future video about I guess how babies are born, and I actually learned a ton about that this past year because a baby was born in our house.
But the placenta is really kind of what the embryo develops inside of, and it's the interface, especially in humans and in mammals, between the developing fetus and its mother, so it kind of is the exchange mechanism that separates their two systems, but allows the necessary functions to go on between them.
But that's not the focus of this video.
The focus of this video is the fact that these cells, which at this point are-- they've differentiated themselves away from the placenta cells, but they still haven't decided what they're going to become.
Maybe this cell and its descendants eventually start becoming part of the nervous system, while these cells right here might become muscle tissue, while these cells right here might become the liver.
These cells right here are called embryonic stem cells, and probably the first time in this video you're hearing a term that you might recognize.
So if I were to just take one of these cells, and actually, just to introduce you to another term, you know, we have this zygote.
As soon as it starts dividing, each of these cells are called a blastomere.
And you're probably wondering, Sal, why does this word blast keep appearing in this kind of embryology video, these development videos?
And that comes from the Greek for spore: blastos.
So the organism is beginning to spore out or grow.
I won't go into the word origins of it, but that's where it comes from and that's why everything has this blast in it.
So these are blastomeres.
So when I talk what embryonic stem cells, I'm talking about the individual blastomeres inside of this embryoblast or inside of this inner cell mass.
These words are actually unusually fun to say.
So each of these is an embryonic stem cell.
Let me write this down in a vibrant color.
So each of these right here are embryonic stem cells, and
I wanted to get to this.
And the reason why these are interesting, and I think you already know, is that there's a huge debate around these.
One, these have the potential to turn into anything, that they have this plasticity.
That's another word that you might hear.
Let me write that down, too: plasticity.
And the word essentially comes from, you know, like a plastic can turn into anything else.
When we say that something has plasticity, we're talking about its potential to turn into a lot of different things.
So the theory is, and there's already some trials that seem to substantiate this, especially in some lower organisms, that, look, if you have some damage at some point in your body-- let me draw a nerve cell.
Let me say I have a-- I won't go into the actual mechanics of a nerve cell, but let's say that we have some damage at some point on a nerve cell right there, and because of that, someone is paralyzed or there's some nerve dysfunction.
We're dealing with multiple sclerosis or who knows what.
The idea is, look, we have these cell here that could turn into anything, and we're just really understanding how it knows what to turn into.
It really has to look at its environment and say, hey, what are the guys around me doing, and maybe that's what helps dictate what it does.
But the idea is you take these things that could turn to anything and you put them where the damage is, you layer them where the damage is, and then they can turn into the cell that they need to turn into.
So in this case, they would turn into nerve cells.
They would turn to nerve cells and repair the damage and maybe cure the paralysis for that individual.
So it's a huge, exciting area of research, and you could even, in theory, grow new organs.
If someone needs a kidney transplant or a heart transplant, maybe in the future, we could take a colony of these embryonic stem cells.
Maybe we can put them in some type of other creature, or who knows what, and we can turn it into a replacement heart or a replacement kidney.
So there's a huge amount of excitement about what these can do.
I mean, they could cure a lot of formerly uncurable diseases or provide hope for a lot of patients who might otherwise die.
But obviously, there's a debate here.
And the debate all revolves around the issue of if you were to go in here and try to extract one of these cells, you're going to kill this embryo.
You're going to kill this developing embryo, and that developing embryo had the potential to become a human being.
It's a potential that obviously has to be in the right environment, and it has to have a willing mother and all of the rest, but it does have the potential.
And so for those, especially, I think, in the pro-life camp, who say, hey, anything that has a potential to be a human being, that is life and it should not be killed.
So people on that side of the camp, they're against the destroying of this embryo.
I'm not making this video to take either side to that argument, but it's a potential to turn to a human being.
It's a potential, right?
So obviously, there's a huge amount of debate, but now, now you know in this video what people are talking about when they say embryonic stem cells.
And obviously, the next question is, hey, well, why don't they just call them stem cells as opposed to embryonic stem cells?
And that's because in all of our bodies, you do have what are called somatic stem cells.
Let me write that down.
Somatic or adults stem cells.
And we all have them.
They're in our bone marrow to help produce red blood cells, other parts of our body, but the problem with somatic stem cells is they're not as plastic, which means that they can't form any type of cell in the human body.
There's an area of research where people are actually maybe trying to make them more plastic, and if they are able to take these somatic stem cells and make them more plastic, it might maybe kill the need to have these embryonic stem cells, although maybe if they do this too good, maybe these will have the potential to turn into human beings as well, so that could become a debatable issue.
But right now, this isn't an area of debate because, left to their own devices, a somatic stem cell or an adult stem cell won't turn into a human being, while an embryonic one, if it is implanted in a willing mother, then, of course, it will turn into a human being.
And I want to make one side note here, because I don't want to take any sides on the debate of-- well, I mean, facts are facts.
This does have the potential to turn into a human being, but it also has the potential to save millions of lives.
Both of those statements are facts, and then you can decide on your own which side of that argument you'd like to or what side of that balance you would like to kind of put your own opinion.
But there's one thing I want to talk about that in the public debate is never brought up.
So you have this notion of when you-- to get an embryonic stem cell line, and when I say a stem cell line, I mean you take a couple of stem cells, or let's say you take one stem cell, and then you put it in a Petri dish, and then you allow it to just duplicate.
So this one turns into two, those two turn to four.
Then someone could take one of these and then put it in their own Petri dish.
These are a stem cell line.
They all came from one unique embryonic stem cell or what initially was a blastomere.
So that's what they call a stem cell line.
So the debate obviously is when you start an embryonic stem cell line, you are destroying an embryo.
But I want to make the point here that embryos are being destroyed in other processes, and namely, in-vitro fertilization.
And maybe this'll be my next video: fertilization.
And this is just the notion that they take a set of eggs out of a mother.
It's usually a couple that's having trouble having a child, and they take a bunch of eggs out of the mother.
So let's say they take maybe 10 to 30 eggs out of the mother.
They actually perform a surgery, take them out of the ovaries of the mother, and then they fertilize them with semen, either it might come from the father or a sperm donor, so then all of these becomes zygotes once they're fertilized with semen.
So these all become zygotes, and then they allow them to develop, and they usually allow them to develop to the blastocyst stage.
So eventually all of these turn into blastocysts.
They have a blastocoel in the center, which is this area of fluid.
They have, of course, the embryo, the inner cell mass in them, and what they do is they look at the ones that they deem are healthier or maybe the ones that are at least just not unhealthy, and they'll take a couple of these and they'll implant these into the mother, so all of this is occurring in a Petri dish.
So maybe these four look good, so they're going to take these four, and they're going to implant these into a mother, and if all goes well, maybe one of these will turn into-- will give the couple a child.
So this one will develop and maybe the other ones won't.
But if you've seen John & Kate Plus 8, you know that many times they implant a lot of them in there, just to increase the probability that you get at least one child.
But every now and then, they implant seven or eight, and then you end up with eight kids.
And that's why in-vitro fertilization often results in kind of these multiple births, or reality television shows on cable.
But what do they do with all of these other perfectly-- well, I won't say perfectly viable, but these are embryos.
They may or may not be perfectly viable, but you have these embryos that have the potential, just like this one right here.
These all have the potential to turn into a human being.
But most fertility clinics, roughly half of them, they either throw these away, they destroy them, they allow them to die.
A lot of these are frozen, but just the process of freezing them kills them and then bonding them kills them again, so most of these, the process of in-vitro fertilization, for every one child that has the potential to develop into a full-fledged human being, you're actually destroying tens of very viable embryos.
So at least my take on it is if you're against-- and I generally don't want to take a side on this, but if you are against research that involves embryonic stem cells because of the destruction of embryos, on that same, I guess, philosophical ground, you should also be against in-vitro fertilization because both of these involve the destruction of zygotes.
I think-- well, I won't talk more about this, because I really don't want to take sides, but I want to show that there is kind of an equivalence here that's completely lost in this debate on whether embryonic stem cells should be used because they have a destruction of embryos, because you're destroying just as many embryos in this-- well, I won't say just as many, but you are destroying embryos.
There's hundreds of thousands of embryos that get destroyed and get frozen and obviously destroyed in that process as well through this in-vitro fertilization process.
So anyway, now hopefully you have the tools to kind of engage in the debate around stem cells, and you see that it all comes from what we learned about meiosis.
They produce these gametes.
The male gamete fertilizes a female gamete.
The zygote happens or gets created and starts splitting up the morula, and then it keeps splitting and it differentiates into the blastocyst, and then this is where the stem cells are.
So you already know enough science to engage in kind of a very heated debate.
Another search problem--
Consider the following search tree, where this is the start node.
Now, assume we search from left to right.
I would like you to tell me the number of nodes expanded from Breadth-First Search and Depth-First Search.
Please do count the start and the goal node, and please give me the same numbers for Right-to-Left Search, for Breadth-First, and Depth-First.
In 2008, Cyclone Nargis devastated Myanmar.
Millions of people were in severe need of help.
The U.N. wanted to rush people and supplies to the area.
But there were no maps, no maps of roads, no maps showing hospitals, no way for help to reach the cyclone victims.
When we look at a map of Los Angeles or London, it is hard to believe that as of 2005, only 15 percent of the world was mapped to a geo-codable level of detail.
The U.N. ran headfirst into a problem that the majority of the world's populous faces: not having detailed maps.
But help was coming.
At Google, 40 volunteers used a new software to map 120,000 kilometers of roads, 3,000 hospitals, logistics and relief points.
And it took them four days.
The new software they used?
Google Mapmaker.
Google Mapmaker is a technology that empowers each of us to map what we know locally.
People have used this software to map everything from roads to rivers, from schools to local businesses, and video stores to the corner store.
Maps matter.
Nobel Prize nominee Hernando De Soto recognized that the key to economic liftoff for most developing countries is to tap the vast amounts of uncapitalized land.
For example, a trillion dollars of real estate remains uncapitalized in India alone.
In the last year alone, thousands of users in 170 countries have mapped millions of pieces of information, and created a map of a level of detail never thought viable.
And this was made possible by the power of passionate users everywhere.
Let's look at some of the maps being created by users right now.
So, as we speak, people are mapping the world in these 170 countries.
You can see Bridget in Africa who just mapped a road in Senegal.
And, closer to home, Chalua, an N.G. road in Bangalore.
This is the result of computational geometry, gesture recognition, and machine learning.
This is a victory of thousands of users, in hundreds of cities, one user, one edit at a time.
This is an invitation to the 70 percent of our unmapped planet.
Welcome to the new world.
(Applause)
We're asked: Do the points on the graph below represent a function?
So in order for the points to represent a function, for every input into our function, we can only get one value.
So if we look here, they've graphed the point--it looks
So if we assume that this is our x-axis, and that is our f(x) axis -- and I'm just assuming it's a function,
I don't know whether it really is just now, this point is telling us that if you put negative 1 into our function, or that thing that might be a function, or maybe our relation, you'll get a 3 So it's telling us that f(x) of negative 1 is equal to 3.
You give me negative 1 and I will map it to 3.
Then they have if x is 2, then our value is negative 2.
This is the point 2, negative 2, so that still seems consistent with being a function.
If you pass me 2, I will map you or I will point you to negative 2.
Let's see this next value here.
This is the point 3, 2 right there.
So once again, that says that, look, if you give me 3 into my function, into my black box, I will output a 2.
Now, what about when we input 4 into the function?
Let me do this in magenta.
So what happens if I input 4 into my function?
So this is 4 right here.
Well, according to these points, there's two points that relate to 4 -- that 4 can be mapped to.
I could map it to the point 4, 5.
So that says if you give me a 4, I'll give you a 5. But it also says if you give me a 4, I could also give you a negative 1 because that's the point 4, negative 1.
So this is not a function.
It cannot be a function if for some input into the function you could give me two different values.
Use less than, greater than, or equal to compare the two fractions 21/28, or 21 over 28, and 6/9, or 6 over 9.
So there's a bunch of ways to do this. The easiest way is if they had the same denominator, you could just compare the numerators.
Unlucky for us, we do not have the same denominator.
So what we could do is we can find a common denominator for both of them and convert both of these fractions to have the same denominator and then compare the numerators.
Or even more simply, we could simplify them first and then try to do it.
So let me do that last one, because I have a feeling that'll be the fastest way to do it. So 21/28-- you can see that they are both divisible by 7.
So let's divide both the numerator and the denominator by 7.
So we could divide 21 by 7. And we can divide-- so let me make the numerator-- and we can divide the denominator by 7.
We're doing the same thing to the numerator and the denominator, so we're not going to change the value of the fraction. So 21 divided by 7 is 3, and 28 divided by 7 is 4.
So 21/28 is the exact same fraction as 3/4. 3/4 is the simplified version of it.
Let's do the same thing for 6/9.
6 and 9 are both divisible by 3.
So let's divide them both by 3 so we can simplify this fraction.
So let's divide both of them by 3. 6 divided by 3 is 2, and 9 divided by 3 is 3. So 21/28 is 3/4.
And 6/9 is the exact same fraction as 2/3. So we really can compare 3/4 and 2/3.
So this is really comparing 3/4 and 2/3. And the real benefit of doing this is now this is much easier to find a common denominator for than 28 and 9. Then we would have to multiply big numbers.
Here we could do fairly small numbers.
The common denominator of 3/4 and 2/3 is going to be the least common multiple of 4 and 3.
And 4 and 3 don't share any prime factors with each other. So their least common multiple is really just going to be the product of the two.
So we can write 3/4 as something over 12. And we can write 2/3 as something over 12.
And I got the 12 by multiplying 3 times 4. They have no common factors.
Another way you could think about it is 4, if you do a prime factorization, is 2 times 2.
And 3-- it's already a prime number, so you can't prime factorize it any more.
So what you want to do is think of a number that has all of the prime factors of 4 and 3. So it needs one 2, another 2, and a 3.
Well, 2 times 2 times 3 is 12.
And either way you think about it, that's how you would get the least common multiple or the common denominator for 4 and 3.
Well, to get from 4 to 12, you've got to multiply by 3.
So we're multiplying the denominator by 3 to get to 12.
So we also have to multiply the numerator by 3. So 3 times 3 is 9.
Over here, to get from 3 to 12, we have to multiply the denominator by 4.
So we also have to multiply the numerator by 4.
So we get 8.
And so now when we compare the fractions, it's pretty straightforward. 21/28 is the exact same thing as 9/12, and 6/9 is the exact same thing as 8/12.
So which of these is a greater quantity?
Well, clearly, we have the same denominator right now.
We have 9/12 is clearly greater than 8/12.
So 9/12 is clearly greater than 8/12. Or if you go back and you realize that 9/12 is the exact same thing as 21/28, we could say 21/28 is definitely greater than-- and 8/12 is the same thing as 6/9-- is definitely greater than 6/9. And we are done.
Another way we could have done it-- we didn't necessarily have to simplify that.
And let me show you that just for fun. So if we were doing it with-- if we didn't think to simplify our two numbers first. I'm trying to find a color I haven't used yet.
So what's the prime factorization of 28? It's 2 times 14. And 14 is 2 times 7.
Prime factorization of 9 is 3 times 3. So the least common multiple of 28 and 9 have to contain a 2, a 2, a 7, a 3 and a 3.
Or essentially, it's going to be 28 times 9. So let's over here multiply 28 times 9. There's a couple of ways you could do it.
You could multiply in your head 28 times 10, which would be 280, and then subtract 28 from that, which would be what? 252. Or we could just multiply it out if that confuses you.
Well, to go from 28 to 252, we had to multiply it by 9. We had to multiply 28 times 9.
So we're multiplying 28 times 9. So we also have to multiply the numerator times 9.
So what is 21 times 9? That's easier to do in your head. 20 times 9 is 180.
To go from 9 to 252, we had to multiply by 28.
So we also have to multiply the numerator by 28 if we don't want to change the value of the fraction.
So 6 times 28-- 6 times 20 is 120. 6 times 8 is 48. So we get 168.
And so we can really just compare the numerators.
And 189 is clearly greater than 168.
654.213의 3의 자릿수는 뭔가요? 좀 생각해 보도록 하죠. 그러려면 일단 다시 써 보고 이번엔 다 다른 색으로 써 보겠습니다. 그러니까 654_ 소수점_213. 제 생각에 우린 소수점 왼쪽이 뭔지 꽤 잘 알고 있을 것 같습니다 우리는 여기 이게_ 좀 더 무난한 색으로 할게요_ 백의 자릿수, 아니면 십의 제곱이라는 것을 알고 있습니다. 그거 여기다 좀 더 큰 글씨로 써 놓을게요. 그러니까 여기 이건 백의 자릿수, 아님 십의 2승의 자릿수이니까 결국 백과 같다는 겁니다. 여기 이건 십의 자릿수입니다, 십의 1승과 똑같은 거죠. 여기 있는 것은 일의 자릿수고, 10의 0승과 같습니다. 그 다음 소수점 오른쪽으로 한 자리 옮기면 10분의 1을 의미하는 것이 됩니다. 이것은 10분의 1 아니면 10의 마이너스 1승이라고 볼 수 있겠죠. 그리고 이 자주색 숫자로 가면, 그러니까 오른쪽으로 두 자리 옮기면 100분의 1 아니면 10의 마이너스 2승입니다. 그리고 마침내, 이 3은 1000분의 1을 뜻합니다.
1000분의 1 아니면 10의 마이너스 3승을 의미하죠. 이제 질문에 대답하자면 654.213에서 3의 자릿수는 무엇인가요? 자릿수는 1000분의 1입니다. 그거면 실질적으로 문제에 대한 답은 나왔죠. 하지만 우리가 이것이 뜻하는 바가 무엇인지 정확히 이해하는지 알기 위해서, 이 숫자를 다시 써 볼 겁니다. 우린 이 숫자를 600으로 다시 쓸 수 있어요.
600 더하기 50 더하기 4 더하기 10분의 2 더하기 1000분의 3으로요. 아니면 자릿수에 대해서 우리가 제대로 알고 있는지 확인하기 위해서 우린 이 숫자를 6 곱하기 100 더하기 5 곱하기 10 더하기 4 곱하기 1_ 계속 잘못된 색깔로 하고 있네요_ 더하기 10분의 1 곱하기 2, 더하기 100분의 1 곱하기 1, 그리고 마지막으로, 더하기 1000분의 1 곱하기 3. 그러니까 희망 사항이지만, 이렇게 적어 놓는다면 우리가 자릿수라고 할 때 어떤 의미인지 이해할 수 있을 겁니다. 소수점에서 왼쪽으로 세 번째 자리에 있는 6은 100의 자릿수이므로, 600을 의미하죠. 이건 10의 자리에 있기 때문에 5 곱하기 10을 의미하고요. 이건 4 곱하기 1을 뜻합니다.
1000분의 1의 자리에 가면 이 3은 실질적으로 3000분의 1을 의미합니다.
Let's say that I love to collect marbles and I love to do it so much that sooner or later my entire room's filled with marbles and it's just this huge mess and when I look at them I have no idea how many marbles I've collected.
So I have all of these marbles, so I decided to do a little bit of organization.
So I could draw how my room looks like initially, but it would fill the screen with marbles.
So I say, you know, maybe I can get organized by... I can take ten marbles at a time.
So let's say... let me draw ten marbles.
One, two, three, four, five six, seven, eight, nine, ten.
And I put them in cans, in marble cans that exactly fit ten marbles. Right, so let's say that they exactly fit ten marbles.
So let me draw this so I can see how well I can draw a marble can Actually let me draw my marble can in purple.
So that's my marble can and let's say that it fits exactly ten marbles.
And of course I can draw my ten. One, two, three, four, five, six, seven, eight, nine, ten. So there I have exactly ten marbles in it.
And I call this a "ten can", so this is not a tin can, a "ten can".
So this is one ten.
One ten.
So good enough, at least this, I put all my marbles in ten cans, I might have a few left over.
Less than ten, if I had ten I would put them in a "ten" can but I put them all in "ten" cans, but I'm such an ambitious marble collecter that I've collected so many "ten" cans that I can't even see how many I've collected. My room is now full of these.
We're asked to add 50 plus 0.
Well, zero is nothing.
So you can imagine that we're starting off with 50 of something, and if we add nothing to that 50, we're still going to have 50 of that something.
If I have three of something and I added nothing, I'm still going to have three, so anything plus zero is going to be whatever you started off with.
So 50 plus 0 is going to still be 50.
Write 7/4 as a mixed number.
So right now it's an improper fraction.
7 is larger than 4.
Let's write it is a mixed number.
So first I'm just going to show you a fairly straightforward way of doing it and then we're going to think a little bit about what it actually means.
So to figure out what 7/4 represents as a mixed number,
let me write it in different colors.
So this is going to be equal to-- the easiest way I do it is you say, well, you divide 4 into 7. so you divide 4 into 7
If we're dealing with fourths, 4 goes into 7 a total of one time.
Let me do this in another color.
A total of one time 1 times 4 is 4.
And then what is our remainder?
7 minus 4 is 3.
So if we wanted to write this in plain-- well, let me just do the problem, and then we'll think about what it means in a second.
So you see that 4 goes into 7 one time, so you have one whole here, you have one whole ,and then how much do you have left over?
Well, you have 3 left over, and that comes from right over there.
That is the remainder when you divide 4 into 7.
3 left over, but it's 3 of your 4, or 3/4 left over.
So that's the way we just converted it from an improper fraction to a mixed number.
Now, it might seem a little bit like voodoo what I just did.
I divided 4 into 7, it goes one time, and then the remainder is 3, so I got 1 and 3/4.
But why does that make sense?
Why does that actually makes sense?
So let's draw fourths.
Let's draw literally 7 fourths and maybe it'll become clear.
So let's do a little square as a fourth.
So I'm gonna do it. Say I have a square like that, and that is 1/4.
Now, let's think about what seven of those mean, so let me copy and paste that.
Copy and then paste it.
So here I have 2 one-fourths, or you could see I have 2/4.
Now I have 3 one-fourths.
Now, I have 4 one-fourths.
Now this is a whole, right?
I have 4 one-fourths.
This is a whole.
So let me start on another whole.
So now I have 5.
Now I have 6 one-fourths, and now I have 7 one-fourths.
Now, what does this look like?
So all I did is I rewrote 7/4, or 7 one-fourths.
I just kind of drew it for you.
Now, what does this represent?
Well, I have 4 fourths here, so this is 4/4.
This right here is 3/4.
Notice, 7/4 is 4/4 with 3/4 left over.
So let me write it this way.
7/4 is 4/4 with 3/4 left over.
Now what is 4/4?
4/4 is one whole.
So you have one whole with 3/4 left over, so you end up with 1 and 3/4.
So that is the 3/4 part and that is your one whole.
Hopefully that makes sense and hopefully you understand why it connects.
Because you say, well, how many wholes do you have?
When you're dividing the 4 into the 7 and getting the one, you're essentially saying how many wholes?
So the number of wholes, or you can imagine, the number of whole pies.
And then how many pieces do we have left over?
Well, we have 3 pieces and each piece is 1/4, so we have 3/4 left over.
So we have one whole pie and three pieces, which are each a fourth left over.
My Aspirations...
My name is Syaiful Bahri
I am 21 years old
I live in Cianjur
I am now working as an administrative staff and also as a teacher
Have you worked abroad?
I was once offered
Not that I wanted it to, but someone offered me
But since I was already working here
And studying in college too
So I turned down the offer
When, where and what kind of work?
It was 2009.
The destination was Korea, to do drawing job
Because I was studying in a Vocational School majoring in drawing
So I was offered to go to Korea to do work in the same field as my major
What was the process to go to Korea?
There was training to learn Korean language
But I didn't stick too long, only around 1-2 days
Then I changed my mind
So I came back home
Do you still want to try your luck abroad?
Not really, I am not interested
After having a long thought about it, I decided I did not want to
Especially after hearing all the news about immigrants that was like...
Gosh, no, I don't want it.
Do you have any family member or friends working as migrant workers?
Only my third sister
Forced by economic situation
That is the first time in the family, my third sister works in Arabic countries
There are friends also, but not my peers
Mostly because of economic situation as well
Most of the men go to Korea
The women usually go to Arabic countries
Besides being migrant worker, what kind of job options available here?
If they don't go abroad, they usually go to Jakarta to work
Or work as farm workers here
Or stay here and do nothing
Because job opportunities are hard to find
There is no work here
At least we should go to the city of Cianjur and work in factories
Otherwise, the young men choose to go to Jakarta
How is the education level in here?
For now, thankfully, many have graduated Senior High School or Vocational School
Before, people only studied until Middle School
Nowadays, since there are colleges that offer distance learning program, more people are pursuing college degrees
What is your education and your aspiration?
I am in semester 5 majoring in Pancasila and Civic Education
I want to be a teacher.
Hopefully I could.
We've seen a reasonable number of acid reactions and base reactions.
So let's just write down a few of them for review and let's see if we can see a general pattern here.
And a lot of this might not be any news to you.
So if we have hydrogen flouride, or if it's in an aqueous solution it's hydrofluoric acid.
We know that this is a weak acid-- it doesn't disassociate completely.
So it's in equilibrium.
Some type of equilibrium.
That doesn't mean the concentrations are equal.
This hydrogen disassociates.
Actually, we know in reality, it tags a ride along with another water molecule and forms hydronium.
And then you have-- and, of course, this is still aqueous.
Everything is going on inside water.
And then you have left over your fluoride anion, or negative ion.
And that's also in an aqueous solution.
And we could have rewritten-- actually, let me write another reaction here, just so you can see the general pattern.
Let me write another acidic reaction.
Let me write ammonium.
So that's NH4 plus-- it's ammonia with an extra hydrogen in an-- let me just write that-- in an aqueous solution.
That can disassociate to one of those hydrogens popping off in an aqueous solution.
And then you have ammonia, NH3.
That's also in an aqueous solution.
Now both of these describe an equilibrium reaction, but it kind of implies that we're dealing with weak acids.
You take an acid, and they're producing hydrogen, which is at least the Arrhenius definition of an acid if you looked at the Bronsted-Lowry definition where they're donating protons to the solution.
They're creating hyrdonium, they're donating protons to the water around it.
But it kind of describes it as an acid.
But we know it's a weak acid, so this reaction goes in two directions.
So we can write the same reaction essentially as a basic reaction.
So we can-- instead of saying hydrofluoric acid is our acid-- we could say hey, if I just have a fluoride anion, if I just have a negative fluoride here, I could say a negative fluoride, if I put that in-- actually, I keep making that same mistake.
The fluorine does not have an I in it.
I do that because chloride does.
Let me erase this.
Hydrogen fluoride is HF.
So it's just F there.
Let me go to the periodic table.
See, I always confused fluorine with chlorine because
F is just for flourine.
But you get the point.
OK.
So I could rewrite the same weak acid equilibrium as a weak base equilibrium.
Or I could say a negative fluorine anion in an aqueous solution is in equilibrium with-- and now we're saying I'm considering this a base, which means that it's going to increase the concentration of OH.
So what this might want to do is it might want to grab some hydrogen from some of the water that's in the aqueous solution.
So it grabs some hydrogen and becomes hydrogen flouride, or hydrofluoric acid.
Let me do that in that magenta color.
It's aqueous.
And where did it get this hydrogen from?
Well, it got it from one of the surrounding water molecules, which was H2O.
Since it gave away one of the hydrogens now it's just OH minus.
So the surrounding water molecule is OH minus aqueous.
Now these might look different.
This is donating a hydrogen to the surrounding medium, and then you're left with just the fluorine molecule.
Well, this is essentially creating a hydroxide molecule out of the surrounding medium so it looks basic, but if you think about it, these reactions are the same.
I mean, you could have just gone in reverse direction.
You could say, hey, this is going to react with some random hydronium molecule or some random, free-standing proton out there.
And then it could form hydrogen fluoride, but we know that hydronium isn't just sitting everywhere, that whenever you take the reverse reaction, whenever you're going in this direction this doesn't have to grab this hydrogen from an H3O.
It could grab it from an H2O.
And then you would have this reaction.
These are equivalent.
And we could do the same thing here for ammonium and amonia.
We could write ammonia as a base.
NH3 is in equilibrium as a weak base with-- it can grab a hydrogen from its surrounding medium and become NH4 plus in an aqueous solution.
And then it would have grabbed that hydrogen, probably from a water molecule because that's what's around it.
And so that water molecule will become an OH minus.
And so now this looks ammonia is a weak base.
Ammonium is a weak acid.
But these are equivalent reactions.
Now, you're probably already seeing a relationship here.
Ammonium is a weak acid.
Ammonia is a weak base.
And what's the difference between the two?
Just an H.
Hydrofluoric acid is a weak acid, just a fluorine anion.
A negative fluorine is a weak base.
And what's the difference between the two?
They're just difference of a hydrogen.
Let me write that down.
So let me write weak acid.
And then you have your weak base.
So your weak base-- let me write our weak acid is first.
We had hydrofluoric acid, and then the weak base is when you essentially just dump the hydrogen, just the hydrogen proton.
You kept the electron, so that's why it's a negative charge right there.
Hydrogen without its one electron is just a proton because it has no neutrons.
The other one was NH4 plus.
You dump one of the hydrogens and you get NH3.
So what's the difference going on?
These are all minus a hydrogen.
Or if you go this way, you're plus a hydrogen.
So you have these kind of conjugates.
And this has all been a long-winded way of introducing you to this idea that you have these conjugate pairs.
Like hydrofluoric acid, or hydrogen fluoride and just the fluorine anions.
So these are conjugate pairs.
Which are essentially two molecules that are identical except for a difference in one hydrogen.
No more than one hydrogen.
One day there might be a test where someone shows you two molecules that are separated by two hydrogens-- those would not be conjugate pairs.
For example, if I show you H2O and OH minus, these are conjugate pairs.
Because this over here is exactly this minus a proton.
And, in fact, let me be clear that it's not just minus the hydrogen-- minus the proton.
One of them is keeping the electron.
So this is minus a hydrogen proton, this is plus a hydrogen proton.
So the difference between these two are just a hydrogen proton.
So these are conjugate pairs.
Now, if I were to say that H3O and OH minus, you might be tempted to say, hey, this is very acidic, this is a base, this is a conjugate pair.
But no, there's a 2 H, 2 proton difference.
This is H3O plus.
There's a 2 proton difference, so these are not conjugate pairs.
So let me just cross that out.
But these are.
Now, you could say, if you have H3O, you might say, hey, what's the conjugate base-- and that's a new word I just introduced you to-- what's the conjugate base for H3O if H3O is an acid?
Well, you take one H from it and you get H2O.
So this is a conjugate pair.
And I just said a word without defining it, so now let me define it.
Within every conjugate pair you have an acid and a base.
And if you say, oh, what is the conjugate base for hydrofluoric acid, you get rid of a hydrogen and you say, oh, it's just this fluorine anion.
If you said, I have some of ammonia, as a base, what is its conjugate acid?
So if someone asks you, what is a conjugate acid, you add a hydrogen proton to it and you get ammonium.
So I could call these the conjugate acid.
Let me just change terminology-- conjugate.
And we'll see that actually, you don't have to be using a weak acid or a weak base.
Conjugate acid, and then you have a conjugate base.
And even though something might be a conjugate acid or conjugate base, it doesn't necessarily mean that they're very basic, for example, or very acidic.
If I have hydrogen chloride, we know this is a strong acid.
Hydrogen chloride.
Its conjugate base, we essentially just get rid of one of these hydrogen protons-- it doesn't take its electron with it.
So it's just going to be the chlorine negative ion.
This is its conjugate.
If I gave you a chlorine negative ion and said, what's its conjugate base-- what's its conjugate acid? you'd say it's hydrochloric acid.
If I gave you hydrochloric acid and I say, what's its conjugate base, you get rid of a hydrogen proton only, and you're left with the chlorine negative ion-- You said that its conjugate base.
Now, with that said, we know that when you put hydrochloric acid, we know this reaction.
This was I think the first reaction we looked at in aqueous solution.
It disassociates completely to form hydrogen protons plus chlorine anions-- everything, of course, in an aqueous solution.
Now, the fact that it disassociates completely, that this is not an equilibrium reaction, this implies that this guy is more basic than water.
He has no temptation-- no, no-- let me say that he is less basic than water.
He has no temptation to grab these hydrogen protons from the surrounding medium to reform hydrochloric acid.
This reaction does not go in this direction.
So even though this chlorine anion, or negative ion of
chlorine, is a "conjugate base of HCL", that doesn't necessarily mean it's that basic.
This is less basic than water.
It wants the hydrogen protons less than, let's say, hydronium.
So if you put some chlorine plus some hydronium, or let's say you have some H plus, you're not going to reform hydrochloric acid.
So this is not really basic even though it's considered a conjugate base.
And that's generally the case whenever you're dealing with strong acids, like in the case of hydrochloric acid.
If I had a big solution of just chlorine anions in water, so I just had tons of a super high concentration of chlorine anions and water, because it's not going to do anything to change the actual hydrogen or hydroxide concentration in the water because it's less basic than the water itself-- it doesn't want to take or give anything to the water-- the PH, so if you have a soup, the PH would be 7.
If you have chlorine minus in an aqueous solution-- and I don't care what its concentration is, you could have 10 molar of it-- the PH is still going to be 7 because it's not going to change its solution.
It's not going to change the PH, just this by itself.
Obviously, if you put hydrochloric acid in an aqueous solution this will change it, because you're going to be dumping all of these hydrogen protons into the solution.
So in general-- I mean, you can kind of remember it, but I think it's maybe common sense-- a strong acid's conjugate base is neutral in water.
Neutral.
So that means no impact on PH.
You say chlorine plus H2O, I mean, you're essentially still going to have chlorine plus H2O.
You're not really changing the concentration.
Now, on the other hand, when you're dealing with weak acids, so this reaction will go in the other direction.
If you put some fluorine in water, it will grab some hydrogen-- not necessarily a ton of it, but it will grab some hydrogen from the surrounding water-- and increase the hydroxide concentration.
It's increasing the concentration of this thing right here.
So it is making, in this case, it is making the solution more basic.
It's increasing the PH of the solution.
So whenever you have a weak acid its conjugate base will be a weak base.
And you could make this statement the other way around.
If you have a conjugate-- let me switch colors, this is getting annoying-- conjugate base-- sorry, a weak base, its conjugate acid is going to be a weak acid.
So hopefully you get the idea here.
It's actually not that fancy of an idea.
It's just that if you have an acid, its conjugate base is just that acid minus a hydrogen.
If you have a base, its conjugate acid is just that thing plus a hydrogen.
Actually, let me just do a bunch of problems here just to really hit the point home of what we're talking about.
Let's just do a bunch of them.
So if this is the acid and this is its conjugate base, so if I have-- I mean, you don't even have to know the words.
If I have that, the conjugate base, well, I'm just going to get rid of a hydrogen proton.
So NO3 minus.
I didn't get rid of the whole neutral hydrogen molecule.
Remember, I just took a proton away, the electrons stay the same, so I have a negative charge.
Let's say we did H2SO4.
So its conjugate base, get rid of a hydrogen.
HSO4 minus.
If I have hydrogen bromide, get rid of a hydrogen.
It's BR minus.
And this is a strong acid.
So this is going to be a neutral-- if you put this in water, it's really not going to do anything even though you are calling it hydrogen bromide's conjugate base.
Now, if we go the other way.
If we give you the base, if I give you OH minus, what's its conjugate acid?
Well, you add a proton to it, you get H2O.
If I have H2O-- we already did that-- you add a proton to it, you get H3O plus.
If you have-- I mean, we could just keep going.
Let's say I have that.
If I add a hydrogen to it, I have H2.
There you go.
And it's neutral now because I added a proton.
Anyway, hopefully I haven't beaten this horse to death and you understand what conjugate acid and bases are all about.
<i>Brought to you by the PKer team @ www.viikii.net
Episode 12
You are leaving already?
It's late so just sleep over.
No, thanks.
I have some books to look over, so I'll just go.
Hey...
You should stop, and move back in now.
I know you are living on your own to find your goal in life, but what about my dream of living happily together, all of us, and living a bustling life?
Your being like this is making it hard on Ha Ni as well.
From her perspective she may be thinking that she is the reason why you won't come home, so be a little more nurturing and caring of her.
Please allow me to make my own decisions regarding my life.
I do not want to be manipulated.
Seung Jo...
I did not want to stay in this house, that's why I left.
You brought Ha Ni back in without even asking, or considering my feelings on the matter.
Because of that, do whatever you want Mother.
Baek Seung Jo...
I am sorry.
I am leaving now.
Dear, understand him...
It's not like I said anything about him not coming back.
He left in search of his dream and to change himself in the process.
But in the end, nothing has changed.
We do not ever see him around.
He is still as cold as ever towards Ha Ni.
Dear, how about you sit down and have another talk with him?
He will at least listen to his father
Even if I talk, does that mean he'll even listen?
Let's just wait, and see what kind of decision he makes.
But, besides that, has he been eating well on his own?
Judging by what I am seeing it seems his face has sunken in.
Let's wait a bit.
At least, he makes his own decision. He should be fine.
You think so?
Enjoy the meal!
We will eat well!
Ah!
It's hot.
What's wrong with your hand?
Housewife's eczema.
This is what happens when you wash the hair of 50 people a day. Oh my gosh...
Oh man does not it hurt?
Yeah it hurts it itches, hurts, and is driving me insane!
But it's better than sitting in class studying boring material!
I am still happy!
Min Ah how is the web comic you are working on?
Well I am drawing characters, and working at a part time job now.
But, what about you guys always being busy and leaving me alone!
I really can not this time.
After messing up, I always end up writing reports.
Aigoo, you should try a little harder.
How is it?
Is it good?
Yes.
Yes, it's really good.
Really?
But, what kind of noodles are these?
Nutrient filled noodles for you youngsters busy working and studying.
It's is especially made for you girls by So Pal Bok Noodles, and it's called Sam Gye Chi Jak Chopped Noodles.
It's a delicacy mixed with the world's best samgyetang and chopped noodles.
Sir, can I have one more bowl please?
But dad...
Huh?
I do not see Joon Gu.
That kid has recently fallen in love with the art of cooking.
He's gone to the market to go personally pick and choose his own ingredients.
Is that really our Bong Joon Gu?
That's really different from back when he was in High School
Did you guys hear?
About what?
Our high school reunion thing?
Reunion?
They have a dress code with a theme of school look.
I heard it too.
I heard.
But I am in trouble, because all my uniforms have gotten smaller because I've gained weight.
I do not know whose idea it is, but I love it.
Our memorable uniforms...
Seung Jo looked good in his uniform.
Especially the winter uniforms.
Baek Seung Jo again?
You heard about it?
What?
That there's a high school reunion, and the dress code is our old uniforms.
Isn't that a fun idea?
Who gave such a childish idea?
I heard it and I do not have any interest in it.
Still,
I am already excited about meeting my old school mates.
Are not you curious about how they are doing?
If you are interested then go.
Really that brat...
I just can not figure out what he is thinking.
Seung Jo said he would not go?
Yes...
Yes, he said it was childish.
Why is he like that?
I totally miss those youthful days.
I had a blind date at a dduk bok gi stand in front of the school.
Omo!
The Ddukbokki in that restaurant is really good!
Many school kids go there.
What was I talking about?
Blind dating!
Aah blind dating!
It was blind dating!
Until I ate the whole plate, that male student could not bring himself to say a word.
So I told him to have some.
He was like "Yes!" and started gulping down all the water.
You were only in high school?!
Yes.
Yes, I am talking about your dad!
Student Baek Soo Chang!
Back then he was so cute!
For me, I can not forget how Seung Jo looked at graduation night when he did his speech!
I am going to have fun and I am going to be happy.
I am going to live like that.
Everybody, where ever you going to be, live having fun.
Omo, Ha Ni!
I have thought of a good idea that would make Seung Jo want to attend the high school reunion.
Really?
What is that smell?
Oh my!
What to do?!
Mhm!
What is it?
Ahh.. heh <I>The thing that allowed me to meet Seung Jo in my dream <i>was the leaf.
But still, he did not give me an F mark.
Parang High School's 14th Graduating Class Reunion
You have become much prettier.
Where are you going? <i>Did Seung Jo come?
Ha Ni!
Why are you so late?
Yeah!
You do not even answer your cell phone!
My mother told me to leave my cell phone at home.
Hand phone?
Why?
I do not know.
I think she has something planned.
But, it's strange coming here wearing our school uniforms.
Yeah?
Why?
Is not it thrillng and fun as if we are ditching, which we never got to do in high school?
You never ditched?
I said I never was able to do it wearing my uniform.
Hmm...
Hey, what about Joon Gu?
Ah, there was a group reservation at the restaurant, so he could not come.
Oooo he is a real chef now?
Seriously.
But... Seung Jo... did not come?
Aigoo!
If you are here to see Seung Jo, then why did not you search for him already?
He is already here.
Over there.
He looks completely uncomfortable.
Oh!
He is here!
Then I am only going to greet him for a bit.
Only greet him?
You said you would not come, but you did.
Why did you leave home without your cell phone?
Huh?
That...
Mother had to quickly leave for Busan to meet her family and you left your keys at home.
She told me to give them to you, so I came.
Is that so?
I did not...
Ah.. sorry. Looks like you went out of your way because of me.
Thank you.
Without you I would not have been able to enter the house tonight.
Well since you are here, spend some time with friends.
No need.
Baek Seung Jo where you going?
Sit down, Sit down.
It's been really a long time.
Long time no see, how have you been?
You are the same as always.
You are making a statement that the school look is childish right?
That's just like you Baek Seung Jo.
Is not that Baek Seung Jo?
Have you been well?
Yes
Punk, it would've been great if we went to Tae San University together.
We could have enjoyed college life together.
I hear you are still being called the prodigy even at Parang University.
Do you know how regretful the head of administration is for losing you?
That's Oh Han Ni right?
Has she become your girlfriend?
Wow Oh Ha Ni, I guess personality does win it.
She's been following you around so long, and eventually even got into Parang University and made it happen!
Seung Jo is the amazing one.
It probably wasn't easy accepting her as a girlfriend.
Girlfriends?
How bothersome.
I don't do that kind of crap.
Then again, I guess a girlfriend doesn't really fit with the almighty Baek Seung Jo.
I see, so Class 7's Oh Ha Ni.
But Baek Seung Jo, what's your major?
There's no such thing.
I'm undecided.
You mean you still haven't decided on a major?
Not yet.
You can inherit your father's company.
Isn't the Chairman's position just waiting for you?
Parang High's best band!
Taking over the Hong Dae indie band scene...
Annyong Bada! <i>Brought to you by PKer team @ www.viikii.net
It must have been fun seeing his friends after such a long time, <i>but he left without a word.
Is he sick?
Seung Jo , I...
I would like it if you would take over my gaming company.
At first as my reliable right-hand man, and later on I would like it if you could take the company in a new direction with your own abilities.
If you wanted, you could easily become a doctor.
So kids like Nu Ri...
I think it would be nice if you became a doctor that fixed the illnesses for many people all around the world.
You forgot this.
Thanks.
May I have a seat?
As you wish.
Thank you.
Are you worried about something?
Tell me.
Don't they say sharing worries could halve them and sharing your happiness will double it?
I will help you.
When I'm worrying about something, or if something good happens, I let Min Ah and Ju Ri know.
Once I do that, it feels like a weight has been lifted off my shoulders.
Then again, sometimes I tell them too much and that becomes a problem.
I'm going to go into the medical field.
I'm going to apply to the med program.
Though I don't know whether or not it's a good match for me, for the first time I've found something I'm interested in.
Seung Jo ah..
Don't tell anyone about it yet.
Especially my parents.
Don't go around spreading rumors all over the place either.
Do you understand?
Of course...
Why would I spread rumors?
Omo!
Then am I the only one who knows that?!
Well, members of the tennis club,
I have some really good news to tell you.
Next week is the 10th year anniversary of our Top Spin tennis club!
So we're thinking of bringing together all the past and current members to host a really great big party.
What do you think?
Aren't you excited!?
Next week is a holiday, so do you think Hae Ra will come?
I got it cheaply because of the holidays.
On top of that, a party with past and current members?
I don't even think I want to go.
Really?
Then should I take that part out?
I think if you could just get Seung Jo to come somehow,
Hae Ra will just come automatically.
That's right!
This is why you have the right to be the captain!
Seung Jo...Hae Ra... That's right!
Then I need to go ask for Ha Ni's advice. <i>So this is the medical department that Seung Jo is trying to get into. <i>I hear it's totally busy here. <i>Doesn't that mean it'll be even harder to see Seung Jo?
Ha Ni!
I've been looking for you everywhere.
Sunbae!
Sunbae, what are you doing here?
What about you?
At the medical department... I mean I came looking for you.
I'm here because of Seung Jo...
Seung Jo?
What about him?
Anyway, why did you come all this way searching for me?
It's nothing big, but next week is our Top Spin's 10th year anniversary.
So I'm planning a party.
Planning a party?
So why are you telling me...
Listen!
For this party, if Seung Jo doesn't show up it becomes a real problem.
Senior, don't tell me you're trying to use Seung Jo again to get to Hae Ra.
You're not trying to use my Seung Jo as bait are you?!
Stop using that method now!
If you're not careful things might just turn for you.
I think you meant turn against you.
Anyways, forcing Seung Jo and Hae Ra together does us absolutely no good.
I know...
I know, I know, but if not for this method I will miss the chance to confess to Hae Ra.
I need Seung Jo, so Han Ni, why don't you...
It's Seung jo!
It's Seung Jo.
Ha Ni!
This is my last favor.
I'm counting on you.
Do you understand?
I'm counting on you.
Were you following me?
No.
I really wanted to visit the medical department at least once.
I mean it may be the place you start attending.
But it's amazing here.
I guess all the people here are going to become doctors in the future.
There are some that don't.
But why did you come here?
It's not time to choose your major yet.
I came to meet a professor.
Why?
To talk about what?
What would you know even if I told you?
Omo, don't look down on me.
Oh yeah, today Dad and Ahjushi went to get a check-up at the hospital.
I don't know how things turned out.
Want to go stop by the house with me later on?
What presents will those two bring back this time?
What do you mean present?
Cake?..
Today is your birthday?
Idiot, I mean an illness.
I want coffee.
Not for you.
I'm absolutely sick and tired of hospitals now.
So how was it?
What about the results?
Here it is.
Show me. Health Examination Results
I can barely understand it.
Induced...
Blood sugar...
It's a cardiac stress test.
It's to check for cardiac infarction or angina.
Let me have a look.
Your blood pressure is high.
Your heart rate is high too.
You've got a bit of cardiac stress.
Your cholesterol is high too.
Father, you have to watch out for your heart.
I heard the exact same thing from the doctor.
Honey, you should be healthy.
You need to think of your family.
Hey, Seung Jo.
How are you so good at it? It's filled with cryptic words!
Though you're my son, you really amaze me.
Hyung could become a doctor too, since he's a genius.
Baek Eun Jo.
Being a genius isn't the only good thing to be.
Honey from now on you're banned from all things sweet and oily things. Then what do I eat?
Dad!
You came.
Did something happen?
Yes?
He used to come running out screaming "Ha Ni" whenever you came.
But he's pretty uncaring lately.
Joon Gu?
Why?
What is he doing?
Hey.
Over there.
Take a look into the kitchen.
Today was the first time Joon Gu made a dish presented to a customer.
What?
Already?
Then does that mean Joon Gu is going to become a chef?
Well, he needs a bit more work with the foods presented to the customers.
That's right.
He may look that way, but his cooking abilities aren't bad at all. And he tries really hard too.
Hey.
Let's watch him Joon Gu.. I just thought he was messing around everyday.
But I need to look again.
True.
See how hard working he is.
It's a bit early but he should do alright.
But he's actually quite good.
He wanted to show you first.
Isn't he commendable? <i>It's my first time to see him like that. <i> He doesn't even know that I've come in.
Here.
It looks delicious.
Ha Ni, here.
Eat well.
Yeah.
I will eat well.
How is it?
Hey!
Success!
It's really delicious, Joon Gu ah.
For real?
Yeah.
It's very delicious! It's the best!
Ha Ni.
If I cooked something well, I wanted you to be the first to taste it.
Wait a moment.
Here.
Try out this dumpling cut noodles.
It's got 3 colored dumplings of green, red, and yellow and the chewy noodles are incredible!
If you try it, you'll definitely like it! Joon Gu ah..
Eat a lot.
Now even I've found something I'm confident in.
There is more.
Wait a second.
Today I saw a new side of Joon Gu. I had always ignored him but
I'm sorry, Joon Gu ah.
Are you.... waiting for someone?
You're not going to sit?
Are you going to go to the 10 year anniversary for the tennis club this week?
Why?
Are you curious?
It's pertaining to the club and there are going to be a lot of Sunbaes coming, so if possible it would be nice if lots of people attended.
I'm not really interested in a meeting where people gather saying things they don't really mean.
Oh! Why don't you go and enjoy it for me?
That should do it.
Do you have anything else to tell me?
Yes?
Well..
I'm curious about something.
We already talked about the 10 year anniversary.
What is it?
Well.
You're undecided on your major, so have you picked one yet?
You're acting funny today.
Why are you curious about my major?
It's just...
To be honest ,you could go anywhere you please as long as you want to, right?
So..
So..
By any chance,
I was wondering if you were going to follow in the foot steps of Seung Jo.
Why do you think about these things?
You're really an idiot.
Just because the person you like is going, doesn't mean you have to go to hell with them too.
Though I'm interested in Seung Jo, I don't care about the major he chooses.
I... will do as I wish, because it's my life.
You don't always have to be together to date.
Unnie will leave now.
See you.
She always ends it like that!
Well.. thinking that way is pretty cool.
Acknowledged.
Pay attention to what you're doing.
What are you doing?
If you're going, leave. If you're staying, sit.
Joon Gu is still working hard to become a chef.
And Hae Ra has things to do. Is that what you mean? o?
Even Eun Jo seems to be worrying about his future.
And you have nothing?
Yeah.
I envy you.
Your carelessness.
I, too... have a dream.
But.. what?
Something you want to do with me?
Tell me... about your dream.
I'll hear you out.
You know...
Seung Jo you're the doctor for a small village and I'm the nurse that helps you.
You're famous so you're always at the hospital.
It's not a big hospital like the university ones, but still, I try my hardest to help you.
Like attending to a crying child or something.
But.. there's a problem within that dream.
For example, if you say you want to become a pilot, then I want to become a stewardess.
And if you say you want to become a pro golfer, then I want to become a caddy. In the end... my dream is simple and does whatever it pleases.
I.. am just moving in the direction of Baek Seung Jo, who is at the center of it.
There exists no such thing as myself.
It's exactly as you said.
But when I decided to become a doctor,
I thought about it a lot too.
So what?
Even an unrealistic dream like that...
A dream is still a dream.
It fits you.
Hey! Is it really that unrealistic?
Do you really think you could become a nurse just because I'm going to be a doctor?
Then again a dream the harder it is to attain . . . the more you want to try it out.
Right? <i>Dad</i>
Have a seat over there.
Today someone from the university, a medical professor, contacted me.
Ah, that?
Is it true that you're going to enter the medical program?
Yes.
I'm planning on entering the medical program starting next semester.
What?
Did you decide on your future without even discussing it with me?!
Have you been ignoring what I told you?
He seems to be angry.
I thought about your company too, Father.
But like you, Father, and like Ha Ni's father...
I've decided I want to put my life on the line in order to do something I want to do.
Seung Jo, what I am saying, my dream is. . .
I have decided to become a doctor.
Even if you say anything, it will be of no use.
I will not inherit your company.
Seung Jo, what did you just say?
Dad!
Dad!
Honey!
Dad!
Dad, what's wrong?
Are you in pain?
Honey! Honey, come back to your senses!
Dad!
They said it's not life threatening.
The examination results are not out yet.
What exactly is wrong?
They say it's angina.
Angina?
Then he should have felt symptoms in his chest, feeling really uncomfortable or something.
He must have been pushing himself too hard.
Lately company work has been really hard.
I see...
Most importantly his condition needs to stabilize.
He will have to stay at the hospital for the time being.
Yes.
There are many good doctors here.
It must be very hard for you.
This person seriously...
Even when he is having such a hard time he won't complain
Since he is always smiling, I didn't know either.
Mother.
Mother.
Oh?
I'll be going back first.
Because Eun Jo is alone.
Right.
Thank you, Ha Ni.
You have to be careful too, Mother.
What if you collapse too?
Ha Ni.
Seung Jo, <Br> you go as well.
Will you be okay?
I'm alright.
Go home.
Alright.
Then, I'll come back tomorrow. <i>Brought to you by the PKer team @ www.viikii.net
Will your father be okay?
It will be hard since he'll be getting physical examinations starting tomorrow.
I'm going to use this opportunity to fully rest up.
I will have to take a break from school too. <i>It's really hard on everyone... <i> Even if for a little, <i>I want to help too.
Sunbaenim, aren't you going to eat?
We'll see.
Sunbaenim, you should eat.
Hae Ra.
Sunbae.
You didn't come to the 10 year anniversary party.
I never said I was going.
Oh, so that's how it was.
I heard the only people that went were you and and the captain.
So I heard the party was a bit down in the dumps.
It turned out like that.
So I hear you had to use a lot of your own money.
I wasn't able to attend but I'll pay the fee.
Please accept it.
Thanks.
Is that what you're having for lunch?
Let's go together.
I will buy lunch for you today.
Ah, no it's okay.
I really like hot dogs.
And it's made from cow meat, and it's really delicious, and If I have just one I'm full.
Is that so?
Then...
Is it not myocardial infarction (heart attack)?
I don't think it'll turn into a myocardial infarction.
But if he continues to overwork himself like this, there's more than a chance for it to turn into a myocardial infarction.
If that happens the chances of surgery--
There's that method of using the femoral artery and doing a bypass graft.
Oh, you know well.
We would want to avoid that path.
So, with patience, we will treat him with medicine.
Yes.
You came?
Who is he?
He is the manager from your dad's company.
Do you not know that he has to stabilize?
This is totally prohibited.
It seems to be really important work.
Even so.
It'll be hard for him to recover like that.
You know how your father can't be at ease if he doesn't make the decision on his own.
He's been dead worried about work, that is why he collapsed like that.
Chairman Dad!
Chairman!
Honey, what's wrong?
Dad!
Honey!
[No visitors allowed]
That was a close one.
There's not many days left until the game is released.
After your father collapsed the game developer left and vanished.
He heard that and that's why he collapsed.
What should we do?
Your father is just laying there and his company is not in good shape.
I will have to go.
Seung Jo.
I'm still young and have no experience, but I'll take care of the company until Dad's health gets better.
Thank you Seung Jo.
Seung Jo said he would work in the company?
That's right.
Seung Jo's dad was happy and his condition is getting more stable.
He is getting better.
That's great.
And Seung Jo is returning to the house too.
He's doing as his father wished.
I guess this is what you call turning a misfortune into an advantage.
Ha Ni I'm going to go to the hospital.
Will it be okay, that I'm leaving everything to you?
Yes, don't worry.
Right, I'll leave it to you.
Ha Ni this is your chance when there's no one to interfere!
Try experiencing what it feels like to be on your honeymoon!
Aigoo, you arrived?
Everyone, Chairman's stand-in is here.
Say hello.
How do you do!
A gaming company's atmosphere is a bit like this...
Ah, yes.
It's good.
This way. Please come this way.
Get up please.
Did you see him smile?
Ah, it's Yon-sama!
They say his IQ is 200. Aigoo, he's not going to fire me because I'm old right?
You should get ready.
Here are the documents regarding our company as well as new games.
Please look over this material.
Should we have the meeting around 11?
There's quite a lot.
Is that so? I'll try to read it fast.
Yes. Then...
Manager.
Yes?
When we're together, please speak comfortably.
Oh no, you are here as the interim CEO.
Then, I will be leaving.
Manager, he didn't talk about restructuring right?
Does he have a girlfriend? Is he dating anyone?
- Are we going to get fired?
- How was he?
Aigoo, do not worry about other people is business and just focus on your work.
- It's because we are worried!
- Get back to work!
No, have you looked through all those documents?
This is the data that is compared to last year's data?
Yes, that's correct.
It looks like the profit has dropped significantly this year.
I think we may have been affected by the large scale push by international gaming companies.
Simply put, at this state, we are in a dangerous stage.
To add to that, the new game that was supposed to launch is gone as well.
We're on thin ice.
If we continue like this it'll be an operational crisis.
We're in a situation where even a merger is impossible.
Without some major support we may just...
Eun Jo, you're really hungry, right? It'll be done in a few minutes.
Let's just order...
What are you talking about?
Restaurant food is high in calories.
With oil and salt, you don't know how much they put in it.
And on top of that, they don't put much vegetables.
I got it, alright! Hurry up!
Next time, don't pretend like you know everything.
Why don't you studying cooking?
Oh. What do I do? What are you going to do if you get both me and Hyung sick too?!
Seung Jo has arrived.
You did well.
Are you very tired?
Hurry and change your clothing.
Shower?
What are you doing?
I am taking off your jacket.
Why are you doing that?
What do you mean? She is acting like a new bride.
What are you saying?
Ahjusshi is at the hospital.
How could I be thinking such indecent thoughts?
You really are an indecent person.
Go get changed quickly!
Today's menu is seasoned taro, grilled mackerel, and bean paste stew.
Eun Jo, eat it.
Here.
Oh gosh it's salty.
Did you pour in the whole bottle of salt?!
Hyung, this does not taste good.
So, I suggest that you do not eat this.
That sound...
The taro.
Taro makes a sound like that?
It's not fully cooked Hyung! Hurry and spit it out!
Do not force yourself.
He swallowed it.
Hyung, you'll get a stomach ache!
Baek Eun Jo, do not just complain.
Hurry and eat it.
Eat it? Which one?
Try poking it with your chopsticks and just eat the ones that are cooked. <i> Even with a horrible meal, <i> Seung Jo did not complain even once and just ate it.
Oh, Ha Ni!
It's Ha Ni?
What, packed lunch?
Why would you need to pack a lunch?!
Ah, Ha Ni's making packed lunch?
How in the world could she do such a thing with such soft hands?!
You're going to what?! I'm on the phone!
Yes, okay.
Seung Jo and Eun Jo's lunches.
Oh. Egg rolls?
- Egg rolls?
- Egg rolls?!
How can you not be able to make something that easy?!
Our Ha Ni is making Baek Seung Jo's lunch?
You're out already. Did you grab your handkerchief? What about your wallet?
I have it.
Here.
Take this.
What is it?
What do you mean? It's lunch.
I'm going to eat at the cafeteria, so it's fine.
No, don't eat that stuff.
I woke up at the break of dawn and prepared this.
The egg rolls are the point.
When you open it, you'll be totally surprised.
See you!
See you.
You probably want to call him "hubby!"
What are you talking about?
Ahjushi is ill. That's so indecent.
New bride Ha Ni, a nickname given to yourself.
I, too, will see you later.
Goodness that youngster just says the darnest things.
Do a good job!
Ha Ni!
Oh.
Come with me for a second.
Oh, I have class...
It'll just take a second.
Is it true that Seung Jo's father has been hospitalized?
That...
But you can't visit him!
He needs to be stabilized. Visitors are prohibited.
How's Seung Jo doing?
I am assuming Seung Jo is not allowed to visit either, right?
He is currently working at Ahjushi's company.
That's why I have not been able to see him.
Thanks.
Yes?
Are you eating lunch?
Yes.
Why don't you join me?
No. It's okay.
Enjoy.
It's a packed lunch.
Did your girlfriend prepare that?
What?
Well then, I'll come back after lunch.
Yes. Alright, a delivery of a special lunch box!
Oh, hey, hey!
Do not eat that.
Bong Joon Gu.
What are you doing?
I can not allow you to eat lunch that Ha Ni packed for you.
Instead, you... eat this.
Grilled eel?
From now on, I will come to this company everyday for the packed lunch Ha Ni made.
I won't leave you alone if you eat the lunch.
Ha Ni's packed lunch is for me.
Well then, thank you.
You did not poison this did you?
I do not play with fresh food!
I'll enjoy.
Do not waste any of the eel and eat it all up.
Let's take a look.
It's not bad.
Seeing Ha Ni's heart for Baek Seung Jo,
My heart is ripping apart.
But then again, I get to try out the lunch that Ha Ni made.
Alright.
Let's try this.
Ha Ni, I'm going to relish this.
Oh Ha Ni, do you truthfully dislike Baek Seung Jo?
How can you possibly feed him this?! But still, Ha Ni made it so I need to eat it.
Oh, I don't think I can eat this. <i>Brought to you by PKer team @ www.viikii.net
What are you doing this late at night without the lights turned on?
I am thinking.
What's the matter?
What's bothering you?
I can help...
Probably not, right?
Then, I am going to sleep first.
Father's not doing well.
Huh?
He might need surgery
Heart surgery?
That's such a big surgery.
I might need to continue working at my father's company for the time being.
It's just too much for father to handle.
Then, what about getting into medical school?
There is no reason that I have to go there.
There is.
This is the first time, is not it, that you wanted to do something, your dream.
It's not much of a dream.
Though I was smitten by it for a bit.
But once I do get into it...
I do not know how it's going to be.
Is it fun working at the company?
No, it's not.
Then, what should we do? You said that you are gg to live an enjoyable life at graduation day.
You promised in front of all those people.
I am not in the least bit interested but if I work at the company, my father will be happy.
Then at least, it is a half successful life.
I am not interesed but if others are happy...
What can you do?
What to do?
Really? Baek Seung Jo?
Seeing he stopped by the student administration offices.
It seems like Seung Jo is planning to take over his father's company.
I thought that if it were Seung Jo, would not do that
His father's condition does noto be good.
How do you know that . . .
Oh my, is that something to be surprised about ?
It's something you can figure out if you put your mind to it.
Especially how Seung Jo must be feeling right now.
I see that he is taken a leave of absence.
I understand.
What?
What do you know about Seung Jo?
I'm thinking about how to help him, that's why I said that.
What can you do ...
Oh Ha Ni...
How are you helping Seung Jo right now when he's going through such a tough time?
Following him around everywhere and getting in his way, or whining, and telling him it's fine and that it's all going to get better...
Comforting him like that?
Right.
You should at least do that.
Because those are the only things that Oh Ha Ni could ever do for Baek Seung Jo.
I'm going.
Living in the 21st century and playing a 2D game is a bit boring, but to play a different game, I mean there aren't many good games.
And when we do it's not that exciting.
Let's use the strategy of turning all the negatives into positives.
I think it would be nice if we create a game that's approachable, graphically appealing, and in 3D.
I heard your IQ was 200, I see you really are a genius.
It's not like that.
You just aren't utilizing your thoughts to their fullest.
Your brains are just a bit rusty because you haven't used them.
Now, shall we start deciding on the name of the game? Rusty...
Rusty...
Rusty?
Rusty?
That's great.
See, see?!
Wow, it's great.
Let's up the skills, actions, and combos.
Yes that's right.
The importance of the main character...
This is where it gets fun.
Mother, did something happen?
What would happen? There is nothing.
I just came to pick up some clothes.
Oh I thought...
Ha Ni, thank you, for filling in my empty place.
It's nothing.
It's something I have to do.
Even so, I'm really relieved.
Seung Jo is taking care of his father's company, and you are taking care of the house,
I feel much more at ease.
Seung Jo goes out to work early in the morning, and keeps working hard until late at night.
Is that so?
Really? It must be hard.
Ha Ni, are you doing okay?
You have to go to school and do the housework.
Of course I have to do it.
Ah, but, Mother.
What? Do you have something to tell me?
I have something to discuss with you.
What?
I'm going to be late, I'm going to be late.
Where are you going?
Seung Jo.
Can you give me a ride today?
Where are you going?
To the same place as you are.
The same place?
No way!
You. . .
I got the approval to work part time at your father's company. Please take care of me.
Oh Ha Ni this Mr. Kim.
Hello. My name is Oh Ha Ni.
Oh, hello!
Everyone, she came in as a new employee.
Say hello.
Hello.
I'm Oh Ha Ni. I will work hard!
Applause.
If you all look after me, I will work hard.
So please take care of me.
Our investor, President Yoon, is waiting downstairs.
Baek Su Chan was always busy bragging about his son, but I see it was all true.
Not at all.
You're too kind.
All right.
How is your father doing in the hospital?
He is getting better, but we thought this was an opportunity for him to take a break.
I guess I'll have to help a bit too.
Yes.
Please do.
Good.
President Yoon this is a document regarding the game we're currently developing.
Oh, I've already read it.
The game's name is "Rusty", right?
Yes.
The idea of the game is very fresh.
Thank you so much.
With an heir like you, I'm sure Baek Su Chang feels relieved.
You've got to make it into an even bigger company than what it is right now.
We've got to get past this hurdle and then think about that.
You have waited for a long time.
It's coffee, right?
Oh right.
Seung Jo-goon, how old are you?
I am 20 years old.
Oh, you're still young.
Don't you have a girl friend?
I don't have one.
Why? It seems that you are very popular.
Yes.
President Baek Seung Jo is really popular.
Oh.
But he doesn't pay any attention to them.
He enjoys reading and listens to mostly classic.
He's also so very good at tennis, at which he's won many matches.
His IQ is 200 too!
He also cooks as well as any chef!
He is all around perfect.
That is amazing.
Miss Oh Ha Ni...
Yes.
Would you leave now?
Yes, President Baek Seung Jo.
You came?
Oh, yes.
Do you have a second?
It seems meeting President Yoon was quite effective.
His employees came by and asked in detail about all the funds we need for the game.
Do you think they'll invest?
But that's...
The chairman has come to like you very much.
Yesterday, he called me and complimented you a lot.
The chairman has a grand-daughter.
He asked me if you could meet with her sometime.
Are you talking about something like an arranged date?
Oh. Yes.
He was saying how it would be a waste to marry off his grand daugther to just anyone.
For our company, we're at a state where we need President Yoon's help.
I was a bit flustterd with his sudden comment.
How should I respond?
Oh!
You're here early.
Huh?
The stuff!
Thank you.
Let's have Bulgogi today.
Lots and lots.
You seem tired these days so I have to pamper you.
And then everything that's giving you a hard time will all go away.
Thank you.
Thank you.
Oh, you arrived Seung Jo-goon.
Hello, Baek Seung Jo. <i>Brought to you by the PKer team @ www.viikii.net
If you had to choose a son in law... who would you choose?
But still, it seems Seung Jo wasn't thinking about it at all.
Divide.
Simplify the answer and write as a mixed number.
And we have 2 and 1/4 divided by 1 and 3/4.
So the first thing we want to do since both of these are mixed numbers is to convert them both into improper fractions.
So let's start with 2 and 1/4.
So we're still going to have 4 in the denominator, but instead of 2 and 1/4, remember, 2 is the same thing as 8/4.
So we have 8/4, and then we have another 1/4.
That gives us 9/4.
Or another way to come up with this 9, you take 4 times 2, which is 8, plus 1.
That gives you 9.
And then the 1 and 3/4, same process.
You're going to have 4 in the denominator, and then the numerator is going to be 4 times 1, which is 4, plus 3, which is 7.
So this is the exact same problem here.
2 and 1/4 divided by 1 and 3/4 is the same thing as 9/4 divided by 7/4.
And we saw in several videos already that dividing by a fraction is the same thing as multiplying by its reciprocal.
So this is equivalent to-- so these are all equivalent.
This is equivalent to 9/4 times the reciprocal of this.
We're changing the division operation to a multiplication, and we're taking the reciprocal of the 7/4.
For the reciprocal of 7/4, you swap the numerator and denominator, or the top number and the bottom number, and you get 4/7.
Now, we could just multiply these.
We could just say this is 9 times 4, which would be 36, over 4 times 7, which is 28, and then try to put it in lowest terms, or we could do it right now because it would be simpler.
We have a 4 in the numerator.
We have a 4 in the denominator, that'll eventually be in the denominator, so let's divide our eventual numerators and our eventual denominators both by 4.
So you divide this 4 by 4, you get 1.
This 4 by 4, you get 1.
So now when you multiply it, you get 9 times 1, which is 9, over 1 times 7, which is 7.
So we have our answer, but right now, it's an improper fraction.
They want us to write it as a mixed number.
And to figure it out as a mixed number, we can do it in our heads now.
I think we've seen this enough times.
We say how many times does 7 go into 9?
Well, it goes into it exactly one time, but when you take 7 into 9 one time, what do you have left over?
Well, you're going to have 2 left over, right?
7 times 1 is 7, and you're going to have 2 left over.
You need 2 more to get to 9.
So you're going to have 2 left over, so this is 1 and 2/7.
And we're done!
Humans have long held a fascination for the human brain.
We chart it, we've described it, we've drawn it, we've mapped it.
Now just like the physical maps of our world that have been highly influenced by technology -- think Google Maps, think GPS -- the same thing is happening for brain mapping through transformation.
So let's take a look at the brain.
Most people, when they first look at a fresh human brain, they say, "It doesn't look what you're typically looking at when someone shows you a brain."
Typically, what you're looking at is a fixed brain.
It's gray.
And this outer layer, this is the vasculature, which is incredible, around a human brain.
This is the blood vessels.
20 percent of the oxygen coming from your lungs, 20 percent of the blood pumped from your heart, is servicing this one organ.
That's basically, if you hold two fists together, it's just slightly larger than the two fists.
Scientists, sort of at the end of the 20th century, learned that they could track blood flow to map non-invasively where activity was going on in the human brain.
So for example, they can see in the back part of the brain, which is just turning around there.
There's the cerebellum; that's keeping you upright right now.
It's keeping me standing.
It's involved in coordinated movement.
On the side here, this is temporal cortex.
This is the area where primary auditory processing -- so you're hearing my words, you're sending it up into higher language processing centers.
Towards the front of the brain is the place in which all of the more complex thought, decision making -- it's the last to mature in late adulthood.
This is where all your decision-making processes are going on.
It's the place where you're deciding right now you probably aren't going to order the steak for dinner.
So if you take a deeper look at the brain, one of the things, if you look at it in cross-section, what you can see is that you can't really see a whole lot of structure there.
But there's actually a lot of structure there.
It's cells and it's wires all wired together.
So about a hundred years ago, some scientists invented a stain that would stain cells.
And that's shown here in the the very light blue.
You can see areas where neuronal cell bodies are being stained.
And what you can see is it's very non-uniform.
You see a lot more structure there.
So the outer part of that brain is the neocortex.
It's one continuous processing unit, if you will.
But you can also see things underneath there as well.
And all of these blank areas are the areas in which the wires are running through.
They're probably less cell dense.
So there's about 86 billion neurons in our brain.
And as you can see, they're very non-uniformly distributed.
And how they're distributed really contributes to their underlying function.
And of course, as I mentioned before, since we can now start to map brain function, we can start to tie these into the individual cells.
So let's take a deeper look.
Let's look at neurons.
So as I mentioned, there are 86 billion neurons.
There are also these smaller cells as you'll see.
These are support cells -- astrocytes glia.
And the nerves themselves are the ones who are receiving input.
They're storing it, they're processing it.
Each neuron is connected via synapses to up to 10,000 other neurons in your brain.
And each neuron itself is largely unique.
The unique character of both individual neurons and neurons within a collection of the brain are driven by fundamental properties of their underlying biochemistry.
These are proteins.
They're proteins that are controlling things like ion channel movement.
They're controlling who nervous system cells partner up with.
And they're controlling basically everything that the nervous system has to do.
So if we zoom in to an even deeper level, all of those proteins are encoded by our genomes.
We each have 23 pairs of chromosomes.
We get one from mom, one from dad.
And on these chromosomes are roughly 25,000 genes.
They're encoded in the DNA.
And the nature of a given cell driving its underlying biochemistry is dictated by which of these 25,000 genes are turned on and at what level they're turned on.
And so our project is seeking to look at this readout, understanding which of these 25,000 genes is turned on.
So in order to undertake such a project, we obviously need brains.
So we sent our lab technician out.
We were seeking normal human brains.
What we actually start with is a medical examiner's office.
This a place where the dead are brought in.
We are seeking normal human brains.
There's a lot of criteria by which we're selecting these brains.
We want to make sure that we have normal humans between the ages of 20 to 60, they died a somewhat natural death with no injury to the brain, no history of psychiatric disease, no drugs on board -- we do a toxicology workup.
And we're very careful about the brains that we do take.
We're also selecting for brains in which we can get the tissue, we can get consent to take the tissue within 24 hours of time of death.
Because what we're trying to measure, the RNA -- which is the readout from our genes -- is very labile, and so we have to move very quickly.
One side note on the collection of brains: because of the way that we collect, and because we require consent, we actually have a lot more male brains than female brains.
Males are much more likely to die an accidental death in the prime of their life.
And men are much more likely to have their significant other, spouse, give consent than the other way around.
(Laughter)
So the first thing that we do at the site of collection is we collect what's called an MR.
This is magnetic resonance imaging -- MRl.
It's a standard template by which we're going to hang the rest of this data.
So we collect this MR.
And you can think of this as our satellite view for our map.
The next thing we do is we collect what's called a diffusion tensor imaging.
This maps the large cabling in the brain.
And again, you can think of this as almost mapping our interstate highways, if you will.
The brain is removed from the skull, and then it's sliced into one-centimeter slices.
And those are frozen solid, and they're shipped to Seattle.
And in Seattle, we take these -- this is a whole human hemisphere -- and we put them into what's basically a glorified meat slicer. There's a blade here that's going to cut across a section of the tissue and transfer it to a microscope slide.
We're going to then apply one of those stains to it, and we scan it.
And then what we get is our first mapping.
So this is where experts come in and they make basic anatomic assignments.
You could consider this state boundaries, if you will, those pretty broad outlines.
From this, we're able to then fragment that brain into further pieces, which then we can put on a smaller cryostat.
And this is just showing this here -- this frozen tissue, and it's being cut.
This is 20 microns thin, so this is about a baby hair's width.
And remember, it's frozen.
And so you can see here, old-fashioned technology of the paintbrush being applied.
We take a microscope slide.
Then we very carefully melt onto the slide.
This will then go onto a robot that's going to apply one of those stains to it.
And our anatomists are going to go in and take a deeper look at this.
So again this is what they can see under the microscope.
You can see collections and configurations of large and small cells in clusters and various places.
And from there it's routine.
They understand where to make these assignments.
And they can make basically what's a reference atlas.
This is a more detailed map.
Our scientists then use this to go back to another piece of that tissue and do what's called laser scanning microdissection.
So the technician takes the instructions.
They scribe along a place there.
And then the laser actually cuts.
You can see that blue dot there cutting.
And that tissue falls off.
You can see on the microscope slide here, that's what's happening in real time.
There's a container underneath that's collecting that tissue.
We take that tissue, we purify the RNA out of it using some basic technology, and then we put a florescent tag on it.
We take that tagged material and we put it on to something called a microarray.
Now this may look like a bunch of dots to you, but each one of these individual dots is actually a unique piece of the human genome that we spotted down on glass. This has roughly 60,000 elements on it, so we repeatedly measure various genes of the 25,000 genes in the genome.
And when we take a sample and we hybridize it to it, we get a unique fingerprint, if you will, quantitatively of what genes are turned on in that sample.
Now we do this over and over again, this process for any given brain.
We're taking over a thousand samples for each brain.
This area shown here is an area called the hippocampus.
It's involved in learning and memory.
And it contributes to about 70 samples of those thousand samples.
So each sample gets us about 50,000 data points with repeat measurements, a thousand samples.
So roughly, we have 50 million data points for a given human brain.
We've done right now two human brains-worth of data.
We've put all of that together into one thing, and I'll show you what that synthesis looks like.
It's basically a large data set of information that's all freely available to any scientist around the world.
They don't even have to log in to come use this tool, mine this data, find interesting things out with this.
So here's the modalities that we put together.
You'll start to recognize these things from what we've collected before.
Here's the MR. It provides the framework.
There's an operator side on the right that allows you to turn, it allows you to zoom in, it allows you to highlight individual structures.
But most importantly, we're now mapping into this anatomic framework, which is a common framework for people to understand where genes are turned on.
So the red levels are where a gene is turned on to a great degree.
Green is the sort of cool areas where it's not turned on.
And each gene gives us a fingerprint.
And remember that we've assayed all the 25,000 genes in the genome and have all of that data available.
So what can scientists learn about this data?
We're just starting to look at this data ourselves.
There's some basic things that you would want to understand.
Two great examples are drugs,
Prozac and Wellbutrin.
These are commonly prescribed antidepressants.
Now remember, we're assaying genes.
Genes send the instructions to make proteins.
Proteins are targets for drugs.
So drugs bind to proteins and either turn them off, etc.
So if you want to understand the action of drugs, you want to understand how they're acting in the ways you want them to, and also in the ways you don't want them to.
In the side effect profile, etc., you want to see where those genes are turned on.
And for the first time, we can actually do that.
We can do that in multiple individuals that we've assayed too.
So now we can look throughout the brain.
We can see this unique fingerprint.
And we get confirmation.
We get confirmation that, indeed, the gene is turned on -- for something like Prozac, in serotonergic structures, things that are already known be affected -- but we also get to see the whole thing.
We also get to see areas that no one has ever looked at before, and we see these genes turned on there.
It's as interesting a side effect as it could be.
One other thing you can do with such a thing is you can, because it's a pattern matching exercise, because there's unique fingerprint, we can actually scan through the entire genome and find other proteins that show a similar fingerprint.
So if you're in drug discovery, for example, you can go through an entire listing of what the genome has on offer to find perhaps better drug targets and optimize.
Most of you are probably familiar with genome-wide association studies in the form of people covering in the news saying, "Scientists have recently discovered the gene or genes which affect X."
And so these kinds of studies are routinely published by scientists and they're great.
They analyze large populations.
They look at their entire genomes, and they try to find hot spots of activity that are linked causally to genes.
But what you get out of such an exercise is simply a list of genes.
It tells you the what, but it doesn't tell you the where.
And so it's very important for those researchers that we've created this resource.
Now they can come in and they can start to get clues about activity.
They can start to look at common pathways -- other things that they simply haven't been able to do before.
So I think this audience in particular can understand the importance of individuality.
And I think every human, we all have different genetic backgrounds, we all have lived separate lives.
But the fact is our genomes are greater than 99 percent similar.
We're similar at the genetic level.
And what we're finding is actually, even at the brain biochemical level, we are quite similar.
And so this shows it's not 99 percent, but it's roughly 90 percent correspondence at a reasonable cutoff, so everything in the cloud is roughly correlated.
And then we find some outliers, some things that lie beyond the cloud.
And those genes are interesting, but they're very subtle.
So I think it's an important message to take home today that even though we celebrate all of our differences, we are quite similar even at the brain level.
Now what do those differences look like?
This is an example of a study that we did to follow up and see what exactly those differences were -- and they're quite subtle.
These are things where genes are turned on in an individual cell type.
These are two genes that we found as good examples.
One is called RELN -- it's involved in early developmental cues.
DlSC1 is a gene that's deleted in schizophrenia.
These aren't schizophrenic individuals, but they do show some population variation.
And so what you're looking at here in donor one and donor four, which are the exceptions to the other two, that genes are being turned on in a very specific subset of cells.
It's this dark purple precipitate within the cell that's telling us a gene is turned on there.
Whether or not that's due to an individual's genetic background or their experiences, we don't know.
Those kinds of studies require much larger populations.
So I'm going to leave you with a final note about the complexity of the brain and how much more we have to go.
I think these resources are incredibly valuable.
They give researchers a handle on where to go.
But we only looked at a handful of individuals at this point.
We're certainly going to be looking at more.
I'll just close by saying that the tools are there, and this is truly an unexplored, undiscovered continent.
This is the new frontier, if you will.
And so for those who are undaunted, but humbled by the complexity of the brain, the future awaits.
Thanks.
(Applause)
Identify all acute, obtuse, and right angles in the image below.
So let's just remind ourselves what an acute, obtuse, or right angle is.
An acute angle is an angle that is less than 90 degrees.
And I'll right it right under the word acute.
A right angle is an angle that is equal to 90 degrees, or who's measure is equal to 90 degrees.
And obtuse angle is an angle that is greater than 90 degrees, greater than 90 degrees, and it is less than 180 degrees.
Or you could do it this way:
Greater than 90 degrees, or 90 degrees is less than an obtuse angle.
And an obtuse angle is less than 180 degrees.
They don't ask us about this, but is you have an angle that is 180 degrees, it forms a straight line.
And that really is called a straight angle.
So let's look at this diagram, and let's start with the acute angles.
And I'll do the acute angles in purple.
Ones that we know are less than 90 degrees.
Well, you look over here the only real information they've given is they've marked this box right over here that this angle right over here is a right angle.
So actually, let's start with the right angle.
Because that actually might be a little more interesting.
So they tell us that this right over here is a right angle.
So we already know one of the right angles is angle QAR.
Where A would be the vertex.
You could also call it angle RAQ. So, angle QAR, QAR, hey actually tell us that the measure is 90 degrees, now there's another 90 degree angle here, that is QAT
This angle right over here, angle QAT and the reason why i know that angle QAt is also right, if you take QAR which is this one and combine it with QAT, you actually form a straight angle all the way around like this and so there some needs to be a 180 degrees so, QAR is 90 degrees, QAT also has to be 90 degrees anothe way to think about it, is so, is because they're next to each other and has a ray and common they are adjacent angle, and if u were put them and if you look at their outer edges they actually form a straight angle you will call this two angle,supplementary or they will add up to 180 degrees another definition of supplementary, they add up to 180 degrees therefore, if one is 90, the other one has to be 90 degress that all the way, now let's look at the acute angles
Cause that actually gives us a lot of information
Because of this entire angle, if QAT is 90 degrees, then any of the angle that make up QAT have to be less than 90 degrees for example, QAP, that angle right over there, the measure of that angle has to be less than 90 degrees because its part of this larger 90 degrees angle, you have add that two right angle over here, that actually 90 degrees, so both of them has to be less than 90 degrees so one acute angle is angle QAP, and another cute angle is angle PAT angle PAT, and once again, we know that because we add this two angle together you get 90 degrees
So each of them have to be less than 90 degrees assuming that this angle are zero degrees now there any other acute angle right over here or another angle that looks acute is angle RAS, angle RAS an the reason that we can feel pretty good that it is less than 90 degrees is because if you keep this line, if AQ is just a ray right now but if u extend all the way, let say u have some mythological point over there called X, angle RAX would be 90 degrees, so RAX is less than that so RAX has to be less that 90 degrees and i think we got all the acute angles here we got the two right angles here now we have to think about the obtuse angle so it was more than 90 degrees and less than 180 degrees so one of the obtuse angle, if you went from
Q, QAS, or SAQ is definitely an obtuse angle cause it contains 90 degree angle rather than its even wider than that so, SAQ, angle SAQ is definitely obtuse i'd be tempted to say SAP, but SAP is a straight angle if you went all the way around like this a 180 degress that would be a straight angle, that's not officially obtuse angle, i notice, this called a straight angle because it forms from a straight lines but two rays, two edges of the angle forms a straight line, so not going to include SAP there now, another obtuse angle, this in a different color this RAP, angle RAP, once again it contains RAQ in it which is 90 degrees which is even wider that that and let's see, RAT is a straight angle, so for all purposes we will not consider that obtuse.
And, have i found everything? am im not missing something? that one, would be straight angles. Oh wait, i just saw one more, of course, you also have this angle over here a big blank spot, and i wasn't paying attention to it you also have this angle TAS and the reason why we know that it's more than 90 degrees is once again we have our mythological point X over here that we just continue, QA in this direction we would know that this is a 90 degree and TAS is opening up more than 90 degree angle, so TAS is also obtuse, and i think i've got all of them now
Let me see.
Yup, we're done.
SelamunAleykum ve Rahmetullah ve Berekatuhu
Shukur YaRabbi Estagfurullah
Elhamdulillah
Asking support from our Shaykh, Sahib ul Saif
Shaykh Abdulkerim el Kibrisi el Rabbani
Who is holding on tightly to the way of our Grand Shaykh to the way our Resullulah SAW bringing the light to the whole world Bringing th elight to the lands where there is no light, because the sun sets in the west it doesn't rise in the west
Specifically he has been sent to the west
To this land to the America
And the light he brought was the light of the Holy Prophet SAW the Icazet that was given to him, when he first came to this country to spread the teachings of real Islam, to spread the teachings of the tariqat, to spread the love of the holy Prophet SAW, to these part of the world where nobody has ever heard of islam and if they did is nothing but lies and slander and wrong things and we are very fortunate
Alhamdulillah Ttat we know him and we are under him and that he has pulled us out from the mess and the jungles of his dunya and this cehennem.
Yes, because this dunya has turned into a cehennem and brought us here to the top of the mountain to live our faith to live Islam to live the lifestyle of the Prophet SAW, according to his teachings according to the way of our Grandsheikh, according to this Tariqat, according to the way of Rasulallah (SAV). We did not come here to the top of the mountain, we did not come to take Beyat with him to show our ego, show our opinions, to show our minds, we came and we gave beyat to him to say Sameena ve ataana we're here and we obey of course our ego that is the worst thing that our ego to our ego to hear and to obey because the ego's nature is to hear and disobey.
But Allah SAT saying to the ego
"step forward," the ego stepped back, opposite.
When He said to the ego "move to the right," ego moved to the left.
When He said to the ego
"move to the left", the ego moved to the right.
When Allah is saying to our egos to you and to mine our ego, saying "who am I, who are you? and our ego says, 'you are you and i am me! you are you, you are existing! I am existing! you are
Lord, I am a Lord!'
So, our egos are declaring that and the ego hates to recognize another Lord, that is the characteristic of sheitan.
Because Sheitan is saying 'Yes, Allah is our Lord but only according to what i wanted to be the way that i want our Lord to be.' And when our lord Allah SWT is saying to Adam, "do not eat from the forbidden fruit" placing restrictions there and Adem AS, with our mother Havva Ana they made the mistake and Adem AS is asking for forgiveness and Adem AS asked for forgiveness when you was sent down to the world standing on one foot on the island of
Sri Lanka for three hundred years, crying and begging to Allah SWT asking for forgiveness and Allah has forgiven, but still. Because that is the nature of the spirit that Allah SWT has created put into man and the nation of the spirit is it does not want to anger that one who has created him.
He does not want to anger it's master, does not want to anger his Lord but the characteristic of the ego is the complete opposite is declaring and always challenging and when Allah SWT is saying to
Shaitan make secde to Adem AS and Shaitan says that doesn't make sense to my idea of what our lord should do or should not do.
How many of us are doing that now, how many muslims are doing that now? how many the people who says they follow a master they follow a Prophet , they follow a master,they follow a Sheik says that now?
It doesn't makes sense to my head, it doesn't make sense to my understanding, it doesn't make sense to my intelligence, what!?
No, I make secde only to you .I am not going to make secde to this one that you have just created who did not even made one secde to you.
Why I should be making secde to him? he should be making secde to me. Of course Shaitan he has a different agenda definitely
Shaitan has a different agenda.
His agenda is to look when he looked at the Makam-il Mahmud that Allah SWT has created and he's saying
I want that it should be for me but he knows that he doesn't fit into that makam and he knows that this new creature that Allah SWT has created this light of Prophet SAV, fits into that Makam.
So, from that time until now Shaitan is going to go opposite to what Allah SWT has prepared for the children of men.
Walakad karamna bani Adam
"And we have honored The bani Adem the children of Adem."
Prophets they came,
Prophet SAV, the seal of the prophets, the holy Prophet SAV came and his inheritors, the EvliyaAllah, and the Sheikhs especially in this most distinguished order, came to make us, to understand, to come in to own reality and to occupy that place of honor. That place of honor that Allah has said
"We have honored the Children of Adem."
That is the purpose of the Sheikhs, that is the purpose of the friends of Allah, that is the purpose of the Murshids.
To change us, to change our nefs from Nefs-i ammaret to Nefs-i mutmain. To change that nefs, that is together allies with the Shaitan, to make our ego to be our vehicle, that the spirit is going to ride on that ego to bring us to higher stations.
We can not do that with books, we cannot do that alone. We can not even do it in a group. We have to do it with a Mursheed, with a sheikh, with a Varis el Enbiya the inheritor of the Prophet SAV.
The Prophet SAV, he came fourteen hundred years ago and, that one is hazir and nazir that one who is fresh and alive, that one who is inside of us, that one who is everywhere has also left inheriters and his inheritors, our Sheikhs they are also following in the same footsteps.
They have veiled from this world from this world but they are hazir and nazir, definitely they are. Because if Holy Prophet SAV is dead, like so many they're claiming that he's dead, then, we're not responsible because we don't follow a dead prophet, we don't.
We don't follow a dead prophet.
That time, we will not be responsible in the day of judgment, Allah SWT is questioning us why we are not following the Shariat of the Rasulallah SAV.
But he's not dead, those who say that he is dead, their hearts are dead .
Definitely, they don't have connection to that one, that Allah SWT has created everything in creation, you and me, the sun and the moon and the galaxies, in everything in creation , that you know and you did not know that Allah is continually creating for the sake of that one.
So, he also has inheritors and his inheritors are teaching us how to come back to own reality, how to come back to our own senses, how to hold on tightly to the lifestyle and the teachings and the sunnat of the
Rasulallah SAV, that is going to fit according to these times, according to this age and according to the group that we're living in.
So Elhamdulillah ,we are here, we've pulled ourselves away from this Dunya, to be on top of the mountain, only to follow the teachings of the Prophet SAV and his advice to his nation in the Ahir zaman, in the Ahir of the ahir zaman, saying,
"O my nation, in the Ahir zaman there's going to be so much fitna everywhere. Pull yourselves back, take a couple of sheep.
Pull yourselves to the mountains ,to the secluded areas, away from the populated areas. Whatever little knowledge that you have, don't go running around, searching and investigating and arguing .
Take that small knowledge that you have and practice it sincerely, live simply and wait because the time of the Sahibul Zaman is right around the corner.
The time of the Sahibul Zaman, it's going to come and we have reached to the ahir of the ahir zaman.
We've reached to the end of the end of the end of times.
And the Ahir of the ahir zaman it is not the time of paradise.
In the ahir of the ahir zaman, it's a time of great tyranny and great confusion everywhere.
From the world, to the countries, through the muslim communities, to the groups, to the families, to the individuals fitna is everywhere.
The fitna of Deccal is everywhere.
Yes, because Deccal is going to appear.
He has already prepared. We're asking the question, why in the month of Ramazan, Shaitan is supposedly locked up but people are still behaving
like shaitans. People are behaving like they're following shaitans.
People are behaving, completely holding on to shaitan .Why is that?
That is because before shaitan has left, he has prepared his deputies.
He has prepared our egos. Trained our egos well, he says "I may be gone, heh but now, you are trained very well by me and be able to continue the work, even if I'm not there."
Deccal, the big one that is coming so many has come, small Deccals. Forty fifty deccals, huh... in these days countless deccals.
That he has, these deccals have prepared the world, prepared countries.
Countries ,nations moving. Communities moving, groups, families, individuals moving and accepting the way of Deccal, the way of fitna, the way of this Dunya, the way of tyranny, so that when Deccal comes, the task, it is so easy for him.
That majority of the people, yes if they don't wake up to themselves, muslims who don't wake up to themselves, they're going to look at Deccal and they are going to say yes, this make sense. We are going to follow you because you are going to give what we're looking for. And what are muslims are looking for these days, ask, think, sit down, ask yourself!
What are you looking for? Are you looking for the Prophet?
If you are looking for the Prophet SAW, you're going to find, look, consult and be with his inheritor, be with his varis be with a
WaliAllah, be with a Sheikh and you're going to say, this one is representing the Prophet I'm looking for.
That one, so now I'm having him, i'm going to hold on tightly to him. Of course he is going to do and he's going to say and he's going to advice things that is not going to be good for my ego. My ego is never going to accept.
My ego is allies with Shaitan but my spirit is going to be free that time.
My spirit is looking for the Prophet SAW and I am looking for the shariat, the shariatullah, the shariat of the Prophet SAW, the way of the Prophet SAW.
Are muslims looking for that?
Are muslims looking for holding on tightly to the shariat that Holy Prophet brought the shariat that is the justice that has been missing from this world especially in the past hundred and less than a hundred fifty years. The shariat there was held on tightly by our ancestors held on tightly especially by the Ottomans who brought justice east, west. north and south.
Do they have enemies? Of course they do, and they will continue to slander them too and all muslims are slandering them, definitely.
Muslims are slandering the Halifa.
Masha'Allah, masha'Allah! Very good for you.
Prepare yourself that time. Because the Holy Prophet SAW is saying, do not against your Halifa. Do not rebel against him. to be awwam (???) to do umum (???)
Do not rebel against him, even if he takes the skin of your back. The whole nation of islam are we running towards that? Looking for shariat,
looking for what? The lands where the sun has set has to offer. You don't have to be a genius to answer that or sing.
Are they looking for a Halifa, a representative of that
Prophet SAW and to live by his words to live by his law.
It's already showing if we are then we will all have
Sheikhs, and we will have masters and we will all hold on tightly to them, and obey them and not have any problems with them. Or do we always have problems with our masters saying,
'I like this part but I don't like that part.'
'This is Ok, but that is not Ok.' I like this one before, now you change it and you like.. No.
So we have to check ourselves, because preparing for the time of Mahdi AS it is not the easy, these are not easy times, these at times of complete darkness.
Sheikh Mawlana Hazretleri said so many times, our Sheikh Efendi Hazretleri said so many times it is time of dark, darkness this is the time sorrow is covering everywhere where the dark clouds are covering everywhere, people are looking muslims are looking, the hadith is saying dark clouds, where is the dark clouds?
Looking with these eyes, but they're not understanding their hearts, our hearts, the muslims' hearts have already been clouded.
It's already dark, because we are not looking to ahirat. We are not looking to the Holy Prophet SAW what he has to say.
We are not looking to the murshids, we are not looking to the sheikhs and we are not looking to Awliya Allah.
But we are looking to what our ego wants, we are looking to what this dunya has to offer to make this dunya to become a paradise, don't we understand?
Don't you understand this is the ahir zaman?
Don't you understand this is the ahir or ahir zaman?
We are following the Prophet of the ahir zaman.
As believers, we should not be preparing ourselves to live in this will world comfortably.
As believers, we should be preparing to make our ahirat better than our dunya.
To live in this dunya as travelers.
Nations have lost their direction.
Nations' leaders have lost their direction, they have lost their compass.
Nations' Alims and Ulamas - they've completely lost their compass. They are under the payroll, and they are looking.
Not what Allah and His Prophet has to say, but who is paying them, who has the power to shut them out or to open their mouth what those ones, what those ones have to say.
Fitna,
Holy Prophet SAW said will come out from the scholars of my nation in the ahir zaman, will come from them and will circle around and they will come back to them, and a big curse is coming to them.
So, not for us to run these times to be come scholars, to know so much, take whatever little knowledge that we have and practice it sincerely, and prepare for the grave. Prepare for the hereafter, make preparation for that, not for this dunya.
Are muslims preparing that?
Definitely not.
Preparing, wishing that this spring is going to turn into summer.
What spring?
They are saying Arab spring.
Eh, it's been a year and a half years already spring is never finishing?
Masha'Allah.
It's spring. No.
It fell down.
It didn't spring, it flopped. Same things happening, why? Gather, be together and ask for the sahibu zaman to come. because only he will come with a divine power to break the system of dajaliyat, to break the system of the shaitan, to break the system where the ego is running completely free, to break the system where everyone is declaring themselves lords.
Where nations' leaders, nations' alims and those ones who are in authority are not warning and keeping their nations in check and to say do not pass your limits.
We are servants, do not cross into that other side to follow what shaitan has been planning for these thousands of years to welcome the time of dajjal.
Yes. We are in the time of dajjal. We are not during the time, we are in the time of Mahdi AS, definitely not.
What, you need proof for that?
Don't you see this whole world?
Right now we are comfortable, we just finished iftar we finished making zikir, we are going to make prayers.
Don't think that this whole world is like this.
Half of this world is burning, half of this world they are suffering, and the leaders of this world they are coming together and they are planning what?
To make this world into a paradise, or they are planning to turn this world into a hell?
To burn this whole world.
So, which type are we living in?
If we are living in a very dangerous times which sad to say not too many people not too many.
Those ones who have authority and those ones have knowledge they are warning the people that we are living in very dangerous times we are living the times of dajjal, they are not warning them.
That is not in their agenda, because this wishing and hoping this world is going to last longer forever if necessary and for them to have more comfort them a luxury from this world but the signs that Holy Prophet SAW has said about the coming of deccal about the cebabire time, it's already here we're living in it we're living dangerous times very dangerous what do we do in dangerous times we sing and we dance we enjoy ourselves uh... are we preparing ourselves for the murids of our Seyh
Holy Prophet SAW has given to us and advise and a warning for us to keep ourselves clean keeping ourselves clean to prepare for the time when the Mehdi AS is going to come prepare for that time to make ourselves to more useful to the Shariat to the laws that Allah SWT has brought
Holy Prophet SAW teaching his nation that is not going to change until Kiyamet prepare ourselves for that get ourselves used for that are we getting more and more used to new and new things Are we getting more used to innovations are we getting more used to new things being introduced our group into tariqat into islam what are we
looking for is that what we're looking for we will find it if that's what we're looking for deccal is going to bring it deccal is going to bring and he's going to say this world it is a paradise but this world it is a hell from the skies to the earth to the waters to the air,this world this planet we have turned it into a hell who's saying otherwise which ignorant one's going to say otherwise and deccal is going to say no we are going to continue with this and we're going to continue to use the world and to suck the world and to make it into a paradise for us but that Sahib ul Zaman is going to come and he's going to say do not believe that because now is a time when black is white and white it's black and unless you are following a Seyh and consulting with him and holding on to him tightly and not being rebellious and challenging when the very dangerous times comes there is no more time for explanation for arguing that is a time insAllah u Rahman we'll be in safety blindfolds will be put to us insAllah for us not to understand that is stepping on the edge of a cliff and we will hear his voice to say just walk don't turn left and right just walk follow me that is the time we're living in those times so we need to check ourselves we need to check ourselves are we preparing ourselves for the Shariat to come uh... we're getting more and more use to Shariat in our lives are we getting more and more use of the laws in the orders that our Seyh has put into our life's and to hold onto that tightly and not change are we looking for an out now especially since his past for a change for uh... adjustment if we are there's a very big danger up ahead it we are it is going to be very difficult times for us if we're holding on tightly he's going to carry us trough insAllah ur Rahman as much faith and as much sincerity that we have and as much obidience that we have we will be in safety here in here after we have a big job ahead of us our job our intension our mission is to continue his mission and his mission is to bring down kufur to bring down disbelief and unbelief that time when the war comes it is no longer with Muslims and Christians or Muslims and Jews and know it is between believers and unbelief because they are believers everywhere in every religion and there are unbeleivers with the appearances that you believe in every belief in every religion in every group if we are preparing ourselves for the time of Mehdi AS when he comes and he's going to come with nothing but the Shariat of the Resullulah SAW we're going to be happy we're going to be in safety it we're looking for changes if we're looking for completely no Shariat but we're looking for mixing everything together then deccal is going to offer as that it is already here it is already because this Shariat this separation of Hak and batil this separation it is very strange to people living these modern times They say we're very backward people we have a strange antiquated we have a strange old fashion people who have no touch with reality if this is a reality this cehennem out there is reality yes we have no touch we're not in touch with that reality but we in touch of the reality that our Seyh that he has brought from our Grand Seyh from Holy Prophet SAW we're in touch with that and we're very happy with that we're not here to please the world we're not here to please this dunya to please this society that we're living in we respect everyone we love everyone and want to live according to that respect and the love that is nothing but is contained in the holy Shariat of Prophet SAW though the Ottomans had brought bringing justice to Muslims Muslim Nations different Muslim Nations and to Christian nations and to Jewish Nations believers and unbelievers giving each one their rights and we are waiting for those days to come insAllah ur Rahman we preparing ourselves for that and to keep ourselves holding on tightly to the way of our Seyh to the way of our grand Seyh to the way of Prophet SAW we're not here wanting to build palaces for ourselves the drive big fancy cars wear nice clothes to eat to drink No that's why we are here on the top of the mountain that is why you have taken biat with our Seyh to say let us begin this first step where we die before we die where we gonna turn away from this world and turn our faces to the Uhva to the reality to the Ahiret to turn our face to that reality that our Seyh has brought from his Grand Seyh from the Holy Prophet SAW that this the reality this is not reality,this is fake and it's passing and this dunya has no value has less value than a wing of a mosquito as Holy Prophet SAW is saying Allah SWT is saying inshaAllah ur Rahman we are asking Allah SWT to bless our Grand Seyh to bless our Seyh to raise their stations higher and higher for us to hold on tightly to them and for the himmet and the Medet come to us for us to continue this way strongly for things to get bigger and to get stronger for us not to deviate for the sake of this holy month for the sake of this holy nights for the sake of the most beloved one in the divine presence
Fatiha to everyone who's watching us inshaAllah ur Rahman this time this day next week we will be celebrating commemorating the fortieth day of of our Seyh
Shaykh AbdulKerim el Kibrisi el Rabbani if Allah gives us long life that is what we're going to do will have Zikr we will continue the program we're not going to change so be with us
Allah has opened the doors Allah has opened the doors also for this technology to be used in the way of islam we are not relying on this technology because we are relying on the technology of our Shaykh technology of the Evliyaullah but this is come to us and we're using it use it for the sake of Allah that time it's going to be blessed but we're not relying on it because the first thing that is going to go when Mehdi AS calls the Tekbir it's electricity that time if you don't build this technology this technology with the Shaykh this technology with a community if we just relying on this camera this electricity easily can be cut that time your connection will be lost and you will be lost will be lost forever big loss coming to us big confusion coming in those days to bigger confusions we don't want to do that because with the end of the race the race is almost done, dont quit now don't turn now there is a tape is there we're running towards the tape now whole world is looking for that foolish olympics are not understanding what it is but that tape there we almost there there's a lot of darkness now definitely but don't suddenly now because you're running there and you seeing something and you running towards to other direction running to the left direction, no dont keep on going straight ahead it may seem because there's a lot of confusion now there's a lot of dust like they say in Turkish you all know when the dust settles whether it is a donkey or a horse so there's a lot of dust covered now as long as we're holding on tightly to our Shaykh inshaallah we will not be the losers
Fatiha Same time next week insAllah if you have any questions you can ask if anything that you want to say, say we are available
InshaAllah if there's anything you wish to do, to participate to make this way stronger and clearer to make this work that we're doing to progress don't hesitate insAllah have a good Teravih and have a good week
Let's do some equations of lines in point-slope form.
And this is different from y or from slope-intercept form.
But they really are just two different ways of writing the same equation.
We'll see that with a couple of examples.
And you might remember that slope-intercept form were equations of the form, y is equal to mx plus b-- we did this in the last video-- where m is the slope, b is the intercept, the y-intercept. That's why it's called slope-intercept.
You have the slope and the intercept. In point-slope form, it takes the form y minus y1-- and I'll tell you what y1 is in a second-- is equal to m times x minus x1, where the coordinate x1, y1 is a point on the line. That's why this is called point-slope form.
And I'll show you that with a couple of examples. But let's just do a few in point-slope form, just to make things concrete in your head.
So here we have a line that has a slope of negative 1 over 10, so m is equal to negative 1 over 10.
And it goes through the point 10 comma 2.
So we can directly go to point-slope form.
A point here is the point 10 comma 2.
So we can immediately go to point-slope form. y minus, this is a y-value that's on the line.
So y minus 2 is going to be equal to the slope, negative 1 over 10 times x minus an x-value, times x minus 10, just like that. And we're done.
We just put it in point-slope form.
There's two things I want to point out to you. One, why this makes sense. And I also want to show you that this is equivalent to that.
So the first thing is why does this make sense? Well, all this is saying, if you divide both sides of this equation by that right over there, you get y2 over x minus 10 is equal to negative 1 over 10. Or you get the change in y between any point and 2, and the point 2, over the change in x.
This is just the definition of your slope. Hopefully I don't confuse you there.
I'm just showing you that this is just using the definition of the slope to create the equation of the line. Now, the other thing I want to show is that this is completely equivalent to this. We can just algebraically manipulate this to get that.
So this right here is the answer to the problem.
But let's play around with it algebraically to get it in that form. So if we get y minus 2 is equal to-- let's distribute the negative 1 over 10.
So it's negative 1 over 10 x, and then negative 1 over 10 times negative 10 is plus 1.
Now we can add 2 to both sides of this equation. And you get y is equal to negative 1 over 10 x plus 3. So just algebraically manipulating it, we were able to put it into slope-intercept form.
So these two things are completely equivalent.
Let's do a couple more problems.
The line contains the points 10 comma 12 and 5, 25. So let's figure out the slope. So the slope, which is equal to change in y over change in x, is equal to-- well, let's just use this point first.
We just knew that the point 5 comma 25 is on the line. So y minus 25 is equal to the slope, which we figured out, times x minus 5. And we're done.
The equation of this line is y is equal to the slope 3/5x, plus the y-intercept, minus 3. And we'd be done.
Well, we know the slope.
But do we know any points on this line? You need a point and a slope to immediately put it into point-slope form. Well, we know one point.
And this is point-slope form. This could be y plus 3 is equal to 3/5 times-- we could write times x minus 0. If you really wanted to make it look like point-slope form, this would be point-slope form, but it's kind of silly to write x minus 0.
It's not 100% clear that you're in point-slope form yet right now. But I think you still need to write x minus 0. And obviously, to go from here to there, you just have to subtract 3 from both sides and you'll get that.
They're even almost equivalent in how you write them. You just have to subtract 3 from both sides of this equation to get to that one. Let's do another one.
It's negative 4 minus 5, over 3 minus negative 7. And this is going to be equal to-- negative 4 minus 5 is negative 9.
And then 3 minus negative 7, that's the same thing as 3 plus 7, that's 10. So slope is negative 9/10.
It's just going to be y-- let's do it this way-- y minus-- I'll color code it-- 3 is equal to-- I'll do this back to the green color-- is equal to the slope, is equal to negative 9 over 10, times this x minus this coordinate, x minus negative 4.
So this is in point-slope form. We obviously can simplify this negative a little bit. We can rewrite it as y minus 3 is equal to negative 9/10 times x, plus 4.
And we are done.
Batu Caves, preparation are underway for the grandest Hindu Festival of the year
Thaipusam is about faith, penance and endurance
More than a million devotees are expected to congregate here over the next few days
Five days before Thaipusam we follow a group of 50 devotees from the Sri Muniswarar Temple in Puchong as they make their climb up the 272 steps to reach the top of the hill where the temple is located.
Hlgh Priest Vasantha, aged 50 is leading a group of devotees to fulfill their vows and to seek forgiveness for their sins from Lord Murugan
She has been doing this for the past 20 years only this year it is a bit different
To avoid the heavy traffic, due to a long stretch of public holidays she is starting early and for many devotees it is never too early to perform this pilgrimage
A contractor is purchasing some stone tiles for a new patio.
Each tile costs $3, and he wants to spend less than $1,000.
And it's less than $1,000, not less than or equal to $1,000.
The size of each tile is one square foot.
Write an inequality that represents the number of tiles he can purchase with a $1,000 limit.
And then figure out how large the stone patio can be.
So let x be equal to the number of tiles purchased.
And so the cost of purchasing x tiles, they're going to be $3 each, so it's going to be 3x.
So 3x is going to be the total cost of purchasing the tiles.
And he wants to spend less than $1,000.
3x is how much he spends if he buys x tiles.
It has to be less than $1,000, we say it right there.
If it was less than or equal to, we'd have a little equal sign right there.
So if we want to solve for x, how many tiles can he buy?
We can divide both sides of this inequality by 3.
And because we're dividing or multiplying-- you could imagine we're multiplying by 1/3 or dividing by 3 -- because this is a positive number, we do not have to swap the inequality sign.
So we are left with x is less than 1,000 over three, which is 333 and 1/3.
So he has to buy less than 333 and 1/3 tiles, that's how many tiles, and each tile is one square foot.
So if he can buy less than 333 and 1/3 tiles, then the patio also has to be less than 333 and 1/3 square feet. Feet squared, we could say square feet.
And we're done.
I come from Lebanon, and I believe that running can change the world.
I know what I have just said is simply not obvious.
You know, Lebanon as a country has been once destroyed by a long and bloody civil war.
Honestly, I don't know why they call it civil war when there is nothing civil about it.
With Syria to the north, Israel and Palestine to the south, and our government even up till this moment is still fragmented and unstable.
For years, the country has been divided between politics and religion.
However, for one day a year, we truly stand united, and that's when the marathon takes place.
I used to be a marathon runner.
Long distance running was not only good for my well-being but it helped me meditate and dream big.
So the longer distances I ran, the bigger my dreams became. Until one fateful morning, and while training, I was hit by a bus.
I nearly died, was in a coma, stayed at the hospital for two years, and underwent 36 surgeries to be able to walk again.
As soon as I came out of my coma,
I realized that I was no longer the same runner I used to be, so I decided, if I couldn't run myself, I wanted to make sure that others could.
So out of my hospital bed, I asked my husband to start taking notes, and a few months later, the marathon was born.
Organizing a marathon as a reaction to an accident may sound strange, but at that time, even during my most vulnerable condition, I needed to dream big.
I needed something to take me out of my pain, an objective to look forward to.
I didn't want to pity myself, nor to be pitied, and I thought by organizing such a marathon, I'll be able to pay back to my community, build bridges with the outside world, and invite runners to come to Lebanon and run under the umbrella of peace.
Organizing a marathon in Lebanon is definitely not like organizing one in New York.
How do you introduce the concept of running to a nation that is constantly at the brink of war?
How do you ask those who were once fighting and killing each other to come together and run next to each other?
More than that, how do you convince people to run a distance of 26.2 miles at a time they were not even familiar with the word "marathon"?
So we had to start from scratch.
For almost two years, we went all over the country and even visited remote villages.
I personally met with people from all walks of life -- mayors, NGOs, schoolchildren, politicians, militiamen, people from mosques, churches, the president of the country, even housewives.
I learned one thing:
When you walk the talk, people believe you.
Many were touched by my personal story, and they shared their stories in return.
It was honesty and transparency that brought us together.
We spoke one common language to each other, and that was from one human to another.
Once that trust was built, everybody wanted to be part of the marathon to show the world the true colors of Lebanon and the Lebanese and their desire to live in peace and harmony.
In October 2003, over 6,000 runners from 49 different nationalities came to the start line, all determined, and when the gunfire went off, this time it was a signal to run in harmony, for a change. The marathon grew.
So did our political problems.
But for every disaster we had, the marathon found ways to bring people together.
In 2005, our prime minister was assassinated, and the country came to a complete standstill, so we organized a five-kilometer United We Run campaign.
Over 60,000 people came to the start line, all wearing white T-shirts with no political slogans.
That was a turning point for the marathon, where people started looking at it as a platform for peace and unity.
Between 2006 up to 2009, our country, Lebanon, went through unstable years, invasions, and more assassinations that brought us close to a civil war.
The country was divided again, so much that our parliament resigned, we had no president for a year, and no prime minister.
But we did have a marathon.
(Applause)
So through the marathon, we learned that political problems can be overcome.
When the opposition party decided to shut down part of the city center, we negotiated alternative routes.
Government protesters became sideline cheerleaders.
They even hosted juice stations. (Laughter)
You know, the marathon has really become one of its kind.
It gained credibility from both the Lebanese and the international community.
Last November 2012, over 33,000 runners from 85 different nationalities came to the start line, but this time, they challenged a very stormy and rainy weather.
The streets were flooded, but people didn't want to miss out on the opportunity of being part of such a national day.
BMA has expanded.
We include everyone: the young, the elderly, the disabled, the mentally challenged, the blind, the elite, the amateur runners, even moms with their babies.
Themes have included runs for the environment, breast cancer, for the love of Lebanon, for peace, or just simply to run.
The first annual all-women-and-girls race for empowerment, which is one of its kind in the region, has just taken place only a few weeks ago, with 4,512 women, including the first lady, and this is only the beginning. Thank you.
(Applause)
BMA has supported charities and volunteers who have helped reshape Lebanon, raising funds for their causes and encouraging others to give.
The culture of giving and doing good has become contagious.
Stereotypes have been broken.
Change-makers and future leaders have been created.
I believe these are the building blocks for future peace.
BMA has become such a respected event in the region that government officials in the region, like Iraq, Egypt and Syria, have asked the organization to help them structure a similar sporting event.
We are now one of the largest running events in the Middle East, but most importantly, it is a platform for hope and cooperation in an ever-fragile and unstable part of the world.
From Boston to Beirut, we stand as one.
(Applause)
After 10 years in Lebanon, from national marathons or from national events to smaller regional races, we've seen that people want to run for a better future.
After all, peacemaking is not a sprint.
It is more of a marathon.
Thank you. (Applause)
Welcome to part two of the presentation on quadratic equations. Well, I think I thoroughly confused you the last time around, so let me see if I can fix that a bit by doing several more examples. Entonces comencemos con una revision de lo que
The quadratic equation says, if I'm trying to solve the equation Ax squared plus Bx plus C equals 0, then the solution or the solutions because there's usually two times that it intersects the x-axis, or two solutions for this equation is x equals minus B plus or minus the square root of B squared minus 4 times A times C. And all of that over 2A. So let's do a problem and hopefully this should make a little more sense.
So in this example what's A?
Well, A is the coefficient on the x squared term. The x squared term is here, the coefficient is minus 9. So let's write that.
A equals minus 9.
What does B equal?
B is the coefficient on the x term, so that's this term here. So B is also equal to minus 9. And C is the constant term, which in this example is 6.
Negative 9 squared.
Minus 4 times negative 9. That's A. Times C, which is 6.
And all of that over 2 times negative 9, which is minus 18, right?
2 times negative 9-- 2A. Let's try to simplify this up here. Well, negative negative 9, that's positive 9.
Negative 4 times negative 9 is positive 36. And then positive 36 times 6 is-- let's see. 30 times 6 is 180.
180 plus 36 is 216. All of that over 2A. 2A we already said is minus 19.
3 times 27. 27-- it goes 33 times, right? So this is the same thing as 9 plus or minus the square root of 9 times 33 over minus 18.
Now we found two x values that would satisfy this equation and make it equal to 0. One x value is x equals 3 plus the square root of 33 over minus 6. And the second value is 3 minus the square root of 33 over minus 6.
Let's say I wanted to solve minus 8x squared plus 5x plus 9.
Now I'm going to assume that you've memorized the quadratic equation because that's something you should do. Or you should write it down on a piece of paper. But the quadratic equation is negative B-- So b is 5, right?
So negative 5, plus or minus the square root of B squared- that's 5 squared, 25.
Minus 4 times A, which is minus 8. Times C, which is 9. And all of that over 2 times A.
288. We have all of that over minus 16. Now simplify it more.
Minus 5 plus or minus the square root-- 25 plus 288 is 313 I believe.
And all of that over minus 16.
That 313 can't be factored into a product of a perfect square and another number. In fact, it actually might be a prime number. That's something that you might want to check out.
Hopefully those two examples will give you a good sense of how to use the quadratic equation. I might add some more modules. And then, once you master this, I'll actually teach you how to solve quadratic equations when you actually get a negative number under the radical.
Deirdre is working with a function that contains the following points. These are the x values, these are y values. They ask us, is this function linear or non-linear?
If something is linear, then the change in y over the change in x always constant.
We go from 1 to 2, 2 to 3, 3 to 4, 4 to 5. So in this example, the change in x is always going to be 1. So in order for this function to be linear, our change in y needs to be constant because we're just going to take that and divide it by 1.
<i>Brought to you by the PKer team @ www.viikii.net
Episode 13.
You arrived, Seung Jo-goon.
Hi, Baek Seung Jo.
Sit down.
You don't have to be that surprised.
I was surprised too when I heard you were my prospective marriage partner.
"I would never have a marriage meeting"
I was positive there would be no way I would marry a man my grandpa picked out for me.
Because of you, now I look funny.
I, too, had no idea that Hae Ra and you knew each other.
Yes, we go to the same school and are the same year.
We're friends.
I did think it was weird that I got her to come out so easily.
But it seems there is a destiny between you and Hae Ra.
Then, let's have something to eat first.
Ah, yes.
Hae Ra, choose something delicious to eat.
Yes, Grandfather.
Seung Jo you also choose what you like.
Yes.
Oh, Seung Jo doesn't really like oily food.
What do you think about this set meal?
It doesn't seem to be too much food either.
That sounds good.
Aigoo, you already get along well just like a married couple.
I'm sorry if I have made you uncomfortable.
I will be leaving early.
What's the matter?
Do you have something else to do?
Do you think this grandfather doesn't have any sense?
Baek Seung Jo!
Hey, Seung Jo!
Mother.
Ha Ni, where is Seung Jo?
He went out.
He went out?
He said he had an appointment, dressed well, and went out.
But why?
You were surprised right?
Yeah...
A bit.
You seem to have delighted my grandpa.
That was the first time he brought a picture and told me to take a look at a guy.
Of course at first, I didn't even look.
But then he said that he was the heir of a successful game company.
And when I saw the picture it was really you!
But how can I not go when it's you?
And it would be so much fun?!
I wanted to see your expression.
How was it?
Your expression was... bitter
So, what do we do next?
If we want to be funded by your grandfather...
Does that mean I need to get married?
With you?
Well, that's possible too.
But you wouldn't like that, right?
Wouldn't you be the one to not like it?
Hey!
What are you doing acting like a kid?
Do you have a handkerchief?
I don't.
In the condition we're in now, a game can't be released.
We're even behind on employees' salaries.
That's why I came out today.
But, since you're the other person, I'm actually relieved.
But don't you dislike it?
Since it's for that reason?
I didn't know these kind of words can come out of Baek Seung Jo's mouth.
Really?
Living is pretty extreme.
It's no joke.
But, I came out because it was you.
You came and you were relieved that it was me, but I came because it was you, even though I knew why you came.
Hey, since I knew the real reason, my pride was hurt so I did actually say that I didn't want to come.
But when this morning came around, I wanted to come out looking pretty.
Doesn't it seem like I really like you?
But don't worry.
Even though the situation seems real, I don't want to go that far.
Let's just take a chance... on each other.
Let's try it out...
Okay, it's good.
Really?
Really?!
It's alright. Be strong.
Right now those people are probably just seeing his fright.
But once they see his true colors, they'll probably say no first.
He's not humane, he's no fun, and he's not good to the ladies.
How is Seung Jo's dad doing lately?
He is getting better.
I'm back.
Let's talk for a bit Baek Seung Jo.
Aren't you going to Father at the hospital?
Just go.
We'll talk next time.
Aigoo, look at that brat.
Who would like someone that cold?
You're probably the only person that can handle that temper of his.
Be strong, okay?
You came back early.
Yeah...
I can't?
Excuse me...
You had a marriage meeting?
Yeah.
How was it?
Did you hear who it was with?
Hae Ra.
I heard it was the granddaughter of Windy Media.
Yeah.
Pretty perfect, isn't it?
Will you... get married?
Get married?
Probably.
Marriage naturally follows a marriage meeting.
Ha Ni!
Oh!
Ha Ni!
What happened now?
I guess something happened again.
Ha Ni, why do you look so down again?
Was Baek Seung Jo mean to you again?
Did you get kicked out of Seung Jo's company?
I said I was sick and that I was going to take a day off today.
So, you're really sick?
You should go to the hospital if you're sick.
Why did you come to school?
It hurts here.
Why?
It's because there's going to be a marriage .
Marriage?
Who?
With who?!
Maybe... Baek Seung Jo?!
Who's the other person?
Yoon Hae Ra.
What?
Yoon Hae Ra?!
Why suddenly with Yoon Hae Ra?
It was a marriage meeting.
One of the big investors of the company, she's his granddaughter.
Oh my goodness.
Yoon Hae Ra is no ordinary girl.
Hey...
So are they going to get married?
He said he likes the idea.
It's the first time I heard Seung Jo say something like that.
Hey!
That's good then!
Now, you can completely forget someone like Baek Seung Jo.
And you can meet a good guy.
Excuse me, President.
How did the meeting go with the chairman's granddaughter?
Fine.
I heard that you two already knew each other.
Yes, that's true.
President Yoon seems to like you quite a lot as a groom.
Is the Powerpoint tutorial going well?
Oh yes, we're working on it right now.
Ah, yes.
Fighting. <i>Acting like a girlfriend...
You've got a text. <i>Looks like you're taking a leave of absence.
Hello!
Really delicious.
Really!
Did you make it all by yourself?
Of course.
I made the soup base on my own, and made the noddles too!
This whole bowl I made all with my power.
How did you already...
You're amazing Bong Joon Gu.
I wanted to let you have the first noodles that I made.
Before I started working, I washed my hands throughly and prepared my heart.
I put all my passion into it.
What am I that you'd go that far for me?
What do you mean what are you?
If it wasn't for you, I wouldn't even wash my face.
It's really true.
Since I never know when you're coming, I dress nicely, wash my hair everday, and work hard at learning how to cook.
To put it in one sentence, Ha Ni, you are the reason that I live.
Thank you.
Since you're saying that to me, I feel like a special person.
And this is really delicious.
You're really cool.
You did well Bong Joon Gu.
Really?
If you think that, we should go on a date sometime..
It would be good to go on a date...
Ok, let's do it.
Let's go on a date.
Re..really?
Rea... Really?
For real?
Date, date.
Ha Ni, thank you!
When will we go on one?
When will we go on the date?
Where is Ha Ni?
She is going on a date.
Date?
She really dolled herself up before leaving.
A red coat, and red shoes.
She went out completely in red.
Really?
Sounds like she went with a guy with strange tastes.
Ha Ni! <BR> Here, here!
Did you come early?
No, it has been about 3 hours?
What?
Did I get the time wrong?
No, it's not that.
At home, I kept looking at the clock but it felt like it wasn't moving.
So I just came.
I see.
You really came.
I'm so touched that I feel like I'm going to die.
Ha Ni is very pretty today.
Where are we going now?
First, the basics of a date...
Let's watch a movie first.
It was a wish of mine to watch a movie with you.
I did too...
Oh, I really wanted to see this movie.
Is that right?
I thought so that's why I got it.
Let's go in.
You want some popcorn?
Here's the Giant Combo.
Let's go! <i>My beating heart <i>Is a mess like my room <i>I just can't get a hold of it
Take this.
How is it?
It's delicious.
How is it? <i>For your own sake, forget all about me <i>I will call you, you <i>I wish to marry you <i>I wish to kiss you <i>I wish to steal your heart
-Should I put it in (your hair?) -I don't want it.
It's pretty, why not?
Do you want to take a picture?
- Watch, watch!
- Hey!
Hey!
I'm sorry, but can you take one picture for us?
-Hey!
-Here.
-You do it too, you do it too. <BR> -Okay okay. <i>My beating heart <i>Like my messy room
Marriage?
Yes.
I found out that the both of them got into Parang University ranked 1st or 2nd in their schools.
During some point in high school,
I heard that they met once at a tennis tournament.
Yes.
It's a match made in heaven isn't it?!
If that's why you think so, then every couple is a match made in heaven!
For a couple to be a match made in--
But this goes for both Seung Jo and Hae Ra.
Maybe after they finish their studies--
Can they not study after they get married?
I'm thinking it might be nice if they study abroad.
If those two get married think about how talented their children would be?
Doing business and all, I've learned that people are the most important factor.
One smart person can do the work of 100 people.
Chairman Baek, no need to worry about money now.
Just carry on with your company.
Yes. <i> Brought to you by the PKer team @ www.viikii.net</i>
Baek Seung Jo!
Yoon Hae Ra!
Laugh while you can!
After today, living will suck.
It's very entertaining.
Keep going.
Ah, I'm so full.
I was going to buy dinner.
What are you talking about?
The man usually pays for the meals.
Today was fun.
The movie was fun as well.
I also had a great time.
This is the best day of my life.
Ha Ni, your smiling face is the best thing in the world.
If I got to see your smiling face everyday,
I'd probably be full even if I didn't eat.
Why?
Is there something on my face?
Then, am I being strange?
Thank you.
Ha Ni.
You really are a good person.
I already knew... but I really feel it these days.
Ha Ni, have you ever been to the Han river?
I haven't been there at night.
I haven't been there since I came up from Busan.
Do you want to go?
Okay.
Wah!
The Han River is so pretty!
It is.
Your mind is everywhere these days, isn't it?
Is the game development going okay?
My grandpa said that the idea was really good.
It's just okay.
I'm going to go at it like a blue frog.
Blue frog?
Since everyone is always saying 3D, 3D,
I'm planning to do something different from 3D.
Like an animation.
That's great.
Everyone's always talking about how to make a game more realistic,
An animation type of game .
That's contrarian.
That's exactly it. Contrarian.
Taking the game's weakest point and making it into the strongest.
I'm thinking about making it look like an animation.
There was a reason that my Grandpa was so interested.
He's really into you.
Do you want to go to a jazz bar in a little bit? Omo, omo.
Ha Ni, let's get going.
Wow, is this really the Han river?
It's really pretty.
Ha Ni, what's this lit up area?
It seems like it's a cafe.
Cafe?
Then, let's go inside the cafe.
Should we have a caramel macchiato?
Okay..
Really...
Let's go.
Let's go.
The cafe is really pretty.
This is the first time I've been someplace like this in my life.
If I didn't know you, I would have never come here.
These places come out on dramas.
Do you like it?
I really like today.
Ha Ni, aren't you cold?
You should have dressed warmly.
Oh, Baek Seung Jo
You're on a date?
Can you not see?
Hey looking at you two, it looks like you're having a good time too.
Yeah. It's good.
Could it be that Seoul is that small?
How did we run into one another here?
I wonder...
Ah!
You wanna go together?
We're going to a jazz bar.
It's just a casual place.
Jazz?
What's wrong?
It'll be annoying for all of us.
You guys should go to some place like an arcade.
Isn't that more comfortable?
Hey, what are you implying?
We have ears too and we know how to listen to music as well.
That's right.
You know me quite well.
Let's go somewhere else, Joon Gu.
Sure.
Oh Ha Ni...
You look quite good together.
Really?
Does it really look that way? You guys are a match made in heaven too! You and your nasty personalities look perfect together!
Let's go.
Good bye!
Ha Ni...
What?
Ah...
Wow!
It's so pretty!
It's really pretty.
Thank you for bringing me here.
Marry me.
What?
What I'm saying is... marry me.
Why?
Do you not have hands?
You'd probably say that if I were Ha Ni.
Probably.
Why are you so mean to Ha Ni? Well...
Oh, am I weird?
Why do I feel that it'd be nice if you were mean to me too? <i>Brought to you by the PKer team @ www.viikii.net
Will you... marry me?
Bong Joon Gu.
I look at you, and you look at Baek Seung Jo.
It's already been 4 years of that.
Of course...
I can wait however long for you.
But, Baek Seung Jo... he's found someone else now.
Both looking at someone else's back like that...
let's stop that now, Ha Ni.
All you have to do it is turn around.
If you just turn around...
I'm right here.
Joon Gu...
Let's get married,
Ha Ni.
He's late.
What is he doing right now?
Jazz bar.
It must be fun.
I'm thinking of Baek Seung Jo again.
You were home.
What time is it right now?!
11 o'clock.
What have you done until now?
You go to a marriage meeting without even telling us.
I heard you went on a date again.
What are you planning to do?
What are you doing right now?
He said he's fine, so what's wrong with you?
You don't have to do that.
Your father's fine.
I'm not doing it because of Father.
What a liar.
You're doing this for your father's company.
Me?
No way.
You really don't know your son?
Then, what's the reason to keep seeing President Yoon's granddaughter?
Are you really curious?
Because I like her.
What?!
That makes no sense.
That reason is enough right?
You... Baek Seung Jo.
Welcome back.
You're late.
You came early.
You looked good together.
Yes, it was good.
It was fun, and he was nice.
Unlike someone, he wasn't mean to me.
I liked it.
That's good then.
Good luck to you.
What?
A proposal?
Bong Joon Gu is amazing.
Marriage?
So, what did you say?
What did you say?
I didn't say anything.
What is this?
I know that Joon Gu is a really good person, but still...
I don't have those feelings for him.
Even when I received that sudden proposal...
I was a little surprised.
But since it passed, I just calmed down.
Hey... where is there a person who thinks about you as much as Joon Gu?
Yeah.
Hey, honestly speaking, instead of Baek Seung Jo, you look much better with Bong Joon Gu.
Baek Seung Jo is getting married with Yoon Hae Ra.
Yeah, Ha Ni.
This time, think carefully about Bong Joon Gu.
He looked at only you for four years.
You probably know how Joon Gu feels, better than anyone.
You know what I'm saying right?
Okay.
Black?
- It's pretty.
- Ah, Seung Jo.
Which one is better?
The white one.
I think so too.
Should I wrap them together?
Please do it separately.
I'll pay for it.
Really?
Thank you.
Ah!
Then, I'll buy dinner.
I know of a few places. <i>The person that looks good with me</i> <i>is not Baek Seung Jo,</i> <i>and it could be Bong Joon Gu.</i> <i>Even if I don't get excited, he's comfortable,</i> <i>like family.</i>
I see you again.
Are you shopping?
We're going to go eat dinner.
Really?
Do you want to come with us?
Oh...
Shall we?
Yes, let's go together.
Whatever you choose.
It's not like I'm begging you to come with us.
Yes, let's go together.
Are you going to look at those all day?
Oh, Chef! I'm sorry.
Clean it up.
Yes!
Welco...
Welcome.
Dad.
Oh!
Ha Ni!
Hello.
Come in.
This place...Ha Ni, this is your...
Yeah.
Yeah that's right.
Oh Ha Ni and Bong Joon Gu...
This place has 60 years of tradition, So Pal Bok Noodles, which Oh Ha Ni and Bong Joon Gu will be taking on!
Ah, but you're friends?
Friends, Chef?
They're getting married.
Is that so?
Sit... sit down please.
I looked it up on the Internet and decided to come here.
Your restaurant is really pretty.
Ah, yes.
Wow pretty.
It's so pretty it feels like a waste to eat it.
Since this rascal came, our chef made something special.
Of course.
If it's Seung Jo and his friend, then they're VlP.
Please eat a lot.
Yes.
I'll eat well.
Ah look at this, look at this.
You don't even know how to eat it.
With this Pyongyang Neng Myun... you put the vinegar right onto the noodles.
And after waiting a little bit for the noodles to soak up the vinegar... you pull them apart and eat them.
Ohhh.
Oh, it's like that.
I didn't know either.
Really?
Well it's okay to not know.
A lot of people don't.
Eat a lot!
Makes me look at him differently.
You must be happy, Oh Ha Ni.
Since your boyfriend knows a lot.
I can't use chopsticks very well.
You can't make fun of me for using them strangely.
Ha Ni.
What are you looking at like that?
Seung Jo's face will fall off. <i>Your Imagination Will Become A Game.
Your imagination will become a game.
We've portrayed many fun features for users within this game.
It's a stylish action with top notch visuals.
With the various missions systems, users can enjoy different levels of enjoyment through the game.
Especially because our games style concept differs from other games.
Action game...
That's the focus and the factor that will differentiate our game.
Then, I will show the demo version.
You have all just experienced the world of imagination.
Just like he said, it looks like an animated movie.
It must not have been easy, but you finished in a short time period.
It was due to the late nights that the employees worked.
-You worked hard.
-Goodbye.
You worked hard.
Should I ask Hae Ra to come out so that we can go eat somewhere?
I'm sorry.
Today is the day that my father gets discharged from the hospital, so I have to go home and eat dinner at home.
Ah is that so?
Then the timing is good!
I'll ask Hae Ra to go over there.
She needs to give her greetings now that he's out of the hospital.
Seung Jo, your mother came out.
-Hello. -Yes.
Why are you here?
Come here.
I've met you once before.
I'm Yoon Hae Ra.
Oh is that so?
It seems like I've seen you before, but I guess your impression wasn't that great.
Ah!
You know that Ha Ni and Seung Jo are living together right?
Yes, of course.
Oh my, you bought cake.
He's (father) forbidden to eat anything sweet.
And Seung Jo doesn't like sweet things.
I bought it, so that you could eat it.
Oh, really?
These are rice cakes.
It's set to eat comfortably.
Please eat it once.
She is different from Oh Ha Ni.
What about rice cakes?
Even if it's simple, rice cakes are rice cakes.
Shall I eat cake?
Then please talk.
I should go in and lay down.
Me too.
Seung Jo.
He is my son, but Seung Jo has a very tiring temper.
He's self centered and naughty...
And he's no fun.
That's not true.
He is fun.
And he can converse well.
You too... must be a boring style.
You talk back well and only talk about things from books.
You must be like that?
Yes, you're right.
We're both rational and logical. But even though people look at us like that, it's fun for us.
More than that, he is not good to women.
He doesn't say a single nice thing.
He's the type of person to fix someone's love letter and give it back.
Really?
I've done that before too.
Wow really?
You really did that before?
Yes.
You guys must be one of a kind.
Baek Seung Jo seems like he's smart, right?
But, he's dumb.
He doesn't know his own feelings.
If he likes someone, he's colder to them and hurts them more.
And he pushes them away.
That's what I see.
That means he's scared.
People's feelings... can't be solved easily like a math equation. that he might get caught.
Are you like that too?
Mother!
You're childish.
What? Childish?
I won't say anything about you liking Oh Ha Ni.
But, why are you pushing me to like her as well?
Were my words wrong?
You are my son.
I know you.
But you don't know yourself.
Even if I don't,
Let me do things the way I want.
Beak Seung Jo.
My career and even my love life.
Please stop your meddling.
Meddling?
I have always respected your decisions.
Isn't that so?
But what is this?
You obviously know Ha Ni's feelings and you still brought her to our house!
This is a problem with courtesy among people.
Are you a kid that doesn't have courtesy?
Mother,
I'm fine.
Now, please
Would you stop this!
Baek Seung Jo, you!
Right.
Since you have always respected my decision, please do so this time as well. <i>Brought to you by the PKer team @ www.viikii.net
I thought that Seung Jo really liked Ha Ni.
Since he is my son I believed that he would eventually come to like her.
You can't control your kids like that.
But don't those two really suit each other well?
They fill the missing spots and share what they have too much of.
Isn't it really like that?
That's how I see it too, but Seung Jo is not going that way.
What to do?
I feel like I did something bad to both Seung Jo and Ha Ni.
He likes her.
What?
Hyung likes Oh Ha Ni.
So don't cry, Mom.
Eun Jo!
What are you talking about?
Baek Eun Jo!
Hyung...
Are you really going to get married to Hae Ra?
Isn't she pretty?
You like pretty Nunas.
Do you like that Nuna?
Won't it turn out like that, if we keep going on?
But still!
Still, the person you like is . . .
That nuna is a woman that suits me very well.
She is smart, and she can play tennis well too.
Hyung!
If you meet her for a couple more times, you'll definitely like her.
Liar.
Sleeping in a place like this...
She's really carefree.
Right!
A bug on top of her hand?
Oh Ha Ni, you'll be surprised for sure.
Oh! <i> Then hyung went back to the pension.
So it was a dream! <i> H..hyung kissed Oh Ha Ni.
After doing that...
I saw everything.
But still I can't tell that to Mom.
Hyung is saying it isn't so.
But this is for sure.
Hyung likes Oh Ha Ni.
Is something going wrong?
No.
There isn't anything that's going well or anything that's going wrong
I'm just playing.
What is this, genius Yoon He Ra?
Should Grandpa put some speed into it?
Put speed?
Yeah, we're the ones that pulled the knife.
He's the one that's supposed to be trying, not us.
I don't want it, Grandpa.
Scaring someone to make them do something, that hurts my pride more.
Really?
Then should Grandpa just stay still?
Yeah.
For now.
If I really think there's nothing I can do, then I might ask you to use a knife.
Yeah.
Don't hold it in.
I won't hold back.
Baek Eun Jo...
I made the pudding that you like!
Here!
Eat it.
Is it good?
That's a relief.
But, Eun Jo... what was that you told me before, about Seung Jo liking Ha Ni.
I'm not eating anymore.
Ah, why?
You're hiding something aren't you? Come here!
Maybe because the weather is clear today, there are many stars in the sky.
Dad.
What do you think about me dating Joon Gu?
Joon Gu?
Why? Did something happen?
No, I was just saying "What if"
What if that's the case.
What if?
Yeah, what if that's the case.
Well, who knows?!
I didn't like him much because he was rough on the edges and all...
He's like a man.
And when he cooks, he really focuses.
As a chef I think he's great.
And more than anything else, he really likes you Ha Ni. He cares for you, so there's nothing not to like.
Is that so?
I guess Seung Jo's getting married?
Yes.
It's that girl who came to the restaurant?
I feel like I've made an unwise decision.
We shouldn't have moved back in no matter how much they tried to convince me.
You know.
If we stay here longer, it will get strange.
It'll get uncomfortable between people.
We won't even be able to talk.
Seung Jo...Well Oh Ha Ni was a really good lady.
Making me really think about it, it was a good opportunity.
Yeah.
There are many stars, right?
Oh, Joon Gu!
At the restaurant?
Why? Today is your day off, isn't it?
What are you doing on your day-off alone?
I'm making a new menu Can you come by after school?
If you say it tastes good, then I want to officially present it to the chef.
You have to come, okay?
These little punks... What are you doing?!
Get up quickly! Move it!
Sunbae, can we not rest for a while?
What did you do so that you can rest?
Training does not stop. Never stop!
It's supposed to rain tomorrow morning.
Are we doing this tomorrow too?
Huh?
You crazy jerk
Why would it rain on a day like this?!
I'll bet my life savings and my left hand that it doesn't rain!
Hurry and get up and stop with the nonsense.
Hurry!
You're the same.
Aigoo! Hey!
Seung Jo! It's really been a long time!
I've heard about your father.
Is he alright now?
Yes, he got through it.
Oh! That's a relief! What to do about this?
Look at this! It's full of men.
Aigoo really.
You came well.
Since you're here, let's play a game.
I came to clean out my locker today.
I don't think I'll be able to come for a while.
Something must be wrong with you.
What kind of freshman is that busy?
I don't see the ball boy today.
Ball boy? Ahhh.
Ha Ni?
She's always skipping these days.
She must be busy dating that guy who works in the cafeteria.
These little punks! What are you doing?! Move it!
This is our school's tennis court. Ah, the tennis court where Ha Ni suffered and got ignored a lot?
Yeah.
This is the place.
-Woah.
-It's good, huh?
Yeah pretty extreme.
Wow, oh. Practicing...
Oh! Baek Seung Jo!
Why are you here?
Shouldn't I be asking you that?
Ah.That's right.
Anyway, we heard you're getting married.
With Yoon Hae Ra?
Today, isn't Ha Ni meeting up with Bong Joon Gu?
Yeah! Bong Joon Gu is making something really yummy for her.
Bong Joon Gu is so great!
I know!
Who knew he'd even ask her to marry him?
Is she responding today?
Ah, that's right!
That's why she dressed up so nicely.
Then won't Ha Ni be the first one to get married?
Ah I know!
So Pal Bok Noodles.
Eat more of this. Ah, I'm full.
How can you be full already? I prepared a lot.
Next time.
But these are really delicious.
Be sure to tell Dad.
It'll be a jackpot.
Is that so?
Drink this.
It's plum juice.
You'll digest nicely.
Joon Gu, you're really great.
It seems like your cooking skills have gotten better than my dad's.
Aigoo what are you talking about?
I still have a long way to go to be like Chef.
But since you're complimenting me, I do feel good.
My heart is beating.
It's raining really hard.
Here...
Ha Ni...
Huh?
What I said last time...
I didn't just say it.
Have you thought about it?
But... I...
A little more ti...
It still can't be?
I'm talking about Seung Jo.
He even went on a marriage meeting.
You can't get rid of your feelings yet?
No, more than that...
Ha Ni...
That cold and bad guy, what do you like so much about him?
I told you last time.
I'm a house.
Whenever you come, I'll be always there.
But if you let the house be empty for too long, you can't use it anymore.
Joon Gu...
Are you okay?
Ha Ni, are you okay?
Ha Ni, I really like you!
Joon Gu...
Ha Ni...
Joon Gu, don't do this.
Joon Gu!
Don't be like this.
No, don't do it.
I told you not to do it! Joon Gu!
I guess... that it can't be me.
I'm sorry, Joon Gu. <i>I really am no good. <i>After making Joon Gu that hopeful, <i>he only ended up getting hurt. <i>What is this?
Did I make it so that if it's not Baek Seung Jo, it can't be anyone?
-What are you doing here?
-What do you mean? Isn't it obvious?
There's no chance that you'd take an umbrella with you.
Then, were you waiting for me?
Are you coming from meeting that guy?
Which answer did you give him?
Huh?
I heard he asked you to marry him.
Why?
I can't do that?
That's why I ask, which answer you gave him.
Whatever I said to him, it's none of your business.
That's right.
I... am going to move out.
I've talked with my father about it.
I'm going to get in your way.
It's a relief that Joon Gu works so hard.
My dad likes him a lot too.
Now, I should help my father at his restaurant with Joon Gu.
Do you like him?
Bong Joon Gu?
Of course I do.
For 4 years, he only liked me.
If someone says they like you, then you just like them like that too?
Why?
I can't do that?
I'm tired of having a crush now.
I want to see a guy that likes me.
I like Joon Gu.
You ...
You like me.
You can't like anyone but me. What is this, that confidence?
Am I not right?
Yes, you are right!
I only like you.
So what am I supposed to do?
You don't ever see me.
Someone like me...
Don't say that you like another guy.
That's the second one.
Second what?
Kiss.
It's the third.
It's fine. you don't have to count those things.
Okay. <i>Brought to you by the PKer team @ www.viikii.net <i>There are actually results from having a crush for four years. <i>Get in. <i>You finally did it. <i>Then what about Bong Joon Gu? <i>You're faster than I thought.
I knew that someday you'd find your true feelings. <i>But you're not having a hard time anymore? <i>I'm not. <i>It became fun. <i>Yoon Hae Ra, what's wrong with you?
I wanted to call you "Father."
I wanted to call you "Father-in-law." <i>Congratulations on your marriage. <i>I'm sorry.
Are you okay? Yeah. Even if you weren't okay, you're not the type who would tell me.
Wait just a little.
This time, honestly, even if I have to leave my home,
I'm going to protect you.
What are you saying?
The Witch's personality isn't the kind to sit back and do nothing.
She's definitely up to something.
I'm just saying that I'll be preparing, too.
Don't do that. what?
Whatever you do, you have to be the reason for it.
I don't want you protecting me.
Why do you not like it?
Because you're my girl, it's a given that I'd protect you.
Someone protecting someone else; someone guarding over someone else...
If it's only sustainable by that... I don't like it.
Until now, I've already received so much from you, F4 sunbaes, even JaeKyung unnie.
At the very least, I want for you and I to be on equal footing.
As I overcome what needs to be overcome.
Do you know?
What?
You're the type of girl on whom
"cuteness" is wasted.
Huh, what's wrong with you?
Chan!
(the boy's name) What's wrong?
Why are you so sad?
What's wrong?
What?!
Is this the time to be laughing?
Hold it in.
You'd better hold it in!
Chan, what is that?
Can you see that?
You can't see it well, huh?
Let me ride on your shoulders, okay? what?
A shoulder ride.
Is it fun? Yeah.
He's going to fall. <BR>No, I'm not going to fall.
It must be spring . . . the weather's mellowed.
It's weird.
What is?
I feel as though
I'm in a vague dream that I've had before.
I'm just saying...
How come this small kid's so heavy! Hey, Manager Jung. Young master, I think you'd better come back now.
Happy birthday to you!
Happy birthday to you!
Happy birthday to YiJung!
Happy birthday to you!
Happy birthday, YiJung.
Come on, you should make a wish and blow out the candles.
This is a gift.
"One meeting, one opportunity "
What does it mean?
A once-in-a-lifetime fate.
GaEul.
YiJung sunbae...
I found it.
What?
I finally found it. *I love you, YiJung*
On that day sunrise was at 7:00 am.
This was only visible right at sunrise, for just a few seconds.
That message.
Idiot.
Even knowing I was an idiot . . . She knew it better than anyone in the whole world.
How could she give me such a tough problem to solve?
YiJung.
I really would like for you to show up.
The breeze... can't go back to a place it has already left, YiJung.
Do it over!
Do it over!
Let me redo it!
Yesterday, the lovely spring weather brought out many families to the city zoo, where flowers were in full bloom.
Mr. President.
Are you serious about keeping this buried?
Even if they say it was an accident that a zealot committed?
It's not as though it would bring these two back to life.
I can't let JiHoo see his father and mother's death be used in political strife.
President.
I had no fear about something that I always believed was right.
But it wasn't until after I lost them that I realized that that was also a form of arrogance. . .
It was because of the fear that I might also lose you...
The years that I was unable to see you was my punishment.
When you should have been blaming your Grandfather, you had been living with that terrible burden.
Now, even if I die,
I have no regrets, child.
Can I ask that you take care of the Foundation and the clinic?
It was your father and mother's wish to cure the heart by the arts and to cure illness by medical practice
Grandfather, I'm not yet...
Come over here!
Spicy fish soup is ready!
He he, that kid sure has a loud voice.
You're going to chase away all the fish with that loud voice of yours!
Is it all done?
Yes.
How is it?
You rascal, know that I'll eat it because I don't want to waste the perfectly good fish.
JiHoo, why don't you taste it?
Amazingly, it tastes a lot like your mom's.
Ok, you two, look over here! one...two...three!
I have good news and bad news.
Which one do you want to hear first?
Ah, I know your style.
Bad news first?
I probably will not be as good as before.
This hand... whether the pottery gods will choose it again,
I don't know.
No, they will.
But, what's the good news?
Even with all that, the fact that I will continue.
I'm not going to avoid it anymore.
If you give up once, how much you regret it...
I learned thanks to you.
Sunbae.
GaEul, you want to try it? How did you know that I would listen bad news first?
Because good girls like happy endings.
I definitely am a cool guy, but not a good guy.
You need to get rid of your misconception that good girls want good guys.
Yes, mom.
What?
Is that true?
All right.
I'll be there right away.
We worked really hard, through the foundation, and the hard efforts of a lot of people went into this.
Jandi, take a walk around.
Okay.
It's quite something, isn't it?
It's so spacious.
Oh!
What's that grandpa?
Over there are all meeting rooms.
Hold on a second.
Yes, it's me.
Hey, is that true?
Who would have the nerve?
How on earth did this situation come about?
No!
Whatever happens, we must take care of the foundation!
No!
Grandpa!
Grandpa!
Grandpa!
Grandpa!
Grandpa, your medicine!
The medicine!
Sunbae!
The hospital, the hospital!
He did not want you to know.
He said he'd be fine as long as he's careful.
Let's go and get Grandfather's stuff.
The preparations are going well, I presume
Chairwoman,
Apart from anything else, could you reconsider about the Sooam Foundation?
You know better than anyone that
I'm not doing this out of greed for the silly foundation.
What are you intending to do?
At this chance, I'm going to pull it out the roots.
It's so fortunate that that little upstart child values something more than money.
I have a proposition.
A proposition?
The fact that the marriage didn't happen...
I'm sorry about that.
But... it's not like the ties are completely cut with JK Group.
I will do my utmost to save it.
Trust in me.
And so what?
Whether you put spies on me or keep me locked up.
I'll take whatever you dish out.
Except.
Except...
leave Jandi alone.
If I don't do anything to Geum Jandi, then is that enough?
Yeah.
I'll make that promise.
I won't lift a finger against Geum Jandi.
In return don't forget what you've said just now.
Don't worry.
This is not the time to be mopping around.
Granny?
Do you still not know your mother?
This is not the time for you to feel at ease.
When you can't even take care of your own girl, how do you plan on taking care of ShinHwa Group in the future?
I did not raise you to be such a pathetic person.
Just because a person is born as a male doesn't mean you're automatically a man.
Since you're furious at your defeat, you can't bear to step back, and you're embarrassed about running away, you overcome your weak character over time. That's how you become a real man.
Do you understand?
Granny!
Thank you. *JiHoo in Kindergarten* * JiHoo in elementary school *
Gaeul
Didn't you say your father had tenure of 20 years at his company?
It hasn't even been that long since he was promoted to assistant manager.
How come they suddenly force only your dad to resign?
Why did they do it?
Seriously?
Shinhwa's Group subcontracting company forced GaEul's dad to resign, all of those things in just one morning?
Looks like it.
I was wondering why she didn't do anything after the wedding.
Then again it seems Jihoo has been put into a mess too.
JiHoo's?
It seems Chairman Kang is going to take over Jihoo's foundation as well.
What?
The development of the new art center in Song-do has already been postponed.
Then...
This is all?
Her plan to destroy, the one, Geum JanDi.
Grandfather...
JanDi, glad you came.
Why?
Did you miss me in that short period of time?
You and your delusional thinking!
JanDi, since you're here, why don't you take that boy out of here?
He's completely stuck on me and won't move an inch.
It's suffocating.
Why aren't you guys both getting out of here?
On such a beautiful spring day! You young, pathetic things,
Get out of here now!
Let's get out of here. <i>The development of the new art center has already been postponed.</i> <i>So, this is . . .</i> <i>Her plan to destroy the one, Geum JanDi.</i>
The desire to protect someone, I never thought it would develop in me.
But since I met you, I started developing it.
Grandfather, the clinic, the foundation,
And... you. <i>Now since Grandpa is with Sunbae, I'm really relieved. <i>Sunbae, you don't know that, right?
Mister,
I don't think I can come here anymore.
I wanted to see you get better.
There were a lot of books I wanted to read to you.
I apologize.
I... can endure hunger. And even being cold, I can endure.
But there is one thing... that I can never endure.
It's seeing those that I love endure hardship because of me.
It's not something that I can make better by trying harder.
Don't you think it's a little unfair this time?
Mister, I'm not running away.
Mister, you know that, right?
Even when I'm not here, you have to get better.
Chairwoman,
Geum JanDi is here.
She came here quicker than I expected.
Let her in.
Hello, Miss.
Oh, Jandi!
Hi!
Has everyone been doing well?
But what's going on?
Is it okay for you to be here?
It's OK.
They won't kill me or bite me!
Geum JanDi! Fighting!
We're all on your side!
Hello Sunbae nim.
Welcome, Miss Geum JanDi.
Why are you acting like that?
It's me, Geum JanDi, your apprentice.
You're a guest when you come to this house now.
But, what brings you here?
Ah..Goo JunPyo....
I mean Master JunPyo....
I came to see Goo JoonPyo.
Young Master is in his room.
Okay...
JunPyo, let's play!
Goo JunPyo, let's play!
Now I'm even hearing Geum JanDi's voice.
Hey, what's going on?
Goo JoonPyo, let's play.
Why are you here?
Did that Witch do something again? Is that it? Let's play, Goo JoonPyo!
Is today a special day
What?
I don't know well but isn't this what it feels like to have a birthday party or to win the lottery?
Are you that happy?
Yeah.
I wish everyday was like today.
Just think about it.
You asked me out on a date.
And we haven't even fought once.
You're right.
While we're on the subject, can I ask you for one more favor?
What is it?
Why haven't you told me that you like me?
I've told you, many times
Do I really have to say it in words
I want to hear it.
What kind of person am I to you?
I like you.
No matter how much I've tried not to like you...
Even though I've tried to erase the feeling, I can't. It's to the point where I'm just frustrated.
Didn't you come because you had something to say?
Leave them alone.
What
My friend GaEul's family
And JiHoo Sunbae's Foundation
Just leave it be
What's your offer?
What are you going to give me in return?
If there's nothing as collateral, I don't have any desire to agree.
I'll leave.
I'll leave Goo JoonPyo.
I'll transfer schools and move.
I'll move to a place Goo JoonPyo can never find me.
Is that enough?
If only you keep that promise..
I'll keep that promise.
Fine.
I think we've come to an agreement.
I'm not losing to you. i'm not running away or stealing either.
You are...
The most evil person I've ever known.
The people that I love....
I don't want them entangled with you. so I'm leaving.
From you, ...the person I love the most
I can't save, and it makes me feel so anxious
Goo JoonPyo
Hmm?
Stop the car here.
Here?
Why?
Just stop the car.
What's up with these bags?
Is this a surprise event?
Goo JoonPyo,
I'm not going to see you anymore.
What
Today was my last day with you
Hey, Geum JanD
Are you bothered that we didn't fight once today?
Even if you're going to joke around, what kind of a joke is this?
I'm not joking.
What's your reason?
Did the witch do something to you again?
No, it was my decision. to take you out of my life.
Geum jandi
Thank you for everything.
Take care.
What's wrong with you?
You said you liked me.
Just a while ago, you said it yourself that you liked me so why...!
It's because of the witch, isn't it?
Right? no
It's because of me.
What?
This time, I realized that you and I live in two separate worlds.
Even though we met in a dream-like fate, but now it's time to return to our separate worlds.
That's a lie.
You're lying to me right now.
Tell me.
I'll solve it.
I'll protect you!
DON'T LEAVE
You said you liked me
Your love is like this
You said that you liked me and you're going to end it so easily?
Maybe it was just this much.
No matter how much I liked you, maybe this is all I could put up with. just this much maybe it was just thatt
Say it.
Aside from ShinHwa and being a plutocrat, have you ever seen me as just a guy?
No.
No matter how much you struggle, you're still ShinHwa Group's Goo JoonPyo.
I never forgot that, not even for a single moment.
Pull Over!
JanDi!
Geum JanDi!
JanDi!
I said pull over!
JanDi! JanDi !
Ever since I've liked you, I've always wished for it... that you were a normal guy that had nothing to do with ShinHwa or being a plutocrat.
Sorry GooJunPyo
For not being able to keep our promise.
I'm really sorry
JanDi!
Grandfather is here.
Where is she?
Jandi?
This child! I'm sorry that I have to leave this way. Thank you for everything.
I'm telling the truth.
Why won't you believe me?
Oh, you're starting again!
If your future son-in-law is some heir to great fortune, what are you doing here?
And not just any heir, ShinHwa Group?!
Then my future daughter-in-law is Jun Sul Group's daughter!
My daughter goes to ShinHwa High School.
I've even made dinner for ShinHwa Group's heir, Goo JoonPyo.
Why won't you believe a word I say? Fine, all right.
Then why don't you go to your future son-in-law and have him take care of your debts?
If you don't, something might happen to you
Oh, welcome.
What can I get you
Give me one of these
Here you go.
Who is that?
He came here in kind of the same situation as you.
He was the president of a startup company...
M, M . . .
However, he lost everything because of some large corporations.
He was divorced and lost his kids, too.
Oh, no.
What to do?
Seeing that he's been hanging around here for the past few months, I think he's hiding from creditors.
That's really too bad.
You've got problems of your own.
You're in no position to worry about others!
Yeah, that's right.
Isn't that JanDi?
Oh, my.
Oh, my!
JanDi!
Mom!
What brought you here?
I wanted to see you.
Is this the daughter that you've been talking about?
Yes, yes.
This is her!
Watch this.
See this?
See?
This is ShinHwa High School uniform!
Oh, my, you said she went to ShinHwa High.
She really does go there!
JanDi, come on.
Let's go talk!
Why don't you all watch over my little store?
Okay, okay, don't worry.
Oh, what kind of luck is that!
Watch it carefully!
How and what brought you here, JanDi?
She looks like she's grown well.
What?
Dad's on a boat?
What were we supposed to do?
Our debt kept growing.
We have to send your brother, KangSan, to school.
It seems like we can't even support the three of us.
Why didn't you tell me then?
What good would it have done except to make you worry?
I could have quit school, gotten a job.
I could have done something.
And that's why I didn't say anything
You need to graduate from ShinHwa High and go to ShinHwa University.
Get married to Master JoonPyo or someone so we can survive.
That's our hope.
Mom... That's rubbish.
Wait, you....why aren't you going to school and why'd you suddenly come here?
I came because I missed you guys.
Mom, dad, San.
Honey!
Our daughter, JanDi, came.
You're doing well, right daddy!
I came.
You're healthy, right?
Please look after your health!
Dad!
Dad!
Have you heard any news about JanDi?
Well....
I've searched just about everywhere.
It's harder to find her than I thought.
I wonder where she's hidden herself so well.
That JoonPyo, I don't think he's been so unreachable ever.
He wasn't even this bad in Macao.
I know...
It's as if he's sitting on a time bomb.
It's hard to watch from above or below.
The weird thing is, JiHoo is the same way.
He's doing well with his grandfather.
Do you think Yoon JiHoo going to work everyday at the Foundation is normal?
For a guy who used to sleep all the time and mess around with his instruments to act like that is....
I think is more strange than how JoonPyo is, and it makes me quite worried.
That is true.
How impressive Geum JanDi is! to put the great F4 into this state and then disappear.
Yes, Grandfather.
It's me.
Yes.
I'll come get you right now
Oh, what to do!
Our JanDi has come to visit and the ban chan (side dishes) are lacking.
What about the ban chan?
Just the fact that I'm having a meal with you makes me so happy I can die!
Noona, how many days will you be staying before you leave?
It'll be nice if you could stay a long time.
I'll be staying a long time.
What do you mean you'll be staying long!
You have to go to school
Stop worrying about your family and accomplish what you need to do.
KangSan's mom?!
I wonder who it is.
We came.
What are you guys doing here?
Oh, she definitely is a future daughter-in-law material of a filthy rich family.
Only the rich attend ShinHwa High, so you must have lots of friends who are rich!
Who cares about the friends?
She's dating the heir to ShinHwa Group!
Living in the country, I never dreamed that I'd come to know the in-laws of ShinHwa Group!
Oh, I know, I know.
Try this
Oh, and the money that you borrowed, just take your time in paying that back.
Oh, really?
Oh, yes.
Of course.
Oh, and take this.
Take this too.
Take it.
Take it.
What's the occasion, this late at night?
- Eat it.
- Okay, we'll eat it well.
You got it!
I got it!
You said you liked me.
Is this how your love is?
Can you really say you like me and end it this easily?
This must have been the limit.
No matter how much I liked you, The amount I could put up with Must've been only this much.
Hey, what are you doing?
Master, why are you doing this?
Why are you breaking somebody else's machine?
Don't touch me!
Why haven't you told me that you like me?
Do I really have to say it in words?
I want to hear it.
What I am to you...
I like you.
No matter how much I've tried not to like you, even though I've tried to erase the feeling, I can't, to the point where I'm just frustrated.
JoonPyo.
So I want to talk today about money and happiness, which are two things that a lot of us spend a lot of our time thinking about, either trying to earn them or trying to increase them.
And a lot of us resonate with this phrase.
So we see it in religions and self-help books, that money can't buy happiness.
And I want to suggest today that, in fact, that's wrong.
(Laughter)
I'm at a business school, so that's what we do.
So that's wrong, and, in fact, if you think that, you're actually just not spending it right.
So that instead of spending it the way you usually spend it, maybe if you spent it differently, that might work a little bit better.
And before I tell you the ways that you can spend it that will make you happier, let's think about the ways we usually spend it that don't, in fact, make us happier.
We had a little natural experiment.
So CNN, a little while ago, wrote this interesting article on what happens to people when they win the lottery.
It turns out people think when they win the lottery their lives are going to be amazing.
This article's about how their lives get ruined.
So what happens when people win the lottery is, number one, they spend all the money and go into debt, and number two, all of their friends and everyone they've ever met find them and bug them for money.
And it ruins their social relationships, in fact.
So they have more debt and worse friendships than they had before they won the lottery.
What was interesting about the article was people started commenting on the article, readers of the thing.
And instead of talking about how it had made them realize that money doesn't lead to happiness, everyone instantly started saying, "You know what I would do if I won the lottery ... ?" and fantasizing about what they'd do.
And here's just two of the ones we saw that are just really interesting to think about.
One person wrote in, "When I win, I'm going to buy my own little mountain and have a little house on top."
(Laughter)
And another person wrote, "I would fill a big bathtub with money and get in the tub while smoking a big fat cigar and sipping a glass of champagne."
"Then I'd have a picture taken and dozens of glossies made.
Anyone begging for money or trying to extort from me would receive a copy of the picture and nothing else."
(Laughter)
And so many of the comments were exactly of this type, where people got money and, in fact, it made them antisocial.
So I told you that it ruins people's lives and that their friends bug them. It also, money often makes us feel very selfish and we do things only for ourselves.
Well maybe the reason that money doesn't make us happy is that we're always spending it on the wrong things, and in particular, that we're always spending it on ourselves.
And we thought, I wonder what would happen if we made people spend more of their money on other people.
So instead of being antisocial with your money, what if you were a little more prosocial with your money?
And we thought, let's make people do it and see what happens.
So let's have some people do what they usually do and spend money on themselves, and let's make some people give money away, and measure their happiness and see if, in fact, they get happier.
So the first way that we did this.
On one Vancouver morning, we went out on the campus at University of British Columbia and we approached people and said, "Do you want to be in an experiment?"
They said, "Yes." We asked them how happy they were, and then we gave them an envelope.
And one of the envelopes had things in it that said, "By 5:00 pm today, spend this money on yourself."
So we gave some examples of what you could spend it on. Other people, in the morning, got a slip of paper that said, "By 5:00 pm today, spend this money on somebody else."
Also inside the envelope was money.
And we manipulated how much money we gave them.
So some people got this slip of paper and five dollars.
Some people got this slip of paper and 20 dollars. We let them go about their day. They did whatever they wanted to do.
We found out that they did in fact spend it in the way that we asked them to. We called them up at night and asked them, "What'd you spend it on, and how happy do you feel now?"
What did they spend it on?
Well these are college undergrads, so a lot of what they spent it on for themselves were things like earrings and makeup.
One woman said she bought a stuffed animal for her niece.
People gave money to homeless people.
Huge effect here of Starbucks.
(Laughter)
So if you give undergraduates five dollars, it looks like coffee to them and they run over to Starbucks and spend it as fast as they can.
But some people bought a coffee for themselves, the way they usually would, but other people said that they bought a coffee for somebody else.
So the very same purchase, just targeted toward yourself or targeted toward somebody else.
What did we find when we called them back at the end of the day?
People who spent money on other people got happier.
People who spent money on themselves, nothing happened.
It didn't make them less happy, it just didn't do much for them.
And the other thing we saw is the amount of money doesn't matter that much.
So people thought that 20 dollars would be way better than five dollars.
In fact, it doesn't matter how much money you spent.
What really matters is that you spent it on somebody else rather than on yourself.
We see this again and again when we give people money to spend on other people instead of on themselves.
Of course, these are undergraduates in Canada -- not the world's most representative population.
They're also fairly wealthy and affluent and all these other sorts of things.
We wanted to see if this holds true everywhere in the world or just among wealthy countries. So we went, in fact, to Uganda and ran a very similar experiment.
So imagine, instead of just people in Canada, we said, "Name the last time you spent money on yourself or other people.
Describe it. How happy did it make you?"
Or in Uganda, "Name the last time you spent money on yourself or other people and describe that."
And then we asked them how happy they are again.
And what we see is sort of amazing because there's human universals on what you do with your money and then real cultural differences on what you do as well.
So for example, one guy from Uganda says this.
He said, "I called a girl I wished to love."
They basically went out on a date, and he says at the end that he didn't "achieve" her up till now.
Here's a guy from Canada.
Very similar thing. "I took my girlfriend out for dinner.
We went to a movie, we left early, and then went back to her room for ... " only cake -- just a piece of cake.
Human universal -- so you spend money on other people, you're being nice to them.
Maybe you have something in mind, maybe not.
But then we see extraordinary differences.
So look at these two.
This is a woman from Canada. We say, "Name a time you spent money on somebody else."
She says, "I bought a present for my mom.
I drove to the mall in my car, bought a present, gave it to my mom."
Perfectly nice thing to do.
It's good to get gifts for people that you know. Compare that to this woman from Uganda.
"I was walking and met a long-time friend whose son was sick with malaria.
They had no money, they went to a clinic and I gave her this money." This isn't $10,000, it's the local currency.
So it's a very small amount of money, in fact.
But enormously different motivations here.
This is a real medical need, literally a life-saving donation.
Above, it's just kind of, I bought a gift for my mother.
What we see again though is that the specific way that you spend on other people isn't nearly as important as the fact that you spend on other people in order to make yourself happy, which is really quite important.
So you don't have to do amazing things with your money to make yourself happy.
You can do small, trivial things and yet still get these benefits from doing this. These are only two countries.
We also wanted to go even broader and look at every country in the world if we could to see what the relationship is between money and happiness.
We got data from the Gallup Organization, which you know from all the political polls that have been happening lately.
They ask people, "Did you donate money to charity recently?" and they ask them, "How happy are you with your life in general?"
And we can see what the relationship is between those two things.
Are they positively correlated?
Giving money makes you happy.
Or are they negatively correlated?
On this map, green will mean they're positively correlated and red means they're negatively correlated.
And you can see, the world is crazily green.
So in almost every country in the world where we have this data, people who give money to charity are happier people that people who don't give money to charity.
I know you're all looking at that red country in the middle.
I would be a jerk and not tell you what it is, but in fact, it's Central African Republic.
You can make up stories. Maybe it's different there for some reason or another.
Just below that to the right is Rwanda though, which is amazingly green.
So almost everywhere we look we see that giving money away makes you happier than keeping it for yourself.
What about your work life, which is where we spend all the rest of our time when we're not with the people we know.
We decided to infiltrate some companies and do a very similar thing.
So these are sales teams in Belgium.
They work in teams; they go out and sell to doctors and try to get them to buy drugs.
So we can look and see how well they sell things as a function of being a member of a team.
Some teams, we give people on the team some money for themselves and say, "Spend it however you want on yourself," just like we did with the undergrads in Canada.
But other teams we say, "Here's 15 euro.
Spend it on one of your teammates this week.
Buy them something as a gift or a present and give it to them.
And then we can see, well now we've got teams that spend on themselves and we've got these prosocial teams who we give money to make the team a little bit better.
The reason I have a ridiculous pinata there is one of the teams pooled their money and bought a pinata, and they all got around and smashed the pinata and all the candy fell out and things like that.
A very silly, trivial thing to do, but think of the difference on a team that didn't do that at all, that got 15 euro, put it in their pocket, maybe bought themselves a coffee, or teams that had this prosocial experience where they all bonded together to buy something and do a group activity.
What we see is that, in fact, the teams that are prosocial sell more stuff than the teams that only got money for themselves.
And one way to think about it is for every 15 euro you give people for themselves, they put it in their pocket, they don't do anything different than they did before.
You don't get any money from that.
You actually lose money because it doesn't motivate them to perform any better.
But when you give them 15 euro to spend on their teammates, they do so much better on their teams that you actually get a huge win on investing this kind of money.
And I realize that you're probably thinking to yourselves, this is all fine, but there's a context that's incredibly important for public policy and I can't imagine it would work there.
And basically that if he doesn't show me that it works here,
I don't believe anything he said.
And I know what you're all thinking about are dodgeball teams.
(Laughter)
This was a huge criticism that we got to say, if you can't show it with dodgeball teams, this is all stupid.
So we went out and found these dodgeball teams and infiltrated them.
And we did the exact same thing as before. So some teams, we give people on the team money, they spend it on themselves.
Other teams, we give them money to spend on their dodgeball teammates.
The teams that spend money on themselves are just the same winning percentages as they were before.
The teams that we give the money to spend on each other, they become different teams and, in fact, they dominate the league by the time they're done.
Across all of these different contexts -- your personal life, you work life, even silly things like intramural sports -- we see spending on other people has a bigger return for you than spending on yourself.
And so I'll just say, I think if you think money can't buy happiness you're not spending it right.
The implication is not you should buy this product instead of that product and that's the way to make yourself happier.
It's in fact, that you should stop thinking about which product to buy for yourself and try giving some of it to other people instead.
And we luckily have an opportunity for you. DonorsChoose.org is a non-profit for mainly public school teachers in low-income schools.
They post projects, so they say, "I want to teach Huckleberry Finn to my class and we don't have the books," or "I want a microscope to teach my students science and we don't have a microscope."
You and I can go on and buy it for them. The teacher writes you a thank you note.
The kids write you a thank you note. Sometimes they send you pictures of them using the microscope.
It's an extraordinary thing.
Go to the website and start yourself on the process of thinking, again, less about "How can I spend money on myself?" and more about "If I've got five dollars or 15 dollars, what can I do to benefit other people?"
Because ultimately when you do that, you'll find that you'll benefit yourself much more.
Thank you.
(Applause)
We've been doing a lot of rotating around the x-axis, so let's start rotating around the y-axis and see what we can do.
Let's me draw my axes.
That's y-axis.
Well let's just do it with an example, but we'll call it f of x too because it'll be generalizable.
Let's just draw y equals x squared.
Let me just draw the positive because we're going to rotate it around the y-axis and it's symmetric anyway, so that's y equals x squared.
This is y-axis.
This is x-axis.
So we'll call this f of x, but clearly this is y equals x squared.
This is f of x.
And we know how to take the volume if I were to rotate this around the x-axis.
But what if I wanted to say-- I guess we could call it the area between 0 and-- I'm trying to determine how general to be.
I think the boundaries might make sense to you.
Roughly this area, and I'm going to rotate it around the y-axis now.
So what's that final figure going to look like?
The base of it-- let me see how well I can draw it.
The base is going to look something like a cylinder like that.
And then the top of it is also going to be-- no, that's not what I wanted to do.
Let me draw the side lines.
So it's going to look something like that.
But it's not just going to be cylinder, right?
If I was doing this entire block it would be a cylinder.
But the inside of it is going to be kind of hollowed out.
So the inside is going to be hollowed out.
It's kind of like on the inside it'll look like a bowl.
On the outside it'll look like a cylinder or a can.
You take this and you rotate this around.
And the curve that specifies the inside would be y is equal to x squared.
It would rotate all the way around.
So how do we do it?
We can't use that disk method, what we were doing before when we were rotating the x-axis, that was the disk method, because we were essentially imagining each of these particular disks and then summing them up.
Now we're going to do something called the shell method.
So what's the shell method?
Instead of taking a bunch of disks and figuring out their combined volumes, we're going to take a bunch of shells.
So what's a shell?
So imagine a rectangle right here.
Let's say it's at the point x,1.
What's its height going to be?
Its height going to be f of x,1.
Now imagine taking that sliver and rotating it around the y-axis.
What's it going to look like?
Well, it's going to look like a shell, it's going to look like a cylinder, just like the outside of a cylinder.
The outside of the shell is going to be solid.
And it'll have some width, but the inside is hollow.
Let me do a different color.
Maybe a darker color to show that that's the inside.
And so what's the height of this ring?
The height is going to be f of x,1.
So let me do a brighter color so you know what I'm saying.
The height of this ring is f of x,1. f of x evaluated at that arbitrary point we picked up.
What is going to be the surface area of this ring?
Well let's think about it.
It'll be the circumference of this ring times it's height.
So what's the circumference of this ring?
Circumference is equal to 2 pi times the radius.
So if we know the radius of it, we know the circumference.
Well what's the radius?
Well the radius is how far we went from the axis of rotation to that point.
So in our particular example the radius is x,1.
It's that x point that we're evaluating it at.
So circumference is going to be equal to 2 pi times that point that we're evaluating at.
And so the surface area-- this magenta thing that I filled in-- that's going to be equal to the circumference times this height, which we already said is f of x,1.
Surface area is equal to circumference times height, which is equal to 2 pi x,1 times f of x,1.
We figured out the surface are of this.
Now how do we figure out the volume?
How thick is this ring?
What's this thickness right here?
But we took this sliver, and this sliver as we learned in previous calculus, the width of this little rectangle is dx.
And you know when we take the integral, it's going to get infinitely smaller and smaller and we'll have infinitely more and more of them.
So the width of this is dx.
Let me draw it big, not so horrible looking.
So if this is a sliver, it's width is dx.
It's height is f of x,1. x,1 will be right in the center.
And then it's distance from the center is of course x,1.
So what's the volume of this shell?
So the volume of the shell-- this shell, not this one-- the volume of the shell is going to be equal to the surface area of the shell times how wide that surface is.
And that width is dx, so it's going to equal this times dx.
So the volume of that shell is 2 pi x,1 times f of x,1 times dx.
So what would be the volume of the entire rotated figure, this thing here?
Well I'm just going to sum up each of these shells.
I have one shell there, then here I'll have a slightly less high shell, and up here I would have a much bigger shell, and I'll add them up.
Here's one shell that goes around.
Then they'll be another shell here, and I'll add them all up.
And that's taking the integral.
So the total volume of the figure when I rotate it around the y-axis is going to be-- and my boundary is from 0 to 1-- 2 pi-- this one I just told you a particular x,1 but we're going to sum them over all of the x's.
So it's going to be 2 pi x f of x dx.
This is just a constant, so you could call it 2 pi times x f of x.
So let's take a particular example.
Let's do it for x squared.
Let's say the function is x squared.
So in this case the volume is going to equal-- let's take the 2 pi out-- 2 pi integral 0 to 1 x times f of x-- f of x in our case is x squared, which I drew earlier-- dx equals 2 pi.
This is just x to the third, right? x to the third.
So it's going to be 2 pi times the antiderivative of x to the third.
Evaluate it at 1 minus evaluate it at 0.
Well that equals 2 pi times 1 to the fourth is 1, so 1/4 and then minus 0.
So it's 2 pi times 1/4.
So that's pi over 2.
That's the volume, and we just rotated it around the y-axis.
I will see you in the next video.
A recipe for oat meal cookies calls for 2 cups of flour for every 3 cups oatmeal.
How much flour is required for a big batch which uses 9 cups of oatmeal.
So 2 cups of flour for every 3 cups of oatmeal.
Now we are going to a situation where we are using 9 cups of oatmeal.
I will let you know a couple of different ways we can think about it.
One way to think about this is we know if we use 3 cups of oatmeal , we need 2 cups of flour.
We do not know how much is required if we use 9 cups of oatmeal
If we are going from 3 cups to 9 cups of oatmeal how much more oatmeal we are using? we are using 3 times more , 3 x 3 = 9
If we want to use flour in the same proportion we need to use, 3 times the flour we need flour times 3 ; 2x3 = 6 cups of flour
Another way to think about it
You can say 2 cups of flour over 3 cups of oatmeal is equal to ? cups of flour over 9 cups of oatmeal.
It is common sense.
If you triple the oatmeal, you have to triple the flour.
Once youset up an equation like this, is to use a little bit of algebra.
In cross multiplication, whenever you set a proportion like this, 2 x 9 = ? x 3 or we get 18 = ? x 3 so the number of cups of flour we need to use times 3 needs to be 18. You divide both sides by 3 to get the answer which is 6
So we get ? = 6 cups of flour.
You might we wondering cross multiplication does not make sense.
If you have setup a proportion like this, why should cross multiplication work.
That comes from algebra.
I am going to rewirte this part as x to simplify we have 2/3 = x/9.
In algebra, all we are saying this quantity over here is equal to this quantity over there.
If you do anything to the left , we need to do the same thing to the right to keep it equal.
So what can we multiply this by, so that we are left with just "x".
So we multiply this times 9, If you multiply right side by 9, you need to multiply the left by 9 for both sides to be equal. on the right hand side the 9 cancel out, you are
left with x. On the left hand side, 9*2/3 = 18/3 = 6
So these are all legitimate ways of doing this.
For really simple problems like this you can use common sense.
If you are increasing oatmeal by 3 times, increase flour also by a factor of 3
 We're asked how many centiliters are in one dekaliter?
So the first thing we want to do is just think about how much is a centiliter relative to a liter, and how much is a dekaliter relative to a liter?
And I'll write the prefixes down.
And really, you should have these memorized because you're going to see these prefixes over and over again for different types of units.
So the prefix, kilo, sometimes [? ki-lo, ?] this means 1,000.
If you see hecto, hecto means 100.
Deka means 10.
If you have nothing, then that just means 1.
Let's put that there.
Then if you have deci, this means 1/10.
If you have centi, this means 1/100.
If you have milli, this means 1/1,000.
So let's go back to what we have. We have centiliters.
Let me write this in a different color.
If you have a centiliter, this is equal to 1/100 of a liter,
Or you could say 1 liter for every 100 centiliters, so you could also write it like this:
1 liter for every 100, or per every 100, centiliters.
So we got the centi, now let's think about the dekaliter. So the deka is right over here.
So a dekaliter means 10 liters.
Or another way to say it is for every 10 liters, you will have 1 dekaliter.
Now, before I actually work out the problem, what's going on here?
We're going from a smaller unit to a larger unit, so there are going to be many of the smaller units in one of the larger ones.
And we can do it multiple ways.
So we want to essentially convert 1 dekaliter into centiliters.
Now, we could just do it by looking at this chart, or we could do it with the dimensional analysis, making sure the dimensions work out.
Let's do it the first way.
So if you have one dekaliter, how many liters is that?
1 dekaliter over here would be the same thing as 10 liters. That's liters. We're assuming that our unit is liters here.
And then 10 liters is going to be how many deciliters?
It's going to be 100 deciliters, right?
Because each of these is 10 deciliters, and you have 10 of them.
So every time you go down, you're going to be multiplying by a factor of 10.
100 deciliters is how many centiliters?
Well, 100 deciliters, each of them is going to be worth 10 centiliters, so that's going to be 1,000 centiliters.
1 dekaliter is 1,000 centiliters.
Now, the other way to do it is you could convert a dekaliter to liters, and then convert a liter to centiliters.
So if we have one dekaliter-- and whenever you do unit things, just make sure that it makes sense.
Sometimes, people, instead of multiplying, they would divide, and then they'd get, oh, 1 dekaliter is equal to 1/1,000 of a centiliter.
And they say, no, no, no, no.
A dekaliter is a much larger unit that a centiliter.
So 1 dekaliter has to be a bunch of centiliters.
This should be a large number, so you should always do that reality check whenever you're dealing with units.
Now, let's do it the dimensional analysis way.
We're starting with one dekaliter.
We want to convert it to liters.
So if you're converting it to liters, you want the dekaliter in the denominator and you want liters in the numerator.
Now, how many liters are 1 dekaliter?
Well, you could say 10 liters is equal to 1 dekaliter.
So 1 dekaliter is equal to-- these cancel out.
1 times 10 is 10 liters.
Now, if we wanted to convert this to centiliters, we're going to want the liters in the denominator, and you want the centiliters in the numerator.
Now, how many centiliters are there per liter?
How many centiliters? Well, 1 liter is 100 centiliters.
Centiliter is 1/100 of a liter.
Notice, this and this are the inverse statements.
They're saying same the exact same thing.
1 liter per 100 centiliters.
Here, writing 1 liter per 100 centiliters.
We've just flipped it, but they're giving the same information.
And the reason why we flipped it is so that the liters cancel out, and then we're just left with 10 times 100 is 1,000 centiliters.
And we are done!
Use the quadratic formula to solve the equation, 0 is equal to negative 7q squared plus 2q plus 9.
Now, the quadratic formula, it applies to any quadratic equation of the form-- we could put the 0 on the left hand side.
0 is equal to ax squared plus bx plus c.
And we generally deal with x's, in this problem we're dealing with q's.
But the quadratic formula says, look, if you have a quadratic equation of this form, that the solutions of this equation are going to be x is going to be equal to negative b plus or minus the square root of b squared minus 4ac-- all of that over 2a.
And this is actually two solutions here, because there's one solution where you take the positive square root and there's another solution where you take the negative root.
So it gives you both roots of this.
So if we look at the quadratic equation that we need to solve here, we can just pattern match.
We're dealing with q's, not x's, but this is the same general idea.
It could be x's if you like.
And if we look at it, negative 7 corresponds to a.
That is our a.
It's the coefficient on the second degree term.
2 corresponds to b.
It is the coefficient on the first degree term.
And then 9 corresponds to c.
It's the constant.
So, let's just apply the quadratic formula.
The quadratic formula will tell us that the solutions-- the q's that satisfy this equation-- q will be equal to negative b. b is 2.
Plus or minus the square root of b squared, of 2 squared, minus 4 times a times negative 7 times c, which is 9.
And all of that over 2a.
All of that over 2 times a, which is once again negative 7.
And then we just have to evaluate this.
So this is going to be equal to negative 2 plus or minus the square root of-- let's see, 2 squared is 4-- and then if we just take this part right here, if we just take the negative 4 times negative 7 times 9, this negative and that negative is going to cancel out.
So it's just going to become a positive number.
And 4 times 7 times 9.
4 times 9 is 36.
36 times 7.
Let's do it up here.
36 times 7.
7 times 6 is 42.
7 times 3, or 3 times 7 is 21.
Plus 4 is 25.
252.
So this becomes 4 plus 252.
Remember, you have a negative 7 and you have a minus out front.
Those cancel out, that's why we have a positive 252 for that part right there.
And then our denominator, 2 times negative 7 is negative 14.
Now what does this equal?
Well, we have this is equal to negative 2 plus or minus the square root of-- what's 4 plus 252?
It's just 256.
All of that over negative 14.
And what's 256?
What's the square root of 256?
It's 16.
You can try it out for yourself.
This is 16 times 16.
So the square root of 256 is 16.
So we can rewrite this whole thing as being equal to negative 2 plus 16 over negative 14.
Or negative 2 minus-- right?
This is plus 16 over negative 14.
Or minus 16 over negative 14.
If you think of it as plus or minus, that plus is that plus right there.
And if you have that minus, that minus is that minus right there.
Now we just have to evaluate these two numbers.
Negative 2 plus 16 is 14 divided by negative 14 is negative 1.
So q could be equal to negative 1.
Or negative 2 minus 16 is negative 18 divided by negative 14 is equal to 18 over 14.
The negatives cancel out, which is equal to 9 over 7.
So q could be equal to negative 1, or it could be equal to 9 over 7.
And you could try these out, substitute these q's back into this original equation, and verify for yourself that they satisfy it.
We could even do it with the first one.
So if you take q is equal to negative 1.
Negative 7 times negative 1 squared-- negative 1 squared is just 1-- so this would be negative 7 times 1, right?
That's negative 1 squared.
Negative 1 times 2 is minus 2 plus 9.
So it's negative 7 minus 2, which is negative 9, plus 9, does indeed equal 0.
So this checks out.
And I'll leave it up to you to verify that 9 over 7 also works out.
We're asked to write this right here in word form, and I'm not saying it out loud because that would give the answer away.
We have 63.15 that we want to write in word form.
Well, the stuff to the left of the decimal point is pretty straightforward.
Let me actually color code it.
So we have 6, 3.
Let me do it all in different colors.
And then we have a decimal, and then we have a 1 and a 5.
There's one common way of doing this, but we'll talk about the different ways you could express this as a word.
But we know how to write this stuff to the left.
This is pretty straightforward.
This is just sixty-three.
Let me write that down.
So this is sixty-three.
Now there's two ways to go here.
We could say, and one tenth and five hundredths, or we could just say, look, this is fifteen hundredths.
One tenth is ten hundredths.
So one tenth and five hundredths is fifteen hundredths.
So maybe I can write it like this: sixty-three and fifteen hundredths.
Now, it might have been a little bit more natural to say, how come I don't say one tenth and then five hundredths?
And you could, but that would just make it a little bit harder for someone's brain to process it when you say it.
So it could have been sixty-three-- so let me copy and paste that.
It could be sixty-three and, and then you would write, one tenth for this digit right there, and five hundredths.
But if you say, fifteen hundredths, people get what you're saying.
Not to beat a dead horse, but this right here, this is 1/10 right here and then this is 5/100, 5 over 100.
But if you were to add these two, If you were to add 1/10 plus 5/100 -- so let's do that.
If you were to add 1/10 plus 5/100, how would you do it?
You need a common denominator.
100 is divisible by both 10 and 100, so multiply both the numerator and denominator of this character by 10.
You get 10 on the top and 100 on the bottom.
1/10 is the same thing as 10 over 100.
10/100 plus 5/100 is equal to 15 over 100, so this piece right here is equal to 15/100.
And that's why we say sixty-three and fifteen hundredths.
Let's say I have the point 3 comma negative 4.
So that would be 1, 2, 3, and then down 4. 1, 2, 3, 4.
So that's 3 comma negative 4.
And I also had the point 6 comma 1.
So 1, 2, 3, 4, 5, 6 comma 1.
6 comma 1.
In the last video, we figured out that we could just use the
Pythagorean theorem if we wanted to figure out the distance between these two points.
We just drew a triangle there and realized that this was the hypotenuse.
In this video, we're going to try to figure out what is the coordinate of the point that is exactly halfway between this point and that point?
So this right here is kind of the distance, the line that connects them.
Now what is the coordinate of the point that is exactly halfway in between the two?
What is this coordinate right here?
It's something comma something.
And to do that-- let me draw it really big here.
Because I think you're going to find out that it's actually pretty straightforward.
Gee, let me use the distance formula with some variables.
But you're going to see, it's actually one of the simplest things you'll learn in algebra and geometry.
So let's say that this is my triangle right there.
This right here is the point 6 comma 1.
This down here is the point 3 comma negative 4.
And we're looking for the point that is smack dab in between those two points.
What are its coordinates?
It seems very hard at first.
But it's easy when you think about it in terms of just the x and the y coordinates.
What's this guy's x-coordinate going to be?
This line out here represents x is equal to 6. This over here-- let me do it in a little darker color-- this over here represents x is equal to 6.
This over here represents x is equal to 3.
What will this guy's x-coordinate be?
Well, his x-coordinate is going to be smack dab in between the two x-coordinates.
This is x is equal to 3, this is x is equal to 6.
He's going to be right in between.
This distance is going to be equal to that distance.
His x-coordinate is going to be right in between the 3 and the 6.
So what do we call the number that's right in between the 3 and the 6?
Well we could call that the midpoint, or we could call it the mean, or the average, or however you want to talk about it.
We just want to know, what's the average of 3 and 6?
So to figure out this point, the point halfway between 3 and 6, you literally just figure out, 3 plus 6 over 2.
Which is equal to 4.5.
So this x-coordinate is going to be 4.5.
Let me draw that on this graph.
1, 2, 3, 4.5.
And you see, it's smack dab in between.
That's its x-coordinate.
Now, by the exact same logic, this guy's y-coordinate is going to be smack dab between y is equal to negative 4 and y is equal to 1.
So this is the x right there.
The y-coordinate is going to be right in between y is equal to negative 4 and y is equal to 1.
So you just take the average.
1 plus negative 4 over 2.
That's equal to negative 3 over 2 or you could say negative 1.5.
You literally take the average of the x's, take the average of the y's, or maybe I should say the mean to be a little bit more specific.
And you will get the midpoint of those two points.
The point that's equidistant from both of them.
It's the midpoint of the line that connects them.
So the coordinates are 4.5 comma negative 1.5.
Let's do a couple more of these.
But just to visualize it, let me graph it.
Let's say I have the point 4, negative 5.
So 1, 2, 3, 4.
And then go down 5.
1, 2, 3, 4, 5.
So that's 4, negative 5.
And I have the point 8 comma 2.
So 1, 2, 3, 4, 5, 6, 7, 8 comma 2.
8 comma 2.
So what is the coordinate of the midpoint of these two points?
Well, we just average the x's, average the y's.
So the midpoint is going to be-- the x values are 8 and 4.
It's going to be 8 plus 4 over 2.
And the y value is going to be-- well, we have a 2 and a negative 5.
So you get 2 plus negative 5 over 2.
And what is this equal to?
This is 12 over 2, which is 6 comma 2 minus 5 is negative 3.
Negative 3 over 2 is negative 1.5.
So that right there is the midpoint.
You literally just average the x's and average the y's, or find their means.
So let's graph it, just to make sure it looks like midpoint.
6, negative 5.
1, 2, 3, 4, 5, 6.
Negative 1.5.
Negative 1, negative 1.5.
Yep, looks pretty good.
It looks like it's equidistant from this point and that point up there.
Now that's all you have to remember.
Average the x, or take the mean of the x, or find the x that's right in between the two.
Average the y's.
You've got the midpoint.
What I'm going to show you now is what's in many textbooks.
They'll write, oh, if I have the point x1 y1, and then I have the point-- actually, I'll just stick it in yellow.
It's kind of painful to switch colors all the time-- and then
I have the point x2 y2, many books will give you something called the midpoint formula.
Just remember, you just average.
Find the x in between, find the y in between.
So midpoint formula.
What they'll really say is the midpoint-- so maybe we'll say the midpoint x-- or maybe I'll call it this way.
I'm just making up notation.
The x midpoint and the y midpoint is going to be equal to-- and they'll give you this formula. x1 plus x2 over 2, and then y1 plus y2 over 2.
And it looks like something you have to memorize.
That's just the average, or the mean, of these two numbers.
I'm adding the two together, dividing by two, adding these two together, dividing by two.
And then I get the midpoint.
That's all the midpoint formula is.
Welcome to the presentation on adding decimals.
Let's do some problems.
So let's say I had point zero zero eight-- that's an eight-- five plus-- and I'm writing it side by side on purpose-- one point seven nine nine.
So at first you're like, these decimals, they confuse me, I give up.
But I'm going to show you that it's actually very staightforward and it's actually no more difficult than doing normal addition.
A true gentleman would never leave such a beautiful lady by herself..
This is a dream, right?
I feel like I'm floating.
It would be nice if she got off of my shoes...
She looks like a completely different person.
Definitely Min Seo Hyun's work.
Maybe I should bring her to my next exhibition as my partner.
What the...
WAHHH!!! Save me!!!
He fell! Senior Goo Joon Pyo fell into the pool!
Come quickly!
What is it?
Why is it such a big deal ?
He can't
Eh?
The only thing the GREAT Goo Joon Pyo cannot do is swim!
Goo Joon Pyo!
Goo Joon Pyo!
Wake up!
Open your eyes!
Ya!
What the..
You're such scum.
You swindling bastard!
Achoo!!
Master, I'm sorry!
I'll prepare the tea again! Please forgive me!
For what?
Have you caught a cold?
Shall I call Doctor Kim?
What cold?
I feel great.
Prepare the car, I should go to school soon.
You want to leave this early sir?
It's never too early for a student going to school.
Don't you know that bugs that wake up early die early?
I'll fire the maid immediately.
But why?
Pardon?
Butler Lee, don't you think you are too uptight?
Relax. Relax.
Ahhh, what wonderful weather!
What the.. Goo Joon Pyo!
Wait until I get my hands on you!
If you get caught, you're done for.
Getting here so early just to work on that.
This is the first time I've seen him try this hard.
Problem is, why must he torture the poor transfer student
Furthermore, if you think about it, isn't she the one who saved his life?
Don't bite the hand that feeds you. This is a situation you use it in, isn't that right?
What are you guys talking about?
This is my way of saying thanks for yesterday.
If not, why would I bother to do such silly things to a low class person.
Normal people may not be grateful for this.
Ji Hoo isn't here.
So now you are picking on me instead, huh?
Right, why isn't that guy here, anyway?
After he came back from Hainan Island, he slipped into depression
Lovers quarrel huh? idiot!
If you like a girl, just grab her.
What's so hard about that?
I'll just leave after I do this...
First, it was Senior Joon Pyo and now, Senior Ji Hoo? Does she have a death wish or something?
Oh, my god!
Look at that fox!
Naturally, that girl is the type that doesn't know when to back off.
What the heck are we supposed to do now?
(Geum Jan Di's ♥)
Hey!
Don't you think you're arriving kind of late? Could you even be on a swim team? You'd be forced off for sure.
Could you even be on a swim team?
You'd be kicked out for sure..
I think they've been meeting up for a while.
There's a reason senior JiHoo is so protective of JanDi .
As time passes, friendships are even being affected because of this girl.
So now you know that even though JanDi looks innocent, her actions are those of a lovely snake.
Shut up!!
If you say one more word, I will twist your neck.
That was brand new...
Disappointed the one you were really hoping to see isn't here?
Goo JoonPyo!
Why are you . . .
What?
Am I not allowed to come here?
Did you two rent this place out or something?
Where are you going?
Since I have nothing to say to you I'm going home. Do you have a problem with that?
I do
What the heck are you doing?!
I have something to say!
Let go.. and talk.
Who do you think you are to fool with me? To mess with us, the great F4 ?
Who fooled whom?
Let go!!
Was I a joke? Just 'cause i went easy on someone like you?
I don't know if you know this about me, but I'm not a charitable person.
It's dissatisfying having to give more than I can take.
What the heck are you doing?
No!
Stop!
No!
Do you hate me that much?
Geum Jan Di, are you going to school or not?
I'm not going!
Would you like to get hit and go? Or just go?
Just hit me and I won't go.
Hit me!
Huh!
You, really!
Would you like to get hit and go? Or just go?
I want to get hit and not go. Hit me! I'm not going!
I'd rather break the ice of the Han river and swim there.
I'm not going back that school! Never!
Do you want me to die?
Isn't today PlaySat.(nol toh= short for "playing saturday")?
And also, some man delivered this for you.
What is that?
What's that?
Invitation. Hello.
I want to invite all of you to my home to celebrate my 23rd birthday. Please free up your schedule so you can attend.. Min SeoHyun
Pa... Party!!
Party?
Then, is our Jan Di finally making her debut in society?
Oh, honey! <BR>Honey, honey, honey...
Give me the card.
Give it to me!
It's not time for us to be doing this right now.
Dress, honey dress, dress
Dress!
Take this one here.
I'm sorry, Jan Di.
I can't even give my daughter a nice evening dress.
I'm sorry, JanDi. Since our neighborhood is poor, they don't bring in decent clothes to be serviced here either!
Ah!
There's a hanbok. How this? Will it do?
Is she going to a traditional wedding?
They said garden party, PARTY!
Isn't this the part where the charming prince comes and takes the girl shopping for a dress?
Hello.
This is a gift from Ms. Min Seo Hyun.
Min Seo Hyun?!
Let's see, let's see.
Does it fit? A little bit lower.
Why didn't you call last time?
You said you were going to call me, but you never did.
Wait a minute, you said the same thing to me too!
Who did you come with tonight?
I don't think you're with someone.
What do you think about me??
What are you talking about?
It's me that he wants!
Ya! Don't touch him. You're funny!
Hold on, hold on, sorry!
Hey, darling, why are you so late?
What brings you here? Seo Hyun unnie invited me here, why?
Did you empty the departmental store ?
I thought this last time too, but doesn't Geum Jan Di look pretty good when she's all dressed up?
Right.
You're the cutest one here.
Cute??!
Can you transform a pumpkin into a watermelon just by drawing some lines on it?
- Huh!
Goo Joon Pyo - has a point.
Happy Birthday to you.
Dear Min Seo Hyun~ Happy Birthday to you~
Thank you all for coming here to celebrate my 23rd birthday
I would like to thank my family and friends for their love and care.
I also have something else to announce to all of you.
That was why I held this huge party, which is not like me.
Where'd that punk Ji Hoo go?
They're not gonna announce their engagement, are they?
I'm going back to Paris next week
And I won't be returning to Korea.
I've already packed and arranged everything and folded model activities.
What's she talking about?
I do not wish to rely on the fruits of my parents' labor.
Instead, I would like to start fresh relying only on my own abilities.
I will not be taking over my parent's law firm.
Because I want a life where I can travel the world and give back as much as I can.
My decision is bound to cause an uproar since it will be hard for those of you with differing views to understand.
Everyone... please be happy for me.
Min SeoHyun, she's always full of surprises!
JiHoo... did he know about this the whole time?
Now we know the reason why he's been so depressed.
It's impressive, but, what's JiHoo gonna do?
Hi.
I can't believe you still have this.
It's from the first time we were separated.
You remember, huh?
It's since then that you stopped calling me noona.
What was I to you?
Our Ji Hoo must be very mad.
I also feel like I'm being thrown away.
If there is something here that can't be so easily thrown away... it's... you.
Don't lie!
If it was a lie, then it wouldn't have bothered me that you're interested in someone else.
What are you talking about?
When you dashed towards that girl, I don't know why but my heart sank.
Funny, right?
I'm not in the mood for jokes.
But isn't it great?
Our JiHoo has really become a man.
Don't joke around!
You'll do what you want anyway.
But you'll tighten me today and loosen me up tomorrow so I can neither go to you nor distance myself from you.
I was just a toy.
If I lost you I would not be able to sleep
Who's interested in whom?
Only looking at Min Seo Hyun for 15 years, it's not enough!
I'm a man, too!
A man who's eager to embrace a woman called Min Seo Hyun!
I know, me too.
Sorry, Ji Hoo.
I'm really sorry.
It would be really embarrassing if you passed out there.
Such behavior really doesn't suit you.
You know that, right?
Who says I was going to faint?
Oh, JanDi, you came... but why didn't you come in?
Ah... that... uh... that's because...
I was about to come to greet you and say thank you.
I came by... just NOW.
The party was chaotic, yes?
We were thinking of going on a quiet drive together.
Would you like to come with us then?
Eh?
Oh, no.. it's ok.
We have somewhere else to go.
We?
Yes both of us were also going to go for a drive.
Drive!
We're going to... Then, goodbye.
See you later.
Let's go. - Unni-
I've paid my debt.
What debt?
Saving me at the pool.
You want to repay me for saving your life just like that?
Then shall we go back?
10%
let's say it's even.. 50 25
I sent them out.
Why?
I rented it out til the morning, so do whatever you want.
Do whatever I want, what?
Yell or cry.
If you want to hit someone, do you want me to call a Mr. portly on standby outside?
Why do I have to do that?
Dldn't you have a heart attack after seeing JiHoo and SeoHyun?
What? no way!
Someone like me can't compete with Min SeoHyun, right.?
I'm not pretty, not smart either.
And I come from a poor family.
And your figure is mediocre and your character sucks too.
THAT'S RlGHT!
How could a girl like me dare to be jealous of Min SeoHyun?
I didn't have a chance against her from the beginning.
Even though there's lots of bad things about you, there are still some good things.
You have potential.
Huh?
I'm certain if Ji Hoo had met you first, he would have fallen for you.
Seriously?
Looks, brains, and background may not be much, but you're the first girl I've approved of.
Full of potential.
Hang on, I need to go use the restroom.
It's warm.
Isn't it warm?
It's warm, I'm thirsty.
Water.
Man, what the heck?
Hey, Dry Cleaner!
Hey, wake up!
What's wrong with her?
Well, it's because of that.
She drank all of it?
Yes.
Hey.
Hey!
Wake up, woman!
Woman?
Yeah, I'm a woman. What?
Can't commoners be women too?
I know that my family background, my physical appearance and my brains are all crap.
Even without you pointing that out, I feel it in my bones every day, you bastard!
What?
Bastard?
No, no.
I don't have time to waste on things like this.
If you only knew how busy I am.
I have to be a loser at an exclusive school where it's not fate, do part-time jobs because of a Dad who causes so much trouble.
And for tuition, I have to swim so I can get a scholarship.
I don't have time to butt into you princes' love lives!
You alcoholic Hey, gangster!
Wake up!
Ya!
I'm so sad lately.
I'm a bit sad.
You bastard!
Goo JoonPyo!
You're the enemy!
Fine, I'll let this go because I feel like it.
50%!
I'm saying that I'll cut in half what you owe to your savior!!
Thank you Goo JoonPyo, for saving me today.
I don't really have anything I can do for you, instead, I will . . . .
Aisshh!
"Charity Auction in aid of Namibian Refugees"
I just know this is a really expensive room just by smelling it.
You have a really good sense of smell.
(geh koh: euphemism short for "you have a nose like a dog")
What happened?
Why am I here?
You're here because I brought you here. That's what I'm saying!
Why am I here and not my house!
You don't remember?
This suit just came from Milan two days ago, and was designed by the famous designer, Yoshikuchi Kenzi, of Ermenegildo Zegna as one of his new works for this spring/summer collection.
The price is . . .
Hey, stop.
There's no reason to shock her.
I'm not exactly in the mood to listen to you brag about your clothes right now in this kind of situation!
That's what I wore yesterday.
What's that got to do with me?!
It was the first time I wore that suit, and my last, thanks to someone.
Do you remember now?
Then, in that state, we needed to come to my house. Or should we have gone to yours?
Sorry.
I already notified your parents.
According to the driver, they didn't seem that concerned.
I'll leave now.
I'm sorry for all the trouble I may have caused you.
Just do what you normally do.
Young master.
What's the matter?
The lady of the house . . .
What about the witch?
She has arrived.
Already?
Why is she here already?
What about JoonPyo?
He is on the second floor.
I'm going to have him take part in the event, so put someone on him to make sure he doesn't run off somewhere.
Yes, ma'am.
What?
It's an emergency!
YJH:
What? GJP: The witch showed up here.
JanDi is in my room right now, but I can't get her out!
Joonpyo, if you get caught, then . .
You're dead meat!
She finds an unfamiliar girl in her son's room, especially someone with Geum JanDi's profile.
I'm really curious.
I'll bet $1,000 that she'll send JoonPyo to Alaska tomorrow morning.
I'll bet $3,000 that she'll send him to Sejong Antarctic Research Center.<BR>
Rather than that, she'll probably hire an asassin first.
What?
Really?
Is she really that scary?
Do you remember the day we ran away from 6th grade camp?
We almost died.
How can I forget?
Don't move!
Bonjour!
Noona!
Is this really So YiJong?
Can you really look this cool?
Noona is the very one whom people call a Korean Vivienne Westwood.
What is it?
Hurry up and tell me,
Hm?
What is it you want?
After all, this is why I like noona so much.
A request to sponsor needy schoolchildren has come in from Seoul City..
Reject.
The Ministry of Education would like to conduct a special selection process for agriculture students at Shinhwa University from next year onwards....
Reject.
You've held up JoonPyo well, right?
Yes.
Hello.
Who is she?
Ah!
Hello.
She's my guest, so don't worry about it.
She's in my house, so she's my guest as well.
Isn't that right, young lady?
She's a friend.
Friend?
Yes, she's our junior at our school.
She's a cute sophomore, so we're specifically training her as the F4 mascot.
Something like that..
Whose daughter are you?
I'm the . .
What does your father do?
My father - has a business.
Really?
What kind?
He's in the clothing business.
No, I mean, fashion business.
It's actually pretty famous within the industry.
That's interesting.
So, do you have any interest in today's auction?
Yes, she has more than an interest.
With the new dress from Bella, she's the darkhorse who will definitely raise a lot of donations tonight..
I guess your mother has a very discerning eye.
What does your mother do?
President, it's time for you to greet your guests.
Joon Pyo, come downstairs and take your place.
The rest of you, since it's for a good cause, do your part before you leave.
Yes ma'm!
Why did you lie?
How are you going to fix this?
We should have told the truth.
Then, should we tell the truth that your dad owns a dry cleaner and your mom, a sauna?
If we did that, then no one knows what would've happened to not only you, but to your family as well.
It's not a joke when we say that you won't survive once you've been singled out.
So it's genetic, huh?
Yes, this next auction item, once you see it, I bet your eyes will jump!
It's coming out now, please look closely.
It's Swimmer Pak Taehwan's goggles!
Pak TaeHwan's goggles?
(Olympic swimmer from Korea)
We're starting at 500,000 won. Yes, 2,000,000 ($2000) won has been bid. $7,000.
1,000,000 ($1000)won has been bid.
200.
Do I hear $7,500? $8,000. Ah, I see $8,000.
Do I hear $8,500?
Yes, $8,500. 10,000$ just came in. Yes, $10,000!
Just now, a 10,000$ bid has come through the phone.
Are there no further bids?
If there are none, we will go onto the count. One, Two, Three!
Sold for $10,000!
This next auction item.
Please look carefully, it's coming out right now. It's the newest item from the young sculptor, So YiJung.
It's a vase.
We will start bidding at 5,000,000 won.
The next auctioned item is the suit of Shinhwa Group's Mr. Goo JunPyo.
The greatest aspect of the suit is that the person wearing it cannot tell whether he is wearing it or not,
We are starting at $10,000.
Yes we have $10,000!
Do we have $15,000?
Yes we have $15,000! <i>[Auctioneer speaking]
Do we have $20,000?
Yes, we have $20,000!
Wow, we are getting tremendous response!! [auctioneer speaking]
Is there $25,000..
Oh! $25,000!
Wow!
Great!
[auctioneer]
What are you doing?Hurry up, it;s your turn now!
[auctioneer speaking]
Yes the next auction item, it's very dazzling
I can't do that!
Please! Please!
You can do it!
I can't!
I can't!
Yes, the light yellow tint, and the lemon-like color will uplift the wearer's glamour..
The gold spangles and beads stress the luxury of the item.
We are starting the bid for this Bella Song dress at $10,000.
Yes, we have $10,000!
Do we have higher bids? $15,000?
How is JoonPyo doing these days?
He has been very quiet.
He is even attending school well.
Do you know that student? <i> [Banditore]
It's a pleasure to finally meet the famous wonder girl.
I didn't push him. Really, I -
Mr. Jung.
Yes?
I know that she is a student of Shin-Hwa High School.
Find out whose daughter she is.
Is this real?
Are these really the goggles that Pak TaeHwan used?
Mmm.
WAHHH!
Noona, noona, big news!
Now what?
Pak Tae Hwan's goggles!
If you sell them, you can get at least $2,000! $2,000?! $2,000 for goggles?
Sell them!
We have to sell them.
Where can you find $2,000?
No way!!
It's worth so much more.
What I'm saying is, this is one of those things that you can't put a price on.
Sell it. $2,000 is $2,000.
I would understand if it were just $20.
What's wrong with you?
But still, if we sell them . . . It's kind of . .
Ah . . . I don't know.
Good night.
Hey!
Why, you little! HEY!
I'm going now. Anyway, thanks.
What?I can't hear you !
I said thank you. What?
What?
I said, THANK YOU!!
Just a plain "thank you" would've sufficed.
For being a commoner, all you have is your big pride.
That's it. I take it back!
What?
I'm taking back the thank you!
What was I thinking? People don't change that easily.
I'm leaving.
Hey, Jandi Baht (field of grass)
You don't drink when I'm not around.
SeoHyun Unni?
What brings you here?
I had to take care of something regarding my dropping out of school.
I wanted to see you one more time before I left.
Dropping out of school? You're really not going to come back?
Most likely.
Tomorrow.
Ah. So soon?
I still haven't been able to say thank you . . .
I haven't even returned the favor.
If you keep saying things like that then I'm going to be sad.
I knew from the moment I saw you, that it was you whom JiHoo talked about with a smile on his face.
Um.. Unni.
JanDi, What are you doing?
I was a fan of yours way before I even met you. So, that's why I know better than anyone why you made this kind of decision.
But...
I'm begging you, please don't leave.
Please stand up.
I know that I have no right to make this kind of request and that you have no reason to listen to me, but if I don't even try . . .
Is it because of JiHoo?
I don't know anything about Senior JiHoo
But, I do know how much he cares about you.
And for some reason, I can see the sad look in his eyes.
But, there are times when he does smile.
He smiles so warmly that whoever is watching him feels that warmth.
The only person who can make him smile is you. If you leave like this, he may never smile again.
Please stand up.
To me, when a person tries to decide what to do, it's similar to buying something in a foreign country.
If you don't buy it at that very moment, then there's no second chance.
I know very well how agonizing that regret is.
JiHoo is an important person to me.
And I also believe that I am to him as well.
That's why I don't believe that he would want me to regret my decision.
What do you think?
I'm sorry. I'm very sorry.
No, I'm really happy you said those things.
Thank you. Unni . . .
Oh, hang on.
Are these . . . for me?
As I told you, shoes are of the utmost importance.
I'll pray that these shoes take you to great places without fail.
I also have a request for you.
Please, make JiHoo . . . smile again.
Who do you think you are?
Who are you to say those things thing!?
Who asked you to make that kind of request?
No, not a request, to beg?
Don't you have any pride?
It's not because I don't have any pride.
It's because you're in such agony.
Because you looked like you would die of sadness.
What's it to you?!
It has nothing to do with you!
Okay, so now you've seen how cool just a short program can be so hopefully you're really excited to keep going with programming on Khan Academy.
We want to give you a little tour of what you can expect.
When we want to teach new concepts we'll use coding talkthroughs where we'll write code on the left side, over here, and we'll see the result on the right side, constantly updating as we change the code. We'll also be talking about what we're writing, so make sure you have your headphones or your speakers on. To get started with a talkthrough, just click Play.
Like maybe, I think that Winston is actually an alien from this crazy planet with purple faces, and I just think that he should have really, really big eyes.
Whoa!
Bug eyes! Programming isn't just about going through the tutorials that we've given you.
Our favorite part about programming is the exploration and the creativity of it. That means that when you wake up in the middle of the night with an idea for a completely new program, just log on and click New Program.
Once you've done that, you'll get a blank editor and a blank canvas, and the world will be your programmatic playground. So, you might not remember how to do things. You can look down at the documentation, and remember, "Oh yeah, okay, I want the ellipse function, and then I'm going to use the draw function, okay."
And then we hope it runs.
Oh! But we got a problem, uh-oh: 'mouseZ is not defined.'
Oh, okay...okay, that's fine.
It's actually supposed to be 'mouseY.' Oh! And now it works.
And so here's the point:
It's totally okay to make mistakes. You should make mistakes. That's what we programmers do, all the time.
Now once I've made my amazing new program, and I'm really satisfied with it, I can save it, give it a really nice, descriptive name, like Circle Drawy ThingyBobber.
Maybe, Mister Circle Drawy ThingyBobber. I can save that, and then other people can actually find it! But creativity isn't just about creating completely new things, it's just as much about building on top of existing things, and taking them in new directions.
I mean, I spend my Friday nights just browsing programs on Khan Academy because I find so many cool things that I would have never thought of!
So some people make games, like Doodle Jump-- you ever played that on the mobile phone? It's a really fun game, and somebody made this version on here, and--
Oh man!!...okay... Ohh!... oh I've almost got it!
Aargh! Alright...alright... I'll play that again later.
People make simulations, so if you want to understand how a pendulum works, like if you're in physics class, you're going to do it in a much more fun way by using this simulation here. And then you can go and modify things on the side to see how different variables affect the pendulum.
People make drawings, like of their favorite cartoon characters.
This is my favorite, the TARDlS from Dr. Who. And if you're not watching Dr. Who yet, you really should, because as you can see, from all the programs and spin-offs on Khan Academy, it's a really cool show.
People make charts or even animated charts.
Some people make really trippy animations, like this one.
I could just watch this for hours, and get hypnotized by it. And you can see that lots of other people liked it, too, because they made all these spin-offs of it, right?
Because that's the thing, if you find a program that you like, you can just start tinkering with it, and seeing, like, "Oh, well what if I change this, and I change this... and maybe I change this, here. How does it change it?"
And you may not even understand it entirely at first, but the more you tinker with it, and the more you play with the code, you get a better feel for it, and then maybe you come up with this variation that you think is really cool, and then you'll save it as a spin-off and say, like, "Alright!
This is my Really Cool version of the Hypnosaic. And then you can save it, and other people can find it. But maybe you want to ask a question about it, right?
"Why did you start your variables with 'i'? Do you work for Apple?" And you can ask your question, and hopefully the person who created it will answer it, and if you find a question that you know the answer to, then answer them, and say, like,
"Hey!
Yeah, you can, here's where I did it:" And a lot of times you can answer with actually a link to another scratchpad, where you actually answered their question. Now if you just want to say how awesome it is, or give a tip, you can go to the Tips & Feedback panel,
This is the coolest thing I've seen today." And then the creator will feel really good because they got this compliment from you. And that's one of the awesome things about programming, is that you can put out these things in the world, and you never know who's going to find them, and whose day you're going to make better, because they found this really cool, creative thing that you came up with.
But as you keep going, you'll be able to do more and more, until one day you realize that, wow!
You can do almost anything in programming!
Find the value of 5 to the third power.
Let me rewrite that.
We have 5 to the third power.
Now, it's important to remember, this does not mean 5 times 3.
This means 5 times itself three times, so this is equal to 5 times 5 times 5.
5 times 3, just as a bit of a refresher so you realize the difference, 5 times 3-- let me write it over here.
5 times 3 is equal to 5 plus 5 plus 5.
So when you multiply by 3, you're adding the number to itself three times.
When you take it to the third power, you're multiplying the number by itself three times.
So 5 times 3, you've seen that before, that's 15.
But 5 to the third power, 5 times itself three times, is equal to-- well, 5 times 5 is 25, and then 25 times 5 is 125, so this is equal to 125.
And we're done!
(Static) Stand by all units.
On her way out
Anyone, help me!
Help me!
Help me!
Victor, GO!
I'm an activist!
Help me!
Head down!
Head down!
Target is secured.
Who are you?
The military?
It's not important who we are!
(Announcer) You there!
Keep the line!
Everyone, yes, come over here
We are for peace and order.
The government is doing everything for the peace and order of our place.
So let us reject trouble-makers in our communities.
Keep the line orderly!
Keep it orderly!
Don't wander around there!
In the last video we touched on the three states of matter that are really most familiar to our everyday experience. The solid, the liquid, and the gas. And I kind of hinted that there is a fourth state, which
But a little bit of a discussion ensued on the message board for that video. So I thought I would at least touch on that fourth stage. And that's plasma.
Plasma. And people consider it a fourth state because it has some properties of gases.
In some ways it's almost a subset of gases. But it also has properties of conductivity that you normally wouldn't associate with a gas.
And just so you know, when you first hear it you think, oh that's a fairly exotic thing, plasma. And in the first video, I said it's only something that occurs at high temperatures, which isn't exactly 100% right.
It doesn't have to be at high temperatures. I really should have said that under extenuating circumstances where you have a very strong electromagnetic field. Or something has to happen to essentially bump the the electrons, or move the electrons off of gases that would've otherwise have kept their electrons.
So it's kind of analogous to what happens in metal. When we talk about metal bonds, we talk about this notion of a sea of electrons. Let's say if we talked about iron.
Although, they don't have to be, that could be under very low pressure. But they're moving around and bumping into each other.
You might say that sounds like a bizarre state of matter, where does it exist?
Well, probably closest to home, it exists in lightning.
And that's worthy of an entire video. But the idea is that you start having a huge potential difference between the clouds and the ground.
And then because you have this huge voltage difference between the two, you have electrons that are essentially wanting to go into the ground. You have a build-up of electrons up here that want to go into the ground. They can't because air is normally a fairly bad conductor.
I thought I would touch on that because it's an interesting subject. And it exists in the universe. On the universal level, because stars are pretty much all plasma, it is actually the most common state of matter in the universe.
And then this has a hydrogen. And it has two electrons, two electron pairs. So I talked about the notion, and we talked about it many times before.
And these are actually the three most electronegative atoms. So the nitrogen, NH3, when it bonds with hydrogen, is essentially so electronegative that you have the same situation. All the electrons hang out here, so you have a partial negative charge, partial positive on the hydrogen ends.
About a year ago, I asked myself a question:
"Knowing what I know, why am I not a vegetarian?"
After all, I'm one of the green guys: I grew up with hippie parents in a log cabin.
I started a site called TreeHugger --
I care about this stuff.
I knew that eating a mere hamburger a day can increase my risk of dying by a third.
Cruelty:
I knew that the 10 billion animals we raise each year for meat are raised in factory farm conditions that we, hypocritically, wouldn't even consider for our own cats, dogs and other pets.
Environmentally, meat, amazingly, causes more emissions than all of transportation combined: cars, trains, planes, buses, boats, all of it.
And beef production uses 100 times the water that most vegetables do.
I also knew that I'm not alone.
We as a society are eating twice as much meat as we did in the 50s.
So what was once the special little side treat now is the main, much more regular.
So really, any of these angles should have been enough to convince me to go vegetarian.
Yet, there I was -- chk, chk, chk -- tucking into a big old steak.
So why was I stalling?
I realized that what I was being pitched was a binary solution.
It was either you're a meat eater or you're a vegetarian, and I guess I just wasn't quite ready.
Imagine your last hamburger.
(Laughter)
So my common sense, my good intentions, were in conflict with my taste buds.
And I'd commit to doing it later, and not surprisingly, later never came.
Sound familiar?
So I wondered, might there be a third solution?
And I thought about it, and I came up with one.
I've been doing it for the last year, and it's great.
It's called weekday veg.
The name says it all:
Nothing with a face Monday through Friday.
On the weekend, your choice.
Simple.
If you want to take it to the next level, remember, the major culprits in terms of environmental damage and health are red and processed meats.
So you want to swap those out with some good, sustainably harvested fish.
It's structured, so it ends up being simple to remember, and it's okay to break it here and there.
After all, cutting five days a week is cutting 70 percent of your meat intake.
The program has been great, weekday veg. My footprint's smaller,
I'm lessening pollution, I feel better about the animals, I'm even saving money.
Best of all, I'm healthier,
I know that I'm going to live longer, and I've even lost a little weight.
So, please ask yourselves, for your health, for your pocketbook, for the environment, for the animals:
What's stopping you from giving weekday veg a shot?
After all, if all of us ate half as much meat, it would be like half of us were vegetarians.
Thank you.
(Applause)
When you're searching for the light
And you see no hope in sight
Be sure and have no doubt
He's always close to you
He's the one who knows you best
He knows what's in your heart
You'll find your peace at last
If you just have faith in Him (Allah) You're always in my heart and mind
Your name is mentioned every day
I'll follow you no matter what
My biggest wish is to see you one day
Coz I believe...
I believe...
I believe
Do you believe, oh do you believe?
Coz I believe
In a man who used to be
So full of love and harmony
He fought for peace and liberty
And never would he hurt anything
He was a mercy for mankind
A teacher till the end of time
No creature could be compared with him
So full of light and blessings (Muhammad)
You're always in my heart and mind
Your name is mentioned every day
I'll follow you no matter what
If God wills we'll meet one day
Coz I believe...
I believe...
I believe
Do you believe, oh do you believe?
If you lose your way
Believe in a better day
Trials will come
But surely they will fade away
If you just believe
What is plain to see
Just open your heart
And let His love flow through
I believe I believe, I believe I believe
And now I feel my heart is at peace
I believe... I believe...
I believe
Do you believe, oh do you believe?
I believe I believe, I believe I believe
We are asked to represent the following function on the coordinate plane.
And they give us domain, and then they give us a range, a set of values that our function can take on.
And the way the question has been phrased, I'm assuming they assume that the negative 8 maps to the 4, the negative 6 maps to the 3, the negative 4 maps to the 2, the negative 2 maps to 1, and the 0 maps to 0.
Because you could have another function with this exact same domain, and this exact same range, where the mapping is different, where negative 8 maps to 3, and negative 6 maps to 4. So this domain and this range could be for many different functions.
But when they say represent the following function, I'm assuming that they want us to assume that they're kind of in order, the pairing.
So let's just graph this function, or represent it using their terminology.
So let me draw some axes here.
So this is the domain, the independent variable, just like that, often known as the x-axis or the horizontal axis. And all of our domain, all of the values, these are all non-positive numbers, so let me give a lot more space to quadrant Il.
You give me a negative 6, I'll give you a 3. Negative 6 and 3.
You give me a negative 4, this function will pop out a 2. Negative 4 comma 2.
And then you give a negative 2, this function will pop out a 1. F of negative 2 is 1. And then finally, f of 0 is 0.
And remember, I just assumed that negative 8 maps to 4, negative 6 maps to 3, but you could have multiple functions that have this domain and range.
But just the way that they said the following function, I'm assuming this is what they want us to do.
This means, "I'm smiling."
So does that.
This means "mouse."
"Cat."
Here we have a story.
The start of the story, where this means guy, and that is a ponytail on a passer-by.
Here's where it happens.
These are when.
This is a cassette tape the girl puts into her cassette-tape player.
She wears it every day.
It's not considered vintage -- she just likes certain music to sound a certain way.
Look at her posture; it's remarkable.
That's because she dances.
Now he, the guy, takes all of this in, figuring,
"Honestly, geez, what are my chances?"
(Laughter)
And he could say, "Oh my God!" or "I heart you!"
"I'm laughing out loud."
"I want to give you a hug."
But he comes up with that, you know.
He tells her, "I'd like to hand-paint your portrait on a coffee mug."
(Laughter)
Put a crab inside it.
Add some water.
Seven different salts.
He means he's got this sudden notion to stand on dry land, but just panhandle at the ocean.
He says, "You look like a mermaid, but you walk like a waltz."
And the girl goes, "Wha'?"
So, the guy replies, "Yeah, I know, I know.
I think my heartbeat might be the Morse code for inappropriate.
At least, that's how it seems.
I'm like a junior varsity cheerleader sometimes -- for swearing, awkward silences, and very simple rhyme schemes.
Right now, talking to you, I'm not even really a guy.
I'm a monkey -- (Laughter) -- blowing kisses at a butterfly.
But I'm still suggesting you and I should meet.
First, soon, and then a lot.
I'm thinking the southwest corner of 5th and 42nd at noon tomorrow, but I'll stay until you show up, ponytail or not.
Hell, ponytail alone.
I don't know what else to tell you.
I got a pencil you can borrow.
You can put it in your phone."
But the girl does not budge, does not smile, does not frown.
She just says, "No thank you."
You know?
[ "i don't need 2 write it down." ] (Applause)
We're asked to find the square root of 100.
Let me write this down bigger.
So the square root is this big check-looking thing.
The square root of 100.
When you see it like this, this means the positive square root.
If you're familiar with negative numbers, you know that there's also a negative square root, but when you just see this symbol, that means the positive square root.
So let's think about what this is saying.
This is asking us find the number, the positive number, that when I multiply that number by itself, I get 100.
So what number when I multiply it by itself do I get 100?
Well, let's see, if I multiply 9 by itself, that's only going to be 81.
If I multiply 10 by itself, that is 100.
So this is equal to-- and let me write it this way.
Normally, you could skip this step.
But you could write this as the square root of-- and instead of 100, 100 is the same thing as 10 times 10.
And then you know, the square root of something times itself, that's just going to be that something.
This is just equal to 10.
So the square root of 100 is 10.
Or another way you could write, I guess, this same truth is that 10 squared, which is equal to 10 times 10, is equal to 100.
Sit
I'll be teaching this class through exams.
We'll find a permanent English teacher during the break.
Who will tell me where you are in the Pritchard textbook?
Mr Anderson?
How a Smartphone Knows Up From Down EngineerGuy Series #4 
I think this is one of the coolest features of today's smartphones.
It knows up from down.
Build into the circuitry is a tiny device that can detect changes in orientation and tell the screen to rotate.
Let me show you what it looks like in an old iPhone.
There it is
It's an accelerometer.
I'll tell you how this kind of chip works and how its made but first, some basics of accelerometers.
They have two fundamental parts
A housing attached to the object whose acceleration we want to measure and a mass that, while tethered to the housing, can still move.
Here its a spring with a heavy metal ball.
If you move the housing up the ball lags behind stretching the spring.
If we measure how much that spring stretches we can calculate the force of gravity.
You can easily see that three of these could determine the orientation of a 3-dimensional object.
While lying with the z-axis perpendicular to gravity only the ball on the x-axis spring shows extension.
Turn this on it side so that z-axis point up and only the accelerometer along the spring on that axis stretches.
So, how does this phone and this chip measure changes in gravity.
While more complex than the simple ball and spring model it has the same fundamental elements.
Inside the chip engineers have created a tiny accelerometer out of silicon.
It has, of course, a housing that's fixed to the phone and a "comb-like" section can move back and forth.
That's the seismic mass equivalent to the ball.
The spring in this case is the flexibility of the thin silicon tethering it to the housing.
Clearly if we can measure the motion of this central section we can detect changes in orientation.
To see how that's done examine three of the fingers on the accelerometer.
The three fingers make up a differential capacitor.
That means that if the center section moves than current will flow.
Engineers correlate the amount of flowing current to acceleration.
This accelerometer fascinates me but even more amazing is how they make such a thing.
It would seem nearly impossible to make such an intricate device as the tiny smartphone accelerometer.
At only 500 microns across no tiny tools could craft such a thing.
Instead, engineers use some unique chemical properties of silicon to etch the accelerometer's fingers and H-shaped section.
To get an idea of how they do this let me show you how to make a single cantilevered beam like a diving board in a solid chunk of silicon.
Empirically, engineers noticed that if they pour potassium hydroxide on a particular surface of crystalline silicon it would eat away at the silicon until it forms a pyramidal-shaped hole.
This occurs because of the unique crystal structure of silicon.
To make a pyramidal hole in silicon engineers cover all but a small square with a mask impervious to the KOH.
Now, it only etches within the square shape cordoned off by the mask.
The KOH dissolves silicon faster in the vertical than in the horizontal direction.
This why it makes a pyramidal hole.
Now, to make a cantilevered beam engineers follow these steps.
First, mask the surface except for a u-shaped section.
At first the KOH will cut two inverse pyramids side-by-side.
As the etching continues the KOH begins to dissolve the silicon between these holes.
If we wash it away at just the right point before it dissolves the silicon just underneath the mask it will leave a small cantilever beam hanging over a hole with a square bottom.
Engineers make smartphone accelerometer using these same methods but as you can picture it takes a series of detailed masks to create the intricate structure of a smartphone accelerometer.
While complex, a key point is that the whole process can be automated.
This is absolutely essential in the miniaturization of technology engineers now make all sorts of amazing things at this tiny scale microengines with gears that rotate 300,000 times a minute nozzles in ink-jet printers, and my favorite micromirrors that focus light in semiconductor lasers.
I'm Bill Hammack, the Engineer guy.
This video is based on a chapter in the book
Eight Amazing Engineering Stories
The chapters features more information about this subject.
This is a work in process, based on some comments that were made at TED two years ago about the need for the storage of vaccine.
(Music) (Video) Narrator:
On this planet, 1.6 billion people don't have access to electricity, refrigeration or stored fuels. This is a problem. It impacts:
the spread of disease, the storage of food and medicine and the quality of life. So here's the plan: inexpensive refrigeration that doesn't use electricity, propane, gas, kerosene or consumables. Time for some thermodynamics.
And the story of the Intermittent Absorption Refrigerator. Adam Grosser: So 29 years ago, I had this thermo teacher who talked about absorption and refrigeration.
It's one of those things that stuck in my head.
It was a lot like the Stirling engine: it was cool, but you didn't know what to do with it.
And it was invented in 1858, by this guy Ferdinand Carre, but he couldn't actually build anything with it because of the tools of the time.
This crazy Canadian named Powel Crosley commercialized this thing called the IcyBall in 1928, and it was a really neat idea, and I'll get to why it didn't work, but here's how it works.
There's two spheres and they're separated in distance.
One has a working fluid, water and ammonia, and the other is a condenser.
You heat up one side, the hot side.
The ammonia evaporates and it re-condenses in the other side.
You let it cool to room temperature, and then, as the ammonia re-evaporates and combines with the water back on the erstwhile hot side, it creates a powerful cooling effect.
So, it was a great idea that didn't work at all: it blew up.
Because using ammonia you get hugely high pressures if you heated them wrong.
It topped 400 psi.
The ammonia was toxic.
It sprayed everywhere.
But it was kind of an interesting thought.
So, the great thing about 2006 is there's a lot of really great computational work you can do.
So, we got the whole thermodynamics department at Stanford involved -- a lot of computational fluid dynamics.
We proved that most of the ammonia refrigeration tables are wrong.
We found some non-toxic refrigerants that worked at very low vapor pressures.
Brought in a team from the U.K. -- there's a lot of great refrigeration people, it turned out, in the U.K. -- and built a test rig, and proved that, in fact, we could make a low pressure, non-toxic refrigerator.
So, this is the way it works.
You put it on a cooking fire.
Most people have cooking fires in the world, whether it's camel dung or wood.
It heats up for about 30 minutes, cools for an hour.
Put it into a container and it will refrigerate for 24 hours.
It looks like this.
This is the fifth prototype.
It's not quite done.
Weighs about eight pounds, and this is the way it works.
You put it into a 15-liter vessel, about three gallons, and it'll cool it down to just above freezing -- three degrees above freezing -- for 24 hours in a 30 degree C environment.
It's really cheap.
We think we can build these in high volumes for about 25 dollars, in low volumes for about 40 dollars.
And we think we can make refrigeration something that everybody can have.
Thank you.
(Applause)
100 is what percent of 80?
These problems tend to kill people because on some level they're kind of simple, they're just 100 and an 80 there, and they're asking what percent.
But then people get confused.
They say, do I divide the 100 by the 80?
The 80 by 100?
Or is it something else going on?
And you really just have to think through what the language is saying.
They're saying that this value right here, this 100, is some percentage of 80, and that some percentage is what we have to figure out.
What percent?
So if we multiply 80 by this what percent, we will get 100.
So let's view it this way.
We have 80.
If we multiply it by something, let's call this something x.
Let me do that in a different color.
If we multiply 80 by something, we are going to get 100.
And we need to figure out what we need to multiply 80 by to get 100.
And if we just solve this equation as it is, we're going to get a value for x.
And what we need to do is then convert it to a percent.
Another way you could have viewed this is 100 is what you get when you multiply what by 80?
And then you would have gotten this number, and then you could convert it to a percent.
So this is essentially the equation and now we can solve it.
If we divide both sides of this equation by 80, so you divide the left-hand side by 80, the right-hand side by 80, you get x. x is equal to 100/80.
They both share a common factor of 20, so 100 divided by 20 is 5, and 80 divided by 20 is 4.
So in simplest form, x is equal to 5/4, but I've only expressed it as a fraction.
But they want to know what percent of 80.
If they just said 100 is what fraction of 80, we would be done.
We could say 100 is 5/4 of 80, and we would be absolutely correct.
But they want to say what percent?
So we have to convert this to a percent, and the easiest thing to do is to first convert it into a decimal, so
let's do that.
5/4 is literally the same thing as 5 divided by 4, so
let's figure out what that is.
Let me do it in magenta.
So 5 divided by 4.
You want to have all the decimals there, so let's put some zeroes out here.
4 goes into 5 one time.
Let me switch up the colors.
1 times 4 is 4.
You subtract.
You get 5 minus 4 is 1.
Bring down the next zero.
And of course, the decimal is sitting right here, so we want to put it right over there.
So you bring down the next zero.
4 goes into 10 two times.
2 times 4 is 8.
You subtract.
10 minus 8 is 2.
Bring down the next zero.
4 goes into 20 five times.
5 times 4 is 20.
Subtract.
No remainder.
So this is equal to 1.25.
5/4 is the same thing as 5 divided by 4, which is equal to 1.25.
So far, we could say, 100 is 1.25 times 80, or 1.25 of 80, you could even say, But we still haven't expressed it as a percentage.
This is really just as a number.
I guess you could call it a decimal, but it's a whole number and a decimal.
It would be a mixed number if we didn't do it as a decimal. It's 1 and 1/4, or 1 and 25 hundredths, however you want to read it.
So to write it as a percent, you literally just have to multiply this times 100, or shift the decimal over twice.
So this is going to be equal to, as a percent, if you just shift the decimal over twice, this is equal to 125%.
And that makes complete sense. 100 is 125% of 80.
80 is 100% of 80.
100% percent is more than 80.
It's actually 1 and 1/4 of 80, and you see that right over there, so it makes sense.
It's 125%.
It's more than 100%.
But we are done. We've solved the problem.
It is a 125% of 80.
Simplify: negative one times this expression in brackets negative seven plus 2 times 3 plus 2 minus 5 in parentheses, squared.
So this is an order of operations problem, and remember in order of operations, you always wanna do parentheses first.
Parentheses.
Parentheses..first.
Then you do exponents.
Exponents.
And there are--there is an exponent in this problem, right over here.
Then you wanna do multiplication... multiplication and division, and then finally you do addition and subtraction.
So let's just try to tackle this as best we can.
So first let's do the parentheses. Let's do the parentheses...
We have a 3+2 here in parentheses, so we can evaluate that to be equal to 5.
And let's see we can do other things in other parts of this expression that won't affect what's going on right here in the parentheses.
We have this negative 5 squared, or actually I should say we have some subtracting of 5 squared.
We wanna do the exponent before we worry about being subtracted, so this 5 squared over here, we can rewrite as 25.
Let's not do too many steps at once, so this whole thing would simplify to negative 1, and then in brackets we have negative 7 plus 2 times 5, plus 2 times 5, and then 2 times 5, and close brackets, minus 25.
Minus 25.
Now, this thing we wanna do multiplication.
You could say,
"hey, we have the parentheses, why don't we do them first" but when we just evaluate what's inside these parentheses you just get a negative 7, it doesn't really change anything.
So we can just leave this as negative 7.
And this expression, we do want to evaluate this whole expression before we anything else.
I mean we could distribute this negative 1 and all that, but let's just do straight up order of operations here.
So let's evaluate this expression.
We want to do multiplication before we add anything.
So we get a 2 times 5 right over there, 2 times 5 is 10. That is 10.
So our whole expression becomes...
Normally you don't have to rewrite the expression this many times, but what we're gonna do at this time to make sure no one gets confused.
So is becomes negative 1 times negative 7 plus 10, plus 10, we close our brackets, minus 25. Minus 25. Now we can evaluate this pretty easily.
Negative 7 plus 10. You can view as starting with negative 7, so I was gonna draw a number line there.
So we're starting - draw a number line - so we're starting at negative 7 and then...
- so this, the length of the line is negative 7 - ... and then we're adding 10 to it.
We are adding 10 to it.
So we're going to move 10 to the right.
If we move 7 to the right we get back to 0, and then we're going to go another 3 after that.
So we're gonna go 7, 8, 9, 10.
So gets us to positive 3.
Another way to think about it is, we are adding integers of different signs, we can view this sum as going to be the difference of the integers, and since our larger integer is positive, the answer will be positive.
So you could literally just view this as 10 minus 7.
10 minus 7 is 3.
So this becomes a 3, so the entire expression becomes negative 1.
Negative 1 times... - and just to be clear: brackets and parentheses are really the same thing
Sometimes people will write brackets around a lot of parentheses just to make it a little bit easier to read, but they are really just the same thing as parentheses.
So these brackets are here, I could just literally write them like that.
And then I have a minus 25 out over here.
Now once again you wanna do multiplication or division before we do addition and subtraction, so it's multiplied the negative 1 times 3, is negative 3.
And now we need to subtract our 25.
So negative 3 minus 25, we are adding two integers of the same sign.
We are already at negative 3, it will become 25 more negative than that.
So you can view this as... we are moving 25 more in the negative direction.
Or you can view this as 3 plus 25 is 28, we're doing it in the negative direction, so it's negative 28.
So this is equal to negative 28.
And we are done!
As the most forward-deployed citizens of the planet at this moment, we, the first expedition crew aboard Space Station Alpha...
We are well started on our journey of exploration and discovery, building a foothold for men and women who will voyage and live in places far away from our home planet.
We are opening a Gateway to Space for all humankind.
As we orbit the planet every 90 minutes, we see a world without borders, and send our wish that all nations will work towards peace and harmony.
Our world has changed dramatically.
Still, the ISS is physical proof that nations can work together in harmony, and should promote peace and global cooperation, and reach goals that are simply out of this world.
On this night, we would like to share with all, our good fortune on this space adventure, our wonder and excitement as we gaze on the Earth's splendor, and our strong sense that the human spirit to do, to explore, to discover has no limit.
Times are hard all over the world, but this is a time when we can all think about being together and treasuring our planet, and we have a pretty nice view of it up here.
We're asked to compute 4,800, or four thousand eight hundred, divided by 80, and then they want us to check our answer, or they say check your answer.
So I'll first do it just the traditional long division way, and then we'll think about if there's maybe a faster way to do this or if we can even do it in our heads.
So let's just do it the traditional way first.
So we have 80 and we want to divide it into 4,800.
Four thousand eight hundred.
Or if we want to know the terminology, 80 is the divisor, 4,800 is the dividend, and in the number that we get, the number of times 80 goes into 4,800, we could call that the quotient.
I always get confused when I start using words like that, so we just think of it as 80 is being divided into 4,800.
Now, the first thing we say:
Well, does 80 go into 4?
No.
Does 80 go into 48?
No, it's bigger than 48.
Does 80 going into 480?
Well, that looks interesting.
Let's see, 6 times 8 is 48, so 6 times 80 is 480.
We could do that right here.
80 times 6.
6 times 0 is 0.
6 times 8 is 48.
Or another way you could have thought about it is 6 times 8 is 48, and we have this extra 0 here, so you add the 0 right there.
So 80 goes into 480 six times, because we're only considering the 480.
We put the 6 right in 480's one spot, which is really the tens place, but if you just think about the 480, it's right above the zero.
Now 6 times 80 is-- we already saw-- 480, and then we can subtract, and we get the zero, and we bring down another zero.
80 goes into 0 how many times?
Well, it goes into it zero times.
0 times 80 is 0.
You subtract.
You get zeroes, and there's nothing left to bring down, so we're done.
4,800 divided by 80 is 60.
When the dividend is 4,800, the divisor-- let me write these words down.
This is divisor.
Then our quotient is 60.
Now they want us to check our answer, so we just have to confirm that 60 times 80 is 4,800 so let's do that.
60 times 80-- now there's two ways you can do it.
You could just literally say 6 times 8 is 48, and then it'll have two zeroes here, one, two.
That's 4,800.
Or we could do it by hand.
0 times 0 is 0.
0 times 6 is 0.
Then we'll put a zero here because we're now in the tens spot.
Put the zero here.
8 times 0 is 0.
8 times 6 is 48.
Add all of this up.
You get 4,800, so it works.
A faster way would just have been to say 8 times 6 is 48, and you have one, two zeroes here, so one, two zeroes right there.
Now, a quick way to think about 4,800 divided by 80 is to divide both of these numbers by 10 first.
And just to think about it this way, what we're doing, this could be written as 4,800/80.
Or this could be written as-- let me write it down here.
4,800/80 could be written as 480 times 10 over 8 times 10.
4,800 is just 480 times 10, and 80 is just 8 times 10.
Now what happens here?
We could view this as being equal to 480/8 times this 10 up here divided by this 10.
Now, what's 10 divided by 10?
What's any non-zero number divided by itself?
Well, this is just going to be 1.
10 goes into 10 one time, so we're just left with 480 over 8.
So essentially, you can just knock off.
You can knock off the same number of zeroes off of the divisor as the dividend.
So we knock off one zero here, one zero there, it becomes 480 divided by 8, and that's an easier problem.
8 goes into 480, and you say 8 goes into-- it doesn't go into 4, so it goes into 48 six times.
6 times 8 is 48.
You have no remainder.
Bring down this zero.
8 goes into 0 zero times.
0 times 8 is 0.
No remainder.
And we get 60 again, so either way would have worked.
This way is a little bit faster.
You might be able to do it in your head, but no matter which way you do it, you get 60 as our answer, and we confirmed that it really works.
Ok, so, it's time for the keynotes and we are very honoured to have Eben Moglen here as first keynote speaker He is a professor of Law and Legal History at Columbia University.
 All of the reactions we've looked at so far have been of the form lowercase a moles of the molecule uppercase A, plus
lowercase b moles of a molecule uppercase B.
They react to form the product or the products.
Let's just say they have a couple of products.
I could have had as many molecules here as I wanted.
Let's say c moles of the molecule C plus d moles of the molecule capital D.
And the idea here is that they went in one direction. And if we did a little energy diagram, just going off of the kinematics video we just did, if that's the reaction, or how the reaction progresses, you could imagine that here you have it at a higher energy state.
You have lowercase a moles of capital A molecule, plus
lowercase b moles of capital B molecule, and you have some activation energy. And then you get to a more stable state or a lower energy
level here, where it's lowercase c moles of C molecule plus lowercase d moles of the D moles, and of course, you had some activation energy.
It only goes in this direction. Once you get here, it's very hard to go back.
So that if you came back and looked at this-- if you get enough of A and B-- you'll just be sitting with molecules of C and D.
But that's not how it happens in reality. In reality-- well, it sometimes happens like this in reality where the reaction can only go in one direction.
But in a lot of cases, the reaction can actually go in both directions.
So we could write, instead of this one-way reaction, we could write a two-way reaction like this.
And not to confuse you too much, these are the number of moles or the ratios of the molecules I'm adding up, and they become relevant in a second.
So let's say I have lowercase a moles of this molecule plus
lowercase b moles of this molecule, and then they react to form lowercase c moles of this molecule plus lowercase d moles of that molecule.
Sometimes the reaction can go in both directions.
And to do that, to just show an equilibrium reaction, you do these arrows that go in both directions. That means that, hey, some of this is going to start forming into some of this. But at the same time, some of this might start forming into some of this.
And at some point, I'm going to be reaching an equilibrium.
When the rate of reaction of molecules going in that direction is equal to the number of molecules going in the other direction, then I'm going to reach some type of equilibrium.
Now, why would this happen as opposed to that? And I can think of one situation.
If we draw this energy diagram again.
Maybe both of these have similar or not so different energy states.
There could be other reasons, but this is the one that comes to my mind.
Maybe the energy states look something like this.
On this side, you have the A plus B, and then you need some activation energy.
And then maybe the C plus D, maybe it's a little bit of a lower potential, but it's not that much lower.
So maybe they're favored to go in this direction, because this is a more stable state.
So this is the A plus B, but here you have the C plus D. But it's not ridiculous to go this way either.
So most of it might go that way, but some of it might go this way.
If some of these molecules just have the right amount of kinetic energy, they can surmount this activation energy and then go backwards to that side of it.
And the study of this is called equilibrium, where you're looking at the concentrations of the different molecules.
And just to compare that to kinetics, kinetics was how fast is this is going to happen?
Or what can I do to change the activation, this hump here?
Equilibrium is studying what will be the concentrations of the different molecules that end up, once the rate going in this direction is equal to the rate going in that direction.
And I want to be clear.
Equilibrium is where the rate going in the forward direction is equal to the rate going in the reverse direction.
It doesn't mean that the concentrations of the two things are equal.
You might end up with 25% of your eventual solution's concentration to be A and B and 75% here.
All we know is that at some point, you've reached an-- equilibrium just means that those concentrations won't change anymore.
And just to give you an example what I mean here, I could have written-- let's see, this is actually the
Haber process. I could write nitrogen gas plus 3 hydrogen gases.
These are all in gas form, so I can put a little g in parentheses.
Actually, it's an equilibrium reaction, and it produces 2 moles of ammonia.
It's called the Haber process. We could talk about that in another video.
So in this case, we could say a is just 1, this lowercase a.
Capital A is the nitrogen molecule.
Lowercase b is 3. Uppercase B is the hydrogen molecule. And then lowercase c is the number of moles of ammonia and uppercase C is the ammonia molecule itself.
I just want you to realize this is just an abstract way of describing a whole set of equations.
Now, what's interesting in equilibrium reactions is that you can define a constant called the equilibrium constant. It's defined as the constant of equilibrium.
Let me switch colors. I'm using this light blue too much.
The equilibrium constant is defined as you take the products, or the right-hand side-- but if it goes in both directions, you can obviously go in either direction.
But let's say that this is the forward direction going from A plus B to C plus D.
So you take the products, you take the concentration of each of the products, and you multiply them by each other, and you raise them to the mole ratios that you're taking.
So in this case, it would be the concentration of big C raised to the lowercase c power and the concentration of big D raised to the lowercase d power.
And when I say concentration, they usually-- especially what you see in your intro chemistry classes, the concentration is going to be measured in molarity, which, just as a review, is moles per liter.
A couple of videos ago, when I taught you what molarity was, I said, you know, moles per liter--- I don't like it so much because the volume of your fluid or your gas you're dealing with is dependent on temperature. So I didn't like using molarity.
But in this case, it's kind of OK.
Because this equilibrium constant is also only true for a given temperature.
We assume it for a given temperature, and I'll show you how we use it in a second.
But it's defined as the concentrations of the products to the powers. And also, if I have time, maybe I'll do it in the next video.
The intuition why you're raising it to the power divided by the concentrations of the reactants, or the things on the left-hand side of the equilibrium reaction.
So capital A to the lowercase a divided by capital B to the lowercase B.
And what's interesting about this, and this is a bit of a simplification, because this doesn't apply to all reactions.
But to most things that you're going to encounter in an intro chemistry class, this is true, that once you establish this equilibrium constant for a certain temperature-- it's only true for a certain temperature-- then you can change the concentrations and then be able to predict what the resulting concentrations are going to be.
Let me give you an example.
So let's say that after you did this equilibrium reaction-- and actually, just to make things hit home a
little bit, let me take this Haber process reaction and write it in the same form. So if I wanted to write the equilibrium constant for the
Haber reaction, or if I wanted to calculate it, I would let this reaction go at some temperature.
So this is only true at-- let's say we're doing it at 25 Celsius, which is roughly room temperature.
So what I would do is I would take the products.
So the only product is ammonia, NH3. I raise it to the power of the number of moles that's produced for every 1 mole of nitrogen gas and 3 moles of hydrogen.
So I raise it to the power of 2. So that's what that gets me.
And I divide it by the reactants.
So 1 mole of nitrogen, so I would just put the concentration of the nitrogen, plus 3 moles of hydrogen-- oh, no, no. I shouldn't write a plus there. It's multiplied.
So times the hydrogen, and I raise it to the third power, because for every 1 mole of nitrogen, I have 3 moles of hydrogen and then 2 moles of ammonia.
And if I were to calculate this, remember, when I put these in brackets, I'm figuring out the concentration. So I would have to figure out the moles per liter.
Or sometimes they say, the molarity of each of these things, and it'll get me some constant.
If I change it, I can go and calculate the rest, so let me just do an example right now.
So let's say I have 1 mole of molecule A plus 2 moles of molecule B are in equilibrium with 3 moles of molecule C.
And let's say that once we're in equilibrium, we go and we measure the concentrations, and we figure out that the concentration of A is 1 molar, which is equal to 1 mole per liter.
That's the concentration of A.
We figure out that once we're in equilibrium, the concentration of B is equal to 3 molar, which means 3 moles per liter. And let's say that once we're in that equilibrium, the concentration of C is equal to point-- well, I don't want to do something too-- let's say it's equal to 1 molar as well.
I should get rid of that point there, because I don't want to say 0.1 molar, so it's just 1 molar.
So if we wanted to calculate the equilibrium constant for this reaction, we just take C, the concentration of C over here, so let's see.
The equilibrium constant is equal to the concentration of
C to the third power divided by the concentration of A to the first power-- because there's only 1 mole of A for every 3 of C and 2 of B-- times the concentration of--
I'll do it in that color-- B to the third power.
So if we needed to calculate this, concentration of C is 1 molar, and we're raising it to the third power, divided by concentration of A is 1 molar times the concentration of B, which is 3 molars, to the third power.
So this is equal to 1/27. There's a couple of things we can think about. The fact that this is less than 1, what does that mean?
Well, that means that our concentration of our reactants is much larger than the concentration of the products, where we view just the products as whatever's on the right-hand side of the equation.
So once this reaction goes to equilibrium, we're still left with a lot more of this than this.
And because we're left with a lot more of that, our equilibrium constant is less than 1, which means that the reaction favors this direction.
Welcome back.
So where I left off, we said that we had this, I guess you could call it, equation or this function, although I didn't write it with the function notation, where I said, the distance is equal to 16 t squared, and I graphed it, it's like a parabola, right, for positive time.
And then we said, well, the velocity, if we know the distance, the velocity is just the change of the distance with respect to time.
It's just, the velocity is always changing, you can't just take the slope, you actually have to take the derivative, right?
So we took the derivative with respect to time of this function, or this equation, and we got 32t, and this is the velocity.
And then we graphed it.
And then I asked a question.
I was like, well, we want to figure out, if we were given this, if we were given just this, and I asked you, what is the distance that this object travels after time, you know, after 10 seconds?
Let's, you know, let's say this t0 is equal to 10 seconds.
I want to know how far is this thing gone after 10 seconds.
And let's say you didn't know that you could just take the antiderivative, let's say we didn't know this at all, and
let's say you didn't know that you could just take the antiderivative, because we just showed that, you know, the derivative of distance is velocity, so the antiderivative of velocity is distance.
So let's say you couldn't just take the antiderivative.
What's a way that you could start to try to approximate how far you've traveled after, say, 10 seconds?
Well [? as I said, ?] you graph this, and you say, let's assume over some change in time, velocity is roughly constant, right?
So you could approximate how far you travel over that small change in time by multiplying that change in time, let's say that's like, you know, a millionth of a second, times the velocity at roughly that time, or maybe even the average velocity over that time, and you'd get the distance you've traveled over that very small fraction of time, right?
And what we said, is if you want to know how far you travel after 10 seconds, you just draw a bunch of these rectangles, and you sum up the area, right?
And you could imagine, and you don't have to imagine, it's actually true, the smaller the bases of these rectangles, and the more of these rectangles you have, the more accurate your approximation will be, and you'll approach 2 things.
You'll approach the area under this curve, right, almost the exact area under this curve, and you'd also get almost the exact value of the distance after, say, 10 seconds in this case, right?
It could have been a variable.
So this is something pretty interesting.
All of a sudden, we see that the antiderivative is pretty darn similar to the area under the curve.
And it actually turns out that they're the same thing.
And this is where I'm going to teach you the indefinite integral.
So the indefinite integral, I don't know how comfortable you are with summation, I remember the first time I learned calculus, I wasn't that comfortable with summation, but it's really, all the indefinite integral, is is you can kind of view it as a sum, right?
So now, you'll maybe understand a little bit more why this symbol looks kind of like a sigma.
But in this case, the indefinite integral is just saying, well, I'm going to take the sum from t equals 0, right, so from t equals 0, to let's say in this example, t equals 10, right, because I said 10.
From t equals 0 to t equals 10. and I'm going to take the sum of each of the heights, the height at any given point, which is the velocity.
It's 32t and then I'm at times the base at each of these rectangles, dt.
The definite integral is literally, and they never do this in math texts, and that's what always kind of confused me, is that you can kind of view it like a sum, like this.
It's kind of the sum of each of these rectangles, but it's the limit, as-- if these were discrete rectangles, you could just do a sum, and you could make the rectangle bases smaller and smaller, and have more and more rectangles, and just do a regular sum.
And actually, that's how, if you ever write a computer program to approximate an integral, or approximate the area under a curve, that's the way a computer program would actually do it.
But the actual indefinite integral says, well, this is a sum, but it's the limit as the bases of these rectangles get smaller and smaller and smaller and smaller, and we have more and more and more of these rectangles.
So as these dt's approach 0, the number of rectangles actually approach infinity.
So I'm actually going to, I'll do that more rigorously later, but I think it's very important to get this intuitive feel of just what an integral is.
So the integral from-- this is now a definite integral, extending from t equals 0 to t equals 10.
This tells us 2 things.
This tells us the area of the curve from t equals zero to t equals 10, right, it tells us this whole area, and it also tells us how far the object has gone after 10 seconds.
So it's very interesting.
The indefinite integral tells us 2 things.
It tells us area, and it also tells us the antiderivative.
We're already familiar with it as an antiderivative.
So let me give you another example.
Actually, maybe I'll stick with this example, but
Maybe, OK, so we have that indefinite integral.
And we could actually figure it out, too.
I mean, well, after t seconds, [UNlNTELLlGIBLE].
So and the way you evaluate an indefinite integral, and let me show you that first, is that you figure out the integral.
So let me just say, let me continue with the problem, actually.
So the way you figure out the indefinite integral, is you say, and sometimes they won't write t equals 0 to t equals t.
They'll just say from 0 to 10 of 32t dt.
And the way you evaluate this, is you figure out the antiderivative, and you really don't have to do the plus c here, so the antiderivative, we know, is 16t squared, right?
It's one half t squared times 32.
So that's 16t squared.
And we evaluate this at ten, and we evaluate it at 0, and then we subtract the difference.
So we evaluate this at 10, so 16 times 100, right?
That's evaluated at 10, and then we subtract it, evaluate at 0.
So 16 times 0 is 0.
So after 10 seconds, we would have gone 1600 feet.
And also, the area under this curve is 1600.
So let's use this to do a couple more examples.
And actually, I want to show you why we do this subtraction.
Actually, I'm going to do that right now.
Let me draw this twice, once for the distance, and once for its derivative.
Let's say you start at some distance, and then it goes off like that.
So let's say we call this distance b.
Well, let's just call this, you know, I don't know, 5.
We start at 5 feet, and then we moved forward from there.
And this axis is of course time, this axis, maybe I shouldn't do 5, because it looks so much like s.
That's 5, 5 feet.
And this is the s, or distance, axis.
So let me continue this in the next presentation.
In the 1980s in the communist Eastern Germany, if you owned a typewriter, you had to register it with the government.
You had to register a sample sheet of text out of the typewriter.
And this was done so the government could track where text was coming from.
If they found a paper which had the wrong kind of thought, they could track down who created that thought.
And we in the West couldn't understand how anybody could do this, how much this would restrict freedom of speech.
We would never do that in our own countries.
But today in 2011, if you go and buy a color laser printer from any major laser printer manufacturer and print a page, that page will end up having slight yellow dots printed on every single page in a pattern which makes the page unique to you and to your printer.
This is happening to us today.
And nobody seems to be making a fuss about it.
And this is an example of the ways that our own governments are using technology against us, the citizens.
And this is one of the main three sources of online problems today.
If we take a look at what's really happening in the online world, we can group the attacks based on the attackers.
We have three main groups.
We have online criminals.
Like here, we have Mr. Dimitry Golubov from the city of Kiev in Ukraine.
And the motives of online criminals are very easy to understand.
These guys make money.
They use online attacks to make lots of money, and lots and lots of it.
We actually have several cases of millionaires online, multimillionaires, who made money with their attacks.
Here's Vladimir Tsastsin form Tartu in Estonia.
This is Alfred Gonzalez.
This is Stephen Watt.
This is Bjorn Sundin.
This is Matthew Anderson, Tariq Al-Daour and so on and so on.
These guys make their fortunes online, but they make it through the illegal means of using things like banking trojans to steal money from our bank accounts while we do online banking, or with keyloggers to collect our credit card information while we are doing online shopping from an infected computer.
The U.S. Secret Service, two months ago, froze the Swiss bank account of Mr. Sam Jain right here, and that bank account had 14.9 million U.S. dollars on it when it was frozen.
Mr. Jain himself is on the loose; nobody knows where he is.
And I claim it's already today that it's more likely for any of us to become the victim of a crime online than here in the real world.
And it's very obvious that this is only going to get worse.
In the future, the majority of crime will be happening online.
The second major group of attackers that we are watching today are not motivated by money.
They're motivated by something else -- motivated by protests, motivated by an opinion, motivated by the laughs.
Groups like Anonymous have risen up over the last 12 months and have become a major player in the field of online attacks.
So those are the three main attackers: criminals who do it for the money, hacktivists like Anonymous doing it for the protest, but then the last group are nation states, governments doing the attacks.
And then we look at cases like what happened in DigiNotar.
This is a prime example of what happens when governments attack against their own citizens.
DigiNotar is a Certificate Authority from The Netherlands -- or actually, it was.
It was running into bankruptcy last fall because they were hacked into.
Somebody broke in and they hacked it thoroughly.
And I asked last week in a meeting with Dutch government representatives, I asked one of the leaders of the team whether he found plausible that people died because of the DigiNotar hack.
And his answer was yes.
So how do people die as the result of a hack like this?
Well DigiNotar is a C.A.
They sell certificates.
What do you do with certificates?
Well you need a certificate if you have a website that has https, SSL encrypted services, services like Gmail.
Now we all, or a big part of us, use Gmail or one of their competitors, but these services are especially popular in totalitarian states like Iran, where dissidents use foreign services like Gmail because they know they are more trustworthy than the local services and they are encrypted over SSL connections, so the local government can't snoop on their discussions.
Except they can if they hack into a foreign C.A. and issue rogue certificates.
And this is exactly what happened with the case of DigiNotar.
What about Arab Spring and things that have been happening, for example, in Egypt?
Well in Egypt, the rioters looted the headquarters of the Egyptian secret police in April 2011, and when they were looting the building they found lots of papers.
Among those papers, was this binder entitled "FlNFlSHER."
And within that binder were notes from a company based in Germany which had sold the Egyptian government a set of tools for intercepting -- and in very large scale -- all the communication of the citizens of the country.
They had sold this tool for 280,000 Euros to the Egyptian government.
The company headquarters are right here.
So Western governments are providing totalitarian governments with tools to do this against their own citizens.
But Western governments are doing it to themselves as well.
For example, in Germany, just a couple of weeks ago the so-called State Trojan was found, which was a trojan used by German government officials to investigate their own citizens.
If you are a suspect in a criminal case, well it's pretty obvious, your phone will be tapped.
But today, it goes beyond that. They will tap your Internet connection. They will even use tools like State Trojan to infect your computer with a trojan, which enables them to watch all your communication, to listen to your online discussions, to collect your passwords.
Now when we think deeper about things like these, the obvious response from people should be that, "Okay, that sounds bad, but that doesn't really affect me because I'm a legal citizen.
Why should I worry?
Because I have nothing to hide."
And this is an argument, which doesn't make sense.
Privacy is implied.
Privacy is not up for discussion.
This is not a question between privacy against security.
It's a question of freedom against control.
And while we might trust our governments right now, right here in 2011, any right we give away will be given away for good.
And do we trust, do we blindly trust, any future government, a government we might have 50 years from now?
And these are the questions that we have to worry about for the next 50 years.
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How many hours are in 549 minutes?
And we can write it as a decimal or a fraction.
So essentially, we're going to take 549 minutes and divide them into groups of 60.
Why 60?
Because we know that one hour is equal to 60 minutes.
So it's essentially saying, how many groups of 60 minutes can we divide 549 into.
Or another way of thinking about that is, well, what is 549 divided into groups of 60.
This is how many hours we're going to have.
So let's do that.
Let's take 549 and divide it by 60.
So let's see, 6 goes into 54 9 times.
So 60 is going to go into 540 9 times.
We're going to have a little bit left over.
So we have 9 times 60 is 540.
We subtract.
We have 9 left over.
And now let's see, we have a little left over, so we're going to get a decimal.
So let's put a decimal place right over here and let's throw some 0's over there.
Let's bring down a 0.
So we bring down a 0.
60 goes into 90 1 time.
1 times 60 is 60.
And we subtract.
We get 30.
Let's bring down another 0.
And so we get to 300.
60 goes into 300 5 times.
5 times 60, 6 times 6 is 30, so 5 times 60 is 300.
Subtract and we are done.
So you divide 549 into groups of 60.
You can divide it into 9.15 groups of 60 minutes.
A group of 60 minutes is an hour.
So this 549 minutes is 9.15 hours.
I want to make sure that we can visualize that properly.
So let's actually construct what 9.15 hours looks like.
So let me draw a little line here, and on the top I'll label Hours, and on the bottom I'll label Minutes.
So this is 0 hours, 0 minutes.
And now we have 1 hour, which is 60 minutes.
Now we have 2 hours, which is 120 minutes.
Then you have 3 hours, which is 180 minutes.
Then you have 4 hours, which is 240 minutes.
5 hours is 300 minutes.
6 hours is 360 minutes.
7 hours, I might be running out of space, is for 420 minutes.
Let me copy and paste this someplace where
I have more real estate.
So let me clear that. And then let me paste that someplace where I don't run into my other math that I did.
All right.
So then you have 8 hours is 480 minutes.
And then you have 9 hours.
Notice, I'm just adding 60 minutes every time.
9 hours is 540 minutes.
Or another way you could think about it is, well, if each hour is 60, 9 times 60 is 540.
And we don't want to go to just 540.
We have another 9 left.
So then we have to go another 9 minutes to go to 549.
So you have 9 minutes left over.
So another way of thinking about this, is that 549 is 9 hours. And then you have 9 minutes left over. And 9 minutes is what fraction of an hour?
Well, 60 minutes is a whole hour.
So 9 minutes is 9/60 of an hour.
So you could write it this way.
It's 9 and 9/60 hours.
Or we could write this as an equivalent fraction.
9/60 is the same thing if we divide the numerator and the denominator by 3, is the same thing as 3/20. So we could write this as 9 and 3/20. And 3/20, well we could figure out what that is going to be.
Let's see, 20 divided by 3.
It's definitely going to be smaller than 1, because 3 is smaller than 20.
So let's throw some 0's on here.
20 doesn't go into 3, but it does go into 30 1 time.
1 times 20 is 20. Subtract, we get a 10.
Bring down a 0.
20 goes into 100 5 times.
5 times 20 is 100.
And we are done.
So notice, 3 over 20 is the exact same thing. So 9 and 3/20 is the exact same thing as 9 and 15/100.
These are all equivalent answers.
Find the perimeter of the parallelogram. We have a parallelogram right over here, opposite sides are parallel.
That side is parallel to that side right over here.
This side is parallel to that side right over here.
And also in a parallelogram, opposite sides have the same length.
Now, we have to worry about the perimeter here.
Which essentially just says that if we had a field the size and shape of this parallelogram, and we wanted to make a fence around the field that was the shape of this parallelogram, how long would that fence have to be?
Obviously, it would be the sum of the lengths of the sides.
So, we wouldn't even have to worry about this thing over here, we can ignore it for the sake of this problem. We don't care about the actual height, or this altitude right over here, we just care about the lengths of the sides.
So the perimeter of this parallelogram is going to be 12 inches, plus 8 inches, plus 12 inches, plus 8 inches.
12 + 8 is 20, 12 + 8 is 20, so this is all going to add up to 40 inches. And we're done. I guess this is a very small field, this is only 8 inches.
I guess it's a little plot of land, a little parallelogram plot of land. Anyway, we're done.
Its perimeter is 40 inches.
Welcome to the presentation on level four division.
So what makes level four division harder than level three division is instead of having a one-digit number being divided into a multi-digit number, we're now going to have a two-digit number divided into a multi-digit number.
So let's get started with some practice problems.
So let's start with what I would say is a relatively straightforward example.
The level four problems you'll see are actually a little harder than this.
But let's say I had twenty-five goes into six thousand two hundred fifty.
So the best way to think about this is you say, okay, I have twenty-five.
Does twenty-five go into six?
Well, no.
Clearly six is smaller than twenty-five, so twenty-five does not go into six.
So then ask yourself well, then if twenty-five doesn't go into six, does twenty-five go into sixty-two?
Well, sure.
Sixty-two is larger than twenty-five, so twenty-five will go into sixty-two.
Well, let's think about it.
Twenty-five times one is twenty-five.
Twenty-five times two is fifty.
So it goes into sixty-two at least two times.
And twenty-five times three is seventy-five.
So that's too much.
So twenty-five goes into sixty-two two times.
And there's really no mechanical way to go about figuring this out.
You have to kind of think about, okay, how many times do I think twenty-five will go into sixty-two?
And sometimes you get it wrong.
Sometimes you'll put a number here.
Say if I didn't know, I would've put a three up here and then I would've said three times twenty-five and I would've gotten a seventy-five here.
And then that would have been too large of a number, so I would have gone back and changed it to a two.
Likewise, if I had done a one and I had done one times twenty-five, when I subtracted it out, the difference I would've gotten would be larger than twenty-five.
And then I would know that, okay, one is too small.
I have to increase it to two.
I hope I didn't confuse you too much.
I just want you to know that you shouldn't get nervous if you're like, boy, you know every time I go through the step it's kind of like--
I kind of have to guess what the number is as opposed to kind of a method.
And that's true. Everyone has to do that.
So anyway, so twenty-five goes into sixty-two two times.
Now let's multiply two times twenty-five.
Well, two times five is ten.
And then two times two plus one is five.
And we know that twenty-five times two is fifty anyway.
Then we subtract.
Two minus zero is two.
Six minus five is one.
And now we bring down the five.
So the rest of the mechanics are pretty much just like a level three division problem.
Now we ask ourselves, how many times does twenty-five go into one hundred twenty-five?
Well, the way I think about it is, twenty-five-- it goes into one hundred about four times-- so it will go into one hundred twenty-five one more time.
It goes into it five times.
If you weren't sure you could try four and then you would see that you would have too much left over.
Or if you tried six you would see that you would actually get-- six times twenty-five is a number larger than one hundred twenty-five.
So you can't use six.
So if we say twenty-five goes into one hundred twenty-five five times, then we just multiply five times five is twenty-five.
Five times two is ten plus two. One hundred twenty five.
So it goes in exact.
So one hundred twenty-five minus one hundred twenty-five is clearly zero.
Then we bring down this zero.
And twenty-five goes into zero zero times.
Zero times twenty-five is zero.
Remainder is zero.
So we see that twenty-five goes into six thousand two hundred fifty exactly two hundred fifty times.
Let's do another problem.
Let's say I had-- let me pick an interesting number. Let's say I had fifteen, and I want to know how many times it goes into two thousand two hundred sixty-five.
Well, we just do the same thing we did before.
We say okay, does fifteen go into two?
No.
So, does fifteen go into twenty-two?
Sure.
Fifteen goes into twenty-two one time.
Notice we wrote the one above the twenty-two.
If it go had gone into two we would've written the one here.
But fifteen goes into twenty-two one time.
One times fifteen is fifteen.
Right?
Twenty-two minus fifteen-- we could do the whole carrying thing-- one, twelve.
Twelve minus five is seven. One minus one is zero.
Twenty-two minus fifteen is seven.
Bring down the six.
Okay, now how many times does fifteen go into seventy-six?
Once again, there isn't a real easy mechanical way to do it.
You can kind of eyeball it and estimate.
Well, fifteen times two is thirty.
Fifteen times four is sixty. Fifteen times five is seventy-five.
That's pretty close, so let's say fifteen goes into seventy-six five times.
So five times five once again, I already figured it out in my head, but I'll just do it again.
Five times one is five.
Plus seven.
Oh, sorry.
Five times five is twenty-five.
Five times one is five.
Plus two is seven.
Now we just subtract.
Seventy-six minus seventy-five is clearly one.
Bring down that five.
Well, fifteen goes into fifteen exactly one time.
One times fifteen is fifteen.
Subtract it and we get a remainder of zero.
So fifteen goes into two thousand two hundred sixty-five exactly one hundred fifty-one times.
So just think about what we're doing here and why it's a little bit harder than when you have a one-digit number here.
Is that you have to kind of think about, well, how many times does this two-digit number go into this larger number?
And since you don't know two-digit multiplication tables-- very few people do-- you have to do a little bit of guesswork.
Sometimes you can look at this first digit and look at the first digit here and make an estimate.
But sometimes it's trial and error.
You'll try and when you multiply it out, you might get it wrong on the first try.
Let's do another problem.
And actually, I'm going to pick numbers at random, so it might not have an easy remainder.
But I think you'll get the point.
I won't teach you decimals now, so I'll just leave the remainder if there is one.
Let's say I had sixty-seven going into five thousand nine hundred seventy-eight.
So I just picked these numbers randomly out of my head, so I'll show you that I also sometimes have to do a little bit of guesswork to figure out how many times one of these two-digit numbers go into a larger number.
So sixty-seven goes into five zero times.
Sixty-seven goes into fifty-nine zero times.
Sixty-seven goes into five hundred ninety-seven-- so let's see.
Sixty-seven is almost seventy and five hundred ninety-seven is almost six hundred.
So if it was seventy goes into-- seventy times nine is six hundred thirty.
Right?
Because seven times nine is sixty-three.
So I'm going to just eyeball approximate.
I'm going to say that it goes into it eight times.
I might be wrong.
And you can always check, but well, we're going to actually check in this step essentially.
Eight times seven-- well that's fifty-six.
And then eight times six is forty-eight.
Plus two is fifty-three.
Seven minus six is one.
Nine minus three is six.
Five minus five is zero.
Sixty-one.
So, good. I got it right.
Because if I got a number here that was larger than-- that was sixty-seven or larger, then that means that this number up here wasn't large enough.
But here, I got a number that's positive, because five hundred thirty-six is less than five hundred ninety-seven.
And it's less than sixty-seven, so I did that step right.
So, now we bring down this eight.
Now this one might be a little bit trickier this time.
Once again, we have almost seventy and here we have almost six hundred thirty.
So maybe it will go into it nine times.
Well, let's give it a try and see if it does.
Nine times seven is sixty-three.
Nine times six is fifty-four.
Plus six is sixty.
Good!
So it did actually go into it nine times because six hundred three is less than six hundred eighteen.
Eight minus three is five.
One minus zero is one.
And six minus six is zero.
We have a remainder of fifteen, which is smaller than sixty-seven.
So I'm not going to teach you decimals right now, so we can just leave that remainder.
So what we could say is that sixty-seven goes into five thousand nine hundred seventy-eight eighty-nine times.
And when it goes into it eighty-nine times, you're left with a remainder of fifteen.
Hopefully you're ready now to try some level four division problems.
Have fun!
Hello. In this series of presentations, I'm gonna try to teach you everything you need to know about triangles and angles and parallel lines and this is probably the highest-yield information that you could ever learn, especially in terms of the standardized tests. And then when we've learned all the rules we'll play something I call the Angle Game, which is essentially what the SAT makes you do over and over again.
In the last video we talked about ionization energy, or the energy required to remove an electron. And we saw the general trend in the periodic table, that when you're in the bottom left-hand side close to cesium, cesium really wants to give up electrons. It's a big atom.
We're on problem 38. Which of the following best describes the graph of this system of equations?
OK, so maybe they're the same line.
Maybe they're parallel.
Maybe they only intersect in one point-- two lines intersecting in only two points.
Well that's impossible. Two lines, I mean that can happen with curves, but that's not going to happen with lines.
So we can already cancel out choice D.
OK, now let's look at these two.
See I have a y here and I have a 5y here. Let's multiply this top equation times 5 and see what it looks like.
So if you multiply the left-hand side by 5, you get 5y.
I'll do it up here. You get 5y is equal to-- 5 times minus 2 is minus 10x, plus 5 times 3 is 15.
So if you multiply the top equation-- both sides of it-- by 5 and it really doesn't fundamentally change the line, the equation might look different, but the equality will still hold in the same universe, which is essentially that line.
So if you just multiply both sides by 5, they become the same equation.
5y is equal to minus 10x plus 15.
We're asked to simplify the cube root of twenty seven a squared times b to the fifth times c to the third power.
Let's do a few more problems that bring together the concepts that we learned in the last two videos.
So let's say we have the inequality 4x plus 3 is less than negative 1.
So let's find all of the x's that satisfy this.
So the first thing I'd like to do is get rid of this 3.
So let's subtract 3 from both sides of this equation.
So the left-hand side is just going to end up being 4x. These 3's cancel out.
That just ends up with a zero.
No reason to change the inequality just yet.
We're just adding and subtracting from both sides, in this case, subtracting.
That doesn't change the inequality as long as we're subtracting the same value.
We have negative 1 minus 3.
That is negative 4.
Negative 1 minus 3 is negative 4.
And then we'll want to-- let's see, we can divide both sides of this equation by 4.
Once again, when you multiply or divide both sides of an inequality by a positive number, it doesn't change the inequality.
So the left-hand side is just x. x is less than negative 4 divided by 4 is negative 1. x is less than negative 1.
Or we could write this in interval notation.
All of the x's from negative infinity to negative 1, but not including negative 1, so we put a parenthesis right there.
Let's do a slightly harder one.
Let's say we have 5x is greater than 8x plus 27.
So let's get all our x's on the left-hand side, and the best way to do that is subtract 8x from both sides.
So you subtract 8x from both sides.
The left-hand side becomes 5x minus 8x.
That's negative 3x.
We still have a greater than sign.
We're just adding or subtracting the same quantities on both sides. These 8x's cancel out and you're just left with a 27.
So you have negative 3x is greater than 27.
Now, to just turn this into an x, we want to divide both sides by negative 3.
But remember, when you multiply or divide both sides of an inequality by a negative number, you swap the inequality.
So if we divide both sides of this by negative 3, we have to swap this inequality.
It will go from being a greater than sign to a less than sign.
And just as a bit of a way that I remember greater than is that the left-hand side just looks bigger.
This is greater than.
If you just imagine this height, that height is greater than that height right there, which is just a point.
I don't know if that confuses you or not.
This is less than.
This little point is less than the distance of that big opening.
That's how I remember it.
But anyway, 3x over negative 3.
So now that we divided both sides by a negative number, by negative 3, we swapped the inequality from greater than to less than.
And the left-hand side, the negative 3's cancel out.
You get x is less than 27 over negative 3, which is negative 9.
Or in interval notation, it would be everything from negative infinity to negative 9, not including negative 9.
If you wanted to do it as a number line, it would look like this.
This would be negative 9, maybe this would be negative 8, maybe this would be negative 10.
You would start at negative 9, not included, because we don't have an equal sign here, and you go everything less than that, all the way down, as we see, to negative infinity.
Let's do a nice, hairy problem.
So let's say we have 8x minus 5 times 4x plus 1 is greater than or equal to negative 1 plus 2 times 4x minus 3.
Now, this might seem very daunting, but if we just simplify it step by step, you'll see it's no harder than any of the other problems we've tackled.
So let's just simplify this.
You get 8x minus-- let's distribute this negative 5.
So let me say 8x, and then distribute the negative 5.
Negative 5 times 4x is negative 20x.
Negative 5-- when I say negative 5, I'm talking about this whole thing.
Negative 5 times 1 is negative 5, and then that's going to be greater than or equal to negative 1 plus 2 times 4x is 8x.
And now we can merge these two terms.
8x minus 20x is negative 12x minus 5 is greater than or equal to-- we can merge these constant terms.
Negative 1 minus 6, that's negative 7, and then we have this plus 8x left over.
Now, I like to get all my x terms on the left-hand side, so let's subtract 8x from both sides of this equation.
I'm subtracting 8x.
This left-hand side, negative 12 minus 8, that's negative 20.
Negative 20x minus 5.
Once again, no reason to change the inequality just yet.
All we're doing is simplifying the sides, or adding and subtracting from them.
The right-hand side becomes-- this thing cancels out, 8x minus 8x, that's 0.
So you're just left with a negative 7.
And now I want to get rid of this negative 5.
So let's add 5 to both sides of this equation.
The left-hand side, you're just left with a negative 20x. These 5's cancel out.
No reason to change the inequality just yet.
Negative 7 plus 5, that's negative 2.
Now, we're at an interesting point.
We have negative 20x is greater than or equal to negative 2.
If this was an equation, or really any type of an inequality, we want to divide both sides by negative 20.
But we have to remember, when you multiply or divide both sides of an inequality by a negative number, you have to swap the inequality. So let's remember that.
So if we divide this side by negative 20 and we divide this side by negative 20, all I did is took both of these sides divided by negative 20, we have to swap the inequality.
The greater than or equal to has to become a less than or equal sign.
And, of course, these cancel out, and you get x is less than or equal to-- the negatives cancel out-- 2/20 is 1/10.
If we were writing it in interval notation, the upper bound would be 1/10.
Notice, we're including it, because we have an equal sign, less than or equal, so we're including 1/10, and we're going to go all the way down to negative infinity, everything less than or equal to 1/10.
This is just another way of writing that.
And just for fun, let's draw the number line.
Let's draw the number line right here.
This is maybe 0, that is 1. 1/10 might be over here.
Everything less than or equal to 1/10.
So we're going to include the 1/10 and everything less than that is included in the solution set.
And you could try out any value less than 1/10 and verify that it will satisfy this inequality.
This film contains graphic images.
Viewer discretion is advised.
On Thursday, the 8th of November
Six days before it launched Operation Pillar of Cloud
Israel killed 13-year-old Ahmed Younes Abu Dagga Also known as Hamid,
He was killed right here while he was playing football with his friends.
He died on the way to hospital
This man, Saleh, witnessed Hamid's death.
Hamid was shot in his stomach and he ran towards the steps of his home.
We took him to the hospital in a car But he died on the way.
At the time, my crew and I were filming a few hundred meters away Near the Israeli-imposed no-go military zone Investigating an incursion into Gaza.
This is the buffer zone.
We are greeted with the sounds of helicopters and Israeli drones.
This is an Israeli tank, part of that incursion, Just hundreds of meters away from Hamid's home.
We heard live fire at the time Hamid was killed and ran to cover.
We had no idea Israel had killed an innocent.
I visited Hamid's school to speak to two boys who were playing with him when he was killed.
On Thursday we were playing football and suddenly I heard Hamid screaming and shouting, "My stomach, my stomach!" And then we saw him run to his home while holding his stomach.
He started to call out for his mum.
His brother was there who started asking us, What's wrong with Hamid?"
So I answered him that they shot him in his stomach.
He was shocked and said, "You mean Hamid?!"
I answered, "Yes!" then the car came to take him.
As recent history has shown, no where in Gaza is safe for Palestinians
But Hamid's family home in Abasan, Khan Yunis is just a few hundred meters from the military buffer zone with Israel.
Its horizons under constant domination by Israel's surveillance balloons.
It's one of the least secure places to live in Gaza
But for the large Abu Dagga family, it's simply always been their home.
It was my shift that night at the hospital.
Suddenly, we heard the noise of shelling and shooting because the hospital is close to the east, near the boarder with Israel.
After five minutes, a casualty arrived to the hospital.
He was a child, and we immediately started treating him.
When we took him, we could see that he appeared to be dead.
We massaged his heart and gave him drugs like adrenalin and a drip to try to restart his heart to beat again or to make him breathe again, to bring him back to life,
But unfortunately the child was injured directly in his heart.
Ahmed was more than a brother to me.
He was my friend.
I spent most of my time with him.
We used to play football together in the streets and always used to play Playstation together.
We were together most of the time.
What happened affected me a lot.
I feel my heart is empty.
Even yesterday, I had my friends visiting me at home and when they wanted to leave, I accidently said, "Hamid, Ahmed, show them downstairs!" I forgot that he was dead.
May his soul rest in peace.
I said to myself, "We put our trust in God, the best of planners."
Near Hamid's home, there's also a sniper outpost.
Although a Hamas official initially reported that a helicopter shooting killed Hamid, It's not clear whether it was shrapnel from a sniper or helicopter bullet, or even shrapnel from a tank shelling that was responsible.
This is just another incident of a suspicious Palestinian child casualty as a result of Israeli force.
We were surprised by the injury because there was no bullet.
When there is a gunshot, there is an entry wound and an exit wound, but the child had only two very small holes on the right side and the left side of his torso, on both sides of his body.
This proves that it was not a gunshot, but shrapnel that killed Hamid, due to a shelling and the shrapnel entered his chest directly.
It hit his heart, and when we examined him, we found two very small holes, two millimeters in size, on both sides.
Here in the hospital, we deal with the children's injuries with our very limited treatment capabilities.
Our limited ability is one of our biggest problems because here in the hospital we are suffering from a shortage of the most basic medical supplies.
Mohammad was another boy playing football with Hamid when he was killed,
I first spoke to his parents
Hamid was here with us, and then suddenly, in seconds, we were surprised, he was gone, he was dead.
My child was with him, I felt bad because my child was in the same place, may Ahmed's soul rest in peace.
I ask the international community to stand up for the rights of Gaza's children.
No one in this world cares about the children or people here in Gaza.
We ask God to finish this occupation, God willing, as soon as possible.
May Ahmed rest in peace in Heaven.
Hamid came to my home and invited me to play football with him.
I accepted.
Before we left my home, he asked me to take photos of him
So I took photos of him and he asked me to put them on Facebook.
After the afternoon prayer, I went to his home, and we played football from 3 until 4 pm.
This is Hamid
Suddenly, we heard shooting and shelling and Hamid fell down as he passed the ball.
I started screaming, saying, "Get down, there is shooting!"
Hamid went to the ground while our other friends ran away.
He started crying and I started calling for his brothers
Then suddenly, he stood up, saying, "Oh, my stomach, my stomach!"
He started running towards his home and I screamed to his brother, "Come, Hamid has been shot!"
Then he started running around his home, screaming.
His brother came and told me to find a car to take him to the hospital.
My child, Mohammed, has his exams these days.
Whenever I ask him to study hard to succeed, he opens his books and then starts crying.
"I can't, I can't study."
All the time, he holds his mobile phone and looks at the photo he took of Hamid.
I told him to focus on his studies, to pray, and I said to him,
"Look how God chose Hamid to be a martyr, and go to Heaven.
He was lucky!".
He always answers, "I can't, I can't because what happened affected me a lot."
He's all the time crying and looking at Hamid's photo.
Now the boys play with Hamid's football, but without Hamid
Human Rights Watch told me they didn't have the resources in Gaza to investigate the killing of Hamid.
Hamid's killing was, of course, barely reported by Western media agencies.
The BBC ran one limited article in which Hamid's killing was reported as just an unverified, alleged incident of collateral damage.
Days after it killed Hamid, Israel launched its November operation Pillar of Cloud, claiming it was responding to rocket fire from Gazan militant groups
Rocket fire that killed no one.
After Hamid's death, in the weekend just preceding the operation,
Israel killed two more Palestinian children when it struck near a funeral parade in North Gaza.
The truth is that the timeline of the recent war started with Israel's killing of Hamid, buried here.
This was Hamid's classroom.
A memorial wreath stands on his chair.
Just before he was killed, he was sitting tests in Geography, and Maths
We all went to school together and went home as a group every day.
Every Thursday, we used to play football together.
Sometimes he would invite me, sometimes I would invite him, and we used to go out a lot together.
My brother was a religious fan of Real Madrid.
He used to download the videos of all their games and goals to watch them play.
Playing football was his biggest hobby.
He always dreamed of becoming a football star.
He always pretended he was Cristiano Ronaldo and he was killed while he was wearing a Real Madrid t-shirt.
Glorious is God: he lived loving football and he died while he was playing it.
What can a child care about except his school and having fun?
These are the only things children think of.
He only cared about wearing his Real Madrid t-shirt, his Real Madrid boots, grabbing his football, and then going to play.
He did not even really care about his studies.
Hamid even said on Thursday morning,
"I have a big responsibility, I have two exams on Saturday!" And Israelis thought that he was thinking about shooting rockets?!
Hamid's mother was motionless with grief.
Some relatives wanted to show me Hamid's bedroom and possessions: his bed, backpack, and mobile.
His schoolbooks, football boots, the t-shirt Hamid was wearing when he was martyred.
The weapons they use are unbelievable.
We have received many injuries of this kind, not only with children
Ahmed is one of them.
They're all the same.
There are very small holes in the chest, stomach, really, anywhere in the body. Sometimes two holes.
But when we resuscitate them, and take them to perform surgery, we see shocking damage, including lacerations in the intestines.
Wherever the injury is, we see incredible damage.
So we saw injuries similar to Ahmed's back during Operation Cast Lead.
Since Hamid was killed, in Gaza alone, a further 61 Palestinian children have been killed by Israeli state violence.
I went to Hamid's funeral parade.
The pupils from his preparatory school arrived.
Glory to our faithful martyrs.
The local police force also paid their respects.
I say to the world, you accepted agreements and protocols to protect Human Rights during wartime and during peacetime, like the Geneva Convention and the jurisdiction of the International Criminal Court in the Hague.
This international community is sitting silently when it comes to Israeli violations against the Palestinian children and people.
They are being killed day and night by the Israelis who think that no power in the world can stop them.
To the soldier that shot my son, he has to know that he killed an innocent child.
Of course, he has his own children.
How would he feel if he saw his son being causelessly killed while he was playing football with his friends?
What's the crime he committed?
Why are our children being unduly killed in front of their homes?
We ask God to end this occupation.
I call on President, Barak Obama, who just won a second term, the new president of the USA that speaks in the name of freedom:
Do the American people accept for a child to be killed while he was playing football in front of his home?
If this happened there, in America, the whole world would stand against it.
If this child has been killed inside Israel, would the state of Israel have stayed silent?
Why does the international community continue its silence?
This is a massacre of children inside Gaza.
The reckless killing or murder of this 13-year-old Real Madrid-supporting child constitutes a prima facie war crime committed by the state of Israel.
One day the International Criminal Court will call for witnesses:
My crew and I will be there.
My message to the world and to everyone listening, pay attention to our plight.
We are poor and oppressed people.
We have lived 65 years suffering from occupation, killing and colonizing.
God willing, people of the world will start to care and put a stop to all of this.
What can I say to the Israeli soldier who killed my brother?
They are not human because they killed a little child playing football.
What kind of terrorism did he commit?
They say they attack terrorists and rocket firers.
My brother Hamid was playing football, not launching a rocket.
They think that when they attack our children that we will be weakened.
It is the opposite.
They raise hatred in our hearts.
Now, don't you think that Hamid's friends will hate the Israelis more and more?
We are like them, we are all humans!
What did he do for them to attack him?!
Those children will grow up and the hate will grow up with them.
God willing, the Israelis will leave our land and the occupation will end soon.
I swear to God that they will not stay here.
The end is coming soon.
As a doctor, as a children's surgeon, I want to say that we are a people of peace and that we love peace.
And my message to the world is please stand by the people of Palestine so that we can live in peace, so our children and their children can live together in peace.
Why do the people of the world live in freedom while the children of Palestine do not know the meaning of freedom or sleep peacefully at night?
So this is my message: stand by the children and the people of Palestine.
We should stop the killing.
Visit GazaReport.com for more insight into the situation afflicting Gaza.
This film's production was made possible by Gaza Report's funders.
Welcome to the presentation on subtracting decimal numbers.
Let's get started with some problems.
The first problem I have here says five point seven three minus point zero eight two one equals who knows?
So the first thing you always want to do with a decimal like this, and I actually kind of inadvertently did this, is that you want to line up the decimals.
So you actually want this decimal to be right above this decimal.
I almost did that when I did it, it must have been my subconscious doing it.
But let me just do it a little bit neater.
So it's five point seven three, and I'll put the decimal here.
Decimal zero eight two one.
And some people say it's good to always put a zero in front of the decimal. My wife's a doctor and she says it's critical otherwise you might give someone the wrong amount of medicine.
So, we've lined up the decimals and now we're ready to subtract.
So one thing that you have to think about when you do decimals is we're going to have to subtract this twenty-one ten thousandths or this two and this one from something.
We can't just subtract it from this blank space.
So we have to add two zeros here.
And as you know, with the decimal when you add zeros to the end of it, it really doesn't change the value of the decimal.
So at this point, we just view this like a level four subtraction problem.
So the first thing we do in any subtraction problem is see if any of the numbers on top are smaller than any of the numbers on the bottom.
Well in this case there are a lot of them.
So this zero is less than this one, this zero is less than this two, this three is less than this eight.
So we're going to have to borrow.
Some people will like to do their borrowing and subtracting, they kind of alternate between the two.
I like to do all of my borrowing ahead of time.
So what I do is I start in the top right and I say okay, zero is less than one.
So that zero becomes a ten.
But in order to become a ten, I would have had to borrow one from some place.
I look to the left of that zero and I say well, can I borrow the one from zero?
Well, no.
This is just the way I do it.
There are people who would actually let you borrow the one from the zero, but I say no, instead of borrowing the one from the zero,
I borrow the one from this entire thirty.
So this thirty -- see right there, this is three zero so I'm going to borrow one from it and it becomes twenty-nine.
So we borrowed one from this thirty to get a ten here, and now let's check again to see if all of our numbers on top are larger than all the numbers on the bottom.
Well ten is larger than one, nine is larger than two, two is not larger than eight.
So we have to borrow again.
So if we're going to borrow, the two becomes a twelve, and the seven-- we borrowed one from that -- becomes a six.
So let's check again.
Ten is larger than one, nine is larger than two, twelve is larger than eight, six is larger than zero, and five is larger than zero.
So now we've done all of our borrowing and we're ready to do some subtraction, and this is the easy part.
Ten minus one is nine.
Nine minus two is seven.
Twelve minus eight is four.
Six minus zero is six.
Five minus zero is five.
And we just bring down the decimal point.
So there's our answer.
Five point seven three minus zero point zero eight two one is equal to five point six four seven nine.
There you go.
I probably confused you, so let's do some more problems.
Here's another one.
Eight -- let me leave some space on top to do the borrowing.
Eight point two five minus zero point zero one zero five.
So what was that first step that I always have to do?
Right. To line up the decimals.
So let me do that.
So it's eight point two five and zero point zero one zero five.
Notice I lined up this decimal right below this decimal.
Now I add the zeros, just because this zero and this five need to be subtracted from something.
Now let me do my borrowing.
So once again, all I do is check to see whether the top number is larger than the number below it.
Well, this zero is smaller than five, so I'm going to have to borrow. So I'm going to borrow.
I can't borrow from this zero, I have to borrow from this entire fifty.
So this fifty, if I borrow one from fifty I get forty-nine.
And this zero will then become a ten, right?
I borrowed one from fifty to get a ten.
Now, am I done?
Ten is larger than five.
Nine is larger than zero.
Four is larger than one.
Two is larger than zero.
Eight is larger than zero.
So I think I'm ready to subtract.
Ten minus five, well that's five.
Nine minus zero is nine.
Four minus one is three.
Two minus zero is two.
Eight minus zero is eight.
And I bring down the decimal point.
So if you mastered level four subtraction, the decimal problems really are just about lining up the decimal point, adding the zeros and then just doing a normal subtraction problem.
In general with subtraction, I think most people have the most trouble with the borrowing.
The way I do it I think is a little bit different than is taught in a lot of schools.
A lot of schools they'll do the subtraction, and they'll borrow alternatively.
But I find this easier when I just borrow ahead of time, and I also, like for example in this problem, when I had to make this zero into a ten, instead of borrowing from the zero, which is not intuitive because I can't really borrow from the zero,
I borrowed from this entire fifty, and I made that into a forty-nine.
Let's do one more problem.
If I have two point six four minus zero point zero four eight six.
So once again, let's line up the decimal points.
Two point six four and it's point zero four eight six.
Lined up the decimal points, include the zeros on top.
You're going to have a zero here, so I have to borrow. Becomes a ten.
Can't borrow from the zero, so I have to borrow from this entire forty.
So this forty becomes a thirty-nine. I think I'm running out of space.
So ten is larger than six.
Nine is larger than eight.
Three is not larger than four.
So this three I'm going to have to borrow. So three becomes a thirteen.
And this six becomes a five.
This is really bad, I shouldn't do it so messy.
But now we say the ten is larger than six, the nine is larger than the eight, this thirteen should be on top of that three.
The thirteen is larger than four, and five is larger than zero.
So we're ready to subtract.
Ten minus six is four.
Nine minus eight is one.
Thirteen minus four is nine.
Five minus zero is five.
Two minus nothing is two.
Bring down the decimal point.
So two point six four minus point zero four eight six is equal to two point five nine one four.
Hope I didn't confuse you too much.
But I think you're ready now to try the subtraction of decimals.
Have fun!
Write 5.1/4 as an improper fraction
Let me remind you an improper fraction is one where the numerator is gretaer than or equal to denominator, absolute value of numerator is greater than or equal to absolute value of denominator
In this situation right here we have a mixed number where 5 is the whole number and 1/4 is a proper fraction as numerator is less than denominator
So write as an improper fraction I will show you the methodology
So 5.1/4, the methodology is simple 5 is the same thing as 20/4
So 20/4 + 1/4 = 21/4
Another way to think is 5 x 4 = 20 + 1 = 21
So its 21/4
You take the mixed number or you take the whole part of the mixed number multiply it with the denominator & add the numerator to it.
So let us see why it works.
lets us see what 5.1/4 is
We have 5 wholes, this is one whole
let me copy it five times
So that is 2, 3, 4 & that is 5
So we have 5 wholes and then we have 1/4 1/4th of a whole is like this
To write it as a improper fraction Divide each of the wholes into 1/4ths
This is 4, 1/4ths, another 4,1/4ths another 4,1/4ths this is another 4, 1/4ths.
So how many 1/4ths we have it is 20 , 1/4ths in green
That is the same thing as 5
and then we can add to that 1/4ths.
Then we will get 21/4.
That is the conceptual way of how it works.
Multiply the whole number by the denominator and add the numertaor to it 5.1/4 = 21/4 5.1/4 =( ( 5x4) + 1)/4
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I've done a bunch of videos now on inflation and deflation and how they can be impacted by capacity utilization.
And the traditional notion of capacity utilization, and this is what my brain does when someone mentions it, is I think of industrial capacity utilization.
I imagine factories.
And when people say low utilization, I imagine idle factories, and when high utilization, I imagine factories that are running at three shifts and things are moving feverishly.
But in a service-based economy like we have here in the U.S. and like we have in a lot of Western societies, most of our real capacity for what we produce, or our GDP, is service based, because we're a service-based economy.
And if you think about it, industrial capacity utilization, it matters, but it matters much more to manufacturing-based economy.
In a service-based economy, the best measure of utilization really is unemployment.
And I guess we could say the best measure of underutilization is unemployment.
With that said, I think it's really important to have a deeper understanding of how unemployment is measured and how it's thought about from the Government, and the numbers you hear on CNN, what they really mean in terms of the real unemployment picture.
And most of these charts, actually all of these charts that I have in this video, I got from Mike Shedlock, who runs the Global Economic Analysis blog.
And I had a conversation with him on Friday and he pointed out some really interesting things.
That's what I really want to cover, and I think it'll give us a good general view of unemployment and give us some clues as to what's going on right now.
But I encourage you to read his blog.
He goes by Mish, and he tells people that the best way to find his blog is to just do a search on Google for Mish.
And he does a lot of this, where he looks at the economic data, but he goes several levels deeper than anyone really would go, especially on TV.
But that's what you really have to do to really discern what matters.
And I want to give him full credit because he really is who pointed out a lot of this to me, but I think it's very instructive to the capacity utilization and inflation-deflation argument that I've been making.
So right here I have a screenshot from the Bureau Of
Labor Statistics and you could go there, just do a search for them.
And what most people don't realize is, just like on the money supply, you have different measures of money supply, you also have different measures of unemployment.
And the number that you hear reported, at least since 1994, is U-3, and that's where we'll start.
That's kind of the official rate of unemployment.
I know you can't read this properly.
My screen capture software doesn't do well with this font.
But U-3 is total unemployed as a percent of the civilian labor force.
So it's very important to realize what they consider unemployed and what they consider the labor force.
They consider you unemployed if you don't have a job and you have looked for work in the past four weeks.
And this is a really important point.
It really is important to think about it relative to everything else I'll go over in this video.
Because we've probably had times in our life where we considered ourselves unemployed or we considered someone else unemployed, but they had maybe gotten dejected and stopped looking a little bit or decided to take a break.
It's important to realize, in the numbers that we hear from the Government, they don't count as part of the civilian labor force.
Well, let's say, you stop looking for a job for five weeks, because you wanted to take a break and maybe redo your resume for awhile, so you're kind of passively looking for a job.
The Government no longer considers you part of the labor force and you're not included in that number.
They do have broader numbers that do include that.
And I think that's important, because we're actually going to study the difference between the different numbers.
U-4 is total unemployed.
So it's the number up here, plus discouraged workers, as a percent of the civilian labor force, plus discouraged workers.
So they're going to add the discouraged workers to the numerator.
Let me do this in a different color.
Before you had-- this is the standard one.
You have unemployed over employed plus unemployed, as defined-- and when we say unemployed, it's someone who doesn't have a job, but you've looked for a job in the last four weeks.
U-4 is now-- let me do it in a different color.
It is unemployed plus discouraged over employed plus unemployed plus discouraged workers.
And their definition of discouraged workers-- I just talked about people who haven't looked or actively looked for a job in more than five weeks or actually more than four weeks.
You're considered discouraged if you give a reason for that, and you say, well, I just haven't looked for it, because I'm discouraged, because I don't think there are jobs for what I want to do anymore, so that's the reason why haven't looked for it.
And that's when you get included into this bucket.
And then U-5 is that same thing, but what they do is they add other marginally attached workers.
And the difference between a discouraged worker and a marginally attached worker, a discouraged worker gives the economic reason.
They say I haven't looked for a job in the past five weeks because I just think it's impossible.
I want to work but it's just impossible find a job as an accountant or an engineer anymore.
While a marginally attached worker also says I haven't looked for a job in the last five weeks, but they don't say it's because they think the economy is making it impossible.
It could just be that they're-- I don't know-- depressed generally or they don't want to-- it could be a whole set of reasons.
The important thing is that on the survey that the Bureau Of
Labor Statistics conducts, that they don't literally give that argument that the only reason that they're not looking for it is economic reasons, and then they'll be put into the marginally attached workers and that's U-5.
And then U-6 is really interesting because it includes all of these above but it actually shifts some people.
So in U-5 you would add marginally attached to the denominator there.
In U-6 what you do is you have total unemployed plus all marginally attached workers plus total employed part-time for economic reasons as a percent of the civilian labor force, plus all marginally attached workers.
So the important thing here is, plus total employed part-time for economic reasons.
That's key, so the denominator doesn't change anymore, but this unemployed number is going to get bigger.
Because there's some part of the employed population who are not working 40 hours a week, or they're not working as much as they want to work, or they're not maybe working in even the field they want to work.
Maybe instead of working as an engineer, they're working 20 hours a week at the local bookstore or at Starbuck's, and these people are included in U-6.
And the reason why I want to really highlight that, and
Mish pointed this out to me, is that this is increasing much faster than this.
And we'll think a little bit about why that's happening and what conclusions we can take.
These are the numbers straight from the Bureau Of Labor Statistics.
I know this screen right here is really hard to see, but if you look at March 2008, the U-3 number was 5.2% and the
U-6 was 9.3%.
So the difference between the two is about 4.1%.
But if you go to the most recent month, the standard unemployment number is 8.5%, but the U-6, the one that includes the discouraged workers, the marginally attached workers and the people who aren't working full time for economic reasons, the difference is now 7.1%, so that spread.
People who would like to work, but they've either stopped looking because they've gotten dejected, or they've just bitten the bullet and taken a job that they otherwise wouldn't want to take or taken fewer hours than they otherwise wouldn't want to take, that's growing.
That really is.
And the reason why we really want to focus on that is because it tells us that even though the unemployment rate, the official unemployment rate-- that is increasing very steeply and I'll show a graph right here, this is actually work Mish did, where he actually shows that the spread between U-6 and U-3 has been increasing, and it's been increasing at an accelerating rate since last February.
That's actually shown right here in this graph.
And he got this from his friend Chris Puplava at Financial Sense, so I want to give him credit for it.
But you see here, U-6, this is the broad measure of unemployment that we talked about right here.
That's increasing at an even faster rate than the standard unemployment measure.
And this green line right here, this is actually the difference between the two.
What's interesting about that is this is kind of measuring the percentage of the labor pool that's getting dejected, that's getting depressed.
So they're either getting depressed or dejected and not looking for work, or they're just saying, you know what?
I can't get a job 40 hours a week anymore as an accountant.
I will now go work part-time at the local department store or do whatever it takes to put some food on the table for their families.
In general, it shows the level of desperation.
And if you look here, and this is really interesting.
This is also from Chris Puplava.
If you look relative to the path, the last major recession that a lot of people talk about is the early 80's, the double dip recession, and even though the headline unemployment rate-- let me make sure I get the right color-- the headline unemployment rate here is the blue line, that is still a good bit below.
We peaked out there, and I don't know what the exact number is, but it looks like about in the mid 10%.
Even though we're a lot lower than that now, we're at 8.2% right now, if you look at U-6, which is the broadest, that's spiked up.
Unfortunately, the data for U-6 doesn't go back before 1994.
They actually changed how a lot of things were measured.
The official headline rate, instead of calling it U-3, it used to be called U-5, but it was, for the most part, the same measure, but that's changed a little bit.
But U-6 did not exist before 1994 so, unfortunately, we can't measure U-6 back then.
But a good, I guess, pseudo-indicator for U-6 that we do have more historical data on is the number of unemployed for more than 15 weeks.
These are people who have been looking for work, but 15 weeks or more, they still haven't found a job even though they've been actively looking for work.
And that, if you look at least while we have U-6 being measured, it has tracked that broad measure quite well.
So if we can make the assumption that U-6 is always on that line or above it as it's graphed here, which it is so far, then U-6 in the early 80's was probably right around where that line is now.
Maybe it was a little higher, maybe it was up here.
But what this graph really does convey is that that broadest measure of unemployment is already as bad as it probably was in the early 80's.
It's just that we don't have that data there.
And if anything, those part-time workers, because they are employed, so in the official unemployment measure, they're actually making the number look a little bit better.
Here you had fewer people.
You were either employed or you were unemployed.
If you're unemployed, you made the number look a little bit bigger.
Here you have a lot more people who are kind of in-between, but they get counted in the employed number.
So they're making the actual reported official unemployment rate a little bit lower than is actually the economic reality.
I think that's a really important thing to realize that you have this accelerating rate of desperation out there in the economy and, if anything, it's telling us that things are getting worse, and it's telling us that things are probably as bad as they've been in some of the worst recessions in history and they're only getting worse.
And going back to where we started this video, in terms of capacity utilization and what that might do to prices, this tells us that labor utilization is low and going down.
What that tells us, is that the price of labor is going down.
And you've probably read multiple news reports already about how this is the first time furloughs are big.
People are actually taking wage cuts.
So you're already seeing deflation in wages.
And when so much of our economy, and even the basket of goods in the CPl-- and I'll do another video on that --is service based, if you're seeing deflation in wages, that's another data point that tells you, at least in the medium term, we're probably going to see further deflation in prices as a whole.
See you in the next video.
Jayda takes 3 hours to deliver 189 newspapers on her paper route.
What is the rate per hour at which she delivers the newspaper?
So this first sentence tells us that she delivers, or she takes, 3 hours to deliver 189 newspapers.
So you have 3 hours for every 189 newspapers.
That's what the first sentence told us.
But we want to figure out the rate per hour, or the newspapers per hour, so we can really just flip this rate right here.
So if we were to just flip it, we would have 189 newspapers for every 3 hours, which is really the same information.
We're just flipping what's in the numerator and what's in the denominator.
Now we want to write it in as simple as possible form, and let's see if this top number is divisible by 3.
1 plus 8 is 9, plus 9 is 18.
So that is divisible by 3.
So let's divide this numerator and this denominator by 3 to simplify things.
So if you divide 189 by 3.
Let's do it over on the side right here.
3 goes into 189.
3 goes into 18 six times.
6 times 3 is 18.
Subtract.
Bring down the 9.
18 minus 18 was nothing.
3 goes into 9 exactly three times.
3 times 3 is 9, no remainder.
So if you divide 189 by 3, you get 63, and if you divide 3 by 3, you're going to get 1.
You have to divide both the numerator and the denominator by the same number.
So now we have 63 newspapers for every 1 hour.
Or we could write this as 63 over 1 newspapers per hour.
Or we could write this as 63, because 63 over 1 is the same thing as 63 newspapers per hour.
In this video I want to familiarize ourselves with negative numbers.
And also learn a bit of how do we add and subtract them.
And when you first encounter them, they look like this deep and mysterious thing.
When we first count things, we're counting positive numbers.
What does a negative number even mean?
But when we think about it, you probably have encountered negative numbers in your everyday life.
So before I give the example, the general idea is a negative number is any number less than zero.
Less than zero.
let's just think about it in a couple of different contexts.
If I have... if we're measuring the temperature ... (and it can be in Celsius or Farenheit, but let's just say we're measuring it in Celsius), and so let me draw a little scale that we can measure the temperature on.
So let's say that this is 0° Celsius, that is 1° Celsius, 2° Celsius, 3° Celsius.
Now, let's say it's a pretty chilly day and it's currently 3° Celsius.
And someone who predicts the future tells you that it is going to get 4° colder the next day.
So how cold will it be?
How can you represent that coldness?
Well, if it only got 1° colder it would be at 2°, but we know we have to go 4° colder.
If we got 2° colder, we would be at 1°.
If we got 3° colder, we would be at 0°.
But 3° isn't enough, we have to get 4° colder, so we actually have to go one more below zero. And that 1 below 0 we call that "negative 1".
And so you can kind of see that the number line, as you go to the right of zero increases in positive values, as you go to the left of zero you're going to have -1, -2, -3.
And you're going to have-depending on how you think about it- you're going to have larger negative numbers.
But I want to make it very clear:
-3 is LESS than -1.
There is less heat in the air at -3° than at -1°.
It is colder---there is less temperature there.
So let me just make it very clear:
-100 is much smaller than -1.
You might look at 100 and you might look at 1 and your gut reaction might be that 100 is much larger than 1.
But when you think about it,
-100: if it's -100° there is a lack of heat, so there is much less heat here than if we had -1°.
Let me give you another example.
Let's say in my bank account today I have $10.
Now, let's say I go out there (because I feel good about my $10), and let's say I go and spend $30.
let's say I have a very flexible bank, one that lets me spend more money than I have (and these actually exist!).
So what's my bank account going to look like?
I will owe the bank some money.
Tomorrow, what is my bank account?
You might immediately say, "if I have $10 and I spend $30, there's $20 that had to come from some place." And that $20 is coming from the bank.
So I'm going to owe the bank $20.
And so, in my bank account, to show how much I have, I could say $10 - $30 is -$20.
So, if I say I have -$20, that means that I owe the bank.
It's going in reverse.
Here, I have something to spend... if my $10 in my bank account means the bank owes me $10.
I've gone the other direction.
If we use a number line here it should hopefully make more sense.
So that is 0.
I'm starting off with $10, and spending $30 means I'm moving 30 spaces to the left.
So if I move 10 spaces to the left--- if I only spend $10 I'll be back at $0.
If I spend another $10, I'll be at -$10.
If I spend another $10 after that, I will be at -$20.
Another $10 I'd be at -$10.
Another $10 I would be at -$20. So this whole distance here is how much I spent.
I spent $30.
So the general idea when you spend or if you subtract, or getting colder, you would move to the left.
The numbers would get smaller.
And we now know they can get even smaller than 0.
They can go to -1, -2---they can even go to -1.5, -1.6.
The more and more negative, the more you lose.
I will move to the right of the number line.
let's just do a couple more pure math problems.
Let's say, 3 - 4.
So once again, this is exactly the situation we did with the temperature.
We're starting with 3 and we're subtracting 4, so we're going to move 4 to the left.
We go 1, 2, 3, 4.
That gets us to -1.
And when you're starting to do this you really understand what a negative number means.
I really encourage you to visualize the number line and really move along it depending on whether you're adding or subtracting.
Let's do a couple more.
Let's say I have 2 - 8 (and we'll think about more ways to do this in future videos), but once again, you just want to do the number line.
You have a 0 here.
We're at (let me draw the spacing a little bit).
If we're subtracting 8, that means we're going to move 8 to the left.
So we're going to go 1 to the left, 2 to the left.
We have to move how many more to the left?
We've already moved 2 to the left, to get to 8, we have to move 6 more to the left.
Well, where is that going to put us?
Well, we were at 0.
This is -1, -2, -3, -4, -5, -6.
So, 2 - 8 is -6.
When you're subtracting 8 you're subtracting another 6.
(and this will be a little less conventional but hopefully it will make sense).
Let us take... (and I'll do this in a new color)...
So we're starting at a negative number and then we're subtracting from that.
Now, if this seems confusing just remember the number line!
This is -1, -2, -3, -4.
So that's where we're starting.
Now we're going to subtract 2 from -4, so we're going to move 2 to the left.
If we subtract another 1 we are going to be at -6.
So this is -6.
Let's do another interesting thing.
Instead of subtracting something from that, let's add 2.
So we're going to move to the right.
But if you add another 1 (which we have to do), you become -1.
You move 2 to the right.
So, -3 + 2 is -1.
And you can see for yourself, this all fits our traditional notion of adding and subtracting.
If we start at -1 and we subtract 2, we should get -3.
Kind of reverses this thing up here. -3 +2 gets us there.
And if we start there and we subtract 2 we should get back to -3. And we see that happens.
In its most popular sense, when people talk about mitosis, they're referring to a cell, a diploid cell.
So diploid just means it has its full complement of chromosomes, so it has 2N chromosomes.
So that's the nucleus.
This is the whole cell.
And so most people are saying, look, the cell itself replicates into two diploid cells, so it turns into two cells, each that have a full complement of chromosomes, 2N chromosomes.
And so when people say a cell has experienced mitosis, they normally mean this.
But I want to make one slight clarification, that formally, mitosis only refers to the process of the replication of the genetic material and the nucleus.
So, for example, if I were to draw this-- let me draw the cell-- and it has now two nucleuses, each with the diploid number of chromosomes, this cell has experienced mitosis.
It has not experienced cytokinesis, which we will talk about in a few moments, but that's the process of the actual cytoplasm of the cell being split into two different cells.
And just as a clarity, the cytoplasm is all the stuff outside of the nucleus.
So I'll talk about that in a second, but just know in everyday usage, this is normally the case when people talk about mitosis.
But if you've got a teacher that likes to get you on a technicality, this is technically what mitosis is.
It's the splitting of the nucleus or the replication of the nucleus into two separate nucleuses.
That's normally accompanied by cytokinesis where the cytoplasms of the cells actually separate.
Now, with that said, let's go into the mechanics of mitosis.
So the first steps that are really necessary for mitosis actually occur outside of mitosis when the cell is just doing its day-to-day life, and that's during the interphase.
And the interphase, literally it's not a phase of mitosis.
It's literally when the cell is just living.
Let's say we have some new cell.
Let me do it in green.
That's a new cell here.
Maybe this is its nucleus.
It's got 2N chromosomes, and then it grows.
It brings in nutrients from the outside and builds proteins and does whatever, and so it grows a bit.
It's obviously got its full chromosomal complement still.
And then at some point during this life cycle, and I'll label these actually, so this phase in interphase, and this might not even be covered in some biology classes, but they give it a label.
They call it G1, which is really just when the cell is growing.
It's just growing, accumulating materials and building itself out, and then it actually replicates its chromosomes.
So you still have a diploid number of chromosomes.
So let me zoom in.
So let me draw this.
This is called the S phase of interphase, so this is S.
And S is where you have replication of the actual chromosomes.
Once again, we're not even in mitosis yet.
So S, you have replication of your chromosomes.
So if I were to zoom in on the nucleus during the S phase, if
I were to start off-- let me just start with some organism that has two chromosomes.
So let's say that at the beginning of S phase, and I'll draw things as chromosomes just to make it clear that things are being replicated.
So let me say it has this chromosome right here and then let's say it has this chromosome right here.
As it goes through S phase, these chromosomes replicate.
And I'm just drawing the nucleus here.
I've zoomed in on just this part right here, where N is 1, where our full diploid complement is two chomosomes.
During S phase, our chromosomes will replicate and will have-- so that green one will completely replicate and generate a copy of itself, and we've learned this a little bit, they're connected at the centromere.
Now, each of those copies are called chromatids, and that magenta one will do the same thing.
Even though we have two chromatids, one for each chromosome, now we have four chromatids, two for each chromosome, we still say we only have two chromosomes.
That's its centromere right there.
This occurs in the S phase, and then the cell will just continue to grow more.
So the cell was already big-- I'll focus on the cell again.
The cell was already big and it gets bigger.
It gets bigger, and that's during the G2 phase, so it's just growing more.
Now, there's another little part of the cell we haven't even talked about yet, but I'll talk about it a little bit.
It's not super-duper important, but it's the idea of these centrosomes.
These are going to be very important later on when the cell is actually dividing, and those also duplicate.
So let's say I have a little centrosome here.
It has centrioles inside it.
You don't have to worry too much about that, but they're these little cylindrical-looking things.
But I just want to-- so you don't get confused if you see the word centriole and centrosomes, not to be confused with centromeres, which are these little points where the two chromatids attach.
Unfortunately, they named many things in this process very similarly, or a lot of the parts of a cell very similarly.
But you have these things called centrosomes that are going to enter the picture very soon, that are sitting outside of the nucleus, and they also replicate.
They also replicate during the interphase.
So you had one before, now you have two of them.
And, of course, they each have their two little centrioles inside, but we're not going to focus too much on those just yet.
So that's what happened in the interphase.
This is most of the cell's life, and it's kind of growing and doing what it wants.
Actually, I'll make a slight point here.
When I drew the DNA here, I drew them as chromosomes.
But the reality is when we're sitting in the interphase, this is not what the DNA would actually look like.
The DNA, if I were to actually draw this, it's in its chromatin form.
It's not all tightly wound like I drew it here.
I drew it tightly wound so that you can see that it got replicated, but the reality is that that green chromosome would actually be all unwound, and if you were looking in a microscope, you would even have trouble seeing it.
This is its chromatin form.
We'll talk a little bit about where it actually organizes itself back into a chromosome, but in its chromatin form, it's just a bunch of DNA and proteins that the DNA is wrapped around a little bit, so you might have some proteins here that the DNA is wrapped around a little bit.
But if you're looking at it in a microscope, it just looks
like a big blur of DNA and proteins.
Same thing for the magenta molecule.
Really, for DNA to do anything, it has to be like this.
It has to be open to its environment in order for the mRNA and the different types of helper proteins to really be able to function with it.
And even for it to be able to replicate, it has to be unwound like this in order for it to function.
It only gets tightly wound like this later on.
I just drew it like this, so really it had one green one, and it's going to replicate to form another green one, and they're going to be attached at some point.
That magenta one is going to replicate to form another magenta one, and they'll be attached at some point, but it's not going to be clear.
I just drew it this way to show that it really happened.
This is the reality.
It's in its chromatin form.
Now, we're ready for mitosis.
So the first stage of mitosis is essentially-- let me draw this.
So I'll draw the cell in green.
I'm going to draw the nucleus a lot bigger than it normally is relative to the cell just because, at least right now, a lot of the action is going in the nucleus.
So the first stage of mitosis is the prophase.
These are somewhat arbitrary names that were assigned.
People looked in a microscope. Oh, that's a certain type of step that we always see when a nucleus is dividing so we'll call this the prophase.
What happens in the prophase is that the actual chromatin starts actually turning into this type of form.
So as I just said, when we're in the interphase, the DNA's in this form where it's all separated and unwound.
It actually starts to wind together, so this is where you'll actually have-- and remember, it's already replicated.
The replication happened before mitosis begins.
So I had that one chromosome there, and then I have another one here.
It has two sister chromatids that we'll see soon get pulled apart.
Now, during prophase, you also start to have these centromeres appear that I was touching on before.
These guys over here, they start to facilitate the generation of what you call microtubules, and you can kind of view these as these sticks or these ropes that are going to be key in moving things around as we divide the cell.
All of this is pretty amazing.
I mean, you think of a cell, you think of something that's inherently pretty simple.
It's the most basic living structure in us or in life.
But even here, you have these complex mechanics going on, and a lot of it still isn't understood.
I mean, we can observe it, but we really don't know what's happening at the atomic level or at the protein level that allows these things to move around in such a nicely choreographed way.
It's still an area of research.
Some of this is understood, some of it isn't.
But you have these two centrosomes, and they facilitate the development of these microtubules, which are literally like these little microstructures.
You can view them as tubes or as some type of rope.
Now as prophase progresses, it eventually gets to the point where-- let me do it.
I don't want this word replication written here.
It makes it confusing.
Let me delete that.
Let me get rid of this replication.
So as prophase progresses, the nuclear envelope actually disappears.
So let me redraw this.
Let me copy and paste what I've done before.
Put it there.
So as prophase progresses-- the nuclear envelope actually starts to disassemble.
So this starts to actually dissolve and disassemble, and then these things start to grow and attach themselves to the centromere.
So actually, let me do that.
So this is all during prophase.
Since all of this happens during prophase, this latter part of prophase, sometimes they'll call it late prophase, sometimes it'll be called prometaphase.
Sometimes it's considered-- I don't think there's a hyphen really there.
So sometimes it's actually considered a separate phase of mitosis, although when I learned it in school, they didn't bother with prometaphase.
They just called it all prophase.
But by the end of prophase, or actually by the end of prometaphase, depending on how you want to view it, the whole situation is going to look something like this.
You have your overall cell.
The nuclear envelope has disassembled, so to some degree, it doesn't exist anymore.
Although the proteins that formed it are still there and they're going to be used later on.
And you have your two chromosomes in this case.
In a human's case, you would have 46 of them.
You have your two chomosomes, each made with sister chromatids, each made with two sister chromatids. Two chromosomes.
They, of course, have their centromeres right there, and then these centrosomes will have migrated roughly on opposite sides of what was once the nucleus.
And these things have kind of spread apart, these microtubules, so they're doing two functions, really.
At this point, they're kind of pushing these two centrosomes apart.
So you have all of these things, and they're connecting the-- you know, some of them are coming from this centrosome, some are coming from this centrosome, some are connecting the two.
And then some of these microtubules, these tubes or these ropes, however you want to view them, attach themselves to the centromeres of the actual chromosomes, and the protein structure that they attach them to is called the kinetochore.
So there's the kinetochore there, and that may or may not be-- kinetochore.
It's a protein structure.
It's actually fascinating.
It's still an open area of research on how exactly the microtubule attaches to the kinetochore, and as we'll see in a second, it's at the kinetochore that the microtubules essentially start to pull at the two separate sister chromatids and actually pull them apart.
And it's actually not understood exactly how that works.
It's just been observed that this actually happens.
Once prophase is done, essentially the cells then just make sure that the chromosomes are well aligned.
I kind of drew them well aligned here, but that just kind of formally occurs during metaphase, which is the next phase.
The first one was prophase.
Now we're in metaphase, and metaphase really is just an aligning of the chromosomes, so all of the chromosomes are going to be aligned at the center of the cell.
So I have my magenta one here, I have my magenta one here, and I have my other one here, my green one there, and, of course, you have your centrosomes, the microspindles that are coming off of them.
Some of them are kinetochore microspindles that are actually attaching to the centromeres of the actual chromosomes.
It's very confusing, right?
The centrosomes are these structures that help direct what happens to these microtubules.
Centrioles are these little structures, these little can-shaped structures inside the centrosomes, and the centromere are the center points where the two chromatids attached to each other within a chromosome.
So this is one sister chromatid, that's another sister chromatid, and they attach at the centromere.
But this is metaphase.
It's fairly easy.
Metaphase, you just have this aligning of the cells, and there's actually some theories, how does the cell know to progress past this point?
How does it know that everything is aligned and attached?
And then there are some theories that there's actually some signaling mechanism that if one of these kinetochore proteins isn't properly attached to one of these ropes, that somehow a signal is sent that mitosis should not continue.
So this is a very intricate process.
You can imagine if you have 46 chromosomes and you have all of this stuff going on in the cell, and it's not like there's some individual pushing stuff, or some computer here.
It's really directed by chemistry and by thermodynamic processes.
But just by the intricacy or the elegance of how these things are, it happens spontaneously with all of the proper checks and balances, so that most of the time, nothing bad happens, which is all quite amazing.
So after metaphase, now we're ready to pull the stuff apart, and that's anaphase.
So in anaphase-- let me write that down.
I've changed the color of my cell.
These guys get pulled apart.
And as soon as they get pulled apart-- so let's see, this guy's getting pulled.
Let me do it in green.
So one of the sister-- nope, that's not green.
One of the sister chromatids is pulling in that direction.
One is getting pulled in that direction.
And then the same is true for the magenta ones.
Pulled in that direction, and one is getting pulled in that direction.
And, of course, you have your centrosomes here and then they're connected to the kinetochores that are right there and that's where they're pulling.
There's also a whole microtubule structure that isn't connected to the actual chromosomes, but they're helping to actually push apart these two centrosomes so that everything is going to opposite sides of the cell.
And so as soon as these two chromatids are separated, and I touched on this a little bit before when we talked about the vocabulary of DNA, then as soon as that happens, these are each referred to as chromosomes.
So now you can say that the cell has what it used to have here.
It has two chromosomes.
It now has four chromosomes.
Because as soon as a chromatid is no longer connected to its sister chromatid, they're then considered sister chromosomes, which is just a naming convention.
I mean, they were there before, they were there after.
They were just attached before.
Now they're not attached, so you kind of consider them their own individual entity.
And then we're almost done.
The last stage is telophase.
I'm going to draw the cell a little bit different here because something is happening simultaneously with telophase most of the time.
So telophase, and actually I'll rotate the cell 90 degrees.
Let's say that this was one centromere.
This is the other centromere.
So at this point, it's essentially pulled the DNA to itself.
So this guy has pulled one copy of that chromosome and one copy of this chromosome.
That guy's done the same up here.
He's pulled over one copy of each-- oh, I used a different color-- one copy of each chromosome to himself.
Let me draw that right there like that.
And now the nuclear membranes start forming around each of these two ends.
So now you start having a nuclear membrane form around each of these two ends.
And so by the end of the telophase-- that's what we're in, the telophase-- we will have completed mitosis.
We will have completely replicated our two original nucleuses and all of the genetic content inside of it.
Now, at the same time telophase is happening, you also normally have this cytokinesis, where this cleavage furrow forms, where essentially-- during telophase, these things are getting pushed further and further apart by those microtubules so that they're already at the ends of the cell, of the cytoplasm of the cell, and you can almost view them as pushing on the sides to elongate the cell.
As that is happening, you have this furrow forming, this little indentation.
By the end of telophase in mitosis, you also have this process of cytokinesis, where this cleavage furrow forms and deepens, deepens, deepens until the cytoplasm is actually split into two separate cells.
So this is cytokinesis, which is formally not a part of mitosis, but it normally occurs with the telophase, so right at the end of mitosis, you do normally have two complete identical cells.
Once you have each of these two cells, then they, each individually, enter their own interphase.
Or they each individually, if we look at just this one, he will then be in his G1 phase.
At some point, these two things are going to replicate, and that's the S phase, and you go to the G2 phase, and then this guy will experience mitosis all over again.
Find the measurement of angle CAD, so angle CAD.. this angle right over here.. measure of that angle, let's just call it x, so that I don't have to keep writing the measure of angle CAD and the other thing that might jump out at you is that the measures of the other angles' measures are given here.. 50 degrees, 45 degrees and 37 degrees.
The other thing that might jump out at you if you take the outer edge of all these angles which are adjacent to each other if you take the outer edge, it forms a straight angle.
So this entire angle is going to be 180 degrees.
Or another way to think about it is the measure of each of these angles, when you add them all together needs to be 180 degrees .. and that's what we need to solve this problem. Because we have x plus 50 (50 in orange), + 45+ 37 is going to be equal to 180 degrees.
And now these, let's see 50+45=95.
So all of that is 132.
We can subtract 132 from both sides.
On our left hand side we are just left with x.
On our right hand side, 180-132 is 48 And we're done!
X is equal to the measure of this angle over here which is equal to 48 degrees.
<i>Brought to you by the PKer team @ www.viikii.net
Episode 10
I will call you, Mother .
Seung Jo, take care of yourself.
Eat your meals, and eat lots of vegetables and fruits.
And don't wander during the night. And...
I know, I know.
If you need anything, call me.
I don't need anything.
You have to come home once in a while, okay ?
I'm going Eun Jo.
Hyung. <i>He left. He really left like that. I was so happy about living in this house with Seung Jo...
Even if he's cold towards me...even if he's says things I don't like... It was nice just being with him .
Ha Ni...don't cry.
Let's wait...
He didn't go far away.
So he'll come back really soon... <i>Now I can't see him anywhere but at school. <i>He'll probably... <i>Seung Jo will probably forget me.
Ha Ni!
Oh Ha Ni!
Hey!
Oh Ha Ni!
Huh?
Did you say something?
Please pull yourself together.
You've lost your mind.
Everyday for a week, you've been like an octopus without bones.
An octopus.
I understand that you're sad because Seung Jo left the house, but this is not my friend, Ha Ni.
Pull yourself together, okay ?
Oh!
It's Seung Jo.
What are you doing?
You missed him so much.
-Hurry up and go act like you know him.
-No.
For some reason I'm scared to talk to him .
Joo Ri is on her lunch break.
Let's go and eat.
Huh?
We need two more King Chops.
Ha Ni went back to where she was a long time ago, huh ?
It's the same as it was in high school .
Here.
Ha Ni, you came? You're humming. You must be in a good mood, Bong Joon Gu .
Of course.
Since I'm working with a stable mind now, Ha Ni will come to me.
This is nothing different than me beating Baek Seung Jo.
Then, Ha Ni will come to me on her knees. please give me a King Cutlet .
Yes.
Eat!
Baek Seung Jo... where is he?
Don't know.
What about where he works?
Don't know.
Hey Oh Ha Ni.
You're saying a girl like you doesn't know that?
I don't know anymore.
Having a crush is really sad.
You're alright Ha Ni?
I'm sorry.
For what?
What happened to Ha Ni?
Isn't she a bit strange?
They say Baek Seung Jo left his house.
She's in shock.
Let's practice. <i>Seung Jo isn't coming for practice. <i>I already knew he wouldn't, but I was thinking maybe...
Hey, Oh Ha Ni!
You can't even pick up the balls properly?
Yes...
Ah really!
Ha Ni!
Do you feel like buying me dinner?
I don't.
Really?
That's a shame.
I was going to let you in on some information about Baek Seung Jo.
If you don't want to, it's fine.
Let's practice.
I'll buy it, sunbae!
I'll buy it, sunbae!
I'll buy it, I'll buy it!
I know a good place.
Yes?
It's not an expensive place, so you don't need to be pressured.
Besides that... the information you were talking about...
Ah information.
As you may already know, Seung Jo doesn't hide anything from me.
So if I tell you, it's pretty good information.
After practice, I'll take you where Seung Jo is working part time.
What !?!?
Seung Jo works here?
Yeah. He's a waiter here.
I introduced him to this place.
I actually work here on the weekends too.
Let's go in. <i>Baek Seung Jo working at a family restaurant... <i>I can't believe it.
Welcome.
How many...?
Oh Kyung Su shi.
Do you work today?
No, I'm here as a customer.
The two of us.
Ah, yeah.
Two persons?
Please come this way.
Yes. Let's go
Ah they added this.
It wasn't here last week.
Ha Ni. Ha Ni!
Yes?
Quit looking around and order.
Yes.
The Fresh Date Salad sounds okay.
The picture of the Garlic Steak Pie looks okay too.
Have you decided?
Why don't you just roughly decide?
Yes, I...
If you have thought about it for 15 minutes, that should be enough.
Baek Seung Jo.
Will it be the Grilled Soy sauce Salmon set?
Or is it the Fresh Date Salad?
Or the Garlic Baked Chicken?
I'll have the Grilled Soy sauce Salmon.
Fresh Date Salad.
Ah, and tea...
What kind of salad dressing would you like?
-Pinenut dressing.. -Would you like peach or lemon for your tea?
Lemon.
Shall I serve the tea after your meal?
Yes.
Please wait a while.
Ha Ni, what do you think? I was right wasn't....
What?
Are you crying now?
Punk, being a baby.
It's been so long since I've talked with Seung Jo.
Did you talk with him just now?
I heard it as ordering.
Excuse me.
Can I get a refill on my cola?
Yes.
Shall I give you more?
Yes.
How can he look so cool in a uniform too?
Sunbae...
Do you by any chance know where Seung Jo is living?
House?
I don't know that much yet.
You have been waiting for long!
Grilled Soy sauce Salmon.
Lemon chicken and fresh date salad for you
Really Looks delicious
Enjoy your meal
Seung Jo
Hello!
Where do you live now?
I'm working now...
Are you angry?
Because I'm here?
I knew you'd come sooner or later, however don't be a tattle-tale about this. <i>Brought to you by the PKer team @ www.viikii.net
That's it!
What?
That!
If I do part-time here,
I can very very casually...
I can be with Seung Jo
But this is quite the opposite of casual.
Just a second.
Oh?
Part time?
Yes.
I'll do my best!
I'm sorry.
What to do?
Yes?
I just hired someone a minute ago, so the positions are all filled.
Yes?!
Sorry, but maybe next time.
You!
Why are you here?
A part time job.
I see you're a second late.
Excuse me, don't you have any other positions?!
Sorry but we don't need any more right now.
Well then, please work hard starting today!
Looks like the tables have turned.
What is?
Ever since Seung Jo left his house, the only place you could meet Seung Jo is at the tennis club, right?
But then again Seung Jo barely ever goes.
I was in the same class and work in a part-time job in the same place as Seung Jo.
Goodness why do I keep feeling like I'm taking candy from you?
Well, I have to go to work so see you!
Oh gosh that was good.
Hey Ha Ni thanks to you, I really enjoyed my meal.
Oh right !
Did you get the part time job?
Great, it's all figured out then.
You have to be thankful to me.
It's all thanks to me.
Let's go now.
You're leaving ma'am?
There's still the tea left in your set meal.
Oh!
Can you just save it for me for tomorrow?
Excuse me?!
The tea...
Can't I come back tomorrow and drink it?
We cannot do that.
And I am not thankful at all if you show up tomorrow as well.
I won't bother you.
In the end, I'm still a customer.
Hey!
Don't you dare tell my family.
Then does that mean I can come?
Busy, huh?
Yeah, probably because there are a lot of customers.
How is living alone?
I just can't leave feeling at ease when Hae Ra is always around.
I need to come tomorrow and the day after as well.
Ha Ni, what are you doing?
Lets go!
Anyway, I'm happy I could see Seung Jo.
I'm back home!
Oh!
Ha Ni
You haven't eaten dinner yet have you?
Come here, let's eat together
I already ate out.
Oh my!
Ha Ni it's been a long time since I've seen you smile
Did something happen?
Huh?
No. Just......
You've been so sad since Seung Jo moved out.
I was worried about you.
Mother, Seung Jo is...
Don't you dare tell my family.
What!
Seung Jo is working part time at a family restaurant!
It was supposed to be a secret.
I had dinner there.
Oh my, oh my, it must have been so much fun!
I want to see it myself.
Right Eun Jo?!
Seung Jo is a waiter!
I want to see him too
Then shall the three of us have dinner there tomorrow?
Huh?
But he said it was a secret...
Oh Ha Ni no need to be shy!
Alright then.
How about all of us disguising ourselves?
We'll sit off to the side.
Yeah! <i> Seung Jo, what are you doing all by yourself? <i>Are you making dinner or are you reading a book? <i> Where in the world are you living right now?
I would like mushrooms and lotus leaves over rice, cabbage salad, and omija tea.
I would like abalone porridge, with grilled green tea mountain roots.
Blueberry sorbet after the meal.
I would like diced hot rice cakes with vegetables.
And please don't add any pepper on my grilled salmon.
I would like the grilled rib steak with 6 pieces of lemon chicken, actually 8 pieces. Instead of the abalone porridge, I would like the chicken breast.
He won't know if we all order like this, so let's clear it up.
What did you get?
Allow me to confirm your orders.
Mushroom and lotus leaves over rice, cabbage salad, and omija tea.
Grilled green tea mountain roots, and the rice cakes with vegetables.
Grilled salmon with no pepper.
Grilled chicken with orange sorbet.
You forgot mine?
Yes, the blueberry sorbet after the meal.
That's all.
I don't think he even jotted it down.
He's so smart, he must have memorized it all!
Hyung, you're so cool!
He's definitely a prodigy.
But he's not very cute.
My Seung Jo is cutest when he smiles.
Do you think Hyung has recognized us?
Hey Ha Ni, there's no way he could recognize us when we're disguised this well!
Excuse me!
Are you ready to order?
Should we eat the lotus leaf steak?
I want half lemon chicken half seasoned chicken.
I want to eat something I haven't tried.
Hurry up!
What is today's special?
Fried yam salad.
Oh I had that yesterday ...
Hey Ha Ni!
Idiot, Hyung probably already recognized us.
Is this you in disguise?
I'm sorry.
Oh it's Seung Jo's mother and Eun Jo.
Welcome.
Oh my gosh, why are you here?!
I work here part time with Seung Jo.
What?!
What were you doing, Ha Ni?!
I'm sorry.
Yoon Hae Ra made a move first!
Son, come home once in awhile.
And be careful not to fall for Hae Ra, not at all!
I get it.
Seung Jo, come on and tell me where you live.
Hurry and leave!
Alright Ha Ni?
You cannot lose to Hae Ra.
Don't you care what he says about you being persistent or tired of you.
You have to meet him everyday.
Stick to him like glue!
Come here every day, alright?
Yes!
There's nothing like a stalker.
My sad Hyung.
Poor Seung Jo.
What?!
Really?!
Yeah, it looks like Hae Ra has attached herself to Seung Jo.
Hae Ra's pretty darn persistent too.
Now that this has happened, you have no choice but to go every day as well.
Don't you think Seung Jo will dislike it?
Oh my gosh!
What in the world are you talking about?!
It's Oh Ha Ni to happily go after him whether he runs away or doesn't like it.
Like a cicada that sticks to a tree like glue and cries all summer long!
Okay. That's it!
A cicada stuck to a tree!
But the problem is...Do you have the time and money to go visit Seung Jo every single day?
Oh...
Are you renting this place?
Are you studying today again?
I have a paper that I have to turn in by next week.
I'll get the order here.
Ah...Okay.
Why did you purposely come?
It seemed like you were going to eat my friend.
What would you like?
Give me anything.
Yes, I understand.
Then, just a little bit...
The food you ordered has come out.
Could you please move your books?
What is this?
This is our restaurant's most popular Super Special Set.
This big... Is this a duck?
Not a duck... a chicken.
Didn't you tell me to get you anything?
Then enjoy your meal.
Thank you, thank you!
Customer!
Should I give you a fifth cup of coffee?
If you drink six cups of black coffee everyday, your stomach will feel terrible.
Aigoo, thank you.
You even worry about me?
It's okay.
I'm nothing if not healthy.
What guy in this world would like a girl that sits here all day wasting her life away watching him.
If I were a guy, I'd probably get really tired of it.
Well anyways, work hard.
Even if you do that, see if I leave. <i>Brought to you by the PKer team @ www.viikii.net</i>
Excuse me, customer!
Customer!
There isn't much time until we close.
Ah... yes.
It's 123,000 won all together.
What's that expensive?
You had a Super Special Set and 7 cups of coffee.
Super... whatever it is... how much is it?
It is 58000 won.
A moment please.
Wait a moment please.
Here.
Yes.
Thank you.
Excuse me.
Until what time does Baek Seung Jo work?
Aye, tell me.
I'm not sure. It's probably until 9 pm.
Ah, really?
Thank you.
At 9 pm?
Since it's 8:30 now...
He should be getting off soon.
Good.
Today, I will go see where Seung Jo lives.
Of course, just slightly.
Were you waiting?
I just came out.
Really?
It is a relief.
Oh, I am tired.
-Let's hurry -Okay.
They're just going together because they live in the same area.
It has to be like that.
What is this?
Seung Jo...
With Hae Ra...
Ha Ni!
What happened?
Why are you so late?
I was worried.
It's past midnight already.
I am sorry.
Was there a club meeting?
Did something happen?
No, everything is alright.
What about a bath?
Should I get the water ready for you?
I am just going to sleep today.
Good night.
Okay.
Good night.
Strange. <i>Seung Jo, who used to be right next door... <i>now lives with Hae Ra now. <i>What was all that talk about not hating me? <i>He doesn't hate me... <i>but he likes He Ra.
Is that it?
Right now, those two...
I'll be back.
Oh my, Ha Ni!
There are dark circles under your eyes!
And your eyes are swollen.
You look a bit sickly.
Really?
I couldn't sleep that well.
Aren't you studying too much?
That could never happen.
Are you okay?
What do you think about taking a day off of school today?
I'm okay.
If you feel worse, ask Seung Jo to bring you home.
If you show that face to our hyung, he'll probably faint.
He probably will.
I better be careful.
Then, I'll be back.
Hey Ha Ni, what about breakfast?
I don't have an appetite.
Then.
What do you think happened to Ha Ni?
It seems like it's not something normal.
What could it be?
Ah, really!
Are you on a diet?
Why aren't you eating these days?!
It's because I don't have an appetite...
What's the matter?
It's because of Baek Seung Jo, isn't it?
Tell us, we will listen.
I... think I'll just give up now.
Aigoo!
I've heard that more than a hundred times before.
Right?
My ears refuse to hear it.
But I really mean it this time...
What?!
Living together?!
Yoon Hae Ra and Beak Seung Jo?!
Didn't you see it wrong or something?
But still, staying at home together for more than one hour and not going out,
Wouldn't they be in that kind of relationship. . .
Seeing that it became like this,
I must have liked Seung Jo very much.
I could feel it all the way in my bones.
Crushes are really painful...
Ha Ni...
What to do?
Hello everyone.
1, 2, 3.
Back to the starting position!
1, 2, 3.
Back to the starting position!
1, 2, 3.
Hey Oh Ha Ni!
Won't you go back to your senses?!
Yes.
1, 2, 3.
Hey!
Baek Seung Jo!
Who are you?
"Who...
Who are you?"
We've been around each other for so long, and you're saying you don't know who we are?
We are Oh Ha Ni's friends.
You have an IQ of 200 but you can't even remember that?
We weren't in the same class, but we went to the same high school!
I immediately erase useless data out of my head, you know.
Ah, I remember!
The two who have the same level of brains as Oh Ha Ni,
Jung Joo Ri and...
Go Min Ah, right?
What's the matter?
Ah really, what did Ha Ni like about a guy like you...
You're right.
What did you want to say?
Hey!
Don't you think, you were too much?
It's about Ha Ni, do you know?
In the last 10 days she looks like she's been through hell and back!
As her friend,
I can't just sit and watch her like this!
So what?
What is it you want to say?
Living together!
Living together?
What?
You want to stand here and deny it now?
That you are living together with Yoon Hae Ra!
Ha Ni said, she followed you two and saw everything with her own eyes!
Ha Ni, the poor thing,
Waited for more than one hour on the street!
Although you know about Ha Ni's feelings,
Did you have to leave home like this, and even live with another woman?
At least clear everything up first!
You're such a coward.
Don't fool around behind her back!
Be a man and tell her the truth!
Fine.
All I have to do is tell her the truth?
If you're too honest then it'll be bad for Ha Ni so...
She's a lot more sensitive than what she looks to be...
So what we're saying is to stop tormenting Ha Ni!
We're not telling you to stop liking Yoon Hae Ra.
You understand, right?
Tell her there's no hope and to give up.
Oh Ha Ni... has been in a one-sided love with you for 4 years.
That's what we wanted to say.
We'll get going now. Let's go.
Here.
You were hungry right?
Wow!
This is abalone.
This is mountain root.
This is duck.
Here Ha Ni eat up, it's a treat from Joon Gu and us.
You have to take care of your body.
And find a new love.
That's right, Ha Ni.
Hey, that's not important.
Is he the only man in this world?
Look around you, there are so many gorgeous man out there...
You're right...
But I have no appetite...
You guys eat up.
Hey, Ha Ni...
You taking it this hard... Is absolutely killing me.
You should eat a little. <i> I haven't seen Seung Jo in two weeks already. <i> Yeah... <i>Without me trying... <i>There was no way for us to meet like this.
What are you doing here?
Are you waiting for someone?
Long time no see...
I haven't seen you around lately.
Yeah that's right...
Then I'm going to go first.
Show some compassion.
Can't you sit with me while I wait for someone?
Well...I guess.
Well... how is it? The new house?
Oh...
It's good.
The rooms are spacious.
Yeah...
What about meals?
Well,
Sometimes I eat at my part-time job.
Sometimes someone cooks for me. <i> C-cooks for him?
When you're suddenly living on your own, it must be quite lonely.
Well, it isn't even like that.
For the most part,
I'm with Yoon Hae Ra quite often.
Ah... yeah...
Teacher!
I'm here!
You're good about being on time.
Coming to Parang University, which is my target...
I'm really starting to think that I need to study really hard.
Omo!
This unnie... are you maybe Oh Ha Ni unnie?
Ah...
- How do you know me?
- I knew it!
She's exactly the way teacher Hae Ra described.
I can recognize her instantly.
I heard a lot about you.
Ah yes...
Huh?!
What did you hear about me?
I heard that you were the bottom of the school, but with the help of teacher Baek Seung Jo that you got into the top 50!
I heard that's still a legend!
Ah.
Well, yes...
Teacher!
Did you wait long?
No, I just came.
I'm getting English tutoring from Hae Ra teacher and math tutoring from Seung Jo teacher, because I'm going to take the entrance exam for this school.
Then your teachers...
They come over at least 3 times a week.
My mom loves them.
She even cooks them meals all the time.
But, it seems like Hae Ra teacher and Ha Ni unnie are not that close.
Then.... the place you went in with Hae Ra... You weren't living together, right?
Live together?!
Making conclusions on your own basis...
It's a good part-time job because it takes care of dinner.
Let's go now.
Then, good-bye.
You were making chocolate??
You give chocolate to special people...
You... perhaps...
Oh my goodness!
Do you know how long I've been waiting for this moment?
It took too long, right?
It's seems like you came back to your own self now.
I was so worried because you kept looking so lifeless these last few days.
This time you really need to make things work.
Yes.
Fighting!
Fighting!
I just can't get it to taste right.
Although the taste is not that important ...
What's wrong...
Is it because I haven't been eating well for the past few days?
Did you make it?
It looks beautiful.
It must be delicious.
Should I put it on your finger?
Seung Jo...
It's even raining on a day like this and I didn't bring my umbrella.
Ahjusshi what's wrong?
What to do?
The car seems to be broken.
What?
Oh, Ha Ni came.
Seung Jo...
I came.
On a day when it's raining this hard!
You're really an amazing person.
There's no use in waiting until Seung Jo has finished.
It seems things just get worse for you.
Today we tutor Ji Yeon.
Ah, it's coffee, right?
A lot of it? <i> When will I be able to give this to him? <i> Here is a little...
And anyhow, Hae Ra is here too.
What's with that face?
What's wrong with my face?
You don't look good.
You should get back home immediately.
I'm fine.
Customer?
Ha Ni?
Ha Ni?
Oh Ha Ni?
Ha Ni?
Oh Ha Ni?!
Hey!
Are you alright?
I'm sorry. Causing trouble.
Will you be okay without calling an ambulance?
Seung Jo Shi already gave you first aid.
That's okay.
I'm better now.
Baek Seung Jo shi, is this a person you know?
Yes.
Is it?
Then both of you should get back home.
You should give this young lady a ride home.
Ah, no.
I'm really fine.
How can you leave by yourself with this situation?
Do as I say Seung Jo shi.
Yes.
I got it.
It seems that you'll leave alone.
I understand.
There is nothing I can do about it.
Getting bumped around by little Miss Trouble everyday, it must be painful.
Oh Ha Ni!
You are amazing.
Anyway take care of yourself.
I'm going.
I'm going.
There aren't many cars around here.
I think it would be hard to find a cab here.
Seung Jo, you're getting wet. Come closer.
Don't go whining about being sick after getting wet so you can just get closer.
Seung Jo...
I'll just walk over to the station so you just go in.
It's a 30 minute walk to the station.
And with rain this harsh...
The trains might come to a halt like last time.
My apartment is 10 min away from here... You wanna come?
In my room, you can call mother and tell her to come here by car.
Wow! It looks better than I expected.
What you even have a full kitchen?!
Here is...
The bathroom.
Hae Ra... came here too?
Here?
You're the first to come over.
How are you doing?
Now I'm okay.
That's what you get for drinking that much coffee on an empty stomach!
It would be amazing if you didn't get a stomachache.
I said I'm alright now.
Here, a towel.
Baek Seung Jo's smell.
What smell? it's brand new. <i>Brought to you by the PKer team @ www.viikii.net
Hello?
It's me, Seung Jo.
I'm at my home
Pardon?
I met her.
She came by my part time job.
She fainted after she drank a cup of coffee.
No, she seems fine right now. <i> The time for us being alone like this, will be over once Mother comes to pick me up. <i> Before that, I have to get a look at Seung Jo's bedroom.
We are together now.
Omo!
Really?!
We couldn't find a cab, therefore please come here to pick her up.
Pardon?
Pardon?!
Are you joking now?
Mom?
Mom?!
Hello...?
Ah what?!
Hanging up like that.
Why?
What did she say?
She doesn't want to come because it's raining too much.
Huh?
She will pick us up tomorrow, so we have to stay here for the night.
That's what she said. <i>He's taking a shower, and from now on it will only be the 2 of us all night long. <i>Ah... <i>A situation that only arises in romance novels! <i> What should I do? <i> This happened before at Seung Jo's parents' house, but the situation is different now. <i>In this house, there is only the two of us! <i> There's also only one bed!
Hey!
Yes?
Are you going to take a shower?
Sh-shower?
Ah, yeah, then... I'll take a shower.
Are you nervous?
Nervous?
No way.
Not at all.
Put that on.
There's only my clothes.
If you don't like it then forget it.
Thank you. <i>I like this feeling of having my heart flutter like this. <i>This spot where Seung Jo was just at...Now I'm here. <i>Is Seung Jo waiting for me outside? <i>Tonight seems like a night that people only experience once in their lifetime.
Joong Gu, answer the phone!
Ah, yes. I understand.
Hello, this is So Pal Bok Noodles.
I'm calling from Seung Jo's house.
I'd like to speak to Ha Ni's father.
Ah, you are Baek Seung Jo's mother?
Oh my, then who would you be?
Joong Goo-goon?
Oh yes it's Bong Joon Gu.
But our chef is extremely busy right now.
Then listen carefully Joon Gu, and please make sure to tell Ha Ni's father.
Yes I got it.
Please tell me.
Ha Ni will be spending the night away from home tonight.
That he need not to worry.
She's going to sleep over at Seung Jo's house.
What?
I just thought it was better for her to stay there than to come home during these windy rains.
What...
What...What did you say?
Are you serious lady?!
H-ha Ni is going to sleep over at Seung Jo's home?!
Where is Baek Seung Jo now?
Omo, what to do... I don't know that.
But although I know it, I'm not gonna tell you~
What?!
Well then, I'm gonna hang up~
Excuse me, hello--
Ahjumma, don't hang up!
Don't hang up!
What's the matter?
Ch-chef!
Do you know where that Baek Seung Jo lives?
How in the world would I know where Seung Jo lives!?
I only know that he's working at that family restaurant.
What's the name of the family restaurant?
I think they're selling Dak (Korean for "chicken") there, ah no, it was chicken, or something like that.
Is it Dak or Chicken?
I'm leaving first!
Hey!
Hey!
Baek Seung Jo!
Hey you!
Joon Gu!
I...
I enjoyed the shower.
Thank you.
Yeah. <i> So... <i> What are we gonna do from now on?
Who are you?
Hello?
Hello?
I wanted... to ask something...
At this restaurant... is there a guy called Seung Jo...
Seung Jo?
Baek Seung Jo?
I must find...
I must find...
Hello?
Sir?
Hello?
Excuse me!
I'm going to go to sleep.
Huh?
Yeah, it's already 12 o'clock...
Well then I will sleep on the floor, so you just sleep in the bed.
Of course.
What?
There's only one blanket. if you're cold, go to the closet
Pull out a coat of mine and go to sleep if you must.
Hey, usually in situations like this, you should say to the girl
"Hey, what are you saying, I'll sleep on the floor, so you can sleep in the bed."
Isn't that common sense?
I don't want to say something like that to you.
What did you say to a sick person?!
You're not even a human!
You crazy cold human!
What?
Hey...
Hey...
What is it?
I hate the dark...
Can't we turn the lights on?
I can't sleep if it's not dark.
A ghost could come out...
Hey...
What now?
Aren't you cold?
Of course I'm cold.
Even my back is cold.
I'll just sleep on the floor.
It's fine, so just go to sleep!
But still...
But it's cold...
Okay!
I can sleep here too, right?
Wait!
Then...
I'll sleep on the floor...
It's fine!
If I do this, then you'll quiet down too!
Sleep!
Are you nervous?
Why do you keep asking that!
Nervous?
Whatever.
I'm not.
Then what's that sound of you swallowing your spit?
Huh?
You're spending a night with me.
You never know if something could happen.
Like a kiss?
Or...
Something beyond that could happen.
You may look forward to it...
Sorry.
But I'm not going to do anything.
Sleep well.
Good night. <i> It's like it all died down, <i> but I think I feel relieved. <i>But still, to not do anything while on a bed with a girl,</i> <i>I wonder if Seung Jo feels numb towards women or something.</i> <i>Maybe it's just because he doesn't see me as an attractive girl.</i> <i>That's it!</i> <i>There's no way a girl like me...</i>
Are you blaming yourself?
Blaming myself?
No...
I...
Don't want to become what my mother thinks of me as.
Say something did happen between us tonight.
We'll totally be caught up in it.
Then we'll forever be controlled by my mother.
That's all.
So...
So don't expect anything and just go to sleep. <i>That's right, he said he didn't dislike me. <i>For some reason I feel warm and happy. <i>Being able to sleep next to Seung Jo... <i>It's so precious I can't fall asleep. <i>Brought to you by the PKer team @ www.viikii.net</i>
Baek Seung Jo!
Yoon Hae Ra!
One two!
It's fun.
Go on.
Alright.
One more match.
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There are two whole Khan Academy videos on what scientific notation is, why we even worry about it.
And it also goes through a few examples.
And what I want to do in this video is just use a ck12.org
Algebra I book to do some more scientific notation examples.
So let's take some things that are written in scientific notation.
Just as a reminder, scientific notation is useful because it allows us to write really large, or really small numbers, in ways that are easy for our brains to, one, write down, and two, understand.
So let's write down some numbers.
So let's say I have 3.102 times 10 to the second.
And I want to write it as just a numerical value.
It's in scientific notation already.
It's written as a product with a power of 10.
So how do I write this?
It's just a numeral.
Well, there's a slow way and the fast way.
The slow way is to say, well, this is the same thing as 3.102 times 100, which means if you multiplied 3.102 times 100, it'll be 3, 1, 0, 2, with two 0's behind it.
And then we have 1, 2, 3 numbers behind the decimal point, and that'd be the right answer.
This is equal to 310.2.
Now, a faster way to do this is just to say, well, look, right now I have only the 3 in front of the decimal point.
When I take something times 10 to the second power, I'm essentially shifting the decimal point 2 to the right.
So 3.102 times 10 to the second power is the same thing as-- if I shift the decimal point 1, and then 2, because this is 10 to the second power-- it's same thing as 310.2.
So this might be a faster way of doing it.
Every time you multiply it by 10, you shift the decimal to the right by 1.
Let's do another example.
Let's say I had 7.4 times 10 to the fourth.
Well, let's just do this the fast way.
Let's shift the decimal 4 to the right.
So 7.4 times 10 to the fourth.
Times 10 to the 1, you're going to get 74.
Then times 10 to the second, you're going to get 740.
We're going to have to add a 0 there, because we have to shift the decimal again.
10 to the third, you're going to have 7,400.
And then 10 to the fourth, you're going to have 74,000.
Notice, I just took this decimal and went 1, 2, 3, 4 spaces.
So this is equal to 74,000.
And when I had 74, and I had to shift the decimal 1 more to the right, I had to throw in a 0 here.
I'm multiplying it by 10.
Another way to think about it is, I need 10 spaces between the leading digit and the decimal.
So right here, I only have 1 space.
I'll need 4 spaces, So, 1, 2, 3, 4.
Let's do a few more examples, because I think the more examples, the more you'll get what's going on.
So I have 1.75 times 10 to the negative 3.
This is in scientific notation, and I want to just write the numerical value of this.
So when you take something to the negative times 10 to the negative power, you shift the decimal to the left.
So this is 1.75.
So if you do it times 10 to the negative 1 power, you'll go 1 to the left.
But if you do times 10 to the negative 2 power, you'll go 2 to the left.
And you'd have to put a 0 here.
And if you do times 10 to the negative 3, you'd go 3 to the left, and you would have to add another 0.
So you take this decimal and go 1, 2, 3 to the left.
So our answer would be 0.00175 is the same thing as 1.75 times 10 to the negative 3.
And another way to check that you got the right answer is if you have a 1 right here, if you count the 1, 1 including the 0's to the right of the decimal should be the same as the negative exponent here.
So you have 1, 2, 3 numbers behind the decimal.
That's the same thing as to the negative 3 power.
You're doing 1,000th, so this is 1,000th right there.
Let's do another example.
Actually let's mix it up.
Let's start with something that's written as a numeral and then write it in scientific notation.
So let's say I have 120,000.
So that's just its numerical value, and I want to write it in scientific notation.
So this I can write as-- I take the leading digit-- 1.2 times 10 to the-- and I just count how many digits there are behind the leading digit.
1, 2, 3, 4, 5.
So 1.2 times 10 to the fifth.
And if you want to internalize why that makes sense, 10 to the fifth is 10,000.
So 1.2-- 10 to the fifth is 100,000.
So it's 1.2 times-- 1, 1, 2, 3, 4, 5.
You have five 0's.
That's 10 to the fifth.
So 1.2 times 100,000 is going to be a 120,000.
It's going to be 1 and 1/5 times 100,000, so 120.
So hopefully that's sinking in.
So let's do another one.
Let's say the numerical value is 1,765,244.
I want to write this in scientific notation, so I take the leading digit, 1, put a decimal sign.
Everything else goes behind the decimal.
7, 6, 5, 2, 4, 4.
And then you count how many digits there were between the leading digit, and I guess, you could imagine, the first decimal sign.
Because you could have numbers that keep going over here.
So between the leading digit and the decimal sign.
And you have 1, 2, 3, 4, 5, 6 digits.
So this is times 10 to the sixth.
And 10 to the sixth is just 1 million.
So it's 1.765244 times 1 million, which makes sense.
Roughly 1.7 times million is roughly 1.7 million.
This is a little bit more than 1.7 million, so it makes sense.
Let's do another one.
How do I write 12 in scientific notation?
Same drill.
It's equal to 1.2 times-- well, we only have 1 digit between the 1 and the decimal spot, or the decimal point.
So it's 1.2 times 10 to the first power, or 1.2 times 10, which is definitely equal to 12.
Let's do a couple of examples where we're taking 10 to a negative power.
So let's say we had 0.00281, and we want to write this in scientific notation.
So what you do, is you just have to think, well, how many digits are there to include the leading numeral in the value?
So what I mean there is count, 1, 2, 3.
So what we want to do is we move the decimal 1, 2, 3 spaces.
So one way you could think about it is, you can multiply.
To move the decimal to the right 3 spaces, you would multiply it by 10 to the third.
But if you're multiplying something by 10 to the third, you're changing its values.
So we also have to multiply by 10 to the negative 3.
Only this way will you not change the value, right?
If I multiply by 10 to the 3, times 10 to the negative 2-- 3 minus 3 is 0-- this is just like multiplying it by 1.
So what is this going to equal?
If I take the decimal and I move it 3 spaces to the right, this part right here is going to be equal to 2.81.
And then we're left with this one, times 10 to the negative 3.
Now, a very quick way to do it is just to say, look, let me count-- including the leading numeral-- how many spaces I have behind the decimal.
1, 2, 3.
So it's going to be 2.81 times 10 to the negative 1, 2, 3 power.
Let's do one more like that.
Let me actually scroll up here.
Let's do one more like that.
Let's say I have 1, 2, 3, 4, 5, 6-- how many 0's do I have in this problem?
Well, I'll just make up something.
0, 2, 7.
And you wanted to write that in scientific notation.
Well, you count all the digits up to the 2, behind the decimal.
So 1, 2, 3, 4, 5, 6, 7, 8.
So this is going to be 2.7 times 10 to the negative 8 power.
Now let's do another one, where we start with the scientific notation value and we want to go to the numeric value.
Just to mix things up.
So let's say you have 2.9 times 10 to the negative fifth.
So one way to think about is, this leading numeral, plus all 0's to the left of the decimal spot, is going to be five digits.
So you have a 2 and a 9, and then you're going to have 4 more 0's.
1, 2, 3, 4.
And then you're going to have your decimal.
And how did I know 4 0's?
Because I'm counting,, this is 1, 2, 3, 4, 5 spaces behind the decimal, including the leading numeral.
And so it's 0.000029.
And just to verify, do the other technique.
How do I write this in scientific notation?
I count all of the digits, all of the leading 0's behind the decimal, including the leading non-zero numeral.
So I have 1, 2, 3, 4, 5 digits.
So it's 10 to the negative 5.
And so it'll be 2.9 times 10 to the negative 5.
And once again, this isn't just some type of black magic here.
This actually makes a lot of sense.
If I wanted to get this number to 2.9, what I would have to do is move the decimal over 1, 2, 3, 4, 5 spots, like that.
And to get the decimal to move over the right by 5 spots-- let's just say with 0, 0, 0, 0, 2, 9.
If I multiply it by 10 to the fifth, I'm also going to have to multiply it by 10 to the negative 5.
So I don't want to change the number.
This right here is just multiplying something by 1.
10 to the fifth times 10 to the negative 5 is 1.
So this right here is essentially going to move the decimal 5 to the right.
1, 2, 3, 4, 5.
So this will be 2.5, and then we're going to be left with times 10 to the negative 5.
Anyway, hopefully, you found that scientific notation drill useful.
Let's do some more percentage problems. Let's say that I start this year in my stock portfolio with $95.00. And I say that my portfolio grows by, let's say, fifteen percent.
How much do I have now?
OK. I think you might be able to figure this out on your own, but of course we'll do some example problems, just in case it's a little confusing. So I'm starting with $95.00, and I'll get rid of the dollar sign.
And I'm going to earn, or I'm going to grow just because I was an excellent stock investor, that ninety-five dollars is going to grow by fifteen percent. So to that ninety-five dollars, I'm going to add another fifteen percent of ninety-five.
95 times 0.15-- I don't want to run out of space. Actually, let me do it up here, I think I'm about to run out of space-- 95 times 0.15. five times five is twenty-five, nine times five is forty-five plus two is forty-seven, one times ninety-five is ninety-five, bring down the five, twelve, carry the one, fifteen. And how many decimals do we have? one, two.
Notice how easy I made this for you to read, especially this two here. 109.25. So if I start off with $95.00 and my portfolio grows-- or the amount of money I have-- grows by fifteen percent, I'll end up with $109.25.
So just like the last problem, I start with x and it grows by twenty-five percent, so x plus twenty-five percent of x is equal to one hundred, and we know this 25% of x we can just rewrite as x plus 0.25 of x is equal to one hundred, and now actually we have a level-- actually this might be level three system, level three linear equation-- but the bottom line, we can just add the coefficients on the x. x is the same thing as onex, right?
So 1.25 times x is equal to 100, so x would equal 100 divided by 1.25.
So x is equal to 100 divided by 1.25.
Actually I think we know what x is and we know how we got to there. If you forgot how we got there, you can I guess rewatch the video.
X equals 100 divided by 1.25, so we say 1.25 goes into 100.00-- I'm going to add a couple of 0's, I don't know how many I'm going to need, probably added too many-- if I move this decimal over two to the right, I need to move this one over two to the right.
And I say how many times does one hundred go into one hundred-- how many times does one hundred and twenty-five go into one hundred? None. How many times does it go into one thousand?
We're on problem 58.
The graph of the equation y is equal to x squared minus 3x minus 4 is shown below.
Fair enough.
For what value or values of x is y equal to 0?
So they're essentially saying is, when does this here equal 0?
They want to know when does y equal 0?
So what values of x does that happen?
And we could factor this and solve for the roots, but they drew us the graph, so let's just inspect it.
So when does y equal 0?
So let me draw the line of y is equal to 0.
So that's right here.
Let me draw it as a line. y equals 0. That's y equals 0 right there.
So what values of x makes y equal 0?
If I can see this properly, it's when x is equal to negative 1 and when x is equal to 4.
So x is equal to negative 1 or 4.
And if we substitute either of these values into this right here, we should get y is equal to 0.
And let's see.
The choices, do they have negative 1 and 4?
Yep, sure enough.
Negative 1 and 4 right there.
I've got five numbers here and the goal is to order them from least to greatest.
And it might be obvious to you that all five of these numbers are negative numbers.
So let's just think about which of these is the greatest number.
And you might be tempted to say:
So you might be tempted to say "negative 40 is the greatest."
But you have to realize what the negative is telling you.
And think about that, think about... if these were your dollar amounts in your bank account... ...would you rather have negative $40 in your bank account or negative $7 in your bank account?
Negative 40 means that you owe the bank $40, so it's $40 less than having nothing.
Negative 7 would mean that you owed the bank only $7, so it's actually the case that -40 is less than -7, and out of all of these numbers, it is the least of all of them.
So -40 is the very least, and you can view that as the least amount of money that you would want, out of these comparisons, in your bank account, or the smallest amount of money.
You owe the bank $40.
Not only do you have nothing, you owe the bank $40.
Then the next smallest number would be -30, and then the next smallest after that would be -25, and then the next smallest after that would be -10, and then finally the greatest of all of these numbers (--the greatest, and I will do it in pink--) ...the greatest of all of these numbers is -7.
And if it's still not obvious to you, you could also think of them in temperature, in temperature terms.
Which of these is the coldest temperature?
(whether you're talking about Celsius or Fahrenheit)
-40 would be the coldest temperature, and -7 would be the warmest temperature.
There would be the most heat in the air at -7.
Another way to think about it is we could draw a number-line.
--So let's draw a number line right over here--
If this is a zero, and you know, we could put maybe +7 up here, +7 isn't one of these numbers, but we can plot all the other numbers.
So this right here might be -7.
If that's -7 then maybe this right over here would be -10.
Notice we go further and further to the left of the zero, and then we go a little bit further to the left we get -25...
A little bit further to the left than that is -30.
Then you go even further to the left and you get to -40.
If you think about it this way, the least of these numbers is the one that's furthest to the left on the number line, and the greatest is the one furthest to the right.
Travelling up the Mekong River, we are heading for the point known as the Golden Triangle where Loas on the right, Thailand on the left and Myanmar up ahead share a common border
When Mao Tse Tung's Red Army swept into Yunnan 10,000 Nationalist from the Kuomintang Army fled into this region led by General Tang, better known as Khunsa
With the fall of Vietnam to Communism in the 1960's the United States and the West were fearful of the Domino Effect in South East Asia, provided Khunsa with funds and arms to enable him to fight Communist expansion.
Instead Khunsa expanded the existing opium cultivation by the hill tribes
He commenced opium cultivation and opium manufacturing to an industrial scale
In the 80's up to 70 % of the heroine in the west came from the Golden Triangle
Kunsa became the most wanted man in the world.
In the early 90's the Royal Thai Army destroyed Khunsa's Opium base and together with the
United Nations International Drug Control Program converted most of the opium fields to tea, coffee and tobacco plantations.
Khunsa surrendered to the Burmese Govt in 1996 and passed away in 2007
All this while the Myanmar refused to extradite him to the USA even though he was charged for opium smuggling in a New York Court.
With the opening of casinos at the Myanmar and Laos borders, the Golden Triangle looks set to regain some of its previous notoriety and reputation.
We're on problem 71. It says, what is the value of x in the triangle below? OK, so we can just pull out the Pythagorean theorem here.
30 degrees, 90 degrees, they have to add up to 180, this one is equal to 60 degrees. And I did that big convoluted drawing where I flipped it and all of that. I think this is a good time to just to memorize the sides of a 30, 60, 90 triangle.
But you could do the Pythagorean theorem here. You could say that 7 squared, which is 49 , plus x squared is going to be equal to the hypotenuse squared. 14 squared is 196.
196. And if you were to subtract 49 from that, this is an 8, this is 16, we have a 7. Sorry, 147.
OK, a square is circumscribed about a circle. What is the ratio of the circle to the area of the square?
Let me draw the circle and the square. Well, if that's my circle, then if I want to draw a square, See if I can, nope that's not what I wanted to do . I wanted to draw a solid square.
The area of the square is just 2r times 2r. Which is 4r squared.
Area of the circle is just pi r squared. You hopefully learned the formula for area of a circle.
Divide the numerator and the denominator by r squared. You're left with pi/4. That's choice D.
CE is equal to 6.
What is the value of DE. Let's call that x. Now, I'm not going to prove it here, just for saving time.
It's going to be equal to x times 6. So you get 60 is equal to 6x. Divide both sides by 6, you get x is equal to 10.
RB is tangent to a circle. Tangent means that it just touches the outside of the circle right there at only one point. And it's actually perpendicular to the radius at that point.
BD is a diameter, OK, fair enough.
Well A is the center, so that's kind of obvious.
So they want to know what is the measure of angle CBR.
So they want to know what this angle is equal to.
We know that when a line is tangent to a circle, it's perpendicular to the radius at that point. So this whole angle is 90 degrees. So the angle that we're trying to figure out,
OK, I'll see you in the next video.
My travels to Afghanistan began many, many years ago on the eastern border of my country, my homeland, Poland.
I was walking through the forests of my grandmother's tales.
A land where every field hides a grave, where millions of people have been deported or killed in the 20th century.
Behind the destruction, I found a soul of places.
I met humble people.
I heard their prayer and ate their bread.
Then I have been walking East for 20 years -- from Eastern Europe to Central Asia -- through the Caucasus Mountains,
Middle East,
North Africa,
Russia.
And I ever met more humble people.
And I shared their bread and their prayer.
This is why I went to Afghanistan.
One day, I crossed the bridge over the Oxus River.
I was alone on foot.
And the Afghan soldier was so surprised to see me that he forgot to stamp my passport.
But he gave me a cup of tea.
And I understood that his surprise was my protection.
So I have been walking and traveling, by horses, by yak, by truck, by hitchhiking, from Iran's border to the bottom, to the edge of the Wakhan Corridor.
And in this way I could find noor, the hidden light of Afghanistan.
My only weapon was my notebook and my Leica.
I heard prayers of the Sufi -- humble Muslims, hated by the Taliban.
Hidden river, interconnected with the mysticism from Gibraltar to India.
The mosque where the respectful foreigner is showered with blessings and with tears, and welcomed as a gift.
What do we know about the country and the people that we pretend to protect, about the villages where the only one medicine to kill the pain and to stop the hunger is opium?
These are opium-addicted people on the roofs of Kabul 10 years after the beginning of our war.
These are the nomad girls who became prostitutes for Afghan businessmen.
What do we know about the women 10 years after the war?
Clothed in this nylon bag, made in China, with the name of burqa.
I saw one day, the largest school in Afghanistan, a girls' school.
13,000 girls studying here in the rooms underground, full of scorpions.
And their love [for studying] was so big that I cried.
What do we know about the death threats by the Taliban nailed on the doors of the people who dare to send their daughters to school as in Balkh?
The region is not secure, but full of the Taliban, and they did it.
My aim is to give a voice to the silent people, to show the hidden lights behind the curtain of the great game, the small worlds ignored by the media and the prophets of a global conflict.
Thanks.
(Applause)
Ok, so you've made a few programs.
You might be wondering, "How on earth am I supposed to remember all of these commands?
Is it oval or circle or ellipse?
Is it width and height, or is it height and width?
Do I have to memorize all of this?"
Thankfully, no!
That's what the computer is for.
The thing is, we always have a computer with us when we're programming, and a computer is really good at remembering things, better than we are.
So what if we just had the computer remember all the details for us, and we can just use it like a dictionary for programming.
Then we can focus on making cool programs, not memorizing a bunch of boring details.
That's what we call 'documentation': a document that explains how to program in a particular language and environment, with examples and gotchas.
You might think it's boring to read documentation, and you're right - it is kind of boring; it's a lot more fun to write code.
But unless you want to memorize absolutely everything (ugh!), you need to learn how to use documentation or be able to code your ideas.
Even great programmers don't try to memorize everything.
In fact, great programmers are usually some of the best at reading documentation.
For example, I'm drawing this smiley face, and I've already drawn the face and the eyes using ellipse, a function I know pretty well.
But I have more work to do.
First, I want to draw the face with thick outlines, like a sticker.
I remember that has something to do with stroke, but I don't remember exactly the name.
So instead of sitting here and trying to invent it, which could take hours or infinity, I'll just go to the documentation tab and look around and try and find what I'm looking for.
I'll look under this Coloring category, because that seems likely, and look at all the functions here, and then finally, at the very end, I find Stroke Weight: to change the thickness of lines and outlines.
So here we see the function name and the parameters - just one in this case. So what I usually do is start off by just copying that code and pasting it into my code. But I immediately get an error: "thickness is not defined."
Regina rode her bike 2 and 1/4 miles from her house to school and then 1 and 5/8 miles to her friend's house.
How many miles did Regina ride in total?
So she first rode 2 and 1/4 miles, and then she rode 1 and 5/8 miles. then she rode 1 and 5/8 miles
So the sum is the total number of miles she rode.
So to take this sum, we've seen that we can add the whole number parts, because this is really the same thing as 2 plus 1/4 plus 1 plus 5/8, so we can just switch the order, if you want to view it that way.
So we can add the 2 plus the 1 first, and then we get-- let me do that here.
So 2 plus the 1, you get 3, and then we need to add the 1/4 plus 5/8.
And to add these two fractions, we have to find the least common multiple of 4 and 8.
That'll be our new denominator.
8 is divisible by both 8 and 4, so that is the least common multiple of 4 and 8, so our common denominator will be 8.
Obviously, 5/8 will still be 5/8.
Now to go from a denominator of 4 to 8, you have to multiply the denominator by 2, so we also need to multiply the numerator by 2, so 1 times 2 is 2.
And, of course, we still have this 3 out there.
So 2 and 1/4 plus 1 and 5/8 is the same thing as this right here, and this is equal to-- we have our 3 plus, and then over 8 we add the 2 plus 5.
We have 7/8.
So this is going to be equal to 3 and 7/8 miles.
She rode a total of 3 and 7/8 miles.
Now, I want to make one thing very clear.
So far when we've been adding these mixed numbers, the fraction part always ended up as a proper fraction.
The numerator was smaller than the denominator.
But I want to do a quick example to show you what you do when the numerator is not smaller than the denominator.
So let's say we had 1 and 5/8 plus 2 and 4/8.
So if you add just the whole number parts, 1 plus 2, you get 3.
Plus 5/8 plus 4/8, 5/8 plus 4/8 is 9/8, so you get 3 plus 9/8.
Now it would be really strange to just say, OK, that's the same thing as 3 and 9/8, because you have a mixed number with a whole number and an improper fraction.
If you're going through the trouble of making it a mixed number, the fraction better be a proper fraction.
So what you need to do is rewrite 9/8, and you know that 9/8 is the same thing as 1 and 1/8, right?
8 goes into 9 one time with 1 left over, so it's 1 and 1/8.
So this is the same thing as 3 plus 1 and 1/8.
So now we can add the whole number parts.
3 plus 1 is equal to 4, and then you have your 1/8 over there: 4 and 1/8.
I just wanted to give you that special circumstance when your fraction part ends up improper.
A recipe for banana oat muffins calls for 3/4 of a cup of old-fashioned oats.
You are making 1/2 of the recipe.
How much oats should you use?
So if the whole recipe requires 3/4 of a cup and you're making half of the recipe, you want half of 3/4, right?
You want half of the number of old-fashioned oats as the whole recipe.
So you want 1/2 of 3/4.
So you just multiply 1/2 times 3/4, and this is equal to-- you multiply the numerators.
1 times 3 is 3.
2 times 4 is 8.
And we're done!
You need 3/8 of a cup of old-fashioned oats.
And let's visualize that a little bit, just so it makes a
little bit more sense.
Let me draw what 3/4 looks like, or essentially how much oats you would need in a normal situation, or if you're doing the whole recipe.
So let me draw.
Let's say this represents a whole cup, and if we put it into fourths-- let me divide it a little bit better.
So if we put it into fourths, 3/4 would represent three of these, so it would represent one, two, three.
It would represent that many oats.
Now, you want half of this, right?
Because you're going to make half of the recipe.
So we can just split this in half.
Let me do this with a new color.
So you would normally use this orange amount of oats, but we're going to do half the recipe, so you'd want half as many oats.
So you would want this many oats.
Now, let's think about what that is relative to a whole cup.
Well, one way we can do it is to turn each of these four buckets, or these four pieces, or these four sections of a cup into eight sections of a cup.
Let's see what happens when we do that.
So we're essentially turning each piece, each fourth, into two pieces.
So let's divide each of them into two.
So this is the first piece.
We're going to divide it into two right there, so now it is two pieces.
And then this is the second piece right here.
We divide it into one piece and then two pieces.
This is the third piece, so we divide it into one, two pieces, and this is the fourth piece, or the fourth section, and we divide it into two sections.
Now, what is this as a fraction of the whole?
Well, we have eight pieces now, right?
One, two, three, four, five, six, seven, eight, because we turned each of the four, we split them again into eight, so we have 8 as the denominator, and we took half of the 3/4, right?
Remember, 3/4 was in orange.
Let me make this very clear because this drawing can get confusing.
This was 3/4 right there.
So that is 3/4.
This area in this purple color is 1/2 of the 3/4.
But let's think about it in terms of the eights. How many of these sections of eight is it?
Well, you have one section of eight here, two sections of eight there, three sections of eight, so it is 3/8.
So hopefully that makes some sense or gives you a more tangible feel for what it means when you take 1/2 of 3/4.
Miranda's Maid Service charges $280 to clean 8 offices.
What is the company's price for cleaning a single office?
So they charge $280 to clean 8 offices.
So it's $280 per every 8 offices.
We could see, well, are both of them divisible by a common factor?
And this one looks like it is divisible by 8.
200 is divisible by 8, and then 80 is divisible by 8 as well.
So let's divide both the numerator and the denominator by 8.
And if we do that, 8 goes into 28 three times.
3 times 8 is 24.
Subtract.
You have 4 left over.
8 minus 4 is 4.
Bring down this 0.
8 goes into 40 exactly five times.
5 times 8 is 40, and you have no remainder.
So when you divide 280 by 8, you get 35.
And if you divide 8 by 8, you get 1.
So this rate simplifies to, this price per office, I guess we could call it, simplifies to $35 for every 1 office, which we could also write as 35 over 1 dollars per office, which is the exact same thing as $35 per office.
And we're done.
That is the company's price for cleaning a single office: $35.
Chapter I. Down the Rabbit-Hole
Alice was beginning to get very tired of sitting by her sister on the bank, and of having nothing to do: once or twice she had peeped into the book her sister was reading, but it had no pictures or conversations in it, 'and what is the use of a book,' thought Alice 'without pictures or conversation?'
So she was considering in her own mind (as well as she could, for the hot day made her feel very sleepy and stupid), whether the pleasure of making a daisy-chain would be worth the trouble of getting up and picking the daisies, when suddenly a White Rabbit with pink eyes ran close by her.
There was nothing so VERY remarkable in that; nor did Alice think it so VERY much out of the way to hear the Rabbit say to itself, 'Oh dear! Oh dear!
I shall be
late!' (when she thought it over afterwards, it occurred to her that she ought to have wondered at this, but at the time it all seemed quite natural); but when the Rabbit actually TOOK A WATCH OUT OF ITS WAlSTCOAT-
POCKET, and looked at it, and then hurried on, Alice started to her feet, for it flashed across her mind that she had never before seen a rabbit with either a waistcoat-pocket, or a watch to take out of it, and burning with curiosity, she ran across the field after it, and fortunately was just in time to see it pop down a large rabbit-hole under the hedge.
In another moment down went Alice after it, never once considering how in the world she was to get out again.
The rabbit-hole went straight on like a tunnel for some way, and then dipped suddenly down, so suddenly that Alice had not a moment to think about stopping herself before she found herself falling down a very deep well.
Either the well was very deep, or she fell very slowly, for she had plenty of time as she went down to look about her and to wonder what was going to happen next.
First, she tried to look down and make out what she was coming to, but it was too dark to see anything; then she looked at the sides of the well, and noticed that they were filled with cupboards and book- shelves; here and there she saw maps and pictures hung upon pegs.
She took down a jar from one of the shelves as she passed; it was labelled 'ORANGE
MARMALADE', but to her great disappointment it was empty: she did not like to drop the jar for fear of killing somebody, so managed to put it into one of the cupboards as she fell past it.
'Well!' thought Alice to herself, 'after such a fall as this, I shall think nothing of tumbling down stairs!
How brave they'll all think me at home!
Why, I wouldn't say anything about it, even if I fell off the top of the house!'
(Which was very likely true.)
Down, down, down.
Would the fall NEVER come to an end!
'I wonder how many miles I've fallen by this time?' she said aloud.
'I must be getting somewhere near the centre of the earth.
Let me see: that would be four thousand miles down, I think--' (for, you see, Alice had learnt several things of this sort in her lessons in the schoolroom, and though this was not a VERY good opportunity for showing off her knowledge, as there was no one to listen to her, still it was good practice to say it over) '--yes, that's about the right distance--but then I wonder what Latitude or Longitude I've got to?'
(Alice had no idea what Latitude was, or Longitude either, but thought they were nice grand words to say.) Presently she began again.
'I wonder if I shall fall right THROUGH the earth!
How funny it'll seem to come out among the people that walk with their heads downward!
The Antipathies, I think--' (she was rather glad there WAS no one listening, this time, as it didn't sound at all the right word) '--but I shall have to ask them what the name of the country is, you know.
Please, Ma'am, is this New Zealand or Australia?' (and she tried to curtsey as she spoke-- fancy CURTSEYlNG as you're falling through the air!
Do you think you could manage it?) 'And what an ignorant little girl she'll think me for asking!
No, it'll never do to ask: perhaps I shall see it written up somewhere.'
Down, down, down.
There was nothing else to do, so Alice soon began talking again.
'Dinah'll miss me very much to-night, I should think!' (Dinah was the cat.) 'I hope they'll remember her saucer of milk at tea-time.
Dinah my dear!
I wish you were down here with me!
There are no mice in the air, I'm afraid, but you might catch a bat, and that's very
like a mouse, you know. But do cats eat bats, I wonder?'
And here Alice began to get rather sleepy, and went on saying to herself, in a dreamy sort of way, 'Do cats eat bats?
Do cats eat bats?' and sometimes,
'Do bats eat cats?' for, you see, as she couldn't answer either question, it didn't much matter which way she put it.
She felt that she was dozing off, and had just begun to dream that she was walking hand in hand with Dinah, and saying to her very earnestly, 'Now, Dinah, tell me the truth: did you ever eat a bat?' when suddenly, thump! thump! down she came upon a heap of sticks and dry leaves, and the fall was over.
Alice was not a bit hurt, and she jumped up on to her feet in a moment: she looked up, but it was all dark overhead; before her was another long passage, and the White
Rabbit was still in sight, hurrying down it.
There was not a moment to be lost: away went Alice like the wind, and was just in time to hear it say, as it turned a corner, 'Oh my ears and whiskers, how late it's getting!'
She was close behind it when she turned the corner, but the Rabbit was no longer to be seen: she found herself in a long, low hall, which was lit up by a row of lamps hanging from the roof.
There were doors all round the hall, but they were all locked; and when Alice had been all the way down one side and up the other, trying every door, she walked sadly down the middle, wondering how she was ever to get out again.
Suddenly she came upon a little three- legged table, all made of solid glass; there was nothing on it except a tiny golden key, and Alice's first thought was that it might belong to one of the doors of the hall; but, alas! either the locks were too large, or the key was too small, but at any rate it would not open any of them.
However, on the second time round, she came upon a low curtain she had not noticed before, and behind it was a little door about fifteen inches high: she tried the little golden key in the lock, and to her great delight it fitted!
Alice opened the door and found that it led into a small passage, not much larger than a rat-hole: she knelt down and looked along the passage into the loveliest garden you ever saw.
How she longed to get out of that dark hall, and wander about among those beds of bright flowers and those cool fountains, but she could not even get her head through the doorway; 'and even if my head would go through,' thought poor Alice, 'it would be of very little use without my shoulders.
Oh, how I wish I could shut up like a telescope!
I think I could, if I only know how to begin.'
For, you see, so many out-of-the-way things had happened lately, that Alice had begun to think that very few things indeed were really impossible.
There seemed to be no use in waiting by the little door, so she went back to the table, half hoping she might find another key on it, or at any rate a book of rules for shutting people up like telescopes: this time she found a little bottle on it, ('which certainly was not here before,' said Alice,) and round the neck of the bottle was a paper label, with the words
'DRlNK ME' beautifully printed on it in large letters.
It was all very well to say 'Drink me,' but the wise little Alice was not going to do
THAT in a hurry.
'No, I'll look first,' she said, 'and see whether it's marked "poison" or not'; for she had read several nice little histories about children who had got burnt, and eaten up by wild beasts and other unpleasant things, all because they WOULD not remember the simple rules their friends had taught them: such as, that a red-hot poker will burn you if you hold it too long; and that if you cut your finger VERY deeply with a knife, it usually bleeds; and she had never forgotten that, if you drink much from a bottle marked 'poison,' it is almost certain to disagree with you, sooner or later.
However, this bottle was NOT marked 'poison,' so Alice ventured to taste it, and finding it very nice, (it had, in fact, a sort of mixed flavour of cherry-tart, custard, pine-apple, roast turkey, toffee, and hot buttered toast,) she very soon finished it off.
'What a curious feeling!' said Alice; 'I must be shutting up like a telescope.'
And so it was indeed: she was now only ten inches high, and her face brightened up at the thought that she was now the right size for going through the little door into that lovely garden.
First, however, she waited for a few minutes to see if she was going to shrink any further: she felt a little nervous about this; 'for it might end, you know,' said Alice to herself, 'in my going out altogether, like a candle.
I wonder what I should be like then?'
And she tried to fancy what the flame of a candle is like after the candle is blown out, for she could not remember ever having seen such a thing.
After a while, finding that nothing more happened, she decided on going into the garden at once; but, alas for poor Alice! when she got to the door, she found she had forgotten the little golden key, and when she went back to the table for it, she found she could not possibly reach it: she could see it quite plainly through the glass, and she tried her best to climb up one of the legs of the table, but it was too slippery; and when she had tired herself out with trying, the poor little thing sat down and cried.
'Come, there's no use in crying like that!' said Alice to herself, rather sharply; 'I advise you to leave off this minute!'
She generally gave herself very good advice, (though she very seldom followed it), and sometimes she scolded herself so severely as to bring tears into her eyes; and once she remembered trying to box her own ears for having cheated herself in a game of croquet she was playing against herself, for this curious child was very fond of pretending to be two people.
'But it's no use now,' thought poor Alice, 'to pretend to be two people!
Why, there's hardly enough of me left to make ONE respectable person!'
Soon her eye fell on a little glass box that was lying under the table: she opened it, and found in it a very small cake, on which the words 'EAT ME' were beautifully marked in currants. 'Well, I'll eat it,' said Alice, 'and if it makes me grow larger, I can reach the key; and if it makes me grow smaller, I can creep under the door; so either way I'll get into the garden, and I don't care which happens!'
She ate a little bit, and said anxiously to herself, 'Which way?
Which way?', holding her hand on the top of her head to feel which way it was growing, and she was quite surprised to find that she remained the same size: to be sure, this generally happens when one eats cake, but Alice had got so much into the way of expecting nothing but out-of-the-way things to happen, that it seemed quite dull and stupid for life to go on in the common way.
So she set to work, and very soon finished off the cake. >
Chapter Il.
The Pool of Tears
'Curiouser and curiouser!' cried Alice (she was so much surprised, that for the moment she quite forgot how to speak good English); 'now I'm opening out like the largest telescope that ever was!
Good-bye, feet!' (for when she looked down at her feet, they seemed to be almost out of sight, they were getting so far off).
'Oh, my poor little feet, I wonder who will put on your shoes and stockings for you now, dears?
I'm sure I shan't be able!
I shall be a great deal too far off to trouble myself about you: you must manage the best way you can;--but I must be kind to them,' thought Alice, 'or perhaps they won't walk the way I want to go!
Let me see: I'll give them a new pair of boots every Christmas.'
And she went on planning to herself how she would manage it.
'They must go by the carrier,' she thought; 'and how funny it'll seem, sending presents to one's own feet!
And how odd the directions will look!
ALlCE'S RlGHT FOOT, ESQ.
HEARTHRUG,
NEAR THE FENDER, (WlTH ALlCE'S LOVE).
Oh dear, what nonsense I'm talking!'
Just then her head struck against the roof of the hall: in fact she was now more than nine feet high, and she at once took up the little golden key and hurried off to the garden door.
It was as much as she could do, lying down on one side, to look through into the garden with one eye; but to get through was more hopeless than ever: she sat down and began to cry again.
'You ought to be ashamed of yourself,' said Alice, 'a great girl like you,' (she might well say this), 'to go on crying in this way!
Stop this moment, I tell you!'
But she went on all the same, shedding gallons of tears, until there was a large pool all round her, about four inches deep and reaching half down the hall.
After a time she heard a little pattering of feet in the distance, and she hastily dried her eyes to see what was coming.
It was the White Rabbit returning, splendidly dressed, with a pair of white kid gloves in one hand and a large fan in the other: he came trotting along in a great hurry, muttering to himself as he came, 'Oh! the Duchess, the Duchess!
Oh! won't she be savage if I've kept her waiting!'
Alice felt so desperate that she was ready to ask help of any one; so, when the Rabbit came near her, she began, in a low, timid voice, 'If you please, sir--' The Rabbit started violently, dropped the white kid gloves and the fan, and skurried away into the darkness as hard as he could go.
Alice took up the fan and gloves, and, as the hall was very hot, she kept fanning herself all the time she went on talking:
'Dear, dear!
How queer everything is to-day!
And yesterday things went on just as usual.
I wonder if I've been changed in the night?
Let me think: was I the same when I got up this morning?
I almost think I can remember feeling a little different.
But if I'm not the same, the next question is, Who in the world am I?
Ah, THAT'S the great puzzle!'
And she began thinking over all the children she knew that were of the same age as herself, to see if she could have been changed for any of them.
'I'm sure I'm not Ada,' she said, 'for her hair goes in such long ringlets, and mine doesn't go in ringlets at all; and I'm sure I can't be Mabel, for I know all sorts of things, and she, oh! she knows such a very little!
Besides, SHE'S she, and I'm I, and--oh dear, how puzzling it all is!
I'll try if I know all the things I used to know.
Let me see: four times five is twelve, and four times six is thirteen, and four times seven is--oh dear!
I shall never get to twenty at that rate!
However, the Multiplication Table doesn't signify: let's try Geography.
London is the capital of Paris, and Paris is the capital of Rome, and Rome--no,
THAT'S all wrong, I'm certain!
I must have been changed for Mabel!
I'll try and say "How doth the little--"' and she crossed her hands on her lap as if she were saying lessons, and began to repeat it, but her voice sounded hoarse and strange, and the words did not come the same as they used to do:--
'How doth the little crocodile Improve his shining tail,
And pour the waters of the Nile On every golden scale!
'How cheerfully he seems to grin, How neatly spread his claws,
And welcome little fishes in With gently smiling jaws!'
'I'm sure those are not the right words,' said poor Alice, and her eyes filled with tears again as she went on, 'I must be Mabel after all, and I shall have to go and live in that poky little house, and have next to no toys to play with, and oh! ever so many lessons to learn!
No, I've made up my mind about it; if I'm Mabel, I'll stay down here!
It'll be no use their putting their heads down and saying "Come up again, dear!"
I shall only look up and say "Who am I then?
Tell me that first, and then, if I like being that person, I'll come up: if not,
I'll stay down here till I'm somebody else"--but, oh dear!' cried Alice, with a sudden burst of tears, 'I do wish they WOULD put their heads down!
I am so VERY tired of being all alone here!'
As she said this she looked down at her hands, and was surprised to see that she had put on one of the Rabbit's little white kid gloves while she was talking.
'How CAN I have done that?' she thought.
'I must be growing small again.'
She got up and went to the table to measure herself by it, and found that, as nearly as she could guess, she was now about two feet high, and was going on shrinking rapidly: she soon found out that the cause of this was the fan she was holding, and she dropped it hastily, just in time to avoid shrinking away altogether.
'That WAS a narrow escape!' said Alice, a good deal frightened at the sudden change, but very glad to find herself still in existence; 'and now for the garden!' and she ran with all speed back to the little door: but, alas! the little door was shut again, and the little golden key was lying on the glass table as before, 'and things are worse than ever,' thought the poor child, 'for I never was so small as this before, never!
And I declare it's too bad, that it is!'
As she said these words her foot slipped, and in another moment, splash! she was up to her chin in salt water.
Her first idea was that she had somehow fallen into the sea, 'and in that case I can go back by railway,' she said to herself.
(Alice had been to the seaside once in her life, and had come to the general conclusion, that wherever you go to on the English coast you find a number of bathing machines in the sea, some children digging in the sand with wooden spades, then a row of lodging houses, and behind them a railway station.)
However, she soon made out that she was in the pool of tears which she had wept when she was nine feet high.
'I wish I hadn't cried so much!' said Alice, as she swam about, trying to find her way out.
'I shall be punished for it now, I suppose, by being drowned in my own tears!
That WlLL be a queer thing, to be sure!
However, everything is queer to-day.'
Just then she heard something splashing about in the pool a little way off, and she swam nearer to make out what it was: at first she thought it must be a walrus or hippopotamus, but then she remembered how small she was now, and she soon made out that it was only a mouse that had slipped in like herself.
'Would it be of any use, now,' thought
Alice, 'to speak to this mouse?
Everything is so out-of-the-way down here, that I should think very likely it can talk: at any rate, there's no harm in trying.'
So she began: 'O Mouse, do you know the way out of this pool?
I am very tired of swimming about here, O Mouse!' (Alice thought this must be the right way of speaking to a mouse: she had never done such a thing before, but she remembered having seen in her brother's Latin Grammar,
'A mouse--of a mouse--to a mouse--a mouse-- O mouse!')
The Mouse looked at her rather inquisitively, and seemed to her to wink with one of its little eyes, but it said nothing.
'Perhaps it doesn't understand English,' thought Alice; 'I daresay it's a French mouse, come over with William the Conqueror.' (For, with all her knowledge of history, Alice had no very clear notion how long ago anything had happened.)
So she began again: 'Ou est ma chatte?' which was the first sentence in her French lesson-book.
The Mouse gave a sudden leap out of the water, and seemed to quiver all over with fright.
'Oh, I beg your pardon!' cried Alice hastily, afraid that she had hurt the poor animal's feelings.
'Not like cats!' cried the Mouse, in a shrill, passionate voice.
'Would YOU like cats if you were me?' 'Well, perhaps not,' said Alice in a soothing tone: 'don't be angry about it.
And yet I wish I could show you our cat Dinah:
I think you'd take a fancy to cats if you could only see her.
She is such a dear quiet thing,' Alice went on, half to herself, as she swam lazily about in the pool, 'and she sits purring so nicely by the fire, licking her paws and washing her face--and she is such a nice soft thing to nurse--and she's such a capital one for catching mice--oh, I beg your pardon!' cried Alice again, for this time the Mouse was bristling all over, and she felt certain it must be really offended.
'We won't talk about her any more if you'd rather not.'
'We indeed!' cried the Mouse, who was trembling down to the end of his tail.
'As if I would talk on such a subject!
Our family always HATED cats: nasty, low, vulgar things!
Don't let me hear the name again!'
'I won't indeed!' said Alice, in a great hurry to change the subject of conversation.
'Are you--are you fond--of--of dogs?'
The Mouse did not answer, so Alice went on eagerly:
'There is such a nice little dog near our house I should like to show you!
A little bright-eyed terrier, you know, with oh, such long curly brown hair!
And it'll fetch things when you throw them, and it'll sit up and beg for its dinner, and all sorts of things--I can't remember half of them--and it belongs to a farmer, you know, and he says it's so useful, it's worth a hundred pounds!
He says it kills all the rats and--oh dear!' cried Alice in a sorrowful tone,
'I'm afraid I've offended it again!'
For the Mouse was swimming away from her as hard as it could go, and making quite a commotion in the pool as it went.
So she called softly after it, 'Mouse dear!
Do come back again, and we won't talk about cats or dogs either, if you don't like them!'
When the Mouse heard this, it turned round and swam slowly back to her: its face was quite pale (with passion, Alice thought), and it said in a low trembling voice, 'Let us get to the shore, and then I'll tell you my history, and you'll understand why it is I hate cats and dogs.'
It was high time to go, for the pool was getting quite crowded with the birds and animals that had fallen into it: there were a Duck and a Dodo, a Lory and an Eaglet, and several other curious creatures.
Alice led the way, and the whole party swam to the shore. >
Chapter ill.
A Caucus-Race and a Long Tale
They were indeed a queer-looking party that assembled on the bank--the birds with draggled feathers, the animals with their fur clinging close to them, and all dripping wet, cross, and uncomfortable.
The first question of course was, how to get dry again: they had a consultation about this, and after a few minutes it seemed quite natural to Alice to find herself talking familiarly with them, as if she had known them all her life.
Indeed, she had quite a long argument with the Lory, who at last turned sulky, and would only say, 'I am older than you, and must know better'; and this Alice would not allow without knowing how old it was, and, as the Lory positively refused to tell its age, there was no more to be said.
At last the Mouse, who seemed to be a person of authority among them, called out,
'Sit down, all of you, and listen to me!
I'LL soon make you dry enough!'
They all sat down at once, in a large ring, with the Mouse in the middle.
Alice kept her eyes anxiously fixed on it, for she felt sure she would catch a bad cold if she did not get dry very soon.
'Ahem!' said the Mouse with an important air, 'are you all ready?
This is the driest thing I know.
Silence all round, if you please!
"William the Conqueror, whose cause was favoured by the pope, was soon submitted to by the English, who wanted leaders, and had been of late much accustomed to usurpation and conquest.
Edwin and Morcar, the earls of Mercia and Northumbria--"'
'Ugh!' said the Lory, with a shiver.
'I beg your pardon!' said the Mouse, frowning, but very politely: 'Did you speak?' 'Not I!' said the Lory hastily.
'I thought you did,' said the Mouse.
'--I proceed.
"Edwin and Morcar, the earls of Mercia and
Northumbria, declared for him: and even Stigand, the patriotic archbishop of
Canterbury, found it advisable--"'
'Found WHAT?' said the Duck.
'Found IT,' the Mouse replied rather crossly: 'of course you know what "it" means.'
The question is, what did the archbishop find?'
The Mouse did not notice this question, but hurriedly went on, '"--found it advisable to go with Edgar Atheling to meet William and offer him the crown.
William's conduct at first was moderate.
But the insolence of his Normans--" How are you getting on now, my dear?' it continued, turning to Alice as it spoke.
'As wet as ever,' said Alice in a melancholy tone: 'it doesn't seem to dry me at all.'
'In that case,' said the Dodo solemnly, rising to its feet, 'I move that the meeting adjourn, for the immediate adoption of more energetic remedies--'
'Speak English!' said the Eaglet.
'I don't know the meaning of half those long words, and, what's more, I don't believe you do either!'
And the Eaglet bent down its head to hide a smile: some of the other birds tittered audibly.
'What I was going to say,' said the Dodo in an offended tone, 'was, that the best thing to get us dry would be a Caucus-race.'
'What IS a Caucus-race?' said Alice; not that she wanted much to know, but the Dodo had paused as if it thought that SOMEBODY ought to speak, and no one else seemed inclined to say anything.
'Why,' said the Dodo, 'the best way to explain it is to do it.'
(And, as you might like to try the thing yourself, some winter day, I will tell you how the Dodo managed it.)
First it marked out a race-course, in a sort of circle, ('the exact shape doesn't matter,' it said,) and then all the party were placed along the course, here and there.
There was no 'One, two, three, and away,' but they began running when they liked, and left off when they liked, so that it was not easy to know when the race was over.
However, when they had been running half an hour or so, and were quite dry again, the
Dodo suddenly called out 'The race is over!' and they all crowded round it, panting, and asking, 'But who has won?'
This question the Dodo could not answer without a great deal of thought, and it sat for a long time with one finger pressed upon its forehead (the position in which you usually see Shakespeare, in the pictures of him), while the rest waited in silence.
At last the Dodo said, 'EVERYBODY has won, and all must have prizes.'
'But who is to give the prizes?' quite a chorus of voices asked.
'Why, SHE, of course,' said the Dodo, pointing to Alice with one finger; and the whole party at once crowded round her, calling out in a confused way, 'Prizes!
Prizes!'
Alice had no idea what to do, and in despair she put her hand in her pocket, and pulled out a box of comfits, (luckily the salt water had not got into it), and handed them round as prizes.
There was exactly one a-piece all round.
'But she must have a prize herself, you know,' said the Mouse.
'Of course,' the Dodo replied very gravely.
'What else have you got in your pocket?' he went on, turning to Alice.
'Only a thimble,' said Alice sadly.
'Hand it over here,' said the Dodo.
Then they all crowded round her once more, while the Dodo solemnly presented the thimble, saying 'We beg your acceptance of this elegant thimble'; and, when it had finished this short speech, they all cheered.
Alice thought the whole thing very absurd, but they all looked so grave that she did not dare to laugh; and, as she could not think of anything to say, she simply bowed, and took the thimble, looking as solemn as she could.
The next thing was to eat the comfits: this caused some noise and confusion, as the large birds complained that they could not taste theirs, and the small ones choked and had to be patted on the back.
However, it was over at last, and they sat down again in a ring, and begged the Mouse to tell them something more.
'You promised to tell me your history, you know,' said Alice, 'and why it is you hate-
-C and D,' she added in a whisper, half afraid that it would be offended again.
'Mine is a long and a sad tale!' said the Mouse, turning to Alice, and sighing.
'It IS a long tail, certainly,' said Alice, looking down with wonder at the Mouse's tail; 'but why do you call it sad?'
And she kept on puzzling about it while the Mouse was speaking, so that her idea of the tale was something like this:--
'Fury said to a mouse, That he met in the house,
"Let us both go to law:
I will prosecute YOU.--Come,
I'll take no denial; We must have a trial:
For really this morning I've nothing to do."
Said the mouse to the cur, "Such a trial, dear Sir,
With no jury or judge, would be wasting our breath."
"I'll be judge, I'll be jury,"
Said cunning old Fury:
"I'll try the whole cause, and condemn you to death."'
'You are not attending!' said the Mouse to Alice severely.
'What are you thinking of?'
'I beg your pardon,' said Alice very humbly: 'you had got to the fifth bend, I think?' 'I had NOT!' cried the Mouse, sharply and very angrily.
'A knot!' said Alice, always ready to make herself useful, and looking anxiously about her.
'Oh, do let me help to undo it!'
'I shall do nothing of the sort,' said the Mouse, getting up and walking away.
'You insult me by talking such nonsense!' 'I didn't mean it!' pleaded poor Alice.
'But you're so easily offended, you know!'
The Mouse only growled in reply.
'Please come back and finish your story!'
Alice called after it; and the others all joined in chorus, 'Yes, please do!' but the
Mouse only shook its head impatiently, and walked a little quicker.
'What a pity it wouldn't stay!' sighed the Lory, as soon as it was quite out of sight; and an old Crab took the opportunity of saying to her daughter 'Ah, my dear!
Let this be a lesson to you never to lose YOUR temper!'
'Hold your tongue, Ma!' said the young Crab, a little snappishly.
'You're enough to try the patience of an oyster!'
'I wish I had our Dinah here, I know I do!' said Alice aloud, addressing nobody in particular.
'She'd soon fetch it back!' 'And who is Dinah, if I might venture to ask the question?' said the Lory.
Alice replied eagerly, for she was always ready to talk about her pet: 'Dinah's our cat.
And she's such a capital one for catching mice you can't think!
And oh, I wish you could see her after the birds!
Why, she'll eat a little bird as soon as look at it!'
This speech caused a remarkable sensation among the party.
Some of the birds hurried off at once: one old Magpie began wrapping itself up very carefully, remarking, 'I really must be getting home; the night-air doesn't suit my throat!' and a Canary called out in a trembling voice to its children, 'Come away, my dears!
It's high time you were all in bed!'
On various pretexts they all moved off, and
Alice was soon left alone.
'I wish I hadn't mentioned Dinah!' she said to herself in a melancholy tone.
'Nobody seems to like her, down here, and I'm sure she's the best cat in the world!
Oh, my dear Dinah!
I wonder if I shall ever see you any more!'
And here poor Alice began to cry again, for she felt very lonely and low-spirited.
In a little while, however, she again heard a little pattering of footsteps in the distance, and she looked up eagerly, half hoping that the Mouse had changed his mind, and was coming back to finish his story. >
Chapter IV.
The Rabbit Sends in a Little Bill
It was the White Rabbit, trotting slowly back again, and looking anxiously about as it went, as if it had lost something; and she heard it muttering to itself 'The
Duchess!
The Duchess!
Oh my dear paws!
Oh my fur and whiskers! She'll get me executed, as sure as ferrets are ferrets!
Where CAN I have dropped them, I wonder?'
Alice guessed in a moment that it was looking for the fan and the pair of white kid gloves, and she very good-naturedly began hunting about for them, but they were nowhere to be seen--everything seemed to have changed since her swim in the pool, and the great hall, with the glass table and the little door, had vanished completely.
Very soon the Rabbit noticed Alice, as she went hunting about, and called out to her in an angry tone, 'Why, Mary Ann, what ARE you doing out here?
Run home this moment, and fetch me a pair of gloves and a fan!
Quick, now!'
And Alice was so much frightened that she ran off at once in the direction it pointed to, without trying to explain the mistake it had made.
'He took me for his housemaid,' she said to herself as she ran.
'How surprised he'll be when he finds out who I am!
But I'd better take him his fan and gloves- -that is, if I can find them.'
As she said this, she came upon a neat little house, on the door of which was a bright brass plate with the name 'W.
RABBlT' engraved upon it.
She went in without knocking, and hurried upstairs, in great fear lest she should meet the real Mary Ann, and be turned out of the house before she had found the fan and gloves.
'How queer it seems,' Alice said to herself, 'to be going messages for a rabbit!
I suppose Dinah'll be sending me on messages next!'
And she began fancying the sort of thing that would happen: '"Miss Alice!
Come here directly, and get ready for your walk!"
"Coming in a minute, nurse!
But I've got to see that the mouse doesn't get out."
Only I don't think,' Alice went on, 'that they'd let Dinah stop in the house if it began ordering people about like that!'
By this time she had found her way into a tidy little room with a table in the window, and on it (as she had hoped) a fan and two or three pairs of tiny white kid gloves: she took up the fan and a pair of the gloves, and was just going to leave the room, when her eye fell upon a little bottle that stood near the looking-glass.
There was no label this time with the words 'DRlNK ME,' but nevertheless she uncorked it and put it to her lips.
'I know SOMETHlNG interesting is sure to happen,' she said to herself, 'whenever I eat or drink anything; so I'll just see what this bottle does.
I do hope it'll make me grow large again, for really I'm quite tired of being such a tiny little thing!'
It did so indeed, and much sooner than she had expected: before she had drunk half the bottle, she found her head pressing against the ceiling, and had to stoop to save her neck from being broken.
She hastily put down the bottle, saying to herself 'That's quite enough--I hope I shan't grow any more--As it is, I can't get out at the door--I do wish I hadn't drunk quite so much!'
Alas! it was too late to wish that!
She went on growing, and growing, and very soon had to kneel down on the floor: in another minute there was not even room for this, and she tried the effect of lying down with one elbow against the door, and the other arm curled round her head.
Still she went on growing, and, as a last resource, she put one arm out of the window, and one foot up the chimney, and said to herself 'Now I can do no more, whatever happens.
What WlLL become of me?'
Luckily for Alice, the little magic bottle had now had its full effect, and she grew no larger: still it was very uncomfortable, and, as there seemed to be no sort of chance of her ever getting out of the room again, no wonder she felt unhappy.
'It was much pleasanter at home,' thought poor Alice, 'when one wasn't always growing
larger and smaller, and being ordered about by mice and rabbits.
I almost wish I hadn't gone down that rabbit-hole--and yet--and yet--it's rather curious, you know, this sort of life!
I do wonder what CAN have happened to me!
When I used to read fairy-tales, I fancied that kind of thing never happened, and now here I am in the middle of one!
There ought to be a book written about me, that there ought!
And when I grow up, I'll write one--but I'm grown up now,' she added in a sorrowful tone; 'at least there's no room to grow up any more HERE.'
'But then,' thought Alice, 'shall I NEVER get any older than I am now?
That'll be a comfort, one way--never to be an old woman--but then--always to have lessons to learn!
Oh, I shouldn't like THAT!' 'Oh, you foolish Alice!' she answered herself.
'How can you learn lessons in here?
Why, there's hardly room for YOU, and no room at all for any lesson-books!'
And so she went on, taking first one side and then the other, and making quite a conversation of it altogether; but after a few minutes she heard a voice outside, and stopped to listen.
'Mary Ann!
Mary Ann!' said the voice.
Then came a little pattering of feet on the stairs.
Alice knew it was the Rabbit coming to look for her, and she trembled till she shook the house, quite forgetting that she was now about a thousand times as large as the
Rabbit, and had no reason to be afraid of it.
Presently the Rabbit came up to the door, and tried to open it; but, as the door opened inwards, and Alice's elbow was pressed hard against it, that attempt proved a failure.
Alice heard it say to itself 'Then I'll go round and get in at the window.'
'THAT you won't' thought Alice, and, after waiting till she fancied she heard the
Rabbit just under the window, she suddenly spread out her hand, and made a snatch in the air.
She did not get hold of anything, but she heard a little shriek and a fall, and a crash of broken glass, from which she concluded that it was just possible it had fallen into a cucumber-frame, or something of the sort.
Next came an angry voice--the Rabbit's-- 'Pat!
Pat!
Where are you?'
And then a voice she had never heard before, 'Sure then I'm here!
Digging for apples, yer honour!'
'Digging for apples, indeed!' said the Rabbit angrily.
'Here! Come and help me out of THlS!' (Sounds of more broken glass.)
'Now tell me, Pat, what's that in the window?'
'Sure, it's an arm, yer honour!' (He pronounced it 'arrum.')
'An arm, you goose!
Who ever saw one that size?
Why, it fills the whole window!'
'Sure, it does, yer honour: but it's an arm for all that.'
'Well, it's got no business there, at any rate: go and take it away!'
There was a long silence after this, and Alice could only hear whispers now and then; such as, 'Sure, I don't like it, yer honour, at all, at all!'
'Do as I tell you, you coward!' and at last she spread out her hand again, and made another snatch in the air.
This time there were TWO little shrieks, and more sounds of broken glass.
'What a number of cucumber-frames there must be!' thought Alice.
'I wonder what they'll do next!
As for pulling me out of the window, I only wish they COULD!
I'm sure I don't want to stay in here any longer!'
She waited for some time without hearing anything more: at last came a rumbling of little cartwheels, and the sound of a good many voices all talking together: she made out the words:
'Where's the other ladder?
--Why, I hadn't to bring but one; Bill's got the other--Bill! fetch it here, lad!
--Here, put 'em up at this corner--No, tie 'em together first--they don't reach half high enough yet--Oh! they'll do well enough; don't be particular--Here, Bill! catch hold of this rope--Will the roof bear?
--Mind that loose slate--Oh, it's coming down!
Heads below!' (a loud crash)--'Now, who did that?
--It was Bill, I fancy--Who's to go down the chimney?
--Nay, I shan't!
YOU do it!
--That I won't, then!
So Bill's got to come down the chimney, has he?' said Alice to herself.
'Shy, they seem to put everything upon Bill!
I wouldn't be in Bill's place for a good deal: this fireplace is narrow, to be sure; but I THlNK I can kick a little!'
She drew her foot as far down the chimney as she could, and waited till she heard a little animal (she couldn't guess of what sort it was) scratching and scrambling about in the chimney close above her: then, saying to herself 'This is Bill,' she gave one sharp kick, and waited to see what would happen next.
The first thing she heard was a general chorus of 'There goes Bill!' then the
Rabbit's voice along--'Catch him, you by the hedge!' then silence, and then another confusion of voices--'Hold up his head--
Brandy now--Don't choke him--How was it, old fellow?
What happened to you?
Tell us all about it!'
Last came a little feeble, squeaking voice, ('That's Bill,' thought Alice,) 'Well, I hardly know--No more, thank ye; I'm better now--but I'm a deal too flustered to tell you--all I know is, something comes at me like a Jack-in-the-box, and up I goes like a sky-rocket!'
'So you did, old fellow!' said the others.
'We must burn the house down!' said the Rabbit's voice; and Alice called out as If they had any sense, they'd take the roof off.'
I'll set Dinah at you!'
There was a dead silence instantly, and Alice thought to herself, 'I wonder what they WlLL do next!
After a minute or two, they began moving about again, and Alice heard the Rabbit say, 'A barrowful will do, to begin with.'
'A barrowful of WHAT?' thought Alice; but she had not long to doubt, for the next moment a shower of little pebbles came rattling in at the window, and some of them hit her in the face.
'I'll put a stop to this,' she said to herself, and shouted out, 'You'd better not do that again!' which produced another dead silence.
Alice noticed with some surprise that the pebbles were all turning into little cakes as they lay on the floor, and a bright idea came into her head.
'If I eat one of these cakes,' she thought, 'it's sure to make SOME change in my size; and as it can't possibly make me larger, it must make me smaller, I suppose.'
So she swallowed one of the cakes, and was delighted to find that she began shrinking directly.
As soon as she was small enough to get through the door, she ran out of the house, and found quite a crowd of little animals and birds waiting outside.
The poor little Lizard, Bill, was in the middle, being held up by two guinea-pigs, who were giving it something out of a bottle.
They all made a rush at Alice the moment she appeared; but she ran off as hard as she could, and soon found herself safe in a thick wood.
'The first thing I've got to do,' said Alice to herself, as she wandered about in the wood, 'is to grow to my right size again; and the second thing is to find my way into that lovely garden.
I think that will be the best plan.'
It sounded an excellent plan, no doubt, and very neatly and simply arranged; the only difficulty was, that she had not the smallest idea how to set about it; and while she was peering about anxiously among the trees, a little sharp bark just over her head made her look up in a great hurry.
An enormous puppy was looking down at her with large round eyes, and feebly stretching out one paw, trying to touch her.
'Poor little thing!' said Alice, in a coaxing tone, and she tried hard to whistle to it; but she was terribly frightened all the time at the thought that it might be hungry, in which case it would be very
likely to eat her up in spite of all her coaxing.
Hardly knowing what she did, she picked up a little bit of stick, and held it out to the puppy; whereupon the puppy jumped into the air off all its feet at once, with a yelp of delight, and rushed at the stick, and made believe to worry it; then Alice dodged behind a great thistle, to keep herself from being run over; and the moment she appeared on the other side, the puppy made another rush at the stick, and tumbled head over heels in its hurry to get hold of it; then Alice, thinking it was very like having a game of play with a cart-horse, and expecting every moment to be trampled under its feet, ran round the thistle again; then the puppy began a series of short charges at the stick, running a very little way forwards each time and a long way back, and barking hoarsely all the while, till at last it sat down a good way off, panting, with its tongue hanging out of its mouth, and its great eyes half shut.
This seemed to Alice a good opportunity for making her escape; so she set off at once, and ran till she was quite tired and out of breath, and till the puppy's bark sounded quite faint in the distance.
'And yet what a dear little puppy it was!' said Alice, as she leant against a buttercup to rest herself, and fanned herself with one of the leaves:
'I should have liked teaching it tricks very much, if--if I'd only been the right size to do it!
I'd nearly forgotten that I've got to grow up again!
Let me see--how IS it to be managed?
I suppose I ought to eat or drink something or other; but the great question is, what?' The great question certainly was, what?
Alice looked all round her at the flowers and the blades of grass, but she did not see anything that looked like the right thing to eat or drink under the circumstances.
There was a large mushroom growing near her, about the same height as herself; and when she had looked under it, and on both sides of it, and behind it, it occurred to her that she might as well look and see what was on the top of it.
She stretched herself up on tiptoe, and peeped over the edge of the mushroom, and her eyes immediately met those of a large caterpillar, that was sitting on the top with its arms folded, quietly smoking a long hookah, and taking not the smallest notice of her or of anything else. >
Chapter V. Advice from a Caterpillar
The Caterpillar and Alice looked at each other for some time in silence: at last the
Caterpillar took the hookah out of its mouth, and addressed her in a languid, sleepy voice.
'Who are YOU?' said the Caterpillar.
This was not an encouraging opening for a conversation.
Alice replied, rather shyly, 'I--I hardly know, sir, just at present--at least I know who I WAS when I got up this morning, but I think I must have been changed several times since then.'
'What do you mean by that?' said the Caterpillar sternly.
'Explain yourself!'
'I can't explain MYSELF, I'm afraid, sir' said Alice, 'because I'm not myself, you see.' 'I don't see,' said the Caterpillar.
'I'm afraid I can't put it more clearly,' Alice replied very politely, 'for I can't understand it myself to begin with; and being so many different sizes in a day is very confusing.'
'It isn't,' said the Caterpillar.
'Well, perhaps you haven't found it so yet,' said Alice; 'but when you have to turn into a chrysalis--you will some day, you know--and then after that into a butterfly, I should think you'll feel it a little queer, won't you?'
'Not a bit,' said the Caterpillar.
'Well, perhaps your feelings may be different,' said Alice; 'all I know is, it would feel very queer to ME.' 'You!' said the Caterpillar contemptuously.
'Who are YOU?'
Which brought them back again to the beginning of the conversation.
Alice felt a little irritated at the Caterpillar's making such VERY short remarks, and she drew herself up and said, very gravely, 'I think, you ought to tell me who YOU are, first.'
'Why?' said the Caterpillar.
Here was another puzzling question; and as Alice could not think of any good reason, and as the Caterpillar seemed to be in a VERY unpleasant state of mind, she turned away.
'Come back!' the Caterpillar called after her.
'I've something important to say!' This sounded promising, certainly:
Alice turned and came back again.
'Keep your temper,' said the Caterpillar.
'Is that all?' said Alice, swallowing down her anger as well as she could.
'No,' said the Caterpillar.
Alice thought she might as well wait, as she had nothing else to do, and perhaps after all it might tell her something worth hearing.
For some minutes it puffed away without speaking, but at last it unfolded its arms, took the hookah out of its mouth again, and said, 'So you think you're changed, do you?'
'I'm afraid I am, sir,' said Alice; 'I can't remember things as I used--and I don't keep the same size for ten minutes together!'
'Can't remember WHAT things?' said the Caterpillar.
'Well, I've tried to say "HOW DOTH THE LlTTLE BUSY BEE," but it all came different!'
Alice replied in a very melancholy voice.
'Repeat, "YOU ARE OLD, FATHER WlLLlAM,"' said the Caterpillar.
Alice folded her hands, and began:-- 'You are old, Father William,' the young man said, 'And your hair has become very white;
And yet you incessantly stand on your head--
Do you think, at your age, it is right?'
'In my youth,' Father William replied to his son,
I feared it might injure the brain;
But, now that I'm perfectly sure I have none,
Why, I do it again and again.'
'You are old,' said the youth, 'as I mentioned before,
And have grown most uncommonly fat;
Yet you turned a back-somersault in at the door--
Pray, what is the reason of that?'
'In my youth,' said the sage, as he shook his grey locks,
'I kept all my limbs very supple
By the use of this ointment-- one shilling the box--
Allow me to sell you a couple?'
'You are old,' said the youth, 'and your jaws are too weak
For anything tougher than suet;
Yet you finished the goose, with the bones and the beak--
Pray how did you manage to do it?'
'In my youth,' said his father, 'I took to the law,
And argued each case with my wife;
And the muscular strength, which it gave to my jaw,
Has lasted the rest of my life.'
'You are old,' said the youth, 'one would hardly suppose
That your eye was as steady as ever;
Yet you balanced an eel on the end of your nose--
What made you so awfully clever?'
'I have answered three questions, and that is enough,'
Said his father; 'don't give yourself airs!
Do you think I can listen all day to such stuff?
Be off, or I'll kick you down stairs!'
'That is not said right,' said the Caterpillar.
'Not QUlTE right, I'm afraid,' said Alice, timidly; 'some of the words have got altered.'
'It is wrong from beginning to end,' said the Caterpillar decidedly, and there was silence for some minutes.
The Caterpillar was the first to speak.
'What size do you want to be?' it asked.
'Oh, I'm not particular as to size,' Alice hastily replied; 'only one doesn't like changing so often, you know.' 'I DON'T know,' said the Caterpillar.
Alice said nothing: she had never been so much contradicted in her life before, and she felt that she was losing her temper.
'Are you content now?' said the
Caterpillar.
'Well, I should like to be a LlTTLE larger, sir, if you wouldn't mind,' said Alice: 'three inches is such a wretched height to be.'
'It is a very good height indeed!' said the Caterpillar angrily, rearing itself upright as it spoke (it was exactly three inches high).
'But I'm not used to it!' pleaded poor Alice in a piteous tone.
And she thought of herself, 'I wish the creatures wouldn't be so easily offended!'
'You'll get used to it in time,' said the Caterpillar; and it put the hookah into its mouth and began smoking again.
This time Alice waited patiently until it chose to speak again.
In a minute or two the Caterpillar took the hookah out of its mouth and yawned once or twice, and shook itself.
Then it got down off the mushroom, and crawled away in the grass, merely remarking as it went, 'One side will make you grow taller, and the other side will make you grow shorter.'
The other side of WHAT?' thought Alice to herself.
'Of the mushroom,' said the Caterpillar, just as if she had asked it aloud; and in another moment it was out of sight.
Alice remained looking thoughtfully at the mushroom for a minute, trying to make out which were the two sides of it; and as it was perfectly round, she found this a very difficult question.
However, at last she stretched her arms round it as far as they would go, and broke off a bit of the edge with each hand.
'And now which is which?' she said to herself, and nibbled a little of the right- hand bit to try the effect: the next moment she felt a violent blow underneath her chin: it had struck her foot!
She was a good deal frightened by this very sudden change, but she felt that there was no time to be lost, as she was shrinking rapidly; so she set to work at once to eat some of the other bit.
Her chin was pressed so closely against her foot, that there was hardly room to open her mouth; but she did it at last, and managed to swallow a morsel of the lefthand bit.
'Come, my head's free at last!' said Alice in a tone of delight, which changed into alarm in another moment, when she found that her shoulders were nowhere to be found: all she could see, when she looked down, was an immense length of neck, which seemed to rise like a stalk out of a sea of green leaves that lay far below her.
'What CAN all that green stuff be?' said And oh, my poor hands, how is it I can't see you?'
'And where HAVE my shoulders got to?
She was moving them about as she spoke, but no result seemed to follow, except a little shaking among the distant green leaves.
As there seemed to be no chance of getting her hands up to her head, she tried to get her head down to them, and was delighted to find that her neck would bend about easily in any direction, like a serpent.
She had just succeeded in curving it down into a graceful zigzag, and was going to dive in among the leaves, which she found to be nothing but the tops of the trees under which she had been wandering, when a sharp hiss made her draw back in a hurry: a large pigeon had flown into her face, and was beating her violently with its wings.
'Serpent!' screamed the Pigeon.
'I'm NOT a serpent!' said Alice indignantly.
'Let me alone!'
'Serpent, I say again!' repeated the Pigeon, but in a more subdued tone, and added with a kind of sob, 'I've tried every way, and nothing seems to suit them!'
'I haven't the least idea what you're talking about,' said Alice.
'I've tried the roots of trees, and I've tried banks, and I've tried hedges,' the
Pigeon went on, without attending to her; 'but those serpents!
There's no pleasing them!'
Alice was more and more puzzled, but she thought there was no use in saying anything more till the Pigeon had finished.
'As if it wasn't trouble enough hatching the eggs,' said the Pigeon; 'but I must be on the look-out for serpents night and day! Why, I haven't had a wink of sleep these three weeks!'
'I'm very sorry you've been annoyed,' said Alice, who was beginning to see its meaning.
'And just as I'd taken the highest tree in the wood,' continued the Pigeon, raising its voice to a shriek, 'and just as I was thinking I should be free of them at last, they must needs come wriggling down from the sky!
Ugh, Serpent!' 'But I'm NOT a serpent, I tell you!' said
Alice.
'I'm a--I'm a--' 'Well!
WHAT are you?' said the Pigeon.
'I can see you're trying to invent something!'
'I--I'm a little girl,' said Alice, rather doubtfully, as she remembered the number of changes she had gone through that day.
'A likely story indeed!' said the Pigeon in a tone of the deepest contempt.
'I've seen a good many little girls in my time, but never ONE with such a neck as that!
No, no!
You're a serpent; and there's no use denying it.
I suppose you'll be telling me next that you never tasted an egg!'
'I HAVE tasted eggs, certainly,' said Alice, who was a very truthful child; 'but little girls eat eggs quite as much as serpents do, you know.'
'I don't believe it,' said the Pigeon; 'but if they do, why then they're a kind of serpent, that's all I can say.'
This was such a new idea to Alice, that she was quite silent for a minute or two, which gave the Pigeon the opportunity of adding, 'You're looking for eggs, I know THAT well enough; and what does it matter to me whether you're a little girl or a serpent?'
'It matters a good deal to ME,' said Alice hastily; 'but I'm not looking for eggs, as it happens; and if I was, I shouldn't want YOURS: I don't like them raw.' 'Well, be off, then!' said the Pigeon in a sulky tone, as it settled down again into its nest.
Alice crouched down among the trees as well as she could, for her neck kept getting entangled among the branches, and every now and then she had to stop and untwist it.
After a while she remembered that she still held the pieces of mushroom in her hands, and she set to work very carefully, nibbling first at one and then at the other, and growing sometimes taller and sometimes shorter, until she had succeeded in bringing herself down to her usual height.
It was so long since she had been anything near the right size, that it felt quite strange at first; but she got used to it in a few minutes, and began talking to herself, as usual.
'Come, there's half my plan done now!
How puzzling all these changes are!
I'm never sure what I'm going to be, from one minute to another!
However, I've got back to my right size: the next thing is, to get into that beautiful garden--how IS that to be done, I wonder?'
As she said this, she came suddenly upon an open place, with a little house in it about four feet high.
'Whoever lives there,' thought Alice, 'it'll never do to come upon them THlS size: why, I should frighten them out of their wits!'
So she began nibbling at the righthand bit again, and did not venture to go near the house till she had brought herself down to nine inches high. >
Chapter Vl.
Pig and Pepper
For a minute or two she stood looking at the house, and wondering what to do next, when suddenly a footman in livery came running out of the wood--(she considered him to be a footman because he was in livery: otherwise, judging by his face only, she would have called him a fish)-- and rapped loudly at the door with his knuckles.
It was opened by another footman in livery, with a round face, and large eyes like a frog; and both footmen, Alice noticed, had powdered hair that curled all over their heads.
She felt very curious to know what it was all about, and crept a little way out of the wood to listen.
The Fish-Footman began by producing from under his arm a great letter, nearly as large as himself, and this he handed over to the other, saying, in a solemn tone,
'For the Duchess.
An invitation from the Queen to play croquet.'
The Frog-Footman repeated, in the same solemn tone, only changing the order of the words a little, 'From the Queen.
An invitation for the Duchess to play croquet.'
Then they both bowed low, and their curls got entangled together.
Alice laughed so much at this, that she had to run back into the wood for fear of their hearing her; and when she next peeped out the Fish-Footman was gone, and the other was sitting on the ground near the door, staring stupidly up into the sky.
Alice went timidly up to the door, and knocked.
'There's no sort of use in knocking,' said the Footman, 'and that for two reasons.
First, because I'm on the same side of the door as you are; secondly, because they're making such a noise inside, no one could possibly hear you.'
And certainly there was a most extraordinary noise going on within--a constant howling and sneezing, and every now and then a great crash, as if a dish or kettle had been broken to pieces.
'Please, then,' said Alice, 'how am I to get in?'
'There might be some sense in your knocking,' the Footman went on without attending to her, 'if we had the door between us.
For instance, if you were INSlDE, you might knock, and I could let you out, you know.'
He was looking up into the sky all the time he was speaking, and this Alice thought decidedly uncivil.
'But perhaps he can't help it,' she said to herself; 'his eyes are so VERY nearly at the top of his head.
But at any rate he might answer questions.
--How am I to get in?' she repeated, aloud.
'I shall sit here,' the Footman remarked, 'till tomorrow--'
At this moment the door of the house opened, and a large plate came skimming out, straight at the Footman's head: it just grazed his nose, and broke to pieces against one of the trees behind him. '--or next day, maybe,' the Footman continued in the same tone, exactly as if nothing had happened.
'How am I to get in?' asked Alice again, in a louder tone.
'ARE you to get in at all?' said the Footman.
'That's the first question, you know.'
It was, no doubt: only Alice did not like to be told so.
'It's really dreadful,' she muttered to herself, 'the way all the creatures argue.
It's enough to drive one crazy!'
The Footman seemed to think this a good opportunity for repeating his remark, with variations. 'I shall sit here,' he said, 'on and off, for days and days.'
'But what am I to do?' said Alice.
'Anything you like,' said the Footman, and began whistling.
'Oh, there's no use in talking to him,' said Alice desperately: 'he's perfectly idiotic!'
And she opened the door and went in.
The door led right into a large kitchen, which was full of smoke from one end to the other: the Duchess was sitting on a three- legged stool in the middle, nursing a baby; the cook was leaning over the fire, stirring a large cauldron which seemed to be full of soup.
'There's certainly too much pepper in that soup!'
Alice said to herself, as well as she could for sneezing.
There was certainly too much of it in the air.
Even the Duchess sneezed occasionally; and as for the baby, it was sneezing and howling alternately without a moment's pause.
The only things in the kitchen that did not sneeze, were the cook, and a large cat which was sitting on the hearth and grinning from ear to ear.
'Please would you tell me,' said Alice, a little timidly, for she was not quite sure whether it was good manners for her to speak first, 'why your cat grins like that?'
'It's a Cheshire cat,' said the Duchess, 'and that's why.
Pig!'
She said the last word with such sudden violence that Alice quite jumped; but she saw in another moment that it was addressed to the baby, and not to her, so she took courage, and went on again:--
'I didn't know that Cheshire cats always grinned; in fact, I didn't know that cats
'They all can,' said the Duchess; 'and most of 'em do.'
'I don't know of any that do,' Alice said very politely, feeling quite pleased to have got into a conversation.
'You don't know much,' said the Duchess;
'and that's a fact.'
Alice did not at all like the tone of this remark, and thought it would be as well to introduce some other subject of conversation.
While she was trying to fix on one, the cook took the cauldron of soup off the fire, and at once set to work throwing everything within her reach at the Duchess and the baby--the fire-irons came first; then followed a shower of saucepans, plates, and dishes.
The Duchess took no notice of them even when they hit her; and the baby was howling so much already, that it was quite impossible to say whether the blows hurt it or not.
'Oh, PLEASE mind what you're doing!' cried Alice, jumping up and down in an agony of terror.
'Oh, there goes his PREClOUS nose'; as an unusually large saucepan flew close by it, and very nearly carried it off.
'If everybody minded their own business,' the Duchess said in a hoarse growl, 'the world would go round a deal faster than it does.'
'Which would NOT be an advantage,' said Alice, who felt very glad to get an opportunity of showing off a little of her knowledge.
'Just think of what work it would make with the day and night!
You see the earth takes twenty-four hours to turn round on its axis--'
'Talking of axes,' said the Duchess, 'chop off her head!'
Alice glanced rather anxiously at the cook, to see if she meant to take the hint; but the cook was busily stirring the soup, and seemed not to be listening, so she went on again:
'Twenty-four hours, I THlNK; or is it twelve?
I--' 'Oh, don't bother ME,' said the Duchess; 'I never could abide figures!'
And with that she began nursing her child again, singing a sort of lullaby to it as she did so, and giving it a violent shake at the end of every line:
'Speak roughly to your little boy, And beat him when he sneezes:
He only does it to annoy, Because he knows it teases.'
CHORUS.
(In which the cook and the baby joined):
'Wow! wow! wow!'
While the Duchess sang the second verse of the song, she kept tossing the baby violently up and down, and the poor little thing howled so, that Alice could hardly hear the words:--
'I speak severely to my boy, I beat him when he sneezes;
For he can thoroughly enjoy The pepper when he pleases!'
CHORUS.
'Wow! wow! wow!'
'Here! you may nurse it a bit, if you like!' the Duchess said to Alice, flinging the baby at her as she spoke.
'I must go and get ready to play croquet with the Queen,' and she hurried out of the room.
The cook threw a frying-pan after her as she went out, but it just missed her.
Alice caught the baby with some difficulty, as it was a queer-shaped little creature, and held out its arms and legs in all directions, 'just like a star-fish,' thought Alice.
The poor little thing was snorting like a steam-engine when she caught it, and kept doubling itself up and straightening itself out again, so that altogether, for the first minute or two, it was as much as she could do to hold it.
As soon as she had made out the proper way of nursing it, (which was to twist it up into a sort of knot, and then keep tight hold of its right ear and left foot, so as to prevent its undoing itself,) she carried it out into the open air.
'IF I don't take this child away with me,' thought Alice, 'they're sure to kill it in a day or two: wouldn't it be murder to leave it behind?'
She said the last words out loud, and the little thing grunted in reply (it had left off sneezing by this time).
'Don't grunt,' said Alice; 'that's not at all a proper way of expressing yourself.'
The baby grunted again, and Alice looked very anxiously into its face to see what was the matter with it.
There could be no doubt that it had a VERY turn-up nose, much more like a snout than a real nose; also its eyes were getting extremely small for a baby: altogether
Alice did not like the look of the thing at all.
'But perhaps it was only sobbing,' she thought, and looked into its eyes again, to see if there were any tears.
No, there were no tears.
'If you're going to turn into a pig, my dear,' said Alice, seriously, 'I'll have nothing more to do with you.
Mind now!'
The poor little thing sobbed again (or grunted, it was impossible to say which), and they went on for some while in silence.
Alice was just beginning to think to herself, 'Now, what am I to do with this creature when I get it home?' when it grunted again, so violently, that she looked down into its face in some alarm.
This time there could be NO mistake about it: it was neither more nor less than a pig, and she felt that it would be quite absurd for her to carry it further.
So she set the little creature down, and felt quite relieved to see it trot away quietly into the wood.
'If it had grown up,' she said to herself, 'it would have made a dreadfully ugly child: but it makes rather a handsome pig, I think.'
And she began thinking over other children she knew, who might do very well as pigs, and was just saying to herself, 'if one only knew the right way to change them--' when she was a little startled by seeing the Cheshire Cat sitting on a bough of a tree a few yards off.
The Cat only grinned when it saw Alice.
It looked good-natured, she thought: still it had VERY long claws and a great many teeth, so she felt that it ought to be treated with respect.
'Cheshire Puss,' she began, rather timidly, as she did not at all know whether it would
like the name: however, it only grinned a little wider.
'Come, it's pleased so far,' thought Alice, and she went on.
'Would you tell me, please, which way I ought to go from here?'
'That depends a good deal on where you want to get to,' said the Cat.
'I don't much care where--' said Alice.
'Then it doesn't matter which way you go,' said the Cat. '--so long as I get SOMEWHERE,' Alice added as an explanation.
'Oh, you're sure to do that,' said the Cat, 'if you only walk long enough.'
Alice felt that this could not be denied, so she tried another question.
'What sort of people live about here?'
'In THAT direction,' the Cat said, waving its right paw round, 'lives a Hatter: and in THAT direction,' waving the other paw, 'lives a March Hare.
Visit either you like: they're both mad.'
'But I don't want to go among mad people,' Alice remarked.
'Oh, you can't help that,' said the Cat: 'we're all mad here.
I'm mad.
You're mad.'
'How do you know I'm mad?' said Alice.
'You must be,' said the Cat, 'or you wouldn't have come here.'
Alice didn't think that proved it at all; however, she went on 'And how do you know that you're mad?' 'To begin with,' said the Cat, 'a dog's not mad.
You grant that?' 'I suppose so,' said Alice.
'Well, then,' the Cat went on, 'you see, a dog growls when it's angry, and wags its tail when it's pleased.
Now I growl when I'm pleased, and wag my tail when I'm angry.
Therefore I'm mad.' 'I call it purring, not growling,' said
Alice.
'Call it what you like,' said the Cat.
'Do you play croquet with the Queen to- day?' 'I should like it very much,' said Alice,
'but I haven't been invited yet.'
'You'll see me there,' said the Cat, and vanished.
Alice was not much surprised at this, she was getting so used to queer things happening.
While she was looking at the place where it had been, it suddenly appeared again.
'By-the-bye, what became of the baby?' said the Cat.
'I'd nearly forgotten to ask.'
'It turned into a pig,' Alice quietly said, just as if it had come back in a natural way.
'I thought it would,' said the Cat, and vanished again.
Alice waited a little, half expecting to see it again, but it did not appear, and after a minute or two she walked on in the direction in which the March Hare was said to live.
'I've seen hatters before,' she said to herself; 'the March Hare will be much the most interesting, and perhaps as this is May it won't be raving mad--at least not so mad as it was in March.'
As she said this, she looked up, and there was the Cat again, sitting on a branch of a tree.
'Did you say pig, or fig?' said the Cat.
'I said pig,' replied Alice; 'and I wish you wouldn't keep appearing and vanishing so suddenly: you make one quite giddy.'
'All right,' said the Cat; and this time it vanished quite slowly, beginning with the end of the tail, and ending with the grin, which remained some time after the rest of it had gone.
It's the most curious thing I ever saw in my life!'
'Well!
She had not gone much farther before she came in sight of the house of the March
Hare: she thought it must be the right house, because the chimneys were shaped like ears and the roof was thatched with fur.
It was so large a house, that she did not like to go nearer till she had nibbled some more of the lefthand bit of mushroom, and raised herself to about two feet high: even then she walked up towards it rather timidly, saying to herself 'Suppose it should be raving mad after all!
I almost wish I'd gone to see the Hatter instead!' >
Chapter VIl.
A Mad Tea-Party
There was a table set out under a tree in front of the house, and the March Hare and the Hatter were having tea at it: a Dormouse was sitting between them, fast asleep, and the other two were using it as a cushion, resting their elbows on it, and talking over its head.
'Very uncomfortable for the Dormouse,' thought Alice; 'only, as it's asleep, I suppose it doesn't mind.'
The table was a large one, but the three were all crowded together at one corner of it:
'No room!
No room!' they cried out when they saw
Alice coming.
'There's PLENTY of room!' said Alice indignantly, and she sat down in a large arm-chair at one end of the table.
'Have some wine,' the March Hare said in an encouraging tone.
Alice looked all round the table, but there was nothing on it but tea.
'I don't see any wine,' she remarked.
'There isn't any,' said the March Hare.
'Then it wasn't very civil of you to offer it,' said Alice angrily.
'It wasn't very civil of you to sit down without being invited,' said the March
Hare.
'I didn't know it was YOUR table,' said Alice; 'it's laid for a great many more than three.' 'Your hair wants cutting,' said the Hatter.
He had been looking at Alice for some time with great curiosity, and this was his first speech.
'You should learn not to make personal remarks,' Alice said with some severity;
'it's very rude.'
The Hatter opened his eyes very wide on hearing this; but all he SAlD was, 'Why is a raven like a writing-desk?'
'Come, we shall have some fun now!' thought
Alice.
'I'm glad they've begun asking riddles.
--I believe I can guess that,' she added aloud.
'Do you mean that you think you can find out the answer to it?' said the March Hare.
'Exactly so,' said Alice.
'Then you should say what you mean,' the
March Hare went on.
'I do,' Alice hastily replied; 'at least-- at least I mean what I say--that's the same thing, you know.'
'Not the same thing a bit!' said the
Hatter.
'You might just as well say that "I see what I eat" is the same thing as "I eat what I see"!'
'You might just as well say,' added the March Hare, 'that "I like what I get" is the same thing as "I get what I like"!'
'You might just as well say,' added the Dormouse, who seemed to be talking in his sleep, 'that "I breathe when I sleep" is the same thing as "I sleep when I breathe"!'
'It IS the same thing with you,' said the Hatter, and here the conversation dropped, and the party sat silent for a minute, while Alice thought over all she could remember about ravens and writing-desks, which wasn't much.
The Hatter was the first to break the silence.
'What day of the month is it?' he said, turning to Alice: he had taken his watch out of his pocket, and was looking at it uneasily, shaking it every now and then, and holding it to his ear.
Alice considered a little, and then said 'The fourth.'
'Two days wrong!' sighed the Hatter.
'I told you butter wouldn't suit the works!' he added looking angrily at the
'It was the BEST butter,' the March Hare meekly replied.
'Yes, but some crumbs must have got in as well,' the Hatter grumbled: 'you shouldn't have put it in with the bread-knife.'
The March Hare took the watch and looked at it gloomily: then he dipped it into his cup of tea, and looked at it again: but he could think of nothing better to say than his first remark, 'It was the BEST butter, you know.'
Alice had been looking over his shoulder with some curiosity.
'What a funny watch!' she remarked.
'It tells the day of the month, and doesn't tell what o'clock it is!'
'Why should it?' muttered the Hatter.
'Does YOUR watch tell you what year it is?'
'Of course not,' Alice replied very readily: 'but that's because it stays the same year for such a long time together.' 'Which is just the case with MlNE,' said the Hatter.
Alice felt dreadfully puzzled. The Hatter's remark seemed to have no sort of meaning in it, and yet it was certainly English.
'I don't quite understand you,' she said, as politely as she could.
'The Dormouse is asleep again,' said the Hatter, and he poured a little hot tea upon its nose.
The Dormouse shook its head impatiently, and said, without opening its eyes, 'Of course, of course; just what I was going to remark myself.'
'Have you guessed the riddle yet?' the Hatter said, turning to Alice again.
'No, I give it up,' Alice replied: 'what's the answer?'
'I haven't the slightest idea,' said the Hatter.
'Nor I,' said the March Hare.
Alice sighed wearily.
'I think you might do something better with the time,' she said, 'than waste it in asking riddles that have no answers.'
'If you knew Time as well as I do,' said the Hatter, 'you wouldn't talk about wasting IT.
It's HlM.'
'I don't know what you mean,' said Alice.
'Of course you don't!' the Hatter said, tossing his head contemptuously.
'I dare say you never even spoke to Time!'
'Perhaps not,' Alice cautiously replied: 'but I know I have to beat time when I learn music.'
'Ah! that accounts for it,' said the
Hatter.
'He won't stand beating.
Now, if you only kept on good terms with him, he'd do almost anything you liked with the clock.
For instance, suppose it were nine o'clock in the morning, just time to begin lessons: you'd only have to whisper a hint to Time, and round goes the clock in a twinkling!
Half-past one, time for dinner!' ('I only wish it was,' the March Hare said to itself in a whisper.)
'That would be grand, certainly,' said Alice thoughtfully: 'but then--I shouldn't be hungry for it, you know.'
'Not at first, perhaps,' said the Hatter: 'but you could keep it to half-past one as long as you liked.'
'Is that the way YOU manage?'
Alice asked.
The Hatter shook his head mournfully.
'Not I!' he replied.
'We quarrelled last March--just before HE went mad, you know--' (pointing with his tea spoon at the March Hare,) '--it was at the great concert given by the Queen of
Hearts, and I had to sing
"Twinkle, twinkle, little bat!
How I wonder what you're at!"
You know the song, perhaps?' 'I've heard something like it,' said Alice.
'It goes on, you know,' the Hatter continued, 'in this way:--
"Up above the world you fly, Like a tea-tray in the sky.
Twinkle, twinkle--"'
Here the Dormouse shook itself, and began singing in its sleep 'Twinkle, twinkle, twinkle, twinkle--' and went on so long that they had to pinch it to make it stop.
'Well, I'd hardly finished the first verse,' said the Hatter, 'when the Queen jumped up and bawled out, "He's murdering the time!
Off with his head!"'
'How dreadfully savage!' exclaimed Alice.
'And ever since that,' the Hatter went on in a mournful tone, 'he won't do a thing I ask!
It's always six o'clock now.'
A bright idea came into Alice's head.
'Is that the reason so many tea-things are put out here?' she asked.
'Yes, that's it,' said the Hatter with a sigh: 'it's always tea-time, and we've no time to wash the things between whiles.'
'Then you keep moving round, I suppose?' said Alice.
'Exactly so,' said the Hatter: 'as the things get used up.'
'But what happens when you come to the beginning again?'
Alice ventured to ask.
'Suppose we change the subject,' the March Hare interrupted, yawning.
'I'm getting tired of this.
I vote the young lady tells us a story.'
'I'm afraid I don't know one,' said Alice, rather alarmed at the proposal.
'Then the Dormouse shall!' they both cried.
'Wake up, Dormouse!'
And they pinched it on both sides at once.
The Dormouse slowly opened his eyes.
'I wasn't asleep,' he said in a hoarse, feeble voice:
'I heard every word you fellows were saying.'
'Tell us a story!' said the March Hare.
'Yes, please do!' pleaded Alice.
'And be quick about it,' added the Hatter,
'or you'll be asleep again before it's done.'
'Once upon a time there were three little sisters,' the Dormouse began in a great hurry; 'and their names were Elsie, Lacie, and Tillie; and they lived at the bottom of a well--'
'What did they live on?' said Alice, who always took a great interest in questions of eating and drinking.
'So they were,' said the Dormouse; 'VERY ill.'
'They couldn't have done that, you know,' Alice gently remarked; 'they'd have been ill.' Alice tried to fancy to herself what such an extraordinary ways of living would be
like, but it puzzled her too much, so she went on:
'But why did they live at the bottom of a well?'
'Take some more tea,' the March Hare said to Alice, very earnestly.
'I've had nothing yet,' Alice replied in an offended tone, 'so I can't take more.'
'You mean you can't take LESS,' said the Hatter: 'it's very easy to take MORE than nothing.' 'Nobody asked YOUR opinion,' said Alice.
'Who's making personal remarks now?' the Hatter asked triumphantly.
Alice did not quite know what to say to this: so she helped herself to some tea and bread-and-butter, and then turned to the Dormouse, and repeated her question.
'Why did they live at the bottom of a well?'
The Dormouse again took a minute or two to think about it, and then said, 'It was a treacle-well.'
'There's no such thing!'
Alice was beginning very angrily, but the Hatter and the March Hare went 'Sh! sh!' and the Dormouse sulkily remarked, 'If you can't be civil, you'd better finish the story for yourself.'
Alice said very humbly; 'I won't interrupt again.
'One, indeed!' said the Dormouse indignantly.
However, he consented to go on.
'And so these three little sisters--they were learning to draw, you know--'
'What did they draw?' said Alice, quite forgetting her promise.
'Treacle,' said the Dormouse, without considering at all this time.
'I want a clean cup,' interrupted the Hatter: 'let's all move one place on.'
He moved on as he spoke, and the Dormouse followed him: the March Hare moved into the
Dormouse's place, and Alice rather unwillingly took the place of the March
Hare.
The Hatter was the only one who got any advantage from the change: and Alice was a good deal worse off than before, as the March Hare had just upset the milk-jug into his plate.
Alice did not wish to offend the Dormouse again, so she began very cautiously:
'But I don't understand.
Where did they draw the treacle from?'
'You can draw water out of a water-well,' said the Hatter; 'so I should think you could draw treacle out of a treacle-well-- eh, stupid?'
'But they were IN the well,' Alice said to the Dormouse, not choosing to notice this last remark.
'Of course they were', said the Dormouse;
'--well in.'
This answer so confused poor Alice, that she let the Dormouse go on for some time without interrupting it.
'They were learning to draw,' the Dormouse went on, yawning and rubbing its eyes, for it was getting very sleepy; 'and they drew all manner of things--everything that begins with an M--'
'Why with an M?' said Alice.
'Why not?' said the March Hare.
Alice was silent.
The Dormouse had closed its eyes by this time, and was going off into a doze; but, on being pinched by the Hatter, it woke up again with a little shriek, and went on: '-
-that begins with an M, such as mouse- traps, and the moon, and memory, and muchness--you know you say things are "much of a muchness"--did you ever see such a thing as a drawing of a muchness?'
'Really, now you ask me,' said Alice, very much confused, 'I don't think--'
'Then you shouldn't talk,' said the Hatter.
This piece of rudeness was more than Alice could bear: she got up in great disgust, and walked off; the Dormouse fell asleep instantly, and neither of the others took the least notice of her going, though she looked back once or twice, half hoping that they would call after her: the last time she saw them, they were trying to put the Dormouse into the teapot.
'At any rate I'll never go THERE again!' said Alice as she picked her way through the wood.
'It's the stupidest tea-party I ever was at in all my life!'
Just as she said this, she noticed that one of the trees had a door leading right into it.
'That's very curious!' she thought.
'But everything's curious today.
I think I may as well go in at once.'
And in she went.
Once more she found herself in the long hall, and close to the little glass table.
'Now, I'll manage better this time,' she said to herself, and began by taking the little golden key, and unlocking the door that led into the garden.
Then she went to work nibbling at the mushroom (she had kept a piece of it in her pocket) till she was about a foot high: then she walked down the little passage: and THEN--she found herself at last in the beautiful garden, among the bright flower- beds and the cool fountains. >
Chapter Vill.
The Queen's Croquet-Ground A large rose-tree stood near the entrance of the garden: the roses growing on it were white, but there were three gardeners at it, busily painting them red.
Alice thought this a very curious thing, and she went nearer to watch them, and just as she came up to them she heard one of them say, 'Look out now, Five!
Don't go splashing paint over me like that!'
'I couldn't help it,' said Five, in a sulky tone; 'Seven jogged my elbow.'
On which Seven looked up and said, 'That's right, Five!
Always lay the blame on others!' 'YOU'D better not talk!' said Five.
'I heard the Queen say only yesterday you deserved to be beheaded!'
'What for?' said the one who had spoken first.
'That's none of YOUR business, Two!' said Seven.
'Yes, it IS his business!' said Five, 'and I'll tell him--it was for bringing the cook tulip-roots instead of onions.'
Seven flung down his brush, and had just begun 'Well, of all the unjust things--' when his eye chanced to fall upon Alice, as she stood watching them, and he checked himself suddenly: the others looked round also, and all of them bowed low.
'Would you tell me,' said Alice, a little timidly, 'why you are painting those roses?'
Five and Seven said nothing, but looked at Two.
Two began in a low voice, 'Why the fact is, you see, Miss, this here ought to have been a RED rose-tree, and we put a white one in by mistake; and if the Queen was to find it out, we should all have our heads cut off, you know.
So you see, Miss, we're doing our best, afore she comes, to--' At this moment Five, who had been anxiously looking across the garden, called out 'The Queen!
The Queen!' and the three gardeners instantly threw themselves flat upon their faces.
Alice looked round, eager to see the Queen.
First came ten soldiers carrying clubs; these were all shaped like the three gardeners, oblong and flat, with their hands and feet at the corners: next the ten courtiers; these were ornamented all over with diamonds, and walked two and two, as the soldiers did.
After these came the royal children; there were ten of them, and the little dears came jumping merrily along hand in hand, in couples: they were all ornamented with hearts.
Next came the guests, mostly Kings and Queens, and among them Alice recognised the
White Rabbit: it was talking in a hurried nervous manner, smiling at everything that was said, and went by without noticing her.
Then followed the Knave of Hearts, carrying the King's crown on a crimson velvet cushion; and, last of all this grand procession, came THE KlNG AND QUEEN OF
HEARTS.
Alice was rather doubtful whether she ought not to lie down on her face like the three gardeners, but she could not remember ever having heard of such a rule at processions;
'and besides, what would be the use of a procession,' thought she, 'if people had all to lie down upon their faces, so that they couldn't see it?'
So she stood still where she was, and waited.
When the procession came opposite to Alice, they all stopped and looked at her, and the
Queen said severely 'Who is this?' She said it to the Knave of Hearts, who only bowed and smiled in reply.
'Idiot!' said the Queen, tossing her head impatiently; and, turning to Alice, she went on, 'What's your name, child?'
'My name is Alice, so please your Majesty,' said Alice very politely; but she added, to herself, 'Why, they're only a pack of cards, after all.
I needn't be afraid of them!'
'And who are THESE?' said the Queen, pointing to the three gardeners who were
lying round the rosetree; for, you see, as they were lying on their faces, and the pattern on their backs was the same as the rest of the pack, she could not tell whether they were gardeners, or soldiers, or courtiers, or three of her own children.
'How should I know?' said Alice, surprised at her own courage.
'It's no business of MlNE.' The Queen turned crimson with fury, and, after glaring at her for a moment like a wild beast, screamed 'Off with her head!
Off--'
'Nonsense!' said Alice, very loudly and decidedly, and the Queen was silent.
The King laid his hand upon her arm, and timidly said 'Consider, my dear: she is only a child!'
The Queen turned angrily away from him, and said to the Knave 'Turn them over!'
The Knave did so, very carefully, with one foot.
'Get up!' said the Queen, in a shrill, loud voice, and the three gardeners instantly jumped up, and began bowing to the King, the Queen, the royal children, and everybody else.
'Leave off that!' screamed the Queen.
'You make me giddy.'
And then, turning to the rose-tree, she went on, 'What HAVE you been doing here?'
'May it please your Majesty,' said Two, in a very humble tone, going down on one knee as he spoke, 'we were trying--' 'I see!' said the Queen, who had meanwhile been examining the roses.
'Off with their heads!' and the procession moved on, three of the soldiers remaining behind to execute the unfortunate gardeners, who ran to Alice for protection.
'You shan't be beheaded!' said Alice, and she put them into a large flower-pot that stood near.
The three soldiers wandered about for a minute or two, looking for them, and then quietly marched off after the others.
'Are their heads off?' shouted the Queen.
'Their heads are gone, if it please your Majesty!' the soldiers shouted in reply.
'That's right!' shouted the Queen.
'Can you play croquet?'
The soldiers were silent, and looked at Alice, as the question was evidently meant for her.
'Yes!' shouted Alice.
'Come on, then!' roared the Queen, and Alice joined the procession, wondering very much what would happen next.
'It's--it's a very fine day!' said a timid voice at her side.
She was walking by the White Rabbit, who was peeping anxiously into her face.
'Very,' said Alice: '--where's the Duchess?'
'Hush!
Hush!' said the Rabbit in a low, hurried tone.
He looked anxiously over his shoulder as he spoke, and then raised himself upon tiptoe, put his mouth close to her ear, and whispered 'She's under sentence of execution.'
'What for?' said Alice.
'Did you say "What a pity!" ?' the Rabbit asked.
'No, I didn't,' said Alice: 'I don't think it's at all a pity.
I said "What for?"' 'She boxed the Queen's ears--' the Rabbit began.
Alice gave a little scream of laughter.
'Oh, hush!' the Rabbit whispered in a frightened tone.
'The Queen will hear you!
You see, she came rather late, and the
Queen said--'
'Get to your places!' shouted the Queen in a voice of thunder, and people began running about in all directions, tumbling up against each other; however, they got settled down in a minute or two, and the game began.
Alice thought she had never seen such a curious croquet-ground in her life; it was all ridges and furrows; the balls were live hedgehogs, the mallets live flamingoes, and the soldiers had to double themselves up and to stand on their hands and feet, to make the arches.
The chief difficulty Alice found at first was in managing her flamingo: she succeeded in getting its body tucked away, comfortably enough, under her arm, with its legs hanging down, but generally, just as she had got its neck nicely straightened out, and was going to give the hedgehog a blow with its head, it WOULD twist itself round and look up in her face, with such a puzzled expression that she could not help bursting out laughing: and when she had got its head down, and was going to begin again, it was very provoking to find that the hedgehog had unrolled itself, and was in the act of crawling away: besides all this, there was generally a ridge or furrow in the way wherever she wanted to send the hedgehog to, and, as the doubled-up soldiers were always getting up and walking off to other parts of the ground, Alice soon came to the conclusion that it was a very difficult game indeed.
The players all played at once without waiting for turns, quarrelling all the while, and fighting for the hedgehogs; and in a very short time the Queen was in a furious passion, and went stamping about, and shouting 'Off with his head!' or 'Off with her head!' about once in a minute.
Alice began to feel very uneasy: to be sure, she had not as yet had any dispute with the Queen, but she knew that it might happen any minute, 'and then,' thought she,
'what would become of me?
They're dreadfully fond of beheading people here; the great wonder is, that there's any one left alive!'
She was looking about for some way of escape, and wondering whether she could get away without being seen, when she noticed a curious appearance in the air: it puzzled her very much at first, but, after watching it a minute or two, she made it out to be a grin, and she said to herself 'It's the
Cheshire Cat: now I shall have somebody to talk to.'
'How are you getting on?' said the Cat, as soon as there was mouth enough for it to speak with.
Alice waited till the eyes appeared, and then nodded.
'It's no use speaking to it,' she thought, 'till its ears have come, or at least one of them.'
In another minute the whole head appeared, and then Alice put down her flamingo, and began an account of the game, feeling very glad she had someone to listen to her.
The Cat seemed to think that there was enough of it now in sight, and no more of it appeared.
'I don't think they play at all fairly,' Alice began, in rather a complaining tone,
'and they all quarrel so dreadfully one can't hear oneself speak--and they don't seem to have any rules in particular; at least, if there are, nobody attends to them--and you've no idea how confusing it is all the things being alive; for instance, there's the arch I've got to go through next walking about at the other end of the ground--and I should have croqueted the Queen's hedgehog just now, only it ran away when it saw mine coming!' 'How do you like the Queen?' said the Cat in a low voice.
'Not at all,' said Alice: 'she's so extremely--' Just then she noticed that the
Queen was close behind her, listening: so she went on, '--likely to win, that it's hardly worth while finishing the game.'
The Queen smiled and passed on.
'Who ARE you talking to?' said the King, going up to Alice, and looking at the Cat's head with great curiosity.
'It's a friend of mine--a Cheshire Cat,' said Alice: 'allow me to introduce it.'
'I don't like the look of it at all,' said the King: 'however, it may kiss my hand if it likes.'
'I'd rather not,' the Cat remarked.
'Don't be impertinent,' said the King, 'and don't look at me like that!'
He got behind Alice as he spoke.
'A cat may look at a king,' said Alice.
'I've read that in some book, but I don't remember where.' 'Well, it must be removed,' said the King very decidedly, and he called the Queen, who was passing at the moment, 'My dear!
I wish you would have this cat removed!'
The Queen had only one way of settling all difficulties, great or small.
'Off with his head!' she said, without even looking round.
'I'll fetch the executioner myself,' said the King eagerly, and he hurried off.
Alice thought she might as well go back, and see how the game was going on, as she heard the Queen's voice in the distance, screaming with passion.
She had already heard her sentence three of the players to be executed for having missed their turns, and she did not like the look of things at all, as the game was in such confusion that she never knew whether it was her turn or not.
So she went in search of her hedgehog.
The hedgehog was engaged in a fight with another hedgehog, which seemed to Alice an excellent opportunity for croqueting one of them with the other: the only difficulty was, that her flamingo was gone across to the other side of the garden, where Alice could see it trying in a helpless sort of way to fly up into a tree.
By the time she had caught the flamingo and brought it back, the fight was over, and both the hedgehogs were out of sight: 'but it doesn't matter much,' thought Alice, 'as all the arches are gone from this side of the ground.'
So she tucked it away under her arm, that it might not escape again, and went back for a little more conversation with her friend.
When she got back to the Cheshire Cat, she was surprised to find quite a large crowd collected round it: there was a dispute going on between the executioner, the King, and the Queen, who were all talking at once, while all the rest were quite silent, and looked very uncomfortable.
The moment Alice appeared, she was appealed to by all three to settle the question, and they repeated their arguments to her, though, as they all spoke at once, she found it very hard indeed to make out exactly what they said.
The executioner's argument was, that you couldn't cut off a head unless there was a body to cut it off from: that he had never had to do such a thing before, and he wasn't going to begin at HlS time of life.
The King's argument was, that anything that had a head could be beheaded, and that you weren't to talk nonsense.
The Queen's argument was, that if something wasn't done about it in less than no time she'd have everybody executed, all round.
(It was this last remark that had made the whole party look so grave and anxious.)
Alice could think of nothing else to say but 'It belongs to the Duchess: you'd better ask HER about it.'
'She's in prison,' the Queen said to the executioner: 'fetch her here.'
And the executioner went off like an arrow.
The Cat's head began fading away the moment he was gone, and, by the time he had come back with the Duchess, it had entirely disappeared; so the King and the executioner ran wildly up and down looking for it, while the rest of the party went back to the game. >
Chapter IX.
The Mock Turtle's Story
'You can't think how glad I am to see you again, you dear old thing!' said the
Duchess, as she tucked her arm affectionately into Alice's, and they walked off together.
Alice was very glad to find her in such a pleasant temper, and thought to herself that perhaps it was only the pepper that had made her so savage when they met in the kitchen.
'When I'M a Duchess,' she said to herself, (not in a very hopeful tone though), 'I won't have any pepper in my kitchen AT ALL.
Soup does very well without--Maybe it's always pepper that makes people hot- tempered,' she went on, very much pleased at having found out a new kind of rule,
'and vinegar that makes them sour--and camomile that makes them bitter--and--and barley-sugar and such things that make children sweet-tempered.
I only wish people knew that: then they wouldn't be so stingy about it, you know--'
She had quite forgotten the Duchess by this time, and was a little startled when she heard her voice close to her ear.
'You're thinking about something, my dear, and that makes you forget to talk.
I can't tell you just now what the moral of that is, but I shall remember it in a bit.'
'Perhaps it hasn't one,' Alice ventured to remark.
'Tut, tut, child!' said the Duchess.
'Everything's got a moral, if only you can find it.'
And she squeezed herself up closer to Alice's side as she spoke.
Alice did not much like keeping so close to her: first, because the Duchess was VERY ugly; and secondly, because she was exactly the right height to rest her chin upon
Alice's shoulder, and it was an uncomfortably sharp chin.
However, she did not like to be rude, so she bore it as well as she could.
'The game's going on rather better now,' she said, by way of keeping up the conversation a little. " Tis so,' said the Duchess: 'and the moral of that is--"Oh, 'tis love, 'tis love, that makes the world go round!"'
'Somebody said,' Alice whispered, 'that it's done by everybody minding their own business!' 'Ah, well!
It means much the same thing,' said the Duchess, digging her sharp little chin into
Alice's shoulder as she added, 'and the moral of THAT is--"Take care of the sense, and the sounds will take care of themselves."'
'How fond she is of finding morals in things!'
Alice thought to herself.
'I dare say you're wondering why I don't put my arm round your waist,' the Duchess said after a pause: 'the reason is, that I'm doubtful about the temper of your flamingo.
Shall I try the experiment?' 'HE might bite,' Alice cautiously replied, not feeling at all anxious to have the experiment tried.
'Very true,' said the Duchess: 'flamingoes and mustard both bite.
And the moral of that is--"Birds of a feather flock together."'
'Only mustard isn't a bird,' Alice remarked.
'Right, as usual,' said the Duchess: 'what a clear way you have of putting things!'
'It's a mineral, I THlNK,' said Alice.
'Of course it is,' said the Duchess, who seemed ready to agree to everything that
Alice said; 'there's a large mustard-mine near here.
And the moral of that is--"The more there is of mine, the less there is of yours."'
'Oh, I know!' exclaimed Alice, who had not attended to this last remark, 'it's a vegetable.
It doesn't look like one, but it is.'
'I quite agree with you,' said the Duchess; 'and the moral of that is--"Be what you would seem to be"--or if you'd like it put more simply--"Never imagine yourself not to be otherwise than what it might appear to others that what you were or might have been was not otherwise than what you had been would have appeared to them to be otherwise."'
'I think I should understand that better,' Alice said very politely, 'if I had it written down: but I can't quite follow it as you say it.'
'That's nothing to what I could say if I chose,' the Duchess replied, in a pleased tone.
'Pray don't trouble yourself to say it any
longer than that,' said Alice.
'Oh, don't talk about trouble!' said the Duchess.
'I make you a present of everything I've said as yet.'
'A cheap sort of present!' thought Alice.
'I'm glad they don't give birthday presents like that!'
But she did not venture to say it out loud.
'Thinking again?' the Duchess asked, with another dig of her sharp little chin.
'I've a right to think,' said Alice sharply, for she was beginning to feel a little worried.
'Just about as much right,' said the
Duchess, 'as pigs have to fly; and the m--'
But here, to Alice's great surprise, the Duchess's voice died away, even in the middle of her favourite word 'moral,' and the arm that was linked into hers began to tremble.
Alice looked up, and there stood the Queen in front of them, with her arms folded, frowning like a thunderstorm.
'A fine day, your Majesty!' the Duchess began in a low, weak voice.
'Now, I give you fair warning,' shouted the Queen, stamping on the ground as she spoke;
'either you or your head must be off, and that in about half no time!
Take your choice!'
The Duchess took her choice, and was gone in a moment.
'Let's go on with the game,' the Queen said to Alice; and Alice was too much frightened to say a word, but slowly followed her back to the croquet-ground.
The other guests had taken advantage of the Queen's absence, and were resting in the shade: however, the moment they saw her, they hurried back to the game, the Queen merely remarking that a moment's delay would cost them their lives.
All the time they were playing the Queen never left off quarrelling with the other players, and shouting 'Off with his head!' or 'Off with her head!'
Those whom she sentenced were taken into custody by the soldiers, who of course had to leave off being arches to do this, so that by the end of half an hour or so there were no arches left, and all the players, except the King, the Queen, and Alice, were in custody and under sentence of execution.
Then the Queen left off, quite out of breath, and said to Alice, 'Have you seen the Mock Turtle yet?'
'No,' said Alice.
'I don't even know what a Mock Turtle is.'
'It's the thing Mock Turtle Soup is made from,' said the Queen.
'I never saw one, or heard of one,' said Alice.
'Come on, then,' said the Queen, 'and he shall tell you his history,'
As they walked off together, Alice heard the King say in a low voice, to the company generally, 'You are all pardoned.'
'Come, THAT'S a good thing!' she said to herself, for she had felt quite unhappy at the number of executions the Queen had ordered.
They very soon came upon a Gryphon, lying fast asleep in the sun.
(IF you don't know what a Gryphon is, look at the picture.)
'Up, lazy thing!' said the Queen, 'and take this young lady to see the Mock Turtle, and to hear his history.
I must go back and see after some executions I have ordered'; and she walked off, leaving Alice alone with the Gryphon.
Alice did not quite like the look of the creature, but on the whole she thought it would be quite as safe to stay with it as to go after that savage Queen: so she waited.
The Gryphon sat up and rubbed its eyes: then it watched the Queen till she was out of sight: then it chuckled.
'What fun!' said the Gryphon, half to itself, half to Alice.
'What IS the fun?' said Alice.
'Why, SHE,' said the Gryphon.
'It's all her fancy, that: they never executes nobody, you know.
Come on!'
'Everybody says "come on!" here,' thought Alice, as she went slowly after it:
'I never was so ordered about in all my life, never!'
They had not gone far before they saw the Mock Turtle in the distance, sitting sad and lonely on a little ledge of rock, and, as they came nearer, Alice could hear him sighing as if his heart would break.
She pitied him deeply.
'What is his sorrow?' she asked the Gryphon, and the Gryphon answered, very nearly in the same words as before, 'It's all his fancy, that: he hasn't got no sorrow, you know.
Come on!'
So they went up to the Mock Turtle, who looked at them with large eyes full of tears, but said nothing.
'This here young lady,' said the Gryphon, 'she wants for to know your history, she do.'
'I'll tell it her,' said the Mock Turtle in a deep, hollow tone: 'sit down, both of you, and don't speak a word till I've finished.'
So they sat down, and nobody spoke for some minutes.
Alice thought to herself, 'I don't see how he can EVEN finish, if he doesn't begin.'
But she waited patiently.
'Once,' said the Mock Turtle at last, with a deep sigh, 'I was a real Turtle.'
These words were followed by a very long silence, broken only by an occasional exclamation of 'Hjckrrh!' from the Gryphon, and the constant heavy sobbing of the Mock
Turtle.
Alice was very nearly getting up and saying, 'Thank you, sir, for your interesting story,' but she could not help thinking there MUST be more to come, so she sat still and said nothing.
'When we were little,' the Mock Turtle went on at last, more calmly, though still sobbing a little now and then, 'we went to school in the sea.
The master was an old Turtle--we used to call him Tortoise--'
'Why did you call him Tortoise, if he wasn't one?'
Alice asked.
'We called him Tortoise because he taught us,' said the Mock Turtle angrily: 'really you are very dull!'
'You ought to be ashamed of yourself for asking such a simple question,' added the
Gryphon; and then they both sat silent and looked at poor Alice, who felt ready to sink into the earth.
At last the Gryphon said to the Mock Turtle, 'Drive on, old fellow!
Don't be all day about it!' and he went on in these words:
'Yes, we went to school in the sea, though you mayn't believe it--'
'I never said I didn't!' interrupted Alice.
'You did,' said the Mock Turtle.
'Hold your tongue!' added the Gryphon, before Alice could speak again.
The Mock Turtle went on.
'We had the best of educations--in fact, we went to school every day--'
'I'VE been to a day-school, too,' said Alice; 'you needn't be so proud as all that.'
'With extras?' asked the Mock Turtle a little anxiously.
'Yes,' said Alice, 'we learned French and music.'
'And washing?' said the Mock Turtle.
'Certainly not!' said Alice indignantly.
'Ah! then yours wasn't a really good school,' said the Mock Turtle in a tone of great relief.
'Now at OURS they had at the end of the bill, "French, music, AND WASHlNG--extra."'
'You couldn't have wanted it much,' said Alice; 'living at the bottom of the sea.'
'I couldn't afford to learn it.' said the Mock Turtle with a sigh.
'I only took the regular course.'
'What was that?' inquired Alice.
'Reeling and Writhing, of course, to begin with,' the Mock Turtle replied; 'and then the different branches of Arithmetic-- Ambition, Distraction, Uglification, and
Derision.'
'I never heard of "Uglification,"' Alice ventured to say.
The Gryphon lifted up both its paws in surprise.
'What!
Never heard of uglifying!' it exclaimed.
'You know what to beautify is, I suppose?' 'Yes,' said Alice doubtfully: 'it means-- to--make--anything--prettier.'
'Well, then,' the Gryphon went on, 'if you don't know what to uglify is, you ARE a simpleton.'
Alice did not feel encouraged to ask any more questions about it, so she turned to the Mock Turtle, and said 'What else had you to learn?'
'Well, there was Mystery,' the Mock Turtle replied, counting off the subjects on his flappers, '--Mystery, ancient and modern, with Seaography: then Drawling--the
Drawling-master was an old conger-eel, that used to come once a week:
HE taught us Drawling, Stretching, and Fainting in
Coils.'
'What was THAT like?' said Alice.
'Well, I can't show it you myself,' the Mock Turtle said:
'I'm too stiff.
And the Gryphon never learnt it.' 'Hadn't time,' said the Gryphon: 'I went to the Classics master, though.
He was an old crab, HE was.' 'I never went to him,' the Mock Turtle said with a sigh: 'he taught Laughing and Grief, they used to say.'
'So he did, so he did,' said the Gryphon, sighing in his turn; and both creatures hid their faces in their paws.
'And how many hours a day did you do lessons?' said Alice, in a hurry to change the subject.
'Ten hours the first day,' said the Mock
Turtle: 'nine the next, and so on.'
'What a curious plan!' exclaimed Alice.
'That's the reason they're called lessons,' the Gryphon remarked: 'because they lessen from day to day.'
This was quite a new idea to Alice, and she thought it over a little before she made her next remark.
'Then the eleventh day must have been a holiday?'
'Of course it was,' said the Mock Turtle.
'And how did you manage on the twelfth?'
Alice went on eagerly.
'That's enough about lessons,' the Gryphon interrupted in a very decided tone: 'tell her something about the games now.' >
Chapter X. The Lobster Quadrille The Mock Turtle sighed deeply, and drew the back of one flapper across his eyes.
'Same as if he had a bone in his throat,' said the Gryphon: and it set to work shaking him and punching him in the back.
At last the Mock Turtle recovered his voice, and, with tears running down his cheeks, he went on again:--
'You may not have lived much under the sea- -' ('I haven't,' said Alice)--'and perhaps you were never even introduced to a lobster--' (Alice began to say 'I once tasted--' but checked herself hastily, and said 'No, never') '--so you can have no idea what a delightful thing a Lobster
Quadrille is!' 'No, indeed,' said Alice.
'What sort of a dance is it?'
'Why,' said the Gryphon, 'you first form into a line along the sea-shore--'
'Two lines!' cried the Mock Turtle.
'Seals, turtles, salmon, and so on; then, when you've cleared all the jelly-fish out of the way--' 'THAT generally takes some time,' interrupted the Gryphon. '--you advance twice--' 'Each with a lobster as a partner!' cried the Gryphon.
'Of course,' the Mock Turtle said: 'advance twice, set to partners--'
'--change lobsters, and retire in same order,' continued the Gryphon.
'Then, you know,' the Mock Turtle went on, 'you throw the--'
'The lobsters!' shouted the Gryphon, with a bound into the air. '--as far out to sea as you can--' 'Swim after them!' screamed the Gryphon.
'Turn a somersault in the sea!' cried the Mock Turtle, capering wildly about.
'Change lobsters again!' yelled the Gryphon at the top of its voice.
'Back to land again, and that's all the first figure,' said the Mock Turtle, suddenly dropping his voice; and the two creatures, who had been jumping about like mad things all this time, sat down again very sadly and quietly, and looked at Alice.
'It must be a very pretty dance,' said Alice timidly.
'Would you like to see a little of it?' said the Mock Turtle.
'Very much indeed,' said Alice.
'Come, let's try the first figure!' said the Mock Turtle to the Gryphon.
'We can do without lobsters, you know.
Which shall sing?'
'Oh, YOU sing,' said the Gryphon.
'I've forgotten the words.'
So they began solemnly dancing round and round Alice, every now and then treading on her toes when they passed too close, and waving their forepaws to mark the time, while the Mock Turtle sang this, very slowly and sadly:--
'"Will you walk a little faster?" said a whiting to a snail.
"There's a porpoise close behind us, and he's treading on my tail.
See how eagerly the lobsters and the turtles all advance!
They are waiting on the shingle--will you come and join the dance?
Will you, won't you, will you, won't you, will you join the dance?
Will you, won't you, will you, won't you, won't you join the dance?
"You can really have no notion how delightful it will be When they take us up and throw us, with the lobsters, out to sea!"
But the snail replied "Too far, too far!" and gave a look askance-- Said he thanked the whiting kindly, but he would not join the dance.
Would not, could not, would not, could not, would not join the dance.
Would not, could not, would not, could not, could not join the dance.
'"What matters it how far we go?" his scaly friend replied.
"There is another shore, you know, upon the other side.
The further off from England the nearer is to France-- Then turn not pale, beloved snail, but come and join the dance.
Will you, won't you, will you, won't you, will you join the dance?
Will you, won't you, will you, won't you, won't you join the dance?"'
'Thank you, it's a very interesting dance to watch,' said Alice, feeling very glad that it was over at last: 'and I do so like that curious song about the whiting!'
'Oh, as to the whiting,' said the Mock Turtle, 'they--you've seen them, of course?' 'Yes,' said Alice, 'I've often seen them at dinn--' she checked herself hastily.
'I don't know where Dinn may be,' said the Mock Turtle, 'but if you've seen them so often, of course you know what they're like.'
'I believe so,' Alice replied thoughtfully.
'They have their tails in their mouths--and they're all over crumbs.'
'You're wrong about the crumbs,' said the Mock Turtle: 'crumbs would all wash off in the sea.
But they HAVE their tails in their mouths; and the reason is--' here the Mock Turtle yawned and shut his eyes.
--'Tell her about the reason and all that,' he said to the Gryphon.
'The reason is,' said the Gryphon, 'that they WOULD go with the lobsters to the dance.
So they got thrown out to sea.
So they had to fall a long way.
So they got their tails fast in their mouths.
So they couldn't get them out again.
That's all.'
'Thank you,' said Alice, 'it's very interesting.
I never knew so much about a whiting before.'
'I can tell you more than that, if you like,' said the Gryphon.
'Do you know why it's called a whiting?' 'I never thought about it,' said Alice.
'Why?'
'IT DOES THE BOOTS AND SHOES.' the Gryphon replied very solemnly.
Alice was thoroughly puzzled.
'Does the boots and shoes!' she repeated in a wondering tone.
'Why, what are YOUR shoes done with?' said the Gryphon.
'I mean, what makes them so shiny?' Alice looked down at them, and considered a little before she gave her answer.
'They're done with blacking, I believe.' 'Boots and shoes under the sea,' the
Gryphon went on in a deep voice, 'are done with a whiting.
Now you know.'
'And what are they made of?'
Alice asked in a tone of great curiosity.
'Soles and eels, of course,' the Gryphon replied rather impatiently: 'any shrimp could have told you that.'
'If I'd been the whiting,' said Alice, whose thoughts were still running on the song, 'I'd have said to the porpoise, "Keep back, please: we don't want YOU with us!"'
'They were obliged to have him with them,' the Mock Turtle said: 'no wise fish would go anywhere without a porpoise.' 'Wouldn't it really?' said Alice in a tone of great surprise.
'Of course not,' said the Mock Turtle: 'why, if a fish came to ME, and told me he was going a journey, I should say "With what porpoise?"'
'Don't you mean "purpose"?' said Alice.
'I mean what I say,' the Mock Turtle replied in an offended tone.
And the Gryphon added 'Come, let's hear some of YOUR adventures.'
'I could tell you my adventures--beginning from this morning,' said Alice a little timidly: 'but it's no use going back to yesterday, because I was a different person then.'
'Explain all that,' said the Mock Turtle.
'No, no!
The adventures first,' said the Gryphon in an impatient tone: 'explanations take such a dreadful time.'
So Alice began telling them her adventures from the time when she first saw the White
Rabbit.
She was a little nervous about it just at first, the two creatures got so close to her, one on each side, and opened their eyes and mouths so VERY wide, but she gained courage as she went on.
Her listeners were perfectly quiet till she got to the part about her repeating 'YOU
ARE OLD, FATHER WlLLlAM,' to the Caterpillar, and the words all coming different, and then the Mock Turtle drew a long breath, and said 'That's very curious.'
'It's all about as curious as it can be,' said the Gryphon.
'It all came different!' the Mock Turtle repeated thoughtfully.
'I should like to hear her try and repeat something now.
Tell her to begin.'
He looked at the Gryphon as if he thought it had some kind of authority over Alice.
'Stand up and repeat "'TlS THE VOlCE OF THE SLUGGARD,"' said the Gryphon.
'How the creatures order one about, and make one repeat lessons!' thought Alice; 'I might as well be at school at once.'
However, she got up, and began to repeat it, but her head was so full of the Lobster
Quadrille, that she hardly knew what she was saying, and the words came very queer indeed:--
" Tis the voice of the Lobster; I heard him declare,
"You have baked me too brown, I must sugar my hair."
As a duck with its eyelids, so he with his nose
Trims his belt and his buttons, and turns out his toes.'
[later editions continued as follows When the sands are all dry, he is gay as a lark, And will talk in contemptuous tones of the Shark,
But, when the tide rises and sharks are around,
His voice has a timid and tremulous sound.]
'That's different from what I used to say when I was a child,' said the Gryphon. 'Well, I never heard it before,' said the Mock Turtle; 'but it sounds uncommon nonsense.'
Alice said nothing; she had sat down with her face in her hands, wondering if anything would EVER happen in a natural way again.
'I should like to have it explained,' said the Mock Turtle.
'She can't explain it,' said the Gryphon hastily.
'Go on with the next verse.'
'But about his toes?' the Mock Turtle persisted.
'How COULD he turn them out with his nose, you know?'
'It's the first position in dancing.'
Alice said; but was dreadfully puzzled by the whole thing, and longed to change the subject.
'Go on with the next verse,' the Gryphon repeated impatiently: 'it begins "I passed by his garden."'
Alice did not dare to disobey, though she felt sure it would all come wrong, and she went on in a trembling voice:--
'I passed by his garden, and marked, with one eye,
How the Owl and the Panther were sharing a pie--'
[later editions continued as follows The Panther took pie-crust, and gravy, and meat, While the Owl had the dish as its share of the treat.
When the pie was all finished, the Owl, as a boon,
Was kindly permitted to pocket the spoon:
While the Panther received knife and fork with a growl,
And concluded the banquet--]
It's by far the most confusing thing I ever heard!'
'Yes, I think you'd better leave off,' said the Gryphon: and Alice was only too glad to do so.
'Shall we try another figure of the Lobster
Quadrille?' the Gryphon went on.
'Or would you like the Mock Turtle to sing you a song?'
'Oh, a song, please, if the Mock Turtle would be so kind,' Alice replied, so eagerly that the Gryphon said, in a rather offended tone, 'Hm!
No accounting for tastes!
Sing her "Turtle Soup," will you, old fellow?'
The Mock Turtle sighed deeply, and began, in a voice sometimes choked with sobs, to sing this:--
'Beautiful Soup, so rich and green, Waiting in a hot tureen!
Who for such dainties would not stoop?
Soup of the evening, beautiful Soup!
Soup of the evening, beautiful Soup!
Beau--ootiful Soo--oop!
Beau--ootiful Soo--oop!
Soo--oop of the e--e--evening, Beautiful, beautiful Soup!
'Beautiful Soup!
Who cares for fish,
Game, or any other dish?
Who would not give all else for two
Pennyworth only of beautiful Soup?
Pennyworth only of beautiful Soup?
Beau--ootiful Soo--oop!
Beau--ootiful Soo--oop!
Soo--oop of the e--e--evening, Beautiful, beauti--FUL SOUP!'
'Chorus again!' cried the Gryphon, and the Mock Turtle had just begun to repeat it, when a cry of 'The trial's beginning!' was heard in the distance.
'Come on!' cried the Gryphon, and, taking Alice by the hand, it hurried off, without waiting for the end of the song.
Alice panted as she ran; but the Gryphon only answered 'Come on!' and ran the faster, while more and more faintly came, carried on the breeze that followed them, the melancholy words:--
'Soo--oop of the e--e--evening, Beautiful, beautiful Soup!' >
Chapter Xl.
Who Stole the Tarts?
The King and Queen of Hearts were seated on their throne when they arrived, with a great crowd assembled about them--all sorts of little birds and beasts, as well as the whole pack of cards: the Knave was standing before them, in chains, with a soldier on each side to guard him; and near the King was the White Rabbit, with a trumpet in one hand, and a scroll of parchment in the other.
In the very middle of the court was a table, with a large dish of tarts upon it: they looked so good, that it made Alice quite hungry to look at them--'I wish they'd get the trial done,' she thought, 'and hand round the refreshments!'
But there seemed to be no chance of this, so she began looking at everything about her, to pass away the time.
Alice had never been in a court of justice before, but she had read about them in books, and she was quite pleased to find that she knew the name of nearly everything there.
'That's the judge,' she said to herself, 'because of his great wig.'
The judge, by the way, was the King; and as he wore his crown over the wig, (look at the frontispiece if you want to see how he did it,) he did not look at all comfortable, and it was certainly not becoming.
'And that's the jury-box,' thought Alice, 'and those twelve creatures,' (she was obliged to say 'creatures,' you see, because some of them were animals, and some were birds,) 'I suppose they are the jurors.'
She said this last word two or three times over to herself, being rather proud of it: for she thought, and rightly too, that very few little girls of her age knew the meaning of it at all.
However, 'jury-men' would have done just as well.
The twelve jurors were all writing very busily on slates.
'What are they doing?'
Alice whispered to the Gryphon. 'They can't have anything to put down yet, before the trial's begun.'
'They're putting down their names,' the Gryphon whispered in reply, 'for fear they should forget them before the end of the trial.'
'Stupid things!'
Alice began in a loud, indignant voice, but she stopped hastily, for the White Rabbit cried out, 'Silence in the court!' and the King put on his spectacles and looked anxiously round, to make out who was talking.
Alice could see, as well as if she were looking over their shoulders, that all the jurors were writing down 'stupid things!' on their slates, and she could even make out that one of them didn't know how to spell 'stupid,' and that he had to ask his neighbour to tell him.
'A nice muddle their slates'll be in before the trial's over!' thought Alice.
One of the jurors had a pencil that squeaked.
This of course, Alice could not stand, and she went round the court and got behind him, and very soon found an opportunity of taking it away.
She did it so quickly that the poor little juror (it was Bill, the Lizard) could not make out at all what had become of it; so, after hunting all about for it, he was obliged to write with one finger for the rest of the day; and this was of very little use, as it left no mark on the slate.
'Herald, read the accusation!' said the
On this the White Rabbit blew three blasts on the trumpet, and then unrolled the parchment scroll, and read as follows:--
'The Queen of Hearts, she made some tarts, All on a summer day:
The Knave of Hearts, he stole those tarts, And took them quite away!'
'Consider your verdict,' the King said to the jury.
'Not yet, not yet!' the Rabbit hastily interrupted.
'There's a great deal to come before that!'
'Call the first witness,' said the King; and the White Rabbit blew three blasts on the trumpet, and called out, 'First witness!'
The first witness was the Hatter.
He came in with a teacup in one hand and a piece of bread-and-butter in the other.
'I beg pardon, your Majesty,' he began, 'for bringing these in: but I hadn't quite finished my tea when I was sent for.'
'You ought to have finished,' said the King.
'When did you begin?'
'Fourteenth of March, I think it was,' he said.
'Fifteenth,' said the March Hare.
'Sixteenth,' added the Dormouse.
'Write that down,' the King said to the jury, and the jury eagerly wrote down all three dates on their slates, and then added them up, and reduced the answer to shillings and pence.
'Take off your hat,' the King said to the Hatter.
'It isn't mine,' said the Hatter.
'Stolen!' the King exclaimed, turning to the jury, who instantly made a memorandum of the fact.
'I keep them to sell,' the Hatter added as an explanation; 'I've none of my own.
I'm a hatter.' Here the Queen put on her spectacles, and began staring at the Hatter, who turned pale and fidgeted.
'Give your evidence,' said the King; 'and don't be nervous, or I'll have you executed on the spot.'
This did not seem to encourage the witness at all: he kept shifting from one foot to the other, looking uneasily at the Queen, and in his confusion he bit a large piece out of his teacup instead of the bread-and- butter.
Just at this moment Alice felt a very curious sensation, which puzzled her a good deal until she made out what it was: she was beginning to grow larger again, and she thought at first she would get up and leave the court; but on second thoughts she decided to remain where she was as long as there was room for her.
'I wish you wouldn't squeeze so.' said the
Dormouse, who was sitting next to her.
'I can hardly breathe.' 'I can't help it,' said Alice very meekly:
'I'm growing.' 'You've no right to grow here,' said the
Dormouse.
'Don't talk nonsense,' said Alice more boldly: 'you know you're growing too.'
'Yes, but I grow at a reasonable pace,' said the Dormouse: 'not in that ridiculous fashion.'
And he got up very sulkily and crossed over to the other side of the court.
All this time the Queen had never left off staring at the Hatter, and, just as the
Dormouse crossed the court, she said to one of the officers of the court, 'Bring me the list of the singers in the last concert!' on which the wretched Hatter trembled so, that he shook both his shoes off.
'Give your evidence,' the King repeated angrily, 'or I'll have you executed, whether you're nervous or not.'
'I'm a poor man, your Majesty,' the Hatter began, in a trembling voice, '--and I hadn't begun my tea--not above a week or so--and what with the bread-and-butter getting so thin--and the twinkling of the tea--'
'It began with the tea,' the Hatter replied.
'Of course twinkling begins with a T!' said the King sharply.
'Do you take me for a dunce?
Go on!'
'I'm a poor man,' the Hatter went on, 'and most things twinkled after that--only the
March Hare said--' 'I didn't!' the March Hare interrupted in a great hurry.
'You did!' said the Hatter.
'I deny it!' said the March Hare.
'He denies it,' said the King: 'leave out that part.'
'Well, at any rate, the Dormouse said--' the Hatter went on, looking anxiously round to see if he would deny it too: but the Dormouse denied nothing, being fast asleep.
'After that,' continued the Hatter, 'I cut some more bread-and-butter--'
'But what did the Dormouse say?' one of the jury asked.
'That I can't remember,' said the Hatter.
'You MUST remember,' remarked the King, 'or I'll have you executed.'
The miserable Hatter dropped his teacup and bread-and-butter, and went down on one knee.
'I'm a poor man, your Majesty,' he began.
'You're a very poor speaker,' said the
King.
Here one of the guinea-pigs cheered, and was immediately suppressed by the officers of the court.
(As that is rather a hard word, I will just explain to you how it was done.
They had a large canvas bag, which tied up at the mouth with strings: into this they slipped the guinea-pig, head first, and then sat upon it.)
'I'm glad I've seen that done,' thought Alice.
'I've so often read in the newspapers, at the end of trials, "There was some attempts at applause, which was immediately suppressed by the officers of the court," and I never understood what it meant till now.'
'If that's all you know about it, you may stand down,' continued the King.
'I can't go no lower,' said the Hatter:
'I'm on the floor, as it is.'
Here the other guinea-pig cheered, and was suppressed.
'Come, that finished the guinea-pigs!' thought Alice.
'Now we shall get on better.'
'I'd rather finish my tea,' said the Hatter, with an anxious look at the Queen, who was reading the list of singers.
'You may go,' said the King, and the Hatter hurriedly left the court, without even waiting to put his shoes on. '--and just take his head off outside,' the Queen added to one of the officers: but the
Hatter was out of sight before the officer could get to the door.
'Call the next witness!' said the King.
The next witness was the Duchess's cook.
She carried the pepper-box in her hand, and
Alice guessed who it was, even before she got into the court, by the way the people near the door began sneezing all at once.
'Give your evidence,' said the King.
'Shan't,' said the cook.
The King looked anxiously at the White Rabbit, who said in a low voice, 'Your
Majesty must cross-examine THlS witness.' 'Well, if I must, I must,' the King said, with a melancholy air, and, after folding his arms and frowning at the cook till his eyes were nearly out of sight, he said in a deep voice, 'What are tarts made of?'
'Pepper, mostly,' said the cook.
'Treacle,' said a sleepy voice behind her.
'Collar that Dormouse,' the Queen shrieked out.
'Behead that Dormouse!
Turn that Dormouse out of court!
Suppress him!
Pinch him!
Off with his whiskers!'
For some minutes the whole court was in confusion, getting the Dormouse turned out, and, by the time they had settled down again, the cook had disappeared.
'Never mind!' said the King, with an air of great relief.
'Call the next witness.'
And he added in an undertone to the Queen, 'Really, my dear, YOU must cross-examine the next witness.
It quite makes my forehead ache!'
Alice watched the White Rabbit as he fumbled over the list, feeling very curious to see what the next witness would be like, '--for they haven't got much evidence YET,' she said to herself.
Imagine her surprise, when the White Rabbit read out, at the top of his shrill little voice, the name 'Alice!' >
Chapter XIl.
Alice's Evidence
'Here!' cried Alice, quite forgetting in the flurry of the moment how large she had grown in the last few minutes, and she jumped up in such a hurry that she tipped over the jury-box with the edge of her skirt, upsetting all the jurymen on to the heads of the crowd below, and there they
'Oh, I BEG your pardon!' she exclaimed in a tone of great dismay, and began picking them up again as quickly as she could, for the accident of the goldfish kept running in her head, and she had a vague sort of idea that they must be collected at once and put back into the jury-box, or they would die.
'The trial cannot proceed,' said the King in a very grave voice, 'until all the jurymen are back in their proper places-- ALL,' he repeated with great emphasis, looking hard at Alice as he said do.
Alice looked at the jury-box, and saw that, in her haste, she had put the Lizard in head downwards, and the poor little thing was waving its tail about in a melancholy way, being quite unable to move.
She soon got it out again, and put it right; 'not that it signifies much,' she said to herself; 'I should think it would be QUlTE as much use in the trial one way up as the other.'
As soon as the jury had a little recovered from the shock of being upset, and their slates and pencils had been found and handed back to them, they set to work very diligently to write out a history of the accident, all except the Lizard, who seemed too much overcome to do anything but sit with its mouth open, gazing up into the roof of the court.
'What do you know about this business?' the King said to Alice.
'Nothing,' said Alice.
'Nothing WHATEVER?' persisted the King.
'Nothing whatever,' said Alice.
'That's very important,' the King said, turning to the jury.
They were just beginning to write this down on their slates, when the White Rabbit interrupted: 'UNimportant, your Majesty means, of course,' he said in a very respectful tone, but frowning and making faces at him as he spoke.
'UNimportant, of course, I meant,' the King hastily said, and went on to himself in an undertone,
'important--unimportant--unimportant-- important--' as if he were trying which word sounded best.
Some of the jury wrote it down 'important,' and some 'unimportant.'
Alice could see this, as she was near enough to look over their slates; 'but it doesn't matter a bit,' she thought to herself.
At this moment the King, who had been for some time busily writing in his note-book, cackled out 'Silence!' and read out from his book, 'Rule Forty-two.
ALL PERSONS MORE THAN A MlLE HlGH TO LEAVE THE COURT.'
Everybody looked at Alice.
'I'M not a mile high,' said Alice.
'You are,' said the King.
'Nearly two miles high,' added the Queen.
'Well, I shan't go, at any rate,' said
Alice: 'besides, that's not a regular rule: you invented it just now.'
'It's the oldest rule in the book,' said the King.
'Then it ought to be Number One,' said Alice.
The King turned pale, and shut his note- book hastily.
'Consider your verdict,' he said to the jury, in a low, trembling voice.
'There's more evidence to come yet, please your Majesty,' said the White Rabbit, jumping up in a great hurry; 'this paper has just been picked up.'
'What's in it?' said the Queen.
'I haven't opened it yet,' said the White Rabbit, 'but it seems to be a letter, written by the prisoner to--to somebody.'
'It must have been that,' said the King, 'unless it was written to nobody, which isn't usual, you know.' 'Who is it directed to?' said one of the jurymen.
'It isn't directed at all,' said the White Rabbit; 'in fact, there's nothing written on the OUTSlDE.'
He unfolded the paper as he spoke, and added 'It isn't a letter, after all: it's a set of verses.'
'Are they in the prisoner's handwriting?' asked another of the jurymen.
'No, they're not,' said the White Rabbit, 'and that's the queerest thing about it.'
(The jury all looked puzzled.) 'He must have imitated somebody else's hand,' said the King.
(The jury all brightened up again.) 'Please your Majesty,' said the Knave, 'I didn't write it, and they can't prove I did: there's no name signed at the end.'
'If you didn't sign it,' said the King, 'that only makes the matter worse.
You MUST have meant some mischief, or else you'd have signed your name like an honest man.'
There was a general clapping of hands at this: it was the first really clever thing the King had said that day.
'That PROVES his guilt,' said the Queen.
'It proves nothing of the sort!' said Alice.
'Why, you don't even know what they're about!' 'Where shall I begin, please your Majesty?' he asked.
The White Rabbit put on his spectacles.
'Begin at the beginning,' the King said gravely, 'and go on till you come to the end: then stop.' These were the verses the White Rabbit read:--
'They told me you had been to her, And mentioned me to him:
She gave me a good character, But said I could not swim.
He sent them word I had not gone (We know it to be true):
If she should push the matter on, What would become of you?
I gave her one, they gave him two, You gave us three or more;
They all returned from him to you, Though they were mine before.
If I or she should chance to be Involved in this affair,
He trusts to you to set them free, Exactly as we were.
My notion was that you had been (Before she had this fit)
An obstacle that came between Him, and ourselves, and it.
Don't let him know she liked them best, For this must ever be
A secret, kept from all the rest, Between yourself and me.'
'That's the most important piece of evidence we've heard yet,' said the King, rubbing his hands; 'so now let the jury--'
'If any one of them can explain it,' said Alice, (she had grown so large in the last few minutes that she wasn't a bit afraid of interrupting him,) 'I'll give him sixpence.
I don't believe there's an atom of meaning in it.'
The jury all wrote down on their slates, 'SHE doesn't believe there's an atom of meaning in it,' but none of them attempted to explain the paper.
'If there's no meaning in it,' said the King, 'that saves a world of trouble, you know, as we needn't try to find any.
And yet I don't know,' he went on, spreading out the verses on his knee, and looking at them with one eye; 'I seem to see some meaning in them, after all. "--SAlD I COULD NOT SWlM--" you can't swim, can you?' he added, turning to the Knave.
The Knave shook his head sadly.
'Do I look like it?' he said.
(Which he certainly did NOT, being made entirely of cardboard.)
'All right, so far,' said the King, and he went on muttering over the verses to himself: '"WE KNOW IT TO BE TRUE--" that's the jury, of course--"I GAVE HER ONE, THEY
GAVE HlM TWO--" why, that must be what he did with the tarts, you know--'
'But, it goes on "THEY ALL RETURNED FROM HlM TO YOU,"' said Alice.
'Why, there they are!' said the King triumphantly, pointing to the tarts on the table.
'Nothing can be clearer than THAT.
Then again--"BEFORE SHE HAD THlS FlT--" you never had fits, my dear, I think?' he said to the Queen.
'Never!' said the Queen furiously, throwing an inkstand at the Lizard as she spoke.
(The unfortunate little Bill had left off writing on his slate with one finger, as he found it made no mark; but he now hastily began again, using the ink, that was trickling down his face, as long as it lasted.)
'Then the words don't FlT you,' said the King, looking round the court with a smile.
There was a dead silence.
'It's a pun!' the King added in an offended tone, and everybody laughed, 'Let the jury consider their verdict,' the King said, for about the twentieth time that day.
'No, no!' said the Queen.
'Sentence first--verdict afterwards.'
'Stuff and nonsense!' said Alice loudly.
'The idea of having the sentence first!'
'Hold your tongue!' said the Queen, turning purple.
'I won't!' said Alice.
'Off with her head!' the Queen shouted at the top of her voice.
Nobody moved.
'Who cares for you?' said Alice, (she had grown to her full size by this time.)
'You're nothing but a pack of cards!'
At this the whole pack rose up into the air, and came flying down upon her: she gave a little scream, half of fright and half of anger, and tried to beat them off, and found herself lying on the bank, with her head in the lap of her sister, who was gently brushing away some dead leaves that had fluttered down from the trees upon her face.
'Wake up, Alice dear!' said her sister; 'Why, what a long sleep you've had!'
'Oh, I've had such a curious dream!' said Alice, and she told her sister, as well as she could remember them, all these strange Adventures of hers that you have just been reading about; and when she had finished, her sister kissed her, and said, 'It WAS a curious dream, dear, certainly: but now run in to your tea; it's getting late.'
So Alice got up and ran off, thinking while she ran, as well she might, what a wonderful dream it had been.
But her sister sat still just as she left her, leaning her head on her hand, watching the setting sun, and thinking of little Alice and all her wonderful Adventures, till she too began dreaming after a fashion, and this was her dream:--
First, she dreamed of little Alice herself, and once again the tiny hands were clasped upon her knee, and the bright eager eyes were looking up into hers--she could hear the very tones of her voice, and see that queer little toss of her head to keep back the wandering hair that WOULD always get into her eyes--and still as she listened, or seemed to listen, the whole place around her became alive the strange creatures of her little sister's dream.
The long grass rustled at her feet as the White Rabbit hurried by--the frightened
Mouse splashed his way through the neighbouring pool--she could hear the rattle of the teacups as the March Hare and his friends shared their never-ending meal, and the shrill voice of the Queen ordering off her unfortunate guests to execution-- once more the pig-baby was sneezing on the
Duchess's knee, while plates and dishes crashed around it--once more the shriek of the Gryphon, the squeaking of the Lizard's slate-pencil, and the choking of the suppressed guinea-pigs, filled the air, mixed up with the distant sobs of the miserable Mock Turtle.
So she sat on, with closed eyes, and half believed herself in Wonderland, though she knew she had but to open them again, and all would change to dull reality--the grass would be only rustling in the wind, and the pool rippling to the waving of the reeds-- the rattling teacups would change to tinkling sheep-bells, and the Queen's shrill cries to the voice of the shepherd boy--and the sneeze of the baby, the shriek of the Gryphon, and all the other queer noises, would change (she knew) to the confused clamour of the busy farm-yard-- while the lowing of the cattle in the distance would take the place of the Mock Turtle's heavy sobs.
Lastly, she pictured to herself how this same little sister of hers would, in the after-time, be herself a grown woman; and how she would keep, through all her riper years, the simple and loving heart of her childhood: and how she would gather about her other little children, and make THElR eyes bright and eager with many a strange tale, perhaps even with the dream of
Wonderland of long ago: and how she would feel with all their simple sorrows, and find a pleasure in all their simple joys, remembering her own child-life, and the happy summer days.
THE END >
My Aspirations...
My name is Syaiful Bahri
I am 21 years old
I live in Cianjur
I am now working as an administrative staff and also as a teacher
Have you worked abroad?
I was once offered
Not that I wanted it to, but someone offered me
But since I was already working here
And studying in college too
So I turned down the offer
When, where and what kind of work?
It was 2009.
The destination was Korea, to do drawing job
Because I was studying in a Vocational School majoring in drawing
So I was offered to go to Korea to do work in the same field as my major
What was the process to go to Korea?
There was training to learn Korean language
But I didn't stick too long, only around 1-2 days
Then I changed my mind
So I came back home
Do you still want to try your luck abroad?
Not really, I am not interested
After having a long thought about it, I decided I did not want to
Especially after hearing all the news about immigrants that was like...
Gosh, no, I don't want it.
Do you have any family member or friends working as migrant workers?
Only my third sister
Forced by economic situation
That is the first time in the family, my third sister works in Arabic countries
There are friends also, but not my peers
Mostly because of economic situation as well
Most of the men go to Korea
The women usually go to Arabic countries
Besides being migrant worker, what kind of job options available here?
If they don't go abroad, they usually go to Jakarta to work
Or work as farm workers here
Or stay here and do nothing
Because job opportunities are hard to find
There is no work here
At least we should go to the city of Cianjur and work in factories
Otherwise, the young men choose to go to Jakarta
How is the education level in here?
For now, thankfully, many have graduated Senior High School or Vocational School
Before, people only studied until Middle School
Nowadays, since there are colleges that offer distance learning program, more people are pursuing college degrees
What is your education and your aspiration?
I am in semester 5 majoring in Pancasila and Civic Education
I want to be a teacher.
Hopefully I could.
Welcome to the presentation on graphing lines.
Let's get started.
So let's say I had the equation-- let me make sure that this line doesn't show up too thick.
Let's say I had the equation-- why isn't that showing up?
Let's see.
Oh, there you go. y is equal to 2x plus 1.
So this is giving a relationship between x and y.
So say x equals 1, then y would be 2 times 1 plus 1 or 3.
So for every x that we can think of we can think of a corresponding y.
So let's do that.
If we said that-- put a little table here. x and y.
And let's just throw out some random numbers for x.
If x was let's say, negative 1, then y would be 2 times negative 1, which is negative 2. Plus 1, which would be negative 1.
If x was 0 that's easy.
It'd be 2 times 0, which is 0. Plus 1, which is 1.
If x was 1, y would be 2 times 1, which is 2. Plus 1, which is 3.
If x was 2, then I think you get the idea here. y would be 5.
And we could keep on going.
Obviously, there are an infinite number of x's we could choose and we could pick a corresponding y.
So now you see we have a little table that gives the relationships between x and y.
What we can do now is actually graph those points on a coordinate axis.
So let me see if I can draw this somewhat neatly.
I'll use this line so I get straight lines.
Okay, that's pretty good.
Okay, let me draw some coordinate points.
So let's say that's 1, that's 2, that's 3.
This is negative 1, negative 2, negative 3.
So this is the x-axis.
We have 1, 2, 3.
Notice we could keep going.
1, 2, 3, and this is the y-axis.
And this would be 1, 2, 3, and so on.
This would be negative 1.
I think you get the idea.
So we can graph each of these points.
So if we have the point x is negative 1, y is negative 1.
So x, we go along the x-axis here, and we go to x is equal to negative 1.
Then we go to y is equal to negative 1, so the point would be right here.
Hope that makes sense to you.
That's the point.
I'll label it: negative 1 comma negative 1.
It's a little messy.
That says negative 1 comma negative 1.
That point I just x'ed right there.
Let's do another one.
That's this point.
I'll do it in a different color this time.
Let's say we had the point 0 comma 1.
Well, x is 0, which is here.
And y is 1, so that point is right there.
Let's do one more.
If we have the point 1 comma 3.
Well, 1 comma 3, x is 1 and we have y is 3.
So we have the point right there.
Hope that's making sense for you.
And we could keep graphing them, but I think you see here, and especially if I had drawn this a little bit neater, that these points are forming a line.
Let me draw that line in.
The line looks something like this.
That's not a good line.
Let me do it better than that.
The line looks something like this.
You see that?
Well, that's actually a pretty bad line that I just drew.
So it would be a line that goes through-- let me change tools.
It'd be a line that goes through here, through here, and through here.
I don't know if I'm making this clear at all.
Let me make these points a little bit.
You see the line will go through all of these points, but it will also go through the point 2 comma 5, which will be up here some place.
For any x that you can think of, if you had x is equal to 10,380,000,000 the corresponding y will also be on this line.
So this pink line, and it keeps going on forever, that represents every possible combination of x's and y's that will satisfy this equation.
And of course, x doesn't have to just be whole numbers or integers. x could be pi-- 3.14159.
In which case it would be someplace here and in which case y would be 2 pi plus 1.
So every number that x could be there's a corresponding y.
Let's do another 1.
So if I had the equation y is equal to-- that's an ugly y. y is equal to negative 3x plus 5.
Well, I'm going to draw it quick and dirty this time.
So that's the x-axis.
That's the y-axis.
Let's put some values here. x and y.
Let's say if x is negative 1, then negative 1 times negative 3 is 3 plus 5 is 8.
If x is 0, then y is 5.
That's pretty easy.
If x is 1, negative 3 times 1 is negative 3.
Then y is 2.
If x is 2, negative 3 times 2 is negative 6.
Then y is 1.
Is that right?
Negative 6-- no, no.
Negative 1.
I knew something was wrong there.
So let's graph some of these points.
So when x = -1, and I'm just kind of approximating, when x = -1, y = -8, so that point will be someplace around here.
And there's a whole module I'm graphing coordinates if you're finding the graphing a coordinate pair to be a little confusing.
Oh, wait.
I just made a mistake.
When x is negative 1, y is 8.
Not negative 8, so ignore this right here.
When x is negative 1, y is positive 8.
So y being up here someplace.
When x is 0, y is 5.
So it'd be here someplace.
When x is 1, y is 2.
So it's like here.
When x is 2, y is negative 1.
So as you can see-- and I've approximated it.
If I had graphing paper or if I had a better drawn chart you could have seen it and it would have been exactly right.
I think this line will do the job.
That every point that satisfies this equation actually falls on this line.
And something interesting here I'll point out.
You notice that this line it slopes downwards.
It goes from the top left to the bottom right.
While the line we had drawn before had gone from the bottom left to the top right.
Is there anything about this equation that seems a little bit different than the last?
I'll give you a little bit of a hint.
This number-- the negative 3, or you could say that the coefficient on x-- that determines whether the line slopes upward, or the line slows downward, and it tells you also how steep the line is.
And that actually, negative 3 is the slope.
And I'm going to do a whole nother module on slope.
And this number here is called the y-intercept.
And that actually tells you where you're going to intersect the y-axis.
And it turns out here, that you intersect the axis at 0 comma 5.
Let's do one more real fast.
y is equal to 2-- we already did 2x. y is equal to 1/2 x plus 2 So real fast. x and y.
And you only need two points for a line, really.
So you could just say let's say, x equals 0.
That's easy. y equals 2.
And if x equals 2 then y equals 3.
So before when we were doing 3 and 4 points that was just to kind of show you, but you really just need two points for a line.
So 0 comma 1 2.
So that's on there.
And then 1, 2 comma 3.
So it's there.
So the line is going to look something like this.
So notice here, once again, we're upward sloping and that's because this 1/2 is positive.
But we're not sloping-- we're not moving up as quickly as when we had y equals 2x. y equals 2x looked something like this.
It was sloping up much, much, much faster.
I hope I'm not confusing you.
And then the y intercept of course is at 0 comma 2, which is right here.
So if you ever want to graph a line it's really easy.
You have to just try out some points and you can graph it.
And now in the next module I'm going to show you a little bit more about slope and y-intercept and you won't even have to do this.
But this gives you good intuitive feel, I think, what a graph of a line is.
I hope you have fun.
 We're asked to solve for x. And we have 9x squared minus 42x, plus 29 is equal to negative 20.
Now, you might be tempted immediately to try to factor the left-hand side of this equation to get the product of two binomials, and that they equal negative 20. But if you think about it, that's not going to help you much. That product of two binomials is only useful if they're equal to 0.
But if we make this a negative 7, because negative 7 would also work, negative 7 squared is also 49. Then 3 times negative 7, times 2 is negative 42. Let me write that down.
Revolution on Represent 107.3 FM My name is Tarek
Now listeners, you may remember not too long ago we had a spoken word artist by the name of Suli Breaks.
Came down and dropped a live session and a lot of you were excited about that.
I was excited this morning when I opened up a package, I had no idea what it was.
Opened it up, put it in the player, pressed play, and it TOTALLY blew me away.
It's his brand new piece from his brand new "The Dormroom Ep".
Ima have to let spoken word do what it does best, and let it speak for itself.
Brand new Suli Breaks!!
Right now, there is a kid finishing parents evening in a heated discussion with his mother.
Saying:
"Why does he have to study subjects he will never, ever use in his life?"
And she will look at him blank eyed stifle a sigh, think for a second, then lie.
She'll say something along the lines of,
"You know to get a good job you need a good degree and these subjects help you get a degree."
"We never had this opportunity when I was younger." and he will reply:
"But you were young a long time ago, weren't you Mum?" and she won't respond although what he implies makes perfect sense that societies needs would have changed since she was 16.
But she will ignore him, grip his hand more sternly, and drag him to the car.
What she doesn't know, is that she didn't ignore him just to shut him up.
She didn't lie because they are just returning him from parents evening, and an argument in the hallway would look bad on her resume.
She won't lie because she had just spent the last hour convincing a stern faced teacher that she would ensure that her child studies more at home.
No!, she will lie simply because she does not know any better herself.
Although all of her adult life she has never used or applied
Pythagoras Theorem of Pathetic Fallacy and still does not know the value of "X"
She will rely on Society to tell her child who has one of the sharpest minds in the school, but is hyperactive, unfocused, easily distracted and wayward.
Students!
How many equations, subjects, or dates did you memorize just before an exam never to use again?
How many "A" grades did you get which were never asked for when applying for a job?
How many times have you remembered something 5 minutes after the Teacher has said "Stop writing." only to receive your results a month later to realize that you were only 1 mark short of the top grade?
Does that mean that remembering 5 minutes earlier would have made you more qualified for a particular job?
Well, on an application form it would have.
We all have different abilities, thought processes, experiences, and genes.
So why is a class full of individuals tested by the same means?
That means Cherrelle thinks she's dumb because she couldn't do a couple sums, and if this issue is not addressed properly, it then becomes a self fulfilling prophecy!
Then every school has the audacity to have policy on equality! "Huh" the irony!!
Exams are Society's methods of telly you what you're worth, but you can't let Society tell you what you are because this is the same Society that tells you that abortion is wrong, but then looks down on teenage parents! The same Society that sells products to promote natural hair, looks and a smooth complexion with the model on the box, half photo-shopped has fake lashes and hair extensions. With Pastors that preach charity, but own private jets.
I'm Michelle, founder of Macchiatto -- a boutique, branding and packaging firm in San Francisco.
I use Evernote Smart Notebook all the time for sketches and inspiration.
Thinking visually can be very cumbersome, so having Evernote helps me keep everything organized in one place.
I literally take it everywhere because you'll never know when a design idea will come.
The project I'm working on right now is seasonal greeting cards that will be sent up to our clients.
I always start by sketching out rough ideas, then I take the most successful sketches and refine them.
When I want to save my designs to Evernote I tag it with a Smart Sticker.
Then snap a picture with Evernote's Page Camera.
My favorite part is that I can take the sticker with me wherever I want.
This sticker here sends my drawing to a shared notebook.
When I need to find it later
I use Evernote Search to bring it up anytime.
As a visual thinker, sketching on paper is a critical part of the process.
My ideas are everywhere.
Being able to save to Evernote quickly and easily helps me stay organized and ultimately makes my work better.
Hi, my name is Jason Cornwell and I'm a User Experience Designer on Gmail.
We've been hard at work to update Gmail with a new look and I'm excited to share with you some of the biggest improvements.
If you prefer a specific display density, you can easily set that as well.
Some people use a lot of labels, others chat a lot.
You can now adjust the size of the label and chat areas to meet your needs.
Even if you do nothing, Gmail adapts to you.
The new look allows themes to really shine and we've updated many of them with new high-resolution imagery.
You may want to take a moment to check out one of the many new high definition themes.
Conversations in Gmail have been redesigned to improve readability and to feel more like a real conversation.
We've also added profile pictures so you can see who said what.
You can also create a filter from the search box.
We're excited to finally share the new Gmail with you and hope you'll enjoy the new design as much as we do.
Let's do some solid geometry and volume problems. so they tell us shown is a triangular prism. and so there's a couple of types of three dimensional figures that deal with triangles.
And this is what a triangular prism looks like it has a triangle on one two faces and they are kind of separated, they kind of have rectangles in between. the other kind of triangular three dimensional figures as you might see would be pyramids this is a rectangular pyramid, cuz it has a rectangular, or it has a square base, just like that you could also have a triangular pyramid where literally every side is a triangle. but this over here is a triangular prism.
I don't want to get to much into the shape classification. if the base of the triangle b is equal to 7 the height of the triangle 'h' is equal to 3 and the lenght of the prism 'l' is equal to 4 what is the total volume of the prism? so they are saying that the base is equal to seven so this right over here is equal to base is equal to seven the height of the triangle is equal to 3 so this right over here this distance right over here
'h' is equal to 3 and the length of the prism is equal to 4 so i'm assuming it is this dimension right over here is equal to 4 so length is equal to four so in this situation what you really just have to do is figure out the area of this triangle right over here we could figure out the area of this triangle and multiply it by how much you go deep so multiply it by this length so the volume is going to be the area of this triangle
let me do it in pink the area of this triangle we know that the area of a triangle is one half, times the base, times the height so the area this area right over here is going to be one half times the base times the height and we are going to multiply it by like kind of our depth of our triangular prism so we have a depth of four so we are going to multiply that times the four times this depth times the four and we get, let's see one half times four is two so these guys cancel out, you'll just have a two and then 2 times 3 is 6 6 times 7 is forty... is forty two and it would be in some kind of cubic unit so if these were in i don't know centimeters, it would be centimeters cubed but they are not making us focus on units in this problem
let's do another one shown is a cube if each side is of equal length 'x' is equal to 3 what is the total volume of the cube? so each side is equal length x which happens to equal to 3 so this side is 3 this side over here x is equal to 3 every side x is equal to 3 so it's actually the same exercise as the triangular prism it is actually a bit easier when you are doing it with a cube where you really just want to find the area of this surface right over here now this is pretty straight forward this is just a square it would be the base times the height or since they are the same it is just 3 times 3 so the volume is going to be the area of this surface 3 times 3 times the depth times the depth so we go 3 deep so times so times three and so we get 3 times 3 times 3 so this is 27 or you might recognize this from exponents this is the same thing as three to the third power and that is why sometimes if you have something to the third power they'll say you cubed it because literally to find the volume of a cube you take the length of one side and you multiply that number by itself three times one for each dimension one for the length, the width, and or I guess the height, the length and the depth. depending on how you want to define them. so it's literally just 3 times 3 times 3
We're asked to subtract and simplify the answer, and we have 8/18 minus 5/18.
So subtracting fractions is very similar to adding fractions.
If we have the same denominator, the denominator in the difference is going to be the same as the denominators in the two numbers that we're subtracting, so it's going to be 18.
And our numerator is going to be the difference between the numerators.
So in this case, it is 8 minus 5, and this will be equal to 3 over 18, which is the answer, but it's not completely simplified, because both 3 and 18 are divisible by 3.
So let's divide them both by 3.
So you divide 3 by 3, you divide 18 by 3, and you get 3 divided by 3 is 1.
18 divided by 3 is 6, so you get 1/6.
And just to see this visually, let me draw 18 parts.
Let me draw 18 parts here.
So it might be a little bit of a messy drawing.
I'll try the best I can.
So let me draw six in this direction.
So that is three right there.
We have another three, so that's six parts.
And then let me split this into three columns.
So there we go.
We have 18 parts.
Now 8/18 is equal to one, two, three, four, five, six, seven, eight.
That's 8/18.
And now we want to subtract five of the eighteenths, so we subtract one, two, three, four, five.
Now, what do we have left over?
Well, we have three of the eighteenths left over, so you have that right there.
You have three of the eighteenths left over.
Now, if you turn three of the eighteenths into one piece, how many of those bigger pieces do you have?
This is one of those big pieces.
Now, where are the other ones?
Well, this is another big piece right here.
This is another big piece right here, another one, another one, and another one.
If you had 18 pieces and you merged three of the pieces into one, then you actually end up with only six pieces.
You end up with six pieces.
Hopefully, you see that each row is one of the pieces now, and the blue is exactly one of the six, so 3/18 is the same as 1/6.
In the last video we got some practice adding what we could consider smaller numbers. For example, if we added 3 + 2 we could imagine that if maybe I had three lemons -- 1, 2, 3 -- and if I were to add to those three lemons maybe two lime-- Is it lime or limes? Let's just -- Well, two green lemons -- or two more tart pieces of fruit
So 3 + 2 = 5. And we also saw that that's the exact same thing as if we add 2 + 3. And I think that makes sense.
You're still going to end up with 5 pieces of fruit.
1, 2, 3, 4, 5. Just like that. So it doesn't matter what order you add in.
You're still going to get five. And this way of thinking about addition I view as the counting way of thinking about addition
The other thing we saw in the last video is the number line version
And they're essentially the same thing So we could draw a line. And all a number line is it lists all of the numbers in order.
Maybe you can think about what that might mean tonight.
But let's use a number line for these addition problems up here.
So in the last video -- just as a bit of a review -- you can view 3 + 2 as starting at 3 -- and then adding 2 to it. Or going two greater than 3. And just going greater -- or adding on the number line -- is just moving to the right -- or moving up by two.
So we started at three and we go up by one.
And then we go up by 2, or we're jumping, and we end up at 5. Which is exactly what we got before. If we have three lemons we add one lemon, we have four lemons.
Whatever you might want to say.
And when you look at this version of it -- when you switched the order -- We started at 2 and we're adding 3 objects to it. In this case, they were lemons or limes.
1, 2, 3. And just like we expected, we got the same thing. We got 5 again.
Now what I want to do in this video -- and hopefully this was just a bit of a review -- -- is I want to tackle harder problems. I want to tackle slightly larger numbers.
Let's say I wanted to add 9 + 3. Well, there are a couple of ways we could do it. We could draw circles again.
And then if you were to count the total number of stars, you would say -- (Let me do that in a different color.)
-- 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12. I now have 12 stars. So, you would say that 9 + 3 = 12.
If you looked at the number line --
If you looked at the number line, you're, starting at 9. Maybe you have 9 stars and you add 1 star, 2 stars, 3 stars to that.
And you end up with 12 stars.
Which is the exact answer we got before. So you can do the same process when you start adding larger numbers, even though that now --
And I want you to notice, the difference now is our answer has two digits in it.
(And we'll talk more about digits in a future video.) But all a digit is is a numeral. Right?
It has a 1 and a 2. That's what 12 is.
I won't go into -- I won't dig too deep into that right now. I think you're pretty familiar with the number 12. But what I want to do is --
For example, if I were to add 27 plus -- let's say -- I don't know -- plus15. (27 + 15.)
Now, if you had a lot of time on your hands and you didn't care about how people judged you you could draw out 27 circles, and then draw out another 15 circles and then count the total number of circles you had. And that would give you an answer.
Or you could draw a number line
You could draw a number line that went all the way to whatever 27 + 15 is.
So it's going to be this really, really large number, but that wouldtake you forever. So what I'm going to do is show you a way to do this type of problem where you really just have to know your addition almost have it memorized, or at least if you don't have it memorized be able to do something like this for relatively small numbers.
And by doing it for the relatively small numbers, you can do the harder problems like this. So what you do, this is the fun part. You add, and I'll talk more about what this means in the future.
You look at each of the digits.
So we call this place, the rightmost place we call that the ones place.
And why do we call that the ones place?
Because 27 is 20 and 7 ones.
It's twenty plus seven.
It's twenty plus seven ones. You could view it as it's twenty plus seven pennies.
And this place right here is called the tens place.
Now why is it called the tens place?
I mean there's a two right there.
It's the place that's called the tens place.
So putting a two here means two tens.
The number twenty, that's two tens.
If I have one dime and you gave me another dime
I now have two dimes, and that's twenty cents
So that's what the tens place is. I don't want to confuse you I just want to show you how to do these problems right now.
We'll dig a little bit deeper in future videos. But I just want to give you that idea.
But the way to do these problems is you look at the numbers in the ones place and add those up first. So you say, OK, I'm not going to worry about this whole thing right now. Let me just add the seven and the five.
So I'm going to add the seven and the five. And if you don't know what that is hopefully you'll be able to do that in your head fairly shortly -- you could look at the number line.
Let's look at the number line here.
So if you add seven if you take seven, and you add five to it. -- 1, 2, 3, 4, 5 -- We end up at twelve.
Or if you started at five and added seven you'd also end up at twelve.
So let's write that down. We know that 7 + 5 = 12. So what we do is we say 7 + 5 is equal to
We write -- we want to write the 12.
7 + 5 is 12. But we just write the 2 here and we carry the 1. 12. one, two
And the reason -- (I'll give you a simple reason for doing that right now.) (I'll give you a better reason in the future.)
-- Is that you only had space to put one digit here and twelve is a two-digit number so we had to think of some other place to put that 1.
If you really want to think about it even more 12 is the same thing as 10 + 2, right?
That's the same thing as 12. So if we say 7 + 5, that's the same thing as 12 which is the same thing as two ones. Right?
Two 1s. 2 pennies, plus 1 dime. Plus 1 ten.
So we really just said 7 + 5 is one 10 plus two 1s.
Or 1 dime plus 2 pennies.
If that confuses you, just write, just say, well I just write the 1s digit of the 2 there and I carry the 1.
And then you do the exact same thing in the 10s place.
You add the 1 plus the 2 plus the 1. So 1 + 2 -- Let's do that on a number line. This is fun.
So we start at one. We're going to add two to it. 1 + 2.
Then you're going to add up another one. So you add another 1. You're going to end up at 4.
So you ended up at 42.
And this was pretty neat, right?
Because we didn't have to draw a number line all the way to 42.
And we'd didn't have to draw 42 objects.
Just by knowing what 7 + 5 was and by knowing what 1 + 2 + 1 was we were able to figure out that 27 + 15 = 42.
Let's do another example. Maybe I'll do a little bit of a simpler example. Let's say I had 78 + 3.
We do the exact same thing as before.
We just look at the 1s place only.
So we look at 8 + 3. What's 8 + 3?
Hopefully, we can do that in our heads at this point. But let's just think about it.
8 + 1 = 9.
8 + 2 = 10.
8 + 3 is going to be equal to 11.
You could do that on the number line if it makes it easier to visualize for you.
So 8 + 3 = 11.
So what we do here, we just have 8 + 3 = 11.
Put this one right here, put that there and carry the other one.
Because eleven is one ten -- one dime -- plus one penny. That's eleven.
And then we add the tens place.
1 dime plus 7 dimes is equal to 8 dimes.
So 78 + 3 = 81.
And now there's one thing I want to show you.
You don't always have to carry numbers like that. Only if the answer to one of these has more than one digit in it. 11 is a two-digit number.
So, for example, if I have 56 + 2. Here, I could just say 6 + 2 is 8. Right?
So 6 + 2 = 8.
And then, I don't have anything to add this 5 to.
So, I just bring the five down here.
So 56 + 2 = 58.
Just like that. And this is one you actually could have drawn on the number line. It wouldn't have been too hard.
So, if you were to draw the number line like that, 0 would be way off to the left some place. But let's say I had 50, no I think you'd have 49 you could keep going to the left but you have 51, 52 -- Actually let me start a little higher than that.
But if we start at fifty-six right there and we add two
We go up one, we go up two. We end up at 58.
So just like, that we're able to do that problem.
I'll see you in the next video.
I have spent my entire life either at the schoolhouse, on the way to the schoolhouse, or talking about what happens in the schoolhouse. (Laughter)
Both my parents were educators, my maternal grandparents were educators, and for the past 40 years, I've done the same thing.
And so, needless to say, over those years I've had a chance to look at education reform from a lot of perspectives.
Some of those reforms have been good.
Some of them have been not so good.
And we know why kids drop out.
We know why kids don't learn.
It's either poverty, low attendance, negative peer influences...
We know why.
But one of the things that we never discuss or we rarely discuss is the value and importance of human connection.
Relationships.
James Comer says that no significant learning can occur without a significant relationship.
George Washington Carver says all learning is understanding relationships.
Everyone in this room has been affected by a teacher or an adult.
For years, I have watched people teach.
I have looked at the best and I've looked at some of the worst.
A colleague said to me one time,
"They don't pay me to like the kids.
They pay me to teach a lesson.
The kids should learn it.
I should teach it, they should learn it,
Case closed."
Well, I said to her,
"You know, kids don't learn from people they don't like."
(Laughter) (Applause)
She said, "That's just a bunch of hooey."
And I said to her, "Well, your year is going to be long and arduous, dear."
Needless to say, it was.
Some people think that you can either have it in you to build a relationship, or you don't.
I think Stephen Covey had the right idea.
He said you ought to just throw in a few simple things, like seeking first to understand, as opposed to being understood. Simple things, like apologizing.
You ever thought about that?
Tell a kid you're sorry, they're in shock. (Laughter)
I taught a lesson once on ratios.
I'm not real good with math, but I was working on it. (Laughter)
And I got back and looked at that teacher edition. I'd taught the whole lesson wrong. (Laughter)
So I came back to class the next day and I said,
"Look, guys, I need to apologize.
I taught the whole lesson wrong.
I'm so sorry."
They said, "That's okay, Ms. Pierson.
You were so excited, we just let you go."
I have had classes that were so low, so academically deficient, that I cried.
I wondered, "How am I going to take this group, in nine months, from where they are to where they need to be?
And it was difficult, it was awfully hard.
How do I raise the self-esteem of a child and his academic achievement at the same time?
One year I came up with a bright idea.
I told all my students,
"You were chosen to be in my class because I am the best teacher and you are the best students, they put us all together so we could show everybody else how to do it."
One of the students said, "Really?"
(Laughter)
I said, "Really.
We have to show the other classes how to do it, so when we walk down the hall, people will notice us, so you can't make noise.
You just have to strut." (Laughter)
And I gave them a saying to say: "I am somebody.
I was somebody when I came.
I'll be a better somebody when I leave.
I am powerful, and I am strong.
I deserve the education that I get here.
I have things to do, people to impress, and places to go."
And they said, "Yeah!" (Laughter)
You say it long enough, it starts to be a part of you.
(Applause)
I gave a quiz, 20 questions.
A student missed 18.
I put a "+2" on his paper and a big smiley face. (Laughter)
He said, "Ms. Pierson, is this an F?"
I said, "Yes." (Laughter)
He said, "Then why'd you put a smiley face?"
I said, "Because you're on a roll.
You got two right.
You didn't miss them all." (Laughter)
I said, "And when we review this, won't you do better?"
He said, "Yes, ma'am, I can do better."
You see, "-18" sucks all the life out of you. "+2" said, "I ain't all bad."
For years, I watched my mother take the time at recess to review, go on home visits in the afternoon, buy combs and brushes and peanut butter and crackers to put in her desk drawer for kids that needed to eat, and a washcloth and some soap for the kids who didn't smell so good.
See, it's hard to teach kids who stink. (Laughter)
And kids can be cruel.
And so she kept those things in her desk, and years later, after she retired,
I watched some of those same kids come through and say to her, "You know, Ms. Walker, you made a difference in my life.
You made it work for me.
You made me feel like I was somebody, when I knew, at the bottom, I wasn't.
And I want you to just see what I've become."
And when my mama died two years ago at 92, there were so many former students at her funeral, it brought tears to my eyes, not because she was gone, but because she left a legacy of relationships that could never disappear.
Can we stand to have more relationships?
Absolutely.
Will you like all your children? Of course not.
(Laughter)
And you know your toughest kids are never absent.
(Laughter)
Never.
You won't like them all, and the tough ones show up for a reason.
It's the connection.
It's the relationships.
So teachers become great actors and great actresses, and we come to work when we don't feel like it, and we're listening to policy that doesn't make sense, and we teach anyway.
We teach anyway, because that's what we do.
Teaching and learning should bring joy.
How powerful would our world be if we had kids who were not afraid to take risks, who were not afraid to think, and who had a champion?
Every child deserves a champion, an adult who will never give up on them, who understands the power of connection, and insists that they become the best that they can possibly be.
Is this job tough? You betcha.
Oh God, you betcha.
But it is not impossible.
We can do this.
We're educators.
We're born to make a difference.
Thank you so much.
(Applause)
I received a problem from Bradley.
I don't know his last name.
I'm assuming it's a he.
I don't know where he lives.
But the problem he gave is interesting.
And I don't think I've covered this before.
So I think it's worth covering. So the problem he gave, if I read his note properly, is this:
3 sine squared of x is equal to 1 plus cosine of x.
So at first cut, this seems like a difficult problem.
How do I-- You can't solve for x.
You would have arcsines and the square roots and cosines et cetera.
Et cetera.
So the way I approached this is-- Any time that if I see a cosine x here but then I see a sine squared x here, I start thinking of what trig identities are at my disposal.
And what trig identities involve a sine squared x?
Well the most basic trig identity, and this comes out of the unit circle definition of trig functions, is that sine squared x plus cosine squared x is equal to 1. And that comes out of the fact that the equation of a circle is x squared plus y squared is equal to the radius squared. But it's the unit circle.
It's equal to 1 squared. But anyway.
Hopefully you have this memorized if you've already been watching the trig videos.
So what does sine squared x equal?
Well let's solve for it.
So sine squared x is equal to 1 minus cosine squared x, right?
So we could substitute this term right here with this.
And what does that get us?
Well we're just playing around at this point, but at least that way, everything is in terms of cosine of x.
So let's do that.
Let's substitute.
So we get 3 times sine squared of x.
We just showed that sine squared of x is the same thing as 1 minus cosine squared of x. Is equal to 1 plus cosine of x.
We can simplify a little bit. 3 minus 3 cosine squared of x is equal to 1 plus cosine of x.
I don't know.
Just for kicks, let's put everything onto the right side of the equation. And you'll see it wasn't just for kicks. 0-- right?
I'm just going to --is equal to-- let's put this onto the right side --3 cosine squared x. And then-- Let's see.
We have to subtract 3 from this side.
Well let's just write the cosine x.
Plus cosine x. And then 1 minus 3 is minus 2.
Let me make sure I didn't make a careless mistake.
We have negative 3 here.
We added 3 cosine x-- 3 cosine squared of x to both sides, right?
We subtracted 3 from both sides.
Minus 2 and this cosine x is this cosine x.
Now what can we do?
Well this is where it gets interesting.
Because this looks an awful lot like a quadratic equation except for the fact that instead of having ax squared plus bx plus c, we have a cosine squared x.
So instead of just having an x squared, we have a whole cosine of x squared.
So what do I mean by that?
Let me make a substitution.
And then I think it'll all become clear to you.
Let's make the substitution that a-- and I'm just picking the letter a arbitrarily --is equal to cosine of x.
So if we were to take the cosine x's of this and replace them with a, what do we get?
And I'm just going to switch it around.
So I want to put the 0 on that side. Equal 0.
So we get 3-- Well cosine squared x.
That's the same thing as cosine of x squared, right?
So we get 3a squared plus a minus 2 is equal to 0.
Well now we have a pure quadratic.
And we can solve it using the quadratic equation.
So what's the quadratic equation?
Let me write it up here.
Negative b plus or minus the square root of b squared minus 4ac.
All of that over 2a.
So what are the roots of this equation?
Well what's minus-- And remember this a is different than this a.
Maybe I shouldn't have used a as a letter. But these-- a, b, and c in the quadratic equation represent the coefficients.
So this is a. b is 1. And c is just minus 2.
So what are the roots of this? So the a's that solve this. a can equal-- And I know I confused you.
I could-- Let me actually write it different.
Let's make this, instead of a is equal to cosine x, let me say that-- I don't know. Let me pick a good letter that's not involved in the-- Let me say d.
So 3d squared plus d minus is 2.
So now the a's, b's and c's are definitely the coefficients.
So the solutions to this are d-- because I didn't want to use a, b, or c --d is equal to minus b.
Well, b is 1. Minus 1. And if this is completely foreign to you, you should review the videos on the quadratic equation.
Minus b squared.
Well that's 1 squared. Minus 4ac.
So minus 4 times a, times 3, times c. Well c is minus 2, right?
So we get a-- That minus cancels there. And we have a 2 there. All of that over 2 times a. a is 3, so we have it over 6.
So this equals minus 1 plus or minus the square root-- What is this?
4 times 3 times 2. 24 plus 1. 25.
Oh.
This works out cleanly. Over 6.
So that equals minus 1 plus or minus 5 over 6.
And so what are the roots?
The roots are-- What's minus 1 minus 5?
That's minus 6 over 6.
So it's minus 1.
What's the other one?
Minus 1 plus 5 is 4. 4 over 6 is 2/3.
So the solution is to the equation-- Let me clear up some space.
Hopefully it'll let me clear up some space here.
Let me see.
What was I doing?
Oh.
Maybe I want to leave-- I can get rid of this.
You know the identity.
And you also know the quadratic formula.
Let's see.
Actually, let me get rid of this too.
Clear up a bunch of space.
I wanted to leave this here because this showed how this turned into a quadratic, but instead of having it in terms of just a variable, we have it in terms of cosine of x. And then we made this d is equal to cosine of x.
Anyway.
So the solution to this equation is that quadratic.
Is d is equal to minus 1 or 2/3, right?
But, of course, we made the substitution long ago that d is equal to cosine of x.
So the solution to this equation, in terms of x, is the solution to this equation.
Cosine of x is equal to minus 1 or cosine of x is equal to 2/3.
Well this one's easy, right? x is equal to arccosine of minus 1.
I always forget if there's two c's when you do arccosine.
Anyway, so what-- At what degree or radian value does the cosine of x equal minus 1?
Well it's at pi, right?
So x could equal pi, which is also or 180 degrees.
This one is not as easy.
I think I will have to use a calculator for this.
Unless I'm-- whoops.
So you may not realize it, but Google is actually a calculator. And a far more advanced calculator than most.
So we could use Google to figure out the arccosine of 2/3.
Let's do that.
Arccosine-- and I don't know if I'm spelling it right --of 2 over 3.
Google tells us that it's 0.841 and a bunch of numbers.
So x is equal to arccosine of 2 over 3.
So x is equal to 0.84106.
Let's see if they work.
Let's, just for fun, let's just see if this one works.
Let's see if we substitute pi into this equation we get the correct answer.
Well what's sine of pi?
Let me erase all of this is so we can check it.
I'm only going to check pi. The 0.84.
And I don't know.
That's messy.
But you could do that in your own time.
So let's check pi. x equals-- No.
That's not what I wanted to do.
So what is-- Let's make sure this works with pi. 3 sine squared of pi is equal to 1 plus cosine of pi.
Well what's sine of pi?
This is equal to 3 sine of pi squared.
This is equal to 1 plus cosine of pi.
Well sine of pi is 0, right?
The y-value when you go 180 degrees is 0.
So this is 0.
And what's cosine of pi?
Cosine of pi is negative 1.
So 1 plus minus 1.
Well this is true.
So pi worked in that equation.
I think if you substitute that 0841068 whatever, you'd also find that that works.
So thanks Bradley for sending this.
I thought this was a neat problem because it looks like it's trigonometry.
And it was trigonometry but you had to know a little bit of identities.
And then you had to recognize it as a quadratic equation.
I will see you in a future video.
For an art project, a pentagon made of construction paper is cut into five equal slices.
Two of the slices are removed.
Write the remaining portion of the pentagon as a fraction.
So let's draw ourselves a pentagon.
A pentagon is just a five-sided figure, so it looks like this.
It's also where the Department of Defense is located, a building that's actually in this shape.
That's why they call it the Pentagon.
Let me draw it a little nicer than that.
It looks something like this.
Eh!
My pentagon drawing skills need some work.
That's a pretty decent shot at a pentagon.
So that's the pentagon made out of construction paper.
Notice it has one, two, three, four, five sides.
That's why it's called a pentagon.
And it's cut into five equals slices, so we could do that.
Maybe that's the center of the pentagon.
Here this is one slice right there.
That is two slices, three slices, four slices, and then a fifth slice, so you can imagine these are all equal slices.
Now, they're saying two of the slices are removed.
Let's say we remove that slice up there.
Let's say we remove the slice right next to it right over there.
And then they want us to write the remaining portion of the pentagon as a fraction.
Well, I have this slice right there, that slice right over here and then this slice.
So you have three slices remaining out of a total possible of how many?
How many slices are in the entire pentagon?
So if you look at the entire pentagon, if you consider all of the slices, we have five slices.
So if you consider the entire pentagon, it is made up of five total slices.
So it's three remaining out of five total slices, so you could say that 3/5 of the pentagon remain.
Or you could say 2/5 were removed.
That's two of the five slices were removed, and then three are remaining, or 3/5 of the pentagon remain.
Now that we know what a solution is, let's think a little bit about what it takes to get a molecule to be soluble into a solution or into a solvent. So let's say I start off with a salt, and I'll do a little side here, because in chemistry, you'll hear the word salt all the time.
And this indeed is both a salt from the Food Channel point of view and from the chemistry point of view, although the chemistry point of view does not care about what it does to season your food. The chemistry point of view, the reason why it's called a salt is because it's a neutral compound that's made with ions. So we all know that this is made when you take sodium.
I could do another oxygen here, and you can kind of see the structure that forms, although what I'm drawing, this is actually more of a-- if you were in a solid state, this would be kind of rigid and they would just vibrate in place. In the liquid state, they're all moving around. They're rubbing up against each other, but they're staying very close.
We know that it becomes smaller as you go to the right of the Periodic Table, so sodium is quite a large atom, while chloride is a good bit smaller, but they're both bigger than oxygen and a lot bigger than hydrogen. So let me draw that. So sodium-- I'll do sodium as a positive.
Sodium is positive and then you have the chloride. The chloride I'll do in purple. They're still pretty big.
So what you need to do is, the warmer the water you have-- I mean, you can fit it into cold water, because at least cold water has some give, but the warmer the better, because you have some kinetic energy, and that essentially gives space. Or it makes room for this sodium ion that's entering in to kind of bump its way into a configuration that's reasonably stable. And a reasonably stable configuration would look something like this.
In order to get as much of the sodium chloride into your water sample, you want to heat up the water as much as possible. Because what that does is it allows these bonds to not be taken as seriously and these relatively huge atoms to kind of bump their way in. So, in general, if you think about solubility of a solute in water-- or especially if you think of a solid solute, which is sodium chloride-- into a liquid solvent, then the higher the temperature while you're in the liquid state, the more of the solid you're going to be able to get into the liquid, or you're going to raise solubility.
Keep putting it into a glass, and at some point it'll dissolve. You could shake it a little bit, just to make sure. You could think about what's happening at the molecular
Now, right when you start seeing that, if you were to put it in the microwave or if you were to heat it up, you would see that even these guys are able to be absorbed in the water, and that's because the extra kinetic energy from the temperature is making it more likely that these guys are going to be able to bump out of configuration for just long enough for these guys to bump in. And just a little side note, when you take these salts, which are just ionic compounds that are neutral, they're made of ions, but they cancel each other out. When you put them in water, these compounds by themselves aren't normally-- when they're in the solid state, they don't normally conduct electricity.
If you were to dissolve carbon dioxide in water-- so if you were to dissolve this in water, so those are some carbon dioxide molecules. I'm just drawing the whole molecule as a circle. What do these molecules want to do?
You want colder temperatures to put more gas into the solution, or you want higher pressure to keep it-- at least in the way my mind works-- from escaping out the top. Anyway, hope you found that useful.
what i want to do in this video is a handful of fairly simple inequality videos. But the real value of it, I think, will be just to get you warmed up in the notation of inequality. So, let's just start with one. we have x minus 5 is less than 35.
And that's one of the distinctions of an inequality. In an equation, you typically have one solution, or at least the ones we've solved so far. In the future, we'll see equations where they have more than one solution.
But in the ones we've solved so far, you solved for a particular x. In the inequalities, there's a whole set of x's that will satisfy this inequality. So they're saying, what are all the x's, that when you subtract 5 from them, it's going to be less than 35?
Minus 100 minus 5. That's less than 35. 5 minus 5.
That won't change the inequality. It won't change the less than sign. If something is less than something else, something plus 5 is still going to be less than the other thing plus 5.
This negative 5 and this positive 5 cancel out. x is less than 35 plus 5, which is 40.
And that's our solution. And to just visualize the set of all numbers that represents, let me draw a number line here.
And I'll do it around-- let's say that's 40, this is 40, 41, 42. And then we could go below 40. 39, 38.
Say we have x plus 15 is greater than or equal to negative 60.
Notice, now we have greater than or equal. So let's solve this the same way we solved that one over there. We can subtract 15 from both sides.
So if I subtract 15 from both sides, so I do a minus 15 there, and I do a minus 15 there. Then the left-hand side just becomes an x. Because obviously you have 15 minus 15.
So we can include the point, because we have this greater than or equal sign.
Notice we're not making it hollow like we did there, we're making it filled in because it can equal negative 75, or it needs to be greater than.
So greater than or equal. We'll shade in everything above negative 75 as well. So in orange is the solution set.
It can be an arbitrarily large number as long as it's greater than or equal to negative 75. Let's do a couple more.
Let's do x minus 2 is less than or equal to 1. Once again, we want to get just our x on the left-hand side. Get rid of this negative 2.
So let me graph the solution set. So let's say this is 0, 1, 2, 3, 4. That's negative 1, negative 2.
The left-hand side just becomes x, and then the right-hand side is less than or equal to 32.
We draw the number line. If this is 32, this is 33, this is 31. I could keep adding things above and below 32.
Remember, the reason why we're filling in this solid, the reason why 32 is an acceptable solution to this original inequality, is because of this less than or equal sign. Over here, you didn't have less than or equal, and that's why 40 wasn't part of the solution set.
This is Randy abandoned at the age of 2 by the family at the Children Loving Association in Klang, Selangor
One day, his grandma sent here, morning six o clock that was one year before grandma not yet come back yet. I heard from grandma, father passed away and mother ran away. The grandma told be when she send him here, his date of birth is 28th March 2009
When he come here he already start crying normally crying and angry person and fighting person
We see on his body lots of burn, now he got improvement can talk Tamil and talk Chinese and can understand all kinds of language
Without the parents and any papers he is considered stateless.
Let's say, the children never get Identity card in the future cannot go to school cannot do anything
So we also cannot do anything and we sent back to the Welfare Department and Welfare will take over.
This home is managed by volunteers and financially supported by the founder Reverend Ani Yeshe Dolma and members of the public
Four workers taking care of the children, 8 children are here 4 working ladies here and 11 volunteers working with the Reverend there sending children to school, office work and the everyday arrange their food and all kinds of activities.
I hope very soon get the IC for Randy we hope can take care of these children they are very happy
We need some support and public help
This is "like".
This is "dislike".
In the 6 years that Thailand's 3 Muslim provinces have been under emergency decree countless numbers of people have been affected by the unjust power and control from government officials
Emergency decree isn't a good law
Those who were arrested got tortured in order to confess
That is not right
Because when being tortured, those who couldn't stand the pain had to admit even though they didn't do anything
That is not right
If they really did wrong, there should be evidence and punishment accordingly
Entering the 8th year of violence in the 3 Muslim provinces, many groups and civil society organizations have been established with the objective and determination to see peace once again
As well as the Civil Society Network Against Emergency Decree that has been continuously campaigning against the decree with different activities from releasing statements
and holding different campaigns like "kicking out" the decree with soccer or by driving classical cars and motorbikes, to organizing a people's forum against the decree.
Recently, the activities have been brought up to the international level with the "Post Peace Campaign"
which allows local people to express their opinions on this emergency decree on postcards as reflections of their feelings and make their voices heard among representatives of international organizations.
Today, we're going to gather the voices of people who want to call for ending the emergency decree
by writing short messages that we want to express to the United Nations on these postcards We'll send all of them to the U.N. Headquarters in Thailand on 10 December which is the Thai Constitution Day and also International Human Rights Day
The campaign to express people's feelings on postcards has received good response from local people, especially those working in city area of Pattani which faced the effects of the decree more.
I hope the situation will be normal soon so I can work more conveniently
When going to pray or elsewhere in the early morning, I don't need to worry that I'll be searched by the army or arrested for investigation
I think there must be a campaign against the emergency decree
This emergency decree has been enforced for a long while and its enforcement has violated the basic rights of the local people
We no longer agree with the emergency decree's enforcement in our areas
If it's still necessary to use the emergency decree then there must be justice
If there's no justice, then it should be repealed
The movement of the Civil Society Network Against Emergency Decree doesn't only aim to have the decree repealed,
but also to reduce the conditions that could lead to endless violence.
Time has proven that the emergency decree couldn't reduce the number of incidents And it even creates hatred among the people who were affected by the unjust power and control of officers
Therefore, should the New Years present that the current government of Ms. Yingluck Chinnawatra
give to people who oppose the emergency decree in the 3 Muslim provinces on this coming 19 December be the repeal of the emergency decree?
We oppose the emergency decree!
We oppose the emergency decree!
We oppose the emergency decree!
Let's start again with a point let's call that point, "Point A." And what I'm curious about is all of the points on my screen that are exactly 2cm away from "Point A." So 2cm on my screen is about that far.
So clearly if I start at "A" and I go 2cm in that direction, this point is 2cm from "A." If I call that
"Point B" then I could say line segment AB is 2cm the length is 2cm.
Remember, this would refer to the actual line segment.
I could say this looks nice but if I talk about it's length, I would get rid of that line on top, and I would just say, "'AB' is equal to 2.
If I wanted to put units, I would say 2cm.
But I'm not curious just about B, I want to think about ALL the points.
The set of ALL of the points that are exactly 2cm away from "A." So I could go 2cm in the other direction, maybe get to point
"C" right over here. So "AC" is also going to be equal to 2cm. But I could go 2cm in any direction.
And so if I find that of all of the points that are exactly 2cm away from "A," I will get a very familiar looking shape, like this:
(I'm drawing this free-hand,) so I would get a shape that looks like this.
Actually, let me draw it in I don't want to make you think that it's only the points where there's white, it's ALL of these points right over here.
Let me clear out all of these and I will just draw a solid line.
It could look something like that (my best attempt.) And this set of all the points that are exactly 2cm away from "A," is a circle, which
I'm sure you are already familiar with.
But that is the formal definition, the set of all points that are a fixed distance from "A." If I said, "The set of all points that are 3cm from "A," it might look something like this:"
That would give us another circle.
(I think you get the general idea.) Now, what I want to introduce to you in this video is ourselves to some of the concepts and words that we use when dealing with circles.
So let me get rid of 3cm circle.
So first of all, let's think about this distance, or one of these line segments that join "A" which we would call the center of the circle.
So we will call "A" the center of the circle, which makes sense just from the way we use the word
'center' in everyday life, what I want to do is think about what line segment "AB" is.
"AB" connects the center and it connects a point on the circle itself.
Remember, the circle itself is all the points that are equal distance from the center. So "AB," any point,
line segment, I should say, that connects the center to a point on the circle we would call a radius.
And so the length of the radius is 2cm.
And you're probably already familiar with the word 'radius,' but I'm just being a little bit more formal.
And what's interesting about geometry, at least when you start learning at the high-school level is that it's probably the first class where you're introduced to a slightly more formal mathematics where we're a little more careful about giving our definitions and then building on those definitions to come up with interesting results and proving to ourselves that we definitely know what we think we know.
And so that's why we're being a little more careful with our language over here.
So "AB" is a radius, line segment "AB," and so is line segment, (let me put another point on here) let's say this is "X" so line segment "AX" is also a radius.
Now you can also have other forms of lines and line segments that interact in interesting ways with the circle.
So you could have a line that just intersects that circle exactly one point.
So let's call that point right over there and let's call that "D." And let's say you have a line and the only point on the circle that the only point in the set of all the points that are equal distance from "A," the only point on that circle that is also on that line is point "D." And we could call that line, "line L." So sometimes you will see lines specified by some of the points on them.
So for example, if I have another point right over here called "E," we could call this line, "line DE," or we could just put a little script letter here with an "L" and say this "line L." But this line that only has one point in common with our circle, we call this 'a tangent line.'
So "Line L" is tangent.
Tangent to the circle.
So let me write it this way, "'line L' is tangent to the circle centered at "A" So this tells us that this is the circle we're talking about, because who knows? maybe we had another circle over here that is centered at "M."
So we have to specify.
It's not tangent to that one, it's tangent to this one.
So this circle with a dot in the middle tells we're talking about circle, and this is a circle centered at point "A." I want to be very clear.
Point "A" is not on the circle, point "A" is the center of the circle.
The points on the circle are the points equal distant from point "A." Now, "L" is tangent because it only intersects the circle in one point.
You could just as easily imagine a line that intersects the circle at two points.
So we could call, maybe this is "F" and this is "G." You could call that
line "FG." And the line that intersects at two points we call this a secant of circle "A." It is a secant line to this circle right here.
Now, if "FG" was just a segment, if it didn't keep on going forever like lines do, if we only spoke about this line segment, between "FG," and not thinking about going on forever, then all the sudden, we have a line segment, which we would specify there, and we would call this a chord of the circle.
A chord of
"circle "A." It starts on a point of the circle, a point that is, in this case, 2cm away and then it finishes at a point on the circle.
So it connects two points on the circle.
Now, you can have cords like this, and you can also have a chord, as you can imagine, a chord that actually goes through the center of the circle.
So let's call this, "point 'H.'" And you have a straight line connecting
"F" to "H" through "A." (That's about as straight as I could draw it.) So if you have a chord like that, that contains actual center of the circle, of course it goes from one point to another point of the circle, and it goes through the center of the circle, we call that a diameter of a circle.
And you've probably seen this in tons of problems before when we were not talking about geometry as formally, but a diameter is made of two radiuses.
We know that a radius connects a point to the center, so you have one radius right over here that connects "F" and "A" that's one radius and you have another radius connecting "A" and "H," a point connecting to the center of the circle.
So the diameter is made of these two radiuses (or radii as I should call it I think that's the plural for radius) and so the length of a diameter is going to be twice the length of a radius.
So we could say, "the length of the diameter, so the length of "FH" (and once again I don't put the
line on top of it when I'm talking about the length) is going to be equal to "FA," the length of segment "FA" plus the length of segment "AH." Now there's one last thing
I want to talk about, when we're dealing with circles, and that's the idea of an arc. So we also have the parts of the circle itself.
(So let me draw another circle over here) Let's center this circle at "B." And I'm going to find some points, all the points that are a given distance from "B." So, it has some radius, I'm not going to specify it right over here.
And let me pick some random points on this circle.
Let's call this, "J," "K," "S," "T," and "U."
Let me center "B" a little bit more in the center here...
Now, one interesting thing is, "what do you call the length of the circle that goes between two points?"
Well, you could imagine in every language, we would call something like that an "arc," which is also what it's called in geometry.
We would call this "JK," the two end points of the arc, the two points on the circle that are the inputs of the arc, and you would use a little notation like that, a little curve on top instead of a strait line.
Now, you can also have another arc that connects "J" and "K," this is called the 'minor arc,' it is the shortest way upon the circle to connect "J" and "K." But you could also go the other way around.
You could also have this thing, that goes all the around the circle.
And that is called the 'major arc.' And usually when we specify the major arc, just to show that you're going kind of the long way around, it's not the shortest way to go between
"J" and "K," you will often specify another point that you're going through.
So for example, this major arc we could specify.
We started "J," we went through, we could have said "U," "T," or "S," but I will put "T" right over there.
We went through "T" and then we went all the way to "K." And so this specifies the major arc.
And this thing could have been the same thing as if I wrote "JUK" these are specifying the same thing, or "JSK." So there are multiple ways to specify this major arc.
The one thing I want to make clear is that the minor arc is the shortest distance, so this is the minor arc, and the longer distance around is the major arc.
I will leave you there. Maybe the next few videos we will starts playing with some of this notation.
Use the discriminant to state the number and type of solutions for the equation
-3x² -3x² + 5x -3x² + 5x - 4
And so just as a reminder you're probably wondering what is the discriminant? And we can just review it by looking at the quadratic formula.
So if I have a quadratic equation in standard form ax² ax² + bx ax² + bx + c ax² + bx + c = 0
We know that the quadratic formula, which is really just derived from completing the square right over here, tells us that the roots of this, or the solutions of this quadratic equation are going to be x = x = (-b) x = (-b ± √()) x = (-b ± √(b²)) x = (-b ± √(b² - 4ac)) all of that over (2a).
Now, you might know from experience applying this a little bit, we're going to get different types of solutions depending on what happens under the radical sign over here.
As you can imagine, if what's under the radical sign over here is positive, then we're going to get an actual, real number as its principal square root.
And when we take the positive and negative version of it, we're going to get two real solutions.
So if b² - 4ac, and this is what the discriminant really is, it's just this expression under the radical sign of the quadratic formula.
If this is greater than zero, then we're going to have two real roots, then we're going to have two real roots, or two real solutions to this equation right here.
If b² - 4ac = 0, then this whole thing is just going to be equal to zero, so plus or minus the square root of zero, (which is just zero) so this is plus or minus zero.
Well, when you add or subtract 0, that doesn't change the solution, so the only solution is going to be -b / 2a
So you're only going to have one real solution.
Now if b² - 4ac were negative - you might already imagine what will happen.
So we would then get an imaginary number right over here. So we would add or subtract the same imaginary number.
So we'll have two complex solutions; not only will we have two complex solutions, but they will be the conjugates of each other.
So if you have one complex solution for a quadratic equation, the other solution will also be a complex solution and will be its complex conjugate.
So here we would have two complex solutions.
And not only are they just complex, but they are the conjugates of each other.
So let's look at b² - 4ac over here.
This is our a, this is our b, and this is our c.
Everything is on one side, in particular the left-hand side, we have a zero on the right-hand side, we've written it in descending power form, or descending degree, where we have our 2nd degree term first, then our 1st degree term, then our constant term.
And so, we can evaluate the discriminant!
b = 5 b = 5, so b² = 5² 5² - 4 5² - 4 • a 5² - 4 • (-3) 5² - 4 • (-3) • c 5² - 4 • (-3) • (-4) c is this whole thing, I have to be careful. c is negative 4, we have to make sure we take the sign into consideration, so times c, which is negative 4 over here.
You can actually figure it out - this is equal to negative 23, negative 23... which is clearly less than zero.
So our discriminant in this situation is less than zero, so we are going to have two complex roots here, and they are going to be each other's conjugates.
Planetary systems outside our own are like distant cities whose lights we can see twinkling, but whose streets we can't walk.
By studying those twinkling lights though, we can learn about how stars and planets interact to form their own ecosystem and make habitats that are amenable to life.
In this image of the Tokyo skyline,
I've hidden data from the newest planet-hunting space telescope on the block, the Kepler Mission.
Can you see it?
There we go.
This is just a tiny part of the sky the Kepler stares at, where it searches for planets by measuring the light from over 150,000 stars, all at once, every half hour, and very precisely.
And what we're looking for is the tiny dimming of light that is caused by a planet passing in front of one of these stars and blocking some of that starlight from getting to us.
In just over two years of operations, we've found over 1,200 potential new planetary systems around other stars.
To give you some perspective, in the previous two decades of searching, we had only known about 400 prior to Kepler.
When we see these little dips in the light, we can determine a number of things.
For one thing, we can determine that there's a planet there, but also how big that planet is and how far it is away from its parent star.
That distance is really important because it tells us how much light the planet receives overall.
And that distance and knowing that amount of light is important because it's a little like you or I sitting around a campfire:
You want to be close enough to the campfire so that you're warm, but not so close that you're too toasty and you get burned.
However, there's more to know about your parent star than just how much light you receive overall.
And I'll tell you why.
This is our star.
This is our Sun.
It's shown here in visible light.
That's the light that you can see with your own human eyes.
You'll notice that it looks pretty much like the iconic yellow ball -- that Sun that we all draw when we're children.
But you'll notice something else, and that's that the face of the Sun has freckles.
These freckles are called sunspots, and they are just one of the manifestations of the Sun's magnetic field.
They also cause the light from the star to vary.
And we can measure this very, very precisely with Kepler and trace their effects.
However, these are just the tip of the iceberg.
If we had UV eyes or X-ray eyes, we would really see the dynamic and dramatic effects of our Sun's magnetic activity -- the kind of thing that happens on other stars as well.
Just think, even when it's cloudy outside, these kind of events are happening in the sky above you all the time.
So when we want to learn whether a planet is habitable, whether it might be amenable to life, we want to know not only how much total light it receives and how warm it is, but we want to know about its space weather -- this high-energy radiation, the UV and the X-rays that are created by its star and that bathe it in this bath of high-energy radiation.
And so, we can't really look at planets around other stars in the same kind of detail that we can look at planets in our own solar system.
I'm showing here Venus, Earth and Mars -- three planets in our own solar system that are roughly the same size, but only one of which is really a good place to live.
But what we can do in the meantime is measure the light from our stars and learn about this relationship between the planets and their parent stars to suss out clues about which planets might be good places to look for life in the universe.
Kepler won't find a planet around every single star it looks at.
But really, every measurement it makes is precious, because it's teaching us about the relationship between stars and planets, and how it's really the starlight that sets the stage for the formation of life in the universe.
While it's Kepler the telescope, the instrument that stares, it's we, life, who are searching.
Thank you.
(Applause)
A carpenter is using a lathe to shape the final leg of a hand-crafted table.
A lathe is this carpentry tool that spins things around, and so it can be used to make things that are, I guess you could say, almost cylindrical in shape, like a leg for a table or something like that.
In order for the leg to fit, it needs to be 150 millimeters wide, allowing for a margin of error of 2.5 millimeters.
So in an ideal world, it'd be exactly 150 millimeters wide, but when you manufacture something, you're not going to get that exact number, so this is saying that we can be 2 and 1/2 millimeters above or below that 150 millimeters.
Now, they want us to write an absolute value inequality that models this relationship, and then find the range of widths that the table leg can be.
So the way to think about this, let's let w be the width of the table leg.
So if we were to take the difference between w and 150, what is this?
This is essentially how much of an error did we make, right?
If w is going to be larger than 150, let's say it's 151, then this difference is going to be 1 millimeter, we were over by 1 millimeter.
If w is less than 150, it's going to be a negative number.
If, say, w was 149, 149 minus 150 is going to be negative 1.
But we just care about the absolute margin.
We don't care if we're above or below, the margin of error says we can be 2 and 1/2 above or below.
So we just really care about the absolute value of the difference between w and 150.
This tells us, how much of an error did we make?
And all we care is that error, that absolute error, has to be a less than 2.5 millimeters.
And I'm assuming less than-- they're saying a margin of error of 2.5 millimeters-- I guess it could be less than or equal to.
We could be exactly 2 and 1/2 millimeters off.
So this is the first part.
We have written an absolute value inequality that models this relationship.
And I really want you to understand this.
All we're saying is look, this right here is the difference between the actual width of our leg and 150.
Now we don't care if it's above or below, we just care about the absolute distance from 150, or the absolute value of that difference, so we took the absolute value.
And that thing, the difference between w a 150, that absolute distance, has to be less than 2 and 1/2.
Now, we've seen examples of solving this before.
This means that this thing has to be either, or it has to be both, less than 2 and 1/2 and greater than negative 2 and 1/2.
So let me write this down.
So this means that w minus 150 has to be less than 2.5 and w minus 150 has to be greater than or equal to negative 2.5.
If the absolute value of something is less than 2 and 1/2, that means its distance from 0 is less than 2 and 1/2. For something's distance from 0 to be less than 2 and 1/2, in the positive direction it has to be less than 2 and 1/2.
But it also cannot be any more negative than negative 2 and 1/2, and we saw that in the last few videos.
So let's solve each of these.
If we add 150 to both sides of these equations, if you add 150-- and we can actually do both of them simultaneously--
let's add 150 on this side, too, what do we get?
What do we get?
The left-hand side of this equation just becomes a w-- these cancel out-- is less than or equal to 150 plus 2.5 is 152.5, and then we still have our and.
And on this side of the equation-- this cancels out-- we just have a w is greater than or equal to negative 2.5 plus 150, that is 147.5. So the width of our leg has to be greater than 147.5 millimeters and less than 152.5 millimeters.
We can write it like this.
The width has to be less than or equal to 152.5 millimeters.
Or it has to be greater than or equal to, or we could say 147.5 millimeters is less than the width.
And that's the range.
And this makes complete sense because we can only be 2 and 1/2 away from 150.
This is saying that the distance between w and 150 can only at most be 2 and 1/2.
And you see, this is 2 and 1/2 less than 150, and this is 2 and 1/2 more than 150.
In the last part of the problem we figured out that the function of the height of the ferris wheel, the people at the ferris wheel at any time is a function of t. h of t is equal to 9 minus 8 cosine of 18t where t is in seconds.
Now the second part of this problem they want us to graph h as a function of t between 0 is less than or equal to t, is less than or equal to 30.
So let me draw axes.
So let's say that that's my h-axis.
Let's say that this is my t-axis.
So this is t equals 0, and this is t is equal to 30 seconds.
I get confused when I see this 18 here or whatever.
So what I'm going to do first of all is I'm going to graph a different function, slightly different function, then I'll translate it to this function.
I'm going to graph h of theta is equal to 9 minus 8 cosine of theta.
I think you'll see where I'm going with this when I'm all done.
So let's try to graph h of theta is equal to 9 minus 8 cosine of theta.
So when t is equal to 30 seconds, what is theta equal to?
So 30 times 18, that's 540.
So this is 540 degrees.
Same thing.
I'll write the thetas in red above the t-axis.
This is 540 degrees, so that's like two times around the circle.
So that's 540 degrees, then this is going to be roughly 270 degrees.
So, 90 degrees will be about 1/3 of this.
That would be 90 degrees, that would be 180, so that would be 90 degrees, that would be 180 degrees, this would be 360 degrees, and this would be 360 plus 90 so this will be 450 degrees.
If you wanted to figure out the corresponding time, you just take this degree and divide by 18.
So it's 90 divided by 18 is what?
It's five, right?
So if I were to write here, this is at 5 seconds, this is at 10 seconds, this is 15 seconds, this is 20 seconds, this is -- sorry, this is 25 seconds, this is 30 seconds.
Actually, a simple thing we could do is let's just figure out what the value of the function is at these points.
Because these are pretty easy degrees to figure out what the cosine value is.
So let's figure out -- let me draw a table.
Tables are always good and I'll do it in yellow.
So I'll draw a t theta and h.
This might be kind of an unconventional way of doing things, but I have a simple mind so this is actually how I like to do it.
So I like to think of theta as 0, 90, 180, 270, 360, 450 and 540.
And t, the corresponding time of those, as 0, 5, 10, 15, 20, 25, 30.
It's not rocket science here.
When t equals 15 seconds, 15 times 18, we're trying to find the cosine of 270 degrees, right?
15 times 18 is 270 degrees.
I'm just doing this because I don't have a calculator and this will help me pick good points.
So when t is equal to 0, what is height?
Or t is equal to 0, theta is equal to 0, so cosine of theta is -- cosine of 0 is 1.
So 9 minus 8 is 1.
I'm going to do h in a different color.
So this is 1.
Cosine of 90 degrees?
Cosine of 90 degrees is 0.
So 9 minus 0 is 9.
Cosine of 180 degrees?
So we're going all the way around the unit circle.
Cosine of 180 degrees is minus 1.
So minus 1 times minus 8 is plus 8, so 9 plus 8, that's 15.
Cosine of 270 degrees are pointing straight down, so the x-coord is going to be 0.
So once again, we're at 9 again. 9 minus 0. 360 degrees.
Cosine of 360 degrees is the same thing as cosine of 0, right?
So once again, I mean we've gone around the circle once.
So it's going to be the same as 0, so it's going to be 1. And 450 is going to be the same thing as 90.
So it's going to be 9 and then 15 degrees.
So let's plot these points.
Actually, let me just draw 15 up here.
So what are the points that keep showing up?
So this is 1, that's 1, that's 1, and then we have 9. 1, there's 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15.
Fair enough.
So let me draw some guidelines just to help us.
Actually, let me do them kind of hard to see, because I don't want to draw too much attention to the guidelines.
I could do one guideline there.
Then I'll do a bottom guideline right there.
Then the 9 keeps showing up.
Oh, you know what, I can't add.
What's 9 plus 8?
It's not 15, it's 17.
Sorry, clearly, I need to practice my addition.
So this is 9 plus 8, this is 17.
And I realized that because I was like, well 9 should be in the middle, so this is actually 17.
Ignore my little marks here.
That's 17, this is 1.
Ignore the marks. 9 would be right in the middle between 1 and 17.
So let me draw kind of mediant point right there.
So this is 9.
Sorry I can't add properly.
Then let's draw the graph or at least plot the points on the graph.
So, t equals 0 where h equals 1, so that's this point.
That's right here.
When t equals 5, h is equal to 9, right here.
When t is equal to 10, h is equal to 17.
When t is equal to 15, h is 9 again.
So it's right here.
At 20 we're back at 1.
I think you see the pattern.
At 25 we're back at 9.
And then at 30 we're back at 17, not 15, because now I have corrected my mistake. And this is going to be sined graph, it's going to look something like this.
Let me do it in a vibrant color so I can overwrite everything and it's going to look something like this.
Go oops, and then up and them down here.
Curve up, come back down, curve up and then come back down. Like that. So that's our graph.
I think in the problem they tell us to approximate.
Actually, let me open up my cousin's problem -- my other account has timed-out on me while I recorded this.
They wanted to approximate when t equals 4 what the height is.
So when t equals 4 the height is like right around there, right?
So the height is a little bit less than 9.
And I don't know, 7 or 8 meters in the air.
And when time is equal to 10 -- well, time equal 10, we figured out exactly, we know that there are 17 meters in the air.
So I know this was kind of a little messy and graphing trick functions tend to be, but hopefully you found this vaguely useful.
Have fun.
A suspension bridge has two towers that rise 500 feet above the road and are connected by cables that hang in the shape of a parabola that can be represented by y is equal to 1/8,960 times x minus 2,100 squared plus 8, where x and y are measured in feet and x is the distance from the left tower in the direction of the right tower.
What is the distance between the two towers?
Let's draw ourselves a diagram.
If we draw the leftmost tower-- I'm going to do it in orange.
So we have the left tower right here.
That tower is at x is equal to 0.
We'll call that x is equal to 0, or maybe just call that the 0 point right there.
Then x is just measuring the distance from that leftmost tower to the rightmost tower, so the rightmost tower in the direction of the right tower.
This right here, maybe the right tower is right over here.
They're both 500 feet high.
The right tower is right over there, and we don't know where it is.
That's we have to figure out.
We have to figure out the distance between the two, but we just need to know that x is measuring this distance.
It's measuring the distance from the left tower in the direction of the right tower, so it's just traditional, just like our coordinate plane.
That is what x is measuring.
If you say x is equal to a million feet, you're going to get something way beyond that second tower.
If you say x is one foot, you're going to get something in the direction of the second tower from the left tower.
So that's x, and then y, we can assume is the height of the towers, or is just the height in general that we're dealing with.
This is the y-axis, so we're just dealing in the first quadrant of the coordinate plane, and that is y.
They're telling us that this parabola, the shape of the parabola, can be represented-- or even better, they're saying that the cable that connects these two is in the shape of a parabola.
Let me draw that parabola right there.
They're the same height, so the parabola will look something like this.
What we can do to figure out, or one possible technique-- let me draw a better parabola there.
That's even worse.
That's about as good as I can do.
One technique for finding the distance between the two is if we could figure out the minimum point of this parabola, which is also going to be the vertex of that parabola, that's going to be halfway between the two towers.
If we can figure out this x-coordinate, we can say that's going to be halfway between the two towers and then just multiply by two.
Let's see if we can figure out this minimum point, because the parabola is symmetric around it, and these are both at the same height.
Let's see if we can figure out that minimum point.
Let me rewrite this equation:
We have y is equal to 1/8,960 times x minus 2,100 squared plus 8.
How do we find the minimum point here?
This whole expression that's squared, this whole expression is always going to be positive, or it's actually always going to be non-negative.
It could be equal to 0, and so this whole thing is always going to be greater than or equal to 0.
This whole thing I'm squaring off in orange is always going to be greater than or equal to 0.
So what is the lowest value that y can take on?
The lowest valued that y can take on will happen when this expression is equal to 0, and this expression equals 0 only when x minus 2,100 squared is equal to 0.
That's only going to be equal to 0 when x minus 2,100 is equal to 0, so x-- let me write it this way-- equals 0, and I'm just talking about this orange part-- when x minus 2,100 is equal to 0, or if you add 2,100 to both sides, or x is equal to 2,100.
When x is equal to 2,100, just out of curiosity, what is y?
If x is 2,100, this thing is 0 times 0, and y is just going to be equal to that 8 there.
So this coordinate right here is the coordinate x is equal to 2,100, y is equal to 8, and it's going to be halfway between our two towers.
If this is at 2,100, how far is this tower away?
Well, it's going to be twice 2,100.
It's going to be 4,200, and everything we're dealing with is feet.
It's going to be 4,200 feet away from that first tower.
So the distance between the two towers is 4,200 feet.
All right, we're on problem number 8. They ask us which equation is equivalent 5x-2(7x+1)＝14x So I'm guessing they just want to simplify this a little bit and see if we get to one of these choices.
This is I think the most obvious thing to simplify. This 2(7x+1) or we can even say -2(7x+1) so then this becomes 5x plus
I'm just going to distribute the -2 times all of this. Plus -2 times 17x is minus 14x. minus 14x
And then -2 times 1 is minus 2 is equal to 14x.
And let's see, on all of these choices they have 14x on the right hand side.
So they just want us to simplify this.
So this simplifies to 5x, plus -14, so that's -14x minus 2 is equal to 14x.
So we have 5x-14x.
What's 5-14?
It's what?
-9, right?
-9x-2＝14x
That is choice A.
Now, one thing that maybe I realized,
I kind of skipped a step.
We could've just...
Let me just do this just so that you understand this step that I did here.
We could have just said minus and then distribute the 2
7 times 5 is 35. 7 times 2 is 14 plus 3 is 17, right. So h has to be less than or equal to 7 hours.
Let's talk about a star search.
Let's assume we have the following grid.
The start state is right here.
And the goal state is right here.
And just for convenience, I will give each here a little number.
A. B. C. D.
Let me draw a heuristic function.
Please take a look for a moment and tell me whether this heuristic function is admissable.
Check here if yes and here if no.
Which one is the first node a star would expand?
B1 or A2?
What's the second node to expand?
B1, C1, A2, A3, or B2?
And finally, what is the third node to expand?
D1, C2, B3, or A4?
-CHAPTER 15
'I did not start in search of Jim at once, only because I had really an appointment which I could not neglect.
Then, as ill-luck would have it, in my agent's office I was fastened upon by a fellow fresh from Madagascar with a little scheme for a wonderful piece of business.
It had something to do with cattle and cartridges and a Prince Ravonalo something; but the pivot of the whole affair was the stupidity of some admiral--Admiral Pierre,
I think.
Everything turned on that, and the chap couldn't find words strong enough to express his confidence.
He had globular eyes starting out of his head with a fishy glitter, bumps on his forehead, and wore his long hair brushed back without a parting.
He had a favourite phrase which he kept on repeating triumphantly, "The minimum of risk with the maximum of profit is my motto.
What?"
He made my head ache, spoiled my tiffin, but got his own out of me all right; and as soon as I had shaken him off, I made straight for the water-side.
I caught sight of Jim leaning over the parapet of the quay.
Three native boatmen quarrelling over five annas were making an awful row at his elbow.
He didn't hear me come up, but spun round as if the slight contact of my finger had released a catch.
"I was looking," he stammered.
I don't remember what I said, not much anyhow, but he made no difficulty in following me to the hotel.
'He followed me as manageable as a little child, with an obedient air, with no sort of manifestation, rather as though he had been waiting for me there to come along and carry him off.
I need not have been so surprised as I was at his tractability.
On all the round earth, which to some seems so big and that others affect to consider as rather smaller than a mustard-seed, he had no place where he could--what shall I say?--where he could withdraw.
That's it!
Withdraw--be alone with his loneliness.
He walked by my side very calm, glancing here and there, and once turned his head to look after a Sidiboy fireman in a cutaway coat and yellowish trousers, whose black face had silky gleams like a lump of anthracite coal.
I doubt, however, whether he saw anything, or even remained all the time aware of my companionship, because if I had not edged him to the left here, or pulled him to the right there, I believe he would have gone straight before him in any direction till stopped by a wall or some other obstacle.
I steered him into my bedroom, and sat down at once to write letters.
This was the only place in the world (unless, perhaps, the Walpole Reef--but that was not so handy) where he could have it out with himself without being bothered by the rest of the universe.
The damned thing--as he had expressed it-- had not made him invisible, but I behaved exactly as though he were.
No sooner in my chair I bent over my writing-desk like a medieval scribe, and, but for the movement of the hand holding the pen, remained anxiously quiet.
I can't say I was frightened; but I certainly kept as still as if there had been something dangerous in the room, that at the first hint of a movement on my part would be provoked to pounce upon me.
There was not much in the room--you know how these bedrooms are--a sort of four- poster bedstead under a mosquito-net, two or three chairs, the table I was writing at, a bare floor.
A glass door opened on an upstairs verandah, and he stood with his face to it, having a hard time with all possible privacy.
Dusk fell; I lit a candle with the greatest economy of movement and as much prudence as though it were an illegal proceeding.
There is no doubt that he had a very hard time of it, and so had I, even to the point, I must own, of wishing him to the devil, or on Walpole Reef at least.
It occurred to me once or twice that, after all, Chester was, perhaps, the man to deal effectively with such a disaster.
That strange idealist had found a practical use for it at once--unerringly, as it were.
It was enough to make one suspect that, maybe, he really could see the true aspect of things that appeared mysterious or utterly hopeless to less imaginative persons.
I wrote and wrote; I liquidated all the arrears of my correspondence, and then went on writing to people who had no reason whatever to expect from me a gossipy letter about nothing at all.
At times I stole a sidelong glance.
He was rooted to the spot, but convulsive shudders ran down his back; his shoulders would heave suddenly.
He was fighting, he was fighting--mostly for his breath, as it seemed.
The massive shadows, cast all one way from the straight flame of the candle, seemed possessed of gloomy consciousness; the immobility of the furniture had to my furtive eye an air of attention.
I was becoming fanciful in the midst of my industrious scribbling; and though, when the scratching of my pen stopped for a moment, there was complete silence and stillness in the room, I suffered from that profound disturbance and confusion of thought which is caused by a violent and menacing uproar--of a heavy gale at sea, for instance.
Some of you may know what I mean: that mingled anxiety, distress, and irritation with a sort of craven feeling creeping in-- not pleasant to acknowledge, but which gives a quite special merit to one's endurance.
I don't claim any merit for standing the stress of Jim's emotions; I could take refuge in the letters; I could have written to strangers if necessary.
Suddenly, as I was taking up a fresh sheet of notepaper, I heard a low sound, the first sound that, since we had been shut up together, had come to my ears in the dim stillness of the room.
I remained with my head down, with my hand arrested.
Those who have kept vigil by a sick-bed have heard such faint sounds in the stillness of the night watches, sounds wrung from a racked body, from a weary soul.
He pushed the glass door with such force that all the panes rang: he stepped out, and I held my breath, straining my ears without knowing what else I expected to hear.
He was really taking too much to heart an empty formality which to Chester's rigorous criticism seemed unworthy the notice of a man who could see things as they were.
An empty formality; a piece of parchment.
Well, well.
As to an inaccessible guano deposit, that was another story altogether.
One could intelligibly break one's heart over that.
A feeble burst of many voices mingled with the tinkle of silver and glass floated up from the dining-room below; through the open door the outer edge of the light from my candle fell on his back faintly; beyond all was black; he stood on the brink of a vast obscurity, like a lonely figure by the shore of a sombre and hopeless ocean.
There was the Walpole Reef in it--to be sure--a speck in the dark void, a straw for the drowning man.
My compassion for him took the shape of the thought that I wouldn't have liked his people to see him at that moment.
I found it trying myself.
His back was no longer shaken by his gasps; he stood straight as an arrow, faintly visible and still; and the meaning of this stillness sank to the bottom of my soul like lead into the water, and made it so heavy that for a second I wished heartily that the only course left open for me was to pay for his funeral.
Even the law had done with him.
To bury him would have been such an easy kindness!
It would have been so much in accordance with the wisdom of life, which consists in putting out of sight all the reminders of our folly, of our weakness, of our mortality; all that makes against our efficiency--the memory of our failures, the hints of our undying fears, the bodies of our dead friends.
Perhaps he did take it too much to heart.
And if so then--Chester's offer....At this point I took up a fresh sheet and began to write resolutely.
There was nothing but myself between him and the dark ocean.
I had a sense of responsibility.
If I spoke, would that motionless and suffering youth leap into the obscurity-- clutch at the straw?
I found out how difficult it may be sometimes to make a sound.
There is a weird power in a spoken word.
And why the devil not?
I was asking myself persistently while I drove on with my writing.
All at once, on the blank page, under the very point of the pen, the two figures of
Chester and his antique partner, very distinct and complete, would dodge into view with stride and gestures, as if reproduced in the field of some optical toy.
I would watch them for a while.
No!
They were too phantasmal and extravagant to enter into any one's fate.
And a word carries far--very far--deals destruction through time as the bullets go flying through space.
I said nothing; and he, out there with his back to the light, as if bound and gagged by all the invisible foes of man, made no stir and made no sound.'
CHAPTER 16
'The time was coming when I should see him loved, trusted, admired, with a legend of strength and prowess forming round his name as though he had been the stuff of a hero.
It's true--I assure you; as true as I'm sitting here talking about him in vain.
He, on his side, had that faculty of beholding at a hint the face of his desire and the shape of his dream, without which the earth would know no lover and no adventurer.
He captured much honour and an Arcadian happiness (I won't say anything about innocence) in the bush, and it was as good to him as the honour and the Arcadian happiness of the streets to another man.
Felicity, felicity--how shall I say it?--is quaffed out of a golden cup in every
latitude: the flavour is with you--with you alone, and you can make it as intoxicating as you please.
He was of the sort that would drink deep, as you may guess from what went before.
I found him, if not exactly intoxicated, then at least flushed with the elixir at his lips.
He had not obtained it at once.
There had been, as you know, a period of probation amongst infernal ship-chandlers, during which he had suffered and I had worried about--about--my trust--you may call it.
I don't know that I am completely reassured now, after beholding him in all his brilliance.
That was my last view of him--in a strong light, dominating, and yet in complete accord with his surroundings--with the life of the forests and with the life of men.
I own that I was impressed, but I must admit to myself that after all this is not the lasting impression.
He was protected by his isolation, alone of his own superior kind, in close touch with
Nature, that keeps faith on such easy terms with her lovers.
But I cannot fix before my eye the image of his safety.
I shall always remember him as seen through the open door of my room, taking, perhaps, too much to heart the mere consequences of his failure.
I am pleased, of course, that some good-- and even some splendour--came out of my endeavours; but at times it seems to me it would have been better for my peace of mind if I had not stood between him and Chester's confoundedly generous offer.
I wonder what his exuberant imagination would have made of Walpole islet--that most hopelessly forsaken crumb of dry land on the face of the waters.
It is not likely I would ever have heard, for I must tell you that Chester, after calling at some Australian port to patch up his brig-rigged sea-anachronism, steamed out into the Pacific with a crew of twenty- two hands all told, and the only news having a possible bearing upon the mystery of his fate was the news of a hurricane which is supposed to have swept in its course over the Walpole shoals, a month or so afterwards.
Not a vestige of the Argonauts ever turned up; not a sound came out of the waste.
Finis!
The Pacific is the most discreet of live, hot-tempered oceans: the chilly Antarctic can keep a secret too, but more in the manner of a grave.
'And there is a sense of blessed finality in such discretion, which is what we all more or less sincerely are ready to admit-- for what else is it that makes the idea of death supportable?
End!
Finis! the potent word that exorcises from the house of life the haunting shadow of fate.
This is what--notwithstanding the testimony of my eyes and his own earnest assurances--
I miss when I look back upon Jim's success.
While there's life there is hope, truly; but there is fear too.
I don't mean to say that I regret my action, nor will I pretend that I can't sleep o' nights in consequence; still, the idea obtrudes itself that he made so much of his disgrace while it is the guilt alone that matters.
He was not--if I may say so--clear to me.
He was not clear.
And there is a suspicion he was not clear to himself either.
There were his fine sensibilities, his fine feelings, his fine longings--a sort of sublimated, idealised selfishness.
He was--if you allow me to say so--very fine; very fine--and very unfortunate.
A little coarser nature would not have borne the strain; it would have had to come to terms with itself--with a sigh, with a grunt, or even with a guffaw; a still coarser one would have remained invulnerably ignorant and completely uninteresting.
'But he was too interesting or too unfortunate to be thrown to the dogs, or even to Chester.
I felt this while I sat with my face over the paper and he fought and gasped, struggling for his breath in that terribly stealthy way, in my room; I felt it when he rushed out on the verandah as if to fling himself over--and didn't; I felt it more and more all the time he remained outside, faintly lighted on the background of night, as if standing on the shore of a sombre and hopeless sea.
'An abrupt heavy rumble made me lift my head.
The noise seemed to roll away, and suddenly a searching and violent glare fell on the blind face of the night.
The sustained and dazzling flickers seemed to last for an unconscionable time.
The growl of the thunder increased steadily while I looked at him, distinct and black, planted solidly upon the shores of a sea of light.
At the moment of greatest brilliance the darkness leaped back with a culminating crash, and he vanished before my dazzled eyes as utterly as though he had been blown to atoms.
A blustering sigh passed; furious hands seemed to tear at the shrubs, shake the tops of the trees below, slam doors, break window-panes, all along the front of the building.
He stepped in, closing the door behind him, and found me bending over the table: my sudden anxiety as to what he would say was very great, and akin to a fright.
"May I have a cigarette?" he asked.
I gave a push to the box without raising my head.
"I want--want--tobacco," he muttered.
I became extremely buoyant.
"Just a moment."
I grunted pleasantly.
He took a few steps here and there.
"That's over," I heard him say.
A single distant clap of thunder came from the sea like a gun of distress.
"The monsoon breaks up early this year," he remarked conversationally, somewhere behind me.
This encouraged me to turn round, which I did as soon as I had finished addressing the last envelope.
He was smoking greedily in the middle of the room, and though he heard the stir I made, he remained with his back to me for a time.
'"Come--I carried it off pretty well," he said, wheeling suddenly.
"Something's paid off--not much.
I wonder what's to come."
His face did not show any emotion, only it appeared a little darkened and swollen, as though he had been holding his breath.
He smiled reluctantly as it were, and went on while I gazed up at him mutely...."Thank you, though--your room--jolly convenient-- for a chap--badly hipped."...
The rain pattered and swished in the garden; a water-pipe (it must have had a hole in it) performed just outside the window a parody of blubbering woe with funny sobs and gurgling lamentations, interrupted by jerky spasms of silence...."A bit of shelter," he mumbled and ceased.
'A flash of faded lightning darted in through the black framework of the windows and ebbed out without any noise.
I was thinking how I had best approach him (I did not want to be flung off again) when he gave a little laugh.
"No better than a vagabond now"...the end of the cigarette smouldered between his fingers..."without a single--single," he pronounced slowly; "and yet ..."
He paused; the rain fell with redoubled violence.
"Some day one's bound to come upon some sort of chance to get it all back again.
Must!" he whispered distinctly, glaring at my boots.
'I did not even know what it was he wished so much to regain, what it was he had so terribly missed.
It might have been so much that it was impossible to say.
A piece of ass's skin, according to Chester....
He looked up at me inquisitively.
If life's long enough," I muttered through my teeth with unreasonable animosity.
"Don't reckon too much on it."
'"Jove!
I feel as if nothing could ever touch me," he said in a tone of sombre conviction.
"If this business couldn't knock me over, then there's no fear of there being not enough time to--climb out, and ..."
He looked upwards.
'It struck me that it is from such as he that the great army of waifs and strays is recruited, the army that marches down, down into all the gutters of the earth.
As soon as he left my room, that "bit of shelter," he would take his place in the ranks, and begin the journey towards the bottomless pit.
I at least had no illusions; but it was I, too, who a moment ago had been so sure of the power of words, and now was afraid to speak, in the same way one dares not move for fear of losing a slippery hold.
It is when we try to grapple with another man's intimate need that we perceive how incomprehensible, wavering, and misty are the beings that share with us the sight of the stars and the warmth of the sun.
It is as if loneliness were a hard and absolute condition of existence; the envelope of flesh and blood on which our eyes are fixed melts before the outstretched hand, and there remains only the capricious, unconsolable, and elusive spirit that no eye can follow, no hand can grasp.
It was the fear of losing him that kept me silent, for it was borne upon me suddenly and with unaccountable force that should I let him slip away into the darkness I would never forgive myself.
'"Well. Thanks--once more.
You've been--er--uncommonly--really there's no word to...Uncommonly!
I don't know why, I am sure.
I am afraid I don't feel as grateful as I would if the whole thing hadn't been so brutally sprung on me.
Because at bottom...you, yourself ..."
He stuttered.
'"Possibly," I struck in.
He frowned.
'"All the same, one is responsible." He watched me like a hawk.
'"And that's true, too," I said. I've gone with it to the end, and I don't intend to let any man cast it in my teeth without--without--resenting it."
He clenched his fist.
'"There's yourself," I said with a smile-- mirthless enough, God knows--but he looked at me menacingly.
"That's my business," he said.
An air of indomitable resolution came and went upon his face like a vain and passing shadow.
Next moment he looked a dear good boy in trouble, as before.
He flung away the cigarette.
"Good-bye," he said, with the sudden haste of a man who had lingered too long in view of a pressing bit of work waiting for him; and then for a second or so he made not the slightest movement.
The downpour fell with the heavy uninterrupted rush of a sweeping flood, with a sound of unchecked overwhelming fury that called to one's mind the images of collapsing bridges, of uprooted trees, of undermined mountains.
No man could breast the colossal and headlong stream that seemed to break and swirl against the dim stillness in which we were precariously sheltered as if on an island.
The perforated pipe gurgled, choked, spat, and splashed in odious ridicule of a swimmer fighting for his life.
"It is raining," I remonstrated, "and I ..."
"Rain or shine," he began brusquely, checked himself, and walked to the window.
"Perfect deluge," he muttered after a while: he leaned his forehead on the glass.
"It's dark, too."
'"Yes, it is very dark," I said.
'He pivoted on his heels, crossed the room, and had actually opened the door leading into the corridor before I leaped up from my chair.
"Wait," I cried, "I want you to ..." "I can't dine with you again to-night," he flung at me, with one leg out of the room already.
"I haven't the slightest intention to ask you," I shouted.
At this he drew back his foot, but remained mistrustfully in the very doorway.
I lost no time in entreating him earnestly not to be absurd; to come in and shut the door.'
CHAPTER 17
'He came in at last; but I believe it was mostly the rain that did it; it was falling just then with a devastating violence which quieted down gradually while we talked.
His manner was very sober and set; his bearing was that of a naturally taciturn man possessed by an idea.
My talk was of the material aspect of his position; it had the sole aim of saving him from the degradation, ruin, and despair that out there close so swiftly upon a friendless, homeless man; I pleaded with him to accept my help; I argued reasonably: and every time I looked up at that absorbed smooth face, so grave and youthful, I had a disturbing sense of being no help but rather an obstacle to some mysterious, inexplicable, impalpable striving of his wounded spirit.
'"I suppose you intend to eat and drink and to sleep under shelter in the usual way,"
I remember saying with irritation.
"You say you won't touch the money that is due to you."...He came as near as his sort can to making a gesture of horror.
(There were three weeks and five days' pay owing him as mate of the Patna.)
"Well, that's too little to matter anyhow; but what will you do to-morrow?
Where will you turn?
You must live ..."
"That isn't the thing," was the comment that escaped him under his breath.
I ignored it, and went on combating what I assumed to be the scruples of an exaggerated delicacy.
"On every conceivable ground," I concluded, "you must let me help you."
"You can't," he said very simply and gently, and holding fast to some deep idea which I could detect shimmering like a pool of water in the dark, but which I despaired of ever approaching near enough to fathom.
I surveyed his well-proportioned bulk.
"At any rate," I said, "I am able to help what I can see of you.
I don't pretend to do more."
He shook his head sceptically without looking at me.
I got very warm.
"But I can," I insisted.
"I can do even more.
I am doing more.
I am trusting you ..."
"The money ..." he began.
"Upon my word you deserve being told to go to the devil," I cried, forcing the note of indignation.
He was startled, smiled, and I pressed my attack home.
"It isn't a question of money at all.
You are too superficial," I said (and at the same time I was thinking to myself: Well, here goes!
And perhaps he is, after all).
"Look at the letter I want you to take.
I am writing to a man of whom I've never asked a favour, and I am writing about you in terms that one only ventures to use when speaking of an intimate friend.
I make myself unreservedly responsible for you.
That's what I am doing. And really if you will only reflect a little what that means ..."
'He lifted his head.
The rain had passed away; only the water- pipe went on shedding tears with an absurd drip, drip outside the window.
It was very quiet in the room, whose shadows huddled together in corners, away from the still flame of the candle flaring upright in the shape of a dagger; his face after a while seemed suffused by a reflection of a soft light as if the dawn had broken already.
'"Jove!" he gasped out.
"It is noble of you!"
'Had he suddenly put out his tongue at me in derision, I could not have felt more humiliated.
I thought to myself--Serve me right for a sneaking humbug....His eyes shone straight into my face, but I perceived it was not a mocking brightness.
All at once he sprang into jerky agitation, like one of those flat wooden figures that are worked by a string.
His arms went up, then came down with a slap.
He became another man altogether.
"And I had never seen," he shouted; then suddenly bit his lip and frowned.
"What a bally ass I've been," he said very slow in an awed tone...."You are a brick!" he cried next in a muffled voice.
He snatched my hand as though he had just then seen it for the first time, and dropped it at once.
"Why! this is what I--you--I ..." he stammered, and then with a return of his old stolid, I may say mulish, manner he began heavily, "I would be a brute now if I ..." and then his voice seemed to break.
"That's all right," I said.
I was almost alarmed by this display of feeling, through which pierced a strange elation.
I had pulled the string accidentally, as it were; I did not fully understand the working of the toy.
"I must go now," he said.
"Jove!
You have helped me.
Can't sit still.
The very thing ..." He looked at me with puzzled admiration.
"The very thing ..."
'Of course it was the thing.
It was ten to one that I had saved him from starvation--of that peculiar sort that is almost invariably associated with drink.
This was all.
I had not a single illusion on that score, but looking at him, I allowed myself to wonder at the nature of the one he had, within the last three minutes, so evidently taken into his bosom.
I had forced into his hand the means to carry on decently the serious business of life, to get food, drink, and shelter of the customary kind while his wounded spirit, like a bird with a broken wing, might hop and flutter into some hole to die quietly of inanition there.
This is what I had thrust upon him: a definitely small thing; and--behold!--by the manner of its reception it loomed in the dim light of the candle like a big, indistinct, perhaps a dangerous shadow.
"You don't mind me not saying anything appropriate," he burst out.
Last night already you had done me no end of good.
Listening to me--you know.
I give you my word I've thought more than once the top of my head would fly off..."
He darted--positively darted--here and there, rammed his hands into his pockets, jerked them out again, flung his cap on his head.
I had no idea it was in him to be so airily brisk.
I thought of a dry leaf imprisoned in an eddy of wind, while a mysterious apprehension, a load of indefinite doubt, weighed me down in my chair.
He stood stock-still, as if struck motionless by a discovery.
"You have given me confidence," he declared, soberly.
"Oh! for God's sake, my dear fellow-- don't!"
I entreated, as though he had hurt me.
"All right.
I'll shut up now and henceforth.
Can't prevent me thinking though....Never mind!...I'll show yet ..."
He went to the door in a hurry, paused with his head down, and came back, stepping deliberately.
"I always thought that if a fellow could begin with a clean slate...And now you...in a measure...yes...clean slate."
I waved my hand, and he marched out without looking back; the sound of his footfalls died out gradually behind the closed door-- the unhesitating tread of a man walking in broad daylight.
'But as to me, left alone with the solitary candle, I remained strangely unenlightened.
I was no longer young enough to behold at every turn the magnificence that besets our insignificant footsteps in good and in evil.
I smiled to think that, after all, it was yet he, of us two, who had the light.
And I felt sad.
A clean slate, did he say?
As if the initial word of each our destiny were not graven in imperishable characters upon the face of a rock.'
At the beginning of the week,
Stewart's checking account had a balance of negative fifteen dollars and eight cents.
On Monday morning he deposited a check for four hundred twenty-six dollars and ninety cents.
On Tuesday morning he deposited another check for [one] hundred dollars.
How much was in Stewart's checking account after the second deposit, so after both of these deposits right over here?
He actually owes the bank money now.
Two minus one is one, and then you have five minus nothing.
So, he is left with five hundred eleven dollars and eighty-two cents, after his second deposit.
Evan from Norway has asked me to do another u substitution problem, and I like these because it gets my momentum going for doing other things that maybe take a little bit more preparation.
This it also be written as-- he wrote it in email, so I don't know how he exactly saw it, but it can also be written as sin of x over cosine squared of x.
But in general you know to do u substitution, or integration by substitution when you see something and you see its derivative sitting there.
We know how to do this integral.
Let me do it on the side.
This integral would be easy.
1 over x squared dx.
We know how to do that.
That would just be the antiderivative of x squared.
This is the same thing as the antiderivative of x to the minus 2 dx, and we know how to take the antiderivative of something like that.
You increase the exponent by 1 and then you multiply by what your new exponent is.
So it would be minus x-- I'm sorry.
You increase your exponent by 1, and then you divide by whatever your new exponent is.
So you would, [? let me do the, ?] increasing the exponent x to the minus 2, you'd increase the exponent, you'd get x to the minus 1.
And then when you divide this by minus 1 you get this minus out front, and then of course you'd have the plus c.
If you don't believe it take the derivative.
Negative 1 times minus 1.
That's a positive.
And then you'd decrease the exponent by 1, you get x to the minus 2.
So if we could get it in a form that looks like this, we'd be all set.
Where this x is you have a cosine there, and then we have cosines derivative there.
So that's the big clue that we should be using u substitution.
So let's do that.
And what we're going to do is we're going to substitute u for cosine of x.
So if we say u is equal to cosine of x, and let's take the derivative of u with respect to x.
So du/dx is equal to what?
What's the derivative of cosine of x? it's not quite sin of x, right?
It's minus sin of x.
And then we can multiply both sides by dx, and you get du is equal to minus sin of x dx.
I just multiplied both sides by dx.
And then up here we have sin of x dx.
We don't have minus sin of x dx.
There we have sin of x dx.
We could have rewritten this top integral, we could have rewritten it like this. Sin of x dx.
All of that over cosine of x squared.
So if we want to substitute for this, here we have a minus.
Let's multiply both sides of this by a negative 1, and you get minus du is equal to sin of x dx. And let's see.
Now I know I'm running out of space.
So we know that u is equal to cosine of x, so let's do that.
So now this integral becomes-- and the denominator, instead of cosine of x squared, u is cosine of x.
That's u, right?
We made that definition.
So that's over u squared.
Cosine of x becomes u.
And then sin of x dx right up there, what is that equal to?
That's equal to minus du.
Sin of x dx is equal to minus du.
So that we can replace with this, minus du.
And then of course this has the exact same form as this thing right here.
You could rewrite this, this is equal to let's say minus 1 over u squared du.
I'm just writing it a bunch of different ways.
The same thing as minus u to the minus 2 du.
And then here we do the same thing we did up here, although now we have a minus out front, that actually makes it a little bit cleaner.
To take the antiderivative, we raise u-- it was to the minus 2 power, let's raise it to 1 power higher than that-- so minus 2 plus 1 is minus 1.
So it's u to the minus 1 power, and then you want to divide by minus 1, and I'll do it explicitly here.
Minus one.
And then you had this negative that was sitting out there before, so that negative is still going to be there.
And of course you're going to have a plus c.
And so you're just left with u to the minus 1 plus c, or 1 over u plus c is the antiderivative-- oh sorry, we're not done yet.
And now we have our substitution to deal with.
What was our substitution that we started with? u is equal to cosine of x.
So if u is equal to cosine of x, this thing is equal to 1 over cosine of x plus c is equal to the antiderivative of our original problem, which was sin of x over cosine of x squared dx.
There you go.
See you in the next video.
>>In the last video, we talked a little bit about compounding interest, and our example was interest that compounds annually, not continuously, like we would see in a lot of banks, but I really just wanted to let you understand that although the idea is simple, every year, you get 10% of the money that you started off with that year, and it's called compounding because the next year, you get money not just on your initial deposit, but you also get money or interest on the interest from previous years.
That's why it's called compounding interest.
Although that idea is pretty simple, we saw that the math can get a little tricky.
If you have a reasonable calculator, you can solve for some of these things, if you know how to do it, but it's nearly impossible to actually do it in your head.
For example, at the end of the last video, we said, "Hey, if I have $100 and if I'm compounding "at 10% a year," that's where this 1 comes from,
"how long does it take for me to double my money?" and end up with this equation.
To solve that equation, most calculators don't have a log (base 1.1), and I have shown this in other videos.
This, you could also say x = log (base 10) 2 / log (base 1.1) 2.
This is another way to calculate log (base 1.1) 2.
I say this ...
Sorry.
This should be log (base 10) 1.1.
I say this because most calculators have a log (base 10) function, and this and this are equivalent, and I have proven it in other videos.
In order to say, "How long does it take "to double my money at 10% a year?" you'd have to put that in your calculator, and let's try it out.
Let's try it out right here.
We're going to have 2, and we're going to take the logarithm of that.
It's 0.3 divided by ... divided by ... ... I'll open parenthesis here just to be careful ... ... divided by 1.1 and the logarithm of that, and we close the parentheses, is equal to 7.27 years, so roughly 7.3 years.
This is roughly equal to 7.3 years.
As we saw in the last video, this not necessarily trivial to set up, but even if you understand the math here, it's not easy to do this in your head.
It's literally almost impossible to do it in your head.
What I will show you is a rule to approximate this question.
How long does it take for you to double your money?
That rule, this is called the Rule of 72.
Sometimes it's the Rule of 70 or the Rule of 69, but Rule of 72 tends to be the most typical one, especially when you're talking about compounding over set periods of time, maybe not continuous compounding.
Continuous compounding, you'll get closer to 69 or 70, but I'll show you what I mean in a second.
To answer that same question, let's say I have 10% compounding annually, compounding, compounding annually, 10% interest compounding annually, using the Rule of 72, I say how long does it take for me to double my money?
I literally take 72.
I take 72.
That's why it's called the Rule of 72.
I divide it by the percentage.
The percentage is 10.
Its decimal position is 0.1, but it's 10 per 100 percentage.
So 72 / 10, and I get 7.2.
It was annual, so 7.2 years.
If this was 10% compounding monthly, it would be 7.2 months.
I got 7.2 years, which is pretty darn close to what we got by doing all of that fancy math.
Similarly, let's say that I am compounding ... Let's do another problem.
Let's say I'm compounding 6.
Let's say 6% compounding annually, compounding annually, so like that.
Well, using the Rule of 72,
I just take 72 / 6, and I get 6 goes into 72 12 times, so it will take 12 years for me to double my money if I am getting 6% on my money compounding annually.
Let's see if that works out.
We learned last time the other way to solve this would literally be we would say x.
The answer to this should be close to log, log base anything really of 2 divided by ...
This is where we get the doubling our money from.
The 2 means 2x our money, divided by log base whatever this is, 10 of, in this case, instead of 1.1, it's going to be 1.06.
You can already see it's a little bit more difficult.
Get our calculator out.
We have 2, log of that divided by 1.06, log of that, is equal to 11.89, so about 11.9.
When you do all the fancy math, we got 11.9.
Once again, you see, this is a pretty good approximation, and this math, this math is much, much, much simpler than this math.
I think most of us can do this in our heads.
This is actually a good way to impress people.
Just to get a better sense of how good this number 72 is, what I did is I plotted on a spreadsheet.
I said, OK, here is the different interest rates.
This is the actual time it would take to double.
I'm actually using this formula right here to figure out the actual, the precise amount of time it will take to double.
Let's say this is in years, if we're compounding annually, so if you get 1%, it will take you 70 years to double your money.
At 25%, it will only take you a little over three years to double your money.
This is the actual, this is the correct, this is the correct, and I'll do this in blue, this is the correct number right here.
This is actual right there.
That right there is the actual.
I plotted it here too.
If you look at the blue line, that's the actual.
I didn't plot all of them.
I think I started at maybe 4%.
If you look at 4%, it takes you 17.6 years to double your money.
So 4%, it takes 17.6 years to double your money.
That's that dot right there on the blue.
At 5%, it takes you, at 5%, it takes you 14 years to double your money.
This is also giving you an appreciation that every percentage really does matter when you're talking about compounding interest.
When it takes 2%, it takes you 35 years to double your money.
1% takes you 70 years, so you double your money twice as fast.
It really is really important, especially if you're thinking about doubling your money, or even tripling your money, for that matter.
Now, in red, in red over here,
I said what does the Rule of 72 predict?
This is what the Rule ...
So if you just take 72 and divide it by 1%, you get 72.
If you take 72 / 4, you get 18.
Rule of 72 says it will take you 18 years to double your money at a 4% interest rate, when the actual answer is 17.7 years, so it's pretty close.
That's what's in red right there.
That's what's in red right there.
You can see, so I have plotted it here, the curves are pretty close.
For low interest rates, for low interest rates, so that's these interest rates over here, the Rule of 72, the Rule of 72 slightly, slightly overestimates how long it will take to double your money.
As you get to higher interest rates, it slightly underestimates how long it will take you to double your money.
Just if you had to think about,
"Gee, is 72 really the best number?" this is what I did.
If you just take the interest rate and you multiply it by the actual doubling time, and here, you get a bunch of numbers.
For low interest rates, 69 works good.
For very high interest rates, 78 works good.
But if you look at this, 72 looks like a pretty good approximation.
You can see it took us pretty well all the way from when I graphed here, 4% all the way to 25%, which is most of the interest rates most of us are going to deal with for most of our lives.
Hopefully, you found that useful.
It's a very easy way to figure out how fast it's going to take you to double your money.
Let's do one more just for fun.
I have a, I don't know, a 4 ... well, I already did that.
Let's say I have a 9% annual compounding.
How long does it take me for me to double my money?
Well, 72 / 9 = 8 years.
It will take me 8 years to double my money.
The actual answer, if this is using ...
This is the approximate answer using the Rule of 72
The actual answer, 9% is 8.04 years.
Once again, in our head, we were able to do a very, very, very good approximation.
In the last video, we learned that if you just leave water to itself, it autoionizes.
H2O, disassociating in itself, really, into a hydrogen ion in an aqueous solution plus a hydroxide anion in an aqueous solution or a negative ion.
These are the same thing, and I write it this way because this is actually the state that happens. That you don't actually have these protons just independently, they actually do join onto another water molecule and form a hydronium ion. But these are the same exact concept.
The concentration of your hydrogen protons-- because that's really what they are, or hydrogen ions-- is 10 to the minus 7 molars. And then we even said, hey, chemists, for whatever reason, don't like dealing with negative exponents. So they defined the pH as equal to the minus log base 10 of your hydrogen concentration.
And of course, that's equal to minus log base 10 of 10 to the minus 7 for pure water, at 25 degrees, which is equal to 7. Fair enough. And you can probably imagine, if people took the trouble of constructing this pH thing and saying it's the negative log, they must really care about what the hydrogen concentration of water is.
Arrhenius.
Arrhenius, with an H. These are Arrhenius acid, Arrhenius base. So for example -- if I were to take --
An aqueous solution plus chloride. So it's just a chloride negative ion in an aqueous solution. And they just float in there.
O4. And these are good to know, because if you see them on a chemistry exam, you know that these are going to completely disassociate. And remember, we keep using this word acid.
Your alkali earth metals are bonded with hydroxide. If you put them in water, the hydroxide pops off. So let me just-- I'll show it with lithium or sodium.
aqueous solution. This completely disassociates. No equilibrium here.
The same thing is if you have sodium.
If you have sodium... Sodium's going to do the same thing. Sodium hydroxide in an aqueous solution.
Now, everything I've done so far-- this is the Arrhenius definition-- where an acid increases your hydrogen concentration, a base increases your hydroxide concentration. Now that is what you're going to see 90% of the time. But there is a slightly broader definition out there.
And I don't know the correct-- I always say just Bronsted, but. If you don't have fancy fonts, it's spelled like this.
Bronsted-Lowry acid or base. If you if you have good fonts, there's usually this little cross at the o. So I don't know.
So let's look at this definition in the context of everything we've just done so far. So if you live by the Bronsted-Lowry definition, what is a proton donor here? Well, this hydrochloric acid is-- let me look at this reaction right here.
Bronsted-Lowry. Well that's because Arrhenius is always-- You're always dealing with water.
And Arrhenius has nothing to say for this. Because everything he deals with is hydronium and water. But the Bronsted-Lowry definition works in this situation.
Bronsted-Lowry and what I'm about to say right now also exists. And that's Lewis acids and bases. Lewis acids and bases.
Now Lewis cares about electrons.
Bronsted-Lowry cared about protons. So Lewis, instead of saying an acid is a proton donor, Lewis acid says it's an electron acceptor. Electron acceptor.
Arrhenius base. Because this doesn't have to happen in water. And what you have here is boron trifluoride, with a fluoride anion.
I have a friend who is an artist, and has sometimes taken a view which I don't agree with very well.
He'll hold up a flower and say "Look how beautiful it is" and I'll agree.
First of all, the beauty that he sees is available to other people and to me too, I believe, although I may not be quite as refined aesthetically as he is; but I can appreciate the beauty of a flower.
At the same time, I see much more about the flower than he sees.
I could imagine the cells in there, the complicated actions inside, which also have a beauty.
I mean, it's not just beauty at this dimension of one centimeter, there's also beauty at smaller dimensions.
The inner structure, also the processes, the fact that the colors and the flower are evolved in order to attract insects to pollinate it is interesting.
It means that insects can see the color.
It adds a question: does this aesthetic sense also exist in the lower forms that... why is it aesthetic... all kinds of interesting questions which with science, knowledge, only adds to the excitement, and mystery, and the awe of a flower.
I don't understand how it subtracts.
If you expected science to give all the answers to the wonderful questions about what we are, where we are going, what the meaning of the universe is, and so on, then I think you could easily become disillusioned and look for some mystic answer to these problems.
How a scientist can take a mystic answer, I don't know, the whole spirit is to understand...
Well, never mind that, I mean I don't understand that.
But anyhow, if you think of it, the way I think of what we're doing is that we are exploring, we're trying to find out as much as we can about the world. People say to me "Are you looking for the ultimate laws of physics?" No I'm not, I'm just looking to find out more about the world, and if it turns out there is a simple ultimate law that explains everything, so be it.
A ball is shot into the air from the edge of a building 50 feet above the ground
It s initial velocity is 20 feet per second
The equation h (height) = -(negative)16t squared+20t+50 can be used to model the height of the ball after t second
And I think in this problem they just want us to accept this formula
Although we do derive formulas like this we show why it works for this type of problem in the Khan academy Physics playlist
But for here we will just go with the flow in this example
So they give us the equation that we use to model the height of the ball after t seconds and then say about how long does it take the ball to hit the ground
So if this is the height, the groudn is when the height is equal to zero
So hitting the ground literally means that h (height) is equal to zero
So we need to figure out at which times does h (height) equal zero
So we are really solving the equation 0 = -16tsquared + 20t + 50
And if you want to simplify this a little bit
Let's see everything here is divisible at least by 2 so let's divide everything by negative 2 just so that we can be rid of this negative coefficient
So you divide the left hand side by negative 2, you still get a zero
Negative 16 divided by negative 2 is eight so 8t squared 20 divided by negative two is negative 10
Minus 10t 50 divided by negative 2 is minus 25 is equal to zero.
If you okay with this on the left hand side you can put it on the left hand side
We can say this is equal to 0
And now we solve
And we can complete the square here or apply the quadratic formula which is derived from completing the square and we have this in standard form, we know that this is our a this our b and this over here is our c
And the quadratic formula tells us that the roots
In this case in terms of the variable t are going to be equal to negative b plus or minus the square root of b squared minus four a c.
All of that over 2 a
So if we apply it we get t is equal to negative b b is negative 10 so negative negative 10 is going to be postitive 10 plus or minus the square root of negative ten squared well thats just positive 100 - 4*a which is 8 times c which is negative 25 and all of that over 2 a a is 8 so 2a is 16 and this over here we have a negative sign negative times a negative... so this is a positive 4 times 25 is 100 100 times 8 is 800 so all that simplifies to 800 and we have 100 + 800 under the radical sign so 10 plus or minus the square root of 900 all of that over 16 is equal to 10 + or - 30 over 16 so we get time is equal to 10+30/16 40-16 which is the same thing if we divide the numerator and denominator by 4 which is 10 over... or even better divide by 8 5 over 2 so thats one solution.
Thats if we add the 30 if we subtract the 30 so or t = 10 -30 which is -20 over 16 divide the numerator and the denominator by 4 and you get -5 over 4
Now we have to remember were trying to find a time and so a time at least in this problem is positve we want to figure out how long it takes for the ball to hit the ground we dont want to go back in time, we dont want negative time we only want to think about our positive answer and so this tells us that the only root that should work is, we have to assume that this is in seconds so 5/2 seconds i woudnt worry to much about the phisics here i think they just want us to apply the quadratic formula into this modeling situation the physics, we go into a lot more depth in the physics playlist so lets verify that we definitley are at a height of 0 at 5/2 seconds so if t=5/2 then this expression is equal to 0 so we have, lets try it out, so we have
-16*5/2^2 +20*5/2 +50 this needs to be equal to 0 so this is -16*25/4 + 50+50=0
-16/4 is -4 4/4 is 1 so -4/25 which is 100, +50 sorry, -4/25 is NEGATlVE 100 100+50+50 so we have -100 plus 100 so thats definatly going to be 0 we get 0 = 0 and it all checks out we hit the ground after 5/2 seconds or another way to think about it is 2.5 seconds
So now we have this graph of this-- what was clearly a trig function. And our task is to figure out what the function is. So let's look at this.
Well, that's just how much does it move up and down above and below the x-axis? Well, the amplitude here is how much it moves up the x-axis. Well, it moves up 1/2 above and below the x-axis.
So let's think about what happens when-- you know, we want to know what this function is. f of x is equal to question mark.
Well, we see that f of 0 is 0. f of 0 is equal to 0.
What does that tell us? Is this a sine or a cosine function? Well, what's cosine of 0?
Let's define another function. Let's define g of x is equal to 1/2 cosine of 2x. What would have this looked like?
This is f of x. f of x is this one right here.
So when x is 0, what is g of 0? Let's put 0 in here. So this whole term will become 0.
It's just like the sine function was just shifted to the left of it.
But if you look at this side, the important thing to realize is that it intersects the y-axis at not 1, but 1/2. And the reason why it doesn't intersect it at 1, even though cosine of 0 is 1, is because we have this 1/2 coefficient right here. I guess you can't call that a coefficient.
In this video, I want to talk a little bit about acceleration.
Acceleration.
And this is probably an idea that you are somewhat familiar with or at least you've heard the term used here or there.
Acceleration is just the change in velocity over time.
Change in velocity over time.
Probably one of the most typical examples of acceleration, if you are at all interested in cars is that many times they will give you acceleration numbers especially for sport cars.
Actually all cars, if you look up in consumer reports or wherever they give stats on different cars they'll tell you something like, I don't know, like a Porsche - and I'm going to make up these numbers right over here.
So let's say we have a Porsche 911. Porsche 911.
They'll say that a Porsche 911 -they'll literally measure it with a stopwatch - can go 0 to 60 miles per hour - and these aren't the exact numbers, although I think it's probably pretty close.
0 to 60 miles per hour in, let's say, three seconds.
In three seconds.
So although officially what they are giving you right here are speeds cause they are only giving you magnitude and no direction, you can assume that it's in the same direction.
And you can say 0 mph to the East to 60 mph to the East in 3 seconds, so what was the acceleration here?
So I just told you the definition of acceleration - it's the change in velocity over time!
So the acceleration, and once again, acceleration is a vector quantity.
You want to know not only how much is velocity changing over time, you also care about the direction!
It also makes sense because the velocity itself is a vector quantity.
Needs magnitude AND direction.
So the acceleration here, and we are just going to assume that we are going to the right, 0 mph and 60 mph to the right.
So what is... It's going to be change in velocity - let me just write it down with different notation, just so you can familiarise yourself if you see it in a textbook this way.
So change in velocity.
This delta symbol right here just means 'change in'.
Change in velocity over time.
Over time.
And it's really, as I've mentioned in previous videos, time, it's really change in time, but we can just write time here.
This 3 seconds is really change in time.
It might have been, you know, if you looked at your second hand, it might have been 5 seconds when it started and it might have been 8 seconds when it stopped, so it took a total of 3 seconds.
So time - it's really a change in seconds.
But we'll just go with time right here,
Or we'll go with 't'.
So what's our change in velocity?
So our final velocity is 60 mph.
Our final velocity is 60 mph.
And our original velocity was 0 mph, so it's 60 minus 0 mph.
And then what is our time?
What is our time over here?
Well, our time is, or we could even say our change in time, our change in time is 3 seconds.
3 seconds.
So this gives us 20 mph per second.
Let me write this down.
So this becomes...
This top part is 60.
60 divided by 3 is 20.
So we get 20... but then the units are a little bit strange.
We have miles... Instead of writing mph I'm going to write miles per hour.
That's the same thing as mph.
And then we also, in the denominator, right over here, we also, right over here in the denominator have seconds.
Which is a little bit strange.
And, as you'll see, the units for acceleration do seem a little strange.
But if we think it through, it actually might make a bit of sense.
So miles per hour, and then we can either put seconds, like this, or we can write per second.
And let's just think about what this is saying, and then we can get it all into seconds, or hours, whatever you like.
This is saying that every second, this Porsche 911 can increase its velocity by 20 mph.
So its acceleration is 20 miles per hour per second.
And actually we should include a direction, cause we're talking about vector quantities.
So this is to the east.
And this is east right over here.
Just so we make sure that we're dealing with vectors.
You're giving it a direction.
So every second, it can increase its velocity by 20 mph.
So hopefully, the way I'm saying it makes a little bit of sense.
20 miles per hour per second.
That's exactly what this is talking about.
Now, we can also write it like this, this is the same thing as 20 miles per hour...
Cause if you take something and divide it by second, that's the same thing as multiplying it by 1 over second.
So that's miles per hour seconds.
And although this is correct, to me this makes a little less intuitive sense.
This one literally says that every second it's increasing in velocity by 20 miles per hour.
20 miles per hour increase in velocity per second.
So that kind of makes sense to me.
Here it's saying 20 miles per hour seconds.
So once again, it's not as intuitive.
But we can make this so it's all in one unit of time.
Althought you don't really have to.
You can change this so you can get rid of maybe the hours in the denominator.
And the best way to get rid of an hour in the denominator is by multiplying it by something that has hours in the numerator.
So hour, and seconds.
And here...
The smaller units are seconds, so it's 3600 seconds for every 1 hour.
Or, one hour is equal to 3600 seconds.
Or, 1/3600 of an hour per second.
All of those are legitime ways to interpret this thing in magenta right over here.
And then you multiply.
Do a little dimensional analysis.
Hour cancels with hour, and then you have...
This will be equal to...
This will be equal to 20/3600.
20/3600.
Miles per seconds times seconds.
Or we could say, miles... Let me write it this way.
Miles per seconds times seconds.
Or you could say, miles per second...
I want to do that in another colour.
Miles per second squared.
Miles per seconds...
Miles per second squared.
And we can simplify this a little bit.
Divide the denominator and numerator by ten.
You get 2 over 360.
Or you could get..
This is the same thing as 1 over... 1 over 180.
Miles per second squared.
Per second squared.
I'll just abbreviate like that.
And once again, this doesn't make... 1 180th of a mile.
How much is that?
You might want to convert it to feet, but the whole point here is, I just wanted to show you that well, one, how do you calculate acceleration, and give you a little bit of sense what it means.
And once again, what you have here, when you have seconds squared in the bottom of the units, it doesn't make a ton sense, but we could rewrite it like this up here.
This is 180... or 1 / 180 miles per second... and then we divide by seconds again: per second.
Or maybe I can write it like this; per second.
Where this whole thing is the numerator.
So this makes a little bit more sense from an acceleration point of view.
One over 180 miles per second...
Every second this Porsche 911 is going to go 1 /180 of a mile per second faster.
And actually it's probably more intuitive to stick to the miles per hour, cause that's something that we have a little bit more sense on.
And another way to visualize it.
Another way to visualize it.
If you were driving that Porsche, and you were looking at the speedometer of that Porsche, and if the acceleration was constant, it's actually not going to be completely constant, and if you looked at this speedometer...
Let me draw it, so this would be 10, 20, 30, 40, 50, 60.
This is probably not what the speedometer for a Porsche looks like, this is probably more analogous to a small four cylinder car's speedometer, I suspect the Porsche's speedometer goes much beyond 60 mph, but you would see, for something accelerating this fast, is right when you're starting, the speedometer would be right there.
And then every second, it would be 20 mph faster.
So after a second, the speedometer would have moved this far.
After another second, the speedometer would have moved this far.
And then after another second, the speedometer would have moved that far.
And the entire time you would have kind of been pasted to the back of your seat.
With all the legitimate concerns about AlDS and avian flu -- and we'll hear about that from the brilliant Dr. Brilliant later today --
I want to talk about the other pandemic, which is cardiovascular disease, diabetes, hypertension -- all of which are completely preventable for at least 95 percent of people just by changing diet and lifestyle.
And what's happening is that there's a globalization of illness occurring, that people are starting to eat like us, and live like us, and die like us.
And in one generation, for example,
Asia's gone from having one of the lowest rates of heart disease and obesity and diabetes to one of the highest.
And in Africa, cardiovascular disease equals the HlV and AlDS deaths in most countries.
So there's a critical window of opportunity we have to make an important difference that can affect the lives of literally millions of people, and practice preventive medicine on a global scale.
Heart and blood vessel diseases still kill more people -- not only in this country, but also worldwide -- than everything else combined, and yet it's completely preventable for almost everybody.
It's not only preventable; it's actually reversible.
And for the last almost 29 years, we've been able to show that by simply changing diet and lifestyle, using these very high-tech, expensive, state-of-the-art measures to prove how powerful these very simple and low-tech and low-cost interventions can be like -- quantitative arteriography, before and after a year, and cardiac PET scans.
We showed a few months ago -- we published the first study showing you can actually stop or reverse the progression of prostate cancer by making changes in diet and lifestyle, and 70 percent regression in the tumor growth, or inhibition of the tumor growth, compared to only nine percent in the control group.
And in the MRI and MR spectroscopy here, the prostate tumor activity is shown in red -- you can see it diminishing after a year.
Now there is an epidemic of obesity: two-thirds of adults and 15 percent of kids.
What's really concerning to me is that diabetes has increased 70 percent in the past 10 years, and this may be the first generation in which our kids live a shorter life span than we do.
That's pitiful, and it's preventable.
Now these are not election returns, these are the people -- the number of the people who are obese by state, beginning in '85, '86, '87 -- these are from the CDC website -- '88, '89, '90, '91 -- you get a new category -- '92, '93, '94, '95, '96,
'97, '98, '99, 2000, 2001 -- it gets worse.
We're kind of devolving.
Now what can we do about this?
Well, you know, the diet that we've found that can reverse heart disease and cancer is an Asian diet.
But the people in Asia are starting to eat like we are, which is why they're starting to get sick like we are.
So I've been working with a lot of the big food companies.
They can make it fun and sexy and hip and crunchy and convenient to eat healthier foods, like -- I chair the advisory boards to McDonald's, and PepsiCo, and ConAgra, and Safeway, and soon
Del Monte, and they're finding that it's good business.
The salads that you see at McDonald's came from the work -- they're going to have an Asian salad.
At
Pepsi, two-thirds of their revenue growth came from their better foods.
And so if we can do that, then we can free up resources for buying drugs that you really do need for treating AlDS and HlV and malaria and for preventing avian flu.
Thank you.
Let's get started and learn how to convert percentages to decimals, and if we have time maybe we'll also learn how to convert decimals into percentages.
So let's get started with what I think is a problem you probably already know how to do.
If I said I have fifty percent.
I don't know if I wanted to write that thick, but we'll go with it.
Actually, let me change it to a thinner one.
And I want to turn that into a decimal.
Well you probably already have a sense of what decimal represents fifty percent.
If I told you we're having a sale and it's fifty percent off, you know that's roughly half off, or another way, how do you say half as a decimal?
Well that's the same thing as zero point five.
So you might have known that in your head, but is there a system for being able to convert this fifty percent to point five?
Well, it turns out it's pretty straightforward.
All you do is you say-- whatever percentage it is, that's the same thing as the number over one hundred.
And fifty over one hundred is the same thing as five over ten or point five.
Now even a simpler way of converting percentage to decimals.
And this, I think, you're going to realize converting a percentage to a decimal or the other way around, you can pretty much do in your head.
If I say, let's say fifty-- and I'm just going to add one decimal of accuracy here just to show you a point-- fifty percent. Right?
If I want to convert that fifty percent into a decimal, all I do is I get rid of the percent sign.
So I'll do it here.
Fifty percent.
I get rid of the percent sign and I take the decimal point and I move it over two spaces to the left.
So I say one, two.
So this is where the new decimal is.
So this equals, we could say zero point five zero zero.
So fifty percent is equal to zero point five zero zero.
And of course, these last two zeros really don't mean anything for our purposes, so we'll get rid of them.
So that's the same thing as zero point five or just point five.
Fifty percent equals point five.
So you're probably saying, well, sure. That looks easy, but what if the problem gets a little harder?
Fifty percent I could have done in my head.
So let's try some, I would say, slightly harder problems.
If I were to tell you that-- let's say sixteen point three two percent.
Well, let's just do it the way I just showed you.
I'll rewrite it down here.
Sixteen point three two percent.
So if we get rid of the percent sign, scratch it out, we just have to move the decimal over two spaces to the left.
So one, two.
This is the new place for the decimal. That decimal goes away.
So it's point one six three two is equal to sixteen point three two percent.
I think you might be getting the idea now.
Let me do another one in green.
Let's say I had-- and this one actually confuses a lot of people.
Let's say I had zero point two five percent.
So the important thing to remember is, I'll rewrite here.
Zero point two five-- and maybe I'll write zero zero point--
And you're probably wondering why I'm doing this, but I think you'll see in a second why I wrote that leading zero there even though it doesn't seem to add much to it.
Zero zero point two five percent.
Well, what's the system I just showed you?
You get rid of the percent sign, and you move the decimal over one, two spaces.
So that equals point zero zero two five.
So point two five percent is equal to point zero zero two five.
And you could put a leading zero here if you want. Actually, I should probably tell you to always do that because it makes it easier to read.
So point two five percent is equal to point zero zero two five.
And I want to just contrast that with twenty-five percent.
Twenty-five percent, what do you think that equals?
Well, you do the same thing that we've been doing.
You get rid of the percent sign and you move the decimal space. In this case-- actually, let me leave that there.
I'll just rewrite it here.
Twenty-five percent.
And you're probably saying, where is the decimal in this?
Well, the decimal is after the number because that twenty-five percent is the same thing as twenty-five point zero percent.
So if we get rid of the percent sign, we move the decimal over two spaces to the left, and that equals point two five as a decimal, or point two five zero, but we can ignore that last zero.
So twenty-five percent equals point two five, while point two five percent is equal to point zero zero two five.
And I want you to maybe sit and think about how small of a number point two five percent is.
Let's do a couple more and maybe we'll convert going the other direction.
Let's say I have the decimal point zero one and I wanted to convert that into a percent.
Well, here we just do it the opposite.
We could look at it two ways.
We could say well, whatever number this is, we multiply it by one hundred and add a percent sign.
So if you say point zero one times one hundred, and then we'll add a percent sign.
So point zero one times one hundred?
Well that's just one.
You could do the math.
You add the percent sign.
Well, that equals one percent.
Or an even easier way, when we go from a percent to a decimal, we move the decimal place over two to the left.
So when you go from a decimal to a percent, we'll do the opposite.
We move the decimal two to the right.
So if we do that, let me just rewrite it.
Point zero one.
Just go one, two.
The new decimal place is here.
If I get rid of that decimal, that's zero one decimal zero zero-- whatever.
Obviously, this leading zero means nothing, so that's the same thing as one point zero zero.
Which is the same thing as one.
And does it make sense that moving the decimal space two to the right-- that's really just the same thing as multiplying it by one hundred, right?
If I multiply something by ten, it's like moving the decimal space one to the right.
If I divide something by ten, it's like moving the decimal space one to left.
Let's do a couple more while I have time.
I think I have three more minutes.
Let's say I had one point two five, and I wanted to convert that to a percent.
Well, the easiest way is just to take-- I'll rewrite it here.
One point two five.
Take the decimal point, move it two to the right.
That's here.
And then I'll add a percent.
So that equals one hundred twenty-five percent.
And if you think about it, the way people talk about percent it makes sense.
If I told you that I'm going to pay one point two five times the price of something.
That makes sense that that's also one hundred twenty-five percent of the price.
Or if it doesn't make sense, hopefully if you do these problems enough it will start to make sense. Let's do a couple of more.
And you can go back and pause this if you think I'm going too fast, which I might be doing.
Let me think.
If I were to say point zero zero three and I want to write this as a percent.
Well, once again, we can move the decimal space two to the right.
So one, two.
And that's analogous to multiplying it by one hundred.
So if we multiply the decimal two to the right we get zero zero decimal point three.
And then we add the percent.
These don't-- at least this first leading zero doesn't mean anything, so that's the same thing as zero point three percent.
The important thing to realize is when you're converting from a percent to a decimal or a decimal to a percent, you're really just moving where that decimal point is.
And if you run out of space, you just have to add or get rid of zeros accordingly.
And the important thing to always have in your mind is, when I convert from a decimal to a percent, the number in front of percent signs going to get bigger.
And when I go from a percent sign to a decimal, I'm going to get a smaller number.
If I say twenty-five percent, that's the same thing as point two five. Right?
So this is a percent, and this is a decimal.
So I went from a bigger number, twenty-five, to a smaller number, point two five.
Twenty-five percent is equal to point two five.
Similarly, if I had a decimal, let's say point one.
When I convert it to a percentage, it's going to be a larger percentage.
So point one is the same thing as ten percent.
And how did I do that again? Well I said point one, I added an extra zero because I'm going to have to move the decimal space over to the right twice.
So I go one, two, and I get a ten.
Ten percent.
Hopefully that answers all your questions for now.
Have fun!
In present days, internet has played important roles in distributing news and information
But at the same time, cases prosecuted from online expression has spiked dramatically since the political crisis in recent years
"Online Witch Hunt" from the screen to prison
According to statistics from Thai Netizens
In 2011, There're 11 cases regarding the Computer Crime Act
Almost all cases' evidences are based on online expression which are relavent to the national security
Only one is the case about technical crime
Meanwhile, the cases persecuted with Article 112 of criminal code which states that whoever defames, insults or threatens the King, Queen, the Heir-apparent or the Regent shall be punished to prison terms from 3-15 years increases from 33 cases in 2005 to 478 cases in 2010 partially of which are from the online expression
After the 2006 coup Thai online society is filled with hatred and full of violent, angry words and unreasonable conversation
We see more of political divides and people want to say things that mainstream media wouldn't say
People wanted to speak about things that are suppressed by the law
During the intense political situations, we would see more intense words on the internet
And also after the coup, lese majeste cases have also increased very much
And it reached is peak in 2010 when the red shirts were crack down
"Kann-thoop" is one of those who was charged with lese majeste from something she posted on facebook
The evidence used against her was gathered from a group called "Social Sanction"
"Social Sanction" is a gathering of facebook users who monitor political expressions on the internet and "hunt" and expose those who expresses critical and defamatory comments against the monarchy
The page's info states that they have around 20,000 members
"Social Sanction" or "Witch Hunt" became common terms to use in online world
It means exposing one's personal information such as names, addresses, photos, workplace, parents' names of "the hunted" by posting them on the Social Santion facebook page
There're a good number of defaming comments and some even led to persecution by the authorities
Mostly, those who were hunted are the facebook users and then make the facebook wall public and not careful about the disclosure of personal information and use real names which are vulnerable to the exposure
So the "hunters" can check out the information and then use the personal data to google
They have intention to just harass or even use the info to press charge with the police
In some cases, the harasser would call up the victim's workplace and said that the person has insulting ideas towards the monarchy, and questioned about the propriety of the employment
This has happened before with the DHL employee
"Norawase" is another person who was "hunted" from content in his personal online blog and personal information was also posted on political online forum called "Serithai"
After that, he was charged with lese majeste and Computer Crime Act
The Social Sanction group has used the information that they obtained and spread out on facebook, webboard and online forum widely the issue has reached my university then the university went to press charge with the police
And then I was given summon notice, and went to see the police after that I got arrested
Firstly when I saw that my personal information is being shared I became afraid because some of them are factual information so I was afraid of personal safety issue
After Kannthoop was being exposed, she lost many opportunities to continue her study at the university
She was also harassed by the society while Norawase must leave his job
When I went to have admission interview at Kasetsart university some people opposing me then was mobilizing to protest against me they don't want the university to admit me,
So as I went there, I saw some people gathering and showing signs that Kasetsart university students are loyal to the monarchy.
I felt unsafe, so I decided not to go and waive my rights to that interview
Then after that I got admitted into Sanakarin Virot Prasanmitr university
So I went to the interview, as I was about to introduce myself
The lecturer/ interviewer then said "stop, I know what you've done, you can go home and wait for the results." and I was like, ok sure.
Thank you.
Goodbye and at Thammasat university where I'm studying now, some classmates will shout at me, if you don't love the king then just get out of this room
Don't come to class, just leave this country
And when I was doing activities with my friends, some people threw shoes at me
The two cases demonstrated the attempts to control the online expression whereby the article 112 and Computer Crime Act open the chances for anyone to press charges against anyone especially targeted are those who are of different political opinion and critical towards the monarchy
The case of "Ipad" also demonstrates such example he challenged the comments posted on news comment section and threaten to press charges against them to the police
It's reported that there 15 people who are pressed charged by Ipad which tops the highest for one person charging
After that, "I pad" would threaten the person charged on the forum
The person who likes to ultra-defend the monarchy likes to think the monarchy belongs to them solely
They didn't earn money from doing it they just do it out of their belief
This is very scary because some people even give out their real identity in exchange to the ability to press charge against people
like the case of "Ipad" who press charges against many people at Roi-et police station
So aside from the harassment by the charge they also have to travel to northeast for the process
As you can see, "Ipad" is very daring in pursuing many cases .
He likes to show off his charging documents.
The state also played important roles in controlling cyberspace such as the Ministry of Information and Communication Technology who founded the Cyber Scout project which trained high school students to monitor information on the internet that's against the monarchy and national security
It's reported that they aimed to train at least 100,000 youth the Cyber Security Operation Center is also established to receive complaints from the public
The complaints filed by general public has made the persecution statistics increased dramatically.
And the accused often don't get bails and proper treatment in prison
Ampon or "Arkong SMS" is the latest case of prisoners who died in jails from cancer
How many times you've requested for bails 6
On what reasons they denied you bails?
Flight risk
These online witch hunters, they just randomly accuse anyone
They just accuse because Thai judicial system is the accuse system
I'm just asking for rights for bail.
I didn't say that if I get bails I must get out guilt-free
I also wanted to fight fairly before the court
I don't know why I would be running away.
The problem of lese majeste law is that it also affects the judicial institutions and personnels
When the accused got charged, the chance of getting bails are very low
I don't know if you can call that an indirect way of social sanction
The police rarely grant bails Both in deep south of Thailand and in Bangkok.
Except those who have high social protection like Sulak Sivaraksa
Some of them have been granted bails, but in general there are very few and when the cases go on trial, some are conducted in secret
like the case of 'Da Torpedo'
People aren't allowed to go observe the trial
And the punishment is very high
like Amphon (uncle SMS) got 20 years
The death of Amphon has raised a lot of questions about the trial of lese majeste cases
In late May 2012, collections of 28,986 has been given to the parliament to request amendment to the article 112 but so far there's been no further progress about the law
However, the monitor and control of online space still continues
While the Thai society hasn't reached the consensus about the limit of the freedom of expression
Hello everyone.
And so the two of us are here to give you an example of creation.
And I'm going to be folding one of Robert Lang's models.
And this is the piece of paper it will be made from, and you can see all of the folds that are needed for it.
And Rufus is going to be doing some improvisation on his custom, five-string electric cello, and it's very exciting to listen to him.
Are you ready to go?
OK.
Just to make it a little bit more exciting.
All right.
Take it away, Rufus.
(Music)
All right.
There you go.
(Laughter) (Applause)
Honey~!
Hey, you can't kick that...
Jeez...
You haven't changed one bit.
Oh it's you, Boeun.
You're a big girl now.
Great body!
Nice curves.
Drop it, okay?
Hey, you little girl!
Hey, give me a break!
They look so nice and shiny...
Stop staring.
You'll sprain your eyes.
No, it's just that they look familiar.
Anyway, what brings you here?
Did you miss me so much that you had to skip school?
No, it's the school's anniversary.
I was forced to come here.
I'm wasting my time when I really have to study.
Yeah, there's only 2 years left till the national exam.
But people like you really make college look undesirable.
What do you mean?
You're a pervert and a playboy.
I may be a playboy, but I'm not a pervert.
Here's your present.
It's just for you!
Keep it a secret to the family.
Okay.
Pretty, isn't it?
It's padded.
Real thick.
You're a pervert!
Should I help you put it on?
- Should I?
- Do you want me to punch you?
- My son!
My son's home!
- How have you been?
- Welcome home.
- Thanks.
- How was your trip?
- Fine.
How have you been?
- Grandfather's waiting.
- Okay.
- Mom, it's heavy.
I'll carry it.
- Okay.
You've changed.
What was all the rush for?
And is grandpa really sick?
Son, brace yourself, okay?
Delicious, isn't it?
I made it myself, just for you, grandfather.
Really tasty.
No one but you can take such good care of me.
Of course, I'm your only granddaughter.
You've really grown.
Now you look like a lady.
She may have grown, but she's still a child.
I'd be married in the old days.
Right grandfather?
Absolutely.
A married woman.
- Sangmin, come sit here.
- Yes, grandfather.
You two, hear me out.
You may have heard this story before...
Sangmin's grandfather was an old friend and war comrade
When we were young, we made a pact,
To marry our kids.
But you two had only sons.
So, our pact was passed down to the next generation.
I hope you two can keep this promise.
What are you saying?
You idiot!
Grandpa wants you to marry Sangmin!
Marriage?
You must be joking grandpa!
Marry Sangmin?
Hey!
Your grandpa's not kidding!
I can die peacefully after you two get married!
This way, I can face Sangmin's grandpa.
How can a high schooler get married!
Anyone over 15 can marry with their parent's consent.
I haven't much time left, you know?
No, I won't.
Never!
Sorry grandpa but I'll forget what you just said.
He hasn't finished speaking!
I'm speechless myself.
It's me.
I'm back.
I'm back in Korea, standing in front of the department office.
Hey, there's lots of new blood in the department
- How are you?
- Oh, yeah.
The chicks are great!
Let's get together after class.
Hey, Sangmin!
What a surprise!
Has it been a year already?
No, I'm back for some family business.
How about you?
Great.
My looks...
- keep me too busy...
- Come on...
Come back when I'm the TA.
It'll help when you skip classes.
Would I, a model student, do that?
Besides, it's my last year...
Friend, my good friend!
- How have you been!
- Great dude!
Look at him!
Life in the West has done you well!
What brought you back?
Problems at home?
- Yeah something's up at home...
- Huh?
What?
- I'm getting married... damn.
- Huh?
Bastard!
Hey, is it a black or white girl?
Pounding!
Only you should know about it~ I'm just 17~
Come, come silently ~ Here and there~
Hey!
They're making such a fuss.
Losers...
- Shh!
They'll hear you.
- Why?
Do you think you're different?
My doctor said I have 20 more years to go!
Really?
Change of plans.
I'll make my move.
Just back me up.
I understand.
Good!
They switched it.
Isn't he the guy?
They switched it.
Remember?
Yeah...
I really wish they wouldn't play those things on TV.
I guess the wedding's really on.
What am I going to do, mom?
Be strong, son.
Grant your grandpa this one wish.
Let's call it a day!
You're Suh Boeun, 1st grade, right?
You were so funny, don't you agree?
Hey, what?
Come on!
Who's he?
He's just a guy I know.
That's what they all say.
I'm telling the truth!
I really thought about it, and I'll speak first.
- Let's just do it.
- Are you crazy?
I'm kidding.
Do you think I'd want to?
I don't want to do it with you!
Even if I did, it's insane.
I'm just 15!
Okay, I got it.
Anyway, I'll buy you dinner.
Or anything else you need.
Mister, you're a sugar daddy, aren't you?
- Boeun.
- Huh?
How can you do this to me?
I may be pretty, but something like this...
Hey...
Hyewon, stop it!
- I'll leave you two to talk.
- Huh?
See you later, Boeun.
- Remember, it's a secret.
- I know.
- Bye.
- Good bye.
- What's her problem?
- It's understandable.
Hello?
Yes...
What!
Good, good.
Grandpa!
- Grandpa!
- Grandpa!
Grandpa, we're here!
Grandpa, Grandpa!
Grandpa, Grandpa!
Wake up, Grandpa!
- Uncle, something's wrong!
- What?
Grandpa!
It's doing it again.
We should've gone to another hospital!
It almost gave me a heart attack!
I was out of myself again.
Are you okay, grandpa?
- Let's have a word outside.
- Okay.
Be by your grandpa's side, okay?
Yeah.
I'm really worried.
I know.
With the kids like that, he's getting worse.
Come on... marriage is out of the question!
They... you have to think about Boeun's future.
Come on, let's just marry the kids.
Let go.
Come on...
This is Sangmin's grandparents.
Soon after this picture was taken, war broke out.
Do you want me to tell you a secret?
Secretly, your grandpa had feelings for Sangmin's grandma.
She was quite a beauty.
However, after Sangmin's grandpa's death, I tucked those feelings away.
That's why I took care of Sangmin's father like my own son.
Your father may not have been so happy about this.
- Boeun!
- Yes?
Keeping this promise is the most important thing for me.
- Grandpa!
- Grandpa!
Grandpa, wake up.
Grandpa!
You can't die!
Open your eyes, grandpa!
Grandpa, I'll get married so open your eyes, grandpa!
I'll keep your promise, grandpa!
I'll get married...
Are you crying?
Stop crying.
You may be behind in your grades, but you're the nation's first to get married at this age.
Congrats, missus.
Right.
Are you scared that Sangmin will discover your lop-sided butt?
A butt that needs cushioning to keep it on balance?
- Hey, get out!
- Ouch, it hurts!
I'm sorry Boeun, for not being much help.
Mom, am I really getting married?
What about school?
I have to go to college...
Marriage won't change anything.
Marriage, accept it with grace.
It's nothing.
Just consider you're getting a new brother.
I'm scared that they'll find out at school.
How will I face everyone?
Don't worry.
Grandpa will take care of it.
Your grandpa was your principal's military senior.
Really?
Behold the face of a wolf who'll eat up a 15 year old virgin.
- Is it satisfaction or disbelief?
- Satisfaction, of course.
Shit, are you really my friends?
I can't be married at this age.
- To Sangmin!
- Cheers~
The chicks here are hot!
Let's go out on the floor!
Hello.
You're here.
Thanks.
You're here.
- Sir!!
- Yes, come in. Over here.
I won't forget this.
How could our field trip be at the same time?
I know.
You shouldn't keep it from your other friends.
If they found out, the whole school will know.
Then I'd have to quit school.
Anyway, you're so pretty today.
I wish I could get married too.
Look here!
Hey, smile!
- How are you doing?
- Hello.
- Don't take my picture.
- Okay, okay.
Good luck!
I'm convinced that grandpa scammed me.
- Boeun, it's just a wedding, okay?
- I can't do it, mom!
Now, don't be a baby.
I'm nervous myself.
I'm telling grandpa, "I can't do it!".
Do you want your wedding turned into a funeral?
I don't know.
I'm scared, mom.
What am I going to do with such a baby?
Now the groom will enter.
Welcome him with a big applause.
The groom, please enter!
She's so beautiful!
Respectable guests, family and relatives.
We are all gathered here to congradulate the new beginning of groom, Park Sangmin and bride, Suh Boeun...
- Dad, we'll be okay.
- Yeah, yeah.
Remember, she's only 15.
- What's your point?
- I know I can trust you.
You forced me into this marriage, so I'll do as I wish!
Boeun is still in high school!
I don't care!
I'll do as I wish with my wife.
Boeun, don't worry.
Your father-in-law has had a word with Sangmin.
About what?
- That you... shouldn't do it...
- What?
I can't say...
- Call us when you get there. - Yes, auntie.
Stop calling her that.
It's mom from now on.
Yes, mom.
Hey, mom!
Can I keep the bouquet?
It was so pretty...
Forget the bouquet...
She's such a child.
What am I going to do with you?
Stop, you promised to be cool.
- Bon voyage~ - Yes, yes...
- Bye~ - Follow right behind, okay?
It's time to board, where is she?
Boeun.
- Boeun?
Where is it?
- Over there...
- Okay, we'll go inside, thanks.
- Okay, go.
- Thanks for everything.
- Don't overdo yourself.
- Have a safe trip.
- Yeah, give me the suitcase.
Have fun, Boeun.
Don't worry, dude.
Be good, okay?
- See you later!
- Bye.
Bon voyage.
- I've never boarded on time...
- Wait.
- What?
- I need to go to the bathroom.
Again?
It's your first time on a plane, isn't it?
Don't worry.
It's only an hour to Jeju Isle.
It won't take long.
You're making such a fuss.
Hurry back.
- I'll be at our seats.
Hurry.
- Okay...
Shit.
Where is she?
- Sir, you must be seated.
- The plane's leaving.
Open the...
Sir, please seat yourself!
Mobiles are prohibited in the cabin.
Thank you for your cooperation.
He must think he owns the plane.
It must be his first flight.
I don't believe this.
Wait sir.
- We're in a hurry.
- Sorry.
Hey!
Did they arrive safely?
Yeah... they did.
I need to be clear about one thing.
Listen!
Until Boeun graduates from college, no grandchildren!
Make this clear to your father as well.
Yes, of course.
When she was little, she would fall and break things, but she seemed to hold herself well at the wedding.
It's a relief.
Why?
Are you disappointed that she didn't fall?
Yes, a little.
Come on...
Not those idiots again!
Having fun?
Hey!
Hey, do you have a place to stay?
Just this once.
Press anything.
Wind it and press.
Say cheese.
Take your best shot.
Uh, Sangmin?
I can't believe this!
What brings you here?
Boeun's on her honeymoon and we're on our fieldtrip.
- Don't you remember?
- Of course I do.
- Where's Boeun?
- Well...
- Hey!
Who's the mister?
- He's just a friend.
- He's cute.
- See you later!
- Hey, stop it.
Wait, come here.
- Oh god...
Hey!
What are you doing on top of her!
You pervert!
You chase after young girls, don't you!
It's not like that.
- I'm not...
- Really.
- Really?
- Really.
Then what are you doing?
- Uh?
- Huh?
Look at him running off!
Aren't you supposed to be on your field trip?
Yes...
Then why are you here?
What are you doing today?
Nothing.
Do you have a boyfriend?
No...I don't.
The cell phone you are tring to reach is off.
You will be transferred to a voice mail...
Pest, how can you do this to me...
Our parents shouldn't find out.
We'll talk later.
Bye.
Then, from now on we're dating.
Okay!
Hey you!
Come here!
Wow!
Looks so fun! Isn't it?
- Where are you from?
- I'm from Canada.
Canada?
I know Canada!
Who am I kidding?
I've never set foot on Canada.
Teacher!
Teacher!
Hi, how are you?
Uh, Hyewon?
What brings you here at this hour?
It's free time for us.
Haven't you ever been on a field trip?
Of course I have.
Anyway, where's Boeun?
Why are you alone?
I don't even know where to begin?
It's like this...
Yes.
Boeun...
You're a serial pervert, aren't you!
Hey!
Come back!
Feels good, doesn't it?
It's been a while... together.
Sit here.
Stop.
Rest your back on this.
I feel great.
It's too late for this but I'm sure that we did a horrible thing to Boeun.
She's only 15, and going through her 1st year of high school.
Come on!
Be more positive.
You were considering him as your son-in-law anyway.
She's not going far away.
Let's have some faith, okay?
Besides, our in-laws love Boeun like their own daughter.
But, she's not their own daughter.
I can understand dad and you, but I still can't forgive you for it.
Okay, okay, that's enough... enough...
Without Boeun, it seems like there's a big hole in my heart.
Everyone looks like Boeun, that one too...
Candy, sir?
Thank you.
Candy, sir?
Boeun, help him.
Honey, honey, here.
Thank you very much.
- Grandpa!
- Dad, come on out.
- Sit, sit and eat.
- Okay.
So, how was your trip?
Good grandpa.
We had a good time.
Yes, Sangmin was kind to me.
I really had fun.
Stop, I didn't do anything.
I'm glad you had fun.
Since you're officially married, love one another so we can see the fruit of your love.
But you don't look so happy, Sangmin.
Are you sick?
Of course I'm not sick.
They're definitely a great couple, aren't they?
Your room's been cleaned, so go get some rest.
Yes sir.
Stop, we should have a drink with the new groom.
How about it dad?
Right.
My grandson-in-law should pour me a drink.
As you wish.
Grandpa, I'll go to bed now.
Yeah, yeah.
Go to your room...
Careful!
Honey!
Let's go!
- Hey!
Boeun's not a thing.
- Good night!
Hey!
Be careful.
Hey!
Hey!
- Have a good night.
- Good night!
Honey!
Ah, you're heavy!
And you stink of liquor!
Hey!
Hey!
- You're tearing my dress.
Stop it!
- Keep still!
He's coming on real strong.
This is the right place.
Come in. Look at this tree.
Come in dad.
Close the door behind you.
What do you think?
Huh?
It's nice right?
Look at this, great isn't it?
It's a great place.
Great place Boeun.
- Hey, you put up that picture!
- Nice, isn't it?
Great huh?
Look at the balcony.
I chose this.
Boeun.
It's so clean.
Hey, look at this picture.
This picture.
Where should I put this picture?
You're having the time of your life, aren't you?
- What's this, Arabian Nights?
- Goodness!
- What's with the pillows...
- Goodness...
Separate rooms until you graduate, okay?
I am so pissed!
I like it...
What's this, a flower garden?
What am I going to do?
Stop it!
Language is part of culture...
Language is... a part of... culture...
When we learn of foreign languages, we should also learn about... that country's culture...
Ah, great!
Hey, stop!
Put something on!
I always take everything off.
Even my underwear.
Get out!
Out where?
This is my room.
What do you mean?
This is my room.
Yours is over there.
Get out!
I don't feel like it.
Let's sleep together.
What, you're crazy!
You sleep together when you get married.
Boeun...
What?
- I think tonight is the night.
- What?
Listen to me.
Stay away from me.
Come on.
We're married.
Boeun, do as I say!
Hey, stop it!
We're married!
Do as I say and stay still.
Shit...
I was just playing with you!
Oh my god!
Good morning, Boeun.
Your eyes are quite a sight!
Morning exercise?
What?
You disappeared from the airport?
Then what did you do during your honeymoon?
Who, me?
Can you keep a secret?
You have too many secrets.
I'm dating Jungwoo.
Jungwoo?
What about your husband?
Husband... are you kidding?
I was forced into it.
Then does Jungwoo know you're married?
No. But I'm sure he'll understand.
Let's go.
If I call her, she'll be here in an instant.
Are you sure she'll come if you call her now?
Of course.
She'll say "Yes master" and then come.
You're such a liar.
Stop, she'll be studying anyway.
- Wait.
I'll show you.
- Dude, that's impolite.
- Tell her to come.
- Wait.
Wife!
It's me!
Your husband commands you to come!
Wow.
- Hurry!
- Wow.
- Hurry!!
- Wow.
Bye!
Now she'll fly here like a bullet.
Guys... let's drink!
I'm Sangmin.
I'm a man, ain't I?
Of course you're a man.
I'm just teaching my wife a lesson, like a real man!
A man of all men.
A real man.
Have a drink, men!
Men!!
Men, drink up!
Drink till we drop!
There'll be an inspection today.
Go home and study.
Wife!
She's my wife.
Come here wife!
- We're married!
- Not today.
He's really her husband.
Welcome, Boeun.
You saw her at the wedding, my wife, Boeun.
How could you call me over to such a place...
like this?
Your husband says it's okay.
Another beer please!
Don't.
Would you like a soda?
Yes...
A soda over here.
You're so adorable.
Thank you.
Of course!
My wife's adorable.
She's a horrible cook, with a bad temper.
And a bad student.
- She also snores.
- Sangmin!
You're drunk.
- Stop drinking, okay?
- No.
I'm jealous.
I have no one to worry about me.
- Wow, I feel great.
Bottoms up!
- Bottoms up, bottoms up!
I never introduced myself.
I'm Sangmin's senior, Han Jisoo.
I'm Suh Boeun.
Boing, boing, Boeun.
She goes boing boing every morning!
Jisoo, do you know what she did to me on our honeymoon?
Hey, Park Sangmin!
Get off your butt!
Pretty please...
I'll see you again, Jisoo.
Yes.
I'm sure we'll be good friends.
Treat me like a little sister.
But you're my senior in life since you're married.
Stop joking.
Stop joking, stop joking.
You know, you two are made for each other.
We were always at each other's throats when we were little.
Hitting and teasing each other.
He's the first boy to flip my skirt.
Funny.
Boys are mean to girls they really like.
Jisoo, Jisoo, kiss me.
At least you could've fixed me something for my hangover.
You deserve it.
Besides, I'm still in high school.
You always use that line when you're cornered.
High school is not a crown, you know.
It is too, so there!
Okay, then I'll show you my cooking talents tonight!
- Hey, Suh Boeun!
- What?
- Let's go.
- Come.
Do you wanna get smacked?
Come!
What do you want?
I heard you were telling everyone you were Jungwoo's girl?
Fucking unbelievable!
She's boasting that she's slept with Jungwoo.
The bitch thinks we're shit.
How dare you, bitch!
Listen up.
Watch your mouth.
If I hear about this again, you're dead meat!
Jungwoo and I are in love!
Have you lost your senses!
Hey!
Didn't you get the message?
I didn't do anything wrong.
I'm leaving!
Hey!
How dare you...
Lose your attitude!
What are you doing!
Fuck off.
What?
Hey, Lee Jungwoo, you can't treat me like that!
You're in no position to say that to me.
Listen up.
It's true that Boeun and I are dating.
Don't mind them.
They think they're princesses.
But you're the real princess.
Sesame oil, sugar!
- A small bottle of oil?
- Yeah!
- This sugar?
- Hurry, hurry.
Okay!
Vinegar, spaghetti, ketchup!
There's the vinegar...
And there's the spaghetti!
Here?
Here, the ketchup's here.
Okay...
Hurry, hurry!
- Olive oil, pickles!
- Olive oil, pickles!
Boeun!
Are you okay, Boeun?
Boeun, Boeun, Are you okay?
Are you okay?
Ow, my leg!
It hurts?
- Does it hurt bad?
- No. Why?
Get off?
Stay put before I change my mind.
Don't touch me there!
I'm not doing it on purpose.
Why should I?
My hand just went there naturally.
What a great excuse!
Now walk straight.
You slant to the right because your butt is lop-sided.
Don't start with me.
I'm not kidding.
Your right butt has grown bigger.
Hey, stop it!
Stop it!
Hey, stop it!
Lop-sided butt~ Lop-sided butt~
- Stop it, stop it!
- Okay, okay!
- Ladies and gentlemen!
- Shut up...
Boeun has a lop-sided butt!
Lop-sided butt~
Look at how you're cutting.
You should put your heart into what you're cooking.
Just be quiet!
- Be quiet?
I'm older than you...
- Stop it!
Stop what?
I'm older...
Hey...
You little...
- What?
- Take my sword.
- Pest... aim at what you can take.
- Hey, come here.
What are you going to do with that?
- Hey, stop it... it's hot.
Hot!
Hey...
- Hey...
Hey... that's not fair!
Ouch!
- It's delicious.
- Yeah.
You got something on your mouth.
The same with you.
Rock, paper, scissors!
Rock, paper, scissors!
Yes!
Make sure everything's spotless.
It's more important than cooking.
Give me a break!
Hey, is it this side?
Hey!
You pervert!
If I were you, I would help!
This picture's great.
I look so handsome.
Gotcha!
Sangmin...
Don't come near me!
Stop it!
Don't come near me!
Stop it, stop...
- Now, I'm taking everything off!
- Stop!
- Thanks, the sushi's great.
- Really?
The baseball field's empty.
Aren't people coming to watch the game?
No one comes to watch high school baseball anymore.
It's pro- baseball or the major league that they go to.
I hope you'll play in the major league some day.
Hey, Lee Jungwoo!
Good luck!
I'm starved.
Double crust seafood...
This is pretty good.
Lee Jungwoo, hurrah~
Give us a break.
Great pitching and now good batting?
She's quite a chick.
Why don't you share?
Shit.
Yes, that player's Lee Jungwoo.
An upcoming star in high school baseball!
Huh?
It's Boeun's high school.
Was I too generous?
That's doesn't look good...
Youngsters with raging hormones.
Something to do without.
But, I guess they'll grow out of it.
One cute student is quite passionate about a player.
- Ah, it's the sushi girl.
- Excuse me?
They were sharing a sushi lunch before the game.
Nice picture.
I see.
Can't you be more early?
- Were you still up?
- I've been waiting for you.
It gets dangerous at night.
Go to bed.
Okay.
- Sleep.
- Go to sleep.
- Yeah.
- Night.
- What's wrong?
- Don't you know?
What?
The whole school knows about you and Jungwoo.
- What's wrong with that?
- Do you think it's right?
You're married.
Just by law!
You know how things are!
What if Sangmin's parents and your's find out about this?
How can you be so selfish?
Why are you crying?
I like Jungwoo too!
There you are.
We're having a meeting at our place tonight.
I know.
You look great.
Your hubby must be treating you well.
- Hey!
- Yes?
- You live in apt.
106, right?
- Yes
There's an important meeting tonight, so tell your mom to come, okay?
- It's apt. 108.
- Okay.
- Hey!
- Yes?
You're such a cute little thing.
Thank you.
- Thanks for everything. Bye.
- Good night.
- Bye.
Take care.
- Thanks for tonight.
Where have you been?
Apartment meeting.
Look at him.
He looks like a sleazebag.
Yeah, he really does.
Looks mean as well.
What did you tell them?
How can you do this to me!
See you later.
Shit, why am I such a loser.
I envy you.
You have a husband and a boyfriend.
Next, next.
No. 2, Hulk, No. 3, Tiger Woods,
- No.
4 Zidane!
- Okay, Zidane!
Zidane, Zidane!
What is it?
Aw shit.
You should've knocked...
- Uh!
Jisoo...
- Jisoo...
You're here.
I have your assigned internship schools.
- Sangmin is Dongin High.
- What?
- Dongin High.
- Shit!
What is it?
What's wrong?
It's Boeun's high school.
Idiot!
Boeun...
Huh?
- You know...
- What!?
- What is it?
I'm late for school!
- Okay.
We'll talk at home, okay?
Bye!
Excuse me, but where is the faculty office?
Faculty office?
I don't know.
I loathe that place.
Wait for me!
Hey, who told you to dye your hair?
What a funky hairstyle!
Come here.
Excuse me!
Hey!
Your tea...
Thank you.
You should have told me.
You seemed too attractive to be a pervert.
Working out?
Sir, this is the new intern Park Sangmin.
Hello, sir.
Miss. Kim, you may be excused.
Yes, we'll be seeing a lot of each other.
- How have you been, sir?
- Good.
- Take good care of Boeun.
- Yes.
- No one knows except for me.
- Right.
Last night I was at a disco club...
Do you know who I met there?
- Who?
- Our room teacher.
What?
She must've gone there to pick up men.
Old maid syndrome!
Quiet!
We have a new intern here.
- Wow, he's so cute.
- He's really cute.
Doesn't he look familiar?
Yeah, he does look familiar.
He's cute, though...
I'm Park Sangmin who will be teaching Art.
- I hope we get along. - Yes!
Don't even think of playing tricks on Mr. Park, okay?
Yes, ma'am...
You all have a bright future, you know what I mean!
- Anything else?
- No, that's all.
Quiet!
Now, let's make a toast!
Cheers!
We'll spend the entire night toasting.
Mr. Park, bottoms up!
Mr. Park!
Now one from your supervisor.
- Here you go~ - Just a little bit.
- How is it, Mr. Park?
- Excuse me?
- The kids are hard to deal with, huh?
- No, I can handle them.
- Are you busy tonight?
- Yes, a bit...
Aw~ come on!
Aw~ come on!
It's a great coincidence that we're teaching the same class.
This calls for a celebration together!
No thank you!
It'll make your internship much easier.
One more round, okay?
Okay...
Mr. Park, let's go!
The second round.
When I first met you in Jeju Isle, I felt weird inside.
Miss Kim!
Wake up.
Please!
Don't take me easy because I'm a spinster!
I'll kill you if you do!
I don't believe this is happening!
Mr. Park...You know...
I went to a fortune teller earliar this year.
I'm supposed to marry a younger man.
What do you think about this?
What do you mean?
We talked about this before!
Don't take me easy!
I'll pound you with a brick if you do!
Miss Kim...
Miss Kim!
Miss... Miss Kim, Miss Kim...
Where are you going Mr. Park?
Nowhere... drive on, mister.
Why are you up?
What?
Why didn't you answer your phone?
Your teachers all drink like fishes!
I couldn't keep up.
- Why of all schools is it mine?
- I know...
If the school finds out, I'm going to die!
Be careful!
I'll be careful.
Don't worry.
There won't be any rumors.
Don't worry.
Go to sleep.
Wash up!
You stink of liquor.
Okay.
Sleep.
Why should I be the only one to be careful?
- Hey!
- What!
I'll be careful.
What?
Sorry, but can I pee next to you?
- No!
- I'll turn around.
Boeun, I can't hold myself!
Oh my god!
What are you doing?
Hey!
Park Sangmin, what are you doing!
Didn't I warn you not to drink too much!
I feel like shit.
Now, focus!
Mr. Park.
Huh?
Get a grip on your wife.
Mr. Park!
Ah, yes, Miss Kim!
Isn't this adorable?
Mr. Park, what are you doing after school?
Well, my grandfather's sick.
- You must be the first son.
- I'm the only son.
Your family must have a weak male line.
We're all sons except for me.
Isn't it funny?
I'm just joking.
Mr. Park...
- It's okay.
- A bright smile.
- The kids are watching.
- Let them watch.
What's with the old maid?
She's caught her prey.
The old maid's pathetic.
She made the physical education teacher transfer to another school.
- Hello, sir.
- Hi.
Was it good?
Were you watching?
You seemed to really enjoy the cozy lunch together.
It was great.
Better than the school store's stale bread.
Jealous?
You're such a loser!
- Hello, sir.
- Uh, yeah.
- Hello, Mr. Park.
- Uh, yeah, hi.
- Is there a Lee Jungwoo here?
- Yes, that will be me.
- Are you Lee Jungwoo?
- Yes.
- So you're Jungwoo...
- Yes, I am Lee Jungwoo.
- Jungwoo, was the sushi good?
- What?
You look good.
Keep it up!
Shit!
- Having fun?
- Yeah.
Hey, I was getting to the fun part!
They're all naked.
How could you say it's fun?
- Don't say that about my hobby!
- You call that a hobby?
- Give it to me!
- Forget it!
It's educational.
Give it back!
You should be ashamed of yourself!
I'm studying!
Then close the door!
- Stop watching!
- Shut up!
- Alright, so give it back.
- No.
- I'm sorry, so give it back.
- You're sorry?
It won't stop you from watching it again!
Gimme.
Okay.
Hey!
Do as you wish!
Hey!
Someone's at the door!
Jeez.
Boeun!
Boeun, Miss Kim's at the door!
Miss Kim?
What did you do to make her come all this way!
I don't know!
Hurry and clean this up.
Hurry!
Underwear, underwear!
Mr. Park~
- Mr. Park!
- Oh god!
- Oh, the door's open~ - Yes...
Oh, your place has everything.
- A woman could just fit in. - Miss Kim, what brings you here?
Mr. Park, I came to do your dirty laundry.
- Is that your bedroom?
- Miss Kim!
- What's that?
- An automatic vacuum cleaner.
Automatic...it does everything by itself...
- Someone's here, Mr. Park.
- No!
It's a ghost, a ghost!
Who was that?
Who was it?
- It's my sister, she's a bit crazy...
- Crazy?
It does seem like it...
Munch is a Norwegian painter.
A pioneer of expressionism, whose paintings were of angst and grief.
- Then there was...
- Mr. Park.
- Huh, what?
- Forget Munch...
Tell us about your first artwork in the deptartment Of romance.
- First artwork...
- Yes!
Let's continue the class!
- Your first love!
- Mr... tell us about your first love
Okay.
My first love was the only visitor during my three years of military service.
But that person doesn't know how much I like her.
Does she still do?
It must be Jisoo.
She may or may not know.
Now back to class.
How's the internship?
I'm so unlucky being stuck with a boys only high school!
How could you be lucky when you're not with the girls?
How about you, Sangmin?
Everything's great, thanks to you.
I felt that you two needed some time together.
The dude's having ball.
He goes to school where he can meet his pretty wife, and be surrounded by young high school girls.
How could he get bored there?
I'm bored out of my brains.
Seeing my bossy wife at school and at home...
Dude, you've got nothing but luck.
Take this.
What is it?
Military service...
It's tomorrow, so don't be late.
And bring coins to play coin games.
Your husband's off to serve his country!
Allegiance!
- No, it's "Victory!"
- Victory!
See you later.
Oh, and don't forget what I asked you to do.
Have fun.
Thank you.
Morning training's over!
Time has passed, but I still got the form, don't I?
Your beer belly is destroying the form.
- They're lining up.
- It's the lunch ration line!
Morons...
Thank you.
Hey, Sangmin, it's noodles...
- Fried tofu noodles?
- Yeah.
Can I have another bowl?
No, it's okay.
You're not eating, right?
Is that sushi?
- Victory!
- Victory!
- Thank you.
- You're welcome.
- I'm sorry.
I just brought only one.
- Don't worry.
It's okay.
Is it good, dude?
Don't talk to me. It's delicious.
At least you could offer some.
- Want a piece of kimchi?
- Kimchi, kimchi...
Another piece would be nice.
A big piece!
Let go!
Aren't you marine Park?
Victory...
Victory!
Victory!
- Invincible!
- Invincible!
- Marines!
- Marines!
Once a marine, always a marine.
What do they want?
Marines are all like that.
- Do something!
- Ah, delicious.
Stop!
Don't touch anything!
Invincible...
Marines...
Mister, what do you think you're doing!
- Get up!
- This won't take long.
A feisty one, aren't you?
Are you his wife or what?
- Yeah, I am his wife!
- Sorry, she's my little sister.
What's there to hide!
How dare you push my hubby around?
Apologize!
- I'm a marine.
- Now!
- I'm a marine.
- My grandpa's a marine, too!
What's your year rank!
What year!?
Hey, Boeun...
Now, I'm leaving for the sea.
Casting a net to catch fish~ I am the romantic cat~
Meow~
My hot lips wish to touch your soft lips.
So my feelings can reach your heart~
If you still don't know.
More than anyone, I will love you ~
- I will love you~ - Forever~
- I will love you~ - Like this moment,
More than anyone, I will love you ~
We can't meet~ The feeling's important~
That's what I think~ I don't want things to be too simple~
Even if it may be just this once~ The feeling's important~
That's what I think~ I don't want things to be too fast~ I still don't know what love is~ Wait a little longer~ If you really love me~ You can wait a little longer~
If you really love me~ You can wait a little longer, even if it may be just once~ The feeling's important ~
I can't meet you, I can't~
Stop it.
Stop.
- Tickle, tickle~ - Stop~
- Nice picture.
- Hullo, hullo!
- Who are you people?
- We're hoodlums.
You're her sugar daddy, aren't you?
- Cute.
- Really cute.
Do you want to die by my hands!
Hey, I'd love to be her sugar daddy.
Sangmin, Sangmin, shit!
You're all dead meat.
Let go!
Can't you file a paper, right?
How can this high schooler be your wife?
They all say they're married to the girl when they're caught.
It's true.
I'm no sugar daddy.
You can check my record then.
Mister, it's true.
We're married.
You're both fucking with me, aren't you?
What is the world coming to?
I'm so pissed.
How could you get beat up like that?
How will you live in the real world!
How come everyone you meet is a bully?
I really worry about you.
- Stop...
- Keep rolling...
How will you go to school with a face like that?
I'm worried about school...
Everything will be okay.
Yeah...
Hello.
Attention!
For this year's school festival, our class is assigned to decorations.
No!
Quiet!
Stage decorations will be done by No. 1 to 15.
The stands and stairways, No. 16 to 21.
The Entrance, No. 23 to 32.
- And No.
22!
- Yes?
No.
22 will do the hall wall.
Alone!
That's all!
But, Miss Kim!
That's unfair.
How will Boeun paint that huge wall by herself?
Right!
I told her to do it herself!
So what!?
With my luck with men, what was I thinking?
You are huge.
Have you thought about what you'll paint?
No.
What do you mean?
Even if I wanted to help you,
I can't, for fear of starting rumors at school.
I'm really worried.
I really worry about you, Boeun.
Do you know what I'm thinking?
Do you?
- Cut it out.
- Boeun!
Shhh!
Follow me.
Oh my...
I must be a lesbian.
I like my friend better than a boy.
If you're a lesbian, I'm a cheating wife.
Hey~ Your husband is so cute.
Stop talking about that loser.
He keeps staring at you during class.
He has a cool side to him.
Cool my ass!
Suh Boeun!
I know you're seeing Jungwoo with romantic feelings, but have you ever thought about Sangmin's feelings?
I really think you like Sangmin.
Am I right?
No...Sangmin's just like a big brother since we were little.
- Stop fooling around.
- You're always on my back.
- Hey, sew her mouth, shut.
- Uh?
Wow, look at all this food.
The table's barely holding up.
- Eat.
- Thank you for the meal.
Thank you for the meal, mom.
Easy.
Have you been skipping meals?
I've really been busy.
I missed your cooking, it's delicious.
You shouldn't say that, your wife's right here.
You'll hurt Boeun's feelings.
Mom, don't worry.
I'm undernourished.
When Boeun reaches twenty, you'll totally forget mom's cooking.
Boeun, I've put food in the fridge, so don't forget, okay?
There'll be more when you're done with it.
Yes...
Okay, it's late.
I'm leaving after dinner.
Yes.
Mom, it's raining.
Sleep over at your son's place.
Yes, mom.
Is it okay?
Sleep over, sleep over.
Eat, mom.
Oh, okay.
It's your son's place.
What's the big deal!
Oh, great.
So comfortable.
Turn around.
No, not this way, but the other.
Okay.
- Stay in that direction.
- Okay, pest.
- Are you asleep, Boeun?
- No...
You can't sleep?
- Sangmin, I thought about it...
- Yeah...
It's not fair to you.
Look at me, Sangmin.
What?
Did you know?
That you're really cute?
You're pretty yourself.
- Sangmin.
- Yeah, Boeun...
Boeun...
Sangmin, what are you doing?
- What do you think?
- Stop!
Wait, Boeun.
Uh, stop it!
Sleep.
Did we paint that much?
Let's hurry up with this.
There's not much time left till the festival.
- Hurry!
- Okay.
Hey, wait!
Gotcha, gotcha!
I see you've been working hard, but can you finish at this pace?
The festival's coming up.
Don't worry.
We'll be done by then.
Yeah, and it'll look great too.
Really?
We'll see about that...
I've seen enough...
Whatever...
The hag has appeared.
To find fault in our wall painting.
Miss Kim,
Miss Kim, with her nasty tone, she will...
I hate to admit it, but we've done a horrible job.
- It's okay.
- Really?
Let's wash our hands and grab some snacks.
Are you taking care of Sangmin's meals?
It's really hard to be an intern you know.
It couldn't be that hard!
Hey, but he's your husband.
Hey, I'm busy myself.
And he'll never skip a meal.
What kind of wife are you?
Then you be his wife.
Mrs. Park Sangmin.
Forget it.
I don't want it.
- Why the sudden interest!
- Shut up.
Hey, Park Sangmin!
Where are you?
Shouldn't you be helping me?
I couldn't believe it myself!
- Coke.
- Thanks.
- Good?
- Yeah.
- Eat up.
We'll be painting until dawn.
- What?
Hey, isn't she a babe?
She's the queen of Sunil Girls' Jr. High.
- Hey, let me see.
- Hey!
I'm going to make a move on her, so nice shots, please.
Okay.
Just don't get blown off.
From this day on, she's Suh Dongku's woman!
Excuse me, but, aren't you going to Sunil Girls' Jr. High?
Hey!
Over there.
Isn't that Dongku's sister?
Where?
It really is his sister.
Her husband looked older than that...
Then, who's that?
She must've fallen for a younger dude.
Nice.
The whole family's fooling around!
I got her number.
Did you get a good shot?
Here.
COME TO THE MONTHLY FAMlLY DlNNER BEFORE IT'S TOO LATE.
Jungwoo, I have to go home.
Already?
Hurry in and sit.
Can't you be more early?
Leave her alone.
It's okay.
Let's eat.
The chili squid was great...
Attention, please.
I'll now show you my girlfriend!
- Do you have a girlfriend?
- Yes, of course.
- Now take a good look.
- That's her?
She's better than your sister.
- Hey, look... look...
- Who's that?
Huh?
Hey, Boeun!
Hey!
Boeun!
When you were little, I always pushed you on this swing here.
You really loved it.
But one day, you fell off the swing while I was pushing.
I actually did it on purpose.
I'm sorry, Sangmin...
Everyone will be worried.
Let's go.
This marriage... it seems like your grandpa forced you into it, but in fact we wanted to have Sangmin as our son-in-law.
Do you remember?
How often you would cry?
But whenever Sangmin came, a smile would spread on your face.
You would fall all the time.
Scraping and breaking yourself.
Sangmin felt worse than I did.
He carried you on his back all the time, that Sangmin.
Anyway, I envy you.
The way he spends more time on your school festival than his graduation exhibition,
I guess he's gone to paint the wall with Yongju and Youngchul...
Sangmin!
Sangmin!
Sangmin!
I came with the family to see you, but an emergency at your squad forces me to turn away.
Are you doing well?
A few days ago, heavy snow came down in Seoul.
The Han River is frozen as well...
It's colder here, right?
Don't catch a cold.
And this is a secret but my mom says that I've become a woman now.
I'm a bit behind than the other girls, but being an idiot that you are, you won't understand what I mean, will you?
It's strange but when you were around, I hated your guts, but your absence has me missing you.
Are you feeling the same?
Then be good to me from now on.
Stupid.
The disappointment of not being able to meet you has your mom crying.
Anyway, this letter, I hope it reaches you.
Where have you been?
I've been looking all over for you.
The wall's great.
- I... have something to say.
- Yeah, what?
I'm sorry.
I've been so selfish.
To you and...
What's got into you?
I'm breaking up with you.
I'm sorry, Jungwoo.
People laugh and dance but I hate to laugh~
While we drink and search for love, we forget about the truth~
Why are you late?
Did you see him?
Who?
Your husband or boyfriend?
I'm not kidding!
There he is.
I like the smiling clown~ Yeah, yeah, yeah, yeah~
I like the clown who embraces sadness~
Aren't they great?
Now, intern, Park Sangmin will share a few words with us.
I thank everyone, the principal, all the teachers... and all the students for helping me finish this internship in one piece.
It may have been a short time, but personally, it has left me with precious memories I will carry for the rest of my life.
Mr. Intern, cut the boring crap and show us some honestly.
Mr. Park Sangmin is a married man.
Didn't you know?
Of course, it's not a sin to be married.
But in fact you're married to a 15 year old high school girl, right?
To Suh Boeun who's sitting right there...
Correct.
We are married.
But Boeun had no choice.
The only crime she's committed was granting her sick grandfather's last wish.
It was against her will to marry me.
She may be married, but she's still a 15 year old high school girl.
She goes crazy over a bowl of chili and spaghetti.
She loves cute stars and sushi- ...loving attractive baseball players.
Everyday, she's stressed over exams, and applying to university.
I hope you won't persecute Boeun's school life over a marriage document.
I beg you all.
Sangmin, I'm not a kid anymore.
Since I was little, you were always at my side.
I was never aware of the strange feelings...inside... but...
I think I'm in love with you...
Our poor Dongku.
She's the end of all your fun and play.
Fun and play...
I knew it since he was fixed on that school queen or whatever...
I can't believe grandpa fell for her grandmother.
- I can't believe it...
- She looks bright though.
Just consider it starting early!
Do it!
Do it!
Oh, shut up and peel the garlic.
I'm in no position to say this, but you can hide a lop-sided butt, but not lop-sized balls.
Anyway, congrats.
It's good that she doesn't have a clue.
Who would marry a lop-sized ball man if they knew, right?
Right.
Oh, you're here!
Oh, dad!
You're here.
I'm really getting into peeling these things...
Did you get married to peel garlic?
Mom!
Okay!
Say cheese.
One, two, three!!
HeIlo
Yes? What?
Sir, kindly switch off your mobile phone
Just one sec, please
Excuse me Sir, please sit down Captain, there's a medical emergency
A passenger has just faIlen down in the aisle
Delhi, Air India 101 returning due to medical emergency Excuse me, sir
Hold on!
I'm fine now, thanks.
Get the car! - Mr. Dhillon? Want the name tattooed?
To the hotel, sir?
Yes, yes, but via Vasant Vihar
Step on the gas, dude! Yeah, Farhan?
Get ready. I'll pick you up in five minutes
What happened?
Chatur called. Remember him?
The 'Silencer'?
Yeah
He said Rancho is coming
What? He said - Come to the campus at 8. On the tank
Oh shucks!
Hurry!
Ok
Honey, I'll be back soon. Oh, shoes
We found our buddy
What? TeIl me later - bye
You forgot your pants Now to the hotel, sir?
Yes, but via Imperial College of Engineering
Ok sir
Forgot my socks
More than just your socks
Your pants
Oh no
Now get my brother from the airport
Same Iast name - Dhillon
This is Dhillon. Where's my cab? On the runway?
Hey Rancho Hey Chatur, where's Rancho?
Rancho
Where's Rancho? Welcome, idiots
Some 'madeira' for you?
The same rum you guzzled those days
Have a drink
Where is Rancho?
Check out the mansion behind, idiots $ 3.5 million
First look at this
Don't eye my wife.
Swimming pooI - heated!
Living room - maple wood flooring
My new Lambhorghini 6496 cc - very fast
Why're you showing us all this?
Forgot?
What's this?
'5th September'. Today's date
I chaIlenge you
We'll meet again after ten years
Same day. Same place
We'll see who's more successful
Have the balls? C'mon, bet!
Remember? I'd challenged that idiot right here
I kept my promise. I'm back
Jackass!
I aborted a flight, he forgot his pants alI to meet Rancho 5 years we've searched. Don't know if he's alive and you think he'll show up for your silly bet
I know he won't show up
You gonna break his jaw or should I
So why'd you caIl us here?
To meet Rancho
Come and see where I've reached and where he rots
So you know where Rancho is?
Yes
Where?
He is in Shimla
Free as the wind was he
Like a soaring kite was he
Where did he go... let's find him
Free as the wind was he
Like a soaring kite was he
Where did he go... let's find him
We were led by the path we took
While he carved a path of his own
Stumbling, rising, carefree walked he We fretted about the morrow
He simply reveled in today Living each moment to the fullest Where did he come from...
He who touched our hearts and vanished...
Where did he go... let's find him In scorching Sun, he was like a patch of shade...
In an endless desert, like an oasis...
On a bruised heart, like soothing balm was he Afraid, we stayed confined in the well
Fearless, he frolicked in the river
Never hesitating to swim against the tide
He wandered lonesome as a cloud ...
Yet he was our dearest friend
Where did he go... let's find him
Rancho
Ranchhoddas Shamaldas Chanchad
He was as unique as his name
From birth we were taught - Life is a race
Run fast or you'll be trampled
Even to be born, one had to race 300 million sperms 1978.
I was born at 5.15 pm
At 5.16, my father announced
My son will be an engineer. - Farhan Qureshi. B.Tech.
And my fate was sealed
What I wanted to be... no one asked
Raju Rastogi... Ranchhoddas Chanchad
Room number?
D-26
C'mon
I'm Man Mohan. MM
These engineers call me MiIlimeter
For eggs, bread, milk, laundry finishing journals, copying assignments
I'm your guy. Fixed rates. No bargaining
Hey wait, hold this
Meet Kilobyte, Megabyte and their mother Gigabyte
Go ahead, click - this family doesn't bite
Check him out... another God-fearing soul
Hi. Farhan Qureshi - I'm Raju Rastogi
Don't worry a few days here and he'll lose faith in God
Then naked babes will be on the wall, and he'll say -
Oh God, give me one chance with her
Get out of here
Four bucks.
Two per bag
Here's five. Keep the change
Thanks boss.
For your tip, here's one in return -
Wear your best underwear tonight
Why?
Your Majesty, thou art great
Accept this humble offering
Ha... here's a He-Man
What a pretty piece.
Cute and compact
A campus tradition - On Day 1...
Freshmen must pay their respects to Seniors in their underwear.
This is when we first saw Rancho
Spiderman
Batman
Fresh meat
Greetings. Drop your pants, get stamped
Name?
'Ranchhoddas Shamaldas Chanchad'
What a mouthful! Needs serious cramming
Come on - pants off
Being stubborn?
Wet pants not good, kiddo.
Take them off
AaI izz well - What's that?
AaI izz Well
What did he say?
Someone tell him.
Hey James Bond
Make him understand
Take off your pants or they are going to piss on you
Hey 007! Ashamed to speak Hindi?
Sorry sir, I was born in Uganda, studied in Pondicherry so little slow in Hindi
So explain slowly. No hurry
Feeling cold?
Pray undress or he'll do 'urine-expulsion' on you
CaIls pissing 'urine-expulsion'!
A true linguist in the land of engineers!
Hey, come out of there
Come out or... or I'Il do 'urine-expulsion' on your door
If you aren't out by the count of ten
I'Il do 'urine-expulsion' on your door alI semester
One
Two
Three
Four
Five
Six
Seven
Eight
Nine
Ten
Salt water is a great conductor of electricity. 8th Grade Physics We had studied it.
Dr. Viru Sahastrabuddhe was the Director of ICE
Students called him Virus, computer Virus
Virus on the way, with eggs
Freshmen are summoned. Come quickly
Virus was the most competitive man we had ever seen
He couldn't bear anyone getting ahead of him
To save time, his shirts had Velcro and his ties had hooks
He'd trained his mind to write with both hands simultaneously
Everyday at 2 pm he took a 7 1/2 minute power nap with an opera as lullaby
Govind, his valet, had instructions to carry out all unproductive tasks such as shaving, nail-cutting etc
What is this?
- Sir, nest
Whose?
- A koel bird's nest, sir
Wrong
A koeI bird never makes her own nest
She lays her eggs in other nests
And when they hatch, what do they do?
They push the other eggs out of the nest
Competition over
Their life begins with murder. That's nature
Compete or die
You also are Iike the koeI birds
And these are the eggs you smashed to get into ICE
Don't forget, ICE gets 400,000 applications a year and only 200 are selected - You!
And these? Finished. Broken eggs
My son... he tried for three years
Rejected. Every time
Remember, life is a race
If you don't run fast, you'lI get trampled
Let me teIl you a very interesting story
This is an astronaut pen
Fountain pens and ballpoint pens don't work in outer space
So scientists spent millions to invent this pen
It can write at any angle, in any temperature, in zero gravity
One day, when I was a student the Director of our institute called me
He said, 'Viru Sahastrabuddhe.' I said, 'Yes sir'
'Come here!' I got scared He showed me this pen
He said, 'This is a symboI of excellence'
'I give it to you'
'When you come across an extraordinary student Iike yourself ...pass it onto him'
For 32 years, I've been waiting for that student But no luck Anyone here, who'll strive to win this pen?
Good. Put your hands down
Shall I post it on the notice board? Hands down
One question, sir
Sir, if pens didn't work in outer space why didn't the astronauts use a pencil?
They'd have saved millions
I wilI get back to you on this
He zaps a Senior's privates at night fingers the Director in the day.
You deflated Virus's erection Your Majesty, thou art great. Accept this humble offering
Buzz off.
You don't have school?
Who'lI pay for it? Your pop?
Keep off my dad! - Relax
For school you don't need tuition money, just a uniform
Pick a school, buy the uniform, slip into class
In that sea of kids, no one will notice
If I get caught?
- Then new uniform, new school
See that? - He was different...
He challenged conventions at every stage
A free-spirited bird had landed in Virus's nest
We were robots, blindly following our professors' commands
He was the only one who was not a machine
What is a machine?
Why're you smiling?
Sir, to study Engineering was a childhood dream
I'm so happy to be here finally
No need to be so happy.
Define a machine
A machine is anything that reduces human effort
WiIl you please elaborate?
Anything that simplifies work, or saves time, is a machine
It's a warm day, press a button, get a blast of air
The fan...
A machine!
Speak to a friend miles away.
The telephone... A machine!
Compute millions in seconds. The calculator... A machine!
We're surrounded by machines
From a pen's nib to a pants' zip - alI machines
Up and down in a second.
Up, down, up, down...
What is the definition?
I just gave it to you, sir
You'lI write this in the exam? This is a machine - up, down...
Idiot! Anybody else?
Yes?
Sir, machines are any combination of bodies so connected that their relative motions are constrained and by which means, force and motion may be transmitted and modified as a screw and its nut, or a lever arranged to turn about a fulcrum or a pulley about its pivot, etc especially, a construction, more or less complex consisting of a combination of moving parts, or simple mechanical elements, as wheels, levers, cams etc
Wonderful
Perfect. Please sit down
Thank you
But sir, I said the same thing, in simple language
If you prefer simple language, join an Arts and Commerce college
But sir, one must get the meaning too
What's the point of blindly cramming a bookish definition
You think you're smarter than the book?
Write the textbook definition, mister, if you want to pass
But there are other books...
Why?
In simple language - Out!
Idiot!
So, we were discussing the machine...
Why're you back?
I forgot something
What?
Instruments that record, analyze, summarize, organize debate and explain information; that are illustrated, non-illustrated hard-bound, paperback, jacketed, non jacketed with foreword, introduction, table-of-contents, index that are intended for the enlightenment, understanding enrichment, enhancement and education of the human brain through the sensory route of vision, sometimes touch
What do you mean?
Books, sir
I forgot my books.
Couldn't you ask simply?
I tried earlier, sir. It simply didn't work
Professors kept Rancho mostly out... seldom in
When thrown out of one class, he'd slip into another
He said - First year or fourth year, it's knowledge.
He was unlike any of us
We fought for a shower every morning
He'd bathe wherever he found water
Morning, sir
Machines were his passion
When he spotted them, he opened them
Some he could re-assemble... some he couldn't
There was another, just like him
Joy Lobo
Sir. Excuse me, sir
Mr. Joy Lobo!
Sir, if I could know the convocation dates...
Why?
Dad wants to make train reservations
I'm the first engineer from my viIlage. Everyone wants to attend
In that case, call your dad
Please hurry up. Don't waste my time
HeIlo
Dad, the Director wants to speak to you
Joy!
Mr. Lobo, your son won't graduate this year
What happened, sir?
He has violated all deadlines
Mr. Lobo, it's an unrealistic project
He is making some nonsense helicopter
I suggest you don't book your tickets. I'm so sorry
Sir, I am this close, sir - Is your project ready?
Is your project ready? - Sir, see it once, please
Submit it, and we'll consider Sir, a small extension... - Why, why should I?
After dad's stroke, I couldn't focus for two months Did you stop eating? No
Stopped bathing?
So why stop studying?
Sir, I'm very close. See it once, please...
Mr. Lobo!
Sunday afternoon, my son feIl off a train and died
Monday morning, I taught a class. So don't give me that nonsense
I can give you sympathy, not an extension
Sir... I'm very close...
Lifelong I lived
The life of another
For just one moment
Let me live as I...
Lifelong I lived
The life of another
For just one moment
Let me live as I...
Give me some sunshine Give me some rain
Give me another chance I wanna grow up once again
Give me some sunshine Give me some rain
Give me another chance I wanna grow up once again
Dude's come up with an amazing design
A wireless camera atop a helicopter
Can be used for traffic updates, security... Wow!
But Virus said it's an impractical design, it won't fly
It wiIl fly! We'll make it fly
Don't tell Joy. It'll be a surprise
We'll fly it up to his window and capture his reaction
If we work on his project, who'lI work on ours?
Tests, vivas, quizzes - 42 exams per semester
You scare easily, bro
Take your hand, put it over your heart, and say, 'Aal izz well'
AlI is well? - Aal izz weIl
Words of wisdom from His Holiness Guru Ranchhoddas
We had an old watchman in our village
On night patrol, he'd calI out, 'Aal izz well'
And we slept peacefully.
Then there was a theft and we learned that he couldn't see at night!
He'd just yeIl 'Aal izz well', and we felt secure
That day I understood this heart scares easily
You have to trick it
However big the problem, teIl your heart, 'All is well, pal'
That resolves the problem?
No.
But you gain courage to face it
Learn it up, bro.
We're gonna reaIly need it here
When life spins out of control Just let your lips roll
Let your lips roll And whistle away the toll
When life spins out of control Just let your lips roll
Just let your lips roll And whistle away the toll
Yell - All is Well...
The chicken's clueless about the egg's fate
Will it hatch or become an omelette
No one knows what the future holds
So let your lips roll And whistle away the toll
Whistle away the toll Yell - All is Well Hey bro - All is Well
Hey mate - All is Well
Hey bro - All is Well
Confusion and more confusion No sign of any solution
Ah... finally a solution But wait... what was the question?
If the timid heart with fear is about to die
Then con it bro, with this simple lie
Heart's an idiot, it will fall under that spell
Let your lips roll And whistle away the toll
Whistle away the toll Yell - All is Well
Hey bro - All is Well
Hey mate - All is Well
Hey bro - All is Well
Blew the scholarship on booze But that did not dispel my blues
Holy incense lit up my plight And yet God's nowhere in sight
The lamb is clueless for what it's destined
Will it be served on skewers or simply minced
No one knows what the future holds
So let your lips roll And whistle away the toll
Whistle away the toll Yell - All is Well
Hey bro - All is Well Hey mate - All is Well
Hey bro - All is Well
When life spins out of control Just let your lips roll
Just let your lips roll And whistle away the toll
All is Well
The chicken's clueless about the egg's fate
Will it hatch or become an omelette
No one knows what the future holds
So let your lips roll And whistle away the toll
Whistle away the toll
Eureka!
Eureka!
Yell - All is Well
Hey Mrs. Chicken - All is Well
Hey Mr. Lamb - All is Well
Hey bro - All is Well
Hey, take it up to Joy's window
Take it higher
Look at Silencer - the nude dude!
Joy, come out
Come to the window
Joy, Iook outside
Good news, sir
The police and Joy's father have no clue
Everyone thinks this is suicide
Intense pressure on windpipe resulting in choking
Cause of Death:
AlI think the pressure on the jugular killed him
What about the mental pressure for the last four years?
That's missing in the report
Engineers are a clever bunch
They haven't made a machine to measure mental pressure
If they had, alI would know... this isn't suicide... it's murder
How dare you blame me for Joy's suicide?
If one student can't handle pressure, is it our fault?
Life is full of pressures. WiIl you always blame others?
I don't blame you, sir. I blame the system
Look at these statistics - India ranks No.1 in suicides
Every 90 minutes, a student attempts suicide
Suicide is a bigger kiIler than disease
Something's terribly wrong, sir
I can't speak for the rest but this is one of the finest colleges in the country
I've run this place for 32 years
We were ranked 28th. Now we're No.1
What's the point, sir?
Here they don't discuss new ideas or inventions
They discuss grades, jobs, settling in the USA
They teach how to get good scores. They don't teach Engineering
Now you will teach me how to teach?
No sir, I...
Sir, my paper...
Vaidyanathan, please sit down
Here is a self-proclaimed professor who thinks he is better than our highly qualified teachers
Professor Ranchhoddas Chanchad wiIl teach us Engineering
We do not have all day
You have 30 seconds to define these terms
You may refer to your books
Raise your hand if you get the answer
Let's see who comes first, who comes last
Your time starts... now
Time up
Time up, sir
No one got the answer?
Now rewind your life by a minute
When I asked this question, were you excited?
Thrilled that you'd learn something new?
Anyone? ... Sir?
No. You all got into a frantic race
What's the use of such methods, even if you come first
WiIl your knowledge increase? No, just the pressure
This is a coIlege, not a pressure cooker
Even a circus lion learns to sit on a chair in fear of the whip
But you call such a lion 'well trained', not 'well educated'
HeIlo!
This is not a philosophy class. Just explain those two words
Sir, these words don't exist
These are my friends' names. Farhan and Raju
Quiet!
Nonsense! Is this how you'lI teach Engineering?
Sir, I wasn't teaching you Engineering
You're an expert at that
I was teaching you... how to teach
And I'm sure one day you'Il learn because unlike you, I never abandon my weak students
Bye, sir
Quiet!
Quiet, I said
I regret to inform you that your son...
Farhan...
Raju... has fallen into bad company
Without urgent corrective steps, his future will be ruined
Virus's letters dropped on our homes like atom bombs
Hiroshima and Nagasaki plunged into gloom
Our parents invited us - for a dressing down
Come in
See that?
We could afford just one air-conditioner
We put it in Farhan's room, so he could study in comfort
I didn't buy a car. I manage with a scooter
We put all our money into Farhan's education
We sacrificed our comforts for Farhan's future.
You took these pictures, Farhan?
He had that useless obsession for a while
Went around taking pictures of animals
Wanted to be a wildlife photographer
Son, what was your score that year?
91%
Hear that? Straight drop from 94% to 91%
You find it funny?
No sir, sorry. I'm just amazed at the photos
Why make him an engineer... Why not a wildlife photographer?
Enough!
I humbly request you - Don't ruin my son's future
Food's on the table, boys.
If you ever visit again, do eat with us
Dad denied us a meal...
So, to fill our bellies with food... and ears with more reprimands, we reached Raju's house
Raju's house was straight out of a 50's black and white film
A small, dingy room... a paralyzed father... a coughing mother... and an unwed sister
A sofa sprouting springs... a 24 hour water supply - from the leaking roof
Mother was a retired school teacher and a tireless complainer
Father was once a postmaster
Paralysis shut down his body partly... his salary completely.
Kammo's turned 28. They demand a car in dowry
If you don't study and earn, how will she marry?
Some okra?
Okra is now 12/- per kilo, cauliflower is 10/-
It's daylight robbery!
What will we eat if we get warnings from your college?
Mom!
Cottage cheese?
Cottage cheese should be sold at the jewelers, in velvet pouches
Cottage cheese? - No, no, it's ok
Mom, please
Alright, I'lI shut up
Earn for the family, slave like a maid and then take the vow of silence
If not with my son, with whom do I share my woes - his friends?
Hey Raju
We were in a huge dilemma
Do we comfort our friend or console his mom?
Screw it, we thought, let's focus on the cottage cheese
Even his eczema cream costs 55/- now
Another roti?
No, thank you. We're through
Okra for 12/- - Cauliflower for 10/-
At least you were offered a meal
Unlike your sadistic dad... 'Hitler' Qureshi!
And your mom is Mother Teresa...
Feeding us 'eczema roti'!
Don't poke fun at my mom!
- Enough, you guys
I'm famished. Let's eat out
It's month end. Who'll pay? His Mother Teresa?
To eat out, you don't need money. Just a uniform. Look...
C'mon - Come
Good evening, good evening
Oh, Uncle
Three large vodkas. - Half soda, half water
If we're caught, we're dead
What's for starters? - Get double portions
Leave this here and start some peppy music
Pia, what the hell!
Why're you wearing this ancient piece of junk?
What'Il people say - My fiancee... a doctor in the making, wearing a cheap, 200/- watch!
Please take it off. Thank you
Hi handsome
Hey Aunty. You're looking good
Don't miss my set, darling - Rubies?
From Mandalay - Mandalay... Wow!
Hey, Iet's go meet David - Of course
Excuse me
Yes?
Flowers
May I take the glass? - Why?
So you don't break it on my head
Why would I do that?
For the free advice I'Il now impart
What?
Don't marry that ass
Excuse me?
He's not a human, he's a price tag
He'll turn your life into a nightmare of brands and prices
He'll ruin your life.
Your future wilI be finished
Want a demonstration?
Shall I find out the price of his shoes?
I won't ask. He'll announce it himself
What the hell... Mint sauce on my $300 shoes!
Run for your life! It's free advice. Take it or leave it
Genuine Italian leather - hand-stitched!
Dad, are they your guests?
My students. What're they doing here?
Hold on, Dad
These beans smeIl great
No room for roti - Just pile it on
Hi - Hey
That was an eye-opener. Thank you so much
It was my moral responsibility
Can I ask you for little more help?
Dad won't let me break off this engagement
You explain so well. Can you give him a demo too?
Certainly. Raju, the mint sauce
You're really sweet
Where is your daddy? - Right behind you
AaI izz well
Run for your life! It's free advice. Take it or leave it
What're you doing here?
We'll hand these gifts to the couple
I'Il do that for you. It's my sister's wedding
Sister?
Sir, what's the sum total of your daughters?
Empty. No gift cheques
Forgot the cheques, Raju ...
Farhan?
We didn't invite you, you must be from the groom's side
No sir, we're here as the emissaries of science
How? Can you explain?
Dad, he explains superbly. I'm sure he'Il give us a demo
Won't you?
WeIl, Delhi has plenty of power cuts that... disrupt wedding celebrations
So I thought of making an inverter that... draws power from guests' cars
I see
Wow
So where's the inverter?
Sir, the design is ready
Where's the design, Farhan?
I gave you the design - I gave it to Raju
Raju, design?
Never mind the design. I'Il make the inverter and show you
You can only invent stories, not an inverter
I'Il make one, I promise
And I'll name it after you. After all, it was invented... at your daughter's wedding.
So it'll be an honor...
Farhan, Raju. I'll see you in my office tomorrow
We'll reimburse you ... in instaIlments
We'll never crash a wedding again - Not even my own
In fact, I won't even marry. Nor will he
Uh... right.
No marriage
Your parents shouldn't have married either
The world would have to feed two Iess idiots
Sit!
Pay attention
This is Ranchhoddas's father's monthly income
Couple of zeroes less, and it's stiIl a sizeable income
But erase another zero, and I would worry a little
Isn't that your fathers income, Farhan?
Yes, sir Now take away another zero... and that's your family income, Raju Rastogi
Big reason to worry
Take my advice and shift into Chatur Ramalingam's room Exams are here. Stay with Rancho and you're sure to fail
Want a shave? - No, sir
Then get lost!
Raju, don't worry. This is Virus's move to split us. Divide and rule
I have to worry
He grades us, and I need good grades for a good job
Unlike you, I don't have a rich dad I can Iive off
Shut up, Raju
Must we follow all his hogwash? 'Aal izz well'
I won't be his flunky... Iike you
You're crossing the line - No, I'm drawing one
I have a family to support
Dad's medicines swallow up mom's pension
My sis can't marry because they want a car in dowry
Mom hasn't bought a single saree in five years
Now don't get your mom's wardrobe into the debate
By the way, how many sarees per annum is reasonable?
Hey... no wisecracks about mom
We'll study with all our heart, but not just for grades
To quote a Wise One - Study to be accomplished, not affluent
FoIlow excellence.
All right, we're on problem 44.
And they said, which is the factored form of 3a squared minus 24ab plus 48b squared? And if this confuses you with a's and b's instead of an x there, I just like to think of in this case, this looks like an x squared.
So I like to think of it the same way I would think of it in terms of if this was an x squared minus some number times x plus some other number.
---
In the last video we took essentially the length of y equals x squared, not the length, but we went from zero to 1 on the x-axis and you can view it as this area.
And we rotated around the y-axis to get this figure here and we figured out the volume, I think our answer if I remember was pi over 2. And we use what I called and what everyone calls the Shell method.
I want to show you that you could actually use the disk method here.
But then we'll just have to switch the ys and xs.
Instead of writing this the function as a function of x, we'll just take the inverse of it and write it as a function of y. so this curve y equals x squared, what it can also be written as, we can just take the squared root of both sides as x is equal to the square root of y.
Just take the square root of both sides.
And now we can use this information to do the disk method, but everywhere where we had an x in the past we'll now have a y.
So let's think about how we would do it.
Once again it's this area-- really the hardest thing about all of these problems is just the visualization.
I think that's why they do it. Just to make sure that you know how to visualize things and maybe understand the calculus.
It's more visualization then calculus really.
So we're still dealing with-- if we take a cross section, if we were to cut this figure this area would be the cross section.
And we're still rotating around the y-axis just like we did in the last video.
We're still rotation around the y-axis, we get this figure.
So how would we deal with disks. Well a disk would look like this at some point-- let me pick another color.
At some point we'd have a disk like that.
That would be the top of the disk, and it would have some depth like we did before.
And its height, or the radius of that disk, would be equal to x.
It's equal to x.
I know you're thinking it looks like the shell method.
But what is x equal to?
It's equal to the square root of y.
It equals the square root of y.
And what would be the width of that disk?
Now we are making everything as a function of y, so the width would be just a very small distance d y, the differential y.
That's essentially all we need to know.
So the volume of that disk would be the radius squared times pi times d y.
Hopefully that makes a little bit sense, but there's another hitch on this problem.
This is actually similar to what we did two videos ago.
Because when you view it in the y-axis, from this y frame of reference, what we're going to do is we're going to take the volume, we take the volume of x is equal to 1.
So what would be the volume of x is equal to 1 rotated around the x-axis?
It would just be the entire cylinder.
It's really important that you visualize this right, what we're doing.
We're going to figure out this volume, volume of x is equal to 1.
Let me draw the axis just so you know what we're doing.
So this would be the y-axis, that would be the x-axis as best as I can draw.
Originally, we can figure out the volume of the entire cylinder.
This is x is equal to 1, x is equal to 1 from what y points?
From the point, well what is this?
This is y equals 1. y equal 1 to zero.
So we would figure out this volume from y equals 1 to zero.
And how would we do that?
What would be the integral?
Remember everything is in y now, so it might seem a little confusing.
For each of these disks, this is going to be made up of a bunch of disks, let me draw one of them.
Let me draw the top one.
The top disk, and it has a width, it's not going to be this entire cylinder, its width is d y, its width is just going to be this. d y, a very small sliver. d y, and its radius is x or you could say f of y.
What would be the volume of that disk?
What would be the surface area of the top?
It would be f of y squared.
Remember we're dealing everything with y. f of y squared times pi, that gives the area of the top.
Put the pi outside of the integral times d y. d y, and we said y is going from zero to 1. y is going from zero to 1.
So that's that entire cylinder.
And what we'll want to do is subtract out, essentially cut out the volume of the inner bowl.
So minus.
How would we figure out the inner bowl?
That's where we will deal with the x is equal to the square root of y function.
Because here, what's each disk?
Once again it's f of y.
I wrote this generally, this is f of y of the outside.
I'm going to now do it for the inside.
I'm going to cut out the inside volume and because I kept it general I could do it.
We're still going from zero to 1, from y equals zero to y equals 1.
Remember we're doing with y now.
I will take f of the inside f of y squared d of y.
You can imagine in this case the inside function, we're going to take the volume.
That original disk I drew is actually one of the disks for the inside function.
Where the height of that disk is d y, that should be d y.
The radius of the disk is f of y.
And of course the area of the top of the desk is pi times the radius squared.
How do we apply it to this particular situation?
What is the outside function? f of y, x is equal to f of y.
We are just switching the variables.
We say that x is equal to 1.
This is just a big cylinder, right?
So f of i is equal go to 1 in this function, so we get pi-- let me switch colors-- times from zero to 1.
1 squared d y minus pi, and we're still going from zero to 1.
Remember, that's the y boundaries.
What's f of y?
Here f of y is square root of y squared d y.
Let's take the pi out.
So pi times, well 1 squared is 1.
What's the anti-derivative of 1?
What function's derivative is 1? It's x, right? x, that's the anti-derivative there.
We can merge these.
We took the pi out.
This square root of y squared, this is just y.
Sorry, we have that derivative 1.
See, even I get quite confused here.
We're taking this with respect to y, right?
The anti-derivative of 1 now is y.
We are setting up a bunch of ys.
I'm sorry.
I find this even a little perplexing when I start switching x and y.
The second function.
Remember, we can merge these because it's the same boundaries and they're both in respect to y.
Square root of y squared is y.
What's the anti-derivative of y, the function y or y d y. Was y squared over 2, minus y squared over 2.
We are going to evaluate that at 1 and zero.
So what does that get us?
We get pi-- we get 1 minus 1/2 minus zero minus zero minus zero plus 0/2.
Whatever these are zero.
1 minus 1/2 that's 1/2 and times pi is equal to pie over 2.
Which is the exact same result.
And I was worried, because you never know when you might make a careless mistake as I often do.
We got the exact same result as I got in the previous video when we used the shell method.
The hardest thing here is just remembering that you're doing everything in terms of y.
When we did the disk method traditionally, the disks were vertical disks.
Now they're horizontal disks but it's the exact same thing.
You just have to get your brain around the idea that we're dealing with the ys, that the boundaries on the integrals are now y values. We're taking the width of the disks, or the height of the disks are d y and the radius is now the function of y.
Hopefully I didn't confuse you too much.
My own brain malfunctioned a bit when I took the anti-derivative of 1 d y, it should have been y.
I will see you in the next video where we will do even more complicated problems, where I'm sure I'll make even more mistakes. See you soon.
First, I am from a coalition of Pengerang NGOs in Johor a fortress for Azalina Othman
I come here with a lot of expectations from the people of Pengerang, for Pakatan Rakyat to win this time around
We in Pengerang are located at the end of the peninsula but be praised to Allah in our continued struggles to bring forward the people's issues only PAS and the other component parties of Pakatan Rakyat that have accepted us and helped us in recognising and tackling issues of the people
In our experience as an NGO we have leaders firstly we have not gone to political parties because we know we have community leaders
But in our campaign to fight for our issues the State executive counsellor, the MP who have been chosen
by us all, and even the PM who we have helped bring to power have not cared for us.
Our experience in Parliament where we had hoped Najib could see us as hardcore BN's hard core voters was completely ignored
That is the value and reward that we have received as hardcore voters of Barisan Nasional, ladies and gentlemen.
This project is perhaps the biggest project during Najib's administration
An oil and gas project that involves RM60 billion and according to Suhakam, the largest displacement of a majority Malay population in Malaysia
And the 2nd largest after Bakun involving 22,500 acres and close to 28,000 mainly Malay inhabitants will be displaced if this project is continued and now it is in the second phase of the hearing on land acquisition
In our campaign, we have faced many trials and tribulations.
Even though this NGO is the platform for the people to demand their rights the party that is with us, will be with us
And we in the coalition of NGOs, we see Pakatan Rakyat or PAS in particular have opened up space for us and have not discriminated on who we are and where we come from but in the principle of openness that have captured our hearts as villagers
And is in coalition, we have veterans who are hardcore MlC and Umno members
And when the character of the party and Pakatan components itself is shown without or asking, is what has attracted us to the party, who have in the past been influenced (by BN) as bogey-man regardless of the image they have displayed.
So today, if we here are still unsure about the struggle that is being led by Pakatan
I feel it would be a waste if we as Malay-Muslims because one of the many issues
Only Parti Islam Se Malaysia (PAS) and the other component parties of the Pakatan Rakyat have received and accepted us and are helping us to address the issues of the people of Pengerang
Our experience in the coalition of NGOs is that we have not approached political parties because we know we have community leaders
But in our battle to bring up the issues of Pengerang, our State executive counsellor whom we have ourselves chosen and even the PM who we had helped put into office have not at all considered us (our plight). was completely ignored.
That was the value and reward that we received as hardcore BN supporters, ladies and gentlemen.
And for your information, the Pengerang project is the largest in Najib's administration.
It's a mega-project for the development of oil and gas that involves RM60 billion according to Petronas' budget.
And according to Suhakam it involves the largest displacement of Malays in Malaysia.
And the second largest (displacement of people) after Bakun involving 22, 500 acres with a largely Malay population.
28,000 people will be moved if this project goes ahead.
Now phase II is in the process of a hearing on land acquisition.
And is the series of our campaign, we have come across many trials and tribulations
And us in the coalition of NGOs we see Pakatan Rakyat and PAS especially, has opened a space for us without discriminating who we are or from where we are from but with an openness and leadership that have captured our hearts as villagers.
And in this coalition, we also lead the veterans of MlC and hardcare UMNO over there
And when the character of Pakatan Rakyat is demonstrated without our request (to help us) but that is the personality and leadership that is present in the Pakatan Rakyat and this is the reason why they have captured and opened up our hearts whereas they (PR) and been portrayed as the bogey-man (by BN) in the past of Pengerang are issues of religion and Malay issues; the majority of lands acquired are Malay lands.
Of the 10 villages that are involved, the majority are Malay villages.
And now the issue that is hot is the relocation of burial grounds
We have never questioned the position of the Mufti, but that is what has happened in the process that has deeply insulted us as Muslims and this was acknowledged by the Mufti when we had met him and the main person that has brought up and brought forward this issue is a Chinese, the treasurer of our coalition.
He was the one who first brought up this issue to awaken us as Malays and Muslims there.
And he is the one who had given us courage as Muslims and Malays to further the cause of the people (of Pengerang).
And we have no differences.
And this is what we have gotten and seen ourselves in the character and leadership of Pakatan Rakyat.
And we from Pengerang are sincere in this.
Over there, we have never been asked by Pakatan Rakyat to vote for them.
But the character they have portrayed will, with Allah's blessing, MlC there will open a PAS supporters club
And that is why this NGO is so required and the party need this NGO and we need the party because we are fighting for the same issues.
So, when we tell the story of hope we are hoping for the support of all of you here to help and spread the information because we are so much challenged by media and how to spread information
When we see in the Chinese papers that they are consistent in our struggle but the Malay media is briddled and I would not be surprised that many do not know the issues of Pengerang.
So I think this is the best platform for me to pass on the message as representative of the the Pengerang community to bring up and to inform the people of the misfortune that has befallen the people of Pengerang and let us together wipe out Barisan Nasional, Allah willing.
A cliff diver dives off of a cliff 85 feet above the water.
If the diver's initial vertical velocity is negative 5 feet per second-- so he's going downward, so they tell us right here-- 5 feet per second downward, and the acceleration of gravity is negative 32 feet per second squared, or 32 feet per second downward-- so that means after every second, you're going 32 feet per second faster in the downward direction-- how long is the diver in the air before entering the water?
So let's just set a variable t to be what we want to solve for, which is how long is the diver in the air?
Let me just write time in the air.
And we have the initial velocity of the diver right here, the initial vertical velocity, and that's what we care about.
We just care about what's going on in the up and down direction, the vertical direction.
So our initial velocity is negative 5 feet per second.
Now, what's going to be his velocity right when he hits the water, right when he enters the water?
What's going to be his final velocity?
He's going to start at negative 5 feet per second, so it's going to be negative 5 feet per second, that's his initial velocity.
And every second that goes by, he's going to be going negative 32 feet per second faster after every second.
He's accelerating downward at that rate.
So if you multiply the acceleration times time, that's how much his velocity is increased.
So it's going to be his initial velocity minus 32 feet per second squared.
That's the acceleration times time-- times the time that he's in the air, times this t.
Obviously, this will be in seconds, so we have 1 second over seconds squared.
You'll just have a second in the denominator, so you'll have feet per second and feet per second.
The units all work out.
But hopefully this makes sense.
He's starting off at moving downward at 5 feet per second.
The negative is telling you the direction is downward, so he's moving downward at 5 feet per second.
So after 1 second, he'll be going 37 feet per second downward.
After 2 seconds, he'll be going-- what, 32 times 2 is 64, plus 9-- 69 feet per second downwards.
So this is his final velocity.
So what's his average velocity?
If his initial velocity is negative 5 feet per second, his final velocity is this.
It's a linear relation.
At every second that goes by, it's linearly increasing, or decreasing, if you want to view it as a negative number.
So the average velocity is just going to be the average of these two values.
We're really just learning a lot of physics here, but this will set us up with a nice quadratic equation that we can use the quadratic formula for.
So our average velocity is going to be the average of those two velocities.
So it's going to be-- and I'll skip the units right now-- it's going to be negative 5 minus 5, minus 32t, all of that over 2.
I'm just averaging these two things.
That's my initial velocity.
This is my final velocity.
I'm just taking the average of the two.
So this is going to be equal to what?
This is negative 10 minus 32t over 2, which is equal to negative 5 minus 16t.
I'm just dividing everything by 2.
So this is my average velocity.
Now, we can just apply our simple distance is equal to rate times time.
Now, what's the distance that he's traveling in this situation?
Well, he's diving off of a cliff 85 feet above the water, so the distance that he's going to be traveling is 85 feet.
He starts 85 feet above the water, but the distance he'll travel, he's going to go 85 feet down.
So the distance he's going to travel is negative 85 feet.
We use negative for down, we use positive for up.
Everything in this problem is happening in the down direction.
So negative 85 feet is going to be equal to the average velocity.
But we just figured out the average velocity.
It's this thing right here.
That's our average velocity.
So it's going to be-- let me do it in another color; let me do it in this blue-- our average velocity is negative 5 minus 16t.
That's our average velocity, velocity average.
And then we want to multiply that times time.
This is our velocity, our rate-- I'm mixing up the colors-- this is our rate, and then we want to multiply it by times, so rate times time is equal to distance travelled.
Let's solve for t.
And we'll skip the units for now, just because that'll kind of get in the way of maybe the learning.
So we have negative 85 is equal to-- when we distribute this t, we get negative 5t minus 16t squared.
And now we can add 85 to both sides of this equation.
Let's add 85 to both sides.
And we are left with 0 is equal to--
let's rearrange this.
So we'll a negative 16t squared minus 5t, plus 85.
So this, essentially, is the equation.
If we solve for t, we'll know how long he's been in the air, because we've used all of the other constraints.
So this is a straight up quadratic equation, so we could use the quadratic formula here.
So it's going to be negative b.
Now what's b? b here is negative 5, so negative b, which is negative negative 5, plus or minus the square root of b squared. Negative 5 squared is 25 minus 4, times a, which is negative 16, times c, which is 85.
All of that over 2 times a. a is negative 16, so 2 times that is negative 32.
So the time is equal to positive 5, right, negative negative 5 is positive 5, plus or minus the square root of-- we probably want to take out our calculator for this.
Let's see, let's evaluate this.
So we have a negative and a negative, so those two are going to cancel-- let put my calculator aside right for a second.
So we have negative out here, and then we have a negative, so these two are going to cancel out.
So it's going to be 25 plus 4, times 16, times 85.
So let's figure out what that is.
So if we have 25 plus-- I'll put some parentheses here-- 4 times 16, times 85 is equal to-- so we got 25 plus 4, times 16, times 85-- is equal to 5,465.
And we could take the square root of this.
So let's just take the square root of it, and we have 73.9.
So let's just stick with 73.9.
So this is going to be equal to-- let me delete this right here-- this is going to be equal to, we already figured out what the square root is, we just evaluated it-- let me delete that right there-- this is going to be equal to plus or minus 73.9, all of that over negative 32.
Now, we can add 73.9, and we can subtract 73.9, but what happens if we subtract 73.9?
Well, actually, let's think about this carefully.
Let's do both of these.
Let's just go through them.
So the two combinations, so the two possibilities for t, is we have 5 plus 73.9, which is 78.9, all of that over negative 32.
That's one possibility for t.
The other one is 5 minus 73.9.
And let's see, what's 73.9 minus 5?
It is negative 68.9.
73 minus 5 is 68, swap the negatives, so it's negative 68.9 over negative 32.
In this case, the negatives cancel out.
So which of these-- can we use both of these times?
Well, this right here is going to be a negative number, and we don't want a negative time.
It's definitely a positive amount of time that he's in the air.
[UNlNTELLlGIBLE]
negative time, are we going back in time?
Who knows?
So we can't even use that.
So the time in the air is going to be this, it's going to be 68.9 divided by 32, so let's figure out what that is.
So it's 68.9 divided by 32 is equal to 2.15 seconds.
So his time in the air is going to be 2.15 seconds.
And we're done.
I'm going to talk today about energy and climate.
And that might seem a bit surprising because my full-time work at the Foundation is mostly about vaccines and seeds, about the things that we need to invent and deliver to help the poorest two billion live better lives.
But energy and climate are extremely important to these people -- in fact, more important than to anyone else on the planet.
The climate getting worse means that many years, their crops won't grow:
There will be too much rain, not enough rain, things will change in ways that their fragile environment simply can't support.
And that leads to starvation, it leads to uncertainty, it leads to unrest.
So, the climate changes will be terrible for them.
Also, the price of energy is very important to them.
In fact, if you could pick just one thing to lower the price of, to reduce poverty, by far you would pick energy.
Now, the price of energy has come down over time.
Really advanced civilization is based on advances in energy.
The coal revolution fueled the Industrial Revolution, and, even in the 1900s we've seen a very rapid decline in the price of electricity, and that's why we have refrigerators, air-conditioning, we can make modern materials and do so many things.
And so, we're in a wonderful situation with electricity in the rich world.
But, as we make it cheaper -- and let's go for making it twice as cheap -- we need to meet a new constraint, and that constraint has to do with CO2.
CO2 is warming the planet, and the equation on CO2 is actually a very straightforward one.
If you sum up the CO2 that gets emitted, that leads to a temperature increase, and that temperature increase leads to some very negative effects: the effects on the weather; perhaps worse, the indirect effects, in that the natural ecosystems can't adjust to these rapid changes, and so you get ecosystem collapses.
Now, the exact amount of how you map from a certain increase of CO2 to what temperature will be and where the positive feedbacks are, there's some uncertainty there, but not very much.
And there's certainly uncertainty about how bad those effects will be, but they will be extremely bad.
I asked the top scientists on this several times: Do we really have to get down to near zero?
Can't we just cut it in half or a quarter?
And the answer is that until we get near to zero, the temperature will continue to rise.
And so that's a big challenge.
It's very different than saying "We're a twelve-foot-high truck trying to get under a ten-foot bridge, and we can just sort of squeeze under."
This is something that has to get to zero.
Now, we put out a lot of carbon dioxide every year, over 26 billion tons.
For each American, it's about 20 tons; for people in poor countries, it's less than one ton.
It's an average of about five tons for everyone on the planet.
And, somehow, we have to make changes that will bring that down to zero.
It's been constantly going up.
It's only various economic changes that have even flattened it at all, so we have to go from rapidly rising to falling, and falling all the way to zero.
This equation has four factors, a little bit of multiplication:
So, you've got a thing on the left, CO2, that you want to get to zero, and that's going to be based on the number of people, the services each person's using on average, the energy on average for each service, and the CO2 being put out per unit of energy.
So, let's look at each one of these and see how we can get this down to zero.
Probably, one of these numbers is going to have to get pretty near to zero.
Now that's back from high school algebra, but let's take a look.
First, we've got population.
The world today has 6.8 billion people.
That's headed up to about nine billion.
Now, if we do a really great job on new vaccines, health care, reproductive health services, we could lower that by, perhaps, 10 or 15 percent, but there we see an increase of about 1.3.
The second factor is the services we use.
This encompasses everything: the food we eat, clothing, TV, heating.
These are very good things: getting rid of poverty means providing these services to almost everyone on the planet.
And it's a great thing for this number to go up.
In the rich world, perhaps the top one billion, we probably could cut back and use less, but every year, this number, on average, is going to go up, and so, over all, that will more than double the services delivered per person.
Here we have a very basic service:
Do you have lighting in your house to be able to read your homework? And, in fact, these kids don't, so they're going out and reading their school work under the street lamps.
Now, efficiency, E, the energy for each service, here finally we have some good news.
We have something that's not going up.
Through various inventions and new ways of doing lighting, through different types of cars, different ways of building buildings -- there are a lot of services where you can bring the energy for that service down quite substantially.
There are other services like how we make fertilizer, or how we do air transport, where the rooms for improvement are far, far less.
And so, overall here, if we're optimistic, we may get a reduction of a factor of three to even, perhaps, a factor of six.
But for these first three factors now, we've gone from 26 billion to, at best, maybe 13 billion tons, and that just won't cut it.
So let's look at this fourth factor -- this is going to be a key one -- and this is the amount of CO2 put out per each unit of energy. And so the question is: Can you actually get that to zero?
If you burn coal, no.
If you burn natural gas, no.
Almost every way we make electricity today, except for the emerging renewables and nuclear, puts out CO2.
And so, what we're going to have to do at a global scale, is create a new system.
And so, we need energy miracles.
Now, when I use the term "miracle," I don't mean something that's impossible. The microprocessor is a miracle.
The personal computer is a miracle.
The Internet and its services are a miracle.
So, the people here have participated in the creation of many miracles.
Usually, we don't have a deadline, where you have to get the miracle by a certain date.
Usually, you just kind of stand by, and some come along, some don't.
This is a case where we actually have to drive at full speed and get a miracle in a pretty tight timeline.
Now, I thought, "How could I really capture this?
Is there some kind of natural illustration, some demonstration that would grab people's imagination here?"
I thought back to a year ago when I brought mosquitos, and somehow people enjoyed that.
(Laughter)
It really got them involved in the idea of, you know, there are people who live with mosquitos.
So, with energy, all I could come up with is this.
I decided that releasing fireflies would be my contribution to the environment here this year.
So here we have some natural fireflies.
I'm told they don't bite; in fact, they might not even leave that jar.
(Laughter)
Now, there's all sorts of gimmicky solutions like that one, but they don't really add up to much.
We need solutions -- either one or several -- that have unbelievable scale and unbelievable reliability, and, although there's many directions people are seeking,
I really only see five that can achieve the big numbers.
I've left out tide, geothermal, fusion, biofuels.
Those may make some contribution, and if they can do better than I expect, so much the better, but my key point here is that we're going to have to work on each of these five, and we can't give up any of them because they look daunting, because they all have significant challenges.
Let's look first at the burning fossil fuels, either burning coal or burning natural gas.
What you need to do there, seems like it might be simple, but it's not, and that's to take all the CO2, after you've burned it, going out the flue, pressurize it, create a liquid, put it somewhere, and hope it stays there.
Now we have some pilot things that do this at the 60 to 80 percent level, but getting up to that full percentage, that will be very tricky, and agreeing on where these CO2 quantities should be put will be hard, but the toughest one here is this long-term issue.
Who's going to be sure?
Who's going to guarantee something that is literally billions of times larger than any type of waste you think of in terms of nuclear or other things?
This is a lot of volume.
So that's a tough one.
Next would be nuclear.
It also has three big problems:
Cost, particularly in highly regulated countries, is high; the issue of the safety, really feeling good about nothing could go wrong, that, even though you have these human operators, that the fuel doesn't get used for weapons.
And then what do you do with the waste?
And, although it's not very large, there are a lot of concerns about that.
People need to feel good about it.
So three very tough problems that might be solvable, and so, should be worked on.
The last three of the five, I've grouped together.
These are what people often refer to as the renewable sources.
And they actually -- although it's great they don't require fuel -- they have some disadvantages.
One is that the density of energy gathered in these technologies is dramatically less than a power plant.
This is energy farming, so you're talking about many square miles, thousands of time more area than you think of as a normal energy plant.
Also, these are intermittent sources.
The sun doesn't shine all day, it doesn't shine every day, and, likewise, the wind doesn't blow all the time.
And so, if you depend on these sources, you have to have some way of getting the energy during those time periods that it's not available.
So, we've got big cost challenges here, we have transmission challenges: for example, say this energy source is outside your country; you not only need the technology, but you have to deal with the risk of the energy coming from elsewhere.
And, finally, this storage problem.
And, to dimensionalize this, I went through and looked at all the types of batteries that get made -- for cars, for computers, for phones, for flashlights, for everything -- and compared that to the amount of electrical energy the world uses, and what I found is that all the batteries we make now could store less than 10 minutes of all the energy.
And so, in fact, we need a big breakthrough here, something that's going to be a factor of 100 better than the approaches we have now.
It's not impossible, but it's not a very easy thing.
Now, this shows up when you try to get the intermittent source to be above, say, 20 to 30 percent of what you're using.
If you're counting on it for 100 percent, you need an incredible miracle battery.
Now, how we're going to go forward on this -- what's the right approach?
Is it a Manhattan Project?
What's the thing that can get us there?
Well, we need lots of companies working on this, hundreds.
In each of these five paths, we need at least a hundred people.
And a lot of them, you'll look at and say, "They're crazy." That's good.
And, I think, here in the TED group, we have many people who are already pursuing this.
Bill Gross has several companies, including one called eSolar that has some great solar thermal technologies.
Vinod Khosla's investing in dozens of companies that are doing great things and have interesting possibilities, and I'm trying to help back that.
Nathan Myhrvold and I actually are backing a company that, perhaps surprisingly, is actually taking the nuclear approach.
There are some innovations in nuclear: modular, liquid. And innovation really stopped in this industry quite some ago, so the idea that there's some good ideas laying around is not all that surprising.
The idea of TerraPower is that, instead of burning a part of uranium -- the one percent, which is the U235 -- we decided, "Let's burn the 99 percent, the U238."
It is kind of a crazy idea.
In fact, people had talked about it for a long time, but they could never simulate properly whether it would work or not, and so it's through the advent of modern supercomputers that now you can simulate and see that, yes, with the right material's approach, this looks like it would work.
And, because you're burning that 99 percent, you have greatly improved cost profile.
You actually burn up the waste, and you can actually use as fuel all the leftover waste from today's reactors.
So, instead of worrying about them, you just take that.
It's a great thing.
It breathes this uranium as it goes along, so it's kind of like a candle.
You can see it's a log there, often referred to as a traveling wave reactor.
In terms of fuel, this really solves the problem.
I've got a picture here of a place in Kentucky.
This is the leftover, the 99 percent, where they've taken out the part they burn now, so it's called depleted uranium.
That would power the U.S. for hundreds of years.
And, simply by filtering seawater in an inexpensive process, you'd have enough fuel for the entire lifetime of the rest of the planet.
So, you know, it's got lots of challenges ahead, but it is an example of the many hundreds and hundreds of ideas that we need to move forward.
So let's think: How should we measure ourselves?
What should our report card look like?
Well, let's go out to where we really need to get, and then look at the intermediate.
For 2050, you've heard many people talk about this 80 percent reduction.
That really is very important, that we get there. And that 20 percent will be used up by things going on in poor countries, still some agriculture, hopefully we will have cleaned up forestry, cement.
So, to get to that 80 percent, the developed countries, including countries like China, will have had to switch their electricity generation altogether.
So, the other grade is: Are we deploying this zero-emission technology, have we deployed it in all the developed countries and we're in the process of getting it elsewhere?
That's super important.
That's a key element of making that report card.
So, backing up from there, what should the 2020 report card look like?
Well, again, it should have the two elements.
We should go through these efficiency measures to start getting reductions:
The less we emit, the less that sum will be of CO2, and, therefore, the less the temperature.
But in some ways, the grade we get there, doing things that don't get us all the way to the big reductions, is only equally, or maybe even slightly less, important than the other, which is the piece of innovation on these breakthroughs.
These breakthroughs, we need to move those at full speed, and we can measure that in terms of companies, pilot projects, regulatory things that have been changed.
There's a lot of great books that have been written about this.
The Al Gore book, "Our Choice" and the David McKay book, "Sustainable Energy Without the Hot Air."
They really go through it and create a framework that this can be discussed broadly, because we need broad backing for this.
There's a lot that has to come together.
So this is a wish.
It's a very concrete wish that we invent this technology.
If you gave me only one wish for the next 50 years -- I could pick who's president, I could pick a vaccine, which is something I love, or I could pick that this thing that's half the cost with no CO2 gets invented -- this is the wish I would pick.
This is the one with the greatest impact.
If we don't get this wish, the division between the people who think short term and long term will be terrible, between the U.S. and China, between poor countries and rich, and most of all the lives of those two billion will be far worse.
So, what do we have to do?
What am I appealing to you to step forward and drive?
We need to go for more research funding.
When countries get together in places like Copenhagen, they shouldn't just discuss the CO2.
They should discuss this innovation agenda, and you'd be stunned at the ridiculously low levels of spending on these innovative approaches.
We do need the market incentives -- CO2 tax, cap and trade -- something that gets that price signal out there.
We need to get the message out.
We need to have this dialogue be a more rational, more understandable dialogue, including the steps that the government takes.
This is an important wish, but it is one I think we can achieve.
Thank you.
(Applause)
Thank you.
Chris Anderson:
Thank you.
Thank you.
(Applause)
Thank you.
So to understand more about TerraPower, right --
I mean, first of all, can you give a sense of what scale of investment this is?
Bil Gates:
To actually do the software, buy the supercomputer, hire all the great scientists, which we've done, that's only tens of millions, and even once we test our materials out in a Russian reactor to make sure that our materials work properly, then you'll only be up in the hundreds of millions.
The tough thing is building the pilot reactor; finding the several billion, finding the regulator, the location that will actually build the first one of these.
Once you get the first one built, if it works as advertised, then it's just clear as day, because the economics, the energy density, are so different than nuclear as we know it.
And so, to understand it right, this involves building deep into the ground almost like a vertical kind of column of nuclear fuel, of this sort of spent uranium, and then the process starts at the top and kind of works down?
BG:
That's right.
Today, you're always refueling the reactor, so you have lots of people and lots of controls that can go wrong: that thing where you're opening it up and moving things in and out, that's not good.
So, if you have very cheap fuel that you can put 60 years in -- just think of it as a log -- put it down and not have those same complexities.
And it just sits there and burns for the 60 years, and then it's done.
CA:
It's a nuclear power plant that is its own waste disposal solution.
Well, what happens with the waste, you can let it sit there -- there's a lot less waste under this approach -- then you can actually take that, and put it into another one and burn that.
Yeah.
And we start off actually by taking the waste that exists today, that's sitting in these cooling pools or dry casking by reactors -- that's our fuel to begin with.
So, the thing that's been a problem from those reactors is actually what gets fed into ours, and you're reducing the volume of the waste quite dramatically as you're going through this process.
I mean, you're talking to different people around the world about the possibilities here.
Well, we haven't picked a particular place, and there's all these interesting disclosure rules about anything that's called "nuclear," so we've got a lot of interest, that people from the company have been in Russia, India, China --
I've been back seeing the secretary of energy here, talking about how this fits into the energy agenda.
So I'm optimistic.
You know, the French and Japanese have done some work.
This is a variant on something that has been done.
It's an important advance, but it's like a fast reactor, and a lot of countries have built them, so anybody who's done a fast reactor is a candidate to be where the first one gets built.
CA:
So, in your mind, timescale and likelihood of actually taking something like this live?
Well, we need -- for one of these high-scale, electro-generation things that's very cheap, we have 20 years to invent and then 20 years to deploy.
That's sort of the deadline that the environmental models have shown us that we have to meet.
And, you know, TerraPower, if things go well -- which is wishing for a lot -- could easily meet that.
And there are, fortunately now, dozens of companies -- we need it to be hundreds -- who, likewise, if their science goes well, if the funding for their pilot plants goes well, that they can compete for this. And it's best if multiple succeed, because then you could use a mix of these things.
We certainly need one to succeed.
CA: In terms of big-scale possible game changes, is this the biggest that you're aware of out there?
BG:
An energy breakthrough is the most important thing.
It would have been, even without the environmental constraint, but the environmental constraint just makes it so much greater.
In the nuclear space, there are other innovators.
You know, we don't know their work as well as we know this one, but the modular people, that's a different approach.
There's a liquid-type reactor, which seems a little hard, but maybe they say that about us.
And so, there are different ones, but the beauty of this is a molecule of uranium has a million times as much energy as a molecule of, say, coal, and so -- if you can deal with the negatives, which are essentially the radiation -- the footprint and cost, the potential, in terms of effect on land and various things, is almost in a class of its own.
CA:
If this doesn't work, then what?
Do we have to start taking emergency measures to try and keep the temperature of the earth stable?
BG: If you get into that situation, it's like if you've been over-eating, and you're about to have a heart attack:
Then where do you go?
You may need heart surgery or something.
There is a line of research on what's called geoengineering, which are various techniques that would delay the heating to buy us 20 or 30 years to get our act together.
Now, that's just an insurance policy.
You hope you don't need to do that.
Some people say you shouldn't even work on the insurance policy because it might make you lazy, that you'll keep eating because you know heart surgery will be there to save you.
I'm not sure that's wise, given the importance of the problem, but there's now the geoengineering discussion about -- should that be in the back pocket in case things happen faster, or this innovation goes a lot slower than we expect?
CA: Climate skeptics: If you had a sentence or two to say to them, how might you persuade them that they're wrong?
BG:
Well, unfortunately, the skeptics come in different camps.
The ones who make scientific arguments are very few.
Are they saying that there's negative feedback effects that have to do with clouds that offset things?
There are very, very few things that they can even say there's a chance in a million of those things.
The main problem we have here, it's kind of like AlDS.
You make the mistake now, and you pay for it a lot later.
And so, when you have all sorts of urgent problems, the idea of taking pain now that has to do with a gain later, and a somewhat uncertain pain thing -- in fact, the IPCC report, that's not necessarily the worst case, and there are people in the rich world who look at IPCC and say, "OK, that isn't that big of a deal."
The fact is it's that uncertain part that should move us towards this.
But my dream here is that, if you can make it economic, and meet the CO2 constraints, then the skeptics say, "OK,
I don't care that it doesn't put out CO2,
I kind of wish it did put out CO2, but I guess I'll accept it because it's cheaper than what's come before."
(Applause)
CA:
And so, that would be your response to the Bjorn Lomborg argument, that basically if you spend all this energy trying to solve the CO2 problem, it's going to take away all your other goals of trying to rid the world of poverty and malaria and so forth, it's a stupid waste of the Earth's resources to put money towards that when there are better things we can do.
Well, the actual spending on the R&D piece -- say the U.S. should spend 10 billion a year more than it is right now -- it's not that dramatic.
It shouldn't take away from other things.
The thing you get into big money on, and this, reasonable people can disagree, is when you have something that's non-economic and you're trying to fund that -- that, to me, mostly is a waste.
Unless you're very close and you're just funding the learning curve and it's going to get very cheap,
I believe we should try more things that have a potential to be far less expensive.
If the trade-off you get into is, "Let's make energy super expensive," then the rich can afford that.
I mean, all of us here could pay five times as much for our energy and not change our lifestyle.
The disaster is for that two billion. And even Lomborg has changed.
His shtick now is, "Why isn't the R&D getting more discussed?"
He's still, because of his earlier stuff, still associated with the skeptic camp, but he's realized that's a pretty lonely camp, and so, he's making the R&D point. And so there is a thread of something that I think is appropriate.
The R&D piece, it's crazy how little it's funded.
Well Bill, I suspect I speak on the behalf of most people here to say I really hope your wish comes true.
Thank you so much.
BG:
Thank you.
(Applause)
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THlS IS YOUR LlFE. Do what you love and do it often. If you don't like something, change it.
Let's learn to multiply.
M U L T I P L Y.
And the best way I think to do anything is just to actually do some examples, and then talk through the examples, and try to figure out what they mean.
In my first example I have two times three.
By now you probably know what two plus three is.
Two plus three.
That's equal to five.
And if you need a bit of a review you could think of if I had two-- I don't know-- two magenta-- this color-- cherries.
And I wanted to add to it three blueberries.
How many total pieces of fruit do I now have?
And you'd say, oh, one, two, three, four, five.
Or likewise, if I had our number line, and you probably don't need this review, but it never hurts.
Never hurts to reinforce the concept.
And it this is zero, one, two, three, four, five.
If you're sitting two to the right of zero and in general when we go positive we go to the right.
And if you were to add three to it, you would move three spaces to the right.
So if I said, if I just moved over three to the right, where do I end up?
One, two, three.
I end up at five.
So either way, you understand that two plus three is equal to five.
So what is two times three?
An easy way to think about multiplication or "timesing" something is it's just a simple way of doing addition over and over again.
So that you means is, and it's a little tricky.
You're not going to add two to three.
You're going to add-- and there's actually two ways to think about it.
You're going to add two to itself three times.
Now what does that mean?
Well, it means you're going to say two plus two plus two.
Now where did the three go?
Well, how many twos do we have here?
Let's see, I have-- this is one two, I have two twos,
I have three twos.
I'm counting the numbers here the same way that I counted blueberries up here.
I had one, two, three blueberries.
I have one, two, three twos.
So this three tells me how many twos I'm going to have.
So what's two times three?
Well, I took two and I added it to itself three times.
So two plus two is four.
Four plus two is equal to six.
Now that's only one way to think about it.
The other way we could have thought about this is we could've said, instead of having two added to itself three times, we could have added three to itself two times!
And I know it's maybe becoming a little bit confusing, but the more practice you do it'll make a little sense.
So this statement up here, let me rewrite it.
Two times three.
It could also be rewritten as three two times.
So three plus three.
And once again, you're like, where did this two go?
You know, I had two times three and whenever you do addition, you see I have two-- oh, I don't know these-- well, I said cherries, but they could be raspberries or anything.
And then I have two things, I have three things and the two and the three never disappear.
And I add them together, I get five.
But here I'm saying that two times three is the same thing as three plus three.
Where did the two go?
Two in this case, in this scenario, is telling me how many times I'm going to add three to itself.
But what's interesting is, regardless of which way I interpret two times three,
I can interpret it as two plus two plus two, or adding two to itself three times.
I can interpret it that way or I can interpret it as adding three to itself two times.
But notice, I get the same answer.
What's three plus three?
That is also equal to six.
And this is probably the first time in mathematics you'll encounter something very neat!
Sometimes, regardless of the path you take, as long as you take a correct path you get the same answer.
So two people can kind of visualize it-- as long as they're visualizing it correctly, two different problems, but they come up with the same solution.
And so you're probably saying,
Sal, when is this multiplication thing even useful?
And this is where it's useful.
Sometimes it simplifies counting.
So let's say I have a-- well, let's stick with our fruit analogy.
An analogy is just when you kind of use something as-- well, I won't go too much into it.
But our fruit example.
Let's say I had lemons.
Let me draw a bunch of lemons.
I'll draw them in rows of three.
So I have one, two, three-- well, I'm not going to count them because that'll give our answer away.
I'm just drawing a bunch of lemons.
Now, if I said, you tell me how many lemons there are here.
And if I did that, you would proceed to just count all of the lemons.
And it wouldn't take you too long to say, that oh, there's one, two, three, four, five, six, seven, eight, nine, ten, eleven, twelve lemons.
I actually already gave you the answer.
We know that there are twelve lemons there.
But there's an easier way and a faster way to count the number of lemons.
Notice: how many lemons are in each row?
And a row is kind of the side to side lemons.
I think you know what a row is.
I don't want to talk down to you.
So how many lemons are there in a row?
Well, there are three lemons in a row.
And now let me ask you another question.
How many rows are there?
Well, this was one row, and this is the second row, this is the third row, and this is the fourth row.
So an easy way to count it is say, I have three lemons per row and I have four of them.
So let's say I have three lemons per row.
I hope I'm not confusing you, but I think you'll enjoy this.
And then I have four rows.
So I have four times three lemons.
Four times three lemons.
And that should be equal to the number of lemons I have-- twelve.
And just to make that gel with what I just did with the addition, let's think about this.
Four times three, literally when you-- and you know, when you actually say the words four times three,
I visualize this.
I visualize four times three.
So three four times.
Three, plus three, plus three, plus three. And if we did that we get:
Three plus three is six.
Six plus three is nine.
Nine plus three is twelve.
And we learned, up here, in this part of the video,
We learned that this same multiplication could also be interpreted as three times four.
You can switch the order.
And this one of the useful and interesting, actually, kind of properties of multiplication.
But this could also be written as four three times.
Four, plus four, plus four.
You add four to itself three times.
Four plus four is eight.
Eight plus four is twelve.
And in the U.S. we always say four times three, but you know, I've met people and a lot of people in my family they kind of learned in the--
I guess you could call it the English system.
And they'll often call this four threes, or three fours.
And that in someways is a lot more intuitive.
It's not intuitive the first time you hear it, but they'll write this multiplication problem, or they'll say this multiplication problem.
They'll say, what are four threes?
And when they say four threes,
They're literally saying, what are four threes?
So this is one three, two threes, three threes, four threes.
So what are four threes when you add them up?
It's twelve.
And you could also say, what are three fours?
So let me write this down.
Let me do it in a different color.
That is four threes.
I mean literally, that's four threes.
If I told you, say, write down four threes and add them up, that's what that is.
And that is four times three.
Or three four times.
And this is-- let me do it in a different color, that is three fours.
And it could also be written as three times four.
And they all equal twelve.
And now you're probably saying, okay, this is nice, it's a cute little trick, Sal, that you've taught me, but it took you less time to count these lemons than to you know, do this problem.
And well first of all, that's only right now because you're new to multiplication.
But what you'll find is that there are times, and there are actually many times--
I don't want to use the word times too much in a video on multiplication-- where each row of lemons, instead of having three, maybe they have one hundred lemons!
Maybe there's one hundred rows!
And it'll take you forever to count all the lemons, and that's where multiplication comes in useful, although we're not going to learn right now how to multiply one hundred times one hundred.
Now the one thing that I want to give you, and this is kind of a trick,
I remember my sister, just to try to show how much smarter she was than me, when I was in kindergarten and she was in third grade,
She would say,"Sal, what is three times one?"
And I would say, because my brain would say,
That's like three plus one, and I would say three plus one is equal to four.
And so I'd say,
Oh!
You know, three times one, that must be four as well.
And she'd say,"No, silly!
It's three!"
And I was like, how can that be?
How can, you know, three times some other number still be the same number?
And think about what this means.
You could view this as three ones.
And what are three ones?
That's one one, plus another one, plus another one.
That's equal to three.
Or you could do this as three one time.
So what's three one time?
It's almost silly how easy it is!
It's just three.
That's one three.
You could write this as one three.
And that's why anything times one, or one times anything, is that anything!
So then, three times one is three.
One times three is three.
And you know, I could say, one hundred times one is equal to one hundred.
I could say that one times thirty-nine is equal to thirty-nine.
And I think you're familiar with numbers this large by now.
So that's interesting.
Now there's one other really interesting thing about multiplication.
And that's when you multiply by zero.
And I'll start with the analogy, or the example, of when you add.
Three plus zero, you've hopefully learned, is three.
Because I'm adding nothing to the three.
If you have three apples, and I give you zero more apples, you still have three apples.
But what is three-- and maybe I'm just fixated on the number three a little too much-- well, so let me switch--
What is four times zero?
Well this is saying zero four times.
So what's zero, plus zero, plus zero, plus zero?
Well, that's zero!
Right?
I have nothing, plus nothing, plus nothing, plus nothing.
So I get nothing!
Another way to think of it,
I could say, four zero times.
So how do I write four zero times?
Well I just don't write anything, right?
Because if I write anything, if I write one four, then I don't have "no fours".
So this is saying-- so this is four-- let me write this-- this is four zeros.
But I could also write zero fours.
And what are zero fours?
Well, I just write a big blank here.
There, I wrote it!
There are no fours here!
So it's just a big blank.
And that's another fun thing.
So, anything times zero is zero!
I could write a huge number.
You know, five million four hundred ninety-three thousand six hundred ninety-two times zero.
What does that equal?
That equals zero.
And by the way, what's this number times one?
Well it's that number again.
What's zero times seventeen?
Once again, that is zero.
Anyway, I think I've talked for long enough.
See you in the next video!
we're asked to simply log base 3 of 27x and frankly this is already quite simple, but I'm assuming they want us to use some logarithm properties and manipulate this some way maybe actually make it a little more complicated and let's give this our best shot at it so the logarithm property that jumps out at me because this, right over here, is saying what power do we have to raise 3 to in order to get 27x 27x is the same thing as 27 times x and so the logarithm property it seems like they want us to use is
log base b of a times c this is equal to the logarithm base b of a plus logarithm base b of c now this comes straight out of the exponent properties that if you have two exponents with the same base you can add the exponents now let me make this a little bit clearer to you now if this part is a little confusing the important part for this example is is that you know how to apply this, but it's even better if you know the intuition so let's say that log, let's say that log base b of a times c is equal to x so this thing right over here evaluates to x
let's say that this thing right over here evaluates to y so log base b of a is equal to y and let's say that that this thing over here evaluates to z so log base b of c is equal to z now, what we know is this thing right over here, this thing right over here or this thing right over here tells us tells us that b, to the x power is equal to a times c now, this right over here is telling us that b to the y power is equal to a and this over here is telling us that b to the z power is equal to c let me do that in that same green so i'm just writing the same truth i'm writing as an exponential function or exponential equation instead of a logarithmic equation so b to the zth power is equal to c these are all, this is the same statement this is the same statement or they're the same truth said in a different way and this is the same truth said in a different way well if we know that, if we know that a is equal to this, is equal to b to the y, we can, and c is equal to b-z then we can write b to the x power is equal to b to the y power that's what a is, we know that already times b to the z power times b to the z power and we know, from our exponent properites we know from our exponent properties That if we take b to the y times b to the z this is the same thing as: b to the, I'll do it in neutral color, b to the y plus z power this came straight out of our exponent properties.
log base 3 of 27 times x -- I'll write it that way -- is equal to log base 3 of 27 plus log base 3 of x. And then this right over here we can evaluate, this tells us: what power do I have to raise 3 to get to 27. You can view it this way:
3 to the question mark is equal to 27. Well, 3 to the 3rd power is equal to 27. 3 times 3 is 9, times 3 is 27.
To this right over here evaluates to 3. So if we were to simplify -- or I guess I wouldn't even call it simplifying, I'll just call it expanding it out or using this property. We now have two terms, where when we started of with one term.
Log base 3 of 27x. So once again -- not clear that this is simpler than this right over here. It's just another way of writing it using logarithm properties.
We're on problem 36. And it says, what is the area in square units of the trapezoid shown below? So, when you just look at this you're like, OK, trapezoid, do
And if I know the dimensions of each of those, I know the area of each of them and then I know the area of the entire thing.
So let's see, what's this height right Here Or this width I should say.
Well we're going from zero to what? x is equal to 8 here. I just went straight down from x is equal to 8, y is equal to 5. So this dimension is 8.
The area of the rectangle part is 8 times 5, that's 40.
The area of this triangle is 5 times 4 times 1/2. If we didn't put that 1/2 we would be figuring out the area of this rectangle right there. So 5 times 4 is 20 times 1/2 is 10.
So the shaded portion is the whole square minus the area of the parallelogram. So the whole square, that's easy, it's 12. And the height is 12, but since you know it's a square we know the width also has to be 12.
And there's no reason why the area of this should be any different than that. We just rearranged its parts. So that's why the area of a parallelogram is just the base times the height.
6 times 6, it's 24. What's the area of each of these triangles?
3 times 4 times 1/2. 3 times 4 is 12 times 1/2 is 6. So the area of that triangle is 6.
The area of this triangle is 6. So 6 plus 24 plus 6 is 36. B.
1/2 times 5 times 5. So it's 25 root 3 over 2 and that's just this triangle right there. Well this triangle's going to have the the exact same area.
So the perimeter of the first square is 4x. x plus x plus x plus x. So the perimeter of the first square is 4x. The perimeter of the second square is 4y.
--(Vic Gundotra) Sergey!
--(Sergey Brin) I've got a really cool event for you.
(cheers and applause) (Sergey)How are you doing?
Guys, we're going to do something pretty magical here.
And we have a special surprise for you.
We've got something pretty special for you.
It's a little bit time sensitive, so I apologize for interrupting.
In this video, I want to tackle some inequalities that involve multiplying and dividing by positive and negative numbers, and you'll see that it's a little bit more tricky than just the adding and subtracting numbers that we saw in the last video. I also want to introduce you to some other types of notations for describing the solution set of an inequality. So let's do a couple of examples.
So let's say I had negative 0.5x is less than or equal to 7.5. Now, if this was an equality, your natural impulse is to say, hey, let's divide both sides by the coefficient on the x term, and that is a completely legitimate thing to do: divide both sides by negative 0.5. The important thing you need to realize, though, when you do it with an inequality is that when you multiply or divide both sides of the equation by a negative number, you swap the inequality. you swap the inequality
I'll do a simple example here. If I were to tell you that 1 is less than 2, I think you would agree with that. 1 is definitely less than 2.
Negative 1 versus negative 2? Well, all of a sudden, negative 2 is more negative than negative 1.
So here, negative 2 is actually less than negative 1.
If something is larger, when you take the negative of both of it, it'll be more negative, or vice versa. So that's why, if we're going to multiply both sides of this equation or divide both sides of the equation by a negative number, we need to swap the sign. So let's multiply both sides of this equation.
And negative 0.5 is the same thing as negative 1/2. The inverse of that is negative 2. So I'm multiplying negative 2 times both sides of this equation.
Negative 16 will not work.
Negative 16 times negative 0.5 is 8, which is not less than 7.5. So the solution set is all of the x's-- let me draw a number line here-- greater than negative 15.
So that is negative 15 there, maybe that's negative 16, that's negative 14.
Greater than or equal to negative 15 is the solution. Now, you might also see solution sets to inequalities written in interval notation.
We want to include negative 15, so our lower bound to our interval is negative 15.
And putting in this bracket here means that we're going to include negative 15. The set includes the bottom boundary. It includes negative 15.
But the parentheses tends to mean that you don't include that boundary, but you also use it with infinity. So this and this are the exact same thing. Sometimes you might also see set notations, where the solution of that, they might say x is a real number such that-- that little line, that vertical line thing, just means such that-- x is greater than or equal to negative 15.
These curly brackets mean the set of all real numbers, or the set of all numbers, where x is a real number, such that x is greater than or equal to negative 15.
All of this, this, and this are all equivalent. Let's keep that in mind and do a couple of more examples. So let's say we had 75x is greater than or equal to 125.
Let's say we have x over negative 3 is greater than negative 10/9. So we want to just isolate the x on the left-hand side. So let's multiply both sides by negative 3, right?
So if you multiply both sides by negative 3, you get negative 3 times-- this you could rewrite it as negative 1/3x, and on this side, you have negative 10/9 times negative 3. And the inequality will switch, because we are multiplying or dividing by a negative number. So the inequality will switch.
This isn't less than or equal to, so we're going to put a parentheses here.
Notice, here it included 5/3. We put a bracket. Here, we're not including 10/3.
Say we have x over negative 15 is less than 8. So once again, let's multiply both sides of this equation by negative 15. So negative 15 times x over negative 15.
And now, this left-hand side just becomes an x, because these guys cancel out. x is greater than 8 times 15 is 80 plus 40 is 120, so negative 120.
Or we could write the solution set as starting at negative 120-- but we're not including negative 120.
And if we were to graph it, let me draw the number line here. I'll do a real quick one. Let's say that that is negative 120.
We are not going to include negative 120, because we don't have an equal sign there, but it's going to be everything greater than negative 120. All of these things that I'm shading in green would satisfy the inequality. And you can even try it out.
0/15? Yeah, that's zero. That's definitely less than 8.
Let's find the volume of a few more solid figures, and if we have time we may be able to do more surface area problems.
So let me draw a cylinder over here.
So that is the top of my cylinder. and then this is the height of my cylinder. this is the bottom right over here. if this was transparent maybe you would be able to see the backside of my cylinder. so you can imagine this kind of looks like a soda can.
And let's say that the height of my cylinder "h" is equal to 8. I'll give some units- 8 cm.
And then let's say that the radius of one of these, of the top of my cylinder, or my soda can
let's say that this radius over here is equal to 4 cm. so what is the volume here. what is the volume going to be? and the idea here is really the exact same thing that we saw in some of the previous problems. if you can find the surface area of one side and the figure out kind of how deep it goes, you'll be able to figure out the volume.
So what we are going to do here is figure out the surface area of the top of this cylinder.
The top of this soda can and then we are going to multiply it by it's height and that'll give us a volume. this will tell us essentially how many square cm fit into this top and then if we know; if we multiply that by how many cm we go down, then that will give us the number of cubic centimeters in this cylinder, or soda can so how do we figure out this area up here well the area on top this is just finding the area of a circle you could imagine drawing it like this if we were just to look at it straight on that's a circle with a radius of 4 cm. the area of a circle with an area of 4 cm area is equal to pie r squared. so it's going to be pie times the radius squared times four cm squared which is equal to 4 squared is 16 times pie and our units now are going to be cm squared or another way to think of these is square cm so that's the area the volume is going to be this area times the height so the volume is going to be equal to 16 pie cm squared times the height times 8 cm times 8 cm and so when you do multiplication you could use the associative property you could kind of rearrange these things it doesn't matter what order you do it. it is all multiplication so this is the same thing as 16 times 8
let's see 8 times 8 is 64 16 times 8 is twice that so it's going to be 128 pi, then you have cm squared times cm so that gives us cm cubed or 128 pi cubic cm. remember, pi is just a number we write it as pi because it is kind of a crazy irrational number that if you were to write it, you could never completely write pi 3.14159 keeps going on never repeats so we just leave it as pi but if you wanted to figure it out you can get a calculator and this would be 3.14 roughtly times 128 so it would be like you know close to 400 cubic cm now, how would we find the surface area of this figure over here well, part of the surface area, are the two surfaces, the top and the bottom. so that would be part of the surface area and then the bottom over here would also be part of the surface area so if we are trying to find the surface area
let's do, surface
let's find the surface area of our cylinder it's deffinitely going to have both of these areas here. so it's going to have the 16 pi cm squared twice this is 16 pi, this is 16 pi square cm. so it's going to have two times 16 pi. cm squared. i'll keep the units still. so that covers the top and the bottom of our soda can. and now we have to figure out the surface area of this thing that goes around and the way I imagine it is imagine if you were trying to wrap this thing with wrapping paper so let me just draw
let me just draw a little dotted line here so imagine if you were to cut it just like that cut the side of the soda can. and if you were to kind of unwind if you were to unwind this thing that goes around it what would you have?
Well you would have something You would end up with a sheet of paper
Where this length right over here This length right over here Is the same thing as this length over here
And then it would be completely unwound
These two ends used to touch each other
These two ends used to touch each other when it was all rolled together And they used to touch each other right over there
So the length of this side and that side is going to be the same thing as the height of my cylinders
This is going to be eight centimeters And then this over here is also going to be eight centimeters
And so the question we'd ask ourselves is is what is going to be this dimension right over here
And remember that dimension is essentially how far did we go around the cylinder
Well if you think about it
That's going to be the exact same thing as the circumference of either the top or the bottom of the cylinder
So what is the circumference?
The circumference of this circle right over here which is the same thing as the circumference of that circle over there.
Or 2pi times the radius. 2pi times 4 cm which is equal to 8 pi cm. So this distance right over here is the circumference of either the top or the bottom of the cylinder.
It's going to be 8 pi cm.
So if you want to find the surface area of just the wrapping. Just the part that goes around the cylinder, not the top or the bottom. It's going to be unwinded, it's going to look like this rectangle.
And so it's area, the area of just that part is going to be equal to 8 cm by 8 pi cm.
So let me does this, it's going to be 8 cm times 8 pi cm. And thats equal to 64 pi. 8 times 8 is 64.
You have your pi centimeters squared.
We just figured that out so it's going to be plus 64 pi cm squared and now we just have to calculate it.
And then 32 plus 64 is 96 pi cm squared. So it's equal to 96 pi square cm is going to be a little over 300 square cm.
And notice when we did surface area. We got our answer in terms of sq cm.
That makes sense because surface area is a 2 dimensional measurement. We think about how many sq cm can we fit on the surface of the cylinder. We did the volume we got cubed centimeters.
1x1x1 cm cubes can we fit inside of this structure so that's why that's why it's cubic centimeters. Anyway hopefully that clarifies things up a little bit.
Dear, how are you? I'm missing you here I hope your love will stay the same because you are the one
Dear promise me that you won't doubt my love Dear I mean what I said because I love you Dear promise me that you take good care of your heart for me
 I've talked a lot about the importance of hemoglobin in our red blood cells so I thought I would dedicate an entire video to hemoglobin. One-- because it's important, but also it explains a lot about how the hemoglobin-- or the red blood cells, depending on what level you want to operate-- know, and I have to use know in quotes.
So this right here, this is actually a picture of a hemoglobin protein.
It's made up of four amino acid chains.
That's one of them.
Those are the other two.
We're not going to go into the detail of that, but these look like little curly ribbons.
If you imagine them, they're a bunch of molecules and amino acids and then they're curled around like that.
So this on some level describes its shape.
And in each of those groups or in each of those chains, you have a heme group here in green.
That's where you get the hem in hemoglobin from.
You have four heme groups and the globins are essentially describing the rest of it-- the protein structures, the four peptide chains
Now, this heme group-- this is pretty interesting. It actually is a porphyrin structure.
And if you watch the video on chlorophyil, you'd remember a porphyrin structure, but at the very center of it, in chlorophyil, we had a magnesium ion, but at the very center of hemoglobin, we have an iron ion and this is where the oxygen binds.
So on this hemoglobin, you have four major binding sites for oxygen.
You have right there, maybe right there, a little bit behind, right there, and right there.
Now why is hemoglobin-- oxygen will bind very well here, but hemoglobin has a several properties that one, make it really good at binding oxygen and then also really good at dumping oxygen when it needs to dump oxygen.
So it exhibits something called cooperative binding.
And this is just the principle that once it binds to one oxygen molecule-- let's say one oxygen molecule binds right there-- it changes the shape in such a way that the other sites are more likely to bind oxygen.
So it just makes it-- one binding makes the other bindings more likely.
Now you say, OK, that's fine. That makes it a very good oxygen acceptor, when it's traveling through the pulmonary capillaries and oxygen is diffusing from the alveoli.
That makes it really good at picking up the oxygen, but how does it know when to dump the oxygen?
This is an interesting question.
It doesn't have eyes or some type of GPS system that says, this guy's running right now and so he's generating a lot of carbon dioxide right now in these capillaries and he needs a lot of oxygen in these capillaries surrounding his quadriceps.
I need to deliver oxygen. It doesn't know it's in the quadraceps.
How does the hemoglobin know to let go of the oxygen there?
And that's a byproduct of what we call allosteric inhibition, which is a very fancy word, but the concept's actually pretty straightforward.
When you talk about allosteric anything-- it's often using the context of enzymes-- you're talking about the idea that things bind to other parts.
Allo means other.
So you're binding to other parts of the protein or the enzyme-- and enzymes are just proteins-- and it affects the ability of the protein or the enzyme to do what it normally does.
So hemoglobin is allosterically inhibited by carbon dioxide and by protons.
So carbon dioxide can bond to other parts of the hemoglobin-- I don't know the exact spots-- and so can protons.
So remember, acidity just means a high concentration of protons.
So if you're in an acidic environment, protons can bond.
Maybe I'll do the protons in this pink color.
Protons-- which are just hydrogen without electrons, right-- protons can bond to certain parts of our protein and it makes it harder for them to hold onto the oxygen.
So when you're in the presence of a lot of carbon dioxide or an acidic environment, this thing is going to let go of its oxygen.
And it just happens to be that that's a really good time to let go of your oxygen.
Let's go back to this guy running.
There's a lot of activity in these cells right here in his quadriceps.
They're releasing a lot of carbon dioxide into the capillaries.
At that point, they're going from arteries into veins and they need a lot of oxygen, which is a great time for the hemoglobin to dump their oxygen.
So it's really good that hemoglobin is allosterically inhibited by carbon dioxide.
Carbon dioxide joins on certain parts of it. It starts letting go of its oxygen, that's exactly where in the body the oxygen is needed.
Now you're saying, wait.
What about this acidic environment? How does this come into play?
Well, it turns out that most of the carbon dioxide is actually disassociated.
It actually disassociates.
It does go into the plasma, but it actually gets turned into carbonic acid.
So I'll just write a little formula right here.
So if you have some CO2 and you mix it with the water-- I mean, most of our blood, the plasma-- it's water.
So you take some carbon dioxide, you mix it with water, and you have it in the presence of an enzyme-- and this enzyme exists in red blood cells.
It's called carbonic anhydrase.
A reaction will occur-- essentially you'll end up with carbonic acid.
We have H2CO3.
It's all balanced. We have three oxygens, two hydrogens, one carbon.
It's called carbonic acid because it gives away hydrogen protons very easily.
Acids disassociate into their conjugate base and hydrogen protons very easily.
So carbonic acid disassociates very easily.
It's an acid, although I'll write in some type of an equilibrium right there. If any of this notation really confuses you or you want more detail on it, watch some of the chemistry videos on acid disassociation and equilibrium reactions and all of that, but it essentially can give away one of these hydrogens, but just the proton and it keeps the electron of that hydrogen so you're left with a hydrogen proton plus-- well, you gave away one of the hydrogens so you just have one hydrogen.
This is actually a bicarbonate ion.
But it only gave away the proton, kept the electron so you have a minus sign.
So all of the charge adds up to neutral and that's neutral over there.
So if I'm in a capillary of the leg-- let me see if I can draw this.
So let's say I'm in the capillary of my leg. Let me do a neutral color.
So this is a capillary of my leg.
I've zoomed in just one part of the capillary. It's always branching off.
And over here, I have a bunch of muscle cells right here that are generating a lot of carbon dioxide and they need oxygen.
Well, what's going to happen?
Well, I have my red blood cells flowing along.
It's actually interesting-- red blood cells-- their diameter's 25% larger than the smallest capillaries.
So essentially they get squeezed as they go through the small capillaries, which a lot of people believe helps them release their contents and maybe some of the oxygen that they have in them.
So you have a red blood cell that's coming in here.
It's being squeezed through this capillary right here.
It has a bunch of hemoglobin-- and when I say a bunch, you might as well know right now, each red blood cell has 270 million hemoglobin proteins.
And if you total up the hemoglobin in the entire body, it's huge because we have 20 to 30 trillion red blood cells.
And each of those 20 to 30 trillion red blood cells have 270 million hemoglobin proteins in them.
So we have a lot of hemoglobin.
So anyway, that was a little bit of a-- so actually, red blood cells make up roughly 25% of all of the cells in our body. We have about 100 trillion or a little bit more, give or take.
I've never sat down and counted them.
But anyway, we have 270 million hemoglobin particles or proteins in each red blood cell-- explains why the red blood cells had to shed their nucleuses to make space for all those hemoglobins.
They're carrying oxygen.
So right here we're dealing with-- this is an artery, right?
It's coming from the heart.
The red blood cell is going in that direction and then it's going to shed its oxygen and then it's going to become a vein.
Now what's going to happen is you have this carbon dioxide.
You have a high concentration of carbon dioxide in the muscle cell.
It eventually, just by diffusion gradient, ends up-- let me do that same color-- ends up in the blood plasma just like that and some of it can make its way across the membrane into the actual red blood cell.
In the red blood cell, you have this carbonic anhydrase which makes the carbon dioxide disassociate into-- or essentially become carbonic acid, which then can release protons.
Well, those protons, we just learned, can allosterically inhibit the uptake of oxygen by hemoglobin.
So those protons start bonding to different parts and even the carbon dioxide that hasn't been reacted with-- that can also allosterically inhibit the hemoglobin.
So it also bonds to other parts.
And that changes the shape of the hemoglobin protein just enough that it can't hold onto its oxygens that well and it starts letting go.
And just as we said we had cooperative binding, the more oxygens you have on, the better it is at accepting more-- the opposite happens.
When you start letting go of oxygen, it becomes harder to retain the other ones.
So then all of the oxygens let go.
So this, at least in my mind, it's a brilliant, brilliant mechanism because the oxygen gets let go just where it needs to let go.
It doesn't just say, I've left an artery and I'm now in a vein. Maybe I've gone through some capillaries right here and I'm going to go back to a vein.
Let me release my oxygen-- because then it would just release the oxygen willy-nilly throughout the body. This system, by being allosterically inhibited by carbon dioxide and an acidic environment, it allows it to release it where it is most needed, where there's the most carbon dioxide, where respiration is occurring most vigorously.
So it's a fascinating, fascinating scheme.
And just to get a better understanding of it, right here I have this little chart right here that shows the oxygen uptake by hemoglobin or how saturated it can be.
And you might see this in maybe your biology class so it's a good thing to understand.
So right here, we have on the x-axis or the horizontal axis, we have the partial pressure of oxygen.
And if you watched the chemistry lectures on partial pressure, you know that partial pressure just means, how frequently are you being bumped into by oxygen?
Pressure is generated by gases or molecules bumping into you.
It doesn't have to be gas, but just molecules bumping into you.
And then the partial pressure of oxygen is the amount of that that's generated by oxygen molecules bumping into you.
So you can imagine as you go to the right, there's just more and more oxygen around so you're going to get more and more bumped into by oxygen.
So this is just essentially saying, how much oxygen is around as you go to the right axis?
And then the vertical axis tells you, how saturated are your hemoglobin molecules?
This 100% would mean all of the heme groups on all of the hemoglobin molecules or proteins have bound to oxygen.
Zero means that none have.
So when you have an environment with very little oxygen-- and this actually shows the cooperative binding-- so let's say we're just dealing with an environment with very little oxygen.
So once a little bit of oxygen binds, then it makes it even more likely that more and more oxygen will bind.
As soon as a little-- that's why the slope is increasing.
I don't want to go into algebra and calculus here, but as you see, we're kind of flattish, and then the slope increases.
So as we bind to some oxygen, it makes it more likely that we'll bind to more.
And at some point, it's hard for oxygens to bump just right into the right hemoglobin molecules, but you can see that it kind of accelerates right around here.
Now, if we have an acidic environment that has a lot of carbon dioxide so that the hemoglobin is allosterically inhibited, it's not going to be as good at this.
So in an acidic environment, this curve for any level of oxygen partial pressure or any amount of oxygen, we're going to have less bound hemoglobin.
Let me do that in a different color.
So then the curve would look like this.
The saturation curve will look like this.
So this is an acidic environment.
Maybe there's some carbon dioxide right here.
So the hemoglobin is being allosterically inhibited so it's more likely to dump the oxygen at this point.
So I don't know. I don't know how exciting you found that, but I find it brilliant because it really is the simplest way for these things to dump their oxygen where needed.
No GPS needed, no robots needed to say, I'm now in the quadriceps and the guy is running. Let me dump my oxygen.
It just does it naturally because it's a more acidic environment with more carbon dioxide.
It gets inhibited and then the oxygen gets dumped and ready to use for respiration.
Let's see if we can learn a thing or two about significant figures, sometimes called significant digits.
And the idea behind significant figures is just to make sure that when you do a big computation and you have a bunch of digits there, that you're not over representing the amount of precision you have that your result isn't more precise than the things that you actually measured - that you usually use to get that result.
But before we go into the depths of it and how you use it with computation let's just do a bunch of examples of identifying significant figures, then we'll try to come up with some rules of thumb.
But the general way to think about it is - "Which digits are really giving me information about how precise my measurement is?"
So on this first thing right over here, the significant figures are this seven-zero-zero.
So over here you have three significant figures.
And it might make you a little uncomfortable that we're not including these zeros that are after the decimal point and before this seven.
That we're not including those - because that does help define the number.
And that is true but it's not telling us how precise our measurement is.
And to try to understand this a little bit better, imagine if this right over here was a measurement of kilometers.
So, if we measured zero point zero zero seven zero zero kilometers.
That same measurement we could have - this would have been the exact same thing as seven point zero zero meters.
Maybe in fact we just used a meter stick.
And we said it's exactly seven point zero zero meters.
So we measured to the nearest centimeter.
And we just felt like writing it in kilometers.
These two numbers are the exact same thing - they're just different units.
But I think when you look over here it makes a lot more sense why you only have three significant figures.
These zeroes are just kind of telling you - are just shifting it based on the units of measurement that you're using. But he numbers that are really giving you the precision are the seven, the zero and the zero.
And the reason why we're counting these trailing zeros is that whoever wrote this number didn't have to write them down.
They wrote them down to explicitly say "Look, I measured this far."
If they didn't measure this far they would have just left these zeros off, and they would have just told you seven meters - not seven point zero zero.
Let's do the next one - so based on the same idea we have the five and the two - the non zero digits are going to be significant figures.
You don't include this leading zero by the same logic that if this was point zero five two kilometers this would be the same thing as fifty two meters, which clearly has two significant figures.
So you don't want to count leading zeros before the first non zero digit, I guess we could say.
You just want to include all the non zero digits and everything in between. and - and trailing zeros - trailing zeros if a decimal point is involved.
I'll make those ideas a little bit more formal. So over here, the person did three hundred seventy, and then they wrote the decimal point.
If they didn't write the decimal point it would be a little unclear on how precise this was.
But becuase they wrote the decimal point it means they measured it to be exactly three hundred seventy.
They didn't get three hundred seventy two and then round down or they didn't have a kind of roughness only to the nearest 10s place.
This decimal tells you that all three of these are significant.
So this is three significant figures over here.
Then on this next one, once again, this decimal tells us that not only did we get to the nearest one, but then we put another trailing zero here which means we got to the nearest tenth.
So in this situation once again we have three significant figures.
Over here - the seven is in the hundreds but we got all the way down - the measurement went all the way down to the thousandths place
And even though there are zeros in between, those zeros are part of our measurement, because they are in between non zero digits.
So in this situation every digit - the way it's written - is a significant digit.
So you have six significant digits.
Now this last one is ambiguous.
The thirty seven thousand - it's not clear whether you measured exactly thirty seven thousand.
Maybe you measured to the nearest one, and you got an exact number - you got exactly thirty seven thousand.
Or, maybe you only measured to the nearest thousand.
So it depends on what - there's a little bit of ambiguity here - if you've just seen something written exactly like this, you'd probably say if you had to guess - or not guess - but if there wasn't any more information, you would say that there's just two significant figures or significant digits.
For this person to be less ambiguous they would want to put a decimal point right over there.
And that let's you know that there was actually five digits of precision - that we actually go to five significant figures.
So if you don't see the decimal point, I would go with two.
Solve for z 5z + 7 is less than 27 OR negative 3z is less than or equal to 18.
So this is a compound inequality.
We have two conditions here.
So z can satisfy this OR z can satisfy this over here.
So lets just solve each of these inequalities and just know that z can satisfy either of them.
So lets just look at this.
So if we look at just this one over here:
We have 5z + 7 is less than 27.
Let's isolate the z's on the left hand side, so lets subtract 7 from both sides to get rid of this 7 on the left hand side.
And so our left hand side is just going to be 5z plus 7, minus 7, those cancel out 5z is less than 27 minus 20, sorry, 27 minus 7, which is 20 so we have 5z less than 20.
Now we can divide both sides of this inequality by 5 and we don't have to swap the inequality because we're dividing by a positive number and so we get z is less than 20 over 5. Z is less than 4.
Now this is only one of the conditions.
Lets go to the other one over here:
We have negative 3z is less than or equal to 18.
Now to isolate the z we can just divide both sides of this inequality by negative 3 but remember when you divide or multiply both sides of an inequality by a negative number, you have to swap the inequality. So we can write negative 3z
We're going to divide by negative 3 and then you go 18 divide by negative 3 but we're going to swap the inequality!
So the left center equals greater than or equal to and so these guys cancel out negative 3 divided by negative 3 equals 1, so we have z is greater than or equal to 18 over negative 3 is negative 6 and remember, it's this constraint OR this constraint and this constraint right over here boils down to this and this one boils down to this so our solution set z is less than 4 OR z is greater than or equal to negative -6.
So let me make this clear.
Let me rewrite it. So z is less than 4 OR z is greater than or equal to negative 6.
It can satisfy either one of these.
This is kind of interesting here.
So, so let's plot these. Let's plot these.
So there's the number line.
Right over there.
Let's say 0 is over here and we have 1, 2, 3, 4 is right over there and negative 6, we have 1, 2 ,3, 4, 5, 6.
That's negative 6 over there.
Now let's think about z being less than 4 Z being less than 4, we put a circle around 4, since we're not including 4 and it'd be everything, everything less than 4. Everything less than 4.
Now lets think about z being greater than or equal to negative 6 would be
That means we can include negative 6 and it's everything... let's do this in a more different color...
It means you can include negative 6... I'm going to do that.... It means you can include negative 6...
Let me do that in a more different color...
I'm going to do it in orange... so z is greater than equal to negative 6 and this means you include negative 6 and its everything greater than that greater than that including 4.
It's everything greater than that.
So we see we've essentially shaded in the entire number line!
Every number will meet either one of these constraints or both of them.
If we're over here, we're going to meet both of the constraints, if we're one of these numbers, if we're a number out here, we're going to meet this constraint if we're a number down here, we're going to meet this constraint.
You can just try it out with a bunch of numbers.
0 will work.
0 plus 7 is 7 which is less than 27.
And three times 0 is less than 18 so it meets both constraints.
If we put 4 here, it should only meet one of the constraints.
Negative 3 times 4 is negative 12, which is less than 18.
So it meets this constraint but won't meet this constraint. Because you do 5 times 4 plus 7 is 27 which is not LESS than 27, it's equal to 27.
Remember this is an OR, so you just have to meet one of the constraints. So 4 meets this constraint so even 4 works.
So it's really the entire the number line will satisfy either one or both of these constraints.
I grew up to study the brain because I have a brother who has been diagnosed with a brain disorder, schizophrenia.
And as a sister and later, as a scientist, I wanted to understand, why is it that I can take my dreams, I can connect them to my reality, and I can make my dreams come true?
What is it about my brother's brain and his schizophrenia that he cannot connect his dreams to a common and shared reality, so they instead become delusion?
So I dedicated my career to research into the severe mental illnesses.
And I moved from my home state of Indiana to Boston, where I was working in the lab of Dr. Francine Benes, in the Harvard Department of Psychiatry.
And in the lab, we were asking the question,
"What are the biological differences between the brains of individuals who would be diagnosed as normal control, as compared with the brains of individuals diagnosed with schizophrenia, schizoaffective or bipolar disorder?"
So we were essentially mapping the microcircuitry of the brain: which cells are communicating with which cells, with which chemicals, and then in what quantities of those chemicals?
So there was a lot of meaning in my life because I was performing this type of research during the day, but then in the evenings and on the weekends,
I traveled as an advocate for NAMl, the National Alliance on Mental illness.
But on the morning of December 10, 1996,
I woke up to discover that I had a brain disorder of my own.
A blood vessel exploded in the left half of my brain.
And in the course of four hours, I watched my brain completely deteriorate in its ability to process all information.
On the morning of the hemorrhage, I could not walk, talk, read, write or recall any of my life.
I essentially became an infant in a woman's body.
If you've ever seen a human brain, it's obvious that the two hemispheres are completely separate from one another.
And I have brought for you a real human brain.
So this is a real human brain.
This is the front of the brain, the back of brain with the spinal cord hanging down, and this is how it would be positioned inside of my head.
And when you look at the brain, it's obvious that the two cerebral cortices are completely separate from one another.
For those of you who understand computers, our right hemisphere functions like a parallel processor, while our left hemisphere functions like a serial processor.
The two hemispheres do communicate with one another through the corpus callosum, which is made up of some 300 million axonal fibers.
But other than that, the two hemispheres are completely separate.
Because they process information differently, each of our hemispheres think about different things, they care about different things, and, dare I say, they have very different personalities.
Excuse me.
Thank you.
It's been a joy. Assistant: It has been.
(Laughter)
Our right human hemisphere is all about this present moment.
It's all about "right here, right now."
Our right hemisphere, it thinks in pictures and it learns kinesthetically through the movement of our bodies.
Information, in the form of energy, streams in simultaneously through all of our sensory systems and then it explodes into this enormous collage of what this present moment looks like, what this present moment smells like and tastes like, what it feels like and what it sounds like.
I am an energy-being connected to the energy all around me through the consciousness of my right hemisphere.
We are energy-beings connected to one another through the consciousness of our right hemispheres as one human family. And right here, right now, we are brothers and sisters on this planet, here to make the world a better place.
And in this moment we are perfect, we are whole and we are beautiful.
My left hemisphere, our left hemisphere, is a very different place.
Our left hemisphere thinks linearly and methodically.
Our left hemisphere is all about the past and it's all about the future.
Our left hemisphere is designed to take that enormous collage of the present moment and start picking out details, and more details about those details.
It then categorizes and organizes all that information, associates it with everything in the past we've ever learned, and projects into the future all of our possibilities.
And our left hemisphere thinks in language.
It's that ongoing brain chatter that connects me and my internal world to my external world.
It's that little voice that says to me, "Hey, you've got to remember to pick up bananas on your way home.
I need them in the morning."
It's that calculating intelligence that reminds me when I have to do my laundry.
But perhaps most important, it's that little voice that says to me,
"I am. I am."
And as soon as my left hemisphere says to me "I am,"
I become separate. I become a single solid individual, separate from the energy flow around me and separate from you.
And this was the portion of my brain that I lost on the morning of my stroke.
On the morning of the stroke, I woke up to a pounding pain behind my left eye.
And it was the kind of caustic pain that you get when you bite into ice cream.
And it just gripped me -- and then it released me.
And then it just gripped me -- and then it released me.
And it was very unusual for me to ever experience any kind of pain, so I thought, "OK, I'll just start my normal routine."
So I got up and I jumped onto my cardio glider, which is a full-body, full-exercise machine.
And I'm jamming away on this thing, and I'm realizing that my hands look like primitive claws grasping onto the bar.
And I thought, "That's very peculiar."
And I looked down at my body and I thought, "Whoa, I'm a weird-looking thing."
And it was as though my consciousness had shifted away from my normal perception of reality, where I'm the person on the machine having the experience, to some esoteric space where I'm witnessing myself having this experience.
And it was all very peculiar, and my headache was just getting worse.
So I get off the machine, and I'm walking across my living room floor, and I realize that everything inside of my body has slowed way down.
And every step is very rigid and very deliberate.
There's no fluidity to my pace, and there's this constriction in my area of perception, so I'm just focused on internal systems.
And I'm standing in my bathroom getting ready to step into the shower, and I could actually hear the dialogue inside of my body.
I heard a little voice saying, "OK. You muscles, you've got to contract.
You muscles, you relax."
And then I lost my balance, and I'm propped up against the wall.
And I look down at my arm and I realize that I can no longer define the boundaries of my body.
I can't define where I begin and where I end, because the atoms and the molecules of my arm blended with the atoms and molecules of the wall.
And all I could detect was this energy -- energy.
And I'm asking myself, "What is wrong with me?
What is going on?" And in that moment, my left hemisphere brain chatter went totally silent.
Just like someone took a remote control and pushed the mute button. Total silence.
And at first I was shocked to find myself inside of a silent mind.
But then I was immediately captivated by the magnificence of the energy around me.
And because I could no longer identify the boundaries of my body,
I felt enormous and expansive. I felt at one with all the energy that was, and it was beautiful there.
Then all of a sudden my left hemisphere comes back online and it says to me, "Hey!
We've got a problem!
We've got to get some help."
And I'm going, "Ahh!
I've got a problem!"
(Laughter)
So it's like, "OK, I've got a problem."
But then I immediately drifted right back out into the consciousness -- and I affectionately refer to this space as La La Land.
But it was beautiful there.
Imagine what it would be like to be totally disconnected from your brain chatter that connects you to the external world.
So here I am in this space, and my job, and any stress related to my job -- it was gone.
And I felt lighter in my body.
And imagine all of the relationships in the external world and any stressors related to any of those -- they were gone.
And I felt this sense of peacefulness.
And imagine what it would feel like to lose 37 years of emotional baggage!
(Laughter) Oh!
I felt euphoria -- euphoria.
It was beautiful.
And again, my left hemisphere comes online and it says,
"Hey! You've got to pay attention.
We've got to get help."
And I'm thinking, "I've got to get help.
I've got to focus." So I get out of the shower and I mechanically dress and I'm walking around my apartment, and I'm thinking, "I've got to get to work.
Can I drive?"
And in that moment, my right arm went totally paralyzed by my side.
Then I realized, "Oh my gosh!
I'm having a stroke!"
And the next thing my brain says to me is, Wow!
This is so cool! (Laughter) This is so cool!
How many brain scientists have the opportunity to study their own brain from the inside out?"
(Laughter)
And then it crosses my mind, "But I'm a very busy woman!"
(Laughter) "I don't have time for a stroke!"
So I'm like, "OK, I can't stop the stroke from happening, so I'll do this for a week or two, and then I'll get back to my routine.
OK.
So I've got to call help.
I've got to call work."
I couldn't remember the number at work, so I remembered, in my office I had a business card with my number.
So I go into my business room, I pull out a three-inch stack of business cards.
And I'm looking at the card on top and even though I could see clearly in my mind's eye what my business card looked like, I couldn't tell if this was my card or not, because all I could see were pixels.
And the pixels of the words blended with the pixels of the background and the pixels of the symbols, and I just couldn't tell.
And then I would wait for what I call a wave of clarity.
And in that moment, I would be able to reattach to normal reality and I could tell that's not the card... that's not the card.
It took me 45 minutes to get one inch down inside of that stack of cards.
In the meantime, for 45 minutes, the hemorrhage is getting bigger in my left hemisphere.
I do not understand numbers, I do not understand the telephone, but it's the only plan I have.
So I take the phone pad and I put it right here.
I take the business card, I put it right here, and I'm matching the shape of the squiggles on the card to the shape of the squiggles on the phone pad.
But then I would drift back out into La La Land, and not remember when I came back if I'd already dialed those numbers.
So I had to wield my paralyzed arm like a stump and cover the numbers as I went along and pushed them, so that as I would come back to normal reality, I'd be able to tell, "Yes, I've already dialed that number."
Eventually, the whole number gets dialed and I'm listening to the phone, and my colleague picks up the phone and he says to me,
"Woo woo woo woo." (Laughter) (Laughter)
And I think to myself, "Oh my gosh, he sounds like a Golden Retriever!" (Laughter)
And so I say to him -- clear in my mind, I say to him:
"This is Jill! I need help!"
And what comes out of my voice is, "Woo woo woo woo woo."
I'm thinking, "Oh my gosh, I sound like a Golden Retriever."
So I couldn't know -- I didn't know that I couldn't speak or understand language until I tried.
So he recognizes that I need help and he gets me help.
And a little while later, I am riding in an ambulance from one hospital across Boston to [Massachusetts] General Hospital.
And I curl up into a little fetal ball.
And just like a balloon with the last bit of air, just right out of the balloon, I just felt my energy lift and just I felt my spirit surrender.
And in that moment, I knew that I was no longer the choreographer of my life.
And either the doctors rescue my body and give me a second chance at life, or this was perhaps my moment of transition.
When I woke later that afternoon, I was shocked to discover that I was still alive.
When I felt my spirit surrender, I said goodbye to my life.
And my mind was now suspended between two very opposite planes of reality.
Stimulation coming in through my sensory systems felt like pure pain.
Light burned my brain like wildfire, and sounds were so loud and chaotic that I could not pick a voice out from the background noise, and I just wanted to escape.
Because I could not identify the position of my body in space, I felt enormous and expansive, like a genie just liberated from her bottle.
And my spirit soared free, like a great whale gliding through the sea of silent euphoria.
Nirvana.
I found Nirvana.
And I remember thinking, there's no way I would ever be able to squeeze the enormousness of myself back inside this tiny little body.
But then I realized, "But I'm still alive!
I'm still alive, and I have found Nirvana.
And if I have found Nirvana and I'm still alive, then everyone who is alive can find Nirvana." And I pictured a world filled with beautiful, peaceful, compassionate, loving people who knew that they could come to this space at any time.
And that they could purposely choose to step to the right of their left hemispheres -- and find this peace.
And then I realized what a tremendous gift this experience could be, what a stroke of insight this could be to how we live our lives. And it motivated me to recover.
Two and a half weeks after the hemorrhage, the surgeons went in, and they removed a blood clot the size of a golf ball that was pushing on my language centers.
Here I am with my mama, who is a true angel in my life.
It took me eight years to completely recover.
So who are we?
We are the life-force power of the universe, with manual dexterity and two cognitive minds.
And we have the power to choose, moment by moment, who and how we want to be in the world.
Right here, right now, I can step into the consciousness of my right hemisphere, where we are.
I am the life-force power of the universe.
I am the life-force power of the 50 trillion beautiful molecular geniuses that make up my form, at one with all that is.
Or, I can choose to step into the consciousness of my left hemisphere, where I become a single individual, a solid.
Separate from the flow, separate from you.
I am Dr. Jill Bolte Taylor: intellectual, neuroanatomist.
These are the "we" inside of me.
Which would you choose?
Which do you choose?
And when?
I believe that the more time we spend choosing to run the deep inner-peace circuitry of our right hemispheres, the more peace we will project into the world, and the more peaceful our planet will be.
And I thought that was an idea worth spreading.
This is an ambucycle.
This is the fastest way to reach any medical emergency.
It has everything an ambulance has except for a bed.
You see the defibrillator. You see the equipment.
We all saw the tragedy that happened in Boston.
When I was looking at these pictures, it brought me back many years to my past when I was a child.
I grew up in a small neighborhood in Jerusalem.
When I was six years old, I was walking back from school on a Friday afternoon with my older brother.
We were passing by a bus stop.
We saw a bus blow up in front of our eyes.
The bus was on fire, and many people were hurt and killed.
I remembered an old man yelling to us and crying to help us get him up.
He just needed someone helping him.
We were so scared and we just ran away.
Growing up, I decided I wanted to become a doctor and save lives.
Maybe that was because of what I saw when I was a child.
When I was 15, I took an EMT course, and I went to volunteer on an ambulance.
For two years, I volunteered on an ambulance in Jerusalem.
I helped many people, but whenever someone really needed help,
The traffic is so bad.
The distance, and everything.
We never got there when somebody really needed us.
One day, we received a call about a seven-year-old child choking from a hot dog.
Traffic was horrific, and we were coming from the other side of town in the north part of Jerusalem.
When we got there, 20 minutes later, we started CPR on the kid.
A doctor comes in from a block away, stop us, checks the kid, and tells us to stop CPR.
That second he declared this child dead.
At that moment, I understood that this child died for nothing.
If this doctor, who lived one block away from there, would have come 20 minutes earlier, not have to wait until that siren he heard before coming from the ambulance, if he would have heard about it way before, he would have saved this child.
He could have run from a block away.
He could have saved this child.
I said to myself, there must be a better way.
Together with 15 of my friends -- we were all EMTs — we decided, let's protect our neighborhood, so when something like that happens again, we will be there running to the scene a lot before the ambulance.
So I went over to the manager of the ambulance company and I told him, "Please, whenever you have a call coming into our neighborhood, we have 15 great guys who are willing to stop everything they're doing and run and save lives.
Just alert us by beeper.
We'll buy these beepers, just tell your dispatch to send us the beeper, and we will run and save lives."
Well, he was laughing.
I was 17 years old. I was a kid.
And he said to me — I remember this like yesterday — he was a great guy, but he said to me,
"Kid, go to school, or go open a falafel stand.
We're not really interested in these kinds of new adventures.
We're not interested in your help."
And he threw me out of the room.
"I don't need your help," he said.
I was a very stubborn kid.
As you see now, I'm walking around like crazy, meshugenah.
(Laughter) (Applause)
So I decided to use the Israeli very famous technique you've probably all heard of, chutzpah. (Laughter)
And the next day, I went and I bought two police scanners, and I said, "The hell with you, if you don't want to give me information, I'll get the information myself."
And we did turns, who's going to listen to the radio scanners.
The next day, while I was listening to the scanners,
I heard about a call coming in of a 70-year-old man hurt by a car only one block away from me on the main street of my neighborhood.
I ran there by foot.
I had no medical equipment.
When I got there, the 70-year-old man was lying on the floor, blood was gushing out of his neck.
He was on Coumadin.
I knew I had to stop his bleeding or else he would die.
I took off my yarmulke, because I had no medical equipment, and with a lot of pressure, I stopped his bleeding.
He was bleeding from his neck.
When the ambulance arrived 15 minutes later,
I gave them over a patient who was alive.
(Applause)
When I went to visit him two days later, he gave me a hug and was crying and thanking me for saving his life.
At that moment, when I realized this is the first person I ever saved in my life after two years volunteering in an ambulance,
I knew this is my life's mission.
So today, 22 years later, we have United Hatzalah.
(Applause)
"Hatzalah" means "rescue," for all of you who don't know Hebrew.
I forgot I'm not in Israel.
So we have thousands of volunteers who are passionate about saving lives, and they're spread all around, so whenever a call comes in, they just stop everything and go and run and save a life.
Our average response time today went down to less than three minutes in Israel.
(Applause)
I'm talking about heart attacks, I'm talking about car accidents, God forbid bomb attacks, shootings, whatever it is, even a woman 3 o'clock in the morning falling in her home and needs someone to help her.
Three minutes, we'll have a guy with his pajamas running to her house and helping her get up.
The reasons why we're so successful are because of three things.
Thousands of passionate volunteers who will leave everything they do and run to help people they don't even know.
We're not there to replace ambulances.
We're just there to get the gap between the ambulance call until they arrive.
And we save people that otherwise would not be saved.
The second reason is because of our technology.
You know, Israelis are good in technology.
Every one of us has on his phone, no matter what kind of phone, a GPS technology done by NowForce, and whenever a call comes in, the closest five volunteers get the call, and they actually get there really quick, and navigated by a traffic navigator to get there and not waste time.
And this is a great technology we use all over the country and reduce the response time.
And the third thing are these ambucycles.
These ambucycles are an ambulance on two wheels.
We don't transfer people, but we stabilize them, and we save their lives.
They never get stuck in traffic.
They could even go on a sidewalk.
They never, literally, get stuck in traffic.
That's why we get there so fast.
A few years after I started this organization, in a Jewish community, two Muslims from east Jerusalem called me up.
They ask me to meet. They wanted to meet with me.
Muhammad Asli and Murad Alyan.
When Muhammad told me his personal story, how his father, 55 years old, collapsed at home, had a cardiac arrest, and it took over an hour for an ambulance arrive, and he saw his father die in front of his eyes, he asked me, "Please start this in east Jerusalem."
I said to myself, I saw so much tragedy, so much hate, and it's not about saving Jews.
It's not about saving Christians. It's about saving people.
So I went ahead, full force -- (Applause) — and I started United Hatzalah in east Jerusalem, and that's why the names United and Hatzalah match so well.
We started hand in hand saving Jews and Arabs.
Arabs were saving Jews. Jews were saving Arabs.
Something special happened.
Arabs and Jews, they don't always get along together, but here in this situation, the communities, literally, it's an unbelievable situation that happened, the diversities, all of a sudden they had a common interest:
Let's save lives together.
Settlers were saving Arabs and Arabs were saving settlers.
It's an unbelievable concept that could work only when you have such a great cause.
And these are all volunteers.
No one is getting money.
They're all doing it for the purpose of saving lives.
When my own father collapsed a few years ago from a cardiac arrest, one of the first volunteers to arrive to save my father was one of these Muslim volunteers from east Jerusalem who was in the first course to join Hatzalah.
And he saved my father.
Could you imagine how I felt in that moment?
When I started this organization, I was 17 years old.
I never imagined that one day I'd be speaking at TEDMED. I never even knew what TEDMED was then.
I don't think it existed, but I never imagined,
I never imagined that it's going to go all around, it's going to spread around, and this last year we started in Panama and Brazil.
All I need is a partner who is a little meshugenah like me, passionate about saving lives, and willing to do it.
And I'm actually starting it in India very soon with a friend who I met in Harvard just a while back.
Hatzalah actually started in Brooklyn by a Hasidic Jew years before us in Williamsburg, and now it's all over the Jewish community in New York, even Australia and Mexico and many other Jewish communities.
But it could spread everywhere.
It's very easy to adopt.
You even saw these volunteers in New York saving lives in the World Trade Center.
Last year alone, we treated in Israel 207,000 people.
Forty-two thousand of them were life-threatening situations.
And we made a difference.
I guess you could call this a lifesaving flash mob, and it works.
When I look all around here, I see lots of people who would go an extra mile, run an extra mile to save other people, no matter who they are, no matter what religion, no matter who, where they come from.
We all want to be heroes.
We just need a good idea, motivation and lots of chutzpah, and we could save millions of people that otherwise would not be saved.
Thank you very much.
(Applause)
Find the place value of 3 in 4,356.
Now, whenever I think about place value, and the more you do practice problems on this it'll become a little bit of second nature, but whenever I see a problem like this, I like to expand out what 4,356 really is, so let me rewrite the number.
So if I were to write it-- and I'll write it in different colors.
So 4,356 is equal to-- and just think about how I just said it. It is equal to 4,000 plus 300 plus 50 plus 6.
And you could come up with that just based on how we said it: four thousand, three hundred, and fifty-six.
Now another way to think about this is this is just like saying this is 4 thousands plus-- or you could even think of "and"-- so plus 3 hundreds plus 50, you could think of it as 5 tens plus 6. And instead of 6, we could say plus 6 ones.
And so if we go back to the original number 4,356, this is the same thing as 4-- I'll write it down.
Let me see how well I can-- I'll write it up like this.
This is the same thing is 4 thousands, 3 hundreds, 5 tens and then 6 ones.
So when they ask what is the place value of 3 into 4,356, we're concerned with this 3 right here, and it's place value.
It's in the hundreds place.
If there was a 4 here, that would mean we're dealing with 4 hundreds.
If there's a 5, 5 hundreds.
It's the third from the right.
This is the ones place.
That's 6 ones, 5 tens, 3 hundreds.
So the answer here is it is in the hundreds place.
I was just looking on the discussion boards on the Khan
Academy Facebook page, and Bud Denny put up this problem, asking for it to be solved. And it seems like a problem of general interest. If the indefinite integral of 2 to the natural log of x over, everything over x, dx.
So the first thing when you see an integral like this, is you say, hey, you know, I have this natural log of x up in the numerator, and where do I start?
And the first thing that should maybe pop out at you, is that this is the same thing as the integral of one over x times 2 to the natural log of x, dx. And so you have an expression here, or it's kind of part of our larger function, and you have its derivative, right? We know that the derivative, let me write it over here, we know that the derivative with respect to x of the natural
log of x is equal to 1/x. So we have some expression, and we have its derivative, which tells us that we can use substitution. Sometimes you can do in your head, but this problem, it's still not trivial to do in your head.
So let's make the substitution. Let's substitute this right here with a u. So let's do that.
In the last video, I told you that if you had a quadratic equation of the form ax squared plus bx, plus c is equal to zero, you could use the quadratic formula to find the solutions to this equation.
And the quadratic formula was x.
The solutions would be equal to negative b plus or minus the square root of b squared minus 4ac, all of that over 2a.
And we learned how to use it.
You literally just substitute the numbers a for a, b for b, c for c, and then it gives you two answers, because you have a plus or a minus right there.
What I want to do in this video is actually prove it to you. Prove that using, essentially completing the square, I can get from that to that right over there.
So the first thing I want to do, so that I can start completing the square from this point right here, is-- let me rewrite the equation right here-- so we have ax--
let me do it in a different color-- I have ax squared plus bx, plus c is equal to 0.
So the first I want to do is divide everything by a, so I just have a 1 out here as a coefficient.
So you divide everything by a, you get x squared plus b over ax, plus c over a, is equal to 0 over a, which is still just 0.
Now we want to-- well, let me get the c over a term on to the right-hand side, so let's subtract c over a from both sides.
And we get x squared plus b over a x, plus-- well, I'll just leave it blank there, because this is gone now; we subtracted it from both sides-- is equal to negative c over a I left a space there so that we can complete the square.
And you saw in the completing the square video, you literally just take 1/2 of this coefficient right here and you square it.
So what is b over a divided by 2?
Or what is 1/2 times b over a?
Well, that is just b over 2a, and, of course, we are going to square it.
You take 1/2 of this and you square it.
Now, of course, we cannot just add the b over 2a squared to the left-hand side.
We have to add it to both sides.
So you have a plus b over 2a squared there as well.
Well, this over here, this expression right over here, this is the exact same thing as x plus b over 2a squared.
And if you don't believe me, I'm going to multiply it out.
That x plus b over 2a squared is x plus b over 2a, times x plus b over 2a. x times x is x squared. x times b over 2a is plus b over 2ax.
You have b over 2a times x, which is another b over 2ax, and then you have b over 2a times b over 2a, that is plus b over 2a squared.
That and this are the same thing, because these two middle terms, b over 2a plus b over 2a, that's the same thing as 2b over 2ax, which is the same thing as b over ax.
So this simplifies to x squared plus b over ax, plus b over 2a squared, which is exactly what we have written right there.
That was the whole point of adding this term to both sides, so it becomes a perfect square.
So the left-hand side simplifies to this.
The right-hand side, maybe not quite as simple.
Maybe we'll leave it the way it is right now.
Actually, let's simplify it a little bit.
So the right-hand side, we can rewrite it.
This is going to be equal to-- well, this is going to be b squared.
This is b-- let me do it in green so we can follow along.
So that term right there can be written as b squared over 4a square.
What would that become?
This would become-- in order to have 4a squared as the denominator, we have to multiply the numerator and the denominator by 4a.
So this term right here will become minus 4ac over 4a squared.
And you can verify for yourself that that is the same thing as that.
I just multiplied the numerator and the denominator by 4a.
In fact, the 4's cancel out and then this a cancels out and you just have a c over a.
So these, this and that are equivalent.
I just switched which I write first. And you might already be seeing the beginnings of the quadratic formula here.
So this I can rewrite.
The right-hand side, right here, I can rewrite as b squared minus 4ac, all of that over 4a squared.
Notice, b squared minus 4ac, it's already appearing.
We don't have a square root yet, but we haven't taken the square root of both sides of this equation, so let's do that.
So if you take the square root of both sides, the left-hand side will just become x plus-- let me scroll down a little bit-- x plus b over 2a is going to be equal to the plus or minus square root of this thing.
And the square root of this is the square root of the numerator over the square root of the denominator.
So it's going to be the plus or minus the square root of b squared minus 4ac over the square root of 4a squared.
Now, what is the square root of 4a squared?
It is 2a, right?
2a squared is 4a squared.
So to go from here to here, I just took the square root of both sides of this equation.
We have a b squared minus 4ac over 2a, now we just essentially have to subtract this b over 2a from both sides of the equation and we're done.
So let's do that.
So if you subtract the b over 2a from both sides of this equation, what do you get?
You get x is equal to negative b over 2a, plus or minus the square root of b squared minus 4ac over 2a, common denominator.
So this is equal to negative b.
Negative b plus or minus the square root of b squared minus 4ac, all of that over 2a.
And we are done!
By completing the square with just general coefficients in front of our a, b and c, we were able to derive the quadratic formula.
Solve for x, 5x - 3 is less than 12 "and" 4x plus 1 is greater than 25.
So let's just solve for X in each of these constraints and keep in mind that any x has to satisfy both of them because it's an "and" over here so first we have this 5 x minus 3 is less than 12 so if we want to isolate the x we can get rid of this negative 3 here by adding 3 to both sides so let's add 3 to both sides of this inequality.
The left-hand side, we're just left with a 5x, the minus 3 and the plus 3 cancel out. 5x is less than 12 plus 3 is 15.
Now we can divide both sides by positive 5, that won't swap the inequality since 5 is positive. So we divide both sides by positive 5 and we are left with just from this constraint that x is less than 15 over 5, which is 3.
So that constraint over here.
But we have the second constraint as well.
We have this one, we have 4x plus 1 is greater than 25.
So very similarly we can substract one from both sides to get rid of that one on the left-hand side.
And we get 4x, the ones cancel out. is greater than 25 minus one is 24.
Divide both sides by positive 4
Don't have to do anything to the inequality since it's a positive number.
And we get x is greater than 24 over 4 is 6.
And remember there was that "and" over here.
We have this "and".
So x has to be less than 3 "and" x has to be greater than 6.
So already your brain might be realizing that this is a little bit strange.
This first constraint says that x needs to be less than 3 so this is 3 on the number line.
We're saying x has to be less than 3 so it has to be in this shaded area right over there.
This second constraint says that x has to be greater than 6.
So if this is 6 over here, it says that x has to greater than 6.
It can't even include 6.
And since we have this "and" here. The only x-es that are a solution for this compound inequality are the ones that satisfy both.
The ones that are in the overlap of their solution set.
But when you look at it right over here it's clear that there is no overlap.
There is no x that is both greater than 6 "and" less than 3.
So in this situation we no solution.
Well this is a really extraordinary honor for me.
I spend most of my time in jails, in prisons, on death row.
I spend most of my time in very low-income communities in the projects and places where there's a great deal of hopelessness.
And being here at TED and seeing the stimulation, hearing it, has been very, very energizing to me.
And one of the things that's emerged in my short time here is that TED has an identity.
And you can actually say things here that have impacts around the world.
And sometimes when it comes through TED, it has meaning and power that it doesn't have when it doesn't.
And I mention that because I think identity is really important.
And we've had some fantastic presentations.
And I think what we've learned is that, if you're a teacher your words can be meaningful, but if you're a compassionate teacher, they can be especially meaningful.
If you're a doctor you can do some good things, but if you're a caring doctor you can do some other things.
And so I want to talk about the power of identity.
And I didn't learn about this actually practicing law and doing the work that I do.
I actually learned about this from my grandmother.
I grew up in a house that was the traditional African-American home that was dominated by a matriarch, and that matriarch was my grandmother.
She was tough, she was strong, she was powerful.
She was the end of every argument in our family.
She was the beginning of a lot of arguments in our family.
She was the daughter of people who were actually enslaved.
Her parents were born in slavery in Virginia in the 1840's.
She was born in the 1880's and the experience of slavery very much shaped the way she saw the world.
And my grandmother was tough, but she was also loving.
When I would see her as a little boy, she'd come up to me and she'd give me these hugs.
And she'd squeeze me so tight I could barely breathe and then she'd let me go.
And an hour or two later, if I saw her, she'd come over to me and she'd say, "Bryan, do you still feel me hugging you?"
And if I said, "No," she'd assault me again, and if I said, "Yes," she'd leave me alone.
And she just had this quality that you always wanted to be near her.
And the only challenge was that she had 10 children.
My mom was the youngest of her 10 kids.
And sometimes when I would go and spend time with her, it would be difficult to get her time and attention.
My cousins would be running around everywhere.
And I remember, when I was about eight or nine years old, waking up one morning, going into the living room, and all of my cousins were running around.
And my grandmother was sitting across the room staring at me.
And at first I thought we were playing a game.
And I would look at her and I'd smile, but she was very serious.
And after about 15 or 20 minutes of this, she got up and she came across the room and she took me by the hand and she said, "Come on, Bryan.
And I remember this just like it happened yesterday.
I never will forget it.
She took me out back and she said, "Bryan, I'm going to tell you something, but you don't tell anybody what I tell you."
I said, "Okay, Mama."
She said, "Now you make sure you don't do that." I said, "Sure."
Then she sat me down and she looked at me and she said, "I want you to know
I've been watching you."
And she said, "I think you're special."
She said, "I think you can do anything you want to do."
I will never forget it.
And then she said, "I just need you to promise me three things, Bryan."
I said, "Okay, Mama."
She said, "The first thing I want you to promise me is that you'll always love your mom."
She said, "That's my baby girl, and you have to promise me now you'll always take care of her."
Well I adored my mom, so I said, "Yes, Mama.
I'll do that."
Then she said, "The second thing I want you to promise me is that you'll always do the right thing even when the right thing is the hard thing."
And I thought about it and I said, "Yes, Mama.
I'll do that."
Then finally she said, "The third thing I want you to promise me is that you'll never drink alcohol."
(Laughter)
Well I was nine years old, so I said, "Yes, Mama.
I'll do that."
I grew up in the country in the rural South, and I have a brother a year older than me and a sister a year younger.
When I was about 14 or 15, one day my brother came home and he had this six-pack of beer --
I don't know where he got it -- and he grabbed me and my sister and we went out in the woods.
And we were kind of just out there doing the stuff we crazily did.
And he had a sip of this beer and he gave some to my sister and she had some, and they offered it to me.
I said, "No, no, no. That's okay. You all go ahead.
My brother said, "Come on. We're doing this today; you always do what we do.
I had some, your sister had some.
Have some beer."
I said, "No, I don't feel right about that.
Y'all go ahead. Y'all go ahead."
And then my brother started staring at me.
He said, "What's wrong with you?
Have some beer."
Then he looked at me real hard and he said,
"Oh, I hope you're not still hung up on that conversation Mama had with you."
(Laughter)
I said, "Well, what are you talking about?"
He said, "Oh, Mama tells all the grandkids that they're special."
(Laughter)
I was devastated.
(Laughter)
And I'm going to admit something to you.
I'm going to tell you something I probably shouldn't.
I know this might be broadcast broadly.
But I'm 52 years old, and I'm going to admit to you that I've never had a drop of alcohol.
(Applause)
I don't say that because I think that's virtuous; I say that because there is power in identity.
When we create the right kind of identity, we can say things to the world around us that they don't actually believe makes sense.
We can get them to do things that they don't think they can do.
When I thought about my grandmother, of course she would think all her grandkids were special.
My grandfather was in prison during prohibition.
My male uncles died of alcohol-related diseases.
And these were the things she thought we needed to commit to.
Well I've been trying to say something about our criminal justice system.
This country is very different today than it was 40 years ago.
In 1972, there were 300,000 people in jails and prisons.
Today, there are 2.3 million.
The United States now has the highest rate of incarceration in the world.
We have seven million people on probation and parole.
And mass incarceration, in my judgment, has fundamentally changed our world.
In poor communities, in communities of color there is this despair, there is this hopelessness, that is being shaped by these outcomes.
One out of three black men between the ages of 18 and 30 is in jail, in prison, on probation or parole.
In urban communities across this country --
Los Angeles, Philadelphia, Baltimore, Washington -- 50 to 60 percent of all young men of color are in jail or prison or on probation or parole.
Our system isn't just being shaped in these ways that seem to be distorting around race, they're also distorted by poverty.
We have a system of justice in this country that treats you much better if you're rich and guilty than if you're poor and innocent.
Wealth, not culpability, shapes outcomes.
And yet, we seem to be very comfortable.
The politics of fear and anger have made us believe that these are problems that are not our problems.
We've been disconnected.
It's interesting to me.
We're looking at some very interesting developments in our work.
My state of Alabama, like a number of states, actually permanently disenfranchises you if you have a criminal conviction.
Right now in Alabama 34 percent of the black male population has permanently lost the right to vote.
We're actually projecting in another 10 years the level of disenfranchisement will be as high as it's been since prior to the passage of the Voting Rights Act.
And there is this stunning silence.
I represent children.
A lot of my clients are very young.
The United States is the only country in the world where we sentence 13-year-old children to die in prison.
We have life imprisonment without parole for kids in this country.
And we're actually doing some litigation.
The only country in the world.
I represent people on death row.
It's interesting, this question of the death penalty.
In many ways, we've been taught to think that the real question is, do people deserve to die for the crimes they've committed?
And that's a very sensible question.
But there's another way of thinking about where we are in our identity.
The other way of thinking about it is not, do people deserve to die for the crimes they commit, but do we deserve to kill?
I mean, it's fascinating.
Death penalty in America is defined by error.
For every nine people who have been executed, we've actually identified one innocent person who's been exonerated and released from death row.
A kind of astonishing error rate -- one out of nine people innocent.
I mean, it's fascinating.
In aviation, we would never let people fly on airplanes if for every nine planes that took off one would crash.
But somehow we can insulate ourselves from this problem.
It's not our problem.
It's not our burden.
It's not our struggle.
I talk a lot about these issues.
I talk about race and this question of whether we deserve to kill.
And it's interesting, when I teach my students about African-American history,
I tell them about slavery.
I tell them about terrorism, the era that began at the end of reconstruction that went on to World War Il.
We don't really know very much about it.
But for African-Americans in this country, that was an era defined by terror.
In many communities, people had to worry about being lynched.
They had to worry about being bombed.
It was the threat of terror that shaped their lives.
And these older people come up to me now and they say, "Mr. Stevenson, you give talks, you make speeches, you tell people to stop saying we're dealing with terrorism for the first time in our nation's history after 9/11."
They tell me to say, "No, tell them that we grew up with that."
And that era of terrorism, of course, was followed by segregation and decades of racial subordination and apartheid.
And yet, we have in this country this dynamic where we really don't like to talk about our problems.
We don't like to talk about our history.
And because of that, we really haven't understood what it's meant to do the things we've done historically.
We're constantly running into each other. We're constantly creating tensions and conflicts.
We have a hard time talking about race, and I believe it's because we are unwilling to commit ourselves to a process of truth and reconciliation.
In South Africa, people understood that we couldn't overcome apartheid without a commitment to truth and reconciliation.
In Rwanda, even after the genocide, there was this commitment, but in this country we haven't done that.
I was giving some lectures in Germany about the death penalty.
It was fascinating because one of the scholars stood up after the presentation and said, "Well you know it's deeply troubling to hear what you're talking about."
He said, "We don't have the death penalty in Germany.
And of course, we can never have the death penalty in Germany."
And the room got very quiet, and this woman said,
"There's no way, with our history, we could ever engage in the systematic killing of human beings.
It would be unconscionable for us to, in an intentional and deliberate way, set about executing people."
And I thought about that.
What would it feel like to be living in a world where the nation state of Germany was executing people, especially if they were disproportionately Jewish?
I couldn't bear it.
It would be unconscionable.
And yet, in this country, in the states of the Old South, we execute people -- where you're 11 times more likely to get the death penalty if the victim is white than if the victim is black, 22 times more likely to get it if the defendant is black and the victim is white -- in the very states where there are buried in the ground the bodies of people who were lynched.
And yet, there is this disconnect.
Well I believe that our identity is at risk.
That when we actually don't care about these difficult things, the positive and wonderful things are nonetheless implicated.
We love innovation.
We love technology.
We love creativity.
We love entertainment.
But ultimately, those realities are shadowed by suffering, abuse, degradation, marginalization.
And for me, it becomes necessary to integrate the two.
Because ultimately we are talking about a need to be more hopeful, more committed, more dedicated to the basic challenges of living in a complex world.
And for me that means spending time thinking and talking about the poor, the disadvantaged, those who will never get to TED.
But thinking about them in a way that is integrated in our own lives.
You know ultimately, we all have to believe things we haven't seen.
We do.
As rational as we are, as committed to intellect as we are.
Innovation, creativity, development comes not from the ideas in our mind alone.
They come from the ideas in our mind that are also fueled by some conviction in our heart.
And it's that mind-heart connection that I believe compels us to not just be attentive to all the bright and dazzly things, but also the dark and difficult things.
Vaclav Havel, the great Czech leader, talked about this.
He said, "When we were in Eastern Europe and dealing with oppression, we wanted all kinds of things, but mostly what we needed was hope, an orientation of the spirit, a willingness to sometimes be in hopeless places and be a witness."
Well that orientation of the spirit is very much at the core of what I believe even TED communities have to be engaged in.
There is no disconnect around technology and design that will allow us to be fully human until we pay attention to suffering, to poverty, to exclusion, to unfairness, to injustice.
Now I will warn you that this kind of identity is a much more challenging identity than ones that don't pay attention to this.
It will get to you.
I had the great privilege, when I was a young lawyer, of meeting Rosa Parks.
And Ms. Parks used to come back to Montgomery every now and then, and she would get together with two of her dearest friends, these older women, Johnnie Carr who was the organizer of the Montgomery bus boycott -- amazing African-American woman -- and Virginia Durr, a white woman, whose husband, Clifford Durr, represented Dr. King.
And these women would get together and just talk.
And every now and then Ms. Carr would call me, and she'd say, "Bryan, Ms. Parks is coming to town.
We're going to get together and talk.
Do you want to come over and listen?"
And I'd say, "Yes, Ma'am, I do."
And she'd say, "Well what are you going to do when you get here?"
I said, "I'm going to listen."
And I'd go over there and I would, I would just listen.
It would be so energizing and so empowering.
And one time I was over there listening to these women talk, and after a couple of hours Ms. Parks turned to me and she said, "Now Bryan, tell me what the Equal Justice Initiative is.
Tell me what you're trying to do."
And I began giving her my rap.
I said, "Well we're trying to challenge injustice.
We're trying to help people who have been wrongly convicted. We're trying to confront bias and discrimination in the administration of criminal justice. We're trying to end life without parole sentences for children.
I gave her my whole rap, and when I finished she looked at me and she said, "Mmm mmm mmm."
She said, "That's going to make you tired, tired, tired."
(Laughter)
And that's when Ms. Carr leaned forward, she put her finger in my face, she said, "That's why you've got to be brave, brave, brave."
And I actually believe that the TED community needs to be more courageous.
We need to find ways to embrace these challenges, these problems, the suffering.
Because ultimately, our humanity depends on everyone's humanity.
I've learned very simple things doing the work that I do.
It's just taught me very simple things.
I've come to understand and to believe that each of us is more than the worst thing we've ever done.
I believe that for every person on the planet.
I think if somebody tells a lie, they're not just a liar.
I think if somebody takes something that doesn't belong to them, they're not just a thief.
I think even if you kill someone, you're not just a killer.
And because of that there's this basic human dignity that must be respected by law.
I also believe that in many parts of this country, and certainly in many parts of this globe, that the opposite of poverty is not wealth.
I don't believe that.
I actually think, in too many places, the opposite of poverty is justice.
And finally, I believe that, despite the fact that it is so dramatic and so beautiful and so inspiring and so stimulating, we will ultimately not be judged by our technology, we won't be judged by our design, we won't be judged by our intellect and reason.
Ultimately, you judge the character of a society, not by how they treat their rich and the powerful and the privileged, but by how they treat the poor, the condemned, the incarcerated.
Because it's in that nexus that we actually begin to understand truly profound things about who we are.
I sometimes get out of balance. I'll end with this story.
I sometimes push too hard.
I do get tired, as we all do.
Sometimes those ideas get ahead of our thinking in ways that are important.
And I've been representing these kids who have been sentenced to do these very harsh sentences.
And I go to the jail and I see my client who's 13 and 14, and he's been certified to stand trial as an adult.
I start thinking, well, how did that happen?
How can a judge turn you into something that you're not?
And the judge has certified him as an adult, but I see this kid.
And I was up too late one night and I starting thinking, well gosh, if the judge can turn you into something that you're not, the judge must have magic power.
Yeah, Bryan, the judge has some magic power.
You should ask for some of that.
And because I was up too late, wasn't thinking real straight, I started working on a motion.
And I had a client who was 14 years old, a young, poor black kid.
And I started working on this motion, and the head of the motion was:
"Motion to try my poor, 14-year-old black male client like a privileged, white 75-year-old corporate executive." (Applause)
And I put in my motion that there was prosecutorial misconduct and police misconduct and judicial misconduct.
There was a crazy line in there about how there's no conduct in this county, it's all misconduct.
And the next morning, I woke up and I thought, now did I dream that crazy motion, or did I actually write it?
And to my horror, not only had I written it, but I had sent it to court.
(Applause)
A couple months went by, and I had just forgotten all about it.
And I finally decided, oh gosh, I've got to go to the court and do this crazy case.
And I got into my car and I was feeling really overwhelmed -- overwhelmed.
And I got in my car and I went to this courthouse.
And I was thinking, this is going to be so difficult, so painful.
And I finally got out of the car and I started walking up to the courthouse.
And as I was walking up the steps of this courthouse, there was an older black man who was the janitor in this courthouse.
When this man saw me, he came over to me and he said, "Who are you?"
I said, "I'm a lawyer." He said, "You're a lawyer?" I said, "Yes, sir."
And this man came over to me and he hugged me.
And he whispered in my ear.
He said, "I'm so proud of you."
And I have to tell you, it was energizing.
It connected deeply with something in me about identity, about the capacity of every person to contribute to a community, to a perspective that is hopeful.
Well I went into the courtroom.
And as soon as I walked inside, the judge saw me coming in.
He said, "Mr. Stevenson, did you write this crazy motion?"
I said, "Yes, sir.
I did." And we started arguing.
And people started coming in because they were just outraged.
I had written these crazy things.
And police officers were coming in and assistant prosecutors and clerk workers.
And before I knew it, the courtroom was filled with people angry that we were talking about race, that we were talking about poverty, that we were talking about inequality.
And out of the corner of my eye, I could see this janitor pacing back and forth.
And he kept looking through the window, and he could hear all of this holler.
He kept pacing back and forth.
And finally, this older black man with this very worried look on his face came into the courtroom and sat down behind me, almost at counsel table.
About 10 minutes later the judge said we would take a break.
And during the break there was a deputy sheriff who was offended that the janitor had come into court.
And this deputy jumped up and he ran over to this older black man.
He said, "Jimmy, what are you doing in this courtroom?"
And this older black man stood up and he looked at that deputy and he looked at me and he said, "I came into this courtroom to tell this young man, keep your eyes on the prize, hold on."
I've come to TED because I believe that many of you understand that the moral arc of the universe is long, but it bends toward justice.
That we cannot be full evolved human beings until we care about human rights and basic dignity.
That all of our survival is tied to the survival of everyone.
That our visions of technology and design and entertainment and creativity have to be married with visions of humanity, compassion and justice.
And more than anything, for those of you who share that,
I've simply come to tell you to keep your eyes on the prize, hold on.
Thank you very much.
(Applause)
Chris Anderson: So you heard and saw an obvious desire by this audience, this community, to help you on your way and to do something on this issue.
Other than writing a check, what could we do?
BS:
Well there are opportunities all around us.
If you live in the state of California, for example, there's a referendum coming up this spring where actually there's going to be an effort to redirect some of the money we spend on the politics of punishment.
For example, here in California we're going to spend one billion dollars on the death penalty in the next five years -- one billion dollars.
And yet, 46 percent of all homicide cases don't result in arrest.
56 percent of all rape cases don't result.
So there's an opportunity to change that.
And this referendum would propose having those dollars go to law enforcement and safety.
And I think that opportunity exists all around us.
CA:
There's been this huge decline in crime in America over the last three decades.
And part of the narrative of that is sometimes that it's about increased incarceration rates.
What would you say to someone who believed that?
Well actually the violent crime rate has remained relatively stable.
The great increase in mass incarceration in this country wasn't really in violent crime categories.
It was this misguided war on drugs.
That's where the dramatic increases have come in our prison population.
And we got carried away with the rhetoric of punishment.
And so we have three strikes laws that put people in prison forever for stealing a bicycle, for low-level property crimes, rather than making them give those resources back to the people who they victimized.
I believe we need to do more to help people who are victimized by crime, not do less.
And I think our current punishment philosophy does nothing for no one.
And I think that's the orientation that we have to change.
(Applause)
CA:
Bryan, you've struck a massive chord here.
You're an inspiring person.
Thank you so much for coming to TED. Thank you.
(Applause)
So we're told that quadrilateral ABCD is a square which tells us that the 4 sides have equal length, and that they are all the interior angles are 90 degrees We also know that FG,FG is a perpendicular bisector of BC so we've already shown that it's perpendicular, that this a 90-degree angle, but it also bisects BC So this length is equal to that length right over there
So this is a circle centered at B So this is the center of the circle, this is part of part of that circle It's really kind of the bottom left corner of that circle and then given that information, they want us to find what the measure of angle BED is
So we need to figure out the measure of this angle right over here
And you might imagine, well I you could pause it and try it without any hints and now I would give you a hint if you if you try it the first time, and you weren't able to do it, and you should pause it again after this hint, is, try to draw some triangles that maybe split up this angle into a couple of different angles and that might be a little bit easier You might be able to use some of what we know about triangles
So the trick is to realize that this is a circle and so any any line that goes between B and any point on this arc is going to be equal to the radius of the circle So AB is equal to the radius of the circle
BE is equal to the radius of the circle And we can keep drawing other things that are equal to the radius of the circle
BC is equal to the radius of the circle
So let me draw segment EC and draw that as straight as possible I can draw a better job of that So the segment EC
And then BG is equal to GC And they both have 90 degree angles They have 90 degree angle here and they have 90 degree angle there
ECG by side angle side congruency, by side angel side congruency
And that also tells that all of the corresponding angles and sides are going to be the same
So, that tells us, that tells us right there that EC that EC is equal to EB, EC is equal to EB So we know that EB, EB is equal to EC, and what is what also is equal to that length?
BE, is one radius of the circle going from the center to the arc But so is BC It is also a radius of the circle going from the center to the arc
BEC is part of the angle BED If we can just figure out the measure of angle CED now, if we can figure out this angle right over here, we just add that to 60 degrees and we're done We figured out the entire the entire BED
We know that this right over here is equal to the radius of the circle And we also know that this length down here, this is a square We know that this length down here is the same as this length up here
BC is the same as that length, is the same as that length, so all 4 sides are gonna be the same as that length because this is a square So let me write, let me write this down Because because it's a square, I'll just write it this way
Because it's a square, we know that CD, we know that cd is equal to BC which is equal to, and we already established this as equal to CEC which is equal to EB, which is equal to EC What's important here is to realize that this and this are the same length And the reason why that is interesting is it let's us know that this is an isosceles triangle
Well we know all the angles of these things off up, we can figure out all the angles of the larger ones up here We know that this is an equilateral triangle So this over here has to be 60 degrees as well
So this is 60 degrees, we know we are dealing with a square So this whole angle over here is a right angle What is the measure of angle ECD?
This angle over here is gonna have to be 30 degrees So that is going to be 30 degrees And now, we are ready to solve
If we call this x, if you call this x, and we know they have to be the same, we have x + x + 30 degrees, x + x + 30 degrees is going to be equal to 180 degrees That is the sum of all the interior angles of a triangle So you get 2x, 2x + 30, + 30 is equal to 180 degrees
This is going to be equal to 75 degrees + 60 degrees which is equal to 135 degrees And we are done
CHAPTER I.
One morning, as Gregor Samsa was waking up from anxious dreams, he discovered that in bed he had been changed into a monstrous verminous bug.
He lay on his armour-hard back and saw, as he lifted his head up a little, his brown, arched abdomen divided up into rigid bow- like sections.
From this height the blanket, just about ready to slide off completely, could hardly stay in place.
His numerous legs, pitifully thin in comparison to the rest of his circumference, flickered helplessly before his eyes.
"What's happened to me," he thought.
It was no dream.
His room, a proper room for a human being, only somewhat too small, lay quietly between the four well-known walls.
Above the table, on which an unpacked collection of sample cloth goods was spread out--Samsa was a travelling salesman--hung the picture which he had cut out of an illustrated magazine a little while ago and set in a pretty gilt frame.
It was a picture of a woman with a fur hat and a fur boa.
She sat erect there, lifting up in the direction of the viewer a solid fur muff into which her entire forearm had disappeared.
Gregor's glance then turned to the window.
The dreary weather--the rain drops were falling audibly down on the metal window
ledge--made him quite melancholy.
"Why don't I keep sleeping for a little while longer and forget all this foolishness," he thought.
But this was entirely impractical, for he was used to sleeping on his right side, and in his present state he couldn't get himself into this position.
No matter how hard he threw himself onto his right side, he always rolled again onto his back.
He must have tried it a hundred times, closing his eyes so that he would not have to see the wriggling legs, and gave up only when he began to feel a light, dull pain in his side which he had never felt before.
"O God," he thought, "what a demanding job I've chosen!
Day in, day out, on the road.
The stresses of selling are much greater than the work going on at head office, and, in addition to that, I have to cope with the problems of travelling, the worries about train connections, irregular bad food, temporary and constantly changing human relationships, which never come from the heart.
To hell with it all!"
He felt a slight itching on the top of his abdomen.
He slowly pushed himself on his back closer to the bed post so that he could lift his head more easily, found the itchy part, which was entirely covered with small white spots--he did not know what to make of them and wanted to feel the place with a leg.
But he retracted it immediately, for the contact felt like a cold shower all over him.
He slid back again into his earlier position.
"This getting up early," he thought, "makes a man quite idiotic.
A man must have his sleep.
Other travelling salesmen live like harem women.
For instance, when I come back to the inn during the course of the morning to write up the necessary orders, these gentlemen are just sitting down to breakfast.
If I were to try that with my boss, I'd be thrown out on the spot.
Still, who knows whether that mightn't be really good for me?
If I didn't hold back for my parents' sake, I'd have quit ages ago.
I would've gone to the boss and told him just what I think from the bottom of my heart.
He would've fallen right off his desk!
How weird it is to sit up at that desk and talk down to the employee from way up there.
The boss has trouble hearing, so the employee has to step up quite close to him.
Anyway, I haven't completely given up that hope yet.
Once I've got together the money to pay off my parents' debt to him--that should take another five or six years--I'll do it for sure.
Then I'll make the big break.
In any case, right now I have to get up.
My train leaves at five o'clock."
He looked over at the alarm clock ticking away by the chest of drawers.
"Good God!" he thought.
It was half past six, and the hands were going quietly on.
It was past the half hour, already nearly quarter to.
Could the alarm have failed to ring?
One saw from the bed that it was properly set for four o'clock.
Certainly it had rung.
Yes, but was it possible to sleep through that noise which made the furniture shake?
Now, it's true he'd not slept quietly, but evidently he'd slept all the more deeply.
Still, what should he do now?
The next train left at seven o'clock.
To catch that one, he would have to go in a mad rush.
The sample collection wasn't packed up yet, and he really didn't feel particularly fresh and active.
And even if he caught the train, there was no avoiding a blow-up with the boss, because the firm's errand boy would've waited for the five o'clock train and reported the news of his absence long ago.
He was the boss's minion, without backbone or intelligence.
Well then, what if he reported in sick?
But that would be extremely embarrassing and suspicious, because during his five years' service Gregor hadn't been sick even once.
The boss would certainly come with the doctor from the health insurance company and would reproach his parents for their lazy son and cut short all objections with the insurance doctor's comments; for him everyone was completely healthy but really lazy about work.
And besides, would the doctor in this case be totally wrong?
Apart from a really excessive drowsiness after the long sleep, Gregor in fact felt quite well and even had a really strong appetite.
As he was thinking all this over in the greatest haste, without being able to make the decision to get out of bed--the alarm clock was indicating exactly quarter to seven--there was a cautious knock on the door by the head of the bed.
"Gregor," a voice called--it was his mother!--"it's quarter to seven.
Don't you want to be on your way?"
The soft voice! Gregor was startled when he heard his voice answering.
It was clearly and unmistakably his earlier voice, but in it was intermingled, as if from below, an irrepressibly painful squeaking, which left the words positively distinct only in the first moment and distorted them in the reverberation, so that one didn't know if one had heard correctly.
Gregor wanted to answer in detail and explain everything, but in these circumstances he confined himself to saying, "Yes, yes, thank you mother.
I'm getting up right away."
Because of the wooden door the change in Gregor's voice was not really noticeable outside, so his mother calmed down with this explanation and shuffled off.
However, as a result of the short conversation, the other family members became aware that Gregor was unexpectedly still at home, and already his father was knocking on one side door, weakly but with his fist.
"Gregor, Gregor," he called out, "what's going on?"
And, after a short while, he urged him on again in a deeper voice:
"Gregor!" Gregor!" At the other side door, however, his sister knocked lightly.
"Gregor?
Are you all right?
Do you need anything?" Gregor directed answers in both directions,
"I'll be ready right away."
He made an effort with the most careful articulation and by inserting long pauses between the individual words to remove everything remarkable from his voice.
His father turned back to his breakfast.
However, the sister whispered, "Gregor, open the door--I beg you."
Gregor had no intention of opening the door, but congratulated himself on his precaution, acquired from travelling, of locking all doors during the night, even at home.
First he wanted to stand up quietly and undisturbed, get dressed, above all have breakfast, and only then consider further action, for--he noticed this clearly--by thinking things over in bed he would not reach a reasonable conclusion.
He remembered that he had already often felt a light pain or other in bed, perhaps the result of an awkward lying position, which later turned out to be purely imaginary when he stood up, and he was eager to see how his present fantasies would gradually dissipate.
That the change in his voice was nothing other than the onset of a real chill, an occupational illness of commercial travellers, of that he had not the slightest doubt.
It was very easy to throw aside the blanket.
He needed only to push himself up a little, and it fell by itself.
But to continue was difficult, particularly because he was so unusually wide.
He needed arms and hands to push himself upright.
Instead of these, however, he had only many small limbs which were incessantly moving with very different motions and which, in addition, he was unable to control.
If he wanted to bend one of them, then it was the first to extend itself, and if he finally succeeded doing what he wanted with this limb, in the meantime all the others, as if left free, moved around in an excessively painful agitation.
"But I must not stay in bed uselessly," said Gregor to himself.
At first he wanted to get out of bed with the lower part of his body, but this lower part--which, by the way, he had not yet looked at and which he also couldn't picture clearly--proved itself too difficult to move.
The attempt went so slowly.
When, having become almost frantic, he finally hurled himself forward with all his force and without thinking, he chose his direction incorrectly, and he hit the lower bedpost hard.
The violent pain he felt revealed to him that the lower part of his body was at the moment probably the most sensitive.
Thus, he tried to get his upper body out of the bed first and turned his head carefully toward the edge of the bed.
He managed to do this easily, and in spite of its width and weight his body mass at last slowly followed the turning of his head.
But as he finally raised his head outside the bed in the open air, he became anxious about moving forward any further in this manner, for if he allowed himself eventually to fall by this process, it would take a miracle to prevent his head from getting injured.
And at all costs he must not lose consciousness right now.
He preferred to remain in bed.
However, after a similar effort, while he lay there again, sighing as before, and once again saw his small limbs fighting one another, if anything worse than earlier, and didn't see any chance of imposing quiet and order on this arbitrary movement, he told himself again that he couldn't possibly remain in bed and that it might be the most reasonable thing to sacrifice everything if there was even the slightest hope of getting himself out of bed in the process.
At the same moment, however, he didn't forget to remind himself from time to time of the fact that calm--indeed the calmest-- reflection might be better than the most confused decisions.
At such moments, he directed his gaze as precisely as he could toward the window, but unfortunately there was little confident cheer to be had from a glance at the morning mist, which concealed even the other side of the narrow street.
"It's already seven o'clock," he told himself at the latest striking of the alarm clock, "already seven o'clock and still such a fog."
And for a little while longer he lay quietly with weak breathing, as if perhaps waiting for normal and natural conditions to re-emerge out of the complete stillness.
But then he said to himself, "Before it strikes a quarter past seven, whatever happens I must be completely out of bed.
Besides, by then someone from the office will arrive to inquire about me, because the office will open before seven o'clock."
And he made an effort then to rock his entire body length out of the bed with a uniform motion.
If he let himself fall out of the bed in this way, his head, which in the course of the fall he intended to lift up sharply, would probably remain uninjured.
His back seemed to be hard; nothing would really happen to that as a result of the fall.
His greatest reservation was a worry about the loud noise which the fall must create and which presumably would arouse, if not fright, then at least concern on the other side of all the doors.
However, it had to be tried.
As Gregor was in the process of lifting himself half out of bed--the new method was more of a game than an effort; he needed only to rock with a constant rhythm--it struck him how easy all this would be if someone were to come to his aid.
Two strong people--he thought of his father and the servant girl--would have been quite sufficient.
They would have only had to push their arms under his arched back to get him out of the bed, to bend down with their load, and then merely to exercise patience and care that he completed the flip onto the floor, where his diminutive legs would then, he hoped, acquire a purpose.
Now, quite apart from the fact that the doors were locked, should he really call out for help?
In spite of all his distress, he was unable to suppress a smile at this idea.
He had already got to the point where, by rocking more strongly, he maintained his equilibrium with difficulty, and very soon he would finally have to decide, for in five minutes it would be a quarter past seven.
Then there was a ring at the door of the apartment.
"That's someone from the office," he told himself, and he almost froze while his small limbs only danced around all the faster.
For one moment everything remained still.
"They aren't opening," Gregor said to himself, caught up in some absurd hope.
But of course then, as usual, the servant girl with her firm tread went to the door and opened it.
Gregor needed to hear only the first word of the visitor's greeting to recognize immediately who it was, the manager himself.
Why was Gregor the only one condemned to work in a firm where, at the slightest
lapse, someone immediately attracted the greatest suspicion?
Were all the employees then collectively, one and all, scoundrels?
Among them was there then no truly devoted person who, if he failed to use just a couple of hours in the morning for office work, would become abnormal from pangs of conscience and really be in no state to get out of bed?
Was it really not enough to let an apprentice make inquiries, if such questioning was even necessary?
Must the manager himself come, and in the process must it be demonstrated to the entire innocent family that the investigation of this suspicious circumstance could be entrusted only to the intelligence of the manager?
And more as a consequence of the excited state in which this idea put Gregor than as a result of an actual decision, he swung himself with all his might out of the bed.
There was a loud thud, but not a real crash.
The fall was absorbed somewhat by the carpet and, in addition, his back was more elastic than Gregor had thought.
For that reason the dull noise was not quite so conspicuous.
But he had not held his head up with sufficient care and had hit it.
He turned his head, irritated and in pain, and rubbed it on the carpet.
"Something has fallen in there," said the manager in the next room on the left.
Gregor tried to imagine to himself whether anything similar to what was happening to him today could have also happened at some point to the manager.
At least one had to concede the possibility of such a thing.
However, as if to give a rough answer to this question, the manager now, with a squeak of his polished boots, took a few determined steps in the next room.
From the neighbouring room on the right the sister was whispering to inform Gregor:
"Gregor, the manager is here." "I know," said Gregor to himself.
But he did not dare make his voice loud enough so that his sister could hear.
"Gregor," his father now said from the neighbouring room on the left, "Mr. Manager has come and is asking why you have not left on the early train.
We don't know what we should tell him.
Besides, he also wants to speak to you personally.
He will be good enough to forgive the mess in your room."
In the middle of all this, the manager called out in a friendly way, "Good morning, Mr. Samsa."
"He is not well," said his mother to the manager, while his father was still talking at the door, "He is not well, believe me, Mr. Manager.
Otherwise how would Gregor miss a train?
The young man has nothing in his head except business.
I'm almost angry that he never goes out at night.
Right now he's been in the city eight days, but he's been at home every evening.
He sits here with us at the table and reads the newspaper quietly or studies his travel schedules.
It's a quite a diversion for him to busy himself with fretwork.
For instance, he cut out a small frame over the course of two or three evenings.
You'd be amazed how pretty it is.
It's hanging right inside the room.
You'll see it immediately, as soon as
Gregor opens the door.
Anyway, I'm happy that you're here, Mr.
Manager.
By ourselves, we would never have made Gregor open the door.
He's so stubborn, and he's certainly not well, although he denied that this morning."
"I'm coming right away," said Gregor slowly and deliberately and didn't move, so as not to lose one word of the conversation.
"My dear lady, I cannot explain it to myself in any other way," said the manager;
"I hope it is nothing serious.
On the other hand, I must also say that we business people, luckily or unluckily, however one looks at it, very often simply have to overcome a slight indisposition for business reasons."
"So can Mr. Manager come in to see you now?" asked his father impatiently and knocked once again on the door.
In the neighbouring room on the left a painful stillness descended.
In the neighbouring room on the right the sister began to sob.
Why didn't his sister go to the others?
She'd probably just gotten up out of bed now and hadn't even started to get dressed yet.
Then why was she crying?
Because he wasn't getting up and wasn't letting the manager in, because he was in danger of losing his position, and because then his boss would badger his parents once again with the old demands?
Those were probably unnecessary worries right now.
Gregor was still here and wasn't thinking at all about abandoning his family.
At the moment he was lying right there on the carpet, and no one who knew about his condition would've seriously demanded that he let the manager in.
But Gregor wouldn't be casually dismissed right way because of this small discourtesy, for which he would find an easy and suitable excuse later on.
It seemed to Gregor that it might be far more reasonable to leave him in peace at the moment, instead of disturbing him with crying and conversation.
But it was the very uncertainty which distressed the others and excused their behaviour.
"Mr. Samsa," the manager was now shouting, his voice raised, "what's the matter?
You are barricading yourself in your room, answer with only a yes and a no, are making serious and unnecessary troubles for your parents, and neglecting (I mention this only incidentally) your commercial duties in a truly unheard of manner.
I am speaking here in the name of your parents and your employer, and I am requesting you in all seriousness for an immediate and clear explanation.
I am amazed.
I am amazed.
I thought I knew you as a calm, reasonable person, and now you appear suddenly to want to start parading around in weird moods.
The Chief indicated to me earlier this very day a possible explanation for your neglect--it concerned the collection of cash entrusted to you a short while ago-- but in truth I almost gave him my word of honour that this explanation could not be correct.
However, now I see here your unimaginable pig headedness, and I am totally losing any desire to speak up for you in the slightest.
And your position is not at all the most secure.
Originally I intended to mention all this to you privately, but since you are letting me waste my time here uselessly, I don't know why the matter shouldn't come to the attention of your parents.
Your productivity has also been very unsatisfactory recently.
Of course, it's not the time of year to conduct exceptional business, we recognize that, but a time of year for conducting no business, there is no such thing at all,
Mr. Samsa, and such a thing must never be."
"But Mr. Manager," called Gregor, beside himself and, in his agitation, forgetting everything else, "I'm opening the door immediately, this very moment.
A slight indisposition, a dizzy spell, has prevented me from getting up.
I'm still lying in bed right now.
But I'm quite refreshed once again.
I'm in the midst of getting out of bed.
Just have patience for a short moment!
Things are not going as well as I thought.
But things are all right.
How suddenly this can overcome someone!
Only yesterday evening everything was fine with me.
My parents certainly know that. Actually just yesterday evening I had a small premonition.
People must have seen that in me.
Why have I not reported that to the office?
But people always think that they'll get over sickness without having to stay at home.
Mr. Manager!
Take it easy on my parents!
There is really no basis for the criticisms which you're now making against me, and really nobody has said a word to me about that.
Perhaps you have not read the latest orders which I shipped.
Besides, now I'm setting out on my trip on the eight o'clock train; the few hours' rest have made me stronger.
Mr. Manager, do not stay.
I will be at the office in person right away.
Please have the goodness to say that and to convey my respects to the Chief."
While Gregor was quickly blurting all this out, hardly aware of what he was saying, he had moved close to the chest of drawers without effort, probably as a result of the practice he had already had in bed, and now he was trying to raise himself up on it.
Actually, he wanted to open the door.
He really wanted to let himself be seen by and to speak with the manager.
He was keen to witness what the others now asking about him would say when they saw him.
If they were startled, then Gregor had no more responsibility and could be calm.
But if they accepted everything quietly, then he would have no reason to get excited and, if he got a move on, could really be at the station around eight o'clock.
At first he slid down a few times on the smooth chest of drawers.
But at last he gave himself a final swing and stood upright there.
He was no longer at all aware of the pains in his lower body, no matter how they might still sting.
Now he let himself fall against the back of a nearby chair, on the edge of which he braced himself with his thin limbs.
By doing this he gained control over himself and kept quiet, for he could now hear the manager.
"Did you understood a single word?" the manager asked the parents, "Is he playing the fool with us?"
"For God's sake," cried the mother already in tears, "perhaps he's very ill and we're upsetting him.
Grete!
Grete!" she yelled at that point.
"Mother?" called the sister from the other side.
They were making themselves understood through Gregor's room.
"You must go to the doctor right away.
Gregor is sick.
Hurry to the doctor.
Have you heard Gregor speak yet?"
"That was an animal's voice," said the manager, remarkably quietly in comparison to the mother's cries.
"Anna!
Anna!' yelled the father through the hall into the kitchen, clapping his hands,
"fetch a locksmith right away!"
The two young women were already running through the hall with swishing skirts--how had his sister dressed herself so quickly?- -and yanked open the doors of the apartment.
One couldn't hear the doors closing at all. They probably had left them open, as is customary in an apartment where a huge misfortune has taken place.
However, Gregor had become much calmer.
All right, people did not understand his words any more, although they seemed clear enough to him, clearer than previously, perhaps because his ears had gotten used to them.
But at least people now thought that things were not all right with him and were prepared to help him.
The confidence and assurance with which the first arrangements had been carried out made him feel good.
He felt himself included once again in the circle of humanity and was expecting from both the doctor and the locksmith, without differentiating between them with any real precision, splendid and surprising results.
In order to get as clear a voice as possible for the critical conversation which was imminent, he coughed a little, and certainly took the trouble to do this in a really subdued way, since it was possible that even this noise sounded like something different from a human cough.
He no longer trusted himself to decide any more.
Meanwhile in the next room it had become really quiet.
Perhaps his parents were sitting with the manager at the table whispering; perhaps they were all leaning against the door listening.
Gregor pushed himself slowly towards the door, with the help of the easy chair, let go of it there, threw himself against the door, held himself upright against it--the balls of his tiny limbs had a little sticky stuff on them--and rested there momentarily from his exertion.
Then he made an effort to turn the key in the lock with his mouth.
Unfortunately it seemed that he had no real teeth.
How then was he to grab hold of the key?
But to make up for that his jaws were naturally very strong; with their help he managed to get the key really moving.
He didn't notice that he was obviously inflicting some damage on himself, for a brown fluid came out of his mouth, flowed over the key, and dripped onto the floor.
"Just listen for a moment," said the manager in the next room; "he's turning the key." For Gregor that was a great encouragement.
But they all should've called out to him, including his father and mother, "Come on,
Gregor," they should've shouted; "keep going, keep working on the lock."
Imagining that all his efforts were being followed with suspense, he bit down frantically on the key with all the force he could muster.
As the key turned more, he danced around the lock.
Now he was holding himself upright only with his mouth, and he had to hang onto the key or then press it down again with the whole weight of his body, as necessary.
The quite distinct click of the lock as it finally snapped really woke Gregor up.
Breathing heavily he said to himself, "So I didn't need the locksmith," and he set his head against the door handle to open the door completely.
Because he had to open the door in this way, it was already open very wide without him yet being really visible.
He first had to turn himself slowly around the edge of the door, very carefully, of course, if he didn't want to fall awkwardly on his back right at the entrance into the room.
He was still preoccupied with this difficult movement and had no time to pay attention to anything else, when he heard the manager exclaim a loud "Oh!"--it sounded like the wind whistling--and now he saw him, nearest to the door, pressing his hand against his open mouth and moving slowly back, as if an invisible constant force was pushing him away.
His mother--in spite of the presence of the manager she was standing here with her hair sticking up on end, still a mess from the night--was looking at his father with her hands clasped.
She then went two steps towards Gregor and collapsed right in the middle of her skirts, which were spread out all around her, her face sunk on her breast, completely concealed.
His father clenched his fist with a hostile expression, as if he wished to push Gregor back into his room, then looked uncertainly around the living room, covered his eyes with his hands, and cried so that his mighty breast shook.
At this point Gregor did not take one step into the room, but leaned his body from the inside against the firmly bolted wing of the door, so that only half his body was visible, as well as his head, tilted sideways, with which he peeped over at the others.
Meanwhile it had become much brighter.
Standing out clearly from the other side of the street was a part of the endless grey- black house situated opposite--it was a hospital--with its severe regular windows breaking up the facade.
The rain was still coming down, but only in large individual drops visibly and firmly thrown down one by one onto the ground.
The breakfast dishes were standing piled around on the table, because for his father breakfast was the most important meal time in the day, which he prolonged for hours by reading various newspapers.
Directly across on the opposite wall hung a photograph of Gregor from the time of his military service; it was a picture of him as a lieutenant, as he, smiling and worry free, with his hand on his sword, demanded respect for his bearing and uniform.
The door to the hall was ajar, and since the door to the apartment was also open, one could see out into the landing of the apartment and the start of the staircase going down.
"Now," said Gregor, well aware that he was the only one who had kept his composure.
"I'll get dressed right away, pack up the collection of samples, and set off.
You'll allow me to set out on my way, will you not?
You see, Mr. Manager, I am not pig-headed, and I am happy to work.
Travelling is exhausting, but I couldn't live without it.
Where are you going, Mr. Manager?
To the office?
Really?
Will you report everything truthfully?
A person can be incapable of work momentarily, but that's precisely the best time to remember the earlier achievements and to consider that later, after the obstacles have been shoved aside, the person will work all the more eagerly and intensely.
I am really so indebted to Mr. Chief--you know that perfectly well.
On the other hand, I am concerned about my parents and my sister.
I'm in a fix, but I'll work myself out of it again.
Don't make things more difficult for me than they already are.
Speak up on my behalf in the office!
People don't like travelling salesmen.
I know that.
People think they earn pots of money and thus lead a fine life.
People don't even have any special reason to think through this judgment more clearly.
But you, Mr. Manager, you have a better perspective on what's involved than other people, even, I tell you in total confidence, a better perspective than Mr.
Chairman himself, who in his capacity as the employer may let his judgment make casual mistakes at the expense of an employee.
You also know well enough that the travelling salesman who is outside the office almost the entire year can become so easily a victim of gossip, coincidences, and groundless complaints, against which it's impossible for him to defend himself, since for the most part he doesn't hear about them at all and only then when he's exhausted after finishing a trip and at home gets to feel in his own body the nasty consequences, which can't be thoroughly explored back to their origins.
Mr. Manager, don't leave without speaking a word telling me that you'll at least concede that I'm a little in the right!"
But at Gregor's first words the manager had already turned away, and now he looked back at Gregor over his twitching shoulders with pursed lips.
During Gregor's speech he was not still for a moment but kept moving away towards the door, without taking his eyes off Gregor, but really gradually, as if there was a secret ban on leaving the room.
He was already in the hall, and given the sudden movement with which he finally pulled his foot out of the living room, one could have believed that he had just burned the sole of his foot.
In the hall, however, he stretched his right hand out away from his body towards the staircase, as if some truly supernatural relief was waiting for him there.
Gregor realized that he must not under any circumstances allow the manager to go away in this frame of mind, especially if his position in the firm was not to be placed in the greatest danger.
His parents did not understand all this very well.
Over the long years, they had developed the conviction that Gregor was set up for life in his firm and, in addition, they had so much to do nowadays with their present troubles that all foresight was foreign to them.
But Gregor had this foresight.
The manager must be held back, calmed down, convinced, and finally won over.
The future of Gregor and his family really depended on it!
If only the sister had been there!
She was clever.
She had already cried while Gregor was still lying quietly on his back.
And the manager, this friend of the ladies, would certainly let himself be guided by her.
She would have closed the door to the apartment and talked him out of his fright in the hall.
But the sister was not even there.
Gregor must deal with it himself.
Without thinking that as yet he didn't know anything about his present ability to move and that his speech possibly--indeed probably--had once again not been understood, he left the wing of the door, pushed himself through the opening, and wanted to go over to the manager, who was already holding tight onto the handrail with both hands on the landing in a ridiculous way.
But as he looked for something to hold onto, with a small scream Gregor immediately fell down onto his numerous little legs.
Scarcely had this happened, when he felt for the first time that morning a general physical well being.
The small limbs had firm floor under them; they obeyed perfectly, as he noticed to his joy, and strove to carry him forward in the direction he wanted.
Right away he believed that the final amelioration of all his suffering was immediately at hand.
But at the very moment when he lay on the floor rocking in a restrained manner quite close and directly across from his mother, who had apparently totally sunk into herself, she suddenly sprang right up with her arms spread far apart and her fingers extended and cried out, "Help, for God's sake, help!"
She held her head bowed down, as if she wanted to view Gregor better, but ran senselessly back, contradicting that gesture, forgetting that behind her stood the table with all the dishes on it.
When she reached the table, she sat down heavily on it, as if absent-mindedly, and did not appear to notice at all that next to her coffee was pouring out onto the carpet in a full stream from the large overturned container.
"Mother, mother," said Gregor quietly, and looked over towards her.
The manager momentarily had disappeared completely from his mind.
At the sight of the flowing coffee Gregor couldn't stop himself snapping his jaws in the air a few times .
At that his mother screamed all over again, hurried from the table, and collapsed into the arms of his father, who was rushing towards her.
But Gregor had no time right now for his parents--the manager was already on the staircase.
His chin level with the banister, the manager looked back for the last time.
Gregor took an initial movement to catch up to him if possible.
But the manager must have suspected something, because he made a leap down over a few stairs and disappeared, still shouting "Huh!"
The sound echoed throughout the entire stairwell.
Now, unfortunately this flight of the manager also seemed to bewilder his father completely.
Earlier he had been relatively calm, for instead of running after the manager himself or at least not hindering Gregor from his pursuit, with his right hand he grabbed hold of the manager's cane, which he had left behind with his hat and overcoat on a chair.
With his left hand, his father picked up a large newspaper from the table and, stamping his feet on the floor, he set out to drive Gregor back into his room by waving the cane and the newspaper.
No request of Gregor's was of any use; no request would even be understood.
No matter how willing he was to turn his head respectfully, his father just stomped all the harder with his feet.
Across the room from him his mother had pulled open a window, in spite of the cool weather, and leaning out with her hands on her cheeks, she pushed her face far outside the window.
Between the alley and the stairwell a strong draught came up, the curtains on the window flew around, the newspapers on the table swished, and individual sheets fluttered down over the floor.
The father relentlessly pressed forward, pushing out sibilants, like a wild man.
Now, Gregor had no practice at all in going backwards--it was really very slow going.
If Gregor only had been allowed to turn himself around, he would have been in his room right away, but he was afraid to make his father impatient by the time-consuming process of turning around, and each moment he faced the threat of a mortal blow on his back or his head from the cane in his father's hand.
Finally Gregor had no other option, for he noticed with horror that he did not understand yet how to maintain his direction going backwards.
And so he began, amid constantly anxious sideways glances in his father's direction, to turn himself around as quickly as possible, although in truth this was only done very slowly.
Perhaps his father noticed his good intentions, for he did not disrupt Gregor in this motion, but with the tip of the cane from a distance he even directed
Gregor's rotating movement here and there.
If only his father had not hissed so unbearably!
Because of that Gregor totally lost his head.
He was already almost totally turned around, when, always with this hissing in his ear, he just made a mistake and turned himself back a little.
But when he finally was successful in getting his head in front of the door opening, it became clear that his body was too wide to go through any further.
Naturally his father, in his present mental state, had no idea of opening the other wing of the door a bit to create a suitable passage for Gregor to get through.
His single fixed thought was that Gregor must get into his room as quickly as possible.
He would never have allowed the elaborate preparations that Gregor required to orient himself and thus perhaps get through the door.
On the contrary, as if there were no obstacle and with a peculiar noise, he now drove Gregor forwards.
Behind Gregor the sound at this point was no longer like the voice of only a single father.
Now it was really no longer a joke, and Gregor forced himself, come what might, into the door.
One side of his body was lifted up.
He lay at an angle in the door opening.
His one flank was sore with the scraping.
On the white door ugly blotches were left.
Soon he was stuck fast and would have not been able to move any more on his own.
The tiny legs on one side hung twitching in the air above, and the ones on the other side were pushed painfully into the floor.
Then his father gave him one really strong liberating push from behind, and he scurried, bleeding severely, far into the interior of his room.
The door was slammed shut with the cane, and finally it was quiet.
Let's do a couple of problems graphing linear equations.
They are a bunch of ways to graph linear equations.
What we'll do in this video is the most basic way.
Where we will just plot a bunch of values and then connect the dots.
I think you'll see what I'm saying.
So here I have an equation, a linear equation.
I'll rewrite it just in case that was too small. y is equal to 2x plus 7.
I want to graph this linear equation.
Before I even take out the graph paper, what I could do is set up a table.
Where I pick a bunch of x values and then I can figure out what y value would correspond to each of those x values.
So for example, if x is equal to-- let me start really low-- if x is equal to minus 2-- or negative 2, I should say-- what is y?
Well, you substitute negative 2 up here.
It would be 2 times negative 2 plus 7.
This is negative 4 plus 7.
This is equal to 3.
If x is equal to-- I'm just picking x values at random that might be indicative of-- I'll probably do three or four points here.
So what happens when x is equal to 0?
Then y is going to be equal to 2 times 0 plus 7.
I just happen to be going up by 2.
You could be going up by 1 or you could be picking numbers at random.
When x is equal to 2, what is y?
It'll be 2 times 2 plus 7.
So 4 plus 7 is equal to 11.
I could keep plotting points if I like.
We should already have enough to graph it.
Actually to plot any line, you actually only need two points.
So we already have one more than necessary.
Actually, let me just do one more just to show you that this really is a line.
So what happens when x is equal to 4?
Actually, just to not go up by 2, let's do x is equal to 8.
Just to pick a random number.
Then y is going to be 2 times 8 plus 7, which is-- well this might go off of our graph paper-- but 2 times 8 is 16 plus 7 is equal to 23.
Now let's graph it.
Let me do my y-axis right there.
That is my y-axis.
Let me do my x-axis.
I have a lot of positive values here, so a lot of space on the positive y-side.
That is my x-axis.
And then I use the points x is equal to negative 2.
That's negative 1.
That's 0, 1, 2, 3, 4, 5, 6, 7, 8.
Those are our x values.
Then we can go up into the y-axis.
I'll do it at a slightly different scale because these numbers get large very quickly.
So maybe I'll do it in increments of 2.
So this could be 2, 4, 6, 8, 10, 12, 14, 16.
I could just keep going up there, but let's plot these points.
So the first coordinate I have is x is equal to negative 2, y is equal to 3.
So I can write my coordinate.
It's going to be the point negative 2, 3. x is negative 2. y is 3.
3 would land right over there.
So that's our first one, negative 2, 3.
Then our next point.
0, 7.
We do it in that color.
0, 7. x is 0. Y is 7. Right there.
0, 7.
We have this one in green here.
Point 2, 11.
2, 11 would be right about there.
And then this last point-- this is actually going to fall off of my graph.
8, 23.
That's going to be way up here someplace.
If you can even see what I'm doing.
This is 8, 23.
If we connect the dots, you'll see a line forms.
Let me connect these dots.
I've obviously hand drawn it, so it might not be a perfectly straight line.
If you had a computer do it, it would be a straight line.
So you could keep picking x values and figuring out the corresponding y values.
In the situation y is a function of our x values.
If you kept plotting every point, you'll get every line.
If you picked every possible x and plotted every one, you get every point on the line.
Let's do another problem.
At the airport, you can change your money from dollars into Euros.
The service costs $5. and for every additional dollar, you get EUR 0.7.
Use your graph to determine how many Euros you would get if you give the office $50.
I will write Euros is equal to-- so let's see, it's going to be dollars.
So you're going to have to give your dollars.
Right off of the bat, they're going to take $5.
So dollars minus 5.
So immediately this service costs $5.
And then everything that's leftover-- this is your
leftover-- you get EUR 0.7 for every leftover dollars.
You get 0.7 for whatever's leftover.
So this is the relationship.
Now we can plot points-- we could actually answer their question right off the bat.
If you give them $50, we don't even have to look at a graph.
But we will look at a graph right after this.
So if you did Euros is equal to-- if you have given them $50-- it would be 0.7 times 50 minus 5.
You gave them 50.
They took 5 as a service fee.
So this is just $45 It would be 0.7 times 45.
I could do that right here.
45 times 0.7. 7 times 5 is 35. 4 times 7 is 28 plus 3 is 31.
And then we have only one number behind the decimal, only this 7.
So it's 31.5.
So if you give them $50, you're going to get EUR 31.5.
Euros, not dollars.
So we answered their question, but let's actually do it graphically.
Let's do a table.
Maybe I'll get a calculator out.
I'll refer to that in a little bit.
So let's say dollars you give them.
And how many Euros do you get?
I'll just put a bunch of random numbers.
If you give them $5, they're just going to take your $5 for the fee.
You're going to get $5 minus 5, which is 0 times 0.7.
So you're going to get nothing back.
So there's really no good reason for you to do that.
Then if you give them $10.
What's going to happen?
If you give them $10, 10 minus 5 is 5 times 0.7.
You're going to get $3-- or I should say EUR 3.50. 3.5 Euros, you'll get.
Now what happens if you give them $30?
Actually let me say 25.
If you give him $25, 25 minus 5 is 20. 20 times 0.7 is $14.
I'll do one more value.
Let's say you gave them $55.
This makes the math easy because then you subtract that 5 out.
55 minus 5 is 50 times 0.7 is $35.
Is that right?
Yep, that's right.
You'll get EUR 35 I should say.
These are all Euros.
I keep wanting to say dollars.
Let's plot this.
All of these values are positive, so I only have to draw the first quadrant here.
And so the dollars-- let's go in increments of 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55.
I made my x-axis a little shorter than I needed to.
All the way up to 55.
And then the y-axis.
I'll go in increments of 5.
So that's 5, 10, 15, 20, 25, 30, 35.
Well that's a little bit too much of an increment.
35.
Now let's plot these points.
I give them $5.
I get EUR 0.
This right here is Euros.
This is the dollars.
The dollars is the independent variable and we figure out the
Euros from it.
Or the Euros I get is dependent on the dollars I get.
If I give $10, I get EUR 3.50. 3.50-- it's hard to read.
Maybe 3.50 would be right around there.
If I give $25, I get EUR 14. 25, 14 is right about there.
Obviously, I'm hand drawing it, so it's not going to be quite exact.
If I get $55, I get EUR 35.
So 55, 35 right there.
If I were to connect to the dots, I should get something that looks pretty close to a line.
If I did it-- if I was a computer, it would be exactly a line.
That looks pretty good.
Then we could eyeball what they asked us to do.
Use your graph to determine how many Euros you would get if you give the office $50.
This is 50 right here.
So you go bam, bam, bam, bam, bam, bam, bam, bam.
I'm at the graph.
Then you go all the way-- actually I drew that last point on the graph a little bit incorrectly.
Let me.
Let me redraw that point.
35 is right there roughly.
So 55, 35 is right there.
So let me redraw my line.
It will look-- I lost 25.
25, 14 is right there.
So my graph looks something like that.
That's my best attempt.
Now let's answer the question.
We give them $50 right there.
You go up, up, up, up, up, up, up. $50.
The person is going to get.
You go all the way to the left-hand side.
That's right about 31.50.
We figured out exactly using the formula.
But you can see, you can eyeball it from the graph and figure out any amount of dollars.
If you give them $20, you're going to go all the way over here.
You'll figure out that it should be-- well $20 should be about 7.50. The imprecision in my graph-- in my drawing the graph makes it a little bit less exact.
When you say 20 minus 5 is 15. 15 times-- actually it'll be a little over $10, which is right.
It's right over there.
If you put $20 in there, 20 minus 5 is 15. 15 times 0.7 is $10.50, which is right there.
So you can look at any point in the graph and figure out how many Euros you'll get.
Let's do this one where we'll do a little bit of reading a graph.
The graph-- I think it said use the graph below.
Oh, the graph below shows a conversion chart for converting between weight in kilograms and weight in pounds.
Use it to convert the following measurements.
We have kilograms here and pounds here.
So they want 4 kilograms into weight into pounds.
So if we look at this right here, 4 kilograms is right there.
We just follow where the graph is.
So 4 kilograms into pounds, it looks like, I don't know, a little bit under 9 pounds.
So a little bit less than-- so almost, I'll write almost 9 pounds.
You can't exactly see.
It's a little less than 9 pounds right there.
4 kilograms.
Now 9 kilograms.
We go over here.
9 kilograms.
Go all the way up.
That looks like almost exactly 20 pounds.
Here they say 12 pounds into weight in kilograms.
Actually kilograms is mass, but I won't get particular.
So 12 pounds.
Go over here.
Pounds.
12 pounds in kilograms looks like 5 1/2.
Approximately 5 1/2.
And then 17 pounds to kilograms.
So 17 is right there.
17 pounds to kilograms looks right about 7 1/2 kilograms.
Anyway, hopefully that these examples made you a little bit more comfortable with graphing equations and reading graphs of equations.
I'll see you in the next video.
I have this problem here from chapter five of the Kotz, Treichel, and Townsend Chemistry and Chemical Reactivity book, and I'm doing this with their permission.
So they tell us that ethanol, C2H5OH, boils at-- let me do this in orange-- it boils at 78.29 degrees Celsius.
How much energy, in joules, is required to raise the temperature of 1 kilogram of ethanol from 20 degrees Celsius to the boiling point and then change the liquid to vapor at that temperature?
So there's really two parts of this problem.
How much energy, in joules, to take the ethanol from 20 degrees to 78.29 degrees Celsius?
That's the first part.
And then once we're there, we're going to have 78.29 degrees Celsius liquid ethanol.
But then we also need the energy to turn it into vapor.
So those are going to be the two parts.
So let's just think about just raising the liquid temperature.
Raising, Raising the liquid temperature
Let's figure out how we're going to do that.
Just the liquid temperature.
So the first thing I looked at is well how many degrees are we raising the temperature?
Well we're going from 20 degrees Celsius-- let me write
Celsius there just so it's clear-- 20 degrees Celsius to 78.29 degrees Celsius.
So how much did we raise it?
Well, 78.29 minus 20 is 58.29.
So our change in temperature is equal to 58.29 degrees Celsius or this could even be 58.29 kelvin.
And the reason why we can do that is because differences on the Celsius scale and the kelvin scale are the same thing.
The kelvin scale is just a shifted version of the Celsius scale.
If you added 273 to each of these numbers you would have the kelvin temperature, but then if you take the difference, it's going to be the exact same difference.
Either way you do it, 78.29 minus 20.
So that's how much we have to raise the temperature.
So let's figure out how much energy is required to raise that temperature.
So we want a delta T.
We want to raise the temperature 58.29.
I'll stay in Celsius.
Actually let me just change it to kelvin because that looks like what our units are given in terms of specific heat.
So let me write that down.
58.29 kelvin is our change in temperature.
I could have converted either of these to kelvin first, then found the difference, and gotten the exact same number.
Because the Celsius scale and the kelvin scale, the increments are the same amount.
Now, that's our change in temperature.
Now how much ethanol are we trying to boil?
Well, it tells us right over here.
It tells us that we're dealing with 1 kilogram of ethanol.
And everything else they give us is in grams.
So let me just write that 1 kilogram, that's the same thing as 1,000 grams.
We could just write it here.
1.00 kilogram is equal to-- or let me write it this way-- times 1,000 grams per 1 kilogram.
These cancel out.
This is the same thing as 1,000 grams.
Although the reality is we only have three significant digits-- this makes it look like we have four.
So we have 1,000 grams times 1,000 grams.
And then we just multiply this times the specific heat of ethanol.
The specific heat capacity of ethanol right here, 2.44 joules per gram kelvin.
So times 2.44 joules.
Let me write it this way, 2.44 joules per gram kelvin.
You see that the units work out.
This kelvin is going to cancel out with that kelvin in the denominator.
This gram in the numerator will cancel out with that grams.
And it makes sense.
Specific heat is the amount of energy per mass per degree that is required to push it that 1 degree.
So here we're doing 58 degrees, 1,000 grams, you just multiply it.
The units cancel out.
So you have kelvin canceling out with kelvin.
You have grams canceling out with grams.
And we are left with-- take out the calculator, put it on the side here.
So we have 58.29 times 1,000-- times one, two, three-- times 2.44 is equal to-- and we only have three significant digits here.
So this is going to be 142-- we'll just round down-- 142,000 kelvin.
So this is 142,000.
Sorry 142,000 joules.
Joules is our units.
We want energy.
So this right here is the amount of energy to take our ethanol, our 1 kilogram of ethanol, from 20 degrees Celsius to 78.29 degrees Celsius.
Or you could view this as from 293 kelvin to whatever this number is plus 273, that temperature in kelvin.
Either way, we've raised its temperature by 58.29 kelvin.
Now, the next step is, it's just a lot warmer ethanol, liquid ethanol.
We now have to vaporize it.
It has to become vapor at that temperature.
So now we have to add the heat of vaporization.
So that's right here.
We should call it the enthalpy of vaporization.
The enthalpy of vaporization, they tell us, is 855 joules per gram.
And this is how much energy you have to do to vaporize a certain amount per gram of ethanol.
Assuming that it's already at the temperature of vaporization, assuming that it's already at its boiling point, how much extra energy per gram do you have to add to actually make it vaporize?
So we have this much.
And we know we have 1,000 grams of enthanol.
The grams cancel out.
855 times 1,000 is 855,000 joules.
So it actually took a lot less energy to make the ethanol go from 20 degrees Celsius to 78.29 degrees Celsius than it took it to stay at 78.29, but go from the liquid form to the vapor form.
This took the bulk of the energy.
But if we want to know the total amount of energy, let's see if we can add this up in our heads.
855,000 plus 142,000.
800 plus 100 is 900.
That's 900,000.
50 plus 40 is 90.
5 plus 2 is 7.
So it's 997,000 joules or 997 kilojoules.
Or we could say it's almost 1 megajoule, if we wanted to speak in those terms.
But that's what it will take for us to vaporize that 1 kilogram of ethanol. ethanol.
I touched on this a little bit in the video on how variation can be introduced into a population, but I think it's fairly common knowledge that all of us-- when I talk about us I'm talking about human beings, and frankly, most eukaryotic organisms-- we're the product of sexual reproduction.
So if this is the first cell that had the potential to become Sal, we know that this first cell-- let me say this is the nucleus of that first cell so I can draw the whole cell and all that, but let's just focus on the nucleus.
It has 23 chromosomes.
Well, let me put it this way.
It has 46 chromosomes, 23 from my father and 23 from my mother, so that's 1, 2 3, 4, 3 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23 from my father.
And then let's say that last one actually helps to determine my gender, or it fully determines my gender.
That's my Y chromosome.
And let's say I had 23 homologous chromosomes, or one chromosome that kind of was the homologue for each of these, but I have 23 of them from my mother, so 1, 2, 3, 4, 5-- oh, you get the idea.
I can just draw a bunch of them, and then have the X chromosome that is essentially one of the gender-determining chromosomes from my mother.
And we learned before that each of these pairs are homologous chromosomes, that they essentially code for the same gene, one from my father and one from my mother.
Now, that first cell that had the potential to become me, it was a product of fertilization, of an egg from my mother-- so an egg from my mother.
I'll just draw the whole egg like that.
I'll just focus on the DNA from now, so my mother's DNA, it had 23 chromosomes.
So it didn't have pairs, and this is key. So there's 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, and then 23 was the X chromosome.
And so it's a combination from my mother, so this is from my mother, and a sperm from my father.
Let me do that here. And I'll draw the sperm much larger than it is normally relatively to the egg.
This is kind of the nucleus of the egg, but let's say that this is the sperm, and it has a tail that helps it swim, and it has 23 chromosomes.
So 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, and then it has that Y chromosome.
Let me do that Y chromosome in a separate color.
Just as an aside, this unification, this fertilization that occurred from this sperm cell to this egg cell, so it essentially penetrates into this egg cell and it creates this zygote, which is a fertilized egg cell from my mother, and this contains all DNA from both my father and my mother.
So this very first cell that was created from this fertilized egg, this is called a zygote.
It's a product of fertilization between two gametes.
So that's a gamete and this is a gamete.
Both a sperm cell or an egg cell, they're both examples of gametes.
Now, the whole reason why I'm doing this is I want to introduce you-- and I already introduced this notion to you when we talked about the variation of population, that, look, this has my full chromosome complement.
It has 23 pairs, and each pair is a pair of homologous chromosomes.
They essentially code for the same things, one from my mother, one from my father, and that is 46 individual chromosomes, 23 from my mother, 23 from my father.
These gametes, they each have only 23 chromosomes, or half the number of a full complement.
Now, everything that I'm talking about here, the number 46, or 23 pairs, or 23 individual chromosomes, this is unique to human beings.
If I talked about other species, they might have 10 chromosomes or they might have 5 chromosomes.
But one thing that is universal for all sexually reproducing organisms is that gametes have half the number of chromosomes as the zygote, or you can kind of view it as the organism itself, the way we conventionally think about it.
So when people talk about half the number of chromosomees, they say it has a haploid number.
And that literally just means half the number of chromosomes.
It's very easy to memorize, because haploid starts with the same two letters as half.
Haploid number for humans is 23 chromosomes.
And so, you say, oh, if you say this is a haploid number, what do you call it when you have the full complement of chromosomes?
Well, that's called the diploid number.
And I remember that because di- often is a prefix associated with having two of something, and so you have twice the number of chromosomes.
So this is haploid, this is diploid number, and this is for humans, right?
For an organism where the diploid number is N, and you'll sometimes see this notation, so I want to make sure you're comfortable with it, there's some organism, or actually any organism.
If the diploid number is 2N, then the haploid number is going to be half of that, or just N.
Now, in the case of humans, the diploid number is 46, so N is equal to 23.
So a fertilized egg or even just a regular somatic cell or a body cell will have a diploid number of chromosome, while a sex cell, and I'll be a little bit clearer about that in a second, will have a haploid number of chromosomes.
So gametes, which are either a sperm or an egg, those are both examples of gametes, they have half the number, they merge, and then you get a zygote, which is that very first cell that had the potential to turn into me, that has a diploid number of chromosomes.
And I actually want to do a little bit of a side here, because it's fascinating.
We talk about natural selection, and we even wonder today to what degree is it occurring, because our society, it's not as tough of an environment as the natural world would be where we're being stalked by predators and we have to live out in the wild and find food and all of that.
But even this process of fertilization is an incredibly competitive process, because this sperm that happened to be the one that kind of won the race from my father to fertilize my mother's egg, it was actually the first of roughly 200 million other sperms.
There were 200 million, roughly. There could've been 200 to 300 million other sperms in that race.
From the moment we're born, we're already the product of an intense competition amongst these male-- I guess we could call them male gametes, or amongst these sperm cells.
Some of them might have had weird mutations, that they didn't know which direction to swim, they happened to go in the wrong direction, maybe some of them had weird tails that didn't allow them to swim as fast, so you're already on some level selecting for fitness within this environment.
So if you had some weird mutations from the get go in some of these sperm cells, it would have been less likely, especially if they affected their ability to kind of swim, it would've been less likely that they would have been the ones to win this race.
So already, you are the product of a race of 280 million organisms, if you consider each of these sperm cells an organism, and you are the product of that winning combination.
So, you know, sometimes we feel lost on this planet. We're one of 6 billion people and all that, or just a number, but we already are the product of a pretty intense accomplishment.
But now with some of this vocabulary thrown out of the way, let's talk a little bit about zygotes and how do zygotes turn into people, and then how do those people essentially produce gametes, which then can fertilize other people's gametes to form more zygotes.
So the general idea: So that very first cell that was essentially my mom's egg fertilized by a sperm cell from my father, that was a zygote, and as soon as it's successfully fertilized, it has 2N, or it has the diploid number of chromosomes in the case of humans, which I believe I am one of them.
I have 46 chromosomes.
And then this cell right here begins to split and divide over and over and over again.
We'll do a whole series of videos on the actual mechanics of that, but it splits by a mechanism called mitosis.
And mitosis literally is just a cell splitting to form copies of itself.
So it just starts splitting into two more cells that are-- and actually, let me do it this way, just because the actual way it works is right when a cell is split, the cells that it splits into aren't that much larger than the original one.
But now each of these have 2N chromosomes, or 46 in the case of humans, and you keep splitting, and it happens over and over and over again.
So eventually-- well, let me just do it this way. This keeps splitting, and then you have-- and I'll go into the words for some of these initial collections of cell, but I won't go into that right now.
2N, all of these are original copies from a genetic point of view of that original cell.
And then eventually, they start to really-- I start to have tons of them.
There's just a gazillion of them that are all duplicates of the cell, and they all contain the 2N number of chromosomes, the diploid number of chromosomes.
They all contain all of my genetic material, but based on how they relate to each other and what they see around them, they start differentiating.
So all of these have 2N number, so they're all diploid.
And mitosis-- this is the process the whole time-- is these divide one cell into two cells and those two cells into four cells and keep going.
And then these begin to differentiate.
Maybe these cells eventually differentiate into things that'll turn to my brain.
These cells right here differentiate into things that'll turn into my heart.
These cells here differentiate into things that will turn into my lungs and so forth and so on.
And eventually, you get a human being.
But it doesn't have to be a human being. It could be whatever species we happen to be talking about.
So let me draw the human being.
So I'll draw my best shot at an outline of a human being.
Now, we're talking about gazillions of cells. You have your human being, and I'll just draw a very simple diagram, outline of a human being.
When I was in high school, I was a class artist, so I don't want to make this representative of my true artistic ability.
I'm doing this here just to kind of give you an idea.
But anyway, eventually, you keep dividing these cells and you end up with a human being, and this human being, you know, you wouldn't even notice the cells on this scale.
Now, most of these cells of this human being, if this is me or you, these are all the product of mitosis that started off with that zygote, and it just kept dividing and dividing and dividing into mitosis.
But it differentiated. I said some of them will turn into brain cells.
Some of them will turn into heart cells.
The whole process of differentiation is actually fascinating, and we'll talk a lot more about that when we talk about stem cells, embryonic stem cells, and maybe we'll even talk about the debate of it.
But the question is, well, how do I then produce those gametes?
How do I produce those things that eventually, if I'm going to reproduce, turn into these kind of haploid number of cells?
And that's what happens in your sexual organs.
So in a male, you have some germ cells, so some of these cells turn into germ cells. And the germ cells exist as part of your reproductive organs.
So let's say those are the germ cells.
In a male, they would be part of the gonads, so they would be there.
In a female, they would be involved in the ovaries.
And these germ cells, they're the product of mitosis.
So let me draw a germ cell.
So a germ cell is the product of mitosis, so it still has 2N number of chromosomes, so it still is a diploid cell or has a diploid number.
But what's special about a germ cell is it has the potential, one, it can either continue to do mitosis and produce more germ cells that are identical to it, so it could produce two germ cells that are identical to it, or it can undergo meiosis.
And meiosis is essentially what a germ cell undergoes to produce gametes.
And so if this germ cell undergoes meiosis, and I'll do a whole video on the mechanics of it, instead of two cells, it'll actually produce four cells that each have half the number of chromosomes in them, so these cells are haploid.
In the case of a male, these would be sperm cells. This would be sperm.
In the case of a female, these would be ova, sperm or ova, and these are the gametes.
So it's an interesting thing to talk about, because in the last several videos, I talked a lot about mutations and what does that do to a species, but think about what happens.
If I have a mutation in some cell here, some somatic cell, some body cell, somatic cell, will that mutation or can that mutation in any way affect what's going to happen to my kids? Will that mutation be carried on to my kids?
Well, no.
Because in no way will what goes on in this cell affect what I actually pass on eventually in the sperm cells.
It'll just be a random mutation.
It could affect my ability to reproduce.
For example, it could be-- God forbid, it could be some type of cancer or something that, especially if you contract it at a young age, it might be some type of terminal form so that might affect your ability to reproduce, but it will not affect the actual DNA that you pass on to your offspring.
So if you have some really bad mutation here, it could affect how you live or it could turn cancerous and start reproducing, but it will not affect what you pass on to your children.
The traits that will be passed on or the changes that will be passed on are those that occur in the germ cells.
So if you have mutations in your germ cells, or during the process of meiosis, you have essentially recombination of DNA because of crossovers, and we saw that in the variation video, then that will introduce new forms or new variants inside that could be passed on to your children.
And I really want to make that point there, because we talk about mutations, but there's different types of mutations.
There's some mutations that won't be passed on to your children, and those are the ones that occur in your somatic cells.
Maybe some of them do nothing so then it really doesn't affect your overall function, but in the mutations that either occur in your germ cells or the recombination or the variation that is introduced during meiosis, that will be passed on to your children.
But even there I want to be careful. Because remember, this is a severe competition.
So out of all of the-- let's say there's 280 million sperm cells that at one time are being competitive for an egg, it's possible that some of them have mutations.
In order for one of those mutations-- let me do the mutations in different colors.
That's a purple mutation.
That's a blue mutation.
But in order for that mutation to truly be passed on to my offspring, the sperm containing the mutation is the one that has to win the race.
So already you have a selection going on at kind of this sexual reproduction level where you're selecting for things that are at least good enough-- I mean, to some degree, the sperm has to be good enough to win this is incredibly, incredibly competitive race.
So that mutation that somehow made the sperm deformed or didn't allow it to swim or made it behave in some weird way, it's very unlikely that that mutation would go on to be the one or that cell would go on to be the one that would successfully fertilize an egg.
So anyway, I wanted to introduce you to these ideas. The main idea is really some of the vocabulary: haploid, diploid.
It's very confusing when you first learn it, but it literally just means half the normal group of chromosomes.
And in the case of humans, that would be 23.
And the cells that have a haploid number of chromosomes are our gametes, which are sperm cells for men, and ova, or egg cells for women.
But everything else in our body, all of our somatic cells, are diploid, which means that the full complement of chromosomes, they all have a copy of our DNA.
And that's why DNA testing is so interesting because you can get any cell from someone anywhere, and you have their full complement of DNA.
You have all of the information that describes them genetically.
Anyway, see you in the next video.
Bu konuya varyasyonların bir populasyonu nasıl etkilediğini anlattığım videoda değinmiştim ama bence hepimiz -bizden kastım bütün insanoğlu ve birçok ökaryot organizma- biz eşeyli üremenin ürünüyüz.
I was speaking to a group of about 300 kids, ages six to eight, at a children's museum, and I brought with me a bag full of legs, similar to the kinds of things you see up here, and had them laid out on a table for the kids.
And, from my experience, you know, kids are naturally curious about what they don't know, or don't understand, or is foreign to them.
They only learn to be frightened of those differences when an adult influences them to behave that way, and maybe censors that natural curiosity, or you know, reins in the question-asking in the hopes of them being polite little kids.
So I just pictured a first grade teacher out in the lobby with these unruly kids, saying, "Now, whatever you do, don't stare at her legs."
But, of course, that's the point.
That's why I was there, I wanted to invite them to look and explore.
So I made a deal with the adults that the kids could come in without any adults for two minutes on their own.
The doors open, the kids descend on this table of legs, and they are poking and prodding, and they're wiggling toes, and they're trying to put their full weight on the sprinting leg to see what happens with that.
And I said, "Kids, really quickly -- I woke up this morning, I decided I wanted to be able to jump over a house -- nothing too big, two or three stories -- but, if you could think of any animal, any superhero, any cartoon character, anything you can dream up right now, what kind of legs would you build me?"
And immediately a voice shouted, "Kangaroo!"
"No, no, no!
Should be a frog!"
"No.
It should be Go Go Gadget!"
"No, no, no!
It should be the Incredibles."
And other things that I don't -- aren't familiar with.
And then, one eight-year-old said,
"Hey, why wouldn't you want to fly too?"
And the whole room, including me, was like, "Yeah." (Laughter)
And just like that, I went from being a woman that these kids would have been trained to see as "disabled" to somebody that had potential that their bodies didn't have yet.
Somebody that might even be super-abled.
Interesting.
So some of you actually saw me at TED, 11 years ago. And there's been a lot of talk about how life-changing this conference is for both speakers and attendees, and I am no exception.
TED literally was the launch pad to the next decade of my life's exploration.
At the time, the legs I presented were groundbreaking in prosthetics.
I had woven carbon fiber sprinting legs modeled after the hind leg of a cheetah, which you may have seen on stage yesterday.
And also these very life-like, intrinsically painted silicone legs.
So at the time, it was my opportunity to put a call out to innovators outside the traditional medical prosthetic community to come bring their talent to the science and to the art of building legs.
So that we can stop compartmentalizing form, function and aesthetic, and assigning them different values.
Well, lucky for me, a lot of people answered that call.
And the journey started, funny enough, with a TED conference attendee --
Chee Pearlman, who hopefully is in the audience somewhere today.
She was the editor then of a magazine called ID, and she gave me a cover story.
This started an incredible journey.
Curious encounters were happening to me at the time;
I'd been accepting numerous invitations to speak on the design of the cheetah legs around the world.
And people would come up to me after the conference, after my talk, men and women.
And the conversation would go something like this,
"You know Aimee, you're very attractive. You don't look disabled."
(Laughter)
I thought, "Well, that's amazing, because I don't feel disabled."
And it really opened my eyes to this conversation that could be explored, about beauty.
What does a beautiful woman have to look like?
What is a sexy body?
And interestingly, from an identity standpoint, what does it mean to have a disability?
I mean, people -- Pamela Anderson has more prosthetic in her body than I do.
Nobody calls her disabled.
(Laughter)
So this magazine, through the hands of graphic designer Peter Saville, went to fashion designer Alexander McQueen, and photographer Nick Knight, who were also interested in exploring that conversation.
So, three months after TED I found myself on a plane to London, doing my first fashion shoot, which resulted in this cover --
"Fashion-able"?
Three months after that, I did my first runway show for Alexander McQueen on a pair of hand-carved wooden legs made from solid ash.
Nobody knew -- everyone thought they were wooden boots.
Actually, I have them on stage with me: grapevines, magnolias -- truly stunning.
Poetry matters.
Poetry is what elevates the banal and neglected object to a realm of art.
It can transform the thing that might have made people fearful into something that invites them to look, and look a little longer, and maybe even understand.
I learned this firsthand with my next adventure.
The artist Matthew Barney, in his film opus called the "The Cremaster Cycle."
This is where it really hit home for me -- that my legs could be wearable sculpture.
And even at this point, I started to move away from the need to replicate human-ness as the only aesthetic ideal.
So we made what people lovingly referred to as glass legs even though they're actually optically clear polyurethane, a.k.a. bowling ball material.
Heavy!
Then we made these legs that are cast in soil with a potato root system growing in them, and beetroots out the top, and a very lovely brass toe.
That's a good close-up of that one.
Then another character was a half-woman, half-cheetah -- a little homage to my life as an athlete. 14 hours of prosthetic make-up to get into a creature that had articulated paws, claws and a tail that whipped around, like a gecko.
(Laughter)
And then another pair of legs we collaborated on were these -- look like jellyfish legs, also polyurethane.
And the only purpose that these legs can serve, outside the context of the film, is to provoke the senses and ignite the imagination.
So whimsy matters.
Today, I have over a dozen pair of prosthetic legs that various people have made for me, and with them I have different negotiations of the terrain under my feet, and I can change my height --
I have a variable of five different heights.
(Laughter)
Today, I'm 6'1".
And I had these legs made a little over a year ago at Dorset Orthopedic in England and when I brought them home to Manhattan, my first night out on the town, I went to a very fancy party.
And a girl was there who has known me for years at my normal 5'8".
Her mouth dropped open when she saw me, and she went, "But you're so tall!"
And I said, "I know.
Isn't it fun?"
I mean, it's a little bit like wearing stilts on stilts, but I have an entirely new relationship to door jams that I never expected I would ever have.
And I was having fun with it.
And she looked at me, and she said, "But, Aimee, that's not fair."
(Laughter) (Applause)
And the incredible thing was she really meant it.
It's not fair that you can change your height, as you want it.
And that's when I knew -- that's when I knew that the conversation with society has changed profoundly in this last decade.
It is no longer a conversation about overcoming deficiency.
It's a conversation about augmentation.
It's a conversation about potential.
A prosthetic limb doesn't represent the need to replace loss anymore.
It can stand as a symbol that the wearer has the power to create whatever it is that they want to create in that space.
So people that society once considered to be disabled can now become the architects of their own identities and indeed continue to change those identities by designing their bodies from a place of empowerment.
And what is exciting to me so much right now is that by combining cutting-edge technology -- robotics, bionics -- with the age-old poetry, we are moving closer to understanding our collective humanity.
I think that if we want to discover the full potential in our humanity, we need to celebrate those heartbreaking strengths and those glorious disabilities that we all have.
I think of Shakespeare's Shylock:
"If you prick us, do we not bleed, and if you tickle us, do we not laugh?"
It is our humanity, and all the potential within it, that makes us beautiful.
Thank you.
(Applause)
I thought I would do another example of partial quotient method for long division So there actually has some positives to do It's actually kind of fun to do
We know what 291 times 10 is. That's clearly 2,910 Let's get some stuff in between here that will help us to try to approximate how many times 291 goes into this crazy thing over here
Let's just say 291 times- let's try 3 out. 291 times 3
Let me do it right over here
So 291 times 3 is- 1 times 3 is 3. 9 times 3 is 27 2 times 3 is 6.
6 plus 2 is 8 So this is equal to 873 It's actually strange that 873 showed up over there
But I'll just calculate it.
291 times 6- 1 times 6 is 6. 9 times 6 is 54.
2 times 6 is 12, plus 5 is 17 So it's 1746 And you might say, Sal why did you go through the trouble of figuring out this and this?
5, 9, 3, 7 minus 3 is 4, 8 minus 7 is 1 9 minus 8 is 1 So now we are left with 1,143,952 So which of these just gets us right under that?
So let's see, if we want to go to- we can't go straight to 1746 That would be too big over here We might want to do 873 again
So 1,2,3 3 times 291 is 873. 3000, is 873000 Let me write this a little bit neater
This is a 2 right over here. 2 minus 0 is 2 And then you subtract again 2 minus 0 is 2.
5 minus 0 is 5.
9 minus 0 is 9.
3 minus 3 is 0 And then you have 4 minus 7 The way I like to do it when I have to start regrouping and borrowing is making sure I go from the left
10 minus 8 is 2 Now 270,952. What's right below that?
We see I'm only using the 6 and 3 because I figured those out ahead of time so I didn't have to do any extra math 2 minus 0 is 2. 5 minus 0 is 5.
9 minus 6 is 3.
0 minus 4-- Well, there are a couple of ways you can think about doing this You could borrow from here.
10 minus 4 is 6 Now this one is lower, so it has to borrow as well
16 minus 7- I have multiple of videos on how to borrow if I'm doing that part too fast But the idea here is to show you a different way of long division
Make this a 16.
Make this an 8 16 minus 7 is 9 And then we have to get close to 9,052 Once again, that 873- those digits look pretty good 873- we still want to multiply 3, and then 10
We subtract again. 2 minus 0 is 2.
5 minus 3 is 2 And then you have 90 minus 87 is 3 I'm doing the subtraction a little fast just so we can get the general idea
32 minus 29 is 3 So you have a remainder of 31 291 cannot go into 31 any more. So that's our remainder
33600.
33900.
33931 33,931
And we're done, assuming I haven't made some silly mistake 291 goes into this thing 33,931 times with a remainder of 31
<i>Brought to you by the PKer team @ www.viikii.net
Episode 9 .
Stop right there!
Hey!
Hey stop right there you punk! Hey! <i>Baek Seung Jo is running with me Oh! it doesn't seem true. <i> It really doesn't seem true.
Thanks to you, I get to experience situations that I never thought I would.
Sorry...
But the work out seems to have had an effect, seeing how you managed to keep up so well.
But, you knew?
That we were following you?
It would be weird if I didn't know. You're obvious.
I didn't have a choice.
When I found out you were going to watch a movie with Hae Ra...
Without knowing...
But if you happen to like Hae Ra,
That is something... I can do nothing about.
Do you want to go somewhere?
What?
I'm asking if you want to go somewhere? <i>It's like a dream... <i>Me being with Seung Jo. <i>With Seung Jo.
It feels like I'm having a life time of happiness on this one day.
I'm happy now
But, it looks like only families are here.
We are the only ones who look like a couple.
Of course.
There is a rumor that says, If a couple comes here together, they would break up in six months.
You didn't know?
What?
You didn't know? It's well known.
After all, we shouldn't care, since we are not dating.
You know what?
Let's just get out of here!
What to do?!
Wear it until your clothes dry.
It's cheap, but it's better than wearing wet clothes.
They were selling them by the road.
You don't like it?
It's the same?
Then, it's couple t-shirts?
Hamburger!
I was so hungry. <i>It's really good. <i> Better than the delicious French or Italian food. <i> I won't be able to eat such a delicious hamburger again. <i> I wish time would stop right here.
Eat!
Don't just look at it
But, why did you take my hand and run earlier?
You were with Hae Ra. . .
That's because. . . You were the one closest to me.
Thank you.
I keep causing trouble all the time.
I haven't really experienced something that was difficult for me.
But after you showed up...
I feel like I'm living in a completely different world.
I feel like I'm solving a sudden problem without an answer.
That may be an ordeal that I should get over.
Something I can't avoid, something I have to solve.
Is the ordeal...possibly me?
At first, I wondered about how to react to it and just wanted to avoid it.
But now, I won't run from it.
If the problem is not wrong, then there has to be an answer.
I'm going to approach it head on.
Huh?
You're going to face me head on?
If you don't get it then forget it.
No, I get it.
So, I am an ordeal to you and you were only trying to run away.
But you changed your mind, and now, you are with me.
Are you proposing to me?!
How could you have come to that conclusion?
I'm telling you that I don't dislike you.
Being with you isn't easy but I'm just saying I don't hate it.
Thank you.
I really thought that you hated me.
Ever since high school, I have only liked you.
I don't know anything about Sartre or Nietzsche . And I can't even cook.
And I'm not glamorous,
But still, I'll try my best.
I'll know to always try my best .
Really?
I'm looking forward to it.
What?
You getting smarter for me... I'm looking forward to it.
Okay.
Since the midterms are not that far away,
That confession...
I'll make sure of it with the test results. Okay?
Midterms?
But I hate exams.
Is there anyone who likes exams?
Then, can I get a C?
C?!
What are you talking about getting a C.
Then C+?
His words were as mischievous as always, but his smile was a little different from before. <i> More than the day I gave him my first love letter, more than the day we first kissed, <i> I think Baek Seung Jo feels closer to me.
Thank you.
You even walked me home.
It's like a perfect date.
Is it okay living here?
Since it is a guest room, it is kind of small.
But it's tolerable.
I'm only staying here for a little bit anyways.
We're staying here until the new house is built.
Will it be okay?
What?
I'm talking about Hae Ra.
She was the one you were meeting today. . .
How could you have parted that way.
Well, since she was with Kyung Su Sunbae.
Excuse me, Hae Ra.
I have something to tell you.
It's really hard for me to say, so I hope you will listen.
I know.
I am not good enough.
Pardon?
Not good enough?
Then have mine too.
I didn't mean... Foo... food is enough.
I'll continue.
I have tried my best not to think about it,
But I keep thinking of you. . .
Should I just leave?
I have a headache.
You have a headache? then, you should take some medicine for it.
Take your time, I will pay and leave now.
Hae Ra.
I know that I lack a lot of things.
That's why
I decided to try hard and not think of you
Recently, thoughts of you just fill my head.
That's what I wanted to say. <i>Brought to you by the PKer team @ www.viikii.net</i>
Dad!
What?
Oh,
Did something good happen today?
Huh?
No, what good thing?
Aigoo, I wish something good happened to us.
Why? <BR><BR>Did something happen?
Oh, it's not that...
I think it's going to take a long time to build the new house.
I can't get insurance on it since it's done by natural disasters.
And the company who was supposed to construct are just shrinking from their responsibility.
Then what should we do, Dad?
Ah, don't worry.
It will be resolved, but it will take some time.
Although it might be uncomfortable, plan on staying here for a while.
Yes.
I am sorry, Ha Ni!
What's there for you to be sorry about?
Don't worry about me.
I am fine.
Okay.
Welcome!
-Hello!
-Hello!
Oh, you two came?
We didn't even open yet!
Sit!
Sit!
What are you doing here at this time?
Ha Ni went to school already.
We know.
We just thought about So Pal Bok Noodles all of a sudden.
Seafood noodles?
With a lot of fresh raw oyster.
I got it, i got it!
Over here!
Two seafood noodles with a lot of fresh raw oyster.
Ooh!
Bong Joon Gu!
Sounds like it's your territory. Super charismatic, huh?
Right, huh?
Should I buy Ha Ni a pair of glasses?
Everyone else says I have charisma, but Ha Ni is the only one that doesn't see it.
Joon Gu, if you're too pushy, Ha Ni will just get bored.
What...what did you say?
Bong Joon Gu, you really don't know women.
Do you know why Ha Ni can't stand up against Seung Jo?
Because Seung Jo is cold.
What? Cold? To women, if a man is far away, they want to get closer.
If they come towards us, we want to run away.
Is that true?
Yeah. If you keep it up, she'll dislike you more and more, Bong Joon Gu.
No, no.
Chef kept talking about being sought after!
So I tried it out...
But it does not really fit the personality
And I can not play, For hard to reach.
I'm a guy from Busan.
I'm doing as I please.
Then someday, won't Ha Ni realize the potential Bong Joon Gu has?
When are the So Pal Bak noodles coming out?
Oh!
Hi!
Did you get home safely?
Yesterday?
Ah yes, of course!
I did get home safely.
I knew you would be safe because of Kyung Sunbae.
But, it seems like you did worry about me.
Anyways, it was fun.
It was like we were shooting a movie.
"Gangsters and Hae Rin"
I'm glad that you got home safely.
Let's go inside.
Look at this.
Wonderful perfection, a goddess.
You sure did take a lot of pictures.
Wow, look at this.
She looks pretty, right?
So, what happened yesterday?
You did have a date, right?
What date?
We just ate and left right after.
Ah, I should have paid for the food.
Ah, what is that?!
How could you when you had the perfect chance?!
You should have confessed.
Confession... I did plan on doing it.
But strangely when I just look at Hae Ra, my mind goes blank.
Nonsense just comes out of my mouth.
And I wonder if a guy like me looking at Hae Ra is just unfulfilled longing.
Why?
You do have charisma.
I know I have charisma.
But strangely in front of Hae Ra...
Then, did you confess to Seung Jo?
I had written a love letter before.
Letter!
Wow, why didn't I think of that?
Letter.
Aigoo, you should never do that!
Hae Ra is like a girl version of Baek Seung Jo.
If you write a letter, you'll just embarrass yourself.
Just look directly into her eyes and confess.
Girls like that the best.
I can't even look at her right.
What do you mean look her in the eyes?
Why?
You can practice.
Here.
Just think that I'm Hae Ra.
Should I?
That won't work.
Why?
You can practice.
Just try it again.
How can I imagine you as Hae Ra?
You try. I'm Baek Seung Jo.
Try it.
I am Baek Sung Jo, Baek Sung Jo.
At a time when she's not even thinking, when she bites her tongue...
That's when it's easy to get them to fall for you!
When she bites her tongue.
Hey, Hey!
What are you doing?
Are you crazy?
Why are you doing this?
This is practice.
Practice?
The timing is important.
Look at this.
If the girl says
What are you doing?!" then you put your hands like this
"If you can forget me, try forgetting me." and just go in for the kiss.
Hey!
You have talent, it's very real.
- Really?
- Wow, so if the girls say "What are you doing?"
Then, slam...
"If you can forget me, try forgetting me"
Wait!
Here, the timing is important.
When the girl lifts her head like this...
Then,
When she lifts her head...
"Why?
What are you doing?"
Slam. " Try to forget me if you can."
That's right.
That's it!
Hey, I'm busy.
Go and let the students practice.
Oh Ha Ni, teach him well.
Yes.
Now, Sunbae, you be the girl.
Okay, girl.
The head is lifted like this.
"What are you doing to me?"
"Try to forget me if you can"
You won't be able to forget it, right?
I won't be able to forget it.
Wow, this is really great!
Yes, I understand the timing now.
But for the kiss... when I watch movies
Do I turn to the left or right.
Or like spiderman...
Do I do it upside down?
The angle?
No, I think kissing is about timing.
Ah, kissing is timing.
Timing...
Ha Ni, you are very good at kissing.
No.
Truthfully, I don't really know about it.
What are you talking about?
If you're at this level, you'll be able to publish a book.
Isn't she hard to understand?
In the tennis club, the girl who follows Baek Seung Jo around.
You heard about that too?
Is that rumor true?
Yes.
There must be a fun rumor going around.
A student at our school left the guy she had a crush on... and supposedly kissed another guy.
On top of that, it was in broad daylight at school.
How could she?
Dumping someone like Baek Seung Jo.
Dumping?!
That doesn't make sense.
With a completely old looking sunbae.
Ah, that girl!
Really!
Oh, look here!
If you just leave like this...
Unnie!
Seung Jo came.
He came.
- It seems like Seung Jo doesn't know about it.
- He doesn't.
Oh Ha Ni even kissed Kyung Sunbae.
Ha Ni to Kyung Sunbae... Kiss?!
That's right, a kiss.
Oh Ha Ni is really great.
She even said to him "Can you do it one more time?".
Then, what happens with Baek Seung Jo?
What do you mean?
Oh Ha Ni dumped him.
Dumped?
What is it you want to say?
Hae Ra, I...
It's fine.
I'll just leave for today.
But, Hae Ra...
Sunbae!
Let go.
I'm going to do it!
If she wants to forget, she'll forget. I'm going to do it!
- Wait a minute.
- Hey!
Put the racket down.
Let go of me!
I'm going to do that.
No, no!
- Ah, no!
- Ha Ni!
Oh Ha Ni ah!
Ha Ni ah!
Ah..
Oh, Ha Ni ah!
- Oh Ha Ni! - You're going to leave already?
What do you mean?
Me with Kyung Sunbae?
They were right?
You did do it?
Kiss?
That's not it.
I was so frustrated that I was just educating him.
Educating?
Educating about what?
Perhaps...
Sex education!
Hey, sex education?! It's not that.
Oh, I'm so sorry.
Rumors have spread everywhere.
Huh?!
Are you sad? Since the girl that was following you has left?
Seung Jo ah!
Oh, it's the main lead of the rumor.
Miss Calm Cat,
When did you become like that with Kyung sunbae?
Have you heard?
The rumor that doesn't make any sense.
I'm leaving first.
Good luck
Congratulations.
Can you stay here by yourself until your brother comes back?
Of course.
I don't know when Seung Jo is coming though.
Do you think I'm a baby?
I also.... need to spend some time alone.
Look at you.
That's right.
Alright, Eun Jo, We'll see you tomorrow.
Hurry!
Don't play too many games.
I won't.
Just leave quickly.
Let's go.
Ok
Aigoo
Alright!
Oh!
"Seung Jo ah" <i>I came all the way here without even realizing it. <i> How did I end up here? <i>And it wasn't that long ago when I was so happy that we had our first date.
What is that sound?
Mother!, Eun Jo ah!
Ouch!!
Eun Jo ah!
You.....Eun Jo ah!
Eun Jo ah!, Eun Jo what's wrong?
My stomach.
Your stomach hurts?
What about you mother?, Where is she?
Vaca...
Vacation?
What to do ?
Hold on!
Hello.
Baek Seung Jo!
Why are you calling from our house?
Eun Jo is...Eun Jo is in pain!
Eun Jo?
What happened to Eun Jo?
He seems very sick.
What to do?
What should I do?!
Oh Han Ni calm down.
Calm down and explain it clearly.
What happened to Eun Jo?
He said his stomach hurts.
He keeps throwing up.
Really?
It might be appendicitis.
Write down what I'm about to tell you and act accordingly.
Place him on his side so he doesn't choke on anything.
Keep his body warm.
Keep in mind how many times he threw up and then, tell the doctor.
Hold on.
Then call the ambulance.
This is 119, right? after that..
Bring him to Parang University Hospital.
He's an elementary school student.
I'll get there as soon as possible.
Oh Ha Ni..
Take care of Eun Jo.
It's a type of intestinal obstruction.
An intussusception has occurred in the affected region.
An intussusception?
It's when part of the intestine folds into another part, sort of like a collapsible telescope.
It's pretty far in so we must operate on it immediately.
Surgery?
Complications can arise due to a perforated intenstine so you need to hurry and make a decision.
But....
What to do?
It's not a serious surgery. <i>Oh Ha Ni, take care of Eun Jo.
I understand.
Begin the surgery.
You came?
Yes.
Eun Jo is having surgery.
I heard about it.
How did it go?
It was as I had thought.
His intestine was folded into itself.
Did the surgery end?
Yes, it went well, you don't have to worry. A part of his intestine was folded into the bottom of it, so we opened up his stomach,
And returned it to normal.
After about a week, you won't be able to notice the cut.
-Baek Eun Jo -No Ri.
Thank you.
My parents... are coming up on an evening flight.
Uhmm..
They must have been very surprised.
The doctor complimented you.
He said your quick actions made the surgery easier.
If you hadn't told me how,
I wouldn't have been able to do anything
It's a type of obstruction to the intestines.
I had no idea.
I really... had no idea that such a scary thing could happen.
I will call my dad.
He must be worried.
Oh Ha Ni!
Ah, my cellphone and my wallet... where did I leave it all?
I, really...
How old am I that I'm already...
You know.. That rumor with Kyung Soo sunbae...
He explained everything to me already.
Thank you Oh Ha Ni.
I was afraid... that I might do something wrong.
So, something might go wrong with Eun Jo.
Everything is alright now. <i> It's the first time that I heard.. <i>warm words from Baek Seung Jo. <i>Since my anxious feelings were all relieved... <i>My eyes and heart... <i>I cried so much they nearly melted away.
Hello!
Hi Eun Jo. Omo! You made it today.
The flowers smells good.
It's Oh Ha Ni again??
She doesn't even get tired and comes very often...
Baek Eun Jo.
How could you talk to your life saver like that??
That's alright.
It seems like you're not getting tested today.
Yes.
In the end, her motive for coming here is about hyung anyways.
Here you go again.
Seung Jo didn't come yet?
See, I told you.
It's all about Seung Jo.
If you keep saying that...
He'll be coming soon.
It seems that Ha Ni should come back home.
Again?
You came?
Baek Seung Jo, even if you talk like that...
Seung Jo, now that you know Ha Ni you feel great right?
Eun Jo, are you okay? <i>Brought to you by the PKer team @ www.viikii.net
How is Eun Jo?
We would be in big trouble if Ha Ni wasn't there.
True.
It would have been a disaster without Ha Ni.
Thank you. Thank you, Oh Ki Dong.
It's a relief that everything is fine.
How is the building of your house coming along?
Is it doing alright?
You know, it's a major pain.
It happened because of the earthquake so the insurance won't really pay for it either.
We're still fighting over it right now.
It'll all go well, I guess.
Well, here.
What is this?
The monthly rent you paid us while you were living in our home.
This person couldn't bring herself to use it.
Why are you giving this back to me?
You shouldn't do this. You helped us so much during that time.
I can't accept this.
Here.
Ki Dong shi, are you really going to be like that?
If you don't accept it, I'm going to be mad.
Yes.
Just as your restaurant was getting really popular..
I know that you were going to build a second floor.
And because of the new house, and Ha Ni...
I also know that you couldn't do anything.
But, still... this.
Ki Dong shi, don't be like that and... just come live with us again?
Yes?
I came out because of Ha Ni.
This is better for Ha Ni.
Pardon?
For Ha Ni?
How can you not know your daughter's heart?
Actually, Ha Ni and Seung Jo... you don't know that they're trying to hide something from us do you?
Pardon?
Hide something?
Those two have even kissed!
And Seung Jo did it first.
Kiss?
Seung Jo did?
Yes.
So, Seung Jo liked Ha Ni all along.
Hello, Eun Jo!
You came again?
Go Ri, hello!
It's not Go Ri, it's No Ri!
That's right.
Hello, No Ri!
Hello.
I brought cake to give to you.
So Ri, you're going to eat too, right?
No Ri, No Ri!
I'm sorry.
I'm not that smart.
No, it's okay.
Everywhere I went, the hospital rooms were so quiet that it was no fun.
But, it's fun and nice here.
No Ri, have you been in the hospital for a long time?
Yes, about 1 year and 2 months.
So, they said I have to repeat fourth grade.
Really?
Then, I'll teach you your homework.
You're going to teach him?
Do you think that makes sense?
He's an elementary school student.
So rash.
Dummy how can you?
I can at least teach him the multiplication table.
I finished the multiplication table in 2nd grade though.
Really?
It's going to be more harmful than anything.
Let's just eat the cake.
Thank you.
Uhjjoo!
No Ri, you too!
She's recognized a dummy!
These guys...
Melong (sticking tongue out/ way of teasing)
Hey!
Baek Eun Jo!
Chef!
Are you worried about something??
Oh!
Your face has a look of concern.
Oh, are you finished?
Yes, of course! I cleaned everything.
Good job.
Perhaps, did something happen to Ha Ni?
Huh?
Why would something happen to Ha Ni?
You can go home now.
Yes, Chef.
I'll be leaving.
Okay.
Good work today.
- Get home safely.
- Yes!
Here we go No Ri, let's check your temperature.
No Ri gets fevers very often.
He's also a patient that was in ICU for over 6 months.
So, you should have been more careful around him.
If you play around with a sick kid like this, what would happen?
I'm sorry.
Please be cautious.
I'm sorry, No Ri.
This is nothing.
I'm already used to it.
After Eun Jo got admitted, everyday is fun.
I can learn from Seung Jo hyung.
And I have laughed a lot because of Ha Ni noona.
I wasn't intending to be funny though...
Okay, let's just rest for today.
When your fever goes down, I'll teach you again.
Yes.
What is his sickness?
It seems like he has a problem with his heart.
Oh, I see.
That little kid has to get shots, take tests, and eat bitter medicine everyday.
He can't even do everything he wants to do.
There's no use in your crying.
That's right.
If it was you, you could have done something to help him.
What can I do?
You're a genius.
So if you put your mind into being a doctor, you can easily do it.
So, it would be great if you could be a doctor, so you could heal many people like No Ri.
Everyone would be grateful towards you.
How does it sound?
If you tell me to become a doctor, does that mean I have to become a doctor?
Yeah, please do it. It's a really good idea right?
Well...
Being a doctor is best for you.
Baek Seung Jo wearing an all white lab coat...
I want to see you like that.
You're incorrigible . . .
You go to the hospital everyday?
So, everyday you're with Baek Seung Jo?
Because Mother leaves during the day, it's just us two.
If only Baek Seung Jo's little brother would be hospitalized a little longer.
Hey, what are you saying...
No?
What no
We can see everything, Oh Ha Ni!
What are you saying?
You're not allowed to fool around with the wheelchairs!
How do you read this?
How much is it?
Yes, what does it mean?
How much is this?
Correct.
Hey guys, let's eat a snack.
What is this?
Hey, what's the use in knowing that?
The No Ri that we love Happy Birthday to you!
Happy Birthday!
No Ri, happy birthday!
Eun Jo, congratulations on being discharged.
Thank you.
Seung Jo hyung and Ha Ni noona, thank you for teaching me.
Okay. If there's something you don't know, always call me.
You know my phone number, right?
Yes, I will.
No Ri, get healed quickly.
Yes, this kind of disease won't be a problem.
No Ri,
No Ri,
Eun Jo, I'm fine. I'm going to get healed quickly and come over to your house.
I will definitely come over too.
Yes. You must come.
Yes, I will definitely come.
No Ri didn't cry... and he held it in really well.
He's probably had to say goodbye to a friend that's gotten discharged first before. Even though he's sad too.
Eun Jo, we're going.
Eun Jo! Congratulations on your discharge from the hospital!
Ha Ni, you came back well!
Dad, what is all this?
It seemed like I didn't know how you felt... and that I was being stubborn about doing things my way.
Dad.
Up til now, the upstairs room... was really uncomfortable, wasn't it?
Seeing you cry (laugh?) at the hospital, I thought that you must be a part of this family.
Welcome Ha Ni.
(Seung Jo's) Mother.
Yeah. Welcome back, Ha Ni!
Thank you, Ahjushi.
Then what about my room?
Your room is with your brother.
No!
I don't want to give up my room again.
You need to say thank you to your noona.
No.
I just did what I had to do.
I'm tired.
Give us dinner.
You can go up now.
Ha Ni, you finished everything too?
Yes, I'll finish up the rest.
Okay, then it's a favor.
Good night.
Ha Ni.
Welcome.
Why aren't you sleeping yet?
I want to drink some water.
Eun Jo, you didn't sleep yet.
This time, you helped with a lot of things.
Thank you.
Punk.
He has some cuteness to him.
You were here.
I guess I ended up moving back in.
Just don't get in the way.
Okay.
Ah, you came?
Why are you still here and not leaving?
I was going to go after finishing this.
Go upstairs first.
Ha Ni, go up.
Ha Ni, wait.
Today, Bong Joon Gu's first piece of work was a success.
Yeah.
Ha Ni, you haven't eaten dinner yet, have you?
I knew it would be like that, so I made these.
Sit down, sit down.
Father, sit down please.
Here.
Look forward to it!
Bong Joon Gu's first piece of work!
Bong(?) Dumplings!
This is called Bong Dumplings.
Inside the dumpling there is another dumpling. I made it after getting special permission from your father.
I'm not sure if it turned out well.
I have one for Father too.
Try it and please critique it.
I was waiting so long for you to come home.
Yeah.
But, what to do?
I already ate dinner.
Really? You already ate?
Ah, what a waste.
Dad.
Oh.
That...
You did quite a good job on the shape.
Does it really look like that?
Father, try it once.
This is kind of embarrassing and I'm nervous.
Oh. Joon Gu.
There... um....
We decided to move back into Seung Jo's house.
It's a bit uncomfortable here, and kind of hard on my back.
And Seung Jo's family wants us too.
We just decided to do it that way.
Just know that. Okay?
Ah yes, yes.
I feel like I'm getting permission from you.
You did well. Good Job. Ha Ni, it is my first piece of work.
So try it at least once.
Eat it, okay?
Okay. <i>I feel sorry towards Joon Gu... <i>but I'm really happy about being able to be next to Seung Jo again. <i>I'm excited but nervous at the same time. <i>Will I be able to do a good job?
Oh. Where did it go?
I know I brought it in.
Is this yours?
Mine.
You took it didn't you?
Dummy.
It was on the ground right here.
Who would steal childish panties like those?
I only wear them once in a while.
I usually wear ones that have a lot of lace.
You don't have a body that can be considered sexy though.
Even the A Cup must be too big...
Did you stop growing after elementary school?
What did you say?
Hey.
Seeing you like that, and not thinking of anything...
Isn't that a big problem?
Is it that fun to make fun of me?
If you don't like living with me, you can just say it.
You just grumpily keep making fun of people.
I'm grumpy?
Yeah.
Why am I doing that?
When I see you I can't help but want to tease you.
But isn't the one with the problem you? You even drop those kinds of things.
It's good that you two have gotten closer... but before marriage, it's good to be a little more careful.
Since Eun Jo is here too. <i>Brought to you by the PKer team @ www.viikii.net
When are you going to select your major?
During my second year.
Then, when you decide what major you're going to take...
Will you be able to do it?
If a bunch of people choose the same major,
They decide using grades, and I'll have to compete in that manner... But it seems that those circumstances are unlikely.
Well, I'm just saying...
It would be nice if you went into business.
I'm not interested in that area.
Ah, Why? Please drop me off right over there.
Are you going into class?
Seung Jo!
Again?
Hey, when you think it's going well with him...
Why is he so fickle?!
Is he being mean again?
This time, it feels different from the last, though.
I don't know.
What- I mean, you said you even kissed.
Like this... you said you hugged too.
But, I mean, why in the world is he being like that??
I don't know if he's interested in me or not. It's very frustrating.
Min Ah, don't you have any good ideas?
To find out if he's interested in me or not.
Ah, then should we try the "yawning method?"
Yawning method?
So, now the word "concluded" is basically the same as "to finish" something.
You start it and it's over, so therefore, it's concluded.
Now, the second sentence we're going to look at
Tariffs lowered on industrial goods and services.
In this particular sentence, <i>Yawning is somewhat contagious.
So if you see someone yawn, you find yourself following. <i>Just use that. <i>You yawn during class. <i>But if Seung Jo yawns after you, <i>then that means he has glanced over at you. <i>If he's not interested, why would he look at you?
Yes!!
So, you're going to make effort to get it.
They're both advocating a deal, it means they both really want the deal.
Is my lesson really that boring guys?
It's ruined.
I haven't suffered from anything so far.
I met my parents well (saying) so I've lived comfortably.
Yeah, You and Me...
I just lived off my greatness. Since all the attention that was supposed to be pointed at the world was actually pointed towards me.
What do we do??
It seems we belong together more and more.
That's when, Oh Ha Ni came to our house.
Looking at her...
I came to realize that maybe the world has different plans for me.
And that is right, and maybe I'm wrong.
It was quite surprising
So I should experience the world more...
I think about it often, lately.
Anyways, thank you He Ra.
That I could talk to someone about this ...
It's a relief
If you can forget me, try forgetting me... if you can forget me... try forgett-
Hey, Ha Ni ah!
It's good that you came.
Come over here.
Ha Ni ah, the thing that you were talking about - the 'timing'
The timing of the kiss
I keep practicing this at home, but It seems there's a problem.
"If you can forget me, try forgetting me." this is 4.3 seconds...
During that time, what if Hae Ra leaves before then.
You'll have to do it before she leaves.
Of course, I have to do it before she leaves.
But you see, that timing doesn't really work out.
Oh, well, what if you were... stand right here for me.
EH?!
No, I don't want to
I did it for you that day, what's the need to do it again?
Please, do it for me.
I'll do it instead.
Ok, then you do it.
Stand right here.
It worked well for Seung Jo.
When I put my hand like this, the head that was facing down, tilt it up .
If you can forget me...
You saw that just now, right?
The timing wasn't right
Before the conversation is over, he already came it.
It's too long, this 4.3 seconds.
Sunbae, do you want to try it holding a racquet?
When you hold a racket, you turn into a completely different person.
Confidence, and burning eyes.
Hae Ra!
Oh my god!
You startled me
Oh, what do we do
Aigoo, you even fold clothes so well.
Hey, when I did all this housework, it got so tiring, but now that I have you to talk to.
It's so fun!
Its really true that a person can't live all by themselves
Yes, it's true.
Oh, Ha Ni!
Can you get the laundry from Seung Jo's room?
Tomorrow is Eun Jo's day to take his P.E. outfit.
It seems I have forgotten!
Sure, I'll be right back
You know that closet towards the inside, right?
I know
OH!
It's the couples T-shirt!
He still has it.
Room for rent
Part time job?
What are you doing in someone else's room?
You came?
She told me to bring Eun Jo's gym clothes.
Then you should have just gotten it and left.
What are you looking through?
Truthfully, I heard something from Kyung Soo Sunbae.
He said that you might even move out of this house.
Cham... anyways, he's a little weird, right?
It's true.
Huh?
I'm going to leave this house.
Why?
What do you mean why?
Do I need to get your permission for that too?
That's not it....
Perhaps, is it because I came in?
Are you leaving because of me?
Anyways, it has nothing to do with you.
Don't relate everything to yourself.
What do you mean you're leaving this house?
Until now, under your supervision...
I have lived comfortably.
But I think it's now time to think about the path ahead of me.
Just once, living by myself, getting a part time job...
I want to throw myself into an absolutely unprotected world and watch over myself.
What kind of person am I?
What can I do?
Okay.
That's not a bad idea.
Aigoo, but still...
It hasn't been long since Ha Ni has come back.
Hey, Seung Jo.
It has nothing to do with her.
It's my life.
Okay.
Go try it out. <i> What should I do? <i> Seung Jo is going to move out of this house. <i> I came back into this house. <i> But this time, Seung Jo... <i> is going to leave. <i>Brought to you by the PKer team @ www.viikii.net
Where is Baek Seung Jo?
If I don't try,
We couldn't even meet like this.
It's Seung Jo. <i> Seung Jo, what are you doing by yourself? <i> In what area are you living right now?
Hey, Baek Seung Jo.
Since she doesn't have a chance, tell her to give up.
Tell her like a man.
Seung Jo!
All of a sudden...
It must be lonely living by yourself.
Well it doesn't seem all that bad since I'm with Yoon Hae Ra.
What?
Roomate?!
Did something happen?
No, I'm fine.
Travelling up the Mekong River, we are heading for the point known as the Golden Triangle where Loas on the right, Thailand on the left and Myanmar up ahead share a common border
When Mao Tse Tung's Red Army swept into Yunnan 10,000 Nationalist from the Kuomintang Army fled into this region led by General Tang, better known as Khunsa
With the fall of Vietnam to Communism in the 1960's the United States and the West were fearful of the Domino Effect in South East Asia, provided Khunsa with funds and arms to enable him to fight Communist expansion.
Instead Khunsa expanded the existing opium cultivation by the hill tribes
He commenced opium cultivation and opium manufacturing to an industrial scale
In the 80's up to 70 % of the heroine in the west came from the Golden Triangle
Kunsa became the most wanted man in the world.
In the early 90's the Royal Thai Army destroyed Khunsa's Opium base and together with the
United Nations International Drug Control Program converted most of the opium fields to tea, coffee and tobacco plantations.
Khunsa surrendered to the Burmese Govt in 1996 and passed away in 2007
All this while the Myanmar refused to extradite him to the USA even though he was charged for opium smuggling in a New York Court.
With the opening of casinos at the Myanmar and Laos borders, the Golden Triangle looks set to regain some of its previous notoriety and reputation.
Hello.
In the last presentation we kind of re-defined the sine, the cosine, and the tangent functions in a broader way where we said if we have a unit circle and our theta is, or our angle, is -- let me use the right tool -- let's say, and our angle is the angle between, say, the x-axis and a radius in the unit circle, and this is our radius. the coordinate of the point where this radius intersects the unit circle is x comma y.
Our new definition of the trig functions was that sine of theta is equal to the y-coordinate, right, this is y-coordinate where it intersects the unit circle.
And remember, this is the unit circle.
It's not just any circle, which means it has a radius of 1.
Cosine of theta is equal to the x-coordinate of this point.
This is the x-coordinate.
And tangent of theta equaled opposite over adjacent or y over x.
That's interesting because that's also equal to sine of theta over cosine of theta.
I'll just do that.
I wasn't even planning on covering that, but just it leaves you something to think about.
So with that said, let's take a look or let's try to see how this defines these functions.
And I guess a good place to start is just with the sine function and we can try to graph it.
So let's write, let's do a little table like we always do when we define a function.
Let's put in values of theta, and let's figure out what sine of theta is.
So when theta is equal to 0 radians, what is sine of theta?
So when theta's 0, right, then the radius between it -- this is the radius and this is the point where the radius intersects the unit circle. And this point has a coordinate 1 comma 0, right?
And so if where it intersects the unit circle is at 1 comma 0, then sine of theta is just the y-coordinate.
So sine of theta is 0.
If we said what is sine of theta when theta is equal to pi over 2.
So now our radius is this radius and we intersect the unit circle right here at the point 0 comma 1.
And what's the y-coordinate at 0 comma 1?
Well it's 1.
What happens when we have theta is equal to pi radians?
So at pi radians we intersect the unit circle right here.
We're at pi radian.
This is the angle, pi.
We intersect with unit circle at negative 1 comma 0.
Because once again, this is the unit circle.
So at negative 1 comma 0, what's the y-coordinate?
Well, it's 0.
So sine of pi is equal to 0.
Let's just keep going around the circle.
When we have the angle, when theta is equal to 3 pi over 4
-- no, sorry, 3 pi over 2.
Because this is pi and this is another half pi.
So this is 3 pi over 2, sorry.
So when theta is equal to 3 pi over 2, what is sine of theta?
Well, now we intersect the unit circle down here at the point 0 comma negative 1.
So now sine of theta is equal to negative 1.
Then if we go all the way around the circle to 2 pi radians, we're back at this point again.
So sine of theta, so we're at 2 pi, sine of theta is now 0 once again.
So let's graph these points out and then we'll try to figure out what the points in between look like, and I'll show you the graph of a sine function is.
So let's draw the x-axis.
This is my x-axis.
And let's draw the y-axis.
Not as clean as I wanted to draw it.
This is y.
And that's x.
But in this case instead of saying that's the x-axis, let's call that the theta axis, because we defined theta as the input or our domains in terms of theta.
So this is the theta axis.
Now we're going to graph sine of theta.
So when we said when theta equaled 0, sine of theta is equal to 0.
So that's this point right here, 0 comma 0.
When theta is equal to pi over 2, sine of theta is equal to 1.
So this is the point pi over 2 comma 1, right?
That's just this 1.
When theta is equal to pi, sine of theta is 0 again.
So this is the point pi comma 0.
And when theta equaled 3 pi over 2, what was sine of theta? I equaled negative 1.
Interesting.
Then when we got to 2 pi -- when we got to theta equal to 2 pi, sine of theta, again, equaled 0.
So we know that these points are on the graph of sine of theta.
And if you actually tried the points in between, and as an exercise it might be interesting for you to do so.
You could actually figure out a lot of the points using 30-60-90 triangles or using the Pythagorean Theorem.
But you actually get a curve that looks something -- let me use a nicer color than this kind of drab grey -- you get a graph that looks something like this.
And you've probably seen that before.
The term for this function is actually a sine wave.
It looks like something that's oscillating or that's moving up and down.
And actually if you were to put in thetas that were less than 0, the sine wave will keep going into the negative theta axis.
It keeps going forever in both directions.
It keeps oscillating between 1 and negative 1 and the points in between.
So that's the graph of the sign function.
In the next module I'll actually do the graph of the cosine function, or actually I might just show you the graph of the cosine function.
Then I'll show you how they relate and how these can describe any kind of, or many types of oscillatory things in the world and how it relates to frequency and amplitude.
So I'll see you in the next module.
And just for fun you might want to sit down with a piece of paper and try to graph the cosine function or the tangent function as well.
Have fun.
In my humble opinion, the single most important biochemical reaction, especially to us, is cellular respiration.
And the reason why I feel so strongly about that is because this is how we derive energy from what we eat, or from our fuel. Or if we want to be specific, from glucose.
At the end of the day, most of what we eat, or at least carbohydrates, end up as glucose.
In future videos I'll talk about how we derive energy from fats or proteins.
But cellular respiration, lets us go from glucose to energy and some other byproducts.
And to be a little bit more specific about it, let me write the chemical reaction right here.
So the chemical formula for glucose, you can have 6 carbons, 12 hydrogens and 6 oxygens.
So that's your glucose right there.
So if you had one mole of glucose-- let me write that, that's your glucose right there-- and then to that one mole of glucose, if you had six moles of molecular oxygen running around the cell, then and this is kind of a gross simplification for cellular respiration.
I think you're going to appreciate over the course of the next few videos, that one can get as involved into this mechanism as possible. I think it's nice to get the big picture.
But if you give me some glucose, if you have one mole of glucose and six moles of oxygen, through the process of cellular respiration and so I'm just writing it as kind of a big black box right now let me pick a nice color.
So this is cellular respiration. Which we'll see is quite involved. But I guess anything can be, if you want to be particular enough about it.
Through cellular respiration, we're going to produce six moles of carbon dioxide. Six moles of water.
And-- this is the super-important part -- we're going to produce energy.
We're going to produce energy.
And this is the energy that can be used to do useful work, to heat our bodies, to provide electrical impulses in our brains.
Whatever energy, especially a human body needs, but it's not just humans, is provided by this cellular respiration mechanism.
And when you say energy, you might say, hey Sal, in the last video didn't you just
--well, if that was the last video you watched you probably saw that I said
ATP is the energy currency for biological systems.
And so you might say hey, well it looks like glucose is the energy currency for biological systems.
And to some degree, both answers would be correct.
But to just see how it fits together is that the process of cellular respiration, it does produce energy directly.
But that energy is used to produce ATP.
So if I were to break down this energy portion of cellular respiration right there, some of it would just be heat.
You know, it just warms up the cell.
And then some of it is used --and this is what the textbooks will tell you. The textbooks will say it produces 38 ATPs.
It can be more readily used by cells to contract muscles or to generate nerve impulses or do whatever else grow, or divide, or whatever else the cell might need.
So really, cellular respiration, to say it produces energy, a little disingenuous. It's really the process of taking glucose and producing ATPs, with maybe heat as a byproduct.
But it's probably nice to have that heat around. We need to be reasonably warm in order for our cells to operate correctly.
So the whole point is really to go from glucose, from one mole of glucose
-- and the textbooks will tell you
-- to 38 ATPs.
And the reality is, this is in the ideal circumstances that you'll produce 38 ATPs.
I was reading up a little bit before doing this video. And the reality is, depending on the efficiency of the cell in performing cellular respiration, it'll probably be more on the order of 29 to 30 ATPs.
But there's a huge variation here and people are really still studying this idea.
But this is all cellular respiration is.
In the next few videos we're going to break it down into its kind of constituent parts.
And I'm going to introduce them to you right now, just so you realize that these are parts of cellular respiration. The first stage is called glycolysis.
Which literally means breaking up glucose.
And just so you know, this part, the glyco for glucose and then lysis means to break up.
When you saw hydrolysis, it means using water to break up a molecule.
Glycolysis means we're going to be breaking up glucose.
And in case you care about things like word origins, glucose comes from, the gluc part of glucose comes from Greek for sweet.
And glucose is indeed sweet.
And then all sugars, we put this ose ending.
So that just means sugar.
So you might think it's kind of a redundant statement to say sweet sugar.
But there are some sugars that aren't sweet.
For example, lactose, Milk, it might be a little bit, but when you actually digest lactose then you can turn it into an actual sweet sugar but it doesn't taste sweet like glucose or fructose or sucrose would taste.
But anyway, that's an aside.
But the first step of cellular respiration is glycolysis breaking up of glucose.
What it does is, it breaks up the glucose molecule from a 6-carbon molecule
-- so it literally takes it from a 6-carbon -- let me draw it like this
-- a 6-carbon molecule that looks like this.
And it's actually a cycle.
Let me show you what glucose actually looks like.
This is glucose right here.
And notice you have one, two, three, four, five, six carbons.
I got this off of Wikipedia.
Just look up glucose and you can see this diagram if you want to kind of see the details.
You can see you have six carbons, six oxygens.
That's one, two, three, four, five, six.
And then all these little small blue things are my hydrogens.
So that's what glucose actually looks like.
But the process of glycolysis, you're essentially just taking-- I'm writing it out as a string, but you could imagine it as a chain -- and it has oxygens and hydrogens added to it, to each of these carbons.
But it has a carbon backbone. And it breaks that carbon backbone into two.
That's what glycolysis does, right there.
So you've kind of lysed the glucose and each of these things. And I haven't drawn all the other stuff that's added on to that.
You know, these things are all bonded to other things, with oxygens and hydrogens and whatever.
But each of these 3-carbon backbone molecules are called pyruvate.
We'll go into a lot more detail on that. But glycolysis, it by itself generates-- well, it needs two ATPs. And it generates four ATPs.
So on a net basis, it generates two -- let me write this in a different color --it generates two net ATPs.
So that's the first stage.
And this can occur completely in the absence of oxygen.
I'll do a whole video on glycolysis in the future.
Then these byproducts, they get re-engineered a little bit.
And then they enter into what's called the Krebs cycle.
Which generates another two ATPs.
And then, and this is kind of the interesting point, there's another process that you can say happens after the Krebs cycle.
But we're in a cell and everything's bumping into everything all of the time. But it's normally viewed to be after glycolysis and the Krebs cycle.
And this requires oxygen.
So let me be clear, glycolysis, this first step, no oxygen required.
Doesn't need oxygen.
It can occur with oxygen or without it. Oxygen not needed.
Or you could say this is called an anaerobic process.
This is the anaerobic part of the respiration.
Let me write that down too.
Anaerobic.
Maybe I'll write that down here.
Glycolysis, since it doesn't need oxygen, we can say it's anaerobic.
You might be familiar with the idea of aerobic exercise.
The whole idea of aerobic exercise is to make you breathe hard because you need a lot of oxygen to do aerobic exercise.
So anaerobic means you don't need oxygen.
Aerobic means it needs oxygen.
Anaerobic means the opposite.
You don't need oxygen.
So, glycolysis anaerobic.
And it produces two ATPs net.
And then you go to the Krebs cycle, there's a little bit of setup involved here.
And we'll do the detail of that in the future.
But then you move over to the Krebs cycle, which is aerobic. It is aerobic.
It requires oxygen to be around.
And then this produces two ATPs.
And then this is the part that, frankly, when I first learned it, confused me a lot.
But I'll just write it in order the way it's traditionally written.
Then you have something called --we're using the same colors too much -- you have something called the electron transport chain.
And this part gets credit for producing the bulk of the ATPs.
34 ATPs.
And this is also aerobic.
It requires oxygen.
So you can see, if you had no oxygen, if the cells weren't getting enough oxygen, you can produce a little bit of energy.
But it's nowhere near as much as you can produce once you have the oxygen.
And actually when you start running out of oxygen, this can't proceed forward, so what happens is some of these byproducts of glycolysis, instead of going into the Krebs cycle and the electron transport chain, where they need oxygen, instead, they go through a side process called fermentation.
For some organisms, this process of fermentation takes your byproducts of glycolysis and literally produces alcohol.
That's where alcohol comes from. That's called alcohol fermentation.
And we, as human beings, I guess fortunately or unfortunately, our muscles do not directly produce alcohol.
They produce lactic acid.
So we do lactic acid fermentation.
Let me write that down.
Lactic acid.
That's humans and probably other mammals.
But other things like yeast will do alcohol fermentation.
So this is when you don't have oxygen.
It's actually this lactic acid that if I were to sprint really hard and not be able to get enough oxygen, that my muscles start to ache because this lactic acid starts to build up.
But that's just a side thing.
If we have oxygen we can move to the Krebs cycle, get our two ATPs, and then go on to the electron transport chain and produce 34 ATPs, which is really the bulk of what happens in respiration.
Now I said this as an aside, that to some degree this isn't fair.
Because while these guys are operating they're also producing these other molecules.
They're not producing them entirely, but what they're doing is, they're taking
-- and I know this gets complicated here but I think over the course of the next few videos we'll get an intuition for it-- in these two parts of the reaction, glycolysis and the Krebs cycle, we're constantly taking NAD
-- I'll write it as NAD plus -- and we're adding hydrogens to it to form NADH.
And this actually happens for one molecule of glucose, this happens to 10 NADs.
Or 10 NAD plusses to become NADHs.
And those are actually what drive the electron transport chain.
And I'll talk a lot more about it and kind of how that happens and why is energy being derived and how is this an oxidative reaction and all of that. And what's getting oxidized and what's being reduced.
But I just wanted to give due credit. These guys aren't just producing two ATPs in each of these stages. They're also producing, actually combined, 10 NADHs, which each produce three ATPs in an ideal situation the electron transport chain.
And they're also doing it to this other molecule, FAD, which is very similar.
But they're producing FADH.
Now I know all of this is very complicated.
I'll make videos on this in the future.
But the important thing to remember is cellular respiration all it is is taking glucose and kind of repackaging the energy in glucose and repackaging it in the form of, your textbooks will tell you, 38 ATPs.
If you're doing an exam, that's a good number to write.
It tends to, in reality be a smaller number. It's also going to produce heat.
Actually most of it is going to be heat.
But 38 ATPs, and it does it through three stages.
The first stage is glycolysis, where you're just literally splitting the glucose into two.
You're generating some ATPs.
But the more important thing is, you're generating some NADHs that are going to be used later in the electron transport chain.
Then those byproducts are split even more in the Krebs cycle, directly producing two ATPs.
But that produces a lot more NADHs.
And all of those NADHs are used in the electron transport chain to produce the bulk of your energy currency, or your 34 ATPs.
Hello.
I will now introduce you to the concept of similar triangles.
Let me write that down.
6 00:00:14,15 --> 00:00:16,35 So in everyday life what does similar mean?
8 00:00:26,89 --> 00:00:29,47 Well, if two things are similar they're kind of the same but they're not the same thing or they're not identical, right?
That's the same thing for triangles.
So similar triangles are two triangles that have all the same angles.
14 00:00:50,46 --> 00:00:57,35 For example, let me draw two similar triangles.
I'll try to make them look kind of the same because they're supposed to look kind of the same, but just maybe be different sizes.
So that's one, and I'll draw another one that's right here.
I'm going to draw it a little smaller to show you that they're not necessarily the same size, they just are same shape essentially.
One way I like to think about similar triangles are they're just triangles that could be kind of scaled up or down in size or flipped around or rotated, but they all have the same angles so they're essentially the same shape.
For example, these two triangles, if I were tell you that this angle -- and this is how they do it in class.
29 00:01:39,99 --> 00:01:44,27 If I were to tell you this angle is equal to this angle
and I told you that this angle here is equal to this angle.
32 00:01:52,52 --> 00:01:54,01 Well, a couple of things.
You already know that this angle's going to be equal to this angle, and why is that?
Well because if two angles are the same, then the third has to be the same, right?
Because all three angles add up to 180.
For example, if this is x, this is y, this one has to be 180 minus x minus y, right?
That's probably too small for you to see.
But that's the same thing here.
If this is x and this is y, then this angle right here is going to be 180 minus x minus y, right?
So if we know that two angles are the same in two triangles, so we know that the third one's also going to be to same.
So we could also say this angle is identical to this angle. And if all the angles are the same, then we know that we are dealing with similar triangles.
What useful thing can we now do once we know that a triangle is similar?
Well, we can use that information to kind of figure out some of the sides.
So, even though they don't have the same sides, the ratio of corresponding side lengths is the same.
I know I've just confused you.
Let me give you an example.
For example, let's say that this side is -- this side is 5.
Let's say that this side is, I don't know, I'm just going to make up some number, 6.
And let's say that this side is 7, right?
And let's say we know that, I don't know, let's say we know that this side here is 2.
64 00:03:37,99 --> 00:03:40,18 So we know the ratio of corresponding sides is the same.
So, if we look at these two triangles, they have completely different sizes but they have corresponding sides.
For example, this side corresponds to this side.
How do we know that?
Well, in this case, they just happen to have the same orientation.
But we know that because these sides are opposite the same angle, right?
This is opposite angle y, and then this side is opposite angle y again.
This whole triangle might be too small for you to see, but hopefully you're getting what I'm saying.
So these are corresponding sides.
Similarly, this side, this blue side, and this blue side are corresponding sides.
Why?
Not because they're kind of on the top left because we could have rotated this and flipped it and whatever else.
It's because it's opposite the same angle.
86 00:04:32,81 --> 00:04:33,895 That's the way I always think about triangles.
It's a good way to think about it, especially when you start doing trigonometry.
So what does that us?
Well, the ratio between corresponding sides is always the same.
So let's say we want to figure out how long this side of the small triangle is.
Well there's a bunch of ways we could do it.
We could say that the ratio of this side to this side, so x to 7 is going to be equal to the ratio of this side to this side
-- is equal to the ratio of 2 to 5. And then we could solve it. And the only reason why we can do this -- you can't do this with just random triangles, you can only do this with similar triangles.
So we could then solve for x, multiply both sides but 7 and you get x is equal to 14 over 5.
So it's a little bit less than 3.
So 14 over 5, so 2.8 or something like that, that equals x. And we could do the same thing to figure out this yellow side.
So if you know two triangles are similar, you know all the sides of one of the triangles, you know one of the sides of the other triangle, you can figure out all the sides.
I think I just confused you with that comment.
So, this side, so let's call this y.
you're doing one triangle's going to be the denominator here, then that same triangle has to be the denominator on the--.
If one triangle is the numerator on the left hand side of the equal sign, right, so the smaller one's the numerator.
Then it's also going to be the numerator on the right hand side of the equal sign.
I just want to make sure you're consistent that way.
If you flip it then you're going to mess everything up. And then we can just solve for, so y is equal to 12 over 5.
127 00:06:30,736 --> 00:06:33,92 So, let's use this information about similar triangles
just to do some problems.
130 00:06:44,75 --> 00:06:47,68 So let's use some of the geometry we've already learned.
I have two parallel lines, then I have a line like that, then I have a line like this.
What did I say, I said that the lines are parallel, so this line is parallel to this line.
And I want to know if this side is length 5, what is -- well,
let's say this length is length 5, let's say that this length is -- let me draw another color.
This length is, I don't know, 8.
140 00:07:45,37 --> 00:07:48,33 I want to know what this side is.
Actually no, let me give you one more side just to make sure you know all of one triangle.
Let's say that this side is 6, and what I want to do is I want to figure out what this side is right here, this purple side.
So how do we do this?
So before we start using any of that ratio stuff, we have to prove to ourselves and prove in general, that these are similar triangles.
So how can we do that?
Let's see if we can figure out which angles are equal to other angles.
So we have this angle here.
Is this angle equal to any of these three angles in this triangle?
Well, yeah sure.
It's opposite this angle right here, so this is going to be equal to this angle right here, right?
So we know that its opposite side is it's corresponding side, so we know that it corresponds to -- we don't know its length, but we know it corresponds to this 8 length, right?
I forgot to give you some information.
I forgot to tell you that this side is -- let me give it a neutral color.
Let's say that this side is 4.
Let's go back to the problem.
So we just figured out these two angles are the same, and that this is that angle's corresponding side.
Can we figure out any other angles are the same?
Let's say we know what this angle is.
172 00:09:12,2 --> 00:09:15,1 I'm going to do kind of a double angle measure here.
So what angle in this triangle -- does any angle here equal that angle?
Sure.
We know that these are parallel lines, so we can use alternate interior angles to figure out which of these angles equals that one.
But I just saw the time and I realize I'm running out of time.
So I will continue this in the next video.
We are on problem 63.
The height of a triangle is 4 inches greater than twice its base.
Let me this triangle in question.
That's the triangle, that's its height, that's its base.
Let's call that b.
So then the height, that's that, is 4 inches greater than twice its base.
So 4 inches more than 2 times the base.
Fair enough.
The area of the triangle is 168 square inches. What is the base of the triangle?
A candy machine creates small chocolate wafers in the shape of circular discs. The Diameter of each wafer is 16 millimeters.
Whats it the area of each candy?
So, the candy they say is in the shape of circular disc and they tell us that the diameter is 16 millimeters.
If i draw a line across the circle, that goes through the center.
The length of the line all the way across the circle through the center is 16 millimeters.
The Diameter here is 16 millimeters.
And they want us to figure out the area of the surface of the candy. Essentially the area of this circle.
When we think about area, we know that the area of the circle is pi times the radius of the circle square.
They gave us the diameter, what is the radius? well, you might remember that the radius is half of the diameter.
Distance from the center of the circle to the outside, to the boundary of the circle.So, it will be this distance over here, which is exactly half of the diameter. So, would be 8 millimeters.
So, where we see the radius, we can put 8milimeters.
So, the Area is going to be equal to pi times 8 millimeters square, which would be 64 pie millimeters square.
And, typically this is written as pi after 64. So, you might often see it as 64 pie millimeter squared.
Now, this is the answer 64 pi millimeters squared.
But sometimes it is not satisfying to leave it as 64 pi millimeter squared.
You might well say, that what number it is close to. I want a decimal representation of this.
And we could start to use the approximate values of pie. So, the most rough approximate value which is tensed to be used is saying that pi, a very rough approximation, is equal to 3.14.
So, in that case we can that this will be equal to 64 times 3.14 millimeters squared.
We can get a calculator to figure out what this will be in decimal form.
So, we have 64 times 3.14, gives us 200.96
So, we can say that the area is approximately equal to 200.96 square millimeters.
Now if we want to get a more accurate representation of this, pi just actually keeps going on and on forever, we could use the calculator's internal representation of pi.
In which case, we will say 64 times, and than we have to look for the pi on the calculator, it's up here this yellow, so I'll use the 2nd function to get the pi there.
Now, we are using the calculator's internal representation of pi which is going to be more precise than what I had in the last one.
And you can 201.06 (to the nearest hundred)
So, more precise is 201.06 square millimeters. So, this is closer to the actual answer, because the calculator's representation is more precise than this very rough approximation of what pi is.
We're told that for the past few months, Old Maple Farms has grown about 1,000 more apples than their chief rival in the region, River Orchards.
Due to cold weather this year, the harvests at both farms were down by about a third.
However, both farms made up for some of the shortfall by purchasing equal quantities of apples from farms in neighboring states.
What can you say about the number of apples available at each farm?
Does one farm have more than the other, or do they have the same amount?
How do I know?
So let's define some variables here.
Let's let M be equal to number of apples at Maple Farms. And then who's the other guy?
River Orchards.
So let's let R be equal to the number of apples at River Orchards.
So this first sentence, they say-- let me do this in a different color-- they say for the past few years, Old Maple
Farms has grown about 1,000 more apples than their chief rival in the region, River Orchards.
So we could say, hey, Maple is approximately Old River, or M is approximately River plus 1,000.
Or since we don't know the exact amount-- it says it's about 1,000 more, so we don't know it's exactly 1,000 more-- we can just say that in a normal year, Old Maple Farms, which we denote by M, has a larger amount of apples than
River Orchard.
So in a normal year, M is greater than R, right?
It has about 1,000 more apples than Old Maple Farms.
Now, they say due to cold weather this year-- so let's talk about this year now-- the harvests at both farms were down about a third.
Let's talk about what's going to happen this year.
In this year, each of these characters are going to be down by 1/3.
Now if I go down by 1/3, that's the same thing as being 2/3 of what I was before.
Let me do an example.
If I'm at x, and I take away 1/3x, I'm left with 2/3x.
So going down by 1/3 is the same thing as multiplying the quantity by 2/3.
So if we multiply each of these quantities by 2/3, we can still hold this inequality, because we're doing the same thing to both sides of this inequality, and we're multiplying by a positive number.
If we were multiplying by a negative number, we would have to swap the inequality. So we can multiply both sides of this by 2/3.
So 2/3 of M is still going to be greater than 2/3 of R.
And you could even draw that in a number line if you like.
Let's do this in a number line.
This all might be a little intuitive for you, and if it is, I apologize, but if it's not, it never hurts.
So that's 0 on our number line.
So in a normal year, M is has 1,000 more than R.
So in a normal year, M might be over here and maybe R is over here.
I don't know, let's say R is over there.
Now, if we take 2/3 of M, that's going to stick us some place around, oh, I don't know, 2/3 is right about there.
So this is M-- let me write this-- this is 2/3 M.
And what's 2/3 of R going to be?
Well, if you take 2/3 of this, you get to right about there, that is 2/3R.
So you can see, 2/3R is still less than 2/3M, or 2/3M is greater than 2/3R.
Now, they say both farms made up for some of the shortfall by purchasing equal quantities of apples from farms in neighboring states.
So let's let a be equal to the quantity of apples both purchased.
So we could add a to both sides of this equation and it will not change the inequality.
As long as you add or subtract the same value to both sides, it will not change the inequality.
So if you add a to both sides, you have a plus 2/3M is a greater than 2/3R plus a.
This is the amount that Old Maple Farms has after purchasing the apples, and this is the amount that River
Orchards has.
So after everything is said and done, Old Maple Farms still has more apples, and you can see that here.
Maple Farms, a normal year, this year they only had 2/3 of the production, but then they purchased a apples.
So let's say a is about, let's say that a is that many apples, so they got back to their normal amount.
So let's say they got back to their normal amount.
So that's how many apples they purchased, so he got back to M.
Now, if R, if River Orchards also purchased a apples, that same distance, a, if you go along here gets you to right about over there.
So once again, this is-- let me do it a little bit different, because I don't like it overlapping, so let me do it like this.
So let's say this guy, M-- I keep forgetting their names--
Old Maple Farms purchases a apples, gets them that far.
So that's a apples.
But River Orchards also purchases a apples, so let's add that same amount.
I'm just going to copy and paste it so it's the exact same amount.
So River Orchards also purchases a, so it also purchases that same amount.
So when all is said and done, River Orchards is going to have this many apples in the year that they had less production but they went and purchased it.
So this, right here, is-- this value right here is 2/3R plus a.
That's what River Orchards has.
And then Old Maple Farms has this value right here, which is 2/3M plus a.
Everything said and done, Old Maple Farms still has more apples.
Let's keep doing some problems.
So in the last time I said, what are the chances of not getting any heads if I flip the coin-- I was going to say dice, but I realized we're dealing with a coin.
If we flip the coin seven times, if you said, well, that's the same thing as getting 7 tails in a row, and that's 1/2 to the seventh power.
Because each trial there's a 1/2 chance of getting the exact thing that we want, which in this case is tails.
And you multiply it times itself seven times and you get 1/128.
It actually turns out that there are actually 1/128 possible results that we can get, equally probable results.
Well, what's the probability of getting-- I don't know-- all heads and then the last flip I get is tails?
So heads, heads, heads, heads-- so I'm doing it seven times, rights?
So 1, 2, 3, 4, 5, 6, and then the last time I get a tails.
If you can think of it, this is exactly 1 particular result out of the total results that we can get.
And what's the probably of this?
Well, there's a 1/2 chance of getting a heads, 1/2 chance of a heads, 1/2 chance of heads-- let me switch colors-- 1/2 chance of a heads, 1/2 chance of a heads, 1/2 chance of a heads, and then 1/2 chance of a tails.
Once again, this is just 1/2 times 1/2 times 1/2 times 1/2 times 1/2 times 1/2, which is equal to 1/128.
So any particular-- I don't want to say combination because we'll learn a little bit about permutations and combinations in future videos.
But any particular set of circumstances we want is 1 out of 128 of the total number of outcomes.
If I have any particular outcome-- so this is a particular outcome, the way to view it is there are 128 particular outcomes, so if I choose one of them my odds of getting it is 1 out of 128.
So let me ask you a question.
What's the probability of getting exactly 1 heads?
This means I could get-- oh, I could get tails, tails, tails and-- let's say we're doing it five times just so I don't waste too much time.
So that could be tails, tails, heads.
That could be-- as you can tell, I switched colors arbitrarily.
That could be tails, tails, tails, head, tails.
Tails, tails, heads, tails, tails.
That could be tails, heads, tails, tails, tails.
That could be heads, tails, tails, tails.
So if we look at this way there's this probability.
There's actually how many events, how many outcomes, would satisfy this statement, exactly 1 heads?
Well, there's 1, 2, 3, 4, 5.
And the way you could think of it is we're going to do 5 flips, exactly 1 of the flips is going to be heads.
It could be any 1 of those 5 flips.
There are 5 situations in which that happens.
And notice, I said exactly one heads. Because if I said at least 1 heads then we would have to take into circumstances where we have 2 heads and then it becomes more complicated.
We'll learn more about that when we do combinations.
So what are the chances of any one of these possible outcomes?
Well, if we just look at this one.
There's a chance of 1/2, 1/2, 1/2, 1/2, 1/2, so it's 1/2 to the fifth power.
Which is equal to 1/32.
And you use the same logic each to these.
This is 1/32, 1/32, 1/32, 1 out of 32.
And in general, when I'm flipping a fair coin five times in a row there are going to be 32 possible outcomes.
And each of these is just 1 of the particular outcome.
And we're essentially saying, out of the 32 outcomes, 5 satisfy the event that we're looking for-- exactly 1 heads out of 5 flips.
So there are 5 that satisfy it out of a total of 32 outcomes.
And so using that definition only if we can say that all of the outcomes are equally probable.
The probability is 5/32.
And then you could say, well, let me make it a little bit more complicated.
What is the probability of not getting exactly one head?
So here there is a lot more circumstances that satisfy it.
So for example, let me throw out a couple that would satisfy it.
Well, you could get all tails.
But also, if you got 2 heads that would satisfy it because you didn't get exactly 1 head, So this would also satisfy it.
And so you might say, well, if we do it like this it's really complicated.
Or you could say, well, these 5/32 are the only outcomes that don't satisfy-- that do not satisfy this condition.
32 minus 5 is what?
The other 27 outcomes will satisfy this.
So you could say that this is equal to-- and this is a common trick in a lot of probability problems.
This is equal to 1 minus the probability of getting exactly one heads out of 5 flips.
And that is equal to-- 1 is the same thing as 32/32.
Minus-- what's the probability of this?
It's 5/32. And that equals 27/32.
So that's just always something to keep in mind.
Sometimes when you get a probability problem it seems difficult to solve that problem, but it's actually not that difficult to solve the opposite problem.
So you say, well, it's hard for me to directly figure out the probability of not getting exactly one heads; I'd have to know combinations and all of this.
But this is the opposite of getting exactly one heads, and that's an easier thing for me to figure out.
So if I can figure out that probability, all of the other outcomes would satisfy the opposite one.
So anyway, everything we've done so far, it's been dealing with coins and fair coins and that's interesting to a certain degree, but let's make it so that the different outcomes have different probabilities.
Let's do free throw percentages because I think this is something that we all-- if we watch basketball or play any basketball, we're familiar with the idea.
So let's say that I, and this is not true, I only could wish-- let's say that I have an 80% free throw percentage.
So that means every time I go to take a free throw there's an 80% chance there's a basket and that there's a 20% chance there's no basket.
Well, we'll do more on statistics later and they're really-- probability and statistics are opposite sides of the same I guess coin, you could say.
But someone says OK, out of the last hundred times Sal took free throws he's made 80.
So in general, he has an 80% chance of making a particular free throw, but it might not have been a hundred.
I might have taken a thousand free throws and I made 800.
So the 80% is p, and then a common notation is the 20% is 1 minus p.
If I have an 80% chance of making the shot, I have a 20% chance of missing the shot.
So my question to you, let's do kind of the same examples we did with the coins.
What's the probability of me making-- I don't know-- 3 shots in a row, 3 baskets in a row, or 3 free throws in a row?
I'm going to say free throws because this is my free throw percentage, not my overall shot percentage.
Well, by the same logic it's going to be equal.
The first one I would have to get right, then the second one I would have to get-- I would have to get a basket and there's a 20% I have no basket.
And then the third one I would have an 80% chance of getting a basket.
But in general, just from the coin example you can just multiply these probabilities.
So 80% is the same thing as 0.8, so you get 0.8 to the third power.
It is 0.8 times 0.8 times 0.8 is equal to 51.2 or 0.512-- 51.2%.
So I have slightly better than even odds of making 3 free throws in a row, which is pretty good.
In the next video I'll do a lot more examples with the free throws and the basket, and we'll even learn a little bit about conditional probability.
See you soon.
It never hurts to get a lot of practice.
So, in this video I'm just going to do a bunch more of essentially what we call long division problems.
And so if you have four divided into two thousand two hundred ninety-two.
And I don't know exactly why they call it long division, and we saw this in the last video a little bit.
I didn't call it long division then, but I think the reason why is it takes you a long time or it takes a long piece of your paper.
As you go along, you kind of have this thing, this long tail that develops on the problem.
So all of those are, at least, reasons in my head why it's called long division.
But we saw in the last video there's a way to tackle any division problem while just knowing your multiplication tables up to maybe ten times ten or twelve times twelve.
But just as a bit of review, this is the same thing as two thousand two hundred ninety-two divided by four.
And it's actually the same thing-- you probably haven't seen this notation before-- as two thousand two hundred ninety-two divided by four.
These-- This, this, and this-- are all equivalent statements on some level.
And you could say, hey Sal, that looks like a fraction.
In case you have seen fractions already.
And that is exactly what it is.
It is a fraction.
But anyway, I'll just focus on this format and in future videos we'll think about other ways to represent division.
So let's do this problem.
So four goes into two how many times?
It goes into two no times, so let's move on to-- let me switch colors-- Let's move on to the twenty-two.
Four goes into twenty-two how many times?
Let's see.
Four times five is equal to twenty.
Four times six is equal to twenty-four.
So six is too much.
So four goes into twenty-two five times.
Five times four is twenty.
There's going to be a little bit of a leftover,
And then we subtract.
Twenty-two minus twenty?
Well that's just two.
And then you bring down this nine.
And you saw in the last video exactly what this means, right?
When you wrote this five up here, notice you wrote hundreds place.
So this is really a five hundred.
But in this video I'm just going to focus more on the process, and you can think more about what it actually means in terms of where I'm writing the numbers.
But I think the process is going to be crystal clear, hopefully, by the end of this video.
So we brought down the nine.
Four goes into twenty-nine how many times?
It goes into it at least six times.
What's four times seven?
Four times seven is twenty-eight.
So it goes into it at least seven times.
What's four times eight?
Four times eight is thirty-two, so it can't go into it eight times.
So it's going to go into it seven.
Four goes into twenty-nine seven times.
Seven times four is twenty-eight.
Twenty-nine minus twenty-eight, to get our remainder for this step in the problem, is one.
And now we're going to bring down this two.
We're going to bring it down and you get a twelve.
Four goes into twelve?
That's easy.
Four times three is twelve.
Four goes into twelve three times.
Three times four is twelve.
Twelve minus twelve is zero.
We have no remainder.
So four goes into two thousand two hundred ninety-two exactly five hundred seventy-three times.
So this two thousand two hundred ninety-two divided by four we can say is equal to five hundred seventy-three.
Or we could say that this thing right here is equal to five hundred and seventy-three.
Let's do a couple of more.
Let's do a few more problems.
So I'll do that red color.
Let's say we had seven going into six thousand four hundred seventy-five.
Maybe it's called long division because you write it nice and long up here and you have this line.
I don't know.
There's multiple reasons why it could be called long division.
So you say seven goes into six zero times.
So we need to keep moving forward.
So then we go to sixty-four.
Seven goes into sixty-four how many times?
Let's see.
Seven times seven is?
Well, that's way too small.
Let me think about it a little bit.
Well seven times nine is sixty-three.
That's pretty close.
And then seven times ten is going to be too big.
Seven times ten is seventy.
So that's too big.
So seven goes into sixty-four nine times.
Nine times seven is sixty-three. Sixty-four minus sixty-three, to get our remainder at this stage, is one.
Bring down the seven.
Seven goes into seventeen how many times?
Well, seven times two is fourteen. And then seven times three is twenty-one. So three is too big.
So seven goes into seventeen two times.
Two times seven is fourteen. Seventeen minus fourteen is three.
And now we bring down the five.
And seven goes into thirty-five-- That's in our seven multiplication tables-- five times.
Five times seven is thirty-five.
And there you go.
So the remainder is zero.
So all the examples I did so far had no remainders.
Let's do one that maybe might have a remainder.
And to ensure it has a remainder, I'll just make up the problem.
It's much easier to make problems that have remainders than the ones that don't have remainders.
So let's say I want to divide three into-- I'm going to divide it into let's say, one seven three five zero nine two.
This will be a nice, beastly problem.
So if we can do this we can handle everything.
So it's one million seven hundred thirty-five thousand ninety-two.
That's what we're dividing three into.
So, three goes into--
And actually, I'm not sure if this will have a remainder.
In the future video I'll show you how to figure out whether something is divisible by three.
Actually, we can do it right now.
We can just add up all these digits.
One plus seven is eight. Eight plus three is eleven. Eleven plus five is sixteen.
So actually, this number is divisible by three.
So if you add up all of the digits, you get twenty-seven.
And then you can add up those digits-- Two plus seven is nine.
So that is divisible by three.
That's a trick that only works for three.
So this number actually is divisible by three.
So let me change it a little bit, so it's not divisible by three.
Let me make this into a one.
Now this number will not be divisible by three.
I definitely want a number where I'll end up with a remainder.
Just so you see what it looks like.
So let's do this one.
Three goes into one zero times.
So we can just move forward. You could write a zero here, and multiply that out.
But that just makes it a little bit messy in my head.
So we just move one to the right.
Three goes into seventeen how many times?
Well, three times five is equal to fifteen.
And three times six is equal to eighteen and that's too big.
So three goes into seventeen right here five times.
Five times three is fifteen.
And we subtract.
Seventeen minus fifteen is two.
And now we bring down this three.
Three goes into twenty-three how many times?
Well, three times seven is equal to twenty-one. And three times eight is too big.
That's equal to twenty-four.
So three goes into twenty-three seven times.
Seven times three is twenty-one.
Then we subtract.
Twenty-three minus twenty-one is two.
Now we bring down the next number.
We bring down the five.
I think you can appreciate why it's called long division now.
We bring down this five.
Three goes into twenty-five how many times?
Well three times eight gets you pretty close and three times nine is too big.
So it goes into it eight times.
Eight times three is twenty-four.
I'm going to run out of space.
You subtract, you get one.
Twenty-five minus twenty-four is one.
Now we can bring down this zero.
You bring down this zero, just like that.
And you get three goes into ten how many times?
That's easy.
It goes into it three times.
Three times three is nine.
That's about as close to ten as we can get.
Three times three is nine. Ten minus nine--
I'm going to have to scroll up and down here a little bit-- Ten minus nine is one, and then we can bring down the next number.
I'm running out of colors.
I can bring down that nine. Three goes into nineteen how many times?
Well, six is about as close as we can get.
That gets us to eighteen.
So three times six. Three goes into nineteen six times.
Six times three-- let me scroll down.
Six times three is eighteen. Nineteen minus eighteen-- we subtract it up here too.
Nineteen minus eighteen is one and then we're almost done.
I can revert back to the pink.
We bring down this one right there.
Three goes into eleven how many times?
Well, that's three times because three times four is too big.
Three times four is twelve, so that's too big.
So it goes into it three times.
So three goes into eleven three times.
Three times three is nine.
And then we subtract and we get a two.
And there's nothing left to bring down.
Right?
When we look up here there's nothing left to bring down.
So we're done!
So we're left with the remainder of two, after doing this entire problem.
So the answer, three goes into one million seven hundred thirty-five thousand ninety-one-- it goes into it five hundred seventy-eight thousand three hundred sixty-three remainder two.
And that remainder two was what we got all the way down there.
So hopefully you now appreciate that you can tackle pretty much any division problem.
And you also, through this exercise, can appreciate why it's called long division.
 Let's continue on with our study of rotation of functions around the x, and we'll soon see the y-axis as well.
So let's do a slightly harder example than what we've been doing, but I think it might be obvious how to approach it.
So there's my y-axis, there's my x-axis, and in a couple of--
I think it was two problems ago-- we figured out if we had the function y is equal to square root of x-- let me try to draw it-- so this is y equals square root of x-- if we were rotate that around the x-axis, what the volume would be between two points, let's say 0 and some other point.
Now let's just pick an arbitrary point 1.
I think you know how to do that at this point.
Now let's make it a slightly more difficult problem.
Let's say I were to also draw the function y is equal to x squared.
So that looks-- if this is 1, they both meet at 1, right?
Because square root of 1 is 1, and 1 squared is 1, so that would look something like this.
So say y equals x squared looks like that.
So my question now is, what is the volume if I were to take this figure and rotate it around?
So this area here, if I were to rotate that about the x-axis, what would the volume be?
So now, what we did just with the square root of x, we had like a solid cup, right?
It would look something like this. It would be like a cup, and it was solid, we were just trying to figure out the volume of it.
Now it's going to be kind of a hollowed-out cup, because we have this inside function, and so the inside of the cup is going to be empty.
Remember you're just taking this and then you're rotating it around the x-axis.
The volume of this figure, which I'm having trouble drawing, it will be the volume formed by the outside rotation of this y equals square root of x.
It'll be the volume formed when that is rotated around, and then the whole solid volume minus the volume when minus this volume.
So if we took the y equals x squared, y equals x squared would look something like that, and then if you rotated it around the axis, it would look something like that.
So if we subtract out this volume when it's rotated around from the volume of y equals square root of x, when that's rotated, we'll get this figure that we're trying to figure out, this area when it's rotated around.
And that should be intuitive for you, hopefully, because when we just did area under a curve, that's how we would figure out the area of this green area.
We would figure out the area under square root of x, and we'd subtract out the area under y equals x squared.
This time, we're going to say the volume of the revolution of y equals square root of x minus the volume of the revolution of y equals x squared.
So let's do the problem.
So the total volume-- let me do a good color, that looks good-- total volume is going to be equal to the volume formed when we rotate y equals square root of x around the x-axis.
I said from 0 to 1, and that's because I picked where they meet.
We're going from 0 to 1, because they also intersect at 0.
0 squared is the same thing as square root of 0.
We're going from 0 to 1, and so what's the volume of the larger?
Or I guess the y equals square root of x rotated around?
I always forget the formula, that's why I always redraw a disk, so if that's the radius of my disk, the disk is going to come around like that, so we know that the radius is a function of the disk, and that's, of course, the dx is the depth of the disk.
So the radius is the function which, for the outside one, is square root of x, and we know area of this disk is pi r squared, so we square the radius, take a pi outside, and then we multiply that times the width, so that's where we get our dx, and of course we sum them all up and that's where we get the integral.
Some people will put them both within the same integral, but I really want to hit the point home that this is the volume of the outside surface, formed by the outside surface or the cup, minus the volume formed by the the inside function.
It's going to be minus pi-- still going to be from 0 to 1--
I drew fairly huge integral signs, I don't know why-- and what's the inside function?
It's x squared, and that's going to be the radius of its own disks, if that's the radius that's the disk, dx is the width, so it'll be x squared, squared, times dx.
So, volume equals-- let's take the pis out.
And then, times the integral, and now we can merge them back, because integrals are additive like that.
So what's square root of x squared?
Well that's just x.
And what's x squared, squared?
That's x to the fourth, right?
You multiply the exponents, exponent rules.
We have a minus sign here.
Minus x to the fourth, all that times dx, we've got that pi on the outside, that equals-- let's keep our pi on the outside.
We're going to have to evaluate the antiderivative at 1 and 0.
So what's the antiderivative of x?
Well, that's x squared over 2, minus-- what's the antiderivative of x to the fourth?
Well, it's x to the fifth over 5.
That's hopefully second nature to you. x to the fifth over 5, and we're going to evaluate that at 1 and 0.
We're going to subtract them.
Fundamental theorem of calculus.
So that equals-- I'm going to switch colors to avoid monotony-- that equals pi times, let's evaluate it at 1, so it's 1/2 minus 1/5 and when you evaluate it at 0, it's 0 minus 0, so when you evaluate 0, you get nothing.
And so what's 1/2 minus 1/5?
That's pi times 2, get a common denominator of 10, 5/2 is 1/2 minus 2/10 is 1/5, so this equals, this would be 3, so we get 3pi over 10.
That's the volume formed.
So it's almost easier to figure out the volume of this figure than to draw it.
Anyway, I think I'll leave you there with this video, and in the next video, we're going to start rotating around the y-axis.
See you soon.
I dont know what the dream is that you have
I dont care how disappointing it may have been as you have been working towards that dream.
But that dream that you're holding in your mind
That is possible.
Some of you already know
That it is hard.
It's not easy.
It's hard changing your life.
Then in the process of working on your dreams
You are going to incur and incur a lot of disappointment,
A lot of failure.
A lot of pain.
The moment when you're going to doubt yourself.
I say God why, why does this happening to me?
I'm just trying to take care of my children and my mother I'm not trying to steal or rob from anybody.
How is this had to happen to me For those of you who had experience some hardships
Don't give up on your dream
There are rough times are going of to come, but they have not come to stay!. They have come to pass Greatness, is not this ,wonderful, esoteric, illusive god like featuring them
<i>Brought to you by the PKer team @ www.viikii.net
Episode 16 - Final
How come you're riding a bike?
Oh, you came.
Yeah.
Oh, hi.
Hi.
Is it a couple bike?
You're making it so obvious.
It's because of my mother.
She tried to make us wear couple clothes as well, but I ran away.
But, you're not wearing the most important thing, the ring.
Oh, later . . .
I'm going to wear it once we get our marriage license.
Marriage license?
Nothing, let's go.
Yeah. <i>
Really?!
Ha Ni . . .
So by law, you're not related specifically to him?
What are you talking about?
The sky and land knows that we married.
Do you know how many witnesses there were?
You came as well.
Because of that paper . . .
That's the power of a document.
The stamp's power.
That means that I have another chance yet. oh~~ yeah yeah, no wonder, I thought that this was too easy.
But is it true?
Yeah.
Is she going to do nursing because of you?Because you are going to be a doctor?
Yeah.
Oh Ha Ni is amazing.
She's like a star that orbits around Baek Seung Jo.
Isn't it expected that the earth orbits around the sun?
Oh my god, Baek Seung Jo you're the macho type?!
What?
Still have a chance?
Can't believe it!
And what?!
You're not going to register me until I'm able to pass the test to change majors?!
So mean and petty.
Okay.
Since it's mean and petty, I will pass.
So we can make it like a buffet, and customers can personally make their own lunches with the food they like.
And if they order something they really like, then I can personally make it a lunch.
Doesn't that sound okay?
Hello.
Welcome! Aigoo.
You came?
Welcome.
Hey.
Eh?
What would you like?
Today, I want to eat Sam Gye Noodles.
Why do you always eat noodles?
You should eat rice, and bread as well.
Better than noodles, I wanted to eat the seasoned cucumber.
It tastes so nice.
Probably I'm addicted to it.
Ah, what should I do?
There's no seasoned cucumber left.
Eh?
Really?
What is that?
It sure does look fancy.
It's a tereré, which you use to drink mate tea cold!
Have some!
Why should I drink what you have been drinking?
We usually share this between people.
It means that you're friends.
Why would people share this one thing?
I'll catch something from it!
Put it away!
You won't get sick.
Tereré has a component that kills bacteria.
Drink it so we can be friends.
I don't want to be your friend.
Just eat the noodles and go okay?
Then be my boyfriend.
What?
I like you Mr. Bong.
I liked you at first sight.
Let's be a couple.
Oh my goodness, this girl is absolutely crazy!
Didn't I say that I have someone that I like?
Liar!
I came everyday and haven't seen her once!
I haven't seen you date as well
If I like someone, do I have to go on dates and be a couple with them?
Just by myself, in my heart, I see this one person.
What is that?
You, don't come from now on.
Alright?
Don't come!
Oh Min Ah.
I'm going right now.
I'll see you later.
Oh!
Ha Ni.
Long time, no see.
Sunbae!
Why don't you come to practice tennis nowadays?
Just because you got married, you're skipping?
It's not that.
Change of major?
Are you being serious?
Yes, I'm desperate.
I know a little about it because one of my friends is in the nursing program.
Employment and competition is really fierce for that program, so not many people get in.
How are you supposed to change into that major when you don't even have a chance?
I know that, then what do I do?
I really have to get in.
You're probably better off just studying again and reapplying at university under that major.
Try again?
No way.
There's no way that the typhoon's gonna come at that time again.
Typhoon?
There's something like that.
Ha Ni!
I, had "something."
Something?
With Hae Ra?
Are you dating?
We're not exactly dating, but we are eating hot dogs together.
Hot dogs?
What is that?
Hot dogs are very important.
Yah, but how could it be like this?
Can a person like another person this much?
Sunbae!
It is very possible a person can like another person that much.
Joo Ri!
You came?
At first, his hair was pretty long.
Maybe up to his shoulders?
Isn't it long?
He comes everyday and tells me to cut it little by little.
That's why it's that short.
But the strange thing is, he comes a bit later after work hours, and that's why I cut it.
He's coming to see you.
It could be like that.
To you who doesn't have certification, pretty great.
I've been studying.
Hey Jung Joo Ri, if you leave me and start dating, it'll be the end of our friendship.
Hey, since you're always in a room drawing all the time, that's why you haven't dated yet.
Aigoo Dok Go Min Ah, it's a waste of your face.
Why?
She's cool.
Your cartoon ratings are really high.
I uploaded a new one yesterday.
Do you want to see it?
Why did you draw me so fat again?
Because you're fat.
-How can you draw like this?
-My arms are so big!
Omo, it's really the same.
Hey!
What is this?
Why did you draw something like this?
This Oh Ha Ni is now Seung Jo's wife.That's something to see while living.
Right?
I found it interesting while I was drawing.
I'm not his wife yet.
Everyone says it's not going to work.
The test to change majors is hard.
But they say there's no way there are spots available in the nursing program.
Really?
What should I do, Mother?
Marriage license.
Ha Ni...!
Follow me.
Marriage license.
We can just do it then.
What is this?
Doing it his own way?
What is he?
But still, I promised.
How is that a promise?
He did it alone.
Oh, it's here.
Marriage license.
Signatures of 2 witnesses.
Well, your father-in-law and I can do that.
Will it be okay?
It's alright, it's alright.
First we'll report it, and then you can take the test.
You pass for the report and the report for your passing.
It's just a different way of going about it.
Is that so?
Of course.
What's the point in waiting when we don't even know when a spot will open up for you!
This is the problem. Identification.
We need Seung Jo's ID.
ID?
Does Seung Jo always carry around his ID?
Good
What are you doing?
Why are you looking at someone else's wallet?
What do you mean looking through?
Your wallet was pretty so I was just looking at it.
Ah, it's so cute!
Should I buy a couple's wallet too?
Hey, Oh Ha Ni.
Are you touching your husband's wallet already?
It's not that.
It seems like there are a couple bills missing.
Hey what are you talking about?
What do you see me as?
Aren't you gonna sleep?
I am. <i>Brought to you by the PKer team @ www.viikii.net
It's already been reported.
What?
That can't be.
This is the first time we've been here.
Really?!
But why is it already done?
Your husband registered it.
Mr. Baek Seung Jo.
Baek Seung Jo?
Did you know that I took it?
Did you not know what was in here?
Seung Jo.
Why do you tease her so much?
It's fun.
I live for teasing Oh Ha Ni.
She tries hard when she has a goal.
Changing into the nursing program isn't easy.
I did it on purpose so that she would set her mind to it.
But then you touch my wallet.
I'm disappointed in you.
No.
I'm gonna do it.
I'll do it!
I'll work hard.
Don't be disappointed.
Well 1,000 hand outs for the time being.
Ok.
Let's see how many lunch boxes...
Hey, but...
When will you finish all this?
The end is right in front of us so I think I'll have to pull an all-nighter.
Hey, but...
After that day, Chris hasn't shown up.
Is that so?
I was so busy I didn't know.
Ah paper cups...
Breathing techniques for the Heimlich maneuver...
Breathe into the mouth...
Ha Ni, Ha Ni.
Hello.
Really?!
Joon Gu?
Sit down.
Joon Gu is so cool!
By any chance, because the food is so good...
You're not confused are you?
That could happen.
No.
I like everything.
I like the way he looks.
I like how he's like a man.
And especially the way he talks.
It's like he's singing.
Oh I see.
I have to go to England on Christmas Eve.
But I don't want to go.
I want to be with him.
If Mr. Bong tells me not to go, I'm not going.
You like him that much?
But Mr. Bong said that he has someone he likes.
Is that true?
Who is it?
He said that?
No.
There's no such person.
Really?!
I knew it!
Then Ha Ni, help me a bit.
Tell Mr. Bong that I'm pretty.
Alright.
So Pal Bok Lunches!
Here, here, here.
Hello!
Hello, welcome to So Pal Bok.
Please go inside.
Wow, this is great Bong Joon Gu.
You had this kind of ability?
This is just for your opening.
Where did you leave Ha Ni and why are you with this girl?
Joon Gu!
Hello.
Ha Ni, you came? Good job!
This is so that your business will unravel into greatness.
Buying this kind of present in this country...
I told her to buy it.
Oh really?
Okay good job, good job!
We actually need this.
Oh it's 3 fold!
Thanks!
Boss Bong! Your honored guests are here so you should say something.
Chef, what would I say?
You may do it
What are you talking about?
Boss Bong has to do it.
Although there may be some that already know...
There's a book known as the Michelin Guide.
It's a book that introduces the best restaurants around the world.
Getting even 1 star in that book is the most honorable thing ever!
The restaurant becomes a worldwide landmark overnight!
At first I thought they were really jerks.
Who are they to put stars next to someone else's food?
Right?
But then the way they rate the food isn't just that it tastes good!
But it's about whether the food is always good no matter when you go.
A star is only given if the taste of the food is always great whether the chef goes through heartache or happiness.
So I too would like to receive a star with So Pal Bok Lunches!
Then the Goddess So Pal Bok in Heaven... would be so happy, right?
Thank you. Thank you.
You're so cool, Mr. Bong.
Ah, Mr. Bong.
I have to go to England, but I don't want to go.
Tell me not to, then I won't.
What the hell are you talking about?!
Did I not tell you? ... ...
I have no one but Ha Ni.
Ha Ni?
Oh Ha Ni?
Yeah, I have no one but Ha Ni.
You're going to England?
Okay, go go go.
Go and don't come back, okay?
Bong Joon Gu.
Oh hey.
Chris!
What should I do?
Chris decided she was going to go to England.
She trusted me and told me everything.
I feel like I betrayed her.
Then why did you get involved in someone else's business?
She told me to help her.
You must like it.
For an ahjumma to have a scandal and all.
Why are you being like that!
But...
What exactly happened?
You and Bong Joon Gu.
What happened... that he's acting that way even though we got married?
Nothing happened.
It's just Joon Gu's character.
During Freshman year in high school...
Are you jealous?
Hey!
Who's jealous?
Jealous?!
Ah just leave it.
Let those two figure it out on their own.
If you keep getting involved... it might get worse.
Maybe?
Yeah.
Just leave them alone, until they figure everything out.
I guess so.
You did that too, didn't you?
What?
You too, after leaving everything alone, you found out your true feelings.
Ah,really.
I'm right, huh?
Hey, just study.
I'm right, aren't I? You were jealous earlier weren't you?
I said I'm not!
I know you were.
Are you crazy?
Hey!
Aigoo cute.
Did you finish all the leftover dishes?
I'll get housewife's eczema like this!
Me too.
But, she's really not coming.
Who?
Chris.
Yeah.
Did she leave already?
Hey, hurry and come!
Let's hurry.
Hello!
Chris is leaving.
You heard, right?
What does that have to do with me?
Tell me honestly.
Do you not like Chris?
Well . . .
There's nothing not to like . . .
Doesn't not seeing her make you curious?
You miss her, right?
No way.
To me, you're the only one.
Didn't I tell you?
I told you that you're my family.
I'm married, Joon Gu.
Now, Seung Jo is my family.
Yeah, that's right.
Ah, in that case
Then insurance!
Think of it like you took on insurance!
Whenever you're having a hard time, then look for me then!
Don't people look to insurance when they're having a hard time or in a sticky situation?
Joon Gu
Sit here.
Hurry.
All this time, Joon Gu, you . . . you've supported me with everything I have done, cheering me on and doing as I asked.
Thank you.
So this time too, just this once, just listen to me once more.
Sit here and calmly think about it.
"My heart feels this way"
"I know myself."
Don't just keep telling yourself that.
Just leave your heart to the swaying swing while looking up at the sky.
They say that then you'll really see your own feelings.
Try it.
And so?
What do you want me to do about you receiving your draft notice?
Ah, no it's not that you should do something, it's just, I don't know either.
For some reason, I thought I should tell you.
Why?
Don't tell me it's because I cried in front of you that day.
You don't think there's something special between us, right?
Oh, no!
Am I a fool?
When I knew why you were crying,
I didn't think that, so don't worry. Then that's a relief.
I
I'm just saying this so don't feel burdened.
Ok.
When you're bored
When you really have nothing to do and you're really bored, a letter . . .
Would you write a letter to me?
I don't want to.
It's bothersome, it's not even e-mail.
Right, it's not even an email.
Where do you have the time to write it, put a stamp on it, find a mailbox?
I probably couldn't do it either.
With that time you might as well sleep!
Yes.
Yeah...
Then, I'll go.
Hae Ra
I have another favor to ask.
This is a real favor.
From now on, don't cry alone.
Back then, you cried into my shoulder. It didn't feel very good,
like my bones were melting or something.
I'm really going now.
Be well.
If I'm really bored . . .
I'll come visit you.
Sleepy . . .
I don't know when a spot will open up, so I don't even want to do it.
No, Seung Jo is expecting me to do this.
Right, I can't disappoint Seung Jo.
S.J HEARTS H.N Happy Love
FlGHTlNG!
Come outside.
Why?
I have something to say.
Really?
I guess there are times the draft comes out this quickly too.
What a pity.
Oh really?
You're the only one sad to hear that I'm going to the army.
Even my parents were glad, because tuition is so expensive.
But I didn't come here to say that.
I wanted to thank you.
To me?
For what?
Didn't you always tell me?
You don't need to prepare special events or anything.
Just sincerely telling the truth is best.
Of course.
Did you confess?
To Hae Ra?
Why would I confess?
But I did do something similar to confessing.
Did you know...
Honestly, watching you I've learned a lot.
I didn't do it at all because I was afraid of failing.
Or being afraid of being rejected so I didn't confess.
I was always like that.
But watching you I began to think, who cares if I fail.
And who cares if I get rejected.
This was my way of thinking, this mindset.
I learned all of this watching you.
There are a few things I know!
In any case, thanks to you I had a fun time.
That's why this older brother of yours would like to.. give my Ha Ni a present.
Really?
Ok, give it to me.
Not that kind.
You said you wanted to get into the nursing program right?
When I go to the army,
I'll open up a spot for you in the nursing program. How could you do that Sunbae?
You're not even in the nursing program.
Ha Ni
In this world our country is the only one that has a very great system known as the accompanying draft system.
Remember last time when I said I had a friend in the nursing program?
He's a man.
He shares a room with me.
When I get drafted, I'll take him with me.
Really?!
He said he'll go with you?!
What's he going to do if he doesn't go?
I'm taking away the room from him!
If I get rid of the room he has nowhere to go!
If I go to the army he has to go to the army too.
If I go to a secluded island, he has to go and catch tuna or something--
Sunbaenim!
So I'll make a spot somehow.
The exam.
I can't do anything with the exam! So you have to do well and get accepted!
Aah of course!
Aaaah!
Assa!
Thank you so much, really!
Sunbae! Thank you!
Sunbaenim!
Thank you!
Are you this happy to see me go into the army?
Yes, I'm so happy.
Please cut it short.
It's already very short.
Do you want to make it shorter?
Oh, okay.
I'm going to the army.
Then . . . we can't do it with this.
It's okay.
Don't worry,
I will wait for you. <i>Brought to you by the PKer team @ www.viikii.net
I requested a change of majors!
The exam is right away.
Yeah.
There aren't many days left.
But what can I do?
The competition is intense.
Do well.
How can you go to sleep already?
What do you want?
You have to help me study!
Pick out the questions you think are going to appear on the exam.
It's your major.
What are you talking about?!
Please Mr. ESP Baek!
I beg of you.
In order to inspect the patient's nutritional status, when is the best time to inspect the patient's abdomen?
4 to 5 hours after a meal.
The 3 premises of setting up a goal in order to motivate someone?
Be detailed.
It must be achievable and yet slightly hard.
Also . . .
By yourself . . .
That's right!
It has to be set on your own.
See, you need a goal to be more motivated.
I even set up a goal for you.
I have a goal!
What is it?
If I pass this time, a date on Christmas Day.
A date?
We got married without even a proper date.
And during the honeymoon, too.
If I pass, let's go on a date.
All right.
All day.
Full.
Fine.
Awesome!
Shall we practice the practical skill portion?
The practical skill is giving CPR.
I read about it, but
I still haven't tried it yet.
About 100 compressions per minute.
So then,
One-Two-Three.
About this much.
Ok, I'll try it.
The Heimlich maneuver.
Uhh, check for breathing.
There's no breath.
Open the airway, mouth to mouth
Hey, what are you doing?
This is an emergency.
You're feeling it?
That's not it!
What do you mean "feeling" it?
Hurry, what's next?
Okay.
Next, chest compressions, 30 times . . .
One-two-three-four-five.
Hey!
Are you treating a sick person or a healthy person right now?
Huh?
I thought it would hurt.
Harder?
One-two. . .
Arms straight.
Four -- how is this?
Five...Six...Seven...Eight...
Rest a bit.
Come here.
I have a lot to do.
This is study as well.
Ah, Eun Joo.
I wanted to ask you something.
Gosh. . . hyung!
Oh Ha Ni sister-in-law!
Next to your room there's a way before adolescence' me
So please watch yourselves
Yeah.
I'm sorry.
Here, take these to relax!
Did you say it was 2 sessions?
The first is the writing exam and the second is the interview.
What would they ask? I'm so nervous.
No there's no need for that.
You'll do fine after eating this!
Hurry and go.
It's almost time.
Ha Ni, Fighting!
Fighting!
She could have taken the easy route, but she chooses the hardest one!
Gosh, how does he know exactly what's on it?
I really must have married an amazing man.
Min Ah, what if I really get into the nursing program like this?
Number 68, Oh Ha Ni.
Yes.
I'll get back to you later. <i>Interviewer</i>
Hello, I'm number 68, Oh Ha Ni.
By any chance are you the snail?
So you eventually got in.
Why should we choose you?
Ah, yes, as an additional acceptee.
Oh, you got lucky.
A quick and accurate act of CPR, increases the probability of survival by 3 times.
But if it's done incorrectly the patient can die as well.
In real life someone gave CPR to someone whose heart stopped.
They did it incorrectly and eventually went to jail.
Really? It had to be done for the person to live.
- After all, murder is murder.
- Murder?!
What would you do?
If someone can live or die by me giving CPR,
I have to try, hoping they'll live.
Is that so?
Then, try it!
You have to check to see if they're conscious first!
Oh?
Are you alright?
You're not going to report it?
Someone please call 119!
Hey, are you treating a sick person or a healthy person here?
Stop. That's enough.
The people of our country will not call it in unless you say, "YOU do it!".
Just a second ago you said "Please report it!", right?
The call probably still hasn't been made yet.
And you have to press in hard enough for it to be 4-5 centimeters deep.
But you nearly crushed them with 6-7 centimeters deep.
This patient probably is 100% dead from a broken rib piercing their lung.
If this was a real situation, you just murdered someone.
We can't choose a murderer as a nurse.
It was announced on the spot.
She said they can't pick a murderer.
Oh my goodness!
What did I say?
I told you that Oh Ha Ni sister-in-law and being a nurse just doesn't match.
That's right.
I was nervous even though it was a mannequin.
When she said the mannequin was dead, my heart dropped.
How in the world could I treat a person?
Ha Ni.
Then, what are you going to do?
I must have reached beyond my abilities, Dad.
I shouldn't have made the decision so easily.
Oh, I should hurry and pick a major.
I will go upstairs first.
It seems Ha Ni is quite upset.
Really.
She must be really ill fated with that professor.
What to do? I guess there's no date after all!
There's nothing we can do.
I'm going crazy because I want to go on a date with Oh Ha Ni!
I can't break it because a promise is a promise.
Shouldn't just having dinner together be alright?
Really?
Hey!
What are you doing in here, doing this?
A young guy like you should be playing outside.
Why should I do anything on Jesus's birthday?
That's right!
Chris is leaving today, right?
That's right, Chris said she was going to leave on Christmas Eve.
That's right.
Really, she said it was a 7:00 o'clock plane. I'm sure of it!
Aigoo!
Right about now, she should be at the airport. <i>Brought to you by the PKer team @ www.viiikii.net
This would be good.
He said that this bag looked pretty.
I'm late!
Cell phone!
Motorcycles are trouble makers!
I'm sorry. Is there any way that I could get there faster?
What can I do with the traffic?
What should I do?
There's an accident.
Anyway, motorcycles cause accidents!
Is that person dead?
Are you alright, young lady?
What should we do? What should we do?
Someone do something.
You've just murdered someone!
Are you alright?
What to do?!
She seems to be unconscious!
Did anybody call the ambulance? Someone call the ambulance!
What should we do?
No air for 5 minutes is brain damage and over 10 minutes is death.
Let her be!
If you wrongly move a hurt person and damage the spine, they can become paralyzed completely.
Did someone call the ambulance?
Someone must have.
No one called?
Ajusshi with the blue jacket.
Phone?
Call 119.
Oh, yes.
Oh. She's alive! She's alive!
That's a relief!
What kind of person is she?
Oh my god, that's such a relief.
Excuse me!
Do you have a ticket?
Did the plane going to the UK leave? Can't I just go in for a second?!
- You can't go in without a ticket.
- It'll just be a minute!
Just for one minute.
What's up with you, Bong Joon Gu?
Why are you here? Are you crazy?
Mr. Bong.
I was right.
So I was right!
I saw everything.
You came here to get me, right? You're here to tell me not to go.
I didn't come here to stop you.
I came here to see you off.
I came here late because there was traffic in the subway.
How come you're here and not inside?<Br> Did I get the time wrong?
No, I went inside and just came back out.
If I went in, then my heart,
I thought it would hurt so much right here.
Tonight, it's really just me.
Ha Ni went to see her husband.
Jong Gu . . . looks like he went to the airport.
That rascal.
Merry Christmas!
She's all right.
You've done well.
Did you learn first aid?
I didn't learn it, I just . . .
If you didn't do it, then something big could have happened.
You saved a person.
Customer,
Business hours are over.
Yeah.
Excuse me.
Yes.
It's nothing.
There was an accident on the way.
If you were going to send a message, you should've sent it fast.
I was worried that something happened.
Are you okay?
Nothing big, right?
Yeah.
I thought you left.
I'm hungry.
Let's at least eat a hamburger somewhere.
Never mind.
Where would we go like this? <Br> We'd better go home.
It's really hard to have one date.
Even though I had told you that before.
Ha Ni is right here.
If not for Ha Ni, I wouldn't have been here right now.
Whether that is loyalty, friendship, or love, whatever it's called, Ha Ni is nailed in right here.
Do you understand?,
So what?
So... so... because of that...
I mean, I can't erase it, ever.
Are you okay with that?
I don't like it!
How can it be okay with me?
Then I can't do anything.
Go!
Then I'm going to nail it in too!,
If Ha Ni is just 1 nail, then I'm going to nail in 10, 20, 100 nails.
I'm going to nail it all over Mr. Bong's body!
Are you trying to kill me?!
With that many nails a person will die, not live!
Even 1 is this hard.
Really? Then . . .
Oh flowers!
I'll cover you with flowers!
Because I don't like it when Mr.Bong is going through a hard time.
Kiddo, give up on the analogies.
I made a new batch of stuffed cucumber.
Why don't you come and have some of that?
Come on, let's go.
Hey, let go! People are watching!
Hurry, hurry!
Hey, wait.
Let's go together.
Aren't cars not allowed here at night time?
Probably.
Then why did you go in? What if we get caught?
Just don't get caught.
Isn't it exciting doing something we're not supposed to do?
As long as we don't get caught. <i>Brought to you by the PKer team @ www.viikii.net
Baek Seung Jo, you had this in you?
I had no idea.
That's cool.
I'm all kinds of charming you don't know about.
You're in big trouble now.
You've totally fallen for the magic that is Baek Seung Jo.
Hello? <i>This is a collect call. . .</i>
Hae Ra, it's Kyung Soo!
Press 1, press 1! <i>If you would like to continue, press 1 and if not, please hang up.<i>
Hae Ra, thanks for accepting the call.
Making a collect call?
Ah, I'm sorry.
It's just that it's Christmas Eve.
What are you doing? Where are you?
I'm out with my friends.
Oh my, why in the world would I think of you, Sunbae?
Really, little by little.
Do you eat well in the army?
I thought this year would be the busiest, but it's the most quiet.
I like it.
It's been awhile since I was able to spend time with you like this.
Does he not have any plans? Why didn't he go out?
Anyway...
Merry Christmas!
You're the Sunbae now.
I still haven't met a patient.
You already saved someone. And killed a mannequin.
Truthfully, I feel weird.
It's really different from practicing on a mannequin.
I didn't get scared.
All I could think about was having to save her.
I even forgot that I had a date with you.
I had purely wanted to get into the nursing program because of you.
It was much more amazing than what I had thought.
I'm thinking about reapplying.
I'll help you.
It's a cool Christmas.
It's Christmas year round, if I'm with you.
Merry Christmas.
Merry Christmas.
Hey, what if someone saw us?
Who's going to see us?
[Hey!]
Hey, they say the calm cats are the first to climb up the wall..
Were you always so quick to move?!
What?
What did you say?
[Hey! Hey Oh Ha Ni...]
Here please.
Yes.
Excuse me. Please give us three more side dishes.
Here you go.
Excuse me!
Okay.
Thank you.
Yes.
Who should I make this out to?
Lee Jin Ki (?)
Salute!
Here.
This is good. What is it?
Who are you here for?
I'm here to visit soldier Wang Kyung Soo.
Yes.
Hey - open the gate.
Have a nice day!
Have a good visit!
Goodbye!
Don't forget to join us on http://www.viikii.net/channels/goto/youtubeplayfulkiss <i>Thank you PKer team who worked so hard.
Rewrite the expression 4 times, and then in parentheses we have 8 plus 3, using the distributive law of multiplication over addition.
Then simplify the expression.
So let's just try to solve this or evaluate this expression, then we'll talk a little bit about the distributive law of multiplication over addition, usually just called the distributive law.
So we have 4 times 8 plus 8 plus 3.
Now there's two ways to do it.
Normally, when you have parentheses, your inclination is, well, let me just evaluate what's in the parentheses first and then worry about what's outside of the parentheses, and we can do that fairly easily here.
We can evaluate what 8 plus 3 is.
8 plus 3 is 11.
So if we do that-- let me do that in this direction.
So if we do that, we get 4 times, and in parentheses we have an 11.
8 plus 3 is 11, and then this is going to be equal to-- well, 4 times 11 is just 44, so you can evaluate it that way.
But they want us to use the distributive law of multiplication.
We did not use the distributive law just now.
We just evaluated the expression.
We used the parentheses first, then multiplied by 4.
In the distributive law, we multiply by 4 first.
And it's called the distributive law because you distribute the 4, and we're going to think about what that means.
So in the distributive law, what this will become, it'll become 4 times 8 plus 4 times 3, and we're going to think about why that is in a second.
So this is going to be equal to 4 times 8 plus 4 times 3.
A lot of people's first instinct is just to multiply the 4 times the 8, but no!
You have to distribute the 4.
You have to multiply it times the 8 and times the 3.
This is right here.
This is the distributive property in action right here.
Distributive property in action.
And then when you evaluate it-- and I'm going to show you in kind of a visual way why this works.
But then when you evaluate it, 4 times 8-- I'll do this in a different color-- 4 times 8 is 32, and then so we have 32 plus 4 times 3.
4 times 3 is 12 and 32 plus 12 is equal to 44.
That is also equal to 44, so you can get it either way.
But when they want us to use the distributive law, you'd distribute the 4 first.
Now let's think about why that happens.
Let's visualize just what 8 plus 3 is.
Let me draw eight of something.
So one, two, three, four, five, six, seven, eight, right?
And then we're going to add to that three of something, of maybe the same thing.
One, two, three.
So you can imagine this is what we have inside of the parentheses.
We have 8 circles plus 3 circles.
Now, when we're multiplying this whole thing, this whole thing times 4, what does that mean?
Well, that means we're just going to add this to itself four times.
Let me do that with a copy and paste.
Copy and paste.
Let me copy and then let me paste.
There you go.
That's two.
That's one, two, three, and then we have four, and we're going to add them all together.
So this is literally what?
Four times, right?
Let me go back to the drawing tool.
We have it one, two, three, four times this expression, which is 8 plus 3.
Now, what is this thing over here?
But what is this thing over here?
Well, that's 8 added to itself four times.
You could imagine you're adding all of these.
So what's 8 added to itself four times?
That is 4 times 8.
So this is 4 times 8, and what is this over here in the orange?
We have one, two, three, four times.
Well, each time we have three.
So it's 4 times this right here.
This right here is 4 times 3.
So you see why the distributive property works.
If you do 4 times 8 plus 3, you have to multiply-- when you, I guess you could imagine, duplicate the thing four times, both the 8 and the 3 is getting duplicated four times or it's being added to itself four times, and that's why we distribute the 4.
Add.
Simplify the answer and write as a mixed number.
And we have three mixed numbers here:
3 and 1/2 plus 11 and 2/5 plus 4 and 3/15.
So we've already seen that we could view this as 3 plus 1/12 plus 11 plus 2/5-- let me write that down.
This is the same thing as 3 plus 1/12 plus 11 plus 2/5 plus 4 plus 3/15.
The mixed number 3 and 1/12 just literally means 3 and 1/12 or 3 plus 1/12.
And since we're just adding a bunch of numbers, order doesn't matter, so we could add all the whole numbers at once.
So we have 3 plus 11 plus 4, and then we can add the fractions: the 1/12 plus 2/5 plus 3/15.
Now, the blue part's pretty straightforward.
We're just adding numbers.
3 plus 11 is 14 plus 4 is 18, so that part right there is just 18.
This will be a little bit trickier, because we know that when we add fractions, we have to have the same denominator.
And now we have to make all three of these characters have the same denominator and that denominator has to be the least common multiple of 12 and 5 and 15.
Now, we could just do it kind of the brute force way.
We could just look at the multiples.
We could pick one of these guys and keep taking their multiples, and then figuring out whether those multiples are both divisible by 5 and 15.
Or the other way we can do it is take the prime factorization of each of these numbers, and just say that the least common multiple has to contain the prime factorization each of these guys, which means it contains each of those numbers.
So let me show you what I'm talking about.
If we take the prime factorization of 12, 12 is 2 times 6, 6 is 2 times 3, so 12 is equal to 2 times 2 times 3.
That's the prime factorization of 12.
Now, if we do 5, prime factorization of 5, well, 5 is just 1 and 5, so 5 is a prime number.
It is the prime factorization of 5.
There's just a 5 there.
This 1 is kind of useless.
So 5 is just 5.
And then 15, let's do 15.
Actually, when I did the prime factorization of 5, I should have said, look, 5 is prime.
There's no number larger than 1 that divides into it, so it's actually silly to even make a tree there.
And now let's do 15, 15's prime factorization.
15 is 3 times 5, and now both of these are prime.
So we need something that has two 2's and a 3, so let's look at the 12 right there.
So our denominator has to have at least two 2's and a 3, so let's write that down.
So it has to be 2 times 2 times 3.
It has to have at least that.
Now, it also has to have a 5 there, right?
Because it has to be a common multiple of 5.
5's another one of those prime factors, so it's got to have a 5 in there.
It didn't already have a 5.
And then it also has to have a 3 and a 5.
Well, we already have a 5.
We already have a 3 from the 12, and we already have a 5 from the 5, so this number will be divisible by all of them, and you can see that because you can see it has a 12 in it, it has a 5 in it, and it has a 15 in it.
So what is this number?
2 times 2 is 4.
4 times 3 is 12.
12 times 5 is 60.
So the least common multiple of 12, 5 and 15 is 60.
So this is going to be plus.
We're going to be over 60.
So all of these are going to be over 60.
All of these three fractions are over 60.
Now, to go from 12 to 60, we have to multiply the denominator by 5, so we also have to multiply the numerator by 5, so 1 times 5 is 5.
5/60 is the same thing as 1/12.
To go from 5 to 60 in the denominator, we have to multiply by 12, so we have to do the same thing for the numerator.
12 times 2 is 24.
The last one, 15 to 60, you have to multiply by 4, so you have to do the same thing in the numerator.
4 times 3 is 12.
And now we have the same denominator.
We are ready to add.
So let's do that.
So this is going to be 18 plus, and then over 60, we have 5 plus 24, which is 29.
29 plus 12, let's see, 29 plus 10 would be 39 plus 2 would be 41.
It would be 41.
And as far as I can tell, 41 and 60 do not have any common factors.
41 actually looks prime to me.
So the final answer is 18 and 41/60.
Suppose marketing experts have determined the relationship between the selling price of an item and the cost of an item can be represented by the linear equation q = -30s + 800, where q is the quantity sold in a year and s is the selling price.
If the cost to produce the item is $20, so the cost to produce an item is $20, what is the selling price that optimizes the yearly, the yearly, profit?
So what's the profit going to be?
So let me write this down.
So a yearly profit is going to be the quantity, is going to be, the quantity that we sell in a year, it's going to be the quantity that we sell in a year, times, times, the price that we sell it at, price, times the price that we sell it at, minus the cost of us actually producing that item, and in this case they tell us it is $20.
So for example, if we sell two items, if q is 2 and we sell them for $25, we're gonna make $5 on each item, 'cause it cost each of them cost us 5, $20 to produce, so 25 minus 20 will be 5.
If we sell two items at that price it'll be 2 times 5 or we'll have a profit of $10.
So what, how can we figure out how to maximize this profit?
Well they gave us the quantity as a function of selling price, so we could, we could express the entire profit as a function of selling price.
So we could say, we can substitute q is equal to -30 s plus 800 right over, right over here. And let's be very clear what this is telling us.
This is telling us that if the selling price increases, then this will become a larger negative number so we're going to sell fewer, we're gonna sell a smaller quantity.
And actually if you believe this, and if you actually made the selling price zero, if you just gave away this product, it tells us that we would sell at most 800.
So it might not be a perfect model but let's just use this for, you know some marketing experts have told us this, so let's just use it.
So if we substitute -30 s plus 800 for q, we get -30 s plus 800 times s minus 20, times, and this is in a different shade of yellow, times s minus 20.
This is profit as a function of selling price. And now we can just, let me be very careful here, let me be very care-- This is just, this is q right here, and so this whole thing is q.
Wanna make sure we're multiplying this whole expression times this entire expression right over there, and so let's do that. So this is going to be equal to, this is going to be equal to -30 s.
So let me just distribute it out.
This is going to be -30 s, times s minus 20, times this whole thing, we're taking this whole term, we're first multiplying it times -30 s. And then we're gonna take this whole term and then multiply it by 800, s minus 20. And so this gives us, this is equal to -30 s times s, we have to distribute again,
-30 s squared, -30 s times -20, is going to be positive, positive, positive 600 s. And then we have 800 times s, so that's plus 800 s, and then 800 times -20, so that is -8 times 2 is 16, and we have one, two, three zeros, one, two, three, zeros. And if we simplify we can add these two terms right over here.
We get -30 s squared plus 1400 s minus 16000.
So we now, we've now expressed, we've now expressed, our profit as a function of selling price. And this is actually going to be a downward opening parabola, and we can tell that because the coefficient on the second degree term, on the quadratic term, is negative.
So if we were to graph this, if we were to graph this...
So over here--let me draw a better graph than that.
Over here, this axis right here is going to be the selling price, And this is profit which is a function of selling price.
This graph, this equation right over here, is going to look like this, is going to look something like this.
We already saw the selling price--let me write, just write it this way. So let me just--is going to look something like this.
I don't know what the exact equation is gonna look like, but it's gonna be downward opening. And what we wanna do is maximize the profit.
We wanna find this maximum point right over here.
You could do it with calculus, if you had, if you had calculus at your, at your, at your fingertips. Or you could just recognize this is the vertex of the parabola. And you could, you could figure out the vertex by putting in the vertex form, but the fastest way is to just know that the normally the x coordinate, or the s coordinate, the s coordinate, of the vertex is going to be -b over 2 a.
Negatives cancel out, we could divide the numerator and the denominator by 10.
So this is the same thing as a 140 over 6.
We can divide the numerator and the denominator by 3, or by, by 2. And you get 70, you get 70 over 3. And then we can just divide that, so 3 goes into 70, 3 goes into 7 two times, 2 times 3 is 6.
Subtract, you get a difference of 1, bring down the zero, 3 goes into 10 three times, 3 times 3 is 9, subtract, you have, bring down, you get a 1.
Now we're in the decimals, we bring down another zero, it becomes a 10 again, 3 goes into 10 three times, I think you see where this is going.
It's 23.3 repeating times.
If we just keep doing this, we'll just keep getting more, more, more threes.
Or if we just wanted to round to the nearest penny, since we're talking about selling something, this optimal profit, this optimal profit, will happen at a selling price of $23 and 30, $23 and 33 cents.
That will optimize the yearly profit.
So the problem's this: f of g of x -- hope I get this right -- is equal to 2 times the square root of x squared plus 1 minus 1, all of that over the square root of x squared plus 1 plus 1.
And f of x is equal to 2x minus 1 over x plus 1.
And the question is, if we know that f of g of x is equal to this fairly complex-looking expression, and that f of x is equal to this, than what is g of x?
Because f of g of x, what we do is, we took -- everywhere we see an x, we replace it with g of x.
So, f of g of x would look like this.
And let's say we don't know what g of x is.
Everywhere where we saw an x, we replace it with g of x.
Because -- so it would be 2 times g of x.
Minus 1 over g of x plus 1.
And we also know that f of g of x is equal to this thing.
Here we just took the g of x and put it in of f of x, and we wrote the g of x in the expression.
So that is also equal to 2 times the square root of x squared plus 1, minus 1, all of that over x squared plus 1 plus 1.
2 times something minus 1. 2 times something minus 1 in the numerator, and that's something plus 1 in the denominator.
So in either case, we have g of x is equal to the square root of x squared plus 1.
And if you were given the choices, then all you have to really do is take each of the choices for g of x and replace them in for x in this expression.
And then see which of those choices for g of x ends up with this expression.
It was given that f of x is 2x minus 1 over x plus 1.
And then they said, which of the following is g of x.
So, g of x is equal to.
And they give these choices. a), square root of x, b), square root of x squared plus 1, which we just figured out was actually the answer. c), x, d), x squared.
looking at it you didn't -- the method we just saw, saw that if you just replaced x with square root of x squared plus 1 everywhere, then you'd get f of g of x.
Well, then you'd get 2 times square root of x minus 1 over the square root of x plus 1.
Then if you took this and you replaced for x everywhere -- so if you took this expression, you replaced it for x everywhere, then you would get this expression.
So you would know that this would be the answer.
If g of x was this, then f of g of x would be -- let's see, everywhere we see an x, you'd put an x squared, so it would be 2x squared minus 1 over x squared plus 1.
Which does not equal this.
And similarly, if g of x was this term right here, then f of g of x would be would be 2 times x squared plus 1 minus 1 over x squared plus 1 plus 1.
And so this, once again, if you're given the choices, you just try this out.
And if you replace this expression everywhere, where you see an x, right?
Romeo and Juliet by William Shakespeare
THE PROLOGUE [Enter Chorus.]
CHORUS Two households, both alike in dignity,
In fair Verona, where we lay our scene, From ancient grudge break to new mutiny,
Where civil blood makes civil hands unclean.
From forth the fatal loins of these two foes
A pair of star-cross'd lovers take their life; Whose misadventur'd piteous overthrows
Doth with their death bury their parents' strife.
The fearful passage of their death-mark'd love,
And the continuance of their parents' rage, Which but their children's end naught could remove,
Is now the two hours' traffic of our stage; The which, if you with patient ears attend,
What here shall miss, our toil shall strive to mend.
[Exeunt.]
ACT I. Scene I. A public place.
[Enter Sampson and Gregory armed with swords and bucklers.]
SAMPSON Gregory, o' my word, we'll not carry coals.
GREGORY No, for then we should be colliers.
SAMPSON I mean, an we be in choler we'll draw.
GREGORY Ay, while you live, draw your neck out o' the collar.
SAMPSON I strike quickly, being moved.
GREGORY But thou art not quickly moved to strike.
SAMPSON A dog of the house of Montague moves me.
GREGORY To move is to stir; and to be valiant is to stand: therefore, if thou art moved, thou runn'st away.
SAMPSON A dog of that house shall move me to stand:
I will take the wall of any man or maid of Montague's.
GREGORY That shows thee a weak slave; for the weakest goes to the wall.
SAMPSON True; and therefore women, being the weaker vessels, are ever thrust to the wall: therefore I will push Montague's men from the wall and thrust his maids to the wall.
GREGORY The quarrel is between our masters and us their men.
SAMPSON 'Tis all one, I will show myself a tyrant: when I have fought with the men I will be cruel with the maids, I will cut off their heads.
GREGORY The heads of the maids?
SAMPSON Ay, the heads of the maids, or their maidenheads; take it in what sense thou wilt.
GREGORY They must take it in sense that feel it.
SAMPSON Me they shall feel while I am able to stand: and 'tis known I am a pretty piece of flesh.
GREGORY 'Tis well thou art not fish; if thou hadst, thou hadst been poor-John.--Draw thy tool; Here comes two of the house of Montagues.
SAMPSON My naked weapon is out: quarrel!
I will back thee.
GREGORY How! turn thy back and run?
SAMPSON Fear me not.
GREGORY No, marry; I fear thee!
SAMPSON Let us take the law of our sides; let them begin.
GREGORY I will frown as I pass by; and let them take it as they list.
SAMPSON Nay, as they dare.
I will bite my thumb at them; which is disgrace to them if they bear it.
[Enter Abraham and Balthasar.]
ABRAHAM Do you bite your thumb at us, sir?
SAMPSON I do bite my thumb, sir.
ABRAHAM Do you bite your thumb at us, sir?
SAMPSON Is the law of our side if I say ay?
GREGORY No.
SAMPSON No, sir, I do not bite my thumb at you, sir; but I bite my thumb, sir.
GREGORY Do you quarrel, sir?
ABRAHAM Quarrel, sir! no, sir.
SAMPSON But if you do, sir, am for you: I serve as good a man as you.
ABRAHAM No better.
SAMPSON Well, sir.
GREGORY Say better; here comes one of my master's kinsmen.
SAMPSON Yes, better, sir.
ABRAHAM You lie.
SAMPSON Draw, if you be men.--Gregory, remember thy swashing blow.
[They fight.]
[Enter Benvolio.]
BENVOLlO Part, fools! put up your swords; you know not what you do.
[Beats down their swords.]
[Enter Tybalt.]
TYBALT What, art thou drawn among these heartless hinds?
Turn thee Benvolio, look upon thy death.
BENVOLlO I do but keep the peace: put up thy sword, Or manage it to part these men with me.
TYBALT What, drawn, and talk of peace!
I hate the word
As I hate hell, all Montagues, and thee:
Have at thee, coward!
[They fight.]
[Enter several of both Houses, who join the fray; then enter
Citizens with clubs.] 1 ClTIZEN Clubs, bills, and partisans! strike! beat them down!
Down with the Capulets! Down with the Montagues!
[Enter Capulet in his gown, and Lady Capulet.]
CAPULET What noise is this?--Give me my long sword, ho!
LADY CAPULET A crutch, a crutch!--Why call you for a sword?
CAPULET My sword, I say!--Old Montague is come,
And flourishes his blade in spite of me.
[Enter Montague and his Lady Montague.]
MONTAGUE Thou villain Capulet!-- Hold me not, let me go.
LADY MONTAGUE Thou shalt not stir one foot to seek a foe.
[Enter Prince, with Attendants.]
PRlNCE Rebellious subjects, enemies to peace, Profaners of this neighbour-stained steel,--
Will they not hear?--What, ho! you men, you beasts, That quench the fire of your pernicious rage
With purple fountains issuing from your veins,-- On pain of torture, from those bloody hands
Throw your mistemper'd weapons to the ground And hear the sentence of your moved prince.--
Three civil brawls, bred of an airy word, By thee, old Capulet, and Montague,
Have thrice disturb'd the quiet of our streets; And made Verona's ancient citizens
Cast by their grave beseeming ornaments, To wield old partisans, in hands as old,
Canker'd with peace, to part your canker'd hate:
If ever you disturb our streets again,
Your lives shall pay the forfeit of the peace.
For this time, all the rest depart away:--
You, Capulet, shall go along with me;-- And, Montague, come you this afternoon,
To know our farther pleasure in this case, To old Free-town, our common judgment-place.--
Once more, on pain of death, all men depart.
[Exeunt Prince and Attendants; Capulet, Lady Capulet, Tybalt,
Citizens, and Servants.]
MONTAGUE Who set this ancient quarrel new abroach?--
Speak, nephew, were you by when it began?
BENVOLlO Here were the servants of your adversary And yours, close fighting ere I did approach:
I drew to part them: in the instant came The fiery Tybalt, with his sword prepar'd;
Which, as he breath'd defiance to my ears, He swung about his head, and cut the winds,
Who, nothing hurt withal, hiss'd him in scorn:
While we were interchanging thrusts and blows,
Came more and more, and fought on part and part, Till the prince came, who parted either part.
LADY MONTAGUE O, where is Romeo?--saw you him to-day?--
Right glad I am he was not at this fray.
BENVOLlO Madam, an hour before the worshipp'd sun Peer'd forth the golden window of the east,
A troubled mind drave me to walk abroad; Where,--underneath the grove of sycamore
That westward rooteth from the city's side,-- So early walking did I see your son:
Towards him I made; but he was ware of me, And stole into the covert of the wood:
I, measuring his affections by my own,-- That most are busied when they're most alone,--
Pursu'd my humour, not pursuing his, And gladly shunn'd who gladly fled from me.
MONTAGUE Many a morning hath he there been seen,
With tears augmenting the fresh morning's dew, Adding to clouds more clouds with his deep sighs:
But all so soon as the all-cheering sun Should in the farthest east begin to draw
The shady curtains from Aurora's bed, Away from light steals home my heavy son,
And private in his chamber pens himself; Shuts up his windows, locks fair daylight out
And makes himself an artificial night: Black and portentous must this humour prove,
Unless good counsel may the cause remove.
BENVOLlO My noble uncle, do you know the cause?
MONTAGUE I neither know it nor can learn of him.
BENVOLlO Have you importun'd him by any means?
MONTAGUE Both by myself and many other friends;
But he, his own affections' counsellor, Is to himself,--I will not say how true,--
But to himself so secret and so close, So far from sounding and discovery,
As is the bud bit with an envious worm Ere he can spread his sweet leaves to the air,
Or dedicate his beauty to the sun.
Could we but learn from whence his sorrows grow,
We would as willingly give cure as know.
BENVOLlO See, where he comes: so please you step aside; I'll know his grievance or be much denied.
MONTAGUE I would thou wert so happy by thy stay
To hear true shrift.--Come, madam, let's away, [Exeunt Montague and Lady.]
[Enter Romeo.]
BENVOLlO Good morrow, cousin.
ROMEO Is the day so young?
BENVOLlO But new struck nine.
ROMEO Ay me! sad hours seem long.
Was that my father that went hence so fast?
BENVOLlO It was.--What sadness lengthens Romeo's hours?
ROMEO Not having that which, having, makes them short.
BENVOLlO In love?
ROMEO Out,--
BENVOLlO Of love?
ROMEO Out of her favour where I am in love.
BENVOLlO Alas, that love, so gentle in his view,
Should be so tyrannous and rough in proof!
ROMEO Alas that love, whose view is muffled still,
Should, without eyes, see pathways to his will!-- Where shall we dine?--O me!--What fray was here?
Yet tell me not, for I have heard it all.
Here's much to do with hate, but more with love:--
Why, then, O brawling love!
O loving hate!
O anything, of nothing first create!
O heavy lightness! serious vanity!
Mis-shapen chaos of well-seeming forms!
Feather of lead, bright smoke, cold fire, sick health!
Still-waking sleep, that is not what it is!--
This love feel I, that feel no love in this.
Dost thou not laugh?
BENVOLlO No, coz, I rather weep.
ROMEO Good heart, at what?
BENVOLlO At thy good heart's oppression.
ROMEO Why, such is love's transgression.--
Griefs of mine own lie heavy in my breast; Which thou wilt propagate, to have it prest
With more of thine: this love that thou hast shown Doth add more grief to too much of mine own.
Love is a smoke rais'd with the fume of sighs; Being purg'd, a fire sparkling in lovers' eyes;
Being vex'd, a sea nourish'd with lovers' tears:
What is it else? a madness most discreet,
A choking gall, and a preserving sweet.-- Farewell, my coz.
[Going.]
BENVOLlO Soft!
I will go along:
An if you leave me so, you do me wrong.
ROMEO Tut!
I have lost myself; I am not here:
This is not Romeo, he's some other where.
BENVOLlO Tell me in sadness who is that you love?
ROMEO What, shall I groan and tell thee?
BENVOLlO Groan! why, no;
But sadly tell me who.
ROMEO Bid a sick man in sadness make his will,--
Ah, word ill urg'd to one that is so ill!-- In sadness, cousin, I do love a woman.
BENVOLlO I aim'd so near when I suppos'd you lov'd.
ROMEO A right good markman!--And she's fair I love.
BENVOLlO A right fair mark, fair coz, is soonest hit.
ROMEO Well, in that hit you miss: she'll not be hit
With Cupid's arrow,--she hath Dian's wit; And, in strong proof of chastity well arm'd,
From love's weak childish bow she lives unharm'd.
She will not stay the siege of loving terms
Nor bide th' encounter of assailing eyes, Nor ope her lap to saint-seducing gold:
O, she's rich in beauty; only poor That, when she dies, with beauty dies her store.
BENVOLlO Then she hath sworn that she will still live chaste?
ROMEO She hath, and in that sparing makes huge waste;
For beauty, starv'd with her severity, Cuts beauty off from all posterity.
She is too fair, too wise; wisely too fair, To merit bliss by making me despair:
She hath forsworn to love; and in that vow Do I live dead that live to tell it now.
BENVOLlO Be rul'd by me, forget to think of her.
ROMEO O, teach me how I should forget to think.
BENVOLlO By giving liberty unto thine eyes;
Examine other beauties.
ROMEO 'Tis the way To call hers, exquisite, in question more:
These happy masks that kiss fair ladies' brows, Being black, puts us in mind they hide the fair;
He that is strucken blind cannot forget The precious treasure of his eyesight lost:
Show me a mistress that is passing fair, What doth her beauty serve but as a note
Where I may read who pass'd that passing fair?
Farewell: thou canst not teach me to forget.
BENVOLlO I'll pay that doctrine, or else die in debt.
[Exeunt.]
Scene Il.
A Street.
[Enter Capulet, Paris, and Servant.]
CAPULET But Montague is bound as well as I,
In penalty alike; and 'tis not hard, I think, For men so old as we to keep the peace.
PARlS Of honourable reckoning are you both;
And pity 'tis you liv'd at odds so long.
But now, my lord, what say you to my suit?
CAPULET But saying o'er what I have said before:
My child is yet a stranger in the world, She hath not seen the change of fourteen years;
Let two more summers wither in their pride Ere we may think her ripe to be a bride.
PARlS Younger than she are happy mothers made.
CAPULET And too soon marr'd are those so early made.
The earth hath swallowed all my hopes but she,-- She is the hopeful lady of my earth:
But woo her, gentle Paris, get her heart, My will to her consent is but a part;
An she agree, within her scope of choice Lies my consent and fair according voice.
This night I hold an old accustom'd feast, Whereto I have invited many a guest,
Such as I love; and you among the store, One more, most welcome, makes my number more.
At my poor house look to behold this night Earth-treading stars that make dark heaven light:
Such comfort as do lusty young men feel When well apparell'd April on the heel
Of limping winter treads, even such delight Among fresh female buds shall you this night
Inherit at my house; hear all, all see, And like her most whose merit most shall be:
Which, among view of many, mine, being one, May stand in number, though in reckoning none.
Come, go with me.--Go, sirrah, trudge about Through fair Verona; find those persons out
Whose names are written there, [gives a paper] and to them say, My house and welcome on their pleasure stay.
[Exeunt Capulet and Paris].
SERVANT Find them out whose names are written here!
It is written that the shoemaker should meddle with his yard and the tailor with his last, the fisher with his pencil, and the painter with his nets; but I am sent to find those persons whose names are here writ, and can never find what names the writing person hath here writ.
I must to the learned:--in good time!
[Enter Benvolio and Romeo.]
BENVOLlO Tut, man, one fire burns out another's burning,
One pain is lessen'd by another's anguish; Turn giddy, and be holp by backward turning;
One desperate grief cures with another's languish:
Take thou some new infection to thy eye,
And the rank poison of the old will die.
ROMEO Your plantain-leaf is excellent for that.
BENVOLlO For what, I pray thee?
ROMEO For your broken shin.
BENVOLlO Why, Romeo, art thou mad?
ROMEO Not mad, but bound more than a madman is;
Shut up in prison, kept without my food, Whipp'd and tormented and--God-den, good fellow.
SERVANT God gi' go-den.--I pray, sir, can you read?
ROMEO Ay, mine own fortune in my misery.
SERVANT Perhaps you have learned it without book: but I pray, can you read anything you see?
ROMEO Ay, If I know the letters and the language.
SERVANT Ye say honestly: rest you merry!
ROMEO Stay, fellow; I can read.
[Reads.]
'Signior Martino and his wife and daughters;
County Anselmo and his beauteous sisters; the lady widow of Vitruvio; Signior Placentio and his lovely nieces; Mercutio and his brother Valentine; mine uncle Capulet, his wife, and daughters; my fair niece Rosaline; Livia; Signior Valentio and his cousin Tybalt; Lucio and the
[Gives back the paper]: whither should they come?
SERVANT Up.
ROMEO Whither?
SERVANT To supper; to our house.
ROMEO Whose house?
SERVANT My master's.
ROMEO Indeed I should have ask'd you that before.
SERVANT Now I'll tell you without asking: my master is the great rich Capulet; and if you be not of the house of Montagues, I pray, come and crush a cup of wine.
Rest you merry!
[Exit.]
BENVOLlO At this same ancient feast of Capulet's Sups the fair Rosaline whom thou so lov'st;
With all the admired beauties of Verona.
Go thither; and, with unattainted eye,
Compare her face with some that I shall show, And I will make thee think thy swan a crow.
ROMEO When the devout religion of mine eye
Maintains such falsehood, then turn tears to fires; And these,--who, often drown'd, could never die,--
Transparent heretics, be burnt for liars!
One fairer than my love? the all-seeing sun
Ne'er saw her match since first the world begun.
BENVOLlO Tut, you saw her fair, none else being by, Herself pois'd with herself in either eye:
But in that crystal scales let there be weigh'd Your lady's love against some other maid
That I will show you shining at this feast, And she shall scant show well that now shows best.
ROMEO I'll go along, no such sight to be shown,
But to rejoice in splendour of my own.
[Exeunt.]
Scene ill.
Room in Capulet's House.
[Enter Lady Capulet, and Nurse.]
LADY CAPULET Nurse, where's my daughter? call her forth to me.
NURSE Now, by my maidenhea,--at twelve year old,--
I bade her come.--What, lamb! what ladybird!-- God forbid!--where's this girl?--what, Juliet!
[Enter Juliet.]
JULlET How now, who calls?
NURSE Your mother.
JULlET Madam, I am here.
What is your will?
LADY CAPULET This is the matter,--Nurse, give leave awhile,
We must talk in secret: nurse, come back again; I have remember'd me, thou's hear our counsel.
Thou knowest my daughter's of a pretty age.
NURSE Faith, I can tell her age unto an hour.
LADY CAPULET She's not fourteen.
NURSE I'll lay fourteen of my teeth,--
And yet, to my teen be it spoken, I have but four,-- She is not fourteen.
How long is it now
To Lammas-tide?
LADY CAPULET A fortnight and odd days.
NURSE Even or odd, of all days in the year,
Come Lammas-eve at night shall she be fourteen.
Susan and she,--God rest all Christian souls!--
Were of an age: well, Susan is with God; She was too good for me:--but, as I said,
On Lammas-eve at night shall she be fourteen; That shall she, marry; I remember it well.
'Tis since the earthquake now eleven years; And she was wean'd,--I never shall forget it--,
Of all the days of the year, upon that day:
For I had then laid wormwood to my dug,
Sitting in the sun under the dove-house wall; My lord and you were then at Mantua:
Nay, I do bear a brain:--but, as I said, When it did taste the wormwood on the nipple
Of my dug and felt it bitter, pretty fool, To see it tetchy, and fall out with the dug!
Shake, quoth the dove-house: 'twas no need, I trow, To bid me trudge.
And since that time it is eleven years; For then she could stand alone; nay, by the rood
She could have run and waddled all about; For even the day before, she broke her brow:
And then my husband,--God be with his soul!
'A was a merry man,--took up the child:
'Yea,' quoth he, 'dost thou fall upon thy face?
Thou wilt fall backward when thou hast more wit; Wilt thou not, Jule?' and, by my holidame, The pretty wretch left crying, and said 'Ay:'
To see now how a jest shall come about!
I warrant, an I should live a thousand yeas,
I never should forget it; 'Wilt thou not, Jule?' quoth he; And, pretty fool, it stinted, and said 'Ay.'
LADY CAPULET Enough of this; I pray thee hold thy peace.
NURSE Yes, madam;--yet I cannot choose but laugh,
To think it should leave crying, and say 'Ay:' And yet, I warrant, it had upon its brow
A bump as big as a young cockerel's stone; A parlous knock; and it cried bitterly.
'Yea,' quoth my husband, 'fall'st upon thy face?
Thou wilt fall backward when thou com'st to age;
Wilt thou not, Jule?' it stinted, and said 'Ay.'
JULlET And stint thou too, I pray thee, nurse, say I.
NURSE Peace, I have done.
God mark thee to his grace!
Thou wast the prettiest babe that e'er I nurs'd:
An I might live to see thee married once, I have my wish.
LADY CAPULET Marry, that marry is the very theme
I came to talk of.--Tell me, daughter Juliet, How stands your disposition to be married?
JULlET It is an honour that I dream not of.
NURSE An honour!--were not I thine only nurse,
I would say thou hadst suck'd wisdom from thy teat.
LADY CAPULET Well, think of marriage now: younger than you,
Here in Verona, ladies of esteem, Are made already mothers: by my count
I was your mother much upon these years That you are now a maid.
Thus, then, in brief;--
The valiant Paris seeks you for his love.
NURSE A man, young lady! lady, such a man
As all the world--why he's a man of wax.
LADY CAPULET Verona's summer hath not such a flower.
NURSE Nay, he's a flower, in faith, a very flower.
LADY CAPULET What say you? can you love the gentleman?
This night you shall behold him at our feast; Read o'er the volume of young Paris' face,
And find delight writ there with beauty's pen; Examine every married lineament,
And see how one another lends content; And what obscur'd in this fair volume lies
Find written in the margent of his eyes.
This precious book of love, this unbound lover,
To beautify him, only lacks a cover: The fish lives in the sea; and 'tis much pride
For fair without the fair within to hide:
That book in many's eyes doth share the glory,
That in gold clasps locks in the golden story; So shall you share all that he doth possess,
By having him, making yourself no less.
NURSE No less! nay, bigger; women grow by men
LADY CAPULET Speak briefly, can you like of Paris' love?
JULlET I'll look to like, if looking liking move:
But no more deep will I endart mine eye
Than your consent gives strength to make it fly.
[Enter a Servant.]
SERVANT Madam, the guests are come, supper served up, you called, my young lady asked for, the nurse cursed in the pantry, and everything in extremity.
I must hence to wait; I beseech you, follow straight.
LADY CAPULET We follow thee.
[Exit Servant.]--
Juliet, the county stays.
NURSE Go, girl, seek happy nights to happy days.
[Exeunt.]
Scene IV.
A Street.
[Enter Romeo, Mercutio, Benvolio, with five or six Maskers;
Torch-bearers, and others.]
ROMEO What, shall this speech be spoke for our excuse?
Or shall we on without apology?
BENVOLlO The date is out of such prolixity:
We'll have no Cupid hoodwink'd with a scarf, Bearing a Tartar's painted bow of lath,
Scaring the ladies like a crow-keeper; Nor no without-book prologue, faintly spoke
After the prompter, for our entrance:
But, let them measure us by what they will,
We'll measure them a measure, and be gone.
ROMEO Give me a torch,--I am not for this ambling;
Being but heavy, I will bear the light.
MERCUTlO Nay, gentle Romeo, we must have you dance.
ROMEO Not I, believe me: you have dancing shoes, With nimble soles; I have a soul of lead
So stakes me to the ground I cannot move.
MERCUTlO You are a lover; borrow Cupid's wings, And soar with them above a common bound.
ROMEO I am too sore enpierced with his shaft
To soar with his light feathers; and so bound, I cannot bound a pitch above dull woe:
Under love's heavy burden do I sink.
MERCUTlO And, to sink in it, should you burden love; Too great oppression for a tender thing.
ROMEO Is love a tender thing? it is too rough,
Too rude, too boisterous; and it pricks like thorn.
MERCUTlO If love be rough with you, be rough with love;
Prick love for pricking, and you beat love down.-- Give me a case to put my visage in:
[Putting on a mask.]
A visard for a visard! what care I What curious eye doth quote deformities?
Here are the beetle-brows shall blush for me.
BENVOLlO Come, knock and enter; and no sooner in
But every man betake him to his legs.
ROMEO A torch for me: let wantons, light of heart, Tickle the senseless rushes with their heels;
For I am proverb'd with a grandsire phrase,-- I'll be a candle-holder and look on,--
The game was ne'er so fair, and I am done.
MERCUTlO Tut, dun's the mouse, the constable's own word:
If thou art dun, we'll draw thee from the mire
Of this--sir-reverence--love, wherein thou stick'st Up to the ears.--Come, we burn daylight, ho.
ROMEO Nay, that's not so.
MERCUTlO I mean, sir, in delay
We waste our lights in vain, like lamps by day.
Take our good meaning, for our judgment sits
Five times in that ere once in our five wits.
ROMEO And we mean well, in going to this mask; But 'tis no wit to go.
MERCUTlO Why, may one ask?
ROMEO I dreamt a dream to-night.
MERCUTlO And so did I.
ROMEO Well, what was yours?
MERCUTlO That dreamers often lie.
ROMEO In bed asleep, while they do dream things true.
MERCUTlO O, then, I see Queen Mab hath been with you.
She is the fairies' midwife; and she comes In shape no bigger than an agate-stone
On the fore-finger of an alderman, Drawn with a team of little atomies
Athwart men's noses as they lie asleep: Her waggon-spokes made of long spinners' legs;
The cover, of the wings of grasshoppers; The traces, of the smallest spider's web;
The collars, of the moonshine's watery beams; Her whip, of cricket's bone; the lash, of film;
Her waggoner, a small grey-coated gnat, Not half so big as a round little worm
Prick'd from the lazy finger of a maid: Her chariot is an empty hazel-nut,
Made by the joiner squirrel or old grub, Time out o' mind the fairies' coachmakers.
And in this state she gallops night by night Through lovers' brains, and then they dream of love;
O'er courtiers' knees, that dream on court'sies straight; O'er lawyers' fingers, who straight dream on fees;
O'er ladies' lips, who straight on kisses dream,-- Which oft the angry Mab with blisters plagues,
Because their breaths with sweetmeats tainted are:
Sometime she gallops o'er a courtier's nose,
And then dreams he of smelling out a suit; And sometime comes she with a tithe-pig's tail,
Tickling a parson's nose as 'a lies asleep, Then dreams he of another benefice:
Sometime she driveth o'er a soldier's neck, And then dreams he of cutting foreign throats,
Of breaches, ambuscadoes, Spanish blades, Of healths five fathom deep; and then anon
Drums in his ear, at which he starts and wakes; And, being thus frighted, swears a prayer or two,
And sleeps again.
This is that very Mab That plats the manes of horses in the night;
And bakes the elf-locks in foul sluttish hairs, Which, once untangled, much misfortune bodes:
This is the hag, when maids lie on their backs, That presses them, and learns them first to bear,
Making them women of good carriage: This is she,--
ROMEO Peace, peace, Mercutio, peace,
Thou talk'st of nothing.
MERCUTlO True, I talk of dreams, Which are the children of an idle brain,
Begot of nothing but vain fantasy; Which is as thin of substance as the air,
And more inconstant than the wind, who wooes Even now the frozen bosom of the north,
And, being anger'd, puffs away from thence, Turning his face to the dew-dropping south.
BENVOLlO This wind you talk of blows us from ourselves:
Supper is done, and we shall come too late.
ROMEO I fear, too early: for my mind misgives
Some consequence, yet hanging in the stars, Shall bitterly begin his fearful date
With this night's revels; and expire the term Of a despised life, clos'd in my breast,
By some vile forfeit of untimely death:
But He that hath the steerage of my course
Direct my sail!--On, lusty gentlemen!
BENVOLlO Strike, drum.
[Exeunt.]
Scene V. A Hall in Capulet's House.
[Musicians waiting.
Enter Servants.] 1 SERVANT Where's Potpan, that he helps not to take away? he shift a trencher! he scrape a trencher!
2 SERVANT When good manners shall lie all in one or two men's hands, and they unwash'd too, 'tis a foul thing.
1 SERVANT Away with the join-stools, remove the court-cupboard, look to the plate:--good thou, save me a piece of marchpane; and as thou loves me, let the porter let in Susan Grindstone and Nell.--
Antony! and Potpan!
2 SERVANT Ay, boy, ready.
1 SERVANT You are looked for and called for, asked for and sought for in the great chamber.
2 SERVANT We cannot be here and there too.--Cheerly, boys; be brisk awhile, and the longer liver take all.
[They retire behind.]
[Enter Capulet, &c. with the Guests the Maskers.]
CAPULET Welcome, gentlemen! ladies that have their toes
Unplagu'd with corns will have a bout with you.-- Ah ha, my mistresses! which of you all
Will now deny to dance? she that makes dainty, she, I'll swear hath corns; am I come near you now?
Welcome, gentlemen!
I have seen the day That I have worn a visard; and could tell
A whispering tale in a fair lady's ear, Such as would please;--'tis gone, 'tis gone, 'tis gone:
You are welcome, gentlemen!--Come, musicians, play.
A hall--a hall! give room! and foot it, girls.--
[Music plays, and they dance.]
More light, you knaves; and turn the tables up,
And quench the fire, the room is grown too hot.-- Ah, sirrah, this unlook'd-for sport comes well.
Nay, sit, nay, sit, good cousin Capulet; For you and I are past our dancing days;
How long is't now since last yourself and I Were in a mask?
2 CAPULET By'r Lady, thirty years.
CAPULET What, man! 'tis not so much, 'tis not so much:
'Tis since the nuptial of Lucentio, Come Pentecost as quickly as it will,
Some five-and-twenty years; and then we mask'd.
2 CAPULET 'Tis more, 'tis more: his son is elder, sir; His son is thirty.
CAPULET Will you tell me that?
His son was but a ward two years ago.
ROMEO What lady is that, which doth enrich the hand Of yonder knight?
SERVANT I know not, sir.
ROMEO O, she doth teach the torches to burn bright!
It seems she hangs upon the cheek of night Like a rich jewel in an Ethiop's ear;
Beauty too rich for use, for earth too dear!
So shows a snowy dove trooping with crows
As yonder lady o'er her fellows shows.
The measure done, I'll watch her place of stand
And, touching hers, make blessed my rude hand.
Did my heart love till now? forswear it, sight!
For I ne'er saw true beauty till this night.
TYBALT This, by his voice, should be a Montague.-- Fetch me my rapier, boy:--what, dares the slave
Come hither, cover'd with an antic face, To fleer and scorn at our solemnity?
Now, by the stock and honour of my kin, To strike him dead I hold it not a sin.
CAPULET Why, how now, kinsman! wherefore storm you so?
TYBALT Uncle, this is a Montague, our foe;
A villain, that is hither come in spite, To scorn at our solemnity this night.
CAPULET Young Romeo, is it?
TYBALT 'Tis he, that villain, Romeo.
CAPULET Content thee, gentle coz, let him alone,
He bears him like a portly gentleman; And, to say truth, Verona brags of him
To be a virtuous and well-govern'd youth:
I would not for the wealth of all the town
Here in my house do him disparagement:
Therefore be patient, take no note of him,--
It is my will; the which if thou respect, Show a fair presence and put off these frowns,
An ill-beseeming semblance for a feast.
TYBALT It fits, when such a villain is a guest:
I'll not endure him.
CAPULET He shall be endur'd:
What, goodman boy!--I say he shall;--go to; Am I the master here, or you? go to.
You'll not endure him!--God shall mend my soul, You'll make a mutiny among my guests!
You will set cock-a-hoop! you'll be the man!
TYBALT Why, uncle, 'tis a shame.
CAPULET Go to, go to!
You are a saucy boy.
Is't so, indeed?-- This trick may chance to scathe you,--I know what:
You must contrary me! marry, 'tis time.-- Well said, my hearts!--You are a princox; go:
Be quiet, or--More light, more light!--For shame!
I'll make you quiet.
What!--cheerly, my hearts.
TYBALT Patience perforce with wilful choler meeting
Makes my flesh tremble in their different greeting.
I will withdraw: but this intrusion shall,
Now seeming sweet, convert to bitter gall.
[Exit.]
ROMEO [To Juliet.]
If I profane with my unworthiest hand
This holy shrine, the gentle fine is this,-- My lips, two blushing pilgrims, ready stand
To smooth that rough touch with a tender kiss.
JULlET Good pilgrim, you do wrong your hand too much, Which mannerly devotion shows in this;
For saints have hands that pilgrims' hands do touch, And palm to palm is holy palmers' kiss.
ROMEO Have not saints lips, and holy palmers too?
JULlET Ay, pilgrim, lips that they must use in prayer.
ROMEO O, then, dear saint, let lips do what hands do;
They pray, grant thou, lest faith turn to despair.
JULlET Saints do not move, though grant for prayers' sake.
ROMEO Then move not while my prayer's effect I take.
Thus from my lips, by thine my sin is purg'd.
[Kissing her.]
JULlET Then have my lips the sin that they have took.
ROMEO Sin from my lips?
O trespass sweetly urg'd!
Give me my sin again.
JULlET You kiss by the book.
NURSE Madam, your mother craves a word with you.
ROMEO What is her mother?
NURSE Marry, bachelor,
Her mother is the lady of the house.
And a good lady, and a wise and virtuous:
I nurs'd her daughter that you talk'd withal; I tell you, he that can lay hold of her
Shall have the chinks.
ROMEO
Is she a Capulet?
O dear account! my life is my foe's debt.
BENVOLlO Away, be gone; the sport is at the best.
ROMEO Ay, so I fear; the more is my unrest.
CAPULET Nay, gentlemen, prepare not to be gone;
We have a trifling foolish banquet towards.-- Is it e'en so? why then, I thank you all;
I thank you, honest gentlemen; good-night.-- More torches here!--Come on then, let's to bed.
Ah, sirrah [to 2 Capulet], by my fay, it waxes late; I'll to my rest.
[Exeunt all but Juliet and Nurse.]
JULlET Come hither, nurse.
What is yond gentleman?
NURSE The son and heir of old Tiberio.
JULlET What's he that now is going out of door?
NURSE Marry, that, I think, be young Petruchio.
JULlET What's he that follows there, that would not dance?
NURSE I know not.
JULlET Go ask his name: if he be married,
My grave is like to be my wedding-bed.
NURSE
His name is Romeo, and a Montague; The only son of your great enemy.
JULlET My only love sprung from my only hate!
Too early seen unknown, and known too late!
Prodigious birth of love it is to me,
That I must love a loathed enemy.
NURSE
What's this?
What's this?
JULlET
A rhyme I learn'd even now Of one I danc'd withal.
[One calls within, 'Juliet.']
NURSE
Anon, anon!
Come, let's away; the strangers all are gone.
[Exeunt.]
[Enter Chorus.]
CHORUS Now old desire doth in his deathbed lie,
And young affection gapes to be his heir; That fair for which love groan'd for, and would die,
With tender Juliet match'd, is now not fair.
Now Romeo is belov'd, and loves again,
Alike bewitched by the charm of looks; But to his foe suppos'd he must complain,
And she steal love's sweet bait from fearful hooks:
Being held a foe, he may not have access
To breathe such vows as lovers us'd to swear; And she as much in love, her means much less
To meet her new beloved anywhere: But passion lends them power, time means, to meet,
Tempering extremities with extreme sweet.
[Exit.] >
ROMEO AND JULlET by William Shakespeare
ACT Il.
Scene I. An open place adjoining Capulet's Garden.
[Enter Romeo.]
ROMEO Can I go forward when my heart is here?
Turn back, dull earth, and find thy centre out.
[He climbs the wall and leaps down within it.]
[Enter Benvolio and Mercutio.]
BENVOLlO Romeo! my cousin Romeo!
MERCUTlO He is wise;
And, on my life, hath stol'n him home to bed.
BENVOLlO He ran this way, and leap'd this orchard wall:
Call, good Mercutio.
MERCUTlO Nay, I'll conjure too.--
Romeo! humours! madman! passion! lover!
Appear thou in the likeness of a sigh:
Speak but one rhyme, and I am satisfied; Cry but 'Ah me!' pronounce but Love and dove;
Speak to my gossip Venus one fair word, One nickname for her purblind son and heir,
Young auburn Cupid, he that shot so trim When King Cophetua lov'd the beggar-maid!--
He heareth not, he stirreth not, he moveth not; The ape is dead, and I must conjure him.--
I conjure thee by Rosaline's bright eyes, By her high forehead and her scarlet lip,
By her fine foot, straight leg, and quivering thigh, And the demesnes that there adjacent lie,
That in thy likeness thou appear to us!
BENVOLlO An if he hear thee, thou wilt anger him.
MERCUTlO This cannot anger him: 'twould anger him To raise a spirit in his mistress' circle,
Of some strange nature, letting it there stand Till she had laid it, and conjur'd it down;
That were some spite: my invocation Is fair and honest, and, in his mistress' name,
I conjure only but to raise up him.
BENVOLlO Come, he hath hid himself among these trees, To be consorted with the humorous night:
Blind is his love, and best befits the dark.
MERCUTlO If love be blind, love cannot hit the mark.
Now will he sit under a medlar tree, And wish his mistress were that kind of fruit
As maids call medlars when they laugh alone.-- Romeo, good night.--I'll to my truckle-bed;
This field-bed is too cold for me to sleep:
Come, shall we go?
BENVOLlO Go then; for 'tis in vain
To seek him here that means not to be found.
[Exeunt.]
Scene Il.
Capulet's Garden.
[Enter Romeo.]
ROMEO He jests at scars that never felt a wound.--
[Juliet appears above at a window.]
But soft! what light through yonder window breaks?
It is the east, and Juliet is the sun!-- Arise, fair sun, and kill the envious moon,
Who is already sick and pale with grief, That thou her maid art far more fair than she:
Be not her maid, since she is envious; Her vestal livery is but sick and green,
And none but fools do wear it; cast it off.-- It is my lady; O, it is my love!
O, that she knew she were!-- She speaks, yet she says nothing: what of that?
Her eye discourses, I will answer it.-- I am too bold, 'tis not to me she speaks:
Two of the fairest stars in all the heaven, Having some business, do entreat her eyes
To twinkle in their spheres till they return.
What if her eyes were there, they in her head?
The brightness of her cheek would shame those stars, As daylight doth a lamp; her eyes in heaven
Would through the airy region stream so bright That birds would sing and think it were not night.--
See how she leans her cheek upon her hand!
O that I were a glove upon that hand,
That I might touch that cheek!
JULlET Ah me!
ROMEO She speaks:--
O, speak again, bright angel! for thou art As glorious to this night, being o'er my head,
As is a winged messenger of heaven Unto the white-upturned wondering eyes
Of mortals that fall back to gaze on him When he bestrides the lazy-pacing clouds
And sails upon the bosom of the air.
JULlET O Romeo, Romeo! wherefore art thou Romeo?
Deny thy father and refuse thy name;
Or, if thou wilt not, be but sworn my love, And I'll no longer be a Capulet.
ROMEO [Aside.]
Shall I hear more, or shall I speak at this?
JULlET 'Tis but thy name that is my enemy;--
Thou art thyself, though not a Montague.
What's Montague?
It is nor hand, nor foot,
Nor arm, nor face, nor any other part Belonging to a man.
O, be some other name!
What's in a name? that which we call a rose By any other name would smell as sweet;
So Romeo would, were he not Romeo call'd, Retain that dear perfection which he owes
Without that title:--Romeo, doff thy name; And for that name, which is no part of thee,
Take all myself.
ROMEO I take thee at thy word:
Call me but love, and I'll be new baptiz'd;
Henceforth I never will be Romeo.
JULlET What man art thou that, thus bescreen'd in night, So stumblest on my counsel?
ROMEO By a name
I know not how to tell thee who I am:
My name, dear saint, is hateful to myself,
Because it is an enemy to thee.
Had I it written, I would tear the word.
JULlET My ears have yet not drunk a hundred words
Of that tongue's utterance, yet I know the sound; Art thou not Romeo, and a Montague?
ROMEO Neither, fair saint, if either thee dislike.
JULlET How cam'st thou hither, tell me, and wherefore?
The orchard walls are high and hard to climb; And the place death, considering who thou art,
If any of my kinsmen find thee here.
ROMEO With love's light wings did I o'erperch these walls; For stony limits cannot hold love out:
And what love can do, that dares love attempt; Therefore thy kinsmen are no let to me.
JULlET If they do see thee, they will murder thee.
ROMEO Alack, there lies more peril in thine eye
Than twenty of their swords: look thou but sweet, And I am proof against their enmity.
JULlET I would not for the world they saw thee here.
ROMEO I have night's cloak to hide me from their sight;
And, but thou love me, let them find me here.
My life were better ended by their hate
Than death prorogued, wanting of thy love.
JULlET By whose direction found'st thou out this place?
ROMEO By love, that first did prompt me to enquire;
He lent me counsel, and I lent him eyes.
I am no pilot; yet, wert thou as far
As that vast shore wash'd with the furthest sea, I would adventure for such merchandise.
JULlET Thou knowest the mask of night is on my face;
Else would a maiden blush bepaint my cheek For that which thou hast heard me speak to-night.
Fain would I dwell on form,fain, fain deny What I have spoke; but farewell compliment!
Dost thou love me, I know thou wilt say Ay; And I will take thy word: yet, if thou swear'st,
Thou mayst prove false; at lovers' perjuries, They say Jove laughs.
O gentle Romeo,
If thou dost love, pronounce it faithfully:
Or if thou thinkest I am too quickly won,
I'll frown, and be perverse, and say thee nay, So thou wilt woo: but else, not for the world.
In truth, fair Montague, I am too fond; And therefore thou mayst think my 'haviour light:
But trust me, gentleman, I'll prove more true Than those that have more cunning to be strange.
I should have been more strange, I must confess, But that thou overheard'st, ere I was 'ware,
My true-love passion: therefore pardon me; And not impute this yielding to light love,
Which the dark night hath so discovered.
ROMEO Lady, by yonder blessed moon I swear,
That tips with silver all these fruit-tree tops,--
JULlET O, swear not by the moon, the inconstant moon, That monthly changes in her circled orb,
Lest that thy love prove likewise variable.
ROMEO What shall I swear by?
JULlET Do not swear at all;
Or if thou wilt, swear by thy gracious self, Which is the god of my idolatry,
And I'll believe thee.
ROMEO If my heart's dear love,--
JULlET Well, do not swear: although I joy in thee,
I have no joy of this contract to-night; It is too rash, too unadvis'd, too sudden;
Too like the lightning, which doth cease to be Ere one can say It lightens.
Sweet, good night!
This bud of love, by summer's ripening breath, May prove a beauteous flower when next we meet.
Good night, good night! as sweet repose and rest Come to thy heart as that within my breast!
ROMEO O, wilt thou leave me so unsatisfied?
JULlET What satisfaction canst thou have to-night?
ROMEO The exchange of thy love's faithful vow for mine.
JULlET I gave thee mine before thou didst request it;
And yet I would it were to give again.
ROMEO Would'st thou withdraw it? for what purpose, love?
JULlET But to be frank and give it thee again.
And yet I wish but for the thing I have; My bounty is as boundless as the sea,
My love as deep; the more I give to thee, The more I have, for both are infinite.
I hear some noise within: dear love, adieu!-- [Nurse calls within.]
Anon, good nurse!--Sweet Montague, be true.
Stay but a little, I will come again.
[Exit.]
ROMEO O blessed, blessed night!
I am afeard, Being in night, all this is but a dream,
Too flattering-sweet to be substantial.
[Enter Juliet above.]
JULlET Three words, dear Romeo, and good night indeed.
If that thy bent of love be honourable, Thy purpose marriage, send me word to-morrow,
By one that I'll procure to come to thee, Where and what time thou wilt perform the rite;
And all my fortunes at thy foot I'll lay And follow thee, my lord, throughout the world.
NURSE [Within.]
Madam!
JULlET I come anon.-- But if thou meanest not well,
I do beseech thee,--
NURSE [Within.]
Madam!
JULlET By-and-by I come:--
To cease thy suit and leave me to my grief: To-morrow will I send.
ROMEO So thrive my soul,--
JULlET A thousand times good night!
[Exit.]
ROMEO A thousand times the worse, to want thy light!-- Love goes toward love as schoolboys from their books;
But love from love, towards school with heavy looks.
[Retiring slowly.]
[Re-enter Juliet, above.]
JULlET Hist!
Romeo, hist!--O for a falconer's voice
To lure this tassel-gentle back again!
Bondage is hoarse and may not speak aloud;
Else would I tear the cave where Echo lies, And make her airy tongue more hoarse than mine
With repetition of my Romeo's name.
ROMEO It is my soul that calls upon my name:
How silver-sweet sound lovers' tongues by night, Like softest music to attending ears!
JULlET Romeo!
ROMEO My dear?
JULlET At what o'clock to-morrow
Shall I send to thee?
ROMEO At the hour of nine.
JULlET I will not fail: 'tis twenty years till then.
I have forgot why I did call thee back.
ROMEO Let me stand here till thou remember it.
JULlET I shall forget, to have thee still stand there,
Remembering how I love thy company.
ROMEO And I'll still stay, to have thee still forget, Forgetting any other home but this.
JULlET 'Tis almost morning; I would have thee gone:
And yet no farther than a wanton's bird; That lets it hop a little from her hand,
Like a poor prisoner in his twisted gyves, And with a silk thread plucks it back again,
So loving-jealous of his liberty.
ROMEO I would I were thy bird.
JULlET Sweet, so would I:
Yet I should kill thee with much cherishing.
Good night, good night! parting is such sweet sorrow
That I shall say good night till it be morrow.
[Exit.]
ROMEO Sleep dwell upon thine eyes, peace in thy breast!--
Would I were sleep and peace, so sweet to rest!
Hence will I to my ghostly father's cell,
His help to crave and my dear hap to tell.
[Exit.]
Scene ill.
Friar Lawrence's Cell.
[Enter Friar Lawrence with a basket.]
FRlAR The grey-ey'd morn smiles on the frowning night,
Chequering the eastern clouds with streaks of light; And flecked darkness like a drunkard reels
From forth day's path and Titan's fiery wheels: Non, ere the sun advance his burning eye,
The day to cheer and night's dank dew to dry, I must up-fill this osier cage of ours
With baleful weeds and precious-juiced flowers.
The earth, that's nature's mother, is her tomb;
What is her burying gave, that is her womb:
And from her womb children of divers kind
We sucking on her natural bosom find; Many for many virtues excellent,
None but for some, and yet all different.
O, mickle is the powerful grace that lies
In plants, herbs, stones, and their true qualities:
For naught so vile that on the earth doth live
But to the earth some special good doth give; Nor aught so good but, strain'd from that fair use,
Revolts from true birth, stumbling on abuse:
Virtue itself turns vice, being misapplied;
And vice sometimes by action dignified.
Within the infant rind of this small flower
Poison hath residence, and medicine power:
For this, being smelt, with that part cheers each part;
Being tasted, slays all senses with the heart.
Two such opposed kings encamp them still
In man as well as herbs,--grace and rude will; And where the worser is predominant,
Full soon the canker death eats up that plant.
[Enter Romeo.]
ROMEO Good morrow, father!
FRlAR Benedicite!
What early tongue so sweet saluteth me?-- Young son, it argues a distemper'd head
So soon to bid good morrow to thy bed:
Care keeps his watch in every old man's eye,
And where care lodges sleep will never lie; But where unbruised youth with unstuff'd brain
Doth couch his limbs, there golden sleep doth reign: Therefore thy earliness doth me assure
Thou art uprous'd with some distemperature; Or if not so, then here I hit it right,--
Our Romeo hath not been in bed to-night.
ROMEO That last is true; the sweeter rest was mine.
FRlAR God pardon sin! wast thou with Rosaline?
ROMEO With Rosaline, my ghostly father? no; I have forgot that name, and that name's woe.
FRlAR That's my good son: but where hast thou been then?
ROMEO I'll tell thee ere thou ask it me again.
I have been feasting with mine enemy; Where, on a sudden, one hath wounded me
That's by me wounded.
Both our remedies Within thy help and holy physic lies;
I bear no hatred, blessed man; for, lo, My intercession likewise steads my foe.
FRlAR Be plain, good son, and homely in thy drift;
Riddling confession finds but riddling shrift.
ROMEO Then plainly know my heart's dear love is set On the fair daughter of rich Capulet:
As mine on hers, so hers is set on mine; And all combin'd, save what thou must combine
By holy marriage: when, and where, and how We met, we woo'd, and made exchange of vow,
I'll tell thee as we pass; but this I pray, That thou consent to marry us to-day.
FRlAR Holy Saint Francis! what a change is here!
Is Rosaline, that thou didst love so dear, So soon forsaken? young men's love, then, lies
Not truly in their hearts, but in their eyes.
Jesu Maria, what a deal of brine
Hath wash'd thy sallow cheeks for Rosaline!
How much salt water thrown away in waste,
To season love, that of it doth not taste!
The sun not yet thy sighs from heaven clears,
Thy old groans ring yet in mine ancient ears; Lo, here upon thy cheek the stain doth sit
Of an old tear that is not wash'd off yet:
If e'er thou wast thyself, and these woes thine,
Thou and these woes were all for Rosaline; And art thou chang'd?
Pronounce this sentence then,--
Women may fall, when there's no strength in men.
ROMEO Thou chidd'st me oft for loving Rosaline.
FRlAR For doting, not for loving, pupil mine.
ROMEO And bad'st me bury love.
FRlAR Not in a grave
To lay one in, another out to have.
ROMEO I pray thee chide not: she whom I love now Doth grace for grace and love for love allow;
The other did not so.
FRlAR O, she knew well Thy love did read by rote, that could not spell.
But come, young waverer, come go with me, In one respect I'll thy assistant be;
For this alliance may so happy prove, To turn your households' rancour to pure love.
ROMEO O, let us hence; I stand on sudden haste.
FRlAR Wisely, and slow; they stumble that run fast.
[Exeunt.]
Scene IV.
A Street.
[Enter Benvolio and Mercutio.]
MERCUTlO Where the devil should this Romeo be?--
Came he not home to-night?
BENVOLlO Not to his father's; I spoke with his man.
MERCUTlO Ah, that same pale hard-hearted wench, that Rosaline,
Torments him so that he will sure run mad.
BENVOLlO Tybalt, the kinsman to old Capulet, Hath sent a letter to his father's house.
MERCUTlO A challenge, on my life.
BENVOLlO Romeo will answer it.
MERCUTlO Any man that can write may answer a letter.
BENVOLlO Nay, he will answer the letter's master, how he dares, being dared.
MERCUTlO Alas, poor Romeo, he is already dead! stabbed with a white wench's black eye; shot through the ear with a love song; the very pin of his heart cleft with the blind bow-boy's butt-shaft: and is he a man to encounter Tybalt?
BENVOLlO Why, what is Tybalt?
MERCUTlO More than prince of cats, I can tell you.
O, he's the courageous captain of compliments.
He fights as you sing prick-song--keeps time, distance, and proportion; rests me his minim rest, one, two, and the third in your bosom: the very butcher of a silk button, a duellist, a duellist; a gentleman of the very first house,--of the first and second cause: ah, the immortal passado! the punto reverso! the hay.--
BENVOLlO The what?
MERCUTlO The pox of such antic, lisping, affecting fantasticoes; these new tuners of accents!--'By Jesu, a very good blade!--a very tall man!--a very good whore!'--Why, is not this a lamentable thing, grandsire, that we should be thus afflicted with these strange flies, these fashion-mongers, these pardonnez-moi's, who stand so much on the new form that they cannot sit at ease on the old bench?
O, their bons, their bons!
BENVOLlO Here comes Romeo, here comes Romeo!
MERCUTlO Without his roe, like a dried herring.--O flesh, flesh, how art thou fishified!--Now is he for the numbers that Petrarch flowed in:
Laura, to his lady, was but a kitchen wench,--marry, she had a better love to be-rhyme her; Dido, a dowdy; Cleopatra, a gypsy; Helen and Hero, hildings and harlots; Thisbe, a gray eye or so, but not to the purpose,-- [Enter Romeo.]
Signior Romeo, bon jour! there's a French salutation to your French slop.
You gave us the counterfeit fairly last night.
ROMEO Good morrow to you both.
What counterfeit did I give you?
MERCUTlO The slip, sir, the slip; can you not conceive?
ROMEO Pardon, good Mercutio, my business was great; and in such a case as mine a man may strain courtesy.
MERCUTlO That's as much as to say, such a case as yours constrains a man to bow in the hams.
ROMEO Meaning, to court'sy.
MERCUTlO Thou hast most kindly hit it.
ROMEO A most courteous exposition.
MERCUTlO Nay, I am the very pink of courtesy.
ROMEO Pink for flower.
MERCUTlO Right.
ROMEO Why, then is my pump well-flowered.
MERCUTlO Well said: follow me this jest now till thou hast worn out thy pump;that, when the single sole of it is worn, the jest may remain, after the wearing, sole singular.
ROMEO O single-soled jest, solely singular for the singleness!
MERCUTlO Come between us, good Benvolio; my wits faint.
ROMEO Swits and spurs, swits and spurs; or I'll cry a match.
MERCUTlO Nay, if thy wits run the wild-goose chase, I have done; for thou hast more of the wild-goose in one of thy wits than, I am sure, I have in my whole five: was I with you there for the goose?
ROMEO Thou wast never with me for anything when thou wast not there for the goose.
MERCUTlO I will bite thee by the ear for that jest.
ROMEO Nay, good goose, bite not.
MERCUTlO Thy wit is a very bitter sweeting; it is a most sharp sauce.
ROMEO And is it not, then, well served in to a sweet goose?
MERCUTlO O, here's a wit of cheveril, that stretches from an inch narrow to an ell broad!
ROMEO I stretch it out for that word broad: which added to the goose, proves thee far and wide a broad goose.
MERCUTlO Why, is not this better now than groaning for love? now art thou sociable, now art thou Romeo; not art thou what thou art, by art as well as by nature: for this drivelling love is like a great natural, that runs lolling up and down to hide his bauble in a hole.
BENVOLlO Stop there, stop there.
MERCUTlO Thou desirest me to stop in my tale against the hair.
BENVOLlO Thou wouldst else have made thy tale large.
MERCUTlO O, thou art deceived; I would have made it short: for I was come to the whole depth of my tale; and meant indeed to occupy the argument no longer.
ROMEO Here's goodly gear!
[Enter Nurse and Peter.]
MERCUTlO A sail, a sail, a sail!
BENVOLlO Two, two; a shirt and a smock.
NURSE Peter!
PETER Anon.
NURSE My fan, Peter.
MERCUTlO Good Peter, to hide her face; for her fan's the fairer face.
NURSE God ye good morrow, gentlemen.
MERCUTlO God ye good-den, fair gentlewoman.
NURSE Is it good-den?
MERCUTlO 'Tis no less, I tell ye; for the bawdy hand of the dial is now upon the prick of noon.
NURSE Out upon you! what a man are you!
ROMEO One, gentlewoman, that God hath made for himself to mar.
NURSE By my troth, it is well said;--for himself to mar, quoth 'a?--Gentlemen, can any of you tell me where I may find the young
Romeo?
ROMEO I can tell you: but young Romeo will be older when you have found him than he was when you sought him:
I am the youngest of that name, for fault of a worse.
NURSE You say well.
MERCUTlO Yea, is the worst well? very well took, i' faith; wisely, wisely.
NURSE If you be he, sir, I desire some confidence with you.
BENVOLlO She will indite him to some supper.
MERCUTlO A bawd, a bawd, a bawd!
So ho!
ROMEO What hast thou found?
MERCUTlO No hare, sir; unless a hare, sir, in a lenten pie, that is something stale and hoar ere it be spent. [Sings.]
An old hare hoar, And an old hare hoar,
Is very good meat in Lent; But a hare that is hoar
Is too much for a score When it hoars ere it be spent.
Romeo, will you come to your father's? we'll to dinner thither.
ROMEO I will follow you.
MERCUTlO Farewell, ancient lady; farewell,-- [singing] lady, lady, lady.
[Exeunt Mercutio, and Benvolio.]
NURSE Marry, farewell!--I pray you, sir, what saucy merchant was this that was so full of his ropery?
ROMEO A gentleman, nurse, that loves to hear himself talk; and will speak more in a minute than he will stand to in a month.
NURSE An 'a speak anything against me, I'll take him down, an'a were lustier than he is, and twenty such Jacks; and if I cannot, I'll find those that shall.
Scurvy knave!
I am none of his flirt-gills; I am none of his skains-mates.--And thou must stand by too, and suffer every knave to use me at his pleasure!
PETER I saw no man use you at his pleasure; if I had, my weapon should quickly have been out, I warrant you:
I dare draw as soon as another man, if I see occasion in a good quarrel, and the law on my side.
NURSE Now, afore God, I am so vexed that every part about me quivers.
Scurvy knave!--Pray you, sir, a word: and, as I told you, my young lady bid me enquire you out; what she bade me say I will keep to myself: but first let me tell ye, if ye should lead her into a fool's paradise, as they say, it were a very gross kind of behaviour, as they say: for the gentlewoman is young; and, therefore, if you should deal double with her, truly it were an ill thing to be offered to any gentlewoman, and very weak dealing.
ROMEO Nurse, commend me to thy lady and mistress.
I protest unto thee,--
NURSE Good heart, and i' faith I will tell her as much:
Lord, Lord, she will be a joyful woman.
ROMEO What wilt thou tell her, nurse? thou dost not mark me.
NURSE I will tell her, sir,--that you do protest: which, as I take it, is a gentlemanlike offer.
ROMEO Bid her devise some means to come to shrift This afternoon;
And there she shall at Friar Lawrence' cell Be shriv'd and married.
Here is for thy pains.
NURSE No, truly, sir; not a penny.
ROMEO Go to; I say you shall.
NURSE This afternoon, sir? well, she shall be there.
ROMEO And stay, good nurse, behind the abbey-wall:
Within this hour my man shall be with thee, And bring thee cords made like a tackled stair;
Which to the high top-gallant of my joy Must be my convoy in the secret night.
Farewell; be trusty, and I'll quit thy pains:
Farewell; commend me to thy mistress.
NURSE Now God in heaven bless thee!--Hark you, sir.
ROMEO What say'st thou, my dear nurse?
NURSE Is your man secret?
Did you ne'er hear say,
Two may keep counsel, putting one away?
ROMEO I warrant thee, my man's as true as steel.
NURSE Well, sir; my mistress is the sweetest lady.--Lord, Lord! when 'twas a little prating thing,--O, there's a nobleman in town, one Paris, that would fain lay knife aboard; but she, good soul, had as lief see a toad, a very toad, as see him.
I anger her sometimes, and tell her that Paris is the properer man; but
I'll warrant you, when I say so, she looks as pale as any clout in the versal world.
Doth not Rosemary and Romeo begin both with a letter?
ROMEO Ay, nurse; what of that? both with an R.
NURSE Ah, mocker! that's the dog's name.
R is for the dog: no; I know it begins with some other letter:--and she hath the prettiest sententious of it, of you and Rosemary, that it would do you good to hear it.
ROMEO Commend me to thy lady.
NURSE Ay, a thousand times.
[Exit Romeo.]
--Peter!
PETER Anon?
NURSE Peter, take my fan, and go before.
[Exeunt.]
Scene V. Capulet's Garden.
[Enter Juliet.]
JULlET The clock struck nine when I did send the nurse;
In half an hour she promis'd to return.
Perchance she cannot meet him: that's not so.--
O, she is lame! love's heralds should be thoughts, Which ten times faster glide than the sun's beams,
Driving back shadows over lowering hills:
Therefore do nimble-pinion'd doves draw love,
And therefore hath the wind-swift Cupid wings.
Now is the sun upon the highmost hill
Of this day's journey; and from nine till twelve Is three long hours,--yet she is not come.
Had she affections and warm youthful blood, She'd be as swift in motion as a ball;
My words would bandy her to my sweet love, And his to me:
But old folks, many feign as they were dead; Unwieldy, slow, heavy and pale as lead.--
O God, she comes!
[Enter Nurse and Peter].
O honey nurse, what news?
Hast thou met with him?
Send thy man away.
NURSE Peter, stay at the gate.
[Exit Peter.]
JULlET Now, good sweet nurse,--O Lord, why look'st thou sad?
Though news be sad, yet tell them merrily;
If good, thou sham'st the music of sweet news By playing it to me with so sour a face.
NURSE I am aweary, give me leave awhile;--
Fie, how my bones ache! what a jaunt have I had!
JULlET I would thou hadst my bones, and I thy news: Nay, come, I pray thee speak;--good, good nurse, speak.
NURSE Jesu, what haste? can you not stay awhile?
Do you not see that I am out of breath?
JULlET How art thou out of breath, when thou hast breath To say to me that thou art out of breath?
The excuse that thou dost make in this delay Is longer than the tale thou dost excuse.
Is thy news good or bad? answer to that; Say either, and I'll stay the circumstance:
Let me be satisfied, is't good or bad?
NURSE Well, you have made a simple choice; you know not how to choose a man:
Romeo! no, not he; though his face be better than any man's, yet his leg excels all men's; and for a hand and a foot, and a body,--though they be not to be talked on, yet they are past compare: he is not the flower of courtesy,--but I'll warrant him as gentle as a lamb.--Go thy ways, wench; serve God.-
-What, have you dined at home?
JULlET No, no: but all this did I know before.
What says he of our marriage? what of that?
NURSE Lord, how my head aches! what a head have I!
It beats as it would fall in twenty pieces.
My back o' t' other side,--O, my back, my back!--
Beshrew your heart for sending me about To catch my death with jauncing up and down!
JULlET I' faith, I am sorry that thou art not well.
Sweet, sweet, sweet nurse, tell me, what says my love?
NURSE Your love says, like an honest gentleman, And a courteous, and a kind, and a handsome;
And, I warrant, a virtuous,--Where is your mother?
JULlET Where is my mother?--why, she is within; Where should she be?
How oddly thou repliest!
'Your love says, like an honest gentleman,-- 'Where is your mother?'
NURSE O God's lady dear!
Are you so hot? marry,come up, I trow; Is this the poultice for my aching bones?
Henceforward, do your messages yourself.
JULlET Here's such a coil!--come, what says Romeo?
NURSE Have you got leave to go to shrift to-day?
JULlET I have.
NURSE Then hie you hence to Friar Lawrence' cell;
There stays a husband to make you a wife:
Now comes the wanton blood up in your cheeks,
They'll be in scarlet straight at any news.
Hie you to church; I must another way,
To fetch a ladder, by the which your love Must climb a bird's nest soon when it is dark:
I am the drudge, and toil in your delight; But you shall bear the burden soon at night.
Go; I'll to dinner; hie you to the cell.
JULlET Hie to high fortune!--honest nurse, farewell.
[Exeunt.]
Scene Vl.
Friar Lawrence's Cell.
[Enter Friar Lawrence and Romeo.]
FRlAR So smile the heavens upon this holy act
That after-hours with sorrow chide us not!
ROMEO Amen, amen! but come what sorrow can, It cannot countervail the exchange of joy
That one short minute gives me in her sight:
Do thou but close our hands with holy words,
Then love-devouring death do what he dare,-- It is enough I may but call her mine.
FRlAR These violent delights have violent ends,
And in their triumph die; like fire and powder, Which, as they kiss, consume: the sweetest honey
Is loathsome in his own deliciousness, And in the taste confounds the appetite:
Therefore love moderately: long love doth so; Too swift arrives as tardy as too slow.
Here comes the lady:--O, so light a foot Will ne'er wear out the everlasting flint:
A lover may bestride the gossamer That idles in the wanton summer air
And yet not fall; so light is vanity.
[Enter Juliet.]
JULlET Good-even to my ghostly confessor.
FRlAR Romeo shall thank thee, daughter, for us both.
JULlET As much to him, else is his thanks too much.
ROMEO Ah, Juliet, if the measure of thy joy
Be heap'd like mine, and that thy skill be more To blazon it, then sweeten with thy breath
This neighbour air, and let rich music's tongue Unfold the imagin'd happiness that both
Receive in either by this dear encounter.
JULlET Conceit, more rich in matter than in words,
Brags of his substance, not of ornament:
They are but beggars that can count their worth;
But my true love is grown to such excess, I cannot sum up sum of half my wealth.
FRlAR Come, come with me, and we will make short work;
For, by your leaves, you shall not stay alone Till holy church incorporate two in one.
[Exeunt.]
>
ROMEO AND JULlET by William Shakespeare
ACT ill.
Scene I. A public Place.
[Enter Mercutio, Benvolio, Page, and Servants.]
BENVOLlO I pray thee, good Mercutio, let's retire: The day is hot, the Capulets abroad,
And, if we meet, we shall not scape a brawl; For now, these hot days, is the mad blood stirring.
MERCUTlO Thou art like one of these fellows that, when he enters the confines of a tavern, claps me his sword upon the table, and says 'God send me no need of thee!' and by the operation of the second cup draws him on the drawer, when indeed there is no need.
BENVOLlO Am I like such a fellow?
MERCUTlO Come, come, thou art as hot a Jack in thy mood as any in
Italy; and as soon moved to be moody, and as soon moody to be moved.
BENVOLlO And what to?
MERCUTlO Nay, an there were two such, we should have none shortly, for one would kill the other.
Thou wilt quarrel with a man for cracking nuts, having no other reason but because thou hast hazel eyes;--what eye but such an eye would spy out such a quarrel?
Thy head is as full of quarrels as an egg is full of meat; and yet thy head hath been beaten as addle as an egg for quarrelling.
Thou hast quarrelled with a man for coughing in the street, because he hath wakened thy dog that hath lain asleep in the sun.
Didst thou not fall out with a tailor for wearing his new doublet before Easter? with another for tying his new shoes with an old riband? and yet thou wilt tutor me from quarrelling!
BENVOLlO An I were so apt to quarrel as thou art, any man should buy the fee simple of my life for an hour and a quarter.
MERCUTlO The fee simple!
O simple!
BENVOLlO By my head, here come the Capulets.
MERCUTlO By my heel, I care not.
[Enter Tybalt and others.]
TYBALT Follow me close, for I will speak to them.--Gentlemen, good-den: a word with one of you.
MERCUTlO And but one word with one of us?
Couple it with something; make it a word and a blow.
TYBALT You shall find me apt enough to that, sir, an you will give me occasion.
MERCUTlO Could you not take some occasion without giving?
TYBALT Mercutio, thou consortest with Romeo,--
MERCUTlO Consort! what, dost thou make us minstrels?
An thou make minstrels of us, look to hear nothing but discords: here's my fiddlestick; here's that shall make you dance.
Zounds, consort!
BENVOLlO We talk here in the public haunt of men:
Either withdraw unto some private place,
And reason coldly of your grievances, Or else depart; here all eyes gaze on us.
MERCUTlO Men's eyes were made to look, and let them gaze;
I will not budge for no man's pleasure, I.
TYBALT Well, peace be with you, sir.--Here comes my man.
[Enter Romeo.]
MERCUTlO But I'll be hanged, sir, if he wear your livery:
Marry, go before to field, he'll be your follower; Your worship in that sense may call him man.
TYBALT Romeo, the love I bear thee can afford
No better term than this,--Thou art a villain.
ROMEO Tybalt, the reason that I have to love thee Doth much excuse the appertaining rage
To such a greeting.
Villain am I none; Therefore farewell; I see thou know'st me not.
TYBALT Boy, this shall not excuse the injuries
That thou hast done me; therefore turn and draw.
ROMEO I do protest I never injur'd thee; But love thee better than thou canst devise
Till thou shalt know the reason of my love:
And so good Capulet,--which name I tender
As dearly as mine own,--be satisfied.
MERCUTlO O calm, dishonourable, vile submission!
Alla stoccata carries it away.
[Draws.]
Tybalt, you rat-catcher, will you walk?
TYBALT What wouldst thou have with me?
MERCUTlO Good king of cats, nothing but one of your nine lives; that I mean to make bold withal, and, as you shall use me hereafter, dry-beat the rest of the eight.
Will you pluck your sword out of his pitcher by the ears? make haste, lest mine be about your ears ere it be out.
TYBALT I am for you.
[Drawing.]
ROMEO Gentle Mercutio, put thy rapier up.
MERCUTlO Come, sir, your passado.
[They fight.]
ROMEO Draw, Benvolio; beat down their weapons.-- Gentlemen, for shame! forbear this outrage!--
Tybalt,--Mercutio,--the prince expressly hath Forbid this bandying in Verona streets.--
Hold, Tybalt!--good Mercutio!-- [Exeunt Tybalt with his Partizans.]
MERCUTlO I am hurt;--
A plague o' both your houses!--I am sped.-- Is he gone, and hath nothing?
BENVOLlO What, art thou hurt?
MERCUTlO Ay, ay, a scratch, a scratch; marry, 'tis enough.--
Where is my page?--go, villain, fetch a surgeon.
[Exit Page.]
ROMEO Courage, man; the hurt cannot be much.
MERCUTlO No, 'tis not so deep as a well, nor so wide as a church door; but 'tis enough, 'twill serve: ask for me to-morrow, and you shall find me a grave man.
I am peppered, I warrant, for this world.--A plague o' both your houses!--Zounds, a dog, a rat, a mouse, a cat, to scratch a man to death! a braggart, a rogue, a villain, that fights by the book of arithmetic!--Why the devil came you between us?
ROMEO I thought all for the best.
MERCUTlO Help me into some house, Benvolio,
Or I shall faint.--A plague o' both your houses!
They have made worms' meat of me:
I have it, and soundly too.--Your houses!
[Exit Mercutio and Benvolio.]
ROMEO This gentleman, the prince's near ally,
My very friend, hath got his mortal hurt In my behalf; my reputation stain'd
With Tybalt's slander,--Tybalt, that an hour Hath been my kinsman.--O sweet Juliet,
Thy beauty hath made me effeminate And in my temper soften'd valour's steel.
[Re-enter Benvolio.]
BENVOLlO O Romeo, Romeo, brave Mercutio's dead!
That gallant spirit hath aspir'd the clouds,
Which too untimely here did scorn the earth.
ROMEO This day's black fate on more days doth depend; This but begins the woe others must end.
BENVOLlO Here comes the furious Tybalt back again.
ROMEO Alive in triumph! and Mercutio slain!
Away to heaven respective lenity, And fire-ey'd fury be my conduct now!--
[Re-enter Tybalt.]
Now, Tybalt, take the 'villain' back again
That late thou gavest me; for Mercutio's soul Is but a little way above our heads,
Staying for thine to keep him company.
Either thou or I, or both, must go with him.
TYBALT Thou, wretched boy, that didst consort him here,
Shalt with him hence.
ROMEO This shall determine that.
[They fight; Tybalt falls.]
BENVOLlO Romeo, away, be gone!
The citizens are up, and Tybalt slain.--
Stand not amaz'd.
The prince will doom thee death If thou art taken.
Hence, be gone, away!
ROMEO O, I am fortune's fool!
BENVOLlO Why dost thou stay?
[Exit Romeo.]
[Enter Citizens, &c.] 1 ClTIZEN Which way ran he that kill'd Mercutio?
Tybalt, that murderer, which way ran he?
BENVOLlO There lies that Tybalt.
1 ClTIZEN Up, sir, go with me; I charge thee in the prince's name obey.
[Enter Prince, attended; Montague, Capulet, their Wives, and others.]
PRlNCE Where are the vile beginners of this fray?
BENVOLlO O noble prince.
I can discover all
The unlucky manage of this fatal brawl: There lies the man, slain by young Romeo,
That slew thy kinsman, brave Mercutio.
LADY CAPULET Tybalt, my cousin!
O my brother's child!--
O prince!--O husband!--O, the blood is spill'd Of my dear kinsman!--Prince, as thou art true,
For blood of ours shed blood of Montague.-- O cousin, cousin!
PRlNCE Benvolio, who began this bloody fray?
BENVOLlO Tybalt, here slain, whom Romeo's hand did slay;
Romeo, that spoke him fair, bid him bethink How nice the quarrel was, and urg'd withal
Your high displeasure.--All this,--uttered With gentle breath, calm look, knees humbly bow'd,--
Could not take truce with the unruly spleen Of Tybalt, deaf to peace, but that he tilts
With piercing steel at bold Mercutio's breast; Who, all as hot, turns deadly point to point,
And, with a martial scorn, with one hand beats Cold death aside, and with the other sends
It back to Tybalt, whose dexterity Retorts it:
Romeo he cries aloud,
'Hold, friends! friends, part!' and swifter than his tongue, His agile arm beats down their fatal points,
And 'twixt them rushes; underneath whose arm An envious thrust from Tybalt hit the life
Of stout Mercutio, and then Tybalt fled:
But by-and-by comes back to Romeo,
Who had but newly entertain'd revenge, And to't they go like lightning; for, ere I
Could draw to part them was stout Tybalt slain; And as he fell did Romeo turn and fly.
This is the truth, or let Benvolio die.
LADY CAPULET He is a kinsman to the Montague, Affection makes him false, he speaks not true:
Some twenty of them fought in this black strife, And all those twenty could but kill one life.
I beg for justice, which thou, prince, must give; Romeo slew Tybalt, Romeo must not live.
PRlNCE Romeo slew him; he slew Mercutio:
Who now the price of his dear blood doth owe?
MONTAGUE Not Romeo, prince; he was Mercutio's friend; His fault concludes but what the law should end,
The life of Tybalt.
PRlNCE And for that offence
Immediately we do exile him hence: I have an interest in your hate's proceeding,
My blood for your rude brawls doth lie a-bleeding; But I'll amerce you with so strong a fine
That you shall all repent the loss of mine:
I will be deaf to pleading and excuses;
Nor tears nor prayers shall purchase out abuses, Therefore use none: let Romeo hence in haste,
Else, when he is found, that hour is his last.
Bear hence this body, and attend our will:
Mercy but murders, pardoning those that kill.
[Exeunt.]
Scene Il.
A Room in Capulet's House.
[Enter Juliet.]
JULlET Gallop apace, you fiery-footed steeds,
Towards Phoebus' lodging; such a waggoner As Phaeton would whip you to the west
And bring in cloudy night immediately.-- Spread thy close curtain, love-performing night!
That rude eyes may wink, and Romeo Leap to these arms, untalk'd of and unseen.--
Lovers can see to do their amorous rites By their own beauties: or, if love be blind,
It best agrees with night.--Come, civil night, Thou sober-suited matron, all in black,
And learn me how to lose a winning match, Play'd for a pair of stainless maidenhoods:
Hood my unmann'd blood, bating in my cheeks, With thy black mantle; till strange love, grown bold,
Think true love acted simple modesty.
Come, night;--come, Romeo;--come, thou day in night;
For thou wilt lie upon the wings of night Whiter than new snow upon a raven's back.--
Come, gentle night;--come, loving, black-brow'd night, Give me my Romeo; and, when he shall die,
Take him and cut him out in little stars, And he will make the face of heaven so fine
That all the world will be in love with night, And pay no worship to the garish sun.--
O, I have bought the mansion of a love, But not possess'd it; and, though I am sold,
Not yet enjoy'd: so tedious is this day As is the night before some festival
To an impatient child that hath new robes, And may not wear them.
O, here comes my nurse,
And she brings news; and every tongue that speaks But Romeo's name speaks heavenly eloquence.--
[Enter Nurse, with cords.] Now, nurse, what news?
What hast thou there? the cords
That Romeo bid thee fetch?
NURSE Ay, ay, the cords.
[Throws them down.]
JULlET Ah me! what news? why dost thou wring thy hands?
NURSE Ah, well-a-day! he's dead, he's dead, he's dead!
We are undone, lady, we are undone!--
Alack the day!--he's gone, he's kill'd, he's dead!
JULlET Can heaven be so envious?
NURSE Romeo can, Though heaven cannot.--O Romeo, Romeo!--
Who ever would have thought it?--Romeo!
JULlET What devil art thou, that dost torment me thus?
This torture should be roar'd in dismal hell.
Hath Romeo slain himself? say thou but I,
And that bare vowel I shall poison more Than the death-darting eye of cockatrice:
I am not I if there be such an I; Or those eyes shut that make thee answer I.
If he be slain, say I; or if not, no: Brief sounds determine of my weal or woe.
NURSE I saw the wound, I saw it with mine eyes,--
God save the mark!--here on his manly breast.
A piteous corse, a bloody piteous corse;
Pale, pale as ashes, all bedaub'd in blood, All in gore-blood;--I swounded at the sight.
JULlET O, break, my heart!--poor bankrout, break at once!
To prison, eyes; ne'er look on liberty!
Vile earth, to earth resign; end motion here;
And thou and Romeo press one heavy bier!
NURSE O Tybalt, Tybalt, the best friend I had!
O courteous Tybalt! honest gentleman!
That ever I should live to see thee dead!
JULlET What storm is this that blows so contrary?
Is Romeo slaughter'd, and is Tybalt dead?
My dear-lov'd cousin, and my dearer lord?-- Then, dreadful trumpet, sound the general doom!
For who is living, if those two are gone?
NURSE Tybalt is gone, and Romeo banished;
Romeo that kill'd him, he is banished.
JULlET O God!--did Romeo's hand shed Tybalt's blood?
NURSE It did, it did; alas the day, it did!
JULlET O serpent heart, hid with a flowering face!
Did ever dragon keep so fair a cave?
Beautiful tyrant! fiend angelical!
Dove-feather'd raven! wolvish-ravening lamb!
Despised substance of divinest show!
Just opposite to what thou justly seem'st, A damned saint, an honourable villain!--
O nature, what hadst thou to do in hell When thou didst bower the spirit of a fiend
In mortal paradise of such sweet flesh?-- Was ever book containing such vile matter
So fairly bound?
O, that deceit should dwell In such a gorgeous palace!
NURSE There's no trust,
No faith, no honesty in men; all perjur'd, All forsworn, all naught, all dissemblers.--
Ah, where's my man?
Give me some aqua vitae.-- These griefs, these woes, these sorrows make me old.
Shame come to Romeo!
JULlET Blister'd be thy tongue For such a wish! he was not born to shame:
Upon his brow shame is asham'd to sit; For 'tis a throne where honour may be crown'd
Sole monarch of the universal earth.
O, what a beast was I to chide at him!
NURSE Will you speak well of him that kill'd your cousin?
JULlET Shall I speak ill of him that is my husband?
Ah, poor my lord, what tongue shall smooth thy name, When I, thy three-hours' wife, have mangled it?--
But wherefore, villain, didst thou kill my cousin?
That villain cousin would have kill'd my husband:
Back, foolish tears, back to your native spring; Your tributary drops belong to woe,
Which you, mistaking, offer up to joy.
My husband lives, that Tybalt would have slain;
And Tybalt's dead, that would have slain my husband:
All this is comfort; wherefore weep I, then?
Some word there was, worser than Tybalt's death, That murder'd me:
I would forget it fain;
But O, it presses to my memory Like damned guilty deeds to sinners' minds:
'Tybalt is dead, and Romeo banished.' That 'banished,' that one word 'banished,'
Hath slain ten thousand Tybalts.
Tybalt's death Was woe enough, if it had ended there:
Or, if sour woe delights in fellowship, And needly will be rank'd with other griefs,--
Why follow'd not, when she said Tybalt's dead, Thy father, or thy mother, nay, or both,
Which modern lamentation might have mov'd?
But with a rear-ward following Tybalt's death,
'Romeo is banished'--to speak that word Is father, mother, Tybalt, Romeo, Juliet,
All slain, all dead:
'Romeo is banished,'-- There is no end, no limit, measure, bound,
In that word's death; no words can that woe sound.-- Where is my father and my mother, nurse?
NURSE Weeping and wailing over Tybalt's corse:
Will you go to them?
I will bring you thither.
JULlET Wash they his wounds with tears: mine shall be spent, When theirs are dry, for Romeo's banishment.
Take up those cords.
Poor ropes, you are beguil'd, Both you and I; for Romeo is exil'd:
He made you for a highway to my bed; But I, a maid, die maiden-widowed.
Come, cords; come, nurse; I'll to my wedding-bed; And death, not Romeo, take my maidenhead!
NURSE Hie to your chamber.
I'll find Romeo
To comfort you:
I wot well where he is.
Hark ye, your Romeo will be here at night:
I'll to him; he is hid at Lawrence' cell.
JULlET O, find him! give this ring to my true knight,
And bid him come to take his last farewell.
[Exeunt.]
Scene ill.
Friar Lawrence's cell.
[Enter Friar Lawrence.]
FRlAR Romeo, come forth; come forth, thou fearful man.
Affliction is enanmour'd of thy parts, And thou art wedded to calamity.
[Enter Romeo.]
ROMEO Father, what news? what is the prince's doom
What sorrow craves acquaintance at my hand, That I yet know not?
FRlAR Too familiar
Is my dear son with such sour company:
I bring thee tidings of the prince's doom.
ROMEO What less than doomsday is the prince's doom?
FRlAR A gentler judgment vanish'd from his lips,--
Not body's death, but body's banishment.
ROMEO Ha, banishment? be merciful, say death; For exile hath more terror in his look,
Much more than death; do not say banishment.
FRlAR Hence from Verona art thou banished:
Be patient, for the world is broad and wide.
ROMEO There is no world without Verona walls,
But purgatory, torture, hell itself.
Hence-banished is banish'd from the world,
And world's exile is death,--then banished Is death mis-term'd: calling death banishment,
Thou cutt'st my head off with a golden axe, And smil'st upon the stroke that murders me.
FRlAR O deadly sin!
O rude unthankfulness!
Thy fault our law calls death; but the kind prince, Taking thy part, hath brush'd aside the law,
And turn'd that black word death to banishment: This is dear mercy, and thou see'st it not.
ROMEO 'Tis torture, and not mercy: heaven is here,
Where Juliet lives; and every cat, and dog, And little mouse, every unworthy thing,
Live here in heaven, and may look on her; But Romeo may not.--More validity,
More honourable state, more courtship lives In carrion flies than Romeo: they may seize
On the white wonder of dear Juliet's hand, And steal immortal blessing from her lips;
Who, even in pure and vestal modesty, Still blush, as thinking their own kisses sin;
But Romeo may not; he is banished,-- This may flies do, when I from this must fly.
And sayest thou yet that exile is not death!
Hadst thou no poison mix'd, no sharp-ground knife,
No sudden mean of death, though ne'er so mean, But banished to kill me; banished?
O friar, the damned use that word in hell; Howlings attend it: how hast thou the heart,
Being a divine, a ghostly confessor, A sin-absolver, and my friend profess'd,
To mangle me with that word banishment?
FRlAR Thou fond mad man, hear me speak a little,--
ROMEO O, thou wilt speak again of banishment.
FRlAR I'll give thee armour to keep off that word; Adversity's sweet milk, philosophy,
To comfort thee, though thou art banished.
ROMEO Yet banished?
Hang up philosophy!
Unless philosophy can make a Juliet,
Displant a town, reverse a prince's doom, It helps not, it prevails not,--talk no more.
FRlAR O, then I see that madmen have no ears.
ROMEO How should they, when that wise men have no eyes?
FRlAR Let me dispute with thee of thy estate.
ROMEO Thou canst not speak of that thou dost not feel:
Wert thou as young as I, Juliet thy love, An hour but married, Tybalt murdered,
Doting like me, and like me banished, Then mightst thou speak, then mightst thou tear thy hair,
And fall upon the ground, as I do now, Taking the measure of an unmade grave.
[Knocking within.]
FRlAR Arise; one knocks.
Good Romeo, hide thyself.
ROMEO Not I; unless the breath of heartsick groans,
Mist-like infold me from the search of eyes.
[Knocking.]
FRlAR Hark, how they knock!--Who's there?--Romeo, arise;
Thou wilt be taken.--Stay awhile;--Stand up; [Knocking.]
Run to my study.--By-and-by!--God's will!
What simpleness is this.--I come, I come!
[Knocking.]
Who knocks so hard? whence come you? what's your will?
NURSE [Within.]
Let me come in, and you shall know my errand;
I come from Lady Juliet.
FRlAR Welcome then.
[Enter Nurse.]
NURSE O holy friar, O, tell me, holy friar, Where is my lady's lord, where's Romeo?
FRlAR There on the ground, with his own tears made drunk.
NURSE O, he is even in my mistress' case,--
Just in her case!
FRlAR O woeful sympathy!
Piteous predicament!
NURSE Even so lies she,
Blubbering and weeping, weeping and blubbering.-- Stand up, stand up; stand, an you be a man:
For Juliet's sake, for her sake, rise and stand; Why should you fall into so deep an O?
ROMEO Nurse!
NURSE Ah sir! ah sir!--Well, death's the end of all.
ROMEO Spakest thou of Juliet? how is it with her?
Doth not she think me an old murderer, Now I have stain'd the childhood of our joy
With blood remov'd but little from her own?
Where is she? and how doth she? and what says
My conceal'd lady to our cancell'd love?
NURSE O, she says nothing, sir, but weeps and weeps;
And now falls on her bed; and then starts up, And Tybalt calls; and then on Romeo cries,
And then down falls again.
ROMEO As if that name, Shot from the deadly level of a gun,
Did murder her; as that name's cursed hand Murder'd her kinsman.--O, tell me, friar, tell me,
In what vile part of this anatomy Doth my name lodge? tell me, that I may sack
The hateful mansion.
[Drawing his sword.]
FRlAR Hold thy desperate hand:
Art thou a man? thy form cries out thou art; Thy tears are womanish; thy wild acts denote
The unreasonable fury of a beast; Unseemly woman in a seeming man!
Or ill-beseeming beast in seeming both!
Thou hast amaz'd me: by my holy order,
I thought thy disposition better temper'd.
Hast thou slain Tybalt? wilt thou slay thyself?
And slay thy lady, too, that lives in thee, By doing damned hate upon thyself?
Why rail'st thou on thy birth, the heaven, and earth?
Since birth and heaven and earth, all three do meet
In thee at once; which thou at once wouldst lose.
Fie, fie, thou sham'st thy shape, thy love, thy wit;
Which, like a usurer, abound'st in all, And usest none in that true use indeed
Which should bedeck thy shape, thy love, thy wit: Thy noble shape is but a form of wax,
Digressing from the valour of a man; Thy dear love sworn, but hollow perjury,
Killing that love which thou hast vow'd to cherish; Thy wit, that ornament to shape and love,
Mis-shapen in the conduct of them both, Like powder in a skilless soldier's flask,
Is set a-fire by thine own ignorance, And thou dismember'd with thine own defence.
What, rouse thee, man! thy Juliet is alive, For whose dear sake thou wast but lately dead;
There art thou happy:
Tybalt would kill thee, But thou slewest Tybalt; there art thou happy too:
The law, that threaten'd death, becomes thy friend, And turns it to exile; there art thou happy:
A pack of blessings lights upon thy back; Happiness courts thee in her best array;
But, like a misbehav'd and sullen wench, Thou pout'st upon thy fortune and thy love:--
Take heed, take heed, for such die miserable.
Go, get thee to thy love, as was decreed,
Ascend her chamber, hence and comfort her:
But, look, thou stay not till the watch be set,
For then thou canst not pass to Mantua; Where thou shalt live till we can find a time
To blaze your marriage, reconcile your friends, Beg pardon of the prince, and call thee back
With twenty hundred thousand times more joy Than thou went'st forth in lamentation.--
Go before, nurse: commend me to thy lady; And bid her hasten all the house to bed,
Which heavy sorrow makes them apt unto.
Romeo is coming.
NURSE O Lord, I could have stay'd here all the night
To hear good counsel:
O, what learning is!-- My lord, I'll tell my lady you will come.
ROMEO Do so, and bid my sweet prepare to chide.
NURSE Here, sir, a ring she bid me give you, sir:
Hie you, make haste, for it grows very late.
[Exit.]
ROMEO How well my comfort is reviv'd by this!
FRlAR Go hence; good night! and here stands all your state:
Either be gone before the watch be set, Or by the break of day disguis'd from hence.
Sojourn in Mantua; I'll find out your man, And he shall signify from time to time
Every good hap to you that chances here:
Give me thy hand; 'tis late; farewell; good night.
ROMEO But that a joy past joy calls out on me,
It were a grief so brief to part with thee: Farewell
[Exeunt.]
Scene IV.
A Room in Capulet's House.
[Enter Capulet, Lady Capulet, and Paris.]
CAPULET Things have fallen out, sir, so unluckily
That we have had no time to move our daughter:
Look you, she lov'd her kinsman Tybalt dearly,
And so did I; well, we were born to die.
'Tis very late; she'll not come down to-night:
I promise you, but for your company, I would have been a-bed an hour ago.
PARlS These times of woe afford no tune to woo.--
Madam, good night: commend me to your daughter.
LADY CAPULET I will, and know her mind early to-morrow; To-night she's mew'd up to her heaviness.
CAPULET Sir Paris, I will make a desperate tender
Of my child's love:
I think she will be rul'd In all respects by me; nay more, I doubt it not.--
Wife, go you to her ere you go to bed; Acquaint her here of my son Paris' love;
And bid her, mark you me, on Wednesday next,-- But, soft! what day is this?
PARlS Monday, my lord.
CAPULET Monday! ha, ha!
Well, Wednesday is too soon,
Thursday let it be;--a Thursday, tell her, She shall be married to this noble earl.--
Will you be ready? do you like this haste?
We'll keep no great ado,--a friend or two;
For, hark you, Tybalt being slain so late, It may be thought we held him carelessly,
Being our kinsman, if we revel much:
Therefore we'll have some half a dozen friends,
And there an end.
But what say you to Thursday?
PARlS My lord, I would that Thursday were to-morrow.
CAPULET Well, get you gone: o' Thursday be it then.--
Go you to Juliet, ere you go to bed, Prepare her, wife, against this wedding-day.--
Farewell, my lord.--Light to my chamber, ho!-- Afore me, it is so very very late
That we may call it early by and by.-- Good night.
[Exeunt.]
Scene V. An open Gallery to Juliet's Chamber, overlooking the Garden.
[Enter Romeo and Juliet.]
JULlET Wilt thou be gone? it is not yet near day:
It was the nightingale, and not the lark,
That pierc'd the fearful hollow of thine ear; Nightly she sings on yond pomegranate tree:
Believe me, love, it was the nightingale.
ROMEO It was the lark, the herald of the morn, No nightingale: look, love, what envious streaks
Do lace the severing clouds in yonder east: Night's candles are burnt out, and jocund day
Stands tiptoe on the misty mountain tops.
I must be gone and live, or stay and die.
JULlET Yond light is not daylight, I know it, I:
It is some meteor that the sun exhales To be to thee this night a torch-bearer
And light thee on the way to Mantua:
Therefore stay yet, thou need'st not to be gone.
ROMEO Let me be ta'en, let me be put to death;
I am content, so thou wilt have it so.
I'll say yon gray is not the morning's eye,
'Tis but the pale reflex of Cynthia's brow; Nor that is not the lark whose notes do beat
The vaulty heaven so high above our heads:
I have more care to stay than will to go.--
Come, death, and welcome!
Juliet wills it so.-- How is't, my soul? let's talk,--it is not day.
JULlET It is, it is!--hie hence, be gone, away!
It is the lark that sings so out of tune, Straining harsh discords and unpleasing sharps.
Some say the lark makes sweet division; This doth not so, for she divideth us:
Some say the lark and loathed toad change eyes; O, now I would they had chang'd voices too!
Since arm from arm that voice doth us affray, Hunting thee hence with hunt's-up to the day.
O, now be gone; more light and light it grows.
ROMEO More light and light,--more dark and dark our woes!
[Enter Nurse.]
NURSE Madam!
JULlET Nurse?
NURSE Your lady mother is coming to your chamber:
The day is broke; be wary, look about.
[Exit.]
JULlET Then, window, let day in, and let life out.
ROMEO Farewell, farewell! one kiss, and I'll descend.
[Descends.]
JULlET Art thou gone so? my lord, my love, my friend!
I must hear from thee every day i' the hour,
For in a minute there are many days:
O, by this count I shall be much in years
Ere I again behold my Romeo!
ROMEO Farewell!
I will omit no opportunity
That may convey my greetings, love, to thee.
JULlET O, think'st thou we shall ever meet again?
ROMEO I doubt it not; and all these woes shall serve
For sweet discourses in our time to come.
JULlET O God!
I have an ill-divining soul!
Methinks I see thee, now thou art below,
As one dead in the bottom of a tomb:
Either my eyesight fails, or thou look'st pale.
ROMEO And trust me, love, in my eye so do you:
Dry sorrow drinks our blood.
Adieu, adieu!
[Exit below.]
JULlET O fortune, fortune! all men call thee fickle:
If thou art fickle, what dost thou with him That is renown'd for faith?
Be fickle, fortune;
For then, I hope, thou wilt not keep him long But send him back.
LADY CAPULET [Within.]
Ho, daughter! are you up?
JULlET Who is't that calls? is it my lady mother?
Is she not down so late, or up so early?
What unaccustom'd cause procures her hither?
[Enter Lady Capulet.]
LADY CAPULET Why, how now, Juliet?
JULlET Madam, I am not well.
LADY CAPULET Evermore weeping for your cousin's death?
What, wilt thou wash him from his grave with tears?
An if thou couldst, thou couldst not make him live; Therefore have done: some grief shows much of love;
But much of grief shows still some want of wit.
JULlET Yet let me weep for such a feeling loss.
LADY CAPULET So shall you feel the loss, but not the friend Which you weep for.
JULlET Feeling so the loss,
I cannot choose but ever weep the friend.
LADY CAPULET Well, girl, thou weep'st not so much for his death As that the villain lives which slaughter'd him.
JULlET What villain, madam?
LADY CAPULET That same villain Romeo.
JULlET Villain and he be many miles asunder.--
God pardon him!
I do, with all my heart; And yet no man like he doth grieve my heart.
LADY CAPULET That is because the traitor murderer lives.
JULlET Ay, madam, from the reach of these my hands.
Would none but I might venge my cousin's death!
LADY CAPULET We will have vengeance for it, fear thou not:
Then weep no more.
I'll send to one in Mantua,--
Where that same banish'd runagate doth live,-- Shall give him such an unaccustom'd dram
That he shall soon keep Tybalt company:
And then I hope thou wilt be satisfied.
JULlET Indeed I never shall be satisfied
With Romeo till I behold him--dead-- Is my poor heart so for a kinsman vex'd:
Madam, if you could find out but a man To bear a poison, I would temper it,
That Romeo should, upon receipt thereof, Soon sleep in quiet.
O, how my heart abhors
To hear him nam'd,--and cannot come to him,-- To wreak the love I bore my cousin Tybalt
Upon his body that hath slaughter'd him!
LADY CAPULET Find thou the means, and I'll find such a man.
But now I'll tell thee joyful tidings, girl.
JULlET And joy comes well in such a needy time:
What are they, I beseech your ladyship?
LADY CAPULET Well, well, thou hast a careful father, child; One who, to put thee from thy heaviness,
Hath sorted out a sudden day of joy That thou expect'st not, nor I look'd not for.
JULlET Madam, in happy time, what day is that?
LADY CAPULET Marry, my child, early next Thursday morn
The gallant, young, and noble gentleman, The County Paris, at St. Peter's Church,
Shall happily make thee there a joyful bride.
JULlET Now by Saint Peter's Church, and Peter too,
He shall not make me there a joyful bride.
I wonder at this haste; that I must wed
Ere he that should be husband comes to woo.
I pray you, tell my lord and father, madam,
I will not marry yet; and when I do, I swear It shall be Romeo, whom you know I hate,
Rather than Paris:--these are news indeed!
LADY CAPULET Here comes your father: tell him so yourself, And see how he will take it at your hands.
[Enter Capulet and Nurse.]
CAPULET When the sun sets, the air doth drizzle dew; But for the sunset of my brother's son
It rains downright.-- How now! a conduit, girl? what, still in tears?
Evermore showering?
In one little body Thou counterfeit'st a bark, a sea, a wind:
For still thy eyes, which I may call the sea, Do ebb and flow with tears; the bark thy body is,
Sailing in this salt flood; the winds, thy sighs; Who,--raging with thy tears and they with them,--
Without a sudden calm, will overset Thy tempest-tossed body.--How now, wife!
Have you deliver'd to her our decree?
LADY CAPULET Ay, sir; but she will none, she gives you thanks.
I would the fool were married to her grave!
CAPULET Soft! take me with you, take me with you, wife.
How! will she none? doth she not give us thanks?
Is she not proud? doth she not count her bles'd,
Unworthy as she is, that we have wrought So worthy a gentleman to be her bridegroom?
JULlET Not proud you have; but thankful that you have:
Proud can I never be of what I hate; But thankful even for hate that is meant love.
CAPULET How now, how now, chop-logic! What is this?
Proud,--and, I thank you,--and I thank you not;-- And yet not proud:--mistress minion, you,
Thank me no thankings, nor proud me no prouds, But fettle your fine joints 'gainst Thursday next
To go with Paris to Saint Peter's Church, Or I will drag thee on a hurdle thither.
Out, you green-sickness carrion! out, you baggage!
You tallow-face!
LADY CAPULET Fie, fie! what, are you mad?
JULlET Good father, I beseech you on my knees,
Hear me with patience but to speak a word.
CAPULET Hang thee, young baggage! disobedient wretch!
I tell thee what,--get thee to church o' Thursday, Or never after look me in the face:
Speak not, reply not, do not answer me; My fingers itch.--Wife, we scarce thought us bles'd
That God had lent us but this only child; But now I see this one is one too much,
And that we have a curse in having her:
Out on her, hilding!
NURSE God in heaven bless her!--
You are to blame, my lord, to rate her so.
CAPULET And why, my lady wisdom? hold your tongue, Good prudence; smatter with your gossips, go.
NURSE I speak no treason.
CAPULET O, God ye good-en!
NURSE May not one speak?
CAPULET Peace, you mumbling fool!
Utter your gravity o'er a gossip's bowl, For here we need it not.
LADY CAPULET You are too hot.
CAPULET God's bread! it makes me mad:
Day, night, hour, time, tide, work, play, Alone, in company, still my care hath been
To have her match'd, and having now provided A gentleman of noble parentage,
Of fair demesnes, youthful, and nobly train'd, Stuff'd, as they say, with honourable parts,
Proportion'd as one's heart would wish a man,-- And then to have a wretched puling fool,
A whining mammet, in her fortune's tender, To answer, 'I'll not wed,--I cannot love,
I am too young,--I pray you pardon me:'-- But, an you will not wed, I'll pardon you:
Graze where you will, you shall not house with me: Look to't, think on't, I do not use to jest.
Thursday is near; lay hand on heart, advise:
An you be mine, I'll give you to my friend;
An you be not, hang, beg, starve, die i' the streets, For, by my soul, I'll ne'er acknowledge thee,
Nor what is mine shall never do thee good:
Trust to't, bethink you, I'll not be forsworn.
[Exit.]
JULlET Is there no pity sitting in the clouds, That sees into the bottom of my grief?
O, sweet my mother, cast me not away!
Delay this marriage for a month, a week;
Or, if you do not, make the bridal bed In that dim monument where Tybalt lies.
LADY CAPULET Talk not to me, for I'll not speak a word;
Do as thou wilt, for I have done with thee.
[Exit.]
JULlET O God!--O nurse! how shall this be prevented?
My husband is on earth, my faith in heaven; How shall that faith return again to earth,
Unless that husband send it me from heaven By leaving earth?--comfort me, counsel me.--
Alack, alack, that heaven should practise stratagems Upon so soft a subject as myself!--
What say'st thou? hast thou not a word of joy?
Some comfort, nurse.
NURSE Faith, here 'tis; Romeo
Is banished; and all the world to nothing That he dares ne'er come back to challenge you;
Or if he do, it needs must be by stealth.
Then, since the case so stands as now it doth,
I think it best you married with the county.
O, he's a lovely gentleman!
Romeo's a dishclout to him; an eagle, madam, Hath not so green, so quick, so fair an eye
As Paris hath.
Beshrew my very heart, I think you are happy in this second match,
For it excels your first: or if it did not, Your first is dead; or 'twere as good he were,
As living here, and you no use of him.
JULlET Speakest thou this from thy heart?
NURSE And from my soul too;
Or else beshrew them both.
JULlET Amen!
NURSE What?
JULlET Well, thou hast comforted me marvellous much.
Go in; and tell my lady I am gone, Having displeas'd my father, to Lawrence' cell,
To make confession and to be absolv'd.
NURSE Marry, I will; and this is wisely done.
[Exit.]
JULlET Ancient damnation!
O most wicked fiend!
Is it more sin to wish me thus forsworn,
Or to dispraise my lord with that same tongue Which she hath prais'd him with above compare
So many thousand times?--Go, counsellor; Thou and my bosom henceforth shall be twain.--
I'll to the friar to know his remedy; If all else fail, myself have power to die.
[Exit.]
>
ROMEO AND JULlET by William Shakespeare
ACT IV.
Scene I. Friar Lawrence's Cell.
[Enter Friar Lawrence and Paris.]
FRlAR On Thursday, sir? the time is very short.
PARlS My father Capulet will have it so; And I am nothing slow to slack his haste.
FRlAR You say you do not know the lady's mind:
Uneven is the course; I like it not.
PARlS Immoderately she weeps for Tybalt's death, And therefore have I little talk'd of love;
For Venus smiles not in a house of tears.
Now, sir, her father counts it dangerous
That she do give her sorrow so much sway; And, in his wisdom, hastes our marriage,
To stop the inundation of her tears; Which, too much minded by herself alone,
May be put from her by society:
Now do you know the reason of this haste.
FRlAR [Aside.]
I would I knew not why it should be slow'd.--
Look, sir, here comes the lady toward my cell.
[Enter Juliet.]
PARlS Happily met, my lady and my wife!
JULlET That may be, sir, when I may be a wife.
PARlS That may be must be, love, on Thursday next.
JULlET What must be shall be.
FRlAR That's a certain text.
PARlS Come you to make confession to this father?
JULlET To answer that, I should confess to you.
PARlS Do not deny to him that you love me.
JULlET I will confess to you that I love him.
PARlS So will ye, I am sure, that you love me.
JULlET If I do so, it will be of more price,
Being spoke behind your back than to your face.
PARlS Poor soul, thy face is much abus'd with tears.
JULlET The tears have got small victory by that; For it was bad enough before their spite.
PARlS Thou wrong'st it more than tears with that report.
JULlET That is no slander, sir, which is a truth;
And what I spake, I spake it to my face.
PARlS Thy face is mine, and thou hast slander'd it.
JULlET It may be so, for it is not mine own.-- Are you at leisure, holy father, now;
Or shall I come to you at evening mass?
FRlAR My leisure serves me, pensive daughter, now.-- My lord, we must entreat the time alone.
PARlS God shield I should disturb devotion!--
Juliet, on Thursday early will I rouse you:
Till then, adieu; and keep this holy kiss.
[Exit.]
JULlET O, shut the door! and when thou hast done so, Come weep with me; past hope, past cure, past help!
FRlAR Ah, Juliet, I already know thy grief;
It strains me past the compass of my wits:
I hear thou must, and nothing may prorogue it,
On Thursday next be married to this county.
JULlET Tell me not, friar, that thou hear'st of this, Unless thou tell me how I may prevent it:
If, in thy wisdom, thou canst give no help, Do thou but call my resolution wise,
And with this knife I'll help it presently.
God join'd my heart and Romeo's, thou our hands;
And ere this hand, by thee to Romeo's seal'd, Shall be the label to another deed,
Or my true heart with treacherous revolt Turn to another, this shall slay them both:
Therefore, out of thy long-experienc'd time, Give me some present counsel; or, behold,
'Twixt my extremes and me this bloody knife Shall play the empire; arbitrating that
Which the commission of thy years and art Could to no issue of true honour bring.
Be not so long to speak; I long to die, If what thou speak'st speak not of remedy.
FRlAR Hold, daughter.
I do spy a kind of hope,
Which craves as desperate an execution As that is desperate which we would prevent.
If, rather than to marry County Paris Thou hast the strength of will to slay thyself,
Then is it likely thou wilt undertake A thing like death to chide away this shame,
That cop'st with death himself to scape from it; And, if thou dar'st, I'll give thee remedy.
JULlET O, bid me leap, rather than marry Paris,
From off the battlements of yonder tower; Or walk in thievish ways; or bid me lurk
Where serpents are; chain me with roaring bears; Or shut me nightly in a charnel-house,
O'er-cover'd quite with dead men's rattling bones, With reeky shanks and yellow chapless skulls;
Or bid me go into a new-made grave, And hide me with a dead man in his shroud;
Things that, to hear them told, have made me tremble; And I will do it without fear or doubt,
To live an unstain'd wife to my sweet love.
FRlAR Hold, then; go home, be merry, give consent To marry Paris:
Wednesday is to-morrow;
To-morrow night look that thou lie alone, Let not thy nurse lie with thee in thy chamber:
Take thou this vial, being then in bed, And this distilled liquor drink thou off:
When, presently, through all thy veins shall run A cold and drowsy humour; for no pulse
Shall keep his native progress, but surcease:
No warmth, no breath, shall testify thou livest;
The roses in thy lips and cheeks shall fade To paly ashes; thy eyes' windows fall,
Like death, when he shuts up the day of life; Each part, depriv'd of supple government,
Shall, stiff and stark and cold, appear like death:
And in this borrow'd likeness of shrunk death
Thou shalt continue two-and-forty hours, And then awake as from a pleasant sleep.
Now, when the bridegroom in the morning comes To rouse thee from thy bed, there art thou dead:
Then,--as the manner of our country is,-- In thy best robes, uncover'd, on the bier,
Thou shalt be borne to that same ancient vault Where all the kindred of the Capulets lie.
In the mean time, against thou shalt awake, Shall Romeo by my letters know our drift;
And hither shall he come: and he and I Will watch thy waking, and that very night
Shall Romeo bear thee hence to Mantua.
And this shall free thee from this present shame,
If no inconstant toy nor womanish fear Abate thy valour in the acting it.
JULlET Give me, give me!
O, tell not me of fear!
FRlAR Hold; get you gone, be strong and prosperous
In this resolve:
I'll send a friar with speed To Mantua, with my letters to thy lord.
JULlET Love give me strength! and strength shall help afford.
Farewell, dear father.
[Exeunt.]
Scene Il.
Hall in Capulet's House.
[Enter Capulet, Lady Capulet, Nurse, and Servants.]
CAPULET So many guests invite as here are writ.--
[Exit first Servant.]
Sirrah, go hire me twenty cunning cooks.
2 SERVANT You shall have none ill, sir; for I'll try if they can lick their fingers.
CAPULET How canst thou try them so?
2 SERVANT Marry, sir, 'tis an ill cook that cannot lick his own fingers: therefore he that cannot lick his fingers goes not with me.
CAPULET Go, begone.--
[Exit second Servant.]
We shall be much unfurnish'd for this time.--
What, is my daughter gone to Friar Lawrence?
NURSE Ay, forsooth.
CAPULET Well, be may chance to do some good on her:
A peevish self-will'd harlotry it is.
NURSE See where she comes from shrift with merry look.
[Enter Juliet.]
CAPULET How now, my headstrong! where have you been gadding?
JULlET Where I have learn'd me to repent the sin Of disobedient opposition
To you and your behests; and am enjoin'd By holy Lawrence to fall prostrate here,
To beg your pardon:--pardon, I beseech you!
Henceforward I am ever rul'd by you.
CAPULET Send for the county; go tell him of this:
I'll have this knot knit up to-morrow morning.
JULlET I met the youthful lord at Lawrence' cell;
And gave him what becomed love I might, Not stepping o'er the bounds of modesty.
CAPULET Why, I am glad on't; this is well,--stand up,--
This is as't should be.--Let me see the county; Ay, marry, go, I say, and fetch him hither.--
Now, afore God, this reverend holy friar, All our whole city is much bound to him.
JULlET Nurse, will you go with me into my closet,
To help me sort such needful ornaments As you think fit to furnish me to-morrow?
LADY CAPULET No, not till Thursday; there is time enough.
CAPULET Go, nurse, go with her.--We'll to church to-morrow.
[Exeunt Juliet and Nurse.]
LADY CAPULET We shall be short in our provision: 'Tis now near night.
CAPULET Tush, I will stir about,
And all things shall be well, I warrant thee, wife:
Go thou to Juliet, help to deck up her;
I'll not to bed to-night;--let me alone; I'll play the housewife for this once.--What, ho!--
They are all forth: well, I will walk myself To County Paris, to prepare him up
Against to-morrow: my heart is wondrous light Since this same wayward girl is so reclaim'd.
[Exeunt.]
Scene ill.
Juliet's Chamber.
[Enter Juliet and Nurse.]
JULlET Ay, those attires are best:--but, gentle nurse,
I pray thee, leave me to myself to-night; For I have need of many orisons
To move the heavens to smile upon my state, Which, well thou know'st, is cross and full of sin.
[Enter Lady Capulet.]
LADY CAPULET What, are you busy, ho? need you my help?
JULlET No, madam; we have cull'd such necessaries As are behoveful for our state to-morrow:
So please you, let me now be left alone, And let the nurse this night sit up with you;
For I am sure you have your hands full all In this so sudden business.
LADY CAPULET Good night:
Get thee to bed, and rest; for thou hast need.
[Exeunt Lady Capulet and Nurse.]
JULlET Farewell!--God knows when we shall meet again.
I have a faint cold fear thrills through my veins That almost freezes up the heat of life:
I'll call them back again to comfort me;-- Nurse!--What should she do here?
My dismal scene I needs must act alone.-- Come, vial.--
What if this mixture do not work at all?
Shall I be married, then, to-morrow morning?--
No, No!--this shall forbid it:--lie thou there.-- [Laying down her dagger.]
What if it be a poison, which the friar Subtly hath minister'd to have me dead,
Lest in this marriage he should be dishonour'd, Because he married me before to Romeo?
I fear it is: and yet methinks it should not, For he hath still been tried a holy man:--
I will not entertain so bad a thought.-- How if, when I am laid into the tomb,
I wake before the time that Romeo Come to redeem me? there's a fearful point!
Shall I not then be stifled in the vault, To whose foul mouth no healthsome air breathes in,
And there die strangled ere my Romeo comes?
Or, if I live, is it not very like
The horrible conceit of death and night, Together with the terror of the place,--
As in a vault, an ancient receptacle, Where, for this many hundred years, the bones
Of all my buried ancestors are pack'd; Where bloody Tybalt, yet but green in earth,
Lies festering in his shroud; where, as they say, At some hours in the night spirits resort;--
Alack, alack, is it not like that I, So early waking,--what with loathsome smells,
And shrieks like mandrakes torn out of the earth, That living mortals, hearing them, run mad;--
O, if I wake, shall I not be distraught, Environed with all these hideous fears?
And madly play with my forefathers' joints?
And pluck the mangled Tybalt from his shroud?
And, in this rage, with some great kinsman's bone, As with a club, dash out my desperate brains?--
O, look! methinks I see my cousin's ghost Seeking out Romeo, that did spit his body
Upon a rapier's point:--stay, Tybalt, stay!-- Romeo, I come! this do I drink to thee.
[Throws herself on the bed.]
Scene IV.
Hall in Capulet's House.
[Enter Lady Capulet and Nurse.]
LADY CAPULET Hold, take these keys and fetch more spices, nurse.
NURSE They call for dates and quinces in the pastry.
[Enter Capulet.]
CAPULET Come, stir, stir, stir!
The second cock hath crow'd,
The curfew bell hath rung, 'tis three o'clock:-- Look to the bak'd meats, good Angelica;
Spare not for cost.
NURSE Go, you cot-quean, go, Get you to bed; faith, you'll be sick to-morrow
For this night's watching.
CAPULET No, not a whit: what!
I have watch'd ere now All night for lesser cause, and ne'er been sick.
LADY CAPULET Ay, you have been a mouse-hunt in your time;
But I will watch you from such watching now.
[Exeunt Lady Capulet and Nurse.]
CAPULET A jealous-hood, a jealous-hood!--Now, fellow,
[Enter Servants, with spits, logs and baskets.]
What's there?
1 SERVANT Things for the cook, sir; but I know not what.
CAPULET Make haste, make haste.
[Exit 1 Servant.]
--Sirrah, fetch drier logs:
Call Peter, he will show thee where they are.
2 SERVANT I have a head, sir, that will find out logs
And never trouble Peter for the matter.
[Exit.]
CAPULET Mass, and well said; a merry whoreson, ha!
Thou shalt be logger-head.--Good faith, 'tis day.
The county will be here with music straight,
For so he said he would:--I hear him near.
[Music within.]
Nurse!--wife!--what, ho!--what, nurse, I say!
[Re-enter Nurse.]
Go, waken Juliet; go and trim her up; I'll go and chat with Paris:--hie, make haste,
Make haste; the bridegroom he is come already:
Make haste, I say.
[Exeunt.]
Scene V. Juliet's Chamber; Juliet on the bed.
[Enter Nurse.]
NURSE Mistress!--what, mistress!--Juliet!--fast, I warrant her, she:--
Why, lamb!--why, lady!--fie, you slug-abed!-- Why, love, I say!--madam! sweetheart!--why, bride!--
What, not a word?--you take your pennyworths now; Sleep for a week; for the next night, I warrant,
The County Paris hath set up his rest That you shall rest but little.--God forgive me!
Marry, and amen, how sound is she asleep!
I needs must wake her.--Madam, madam, madam!--
Ay, let the county take you in your bed; He'll fright you up, i' faith.--Will it not be?
What, dress'd! and in your clothes! and down again!
I must needs wake you.--lady! lady! lady!--
Alas, alas!--Help, help!
My lady's dead!-- O, well-a-day that ever I was born!--
Some aqua-vitae, ho!--my lord! my lady!
[Enter Lady Capulet.]
LADY CAPULET What noise is here?
NURSE O lamentable day!
LADY CAPULET What is the matter?
NURSE Look, look!
O heavy day!
LADY CAPULET O me, O me!--my child, my only life!
Revive, look up, or I will die with thee!-- Help, help!--call help.
[Enter Capulet.]
CAPULET For shame, bring Juliet forth; her lord is come.
NURSE She's dead, deceas'd, she's dead; alack the day!
LADY CAPULET Alack the day, she's dead, she's dead, she's dead!
CAPULET Ha! let me see her:--out alas! she's cold;
Her blood is settled, and her joints are stiff; Life and these lips have long been separated:
Death lies on her like an untimely frost Upon the sweetest flower of all the field.
Accursed time! unfortunate old man!
NURSE O lamentable day!
LADY CAPULET O woful time!
CAPULET Death, that hath ta'en her hence to make me wail,
Ties up my tongue and will not let me speak.
[Enter Friar Lawrence and Paris, with Musicians.]
FRlAR Come, is the bride ready to go to church?
CAPULET Ready to go, but never to return:--
O son, the night before thy wedding day Hath death lain with thy bride:--there she lies,
Flower as she was, deflowered by him.
Death is my son-in-law, death is my heir;
My daughter he hath wedded: I will die.
And leave him all; life, living, all is death's.
PARlS Have I thought long to see this morning's face,
And doth it give me such a sight as this?
LADY CAPULET Accurs'd, unhappy, wretched, hateful day!
Most miserable hour that e'er time saw
In lasting labour of his pilgrimage!
But one, poor one, one poor and loving child,
But one thing to rejoice and solace in, And cruel death hath catch'd it from my sight!
NURSE O woe!
O woeful, woeful, woeful day!
Most lamentable day, most woeful day That ever, ever, I did yet behold!
O day!
O day!
O day!
O hateful day!
Never was seen so black a day as this:
O woeful day!
O woeful day!
PARlS Beguil'd, divorced, wronged, spited, slain!
Most detestable death, by thee beguil'd,
By cruel cruel thee quite overthrown!-- O love!
O life!--not life, but love in death!
CAPULET Despis'd, distressed, hated, martyr'd, kill'd!--
Uncomfortable time, why cam'st thou now To murder, murder our solemnity?--
O child!
O child!--my soul, and not my child!-- Dead art thou, dead!--alack, my child is dead;
And with my child my joys are buried!
FRlAR Peace, ho, for shame! confusion's cure lives not
In these confusions.
Heaven and yourself Had part in this fair maid; now heaven hath all,
And all the better is it for the maid: Your part in her you could not keep from death;
But heaven keeps his part in eternal life.
The most you sought was her promotion;
For 'twas your heaven she should be advanc'd:
And weep ye now, seeing she is advanc'd
Above the clouds, as high as heaven itself?
O, in this love, you love your child so ill
That you run mad, seeing that she is well:
She's not well married that lives married long:
But she's best married that dies married young.
Dry up your tears, and stick your rosemary
On this fair corse; and, as the custom is, In all her best array bear her to church;
For though fond nature bids us all lament, Yet nature's tears are reason's merriment.
CAPULET All things that we ordained festival
Turn from their office to black funeral: Our instruments to melancholy bells;
Our wedding cheer to a sad burial feast; Our solemn hymns to sullen dirges change;
Our bridal flowers serve for a buried corse, And all things change them to the contrary.
FRlAR Sir, go you in,--and, madam, go with him;--
And go, Sir Paris;--every one prepare To follow this fair corse unto her grave:
The heavens do lower upon you for some ill; Move them no more by crossing their high will.
[Exeunt Capulet, Lady Capulet, Paris, and Friar.] 1 MUSlCIAN Faith, we may put up our pipes and be gone.
NURSE Honest good fellows, ah, put up, put up; For well you know this is a pitiful case.
[Exit.]
1 MUSlCIAN Ay, by my troth, the case may be amended.
[Enter Peter.]
PETER Musicians, O, musicians, 'Heart's ease,' 'Heart's ease':
O, an you will have me live, play 'Heart's ease.'
1 MUSlCIAN Why 'Heart's ease'?
PETER O, musicians, because my heart itself plays 'My heart is full of woe':
O, play me some merry dump to comfort me.
1 MUSlCIAN Not a dump we: 'tis no time to play now.
PETER You will not then?
1 MUSlCIAN No.
PETER I will then give it you soundly.
1 MUSlCIAN What will you give us?
PETER No money, on my faith; but the gleek,--I will give you the minstrel.
1 MUSlCIAN Then will I give you the serving-creature.
PETER Then will I lay the serving-creature's dagger on your pate.
I will carry no crotchets:
I'll re you, I'll fa you: do you note me?
1 MUSlCIAN An you re us and fa us, you note us.
2 MUSlCIAN Pray you put up your dagger, and put out your wit.
PETER Then have at you with my wit!
I will dry-beat you with an iron wit, and put up my iron dagger.--Answer me like men:
'When griping grief the heart doth wound, And doleful dumps the mind oppress,
Then music with her silver sound'-- why 'silver sound'? why 'music with her silver sound'?--
What say you, Simon Catling?
1 MUSlCIAN Marry, sir, because silver hath a sweet sound.
PETER Pretty!--What say you, Hugh Rebeck?
2 MUSlCIAN I say 'silver sound' because musicians sound for silver.
PETER Pretty too!--What say you, James Soundpost?
3 MUSlCIAN Faith, I know not what to say.
PETER O, I cry you mercy; you are the singer:
I will say for you.
It is 'music with her silver sound' because musicians have no gold for sounding:--
'Then music with her silver sound With speedy help doth lend redress.'
[Exit.]
1 MUSlCIAN What a pestilent knave is this same!
2 MUSlCIAN Hang him, Jack!--Come, we'll in here; tarry for the mourners, and stay dinner.
[Exeunt.] >
ROMEO AND JULlET by William Shakespeare
Act V. Scene I. Mantua.
A Street.
[Enter Romeo.]
ROMEO If I may trust the flattering eye of sleep, My dreams presage some joyful news at hand;
My bosom's lord sits lightly in his throne; And all this day an unaccustom'd spirit
Lifts me above the ground with cheerful thoughts.
I dreamt my lady came and found me dead,--
Strange dream, that gives a dead man leave to think!-- And breath'd such life with kisses in my lips,
That I reviv'd, and was an emperor.
Ah me! how sweet is love itself possess'd,
When but love's shadows are so rich in joy!
[Enter Balthasar.]
News from Verona!--How now, Balthasar?
Dost thou not bring me letters from the friar?
How doth my lady?
Is my father well?
How fares my Juliet? that I ask again;
For nothing can be ill if she be well.
BALTHASAR Then she is well, and nothing can be ill: Her body sleeps in Capel's monument,
And her immortal part with angels lives.
I saw her laid low in her kindred's vault,
And presently took post to tell it you:
O, pardon me for bringing these ill news,
Since you did leave it for my office, sir.
ROMEO Is it even so? then I defy you, stars!-- Thou know'st my lodging: get me ink and paper,
And hire post-horses.
I will hence to-night.
BALTHASAR
I do beseech you, sir, have patience: Your looks are pale and wild, and do import
Some misadventure.
ROMEO Tush, thou art deceiv'd:
Leave me, and do the thing I bid thee do.
Hast thou no letters to me from the friar?
BALTHASAR No, my good lord.
ROMEO No matter: get thee gone, And hire those horses; I'll be with thee straight.
[Exit Balthasar.]
Well, Juliet, I will lie with thee to-night.
Let's see for means;--O mischief, thou art swift To enter in the thoughts of desperate men!
I do remember an apothecary,-- And hereabouts he dwells,--which late I noted
In tatter'd weeds, with overwhelming brows, Culling of simples; meagre were his looks,
Sharp misery had worn him to the bones; And in his needy shop a tortoise hung,
An alligator stuff'd, and other skins Of ill-shaped fishes; and about his shelves
A beggarly account of empty boxes, Green earthen pots, bladders, and musty seeds,
Remnants of packthread, and old cakes of roses, Were thinly scatter'd, to make up a show.
Noting this penury, to myself I said, An if a man did need a poison now,
Whose sale is present death in Mantua, Here lives a caitiff wretch would sell it him.
O, this same thought did but forerun my need; And this same needy man must sell it me.
As I remember, this should be the house:
Being holiday, the beggar's shop is shut.--
What, ho! apothecary!
[Enter Apothecary.]
APOTHECARY Who calls so loud?
ROMEO Come hither, man.--I see that thou art poor;
Hold, there is forty ducats: let me have A dram of poison; such soon-speeding gear
As will disperse itself through all the veins That the life-weary taker mall fall dead;
And that the trunk may be discharg'd of breath As violently as hasty powder fir'd
Doth hurry from the fatal cannon's womb.
APOTHECARY Such mortal drugs I have; but Mantua's law Is death to any he that utters them.
ROMEO Art thou so bare and full of wretchedness
And fear'st to die? famine is in thy cheeks, Need and oppression starveth in thine eyes,
Contempt and beggary hangs upon thy back, The world is not thy friend, nor the world's law:
The world affords no law to make thee rich; Then be not poor, but break it and take this.
APOTHECARY My poverty, but not my will consents.
ROMEO I pay thy poverty, and not thy will.
APOTHECARY Put this in any liquid thing you will,
And drink it off; and, if you had the strength Of twenty men, it would despatch you straight.
ROMEO There is thy gold; worse poison to men's souls,
Doing more murders in this loathsome world Than these poor compounds that thou mayst not sell:
I sell thee poison; thou hast sold me none.
Farewell: buy food and get thyself in flesh.--
Come, cordial and not poison, go with me To Juliet's grave; for there must I use thee.
[Exeunt.]
Scene Il.
Friar Lawrence's Cell.
[Enter Friar John.]
FRlAR JOHN Holy Franciscan friar! brother, ho!
[Enter Friar Lawrence.]
FRlAR LAWRENCE This same should be the voice of Friar John.
Welcome from Mantua: what says Romeo?
Or, if his mind be writ, give me his letter.
FRlAR JOHN Going to find a barefoot brother out, One of our order, to associate me,
Here in this city visiting the sick, And finding him, the searchers of the town,
Suspecting that we both were in a house Where the infectious pestilence did reign,
Seal'd up the doors, and would not let us forth; So that my speed to Mantua there was stay'd.
FRlAR LAWRENCE Who bare my letter, then, to Romeo?
FRlAR JOHN I could not send it,--here it is again,--
Nor get a messenger to bring it thee, So fearful were they of infection.
FRlAR LAWRENCE Unhappy fortune! by my brotherhood,
The letter was not nice, but full of charge Of dear import; and the neglecting it
May do much danger.
Friar John, go hence; Get me an iron crow and bring it straight
Unto my cell.
FRlAR JOHN Brother, I'll go and bring it thee.
[Exit.]
FRlAR LAWRENCE Now must I to the monument alone; Within this three hours will fair Juliet wake:
She will beshrew me much that Romeo Hath had no notice of these accidents;
But I will write again to Mantua, And keep her at my cell till Romeo come;--
Poor living corse, clos'd in a dead man's tomb!
[Exit.]
Scene ill.
A churchyard; in it a Monument belonging to the Capulets.
[Enter Paris, and his Page bearing flowers and a torch.]
PARlS Give me thy torch, boy: hence, and stand aloof;-- Yet put it out, for I would not be seen.
Under yond yew tree lay thee all along, Holding thine ear close to the hollow ground;
So shall no foot upon the churchyard tread,-- Being loose, unfirm, with digging up of graves,--
But thou shalt hear it: whistle then to me, As signal that thou hear'st something approach.
Give me those flowers.
Do as I bid thee, go.
PAGE [Aside.]
I am almost afraid to stand alone Here in the churchyard; yet I will adventure.
[Retires.]
PARlS Sweet flower, with flowers thy bridal bed I strew:
O woe! thy canopy is dust and stones!
Which with sweet water nightly I will dew; Or, wanting that, with tears distill'd by moans:
The obsequies that I for thee will keep, Nightly shall be to strew thy grave and weep.
[The Page whistles.]
The boy gives warning something doth approach.
What cursed foot wanders this way to-night, To cross my obsequies and true love's rite?
What, with a torch! muffle me, night, awhile.
[Retires.]
[Enter Romeo and Balthasar with a torch, mattock, &c.]
ROMEO Give me that mattock and the wrenching iron.
Hold, take this letter; early in the morning See thou deliver it to my lord and father.
Give me the light; upon thy life I charge thee, Whate'er thou hear'st or seest, stand all aloof
And do not interrupt me in my course.
Why I descend into this bed of death
Is partly to behold my lady's face, But chiefly to take thence from her dead finger
A precious ring,--a ring that I must use In dear employment: therefore hence, be gone:--
But if thou, jealous, dost return to pry In what I further shall intend to do,
By heaven, I will tear thee joint by joint, And strew this hungry churchyard with thy limbs:
The time and my intents are savage-wild; More fierce and more inexorable far
Than empty tigers or the roaring sea.
BALTHASAR I will be gone, sir, and not trouble you.
ROMEO So shalt thou show me friendship.--Take thou that:
Live, and be prosperous: and farewell, good fellow.
BALTHASAR For all this same, I'll hide me hereabout:
His looks I fear, and his intents I doubt.
[Retires.]
ROMEO Thou detestable maw, thou womb of death,
Gorg'd with the dearest morsel of the earth, Thus I enforce thy rotten jaws to open,
[Breaking open the door of the monument.]
And, in despite, I'll cram thee with more food!
PARlS This is that banish'd haughty Montague
That murder'd my love's cousin,--with which grief, It is supposed, the fair creature died,--
And here is come to do some villanous shame To the dead bodies:
I will apprehend him.--
[Advances.]
Stop thy unhallow'd toil, vile Montague!
Can vengeance be pursu'd further than death?
Condemned villain, I do apprehend thee;
Obey, and go with me; for thou must die.
ROMEO I must indeed; and therefore came I hither.-- Good gentle youth, tempt not a desperate man;
Fly hence and leave me:--think upon these gone; Let them affright thee.--I beseech thee, youth,
Put not another sin upon my head By urging me to fury:
O, be gone!
By heaven, I love thee better than myself; For I come hither arm'd against myself:
Stay not, be gone;--live, and hereafter say, A madman's mercy bid thee run away.
PARlS I do defy thy conjurations,
And apprehend thee for a felon here.
ROMEO Wilt thou provoke me? then have at thee, boy!
[They fight.]
PAGE O lord, they fight!
I will go call the watch.
[Exit.]
PARlS O, I am slain!
[Falls.]
If thou be merciful, Open the tomb, lay me with Juliet.
[Dies.]
ROMEO In faith, I will.--Let me peruse this face:-- Mercutio's kinsman, noble County Paris!--
What said my man, when my betossed soul Did not attend him as we rode?
I think
He told me Paris should have married Juliet: Said he not so? or did I dream it so?
Or am I mad, hearing him talk of Juliet, To think it was so?--O, give me thy hand,
One writ with me in sour misfortune's book!
I'll bury thee in a triumphant grave;--
A grave?
O, no, a lanthorn, slaught'red youth, For here lies Juliet, and her beauty makes
This vault a feasting presence full of light.
Death, lie thou there, by a dead man interr'd.
[Laying Paris in the monument.]
How oft when men are at the point of death
Have they been merry! which their keepers call A lightning before death:
Call this a lightning?--O my love! my wife!
Death, that hath suck'd the honey of thy breath,
Hath had no power yet upon thy beauty:
Thou art not conquer'd; beauty's ensign yet
Is crimson in thy lips and in thy cheeks, And death's pale flag is not advanced there.--
Tybalt, liest thou there in thy bloody sheet?
O, what more favour can I do to thee
Than with that hand that cut thy youth in twain To sunder his that was thine enemy?
Forgive me, cousin!--Ah, dear Juliet, Why art thou yet so fair?
Shall I believe
That unsubstantial death is amorous; And that the lean abhorred monster keeps
Thee here in dark to be his paramour?
For fear of that I still will stay with thee,
And never from this palace of dim night Depart again: here, here will I remain
With worms that are thy chambermaids:
O, here Will I set up my everlasting rest;
And shake the yoke of inauspicious stars From this world-wearied flesh.--Eyes, look your last!
Arms, take your last embrace! and, lips, O you The doors of breath, seal with a righteous kiss
A dateless bargain to engrossing death!-- Come, bitter conduct, come, unsavoury guide!
Thou desperate pilot, now at once run on The dashing rocks thy sea-sick weary bark!
Here's to my love! [Drinks.]
--O true apothecary!
Thy drugs are quick.--Thus with a kiss I die.
[Dies.]
[Enter, at the other end of the Churchyard, Friar Lawrence, with a lantern, crow, and spade.]
FRlAR Saint Francis be my speed! how oft to-night Have my old feet stumbled at graves!--Who's there?
Who is it that consorts, so late, the dead?
BALTHASAR Here's one, a friend, and one that knows you well.
FRlAR Bliss be upon you!
Tell me, good my friend,
What torch is yond that vainly lends his light To grubs and eyeless skulls? as I discern,
It burneth in the Capels' monument.
BALTHASAR It doth so, holy sir; and there's my master, One that you love.
FRlAR Who is it?
BALTHASAR Romeo.
FRlAR How long hath he been there?
BALTHASAR Full half an hour.
FRlAR Go with me to the vault.
BALTHASAR I dare not, sir;
My master knows not but I am gone hence; And fearfully did menace me with death
If I did stay to look on his intents.
FRlAR Stay then; I'll go alone:--fear comes upon me;
O, much I fear some ill unlucky thing.
BALTHASAR As I did sleep under this yew tree here, I dreamt my master and another fought,
And that my master slew him.
FRlAR Romeo!
[Advances.]
Alack, alack! what blood is this which stains The stony entrance of this sepulchre?--
What mean these masterless and gory swords To lie discolour'd by this place of peace?
[Enters the monument.]
Romeo! O, pale!--Who else? what, Paris too?
And steep'd in blood?--Ah, what an unkind hour Is guilty of this lamentable chance!--The lady stirs.
[Juliet wakes and stirs.]
JULlET O comfortable friar! where is my lord?-- I do remember well where I should be,
And there I am:--where is my Romeo?
[Noise within.]
FRlAR I hear some noise.--Lady, come from that nest
Of death, contagion, and unnatural sleep: A greater power than we can contradict
Hath thwarted our intents:--come, come away!
Thy husband in thy bosom there lies dead;
And Paris too:--come, I'll dispose of thee Among a sisterhood of holy nuns:
Stay not to question, for the watch is coming.
Come, go, good Juliet [noise within],--I dare no longer stay.
JULlET Go, get thee hence, for I will not away.--
[Exit Friar Lawrence.]
What's here? a cup, clos'd in my true love's hand?
Poison, I see, hath been his timeless end:-- O churl! drink all, and left no friendly drop
To help me after?--I will kiss thy lips; Haply some poison yet doth hang on them,
To make me die with a restorative.
[Kisses him.]
Thy lips are warm!
1 WATCH [Within.] Lead, boy:--which way?
JULlET Yea, noise?--Then I'll be brief.--O happy dagger!
[Snatching Romeo's dagger.]
This is thy sheath [stabs herself]; there rest, and let me die.
[Falls on Romeo's body and dies.]
[Enter Watch, with the Page of Paris.]
PAGE This is the place; there, where the torch doth burn.
1 WATCH The ground is bloody; search about the churchyard:
Go, some of you, whoe'er you find attach.
[Exeunt some of the Watch.]
Pitiful sight! here lies the county slain;-- And Juliet bleeding; warm, and newly dead,
Who here hath lain this two days buried.-- Go, tell the prince;--run to the Capulets,--
Raise up the Montagues,--some others search:-- [Exeunt others of the Watch.]
We see the ground whereon these woes do lie; But the true ground of all these piteous woes
We cannot without circumstance descry.
[Re-enter some of the Watch with Balthasar.] 2 WATCH Here's Romeo's man; we found him in the churchyard.
1 WATCH Hold him in safety till the prince come hither.
[Re-enter others of the Watch with Friar Lawrence.] 3 WATCH Here is a friar, that trembles, sighs, and weeps:
We took this mattock and this spade from him
As he was coming from this churchyard side.
1 WATCH A great suspicion: stay the friar too.
[Enter the Prince and Attendants.]
PRlNCE What misadventure is so early up, That calls our person from our morning's rest?
[Enter Capulet, Lady Capulet, and others.]
CAPULET What should it be, that they so shriek abroad?
LADY CAPULET The people in the street cry Romeo,
Some Juliet, and some Paris; and all run, With open outcry, toward our monument.
PRlNCE What fear is this which startles in our ears?
1 WATCH Sovereign, here lies the County Paris slain;
And Romeo dead; and Juliet, dead before, Warm and new kill'd.
PRlNCE Search, seek, and know how this foul murder comes.
1 WATCH Here is a friar, and slaughter'd Romeo's man,
With instruments upon them fit to open These dead men's tombs.
CAPULET O heaven!--O wife, look how our daughter bleeds!
This dagger hath mista'en,--for, lo, his house Is empty on the back of Montague,--
And it mis-sheathed in my daughter's bosom!
LADY CAPULET O me! this sight of death is as a bell
That warns my old age to a sepulchre.
[Enter Montague and others.]
PRlNCE Come, Montague; for thou art early up,
To see thy son and heir more early down.
MONTAGUE Alas, my liege, my wife is dead to-night;
Grief of my son's exile hath stopp'd her breath:
What further woe conspires against mine age?
PRlNCE Look, and thou shalt see.
MONTAGUE O thou untaught! what manners is in this,
To press before thy father to a grave?
PRlNCE Seal up the mouth of outrage for a while, Till we can clear these ambiguities,
And know their spring, their head, their true descent; And then will I be general of your woes,
And lead you even to death: meantime forbear, And let mischance be slave to patience.--
Bring forth the parties of suspicion.
FRlAR I am the greatest, able to do least, Yet most suspected, as the time and place
Doth make against me, of this direful murder; And here I stand, both to impeach and purge
Myself condemned and myself excus'd.
PRlNCE Then say at once what thou dost know in this.
FRlAR I will be brief, for my short date of breath
Is not so long as is a tedious tale.
Romeo, there dead, was husband to that Juliet;
And she, there dead, that Romeo's faithful wife:
I married them; and their stol'n marriage day
Was Tybalt's doomsday, whose untimely death Banish'd the new-made bridegroom from this city;
For whom, and not for Tybalt, Juliet pin'd.
You, to remove that siege of grief from her,
Betroth'd, and would have married her perforce, To County Paris:--then comes she to me,
And with wild looks, bid me devise some means To rid her from this second marriage,
Or in my cell there would she kill herself.
Then gave I her, so tutored by my art,
A sleeping potion; which so took effect As I intended, for it wrought on her
The form of death: meantime I writ to Romeo That he should hither come as this dire night,
To help to take her from her borrow'd grave, Being the time the potion's force should cease.
But he which bore my letter, Friar John, Was stay'd by accident; and yesternight
Return'd my letter back.
Then all alone At the prefixed hour of her waking
Came I to take her from her kindred's vault; Meaning to keep her closely at my cell
Till I conveniently could send to Romeo:
But when I came,--some minute ere the time
Of her awaking,--here untimely lay The noble Paris and true Romeo dead.
She wakes; and I entreated her come forth And bear this work of heaven with patience:
But then a noise did scare me from the tomb; And she, too desperate, would not go with me,
But, as it seems, did violence on herself.
All this I know; and to the marriage
Her nurse is privy: and if ought in this Miscarried by my fault, let my old life
Be sacrific'd, some hour before his time, Unto the rigour of severest law.
PRlNCE We still have known thee for a holy man.--
Where's Romeo's man? what can he say in this?
BALTHASAR I brought my master news of Juliet's death;
And then in post he came from Mantua To this same place, to this same monument.
This letter he early bid me give his father; And threaten'd me with death, going in the vault,
If I departed not, and left him there.
PRlNCE Give me the letter,--I will look on it.--
Where is the county's page that rais'd the watch?-- Sirrah, what made your master in this place?
BOY He came with flowers to strew his lady's grave;
And bid me stand aloof, and so I did:
Anon comes one with light to ope the tomb;
And by-and-by my master drew on him; And then I ran away to call the watch.
PRlNCE This letter doth make good the friar's words,
Their course of love, the tidings of her death:
And here he writes that he did buy a poison
Of a poor 'pothecary, and therewithal Came to this vault to die, and lie with Juliet.--
Where be these enemies?--Capulet,--Montague,-- See what a scourge is laid upon your hate,
That heaven finds means to kill your joys with love!
And I, for winking at your discords too,
Have lost a brace of kinsmen:--all are punish'd.
CAPULET O brother Montague, give me thy hand:
This is my daughter's jointure, for no more
Can I demand.
MONTAGUE But I can give thee more:
For I will raise her statue in pure gold;
That while Verona by that name is known, There shall no figure at such rate be set
As that of true and faithful Juliet.
CAPULET As rich shall Romeo's by his lady's lie;
Poor sacrifices of our enmity!
PRlNCE A glooming peace this morning with it brings; The sun for sorrow will not show his head.
Go hence, to have more talk of these sad things; Some shall be pardon'd, and some punished;
For never was a story of more woe Than this of Juliet and her Romeo.
[Exeunt.]
>
Let's do a bunch more of these addition problems.
So let's say I have 9,367 plus 2,459.
We start in the 1's place or you can even think of it as the 1's column.
So you're going to add the 7 1's plus the 9 1's.
So you're going to have 7 plus 9, which we hopefully know by now is 16.
So what we do is we write the 6 in the 1's place and we carry the 1.
Let me switch-- if this 1 is going to be the same thing as that 1 right there.
And this might look like a little bit of a mystery or magic, and the whole reason we did that is that this is the 10's place.
And when you write 16 you have six 1's and one 10.
If you view this as money, what's the best way to get $16 in a world where there weren't $5 bills?
Where you only had $1 bills, $10 bills, $100 bills, and so on. Only multiples of 10.
And we don't have any $5 bills. In that world you would represent 16 as one $10 bill just like that.
And then six $1 bills.
So that's two $1 bills.
That's two more $1 bills.
And then that's two more $1 bills. The whole reason why I'm drawing it this way or I'm even using this analogy or drawing the dollar bills is to show you what these places mean.
When I say that this right here is the 10's place,
I'm essentially telling you how many $10 bills do I have? If I've $16 and I'm doing it as efficiently as I can in a world without $5 bills.
I only have $1's, $10's, and $100's and $1,000's bills and so forth.
And this is the 1's. So when I write it this way I'm literally telling you,
I have one $10 bill and I have six $1 bills. That's what $16 is.
And so when I have 7 plus 9 is equal to 16
I say that I have six $1 bills and I have one $10 bill.
We're on problem 14.
And it asks us what is the solution to the inequality x minus 5 is greater than 14?
Well, to do this, this is just like solving any equality or equation.
What we do to one side, we have to do the other side.
And we want to get rid of this minus 5, and the best way to get rid of a minus 5 is to add 5, so lets add 5 to both sides of this equation.
So 5 plus and then a plus 5.
And then a 5 plus a minus 5, that's 0.
That's why we added the 5 in the first place.
So we're just left with an x on that side. We get x is greater than 14 plus 5, which is 19.
That's choice B.
Problem 15.
The lengths of the sides of a triangle are-- so we have a triangle.
They tell us the lengths of the sides are y, y plus 1, and 7 centimeters.
They also tell us the perimeter is 56 centimeters.
The perimeter is equal to 56 centimeters.
What is the value of y?
So the perimeter of any shape is just the sum of the sides.
So y plus y plus 1 plus 7.
That's the distance around the triangle.
And that is equal to the perimeter, which is equal to 56.
Let's see, we get y plus y is 2y, plus 1 plus 7 is 8, is equal to 56, so you get 2y is equal to what is that?
56.
So if we subtract 8 from both sides of this equation, on the left-hand side, we just get 2y.
On the right-hand side, 56 minus 8, that's 48.
Divide both sides by 2 and you get y is equal to 24.
And that is choice A.
Problem 16.
Now what do they want us to do?
All right, I think this is one I should copy and paste.
Which number serves as a counterexample to the statement below?
So, a counterexample, an example that shows that this isn't always true.
So the statement is all positive integers are divisible by 2 or 3.
So we just have to find a positive integer that is not divisible by 2 or 3, by neither 2 nor 3.
Well, 100 is divisible by 2, right?
So that just verifies or it's just another example of a positive integer that's divisible by one of these two, so it's not choice A.
It's not a counterexample.
57, It's not divisible by 2, but it is divisible by 3.
19 times 3 is 57.
So it's not choice B. 57 is another positive integer that's divisible by 2 or 3.
It's divisible by 3, so it's not that.
30's divisible by both, so that's definitely not a counterexample.
But here we have 25.
It's a positive integer and it is neither divisible by 2 nor 3, so it disproves the statement.
So it is a counterexample.
And so the answer is D.
Problem 17.
All right.
What is the conclusion of the statement in the box below?
OK, they say if x squared is equal to 4.
So if we know that x squared is equal to 4, then we know, and we know this from algebra, we could have solved it, that x is equal to minus 2 or 2.
All right, so what is the conclusion of the statement in the box below?
Oh, OK.
This is the condition and this is the conclusion.
They're saying if this has happened, then we conclude that.
So they're actually just asking us to label it.
This is the conclusion.
Then x is equal to minus 2 or 2.
I don't like that question so much.
My reaction was, OK, if this is the whole statement, what can I conclude from it?
And there's not a lot that I could conclude from it unless they told me that this indeed was true.
But anyway, I don't want to get too complicated.
They're just saying that if this is true, then we can conclude this. And they're actually just saying what is the conclusion? So what part of this statement can we label as the conclusion?
Anyway, see you in the next video.
Why do so many people reach success and then fail?
One of the big reasons is, we think success is a one-way street.
So we do everything that leads up to success, but then we get there.
We figure we've made it, we sit back in our comfort zone, and we actually stop doing everything that made us successful.
And it doesn't take long to go downhill.
And I can tell you this happens, because it happened to me.
Reaching success, I worked hard, I pushed myself.
But then I stopped, because I figured, "Oh, you know, I made it.
I can just sit back and relax."
Reaching success, I always tried to improve and do good work.
But then I stopped because I figured, "Hey, I'm good enough.
I don't need to improve any more."
Reaching success, I was pretty good at coming up with good ideas.
Because I did all these simple things that led to ideas.
But then I stopped, because I figured I was this hot-shot guy and I shouldn't have to work at ideas, they should just come like magic.
And the only thing that came was creative block.
I couldn't come up with any ideas.
Reaching success, I always focused on clients and projects, and ignored the money.
Then all this money started pouring in.
And I got distracted by it.
And suddenly I was on the phone to my stockbroker and my real estate agent, when I should have been talking to my clients.
And reaching success, I always did what I loved.
But then I got into stuff that I didn't love, like management.
I am the world's worst manager, but I figured I should be doing it, because I was, after all, the president of the company.
Well, soon a black cloud formed over my head and here I was, outwardly very successful, but inwardly very depressed.
But I'm a guy; I knew how to fix it.
I bought a fast car.
(Laughter)
It didn't help.
I was faster but just as depressed.
So I went to my doctor.
I said, "Doc, I can buy anything I want.
But I'm not happy.
I'm depressed.
It's true what they say, and I didn't believe it until it happened to me.
But money can't buy happiness."
He said, "No.
But it can buy Prozac."
And he put me on anti-depressants.
And yeah, the black cloud faded a little bit, but so did all the work, because I was just floating along.
I couldn't care less if clients ever called.
(Laughter)
And clients didn't call.
(Laughter)
Because they could see I was no longer serving them,
I was only serving myself.
So they took their money and their projects to others who would serve them better.
Well, it didn't take long for business to drop like a rock.
My partner and I, Thom, we had to let all our employees go.
It was down to just the two of us, and we were about to go under.
And that was great.
Because with no employees, there was nobody for me to manage.
So I went back to doing the projects I loved.
I had fun again, I worked harder and, to cut a long story short, did all the things that took me back up to success.
But it wasn't a quick trip.
It took seven years.
But in the end, business grew bigger than ever.
And when I went back to following these eight principles, the black cloud over my head disappeared altogether.
And I woke up one day and I said,
"I don't need Prozac anymore."
And I threw it away and haven't needed it since.
I learned that success isn't a one-way street.
It doesn't look like this; it really looks more like this.
It's a continuous journey.
And if we want to avoid "success-to-failure-syndrome," we just keep following these eight principles, because that is not only how we achieve success, it's how we sustain it.
So here is to your continued success.
Thank you very much.
(Applause)
At 9:50am Haitham Ziad Al-Mis'hal was targeted by an unmanned Israeli aircraft in North Gaza, just North of the Beach refugee camp where he resided, right outside a Hamas training site
The targeted assassination was the first of its kind since the eight-day war of
The hamas government in Gaza condemned the targeting in a relatively measured statement.
According to the Occupying state of Israel
Haitham was responsible for a rocket firing incident in Egypt's Sinai desert a fortnight ago.
No israelis were injured or killed went two Grad rockets landed in the Israeli town of Eilat.
Some of Haitham's friends and relatives arrived at the morgue to see his body.
At the mortuary Haitham's father confirmed his son's involvement with various resistance groups.
All of his life he worked with the resistance and he always aspired to be martyred like his relative Ahmad al-Mis'hal.
Now he followed Ahmad.
The targeting of Haitham was apparently a joint Israeli military and secret service intelligence operation.
Israel further claimed that Hamas knew about Haitham's militant activities and failed to stop him
Israel holds the Hamas government responsible for any attacks emanating from Gaza
Hamas hasn't been able to restrain the armed activities of some resistance groups since it came to power in 2007.
Men carried Haitham's body from the morgue to his family home
The women of the family and neighbourhood received the body
His ankles, torn off by two drone missiles.
Haitham's mother said that 20 more resistance fighters will rise up in his place.
She added that she hopes that the resistance groups will destroy Israel
She herself hopes to be killed defending Palestinian land
His older sister exclaimed: where is the cease-fire?
Then she said Gaza doesn't need a cease-fire anyway.
Today was Haitham's [25th] birthday
Haitham had four brothers and three sisters.
We spoke with his middle sister
Twelve-year-old Aya who said he was the family's only breadwinner
Honestly Haitham was a good guy.
He was like a caring father figure and brother.
Now he is a martyr with his Lord.
We have not lost out because this was God's will.
God's will governs even the lives of the collaborators.
I hope that God kills all those who betrayed our people.
In the Catastrophe of 1948 Haitham's family was displaced from al-Jorah near Ashkelon, now inside Israel, a few miles north from his family home
According to his family Haitham was riding a motorbike when he received a mobile phone call telling him to ride north to visit the unknown caller.
He was targeted en route.
I'm the wife of Haitham
We married 3 months ago.
I am proud of his martyrdom.
I'm pregnant.
Who's the one who's going to raise the baby inside me?
God is the best of planners.
The family fears Haitham's wife will miscarry because of the grief and stress
The men then proceeded to a graveyard in Sheikh Redwan where he was buried.
Um Amar Abu Sharaekh lives directly opposite Haitham's home and helped raise him.
Haitham was not the first to be martyred and he won't be the last
And many will rise up like Haitham.
Israel shouldn't think that our youth and our resistance will stop rising up and the one who taught Haitham will teach many more.
In the future the the rocket firers will strike further away than Tel Aviv. They will respond. Anyone from the Muslim youth is our son too.
Israel maintains that they it preemptively target anyone involved in planned rocket attacks from
Gaza or Egypt
Meanwhile various militant groups here in Gaza have issued statements saying that they will answer today's targeting
It's now more likely the things will escalate in Gaza in the coming days
Visit GazaReport.com for more insight into the situation afflicting Gaza
This films production was made possible by Gaza Report's funders
Let's just do a ton of more examples, just so we make sure that we're getting this trig function thing down well. So let's construct ourselves some right triangles. Let's construct ourselves some right triangles, and I want to be very clear.
So if you're trying to find the trig functions of angles that aren't part of right triangles, we're going to see that we're going to have to construct right triangles, but let's just focus on the right triangles for now. So let's say that I have a triangle, where let's say this length down here is seven, and let's say the length of this side up here, let's say that that is four.
Let's figure out what the hypotenuse over here is going to be. So we know -let's call the hypotenuse, "h"- we know that h squared is going to be equal to seven squared plus four squared, we know that from the Pythagorean theorem, that the hypotenuse squared is equal to the square of each of the sum of the squares of the other two sides. h squared is equal to seven squared plus four squared.
So this is equal to forty-nine plus sixteen, forty-nine plus sixteen, forty nine plus ten is fifty-nine, plus six is sixty-five.
It is sixty five. So this h squared, let me write: h squared -that's different shade of yellow- so we have h squared is equal to sixty-five.
Did I do that right?
Forty nine plus ten is fifty nine, plus another six is sixty-five, or we could say that h is equal to, if we take the square root of both sides, square root square root of sixty five.
And we really can't simplify this at all. This is thirteen. This is the same thing as thirteen times five, both of those are not perfect squares and they're both prime so you can't simplify this any more.
So this is equal to the square root of sixty five.
Now let's find the trig, let's find the trig functions for this angle up here.
Let's call that angle up there theta.
So whenever you do it you always want to write down - at least for me it works out to write down -
"soh cah toa". soh... ...soh cah toa.
I don't know - you know, some... about some type of indian princess named "soh cah toa" or whatever, but it's a very useful mnemonic, so we can apply "soh cah toa".
Let's find, let's say we want to find the cosine. We want to find the cosine of our angle.
We wanna find the cosine of our angle, you say: "soh cah toa!"
"Cah" tells us what to do with cosine, the "cah" part tells us that cosine is adjacent over hypotenuse.
Cosine is equal to adjacent over hypotenuse. So let's look over here to theta; what side is adjacent?
Well we know that the hypotenuse, we know that that hypotenuse is this side over here.
So it can't be that side.
The only other side that's kind of adjacent to it that isn't the hypotenuse, is this four.
So the adjacent side over here, that side is, it's literally right next to the angle, it's one of the sides that kind of forms the angle it's four over the hypotenuse.
The hypotenuse we already know is square root of sixty-five. so it's four over the square root of sixty-five.
And sometimes people will want you to rationalize the denominator which means they don't like to have an irrational number in the denominator, like the square root of sixty five, and if they - if you wanna rewrite this without a irrational number in the denominator, you can multiply the numerator and the denominator by the square root of sixty-five.
This clearly will not change the number, because we're multiplying it by something over itself, so we're multiplying the number by one.
That won't change the number, but at least it gets rid of the irrational number in the denominator.
So the numerator becomes four times the square root of sixty-five, and the denominator, square root of 65 times square root of 65, is just going to be 65.
We didn't get rid of the irrational number, it's still there, but it's now in the numerator.
Now let's do the other trig functions or at least the other core trig functions.
We'll learn in the future that there's actually a ton of them but they're all derived from these. so let's think about what the sign of theta is.
Once again go to "soh cah toa".
The "soh" tells what to do with sine.
Sine is opposite over hypotenuse.
Sine is equal to opposite over hypotenuse.
Sine is opposite over hypotenuse.
So for this angle what side is opposite?
We just go opposite it, what it opens into, it's opposite the seven so the opposite side is the seven.
This is, right here - that is the opposite side and then the hypotenuse, it's opposite over hypotenuse.
The hypotenuse is the square root of sixty-five.
Square root of sixty-five. and once again if we wanted to rationalize this, we could multiply times the square root of 65 over the square root of 65 and the the numerator, we will get seven square root of 65 and in the denominator we will get just sixty-five again.
Now let's do tangent!
Let us do tangent.
So if i ask you the tangent of - the tangent of theta once again go back to "soh cah toa".
The toa part tells us what to do with tangent it tells us... it tells us that tangent is equal to opposite over adjacent is equal to opposite over opposite over adjacent
So for this angle, what is opposite?
We've already figured it out. it's seven.
It opens into the seven.
It is opposite the seven.
So it's seven over what side is adjacent. well this four is adjacent.
So the adjacent side is four. so it's seven over four, and we're done.
We figured out all of the trig ratios for theta. let's do another one.
Let's do another one. i'll make it a little bit concrete 'cause right now we've been saying,
"oh, what's tangent of x, tangent of theta." let's make it a little bit more concrete.
Let's say... let's say, let me draw another right triangle, that's another right triangle here.
Everything we're dealing with, these are going to be right triangles. let's say the hypotenuse has length four, let's say that this side over here has length two, and let's say that this length over here is going to be two times the square root of three.
We can verify that this works.
If you have this side squared, so you have - let me write it down - two times the square root of three squared plus two squared, is equal to what? this is two. There's going to be four times three. four times three plus four, and this is going to be equal to twelve plus four is equal to sixteen and sixteen is indeed four squared.
So this does equal four squared, it does equal four squared.
It satisfies the pythagorean theorem and if you remember some of your work from 30 60 90 triangles that you might have learned in geometry, you might recognize that this is a 30 60 90 triangle.
This right here is our right angle,
- i should have drawn it from the get go to show that this is a right triangle - this angle right over here is our thirty degree angle and then this angle up here, this angle up here is a sixty degree angle, and it's a thirty sixteen ninety because the side opposite the thirty degrees is half the hypotenuse and then the side opposite the 60 degrees is a squared of 3 times the other side that's not the hypotenuse.
So that said, we're not gonna ... this isn't supposed to be a review of 30 60 90 triangles although i just did it.
Let's actually find the trig ratios for the different angles.
So if i were to ask you or if anyone were to ask you, what is... what is the sine of thirty degrees? and remember 30 degrees is one of the angles in this triangle but it would apply whenever you have a 30 degree angle and you're dealing with the right triangle.
We'll have broader definitions in the future but if you say sine of thirty degrees, hey, this angle right over here is thirty degrees so i can use this right triangle, and we just have to remember "soh cah toa"
We rewrite it. soh, cah, toa. "sine tells us" (correction). soh tells us what to do with sine. sine is opposite over hypotenuse. sine of thirty degrees is the opposite side, that is the opposite side which is two over the hypotenuse.
The hypotenuse here is four. it is two fourths which is the same thing as one-half. sine of thirty degrees you'll see is always going to be equal to one-half. now what is the cosine?
What is the cosine of thirty degrees?
Once again go back to "soh cah toa".
The cah tells us what to do with cosine.
Cosine is adjacent over hypotenuse.
So for looking at the thirty degree angle it's the adjacent.
This, right over here is adjacent. it's right next to it. it's not the hypotenuse. it's the adjacent over the hypotenuse. so it's two square roots of three adjacent over...over the hypotenuse, over four. or if we simplify that, we divide the numerator and the denominator by two it's the square root of three over two.
Finally, let's do the tangent.
The tangent of thirty degrees, we go back to "soh cah toa". soh cah toa toa tells us what to do with tangent. It's opposite over adjacent you go to the 30 degree angle because that's what we care about, tangent of 30. tangent of thirty.
Opposite is two, opposite is two and the adjacent is two square roots of three.
It's right next to it. It's adjacent to it. adjacent means next to. so two square roots of three so this is equal to... the twos cancel out one over the square root of three or we could multiply the numerator and the denominator by the square root of three.
So we have square root of three over square root of three and so this is going to be equal to the numerator square root of three and then the denominator right over here is just going to be three.
So that we've rationalized a square root of three over three.
Fair enough.
Now lets use the same triangle to figure out the trig ratios for the sixty degrees, since we've already drawn it. so what is... what is the sine of the sixty degrees? and i think you're hopefully getting the hang of it now.
Sine is opposite over adjacent. soh from the "soh cah toa". for the sixty degree angle what side is opposite? what opens out into the two square roots of three, so the opposite side is two square roots of three, and from the sixty degree angle the adj-oh sorry its the opposite over hypotenuse, don't want to confuse you. so it is opposite over hypotenuse so it's two square roots of three over four. four is the hypotenuse. so it is equal to, this simplifies to square root of three over two.
What is the cosine of sixty degrees? cosine of sixty degrees. so remember "soh cah toa". cosine is adjacent over hypotenuse. adjacent is the two sides, right next to the sixty degree angle.
So it's two over the hypotenuse which is four.
So this is equal to one-half and then finally, what is the tangent? what is the tangent of sixty degrees?
Well tangent, "soh cah toa".
Tangent is opposite over adjacent opposite the sixty degrees is two square roots of three two square roots of three and adjacent to that adjacent to that is two. Adjacent to sixty degrees is two.
So its opposite over adjacent, two square roots of three over two which is just equal to the square root of three.
And I just wanted to -look how these are related- the sine of thirty degrees is the same as the cosine of sixty degrees.
The cosine of 30 degrees is the same thing as the sine of 60 degrees and then these guys are the inverse of each other and i think if you think a little bit about this triangle it will start to make sense why. we'll keep extending this and give you a lot more practice in the next few videos.
A standard elevator in a mid-rise building can hold a maximum weight of 1 and 1/2 tons. Assuming an average adult weight of 160 pounds, what is the maximum number of adults who could safely ride the elevator?
So what we need to do is we have to get the maximum weight that the elevator could hold in terms of pounds.
And then say, OK, well, how many adults is that?
So they gave us the maximum weight in terms of tons.
So they say it is 1 and 1/2 tons. And it's always easier to deal with improper fractions than mixed numbers, so let's write this as an improper fraction.
1 and 1/2 tons is the same thing as-- well, 1 ton is 2 halves, and then you add another 1 half, that's 3 halves.
So you get 3/2 tons.
Or another way to think about it is 2 times 1 is 2, plus 1 is 3.
So the maximum capacity is 3/2 tons.
Let's think about how many pounds that is. And to do that, we have to know that there are 2,000 pounds per ton.
Let me write this up here.
We know that there are 2,000 pounds per ton.
This wasn't given in the problem anywhere. This is something I knew from past experience, and it's a good thing to know, in general, that a ton is 2,000 pounds.
So I'm going to write it right over here.
Now, how do we convert these 3/2 tons into pounds? Well, we're going to multiply it by something, and the units that we're going to multiply by, we want the tons to cancel out.
So we're going to want to have tons in the denominator, so it cancels out with this tons up here.
And then we want pounds in the numerator.
And that's exactly what we wrote up here. There are 2,000 pounds for every 1 ton, or you could just say 2,000 pounds per ton.
You could put the 1 there, but it doesn't really change the expression.
Now, if we multiply 3/2 tons times 2,000 pounds per ton, what'll happen is that the tons cancel out.
That was the whole point of multiplying it by this. And we would be left with 3/2 times 2,000, and the only unit
left is pounds.
And if you do it this way, you'll never get confused. You'll know that the units cancel out so you're getting the right units.
But if you just think about it in your mind, it should also make sense.
If there are 2,000 pounds per ton and there are 1 and 1/2 tons, I should multiply 1 and 1/2 times 2,000 to get the number of pounds.
That makes sense. And we know 1 and 1/2 times 2,000 is 3,000, but we'll figure it out right here.
So what is 3/2 times 2,000?
Well, I just told you answer.
We can actually simplify it right over here.
This is going to be 3 times 2,000/2 pounds.
We can divide the numerator and the denominator by 2.
This will become 1,000, and this will become 1, so it's 3 times 1,000 pounds, or this is equal to 3,000 pounds. So what we've done so far, we've just figured out the maximum capacity of the elevator.
It can hold 1 and 1/2 tons, which is the exact same thing as 3,000 pounds.
Now, what we need to figure out is 3,000 pounds is the equivalent to how many average adults of 160 pounds?
Or how many 160 pound people would it take to weigh a total of 3,000 pounds?
Well, we can just divide by 160. And if you want to make sure that the units work out, remember, we want our answer to be in terms of people, and we want the pounds to cancel out.
So we have pounds in the numerator here, so if we divide by pounds, the pounds will cancel out.
And then we want our leftover to be people, or maybe person.
Person, people, same thing.
Let me do people. The grammar of it, singular, plural, might make it a little confusing, but I think you get the general idea.
Now, if we were to write this out, what does it tell us? 1 person weighs 160 pounds, so there's one person for every 160 pounds.
So notice, if we multiply these two expressions, the pounds will cancel out.
We'll be just left with people. We're multiplying 3,000 times 1/160, but it's really just taking 3,000 and dividing by 160, which makes sense.
We have a capacity of 3,000.
Each of our people weighs 160 pounds.
Divide by 160.
It tells you how many people.
But this way, you know that the units are working out.
So this is going to be equal to 3,000/160 people. That is the maximum capacity of the elevator in terms of average people.
Now, what is this?
Well, we can divide the numerator and the denominator by 10.
If we divide the numerator and the denominator by 10, this becomes 300/16.
If we divide 300 by 2, this becomes 150.
If we divide 16 by 2, this becomes 8.
Now, let's see, what can we do more here?
We could divide by 2 again.
Let me rewrite it.
So this is the same thing as 150/8 people.
150, we can divide by 2.
It gives us 75.
And if you take 8 divided by 2, that is 4.
So we have 75 divided by 4 people.
Let me just do that, work it out. So you have 75 divided by 4.
4 goes into 7 one time.
1 times 4 is 4. You subtract.
7 minus 4 is 3. Bring down this 5.
4 goes into 35 eight times.
8 times 4 is 32. Subtract.
5 minutes 2 is 3.
And then you have the decimal.
We're going to the right of the ones place.
We're going to the tenths place now.
So we can bring down a zero over here.
4 goes into 30 seven times.
7 times 4 is 28.
You subtract.
You get 2. Bring down another zero. 4 goes into 20 exactly five times.
5 times 4 is 20, and then we are done. So this expression is exactly-- the 3,000 divided by 160, or the 150 divided by 8, the 75 divided by 4, it all turns out to be 18.75 people is the capacity of the elevator.
18.75 average 160-pound people would weigh 3,000 pounds.
Now, do they want a decimal?
What is the maximum number of adults who could safely ride the elevator?
Well, if they're all going to be average, then the maximum number of adults, since you can't have 3/4 of a person, or 75/100 of a person, the maximum number is going to be 18.
A baby's T-shirt requires 4/5 yards of fabric, or 4/5 of a yard of fabric.
How many T-shirts can be made from 48 yards?
So what we want to do is we essentially want to say how many groups of 4/5 of a yard can we make with 48 yards?
So you literally view this as we want to take 48 yards and divide it into groups of 4/5 of a yard, and say how many groups are there?
Because each of those groups can make one to baby's T-shirt.
If you give me 4/5 of a yard, one baby's T-shirt, so the number of groups of 4/5 is the number of babies' T-shirts.
Now, when we divide by a fraction, we just have to remember that that is the same thing, that is completely equivalent to multiplying times the reciprocal of the fraction.
So if we have 4/5 here, that'll be 5/4, the reciprocal.
Now, you still might say, hey, I have a whole number here and a fraction, and you just have to remember any whole number can be written as a fraction.
This is the same thing as 48/1 times 5/4.
Now, we could just multiply it out at this point and figure out what 48 times 5 is and that'll be over 4, but that'll get big numbers and it'll be hard to kind of divide and all that, but we could divide at this stage right here. We could divide the numerator and the denominator by 4.
Or we could say, look, this is going to be equal to 48 times 5, whatever that is, over 4.
Now, let's divide the numerator by 4.
Well, we could divide 48 by 4, and we will get to 12, and whatever we did to the numerator, we have to do to the denominator, so if we divide 4 by 4, we get 1.
So then we're left with 12 times 5, which is equal to 60.
12 times 5, which is equal to 60/1, which is the exact same thing as 60.
So you can actually make 60 children's or babies' T-shirts from 48 yards if each of them use 4/5 of a yard.
Jamir is training for a race and is running laps around a field.
If the distance around the field is 300 yards, how many complete laps would he need to do to run at least 2 miles?
So they tell us how far one lap is, it's 300 yards, but we need to figure out how many laps to go 2 miles.
So a good starting point would be to get everything into the same units.
We have distance here in terms of miles, we have it here in terms of yards.
So let's just get everything into yards.
So he needs to run 2 miles.
How do we convert that to yards?
Well, I don't have it memorized how many yards there are per mile, but I do have it memorized how many feet there are per mile.
And it's a good thing to have in the back of your brain someplace, that in general you have 5,280 feet per mile.
It's a good number to know. 5,280 feet per mile.
So if we want to convert, we can first convert the miles to feet, and then we know that there are 3 feet per yard, and then we'll have 2 miles in terms of yards.
So 2 miles, if we want it converted to feet, we want miles in the denominator and we want feet in the numerator.
And the reason why I say that is so that this miles will cancel out with that miles, and we'll just have feet there.
And I just wrote down, there's 5,280 feet per mile, or you say 5,280 feet for every 1 mile.
You can write it either way, but let's just write it like that.
And then we can multiply.
So this is going to give us what?
If we just multiply the numbers 2 times 5,280.
So what is that going to be?
Maybe I should get a calculator out.
Or we could do that in our head.
Let's think of it this way:
2 times 80 is 160. 2 times 200 is 400.
So it's going to be 400 plus 160 is going to be 560.
And then 2 times 5,000 thousand is 10,000.
So it's 10,560.
And then the miles cancel out, and we are just left with feet.
And let me actually multiply it out.
I did it in my head that time, but that's not always useful.
Let me verify for you that 5,280 times 2 is indeed 10,560.
So 2 times 0 is 0. 2 times 8 is 16.
Carry the 1. 2 times 2 is 4, plus 1 is 5. 2 times 5 is 10.
So he needs to run 10,560 feet.
Now, we want this in terms of yards.
So 10,560 feet.
Let's convert this to yards.
Well, we want it in yards.
So we want yards in the numerator, and we want feet in the denominator, so that the feet cancel out with that feet right there.
And we know that there are 3 feet for every 1 yard.
Or another way to read this is that you have 1/3 of a yard for every foot.
And now we can multiply.
And it makes sense.
If you're going from feet to yards, the number should get smaller because yards is a bigger unit.
You need fewer yards to go the same distance as a certain number of feet.
So it makes sense that we're dividing.
Same thing:
2 miles is a ton of feet, so it made sense that we were multiplying by a large number.
Here it makes sense that we're dividing.
So let's do this.
So this becomes 10,560 times 1 divided by 3.
So it's 10,560/3. That's that and that part.
And then the feet cancel out, and we are just left with yards.
So 2 miles is 10,560 divided by 3.
And let's figure out what that is.
So 3 goes into 10,560.
It doesn't go into 1.
It goes into 10 three times. 3 times 3 is 9.
And we subtract.
We get 1. Bring down this 5.
It becomes a 15. 3 goes into 15 five times. 5 times 3 is 15.
We have no remainder, or 0.
You bring down the 6. 3 goes into 6 two times.
Let me scroll down a little bit. 2 times 3 is 6. Subtract.
No remainder.
Bring down this last 0. 3 goes into 0 zero times. 0 times 3 is 0.
And we have no remainder.
So 2 miles is the equivalent to 3,520 yards.
That's the total distance he has to travel.
That's the equivalent of 2 miles.
Now we want to figure out how many laps there are.
We want this in terms of laps, not in terms of yards.
So we want the yards to cancel out.
And we want laps in the numerator, right?
Because when you multiply, the yards will cancel out, and we'll just be left with laps.
Now, how many laps are there per yard or yards per lap?
Well, they say the distance around the field is 300 yards.
So we have 300 yards for every 1 lap.
So now, multiply this right here.
The yards will cancel out, and we will get 3,520.
Let me do that in a different color.
We will get 3,520, that right there, times 1/300.
When you multiply it times 1, it just becomes 3,520 divided by 300.
And in terms of the units, the yards canceled out.
We're just left with the laps.
So this is how many laps he needs to run.
So 3,520 divided by 300.
Well, we can eyeball this right here.
What is 11 times 300?
Let's just approximate this right here.
So if we did 11 times 300, what is that going to be equal to?
Well, 11 times 3 is 33, and then we have two zeroes here.
So this will be 3,300.
So it's a little bit smaller than that.
If we have 12 times 300, what is that going to be?
12 times 3 is 36, and then we have these two zeroes, so it's equal to 3,600.
So this is going to be 11 point something.
It's larger than 11, right?
3,520 is larger than 3,300.
So when you divide by 300 you're going to get something
larger than 11.
But this number right here is smaller than 3,600 so when you divide it by 300, you're going to get something a little bit smaller than 12.
So the exact number of laps is going to be a little bit lower than 12 laps.
So 2 miles is a little bit lower than 12 laps.
But let's make sure we're answering their question.
How many complete laps would he need to do to run at least 2 miles?
So they're telling us that, look, this might be, 11 point something, something, something laps.
That would be the exact number of laps to run 2 miles.
But they say how many complete laps does he have to run?
11 complete laps would not be enough.
He would have to run 12.
So our answer here is 12 complete laps.
That complete tells us that they want a whole number of laps.
We can't just divide this.
If we divide this, we're going to get some 11 point something, something.
You can do with the calculator or do it by hand if you're interested.
But we have to do at least 12 because that's the smallest whole number of laps that will get us to at least this distance right here, or this number of laps, or the equivalent of 2 miles.
A card game using 36 unique cards, four suits, diamonds, hearts, clubs, and spades, with cards numbered from 1 to 9 in each suit.
So there's four suits.
Each of them have nine cards, so that gives us 36 unique cards.
A hand is a collection of nine cards, which can be sorted however the player chooses.
So they're essentially telling us that order does not matter.
What is the probability of getting all four of the 1's?
So they want to know the probability of getting all four of the 1's.
So all four 1's in my hand of 9.
Now this is kind of daunting at first. You're like, gee you know, I've got nine cards and I'm taking them out of 36 and I have to figure out how do I get all of the 1's.
But if we think about it just very, very, in very simple terms, all a probability is saying is, the number of events-- or I guess you could say-- the number of ways in which this action or this event happens.
So this is what the definition of the probability is.
It's going to be the number of ways in which event can happen and when we talk about the event, we're talking about having all four 1's in my hand.
That's the event.
And all of these different ways, that's sometimes called the event space.
But we actually want to count how many ways that, if I get a hand of 9 picking from 36, that I can get the four 1's in it.
So it is the number of ways in which my event can happen and we want to divide that into all of the possibilities-- or maybe I should write it this way-- the total number of hands that I can get.
So the numerator in blue is the number of different hands where I have the four 1's and we're dividing the total number of hands.
Now let's figure out the total number of hands first, because on some level this might be more intuitive and we've actually done this before.
Now, the total number of hands, we're picking nine cards.
And we're picking them from a set of 36 unique cards.
And we've done this many, many times.
Let me write this, total number of hands, or total number of possible hands.
That's equal to-- you can imagine, you have nine cards to pick from.
The first card you pick, it's going to be 1 of 36 cards.
Then the next one is going to be 1 of 35.
Then the next one is going to be 1 of 34, 33, 32, 31.
We're going to do this nine times, one, two, three, four, five, six, seven, eight, and nine.
So that would be the total number of hands if order mattered.
But we know-- and we've gone over this before-- that we don't care about the order.
All we care about are the actual cars that are in there.
So we're overcounting here.
We're overcounting for all of the different rearrangements that these cards could have.
It doesn't matter whether the Ace of diamonds is the first card I pick or the last card I pick.
The way I've counted them right now, we are counting those as two separate hands.
But they aren't two separate hands, so order doesn't matter.
So we have to do is, we have to divide this by the number of ways you can arrange nine things.
So you could put nine of the things in the first position, then eight in the second, seven in the third, so forth and so on.
It essentially becomes 9 factorial times 2 times 1.
And we've seen this multiple times.
This is essentially 36 choose 9.
This expression right here is the same thing-- just you can relate it to the combinatorics formulas that you might be familiar with-- this is the same thing as 36 factorial over 36 minus 9 factorial-- that's what this orange part is over here-- divided by 9 factorial or over 9 factorial.
What's green is what's green and what is orange is what's orange there.
So that's the total number of hands.
Now a little bit more of a nuanced thought process is, how do we figure out the number of ways in which the event can happen, in which we can have all four 1's.
So let's figure that out.
So number of ways-- or maybe we should say this-- number of hands with four 1's.
And just as a little bit of a thought experiment, imagine if we were only taking four cards, if a hand only had four cards in it.
Well if a hand only had four cards in it, then the number of ways to get a hand with four 1's, there'd only be one way, one combination.
You'd just have four 1's.
That's the only combination with four 1's, if we were only picking four cards.
But here, we're not only picking four cards.
Four of the cards are going to be 1's.
One, two, three, four.
But the other five cards are going to be different.
So one, two, three, four, five.
So for the other five cards-- if you imagine this slot-- considering that of the 36 we would have to pick four of them already in order for us to have four 1's.
Well, we've used up four of them, so there's 32 possible cards over in that position of the hand.
And then there'd be 31 in that position of the hand.
And then there'd be 30 because every time we're picking a card, were using it up.
And now we only have 30 to pick from.
Then we only have 29 to pick from.
And then we have 28 to pick from.
And just like we did before, we don't care about order.
We don't care if we pick the 5 of clubs first or whether we pick the 5 of clubs last.
So we shouldn't double count it.
So we have to divide by the different number of ways that five cards can be arranged.
So we have to divide this by the different ways that five cards can be arranged.
The first card or the first position can be any one of five cards, then four cards, then three cards, then two cards, then one cards.
So the number of hands with four 1's is actually just this number.
You're actually looking at all of the different ways you can fill up the remaining cards.
These four 1's are just going to be four 1's.
There's only one way to get that if the remaining cards that's going to give all of the different combinations of having four 1's.
So this will be a count of all of the different combinations because all of the different extra stuff that you have will be all of the different hands.
Now we know the total number of hands with four 1's is this number.
And now we can divide it by the total number of possible hands.
And I didn't multiply them out on purpose so that we can cancel things out.
So let's do that.
Let's take this and divide by that.
So let me just copy and paste it.
Let's take that and let's divide it by that.
But dividing by a fraction is the same thing as multiplying by the reciprocal.
So let's just multiply by the reciprocal.
So let's multiply-- so this is the denominator.
Let's make this the numerator.
So let me copy it and then let me paste it.
So that's the numerator and then that's the denominator up there.
Because we're dividing by that expression.
So let me-- whoops. Let me put that there.
Let me get the select tool and then let me make sure I'm selecting all of the numbers.
Let me copy it and then let me paste that.
It's a little messy with those lines there, but I think this'll suit our purposes.
This'll suit our purposes just fine.
So when we're multiplying by this, we're essentially dividing by this expression up here.
Now this we can simplify pretty easily.
We have a-- well actually I forgot to do-- this should be 9 factorial.
This should be 9 times 8 times 7 times 6 times 5 times 4 times 3 times 2 times 1.
Let me put that in both places.
Actually let me just-- let me clear that both places.
Clear.
Don't want to confuse people.
Clear.
I'm sorry if that confused you when I wrote it earlier.
This would be 9 factorial.
9 times 8 times 7 times 6 times 5 times 4 times 3 times 2 times 1.
Let me copy and paste that now.
Copy and then you paste.
It That's that, right there.
And then we have this in the numerator.
We have 5 times 4 times 3 times 1 in the denominator.
So this will cancel out with that part right over there.
And then we have 32 times 31 times 30 times 29 times 28.
That is going to cancel with that.
That and that cancels out.
So what we're left with is just this part over here.
Let me rewrite it.
So we're left with 9 times 8 times 7 times 6 over-- and this will just be an exercise in simplifying this expression-- 36 times 35 times 34 times 33.
And let's see, if we divide the numerator and denominator by 9, that becomes a 1, this becomes a 4.
You can divide the numerator and denominator by 4, this becomes a 2.
This becomes a 1.
You divide numerator and denominator by 7, this becomes a 1, this becomes a 5.
You can divide both by 2 again and then this becomes a 1.
This becomes a 17.
And you could divide this and this by 3.
This becomes a 2 and then this becomes an 11.
So we're left with, the probability of having all four 1's in my hand of 9 that I'm selecting from 36 unique cards is equal to-- in the numerator, I'm just left with this 2 times 1 times 1 times 1-- so it's equal to 2 over 5 times 17 times 11.
And that is-- so drum roll, this was kind of an involved problem-- 5 times 17 times 11 is equal to 935.
So it's equal to 2 over 935.
So about roughly 2 in a thousand chance or 1 in a 500-- roughly speaking, this isn't exact odds-- you have a roughly 1 in 500 chance of getting all four of the 1's in your hand of 9 when you're selecting from 36 unique cards.
בוידאו הראשון על In the first video on evolution, I gave the example of the peppered moth during the Industrial Revolution in England and how, before the Industrial Revolution, there were a bunch of moths: some were dark, some were light, some were in between.
But then once everything became soot filled, all of a sudden, the dark moths were less likely to be caught by predators and so all of the white moths were less likely to be able to reproduce successfully, so the black moth trait, or that variant, dominated.
And then if you came a little bit later and you saw all the moths had turned black, you'd say all these moths are geniuses.
They appear to have somehow engineered their way to stay camouflaged.
And the point I was making there is that, look, that wasn't engineered or an explicit move on the part of the moths or the DNA, that was just a natural byproduct of them having some variation, and some of that variation was selected for.
So that example, that was pretty simple: black or white.
But what about more complicated things?
So, for example, here I've got a couple of pictures of what's commonly called the owl butterfly.
And what's amazing here, and it's pretty obvious, as I probably don't have to point out to you, is its wing looks like half of an owl's eye.
I can almost draw a beak here and draw another wing there and you can imagine an owl staring at us, right?
And here, too, I could imagine a beak here and you would think an owl there, too.
And so the question is how does something this good show up randomly, right?
I mean, you could imagine, OK, little spots or black and white or grey, but how does something that looks so much like an eye generate randomly?
Now the answer is-- well, there's a couple of answers.
One is why does this eye exist, or this eye-like pattern or this owl-like eye's pattern?
And there, the jury's still out on that.
I read a little bit about it on Wikipedia and all of these images I got from Wikipedia.
In Wikipedia, they said, look, there's two competing theories here.
One theory is that this, even though to us humans, the way we see things, it looks like an owl's eye, that this is actually a decoy.
When some predator wants to eat one of these things, they go for the thing that looks most substantive.
So instead of going for the butterfly's body, which doesn't look that substantive, they go for the big, black thing.
They say, oh, that looks like it's protein rich and it'll be a good meal.
So they try to snap and bite at that, and if they bite at that, sure, the guy's wing's going to be clipped a little bit and it's going to suck, but the animal itself, the actual butterfly, would survive, and maybe it can repair its swings.
I don't know the actual biology of the owl butterfly. That's one theory, and then the argument against it goes, well, no, if that was the case, then you would want the black spot even further back along its-- you'd want the spot way far away from the body.
You'd want it back here instead of right here, because there's still a chance, if something chomps at this little black spot, that it'll still get the abdomen of the butterfly.
Now, the other theory as to why this exists-- and, you know, who knows?
Maybe it's a little bit of both.
Maybe both of these are true.
Maybe this offers two advantages.
The other theory, and this is kind of the one that jumps out at us when we see this , is, hey, this looks like an owl.
Maybe this is to scare away the things that are likely to eat this dude.
And it does turn out in my reading that there are lizards that like to eat these type of butterflies, and those lizards probably don't like to be around birds or owls because those owls eat them, so that might be a deterrent.
And then the other example, they said is, look, they tend to be eaten by this lizard right here-- this is what
Wikipedia told me-- and that this lizard tends to be eaten by this frog right there, and that the eyes of this butterfly are not too dissimilar to the eyes of this frog.
And, you know, we can debate whether or not that's the case, and if this was the predator we're trying to mimic, you could make an argument that maybe we would have had more green on our wing, but that's not the point of this video.
But it's a fun discussion to have as to what is useful about this eye.
But let's have the question: How did that eye come about?
And when I say that eye, I mean the pattern on that wing.
What set of events allowed this to happen?
Because when I described evolution, and we know that everything in our biological kingdom is just a set of proteins and then stuff that maybe the protein-- but mainly protein, and that protein's all coded for by DNA.
I'm going to do future videos on DNA, but DNA is just a sequence of base pairs.
It's a sequence of these molecules.
And we represent adenine, and guanine and cytosine and thymine.
Then maybe you have a couple of adenines in a row and some guanine and thymine.
I'll do a lot more on this in the future, but the idea is it's just coded for by this sequence of these molecules.
How do you go from a butterfly that has no eye to all of a sudden an eye that goes there?
Obviously, just one change that happens from a random mutation.
Maybe that G turns into an A or maybe this C and this T get deleted so everything-- that alone isn't going to develop this beautiful of a pattern or this useful of a pattern.
So how do the random changes explain something that's this intricate?
And this is my explanation.
And obviously, I wasn't sitting there watching over the thousands or millions of years as these owl butterflies emerged, so this is just my theory of how natural selection does explain this type of phenomenon.
You have a world where in some environment you have butterflies, and their wings look like-- let's say you have some butterflies that are generally like this.
That's their wing, and it's a very bad drawing, but I think you get the idea, and there's just some general patterns.
We've seen it before. There's variation.
And the variation does show up from these little random changes in DNA.
I think we can all believe that, that most of these changes are kind of benign.
Maybe they just set up differently where a little pattern will show up or a little speck of pigment will show up with a slightly different color.
And we even see amongst these owl butterflies, there is variation.
This dude's wing is different than that guy's wing with the commonality that they do have these eye-looking shapes.
And there's not just one; there's actually multiple.
This guy has this other thing up here that looks interesting, and they have multiple things, but the one really noticeable feature is this eye-looking thing.
So how do we go from this to an eye-looking thing?
So the idea is you have some variation.
One guy might look like that.
Another guy, or gal, might-- just randomly, their dot might be something like that.
Another gal or guy-- these wings are really badly drawn, but you get the idea.
This is the butterfly.
This is its antenna right there.
That's its body.
Another butterfly's patterns might look like this, right?
And so, they're just random.
But when they go into a certain environment for whatever reason, maybe one of its predators-- maybe that theory that these are supposed to look like eyes is true.
And so, actually, maybe this guy just has a random pattern here.
And so this guy-- and I'm not saying that it's like definitely better. They're both going to be found and killed by predators, but it's all probablistic, right?
Maybe this guy has a 1% less chance of getting a predator, because when a predator just looks at him out of the corner of that eye, that little really hazy region kind of looks like an eye and the predator would be better off just not messing with it, and they'd rather go after the dude that looks like this.
So it's just a slight probability.
Now, you might, say, OK, what's 1% going to do?
But when you compound that 1% over thousands and thousands of generations, all of a sudden, this trait might dominate because he's just going to be killed that less frequently, 1% less frequently.
Now, maybe this guy has a similar trait, but his spot is closer to the abdomen.
And here, it's a tradeoff, because maybe some predators get scared away by this concentration of pigment.
And once again, I'm not saying that we're here yet.
We're not at this very advanced, sophisticated pattern yet.
We're at this random concentration of pigment that just shows up.
So we see that people who have this concentration of pigment further away from their abdomen, they do well.
But when it's too close, maybe some predators think that that's actually an insect and they want to eat it, so that's actually a bad trait.
So what happens is this guy dominates, and so within this population, you start having a lot of variation, because he starts representing-- he's more likely to pass on these traits.
And I want to make that point very clear.
This isn't what happens over the course of an animal's lifetime.
It's not like if somehow I experience something, or at least our current theory if I experience something, that I could somehow pass on that knowledge to my child.
What it says is if my DNA just happens to have just some variation that happens to be more useful or more likely for me to survive to reproduction and for my children to survive, then that will start to dominate in the population.
So then the population, you're going to have variations within that.
Maybe some guys, you know, it's going to get a little bit to look like that.
Maybe another one's going to look a little bit like that.
Maybe it has some spots there.
You can kind of view it as the variation as "exploring." But
I want to be very clear not to use any active verbs here because this is all being done really as almost a common sense process, where everything changes.
The changes that are most suited are the ones that are going to survive more frequently.
And then the next generation's going to have more of that and then you'll have variation within that change.
And then this one might be like that, and maybe this is the one.
These were good compared to that, but now when you're competing amongst themselves, this one is able to reproduce 1% more than this guy or this guy.
And so this guy becomes-- and maybe it's some combination of all of the above, and they mix and match.
It's a hugely complex system.
But then this guy represents most of the population, when I say this guy, I'm saying this guy's genetic information, at least as it pertains to his wings.
And then you get variation amongst that.
Maybe some of it, they have a little small dot and there's some dots around it.
Maybe it's like this.
Maybe one of them digresses and goes back here, but then he has trouble competing so he gets knocked out again.
And then some other people have it back here.
I think you get the point that this isn't happening overnight.
These changes can be fairly incremental, but we're doing it over thousands of generations.
So when you're talking about thousands of generations, or even millions of generations, even a 1% advantage can be significant, and when you accumulate those variations over a large period of time, you can get to fairly intricate patterns like this.
So I just wanted to explain that, because this is often used as, sure, I can believe the butterfly moth or I can even maybe believe the examples of the antibiotics and the bacteria or the flu, because those are kind of real-time examples.
But how does something this intricate show up?
And I actually want to make a point here.
We think this is more intricate because we can relate to it in our everyday lives.
But if you actually look at a structure of a bacteria and how it operates or what a virus does to infiltrate an immune system or a cell, that's actually on a lot more
levels a lot more intricate than a design.
In fact, the whole reason why I'm using this as an example is because this is a fairly simple example as opposed to kind of explaining the metabolism of a certain type of bacteria and how that might change and how it might become immune to penicillin or whatever else.
But I want to make this very clear that these very intricate things, they don't happen overnight.
It's not like one butterfly was completely one uniform hot-pink color and then all of a sudden they have a child whose wings looked just like this.
No!
It happens over large periods of time, although there might be some little weird hormonal change that does this, but I'm not going to go there, but that is possible.
But I just wanted to make this point because I think the more examples we see, the more it'll kind of hit home that this is a passive process.
We're not talking about these things happening overnight.
And it's actually really interesting to look at our world around us and look at ecosystems as they are today and try to think really hard about how something came to be, what it's useful for, why it might have been selected for.
For example, are traits that occur after reproduction selected for?
Well, probably not unless they affect the reproduction of the next cycle.
For example, you might say, oh, well, the trait to be nurturing after your reproductive years, that's after reproductive years.
No, but it helps your offspring reproduce.
But we already see a lot of diseases, especially once we get beyond our reproductive and our child-rearing years.
So once we get into our fifties and sixties, the incidences of diseases increases exponentially from when we're younger and because they're no longer being selected for, because it no longer affects our ability to reproduce, because we've already reproduced.
We've already raised our children so that they could reproduce.
So the only thing that happens at that point is now not being selected for.
So anyway, hopefully, this video will give you a little bit more nuance on evolution, and I want to do a couple of videos like this, because I really want to make it clear that it's not making some wild claim that all of a sudden this appears spontaneously, that it really is a thing that happens over millennia and eons and very gradually.
Welcome to my presentation on equivalent fractions.
So equivalent fractions are essentially what they sound like They're two fractions that although they use different numbers, they actually represent the same thing.
Let me show you an example.
Let's say I had the fraction 1/2.
Why isn't it writing.
Let me make sure I get the right color here.
Let's say I had the fraction 1/2.
So graphically, if we to draw that, if I had a pie and I would have cut it into two pieces.
That's the denominator there, 2.
And then if I were to eat 1 of the 2 pieces I would have eaten 1/2 of this pie.
Makes sense.
Nothing too complicated there.
Well, what if instead of dividing the pie into two pieces, let me just draw that same pie again.
Instead of dividing it in two pieces, what if I divided that pie into 4 pieces?
So here in the denominator I have a possibility of-- total of 4 pieces in the pie.
And instead of eating one piece, this time I actually ate 2 of the 4 pieces.
Or I ate 2/4 of the pie.
Well if we look at these two pictures, we can see that I've eaten the same amount of the pie.
So these fractions are the same thing.
If someone told you that they ate 1/2 of a pie or if they told you that they ate 2/4 of a pie, it turns out of that they ate the same amount of pie.
So that's why we're saying those two fractions are equivalent.
Another way, if we actually had-- let's do another one.
Let's say-- and that pie is quite ugly, but let's assume it's the same type of pie.
Let's say we divided that pie into 8 pieces.
And now, instead of eating 2 we ate 4 of those 8 pieces.
So we ate 4 out of 8 pieces.
Well, we still ended up eating the same amount of the pie.
We ate half of the pie.
So we see that 1/2 will equal 2/4, and that equals 4/8.
Now do you see a pattern here if we just look at the numerical relationships between 1/2, 2/4, and 4/8?
Well, to go from 1/2 to 2/4 we multiply the denominator-- the denominator just as review is the number on the bottom of the fraction.
We multiply the denominator by 2.
And when you multiply the denominator by 2, we also multiply the numerator by 2.
We did the same thing here.
And that makes sense because well, if I double the number of
pieces in the pie, then I have to eat twice as many pieces to eat the same amount of pie.
Let's do some more examples of equivalent fractions and hopefully it'll hit the point home.
Let me erase this.
Why isn't it letting me erase?
Let me use the regular mouse.
OK, good.
Sorry for that.
So let's say I had the fraction 3/5.
Well, by the same principle, as long as we multiply the numerator and the denominator by the same numbers, we'll get an equivalent fraction.
So if we multiply the numerator times 7 and the denominator times 7, we'll get 21-- because 3 times 7 is 21-- over 35.
And so 3/5 and 21/35 are equivalent fractions.
And we essentially, and I don't know if you already know how to multiply fractions, but all we did is we multiplied 3/5 times 7/7 to get 21/35.
And if you look at this, what we're doing here isn't magic.
7/7, well what's 7/7?
If I had 7 pieces in a pie and I were to eat 7 of them; I ate the whole pie.
So 7/7, this is the same thing as 1.
So all we've essentially said is well, 3/5 and we multiplied it times 1.
Which is the same thing as 7/7.
Oh boy, this thing is messing up.
And that's how we got 21/35.
So it's interesting.
All we did is multiply the number by 1 and we know that any number times 1 is still that number.
And all we did is we figured out a different way of writing 21/35.
Let's start with a fraction 5/12.
And I wanted to write that with the denominator-- let's say I wanted to write that with the denominator 36.
Well, to go from 12 to 36, what do we have to multiply by?
Well 12 goes into 36 three times.
So if we multiply the denominator by 3, we also have to multiply the numerator by 3.
Times 3.
We get 15.
So we get 15/36 is the same thing as 5/12.
And just going to our original example, all that's saying is, if I had a pie with 12 pieces and I ate 5 of them.
Let's say I did that.
And then you had a pie, the same size pie, you had a pie with 36 pieces and you ate 15 of them.
Then we actually ate the same amount of pie.
Well now you've learned what I think is quite possibly one of the most useful concepts in life, and you might already be familiar with it, but if you're not this will hopefully keep you from one day filing for bankruptcy.
So anyway, I will talk about interest, and then simple versus compound interest.
So what's interest?
We all have heard of it.
Interest rates, or interest on your mortgage, or how much interest do I owe on my credit card.
So interest-- I don't know what the actual formal definition, maybe I should look it up on Wikipedia-- but it's essentially rent on money.
So it's money that you pay in order to keep money for some period of time.
That's probably not the most obvious definition, but let me put it this way.
Let's say that I want to borrow $100 from you.
So this is now.
And let's say that this is one year from now.
One year.
And this is you, and this is me.
So now you give me $100.
And then I have the $100 and a year goes by, and I have $100 here.
And if I were to just give you that $100 back, you would have collected no rent.
You would have just got your money back.
You would have collected no interest.
But if you said, Sal I'm willing to give you $100 now if you give me $110 a year later.
So in this situation, how much did I pay you to keep that $100 for a year?
Well I'm paying you $10 more, right?
I'm returning the $100, and I'm returning another $10.
And so this extra $10 that I'm returning to you is essentially the fee that I paid to be able to keep that money and do whatever I wanted with that money, and maybe save it, maybe invest it, do whatever for a year.
And that $10 is essentially the interest.
And a way that it's often calculated is a percentage of the original amount that I borrowed.
And the original amount that I borrowed in fancy banker or finance terminology is just called principal.
So in this case the rent on the money or the interest was $10. And if I wanted to do it as a percentage, I would say 10 over the principal-- over 100-- which is equal to 10%.
So you might have said, hey Sal I'm willing to lend you $100 if you pay me 10% interest on it.
So 10% of $100 was $10, so after a year I pay you $100, plus the 10%.
And likewise.
So for any amount of money, say you're willing to lend me any amount of money for a 10% interest.
Well then if you were to lend me $1,000, then the interest would be 10% of that, which would be $100.
So then after a year I would owe you $1,000 plus 10% times $1,000, and that's equal to $1,100.
All right, I just added a zero to everything.
In this case $100 would be the interest, but it would still be 10%.
So let me now make a distinction between simple interest and compound interest.
So we just did a fairly simple example where you lent money for me for a year at 10% percent, right?
So let's say that someone were to say that my interest rate that they charge-- or the interest rate they charge to other people-- is-- well 10% is a good number-- 10% per year.
And let's say the principal that I'm going to borrow from this person is $100.
So my question to you-- and maybe you want to pause it after I pose it-- is how much do I owe in 10 years?
How much do I owe in 10 years?
So there's really two ways of thinking about it.
You could say, OK in years at times zero-- like if I just borrowed the money, I just paid it back immediately, it'd be $100, right?
I'm not going to do that, I'm going to keep it for at least a year.
So after a year, just based on the example that we just did, I could add 10% of that amount to the $100, and I would then owe $110.
And then after two years, I could add another 10% of the original principal, right?
So every year I'm just adding $10.
So in this case it would be $120, and in year three, I would owe $130.
Essentially my rent per year to borrow this $100 is $10, right?
Because I'm always taking 10% of the original amount.
And after 10 years-- because each year I would have had to pay an extra $10 in interest-- after 10 years I would owe $200.
Right?
And that $200 is equal to $100 of principal, plus $100 of interest, because I paid $10 a year of interest.
And this notion which I just did here, this is actually called simple interest.
Which is essentially you take the original amount you borrowed, the interest rate, the amount, the fee that you pay every year is the interest rate times that original amount, and you just incrementally pay that every year.
But if you think about it, you're actually paying a smaller and smaller percentage of what you owe going into that year.
And maybe when I show you compound interest that will make sense.
So this is one way to interpret 10% interest a year.
Another way to interpret it is, OK, so in year zero it's $100 that you're borrowing, or if they handed the money, you say oh no, no, I don't want it and you just paid it back, you'd owe $100.
After a year, you would essentially pay the $100 plus 10% of $100, right, which is $110.
So that's $100, plus 10% of $100.
Let me switch colors, because it's monotonous.
Right, but I think this make sense to you.
And this is where simple and compound interest starts to diverge.
In the last situation we just kept adding 10% of the original $100.
In compound interest now, we don't take 10% of the original amount.
We now take 10% of this amount.
So now we're going to take $110.
You can almost view it as our new principal.
This is how much we offer a year, and then we would reborrow it.
So now we're going to owe $110 plus 10% times 110.
You could actually undistribute the 110 out, and that's equal to 110 times 110.
Actually 110 times 1.1.
And actually I could rewrite it this way too.
I could rewrite it as 100 times 1.1 squared, and that equals $121.
And then in year two, this is my new principal-- this is $121-- this is my new principal.
And now I have to in year three-- so this is year two.
I'm taking more space, so this is year two.
And now in year three, I'm going to have to pay the $121 that I owed at the end of year two, plus 10% times the amount of money I owed going into the year, $121.
And so that's the same thing-- we could put parentheses around here-- so that's the same thing as 1 times 121 plus 0.1 times 121, so that's the same thing as 1.1 times 121.
Or another way of viewing it, that's equal to our original principal times 1.1 to the third power. And if you keep doing this-- and I encourage you do it, because it'll really give you a hands-on sense-- at the end of 10 years, we will owe-- or you, I forgot who's borrowing from whom-- $100 times 1.1 to the 10th power.
And what does that equal?
Let me get my spreadsheet out.
Let me just pick a random cell.
So plus 100 times 1.1 to the 10th power.
So $259 and some change.
So it might seem like a very subtle distinction, but it ends up being a very big difference.
When I compounded it 10% for 10 years using compound interest, I owe $259.
When I did it using simple interest, I only owe $200.
So that $59 was kind of the increment of how much more compound interest cost me.
I'm about to run out of time, so I'll do a couple more examples in the next video, just you really get a deep understanding of how to do compound interest, how the exponents work, and what really is the difference.
Let's say that we have the number 5 and we're asked... what number do we need to add to the number 5 to get to 0 and you might already know this but let's draw it out so let's say we have a number line over here and 0 is sitting right over there we are already sitting here at 5 so to go from 5 to 0 we have to go 5 spaces to the left and if we are going 5 space to the left that means we are adding negative 5 (-5) so if we add negative 5 right here than that is going to bring us back to 0 and you probably already knew this and this is a pretty... maybe common sense thing here but there is a fancy word for it called the additive inverse property and i'll just right it down, i think it's ridiculous that this is given such a fancy word for such a simple idea additive inverse property, and it is just the idea that if you have a number and if you add the additive inverse of the number, which most people call the negative of the number you add the negative of your number you will get back to 0 because they have the same size, you could view it that way, they both have a magnitude of 5, but this is going 5 to the right and this is going 5 to the left
Similarly, if you started at negative 3 (-3) if your starting over here at -3 so you already moved 3 spaces to the left. and someone says...
"What do i have to add to -3 to get back to 0?" well i have to move 3 spaces to the right now. and 3 spaces to the right is in the positive direction so i have to add positive 3 (+3) so if i add positive 3 to negative 3 i will get 0 so in general, if i have any number... 1 million seven hundred twenty five thousand three hundred and fourteen (1,725,314) and i say... what do i need to add to this to get back to zero well i have to essentially go in the opposite direction, i have to go in the leftwards direction so i'm going to subtract the same amount. or i can say i can add the additive inverse or add the negative version of it. so this is going to be the same thing as adding -1,725,314 and that will get me back to zero (0) similarly, what number do i need to add to -7 to get to 0. well if i'm already at -7 i need to add positive 7 ( 7 to the right) so this is going to be equal to 0 and this all comes form the general idea.
5+-5 : 5+ the - of 5: or 5 + the additive inverse of 5 you can just view this, and as another way as 5 - 5 and if you have 5 of something then you take you take away 5 then you learned many many years ago that, that is going to get you 0
Quadrilateral ABCD they're telling us it is a rhombus
To prove that the area of this rhombus is equal to one half times x AC x BD, essentially proving that the area of a rhombus is one half times the product of the lengths of its diagonals
Let' s see what we can do over here
There's a bunch of things we know about rhombi
All rhombi are parallelograms and there's tons of things that we know about parallelograms
First of all, if it's a rhombus, we know that all of the sides are congruent
That side length is equal to that side length, is equal to that side length, is equal to that side length
Because it's a parallelogram, we know that the diagonals bisect each other
Let's call this point over here E
We know that BE is going to be equal to ED and we know that AE is equal to EC
We also know because this is a rhombus and we proved this in the last video: that the diagonals, not only do they bisect each other, but they're also perpendicular
So we know that this is a right angle
This is a right angle
That is a right angle and then this is a right angle
The easiest way to think about it is, if we can show that this triangle ADC is congruent to triangle ABC and if we can figure out the area of one of them, we can just double it
The first part is pretty straightforward
We know that triangle ADC is going to be congruent to triangle ABC and we know that by side-side-side congruency
This side is congruent to that side
This side is congruent to that side and they both share AC right over here
So, this is by side-side-side
Because of that, we know that the area of ABCD is just going to be equal to 2 times the area of, we can pick either one of these, ABC
Let me write it this way
The area of ABCD is equal to the area of ADC plus the area of ABC but since they're congruent, these 2 are going to be the same thing so it's just going to be 2 times the area of ABC
Now what is the area of ABC
The area of a triangle is just one half of base times height
The area of ABC is just equal to times the base of that triangle times its height
What is the length of the base
The length of the base is AC
I'll color code it
The base is AC and then what is the height here
We know that this diagonal line over here is a perpendicular bisector so the height is just the distance from BE
So, it's AC times BE, that is the height
This is an altitude
It intersects this base at a 90 degree angle
Or we can say BE is the same thing as times BD
This is equal to times AC, that's our base
Our height is BE, which is times BD
So that's the area of just ABC, that broader, larger triangle right up there
That half of the rhombus
We just said that the area of the whole thing is 2 times that
If we go back, if we use both this information and this information right over here We have the area of ABCD is going to be equal to 2 times the area of ABC, this thing right over here
It is 2 times the area of ABC, right over there
So times is , times AC times BD
Then you see where this is going 2 times is , times AC times BD
Fairly straightforward, there's a neat result
Actually, I haven't done this in a video
I'll do it in the next video
There are other ways of finding the areas of parallelograms
Generally, it's essentially, base times height
But for rhombus, we could do that because it is a parallelogram, but we also have this other neat little result that we proved in this video
And if we know that lengths of the diagonals, the area of the rhombus is times the products of the lengths of the diagonals, which is kind of a neat result
We're asked to move the orange dot to -0.6 on the number line So the point, the dot, right now is at zero... and let's see this is -2, this is positive 2. So, each of these big slashes looks like it's 1
This gets us to 1; in fact, this is 0.5, 1, 1.5... and 1.9 is only going to be a tenth less than 2
And assuming that it is locking us to the tenths, and it looks like it is, so that looks pretty close to 1.9. Let's do one more of these. "Move the orange dot to 0.5 on the number line."
On a multiple choice test, problem 1 has 4 choices, and problem 2 has 3 choices.
Each problem has only one correct answer.
What is the probability of randomly guessing the correct answer on both problems?
Now, the probability of guessing the correct answer on each problem-- these are independent events.
So let's write this down.
The probability of correct on problem number 1 is independent.
Or let me write it this way.
Probability of correct on number 1 and probability of correct on number 2, on problem 2, are independent.
Which means that the outcome of one of the events, of guessing on the first problem, isn't going to affect the probability of guessing correctly on the second problem.
Independent events.
So the probability of guessing on both of them-- so that means that the probability of being correct-- on guessing correct on 1 and number 2 is going to be equal to the product of these probabilities.
And we're going to see why that is visually in a second.
But it's going to be the probability of correct on number 1 times the probability of being correct on number 2.
Now, what are each of these probabilities?
On number 1, there are 4 choices, there are 4 possible outcomes, and only one of them is going to be correct.
Each one only has one correct answer.
So the probability of being correct on problem 1 is 1/4.
And then the probability of being correct on problem number 2-- problem number 2 has three choices, so there's three possible outcomes.
And there's only one correct one, so only one of them are correct.
So probability of correct on number 2 is 1/3.
Probability of guessing correct on number 1 is 1/4.
The probability of doing on both of them is going to be its product.
So it's going to be equal to 1/4 times 1/3 is 1/12.
Now, to see kind of visually why this make sense, let's draw a little chart here.
And we did a similar thing for when we thought about rolling two separate dice.
So let's think about problem number 1.
Problem number 1 has 4 choices, only one of which is correct.
So let's write-- so it has 4 choices.
So it has 1-- let's write incorrect choice 1, incorrect choice 2, incorrect choice 3, and then it has the correct choice over there.
So those are the 4 choices.
They're not going to necessarily be in that order on the exam, but we can just list them in this order.
Now problem number 2 has 3 choices, only one of which is correct.
So problem number 2 has incorrect choice 1, incorrect choice 2, and then let's say the third choice is correct.
It's not necessarily in that order, but we know it has 2 incorrect and 1 correct choices.
Now, what are all of the different possible outcomes?
We can draw a little bit of a grid here.
All of these possible outcomes.
Let's draw all of the outcomes.
Each of these cells or each of these boxes in a grid are a possible outcome.
You could-- you're just guessing.
You're randomly choosing one of these 4, you're randomly choosing one of these 4.
So you might get incorrect choice 1 and incorrect choice 1-- incorrect choice in problem number 1 and then incorrect choice in problem number 2.
That would be that cell right there.
Maybe you get this-- maybe you get problem number 1 correct, but you get incorrect choice number 2 in problem number 2.
So these would represent all of the possible outcomes when you guess on each problem.
And which of these outcomes represent getting correct on both?
Well, getting correct on both is only this one, correct on choice 1 and correct on choice-- on problem number 2.
And so that's one of the possible outcomes and how many total outcomes are there?
There's 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, out of 12 possible outcomes.
Or since these are independent events, you can multiply.
You see that they're 12 outcomes because there's 12 possible outcomes.
So there's 4 possible outcomes for problem number 1, times the 3 possible outcomes for problem number 2, and that's also where you get a 12.
Whether you use it to fry your eggs, melt and bake potatoes, use on popcorn or simply spread on toast. Chances are butter has been part of your life and diet.
What is the difference between butter and margarine and is one healthier than the other?
Butter, made from cream or milk has been used for thousands of years.
But scientists eventually took notice of its high levels of saturated fat.
With more than 35 calories per teaspoon, butter is fattening.
When we look at the molecules of butter we see some of the building blocks of life, carbon, hydrogen and oxygen.
But these carbon atoms are completely surrounded by the hydrogen atoms.
And this saturation level quickly became associated with, and commonly believed to contribute to cardiovascular disease.
Margarine on the other hand is created primarily from plant oils which have a similar but different chemical composition. The carbons double bond with each other so that fewer hydrogen can fit and we call this unsaturated fat.
So far so good, a similar tasting substitute with less saturated fat.
Right? Not so fast, unsaturated fat has a lower melting point and so its natural state is less solid, like vegetable oil.
In order to get the consistency of butter scientists decided to make it a little more saturated.
The problem is through this process called hydrogenation where more hydrogen is added and the oil becomes more solid, high temperatures are used which cause some troublesome changes.
You see, most of these double bonds are in a configuration known as "cis bonds", but hydrogenation often flips them into something called a "trans configuration".
Ah, the dawn of trans fats. And while it may seem trivial, this simple yet unwitting flip from "cis" to
"trans" leads to significant changes in the way our body processes and metabolizes the molecules.
Essentially trans fats lower good cholesterol and higher the bad cholesterol which increases the risk of coronary heart disease.
So while margarine was initially seen as a healthier option, it's own hazards slowly came to light.
But the truth is that many margarine companies claim to be trans fat-free nowadays, and some are.
At the end of the day if we compare them side by side there are pros and cons for each.
Butter is completely natural and typically made from one ingredient, whereas margarine is processed and has many ingrediants.
Butter also has some essential vitamins and minerals such as vitamin a and e.
But margarines now vary so much it is difficult to make an accurate comparison.
Many hard stick margarines are still high in trans fats and much worse than butter.
But some newer margarines are much lower in saturated fat, lower their calorie count and contain zero trans fats.
The bottom line is to be aware of what you are eating.
Margarine can vary so drastically that looking at the label to understand what is or isn't and it will help you make informed decisions.
And there are healthier alternatives to both, such as vegetable oil spreads or using olive oil to dip your bread instead of buttering up.
No matter what you choose, the recommended goal is to limit the intake of saturated fat and avoid trans fats altogether.
This episode of AsapSClENCE is supported by audible.com, a leading provider of audiobooks with over one hundred thousand downloadable titles across all types of literature.
If you would like to learn more about food science I recommend the book "What Einstein Told His Cook" by Robert Wolke.
You can download this audiobook or another of your choice for free at audible.com/asap.
Special thanks to audible.com for making these videos possible and for offering you every audiobook at audible.com/asap, and subscribe for more weekly science videos.
In the last video we learned a little bit about photosynthesis.
And we know in very general terms, it's the process where we start off with photons and water and carbon dioxide, and we use that energy in the photons to fix the carbon.
And now, this idea of carbon fixation is essentially taking carbon in the gaseous form, in this case carbon dioxide, and fixing it into a solid structure.
And that solid structure we fix it into is a carbohydrate.
The first end-product of photosynthesis was this 3-carbon chain, this glyceraldehyde 3-phosphate.
But then you can use that to build up glucose or any other carbohydrate.
So, with that said, let's try to dig a little bit deeper and understand what's actually going on in these stages of photosynthesis.
Remember, we said there's two stages. The light-dependent reactions and then you have the light independent reactions.
I don't like using the word dark reaction because it actually occurs while the sun is outside.
It's actually occurring simultaneously with the light reactions.
It just doesn't need the photons from the sun.
But let's focus first on the light-dependent reactions. The part that actually uses photons from the sun. Or actually, I guess, even photons from the heat lamp that you might have in your greenhouse.
Remember, reduction is gaining electrons or hydrogen atoms.
And it's the same thing, because when you gain a hydrogen atom, including its electron, since hydrogen is not too electronegative, you get to hog its electron.
So this is both gaining a hydrogen and gaining electron.
But let's study it a little bit more.
So before we dig a little deeper, I think it's good to know a little bit about the anatomy of a plant.
So let me draw some plant cells.
So plant cells actually have cell walls, so I can draw them a little bit rigid.
So let's say that these are plant cells right here.
Each of these squares, each of these quadrilaterals is a plant cell.
And then in these plant cells you have these organelles called chloroplasts.
Remember organelles are like organs of a cell.
They are subunits, membrane-bound subunits of cells.
And of course, these cells have nucleuses and DNA and all of the other things you normally associate with cells. But I'm not going to draw them here.
I'm just going to draw the chloroplasts.
And your average plant cell-- and there are other types of living organisms that perform photosynthesis, but we'll focus on plants. Because that's what we tend to associate it with.
Each plant cell will contain 10 to 50 chloroplasts.
I make them green on purpose because the chloroplasts contain chlorophyil.
Which to our eyes, appear green.
But remember, they're green because they reflect green light and they absorb red and blue and other wavelengths of light.
That's why it looks green.
Because it's reflecting.
But it's absorbing all the other wavelengths.
But anyway, we'll talk more about that in detail.
But you'll have 10 to 50 of these chloroplasts right here.
And then let's zoom in on one chloroplast.
So if we zoom in on one chloroplast. So let me be very clear.
This thing right here is a plant cell.
That is a plant cell.
And then each of these green things right here is an organelle called the chloroplast.
And let's zoom in on the chloroplast itself.
If we zoom in on one chloroplast, it has a membrane like that.
And then the fluid inside of the chloroplast, inside of its membrane, so this fluid right here.
All of this fluid.
That's called the stroma.
The stroma of the chloroplast.
And then within the chloroplast itself, you have these little stacks of these folded membranes, These little folded stacks.
Let me see if I can do justice here.
So maybe that's one, two, doing these stacks.
Each of these membrane-bound-- you can almost view them as pancakes-- let me draw a couple more.
Maybe we have some over here, just so you-- maybe you have some over here, maybe some over here.
So each of these flattish looking pancakes right here, these are called thylakoids.
So this right here is a thylakoid.
That is a thylakoid.
The thylakoid has a membrane.
And this membrane is especially important.
We're going to zoom in on that in a second.
So it has a membrane, I'll color that in a little bit.
The inside of the thylakoid, so the space, the fluid inside of the thylakoid, right there that area. This light green color right there. That's called the thylakoid space or the thylakoid lumen.
And just to get all of our terminology out of the way, a stack of several thylakoids just like that, that is called a grana.
That's a stack of thylakoids.
That is a grana.
And this is an organelle.
And evolutionary biologists, they believe that organelles were once independent organisms that then, essentially, teamed up with other organisms and started living inside of their cells.
So there's actually, they have their own DNA.
So mitochondria is another example of an organelle that people believe that one time mitochondria, or the ancestors of mitochondria, were independent organisms.
That then teamed up with other cells and said, hey, if I produce your energy maybe you'll give me some food or whatnot.
And so they started evolving together. And they turned into one organism.
Which makes you wonder what we might evolve-- well anyway, that's a separate thing.
So there's actually ribosomes out here.
That's good to think about.
Just realize that at one point in the evolutionary past, this organelle's ancestor might have been an independent organism.
But anyway, enough about that speculation.
Let's zoom in again on one of these thylakoid membranes.
So I'm going to zoom in.
Let me make a box.
Let me zoom in right there.
So that's going to be my zoom-in box.
So let me make it really big. Just like this.
So this is my zoom-in box.
So that little box is the same thing as this whole box.
So we're zoomed in on the thylakoid membrane.
So this is the thylakoid membrane right there.
That's actually a phospho-bilipd layer.
It has your hydrophilic, hydrophobic tails.
I mean, I could draw it like that if you like.
The important thing from the photosynthesis point of view is that it's this membrane.
And on the outside of the membrane, right here on the outside, you have the fluid that fills up the entire chloroplast.
So here you have the stroma.
And then this space right here, this is the inside of your thylakoid.
So this is the lumen.
So if I were to color it pink, right there.
This is your lumen. Your thylakoid space.
And in this membrane, and this might look a little bit familiar if you think about mitochondria and the electron transport chain.
What I'm going to describe in this video actually is an electron transport chain.
Many people might not consider it the electron transport chain, but it's the same idea.
Same general idea.
So on this membrane you have these proteins and these complexes of proteins and molecules that span this membrane.
So let me draw a couple of them.
So maybe I'll call this one, photosystem Il.
And I'm calling it that because that's what it is. Photosystem Il.
You have maybe another complex.
And these are hugely complicated.
I'll do a sneak peek of what photosystem II actually looks like.
This is actually what photosystem II looks like.
So, as you can see, it truly is a complex.
These cylindrical things, these are proteins.
These green things are chlorophyil molecules.
I mean, there's all sorts of things going here.
And they're all jumbled together.
I think a complex probably is the best word.
It's a bunch of proteins, a bunch of molecules just jumbled together to perform a very particular function.
We're going to describe that in a few seconds.
So that's what photosystem II looks like.
Then you also have photosystem I.
And then you have other molecules, other complexes.
You have the cytochrome B6F complex and I'll draw this in a different color right here.
I don't want to get too much into the weeds. Because the most important thing is just to understand.
So you have other protein complexes, protein molecular complexes here that also span the membrane.
But the general idea-- I'll tell you the general idea and then we'll go into the specifics-- of what happens during the light reaction, or the light dependent reaction, is you have some photons.
Photons from the sun.
They've traveled 93 million miles. so you have some photons that go here and they excite electrons in a chlorophyil molecule, in a chlorophyil A molecule.
And actually in photosystem Il-- well, I won't go into the details just yet-- but they excite a chlorophyil molecule so those electrons enter into a high energy state.
Maybe I shouldn't draw it like that.
They enter into a high energy state.
And then as they go from molecule to molecule they keep going down in energy state.
But as they go down in energy state, you have hydrogen atoms, or actually I should say hydrogen protons without the electrons.
So you have all of these hydrogen protons.
Hydrogen protons get pumped into the lumen.
They get pumped into the lumen and so you might remember this from the electron transport chain.
In the electron transport chain, as electrons went from a high potential, a high energy state, to a low energy state, that energy was used to pump hydrogens through a membrane.
And in that case it was in the mitochondria, here the membrane is the thylakoid membrane.
But either case, you're creating this gradient where-- because of the energy from, essentially the photons-- the electrons enter a high energy state, they keep going into a lower energy state.
And then they actually go to photosystem I and they get hit by another photon.
Well, that's a simplification, but that's how you can think of it.
Enter another high energy state, then they go to a lower, lower and lower energy state.
But the whole time, that energy from the electrons going from a high energy state to a low energy state is used to pump hydrogen protons into the lumen.
So you have this huge concentration of hydrogen protons.
And just like what we saw in the electron transport chain, that concentration is then-- of hydrogen protons-- is then used to drive ATP synthase.
So the exact same-- let me see if I can draw that ATP synthase here.
You might remember ATP synthase looks something like this.
Where literally, so here you have a huge concentration of hydrogen protons.
So they'll want to go back into the stroma from the lumen.
And they do.
And they go through the ATP synthase.
Let me do it in a new color.
So these hydrogen protons are going to make their way back.
Go back down the gradient.
And as they go down the gradient, they literally-- it's like an engine.
And I go into detail on this when I talk about respiration.
And that turns, literally mechanically turns, this top part-- the way I drew it-- of the ATP synthase.
And it puts ADP and phosphate groups together.
It puts ADP plus phosphate groups together to produce ATP.
So that's the general, very high overview.
And I'm going to go into more detail in a second.
But this process that I just described is called photophosphorylation.
Let me do it in a nice color.
Why is it called that?
Well, because we're using photons.
That's the photo part.
We're using light.
We're using photons to excite electrons in chlorophyil.
As those electrons get passed from one molecule, from one electron acceptor to another, they enter into lower and lower energy states.
As they go into lower energy states, that's used to drive, literally, pumps that allow hydrogen protons to go from the stroma to the lumen.
Then the hydrogen protons want to go back.
They want to-- I guess you could call it-- chemiosmosis. They want to go back into the stroma and then that drives ATP synthase.
Right here, this is ATP synthase.
ATP synthase to essentially jam together ADPs and phosphate groups to produce ATP.
Now, when I originally talked about the light reactions and dark reactions I said, well the light reactions have two byproducts.
It has ATP and it also has-- actually it has three.
It has ATP, and it also has NADPH.
NADP is reduced.
It gains these electrons and these hydrogens.
So where does that show up?
Well, if we're talking about non-cyclic oxidative photophosphorylation, or non-cyclic light reactions, the final electron acceptor.
So after that electron keeps entering lower and lower energy states, the final electron acceptor is NADP plus.
So once it accepts the electrons and a hydrogen proton with it, it becomes NADPH.
Now, I also said that part of this process, water-- and this is actually a very interesting thing-- water gets oxidized to molecular oxygen.
So where does that happen?
So when I said, up here in photosystem I, that we have a chlorophyil molecule that has an electron excited, and it goes into a higher energy state.
And then that electron essentially gets passed from one guy to the next, that begs the question, what can we use to replace that electron?
And it turns out that we use, we literally use, the electrons in water.
So over here you literally have H2O.
And H2O donates the hydrogens and the electrons with it.
So you can kind of imagine it donates two hydrogen protons and two electrons to replace the electron that got excited by the photons.
Because that electron got passed all the way over to photosystem I and eventually ends up in NADPH.
So, you're literally stripping electrons off of water.
And when you strip off the electrons and the hydrogens, you're just left with molecular oxygen.
Now, the reason why I want to really focus on this is that there's something profound happening here.
Or at least on a chemistry level, something profound is happening.
You're oxidizing water.
And in the entire biological kingdom, the only place where we know something that is strong enough of an oxidizing agent to oxidize water, to literally take away electrons from water. Which means you're really taking electrons away from oxygen. So you're oxidizing oxygen.
So it's a very profound idea, that normally electrons are very happy in water.
They're very happy circulating around oxygens.
Oxygen is a very electronegative atom.
That's why we even call it oxidizing, because oxygen is very good at oxidizing things.
But all of a sudden we've found something that can oxidize oxygen, that can strip electrons off of oxygen and then give those electrons to the chlorophyil.
The electron gets excited by photons.
Then those photons enter lower and lower and lower energy states.
Get excited again in photosystem I by another set of photons and then enter lower and lower and lower energy states.
And then finally, end up at NADPH.
And the whole time it entered lower and lower energy states, that energy was being used to pump hydrogen across this membrane from the stroma to lumen.
And then that gradient is used to actually produce ATP.
So in the next video I'm going to give a little bit more context about what this means in terms of energy states of electrons and what's at a higher or lower energy state.
But this is essentially all that's happening.
Electrons get excited.
Those electrons eventually end up at NADPH.
And as the electron gets excited and goes into lower and lower energy states, it pumps hydrogen across the gradient.
And then that gradient is used to drive ATP synthase, to generate ATP.
And then that original electron that got excited, it had to be replaced.
And that replaced electron is actually stripped off of H2O.
So the hydrogen protons and the electrons of H2O are stripped away and you're just left with molecular oxygen.
And just to get a nice appreciation of the complexity of all of this-- I showed you this earlier in the video-- but this is literally a-- I mean this isn't a picture of photosystem Il.
You actually don't have cylinders like this.
But these cylinders represent proteins.
Right here, these green kind of scaffold-like molecules, that's chlorophyil A.
And what literally happens, is you have photons hitting-- actually it doesn't always have to hit chlorophyil A.
It can also hit what's called antenna molecules.
So antenna molecules are other types of chlorophyil, and actually other types of molecules.
And so a photon, or a set of photons, comes here and maybe it excites some electrons, it doesn't have to be in chlorophyil A.
It could be in some of these other types of chlorophyil.
Or in some of these other I guess you could call them, pigment molecules that will absorb these photons.
And then their electrons get excited.
And you can almost imagine it as a vibration.
But when you're talking about things on the quantum level, vibrations really don't make sense.
But it's a good analogy.
They kind of vibrate their way to chlorophyil A.
And this is called resonance energy.
They vibrate their way, eventually, to chlorophyil A.
And then in chlorophyil A, you have the electron get excited.
The primary electron acceptor is actually this molecule right here. Pheophytin. Some people call it pheo.
And then from there, it keeps getting passed on from one molecule to another.
I'll talk a little bit more about that in the next video.
But this is fascinating.
Look how complicated this is.
In order to essentially excite electrons and then use those electrons to start the process of pumping hydrogens across a membrane.
And this is an interesting place right here.
This is the water oxidation site.
So I got very excited about the idea of oxidizing water.
And so this is actually where it occurs in the photosystem II complex.
And you actually have this very complicated mechanism.
Because it's no joke to actually strip away electrons and hydrogens from an actual water molecule.
I'll leave you there.
And in the next video I'll talk a little bit more about these energy states.
And I'll fill in a little bit of the gaps about what some of these other molecules that act as hydrogen acceptors. Or you can also view them as electron acceptors along the way.
We humans like to get our heads around all of the complexity around us by classifying things. And you could imagine there's no more obvious thing to classify than all of the living things around us, than all of the life that surrounds us. So what I want to start talking about is, how do we classify all of the life around us?
But that, by itself, is not a good enough definition for a species. Things that look like each other or things that act like each other, because what we'll see is that there's some things that could be very different, at least in and how they look or act, but are actually closely related. And we'll talk about what it means to be closely related.
In general, ligers can't interbreed. And in general, this combination isn't going to produce offspring that can keep interbreeding or that are fertile. So that's why we say that lions and tigers are different species.
And that liger, we wouldn't even call it as a species at all. We would actually call it a hybrid between two species. Now the same thing is true-- and actually you might be asking yourself, well, this was a male lion and a female tigress, what if we went the other way around?
Welcome to the presentation on units.
Let's get started.
So if I were to ask you, or if I were to say, I have traveled 0.05 kilometers-- some people say KlL-ometers or kil-O-meters. If I have traveled 0.05 kilometers, how many
centimeters have I traveled?
So before we break into the math, it's important to just know what these prefixes centi and kilo mean. And it's good to memorize this, or when you're first starting to do these problems, you can just write them down on a piece of paper, just so you have a reference. So kilo means 1,000, hecto means 100, deca means 10.
No prefix equals 1. deci is equal to 0.1 or 1/10. centi-- I keep changing between cases. centi is equal to 0.01, or 1/100. And then milli is equal to 0.001, and that's the same thing as 1/1,000. And the way I remember, I mean, centi, if you think of a centipede, it has a 100 feet.
If I have 0.05 kilometers, how many centimeters do I have? Whenever I do a problem like this, I like to actually convert my number to meters because that's very easy for me. And actually, I'm going to abbreviate this is km, and we can abbreviate this as cm for centimeters.
Well, if I want to convert this into meters, is it going to be more than 0.05 meters or less than 0.05? Well, a kilometer is a very large distance, so in terms of meters, it's going to be a much bigger number.
So we can multiply this times 1,000 meters, and I'll do it over 1, per kilometer. And what does that get?
Well, 0.05 times 1,000 is equal to 50, right? I just multiplied 0.05 times 1,000. And with the units, I now have kilometers times meters over kilometers.
One gram is actually a very small amount. That's what you measure-- I guess in the metric system, they measure gold in terms of grams. And I want to convert this into milligrams.
Well, a milligram, as we see here, is 100 times smaller, right? To go from 1/10 to 1/1,000, you have to decrease in size by 100. So we could just say 422 decigrams times 100 milligrams per decigram.
times 100, 42,200 milligrams. Now, another way you could have done it is the way we just did that last problem. We could say 422 decigrams, we could convert that to grams.
Well, 1 decigram is equal to-- no, sorry. 1 gram is equal to how many decigrams?
Well, 1 gram is equal to 10 decigrams. And the reason why this makes sense is if we have a decigram in the numerator here, we want a decigram in the denominator here. So if we have decigrams cancel out, 422 decigrams will equal-- that divided by 10 is equal to 42.2 grams.
1 gram is equal to 1,000 milligrams, so we could say times 1,000 milligram per gram. The grams cancel out, and we're left with 42,200 milligrams, right?
42.2 times 1,000. Hopefully, that doesn't confuse you too much. The important thing is to always take a step back and really visualize and think about, should I be getting a
Look at the two thermometers below.
Identify which is Celsius and which is Fahrenheit, and then
label the boiling and freezing points of water on each.
Now, the Celsius scale is what's used in the most of the world.
And the easy way to tell that you're dealing with the Celsius scale is on the Celsius scale, 0 degrees is freezing of water at standard temperature and pressure, and 100 degrees is the boiling point of water at standard temperature and pressure.
Now, on the Fahrenheit scale, which is used mainly in the
United States, the freezing point of water is 32 degrees, and boiling of water is 212 degrees.
As you could tell, Celsius, the whole scale came from using freezing as 0 of regular water at standard temperature and pressure and setting 100 to be boiling. On some level, it makes a little bit more logical sense, but at least here in the U.S., we still use Fahrenheit.
Now let's figure out which of these are Fahrenheit and which are Celsius.
Now remember, regardless of which thermometer you're using, water will always actually boil at the exact same temperature.
So Fahrenheit, 32 degrees, this has to be the same thing as Celsius 0 degrees.
So let's see what happens.
So when this temperature right here is 0, this one over here, it looks like it's negative something.
So this one right here doesn't look like Celsius.
Here, if we say this is Celsius, this looks pretty close to 32 on this one.
Let me do that in a darker color.
So this one right here looks like Celsius, and this one right here looks like Fahrenheit.
And the way I was able to tell is that the 0 degrees Celsius needs to be the same thing as 32 degrees Fahrenheit.
In both cases, this is where water freezes, the freezing point.
That is water freezing.
And let's make sure we're right.
So if this is the Celsius scale, this is where water will boil, 100 degrees Celsius, and that looks like it is right about 212 on the other scale.
So right there is where water is boiling at standard temperature and pressure.
So this thing on the right, right here, I guess I'll circle it in orange, that is Celsius.
And then the one on the left, I'll do it in magenta, the one on the left is Fahrenheit.
In this video I wanna give you the basics of Trigonometry.
It's sounds like a very complicated topic but you're gonna see this is just the study of the ratios of sides of Triangles. The "Trig" part of "Trigonometry" literally means
Triangle and the "metry" part literally means Measure. So let me just give you some examples here.
I think it'll make everything pretty clear. So let me draw some right triangles, let me just draw one right triangle.
So this is a right triangle.
When I say it's a right triangle, it's because one of the angles here is 90 degrees.
This right here is a right angle.
It is equal to 90 degrees.
And we will talk about other ways to show the magnitude of angles in future videos.
So we have a 90 degree angle. It's a right triangle, let me put some
lengths to the sides here. So this side over here is maybe 3.
This height right over there is 3.
Maybe the base of the triangle right over here is 4. and then the hypotenuse of the triangle over here is 5.
You only have a hypotenuse when you have a right triangle.
It is the side opposite the right angle and it is the longest side of a right triangle. So that right there is the hypotenuse.
You've probably learned that already from geometry.
And you can verify that this right triangle - the sides work out - we know from the Pythagorean theorem, that 3 squared plus 4 squared, has got to be equal to the length of the longest side, the length of the hypotenuse squared is equal to 5 squared so you can verify that this works out that this satisfies the Pythagorean theorem. Now with that out of the way let's learn a little bit of Trigonometry.
The core functions of trigonometry, we're going to learn a little more about what these functions mean.
There is the sine, the sine function.
There is the cosine function, and there is the tangent function.
And you write sin, or S-I-N, C-O-S, and "tan" for short.
And these really just specify, for any angle in this triangle, it will specify the ratios of certain sides. So let me just write something out.
This is really something of a mnemonic here, so something just to help you remember the definitions of these functions, but I'm going to write down something called "soh cah toa", you'll be amazed how far this mnemonic will take you in trigonometry.
"soh" tells us that "sine" is equal to opposite over hypotenuse.
It's telling us.
And this won't make a lot of sense just now,
I'll do it in a little more detail in a second.
And then cosine is equal to adjacent over hypotenuse.
And then you finally have tangent, tangent is equal to opposite over adjacent.
So you're probably saying, "hey, Sal, what is all this "opposite"
"hypotenuse", "adjacent", what are we talking about?" Well, let's take an angle here.
Let's say that this angle right over here is theta, between the side of the length 4, and the side of length 5. This is theta.
So lets figure out the sine of theta, the cosine of theta, and what the tangent of theta are.
So if we first want to focus on the sine of theta, we just have to remember "soh cah toa", sine is opposit over hypotonuse, so sine of theta is equal to the opposite - so what is the opposite side to the angle?
So this is our angle right here, the opposite side, if we just go to the opposite side, not one of the sides that are kind of adjacent to the angle, the opposite side is the 3, if you're just kinda - it's opening on to that 3, so the opposite side is 3.
And then what is the hypotenuse? Well, we already know - the hypotenuse here is 5.
So it's 3 over 5.
The sine of theta is 3/5.
And I'm going to show you in a second, that the sine of theta - if this angle is a certain angle - it's always going to be 3/5.
The ratio of the opposite to the hypotenuse is always going to be the same, even if the actual triangle were a larger triangle or a smaller one. So I'll show you that in a second.
So let's go throught all of the trig functions.
Let's think about what the cosine of theta is.
Cosine is adjacent over hypotenuse, so remember - let me label them.
We already figured out that the 3 was the opposite side.
This is the opposite side.
And only when we're talking about this angle. When we're talking about this angle - this side is opposite to it.
When we're talking about this angle, this 4 side is adjacent to it, it's one of the sides that kind of make up - that kind of form the vertex here.
So this right here is the adjacent side.
And I want to be very clear, this only applies to this angle.
If we're talking about that angle, then this green side would be opposite, and this yellow side would be adjacent.
But we're just focusing on this angle right over here.
So cosine of this angle - so the adjacent side of this angle is 4, so the adjacent over the hypotenuse, the adjacent, which is 4, over the hypotenuse, 4 over 5.
Now let's do the tangent.
Let's do the tangent.
The tangent of theta: opposite over adjacent.
The opposite side is 3.
What is the adjacent side?
We've already figured that out, the adjacent side is 4.
So knwoing the sides of this right triangle, we were able to figure out the major trig ratios.
And we'll see that there are other trig ratios, but they can all be derived from these three basic trig functions.
Now, let's think about another angle in this triangle, and I'll re-draw it, because my triangle is getting a little bit messy.
So I'll re-draw the exact same triangle.
The exact same triangle.
And, once again, the lengths of this triangle are - we have length 4 there, we have length 3 there, we have length 5 there.
In the last example we used this theta.
But let's do another angle, let's do another angle up here, and let's call this angle - I don't know, I'll think of something, a random Greek letter. So let's say it's psi. It's, I know, a little bit bizarre.
Theta is what you normally use, but since I've already used theta, let's use psi.
Or actually - let me simplify it, let me call this angle x.
Let's call that angle x.
So let's figure out the trig functions for that angle x. So we have sine of x, is going to be equal to what?
Well sine is opposite over hypotenuse.
So what side is opposite to x?
4 was adjacent to this theta, but it's opposite to x.
So in this context, this is now the opposite, this is now the opposite side.
Remember: So it's going to be 4 over - now what's the hypotenuse?
Well, the hypotenuse is going to be the same regardless of which angle you pick, so the hypotenuse is now going to be 5, so it's 4/5.
Now let's do another one; what is the cosine of x?
So cosine is adjacent over hypotenuse.
What side is adjacent to x, that's not the hypotenuse?
You have the hypotenuse here. Well the 3 side, it's one of the sides that forms the vertex that x is at, that's not the hypotenuse, so this is the adjacent side.
That is the adjacent.
So it's 3 over the hypotenuse, the hypotenuse is 5.
And then finally, the tangent.
We want to figure out the tangent of x.
Tangent is opposite over adjacent,
"soh cah toa", tangent is opposite over adjacent, opposite over adjacent. The opposite side is 4.
The opposite side is 4, and the adjacent side is 3.
And we're done!
And in the next video I'll do a ton of more examples of this, just so that we really get a feel for it.
But I'll leave you thinking of what happens when these angle start to approach 90 degrees, or how could they even get larger than 90 degrees.
And we'll see that this definition, the "soh cah toa" definition takes us a long way for angles that are between 0 and 90 degrees, or that are less than 90 degrees.
But they kind of start to mess up really at the boundries.
And we're going to introduce a new definition, that's kind of derived from the "soh cah toa" definition for finding the sine, cosine and tangent of really any angle.
What we're going to prove in this video is a couple of fairly straight forward parallelogram related proofs And this first one we're gonna say, "Hey, if we have this parallelogram ABCD,
So, if we look, view DB, this diagonal DB, we can view it as a transversal for the parallel lines AB and DC And if you view it that way, you can pick out that angle ABD is going to be congruent So, angle ABD, that's that angle right there is going to be congruent to angle BDC because they are alternate interior angles
Now you can also view this diagonal DB, you can view this as a transversal of these two parallel lines, of the other two pair of parallel lines, AD and BC And if you look at it that way you'll immediately see that angle
DBC, right over here, angle DBC is going to be congruent to angle
ADB for the exact same reason, they are alternate interior angles of a transversal intersecting these two parallel lines So, I could write this This is alternate interior angles are congruent when you have a transversal intersecting two parallel lines
non-labeled to pink to green -- CBD and this comes out of angle-side-angle congruency So, this is from angle-side-angle congruency Well, what does that do for us
In particular, side DC corresponds to side BA -- side DC on this bottom triangle corresponds to side BA on the top triangle So, they need to be congruent So, DC
So, we get DC is going to be equal to BA and that's because they are corresponding sides of congruent triangles So, this is going to be equal to that and by that exact same logic,
AD corresponds to CB
AD is equal to CB and for the exact same reason: corresponding sides of congruent triangles And then we're done! We've proven that opposite sides are congruent
Alright So, we obviously know that CB is going to be equal to itself So, I'll draw it like that
We've split this quadrilateral to two triangles: triangle ACB and triangle DBC
And notice, they have all three sides of these two triangles are equal to each other So, we know that by side-side-side that they are congruent So, we know that triangle, I'm gonna start at A and I'm going to the one half side, so, ACB is congruent to triangle DBC and this is by side-side-side congruency
you can see ABC -- is going to be congruent to DCB, angle DCB and you can say by you can say corresponding angles congruent of congruent triangles
So, ABC is going to be congruent to DCB So, these two angles are going to be congruent Well, this is interesting because here you have a long line and it's intersecting AB and CD and we clearly see that these things that could be alternate angles, alternate interior angles, are congruent
angle ACB is congruent to angle DBC
and we know that by corresponding angles congruent of congruent triangles So, we're just saying that this angle is equal to that angle Well, once again these could be alternate interior angles, they look like they could be, this is a transversal and here's two lines here which we're not sure they're parallel but because the alternate interior angles are congruent we know that they are parallel
And we're done! So, what we've done is interesting We've shown if you have a parallelogram, opposite sides are, opposite sides have the same length
We're told to graph all possible values for h on the number line. And this is a especially interesting inequality because we also have an absolute value here. So the way we're going to do it, we're going to solve this inequality in terms of the absolute value of h, and from there we can solve it for h.
So now we have that the absolute value of h is less than 7 and 1/2. So what does this tell us? This means that the distance, another way to interpret this-- remember, absolute value is the same thing as distance from 0-- so another way to interpret this statement is that the distance from h to 0 has to be less than 7 and 1/2.
But if it gets too far negative, if it goes to negative 3, we're cool, negative 4, negative 5, negative 6, negative 7, we're still cool, but then at negative 8, all of a sudden the absolute value isn't going to be less than this.
So it also has to be greater than negative 7 and 1/2. If you give me any number in this interval, its absolute value is going to be less than 7 and 1/2 because all of these numbers are less than 7 and 1/2 away from 0. Let me draw it on the number line, which they want us to do anyway.
So if this is the number line right there, that is 0, and we draw some points, let's say that this is 7, that is 8, that is negative 7, that is negative 8. What numbers are less than 7 and 1/2 away from 0? Well, you have everything all the way up to-- 7 and 1/2 is exactly 7 and 1/2 away, so you can't count that, so 7 and 1/2, you'll put a circle around it.
Identify all sets of parallel and perpendicular lines in the image below. So let's start with the parallel lines and, just as a reminder, two lines are parallel if they're in the same plane, and all of these lines are clearly in the same plane.
But they are two lines that never intersect. And one way to verify: because it sometimes looks like two lines will intersect, but you can't just always assume just based on how it looks. You really have to some information given to you in the diagram or the problem that tells you that they are definitely parallel, that they're definitely never going to intersect.
UV (make sure I specify these as lines) is perpendicular to CD.
And so UV, ST they're perpendicular to CD. And then after that, the only other information where they definitely tell us that two lines are intersecting at right angles are Line AB and WX. So Line AB is definitely perpendicular to Line WX.
So, if somehow they told us that this was a right angle, even though it doesn't look anything like a right angle, then we would have to suspend our judgement based on how it actually looks and say, huh I guess maybe those things are perpendicular. And maybe these two things are parallel. They didn't actually tell us that, and that would actually be bizarre because these lines are so not parallel.
Based on the information they gave us, these are the parallel and perpendicular lines.
18 minutes is an absolutely brutal time limit, so I'm going to dive straight in, right at the point where I get this thing to work.
Here we go.
I'm going to talk about five different things.
I'm going to talk about why defeating aging is desirable.
I'm going to talk about why we have to get our shit together, and actually talk about this a bit more than we do.
I'm going to talk about feasibility as well, of course.
I'm going to talk about why we are so fatalistic about doing anything about aging.
And then I'm going spend perhaps the second half of the talk talking about, you know, how we might actually be able to prove that fatalism is wrong, namely, by actually doing something about it.
I'm going to do that in two steps.
The first one I'm going to talk about is how to get from a relatively modest amount of life extension -- which I'm going to define as 30 years, applied to people who are already in middle-age when you start -- to a point which can genuinely be called defeating aging.
Namely, essentially an elimination of the relationship between how old you are and how likely you are to die in the next year -- or indeed, to get sick in the first place.
And of course, the last thing I'm going to talk about is how to reach that intermediate step, that point of maybe 30 years life extension.
So I'm going to start with why we should.
Now, I want to ask a question.
Hands up: anyone in the audience who is in favor of malaria?
That was easy.
OK.
OK. Hands up: anyone in the audience who's not sure whether malaria is a good thing or a bad thing?
OK.
So we all think malaria is a bad thing.
That's very good news, because I thought that was what the answer would be.
Now the thing is, I would like to put it to you that the main reason why we think that malaria is a bad thing is because of a characteristic of malaria that it shares with aging.
And here is that characteristic.
The only real difference is that aging kills considerably more people than malaria does.
Now, I like in an audience, in Britain especially, to talk about the comparison with foxhunting, which is something that was banned after a long struggle, by the government not very many months ago.
I mean, I know I'm with a sympathetic audience here, but, as we know, a lot of people are not entirely persuaded by this logic.
And this is actually a rather good comparison, it seems to me.
You know, a lot of people said, "Well, you know, city boys have no business telling us rural types what to do with our time.
It's a traditional part of the way of life, and we should be allowed to carry on doing it.
It's ecologically sound; it stops the population explosion of foxes."
But ultimately, the government prevailed in the end, because the majority of the British public, and certainly the majority of members of Parliament, came to the conclusion that it was really something that should not be tolerated in a civilized society.
And I think that human aging shares all of these characteristics in spades.
What part of this do people not understand?
It's not just about life, of course -- (Laughter) -- it's about healthy life, you know -- getting frail and miserable and dependent is no fun, whether or not dying may be fun.
So really, this is how I would like to describe it.
It's a global trance.
These are the sorts of unbelievable excuses that people give for aging.
And, I mean, OK, I'm not actually saying that these excuses are completely valueless.
There are some good points to be made here, things that we ought to be thinking about, forward planning so that nothing goes too -- well, so that we minimize the turbulence when we actually figure out how to fix aging.
But these are completely crazy, when you actually remember your sense of proportion.
You know, these are arguments; these are things that would be legitimate to be concerned about.
But the question is, are they so dangerous -- these risks of doing something about aging -- that they outweigh the downside of doing the opposite, namely, leaving aging as it is?
Are these so bad that they outweigh condemning 100,000 people a day to an unnecessarily early death?
You know, if you haven't got an argument that's that strong, then just don't waste my time, is what I say.
(Laughter)
Now, there is one argument that some people do think really is that strong, and here it is.
People worry about overpopulation; they say,
"Well, if we fix aging, no one's going to die to speak of, or at least the death toll is going to be much lower, only from crossing St. Giles carelessly.
And therefore, we're not going to be able to have many kids, and kids are really important to most people."
And that's true.
And you know, a lot of people try to fudge this question, and give answers like this.
I don't agree with those answers.
I think they basically don't work.
I think it's true, that we will face a dilemma in this respect.
We will have to decide whether to have a low birth rate, or a high death rate.
A high death rate will, of course, arise from simply rejecting these therapies, in favor of carrying on having a lot of kids.
And, I say that that's fine -- the future of humanity is entitled to make that choice.
What's not fine is for us to make that choice on behalf of the future.
If we vacillate, hesitate, and do not actually develop these therapies, then we are condemning a whole cohort of people -- who would have been young enough and healthy enough to benefit from those therapies, but will not be, because we haven't developed them as quickly as we could -- we'll be denying those people an indefinite life span, and I consider that that is immoral.
That's my answer to the overpopulation question.
Right.
So the next thing is, now why should we get a little bit more active on this?
And the fundamental answer is that the pro-aging trance is not as dumb as it looks.
It's actually a sensible way of coping with the inevitability of aging.
Aging is ghastly, but it's inevitable, so, you know, we've got to find some way to put it out of our minds, and it's rational to do anything that we might want to do, to do that.
Like, for example, making up these ridiculous reasons why aging is actually a good thing after all.
But of course, that only works when we have both of these components.
And as soon as the inevitability bit becomes a little bit unclear -- and we might be in range of doing something about aging -- this becomes part of the problem.
This pro-aging trance is what stops us from agitating about these things.
And that's why we have to really talk about this a lot -- evangelize, I will go so far as to say, quite a lot -- in order to get people's attention, and make people realize that they are in a trance in this regard.
So that's all I'm going to say about that.
I'm now going to talk about feasibility.
And the fundamental reason, I think, why we feel that aging is inevitable is summed up in a definition of aging that I'm giving here.
A very simple definition.
Aging is a side effect of being alive in the first place, which is to say, metabolism.
This is not a completely tautological statement; it's a reasonable statement.
Aging is basically a process that happens to inanimate objects like cars, and it also happens to us, despite the fact that we have a lot of clever self-repair mechanisms, because those self-repair mechanisms are not perfect.
So basically, metabolism, which is defined as basically everything that keeps us alive from one day to the next, has side effects.
Those side effects accumulate and eventually cause pathology.
That's a fine definition.
So we can put it this way: we can say that, you know, we have this chain of events.
And there are really two games in town, according to most people, with regard to postponing aging.
They're what I'm calling here the "gerontology approach" and the "geriatrics approach."
The geriatrician will intervene late in the day, when pathology is becoming evident, and the geriatrician will try and hold back the sands of time, and stop the accumulation of side effects from causing the pathology quite so soon.
Of course, it's a very short-term-ist strategy; it's a losing battle, because the things that are causing the pathology are becoming more abundant as time goes on.
The gerontology approach looks much more promising on the surface, because, you know, prevention is better than cure.
But unfortunately the thing is that we don't understand metabolism very well.
In fact, we have a pitifully poor understanding of how organisms work -- even cells we're not really too good on yet.
We've discovered things like, for example, RNA interference only a few years ago, and this is a really fundamental component of how cells work.
Basically, gerontology is a fine approach in the end, but it is not an approach whose time has come when we're talking about intervention.
So then, what do we do about that?
I mean, that's a fine logic, that sounds pretty convincing, pretty ironclad, doesn't it?
But it isn't.
Before I tell you why it isn't, I'm going to go a little bit into what I'm calling step two.
Just suppose, as I said, that we do acquire -- let's say we do it today for the sake of argument -- the ability to confer 30 extra years of healthy life on people who are already in middle age, let's say 55.
I'm going to call that "robust human rejuvenation." OK.
What would that actually mean for how long people of various ages today -- or equivalently, of various ages at the time that these therapies arrive -- would actually live?
In order to answer that question -- you might think it's simple, but it's not simple.
We can't just say, "Well, if they're young enough to benefit from these therapies, then they'll live 30 years longer."
That's the wrong answer.
And the reason it's the wrong answer is because of progress.
There are two sorts of technological progress really, for this purpose.
There are fundamental, major breakthroughs, and there are incremental refinements of those breakthroughs.
Now, they differ a great deal in terms of the predictability of time frames.
Fundamental breakthroughs: very hard to predict how long it's going to take to make a fundamental breakthrough.
It was a very long time ago that we decided that flying would be fun, and it took us until 1903 to actually work out how to do it.
But after that, things were pretty steady and pretty uniform.
I think this is a reasonable sequence of events that happened in the progression of the technology of powered flight.
We can think, really, that each one is sort of beyond the imagination of the inventor of the previous one, if you like.
The incremental advances have added up to something which is not incremental anymore.
This is the sort of thing you see after a fundamental breakthrough.
And you see it in all sorts of technologies.
Computers: you can look at a more or less parallel time line, happening of course a bit later.
You can look at medical care.
I mean, hygiene, vaccines, antibiotics -- you know, the same sort of time frame.
So I think that actually step two, that I called a step a moment ago, isn't a step at all.
That in fact, the people who are young enough to benefit from these first therapies that give this moderate amount of life extension, even though those people are already middle-aged when the therapies arrive, will be at some sort of cusp.
They will mostly survive long enough to receive improved treatments that will give them a further 30 or maybe 50 years.
In other words, they will be staying ahead of the game.
The therapies will be improving faster than the remaining imperfections in the therapies are catching up with us.
This is a very important point for me to get across.
Because, you know, most people, when they hear that I predict that a lot of people alive today are going to live to 1,000 or more, they think that I'm saying that we're going to invent therapies in the next few decades that are so thoroughly eliminating aging that those therapies will let us live to 1,000 or more.
I'm not saying that at all.
I'm saying that the rate of improvement of those therapies will be enough.
They'll never be perfect, but we'll be able to fix the things that 200-year-olds die of, before we have any 200-year-olds.
And the same for 300 and 400 and so on.
I decided to give this a little name, which is "longevity escape velocity."
(Laughter)
Well, it seems to get the point across.
So, these trajectories here are basically how we would expect people to live, in terms of remaining life expectancy, as measured by their health, for given ages that they were at the time that these therapies arrive.
If you're already 100, or even if you're 80 -- and an average 80-year-old, we probably can't do a lot for you with these therapies, because you're too close to death's door for the really initial, experimental therapies to be good enough for you.
You won't be able to withstand them.
But if you're only 50, then there's a chance that you might be able to pull out of the dive and, you know -- (Laughter) -- eventually get through this and start becoming biologically younger in a meaningful sense, in terms of your youthfulness, both physical and mental, and in terms of your risk of death from age-related causes.
And of course, if you're a bit younger than that, then you're never really even going to get near to being fragile enough to die of age-related causes.
So this is a genuine conclusion that I come to, that the first 150-year-old -- we don't know how old that person is today, because we don't know how long it's going to take to get these first-generation therapies.
But irrespective of that age, I'm claiming that the first person to live to 1,000 -- subject of course, to, you know, global catastrophes -- is actually, probably, only about 10 years younger than the first 150-year-old.
And that's quite a thought.
Alright, so finally I'm going to spend the rest of the talk, my last seven-and-a-half minutes, on step one; namely, how do we actually get to this moderate amount of life extension that will allow us to get to escape velocity?
And in order to do that, I need to talk about mice a little bit.
I have a corresponding milestone to robust human rejuvenation.
I'm calling it "robust mouse rejuvenation," not very imaginatively.
And this is what it is.
I say we're going to take a long-lived strain of mouse, which basically means mice that live about three years on average.
We do exactly nothing to them until they're already two years old.
And then we do a whole bunch of stuff to them, and with those therapies, we get them to live, on average, to their fifth birthday.
So, in other words, we add two years -- we treble their remaining lifespan, starting from the point that we started the therapies.
The question then is, what would that actually mean for the time frame until we get to the milestone I talked about earlier for humans?
Which we can now, as I've explained, equivalently call either robust human rejuvenation or longevity escape velocity.
Secondly, what does it mean for the public's perception of how long it's going to take for us to get to those things, starting from the time we get the mice?
And thirdly, the question is, what will it do to actually how much people want it?
And it seems to me that the first question is entirely a biology question, and it's extremely hard to answer.
One has to be very speculative, and many of my colleagues would say that we should not do this speculation, that we should simply keep our counsel until we know more.
I say that's nonsense.
I say we absolutely are irresponsible if we stay silent on this.
We need to give our best guess as to the time frame, in order to give people a sense of proportion so that they can assess their priorities.
So, I say that we have a 50/50 chance of reaching this RHR milestone, robust human rejuvenation, within 15 years from the point that we get to robust mouse rejuvenation.
15 years from the robust mouse.
The public's perception will probably be somewhat better than that.
The public tends to underestimate how difficult scientific things are.
So they'll probably think it's five years away.
They'll be wrong, but that actually won't matter too much.
And finally, of course, I think it's fair to say that a large part of the reason why the public is so ambivalent about aging now is the global trance I spoke about earlier, the coping strategy.
That will be history at this point, because it will no longer be possible to believe that aging is inevitable in humans, since it's been postponed so very effectively in mice.
So we're likely to end up with a very strong change in people's attitudes, and of course that has enormous implications.
So in order to tell you now how we're going to get these mice, I'm going to add a little bit to my description of aging.
I'm going to use this word "damage" to denote these intermediate things that are caused by metabolism and that eventually cause pathology.
Because the critical thing about this is that even though the damage only eventually causes pathology, the damage itself is caused ongoing-ly throughout life, starting before we're born.
But it is not part of metabolism itself.
And this turns out to be useful.
Because we can re-draw our original diagram this way.
We can say that, fundamentally, the difference between gerontology and geriatrics is that gerontology tries to inhibit the rate at which metabolism lays down this damage.
And I'm going to explain exactly what damage is in concrete biological terms in a moment.
And geriatricians try to hold back the sands of time by stopping the damage converting into pathology.
And the reason it's a losing battle is because the damage is continuing to accumulate.
So there's a third approach, if we look at it this way.
We can call it the "engineering approach," and I claim that the engineering approach is within range.
The engineering approach does not intervene in any processes.
It does not intervene in this process or this one.
And that's good because it means that it's not a losing battle, and it's something that we are within range of being able to do, because it doesn't involve improving on evolution.
The engineering approach simply says,
"Let's go and periodically repair all of these various types of damage -- not necessarily repair them completely, but repair them quite a lot, so that we keep the level of damage down below the threshold that must exist, that causes it to be pathogenic."
We know that this threshold exists, because we don't get age-related diseases until we're in middle age, even though the damage has been accumulating since before we were born.
Why do I say that we're in range?
Well, this is basically it.
The point about this slide is actually the bottom.
If we try to say which bits of metabolism are important for aging, we will be here all night, because basically all of metabolism is important for aging in one way or another.
This list is just for illustration; it is incomplete.
The list on the right is also incomplete.
It's a list of types of pathology that are age-related, and it's just an incomplete list.
But I would like to claim to you that this list in the middle is actually complete -- this is the list of types of thing that qualify as damage, side effects of metabolism that cause pathology in the end, or that might cause pathology.
And there are only seven of them.
They're categories of things, of course, but there's only seven of them.
Cell loss, mutations in chromosomes, mutations in the mitochondria and so on.
First of all, I'd like to give you an argument for why that list is complete.
Of course one can make a biological argument.
One can say, "OK, what are we made of?"
We're made of cells and stuff between cells.
What can damage accumulate in?
The answer is: long-lived molecules, because if a short-lived molecule undergoes damage, but then the molecule is destroyed -- like by a protein being destroyed by proteolysis -- then the damage is gone, too.
It's got to be long-lived molecules.
So, these seven things were all under discussion in gerontology a long time ago and that is pretty good news, because it means that, you know, we've come a long way in biology in these 20 years, so the fact that we haven't extended this list is a pretty good indication that there's no extension to be done.
However, it's better than that; we actually know how to fix them all, in mice, in principle -- and what I mean by in principle is, we probably can actually implement these fixes within a decade.
Some of them are partially implemented already, the ones at the top.
I haven't got time to go through them at all, but my conclusion is that, if we can actually get suitable funding for this, then we can probably develop robust mouse rejuvenation in only 10 years, but we do need to get serious about it.
We do need to really start trying.
So of course, there are some biologists in the audience, and I want to give some answers to some of the questions that you may have.
You may have been dissatisfied with this talk, but fundamentally you have to go and read this stuff.
I've published a great deal on this;
I cite the experimental work on which my optimism is based, and there's quite a lot of detail there.
The detail is what makes me confident of my rather aggressive time frames that I'm predicting here.
So if you think that I'm wrong, you'd better damn well go and find out why you think I'm wrong.
And of course the main thing is that you shouldn't trust people who call themselves gerontologists because, as with any radical departure from previous thinking within a particular field, you know, you expect people in the mainstream to be a bit resistant and not really to take it seriously.
So, you know, you've got to actually do your homework, in order to understand whether this is true.
And we'll just end with a few things.
One thing is, you know, you'll be hearing from a guy in the next session who said some time ago that he could sequence the human genome in half no time, and everyone said, "Well, it's obviously impossible."
And you know what happened.
So, you know, this does happen.
We have various strategies -- there's the Methuselah Mouse Prize, which is basically an incentive to innovate, and to do what you think is going to work, and you get money for it if you win.
There's a proposal to actually put together an institute.
This is what's going to take a bit of money.
But, I mean, look -- how long does it take to spend that on the war in Iraq?
Not very long.
OK.
(Laughter)
It's got to be philanthropic, because profits distract biotech, but it's basically got a 90 percent chance, I think, of succeeding in this.
And I think we know how to do it.
And I'll stop there.
Thank you.
(Applause)
Chris Anderson:
OK.
I don't know if there's going to be any questions but I thought I would give people the chance.
Since you've been talking about aging and trying to defeat it, why is it that you make yourself appear like an old man?
(Laughter)
AG:
Because I am an old man.
I am actually 158.
(Laughter) (Applause)
Audience:
Species on this planet have evolved with immune systems to fight off all the diseases so that individuals live long enough to procreate.
However, as far as I know, all the species have evolved to actually die, so when cells divide, the telomerase get shorter, and eventually species die.
So, why does -- evolution has -- seems to have selected against immortality, when it is so advantageous, or is evolution just incomplete?
AG:
Brilliant.
Thank you for asking a question that I can answer with an uncontroversial answer.
I'm going to tell you the genuine mainstream answer to your question, which I happen to agree with, which is that, no, aging is not a product of selection, evolution; [aging] is simply a product of evolutionary neglect.
In other words, we have aging because it's hard work not to have aging; you need more genetic pathways, more sophistication in your genes in order to age more slowly, and that carries on being true the longer you push it out.
So, to the extent that evolution doesn't matter, doesn't care whether genes are passed on by individuals, living a long time or by procreation, there's a certain amount of modulation of that, which is why different species have different lifespans, but that's why there are no immortal species.
CA:
The genes don't care but we do?
AG:
That's right.
Audience:
Hello. I read somewhere that in the last 20 years, the average lifespan of basically anyone on the planet has grown by 10 years.
If I project that, that would make me think that I would live until 120 if I don't crash on my motorbike.
That means that I'm one of your subjects to become a 1,000-year-old?
AG:
If you lose a bit of weight.
(Laughter)
Your numbers are a bit out.
The standard numbers are that lifespans have been growing at between one and two years per decade.
So, it's not quite as good as you might think, you might hope.
But I intend to move it up to one year per year as soon as possible.
Audience: I was told that many of the brain cells we have as adults are actually in the human embryo, and that the brain cells last 80 years or so.
If that is indeed true, biologically are there implications in the world of rejuvenation?
If there are cells in my body that live all 80 years, as opposed to a typical, you know, couple of months?
AG:
There are technical implications certainly.
Basically what we need to do is replace cells in those few areas of the brain that lose cells at a respectable rate, especially neurons, but we don't want to replace them any faster than that -- or not much faster anyway, because replacing them too fast would degrade cognitive function.
What I said about there being no non-aging species earlier on was a little bit of an oversimplification.
There are species that have no aging -- Hydra for example -- but they do it by not having a nervous system -- and not having any tissues in fact that rely for their function on very long-lived cells.
What I want to do in this video is think a little bit about how the unemployment rate is actually computed by the bureau of labor statistics.
So to figure that out, let's just start off with the entire US population.
So let me draw a big circle here that represents the entire US population.
US population, and right now, if my numbers are correct the latest numbers are 304,000,000 people.
Now, not all of those 304 million people are capable of working including my 2 1/2 year old son, or my new born daughter, so, you have to think, when you think of unemployment you want to think about the percentage of these people that are actually old enough to work, that actually can be employed theoretically.
So let's take a subset of that US population and let's think about who's essentially an adult who's working age?
So this subset right over here is 16 years and older.
So people who can legally work and the numbers I have here, this is 100 sorry, this right here is 237,000,000 people
Now, we can't just say all of these people could possibly work because a lot of them are in college some of them are in high school, some of them might not have the ability to work, some of them might be retired, so what we want to do is take a subset of this population that is essentially you could say, part of the labor force, in that they are working or they are actively looking for work.
Let me draw that right over here.
So this right over here is the labor force.
So these are not retirees, or people who are in college those people would be sitting right over there assuming they are 16 years or older.
The labor force, this is working and actively looking for work and we'll think about what actively looking for work means in a little bit more depth in a few minutes.
Actively looking for work.
And that number, if my numbers are correct, is right around 154,000,000. Although the numbers here are not so important, the more important thing is the idea of how the unemployment rate itself is calculated.
And then so within the labor force, you have a subset
So this is working and actively looking for work.
So you have a subset of the labor force that is actively looking for work.
So they don't have a job, but they're actively looking.
So this right here is unemployed and actively looking, this actively looking is probably more important than you might realize at first.
And this number, let's just say for the sake of argument this is sitting around 15,000,000 people.
So if you have a job, you're right over here, if you don't have a job, but are actively looking you're going to be right over here.
What we're going to see in a little bit is if you have, if you don't have a job, but you are not actively looking, you could be working you would actually be sitting out here.
This is going to be interesting when we think of trends and the unemployment rate, when it goes up or down.
But just to see how the unemployment is calculated let's use, let's do it for this example.
So the unemployment rate is literally just the number of unemployed, over the entire labor force.
So in this situation, it would be 15,000,000, so that's just the number of unemployed and actively looking, over the entire labor force
Over 154,000,000. So if we get my handy TI 85 out that gives us in this example right over here and unemployment rate of 15 divided by 154 million.
So it's about 9.7, if we write it as a decimal, it would be 0.097 if we write it as a percentage, this would be 9.7% so this is approximately 9.7%.
Now I told you that the details are going to be important
And the reason why they are is interesting things happen when people stop looking for work, or when they start looking for work.
So I said "unemployed and actively looking" puts you in this bucket over here.
If you're unemployed, if you don't have a job and you're not actively looking you're actually not in the labor force.
And so you might be saying, "Sal, what does it mean to be actively looking for work?"
And this means that you've looked for a job or you're actively searching in the past
We'll do this in a new color in the past 4 weeks
And you might say "Sal, how do they know whether these 15 million people, have actively searched for jobs in the past 4 weeks?"
And the answer is they do a survey.
They're not going to survey every human being in the labor force or the US population, or all 15 million that are unemployed, that would be logistically impossible what they do is they do a survey and right now they do about 60,000 every month and they essentially ask them, are you employed? are you unemployed? if you are unemployed, have you looked for a job in the past 4 weeks?
If you have looked for a job in the past 4 weeks as an unemployed person, you'd get thrown into this bucket right here, you're actively looking, you're still part of the labor force but if you've got so discouraged that you're no longer
looking for work, maybe you've given up then you get thrown out of here, you get thrown out of the labor force. And that is what most people don't realize, when things get bad enough and people get really discouraged, you have people not going, you have people actually exiting the entire labor force and see how that affects the numbers imagine a situation, so this is the unemployment rate right now, there's 15,000,000 who are unemployed and actively looking for work.
Let's say that this is just a horrible recession or depression and 5,000,000 of these people get so discouraged, they don't, in the last 4 weeks they do not look for work anymore.
So they've maybe stopped altogether or they want to take a break so what we're gonna do, is we're going to take 5,000,000 people out of this bucket over here, so we're going to take 5,000,000 people and move them out over here.
Outside of the labor force.
If you did that what happens?
Well now, the number, the official unemployed number is now going to be 10,000,000 and what's the labor force number?
Remember, they went completely out of this green circle over here
So they also left the labor force, so the labor force number is now 149,000,000
So in this bad situation, where people have left the labor force the unemployment rate would now be 10 million people unemployed and actively looking for work over a labor force of 149,000,000.
The labor force has shrunk because they're so discouraged so what do we get there as our unemployment rate?
We have 10 divided by 149 it gives us 6.7%
So this is fascinating, if things get bad enough and people actually exit the labor force then the unemployment rate could actually go down because the labor force is shrinking.
The other thing could also happen, maybe things get really good and you have 10,000,000 people who are sitting out here they're either marginally attached to workers, which are people who are hoping to get a job, but haven't looked for a job in the past 4 weeks or they could be discouraged workers who would mind working, but they've given up altogether looking but you can imagine when the economy gets good
let's say we're starting from this baseline here, the economy gets good, and all these people who are unemployed, but not part of the labor force, all of a sudden start looking for work.
So then they'd be part of the official unemployed
So 10,000,000 would grow to 20,000,000
So now this number is 20 million, and this green area would go up by 10 million, so now this would be 159 million, so in this situation, the official unemployed would be 20 million, and the entire labor force would be 159 million, and now you get a situation so you have 20 divided by 159 million, which is 12.6%
Approximately 12.6%
So the whole point of this video, I'm not saying that the unemployment rate is the way it's calculated is wrong, or that it's supposed to be misleading, I just want to give you a little bit of nuance that it doesn't always give the complete picture in particular, that one number, just this and there's other unemployment rates that give a little bit more nuance here, but this one headline unemployment rate that's typically given on the news doesn't capture the whole story, in particular it doesn't capture the people who might be exiting the labor force when things are bad, so in that situation the unemployment rate would probably be understating how bad things are.
And it also doesn't capture the people who are entering the labor force in that situation the unemployment rate would probably make things look worse than they are when things might actually be improving.
We are asked how many inches are in four and a half yards. We can do it in a couple of ways. One we could do is to see how many inches are in four yards and how many inches are there in half a yard. and this is really four plus one half yards.
Find the slope of the line pictured on the graph.
So the slope of a line is defined to be rise over run.
Or you can also view it as change in y over change in x.
And let me show you what that means.
So let's start as some arbitrary point on this line.
And they kind of highlight some of these points.
So let's start at one of these points right over here.
So if we wanted to start at one of these points.
Let's say we want to change our x in the positive direction.
So we want to go to the right.
So let's say we want to go from this point to this point over here.
How much do we have to move in x?
So if we want to move in x, we have to go from this point to this point.
We are going from -3 to 0.
So we are going from -3 to 0.
So our change in x, and this triangle, that's delta.
That means change in.
Our change in x is equal to 3.
So our change in x over here is equal to 3.
So what was our change in y when our change in x is equal to 3?
Well when we moved from this point to this point, our x value changed by 3.
But what happened to our y value?
Well, our y value went down. It went from positive 3 to positive 2. Our y value went down by 1.
So our change in y is equal to -1.
So we rose -1.
We actually went down.
So our rise is -1 when our run, our change in x, is 3.
The change in y over the change in x is -1 over 3.
Or we could say that our slope is -1/3.
It is -1/3.
And I want to show you that we can do this with any two points on the line.
We can even go further than 3 in the x direction.
Let's go the other way.
Let's start at this point right over here.
And then move backwards to this point over here just to show you we will still get the same result.
So to go from this point to that point, what is our change in x?
So our change in x is this right over here.
Our change in x is that distance right over there.
We started at 3 and we went to -3.
We went back 6.
Over here, our change in x is equal to -6.
We starting at this point now.
So over here our change in x is -6.
And then when our change in x is -6, when we start at this point and we move 6 back
What is our change of y to get to that point?
Well, our y-value went from 1, that was our y-value at this point,
And then we go back to this point our y-value is 3.
So now our y-value is 3.
So what did we do?
We moved up by 2.
Our change in y is equal to 2.
So over here, our change in y is equal to 2.
Slope is change in y over change in x.
Or, rise over run.
Change in y is just rise.
Change in x is just run, how much you're moving in the horizontal direction.
So rise over run in this example here is going to be 2 over -6, which is the same thing as -1/3.
And you could verify it for yourself.
Take any of these two points.
Start at one of these two points and figure out what is the run to get to the next point.
And then what is the rise to get to the next point.
And for any line, the slope won't change.
Let me do it again.
Over here, we had to move in the +3 direction.
So that is our run.
So this right here is +3.
That's our run.
But what's our rise?
Well, we actually went down.
So we have a negative rise.
Our rise is -1.
So we have -1 as our rise.
We went down.
Our run was +3. So our slope here is -1/3.
The answer is that soup occurs in most of these phrases but not 100% of them.
It's missing in this phrase.
Equivalently, on the Chinese side we see this character occurs in most of the phrases, but it's missing here.
So we see that the correspondence doesn't have to be 100% to tell us that there is still a good chance of a correlation.
When we're learning to do machine translation we use these kinds of alignments to learn probability tables of what is the probability of one phrase in one language corresponding to the phrase in another language.
Moanin' Low, my sweet man I love him so though he's mean as can be He's the kind of man needs a kind of woman like me a woman like me... a woman like me... a woman like me... a woman like me... a woman like me... a woman like me... (etc...) Rick wants to hire me!
Welcome to our programming tutorials on Khan Academy.
Are you completely new to computer programming?
Well, don't worry--that means that you're like 99.5% of the world.
And we're here to help.
I bet you're wondering what programming actually is.
When we write a program, we're giving a computer a series of commands, that kind of look like a weird form of English.
You could just think of a computer as a really obedient dog, listening to your commands, and doing whatever you tell it to do.
Thankfully, programming isn't this obscure skill that only special people can do--
It's something that we can all learn.
Kids, teens, adults from all over the world are learning programming today.
What's so "cool" about programming?
Why are all those people learning it?
Well, it really depends on what you think is "cool," because, as it turns out, you can use programming for almost everything.
Today people write programs to do everything from helping doctors and patients cure diseases; helping save endangered species all over the world; making self-driving cars, so that you never have to worry about learning to drive when you get older; creating algorithmic jewelry; designing robots that can take care of patients, or robots that can roam around Mars and look for water on the surface; making really fun games, like Doodle Jump, Draw Something, Angry Birds, any game that you've played; making movies like all those awesome 3-D movies from Pixar, like Avatar, or making computer graphics to go inside live-action movies like Gollum, in Lord of the Rings; making the websites and apps that you use everyday, all the time,
Use less than or greater than for this little brackets thing to write a true sentence.
So they essentially want us to say whether 45.675 is greater than or less than 45.645.
So let's look at each of these numbers. I'm just going to write them on top of each other.
So the first a number is forty-five and six hundred and seventy-five thousandths. and the second number is forty-five and six hundred and forty-five thousandths.
Now when you look at everything, here, the only place, where these two numbers are different is in the hundredths place.
We have 7 hundredths here and we have 4 hundredths here.
Everything is the same, so this number is going to be greater.
This number is a greater than 45.645, or six-hundred and forty-five thousandths.
Let me write that down just to make sure, we know what we're doing.
Forty-five and six hundred and seventy-five thousandths, or 45.675, is definitely greater than 45.645, or forty-five and six hundred and forty-five thousandths.
Several videos ago I had a figure that looked something like this, I believe it was a pentagon or a hexagon. and what we had to do is figure out the sum of the in particular exterior angles of the hexagon so that this angle equaled A, this angle B, C, D and E. The way that we did it the last time we said, well A is going to be 180 degrees, minus the interior angle that is supplementary to A, and then we did that for each of the angles and then we figured out, we were able to algebraically manipulate it, we were able to figure out what the sum of the interior angles were, using... dividing it up into triangles and then use that to figure out the exterior angle.
So it was a bit of an involved process.
So lets just draw each of them, so let me draw this angle right over here, we'll call it angle A or the measure of this angle's A, either way let me draw right over here.
So this going to be a convex angle right over here it's going to have a measure of A, now let me draw angle B, angle B, and i going to draw adjacent to angle A, and what you could do is just to think about it maybe if we draw a line over here, if we draw a line over here that is parallel to this line then the measure over here would also be B,because this is obviously a straight line, it would be like transversal, this of course a responding angles, so if u want to draw adjacent angle, the adjacent to A, do it like that, or whatever angle this is the measure of B and now it is adjacent to A, now let's draw the same thing to C
We can draw a parallel line to that right over here.
And this angle would also be C and if we want it to be adjacent to that, we could draw it there, so that angle is C
C would look something like this, like that then we can move on to D, once again we do it in different color, you could do D, right over here or you could shift it over here it'll look like that, or shift over here, it'll look like that
If we just kept thinking of parallel, if all of this line were parallel to each other
So, let's just draw D like this, so this line is going to parallel to that line
Finally, you have E, and again u can draw a line that is parallel to this right over here and this right over here would be angle E or you could draw right over here, right over here And when you see it drawn this way, it's clear that when you add up, the measure, this angle A,B,C,D and E going all the way around the circle, either way it could be going clockwise or it could be counter clockwise but it will going all the way around the circle.
And some of this angle, A+B+C+D+E is just going to be 360 degree
And this is work for any convex polygon, and when I say convex polygon I mean it is not that dented words
Just to be clear what I'm talking about, it would work for any convex polygon that is kind of
I don't want to say regular, regular means it has the same size and angle, but it is not dented, this is a convex polygon.
This right here is a concave polygon
Let me draw this, right this way, so this would be a concave polygon
Let me draw as it having the same number of side, So i just going to dent this two sides right very here.
Is it right? Let me do the same number sides, So i do that, that, that, that and then that's the same side over there, Let me do that and then like that.
This has 1,2,3,4,5,6, sides and this has 1,2,3,4,5,6 sides.
This is concave, sorry this is a convex polygon, this is concave polygon, All you have to remember is kind of cave in words
And so, what we just did is applied to any exterior angle of any convex polygon.
I Am a bit confused.
This applied to any convex polygon and once again if you take this angle and added to this angle and added to this angle, this angle, that angle and that angle and I'm not applying that all
It's going to be the same and I just drew it in that way I could show u that they are different angles, i could say that one green, and that one some other colour they can all be different but if you shift the angle like this you can see that they just go round the circle.
 We could have a debate about what the most interesting cell in the human body is, but I think easily the neuron would make the top five, and it's not just because the cell itself is interesting.
The fact that it essentially makes up our brain and our nervous system and is responsible for the thoughts and our feelings and maybe for all of our sentience, I think, would easily make it the top one or two cells.
So what I want to do is first to show you what a neuron looks like. And, of course, this is kind of the perfect example.
And then we're going to talk a little bit about how it performs its function, which is essentially communication, essentially transmitting signals across its length, depending on the signals it receives.
So if I were to draw a neuron-- let me pick a better color.
So in the middle you have your soma and then from the soma-- let me draw the nucleus.
This is a nucleus, just like any cell's nucleus.
And then the soma's considered the body of the neuron and then the neuron has these little things sticking out from it that keep branching off.
Maybe they look something like this.
I don't want to spend too much time just drawing the neuron, but you've probably seen drawings like this before.
And these branches off of the soma of the neuron, off of its body, these are called dendrites.
They can keep splitting off like that.
I want to do a fairly reasonable drawing so I'll spend a little time doing that.
And these tend to be-- and nothing is always the case in biology. Sometimes different parts of different cells perform other functions, but these tend to be where the neuron receives its signal.
And we'll talk more about what it means to receive and transmit a signal in this video and probably in the next few.
So this is where it receives the signal.
So this is the dendrite.
This right here is the soma. Soma means body. This is the body of the neuron.
And then we have kind of a-- you can almost view it as a tail of the neuron.
It's called the axon.
A neuron can be a reasonably normal sized cell, although there is a huge range, but the axons can be quite long. They could be short.
Sometimes in the brain you might have very small axons, but you might have axons that go down the spinal column or that go along one of your limbs-- or if you're talking about one of a dinosaur's limbs.
So the axon can actually stretch several feet. Not all neurons' axons are several feet, but they could be.
And this is really where a lot of the distance of the signal gets traveled.
Let me draw the axon.
So the axon will look something like this.
And at the end, it ends at the axon terminal where it can connect to other dendrites or maybe to other types of tissue or muscle if the point of this neuron is to tell a muscle to do something.
So at the end of the axon, you have the axon terminal right there.
I'll do my best to draw it like that.
Let me label it. So this is the axon.
This is the axon terminal.
And you'll sometimes hear the word-- the point at which the soma or the body of the neuron connects to the axon is as often referred to as the axon hillock-- maybe you can kind of view it as kind of a lump. It starts to form the axon.
And then we're going to talk about how the impulses travel. And a huge part in what allows them to travel efficiently are these insulating cells around the axon.
We're going to talk about this in detail and how they actually work, but it's good just to have the anatomical structure first.
So these are called Schwann cells and they're covering-- they make up the myelin sheath. So this covering, this insulation, at different intervals around the axon, this is called the myelin sheath.
So Schwann cells make up the myelin sheath.
I'll do one more just like that.
And then these little spaces between the myelin sheath-- just so we have all of the terminology from-- so we know the entire anatomy of the neuron-- these are called the nodes of Ranvier.
I guess they're named after Ranvier. Maybe he was the guy who looked and saw they had these little slots here where you don't have myelin sheath.
So these are the nodes of Ranvier.
So the general idea, as I mentioned, is that you get a signal here. We're going to talk more about what the signal means-- and then that signal gets-- actually, the signals can be summed, so you might have one little signal right there, another signal right there, and then you'll have maybe a larger signal there and there-- and that the combined effects of these signals get summed up and they travel to the hillock and if they're a large enough, they're going to trigger an action potential on the axon, which will cause a signal to travel down the balance of the axon and then over here it might be connected via synapses to other dendrites or muscles.
And we'll talk more about synapses and those might help trigger other things.
So you're saying, what's triggering these things here? Well, this could be the terminal end of other neurons' axons, like in the brain.
This could be some type of sensory neuron.
This could be on a taste bud someplace, so a salt molecule somehow can trigger it or a sugar molecule-- or this might be some type of sensor.
It could be a whole bunch of different things and we'll talk more about the different types of neurons.
On the 4th of July, 2011 we posted a request online to participate in a short film about interdependence.
Artwork and videos emerged from around the world.
Here is what unfolded...
When in the course of human events...
It becomes increasingly necessary to recognize the fundamental qualities that connect us.
Then we must reevaluate the truths we hold to be self evident.
That all humans are created equal and all are connected
That all humans are created equal and all are connected.
That we share the pursuits of life liberty happiness food water shelter safety education justice and hopes for a better future.
That our collective knowledge economy technology and environment are fundamentally interdependent.
Interdependent.
That what will propel us forward as a species is our curiosity our ability to forgive our ability to appreciate our courage and our desire to connect.
That these things we share will ultimately help us evolve to our fullest common potential.
And whereas we should take our problems seriously we should never take ourselves too seriously
Because another thing that connects us is our ability to laugh and our attempt to learn from our mistakes.
So that we can learn from the past understand our place in the world and use our collective knowledge to create a better future
So perhaps it's time that we as a species who love to laugh ask questions and connect do something radical and true.
For centuries we have declared independence
Perhaps it's now time that we as humans declare our interdependence
Interdependence
To declare your Interdependence...
let it ripple [letitripple.org]
let it ripple [letitripple.org] -- declare
Let it Ripple:
Global Films for Mobile Change
Let's learn about matrices.
So, what is a, well, what I do I mean when I say matrices?
Well, matrices is just the plural for matrix.
Which is probably a word you're familiar with more because of Hollywood than because of mathematics.
So, what is a matrix?
Well, it's actually a pretty simple idea.
It's just a table of numbers.
That's all a matrix is.
So, let me draw a matrix for you.
I don't like that toothpaste colored blue, so, let me use another color.
This is an example of a matrix.
If I said, I don't know I'm going to pick some random numbers;
Five, one, two, three, zero, minus five.
That is a matrix. And all it is is a table of numbers and, oftentimes if you want to have a variable for a matrix, you use a capital letter.
So, you could use a capital 'A'.
Sometimes in some books they make it extra bold.
So it could be a bold 'A', would be a matrix.
And, just a little bit of notation, So, they would call this matrix.
Or, we would call this matrix, just by convention, you would call this a two by three matrix.
And, sometimes they actually write it '2 by 3' below the bold letter they use to represent the matrix
What is two?
And, what is three?
Well, two is the number of rows.
We have one row, two row.
This is a row, this is a row.
We have three columns; one, two , three.
So, that's why it's called a two by three matrix.
When you say, you know, if I said, if I said that B, I'll put it extra bold.
If B is a five by two matrix, that means that B would have, I can, let me do one
I'll just type in numbers; zero, minus five, ten.
So, it has five rows, it has two columns.
We'll have another column here.
So, let's see; minus ten, three,
I'm justing putting in random numbers here.
Seven, two, pi.
That is a five by two matrix.
So, I think you'd now have a kind of a convention that all a matrix is is a table of numbers.
You can represent it when you're doing it in variable form you represent it as bold face capital letter.
Sometimes you'd write two by three there.
And, you can actually reference the terms of the matrix.
In this example, the top example, where we have matrix A.
If someone wanted to reference, let's say, this, this element of the matrix.
So, what is that?
That is in the second row.
It's in row two.
And, it's in column two. Right?
This is column one, this is column two.
Row one, row two.
So, it's in the second row, second column.
So, sometimes people will write that A, then they'll write, you know two comma two is equal to zero.
Or, they might write, sometimes they'll write a lowercase a, two comma two is equal to zero.
Well, what is A?
These are just the same thing.
I'm just doing this to expose you to the notation, because a lot of this really is just notation.
So, what is a, one comma three?
Well, that means we're in the first row and the third column.
First row; one, two, three.
It's this value right here.
So, that equals two.
So, this is just all notation of what a matrix is; it's a table of numbers, it can be represented this way.
We can represent its different elements that way.
So, you might be asking
"Sal, well, that's nice, a table of numbers with fancy words and fancy notations.
But, what is it good for?"
And that's the interesting point.
A matrix is just a data representation.
It's just a way of writing down data.
That's all it is.
It's a table of numbers.
But, it can be used to represent a whole set of phenomenon.
And if you're doing this in you Algebra 1 or your Algebra 2 class you're probably using it to represent linear equations.
But, we will learn, later, that it, and I'll do a whole set of videos on applying matrices to a whole bunch of different things.
But, it can represent, it's very powerful and if you're doing computer graphics, that matrixes...The elements can represent pixels on your screen, they can represent points in coordinate space, they can represent...Who knows!
There's tonnes of things that they can represent.
But, the important thing to realize is that a matrix isn't, it's not a natural phenomenon.
It's not like a lot of the mathematical concepts we've been looking at.
It's a way to represent a mathematical concept.
Or, a way of representing values.
But you kinda have to define what it's representing.
But, lets put that on the back burner a little bit in terms of what it actually represents.
And the, oh, my wife is here.
She's looking for our filing cabinet.
But anyway, back to what I was doing.
So, so, lets put on the back burner what a matrix is actually representing.
Let's learn the conventions.
Because, I think, uhm, at least initially, that tends to be the hardest part, How do you add matrices?
How do you multiple matrices?
How do you invert a matrices?
How do you find the determinant of a matrix?
I know all of those words might sound unfamiliar.
Unless, you've already been confused by then in your algebra class.
So. I'm gonna teach you all of those things first.
Which are all really human-defined conventions.
And then, later on, I'll make a whole bunch of videos on the intuition behind them, and what they actually represent.
So, let's get started.
So, lets say I wanted to add these two matrices.
Let's say, the first one, let me switch colors.
Let's say, I'll do relatively small ones, just, not to waste space.
So, you have the matrix; three, negative one, I don't know, two, zero.
I don't know, let's call that A, capital A.
And let's say matrix B, and I'm just making up numbers.
Matrix B is equal to; minus seven, two, three, five.
So, my question to you is:
What is A, so I'm doing it bold like they do in the text books, plus matrix B?
So, I'm adding two matrices.
And, once again this is just human convention.
Someone defined how matrices add.
They could've defined it some other way.
But, they said; we're gonna make matrices add the way I'm about to show you because it's useful for a whole set of phenomenon.
So, when you add two matrices you essentially just add the corresponding elements.
So, how does that work?
Well, you add the element that's in row one column one with the element that's in row one column one.
Alright, so, it's three plus minus seven. So, three plus minus seven.
Then, the row one column two element will be minus one plus two.
Put parenthesis around them so you know that these are separate elements.
And, you could guess how this keeps going.
This element will be two plus three.
This element, this last element will be zero plus five.
So, that equals what?
Three plus minus seven, that is minus four.
Minus one plus two, that's one.
Two plus three is five.
And, zero plus five is five.
So, there we have it, that is how we humans have defined the addition of two matrices.
And, by this definition, you can imagine that this is going to be the same thing as B plus A. Right?
And remember, this is something we have to think about because we're not adding numbers anymore.
You know one plus two is the same as two plus one.
Or, any two normal numbers, it doesn't matter what order you add them in.
But matrices it's not completely obvious.
But, when you define it in this way it doesn't matter if we do A plus B or B plus A. Right?
If we did B plus A, this would just say negative seven plus three.
This would just say two plus negative one.
But, it would come out to the same values.
That is matrix addition.
And, you can imagine, matrix subtraction, it's essentially the same thing.
We would...Well, actually let me show you.
What would be A minus B?
Well, you can also view that, this is capital B, it's a matrix that's why I'm making it extra bold.
A plus minus one, times B. What's B?
Well, B is; minus seven, two, three, five.
And, when you multiply a scalar, when you just multiply a number times the matrix, you just multiply that number times every one of its elements.
So, that equals A, matrix A, plus the matrix, we just multiply the negative one times every element in here.
So, seven, minus two, minus three, five.
And then we can do what we just did up there.
We know what A is.
So, this would equal, let's see, A is up here.
So, three plus seven is ten, negative one, plus negative two is minus three, two plus minus three is minus one and zero plus five is five.
And, you didn't have to go through this exercise right here.
You could have, literally, just subtracted these elements from these elements and you would have gotten the same value.
I did this because I wanted to show you also that multiplying a scalar times, or just a value or a number, times a matrix is just multiplying that number times all of the elements of that matrix.
And, so what...By this definition of matrix addition what do we know?
Well, we know that both matrices have to be the same size, by this definition of the way we're adding.
So, for example you could add these two matrices, You could add, I don't know, one, two, three, four, five, six, seven, eight, nine to this matrix; to, I don't know, minus ten, minus one hundred, minus one thousand.
I'm making up numbers. One, zero, zero, one ,zero, one.
You can add these two matrices. Right?
Because they have the same number of rows and the same number of columns.
So, for example, if you were to add them.
The first term up here would be one plus minus ten, so, it would be minus nine.
Two plus minus one hundred, minus ninety-eight.
I think you get the point.
You'd have exactly nine elements and you'd have three rows of three columns.
But, you could not add these two matrices.
You could not add...
Let me do it in a different color, just to show it is different,
You could not add, this blue, you could not add this matrix; minus three, two to the matrix; I don't know, nine, seven.
And why can you not add them?
Well, they don't have corresponding elements to add up.
This is a one row by two column, this is one by two and this is two by one.
So, they don't have the same dimensions so we can't add or subtract these matrices.
And, just as a side note, when a matrix has...when one of its dimensions is one.
So, for example, here you have one row and multiple columns.
This is actually called a row vector.
A vector is essentially a one dimensional matrix, where one of the dimensions is one.
So, this is a row vector and similarly, this is a column vector.
That's just a little extra terminology that you should know.
Uhm, if you take linear algebra and calculus your professor might use those terms and it's good to be familiar with it.
Anyway, I'm pushing eleven minutes, so I will continue this in the next video. See you soon.
So far we've been dealing with one way of Probability, that was the probability of (A) occur,
The number of events that satisfy A over all number of the equally likely events
All of the equally likely events.
And so in the case of a coin, The Probability of heads was a fair coin
With 2 equally likely events, satisfies being "Heads"
So there's a half chance of having a "Heads"
Similarly for tails, if you took a die
The probability of getting an even number.
Well there's 6 equally likely events, and there are three even numbers you can get
Which are, two, four and six
So there's three over six, or simply, One half chance And this is a really good model of equally likely events.
I'll draw a line, this was just one way about thinking of probability
Now we're going to talk of probability where we can think of equally likely events
And in particular I'm going to set up an unfair coin
So this right over here, is supposed to be my unfair coin.
One side of that coin is heavier than the other, So this is the head's side
As I said, this is an UNFAlR coin
Now I'm going to make an interesting statement about this unfair coin It doesn't fit into the model I've created above, And this interesting statement is, above we had a 50-50 chance of getting heads
I'm going to say, here, that the probability of getting Heads, for this coin right here, is 60% (Sixty Per Cent)
Or another way to say, 0.6 or 6 upon 10.
Or another way to say this is 3/5 or three-fifths
Now we can't say there are two equally likely events
There are two possible events
The coin may fall on the heads, or tails
So it is obvious that either we'll get Heads or Tails
But there aren't really two equally likely events
Counting the number of events that satisfy, over all the possible events
In this situation, we can visualize the probability.
This is fundamentally different from the model we talked about above.
We have to kind of take, a frequentive approach
Think about it in terms of frequency, And the way to conceptualize, 60% chance of getting heads
If we had a super large number of trials.
This means if we are to flip this coin Like a zillion times
We would expect, 60% of those would come up as heads
So I'm clear how I determine, that this is60%!
Maybe I ran a computer stimulation, maybe I should know exactly all about physics
Of this, and I can completely marvel how it's going to fall everytime
Or maybe it's like, I have a tonne of trials, I flip the coin a million times And I said, well, 60%
Of those, therefore, came up heads.
And we can make a similar statement about Tails!
So, the probability of Heads is 60%
The Probability of Tails, well there're only two possibilities, whether there can be heads or tails!
So if I say the probability of heads or tails, is going to be equal to 1 !
Because there also can be a chance of getting hundred percent Heads or tails
And these are mutually exclusive events, you can't have both of them
So this is going to be, the probability of tails is, going to be 100% - Probability of Heads which of course is 60% (as above)
Which is equal to 40% or as a decimal, it is 0.4
Or as a fraction, four tenths, or Four upon Ten, or in its simplest form, it is Two Fifths, 2 over 5
So once again, we can't call them equally likely events.
If we toss a coin a zillion times, and we get 60% of the coins as heads, it is obvious that the rest coins have to be tails
It's time for some problems now,
The probability of getting heads on our first flip and heads on our second flip.
So once again these are independent flips.
The coin has no memory, regardless what I got on the first flip, I have equal chance of getting heads on the second flip.
I can get heads and tails on the first as well, so the probability of heads on the first flip X Probability of getting heads on the second flip.
Now we already know that the probability of getting heads on the first flip is 60%
Or let's write it in the decimal form, it is 0.6 Also, P(H2) is 0.6.
I'll do it right here, so this is 0.6 x 0.6
It is equal to 0.36.
We're taking 60% of 0.6.
0.36, or another way to say it that we have 36% of getting two heads in a row
Given this unfair coin, remember if it was a fair coin, one half times which is one over four which 1/4 or 25%.
Now let's see a slightly complicated example;
Let's say, the Probability of getting a tails on the first flip, getting a heads on the second flip, And getting a tails on the third flip. So this is going to be equal to the probability of getting a tails on the first and third flip, and a heads on the second
It is equal to The Probability of Getting Tails on the First flip, multiplied by the probability of getting
heads on the second flip, heads being on the second time doesn't affect the probability of heads and similarly, a tails, again, on the third flip
And we know that the probability of getting a tails is 0.4
The Probability of getting a heads(on any flip) is 0.6 and the probability of getting tails on the third flip is 0.4
So once again we just have to multiply all these probabilities,
So 0.4 X 0.4 X 0.6 = 0.096
Or another way it to write is 9.6%, a little less than 10%.
We have a 9.6% chance of getting this probability
Remember, in this case, the position of heads or tails, first, second or third does not affect
Their probability
In the last video on the lungs or the gas exchange in our bodies or on the pulmonary system, we left off with the alveolar sacs.
Let me draw one right here.
So we have these alveolar sacs that I talked about and they're in these little clumps like this.
Let me draw a couple of them just so you get the idea.
And if you remember from the last video, these are kind of where air goes in through our trachea, then that splits up into our bronchi, and then those split into the bronchioles, and the bronchioles terminate at these alveoli.
So that's the alveoli.
These are these super-small sacs that we talked about in the last video on the pulmonary system.
You might want to watch that video if none of this sounds familiar.
And then of course we have our bronchiole that feeds into this, and then that might have branched off from another one that feeds into another set of alveolar sacs, but I don't want to get too focused on that.
I covered that in the last video.
In the last video, we saw that air, when we breathe in, when our diaphragm contracts and makes our lungs expand and fill up that space, air comes in.
Air comes in and that air that comes in is going to be-- as we're breathing atmospheric air-- it's going to be 21% oxygen and it's going to be 78% nitrogen.
And actually, in our atmosphere, carbon dioxide is actually almost a trace gas.
It's less than 1%.
So any time you breathe in on Earth, this is what you're going to get.
And we said in the last video that you have these capillaries, these pulmonary capillaries that are running all along the side of these alveoli.
So let me draw those pulmonary capillaries-- and so when they are de-oxygenated-- so they come here to be oxygenated.
So when they're de-oxygenated, they might look a little purplish.
And then they pick up the oxygen from inside the alveoli-- or the oxygen diffuses across the membrane of the alveoli, into these capillaries, into these super small tubes.
And then once they do, that makes the blood red.
I'm going to talk in a little bit about why it becomes red.
So then it becomes red, and now that the blood is red, it has its oxygen.
The whole point is to get the oxygen.
It's ready to go back to the heart.
So that's just one little part of it.
And we learned in the last video that something that goes away from the heart-- so this is going away from the heart-- that is an artery.
"A" for "way".
Artery.
And something that's going towards the heart is a vein.
So this right here is a vein.
Now one question-- and this actually came up in the last video.
Someone asked-- which I think is a very good question-- is, gee, when we breathe in, most of the air is nitrogen.
Only 21% is oxygen.
What happens to all that nitrogen there?
How come that doesn't go into our blood?
And that's actually an excellent question.
So to answer that, I think that actually helps explain what's going on here.
Let's draw a little bit bigger.
This is the inside of of an alveolus.
This is its membrane right here, super thin, almost one cell thick.
And then you have a capillary running right next to it.
Let me do that in a neutral color.
So you have a capillary that's maybe running right along the surface.
And this is porous to gases like oxygen, and nitrogen, carbon dioxide.
And what we have here-- let's say that this is-- so the heart is over here.
So this is blood coming from the heart and then this is going to go back to the heart.
Well, the heart's on both sides.
So let me write it this way.
From the heart and to the heart.
And what you have here is-- when we're coming from the heart, this is de-oxygenated blood and it's actually going to have a high concentration of carbon dioxide.
I already did nitrogen as green.
Let me do carbon dioxide as orange.
There's a lot of carbon dioxide and actually carbon dioxide actually gets diffused in the blood.
It actually is carried in the plasma of the blood.
It's not carried by red blood cells that we're going to talk about in a second.
So that's a bunch of carbon dioxide here.
And the concentration of carbon dioxide in the de-oxygenated blood is going to be higher than the concentration of carbon dioxide in the alveolus. so if this is porous to carbon dioxide, this membrane-- and it is, these carbon dioxide molecules are going to diffuse into the alveolus.
Now on the other side of that-- we have oxygen here.
We're breathing it in.
The air is 21% oxygen so you're actually going to have a lot more oxygen than carbon dioxide.
And this is de-oxygenated blood.
We used all of the oxygen in our body and we'll talk more about that either at the end of this video or in a future video on how we use it or where it goes in our body, but there's no oxygen here so the oxygen is going to be taken-- it's going to diffuse across this membrane because the concentration of oxygen is low.
Now the question is-- so immediately you see that as the oxygen diffuses across this membrane, all of a sudden, this is oxygenated blood ready to go back to the heart.
So this transition between artery and vein is a very subtle thing.
Very clearly here, you say that, OK, this is going from the heart.
This is our vein.
This is going to the heart-- sorry.
I always get confused.
This is going away from the heart-- and I was looking for an A and I wrote from.
This is away from the heart so this is an artery.
And this is going to the heart so this is a vein.
So you could make the division.
You could say, OK, once it's oxygenated, maybe we're going back to the heart, but it's kind of an arbitrary-- sorry.
I spelled artery wrong.
These are my flaws.
Spelling was never my strong suit.
So it's hard to say where the artery ends and the vein begins.
A good demarcation is when the carbon dioxide concentration goes low and that the oxygen concentration goes high.
That's a good time, where we start from the pulmonary artery.
Probably in the next video, I will a make a very-- you'll see why the pulmonary arteries are special, because pulmonary arteries coming away from the heart have no oxygen or very
So pulmonary veins, which is-- it's arbitrary where the artery turns into a vein.
Once it gets oxygenated, it's ready to go back to the heart.
It's a pulmonary vein and it is oxygenated.
So it has oxygenated-- and we could write de-oxygenated.
Now the reason why I say it's special besides the fact that pulmonary arteries and veins go to and from the lungs, is that they're kind of the opposite.
Because in the rest of the body when we're going away from the heart or we're talking about arteries, you're going to see that that's oxygenated blood, while when we're going away from the heart to the lungs, that's de-oxygenated blood.
Similarly in the rest of the body, when we're going to the heart, where you're to see that that's de-oxygenated blood, but in the pulmonary vein, when we're going to the heart, it's oxygenated because the lungs are what take up the carbon dioxide and give us the oxygen.
Now I still haven't answered that interesting question that rose on the message board on the last video.
What happens to the 78% of nitrogen that's sitting here?
There's just a ton of nitrogen over here, more than the oxygen, a lot more than the carbon dioxide.
What happens to all of these nitrogen molecules?
And the answer is, nitrogen can diffuse and does diffuse into the blood, but the blood's ability to take in nitrogen isn't that high.
And you might say, well, why is oxygen special?
Why can the blood take up oxygen so much easier than nitrogen?
And that's where the red blood cells come into play.
Let me write this down.
I'll write it in red.
Red blood cells, which are fascinating on a whole set of levels.
What red blood cells-- these are these cells that are sitting in-- they're flowing through our circulatory system and they look kind of like lozenges, if I were to draw one.
They're kind of like a flattened sphere with a little divot on either side of it-- a lot like a lozenge.
So if I were to draw it from the side, it might look something like-- well, from the side, it would look like that and if you could see through it, there'd be a
If I were to draw it at an angle, it would look something like this.
There'd be a little divot on that side and there'd be a similar divot on the other side.
And red blood cells-- and I could do a whole set of videos just on red blood cells-- they contain hemoglobin.
Maybe we'll do a whole video on hemoglobin.
The hemoglobin are these small proteins that contain four hem groups.
So inside of red blood cells, you have millions of hemoglobin proteins.
And the hemoglobin proteins-- I'll just draw them as this-- they have these four heme groups.
And heme groups, the main component is iron.
And that's why iron is so important.
If you don't have enough iron, you're going to have trouble processing oxygen in your blood and your hemoglobin won't be functional enough.
But it has iron on it.
It has four of these heme groups.
And each of these heme groups can bond to oxygen molecules.
They're very good binders of oxygen.
And we're going to see in a little bit-- probably the next video-- how they release the oxygen, but this has tons, this has millions of heme groups in it and the oxygen diffuses across the membrane of the red blood cells and bonds to to the heme groups on your hemoglobin.
So because the red blood cells have the hemoglobin inside of them, they're like these sponges for oxygen because hemoglobin is so good at taking in oxygen.
So the red blood cells are able to essentially suck up all of the oxygen out of the plasma.
The plasma we can view as just the general fluid of the blood, not including the red blood cells.
So the red blood cell here isn't so red.
And the reason-- and this is the key point-- the reason why it's not so red-- maybe we had a red blood cell over here--
let me make it clear.
Carbon dioxide for the most part is traveling within the plasma.
It gets absorbed into the actual fluid and I'll talk about it in a future video.
It's actually in a slightly different form.
It's as carbonic acid and that's actually a key point for how the plasma knows where to dump the oxygen, but I'll talk about that in a future video.
But over here, this red blood cell has a bunch of hemoglobin proteins in it, but those hemoglobin proteins have dumped their oxygen.
And it actually turns out it's the hemoglobin-- so with oxygen, hemoglobin looks red.
It reflects red light.
When it doesn't have oxygen, hemoglobin does not look red.
It looks kind of purplish, bluish, darkish-- something.
And that's why in most of your body, your veins that have de-oxygenated red blood cells look kind of bluish.
And the reason why it changes color is that when the oxygen bonds to the hem sites on the hemoglobin, it actually changes the entire confirmation, the entire structure of the protein.
We've see that multiple times.
The whole protein folds in such a way that all of a sudden, instead of purplish or dark light being reflected, now red light is reflected.
And that's why red blood cells will become red once they take the oxygen.
But I'm going on a tangent.
The whole point here is saying, why we taking up so much more oxygen than nitrogen, given that there's
less oxygen in the atmosphere than nitrogen?
And the key is these red blood cells.
These red blood cells have these millions of hemoglobin proteins inside of them and they take them up and they sop up all of the oxygen out of the plasma.
Actually, they sop about 98.5% of the oxygen.
So these red blood cells are just traveling and they're going to go back to the heart.
They are what make our blood red.
So you have this thing, hemoglobin, that's sitting in red blood cells.
It's sopping up all the oxygen.
So it keeps the oxygen concentration and the actual plasma low.
You have nothing like that for nitrogen.
There is no cell that's sopping up the nitrogen.
Nitrogen does not bond to hemoglobin.
So that's why oxygen is taken up so much better than nitrogen.
It's a very interesting question because if you just think about how much nitrogen is, it's kind of a very natural idea.
Now I want to focus a little bit on the red blood cell itself because it's fascinating.
In the video on the structure of the cell, I start off saying, all cells have a membrane and they all have DNA.
Now, the fascinating thing about a red blood cell-- I already said it has millions of hemoglobin molecules or proteins inside of it.
The fascinating thing about a red blood cell-- it has no nucleus.
And no DNA.
This is mind boggling when I first found out.
I was like, well, why is it a cell?
Is it really even a living thing?
And it turns out when it's growing, it does have a nucleus.
All cells need a nucleus with DNA in order to generate the proteins that build it up, in order to exist and structurally make itself the way it needs to be made, but the whole point of a red blood cell is to contain as much hemoglobin as possible.
And so you can imagine, this is actually a favorable evolutionary trait, that as red blood cells are ready to go into business, you've built the whole structure, they actually get rid of their nucleus.
They actually push their nucleus out of the cell and the whole reason why that's beneficial is, that's more space for hemoglobin.
Because the more hemoglobin you have, the more oxygen you can take up.
And I can do a ton of videos on hemoglobin and all of that-- and actually, I'm going to do a lot more on the circulatory system so don't worry about that, but I want to go over one other really interesting thing about hemoglobin.
We already talked about red blood cells.
I think it's fascinating that they actually don't have a nucleus in their mature form.
They actually have very short lives.
They live maybe 80, 120 days so they're not these long
lived cells-- so it's almost a philosophical question.
Are are they still alive once they've lost their DNA or are they just vessels for oxygen that aren't really alive because they aren't regenerating and producing their own DNA?
So actually, instead of going into the hemoglobin discussion right now, I'll leave you there in this video.
I realize I've been making 20-minute videos where my goal is really to make ten-minute ones.
So I'll leave you here and in the next video, we'll talk more about hemoglobin and the circulatory system.
Welcome to the presentation on using the quadratic equation.
So the quadratic equation, it sounds like something very complicated.
And when you actually first see the quadratic equation, you'll say, well, not only does it sound like something complicated, but it is something complicated.
But hopefully you'll see, over the course of this presentation, that it's actually not hard to use.
And in a future presentation I'll actually show you how it was derived.
So, in general, you've already learned how to factor a second degree equation.
You've learned that if I had, say, x squared minus x, minus 6, equals 0.
If I had this equation. x squared minus x minus x equals zero, that you could factor that as x minus 3 and x plus 2 equals 0.
Which either means that x minus 3 equals 0 or x plus 2 equals 0.
So x minus 3 equals 0 or x plus 2 equals 0.
So, x equals 3 or negative 2.
And, a graphical representation of this would be, if I had the function f of x is equal to x squared minus x minus 6.
So this axis is the f of x axis.
You might be more familiar with the y axis, and for the purpose of this type of problem, it doesn't matter.
And this is the x axis.
And if I were to graph this equation, x squared minus x, minus 6, it would look something like this.
A bit like -- this is f of x equals minus 6.
And the graph will kind of do something like this.
34 00:01:57,15 --> 00:02:00,03 Go up, it will keep going up in that direction.
And know it goes through minus 6, because when x equals 0, f of x is equal to minus 6.
So I know it goes through this point.
And I know that when f of x is equal to 0, so f of x is equal to 0 along the x axis, right?
Because this is 1.
This is 0.
This is negative 1.
So this is where f of x is equal to 0, along this x axis, right?
And we know it equals 0 at the points x is equal to 3 and x is equal to minus 2.
That's actually what we solved here.
Maybe when we were doing the factoring problems we didn't realize graphically what we were doing.
But if we said that f of x is equal to this function, we're setting that equal to 0.
So we're saying this function, when does this function equal 0?
When is it equal to 0?
Well, it's equal to 0 at these points, right?
Because this is where f of x is equal to 0.
And then what we were doing when we solved this by factoring is, we figured out, the x values that made f of x equal to 0, which is these two points.
And, just a little terminology, these are also called the zeroes, or the roots, of f of x.
63 00:03:12,47 --> 00:03:14,81 Let's review that a little bit.
So, if I had something like f of x is equal to x squared plus 4x plus 4, and I asked you, where are the zeroes, or the roots, of f of x.
That's the same thing as saying, where does f of x interject intersect the x axis?
And it intersects the x axis when f of x is equal to 0, right?
If you think about the graph I had just drawn.
So, let's say if f of x is equal to 0, then we could just say, 0 is equal to x squared plus 4x plus 4.
And we know, we could just factor that, that's x plus 2 times x plus 2. And we know that it's equal to 0 at x equals minus 2. 78 00:04:10,17 --> 00:04:13,94 x equals minus 2.
Well, that's a little -- x equals minus 2.
So now, we know how to find the 0's when the the actual equation is easy to factor.
But let's do a situation where the equation is actually not so easy to factor.
85 00:04:32,12 --> 00:04:39,75 Let's say we had f of x is equal to minus 10x
squared minus 9x plus 1.
Well, when I look at this, even if I were to divide it by 10 I would get some fractions here.
And it's very hard to imagine factoring this quadratic.
And that's what's actually called a quadratic equation, or this second degree polynomial.
But let's set it -- So we're trying to solve this.
Because we want to find out when it equals 0.
Minus 10x squared minus 9x plus 1.
We want to find out what x values make this equation equal to zero.
And here we can use a tool called a quadratic equation. And now I'm going to give you one of the few things in math that's probably a good idea to memorize.
The quadratic equation says that the roots of a quadratic are equal to -- and let's say that the quadratic equation is a x squared plus b x plus c equals 0.
So, in this example, a is minus 10. b is minus 9, and c is 1.
The formula is the roots x equals negative b plus or minus the square root of b squared minus 4 times a times c, all of that over 2a.
I know that looks complicated, but the more you use it, you'll see it's actually not that bad.
And this is a good idea to memorize.
So let's apply the quadratic equation to this equation that we just wrote down.
So, I just said -- and look, the a is just the coefficient on the x term, right? a is the coefficient on the x squared term. b is the coefficient on the x term, and c is the constant.
So let's apply it tot this equation.
What's b? Well, b is negative 9.
We could see here. b is negative 9, a is negative 10. c is 1. Right?
So if b is negative 9 -- so let's say, that's negative 9. Plus or minus the square root of negative 9 squared.
Well, that's 81.
128 00:06:53,14 --> 00:06:56,94 Minus 4 times a.
a is minus 10.
Minus 10 times c, which is 1.
I know this is messy, but hopefully you're understanding it.
And all of that over 2 times a.
Well, a is minus 10, so 2 times a is minus 20.
So let's simplify that.
Negative times negative 9, that's positive 9.
Plus or minus the square root of 81.
We have a negative 4 times a negative 10.
This is a minus 10.
I know it's very messy, I really apologize for that, times 1.
So negative 4 times negative 10 is 40, positive 40.
Positive 40.
And then we have all of that over negative 20. Well, 81 plus 40 is 121.
So this is 9 plus or minus the square root of 121 over minus 20.
Square root of 121 is 11. So I'll go here.
Hopefully you won't lose track of what I'm doing.
So this is 9 plus or minus 11, over minus 20.
And so if we said 9 plus 11 over minus 20, that is 9 plus 11 is 20, so this is 20 over minus 20. Which equals negative 1.
So that's one root.
That's 9 plus -- because this is plus or minus. And the other root would be 9 minus 11 over negative 20.
Which equals minus 2 over minus 20.
Which equals 1 over 10.
So that's the other root.
So if we were to graph this equation, we would see that it actually intersects the x axis.
Or f of x equals 0 at the point x equals negative 1 and x equals 1/10.
I'm going to do a lot more examples in part 2, because I think, if anything, I might have just confused you with this one. So, I'll see you in the part 2 of using the quadratic equation.
Welcome to the presentation on level four linear equations.
So, let's start doing some problems.
Let's say I had the situation-- let me give me a couple of problems-- if I said three over x is equal to, let's just say five.
So, what we want to do -- this problem's a little unusual from everything we've ever seen. Because here, instead of having x in the numerator, we actually have x in the denominator.
So, I personally don't like having x's in my denominators, so we want to get it outside of the denominator into a numerator or at least not in the denominator as soon as possible.
So, one way to get a number out of the denominator is, if we were to multiply both sides of this equation by x, you see that on the left-hand side of the equation these two x's will cancel out.
And in the right side, you'll just get five times x.
So this equals -- the two x's cancel out.
And you get three is equal to fivex.
Now, we could also write that as fivex is equal to three.
And then we can think about this two ways.
We either just multiply both sides by one / five, or you could just do that as dividing by five.
If you multiply both sides by one / five. The left-hand side becomes x.
And the right-hand side, three times one / five, is equal to three / five.
All we had to do is multiply both sides of this equation by x.
And we got the x's out of the denominator.
Let's do another problem.
Let's have -- let me say, x plus two over x plus one is equal to, let's say, seven.
So, here, instead of having just an x in the denominator, we have a whole x plus one in the denominator.
But we're going to do it the same way.
To get that x plus one out of the denominator, we multiply both sides of this equation times x plus one over one times this side.
Since we did it on the left-hand side we also have to do it on the right-hand side, and this is just seven / one, times x plus one over one.
And you're just left with x plus two.
And that equals seven times x plus one.
And that's the same thing as x plus two.
And, remember, it's seven times the whole thing, x plus one.
And that equals sevenx plus seven.
And now all we do is, we say well let's get all the x's on one side of the equation.
So I'm going to choose to get the x's on the left.
So let's bring that sevenx onto the left.
And we can do that by subtracting sevenx from both sides.
The right-hand side, these two sevenx's will cancel out.
And on the left-hand side we have minus sevenx plus x. Well, that's minus six plus two is equal to, and on the right all we have left is seven.
And we can just do that by subtracting two from both sides.
And we're left with minus six x is equal to six.
We just have to multiply both sides times the reciprocal of the coefficient on the left-hand side.
So we multiply both sides of the equation by negative one / six.
The left-hand side, negative one over six times negative six. Well that just equals one.
So we just get x is equal to five times negative one / six. Well, that's negative five / six.
And we're done.
Let's do another one.
Let me think. three times x plus five is equal to eight times x plus two.
Well, we do the same thing here.
We want to get x plus five out and we want to get this x plus two out.
So let's do the x plus five first.
Well, just like we did before, we multiply both sides of this equation by x plus five.
You can say x plus five over one.
Times x plus five over one.
On the left-hand side, they get canceled out.
So we're left with three is equal to eight times x plus five. All of that over x plus two.
Now, on the top, just to simplify, we once again just multiply the eight times the whole expression.
So it's eightx plus forty over x plus two.
Now, we want to get rid of this x plus two.
We can multiply both sides of this equation by x plus two over one. x plus two.
So the left-hand side becomes threex plus six.
Remember, always distribute three times, because you're multiplying it times the whole expression. x plus two.
And on the right-hand side. Well, this x plus two and this x plus two will cancel out.
And we're left with eightx plus forty.
Well, if we subtract eightx from both sides, minus eightx, plus-- I think I'm running out of space.
Well, on the right-hand side the eightx's cancel out.
On the left-hand side we have minus fivex plus six is equal to, on the right-hand side all we have left is forty.
Now we can subtract six from both sides of this equation. Let me just write out here. Minus six plus minus six.
But if we subtract minus six from both sides, on the left-hand side we're just left with minus fivex equals, and on the right-hand side we have thirty-four.
We just multiply both sides times negative one / five.
On the left-hand side we have x.
And on the right-hand side we have negative thirty-four / five.
Unless I made some careless mistakes, I think that's right.
And I think if you understood what we just did here, you're ready to tackle some level four linear equations. Have fun.
What I want to do in this video is review all the neat and bizarre things that we have learned about triangles so first we learned
So let me just draw a bunch of triangles for ourselves so let's have a triangle right over there the first thing that we talked about is the perpendicular bisectors of the sides of the triangles, so if we take, so let's take
let's bisect this side over here, and let's draw a perpendicular line to it, so this line right over here would be the perpendicular bisector of this side right over here, so it's bisecting and it's perpendicular, let's draw another perpendicular bisector right over here, so we're learning that this is the midpoint of that side, let's draw a perpendicular bisector and this length is equal to this length, and then let's do one, let's do one over here, this is the midpoint of that side right over there, and then we will draw a perpendicular - we know that this length is equal to this length right over here, and what we learned is where all these perpendicular bisectors intersect, what's neat about this and frankly, all the things we're going to talk about in this videos is they do intersect in one unique point that one unique point is equidistant from the vertices of this triangle, so this distance is going to be equal to this distance, which is going to be equal to that distance, and because it's equidistant to the vertices, you could draw a circle of that radius that goes through the vertices, so you could draw a circle of that radius that goes through, that goes through the vertices, and that's why we call this right over here, that point, that intersection of the perpendicular bisectors
let me write this down so we can keep track of things, perpendicular bisectors, perpendicular bisectors, we call this point right over here our circumcenter, because it is the center of our circumcircle, a circle that can be circumscribed about this triangle, so this is our circumcircle.
And the radius of the circumcircle, the distance between the circumcenter and the vertices is the circumradius, so that was the perpendicular bisectors.
Now the next thing we learn is the whole point of this video is to make sure we differentiate between these things and not get too confused
let me draw another arbitrary triangle right over here, the next thing we thought about is, well, what about if we were to bisect the angles?
Now, we're not talking about perpendicular bisecting the sides, we're talking about bisecting the angles themselves, so we can bisect this angle right over here, my best attempt to draw it- so this angle is going to be equal to that angle, we could bisect this angle right over here, we could bisect- oh, that's - I could do a better version of that so that looks- well, one more try.
So I could bisect it like that, and then if I'm bisecting it, this angle is going to be equal to that angle and then if I bisect this one, we know that this angle is going to be equal to that angle over there, and once again, we have proven to ourselves that they all intersect in a unique point, and this point, instead of being equidistant from the vertices, this point is equidistant from the sides of the triangle, so if you drop a perpendicular to each of the sides, this distance is going to be equal to that distance, which is going to be equal to that distance, and because of that, we can draw a circle that is tangent to the side that has this radius, we can draw a circle, we can draw a circle that looks like this, and we call this circle, because it's kind of inside the triangle we call it an incircle, incircle, and this point, we can call, which is the intersection of these angle bisectors, we can call this, we can call this the in-radius, now the other thing we learned about angle bisectors and this was - we just have to draw one- so let me just draw another triangle right over here, and let me draw an angle bisector, so I'm going to bisect this angle, so this angle is equal to that angle, and let me label some points here, so let's say that this is- change the colors, let's say that is A, this is B,this is C, and this is D, we learned that if AC is really the angle bisector of angle BAD, that the ratio between AB over BC, is going to be equal to the ratio
AD to DC, sometimes this is called the angle bisector here, so that- that's neat so the next thing we learned is - let's draw another triangle here, this is to be a full review of everything we've been covering in the last few videos- so let me draw another triangle here- so now, instead of drawing the perpendicular bisectors
let me label everything, this is angle bisectors, this is angle bisectors, and now what I'm going to think about are the medians, the medians.
So the perpendicular bisectors were lines that bisect the sides, and they are perpendicular, but don't necessarily go through the vertices.
When we talk about medians, we are talking about- we are talking about points that bisect the sides, but they go to the vertices, and they are not necessarily perpendicular.
So let's draw some medians here.
So let's say this is the midpoint of that side right over there, so we can draw the median like that, notice it's going through the vertices, these did not necessarily go through the vertices this right over here is not necessarily perpendicular but we do know that this length is equal to that length right over there and we draw a couple of more medians, right over here, so this, the midpoint looks like it's right about here, the midpoint looks
looks like it's right about, well, right about there, and once again, all of these are concurrent, they all intersect at one point right over here, so this length right over here is equal to this length right over here.
There is a bunch of neat things about medians- when you draw the three medians
like this, that unique point where they intersect we call this a centroid, centroid, and as I mentioned, and you might learn this
later on in physics, is if this was a uniform triangle, and it had a uniform density, and if were to throw it or rotate it in the air, it would rotate around it's centroid,which is essentially- it would essentially be its center of mass, it would rotate around that as it's flying through the air, if it had some type of rotational or I guess you'd say angular momentum, but the neat thing about this is it also divides this triangle into six triangles of equal area, so this, this triangle has the same area as that triangle, we proved this in several videos ago, each of these 6 triangles all have all have the same area.
The other thing that we learned about medians is that where the centroid sits on each of the medians is two thirds along the median, so the ratio of this side of this length to this length is two to one, or this is two thirds along the way of the median- this is two thirds of the median, this is one third of the median, so the ratio is two to one.
Another related thing we learned, this wasn't necessarily about medians, but a related concept, was the idea of medial triangle, a medial triangle like this, where you take the midpoint of each side the midpoint of each side, and you draw a triangle that connects the midpoints of each side, we call this triangle a medial triangle, a medial triangle, and we've proved to ourselves that this- when you draw a medial triangle, it separates this triangle into four triangles that not only have equal area, but the four triangles here are actually, they are actually congruent triangles, and not only are they congruent, but we've shown that this side is parallel to this side,that's what we do, use some more colors here, this side is parallel - actually, I should draw two arrows like that, that side is parallel to that side,this side is parallel to this side, and then you have this side is parallel to this side right here, and this length is half that length, this length is half of that length, and it really just comes out of the fact that these are four congruent triangles.
There's a last thing that we touched on is drawing altitudes of a triangle, so there's medians, medial triangles,and
I'll draw one last triangle over here, and here I'm going to go from each of the vertex, and I'm not going to go to the midpoint
I'm going to drop a perpendicular to the other side.
So here I will drop a perpendicular but this isn't necessarily bisecting the other side, once again, we're going to drop a perpendicular but not necessarily bisecting the other side, and then drop a perpendicular but not necessarily bisecting the other side and we have also proven to ourselves that these are the altitudes of the triangle, altitudes of the triangle, and these also intersect in a unique- these also intersect in a unique point.
And I want to be clear, this unique point does not necessarily have to be inside of the triangle.
The same thing was true of the perpendicular bisectors, it actually could be outside of the triangle, and this unique point we call an ortho, orthocenter.
So I'll leave you there, and hopefully this is useful, cause I know it can get confusing, you know, how's a median different than a circumcenter, which is different than an orthocenter, or inrays, or any of these type of things, so hopefully, this clarifies things a little bit.
[cheers]
Thank you. [cheers]
Thank you.
[cheers]
Thank you so much.
[cheers]
Thank you.
[cheers]
To Graça Machel and the Mandela family;
To President Zuma and members of the government; to heads of states and goverments
-- past and present -- distinguished guests.
It is a singular honor to be with you today to celebrate a life like no other
To the people of South Africa [cheers] People of every race and every walk of life the world thanks you for sharing Nelson Mandela with us His struggle was your struggle his triumph was your triumph, your dignity and your hope found expression in his life and your freedom
The Case by JL Burgos
Go ahead tell to attorney what happened.
They forced me.
The case is strong.
The case is strong.
The case is strong.
The case is strong.
The case is so strong.
The case is strong.
The case is strong.
American soldier.
The case is dead.
Justice will remain elusive in a country repeatedly raped by abusive nations.
Scrap the One Sided RP-US Visiting Forces Agreement!
We are here to celebrate Women's Aid Organization's 30th anniversary
In 1982 it broke the silence of domestic violence as it opened its first shelter
A refuge for battered wives and domestic mothers and their children
So we're here 30 years later, domestic violence is still a problem
We're still going strong
<i>Brought to you by the PKer team @ www.viki.com.
Episode 14
What are you doing here?
I...am going to move out.
I'm going to get in your way.
It's a relief that Joon Gu works so hard.
My dad likes him a lot too.
Now, I should help my father at his restaurant with Joon Gu.
You like him?
Bong Joon Gu?
Of course I do.
He liked only me for 4 years.
If someone says they like you, then you just like them like that too?
Why?
I can't do that?
I'm tired of having a crush now.
I want to see a guy that likes me.
I like Joon Gu.
You... like me.
You can't like anyone but me.
What is this, that confidence?
Am I not right?
Yes, you're right!
I only like you.
So what am I supposed to do?
You don't ever see me.
Someone like me...
Don't say that you like another guy.
That's the second one.
Second what?
Kiss...
It's the third.
It's fine.
I'm not going to count any more.
Okay.
It's still not that time.
They're kids.
There is no need for that.
Just because there are marriage talks, doesn't mean anything is going to happen right away.
It will be uncomfortable, no, I'm the one who is uncomfortable.
Gi Dong-shii !
Thanks for what you've done.
Twice already...
I will definitely pay you back.
Hyung!
Oh dear!
What happened to you two?
You'll catch a cold.
Hurry, go upstairs and get changed.
Yes.
Hyung!
Oh Ha Ni is going to move out.
I have something to say.
To me?
Well, get changed first, then. . .
I . . . want to marry Oh Ha Ni.
What?
Seung Jo...
Of course, not right away, but after we graduate, and Father's company is in a better state, if you were to approve, Father.
A... are you being serious now?
Yes.
You already know, but our Ha Ni is not very good at anything.
I know.
And she is not very bright.
I know.
And she can't cook.
I know it well.
She's careless and accident prone.
The best.
Even so, she's bright and is very good about doing the right thing.
She has a cute side to her.
Yes.
I know it very well.
Well since Ha Ni likes you so much.
Ha Ni!
It really turned out well!
This is great!
Hey Baek Seung Jo!
Why are you so cool?
What to do?
Ha Ni!
I knew it would be like this.
You didn't go to sleep?
Yeah...
It stopped raining.
Oh...
Since it stopped raining, the sky seems clearer.
That's right.
You're not cold?
I'm going to sleep first.
What?
What is it?
It's just that if you go to sleep like this, once it's morning,
"What if you go back to being the cold Baek Seung Jo?"
That is what I was thinking.
Then, do you want us to sleep together tonight?
N... No.
It's not like that.
Right.
Let's just wait for a while.
I couldn't even imagine it, that you would come to like me.
Me too.
I like you.
I like you very very much.
Mom, would you stop it?
Hey!
Shh! <i>Don't be like this...
Joon Gu... <i>Hey, don't. <i>I told you to not do this Joon Gu!
Why did I do that?!
If I come onto her all of a sudden like that, then her feelings for me will just drop.
Joon Gu, really, what is wrong with you?
You're not sleeping?
Ha Ni...
I did wrong yesterday.
Eat this and forgive me, okay?
Someone is already here?
Aigoo!
Hey Joon Gu!
Why are you here already?
Oh Chef, did you go to the morning market?
Yeah, that's right.
But what is all of this?
This early in the morning?
Why are you packing a lunch?
Hey, there are even chicken wings.
I was preparing it to give to Ha Ni.
Ha Ni?
Ah, yes.
Actually, I ... to Ha Ni ...
It's nothing!
This is so fancy.
They've got titles to them too.
This is sweetened with honey so it's called "Oh Ha Ni."
Oh.
Ha.
Ni.
The focus of this one is the fried chicken wings so it's called, "Bong Joon Gu!"
Oh Ha Ni, Bong Joon Gu
How about we make a Sok Pal Book Lunch box?
Sok Pal Book Lunch box?
Ah, let me think about it.
Yes!
Oh Ha Ni~ Bong Joon Gu~ !
Done.
What?
Is this a joke?
It's the truth!
He said it right in front of all of the adults!
Baek Seung Jo?
Not Bong Joon Gu?
Yeah.
Why?
Why does he want to marry you suddenly?
I'm not sure.
Maybe he finally realized my feelings.
He found out it was love.
A story like that.
Then are you going to get married right away?
It's still far away Not before we graduate.
Wow, Oh Ha Ni, that's great!
Hey!
I want to make you my life's mentor!
What's wrong with you!
Anyway, Congratulations The crush you had for 4 years is finally paying off!
So you finally did it!
Congrats!
Thanks.
You like it that much?!
Yeah, she's loving it!
Ah, then... what about Bong Joon Gu?
Ah, right.
And Yoon Hae Ra...?
Seung Jo said he's gonna tell Hae Ra.
And I have to tell Joon Gu.
Oh Ha Ni? <i> Oh Ha Ni / Baek Seung Jo After 4 years of passionate love, finally the engagement.
I wonder who confessed first?
It must be Oh Ha Ni.
It came faster than I thought
I knew that someday you would figure out your true feelings, but this day came sooner than I thought.
I didn't know either that this was going to happen.
Did you know?
Your mother knew too, didn't she?
Oh Ha Ni was really difficult.
It was like solving a problem with no answer.
That's why it was so hard.
But you didn't want to admit that, right?
That Baek Seung Jo had a problem that, no matter how hard he tried, he couldn't find an answer to.
How come you know me so well?
But now it isn't hard anymore?
It was hard when I was trying not to be shaken by those feelings
But when I admitted, "I've completely given up to this kid."
Once I surrendered to that, it's not hard any more.
Now it's fun.
Hey!
You came to apologize, but aren't you just bragging too much?
Is that so?
Okay.
I'm sincerely apologizing.
But I wasn't joking around.
I really thought we two would match well.
When I was with you, I was really comfortable.
You were running away from Oh Ha Ni and finding comfort in me right?
I'm sorry.
You're not saying you weren't.
But what to do?
"I'm fine." I can't say that.
Scared?
Okay.
I've accepted it.
Congratutlations on your marriage.
It's still far away!
I'm congratulating you early then.
Okay.
What is this?
I'm trying to throw away my feelings.
Why is your hand so warm?
You're really a nice girl.
I know.
Joon Gu, let's eat.
I don't feel like it.
Go ahead.
Does a person working in the cafeteria bother to think about eating?
While we're not busy we have to eat and clean up.
Hurry and come.
Oh, what's that?
It looks like a lunch box.
Is he saying he doesn't feel like it since he brought his lunch?
- Hey, is this octopus or rice cake?
- It's rice cake!
Look at the way he wrapped this meat?!
I bet it's delicious!
It's really delicious!
I'm being truly honest when I say this... apart from how Bong looks...
I can't believe it's to this point!
I would pay over 10 times to eat this.
I feel the same way.
It's so good.
Joon Gu you could sell this right away!
Quit that noodle place and let's open up a lunch box shop?!
What do you think?!
Ha Ni, have you eaten?
I don't know.
I should have told him in person first.
I left after what happened last night too.
Did Seung Jo tell her yet?
It seemed like Hae Ra really liked Seung Jo a lot, too.
That's probably why she was like that to me.
Why is dating so difficult?
"Oh Ha Ni, Baek Seung Jo"?!
"After 4 years of passionate love, finally the engagement"?!
What does this Oh Ha Ni look like?!
What does she look like that she was able to accomplish this feat?!
That's freaking amazing!
But she's so ugly, she's really ugly!
I like you. <i>Let's just take a chance, <i>on each other. <i>Let's... start. <i> You're a really fine woman.
Where are the beverages?
Ah, yeah.
She must be really thirsty.
I have to know what she likes so that I can buy it.
Water?
No, not water.
It's not cold!
Oh this is cold, this is cold!
I don't even know if she likes that.
A drink like this?!
Just because she was exercising doesn't mean I can give her a sports drink!
Coke, Coke, Coke!
Ah, right, Diet Coke.
That would imply that she has to lose weight.
There's nothing for her to lose!
What should I buy?
Excuse me!
When you're really thirsty, what do you like to drink?
Yoon Hae Ra, why are you like this, really?
Are you okay?
Beer?
It was cool, earlier on...
Fine.
I'm thirsty.
Why won't this open!
Should I open it up for you?
It's fine.
Ah. It's really annoying.
It's okay if you sob,
I'm okay with it.
Don't hold it back.
Ha Ni, I really wanted to do this together with you.
You are my life's navigation system
You guide me through the paths I have to.. to take.
Yes, Chef!
I'm out for some fresh air now .
Yes, I understand.
I'll be coming back now.
Make sure to clean up nicely before you go in.
I understand
Great job.
You came!
Good thing you came.
Chef left his wallet.
Where was it...Oh here it is.
Here.
Wallet?
The colour is pretty.
What is it?
Chlorella.
Joon Gu, I ...
I have something to say.
I'm sorry, but today you have to go home.
I'm really busy.
Bong Joon Gu.
Let's have a talk.
You must be kidding.
What do I have to talk with you about?
Just go.
Then I'll say it right here.
I...
like Oh Ha Ni.
We don't need your permission to date, but it's important for Ha Ni.
It would be good if you let it go.
If you let her go, everything will be fine.
Hey!
That's something stupid to say.
Let go... let go of what?
Hey Baek Seung Jo.
All this time you've been so mean to Ha Ni.
Now what are you trying to say? It seems like you don't know, but for 4 years, I liked Ha Ni. Joon Gu.
I'm sorry. Why are you sorry?
Of course I'm sorry and thankful.
But I really...
It's fine.
Don't say it.
I already know.
I already saw it.
Ah Oh Ha Ni, really...
You really have no taste in guys.
Later,even if you regret it,
I'm not going to give in.
Will you be okay with that?
See?
You can't even respond quickly enough.
Baek Seung Jo.
What are you going to do?
Ha Ni isn't able to respond.
Yeah.
I'm getting nervous.
Seung Jo.
Just know that I'm always going to be watching you.
If you make tears come out of Ha Ni's eyes,
I'll make bloody tears come out of your eyes.
I'll keep that in mind. <i>Brought to you by the PKer team @ www.viki.com
What is this?
Get in.
What car is this?
It's a company car.
I'm using it for now.
It just didn't feel right in my father's car.
Wow... it's nice!
Then should we go driving?
Don't think like that.
This car is for company use only.
Here.
Something to eat while you drink.
Chef...
Yes, Joon Gu?
You know, I ... wanted to call you Father.
I truly wanted to call you "Father-in-law."
My father-in-law.
I'm really sorry about what happened with your grand daughter.
It's all my fault.
Collapsing and all.
Seung Jo may be reliable, but he's still very young.
He's not ...
You don't need to beat around the bush.
My investment was on the line, and since that all happened, my investment is no longer there.
It's simple.
But still... the game is almost complete and you really enjoyed it...
I'm not that great of a person.
I can't separate how I feel and what I'm supposed to do!
Since there was interest, the game is probably liked.
Seung Jo!
Did you come to witness the punishment for yourself?
No.
I settled the matter with your granddaughter myself.
Today, I came to talk about business.
Seung Jo.
What?!
Saying sorry for what happened, I don't think Hae Ra would want that.
For whatever reason, putting herself in a hurtful position... a position to accept an apology, I don't think she'd like it.
I have a similar personality so I know her quite well.
So?
You're not going to apologize for Hae Ra but you still want me to invest?
Yes.
Seung Jo!
Please invest, but you don't necessarily need to invest in our company.
Our game, we can pass it on to a different company, or your company can service it completely.
Wherever it may be, please allow us to have game service.
For the last 2 months our employees have worked day and night, even forgoing their paychecks.
They worked very hard, and the results came out nicely.
It's fine if you throw out our company, but please at least allow this game to see the spotlight, and please save our developers.
To give up on those below me because you dislike me...
It's childish?
You're teaching me right now, aren't you?
It's not that.
Baek Seung Jo!
I don't like you.
I'm very sorry.
You should at least plead for something.
Invest in us or it's the end for us.
I did wrong with Hae Ra.
Please forgive me.
You need to plead like that, rascal.
That way I'll waver and sign the contract.
Idiot. <i>Yes, President?
Bring the stamp (used to sign contracts).
Thank you very much.
You can't mooch off my money.
Pay me back multiples.
Yes, I'll do that.
Thank you.
Thank you.
So the launch is next week?
Yes.
As long as there are no problems.
Seung Jo you're amazing.
I'm really indebted to you this time.
I was very surprised.
Made me wonder whether you are really my son.
You're cool.
But you can't brag in front of me.
Do you think I've been through this only once or twice?
Yes, it must have been like that.
Yes that's why you should quit now.
You did enough so you can stop.
It's time for you to pick a major for next year.
You have to go to med school.
But there's no guarantee that this game will be successful.
Then we'll just be in debt.
And your health...
I just told you not to brag!
I'm fairly famous in the gaming industry within our country!
Don't you try to overstep me!
Seung Jo, don't you dare steal my place.
I'm going to do this for the next 20 years.
20 years?
And after that?
I'm here!
I'm better at gaming than my brother.
He doesn't like games, and he doesn't like them.
If I work hard from now on, I can become a great heir.
So, Seung jo, become a doctor.
Become a doctor and help NoRi.
No Ri is sick again.
I saved this nearly collapsing company, but seems I've been instantly kicked out.
Yes, as soon as this new game launches, let's shoot him off to med school!
Poor you...
There isn't a day where your hands are normal.
Lately I always hurt myself because of the cutting exercises.
And this one I was curling...
Did you say the qualification test was next month?
When I finish school, you two have to buy me a set of scissors (hair cutting)
But that's expensive.
Buy it anyway!
That's what people get when they graduate!
You two start saving your money.
Got it!
I'll have to take on a part-time job.
Then buy me a tablet.
What's a tablet?
There's this thing you use to draw when using a computer.
Ah, Min Ah I saw your webtoon!
"Pitpatting Parang High." It was totally about us!
It was so amusing.
Hey, what are you?
You drew me like that, am I that fat?!
Why?
The feedback was really good.
Hey, in her webtoon your character is the most popular.
Really?
Dok Go Min Ah, are you going to become a famous cartoonist then?
Looks like I'll have to get a signature. Hurry up and give me a signature.
Hurry!
The game we are launching this month is a new MMORPG with realistic visual action aspects to it.
We will be implementing real time play within the existing market, which will make a big impact and change the way games are played.
It's a taste of a game that none other possesses with focus on animation like graphics.
Then, we'll start now.
These days online games are exported just as much as cars, maybe more, and therefore quality has gone down causing concern.
But a new game was released that could be the new face of this declining industry.
Within this gaming industry that's filled with games that require boring time commitments and nothing more than extravagant graphics..
We have created a fun animation game that is easy to enjoy.
As expected!
Isn't he fine, Grandfather?
Yeah.
He is desirable.
Of course!
Would I have liked a trivial person?
It's in past tense.
Then, have you cleared up your feelings?
You were really upset over it.
Seeing him again, I'm getting greedy again.
Ah, how tiring.
Joon Gu, it's a favor.
Joon Gu, hurry with the dishes...
Cut up some scallions, and cook some more noodles.
Yes, I understand.
Right Baek Seung Jo.
Let's try our best.
You can enjoy all aspects of action with our game.
Hey, you being around motivates me even more.
Just wait and see.
I'll become a great person too.
On the Internet, the feedback from the game is explosive.
Even if he is my son, Seung Jo is really amazing.
Ha Ni, I saw the webtoon Min Ah put on the Internet.
It was so funny.
Isn't it? Lately that webtoon has been really popular.
I think in good time she should be amongst some of the most popular cartoonists.
That's great.
I know. I'm so happy for her.
I see because she's so talented she's already making a name for herself.
I hear getting a job for university grads is real hard these days so they're interviewing like crazy. Good for her.
Despite these hard times I hear there are tons of students that don't give a care in the world.
That friend of yours must be working really hard.
Yes, they're working hard
That doesn't "care for a thing" student, we have one at our house too.
You...again!
Oh, Ha Ni, something came from the school for you
Eun Jo, give me that thing on the very top over there.
Here.
Yes.
What is it?
What is it?
Report card...
Huh?
It's probably obvious.
What do I do!?
I calculated my credits and was reassured. I thought it was okay.
I don't have enough credits.
Then the credits on there were probably calculated incorrectly.
Huh?
It seems like it.
What do I do?
If you don't have enough credits, then you have to push through again.
There's no use in coming to me and crying.
You caused these results by yourself, so you're the only one that can take care of this.
Yes.
I know that much.
Then, it is fine.
Excuse me...
I think I'm just no good at studying
Should I just give up school?
I tried on my own.
It seems like my grades aren't going up.
Because if you do that then you could spend a bit more time following me around?
It's not exactly like that.
What about when everyone around you was studying like crazy to get good grades so they could get a job?
What were you doing?
Have you thought about your future career?
You don't think things through enough and that's why your calculations are wrong, and your credits don't add up.
Baek Seung Jo!
Am I wrong?
You don't know my feelings.
You're good at everything without even trying whether it's grades or sports.
You're popular with girls
Baek Seung Jo, you don't understand others' struggles.
Someone like you can't understand my feelings.
If you didn't have perseverance what would be left of you?
Then you... don't have any charm.
You were this cold of a person,
Baek Seung Jo.
Where are you going? Wherever
Is there even a place for you to go this late at night?
I have.
I might just go to a different guy!
So you have that kind of courage?
Bong Joong Gu or...
Kyung Su sunbae?
Even if you regret it later, I won't care.
Do as you wish. <i>You are too much Baek Seung Jo!</i> <i>I'm already upset because of my credits, <i>and you stepped all over that. <i>As happy as I am, I still get hurt too. <i>All I wanted was for you to comfort me a bit. <i>Cold blooded Baek Seung Jo!
What did you say to Ha Ni?
She's the kind of girl who didn't give up, even when you were so mean to her.
Tell me. What did you say to her?
What could you have said to make her leave?
She probably went to her friends.
Besides, I didn't say much.
I just gave her some motivation because it seemed like she was given an academic warning.
You really. I thought you were doing well.
Why are you like that again?
This is a good chance.
She needs to be apart from me a little, so that she can think for herself.
Joo Ri!
Oh!
Ha Ni!
Why are you here at this time?
I . . .
left the house.
What?
Yah!
You failed one of your classes, didn't you?
So you fought with Baek Seung Jo?
Lovers' quarrel?
Hey! I'm not in the mood for joking!
Even if you're really mad, who would just leave the house like that?
He'll probably come get her.
Really?
I don't know It's been a long time we had such good beer, let's drink up!
Right! Drink up!!
Don't worry and just drink. You can spend the night at my place.
Thank you. <i> Did Seung Jo already go to sleep? <i>No, that is not possible. <i> Because I left like that, he must be worried and not able to sleep. <i> Would he come looking for me? <i> Should I send him a message to let him know at least where I am? <i> No matter how, it seems like I overreacted <i> saying I'll go to another man. <i> He'll come to get me tomorrow, right? <i>He's probably reflecting, right? <i> Baek Seung Jo, <i> I'm lonely without you. <i>It's upsetting but . . . <i> I miss you, Seung Jo!
Really?
Yeah.
Oh Ha Ni, it looks like you didn't sleep well.
If you miss Seung Jo, just go back home.
I can't give in first now that I've come this far.
It's a good chance to make Seung Jo realize how large my presence was.
I can't keep on being the only one saying I like him.
Aigoo, Oh Ha Ni! Only now did you return to your senses?
I have to go now. I'll be late.
Bye!
Fighting! Work hard.
Call me.
Bye!
Right, you thought well.
You should be able to do that too.
But how is Seung Jo doing?
Should I take a small look from afar?
Oh Ha Ni!
Why? It's fun!
To see Baek Seung Jo's struggling face because he misses me.
Let's go, okay?
He's over there.
He looks like he's having fun.
He's not struggling at all.
I'm definitely not going back home!
Never ever!
Are you sighing again?
Ha Ni left yesterday and hasn't called.
I am back!
Oh, you're here early!
What about Ha Ni? Did you find her?
No.
How about putting an end to this and bringing her back home?
Ha Ni is also just being stubborn right now.
She wants to come back but hasn't had the chance, so she's having a hard time.
You don't even know that?
How can someone be that cold?
Oh poor Ha Ni!
Ah let's just leave them.
After all, it's something that concerns only them.
Won't something good come out of Ha Ni being apart for a little while?
If Gi Dong shi says that too, then what are we going to do?
Ha Ni!
She's only been gone one day and I miss her this much.
I'm sorry.
My family came all of a sudden.
You're going home, right?
Huh?
Don't be like that and just go back home.
He might have been a little harsh, but I think he said all that for your own good.
Go home.
Okay.
You go back in first.
I am sorry Ha Ni.
Cheer up!
Yes.
I'm going.
Go back in first.
They're waiting for you.
Huh?
I'm going.
Go back home.
Ok.
I love you!
Me too!
Go!
Where I am going to go now?
Bad Beak Seung Jo!
He's not even worried!
How could he not even call? <i>Brought to you by the PKer team @ www.viikii.net
Come to our club! We will escort you.
I ...
It's really great.
Where are you going in the middle of the night?
Since you're not looking for her, the least I can do is to go out and look for her myself.
I'm worried too, but since it's happened, you should leave her to solve this herself.
For Ha Ni's sake, it's a good thing
I understand.
But you... do you know...?
A person's feelings don't have one answer like a math problem.
What the right answer is...I don't know either. <i>Seung Jo's words are right...
Thanks for coming! Please come again!
Workers needed!
Did you finish?
Yes.
But will a young lady like you be able to do it?
Though it looks like this, it's going to be pretty hard.
If it's hard, the harder it is the better.
If there are a lot of orders you might even have to cook
Now, don't worry about that.
My dad is a chef, and his noodle restaurant has a 60 year old history.
Is that so?
So, can you start today?
Actually, one of the ladies quit so we do need help.
Yes.
Of course.
I'll do my best.
It's okay.
Let me do this.
Okay.
You do it.
Aunty, I'll do the dishes too
Just leave them.
Working part-time in a restaurant?
I thought she went back home, but she is working in that restaurant.
Oh Ha Ni is out looking for trouble again.
She said that this should be kept a secret from Seung Jo.
So she doesn't want to see Baek Seung Jo until she makes something great out of herself?
No, apparently the restaurant is a bit grungy
The dirty aprons don't make her feel right
What is this? Ah.
But how is she going to go to school?
She did say something about dropping out.
Is she going to continue working there?
Oh my.
Baek Seung Jo
I'll be going now!
I'm back!
Welcome!
What should we have?
Our bean-paste soup is really good.
Then should we have that? Two bean-paste soups please.
Ah, yes.
Aunty, two bean-paste soups please.
Please enjoy your meals!
Oh Ha Ni?
Aren't you Oh Ha Ni?
No, I'm not.
You are. You are Ha Ni.
What are you doing here, Ha Ni?
Are you working?
Something like that.
I heard you got into the law program.
You must be studying for the licensing exam, right?
I heard it was really hard.
If you're not someone like the genius Baek Seung Jo, then it'll be difficult to pass with one try.
There are even people who've been taking the test for 12 years.
You guys are lucky that everything comes so easy to you guys.
A lot of people say it like that.
But doesn't matter how smart you are, it's hard following the masses.
I'm not sure, but Seung Jo is probably trying really hard on his own too.
Nothing comes free in life, kiddo.
Since you have such a hard time studying, you're trying to find something else to do?!
What would it be?
By any chance... housewife?
That's perfect Ha Ni.
You and the tray look perfect together.
Work hard.
I'm rooting for you.
Unnie is going to go.
I've got to study.
Please continue.
Aunty, I'm back.
Oh good job.
Customer at table 9 ordered bean paste soup.
I'll go out for a sec.
Please enjoy your meal!
It's tasteless.
Is that so? I'll make it again.
Even if you make it again, it will probably taste the same.
Seung Jo.
Your friends said that the food here is delicious?
What's wrong with the taste?
Okay.
What are you going to do in the future?
Being apart from you for a couple days...
I realized how tiring I am towards you and how childish I was.
I think I thought too much of my comfort.
So, you've made a decision after thinking it over?
What is the thing I want to do the most?
I thought about it.
What is that?
Seung Jo, you may think it's ridiculous and laugh in my face.
No matter how much I think about it, this is the only thing I want.
Helping with Baek Seung Jo's work.
I'm going to become a nurse.
Since it has to do with life (the living), you might think it's too much for me.
Even so, I'm seriously thinking about it.
I want to become a wife who would suit you.
So you've thought a lot about it.
Trying your best to become a nurse.
Seung Jo.
Stop it and come back home now.
Is it fine if I do?
The truth is, I missed you so much I thought I would die.
I know, I know it all.
You must really be busy with school Seung Jo.
Its going to be hard seeing you around.
It seems that I will be out of it until graduation.
I . . .
That's right! The game Seung Jo developed, it's going to an American game show next year!
Wow!
That's great.
I have something to say everyone.
Please empty your schedule for this coming Wednesday
Wednesday? I have a golf appointment with Chairman Yoon that day.
The restaurant workers and I are going out
I can't either.
I'm invited to a birthday party.
Me too.
Okay. You all cancel.
What's this?
What is happening on that day?
Your wedding!
Wedding?! <i>Brought to you by the PKer team @ www.viikii.net
Welcome. Well what I want to do now is actually I'm going to use this graphing application to explore the trigonometric functions or explore the graphs of them. And just to start off or just to let you, this application
So let's start off just graphing some functions. Let's start off with the sine function. So let's say sine of x.
So when x is 0, y is also 0.
That the sine of 0 radians is 0. And now as we move on, or move along the curve, I have the trace function on. This is when x is equal-- if we look in the grey area at the bottom left it says 1.57.
If you're familiar with the-- 1.57 is more commonly known as what?
It's 1/2 of what famous number? Right. It's half of pi.
Let me see if I can-- no. I don't know how to trace the cosine function, so I'll just do it here.
Well, look at that. So the blue line is the tangent function. And why does it do this crazy thing?
Or since the y is the sine and cosine is the x, it also equals the sine over the cosine. So here, tangent is 0 whatever sine is 0 because that makes sense. Because tangent is equal to sine over cosine.
I drew the sine function before. Let me draw the sine of let's say, 2x. Whoops, that's not right. sine of 2-- maybe I need to put some parentheses in.
Let's start off with sine of x again. And now, instead of making the coefficient larger, let's make the coefficient less. Let's make it sine of 0.5x.
Look at that. Now, all of a sudden, it takes 4 pi radians to complete one cycle. And I want you to think about why that is.
Evaluate 1x when x is equal to -1,0,and 1.
So let's do the scenario x is equal to 1.
So 1x becomes 1 times.. one-which is now negative 1
So it's one times negative one.
There a couple of ways to think about it.
One times anything is going to be that anything.
So one times negative one is going to be equal to negative one
Another way you could have thought about it is that you could just look at the absolute value of each number so you say one times one is one they have different signs so it's going to be negative which have gotten you the same answer either way
So now with the scenario that x is equal to 0
So one times x is going to be the same thing as one times 0
We subsitute the 0 for x.
So once again,one times anything is going to be that anything.
This is going to become 0
Another way to think about this is that 0 times anything is going to become 0.
So either one of the ways of thinking about it would have gotten you the same answer.
Actually we can even write 1*x =x
So really when you value these numbers in x x is equal to -1,0 or1
It's going to equal that number one times anything is going to be that anything right overthere.
To make it clear 0 times anything is 0 (0x=0)
Just for good measure we kind or already went through the answers.
But let's try x is equal to 1
So this will give us 1 times 1 which you probably learned a while ago. 1 times anything is going to become that number! so it's equal to 1
20,000 years ago, the world suffered in the depths of the last ice age.
For several thousand years, global average temperatures stayed 15 degrees Fahrenheit, that's about 8 degrees celcius below what they're today, and mile thick glaciers covered much of North America, Europe, and Asia; outside the ice-covered regions, it was so dry that survival became difficult in most areas.
Some areas where people'd been living became inhospitable, and in some other places, new barriers of ice or desert separated groups of people, but against all odds, some people found ways to survive in severe conditions as far north as Siberia.
The ice age not only created barriers, it also created bridges with so much water locked up in ice, sea levels dropped, exposing land and connected Siberia and Alaska, a few people in Siberia took advantage of this bridge, moving into present-day Alaska, and later, down into other parts of North America, maybe they followed migrating herds or maybe, they traveled in small boats, down the Pacific coast, or maybe they did both.
No matter how they got there, those people who get there became the ancestors of today's Americans.
In just a short time, humans from a small corner of Africa had populated all continents except Antarctica, and in there new homes, their languages began to differentiate to form the precursors of today's languages.
Some populations probably didn't survived the ice age and those that did often became more isolated from other groups, scattered around the world, these small populations became more being culturally, and genetically distinct from one another.
How would cultural innovations helped a few of these groups to expand dramatically over the next several thousands years.
 Welcome back. I'm now going to do a bit of a review of everything we've
But anyway, so that's equal to the hypotenuse over the adjacent, which is equal to 1 over cosine of theta. And then, of course, cotangent of theta is equal to the adjacent over the opposite, which is equal to 1 over tan theta. And of course, that's also equal to cosine of theta over sine theta.
What I want to do in this video is one, just do a bunch of addition examples so that we really get some good practice and we really get warmed up with addition.
And what I even more want to show you is that we now have all the tools we need to really tackle any addition problem.
So let's just get warmed up with some one-digit addition problems, but these are the ones that always give me a
Let's start with a really, relatively straightforward one.
I want to say two plus four.
I don't think we need to draw the number line at this point, but you can if you need to remember this.
Two plus four is six.
What about nine plus three?
We saw that in the last video. Nine plus one is ten. Plus another one is eleven.
Nine plus three is twelve.
It's good to visualize what's happening here, but it's also not a bad idea to be able to do these very fast.
To be able to memorize, at least what the one-digit addition problems end up being.
Let's do a couple of harder ones.
Six plus seven.
But six plus seven is thirteen.
Eight plus six or six plus eight is going to be fourteen.
And that's the same thing as seven plus seven -- is also going to be fourteen.
And if you think about it, we got the same number here as there.
And it makes sense, right?
Because we took one away from eight, but we had one more than six.
That's why we got the same answer.
Let's just do a couple of more of these.
So eight plus eight is sixteen.
These are things that hopefully you'll be able to do super fast in the not too far off future.
Five plus six.
Well, that's eleven.
Let me just do a couple of more really fast.
So let's say seven plus nine is going to be sxiteen.
And that's going to be the same thing as eight plus eight, is also sixteen.
And then nine plus nine is eighteen.
And then nine plus eight is seventeen.
And that's just a little bit of warm up.
We didn't do all of the possible combinations of one-digit numbers, but these are some of the ones that give people a little bit more headache.
So now that we've done that let's tackle some larger digit numbers that we started doing in the previous video.
Let's do twenty-two plus three.
So we go to the ones place.
Two plus three is five.
We didn't have to carry anything.
And then in the tens place we just have this two sitting here.
Two plus nothing -- it's two tens.
It's two dimes.
So then we put that down there.
So we get twenty-five.
Two dimes and five pennies, or twenty-five cents depending -- a lot of people, money makes it easier to understand things or maybe to be motivated to understand things.
What is thirty-eight plus seventeen?
So we look at just the ones place.
What is eight plus seven?
We haven't done that one yet; I'll do it up here. Eight plus seven is equal to-- it's going to be one more than eight plus six.
Eight plus six is fourteen, then eight plus seven is going to be one more than that. So it's going to be equal to fifteen.
So in this problem we write the five here. Let me write this in a different color. So the five in the fifteen we'd write right down there in the ones place.
And we would carry the one because that's one dime.
That's one ten.
You know, this fifteen, this is ten plus five.
So this one really means one ten or one dime.
So we put that one up there in the tens place.
We have one plus three is four.
Plus one is five.
So you get fifty-five.
Thirty-eight plus seventeen is fifty-five.
Or five tens and five ones. That's the same thing as fifty-five.
Let's do a couple more problems.
Let's say we have forty-seven. Let me switch colors just so it stays interesting. Forty-seven plus nine.
We just look at the ones place.
Seven plus nine.
We know what that is already. We did that problem already.
Seven plus nine is sixteen.
So you write the six in the ones place and carry the one. And now it's in the tens place.
Because this is one ten right there.
So one dime plus four dimes is five dimes.
So it's five dimes and six pennies. It's fifty-six.
All right, let's do something hard.
Ninety-nine plus eighty-eight.
You say, what's nine plus eight?
We did that up here.
Nine plus eight we know already is seventeen.
Nine plus eight is seventeen, but it's always good to be able to visualize it as well.
So nine plus eight is seventeen.
Carry the one.
And then we have one plus nine is ten.
Ten plus eight is eighteen.
Now this is interesting.
So we write our eight down there.
We have one plus nine plus eight. One plus nine plus eight is equal to eighteen.
We wrote the eight down there and we say, let's carry the one. We carry the one, but we carry it into the hundreds place.
This was the ones place, the tens place, now we're in the hundreds place.
But there's nothing else in the hundreds place.
So it just drops straight down.
So you could almost just write the eighteen just like that.
So ninety-nine plus eighty-eight is one hundred and eighty-seven.
Let's keep doing some examples.
You could see, it's all the same pattern.
We could add two ten-digit numbers to each other as long as we're just careful about carrying our digits.
Let's do a four-digit number.
So let's do four thousand, three hundred and sixty-eight plus five hundred and seventy two.
I'll write it down here.
Eight plus two.
We know that that is equal to ten.
You can do the number line if you need to.
Eight plus two is equal to ten.
Put the zero in the ones place, carry the one. Now we're in the tens place.
This is really one ten.
This is six tens.
This is seven tens.
So one dime plus six dimes is seven dimes.
Seven dimes plus seven dimes is fourteen.
Let me write it like this.
We could write one plus six plus seven is equal to -- one plus six is seven. Seven plus seven is fourteen.
So this right here is going to be equal to fourteen.
Carry the one.
We have one plus three. We're in the hundreds place now. Plus five.
Well, one plus three is four. Plus five is nine.
Nothing to carry.
And then we go to the thousands place.
Nothing to add to the thousands place.
So you just take this four thousand -- you see a four here, but since it's in the fourth digit to the left, this means four thousand.
So this four thousand right here, we don't have any other thousands to add it to, so we just bring it straight down.
So four thousand, three hundred and sixty-eight plus five hundred and seventy-two is four thousand -- we'll put a comma there to make it easy to read -- four thousand, nine hundred and forty.
So, imagine you're standing on a street anywhere in America and a Japanese man comes up to you and says,
"Excuse me, what is the name of this block?"
And you say, "I'm sorry, well, this is Oak Street, that's Elm Street.
This is 26th, that's 27th."
He says, "OK, but what is the name of that block?"
You say, "Well, blocks don't have names.
Streets have names; blocks are just the unnamed spaces in between streets."
He leaves, a little confused and disappointed.
So, now imagine you're standing on a street, anywhere in Japan, you turn to a person next to you and say,
"Excuse me, what is the name of this street?"
They say, "Oh, well that's Block 17 and this is Block 16."
And you say, "OK, but what is the name of this street?"
And they say, "Well, streets don't have names.
Blocks have names.
Just look at Google Maps here.
There's Block 14, 15, 16, 17, 18, 19.
All of these blocks have names, and the streets are just the unnamed spaces in between the blocks.
And you say then, "OK, then how do you know your home address?"
He said, "Well, easy, this is District Eight.
There's Block 17, house number one."
You say, "OK, but walking around the neighborhood,
I noticed that the house numbers don't go in order."
He says, "Of course they do.
They go in the order in which they were built.
The first house ever built on a block is house number one.
The second house ever built is house number two.
Third is house number three.
It's easy.
It's obvious."
So, I love that sometimes we need to go to the opposite side of the world to realize assumptions we didn't even know we had, and realize that the opposite of them may also be true.
So, for example, there are doctors in China who believe that it's their job to keep you healthy.
So, any month you are healthy you pay them, and when you're sick you don't have to pay them because they failed at their job.
They get rich when you're healthy, not sick.
(Applause)
In most music, we think of the "one" as the downbeat, the beginning of the musical phrase: one, two, three, four.
But in West African music, the "one" is thought of as the end of the phrase, like the period at the end of a sentence.
So, you can hear it not just in the phrasing, but the way they count off their music: two, three, four, one.
And this map is also accurate.
(Laughter)
There's a saying that whatever true thing you can say about India, the opposite is also true.
So, let's never forget, whether at TED, or anywhere else, that whatever brilliant ideas you have or hear, that the opposite may also be true.
Domo arigato gozaimashita.
Hill tribes in the Golden Triangle were once cultivating opium as a cash crop.
In 1984, with the encouragement of the Thai monarch, King Bhumibol, they switched to Arabica Coffee.
So successful was this initiative that some of the best coffee in the world are to be found growing in this region.
In Doi Chaang or Elephant Mountain in Northern Thailand, the Akha hill tribes have been a role model for successfully cultivating, processing and marketing of their coffee worldwide.
Here, in the cool highlands, amidst pear, peach and macadamia nut plants,
Arabica coffee thrives best, producing coffee cherries that have a more complex and intense flavour, low in caffeine and therefore less bitter.
The Akha hill tribes together with other tribes have been living along the borders of Thailand, Laos and Myanmar for 2000 years.
Recently they have settled in Northern Thailand to avoid persecution and harassment from other Governments.
After 20 years of successful cultivation, the Akha villagers have established themselves as independent coffee producers building their own processing, R & D facilities and marketing outlets, selling their coffee throughout Thailand, Asia and America.
If you are searching for that best cup of coffee then you have to look no further than in the Golden Triangle.
If x is a whole number, what other sets does x belong to?
And we saw a couple of videos ago that I mentioned that the notion of the set of whole numbers is a little bit ambiguous.
Sometimes whole number means non-negative integers.
And sometimes it means all integers.
But in this context, and I actually looked at what the writers of this question are looking for and the standards that they care about.
So from their point of view, when they refer to whole numbers, they're referring to non-negative integers.
So they're referring to 0, 1, 2, 3, so on and so forth.
And I also looked at what they referred to-- And remember, this is just according to the writers of this question. This isn't according to how everyone views these things.
But they view natural numbers as just the positive numbers.
I told you two videos ago that some people view natural numbers as just the positive, but some people include 0 as a natural number.
But in this context it's just the positive integers.
I shouldn't have said positive numbers, I should have said positive integers.
It obviously doesn't include the numbers in between the integers.
So natural are there the numbers in this context.
You'll see other contexts where this would be described as natural.
In this context the natural numbers are 1, 2, 3, 4, so on and so forth.
And of course, there's no ambiguity about what integers are; everyone agrees on that.
Integers are-- you know, you could go arbitrarily negative and then negative 3, negative 2, negative 1, 0, 1, 2, 3.
And you can just keep going in the positive direction.
So if x is a whole number, when they say whole numbers they mean it is non-negative.
What other sets does x belong to?
Well, if it's a whole number, it's anyone of these numbers. And all of these numbers are also integers.
The set of whole numbers, by the convention they're using, is this set right here. It is a subset of integers.
So we know that x is also an integer. x is also a member of integers. That means a member, a member of a set. x is also a member of integers.
But it will not be a member of natural numbers, or at least the way that they've defined it.
Because x could be 0.
0 is considered a whole number, but if x were 0, it would not be a member of the natural numbers.
So we can't say it's natural.
All we can say is, that it's definitely integers, it's definitely rational.
Because any whole number, you can just divide it by 1 and represent it as a fraction.
So x is a member of rationals.
And of course, it's also a member of the real, which is the broadest set that we know of.
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So, we have a parallelogram right over here So, what we wanna prove is that it's diagonals bisect each other So, the first thing we can think about; these aren't just diagonals, these are lines that are intersecting parallel lines
So, angle DEC must be --- let me write this down --- angle DEC must be congruent to angle BAE
If we look this top triangle over here and this bottom triangle, we have one set of corresponding angles that are congruent We have a side in between that's going to be congruent Actually, let me write that down explicitly
What we know if two triangles are congruent, all of their corresponding features especially all of the corresponding sides are congruent So, we know that side EC corresponds to EA Or I could say side AE, we could say side AE,
corresponds to side CE They're corresponding sides of congruent triangle So, their measures or their lengths must be the same
let me focus on this -- we know that BE must be equal to DE Once again they're corresponding sides of two congruent triangles so they must have the same length So, this is corresponding sides of congruent triangles
We've showed that, look, diagonal DB is splitting AC into two segments of equal length and vice versa
AC is splitting DB into two segments of equal lengths So, they are bisecting each other Now, let's go the other way around
C -- label this point -- angle CED is going to be equal to or is congruent to angle, so I started is BEA, angle BEA And that, what is that, well that shows us that these two triangles are congruent 'cause we have a corresponding sides of a congruent and angle in between and on the other side So, we now know that the triangle, I'll keep this in yellow, triangle AEB is congruent to triangle DEC by side-angle-side congruency, by SAS congruent triangles
And this is just corresponding angles of congruent triangles And now we have this kind of transversal of these two lines that could be parallel if the alternate interior angles are congruent And we see that they are
by alternate interior angles congruent of parallel lines
And so we can then do the exact same -- while we just shown that these two sides are parallel -- we can do that exact same logic to show that these two sides are parallel
So, first of all, we know that this angle is congruent to that angle right over there And then we know, actually let me write it out, we know that angle AEC is congruent to angle DEB, I should say
They are vertical angles
And then we see that triangle AEC must be congruent to triangle DEB by side-angle-side So, then we have triangle AEC must be congruent to triangle
DEB by SAScongruency Now, we know that corresponding angles must be congruent So, that we know that angle, so, for example angle CAE
must be congruent to angle BDE and this is the corresponding angles of congruent triangles So, CAE, let me use a new color
CAE must be congruent to BDE And now we have a transversal The alternate interior angles are congruent
In this video we're going to talk about another way of visualizing data called the histogram, which is a very fancy word for a not so fancy thing.
I think it's probably fair to say that the histogram is the most used way of representing statistical data. Let me just show you how to figure out a histogram for some data, and I think you're going to get the point pretty easily. So I have some data here and I want to represent it with a histogram.
So I have the numbers 0, 1, 2, 3, 4-- we could even throw 5 in there, although 5 has a frequency of 0. And we have a 6. So the 0 showed up four times in this data set.
One, two, three, four, five, six, seven times. That's what we mean by frequency. Now a histogram is really just a plot, kind of a bar graph, plotting the frequency of each of these numbers.
Draw it just like that. 0 shows up four times. That is that information right there.
2-- I'll do it in a different color-- 2 shows up five times.
Do a bar graph, go all the way up to five. 2 shows up five times.
We have one 3, two 3's.
5 doesn't show up at all. So it doesn't even get any height there. And then finally, 6 shows up one time.
Very fancy word, but I think you will agree it's a fairly simple idea. Figure out the frequency of each of these numbers and then plot the frequency of each of these numbers and you get yourself a histogram.
We're asked to multiply 5/6 times 2/3 and then simplify our answer.
So let's just multiply these two numbers.
So we have 5/6 times 2/3.
Now when you're multiplying fractions, it's actually a pretty straightforward process.
The new numerator, or the numerator of the product, is just the product of the two numerators, or your new top number is a product of the other two top numbers.
So the numerator in our product is just 5 times 2.
So it's equal to 5 times 2 over 6 times 3, which is equal to: 5 times 2 is 10 and 6 times 3 is 18, so it's equal to 10/18.
And you could view this as either 2/3 of 5/6, or 5/6 of 2/3, depending on how you want to think about it.
And this is the right answer.
It is 10/18, but when you look at these two numbers, you immediately or you might immediately see that they share some common factors.
They're both divisible by 2, so if we want it in lowest terms, we want to divide them both by 2.
So divide 10 by 2, divide 18 by 2, and you get 10 divided by 2 is 5, 18 divided by 2 is 9.
Now, you could have essentially done this step earlier on.
You could've done it actually before we did the multiplication.
You could've done it over here.
You could've said, well, I have a 2 in the numerator and I have something divisible by 2 into the denominator, so let me divide the numerator by 2, and this becomes a 1.
Let me divide the denominator by 2, and this becomes a 3.
And then you have 5 times 1 is 5, and 3 times 3 is 9.
So it's really the same thing we did right here.
We just did it before we actually took the product.
You could actually do it right here.
So if you did it right over here, you'd say, well, look, 6 times 3 is eventually going to be the denominator.
5 times 2 is eventually going to be the numerator.
So let's divide the numerator by 2, so this will become a 1.
Let's divide the denominator by 2.
This is divisible by 2, so that'll become a 3.
And it'll become 5 times 1 is 5 and 3 times 3 is 9.
So either way you do it, it'll work.
If you do it this way, you get to see the things factored out a little bit more, so it's usually easier to recognize what's divisible by what, or you could do it at the end and put things in lowest terms.
I promised you that I'd give you some more Pythagorean theorem problems, so I will now give you more Pythagorean theorem problems.
And once again, this is all about practice. Let's say I had a triangle-- that's an ugly looking right triangle, let me draw another one --and if I were to tell you that that side is 7, the side is 6, and I want to figure out this side.
Well, we learned in the last presentation: which of these sides is the hypotenuse?
Well, here's the right angle, so the side opposite the right angle is the hypotenuse.
So what we want to do is actually figure out the hypotenuse. So we know that 6 squared plus 7 squared is equal to the hypotenuse squared.
And in the Pythagorean theorem they use C to represent the hypotenuse, so we'll use C here as well.
And 36 plus 49 is equal to C squared.
Or C is equal to the square root of 85.
And this is the part that most people have trouble with, is actually simplifying the radical.
So the square root of 85: can I factor 85 so it's a product of a perfect square and another number?
85 isn't divisible by 4.
So it won't be divisible by 16 or any of the multiples of 4.
5 goes into 85 how many times?
No, that's not perfect square, either. I don't think 85 can be factored further as a product of a perfect square and another number.
So you might correct me; I might be wrong. This might be good exercise for you to do later, but as far as I can tell we have gotten our answer.
And if we actually wanted to estimate what that is, let's think about it: the square root of 81 is 9, and the square root of 100 is 10 , so it's some place in between 9 and 10, and it's probably a little bit closer to 9.
So it's 9 point something, something, something.
And that's a good reality check; that makes sense.
If this side is 6, this side is 7, 9 point something, something, something makes sense for that length.
Let me give you another problem.
[DRAWlNG]
Let's say that this is 10 . This is 3.
What is this side?
First, let's identify our hypotenuse. We have our right angle here, so the side opposite the right angle is the hypotenuse and it's also the longest side.
So it's 10.
So 10 squared is equal to the sum of the squares of the other two sides.
This is equal to 3 squared-- let's call this A.
Pick it arbitrarily. --plus A squared.
Well, this is 100, is equal to 9 plus A squared, or A squared is equal to 100 minus 9.
A squared is equal to 91.
I don't think that can be simplified further, either.
3 doesn't go into it. I wonder, is 91 a prime number?
I'm not sure.
As far as I know, we're done with this problem.
Let me give you another problem, And actually, this time I'm going to include one extra step just to confuse you because I think you're getting this a little bit too easily.
Let's say I have a triangle. And once again, we're dealing all with right triangles now.
And never are you going to attempt to use the Pythagorean theorem unless you know for a fact that's all right triangle. But this example, we know that this is right triangle.
If I would tell you the length of this side is 5, and if our tell you that this angle is 45 degrees, can we figure out the other two sides of this triangle?
Well, we can't use the Pythagorean theorem directly because the Pythagorean theorem tells us that if have a right triangle and we know two of the sides that we can figure out the third side.
Here we have a right triangle and we only know one of the sides.
So we can't figure out the other two just yet.
But maybe we can use this extra information right here, this 45 degrees, to figure out another side, and then we'd be able use the Pythagorean theorem.
Well, we know that the angles in a triangle add up to 180 degrees.
Well, hopefully you know the angles in a triangle add up to 180 degrees.
If you don't it's my fault because I haven't taught you that already. So let's figure out what the angles of this triangle add up to.
Well, I mean we know they add up to 180, but using that information, we could figure out what this angle is.
Because we know that this angle is 90, this angle is 45.
So we say 45-- lets call this angle x; I'm trying to make it messy --45 plus 90-- this just symbolizes a 90 degree angle --plus x is equal to 180 degrees.
And that's because the angles in a triangle always add up to 180 degrees.
So if we just solve for x, we get 135 plus x is equal to 180. Subtract 135 from both sides.
We get x is equal to 45 degrees.
Interesting. x is also 45 degrees.
So we have a 90 degree angle and two 45 degree angles.
Now I'm going to give you another theorem that's not named after the head of a religion or the founder of religion.
I actually don't think this theorem doesn't have a name at.
All It's the fact that if I have another triangle --I'm going to draw another triangle out here --where two of the base angles are the same-- and when I say base angle, I just mean if these two angles are the same, let's call it a.
They're both a --then the sides that they don't share-- these angles share this side, right? --but if we look at the sides that they don't share, we know that these sides are equal.
Maybe I'll look it up in another presentation; I'll let you know.
But I got this far without knowing what the name of the theorem is.
And it makes sense; you don't even need me to tell you that.
If I were to change one of these angles, the length would also change.
Or another way to think about it, the only way-- no, I don't confuse you too much.
But you can visually see that if these two sides are the same, then these two angles are going to be the same. If you changed one of these sides' lengths, then the angles will also change, or the angles will not be equal anymore.
But I'll leave that for you to think about.
But just take my word for it right now that if two angles in a triangle are equivalent, then the sides that they don't share are also equal in length.
Make sure you remember: not the side that they share-- because that can't be equal to anything --it's the side that they don't share are equal in length.
So here we have an example where we have to equal angles.
They're both 45 degrees. So that means that the sides that they don't share-- this is the side they share, right?
Both angle share this side --so that means that the side that they don't share are equal.
So this side is equal to this side. And I think you might be experiencing an ah-hah moment that right now.
Well this side is equal to this side-- I gave you at the beginning of this problem that this side is equal to 5 --so then we know that this side is equal to 5.
And now we can do the Pythagorean theorem.
We know this is the hypotenuse, right?
So we can say 5 squared plus 5 squared is equal to-- let's say
C squared, where C is the length of the hypotenuse --5 squared plus 5 squared-- that's just 50 --is equal to C squared.
And then we get C is equal to the square root of 50. And 50 is 2 times 25, so C is equal to 5 square roots of 2.
Interesting. So I think I might have given you a lot of information there. If you get confused, maybe you want to re-watch this video.
But on the next video I'm actually going to give you more information about this type of triangle, which is actually a very common type of triangle you'll see in geometry and trigonometry 45, 45, 90 triangle.
Welcome to the playlist on statistics.
Something I've been meaning to do for some time.
So anyway, I just want to get right into the meat of it and I'll try to do as many examples as possible and hopefully give you the feel for what statistics is all about.
And, really, just to kind of start off in case you're not familiar with it -- although, I think a lot of people have an intuitive feel for what statistics is about.
And essentially -- well in very general terms it's kind of getting your head around data.
And it can broadly be classified. Well there are maybe three categories.
You have descriptive.
So say you have a lot of data and you wanted to tell someone about it without giving them all of the data.
Maybe you can kind of find indicative numbers that somehow represent all of that data without having to go over all of the data.
That would be descriptive statistics.
There's also predictive.
Well, I'll kind of group them together.
There's inferential statistics.
And this is when you use data to essentially make conclusions about things.
So let's say you've sampled some data from a population -- and we'll talk a lot about samples versus populations but
I think you have just a basic sense of what that is, right?
If I survey three people who are going to vote for president, I clearly haven't surveyed the entire population.
I've surveyed a sample.
But what inferential statistics are all about are if we can do some math on the samples, maybe we can make inferences or conclusions about the population as a whole.
Well, anyway, that's just a big picture of what statistics is all about.
Let's just get into the meat of it and we'll start with the descriptive.
So the first thing that, I don't know, that I would want to do or I think most people would want to do when they are given a whole set of numbers in they're told to describe it. Well, maybe I can come up with some number that is most indicative of all of the numbers in that set.
Or some number that represents, kind of, the central tendency
-- this is a word you'll see a lot in statistics books.
The central tendency of a set of numbers.
And this is also called the average. And I'll be a little bit more exact here than I normally am with the word "average." When I talk about it in this context, it just means that the average is a number that somehow is giving us a sense of the central tendency. Or maybe a number that is most representative of a set.
So there's a bunch of ways that you can actually measure the central tendency or the average of a set of numbers.
And you've probably seen these before.
They are the mean. And actually, there's types of means but we'll stick with the arithmetic mean. geometric means and maybe we'll cover the harmonic mean one day.
There's a mean, the median, and the mode.
And in statistics speak, these all can kind of be representative of a data sets or population central tendency or a sample central tendency.
And they all are collectively -- they can all be forms of an average.
And I think when we see examples, it'll make a
little bit more sense.
In every day speak, when people talk about an average, I think you've already computed averages in your life, they're usually talking about the arithmetic mean. So normally when someone says, "Let's take the average of these numbers." And they expect you to do something, they want you to figure out the arithmetic mean.
They don't want you figure out the median or the mode. But before we go any further, let's figure out what these things are. Let me make up a set of numbers.
Let's say I have the number 1.
Let's say I have another 1, a 2, a 3. Let's say I have a 4. That's good enough.
And that's essentially -- you add up all the numbers and you divide by the numbers that there are.
So in this case, it would be 1 plus 1 plus 2 plus 3 plus 4. And you're going to divide by one, two, three, four, five numbers. It's what?
1 plus 1 is 2. 2 plus 2 is 4. 4 plus 3 is 7.
That's the number that all of these numbers you can kind of say are closest to." Or, 2.2 represents the central tendency of this set.
And in common speak, that would be the average.
But if we're being a little bit more particular, this is the arithmetic mean of this set of numbers. And you see it kind of represents them. If I didn't want to give you the list of five numbers, I could say, "Well, you know, I have a set of five numbers and their mean is 2.2." It kind of tells you a little bit of at
So that's one measure.
Another measure, instead of averaging it in this way, you can average it by putting the numbers in order, which I actually already did.
So let's just write them down in order again.
1, 1, 2, 3, 4.
And you just take the middle number.
So let's see, there's one, two, three, four, five numbers.
So the middle number's going to be right here, right?
The middle number is 2.
There's two numbers greater than 2 and there's two numbers less than 2.
And this is called the median. So it's actually very little computation.
You just have to essentially sort the numbers. And then you find whatever number where you have an equal number greater than or less than that number.
So the median of this set is 2.
And you see, I mean, that's actually fairly close to the mean.
And there's no right answer.
One of these isn't a better answer for the average.
They're just different ways of measuring the average. So here it's the median.
And I know what you might be thinking. "Well, that was easy enough when we had five numbers.
What if we had six numbers?" What if it was like this?
What if this was our set of numbers? 1, 1, 2, 3, let's add another 4 there.
So now, there's no middle number, right?
I mean 2 is not the middle number because there's two less than and three larger than it.
And then 3's not the middle number because there's three larger and -- sorry, there's two larger and three smaller than it.
So there's no middle number.
So when you have a set with even numbers and someone tells you to figure out the median, what you do is you take the middle two numbers and then you take the arithmetic mean of those two numbers.
So in this case of this set, the median would be 2.5. Fair enough.
But let's put this aside because I want to compare the median and the means and the modes for the same set of numbers. But that's a good thing to know because sometimes it can be a little confusing. And these are all definitions.
Anyway, before I talk more about that, let me tell you what the mode is. And the mode to some degree, it's the one I think most people probably forget or never learn and when they see it on an exam, it confuses them because they're like, "Oh, that sounds very advanced." But in some ways, it is the easiest of all of the measures of central tendency or of average.
The mode is essentially what number is most common in a set.
So in this example, there's two 1's and then there's one of everything else, right?
So the mode here is 1. So mode is the most common number. And then you could kind of say, "Whoa, hey Sal, what if this was our set?
1, 1, 2, 3, 4, 4." Here I have two 1's and I have two 4's.
And this is where the mode gets a little bit tricky because either of these would have been a decent answer for the mode. You could have actually said the mode of this is 1 or the mode of this is 4 and it gets a little bit ambiguous. And you probably want a little clarity from the person asking you.
Most times on a test when they ask you, there's not going to be this ambiguity.
There will be a most common number in the set. So now it's like oh, well you know, why wasn't just one of these good enough?
You know why we learned averages, why don't we just use averages?
Or why don't we use arithmetic mean all the time?
What's median and mode good for?
Well, I'll try to do one example of that and see if it rings true with you. And then you can think a little bit more.
Let's say I had this set of numbers.
3, 3, 3, 3, 3, and, I don't know, 100.
So what's the arithmetic mean here?
I have one, two, three, four, five 3's and 100.
So it would be 115 divided by 6, right? I could have one, two, three, four, five, six numbers. 115 is just the sum of all of these.
So it's equal to 19 1/6. Fair enough.
I just added all the numbers and divided by how many there are.
But my question is, is this really representative of this set? I mean, I have a ton of 3's and then I have 100 all of a sudden, and we're saying that the central tendency is 19 1/6. And, I mean, 19 1/6 doesn't really seem indicative of the set.
I mean, my intuition would be that the central tendency is something closer to 3 because there's a lot of 3's here.
So what would the median tell us?
I already put these numbers in order, right?
If I give it to you out of order, you'd want to put it in this order and you'd say what's the middle number?
Let's see, the middle two numbers, since I have an even number, are 3 and 3.
So if I take the average of 3 and 3 -- or I should be particular with my language. If I take the arithmetic mean of 3 and 3, I get 3.
And this is maybe a better measurement of the central tendency or of the average of this set of numbers, right?
Essentially, what it does is by taking the median, I wasn't so much affected by this really large number that's very different than the others.
In statistics they call that an outlier.
A number that, you know, if you talked about average home prices, maybe every house in the city is $100,000 and then there's one house that costs $1 trillion.
And then if someone told you the average house price was, I don't know, $1 million, you might have a very wrong perception of that city.
But the median house price would be $100,000 and you get a better sense of what the houses in that city are like.
So similarly, this median, maybe, gives you a better sense of what the numbers in this set are like.
Because the arithmetic mean was skewed by this, what they call an outlier. And being able to tell what an outlier is, it's kind of one of those things that a statistician will say, well, I know it when I see it.
There isn't really a formal definition for it but it tends to be a number that really kind of sticks out and sometimes it's due to, you know, a measurement error or whatever.
And then finally, the mode.
What is the most common number in this set? Well there's five 3's and there's 100.
So the most common number is, once again, it's a 3.
So in this case, when you had this outlier, the median and the mode tend to be, you know, maybe they're a little bit better about giving you an indication of what these numbers represent.
If these are house prices, then I would argue that these are probably more indicative measures of what the houses in a area cost.
But if this is something else, if this is scores on a test, maybe, you know, maybe there is one kid in the class -- one out of six kids who did really, really well and everyone else didn't study.
And this is more indicative of, kind of, how students at that level do on average.
Anyway, I'm done talking about all of this.
And I encourage you to play with a lot of numbers and deal with the concepts yourself.
In the next video, we'll explore more descriptive statistics.
Instead of talking about the central tendency, we'll talk about how spread apart things are away from the central tendency.
See you in the next video.
Based on the examples in the last video let's see if we can come up with some rules of thumb for figuring out how many significant figures, or how many significant digits, there are in a number - or a measurement.
So the first thing that is pretty obvious is that any non-zero digit, and any of the zero digits in between are significant.
Really the 7 and the 5 here are significant and the zero's in between them, it's also going to be significant.
So let's write this over here: so, any non-zero digits and zero's in between are going to be significant.
That's pretty straightforward. Now the zero's that are not in between non-zero digits, these become a little bit more confusing.
So let's just make sure we can rule out some of them.
So you can always rule out - when you're thinking about significant figures - the leading zero's.
And when I talk about leading zero's, I'm talking about the zero's that come before your non-zero digit.
So these are leading zero's here, these are leading zero's.
There's no leading zero's here, no leading zero's in this one, this one, and this one.
But in any situation, the leading zero's are not significant.
So leading zero's not significant.
And so the last question, all you have left, I mean, you only have non-zero digits and zero's in between; you could have some leading zero's which you've already said are not significant.
And so the only thing left that you have to figure out is what do you do with the trailing zero's, the zero's behind the last non-zero, or to the right of, the last non-zero digit.
So that these trailing zero's here, there's actually two trailing zero's over, and then there is three trailing zero's over here.
So let me make a little... so trailing zero's.
What do we do with them?
So the easy way to think about is, if you have a decimal, if there is a decimal anywhere in your number, count them.
If you have a decimal count them as significant. they are significant. Count them as significant.
If there is no decimal anywhere in the number, then it's kind of ambiguous.
You're kind of not sure, and this is the situation.
So clearly, over here, there's a decimal in the number so you count the trailing zeros - these are adding to the precision.
Over here, there's a decimal so you count the trailing zero.
There's a decimal here so you count the trailing zero's.
There are no trailing zero's here.
And over here, well the way I later put a decimal here, here you would count it, so if you have a decimal there you would count all five.
If you didn't have the decimal, if you just had 37,000 like that it's ambiguous, and if someone doesn't give you more information you're best assumption is probably that they just measured to the nearest thousand, that they didn't measure exactly to the one and just happened to get exactly on 37,000.
So if there's no decimal, let me write it this way, it's ambiguous, which means that you're really not sure what it means, it's not clear what it means, and you're proabably safer assuming to not count the trailing zero's.
If someone really does measure, if you were to really measure something to the exact one, then you should put a decimal at the end like that.
And there is a notation for specifying: let's say you do measure - let me do a different number - let's say you do measure 56,000 and there is a notation for specifying that 6 definitely is the last significant digit and sometimes you'll see a bar put over the 6, sometimes you'll see a bar put under the 6.
And that could be useful, because maybe, you're last significant digit is this zero over here, maybe you were able to measure to the 100's with a reasonable level of precision.
And so then you would write something like, you'd still write 56,000, but then you would put the bar above that zero or the bar below that zero to say that that was the last significat digit.
So if you saw something like this, you would say 3 significant digits.
This isn't used so frequently. A better way to show that you've measured to 3 significant digits would be to write it in scientific notation.
There's a whole video on that.
But to write this in scientific notation, you could write this as 5.60 times 10 to the fourth power, right?
Cause if you multiply this by 10 to the fourth you'd move this decimal over four spaces and get us to 56,000.
So 5.60 times 10 to the fourth; and if this confuses you, watch the video on scientific notation.
Hopefully it will clarify things a little bit.
But when you write a number in scientific notation, it makes it very clear about your precision and how many significant digits you're dealing with.
So instead of doing this notation that's a little bit outdated,
I haven't seen it used much, with these bars below or above the high significant digit, instead you can represent it with a decimal in scientific notation and then it's very clear you have 3 significant digits.
So hopefully that helps you out.
In the next couple of videos, we'll explore a little bit more why significant digits are important especially when you do calculations with multiple measurements.
Find the volume of a sphere with a diameter of 14 centimeters. So if I have a sphere, so this isn't just a circle.
This is a sphere.
You can view it as a globe of some kind.
So i'm gonna shad it a little bit so you can tell it's three-dimensional.
They're giving us the diameter so if we go from on side of the sphere straight through the center of it, so we're imagining we can see through the sphere.
And we go straight through the centimeter that distance right over there is 14 centimeters.
Now, to find the volume of a sphere, we prove this or you will see a proof for this later when you learn calculus, but the formula for the volume of a sphere is volume is equal to 4 thirds pi*r^3.
So they 've given us the diameter and just like for circles, the radius of the sphere, the radius of the sphere is half the diameter.
So in this example, our radius is going to be 7 centimeters.
In fact, the sphere itself is the set of all points in three dimensions that is exactly the radius away from the center.
With that out of the way, let's just apply this radius being 7 centimeters to this formular right over here.
So we're going to have a volume is equal to 4 thirds pi*7. cm^3.
And, since it already involves pi, and you can approximate pi with 3.14, some people even approximate it with 22/7, but we'll actually just get the calculator out to get the exact value for this volume.
My volume is going to be 4/3...And then I don't want to just put a pi there because that might interprit it as 4 divided by 3 pi.
So four divided by three times pi times seven to the third power. In order of operations it will do the exponent first so this should work out.
An the units are going to be in centimeters cubed or cubic centimeters.
So we get 1436, they don't tell us what to round it to so I'll just round it to the nearest tenth. 1436.8 So this is equal to 1436.8 centimeters cubed.
And we're done!
The beginning of any collaboration starts with a conversation.
And I would like to share with you some of the bits of the conversation that we started with.
I grew up in a log cabin in Washington state with too much time on my hands.
Yves Behar:
And in scenic Switzerland for me.
FN:
I always had a passion for alternative vehicles.
This is a land yacht racing across the desert in Nevada.
YB:
Combination of windsurfing and skiing into this invention there.
FN:
And I also had an interest in dangerous inventions.
This is a 100,000-volt Tesla coil that I built in my bedroom, much to the dismay of my mother.
YB:
To the dismay of my mother, this is dangerous teenage fashion right there.
(Laughter)
FN:
And I brought this all together, this passion with alternative energy and raced a solar car across Australia -- also the U.S. and Japan.
YB:
So, wind power, solar power -- we had a lot to talk about.
We had a lot that got us excited.
So we decided to do a special project together.
To combine engineering and design and ...
FN:
Really make a fully integrated product, something beautiful.
YB:
And we made a baby.
(Laughter)
FN:
Can you bring out our baby?
(Applause)
This baby is fully electric.
It goes 150 miles an hour.
It's twice the range of any electric motorcycle.
Really the exciting thing about a motorcycle is just the beautiful integration of engineering and design.
It's got an amazing user experience.
It was wonderful working with Yves Behar.
He came up with our name and logo.
We're Mission Motors.
And we've only got three minutes, but we could talk about it for hours.
YB:
Thank you.
FN:
Thank you TED.
And thank you Chris, for having us.
(Applause)
In this video I want to talk a little bit about what it means to be a prime number and what you will hopefully see in this video is this pretty straightforward concept but as you progress through your mathematical career you'll see that there is actually fairly sophisticated concepts that can be built on top of the idea of the prime number and that includes the idea of cryptography and maybe some of the encryption that your computer uses right now could be based on prime numbers.
If you don't know what encryption means you don't have to worry about it right now you just need to know that prime numbers are pretty important.
So I'll give you the definition and the definition might be a little confusing but when we see it with examples it should be pretty straightforward
A number is prime if it is a natural number for example 1, 2 or 3 (the counting numbers starting at 1) or you could also say "the positive integers" it is a natural number divisible by exactly two natural numbers: itself and 1.
Those are the two numbers that it's divisible by. If this does not make sense for you lets just do some examples.
Lets figure out if some numbers are prime or not.
So lets start with the smallest natural numbers.
The number 1.
So you might say "1 is divisible by 1" and "1 is divisible by itself", hey!
1 is a prime number! But remember, part of our definition, it needs to be divisible by exactly two natural numbers.
1 is divisible only by one natural number, only by 1.
So 1, even it may be a little counter intuitive, is not prime.
Lets move on to 2.
So 2 is divisible by 1 and by 2, and not by any other natural numbers.
So it seems to fit our constraints.
It's divisible by exactly two natural numbers.
Itself and 1. So the number 2 is prime.
I will circle the numbers that are prime.
The number 2 is interesting because it's the only even number that is prime.
If you think about it, any other even number is also going to be divisible by 2., so it won't be prime.
We'll think about that more in future videos. Lets try out 3.
Well, 3 is definitely divisible by 1 and 3 and it's not divisible by anything in between. it's not divisible by 2.
So 3 is also a prime number.
Lets try 4.
4 is definitely divisible by 1 and 4, but it's also divisible by 2.
So it's divisible by three natural numbers:
1, 2 and 4.
So it does not meet our constraints for being prime.
Lets try out 5. 5 is definitely divisible by 1,
It's not divisible by 2, 3 or 4 (you could divide 5 / 4 but you would get a remainder) And it is exactly divisible by 5, obviously.
So once again, 5 is divisible by exactly two natural numbers:
So once again, 5 is prime.
Lets keep going, so that we see if there is any kind of a pattern here and then maybe I'll try a really hard one that tends to trip people up.
So lets try the number 6.
It is divisible by 1, 2, 3 and 6.
So it has four natural number "factors", I guess you could say it that way
So it does not have exactly two numbers that it's divisible by, it has four, so it is not prime. Lets move on to 7.
7 is divisible by 1, not 2, 3, 4, 5 or 6, but it's also divisible by 7 so 7 is prime.
How many natural numbers, numbers like 1, 2, 3, 4, 5, the numbers that you learn when you are two years old not including zero, not including negative numbers, not including fractions and irrational numbers, and decimals and all the rest, just regular counting positive numbers.
If you have only two of them, if you are only divisible by yourself and by 1, then you are prime. and the way I think about it, if we don't think of the special case of 1, prime numbers are kind of these building blocks of numbers.
You can't break them down anymore. They are almost like the atoms.
If you think about what the atom is, or what people thought atoms were when they first... they thought they were these things you couldn't divide anymore.
We now know we could divide atoms and actually if you do you may create a nuclear explosion. But it's the same idea behind prime numbers.
In theory, no prime number is not a theory.
You can't break them down into products of smaller natural numbers.
Things like 6 you can say, hey, 6 is 2 times 3, you can break it down, and notice, we can break it down as a product of prime numbers.
We've kind of broken it down into it's parts. 7 you can't break it down anymore.
All you can say is 7 equals 1 times 7.
And in that case you haven't really broken it down much. You just have the 7 there again. 6 you can actually break it down.
4 you can actually break it down as 2 times 2.
Now with that out of the way lets think about some larger numbers, and think about whether those larger numbers are prime.
So lets try 16.
So clearly any natural number is divisible by 1 and itself.
So you are going to start with two, so if you can find anything else that goes into this then you know you are not prime.
And for 16 you could have 2 times 8, you can have 4 times 4, so it has a ton of factors here, above and beyond just the 1 and 16.
So 16 is not prime.
What about 17?
1 and 17 will definitely go into 17, 2 doesn't go into 17, 3 doesn't go, 4, 5, 6, 7, 8, ... none of those numbers, nothing between 1 and 17 goes into 17, so 17 is prime.
And now I'll give you a hard one.
This one can trick a lot of people.
What about 51?
Is 51 prime?
And if you are interested you can pause the video here and try to figure out by yourself if 51 is a prime number.
If you can find anything other than 1 or 51 that is divisible into 51. It seems like... wow this is kind of a strange number
You might be tempted to think it's prime, but I'm now going to give you the answer.
It is not prime, because it is also divisible by 3 and 17 3 times 17 is 51.
So hopefully this gives you a good idea of what prime numbers are all about, and hopefully we can give you some practice on that in future videos and maybe in some of our exercises.
I've got a square here.
What makes it a square is all of the sides are equal.
I haven't gone in depth into angles yet, but these are at right angles to each other.
That means that if this bottom side goes straight left and right, that this left side will go straight up and down.
That's all the right angle really means.
Let's say that the side down here is equal to 8 meters.
And this is a square.
And I were to ask you what is the area of the square?
Well, the area is essentially how much space the square takes up, let's say, on your screen right now.
So it's essentially a way of measuring how much space something takes up on kind of a two-dimensional surface.
A two-dimensional surface would just be this computer screen or your piece of paper, if you're also doing this problem.
An analogy would be if you had an 8 meter by 8 meter room, how much carpeting would you need is kind of the size of the space you need to fill out in two dimensions on some type of surface.
So the area here is literally how much is this size that you're filling up, and it's very easy to figure out for a square.
It's literally going to be your base times your height -- and this is true for any rectangle -- but since this is a square, your base and your height are going to be the same number.
It's going to be 8 meters.
So your area is going to be 8 meters times 8 meters, which is equal to 8 times 8 is 64, and then your meters times your meters -- you have to do the same thing with your units -- you get 64 meters squared.
You might be asking where are those 64 square meters?
Well, you can actually break it out here.
So let me draw it a little bit bigger than
So let's say that's my same square.
I'm going to draw a little bit, so let me divide it in the middle.
Let me see, I have -- and we divide them again.
Then we divide each side again just like that.
Divide these just like that, and then divide these just like that.
There you go.
Now the reason why I did this is to show you the dimensions along the base and the height.
We said this is 8 meters, and notice I have 1, 2, 3, 4, 5, 6, 7, 8 meters.
And the same thing along this side. 1, 2, 3, 4, 5, 6, 7, 8 meters.
So when we're talking about 64 square meters, we're literally counting each of the square meters.
A square meter is a two-dimensional measurement, that's 1 meter on each side.
That's 1 meter, that's 1 meter.
What I'm shading here in yellow is 1 square meter.
And you could imagine just counting the square meters.
In each row we're going to have 1, 2, 3, 4, 5, 6, 7, 8 square meters.
And then we have 8 rows.
So we're going to have 8 times 8 square meters or 64 meters square.
Which is essentially if you sat here and just counted each of these, you would count 64 square meters.
Now, what happens if I were to ask you the perimeter of my square?
The perimeter is the distance you need to go to go around the square. It's not measuring, for example, how much carpeting you need.
It's measuring, for example, if you wanted to put a fence around your carpet -- I'm kind of mixing the indoor and outdoor analogies -- it would be how much fencing you would need. So it would be the distance around.
So it would be that distance plus that distance plus that distance plus that distance.
But we already know this distance right here on the bottom, we already know this distance is 8 meters.
Then we know that the height right here is 8 meters.
It's a square. This distance up here is going to be the same as this distance down here -- it's going to be another 8 meters.
Then when you go down the left hand side it's going to be another 8 meters.
We have four sides -- 1, 2, 3, 4 -- each of them are 8 meters.
So you add 8 to itself 4 times, that's the same thing as 8 times 4, you get 36 meters.
Now notice, when we measured just the amount of fencing we needed, we ended up just with meters, just with kind of a one-dimensional measurement.
That's because we're not measuring square meters here. We're not measuring how much area we're taking up.
We're measuring a distance -- a distance to go around.
We are taking turns, but you can imagine straightening out this fence, and it would just become one big fence like this, which would have the same length of 36 meters.
So that's why we just have meters there for perimeter.
But for area we got square meters, because we're counting these two-dimensional measurements.
What happens if instead of a square I have a rectangle like this?
Let's say that this side over here is 7 centimeters. And let's say that the height right here is 4 centimeters.
So what is the area of this rectangle going to be?
It's going to be 7 times 4 centimeters. 7 centimeters times 4 centimeters.
Remember, we could draw 7 rows, right, and each of them is going to have 4 square centimeters -- each of those is a square centimeter.
So if you were to count them all out, you'd have 7 times 4 square centimeters.
So it's equal to 28 centimeters square or squared centimeters.
What's the perimeter?
Well, it's going to be equal to this distance down here, which is 7 centimeters, plus this distance over here which is 4 centimeters, plus the distance on the top -- this is a rectangle, it's going to be the same distance as this one over here.
So plus another 7 centimeters. Then you're going to have this distance on the left hand side. But this distance on the left hand side is the same as this distance right here -- this is also 4 centimeters.
So plus another 4 centimeters.
And what do you get?
You get 7 plus 4 which is 11, and then you have another 7 plus 4. You have 11 plus 11, so you have 22 centimeters.
Once again, it's not a square centimeter.
Now let's divert -- let's go away from our rectangle analogy or our rectangle examples.
That's my triangle.
And let's say that this distance right here is 7 centimeters right down there.
And let's say that the height of this triangle is 4 centimeters.
And I were to ask you what is the area of the triangle?
Well, when we had a rectangle like this, we just multiplied 7 times 4.
But what would that give us? That would give us the area of an entire rectangle. If we did 7 times 4, that would give us the area of this entire rectangle.
You could imagine extending my triangle up like this.
So you could almost view it as it's 1/2 of this rectangle. Not really almost, it is.
Because if you just double this guy, you could imagine if you flip this triangle over, you get the same triangle but it's just upside down and flipped over.
So if you think about when you multiply 7 times 4, you're getting the area of this entire rectangle, which we just did up here.
We want to know just this area right here.
You can see, hopefully, from this drawing that the area of this triangle is exactly 1/2 of the area of the entire rectangle.
So the area for a triangle is equal to the base times the height -- now this so far, base times height is the area of a rectangle. So in order to get the area of the triangle, you're going to multiply that times 1/2.
So 1/2 base times height.
So in our example it's going to be 1/2 times 7 centimeters times 4 centimeters.
We know what 7 times 4 is. We already know it's 28 centimeters -- we did that up there.
So this right here is 28 centimeters.
Then we want centimeters and we want to multiply that by 1/2. So that's going to be 14 centimeters just like that.
So the area of this triangle is exactly 1/2 of the area of that rectangle.
Now, the perimeter of this triangle becomes a little bit more complicated because figuring out this distance isn't the easiest thing in the world.
Well, it will be easy for you once you get exposed to the Pythagorean Theorem.
Let me just give you one more area of a triangle. Let's say I have a triangle that looks like this.
Let's say we had a triangle that looks like this. It's a little bit more skewed looking like this.
And let's say that this distance down here is 3 meters -- that distance is 3 meters.
Let's say we don't know what that distance is and we don't know what that distance is.
But we do know that if we were to kind of drop a line straight down like this -- if you imagine this was a building or some type of mountain and you just drop something straight down onto the ground like that, we know that this distance is equal to -- let's say it's equal to 4 meters.
Well, we apply the same formula.
Area is equal to 1/2 base times height.
So 1/2 times 3 times 4.
Which is equal to 3 times 4 is 12 times 1/2 is equal to 6.
We're going to be dealing with square meters.
I really want to highlight the idea, because if I gave you a triangle that looked like this, where if this was 3 meters down here, and then if I were to tell you that this side over here is 4 meters, this is not something that you can just apply this formula to and figure out.
In fact, you'd have to know some of the angles and whatnot to really be able to figure out the area, or you'd have to know this other side here.
So this is not easy.
You have to know what the altitude or the height of the triangle is.
In this case, it was one of the sides, but in this case it's not one of the sides.
You'd have to figure out what that side right there on the right hand side is in order to apply this formula.
Translated by (your name here) Last time...
It was supposed to be a standard mission.
Get in.
Get out.
Get paid.
Now my men are dead.
Who killed my mates?
The name is Bobby-
Kotickovich!
ActivistSun is proud to announce our acquisition of Outer Heaven.
Liquid and Makarov are creating a new weapon.
Modern Gear!
The Boss is arming Modern Gear as we speak.
Act 3:
Sun Down
Sorry it's taken so long.
But I've finally found him.
That bastard who betrayed us.
His name...is Bobby Kotickovich.
Isn't he that guy that clubs baby seals?
Well, yes, but he's also the head of ActivistSun.
A powerful shadow military.
And it's our job to bring them to light.
Kotickovich has stayed one step ahead of us. But we've tracked him down.
Booyah!
It wasn't hard to follow the trail of bodies.
We believe he's using this abandoned arms depot to launch his new weapon.
Modern Gear!
Once Modern Gear is finished, Kotickovich will be unstoppable.
We have to face reality.
It's unlikely that you'll be coming back from this mission.
But when they speak of this moment
It won't be us that stood idly by while Kotickovich destroys everything we stand for.
Snake.
Ghost.
The fate of the world is in your hands now.
I won't stop until I've brought that bastard down.
I swear it.
You will be avenged.
No matter what the cost.
Even if I have to sacrifice everything.
We're not sending you in empty-handed.
We've been working on some new gear for you.
Whoah, what is it!?
I hope it's a puppy. I'm gonna name it Solid Dog.
(Ghost:) Oh yeah, nice one brother!
Whoah!
Sweet!
Thanks Naomi!
We got something for you too, Ghost.
Oh thanks mate, you shouldn't have-
-Uhhhhh. . . . .alright.
It's a bit small, innit?
Uhh...
I thought they'd go well with your mask.
(sigh)
Well, try them on!
(sigh) (Snake hums)
This may be a suicide mission.
But the world will remember us...for this.
We...will...kill him!
(Snake:) In position.
Don't you just love this weather?
Make's you feel good to be alive.
Hey, what is that?
Awww, it's just a box.
What's it doing out here?
Beats me.
Did you order anything?
No.
Hey, you cardboard son of a-
Hello!
Sleepy time!
Moving out.
Got you covered!
Let's go.
Clear!
Watch your corners.
Kotickovich could be anywhere.
I'm gonna kick his puny ass.
Clear!
Whoah.
Do you hear something?
(industrial noises)
Holy --CENSORED-- What is that!?
Modern Gear
Oh, this was a bad idea.... (snake groans)
Well well well, look what we have here!
Snake and Ghost!
Kotickovich!
We have some unfinished business, you and I, Ghost!
Right, I forgot to send you back to hell!
Seriously, is that it?
Is that all you got?
My turn!
Aw crap.
How do you not see him!?
Where are you going, Ghost?
(evil laughter)
No.
No!
NO!
Oy, toaster oven!
Where's my pop-tarts?
Hey, that's not my name!
No-no-no-no-no-no-no-no!
Die already!
Oh crap!
Stop hiding, Ghost!
Oh no.
Damn it!
This is not gonna work.
Oh crap- oh crap- oh crap- oh crap- oh crap- oh crap!
Oh this is not fair!
Come on Ghost!
No.
It can't end like this.
(Ghost yells)
Ghost!
Come out and play!
I'm gonna finish what I started with your team!
What's this?
(Ghost laughs) Oh yeah!
It's been a long time, old friend. On the next episode...
Translated by (your name here).
Let's say we have two lines over here.
Let's call this line right over here line AB.
So A and B both sit on this line.
And let's say we have this other line over here.
We'll call this line CD.
So it goes through point C and it goes through point D and it just keeps on going forever.
Now let's say that these lines both sit on the same plane and in this case the plane is our screen or this little piece of paper we're looking at right over here.
And they never intersect!
They never intersect.
So they're on the same plane but they never intersect each other.
If those two things are true, their not the same line, they never intersect, they can be on the same plane, then we say that these lines are parallel.
They are moving in the same general direction, in fact the exact same general direction, if we are looking at it from an algebraic point of view, we would say they have the same slope, but they have different intersect, they involve different points.
If we do accorded axes here they would intersect that in a different point but they would have the same exact slope.
What I want to do is think how angles relate to paralel lines.
So right over here we have this two paralel lines.
We can say that line AB is paralel to line CD
Sometimes you'll see it specified on geometric drawings like this.
I'll put a little arrow here to show that this two lines are paralel and if you already used the single arrow then you might put a double arrow to show that this line is paralel to that line right over there.
Now what I want to do is draw a line that intersects both of this paralel lines.
So here's a line that intersects both of them.
Let me draw it a bit near than that.
And I'll just call that line "L".
And this line that intersects both of this paralel lines we call that a transversal.
This is a transversal line.
It's transversing both of this paralel lines.
And what I want to think about is the angles that are formed and how they relate to each other.
The angles that are formed at intersection between this transversal line and the two paralel lines.
So we can first of all start of this angle right over here.
That angle right over there we can call that angle... well if we make some labels here that would be D, this point and then something else but I'll just call of this angle right over here.
We know that this is going to be equal to it's vertical angle.
So this angle is vertical with that one, so it's going to be equal to that angle right over there.
We also know that this angle here is going to be equal to the angle that is it's vertical angle or the angle that is opposite the intersection so it's going to be equal to that.
And sometimes you will see it specified like this, you will see a double angle mark like that or sometimes you will see someone write this to show that this two are equal and this two are equal right over here.
Now the other thing we know is we can do the exact same exersise up here - this two are gonna be equal to each other and this two are gonna be equal to each other.
They are all vertical angles.
What's interesting here is thinking about the relationship between this angle right over here and this angle right up over there.
And if you just look at it it's actually obvious what that relationship is.
They are going to be the same exact angle.
And if you put a protractor here and measure it you'd get the exact same measure up here.
And if i drew parallel lines, maybe I'll draw it straight left and right, it might be a little bit ore obvious so if I assume that these two lines are parallel and I have a transversal here what I'm saying is this angle is going to be the exact same measure as that angle there.
And to visualize that, just imagine tilting this line, and as you take different, so it looks like its the case over there, if you take the line like this and you look at it over here, it's clear that this is equal to this and there's actually no proof for this.
This is one of those things that a mathematician would say intuitively obvious.
That if you look at it, as you tilt these lines, you would say that these angles are the same.
Or think about putting a protractor here to actually measure these angles.
If you put a protractor here, you would have one side here of the angle at the 0 degree and the other side would specify that point and if you put the protractor over here, the exact same thing would happen.
One side would be on this parallel line and the other side would point at the exact same point.
So given that, we not that not only this side is equivalent to this side it is also equivalent to this side over here, and that tells us that's also equivalent to that side over there.
So all of these things in green are equivalent and by the same exact argument, this side over here or this angle is going to have the same measure as this angle and that's going to be the same as this angle, because they're opposite, or they're vertical angles.
Now the important thing to realize is the vertical angles are equal and the corresponding angles at the same point of intersection are also equal.
So that's a new word I'm introducing right over here.
This angle and this angle are corresponding.
They represent kind of the top right corner in this example where we intersected.
Here they represent the top right corner of the intersection.
This would be the top left corner.
They're always gonna be equal, corresponding angles.
And once again, really it is a bit obvious.
Now on top of that, there are other words that people would see, essentially just proven that not only is this angle equivalent to this angle, but it's also equivalent to this angle right over here.
And these two angles, maybe if I call this
Let me label them so that we can make some headway here.
So I'm gonna use lower case letters for the angles themselves. Let's call this lowercase a, lowercase b, lowercase c..so lowercase c for the angle, lowercase d and then let me call this e, f, g, h.
So we know from vertical angles that b is equal to c, but we also know that b is equal to f, because they're corresponding angles.
And then f is equal to g.
So vertical angles are equivalent.
Corresponding angles are equivalent and so we also know that obviously that b is equal to g.
And so we say that alternate interior angles are equivalent.
So you see that there are kind of on the interior of the intersection.
They're between the two lines but they're all on the opposite sides of the transversal.
Now you don't have to know that fancy word - alternate interior angles - you really just have to deduce what we just saw over here, that vertical angles are gonna be equal and corresponding angles are gonna be equal.
And you see it with the other ones too.
We know that a is gonna be equal to d, which is going to be equal to h, which is going to be equal to e.
Hey.
Hey Square.
Where have you been all this time?
With you we sang.
And with you we labored.
We fought our fears.
And we prayed.
All as one hand.
Day and night.
And with you nothing is impossible.
The voice of freedom brings us together.
Finally our lives have a meaning.
There is no going back.
Our voices are heard.
And the dream is not forbidden anymore.
Hey.
Hey Square.
Where have you been all this time?
You brought down the wall.
You lit the light.
You gathered around you a broken people.
We were born anew.
And a stubborn dream has been born.
We've disagreed with good intentions.
Sometimes things weren't clear.
We'll protect our country and our children's children.
We'll protect the rights of the lost lives of our youth.
Hey.
Hey Square.
Where have you been all this time?
With you we felt and started
After we had been far and had come to the end.
We have to change ourselves with our hands.
You gave us a lot and the rest is up to us.
Sometime I worry that you'll become a memory.
That you'll become distant from us and the idea will die.
And we'll go back and forget what happened.
And tell stories about you in our tales.
Hey.
Hey Square.
Where have you been all this time?
The Square is full.
With all kinds.
The reckless one.
And the courageous.
There is the passionate one.
And the one who are on a ride.
The loud one.
The quiet one.
We get together.
Drink tea.
We now know how to get our rights.
You let the world hear us.
And you let the neighbors get together.
Hey.
Hey Square.
Where have you been all this time?
Our idea is our strength.
Our weapon is our unity.
The square says the truth.
It always says no the oppressor.
The square is like a wave.
There are people riding it. Others are pulled in by it.
People outside of it calling it chaotic.
And what has been done is now written.
Hey.
Hey Square.
Where have you been all this time?
Rewrite the equation 6x^2 + 3 = 2x - 6 in standard form and identify a, b, and c.
So standard form for a quadratic equation is ax squared plus bx plus c is equal to zero.
So essentially you wanna get all of the terms on the left-hand side, and then we want to write them so that we have the x terms...where their exponents are in decreasing order.
So we have the x squared term and then the x term and then we have the constant term.
So let's try to do this over here.
So let me rewrite our original equation.
We have 6x squared plus 3 is equal to 2x minus 6.
So essentially we wanna get everything on the left-hand side. so I could subtract 2x from both sides, so I could subtract 2x from both sides, so let me just...I'll take one step at a time.
So I can subtract 2x from both sides.
And then I'll get...and I'm gonna write it in descending order for the exponents on x.
So the highest exponent is x squared.
So I'll write that first.
6x squared, and then we have minus 2x, and then we have plus 3 is equal to... the 2 'x's on the right cancel out...equal to negative 6.
And now, to get rid of this negative 6 on the right-hand side, we can add 6 to both sides.
So let's add 6 to both sides... ...and then this simplifies to 6x squared, minus 2x, plus nine is equal to...zero.
So let's make sure we're already in standard form.
All of our terms, our non-zero terms are on the left-hand side, we've done that.
We have a zero on the right-hand side, we've done that.
And, we have the x squared term first, then the x to the first power term, then the constant term. x squared, then x to the first, then the constant term.
So we are in standard form.
And so we can say that a is equal to 6, a is equal to 6.
We could say that b is equal to, and this is key, it's not just the 2, it's the negative 2. B is equal to negative 2, 'cause notice this says plus bx, but over here we have minus 2x.
So the b is a negative 2 here. B is negative 2.
And then c, c is going to be, c is going to be 9.
Well we already know that definite integrals can help us figure out areas underneath curves or between curves.
What we'll show in this video is that you can actually use pretty much the exact same principles to figure out the volumes of rotational solids.
So what do I mean?
So let me just draw a couple of examples.
So let me start with a fairly straightforward function.
That's my y-axis.
This is my x-axis.
Let me draw my function.
So y equals the square root of x looks something like that.
Actually, let me redraw that, because I didn't want it to curve down like that at the end.
So we'll call that f of x.
This is our x-axis.
This is our y-axis.
And we already know that if we wanted to figure out the area under this curve between two points.
Let's say between the point a-- well, we can do it between any two points.
Let's say this point a and this point b, and we wanted to find this area between the two curves.
If we wanted this area right here, we would essentially just be-- just as a review-- be summing up a bunch of small squares, where each square has a bunch of rectangles, has a width dx, and its height at that point would be whatever x value here is-- it would be f of x.
And if we take the sum of all of these areas, of all of these rectangles, we would get the area to this curve.
And we learned in the definite integral video that that's just equal to the definite integral from a-- that's a lower bound-- from a to b of f of x times d of x.
Where each [? rafter ?] angle is f of x times d of x.
What if we took this function and we rotated it about the x-axis.
So this might take a little bit of visualization, but what you imagine is-- let me see if I can draw.
So I take this curve and if I were to rotate it about the x-axis, it would look something like this.
That would be the opening on the inside.
You know, that would be the y-axis there, and the x-axis would pop out the middle.
So let me draw an arrow to show that we're rotating it around.
So if we took this piece and we rotated it around, what would it look like between a and b.
It would look something like this.
It'd be kind of a circle on one end, and then it would curve down a little bit and it would be another circle on the other end.
And if I were to draw the x-axis, the x-axis would kind of pop out of the middle right there.
That right there would be the point b, x equals b.
If we were to kind of go behind or look into the object we would see the other surface of this rotational solid.
And this point right here, that would be a.
And then of course the x-axis would keep going, and then that would be the y-axis.
The visualization really is the hardest part about these problems.
So I just did this section, if I rotated it about the x-axis.
But if I were to draw the whole curve, the whole curve would look something like this.
We're rotating it around that way.
So how do we do that?
Well we use the exact same principle.
When we figured out the area, we would figure out the area of each of these small squares, and then we would take the sum of an infinite number of infinitely small squares, and we got this.
So to do the volume, what we do is instead of having each rectangle, we kind of rotate each of these rectangles around the x-axis.
If that's the rectangle, it has width dx, and it has height f of x.
So this height right here, that's f of x at this point.
If I were to rotate this rectangle around the x-axis, what do I end up with?
Well I'll end up with a disk.
I'm trying to show you some perspective when I draw.
So that would be the top surface of the disk.
And this would be the side of the disk.
And so this is the top surface at the disk.
And what would be the radius of this disk, what would be this height right here?
Well that radius, that's going to be f of x.
That's this height.
Imagine if you took this and rotated it around, that's the same thing as this height right here, right?
So that height or the radius of the disk is f of x.
And then what's the width of the disk?
Well that's just d of x.
That's the same thing as this.
We just rotated it around.
So what would be the volume of this disk?
It would be the area of this side.
It'll be this area right here times this height.
Well what's the area?
Well we know the radius, right?
Area is equal to pi r squared.
My radius is f of x, right?
So the area of this disk is equal to pi times the radius squared, it so it's pi times f of x, the whole thing squared.
So what would be the volume of this entire disk?
So it'll just be this area times dx.
So the volume of that disk is going to be equal to area of that disk, pi f of x squared.
The whole function, whatever length this is at any point squared, that gives us the area, times the depth you can say, so that's d of x.
Now that gives us just the volume of this one disk when it's rotated around.
So if we wanted the volume of this entire object that I drew here, we would just sum up a bunch of these disks.
We would take each of these rectangles, rotate them around, figure out the volume of that disk it creates, and then sum them up.
And so essentially we're going to take an infinite sum of a bunch of these small little disks so we can take the integral.
So this is the volume of each disk.
We could call that a volume of a disk.
So what's the volume of the whole thing?
Well we just take a sum, an integral sum of each of these disks.
So the volume when you rotate it is going to be equal to the definite integral between-- and remember, our boundaries were a and b-- between a and b of this quantity right here-- pi f of x squared dx.
Just remember, this is the width of each disk.
This is the radius of the disk, or the radius of the surface, so it would be squared, and that makes sense, that's the height, f of x.
And we have pi r squared, so that's where the pi comes from.
In the next video I'll actually apply this to an actual problem.
See you soon.
Solve the following application problem using three equations with three unknowns.
And they tell us the second angle of a triangle is 50 degrees less than 4 times the first angle.
The third angle is 40 degrees less than the first.
Find the measures of the three angles.
Let's draw ourselves a triangle here.
And let's call the first angle "a", the second angle "b", and then the third angle "c".
And before we even look at these constraints, one property we know of triangles is that the sum of their angles must be 180 degrees.
So we know that a + b + c must be equal to 180 degrees.
Now with that out of the way let's look at these other constraints.
So they tell us the second angle of a triangle is 50 degrees less than 4 times the first angle.
So we're saying b is the second angle.
So they're second the angle of a triangle is 50 degrees less than 4 times the first angle.
So 4 times the first angle would be 4a (we're calling a the first angle). So 4 times the first angle is 4a but its 50 degrees less than that so minus 50.
Now the next constraint they give us: the third angle is 40 degrees less than the first.
So the third angle is 40 degrees less than the first.
So the first angle is a and it's going to be 40 degrees less than that.
So we have 3 equations with 3 unknowns and so we just have to solve for them.
Let's see, what's a good first variable to try to eliminate. And just to try to visualize that a little bit better,
I'm going to bring these a's onto the left-hand side of each of these equations over here.
So I'm going to rewrite the first equation.
We have a + b + c = 180 and then this equation, if we subtract 4a from both sides of this equation we have
-4a + b = -50.
And then this equation right over here, if we subtract a from both sides we get
-a + c = -40.
I just subtracted a from both sides.
So we now want to eliminate variables.
And we already have this third equation here is only in terms of a and c, this is only in terms of a and b, and this first one is in terms of a, b and c.
Let's see, this is already in terms of a and c; if we could turn these first two equations, if we could use the information in these first two equations to end up with an equation that's only in terms of a and c, then we could use whatever we end up with along with this third equation right over here and we'll have a system of 2 equations with 2 unknowns.
So let's do that.
So if we wanted to just end up with an equation only in terms of a and c using only these first 2, we would want to eliminate the b's... so we could multiply one of these equations time negative 1 and one of these positives b's would turn into a negative b.
So let's do that.
Let's multiply this first equation over here times -1.
So it will become
-a - b - c = -180, and then we have this green equation right over here which is really just this equation, just rearranged.
So we have
-4a + b = -50 and now we can add these two equations. Actually let me do that in the other color just so you see where that's coming from.
This is
-4a + b = -50.
We can add these two up now and we get
-a - 4a = - 5a, the b's cancel out, we have a minus c, is equal to
-180 - 50 = -230
So now using these top two equations we have an equation only in terms of a and c, we have another equation only in terms of a and c, and it looks like if we add them together the c's will cancel out.
So let me just rewrite this equation over here.
And you have to be careful that you're using all of the equations otherwise you'll kind of do a circular argument.
You have to be careful that over here, this first equation came from these two over here
Now I want to combine that with this third constraint, a constraint that's not already baked into this equation right over here. So we have
-a + c = -40
We add these two equations:
-5a - a = -6a, the c's cancel out, and then you have -230 - 40, this is equal to -270, we can divide both sides by -6, and we get a is equal to -270 over -6.
270 is divisible by both 3 and 2 so it should be divisible by 6, so let me just divide it; the negative signs obviously will cancel, a negative divided by a negative is going to be a positive.
If we take 6 into 270, 6 goes into 27 four time 4 x 6 = 24 we subtract we get 3, bring down the zero 6 goes into 30, 5 times
So we get a is equal to 45.
Now let's look at the other ones.
We can substitute back into to solve for c. c is equal to a minus 40 degrees.
So that is equal to, in yellow, so c is equal to 45 minus 40 which is equal to 5 degrees.
So, so far we have a = 45 degrees, c = 5 degrees, and then you can substitute into either one of these other ones to figure out b.
We can use this one right over here in green: b = 4a - 50
So b is going to be equal to 4 times 45... let's see, 2 x 45 is 90, so 4 x 45 is 180 so it's going to 180 minus 50 by this equation right over here which is equal to 130 degrees.
So we get b is equal to 130 degrees.
So let me write it right over here.
So a is equal to 45.
If I wanted to draw this triangle it would actually look something like this: a is a 45 degree angle, b is a 130 degree angle, and c is 5.
So it'll look something like this where this is a at 45 degrees, b is 135 degrees [oops], and then c is 5 degrees.
And you can verify that it works.
One, you could just add up the angles 45 + 5 is 50.
Oh, sorry, this isn't 135, it's 130.
We solved it right over here and this is 5.
So when you add them all up 45 + 130 + 5 that does indeed equal 180 degrees; 45 + 5 is 50 plus 130 so this does definitely equal 180.
So it meets our first constraint.
Then on our second constraint b needs to be equal to 4a - 50 well 4 x a = 180 180 - 50 = 130 degrees so it meets our second constraint.
And then our third constraint c = a - 40 degrees
Well a is 45, c is 5, so if subtract 40 from 45 you get 5 which is c so it meets all of our constraints and we are done.
In this video I'm going to do a bunch of examples of finding the equations of lines in slope-intercept form.
Just as a bit of a review, that means equations of lines in the form of y is equal to mx plus b where m is the slope and b is the y-intercept.
So let's just do a bunch of these problems.
So here they tell us that a line has a slope of negative 5, so m is equal to negative 5.
And it has a y-intercept of 6.
So b is equal to 6.
So this is pretty straightforward.
The equation of this line is y is equal to negative 5x plus 6.
That wasn't too bad. Let's do this next one over here.
The line has a slope of negative 1 and contains the point 4/5 comma 0.
So they're telling us the slope, slope of negative 1.
So we know that m is equal to negative 1, but we're not 100% sure about where the y-intercept is just yet.
So we know that this equation is going to be of the form y is equal to the slope negative 1x plus b, where b is the y-intercept.
Now, we can use this coordinate information, the fact that it contains this point, we can use that information to solve for b.
The fact that the line contains this point means that the value x is equal to 4/5, y is equal to 0 must satisfy this equation.
So let's substitute those in. y is equal to 0 when x is equal to 4/5.
So 0 is equal to negative 1 times 4/5 plus b.
I'll scroll down a little bit. So let's see, we get a 0 is equal to negative 4/5 plus b.
We can add 4/5 to both sides of this equation.
So we get add a 4/5 there. We could add a 4/5 to that side as well.
The whole reason I did that is so that cancels out with that.
You get b is equal to 4/5.
So we now have the equation of the line. y is equal to negative 1 times x, which we write as negative x, plus b, which is 4/5, just like that.
Now we have this one.
The line contains the point 2 comma 6 and 5 comma 0.
So they haven't given us the slope or the y-intercept explicitly.
But we could figure out both of them from these coordinates.
So the first thing we can do is figure out the slope.
So we know that the slope m is equal to change in y over change in x, which is equal to-- What is the change in y?
Let's start with this one right here.
So we do 6 minus 0.
Let me do it this way. So that's a 6-- I want to make it color-coded-- minus 0.
So 6 minus 0, that's our change in y.
Our change in x is 2 minus 5.
The reason why I color-coded it is I wanted to show you when I used this y term first, I used the 6 up here, that I have to use this x term first as well.
So I wanted to show you, this is the coordinate 2 comma 6. This is the coordinate 5 comma 0.
I couldn't have swapped the 2 and the 5 then.
Then I would have gotten the negative of the answer.
But what do we get here?
This is equal to 6 minus 0 is 6.
2 minus 5 is negative 3.
So this becomes negative 6 over 3, which is the same thing as negative 2.
So that's our slope.
So, so far we know that the line must be, y is equal to the slope-- I'll do that in orange-- negative 2 times x plus our y-intercept.
Now we can do exactly what we did in the last problem.
We can use one of these points to solve for b.
We can use either one.
Both of these are on the line, so both of these must satisfy this equation.
I'll use the 5 comma 0 because it's always nice when you have a 0 there.
The math is a little bit easier.
So let's put the 5 comma 0 there.
So y is equal to 0 when x is equal to 5.
So y is equal to 0 when you have negative 2 times 5, when x is equal to 5 plus b.
So you get 0 is equal to -10 plus b.
If you add 10 to both sides of this equation, let's add 10 to both sides, these two cancel out.
You get b is equal to 10 plus 0 or 10. So you get b is equal to 10.
Now we know the equation for the line.
The equation is y-- let me do it in a new color-- y is equal to negative 2x plus b plus 10.
We are done.
Let's do another one of these.
All right, the line contains the points 3 comma 5 and negative 3 comma 0.
Just like the last problem, we start by figuring out the slope, which we will call m.
It's the same thing as the rise over the run, which is the same thing as the change in y over the change in x.
If you were doing this for your homework, you wouldn't have to write all this. I just want to make sure that you understand that these are all the same things.
Then what is our change in y over change in x?
This is equal to, let's start with this side first. It's just to show you I could pick either of these points.
So let's say it's 0 minus 5 just like that.
I'm kind of viewing it as the endpoint.
Remember when I first learned this, I would always be tempted to do the x in the numerator.
No, you use the y's in the numerator.
So that's the second of the coordinates.
That is going to be over negative 3 minus 3.
This is the coordinate negative 3, 0.
This is the coordinate 3, 5.
We're subtracting that.
So what are we going to get? This is going to be equal to-- I'll do it in a neutral color-- this is going to be equal to the numerator is negative 5 over negative 3 minus 3 is negative 6.
So the negatives cancel out.
You get 5/6.
So we know that the equation is going to be of the form y is equal to 5/6 x plus b.
Now we can substitute one of these coordinates in for b.
So let's do.
I always like to use the one that has the 0 in it.
So y is a zero when x is negative 3 plus b. So all I did is I substituted negative 3 for x, 0 for y.
I know I can do that because this is on the line.
This must satisfy the equation of the line.
Let's solve for b. So we get zero is equal to, well if we divide negative 3 by 3, that becomes a 1.
If you divide 6 by 3, that becomes a 2.
So it becomes negative 5/2 plus b.
We could add 5/2 to both sides of the equation, plus 5/2, plus 5/2. I like to change my notation just so you get familiar with both.
So the equation becomes 5/2 is equal to-- that's a 0-- is equal to b. b is 5/2.
So the equation of our line is y is equal to 5/6 x plus b, which we just figured out is 5/2, plus 5/2.
We are done.
Let's do another one.
We have a graph here.
Let's figure out the equation of this graph.
This is actually, on some level, a little bit easier.
What's the slope?
Slope is change in y over change it x.
So let's see what happens.
When we move in x, when our change in x is 1, so that is our change in x. So change in x is 1.
I'm just deciding to change my x by 1, increment by 1.
What is the change in y?
It looks like y changes exactly by 4.
It looks like my delta y, my change in y, is equal to 4 when my delta x is equal to 1.
So change in y over change in x, change in y is 4 when change in x is 1.
So the slope is equal to 4.
Now what's its y-intercept?
Well here we can just look at the graph.
It looks like it intersects y-axis at y is equal to negative 6, or at the point 0, negative 6.
So we know that b is equal to negative 6.
So we know the equation of the line.
The equation of the line is y is equal to the slope times x plus the y-intercept. I should write that.
So minus 6, that is plus negative 6 So that is the equation of our line.
Let's do one more of these.
So they tell us that f of 1.5 is negative 3, f of negative 1 is 2.
What is that?
Well, all this is just a fancy way of telling you that the point when x is 1.5, when you put 1.5 into the function, the function evaluates as negative 3.
So this tells us that the coordinate 1.5, negative 3 is on the line.
Then this tells us that the point when x is negative 1, f of x is equal to 2.
This is just a fancy way of saying that both of these two points are on the line, nothing unusual.
I think the point of this problem is to get you familiar with function notation, for you to not get intimidated if you see something like this.
If you evaluate the function at 1.5, you get negative 3.
So that's the coordinate if you imagine that y is equal to f of x.
So this would be the y-coordinate.
It would be equal to negative 3 when x is 1.5.
Anyway, I've said it multiple times.
Let's figure out the slope of this line.
The slope which is change in y over change in x is equal to, let's start with 2 minus this guy, negative 3-- these are the y-values-- over, all of that over, negative 1 minus this guy.
Let me write it this way, negative 1 minus that guy, minus 1.5.
I do the colors because I want to show you that the negative 1 and the 2 are both coming from this, that's why I use both of them first.
If I used these guys first, I would have to use both the x and the y first.
If I use the 2 first, I have to use the negative 1 first.
That's why I'm color-coding it.
So this is going to be equal to 2 minus negative 3. That's the same thing as 2 plus 3.
So that is 5.
Negative 1 minus 1.5 is negative 2.5.
5 divided by 2.5 is equal to 2.
So the slope of this line is negative 2.
Actually I'll take a little aside to show you it doesn't matter what order I do this in.
If I use this coordinate first, then I have to use that coordinate first.
Let's do it the other way.
If I did it as negative 3 minus 2 over 1.5 minus negative 1, this should be minus the 2 over 1.5 minus the negative 1.
This should give me the same answer.
This is equal to what? Negative 3 minus 2 is negative 5 over 1.5 minus negative 1. That's 1.5 plus 1.
So once again, this is equal the negative 2.
So I just wanted to show you, it doesn't matter which one you pick as the starting or the endpoint, as long as you're consistent.
If this is the starting y, this is the starting x.
If this is the finishing y, this has to be the finishing x.
But anyway, we know that the slope is negative 2.
So we know the equation is y is equal to negative 2x plus some y-intercept.
Let's use one of these coordinates.
I'll use this one since it doesn't have a decimal in it.
So we know that y is equal to 2. So y is equal to 2 when x is equal to negative 1.
Of course you have your plus b.
So 2 is equal to negative 2 times negative 1 is 2 plus b.
If you subtract 2 from both sides of this equation, minus 2, minus 2, you're subtracting it from both sides of this equation, you're going to get 0 on the left-hand side is equal to b.
So b is 0.
So the equation of our line is just y is equal to negative 2x.
Actually if you wanted to write it in function notation, it would be that f of x is equal to negative 2x.
I kind of just assumed that y is equal to f of x.
But this is really the equation.
They never mentioned y's here.
So you could just write f of x is equal to 2x right here.
Each of these coordinates are the coordinates of x and f of x.
So you could even view the definition of slope as change in f of x over change in x.
These are all equivalent ways of viewing the same thing.
I seek refuge from Allah from the Shaytan
In the Name of Allah The Most Gracious The Most Merciful
Ha Mim.
The revelation of the Book is from Allah the Exalted in Power, Full of Wisdom.
Verily in the heavens and the earth, are Signs for those who believe.
And in the creation of yourselves and the fact that animals are scattered (through the earth), are Signs for those of assured Faith.
The general atmosphere of the revolution cause the youths to want to put the meter back to zero Begin from zero.
There is a feeling that we could went against everything: what is called the basic assumption in psychology belief and religion itself.
I'm not afraid for the sake of religion of our God
The aim of these words is not to protect the religion
We are not the protectors of the religion, it's our God who protect us by the deen. surah...
But the faith of the people which is going to split from them because of us because we do not comprehend the next generation their wondering their inability to mix between their civilization and identity which become ambiguous with other civilization and the globalized world they live in. sometimes, actually one is surprised by things discussed by the youths while we mistaken it as so much self-evident it is not so obvious to them we need to talk and transmit our intellectual experience to help anyone to see the path in their condition. the core of the issue we live by in Egypt and all Arabs countries is to build the principles of... the human mind is unable at his level to understand everything that occur around him and to relate them
All these questions need a ray to enlighten and make us see
So to live believing the deen while at the same time my wondering unable me to have certainty is not normal condition actually
You were not asked to do so
It's our mistake, probably the general religious speech due to importation of another culture and open another world without fortifying ourselves by 'aqidah'
It's the sin of the entire ummah nowadays not a specific individual
It's not correct to judge a person for the mistake of the ummah when he shows symptoms:
I'm wondering and I have no answers
We shut him "Dont ask", so they keep the questions and dont speak.
[Instrumental intro of the "I Was Here" song]
[Beyoncé, over the music]
On August 19, 2012, it's high time we rise together.
Do one thing for another human being.
Nothing is too small.
It begins with each of us.
Make your mark and say "I was here."
Go to whd-iwashere.org and together, we'll make our stories known. ♪ I was here.
I lived, I loved ♪ <P align="right">[Over the song:] <i>One day,</i></P> one message, one billion people take an action ♪ I did, I've done ♪ <P align="right">[Over the song:] <i>for each other.</i> ♪ I was here ♪
I'll see you then.
[Cymbals + echo]
(I Was Here World Humanitarian Day August 19 whd-iwashere.org)
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I'll now introduce you to the concept of a random variable.
And for me this is something that I always had a lot of trouble getting my head around, and that's really because it's a byproduct of what it's called.
It's called a variable and we're used to variables as kind of an unknown in the equation.
If I write x plus 3 is equal to 7, the variable was x.
Maybe you could solve for it or maybe you could have an equation y is equal to 3x minus 2.
And then, here y and x are both variables.
If you input 1x you could solve for the other variable, y.
And you can change them.
And variables were kind of things that could change and that you could solve for.
And they could take on particular values.
A random variable is kind of the same thing in that it can take on multiple values, but it's not something that you really ever solve for.
So just so you get used to the notation, a random variable is usually a capital letter.
Usually a Capital X, Y, or Z.
Usually a capital X.
And where it really defers from a traditional variable is that it can take on a bunch of different values, like a traditional variable but you never solve for it.
And really, it's a little misleading to call it a variable at all.
It's really a function.
And it's a function that maps you from the world of random processes to an actual number.
So let's say-- I don't know-- I wanted to somehow quantify a random process.
Is it going to rain or not tomorrow?
So let's see-- rain tomorrow.
So you could observe that.
You could wait until tomorrow and see if it rains or not, but then, how do you quantify it?
Well, we can define a random variable that will quantify it.
We can say this random variable is going to be equal to 1 if it rains tomorrow and it equals 0 if it doesn't rain tomorrow.
We didn't have to assign 1 and 0; those tend to be a little bit more useful.
They make sense.
But we could have assigned this as-- I don't know-- we could have said that this is 21 and that this is 100.
It's however you define it.
So it's important to keep this distinction in mind, that a random variable-- it isn't a variable in the traditional sense of the world.
Inboxes can be overwhelming.
Unless you have the new Gmail inbox.
One tab for social sites
One tab for promotions and offers
One tab for updates, bills and receipts
And one tab for the mail you really, really want.
The inbox has gone Google.
Again.
Write six hundred forty-five million five hundred eighty-four thousand four hundred sixty-two in standard form.
So let's tackle this piece by piece. So the first part we have six hundred and forty-five million.
So let's think about that.
So we have six hundred and forty-five.
We have six hundred forty-five millions.
So we could view that as 645 times 1,000,000.
One million is one followed by six zeroes. So this piece right here is this right over here. That is six hundred and forty-five million.
And what is that when we write it out?
If we were to multiply this out, this is equal to-- it would be 645 times this 1 with six zeroes behind it. So this would be equal to 600-- I'll write it like this.
This is equal to 645, and then we have our six zeroes.
One, two, three, one, two, three.
That's just this part of the number.
And I'm going to do it kind of slow and do all of the different parts of the problem, but once you get some practice, you'll find that these are a bit second nature, and you won't have to go through all of these steps.
You'll just be able to write the number.
Now, let's move on to the next part.
We have five hundred and eighty-four.
Let me write that down.
584 thousand.
So let me write the thousand.
So 584 thousand.
So it's 584 times 1,000.
And what's that going to look like?
So that's this whole part right here.
So 584 times 1,000 is equal to what?
Well, it's going to be 584 with three zeroes behind it, or you could view it as 584 times the 1, and then you're going to have three zeroes in the final answer.
So it's going to be 584,000.
We have our three zeroes at the end.
584, three zeroes.
So that's that part.
And then finally, we have four hundred sixty-two, and that's just 462, straight up.
You could view it as 462 ones.
So then you just have 462, which obviously equals just 462.
Now our number is all of these combined.
It is 645,000,000 and 584,000 and 462.
So one way to think about it is that you could add these three numbers.
So if we were to add them, we get 645,584,462.
Now, I said it'll become a little bit of second nature to you in a little bit, and the way to think about that, the easiest way to think about that, is millions will have six zeroes behind them, thousands will have three zeroes behind them, and just regular numbers have no zeroes behind them.
So what you can do when you kind of want to learn it second nature, you'll just look at the six hundred and forty-five million, so you'll write 645, and you'll kind of keep in the back of your mind that you're going to have to have six more digits to the right of this.
And then you say five hundred and eighty-four thousand, so then you have your five hundred and eighty-four thousand, so then you write that down, 584,000, keeping in mind that you're going to need three digits to the right of that.
And so if they didn't tell us 462, we would just put three zeroes here, and that would also fulfill the six zeroes we need behind 645,000,000.
But then they tell us 462, so we just write that right here.
Graph x is less than 4.
So, let's draw ourselves a numberline overhere.
So let me draw a number line.
Let me put ....I'll start here 0. 1-2-3-4-5
And we can go below 0
-1,-2,-3,-4 and I can go on now we wanna graph all of the Xs that are less than 4 but we're not including 4 it's not less or equal than 4 it's less than 4 and to show that we're not including 4 what we're going to do is that we're going to draw a circle around 4 so this shows us that we're not including 4 if we were including 4
I would make that a solid dot
To show that we're going to do all of the values less than 4 we'll shade in the number line below 4 going down from 4 just like that just like that and we can shade in the arrow just like that here is all of the values less than 4 and you can test it out take any value where there is blue so there is blue overhere
-2,-2 is definitely less than 4 if you take this value right here, this 2. It's definitely less than 4.
4 is not included, because 4 is not less than 4. It's equal to 4. 5 is not included because 5 is not less than 4.
Presented by SHOWEAST
Produced by BLUE STORM A light on channel 3 isn't coming on.
Gwang-il can you finish up here alone? Can you?
Yes. Something urgent came up. - I'll call you later.
April Snow
BAE Yong-joon
SON Ye-jin Operating Room Intensive Care Unit
I'll try reaching Mr. Kim again later. But I can't...
You can do it kid. I'll try.
Okay, bye.
We still don't know who was driving. They were both found outside the car. It was a big accident.
Ms. Kang was intoxicated at the time.
Samchuk Hospital Hello?
Design Sai. Is this the main office? Yes.
I'm calling about Kang Su-jin. Um... She's on vacation.
Hello, sir. She was out here on business?
Yes... I need to go to Seoul for a day or so. Try to have some more, Dad.
Look, ln-su. I understand, but... The production isn't happy with you running out on last nights show.
Okay.
Sam-heung Motel Excuse me? Yes?
What is it? Was your husband really here on business?
Yes, that's right. My wife was on vacation. But I said she was here on a side job.
Samchuk Hospital What are you doing? Have you had a lot of stress recently?
Yes...
Hello. Do you want something strong or mild? Something that works well. $2 please.
Yes. I'm having trouble sleeping. I have something to ask you.
Could I read your husband's messages? Let's go away together. Can you take time off?
I'm worn out from last night. KANG Su-jin
I'm filming us now...
Hey.
Did you eat? No. Then let's go eat.
Gwang-il... When I saw Su-jin at the hospital, I wished that I'd been hurt instead.
Yeah, right...
Gwang-il... Just leave... Just leave...
Hey. Please... Open the door.
Hey... I... uhm... I'd like to apologize.
I'm very sorry.
One, two, three. Why'd you have to do it, Su-jin? I just don't get it.
Oh, that. No, I'm a lighting director for stages. Like at concerts.
Joong-ang University.
Then, they must've been in the same club. Would you like some more? I'll have the beer.
Here you are.
Hello. Have you eaten? Yes.
So you're going to Seoul?
Hello. Hi.
Are things going okay? Yes.
I knew you could do it. Thanks. Let's take it from the top.
Okay. Do you like to walk?
Yes, I do. Do you? I do, too.
Yes, aren't you? Just a little. Should we go back?
Then, I guess it should snow in spring. Think that'd ever happen? Want to take a picture?
Look here? Yes.
One, two, three...
Here, let me do it. Who is it? It's your father-in-law, son.
Yes, sir. Just a moment. Okay.
Hello, sir. I didn't know you were coming.
Holding up okay? Yes.
Ah... did you eat? No, not yet. I was just on my way out for dinner.
Su-jin looks a lot better.
She does.
Ah, Dad? I think I forgot to lock the door. I'll wait downstairs.
Hello?
Yes, I'll be right there.
Su-jin.
Su-jin. It might take a few weeks for the patient to talk. You said you'd be back late.
Okay. I almost forgot, his blood pressure went down this afternoon. Thank you...
Yes, it's me. No. Something came up.
Please take good care of him. Bye.
4, 7, 8, 9... 20. ...40. Square that all up and it comes to 1 60 points. Are you sure?
It's right. Look, 3, 4.
It's 7.
7, 8... He passed away at 3:23 p.m. Would you like to go in and see him?
"The departed saint" - "YOON Kyung-ho" "The chief mourner" - "HANG Seo-young" Honey, I want a cigarette. Are you okay to smoke?
- Where are you going?
Seoul! Last call to Seoul!
Seoul!
Seoul! Last call to Seoul! Thank you.
In-su, isn't there something you want to ask me? How long are you going to hold it back? At first, I wanted to know...
Su-jin... He died.
Gwang-il. Yes?
Check on the bank. Right on it, sir! Good.
A great snow squall is falling far into spring.
Tae-Baek Mts are about to embrace the spring warm but it seems he has decided to hibernate again. The spring flowers are being helplessly buried in the snow... Where should we go?
<i>Brought to you by the PKer team @ www.viikii.net
Episode 15
Everybody listen here!
Yes ?
I also have something to say.
Everyone please free your schedule on next Wednesday.
But... I'm going to play golf with Mr. Yoon on that day.
Ah, me too.
I have to go somewhere with the shop workers on that day.
I can't either.
I got invited to a birthday party.
Me too.
Ah okay.
Cancel it all.
Why?
Why?
What's happening that day?
Your wedding.
W-w-wedding?!
Ah, please stop controlling us any which way you please.
Omo!
Who's deciding?
You said you want to get married.
I said after graduation!
When will that be?
You have to become an intern, then a resident and you have to do your military service, too.
What's the point of delaying?
It's better to do it now, when you're still pretty and youthful.
But....
- The birthday party ....
- Stop! don't say anything else right now!
Do you have any idea how hard it is for me to reserve a wedding hall?
On that day, clear out all your schedules and you need to help each other out, alright?
You're still awake?
Ah...
Yes.. .Yes.
What is it?
Did I go overboard by doing what I please?
That... that's not it.
We're living together anyway.
I thought they might as well be married, and it would look better in the eyes of others too.
Oh I see.
Honestly that was bothering me a bit too.
Thank you for everything.
But...
Why are you like this?
Your expression doesn't look good.
No, I'm doing good.
It's just that I don't know what to start preparing first.
What is there to prepare?We already live together so there is nothing to buy, and the wedding hall has been booked.
We just need a dress and a ring, then everything will be fine.
Still...
Next Wednesday?!!!
Yeah.
Seung Jo's mother has some serious drive.
That's right.
Hey, did you guys cause some sort of accident?
Ya!
It's not that!
Ah yes.
Does Bong Joon Gu knows?
Um... My dad has told him.
So that's why he looked so down in the dumps.
He didn't even notice us when we came.
Hey, did you pick your dress?
You have to buy your ring too.
We have to start now.
I'm busy.
Welc....
Sir!
Hey hurry and talk to me.
Hey, let's eat!
Eat well!
Sir, sir!
A foreigner came!
She is right over there, a foreigner!
Oh.
Quickly, quickly, quickly!
Hurry!
Hi.
Hi.
Thank you.
Ha Ni, hurry up and take her order.
Me?
I can't speak English.
But, you're a college student.
Hurry up!
Hi.
Hi.
How are you?
I . . . want to eat noodles!
Please give me chopped noodles.
She speaks korean very well.
What is it?
It's mushroom.
Pine mushrooms.
Ah, pine mushrooms.
The scent . . .
The scent is very nice!
She said pine mushrooms.
Her accent is so cute!
It's good for your health too.
This is called oyster.
Ah yes, oyster.
I usually don't eat this.
This tastes good.
How do you speak Korean so well?
My mom is Korean, but my dad is English.
I came to Korea to see my mother's hometown.
I have to go home in 10 days.
Ah... yeah.
It's delicious.
Very, very delicious.
That's stuffed cucumber kimchi.
That guy over there made it!
This tastes good!
It's killer!
He is from Busan, so he's a little curt.
Ah...
Yes...
How was the one we saw before?
It's too showy.
Really ?
Then what about this one?
This one is pretty.
I don't like it.
It's too shiny.
Then, you choose it.
Hey!
Do we have to get rings?
What are you talking about?
It's a symbol of love.
A symbol of love?
Hey!
How can something so materialistic be a symbol of love?
I'm not doing this!
No!
You have to do it!
There needs to be a sign that you're a married man.
So it's not really a symbol of love but more like shackles.
Forget it!
What's there to buy when you only wear it that one day?
I have a suit already.
Still!
Let's go in!
I'm going to look for a dress.
Then go buy it and come back.
I'll go somewhere and wait for you.
OK!
Then, let's go to the studio.
Studio?
Why?
Why?
It's for the photo album shoot.
Photo album shoot?
Hey!
I'm not doing that.
Husband look over here, bride smile a bit more...
You want me to do that silly thing?
Never.
This isn't fair. You don't want to match rings.
You don't want to do the album photo shoot as well.
Why did you come out with me if you were going to be like this?
Do you think I came because I wanted to?
I came out just because they wanted me to.
Anyways, you came out.
Can't you just put up with it and help?
You've only been irritated and saying you don't like this and that!
Hey.
Why are you speaking like this in the street?
It's embarrassing.
Embarrassing?
I'm embarrassed too!
What do you think the people at the rings store thought about us?
Why should I have to continually match your wants and needs?
Don't then.
If I don't... .What if I don't hold it in either?!
Now I see why couples break up before even getting married.
What?
I'm telling you now.
Even after marrying you, I won't be able to just look to you.
I can't adjust myself for you.
When did you ever?
Really...
What's all this?
It's because of my mom.
It's not because of Mother (in-law).
If so, why did you say you were going to marry me?
Yeah.
I'm regretting why I said that.
I think we should think about it again.
Really?
So you weren't able to get your dress yet?
He doesn't even talk to me at home.
When we run into one another he avoids me.
What?
There's not many days left...
He said he regrets asking me to marry him, and that we should think it over.
No, you know how Baek Seung Jo is normally cold like that.
Even if he says that, he doesn't mean it.
The business hours are over.
Oh, Seung Jo!
Come on in!
Have a seat.
You were reading a book?
From a dad to his daughter...
I wanted to talk to her about it.
What brought you here at this time?
I have something to tell you.
Doesn't it look beautiful?
It would be nice drinking coffee with those cups.
Yes, it looks beautiful.
Why does a bride-to-be's face look so upset?
Is Seung Jo being a pain?
No.
Wow, how beautiful.
Hey Dad.
Ha Ni, what are you doing?
Oh, is that so?
Then come here for a moment.
Now?
Why, did something happen?
Date?
I understand.
I'm coming now.
Dad..
Oh!
Ha Ni.
Where are we going?
Where are we going, exactly?
You will find out once we get there. <i>Brought to you by the PKer team @ www.viikii.net
Seung Jo wanted to greet your grandmother and mother.
I was busy so I forgot about it.
Nice to meet you, Mother.
Grandmother...
Your grandson-in-law is here.
Do you like it?
I'm worried because Oh Ha Ni isn't listening to me already, but you don't have to worry.
I will take care of her.
I hate you.
Hate ?
I like it.
Thank you.
Mom..
Grandmom..
I'm getting married.
Kyung Soo sunbae is going to be the host.
Officiator.
Let's not have an officiator.
What about our honeymoon?
Where are we going for our honeymoon?
Do we have to go?
We don't have much time.
There you go again!
Fine, fine.
Where?
Is there a place you would like to go?
Yes!
Italy?
Perhaps Rome!
Rome?
Rome? In your dreams.
I was just joking.
Even if it's not far away, I hope we go to an island.
Island.
Okay then
Alright then.
How about Yeo Eui Do?
Yeo Eui Do?
Why?
Yeo Eui Do was once an island as well
Or...Bam Island?
Right!...Ddook I sland!
Ddook Island?!
How annoying.
Fine.
Let's determine with this.
If 3 of the same pictures appear after a shake... we'll go to the place you wish.
Okay.
But isn't there only a small possibility?
No.
Jeju island, jeju island, jeju island.
Yeo Eui Do...
Jeju Island!
Jeju Island!
It's Jeju Island.
Wow!!
Hooray!
Yes!
Jeju Island!
Yay!
Hurray!
How does it feel? It's tomorrow.
I don't know.
It still hasn't hit me yet.
Have you packed your bag?
Yeah, just the basics.
Surprise!
What ,is it?
Open it.
Oh my.
Just rip it open, like this.
Okay.
Hey!!
What do you mean "Hey"?
We searched on the Internet.
They said that the most important thing on the honeymoon is underwear and nightwear.
And fragrance.
See.
You take a shower first.
Seung Jo oppa!
Then you wear this underwear all sexy, like this.
And you spray some of the fragrance.
Put on make up lightly as well.
When you take a shower, there is an important point.
What is it?
Never, ever, hum to yourself.
Why is that?
Men get scared when you are too powerful.
I see.
Hey, does Baek Seung Jo kiss well?
Hey!
- Tell me.
- Does he kiss well?
Hey!
Was he good?!
Was he good?!
How did he do it?!
Stop!
Here...
What is that?
It's just silverware and a china set.
Hey!
Why did you buy this?
I hear even if you do nothing, this is something you have to do.
I also bought a set of blankets.
It's in the room, but I don't know if you'll like it.
Oh my!
In law, please look to us kindly!
Yes.
Please look to me kindly too, in law!
What to do.
Hyung.
Are you asleep?
No.
So you're eventually getting married to Oh Ha Ni.
It seems so.
Why, you don't like it?
Of course.
Oh Ha Ni isn't smart and she's clumsy.
More than anything, she's stupid.
Doesn't even know how to swim but tried to save me.
Even though you're mean to her, she smiles about liking you.
I'm going to marry a girl much smarter and prettier than Oh Ha Ni.
Okay.
But, I'm all for Hyung and Oh Ha Ni getting married.
I like you very much, but to be honest, it is quite true that your personality has a few issues.
And so, I think that you should marry a person like Oh Ha Ni.
You're doing the right thing.
Congrats.
Ha Ni,
I'm really happy right now, because you're probably really happy right now.
When you're happy,
I'm happy as well.
Congratulations, Oh Ha Ni.
Have beautiful dreams and I'll see you tomorrow.
What?
They're the ones that wanted to stay up all night and talk. <i>Brought to you by the PKer team @ www.viikii.net
Dad.
Why aren't you sleeping?
I can't sleep.
How about you?
Me too.
Dad.
Yes?
Thank you for raising me this well.
Oh
Don't cry.
If your eyes get swollen, other people tomorrow will say that the bride's not pretty.
Oh ?
I said not to cry.
Why do you cry when it's such a happy day?
I will smile too.
You too, have to smile tomorrow, ok?
The only daughter of a widowed father.
If she cries on her wedding day her life will be rainy.
Okay.
I will smile.
Yeah.
Dad...
Mm?
Do you want to practice?
Oh..
Yeah.
S....s...
Ready, start.
Aigoo.
Hello.
Hello.
You must be very happy to get a new daughter-in-law.
This is my son.
Congratulations.
I hear you're working on a new business.
- Oh sir you're here!
-Congratulations.
- I need to come even if I'm busy!
- Oh thank yoU!
One, two, three!
Me too!
-Min Ah, Min Ah come here!
- Stand next to Ju Ri.
I'll be compared to Min Ah then.
I'm going to take it!
Teacher!
Teacher.
Hi!
Congratulations, Ha Ni!
Congratulations.
You are pregnant?
What happened to you!??
It's embarrassing!
Ha Ni, congratulations!
Marrying with Seung Jo, you're epic!!
You've succeeded!
You've done it!
Ha Ni, see you later.
Thank you for coming.
You look pretty!
Ha Ni, congratulations!
You look really beautiful!
Teachers getting married is pretty epic too.
Did you see that?
You will one day get pregnant, too Won't you?
You look pretty.
You too.
I feel good that it's you.
Hmm?
I feel good that Baek Seung Jo chose you, not me.
Yeah.
This is why I like him.
I'm thinking like that.
It's hard.
What's hard?
Baek Seung Jo has good taste in girls.
That's what I mean.
Hae Ra.
Be happy, so I become jealous and marry quickly.
Okay, I'll try hard.
Don't try hard.
I feel scared when you say that you're going to try hard.
Oh Ha Ni's patience and perseverance...
To top that off if Oh Ha Ni tries hard too...
Everyone's dead...
All right.
Congratulations.
Thank you.
See you later.
You came?
Ya, you look happy.
You're smiling very wide.
Your mouth looks like it's going to rip.
You look good.
Of course.
Be careful, Ha Ni might change her mind after seeing me.
I could run away with her.
Ladies and gentlemen.
Soon, bridegroom Baek Seung Jo and the bride Oh Ha Ni's wedding will start.
What do I do, Eun Jo?
It's going to start.
Are you nervous?
Don't make mistakes again, whether you drop the ring or you step on your own dress and slip.
Hey.
Don't say things like that.
Do you want me to give you a wedding present?
Gift?
Yeah.
What is it?
Give me your ears.
What?!
Ah, as you see, there's no officiator in this wedding, so we'll have the two of them doing their own officiating.
Start.
I, Baek Seung Jo, will respect and love my bride, Oh Ha Ni, whatever it takes, will respect the elders, will be a good husband to her,
I promise.
I, Oh Ha Ni, with groom Baek Seung Jo, will love and respect forever whatever it takes.
I promise I will respect the elders, and be a good wife to him.
This bride's dad is a very old friend of mine.
Until junior high, it was as if I lived at his house.
He's done a lot for me.
It was like that back then, and it was like that once we met again too.
I always thought that there couldn't be a warmer and nicer person than him.
This amazing friend of mine has now become my in law.
My friend, thank you for letting your well raised daughter marry my son.
After thinking about what I should say,
I remembered my short married life.
On our wedding day, it snowed a lot.
And on Christmas eve, while we were eating the leftover noodles, we said "Merry Christmas" to each other.
After that, Ha Ni came and my wife passed.
I was holding Ha Ni and crying.
I remembered all that.
It doesn't seem like such a big deal, but I was very happy.
It was probably because of the hardships we endured together.
Like how my mother-in-law would call her Noah's snail all the time.
She knew what road to take, and she is a child who took that road smiling.
I was always sad and sorry about her being alone.
From today, since a caring and cool groom is going with her, my heart is put at ease and I'm reassured.
Thank you, Seung Jo.
Go with Ha Ni to the end.
It is time for the ring exchange.
Groom and bride, please exchange rings.
What to do?
Here it is!
Thank you.
Dummy.
Don't tease me, Baek Seung Jo, when you actually like me a lot, starting from a long time ago too.
What?
What are you talking about?
The second kiss.
Instead of in the rain, it was at the pension wasn't it?
I was sleeping, how childish.
After doing that, being so coy.
What is this?
Everyone, the bride is really bold!
Look at you now.
Everyone let's give the bride and groom a round of applause!
Wow! It's so cool!
Can we get out and see the ocean for a little while and then go?
Let's see it and go, huh?
Let's see the ocean and go!
It's so pretty!
Look at the color of the ocean.
It's really pretty, isn't it?
I feel like I've come to the South Pacific.
How can the ocean be that blue?
What?
Are you still mad?
If you're done looking, let's go.
The growing of our two lovebirds, the bride and groom, has been prepared through a video.
Please continue eating the food in front of you, and let's appreciate this together.
Since she was a baby, her beauty was different from others
This child, grew up to be a man over there.
Is that hyung?!
Right.
That's hyung.
I feel so much better. From now on, I don't think I can live holding a secret.
Seung Jo, you live lightly too from now on.
Carefree!
Mother-in-law, really.
She went overboard.
Even though she was well aware of your temper.
Hey!
Where are you going?!
Hey!
Stop there!
Hey, Baek Seung Jo!!
How long are you going to keep on following me?
Ah, about that...
Hae Ra!
Are you not hungry?
I noticed earlier that you hadn't eaten anything.
Do you want me to buy you food? <i> Brought to you by the PKer team @ www.viikii.net</i>
It's different from the hotel that I thought of. It's really pretty.
We're over there.
Oh, how frustrating!
What kind of man has so little strength?
I'm sorry.
Oh, what's up with this? Are you staying here?
Do you not remember?
We sat next to each other on the plane.
Ah, yes.
Ah, check-in. Check-in!
Oh okay.
Couldn't even find the hotel gate. Making me come in through the back.
Ah, I'm really going to go crazy.
I didn't notice while I was sitting next to you earlier, but you're really handsome.
You could be an actor!
Ah, then we'll be leaving first.
Let's go.
Oh, excuse me!
You must really like hot dogs.
Do you not like hot dogs that much?
Should we go eat something else?
No, it's okay.
Please eat.
Do you want me to tell you something fun?
Eye booger.
What?
What is this?
What is this?
Hot Dog Eating Competition.
If you can eat 30 in ten minutes, you qualify for the competition in New York.
They can go to New York.
Between the ages of 20 and 40.
I can do it, I'm 21. Right, right?
Hey this...
Hae Ra, Hae Ra!
If it's 30 hotdogs in 10 minutes, then it's 1 hotdog per 20 seconds.
It can't be done? I think it's possible.
You're going to do it?
I should go for things like that.
I get to eat a lot of hot dogs, I get to go to New York, and I win, the prize which will probably be really big.
If I win and get a prize, I'll buy you yummy stuff.
Let's practice.
I'll eat this.
Count from 1 to 20 okay.
1... 2...
You laughed.
Did you not get sick that day?
You practiced tennis real hard for a long time.
I don't get sick over something like that.
What do you mean something like that?
You practiced for four hours.
You were there for four hours, sunbae?
Let's eat... hotdog. <i>Brought to you by the PKer team @ www.viikii.net.
It's so nice here.
And the ocean is right in front of our noses.
It is really beautiful!
Excuse me...
I'll try hard.
I know I'm not that great with a lot of things, but I'll try!
I'll be a good wife. <i>Oh, what do I do! <i>The environment seems so good.
Oh! Ah, you're in that room.
Our room is over there.
It is really fate!
What is this candle light event?
It's our hotel's most popular program for newlyweds on their honeymoon.
You should be pretty pleased with just the meal alone.
The feedback is really good.
Grilled pork, eel, and lobster marinade.
Caesar salad as well as live music and picture service.
Should we try this?
On a weekday like today we have a wonderful wine service that's on the house.
Really?
A candle light dinner and free wine too?!
It is good.
What do you think?
Alright, we'll take this for our dinner tonight.
Yes, I got it.
We'll contact your room as soon as it's ready.
All you have to do is come to the restaurant next to the pond.
Yes.
There's only 1 other couple that requested this aside from you.
Seeing there's only 2 couples it should be quite cozy.
There's another honeymoon couple?
Oh my goodness!
I heard there was an event the hotel prepared for honeymooning couples.
I thought it was going to be real lame.
Isn't it really romantic?!
Our fates are really entwined, don't you think?
We should have just come together from the airport.
We had a really hard time finding it.
I'm not too good with roads.
Is that all?!
But both of you look young.
Yes, we're 21.
Oh we're the same age!
It is really our fate!
But you got married real early.
Yes well...
Shotgun wedding?
We're 11 years apart, but it looks more doesn't it?
- Please have some. - Yes.
You're even good at pouring wine.
Since we're the same age shall we talk informally?
Do as you wish.
Are you taking a shot?!
I don't know too much about drinking wine.
Ah, slowly!
Slowly!
I think I'm going to throw up.
Why did you drink so much?
Are you alright?
Here you go pork chopped noodles.
Ah!
Give me a fork please!
A fork?
Do you think this is spaghetti?!
There's a way to eat all foods.
Noodles like this you use chopsticks and go whoosh whoosh.
You need to eat it like that to get the full taste!
Here.
I don't know how to use chopsticks.
Didn't you say your mother is Korean?
Haven't you learned how to use chopsticks?
Look!
Chopsticks...
You need to know the fundamentals.
Fundamentals, okay?
Do you know what fundamentals are?
What?
You place the chopstick like this and you only add pressure to here and here.
And the other one you hang it off of here.
And you just move this one like this.
Where in the world are you looking when I'm here explaining it to you?
Here.
Not like that, over here.
-Here, here! -Here!
That's right.
Wow the building looks unique.
They made it after the Great Mosque of Djenné.
Djenné?
It's an Islamic mosque in western Africa.
It's the biggest adobe building in the world.
Oh adobe.
Wow!
How could they build such a big building with adobe?
Once a year they paint the adobe.
You see that thing sticking out?
Yes.
They step on that to climb up--
Oh I see.
How do you know so much, Seung Jo?
Is it because you are a medical student?
It'll be fun if we go around together.
I'm going to follow you around like crazy.
Ah!
Are you alright?
Do you know you downed two bottles of wine all on your own last night?
Ah! Really?
That's really interesting, right?
Look at this!
It's so pretty.
Right?
I am sorry!
Over there, over there!
Hurry!
This place is so fun!
Over there! Should we go over there?
Look here!
Yes!
If you're the husband, take care of your wife!
Why am I stuck in this situation because of your wife?!
I am sorry , Miss Ha Ni!
Truthfully, I am worried too.
Seung Jo is after my wife.
What?
Seung Jo?
Seung Jo isn't into women like that! Especially ones that force themselves like that.
Women like that?!
Force herself?! My Hyun Ah is friendly and very affectionate.
She's misunderstood like that a lot, but she's a genuinely nice girl.
She's too good for me!
Omo!
Those two match really well.
Once we're done here do you want to head to the other museum?
I hear it's totally fun there.
Let's go to see!
Let's go!
-Oh, I am sorry!
-What is this?
Wow! It is really cute!
Should we buy this for Eun Jo?
I don't think we need to buy it for him.
Put it down.
Did you see me looking at you?!
Oh, really!
I'm here now!
Then you should have dressed better!
What in the world is this?!
We went to so many places today.
I don't know how many museums we went to.
Aren't you tired?
You had to drive too.
Want to wash up first?
Oh!
Shall I?
What do I do!
The time has finally come.
What to do?
Who is it?
It is me. Open the door, please.
What is it?
Let's have some champagne.
This is really good stuff. <i>Brought to you by the PKer team @ www.viiikii.net
Hello.
You're a bit late.
Would you like a glass of wine?
That's okay.
Have a nice time
Today's the last day.
What is this?
We haven't even been able to take a single picture yet.
You probably don't have to worry about that.
Huh?
Why?
I didn't have time to be with you, only us two.
So, let's hang around with only us two for today, okay?
Okay.
Truly?
I look pretty!
This is why he married me I guess
Seung Jo. Seung Jo.
What is it? Who is it?
I wonder.
Seung Jo.
Please help.
It hurts.
It hurts.
Where does it hurt?
I don't know.
It hurts all over.
Hyun Ah...
Just hold on.
Is it here?
No, I don't think it's over there.
Then, here?
Here? <i>No, don't touch her. <i>Stop.
How about here?
Here, this is where it hurts.
Stop It!
Don't touch a woman like that!
Oh Ha Ni.
What are you doing now?
I don't like it when you touch some other woman's body.
I don't like that.
Oh Ha Ni! You married a person that's going to be become a doctor.
What are you going to do if you're jealous of a sick person?
Because I've touched them?!
Aren't you even embarrassed?
If you don't like it, then you cannot live with me.
Do you understand?
Miss Ha Ni!
Hurry up and go follow her.
What the!
Gospodična Ha Ni!
Finally, its only us two.
Seung Jo, you don't like Ha Ni right?
You don't want to touch her either, do you?
How unfortunate.
You should have met me before Ha Ni.
If that's the case, Then, I wouldn't have even glanced at you probably.
What?
I have no choice but to deal with you because of where we are right now.
Don't you dare compare something like you to Ha Ni.
I couldn't catch her.
I thought you wanted it to be just the two of us? So why are you leaving on your own?
Are you still angry?
Put yourself in my shoes.
It would be weird not to get angry.
But you're pretty when you smile.
When you smile I start to feel good.
It tickles!
Hey, stop it!
Don't!
Don't!
I'm sorry
I'm sorry.
That I acted stupid.
Getting jealous at those things...
Dork.
You're cute.
Every now and then.
There are also times when you're beautiful.
From time to time.
But ...
Why do I like you?
You're not that pretty and you're only cute now and then.
Why would I always miss you?
You... What did you do to me?
Hey...
Wait a minute...
I have something to prepare...
Prepare what?
See... A girl has things to prepare--
It's fine.
I can't wait any longer.
Good morning!
Why? You should have slept more.
You must be tired.
I'm sorry.
What happened? The alarm went off at 5am.
I was looking forward to what you would make for breakfast.
Hyung you can rethink all this.
Ha Ni, you sit down too.
Do you want to wash up before you eat?
Yes.
I'm sorry.
Absolutely no need for that!
You're going to the library, right? I'll be quick so lets go together.
Going to study to get into the nursing program?
Yes.
The son will be a doctor and the daughter-in-law a nurse.
That's so great!
Well I can't take the certification until I get into the program.
If I don't then I may not be able to take it at all.
Oh really?!
Just because she takes it doesn't mean she's going to pass.
She's better off not being able to take it.
Baek Eun Jo fix that mouth of yours!
She's your sister-in-law now.
Oh that's right!
We have to register your marriage!
Well...
What kind of reply is that?
I know you're busy, but there are priorities you know!
Hey Ha Ni later go with Seung Jo and--
I'll think about it first.
What?! Think about what?!
About putting her on our family register.
I want to wait and see.
Is that something to say for someone that just came back from their honeymoon?!
That was something that you forced on us, Mother.
Baek Seung Jo does any of this make any sense?!
Thank God Ha Ni's father isn't here!
What is it that you want to think over?
Well...
I don't know but something isn't right at all.
It just feels like we're rushing through it all.
You don't want that either right?
Is that so...
Then what do we do?
Changing your major to nursing.
Let's register once you pass the test to change majors.
What does that have to do with your marriage registration?!
No way!
What? Are you not confident?
You jumped into it and this is it?
No that's not it. There's a chance I may not be able to take it at all!
I'm sure it'll happen, some day. <i>Thanks to the amazing PKer team for all their hard work today.
Thank you to all the viewers who waited until the channel went green for GO to watch this episode.
What?
You won't put me on your family register until I pass?!
We can just do it!
Family register.
I like you Mr. Bong! What?!
It was love at first sight!
But Mr. Bong says he likes someone.
Is it true?
You must love it.
The old lady gets a scandal and everything.
By chance are you jealous? You're jealous right?!
- I said I'm not!
- Whatever it totally is!
Ever since that day Chris isn't around much.
What the hell Bong Joon Gu? Why are you here?!
Are you crazy?!
I applied to change majors!
If I pass this time then go on a date with me on Christmas.
Hey what are you doing?
- Come here.
- Hyung!
Yeah! Yeah, Eun Jo!
Man, I'm going crazy because I want to go on a date with Oh Ha Ni!
I'm late!
<i>Brought to you by the PKer team @ www.viikii.net</i> <i>Episode 4
Is it that house?
That's enough, okay?
Hurry and leave! If Baek Seung Jo sees us, we're dead.
Hurry, hurry.
Where's your room ?
Is it over there?
Or there?
Where is it?
Spare me, please!
It seems like it's over there. Right there.
If that's Ha Ni's room, that one must be Baek Seung Jo's room?!
Please, please!
Spare me!
Just go already!
Ha Ni, you came?
You're here early!
Ah, yes.
Why aren't you coming in?
Well, today is just...
Are they your friends ?
Ah, hello.
Ah!
You, you're Lady Gaga, right?
Oh, yes.
Aaah, the pizza lady!
That's right!
Ah!
Hello.
And you?
You're the friend who was in the relay. Right?
Yes. Hello.
They were curious about where I'm living, but they're leaving now, right?
Bye!
Omo, go where? Come in.
Okay.
Shall I make some strawberry Bingsu (a mixture of fruits, ice cream and shaved ice) for you?
You can leave after you eat it.
Aigoo!
Aigoo!
Oh!
This looks really delicious!
Really?
For real?
You're just loving this, aren't you?
Oh! Son, you came?
Hyung!
Spreading rumors wasn't enough, so you even brought them here?
No, that's...
You should know I've already scolded her.
Is this your house?
I invited them in.
It's so much fun!
It feels like there are actually people living here.
But these friends asked me if I'm really your mom.
They asked if I'm not really your older sister.
Oh Ha Ni.
Are you testing my patience?
Oh?
I told you to stop doing this to me. And not to interfere with my life anymore!
How far do you intend to go with this?
Just give it a rest!
What do you think you're doing now?
It was me who took that picture, and it was me who put that picture in the book without telling anyone.
Why are you scolding Ha Ni?!
You too, Mom, please!
Take down that blog right this instant.
Omo?
What makes you so mighty that you can tell me what to do with my hobby?
Is ruining your son's life really your hobby?
By chance, I heard what's going around school.
So what if rumors were to spread?
What's there to feel sorry about?
Then, we will... ...be leaving now.
Ah, why?
You should have dinner with us.
- Ah, no it's alright.
-Goodbye.
Ah, why?
You should stay and have dinner here!
Ah, right!
This weekend, we're going to the beach.
Let's go together!
Sorry?
But we have class this week.
Omo!
It's okay to miss just one day.
Oh!
It's going to be fun!
You girls only need to prepare your bathing suits because I'll prepare everything else!
Okay?!
Oh come on, please come on!
Don't ask me the reason.
Can't you just do it for me?
Why?
Did you mess something up again?!
No.
Perhaps, are you sick?
Ah no, I'm not sick at all.
Fine then.
How much do you need?
Ah, 1,000?
No, no. 2,000?
Ah, no, no. 3,000?!
Yes, 3,000 would be good!
3,000?!
Just think of it as spending money for my wedding just a little early.
I just need 3,000.
Will 3,000 be enough?
Yes, 3,000 will be fine!
Then, I'll give it to you!
Oh really?!
Thank you so much, Father!
But, why are you so worked up over 3,000 won (about $2.50)?
Ah, the truth is...
I wanted to get a room.
What?!
3,000, 3,000 won?
Father, are you kidding me right now?!
Kidding? You punk?!
You little ungrateful, shameless rascal!
Are you crazy?!
You little punk!
You want 30,000,000 won ($25,600)!?
Are you stupid?
For what? To rent a room?
Don't waste your time on such unnecessary things and go do something productive.
I'm going to hang up now.
HANG UP!
Don't you know that in order to protect your love you need to have money?
Aish!
Shut up!
Oh, what a fright!
Would you move from there?
That is my place, young man.
Oh! What's this, ahjussi?
So smelly!
Why did you lose your love, young one?
Because of money?
Forget it!
Just go back to sleep!
Love is lonely because fate is on the line.
One puts everything on the line, which is why it's lonely.
What?
When living life is hard and you feel alone, love is what makes such a world look beautiful.
Excuse me? You say that because you don't realize how lonely that kind of love makes oneself.
But... ...does that mean you should give up on love?
Such a bright youth!
Wouldn't you feel sorry towards (Van) Gogh who lived his life more unhappily than we do ours?
What?
Gogh?
Do you know about Gogh's love?
Putting everything you have on the line.
To have no regrets despite losing everything.
You must be able to do that in order to really say that you've been in love.
Wait, wait!
Can't you tell me anything else?!
That's right!
Bong Joon Gu.
Can you really say your love has been tested by fate?
You still haven't even properly confessed your feelings to Ha Ni!
And even if you had, what would be the point?
To not regret loving despite losing everything.
Listen carefully to what I have to say.
While you've been living here there's something I've really come to hate.
People with a bad head, like you, who aren't able to take in the situation, let alone understand their own situation, acting as if they know what's going on and bothering other people.
Don't make me repeat myself.
What I said about you being out of your mind wasn't just empty words. <i>Because of the letter, <i>he embarrassed me in front of all those students and teachers.
Even after going through such shame, I didn't cry.
No, it's alright.
It's totally understandable.
He has every right to do so.
He must be thinking that I planned everything out.
(Sigh!)
I said that's not how it is!
If I were him, I would be really angry too!
It must've been a pretty big shock.
Alright, bye!
Oh Ha Ni?
Are you Oh Ha Ni?
I hate stupid girls. <i>Brought to you by the PKer team @ www.viikii.net</i> <i>I don't know when it was, <i>Ever since I first saw you, <i>Every minute, every second, I keep thinking about you. <i>What you are doing... <i> Where you are right now.
Thank you. <i>Even when I try looking here and there, <i> And stomp on this and that. <i> I keep on liking you, I think I'm going crazy, Ooh. <i> I wonder if you know how I feel,
I'm telling you not to interfere with my life anymore!
How far do you want to keep going with this?!
Will you give it up!? <i> Every day stay by my side and protect me. <i> I love you too much for us to be just friends. <i> So can you please tell me that one word, I love you right now? <i>I love every day, only love me, <i> Please kiss me.
It really looks pretty!
Um.
How is it?
Hi!
Seung Jo, you came down.
They said they're ready and that we should come out.
Oh, really?
Then shall we get going?
Seung Jo, you too.
Put your bag down and quickly come with us!
Go?
Go where?
We're going camping for two days and one night.
I present you...
Auto-Camping.
What?
What about school?
I already called them.
Hyung, I've been kidnapped!
I woke up and found myself in the car!
Come out quickly.
That is the only way to save his life.
Quickly!
I've already packed your luggage.
Your bathing suit too!
You are too much, seriously.
Who is it?!
Ha Ni!
This girl suddenly says she's coming too.
Hello!
I'm comming too!
Who is she?
Hey.
What is this?
Why isn't she here yet?
None of them are here.
Argh, really!
Good morning!
Nothing going on, right?
Teacher, Ha Ni isn't here yet!
Go Min Ah isn't here either.
Jung Ju Ri as well!
They've all gone to have fun.
They said they're going to the beach!
Jealous, right?!
Gone to have fun you said?
Teacher, do you know how scary this world is?!
How could you allow three girls to go to the beach alone?!
It wasn't just the girls; they all went with Baek Seung Jo's family.
Did you say Baek...BAEK SEUNG JO?!
Just kill me instead!
Kill me!
What?
They went on a trip?!
And to add to that, for one night and two days?!
What am I going to do?
Am I going to have to earn some money?
Argh!
What to do now?
What is it, Bong Joon Gu?
You, did you just get here?!
That's not it, Sir.
I'm in a rush and am leaving early.
Leaving early?!
Vice Principal, you see...
Aigoo, my aunt got into a traffic accident so suddenly!
I have to go really quickly now.
R-really?
Then hurry up and go.
Ah yes.
Aigoo, but although I have to go really quickly, I have no money!
Can I borrow this just this once?
Aigoo, this?!
Yes. They said she might pass away any second!
Man, even if this is a piece of crap, it's still something!
The heavens are definitely on my side!
Ha Ni, I'm coming!
Okay, kids, raise your hands!
Quickly cross the road! It's dangerous.
Aigoo, how cute they are!
Alright, let's go!
Oppa!
Oppa!
Oh.
What is it?
We just opened right next to the subway station.
Here.
Be sure to come and have fun!!
But I'm still a student.
Many university students come as well.
But, Oppa, you're really cute.
Ah, yes, thank you.
You should definitely come!
Massage Palace?
Eh?
What's that?
Protect the youth.
Is this a good thing?
Yaah, really!
Let's go!
Ah.
Oppa, do you want to eat some watermelon?
I cut it up nicely so it's easy to eat!
There's a ridiculous amount of watermelon in the fridge.
Oh, but mine is super sweet!
It tastes like honey!
A watermelon should taste like watermelon.
If it tastes like honey, how could it be watermelon?
Wouldn't it be honey?!
So, how did you know we were going to the beach?
Everyone has their ways.
First, you need to have a bathing suit.
Ah, also hairspray and a hairdryer and...
And what else?
Ha Ni, do you have a swimsuit?
Yeah.
I bought it last year, remember?
Hey! Just buy a new one!
Omo, there is even a Noraebang (Karaoke) there?
Should we try out a song, Oppa?!
What is this, a tour bus?
Why would you sing?
Then should we play the "End Letter" game?!
Huh?
Why that?
It's so childish!
Omo!
That's a great idea!
Ha Ni, you really thought well!
Then, let's have the topic be four character sayings!
Mi Na first!
Ee Shim Jun Shim!
(tactic understanding)
Ee Shim Jun Shim?
"Shim"?
Ooh...
"Shim Shim Pur Ee!
(to kill time)
Is "kill time" a four character saying, Mom?
Of course!
Shim Shim Pur Ee!
Hurry up and do it, if you don't you'll be punished!!
You'll have to write your name with your butt!
You're really immature!
One, two...
Ee Shil Jik Go!
(telling the truth!)
Seung Jo.
Ah!
Are you really doing this?
One, two!
Go...
"Go Jang Nan Myeong" ("It takes two to tango" or "One needs help to accomplish anything")
"GojangNanMyeong"?
What does that mean?
It should just be Go Jang Nan Cha! (broken car) instead.
He didn't say "Go Jang Nan Byung" (broken disease), he said "Go Jang Nan Myeong"!
"Go Jang Nan Myeong". It means you can't make sound with just one hand!
Oh.
You're so smart!
Did you guys get that?
So stupid!
Yu Yu Sang Jong!
(Birds of a feather flock together!)
Hey!
Hurry and go.
"Go Jang Nan Myeong"!
- One - Myeong, Myeong?
Two.
"Myeong Myeong Baek Baek!"
(Crystal clear!)
Baek?
Baek.
One.
Wait a second.
What starts with Baek?
Baek?!
Two.
Three!
"Baek Seung Jo Jjang!"
(Baek Seung Jo is the best!)
You wanted to say those words so badly, that's why you asked to play this game, right?!
No.
Are you crazy?!
It's just that there were no other words! <i>Brought to you by the PKer team @ www.viikii.net
Is it ready?!
Aigoo, thank you!
Whoa! This is great!
Kids, come get some drinks!
Yes!
I should have bought Ha Ni a bikini!
She looks pure and pretty! A high school girl's charm is her innocence.
- Oh.
- Oh.
What's that, Oh Ha Ni?!
You have to use a tube?!
I don't even need one.
Yeah, I can't swim very well.
Seung Jo, does Ha Ni look pretty?
Doesn't she look like a high school student?
She looks like an elementary student.
You're pretty, Ha Ni.
You're the prettiest!
That's right.
Ha Ni is the prettiest.
Our Ha Ni is in bikini season. "Best"! I mean best.
I forgot.
You need these.
What is this!
They're socks.
Why did he give these to you? <i>What is that?
They look like socks.
God, I will kill that guy today and go to hell!
HEY!!
Ha Ni!
Oh, Ha Ni!
Are you okay?
Are you okay?
Nothing happened, right?
Those socks were for you to wear.
Aren't you going to come here?
BAEK SEUNG JO!!
What is this? What's wrong with you?
Why is this suddenly being like this?!
Has it already lived its life?
We're almost there, so why are you being like this?
Aish!
Is it out of gas?
I don't have any money, what will I do?
Really!
Is there any gas?
Let's see, let's see.
Is it there, or is it empty?
It's too dark, I can't see anything.
Ah, that's right.
Aish.
Oh, what's up with this?
This is interesting.
Here. Let's see, let's see.
Here.
Oh!
Dad, what is that?
Don't know.
Did it fall from the sky?!
No.
I'm taking the picture!
Kimchi!
Is it done?!
Yeah!
Next time, we should ask someone else to take the photo.
Go Mi didn't come.
Seung Jo Oppa!
Hyung!
Oh.
Well done!
Man.
That dung fly, Hong Jang Mi, is getting in the way.
I absolutely hate her!
Look at that!
Kids!
Let's eat some watermelon!
I think she's calling us!
Ha Ni!
Come!
Let's go!
I'm so hungry!
The watermelon looks yummy!
Oh.
Wait just a second!
Hey!
Bbong (padding) Ha Ni!
What?
Stop kidding around!
Bbong!
A tree goes plop and farts, "Bbong!!"
HEY!
Baek Eun Jo! <i>Bbong bboro bbong bbong, bbong bbong!
You really, to your Noona?! <i>Bbong bboro bbong bbong, bbong bbong!</i>
What?!
I'll scold you!
HEY!
What's wrong with you?
Try and catch me!
Just try.
Come in. You can't swim, can you?!
Just try and come!
HEY!
Baek Eun Jo.
Just try and come out!
Hey!
Are you faking this?!
You've got to better than that if you're just fooling around.
HELP ME!
HELP ME, PLEASE!
What?!
Is this real?!
Hey!
Baek Eun Jo!
Hey!
Someone fell in the water!
Someone help!
Dad!
After telling them to come eat watermelon, they go right back in. Their maturity level is the same.
They're just innocent!
Honey, our throats are getting dry!
Watermelon for me, too!!
I'll give you watermelon.
Here's some. Say "ah".
Eat some watermelon!
What?!
They fell?!?!
What?!
Honey, what's going on?!
What?!
Hey!
Ha Ni!
Ha Ni!
Just stay still!
Eun Jo!
Eun Jo!
Are you alright?!
Are you okay?!
Eun Jo!
You're okay?!
Yes?!
Our son!
Wow! This looks so good!
Seung Jo.
Go give Ha Ni some water.
Warm water.
I'll go give it to her.
Oh no, no!
Jang Mi, you cook the beef.
Pardon?
Baek Seung Jo, quickly!
My goodness.
Are you okay, Ha Ni?!
You don't have to go to the hospital?
No. You were scared, weren't you?
Of course!
I was so surprised, my heart is still pounding.
It had to be when I was under the sand.
It's okay.
I came right out.
What do you mean "it's okay"?
I couldn't move because of the sand, but there you were right in front of me flailing around!
At that moment, I was thinking...
"This is what they call hell."
I'm sorry, Dad.
Do you want some water?
Seung Jo, thank you so much.
If you hadn't been there, what would have happened?
It was nothing.
For that, I will pay you back with a killer dinner.
You can't swim and without fear...
What was I supposed to do?
Even when I yelled, no one could hear me.
You are an accident prone troublemaker.
I haven't had a days rest since meeting you.
Why are you being mean again?
I'm still sick.
Sick...
Who... Who are you?
Where is my Ha Ni?
Is it all ready?
Yes.
Then, all of the men go to the tent!
What about Eun Jo?
Since Eun Jo's sick, he has to sleep with me.
Yes.
Yes.
Children!
Wow, it's our sleeping quarters.
Wow, this is great!
I get top bunk.
Wow, jackpot! So great!
I call this spot!
It really changed!
Go, go, go!
You got the top bunk.
Must be nice!
Must be nice!
You're not tired?
I'm okay.
What?
Hey, hey, you took one!
Hey! <i>Brought to you by the Pker team @ www.viikii.net
You know how to play guitar too?
I borrowed some of your clothes.
Okay.
I heard that you saved Ha Ni.
I should have come a little earlier.
Well, I guess you did your fair share.
Did you come all the way here because of Oh Ha Ni?
Of course I did!
I don't care what a stiff genius you are; you're still a puberty stricken 18 year old!
I don't know when you'll turn into a beast, so I've got to watch you day and night.
Why?
You should just move into our house then.
Do you have an empty room?
I'm warning you!
Don't you dare make a move on her!
Remember that I'm always watching from somewhere.
Got it?
You like Oh Ha Ni that much?
Man, if you ask me that directly, it's a bit overwhelming.
Whatever I become, I need to hurry up and get a job.
My dream is to make Ha Ni happy. Yeah.
You guys look good together, you and Oh Ha Ni.
Really?
You think so?
You're different than what I thought, Baek Seung Jo.
Definitely different.
Yeah, really different.
You have some taste.
Yeah.
Ha Ni doesn't look good with you.
Doesn't matter how much Ha Ni likes you.
That'll end in good time.
Huh.
Baek Seung Jo, should we be friends?
No.
Why?
Okay, okay.
Do whatever you want.
I don't need a friend like you. As long as I have Ha Ni, I'm good.
Hey, sing a song. <i>Once again, he has come a long way in order to protect you. <i>Playful Kiss.
Ha Ni.
It was great when we were playing.
Seriously.
There are so many colleges, we'll get into one, right?
Of course.
Is this arrogance I see because you got into the top fifty within a week?
It's not that.
Ah!
You guys should be playing at this age. What kind of suffering is this? So sad.
It is, huh?
You feel really sad for us, don't you?
We'll eat well.
Thank you very much.
Kids, if there's something you don't know, ask him.
What else would you use a smart kid for?
Fighting.
Fighting.
Thank you.
Did you see?
Her face is the size of my fist.
Whoa.
Ha Ni, this is no joke for you.
No.
It's mother's (Seung Jo's mother) preferences.
Oh, mother?
What?
It's my friend's mother.
Oh, look at this.
What is this?
"Things To Do With Seung Jo."
- "A date at the Nam Mountains."
- Hey!
- "Piggyback ride amongst a lot of people."
- Hey, hey!
- "Holding hands." - "Talking on the phone all night long!"
"Getting married!"
It's completely decorated with Baek Seung Jo.
Give it to me!
Ha Ni!
Hey, what are you doing?
I thought Baek Seung Jo was really skinny, but ever since we went on the trip, I found out he's a man.
Oh.
He must work out. His back muscles look really firm.
Hey.
Even talking about him gets you excited?!
You like him that much?
Ah, really.
Study, study!
Right.
Number 1.
1/4 of this...
That's the equation.
The answer...
What are you talking about?
Should we start with number 2?
What?
What? <i>What?</i>
Hurry and go.
Hurry, hurry, hurry.
Get up, get up.
Yes?
Eun Jo, not there, but higher.
Here?
Excuse me.
Do you have a bit of time?
No.
Right? Okay.
Hi!
What the heck, Oh Ha Ni?!
You see, I'm studying with my friends and there's a problem we don't understand.
We just can't seem to get it.
I don't want to.
Come on, it won't even take you a minute.
30 seconds, just 30 seconds!
Even 30 seconds is a waste of my time.
A waste of your time?
Our lives depend on your 30 seconds.
At least you speak well.
It's this one! What about this do you not understand?
Huh? <i>Brought to you by the PKer team @ www.viikii.net
There, right?
Wow!
Yes.
Thanks.
Thanks a lot!
Oh, I see.
He solved it so simply, even I can understand it.
Alright then, the next problem!
Let's go for the next one!
Excuse me.
Excuse me.
Just one more.
You're going to sleep?
The next equation as well...
I'm sorry!
Hey!
Come back in 15 minutes!
Try going in.
Yeah, it's been 15 minutes...
I'm scared.
Hurry up!
I just can't do it!
Hurry up and go in!
Oh my, oh my!
Are you happy?!
Don't you dare come near my room now!
Ah, I see.
What if I actually get into a university like this?!
It would be nice if he could help with our other subjects too.
That's right!
We have free time this week!
Are you out of your minds?!
How can you ask that after seeing how he reacted last night?
Hey.
What's this?
Wow!
Hey, what are you doing?!
Why are you bothering Ha Ni?
Oh Ha Ni.
Who solved these for you?
Baek Seung Jo worked them out for you, didn't he?
I heard you two live together.
No, that is...
Move it, move it, move it!
That's right, the god, Baek Seung Jo solved them!
Why?
Are you guys jealous?!
You guys study with Baek Seung Jo?!
What is it? What are they talking about?
Oh Ha Ni.
Let me in too.
Huh?
Me too! Me too!
Me too!
What are you talking about?
Don't you guys have any pride?!
Joon Gu!
What?!
Does pride get you into university?
What?! Pride?!
You little! You're supposed to study on your own!
Who are you asking to teach you?!
Isn't that right?
Right, right?
Hey, you, yellow head!
You're going to go too?
Just look at them! Fine! Go, go!
Oh really?
Fine!
Just go, go, go!
Hey. Hey. One.
What? Man!
Why are there so many shoes?
- He's here!
- Hello, Teacher!
Mom, what the heck are these--?
They all came to see you.
Baek Seung Jo!
Tutor us too.
- Me too!
- Me too!
- Me too!
Jeez!
Oh Ha Ni.
No way.
I'm a bit tired.
Dear, where are you going?
Mom is so very happy! That my son, can be of help to someone like this.
You're happy?!
Hey, Oh Ha Ni!
You better come out!
Just this once?
Oh Ha Ni, you really...
Save our class, just this once! I will never forget your kindness!
We'll never forget!
Please help us!
Please save us!
The object on the ground, has a mass of 2 kilograms.
If 10 newtons of force are applied, with a frictional force of 4 newtons, what is the highest speed this object can reach?
With this problem, you use the equation of F = ma.
Ahhh~
If F = ma, what is F?
Force.
M is mass.
Ah.
A is acceleration.
Oh, I see!
What we're looking for is the value of "a".
Therefore A = F/M.
In this case, force is 10 newtons and mass is 2 kilograms.
Oh?
I'll do the dishes!
I'm all done.
Your friends left?
I told you to have them over for dinner.
I couldn't.
You even made lunch for all of them.
Do you think studying is going to get you anywhere?
Baek Eun Jo, that's a yellow card for you.
One more time and you're out.
What should we have for dinner?
Sweet and sour pork!
No way!
It seems like Seung Jo doesn't like sweet and sour pork very much.
When we have it for lunch, he barely eats any of it.
I like it!
That's right.
Seung Jo doesn't really like it.
I said that I like it!
Are you tired?
Obviously.
Water?
You want water?!
This one is cold.
Never mind.
Here.
Oh, really!
That one was just put in.
Stop.
Hello.
Yes! What's happening?
Really?
What should I do?
I'll leave right away!
Yes. I'm hanging up.
What should I do?
What am I going to do?
What should I do?
What to do, what to do?
My husband is going to go straight there as well!
So you two figure out your own dinners, alright?
- Why isn't Hyung going?
- Hyung has to study, he's a senior.
Don't come out! You two stay here!
Hey.
Hurry.
Sorry, Ha Ni.
Bye. <i>Brought to you by the PKer team @ www.viikii.net</i>
Where are you going?
I'm going to go get food.
I'll make it!
As a thank you for yesterday as well as today.
You're going to?
What's with you?
Even though I look like this, I am Oh Gi Dong's daughter!
Always treating me like an idiot.
This time...
"Hawaiian Loco Moco"?
"On a bed of warm rice..."
"...place a thick patty of meat."
"Pour a generous amount..."
"...of gravy sauce."
"Place a sunny side up fried egg on top."
"The point is to dip the meat in the yolk."
Awesome!
Baek Seung Jo, you're going to be absolutely amazed.
What? The big problem was this?
Mom's good at acting, isn't she?
The bank lady called.
She must be wondering what I was talking about.
You told me to come here all of a sudden, so I thought something had happened too.
But something did happen.
Her whole class came over.
Oh really.
Hey, Ha Ni is something else.
That's what I said.
Ha Ni, she's got strength.
She's got bad grades.
All she has is strength.
Hey, you rascal!
Are you just going to keep saying what's true?
Oh, that picture?
We took it right in front here, when we were going to start remodeling the restaurant.
It was around the time my wife passed away so Ha Ni must have been... ...it was when she was four years old.
You're not interested in getting remarried?
Well, if someone as great as you appears.
But really, if Ha Ni gets married, you'll be lonely by yourself.
Married?
Just hearing the word brings tears to my eyes.
There's no need for that!
We can live together!
Huh?
Then again, I don't know if we should leave those two alone like that.
I left the two home on purpose.
The air between those two seemed so bad.
Guys and girls, if they're alone, it all works itself out naturally.
Hey, are you going to give me food or not?
Hey, what's happening?
I'm sorry.
It' got slightly burned.
This burnt thing, what is it supposed to be?
Hawaiian Loco Moco.
Hawaiian what?
Loco Moco.
This is only slightly burned?
This isn't dinner, this is just mush.
Why?
You don't like mush?
Hey!
Are you telling me to eat this right now?
When do we spray this on?
Just bring the water.
Yes.
Wow.
It's amazing.
It's just like the ones in a restaurant.
It's really good!
How did you cook the egg so it's so soft?
And so quickly!
It didn't even take 30 minutes.
Because I'm smart.
Huh?
Cooking is all smarts too.
Ah, really?
Then my dad must be super smart.
Then is Bong Joon Gu smart too?
Joon Gu is really good at cooking too.
No way.
It's true.
He sold Dduk Bokk Gi and Ma Tang for the festival and it was totally good.
Hey!
Is making Dduk Bokk Gi cooking?
It is. Those types of food are the hardest.
The dishes that are eaten by a lot of people, it's hard to accommodate each person's tastes.
Even the Ma Tang, the outside was really crispy and the inside so very soft.
You know how typically it's really mushy and sticky--
You're already done?
I only had a spoonful!
Clean it all up, and do the dishes too!
I really only had one bite.
[So Pal Bok Noodles]
Thank you!
Let's go to Noraebong (karaoke)!
Noraebong?
I'm tired, let's go home. It's only 10:00!
Let's go to Noraebong.
Noraebong?
Oh my, seems like you're having fun.
I can't, I have an important English test.
I've got to prepare for it.
Don't worry about me and have fun.
Teddy.
Though he's always so fussy, he still does everything.
Where did my English book go?!
Why is that the only one missing?
"Talk all night! Get married!"
No one can see that!
It's so embarassing!
What will I do?
I'm going to get made fun of so much!
Oh, yeah! He's sleeping.
You rascal, so nice of you!
Where is it?
He sleeps so beautifully.
What is this?
He only reads the original editions?
Why are you acting like a thief?
That's not it.
I had to look for something.
Do you expect me to believe that?
Of all times, when no one was in the house but the two of us, you suddenly have something to look for?
What?
No. Really.
Bong Joon Gu said... ...that we're all puberty stricken 18 year olds.
Why are you acting like this?
What do you mean "why are you acting like this"?
Isn't this why you came in here?
What?
No way!
What's it matter?
We're the only ones in the house right now.
Seung Jo, why are you acting like this?
Seung Jo ssi! <i>Brought to you by the PKer team @ www.viikii.net</i>
What major?
Why would you go to university?
When you find something you like, your heart starts to beat fast.
What's going on?
Shut up!
I knew we would be far apart.
Hello?
Yes, yes, yes, I will go!
I'll be there! Thank you!
Where are you?
Ha Ni, why don't you go in first for now?
You got it!
You got it!
Seung Jo got it for me.
Do you think I won this so I could play with it?
If you come to my university, I could keep you entertained.
You're going to take the exam tomorrow, right?
Did you catch a cold?
This won't make me drowsy, right?
I hear you fed Seung Jo Oppa sleeping pills.
Please tell me it's not like that.
That nothing happened.
Mawlaya salli wa sallim da'iman abadan (My Lord send Your peace and blessings always and forever)
'Ala habibika khayril khalqi kullihimi (Upon Your beloved, the best of the entire creation)
Mawlaya salli wa sallim da'iman abadan (My Lord send Your peace and blessings always and forever)
'Ala habibika khayril khalqi kullihimi (Upon Your beloved, the best of the entire creation)
Ya Rabbee salli 'aleeh (My Lord send Your peace upon him)
Salawatu Allahi 'aleeh (May Allah's salutations be upon him)
All the poetry ever written
Every verse and every line
All the love songs in the world
And every melody and rhyme
If they were combined
They would still be unable to express
What I want to define
When I try to describe my love for you
Mawlaya salli wa sallim da'iman abadan (My Lord send Your peace and blessings always and forever)
'Ala habibika khayril khalqi kullihimi (Upon Your beloved, the best of the entire creation)
Mawlaya salli wa sallim da'iman abadan (My Lord send Your peace and blessings always and forever)
'Ala habibika khayril khalqi kullihimi (Upon Your beloved, the best of the entire creation)
Ya Rabbee salli 'aleeh (My Lord send Your peace upon him)
Salawatu Allahi 'aleeh (May Allah's salutations be upon him)
Every sound and every voice
In every language ever heard
Each drop of ink that has been used
To write every single word
They could never portray
Everything I feel in my heart and want to say
And it's hard to explain
Why I could never describe my love for you
Mawlaya salli wa sallim da'iman abadan (My Lord send Your peace and blessings always and forever)
'Ala habibika khayril khalqi kullihimi (Upon Your beloved, the best of the entire creation)
Mawlaya salli wa sallim da'iman abadan (My Lord send Your peace and blessings always and forever)
'Ala habibika khayril khalqi kullihimi (Upon Your beloved, the best of the entire creation)
Ya Rabbee salli 'aleeh (My Lord send Your peace upon him)
Salawatu Allahi 'aleeh (May Allah's salutations be upon him)
There's not a single person Who can ever match his worth
In character and beauty To ever walk on earth
I envy every rock and tree And every grain of sand
That embraced his noble feet
Or that kissed his blessed hands
Ya Rasool Allah (O Messenger of Allah)
Ya Habiba Allah (O Allah's Beloved)
Grant us the chance to be with him
We pray to You Allah
Mawlaya salli wa sallim da'iman abadan (My Lord send Your peace and blessings always and forever)
'Ala habibika khayril khalqi kullihimi (Upon Your beloved, the best of the entire creation)
Mawlaya salli wa sallim da'iman abadan (My Lord send Your peace and blessings always and forever)
'Ala habibika khayril khalqi kullihimi (Upon Your beloved, the best of the entire creation)
Ya Rabbee salli 'aleeh (My Lord send Your peace upon him)
Salawatu Allahi 'aleeh (May Allah's salutations be upon him)
Mawlaya salli wa sallim da'iman abadan (My Lord send Your peace and blessings always and forever)
'Ala habibika khayril khalqi kullihimi (Upon Your beloved, the best of the entire creation)
Mawlaya salli wa sallim da'iman abadan (My Lord send Your peace and blessings always and forever)
'Ala habibika khayril khalqi kullihimi (Upon Your beloved, the best of the entire creation)
Ya Rabbee salli 'aleeh (My Lord send Your peace upon him)
Salawatu Allahi 'aleeh (May Allah's salutations be upon him)
We're told to find the x- and y-intercepts for the graph of this equation:
2 y plus 1/3x is equal to 12. And just as a bit of a refresher, the x-intercept is the point on the graph that intersects the x-axis. So we're not above or below the x-axis, so our y value must be equal to 0.
So let's set each of these values to 0 and then solve for what the other one has to be at that point. So for the x-intercept, when y is equal to 0, let's solve this. So we get 2 times 0, plus 1/3x is equal to 12.
I'm trying my best to draw a straight line.
And notice where the line intercepted or intersected the y-axis, that's the y-intercept, x is 0, because we're not to the right or the left of it. Where the line intersected the x-axis, y is 0, because we're not above or below it.
Solve for C and graph the solution.
We have have -5C is less than or equal to 15.
So -5C is less than or equal to 15.
I just rewrote it a little bit bigger.
So if we want to solve for C, we just want to isolate this C right over here, maybe on the left -hand side.
Its right now being multiplied by -5
So the best way to just have a C on the left-hand side is we can multiply both sides of this inequality by the inverse of -5 or by -(1/5).
So we want to multiply -(1/5) times -5C and we also want to multiply 15 times - (1/5).
I'm just multiplying both sides of the inequality by the inverse of -5, because this will cancel out with -5 and will leave me just with C. Now I didn't draw the inequality here, because we have to remember if we multiply or divide both sides of an inequality by a negative number, you have to flip the inequality and we are doing that.
So we need to turn this from a less than or equal to a greater than or equal.
And now we can proceed solving for C. So -(1/5) times -5 is 1, so the left-hand side is just going to be
C is greater than or equal to 15 times -(1/5). That's the same thing as 15 divided by -5.
And so that is -3.
So our solution is C is greater than or equal to -3 and let's graph it.
So that is my number line.
Let's say that is 0, -1, -2, -3 and that can go above 1 too.
And so C is greater than or equal to -3, so it can be equal to -3, so I'll fill that in right over there. Let me do it in a different color.
So I'll fill it in right over there and then its greater than as well.
So its all of these values I am filling in in green.
And you can verify that it works in the original inequality.
Pick something that should work.
Well 0 should work.
0 is one of the numbers that we filled in.
-5 times 0 is 0, which is less than or equal to 15, its less than 15.
Now let's try a number that's outside of it.
And I haven't drawn it here, I could continue with the number line in this direction. You would have a -4 here.
-4 times -5 is +20 and +20 is not less than 15 so its good that we did not include -4.
So this is our solution and this is that solution graphed.
And I wanted to do that in the other green color.
Here you go, that's what it looks like.
I'm going to do a quick argument or proof, as to why the diagonals of a rhombus are perpendicular.
So remember, a rhombus is just a parallelogram, where all four sides are equal.
In fact, if all four sides are equal, it has to be a parallelogram.
Just to make things clear, some rhombuses are squares, but not all of them, because you could have a rhombus like this, that comes in where the angles aren't 90°.
But squares are rhombuses, because all squares they have 90° angles, that's not what makes them a rhombus, but all of the sides are equal.
So all squares are rhombuses, but not all rhombuses are squares.
Now, with that said, let's think about the diagonals of a rhombus, to think about that a little bit clearer,
I'm going to draw the dia- I'm going to draw the rhombus really as kind of,
I'm going to rotate it a little bit, so it looks a little bit like a diamond shape.
But notice, I'm not really changing the properties of the rhombus, I'm just changing its orientation a little bit.
I'm just changing its orientation.
So, a rhombus, by definition, the four sides are going to be equal.
Now, let me draw one of its diagonals, and the way I drew it right here is kind of a diamond.
One of its diagonals will be right along the horizontal, right like that.
Now this triangle on the top and the triangle on the bottom both share this side.
So that side is obviously is going to be the same length for both of these triangles.
In the other two sides of the triangles are also the same thing, they're sides of the actual rhombus.
So all three sides of this top triangle and the bottom triangle are the same.
So this top triangle and this bottom triangle are congruent.
They are congruent triangles.
If you go back to your 9th grade Geometry unit, you'd use the Side-Side-Side (SSS) theorem: if three sides are congruent, then the triangles themselves are congruent.
That also means all of the angles in the triangle are congruent.
So the angle that is opposite this side, this shared side, right over here will be congruent to the corresponding angle in the other triangle.
The angle opposite this side would be the same thing as that.
Now, both of these triangles are also isosceles triangles, so their base angles are going to be the same.
So that's one base angle, that's the other base angle.
This is an upside down isosceles triangle, this is a right-side-up one.
And so, if these two are the same then these are also going to be the same.
They are going to be the same to each other, because this is an isosceles triangle.
And, they're also going to be the same to these other characters, down here, because these are congruent triangles.
Now, if we take an altitude...
No, actually I don't have to talk about that since, I don't think that will be relevant when we actually prove what we want to prove.
If we take an altitude from each of these vertices, down to this side, so an altitude by definition.
An altitude by definition is going to be perpendicular down here.
Now, an isosceles triangle is perfectly symmetrical.
If you drop an altitude from the the top, or the unique angle, or the unique vertex in an isosceles triangle you will split it into two symmetric right triangles.
Two right triangles that are essentially the mirror images of each other.
You will also bisect the opposite side.
This altitude is, in fact, a median of the triangle.
Now, we could do it on the other side, the same exact thing is going to happen. We are bisecting this side over here, this is a right angle.
And so essentially, the combination of these two altitudes is really just a diagonal of this rhombus, and it's at a right angle to the other diagonal of the rhombus. And it bisects that other diagonal of the rhombus. We can make the exact same argument over here.
You could think of an isosceles triangle, over here.
This is an altitude of it, it splits it into two symmetric right triangles, it bisects the opposite side, it's essentially a median of that triangle.
Any isosceles triangle, of that side equal to that side, if you drop an altitude, these two triangles are going to be symmetric, and you will have bisected the opposite side. So, by the same argument, that side is equal to that side.
So the two diagonals of any rhombus are perpendicular to each other and they bisect each other.
Anyway, hopefully you found that useful.
I have here a bunch of radical expressions, or square root expressions.
And what I'm going to do is go through all of them and simplify them.
And we'll talk about whether these are rational or irrational numbers.
So let's start with A.
A is equal to the square root of 25.
Well that's the same thing as the square root of 5 times 5, which is a clearly going to be 5.
We're focusing on the positive square root here.
Now let's do B.
B I'll do in a different color, for the principal root, when we say positive square root.
B, we have the square root of 24.
So what you want to do, is you want to get the prime factorization of this number right here.
So 24, let's do its prime factorization.
This is 2 times 12.
12 is 2 times 6.
6 is 2 times 3.
So the square root of 24, this is the same thing as the square root of 2 times 2 times 2 times 3.
That's the same thing as 24.
Well, we see here, we have one perfect square right there.
So we could rewrite this.
This is the same thing as the square root of 2 times 2 times the square root of 2 times 3.
Now this is clearly 2.
This is the square root of 4.
The square root of 4 is 2.
And then this we can't simplify anymore.
We don't see two numbers multiplied by itself here.
So this is going to be times the square root of 6.
Or we could even right this as the square root of 2 times the square root of 3.
Now I said I would talk about whether things are rational or not.
This is rational.
This part A can be expressed as the ratio of 2 integers.
Namely 5/1.
This is rational.
This is irrational.
I'm not going to prove it in this video.
But anything that is the product of irrational numbers. And the square root of any prime number is irrational.
I'm not proving it here.
This is the square root of 2 times the square root of 3.
That's what the square root of 6 is.
And that's what makes this irrational.
I cannot express this as any type of fraction.
I can't express this as some integer over some other integer like I did there.
And I'm not proving it here.
I'm just giving you a little bit of practice.
And a quicker way to do this.
You could say, hey, 4 goes into this.
4 is a perfect square.
Let me take a 4 out.
This is 4 times 6.
The square root of 4 is 2, leave the 6 in, and you would have gotten the 2 square roots of 6.
Which you will get the hang of it eventually, but I want to do it systematically first.
Let's do part C.
Square root of 20.
Once again, 20 is 2 times 10, which is 2 times 5.
So this is the same thing as the square root of 2 times 2, right, times 5.
Now, the square root of 2 times 2, that's clearly just going to be 2.
It's going to be the square root of this times square root of that.
2 times the square root of 5.
And once again, you could probably do that in your head with a little practice.
The square root of the 20 is 4 times 5.
The square root of 4 is 2.
You leave the 5 in the radical.
So let's do part D.
We have to do the square root of 200.
Same process.
Let's take the prime factors of it.
So it's 2 times 100, which is 2 times 50, which is 2 times 25, which is 5 times 5.
So this right here, we can rewrite it.
Let me scroll to the right a little bit.
This is equal to the square root of 2 times 2 times 2 times 5 times 5.
Well we have one perfect square there, and we have another perfect square there.
So if I just want to write out all the steps, this would be the square root of 2 times 2 times the square root of 2 times the square root of 5 times 5.
The square root of 2 times 2 is 2.
The square root of 2 is just the square root of 2.
The square root of 5 times 5, that's the square root of 25, that's just going to be 5.
So you can rearrange these.
2 times 5 is 10.
10 square roots of 2.
And once again, this is irrational.
You can't express it as a fraction with an integer and a numerator and the denominator.
And if you were to actually try to express this number, it will just keep going on and on and on, and never repeating.
Well let's do part E.
The square root of 2000.
I'll do it down here.
Part E, the square root of 2000.
Same exact process that we've been doing so far.
Let's do the prime factorization.
That is 2 times 1000, which is 2 times 500, which is 2 times 250, which is 2 times 125, which is 5 times 25, which is 5 times 5.
And we're done.
So this is going to be equal to the square root of 2 times 2-- I'll put it in parentheses-- 2 times 2, times 2 times 2, times 2 times 2, times 5 times 5, times 5 times 5, right?
We have 1, 2, 3, 4, 2's, and then 3, 5's, times 5.
Now what is this going to be equal to?
Well, one thing you might see is, hey, I could write this as, this is a 4, this is a 4.
So we're going to have a 4 repeated.
And so this the same thing as the square root of 4 times 4 times the square root of 5 times 5 times the square root of 5.
So this right here is obviously 4.
This right here is 5.
And then times the square root of 5.
So 4 times 5 is 20 square roots of 5.
And once again, this is irrational.
Well, let's do F.
The square root of 1/4, which we can view this is the same thing as the square root of 1 over the square root of 4, which is equal to 1/2.
Which is clearly rational.
It can be expressed as a fraction.
So that's clearly rational.
Part G is the square root of 9/4.
Same logic.
This is equal to the square root of 9 over the square root of 4, which is equal to 3/2.
Let's do part H.
The square root of 0.16.
Now you could do this in your head if you immediately recognize that, gee, if I multiply 0.4 times 0.4, I'll get this.
But I'll show you a more systematic way of doing it, if that wasn't obvious to you.
So this is the same thing as the square root of 16/100, right?
That's what 0.16 is.
So this is equal to the square root of 16 over the square root of 100, which is equal to 4/10, which is equal to 0.4.
Let's do a couple more like that.
OK.
Part I was the square root of 0.1, which is equal to the square root of 1/10, which is equal to the square root of 1 over the square root of 10, which is equal to 1 over-- now, the square root of 10-- 10 is just 2 times 5.
So that doesn't really help us much.
So that's just the square root of 10 like that.
A lot of math teachers don't like you leaving that radical in the denominator.
But I can already tell you that this is irrational.
You'll just keep getting numbers.
You can try it on your calculator, and it will never repeat.
Your calculator will just give you an approximation.
Because in order to give the exact value, you'd have to have an infinite number of digits.
But if you wanted to rationalize this, just to show you.
If you want to get rid of the radical in the denominator, you can multiply this times the square root of 10 over the square root of 10, right?
This is just 1.
So you get the square root of 10/10.
These are equivalent statements, but both of them are irrational.
You take an irrational number, divide it by 10, you still have an irrational number.
Let's do J.
We have the square root of 0.01.
This is the same thing as the square root of 1/100.
Which is equal to the square root of 1 over the square root of 100, which is equal to 1/10, or 0.1.
Clearly once again this is rational.
It's being written as a fraction.
This one up here was also rational.
It can be written expressed as a fraction.
Please close your eyes, and open your hands.
Now imagine what you could place in your hands: an apple, maybe your wallet.
Now open your eyes.
What about a life?
What you see here is a premature baby.
He looks like he's resting peacefully, but in fact he's struggling to stay alive because he can't regulate his own body temperature.
This baby is so tiny he doesn't have enough fat on his body to stay warm.
Sadly, 20 million babies like this are born every year around the world.
Four million of these babies die annually.
But the bigger problem is that the ones who do survive grow up with severe, long-term health problems.
The reason is because in the first month of a baby's life, its only job is to grow.
If it's battling hypothermia, its organs can't develop normally, resulting in a range of health problems from diabetes, to heart disease, to low I.Q.
Many of these problems could be prevented if these babies were just kept warm.
That is the primary function of an incubator.
But traditional incubators require electricity and cost up to 20 thousand dollars.
So, you're not going to find them in rural areas of developing countries.
As a result, parents resort to local solutions like tying hot water bottles around their babies' bodies, or placing them under light bulbs like the ones you see here -- methods that are both ineffective and unsafe.
I've seen this firsthand over and over again.
On one of my first trips to India, I met this young woman, Sevitha, who had just given birth to a tiny premature baby, Rani.
She took her baby to the nearest village clinic, and the doctor advised her to take Rani to a city hospital so she could be placed in an incubator.
But that hospital was over four hours away, and Sevitha didn't have the means to get there, so her baby died.
Inspired by this story, and dozens of other similar stories like this, my team and I realized what was needed was a local solution, something that could work without electricity, that was simple enough for a mother or a midwife to use, given that the majority of births still take place in the home.
We needed something that was portable, something that could be sterilized and reused across multiple babies and something ultra-low-cost, compared to the 20,000 dollars that an incubator in the U.S. costs.
So, this is what we came up with.
What you see here looks nothing like an incubator.
It looks like a small sleeping bag for a baby.
You can open it up completely.
It's waterproof.
There's no seams inside so you can sterilize it very easily.
But the magic is in this pouch of wax.
This is a phase-change material.
It's a wax-like substance with a melting point of human body temperature, 37 degrees Celsius.
You can melt this simply using hot water and then when it melts it's able to maintain one constant temperature for four to six hours at a time, after which you simply reheat the pouch.
So, you then place it into this little pocket back here, and it creates a warm micro-environment for the baby.
Looks simple, but we've reiterated this dozens of times by going into the field to talk to doctors, moms and clinicians to ensure that this really meets the needs of the local communities.
We plan to launch this product in India in 2010, and the target price point will be 25 dollars,
less than 0.1 percent of the cost of a traditional incubator.
Over the next five years we hope to save the lives of almost a million babies.
But the longer-term social impact is a reduction in population growth.
This seems counterintuitive, but turns out that as infant mortality is reduced, population sizes also decrease, because parents don't need to anticipate that their babies are going to die.
We hope that the Embrace infant warmer and other simple innovations like this represent a new trend for the future of technology: simple, localized, affordable solutions that have the potential to make huge social impact.
In designing this we followed a few basic principles.
We really tried to understand the end user, in this case, people like Sevitha.
We tried to understand the root of the problem rather than being biased by what already exists.
And then we thought of the most simple solution we could to address this problem.
In doing this, I believe we can truly bring technology to the masses.
And we can save millions of lives through the simple warmth of an Embrace.
In this presentation we're going to learn how to graph trig functions without having to kind of graph point by point. And hopefully after this presentation you can also look at a trig function and be able to figure out the actual analytic definition of the function as well.
So let's start.
Let's say f of x.
Let me make sure I'm using all the right tools.
So let's say that f of x is equal to 2 sine of 1/2 x.
So when we look at this, a couple interesting things here.
How is this different than just the regular sine function?
Well, here we're multiplying the whole function by 2, and also the coefficient on the x-term is 1/2.
And if you've seen some of the videos I've made, you'll know that this term affects the amplitude and this term affects the period, or the inverse of the period, which is the frequency.
Either way.
It depends whether you're talking about one or the inverse of the other one.
So let's start with the amplitude. This 2 tells us that the amplitude of this function is going to be 2. Because if it was just a 1 there the amplitude would be 1.
So it's going to be 2 times that.
So let's draw a little dotted line up here at y equals 2.
And then another dotted line at y equals negative 2.
So we know this is the amplitude.
We know that the function is going to somehow oscillate between these two points, but we have to figure out how fast is it going to oscillate between the two points, or what's its period.
And I'll give you a little formula here.
The function is equal to the amplitude times, let's say, sine, but it would also work with cosine.
The amplitude of the function times sine of 2pi divided by the period of the function, times x.
This right here is a "p."
So it might not be completely obvious where this comes from.
But what I want you to do is maybe after this video or maybe in future videos we'll experiment when we see what happens when we change this coefficient on the x-term.
And I think it'll start to make sense to you why this equation holds.
But let's just take this as kind of an act of faith right now, that 2pi divided by the period is the coefficient on x.
So if we say that 2pi divided by the period is equal to the coefficient, which is 1/2.
I know this is extremely messy.
And this is separate from this.
So 2pi divided by the period is equal to 1/2. Or we could say 1/2 the period is equal to 2pi. Or, the period is equal to 4pi.
So we know the amplitude is equal to 2 and the period is equal to 4pi.
And once again, how did we figure out that the period is equal to 4pi?
We used this formula:
2pi divided by the period is the coefficient on the x-term.
So we set 2pi divided by the period equal to 1/2, and then we solved that the period is 4pi.
So where do we start?
Well, what is f of 0? Well, when x is equal to 0 this whole term is 0.
So what's sine of 0?
Sine of 0 is 0, if you remember.
I guess you could use a calculator, but that's something you should remember.
Or you could re-look at the unit circle to remind yourself.
Sine of 0 is 0. And then 0 times 2 is 0.
So f of 0 is 0.
Right?
We'll draw it right there.
And we know that it has a period of 4pi.
That means that the function is going to repeat after 4pi.
So if we go out it should repeat back out here, at 4pi.
And now we can just kind of draw the function.
And this will take a little bit of practice, but-- actually I'm going to draw it, and then we can explore it a little bit more as well.
So the function's going to look like this.
Oh, boy.
This is more difficult than I thought. And it'll keep going in this direction as well. And notice, the period here you could do it from here to here.
This distance is 4pi.
That's how long it takes for the function to repeat, or to go through one cycle. Or you could also, if you want, you could measure this distance to this distance.
This would also be 4pi. And that's the period of the function.
And then, of course, the amplitude of the function, which is this right here, is 2.
Here's the amplitude.
And then the period of 4pi we figured out from this equation.
Another way we could have thought about it, let's say that-- let me erase some of the stuff-- let's say I didn't have this stuff right here.
Let's say I didn't know what the function was.
Let me get rid of all of this stuff.
And all I saw was this graph, and I asked you to go the other way.
Using this graph, try to figure out what the function is.
Then we would just see, how long does it take for the function to repeat?
Well, it takes 4pi radians for the function to repeat, so you'd be able to just visually realize that the period of this function is 4pi.
And then you would say, well what's the amplitude?
The amplitude is easy.
You would just see how high it goes up or down.
And it goes up 2, right?
When you're doing the amplitude you don't do the whole swing, you just do how much it swings in the positive or negative direction.
So the amplitude is 2.
I'm using the wrong color.
The period is 4pi.
And then your question would be, well this is an oscillating, this is a periodic function.
Is it a sine or is it a cosine function?
Well, cosine function, assuming we're not doing any shifting-- and in a future module I will shift along the x-axis-- but assuming we're not doing any shifting, cosine of 0 is 1.
Right?
And sine of 0 is 0. And what's this function at 0?
Well, it's 0.
Right?
So this is going to be a sine function.
So we would use this formula here. f of x is equal to the amplitude times the sine of 2pi divided by the period times x.
So we would know that the function is f of x is equal to the amplitude times sine of 2pi over the period-- 4pi-- x. And, of course, these cancel out.
And then this cancels out and becomes 2 sine of 1/2 x.
I know this is a little difficult to read.
My apologies. And I'll ask a question.
What would this function look like? f of x equals 2 cosine of 1/2 x.
Well, it's going to look the same but we're going to start at a different point.
What's cosine of 0?
When x is equal to 0 this whole term is equal to 0.
Cosine of 0, we learned before, is 1.
So f of 0 is equal to 2.
Let me write that. f of 0 is equal to 2.
Let me do this in a different color.
Let me draw the cosine function in a different color.
We would start here. f of 0 is equal to 2, but everything else is the same.
The amplitude is the same and the period is the same.
So now it's going to look like this.
I hope I don't mess this up.
This is difficult.
So now the function is going to look like this. And you're going to go down here, and you're going to rise up again here. And on this side you're going to do the same thing.
So notice, the cosine and the sine functions look awfully similar. And the way to differentiate them is what they do-- well, what they do in general.
But the easiest way is, what happens when you input a 0 into the function?
What happens at the y-axis, or when x is equal to 0, or when the angle that you input into it is equal 0?
Unless we're doing shifting-- and don't worry about shifting for now, I'll do that in future modules-- sine of 0 is 0 while cosine of 0 would be 1. And since we're multiplying it times this factor right here, times this number right here, the 1 becomes a 2.
And so this is the graph of cosine of x.
This is this graph of sine of x.
And this is a little bit of a preview for shifting.
Notice that the pink graph, or cosine of x, is very similar to the green graph. And it's just shifted this way by-- well, in this case it's shifted by pi.
Right? And this actually has something to do with the period of the coefficient.
In general, cosine of x is actually sine of x shifted to the left by pi/2.
But I don't want to confuse you too much.
That's all the time I have for this video.
I will now do another video with a couple of more examples like this.
Let's say we have the equation 7 times x is equal to 14.
Now before even trying to solve this equation, what I want to do is think a little bit about what this actually means.
7x equals 14, this is the exact same thing as saying 7 times x
-- let me write it this way -- 7 times x -- we'll do the x in orange again -- 7 times x is equal to 14.
Now you might be able to do this in your head.
You could literally go through the 7 times table.
You say well 7 times 1 is equal to 7, so that won't work.
7 times 2 is equal to 14, so 2 works here.
So you would immediately be able to solve it.
You would immediately, just by trying different numbers out, say hey, that's going to be a 2.
But what we're going to do in this video is to think about how to solve this systematically.
Because what we're going to find is as these equations get more and more complicated, you're not going to be able to just think about it and do it in your head.
So it's really important that one, you understand how to manipulate these equations, but even more important to understand what they actually represent.
This literally just says 7 times x is equal to 14.
In algebra we don't write the times there.
When you write two numbers next to each other or a number next to a variable like this, it just means that you are multiplying.
It's just a shorthand, a shorthand notation.
And in general we don't use the multiplication sign because it's confusing, because x is the most common variable used in algebra.
And if I were to write 7 times x is equal to 14, if I write my times sign or my x a little bit strange, it might look like xx or times times.
So in general when you're dealing with equations, especially when one of the variables is an x, you wouldn't use the traditional multiplication sign.
You might use something like this -- you might use dot to represent multiplication.
So you might have 7 times is equal to 14.
But this is still a little unusual.
If you have something multiplying by a variable you'll just write 7x.
That literally means 7 times x.
Now, to understand how you can manipulate this equation to solve it, let's visualize this.
So 7 times x, what is that?
That's the same thing -- so I'm just going to re-write this equation, but I'm going to re-write it in visual form. So 7 times x.
So that literally means x added to itself 7 times.
That's the definition of multiplication.
So it's literally x plus x plus x plus x plus x -- let's see, that's 5 x's -- plus x plus x.
So that right there is literally 7 x's.
This is 7x right there.
Let me re-write it down.
This right here is 7x.
Now this equation tells us that 7x is equal to 14.
So just saying that this is equal to 14.
Let me draw 14 objects here.
So let's say I have 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14.
So literally we're saying 7x is equal to 14 things.
These are equivalent statements.
Now the reason why I drew it out this way is so that you really understand what we're going to do when we divide both sides by 7.
So let me erase this right here.
So the standard step whenever -- I didn't want to do that,
let me do this, let me draw that last circle.
So in general, whenever you simplify an equation down to a
-- a coefficient is just the number multiplying the variable.
So some number multiplying the variable or we could call that the coefficient times a variable equal to something else.
What you want to do is just divide both sides by 7 in this case, or divide both sides by the coefficient.
So if you divide both sides by 7, what do you get?
7 times something divided by 7 is just going to be that original something.
7's cancel out and 14 divided by 7 is 2.
So your solution is going to be x is equal to 2.
But just to make it very tangible in your head, what's going on here is when we're dividing both sides of the equation by 7, we're literally dividing both sides by 7.
This is an equation.
It's saying that this is equal to that.
Anything I do to the left hand side I have to do to the right.
If they start off being equal, I can't just do an operation to one side and have it still be equal.
They were the same thing.
So if I divide the left hand side by 7, so let me divide it into seven groups.
So there are seven x's here, so that's one, two, three, four, five, six, seven.
So it's one, two, three, four, five, six, seven groups.
Now if I divide that into seven groups, I'll also want to divide the right hand side into seven groups.
One, two, three, four, five, six, seven.
So if this whole thing is equal to this whole thing, then each of these little chunks that we broke into, these seven chunks, are going to be equivalent.
So this chunk you could say is equal to that chunk.
This chunk is equal to this chunk -- they're all equivalent chunks.
There are seven chunks here, seven chunks here.
So each x must be equal to two of these objects.
So we get x is equal to, in this case -- in this case we had the objects drawn out where there's two of them. x is equal to 2.
Now, let's just do a couple more examples here just so it really gets in your mind that we're dealing with an equation, and any operation that you do on one side of the equation you should do to the other.
So let me scroll down a little bit.
So let's say I have I say I have 3x is equal to 15.
Now once again, you might be able to do is in your head.
You're saying this is saying 3 times some number is equal to 15.
You could go through your 3 times tables and figure it out.
But if you just wanted to do this systematically, and it is good to understand it systematically, say OK, this thing on the left is equal to this thing on the right.
What do I have to do to this thing on the left to have just an x there?
Well to have just an x there, I want to divide it by 3.
And my whole motivation for doing that is that 3 times something divided by 3, the 3's will cancel out and I'm just going to be left with an x.
Now, 3x was equal to 15.
If I'm dividing the left side by 3, in order for the equality to still hold, I also have to divide the right side by 3.
Now what does that give us?
Well the left hand side, we're just going to be left with an x, so it's just going to be an x.
And then the right hand side, what is 15 divided by 3?
Well it is just 5.
Now you could also done this equation in a slightly different way, although they are really equivalent.
If I start with 3x is equal to 15, you might say hey, Sal, instead of dividing by 3, I could also get rid of this 3, I could just be left with an x if I multiply both sides of this equation by 1/3.
So if I multiply both sides of this equation by 1/3 that should also work.
You say look, 1/3 of 3 is 1.
When you just multiply this part right here, 1/3 times 3, that is just 1, 1x.
1x is equal to 15 times 1/3 third is equal to 5.
And 1 times x is the same thing as just x, so this is the same thing as x is equal to 5.
And these are actually equivalent ways of doing it.
If you divide both sides by 3, that is equivalent to multiplying both sides of the equation by 1/3.
Now let's do one more and I'm going to make it a little bit more complicated.
And I'm going to change the variable a little bit.
So let's say I have 2y plus 4y is equal to 18.
Now all of a sudden it's a little harder to do it in your head.
We're saying 2 times something plus 4 times that same something is going to be equal to 18.
So it's harder to think about what number that is.
You could try them.
Say if y was 1, it'd be 2 times 1 plus 4 times 1, well that doesn't work.
But let's think about how to do it systematically.
You could keep guessing and you might eventually get the answer, but how do you do this systematically.
Let's visualize it.
So if I have two y's, what does that mean?
It literally means I have two y's added to each other.
So it's literally y plus y.
And then to that I'm adding four y's.
To that I'm heading four y's, which are literally four y's added to each other.
So it's y plus y plus y plus y.
And that has got to be equal to 18.
So that is equal to 18.
Now, how many y's do I have here on the left hand side?
How many y's do I have?
I have one, two, three, four, five, six y's.
So you could simplify this as 6y is equal to 18.
And if you think about it it makes complete sense.
So this thing right here, the 2y plus the 4y is 6y.
So 2y plus 4y is 6y, which makes sense.
If I have 2 apples plus 4 apples, I'm going to have 6 apples.
If I have 2 y's plus 4 y's I'm going to have 6 y's.
Now that's going to be equal to 18.
And now, hopefully, we understand how to do this.
If I have 6 times something is equal to 18, if I divide both sides of this equation by 6, I'll solve for the something.
So divide the left hand side by 6, and divide the right hand side by 6.
And we are left with y is equal to 3.
And you could try it out.
That's what's cool about an equation.
You can always check to see if you got the right answer.
Let's see if that works.
2 times 3 plus 4 times 3 is equal to what?
2 times 3, this right here is 6.
And then 4 times 3 is 12.
6 plus 12 is, indeed, equal to 18.
So it works out.
So you may or may not already know that any linear equation can be written in the form y is equal to mx plus b. Where m is the slope of the line. The same slope that we've been dealing with the last few videos.
The line will intercept the y-axis at the point y is equal to b. We'll see that with actual numbers in the next few videos. Just to verify for you that m is really the slope, let's just try some numbers out.
You get y is equal to m times 1. Or it's equal to m plus b. So we also know that the point 1, m plus b is also on the line.
Our delta y-- and I'm just doing it because I want to hit an even number here-- our delta y is equal to-- we go down by 2-- it's equal to negative 2. So for A, change in y for change in x. When our change in x is 3, our change in y is negative 2.
A little bit more than 1. About 1 1/3. So we could say b is equal to 4/3.
Let's figure out its slope first. Let's start at some reasonable point. We could start at that point.
B. Equation B.
So our delta x could be 1. When we move over 1 to the right, what happens to our delta y? We go up by 3. delta x. delta y.
That's our y-intercept when x is equal to 0. This tells us that for every 5 we move to the right, we move down 1. We can view this as negative 1/5.
Where is this x term? It's completely gone. Well the reality here is, this could be rewritten as y is equal to 0x plus 3.75.
The slope is 0. No matter how much we change our x, y does not change. Delta y over delta x is equal to 0.
You want to get close. 3 3/4. As I change x, y will not change. y is always going to be 3.75.
It's just going to be a horizontal line at y is equal to 3.75. Anyway, hopefully you found this useful.
By 14,000 years ago, the Ice Age was winding down.
As the ice melted, oceans rose, and coastlines changed, some environmental barriers between populations vanished.
While elsewhere, new ones appeared.
Temperatures and rainfall increased dramatically. And some areas became so rich in plants and animals, that people no longer had to travel in search of food. Instead, people settled into more permanent villages based on foraging.
By planting the seeds from wild grains near their homes, they could supplement their food supplies, and stay in the same spot year round.
Perhaps as they became more sedentary, they had more opportunities for other, ahem, pursuits.
In any case, populations grew and pretty soon, growing families in these villages became less suited to the nomadic lifestyle.
In some places, during droughts or harsh winters, local wild plants and animals could no longer support everyone.
Independently and all over the world, people began making the same discovery, which would change human societies and the natural environment forever.
They developed AGRlCULTURE!
It's not an obvious choice, hunter-gatherers can provide food for their families, by working only a few days a week.
Farming, on the other hand, is hard work, and a full-time job.
But farming provided more food to feed larger populations consistently
Villages began relying more and more on their gardens.
As mutant varieties of wild grains occured, these early agriculturists chose the crops with larger seeds and grain ears that were easier to gather.
People also domesticated docile, local animals.
Villages grew, especially in areas with fertile soil, and became cities.
And settled people became more detached from the natural world.
By 6,000 years ago, in Mesopotamia, there were cities with wealth, power, and a new social order.
Whoever controlled grain supplies wielded power.
And some people no longer had to find or produce their own food, but rather exchange their services for dinner.
Agricultural societies soon became the dominant way of life for people throughout the world.
World populations exploded, creating more laborers to produce more crops, to feed more mouths, more land had to be cleared for farming.
Sometimes, whole towns relocated when soils couldn't sustain repeated cultivation.
And each year, people took their livestock farther and farther afield to graze.
Groups who had been separated for thousands of years came in contact as they traveled in search of land, labor, and trade goods.
New means of transportation brought distant cultures in contact.
New families produced from these contacts blurred genetic distinctions within continents, and all around the world.
Migrating farmers encountered hunter-gatherers. In sub-Saharan Africa, for example, farmers spread east and south from present-day Cameroon around 5,000 years ago.
Along the way, they met and absorbed many of the people whose ancestors had been living there for thousands of years.
Some hunter-gatherers who lived next to farming communities took up farming themselves. But others followed game to areas unsuited to agriculture.
By 1,500 years ago, agriculture dominated most of sub-Saharan Africa.
But the Calahari Desert, too harsh for farming, remained a home of hunter-gatherers, who kept not only much of their lifestyle, but also their unique click languages.
In most places throughout the world, however, agriculture triumphed. As the new farmers on each continent expanded and absorbed other hunter-gatherer groups.
Genetic differences within continents began disappearing, setting the stage for the most recent chapter in our human story.
Evaluate 0 plus y plus -7 when y is equal to -3 and y is equal to 0 and y is equal to 7.
So let's take the first situation where y is equal to -3...
Then this expression right here would be... 0 plus -3 (because that's our "y" now) plus -7.
Now 0 plus or minus anything won't change its value
So you can really just ignore the 0 here.
This is going to be the same thing, this is going to be the exact same thing, as -3 plus -7.
-3 plus -7
Now we could draw a number line here, just to help us visualize it
But even if we didn't have the number line, we could say "Look, we're already 3 below zero... We're going to go another 7 to the left... another 7 more negative."
So we're 3 away from zero, we're going to go 7 more away from zero
So we're going to be 10 to the left of zero, or -10.
Or another way to think of it...
Lemme draw the number line there (always better to have the visual).
So we're starting (this is zero)
We're starting at -3, and to that we're adding -7
So we're starting at -3, the absolute value is -3[sic] is our starting point. To that we're adding another negative 7
We're going to move another 7 to the left.
So we're adding (let me draw this)... we're adding a negative 7 right over here
We're adding a negative 7 right over here
So what's the length of this over here?
The absolute value of -7 is equal to 7... that's the length of this arrow.
But we're moving it to the left.
The abolsute value of this arrow right here (the absolute value of negative 3) is 3.
So we're already 3 to the left, now we're moving 7 more to left
So now we're going to be 10 to the left.
We are going to be 10 to left.
10 to the left.
This is literally, this is equal to the absolute value of -7...
Let me do it in the order that we wrote it in the problem...
So this is equal to the absolute value of -3 (you'd want to use the same colors)
The absolute value of -3 plus the absolute value of -7.
But we're to the left of zero (we've been moving to the left) so it's the negative of that which is -10
So if your signs are the same, you can just take the absolute value of them say "ok, that's how far we're going to move, total. and we're that far from zero to the left"
So the answer here is -10
That was when y is -3.
Let's think about when y is equal to 0.
When y is equal to 0, this expression up here becomes 0 plus 0 (our y here is going to be zero)... (We'll do it in that same blue color.) .... plus 0 plus -7.
Now, if you add 0 to anything it's not going to change the value.
So this thing over here, this is pretty straight-forward, these don't matter
It's just going to be equal to -7
Now let's do the last one (when y is equal to 7)
It's going to be 0 plus (our y is equal to 7) so 0 plus 7 and then we have plus -7
Now there's a couple of ways to do this...
You could literally just say "now adding a negative number is equivalent to subtracting the number".
You could say this is equivalent to 0 plus 7 minus 7
Plus -7 is the same thing as subtracting a 7
The zero doesn't matter, so this is equal to 7 minus 7... which is equal to zero!
Another way to think about it...
Let's draw a number line
So let's say that this is zero
We're starting off at 7.
We're 7 to the right of zero.
And to that we're adding a -7.
So we're going to move 7 to the left of where we were.
7 to the left of 7 which was 7 to the right of 0!
This gets us back to 0.
So the answer is... zero.
There's no fear in my heart
Got nothing left to lose
I saw my loved ones die
Oh, I swear that I won't give in
By God you'll never win
I'll fight for what's right
And nothing can stand in my way
Even if I get knocked down
I will stand my ground
And I'll never
Hide or run away
Love will prevail
By God it will
Love will prevail
I refuse to fail
Love will prevail
Life's become so cheap
So many orphans weep
They forgot how to smile
Oh, I cannot understand
Just how somebody can
Murder an innocent child
I swear their lives won't be lost in vain
Even if I get knocked down
I will stand my ground
And I'll never
Hide or run away
Love will prevail
By God it will
Love will prevail
I refuse to fail
Love will prevail
God made me free
You can't take that away from me
Freedom is my destiny
I have a dream
And my dream is to see
To see all my people smile
See all of them free and proud
I feel the wind of peace
"Cause with hardship comes ease
That's why I won't lose faith
And I know that God is Great
So, I'll never Hide or run away
Love will prevail
By God it will
Love will prevail
I refuse to fail
Love will prevail
I won't run away
Love will prevail
By God it will
Love will prevail
I refuse to fail
Love will prevail
In 926, the capital of Balhae fell to Georan.
On the territory Georan founded a new country called Dongranguk, which means 'Georan of East'.
The survivals of Balhae, however, kept struggling fiercely to restore their country.
In 927, Autumn A raid by the Killer-Blade Army of Dongranguk!
Form a defense line!
Don't give an inch, just fight back!
Gunhwapyeong!
I'm honored.
The commander of the Killer-Blade Army has come to pay a personal visit.
I came all the way to ask you something.
Wouldn't you rather cooperate with Dongranguk?
I'm a human being.
You want me to be a dog for Georan, like you?
Any last words?
I'm sad to announce that even our future king, Prince Suhyeon, has been assassinated by Gunhwapyeong.
Gunhwapyeong, that traitor is killing off everyone from the royal family, cutting off the lineage.
Son of a Bitch!
I heard the news has spread all over, hurting the morale of the people.
It's a big problem.
We need a king at a time like this.
With Prince Suhyeon dead, who can become our king?
Who else is left?
I've found a prince whose whereabouts were unknown.
Oh, is there a prince?
Who is he?
Do you remember Prince Jeonghyeon?
What happened?
As you ordered, I sent Maeyoungok and Mabul to Jungwon.
Youngok...
She always works hard.
According to a secret agent,
Balhae has also dispatched an excellent fighter...
Who's that?
We don't know yet.
Does anybody have any idea who it could be?
This time you have to go far.
He's the son of LADY OH.
He was involved in some political strife 14 years ago, and sent to Jungwon.
He was exiled.
The Killer-Blade Army will be coming.
We must find him before the they do.
We must have a king to unite our people.
If we can unite our people and soldiers, instead of fighting all over the place, we can never lose...
Don't forget that.
Balhae's fate depends on him.
How was today?
What about the girl?
- Sosam?
- Yes.
What have you got?
What do you need to sell?
I'll meet the gentleman first and tell him.
Gentleman?
Sit over there and wait.
There's no need to doubt.
Just tell me how much you can pay.
There are others who are doing this kind of business.
Why did you come to me?
I heard there's no later trouble with you.
No trouble when dealing with Sosam.
That's right.
The important thing is whether there will be trouble or not.
The price is the next concern.
So, how much are you asking?
Fifty jeon...
You rat!
That's too cheap!
Is about right, but I'll give you up to 80 jeon.
Fine.
Hey, Sosam, well...
I'm not sure where you heard of me but you found the right person.
It's very important who you deal with here.
You have to find a credible person...
I have a question to ask you.
What is your honorable name?
You were looking for Sosam.
I'm asking for your real name.
There are too many eyes here.
Follow me.
What you have, only two of them were existed.
I thought I've been seeing strangers lately.
Your Highness, there must be a misunderstanding.
I'd never misunderstand assassins.
Do me a favor.
Hey, Sosam.
That's no favor...
I thank you.
Don't worry and just go!
A misunderstanding?
Aren't you going to follow him?
I don't think anything I say will matter right now.
Please, you guys need to help me.
Before that, you must help us first.
We're desperate.
I don't think so
All I have learned is how to kill.
No need to talk to you.
Kill her.
I said "I don't think so".
Okay, okay!
Understood.
I would like to know something.
There is so called "Rules" on the back street.
I know 10 ways to make you speak.
But, I'm not sure you can bear it.
Calm down.
I'm willing to give out everything.
Please sit down.
I'm Yeon Soha, officer first class of Biseonwon.
Please forgive my discourtesy, Your Highness.
Of course, I have to forgive in this situation.
I don't know why you think so, but I'm not an assassin.
- All the other princes are... are no more.
They'll leave an exiled prince alive?
- What if other princes...
Your Highness!
You must become the king of Balhae.
I will be escorting you to Balhae.
I've lived in a place like this, hiding from assassins for 14 years.
And now that painful time is all gone and I am to be the king of Balhae, right?
Do you think I believe that?
OK.
Let's say that's all true.
Do you think I'm crazy?
That's only a title.
You're saying that I should become the king to be chased by Georan, not knowing when I will be killed?
Do you know what I believe in?
"Survival, above all else."
That's all I'm interested in.
Your Highness!
My kids came back almost all crippled, which means I lose face.
What are we supposed to do now, huh?
I didn't do it.
Did I say you did it, Prince?
You ain't from battle field, are you?
Tell me.
About what?
Tell me the details so I can decide on the price.
How much money will you bring me when I hand you over?
Always the same routine...
They need to be beaten to start speaking.
You...
Stop!
She...
She's the one!
She attacked us!
Welcome.
I've heard interesting stories about your skills.
I'm the boss of...
I told you to take your hands off of him.
Not gonna work.
You should talk to me.
I'm the boss of...
Oh, Shit!
Your Highness, are you okay?
What's going on?
They're on the same team!
Please don't worry.
I will protect you.
Bo...
Boss...
Yeon Soha...
It's you.
You came here.
We've passed a couple of times, but this is the first time we've said hello.
What do we do?
There are more than two of them now.
Don't worry.
This is our region.
And we've got more people.
Who are they now?
They're Dongranguk's Killer-Blade army.
Officer Yeon, wouldn't it be better if we avoided any unnecessary killings?
Give us Prince Jeonghyeon and we'll guarantee your life.
I can never allow you to take him.
It's not going to work by talking.
Everyone stop!
What?
Looking at the current situation, I think you're the one we should join up with.
Get out!
Lt'll be better to talk.
I'm the boss of...
What are we doing?
Kill them!
Your Highness, please run!
What?
We have to run away.
Hurry!
What is the matter?
Your Highness!
They'll keep coming.
You have to keep away from them!
Follow me!
Tell me.
Who are you?
What do you have to do with the Killer-Blade Army?
Most of them are traitors to Balhae.
In the past, I've seen them in the military.
Is that why you introduced yourself like that?
Is there something wrong with how I introduced myself?
Then, how are you related to my brother Suhyeon?
I've once guarded the Crown Prince for a while.
We must go now.
Where to?
This is the safest place.
There is no safe place.
As long as we are here, they'll eventually find you.
They will kill everyone on Wolnak street if they need to...
That is the Killer-Blade army's way.
Didn't you say that surviving is your only interest?
Then there's no other way.
Then follow me, I know a shortcut out of here.
You want a drink?
Is this the fast way you've mentioned?
We must eat well to go fast.
How can we travel far without eating?
They are the Bidomun, a branch of Heukdobang's gang.
I recognize the symbol.
I heard they are out of their minds because their boss was killed.
Let's go now.
We don't have much time.
I will decide whether to go or not.
If I don't like it, I won't go.
Who the hell are you?
My boss here told me to ask you something!
What?
That girl?
What did she say?
She wonders if it's true that your boss died from overdoing it with women.
That bitch!
Please just ignore him and let it go.
Too late.
We already heard him!
What are you doing?
We are still in mourning for my father.
That guy picked a fight with us.
We didn't have a choice.
I gave you an order to be cautious, no matter what happened!
Say again what you just said.
I found him!
Here!
Here!
It's very late.
Let's go now.
Uh...
OK...
Go quickly.
I appreciate your help very much.
Don't say that.
How can I just ignore this kind of thing?
I wish...
I wish I could cut him though for your sake...
Everything will be okay, don't worry.
Let's go.
What happened?
After listening to our story, she said she would help us.
Story?
You told her everything?
Are you out of your mind?
You have no idea how fast rumors spread in this town.
I said that you abandoned your wife and children to run away with a widow, stealing your ill mother's money.
Hey!
You're a warrior.
How can you lie to people like that?
Sword is not the only thing you need in the battle field.
Put these on.
It's going to be a tough walk and quite cold from now on.
That's okay.
I'm not going to care if you get cold later on.
Let's go.
How did you learn martial art?
I've only trained to use sword.
Where did you learn to use it?
I learned from a military camp.
I had learned from many soldiers since I was little.
You had one rough life.
I would've give up.
What is going on?
I need to get horses.
I don't think it is possible.
It is not like stealing clothes.
It is way too difficult to steal them.
We have to wait till dawn, and...
Don't worry, I can pay.
Damn, it's hot!
It's killing me...
Wow, who's this!
Brother Sosam!
- I brought you a customer.
- Customer?
Do you like any of them?
I want to buy the one on the far right and the fourth one.
You know your horses.
But they are quite expensive...
Since you came with Brother Sosam, I'll give you a good deal.
For the two, give me 300 jeon.
I live off of you, Brother.
But they're real good horses!
- But they're stolen.
- Shhh!
Come on...
She's fine.
Who is she?
A devil from hell.
Come to take me to die.
What?
Never understand a single word...
Anyway let me take a sword.
I'd better carry one since someone's trying to kill me...
Let's see.
This one should be good.
Why did you choose that one?
Take a better one.
I'll pick one for you.
Doesn't matter.
I'll never use it anyhow.
You surprised me...
You're here again.
No word from the Deputy Commander yet?
Please don't worry...
Maeyoungok has never lost her quarry.
Wouldn't it depend on who the quarry is?
- Have you found out?
- Of course!
Do you know a female warrior called Yeon Soha?
I'll go myself.
Are you going to kill the prince again this time?
The royal court wants Balhae's royal family to cooperate.
To help calm the conflicts and uprisings all around the country.
But because you've been killing every member of the royal family, the court can't trust you.
If you want to gain something big, you'd better control your vengeful spirit.
Understand?
Father!
Welcome!
How can I help you?
We don't need dinner.
Give us a place to stay.
Yes!
How many rooms...
Can't you see?
There are two people.
Then I'll prepare...
Give us one room.
One's enough.
Are you going to stay like that all night?
This is the way Biseonwon warriors guard the door of the king until he falls asleep.
Please do not worry.
If you're going to be silly, you'd better come in and be silly.
You're going to be the king.
There shouldn't be any kind of scandalous rumors.
Are we in Balhae?
Who's going to see?
Whoever's watching or not is not important.
Under the heavens, The king should have nothing to hide.
You speak as if I'm going to be the king.
When did I say I would?
I'm not going to.
He said they went to Hadong.
The Chief Commander is coming.
Hey, Officer Yeon Soha!
You said you grew up in the military.
Was your father a soldier?
No, Sir.
Then, why?
I didn't have anywhere else to go.
Georan soldiers killed my father when I was 9, my mother when I was 10...
I didn't have any other relatives.
It'll be tough to get to Hadong today.
There's a place to stay near there.
A very cozy place.
What's that?
That incense...
It's my habit to comfort the dead.
Those who I used to know and the enemies who have been killed by my sword.
You comfort even the souls of your enemies?
With no hatred or resentment?
At least you won't be eaten by an evil spirit.
Why?
I also learned how to use the sword in Balhae.
I know the story that evil spirits born from the resentment, spite, and hatred, that lives on in your sword.
Grown-ups used to scare me with the story that an evil spirit grows by drinking blood and finally makes the owner of the sword evil as well.
I learned when I grew up that the story meant one shouldn't lose serenity because of hatred.
I believe evil spirits grow in the sword.
Do you still believe what you were told when you were little?
That is why you treat it so carefully.
It protects you from evil spirits.
Yes.
I believe I have to use the sword to protect my important things.
Hey...
What would people think when they hold the sword?
Protecting?
No way...
Killing comes the first.
That is instinct.
I have tried to tell a couple of times, don't give me that look.
Don't give me that pity look.
I have had a fairly great life until I met you.
I need to meet someone.
Wait here for a while.
We don't have much time.
There's still a long way to go...
It's the owner of this shop.
Don't go anywhere, just wait here.
It'll only take me a moment.
Hey, who's this?
Here you go!
What are you doing here, without telling us you were coming?
I'd like to get back my money that you're keeping for me.
It looks like I'll have to go in hiding for a while.
What have you done?
It's a long story.
I'll tell you later.
So where are you going this time?
Well...
For now, quite far...
Sosam, to be honest, some people came by here yesterday.
Who?
They...
Said they were with the Killer-Blade Army.
And they're looking for you!
Let's talk.
Did you think you could get away from me?
Let me ask you one thing.
Would you like to cooperate with Dongranguk?
Negotiate?
I don't know what you mean by that...
You...
Why are you trying so hard to take me?
Because you're going to be Balhae's king.
You've seen how I live.
Do you think the throne fits me?
You'll be an excellent king.
Thank you for thinking highly of me, but let me tell you one thing.
I was going to leave you here and run away.
I failed because my friend betrayed me.
If you were really going to do that, there were a lot of chances.
Why do you think I'm telling you this?
I have no intention to go to Balhae.
If I hope to survive, there are many other ways.
You have to go no matter what.
Then tell me one good reason why I must go to Balhae.
Why do I have to go there?
As far as I know, you weren't present at your mother's deathbed.
We'll pass by Cheonaegok on the way.
There is a graveyard.
Your Highness!
Long time no see.
I know only one thing.
My father and family were dishonored and brutally killed by the royal family of Balhae.
The charges against them were not false.
I don't care who says what.
I will kill whoever insulted my father and family.
Your Highness, are you OK?
No, I'm not OK.
Do you know how terrible it is to be stabbed from behind?
A message came from headquarters.
What would you like to do?
Say we haven't found them.
I'm not going back before I kill Yeon Soha.
Kill Yeon Soha?
As long as I'm under orders, I want to take care of it on my own.
And...
I don't want to cause trouble to you, most of all.
I will give you four days.
If I see Yeon Soha, you'll have no more chances.
It was quite close.
I guess it may not be that serious...
It is from the street fight.
It is from the battle field.
What made you think...
I wouldn't even get close to it.
I was told you joined the majesty, your father, for the battle against Georan when you were only fifteen.
Georan soldiers!
They seem dropping out of the headquarters.
Your highness!
Look at this chaos.
They wouldn't have time to pack.
They wouldn't even dare to fight, but run.
What is that for?
It is for you since you are not well.
It seems so convenience.
Hand it over.
I will do, your highness.
Why?
Have you ever done carpenter's work?
I had to fix stuffs to sell.
Some dorks broke things when they stole goods.
What?
This is what I have been doing.
You see!
I'm not even close to be a King.
You made wrong decision.
General KeumHwee.
For the fifteen years old prince who was brave and fought in the battle field, every soldiers called you by that name.
With glint helmet,
You were surely stand out in the battle field.
How well do you know about me?
There were many princes who fought in the field but no one could even get close to what you had done.
You are the one people rely on in this harsh time.
I'm nobody.
All that is left is useless myself, Sosam.
Your real nature wouldn't have changed.
That is wrong.
I have confidence in you.
Don't be silly.
What if you are wrong?
I bet my life on that.
Do we have to do that?
Going across the border is the fastest way to Balhae.
We could get into big trouble unless we put on Georan costumes.
Don't reveal your emotions.
They are looking for Balhae's militia corp soldiers.
Those who fought here were not from regular army of Balhae.
They were from militia corp.
They used to be normal farmers or wood gatherers.
Give me the reins now.
I'll take it from here.
That's okay.
I'm bored.
I'm bored to death.
Take a nap.
Or sing a song.
What is wrong with you?
You seem so upset.
With all your help, I try to help you back, but all I get is your angry look.
What is wrong with me, you asked?
Your highness, you were almost killed.
You should be a king.
Your life does not only belong to you, but to all people.
What you have done would have kill more people.
You shouldn't worry too much.
Reason why I'm heading that way is to visit my mother's graveyard.
We are almost there.
There should be a person from Balhae waiting for us.
What's wrong?
You don't look well.
I'm okay.
Let's rest for a moment.
We must go.
We can't slow down because of me.
Take it.
I may not be able to protect you, but I can avoid causing you more trouble.
Let's go, please.
You said the life of a king is not his own, and said that he should run away, even if the man who would protect him is dying.
Let's say I'm the king of Balhae.
You're telling me I should become a king who only thinks about himself, although his man is dying?
Is that a king?
If that is...
I will never become the king.
Please let me go.
You have to receive a bow in welcome.
I, Jocheonsu, under General lmsunji, greet Prince Jeonghyeon, Your Highness.
What happened to you?
- Uncle...
- Yes.
Please take care of the prince.
Soha!
Why is she sick?
Is it serious?
Tell me what's happened.
She's been poisoned by snake venom.
I think it's too late.
I heard that lmseonju moved to protect the prince.
With his army...
Do you understand what this means?
Once they arrive here, there'll be no chance!
I'll finish before they arrive.
The royal court wants something more specific.
They sent the Golden Boy Army here!
The Golden Bow Army will catch the prince.
The Killer-Blade Army can wait for a new mission.
But...
It's the orders of the court!
Are you going to go against them?
I called you because of Gunhwapyeong.
The Killer-Blade Army should have taken care of this job.
But the Golden Bow Army has been sent already...
If the Golden Bow Army takes the honor of victory,
I cannot keep my promise with Gunhwapyeong.
Send us please.
We are sure to succeed!
I wish I could.
But I already have my orders.
Well, there may be a way...
Can you give me your life for it?
Of course!
Do you know what I mean?
I...
I am a warrior!
If there is any way for you to succeed, you must take it, don't you think?
Don't you regret?
About changing your country...
Why... don't you like it?
I don't care about country.
My only concern is to serve you.
Whatever your position is, you're always the same person to me.
It won't take long...
Once the last prince is killed the dream will come true...
I will establish my own country on the territory of current Balhae with a help of Georan.
Now she passed the crucial moment.
She will wake up soon.
Now you should go meet your mother.
Yayul cheolla said we have to leave before the Golden Bow Army arrives.
I will never forget what you wished for, Maeyoungok...
Have you contacted the Golden Bow Army?
Of course.
They might attack you Killer Blades unless they know you're coming.
Prince Jeonghyeon will be dead...
No matter who finds him, the Killer Blades or the Golden Bows.
What do you mean?
You're still thinking like that?
The court wants the prince alive...
You... think you'll be okay after this?
The Balhae people killed you.
Or, better yet, Prince Jeonghyeon.
So I killed Jeonghyeon to avenge you.
It's a simple story.
You...
Ingrate...
He is dead.
Send this message of his death to the Gloden Bow Army.
I think you should go.
She may be awake.
I should.
Your name is Jocheonsu, right?
Yes, your highness.
You look familiar.
I have seen you a couple of times in the battle field,
General Keumhwee.
How is the wound on your back?
Your Highness.
There is a person from headquarters.
Chief of assault team, Jochensu.
I came here to see you, your highness.
You are deeply wounded.
I will call medic to bring you to headquarters.
It wouldn't take long, your highness.
I remember you, now.
Chief of assault team, Jochensu.
Please take your time to see her.
I will.
Soha!
You're awake.
Good.
The prince is not here.
He went to Lady Oh's grave.
He was on guard for you all night.
Gunhwapyeong's here!
Is that how Gunhwapyeong indicates he's on the hunt?
The prince is in danger!
Mother, I'm here.
I survived no matter what as I promised to you.
Are you satisfied now?
Aren't you...
Jocheonsu, the one who used to be called the One-Strike-Killer?
It's been a long time, Gunhwapyeong.
I've heard enough about your brutal killings.
Take off.
I'll catch you up later.
Hurry!
Now that you've met me, I think you're killing days are over.
We must hurry.
Have you recovered?
Are you ok?
Yes, I'm fine.
Let's go.
Better than expected, Gunhwapyeong.
But you're just an old tiger now...
This...
This is...
To the victor goes the spoils...
Your Highness!
No more energy, already?
I know what's happening to you.
If you overuse your energy when you're poisoned, your blood gets all twisted.
If you practice your military techniques, you'll die.
You're wrong.
There's difference between not being able to use the techniques and not being allowed to use them.
You...
What's going on?
Stop right there, Commander Gunhwapyeong.
Jocheonsu is dead.
I killed him...
And now I'm going to kill that prince...
There's only one way.
There's one attack, but it will cost you your life.
Do you know what you need for that one blow?
You need the will to kill.
Think of how much you want to kill.
That's all.
The sword... it's not for killing.
It is for protecting valuable things.
But nobody can block my way...
Just sit there... and watch the prince die helplessly.
That... sword...
You know it well...
Your father gave the same sword to two young princes.
How...
How did you...
Because I killed Daesuhyeon.
Your Highness.
Teach me how to use the sword.
Why do you want to learn?
My father and mother, both were killed by the Georan people.
I...
I want to learn.
The sword is not for killing or hurting people.
Rather, it's for protecting something valuable.
Let me ask you one thing.
Why do you have it?
I saved it to kill you... the last in the lineage.
That's wrong...
That sword is not the secret sword you think it is.
But the sword you were lookin for is...
The true sword is the valuable spirit of Soha's.
I must save that spirit.
No matter what.
There's this thing called the Body-Attack technique.
Both Daesuhyeon and Jocheonsu...
I killed them with this skill.
With this skill...
I will also kill you.
Slowly.
With the secret skill of the Balhae royal family.
You know, this was the only military technique that I learned completely.
I guess you haven't learned how to overcome the inner shock.
From the beginning, you couldn't beat me.
Why...
Why didn't you tell me?
You must pass Cheonaegok now.
I'm asking you why...
You...
You really thought I'd be the king?
Since the day I met you in Junwon, I've never doubted. Not even once...
Because you must be... the same person you were 14 years ago.
Without you...
I wouldn't be here.
You brought me a reason to live... to me who lost everything.
You were my life for 14 years.
It's General lmsunji and soldier of Balhae.
Please get ready to meet them.
Soha!
Soha!
I...
I have no chance.
What are you talking about?
Everything is over!
We're almost there!
Please don't say anything.
Please stay like this for a while.
I beg you...
Your Highness, I kept my promise.
But...
You didn't...
Save your life.
I saved something more valuable than my life.
Sword is to protect important things to you.
Am I right?
Soha...
Soha!
We were robbed our castles, our land and our country.
They even stole our capital and changed the name of the palace.
A lot of people have died.
They're telling us to recover the valuable things the things they lost.
So, in this battle, we are not going to falter or fail in!
If we have no strength and are caught, our eyes will pierce the enemies.
If our eyes get plucked out...
We'll speak about their sins to the heavens!
We'll let them know they can never take us from this land!
Now this castle will again be called Holhan Palace and we'll restore our country!
Charge!
In 928, Dongranguk withdrew to Leaotong area.
Post-Balhae and Jeongahnguk were founded on the territory.
Both of them proudly called themselves the descendants of Balhae.
The medics have arrived to escort you.
- Genera Jo.
- Please speak freely.
This kid lost both parents.
Please take care of her.
Yes, sir.
You remember everything I told you?
Yes.
Can you promise you won't forget?
Yes, I promise.
In this video I want to do a bunch of example problems that show up on standardized exams and definitely will help you with our divisibility module because it's asking questions like this
All numbers, and this is just one of the examples, All numbers divisible by both 12 and 20 are also divisible by and the trick here is to realize that if a number is both divisible by 12 and 20 it has to be divisible by each of these guy's prime factors
So let's take their prime factorization.
The prime factorization of 12 is 2 time 6 6 isn't prime yet, so 6 is 2 times 3,
So that is prime so any number divisible by 12 needs to be divisible by 2 times 2 times 3.
So it's prime factorization needs to have a 2 times a 2 times a 3 in it any number that's divisible by 12
Now, any number that's divisible by 20, needs to be divisible by
Let's take it's prime factorization 2 times 10, 10 is 2 times 5 so any number divisible by 20, needs to also be divisible by 2 times 2 times 5 or another way of thinking about it, it needs to have two 2's, and a 5 in it's prime factorization
Now if you're divisible by both, you need to have two 2's, a 3, and a 5. two 2's and a 3 for 12, and then two 2's and a 5 for 20 and you can verify this for yourself if this is divisible by both
Obviously, if you divide it by 20, is the same thing as dividing it by 2 times 2 times 5
So you're going to have, the 2's are going to cancel out, the 5's are going to cancel out your just going to have a 3 leftover, so it's clearly divisible by 20 and if you were to divide it by 12, you'd divide it by 2 times 2 times 3 this is the same thing as 12 and so these guys would cancel out, and you would just have a 5 leftover so it's clearly divisible by both, and this number right here is 60 it's 4 times 3, which is 12, times 5.
This right here is actually the least common multiple of 12 and 20
Here we are, 2013. We ALL depend on technology. To Communicate.
That's it!
We're asked to subtract. And we have the problem 68 - 42. And what I want to do here, is 1) just show you how I would do this problem, and then, talk a little bit about why it actually works.
And later in this video it should be clear - or I'll hopefully make it clear - why that's a good thing to do.
Alright. So then we go to the 1's place, and we see an 8. And from that, we're going to subtract a 2.
(8 - 2 = 6) I'll write that over here.
Let me write that over here.
8-2 is 6. 8 - 2 is equal to 6. (Repeating:
And then we go to the 10's place. We have 6 - 4.
And since they're in the 10's place, this is really 60 - 40.
But 6 - 4 is 2. 6 - 4 = 2. And since these are in the 10's place, this is really saying 60 - 40 = 20.
And I'll make that a little bit clearer in a second.
So we're actually done here.
68 - 42 = 26. And you can check that for yourself. If you add 26 + 42, you should get 68.
Or if you subtract 26 from 68 you should get 42.
So I encourage you do that in your own time after this video - verify that 42 + 26 = 68. And also verify what 68 - 26 is equal to. And you should see that is equal to 42.
So these are two things for you to check on your own.
Now, the last thing I want to do in this video is just to explain in a little bit more depth why this actually works. And, at least in my mind, I like to visualize 68 - (You won't to have write it out like this - but it's one way to make sure you really understand what is going on here.) 68 is the same thing as 60 + 8, or 60 and 8. And from that, we're subtracting 42.
The things we make have one supreme quality -- they live longer than us.
We perish, they survive; we have one life, they have many lives, and in each life they can mean different things.
Which means that, while we all have one biography, they have many.
I want this morning to talk about the story, the biography -- or rather the biographies -- of one particular object, one remarkable thing.
It doesn't, I agree,
look very much.
It's about the size of a rugby ball.
It's made of clay, and it's been fashioned into a cylinder shape, covered with close writing and then baked dry in the sun.
And as you can see, it's been knocked about a bit, which is not surprising because it was made two and a half thousand years ago and was dug up in 1879.
But today, this thing is, I believe, a major player in the politics of the Middle East.
And it's an object with fascinating stories and stories that are by no means over yet.
The story begins in the Iran-Iraq war and that series of events that culminated in the invasion of Iraq by foreign forces, the removal of a despotic ruler and instant regime change.
And I want to begin with one episode from that sequence of events that most of you would be very familiar with,
Belshazzar's feast -- because we're talking about the Iran-Iraq war of 539 BC.
And the parallels between the events of 539 BC and 2003 and in between are startling.
What you're looking at is Rembrandt's painting, now in the National Gallery in London, illustrating the text from the prophet Daniel in the Hebrew scriptures.
And you all know roughly the story.
Belshazzar, the son of Nebuchadnezzar,
Nebuchadnezzar who'd conquered Israel, sacked Jerusalem and captured the people and taken the Jews back to Babylon.
Not only the Jews, he'd taken the temple vessels.
He'd ransacked, desecrated the temple.
And the great gold vessels of the temple in Jerusalem had been taken to Babylon.
Belshazzar, his son, decides to have a feast.
And in order to make it even more exciting, he added a bit of sacrilege to the rest of the fun, and he brings out the temple vessels.
He's already at war with the Iranians, with the king of Persia.
And that night, Daniel tells us, at the height of the festivities a hand appeared and wrote on the wall,
"You are weighed in the balance and found wanting, and your kingdom is handed over to the Medes and the Persians."
And that very night
Cyrus, king of the Persians, entered Babylon and the whole regime of Belshazzar fell.
It is, of course, a great moment in the history of the Jewish people.
It's a great story. It's story we all know.
"The writing on the wall" is part of our everyday language.
What happened next was remarkable, and it's where our cylinder enters the story.
Cyrus, king of the Persians, has entered Babylon without a fight -- the great empire of Babylon, which ran from central southern Iraq to the Mediterranean, falls to Cyrus.
And Cyrus makes a declaration.
And that is what this cylinder is, the declaration made by the ruler guided by God who had toppled the Iraqi despot and was going to bring freedom to the people.
In ringing Babylonian -- it was written in Babylonian -- he says, "I am Cyrus, king of all the universe, the great king, the powerful king, king of Babylon, king of the four quarters of the world."
They're not shy of hyperbole as you can see.
This is probably the first real press release by a victorious army that we've got.
And it's written, as we'll see in due course, by very skilled P.R. consultants.
So the hyperbole is not actually surprising.
And what is the great king, the powerful king, the king of the four quarters of the world going to do?
He goes on to say that, having conquered Babylon, he will at once let all the peoples that the Babylonians -- Nebuchadnezzar and Belshazzar -- have captured and enslaved go free.
He'll let them return to their countries.
And more important, he will let them all recover the gods, the statues, the temple vessels that had been confiscated.
All the peoples that the Babylonians had repressed and removed will go home, and they'll take with them their gods.
And they'll be able to restore their altars and to worship their gods in their own way, in their own place.
This is the decree, this object is the evidence for the fact that the Jews, after the exile in Babylon, the years they'd spent sitting by the waters of Babylon, weeping when they remembered Jerusalem, those Jews were allowed to go home.
They were allowed to return to Jerusalem and to rebuild the temple.
It's a central document in Jewish history.
And the Book of Chronicles, the Book of Ezra in the Hebrew scriptures reported in ringing terms.
This is the Jewish version of the same story.
"Thus said Cyrus, king of Persia,
'All the kingdoms of the earth have the Lord God of heaven given thee, and he has charged me to build him a house in Jerusalem.
Who is there among you of his people?
The Lord God be with him, and let him go up.'"
"Go up" -- aaleh.
The central element, still, of the notion of return, a central part of the life of Judaism.
As you all know, that return from exile, the second temple, reshaped Judaism.
And that change, that great historic moment, was made possible by Cyrus, the king of Persia, reported for us in Hebrew in scripture and in Babylonian in clay.
Two great texts, what about the politics?
What was going on was the fundamental shift in Middle Eastern history.
The empire of Iran, the Medes and the Persians, united under Cyrus, became the first great world empire.
Cyrus begins in the 530s BC.
And by the time of his son Darius, the whole of the eastern Mediterranean is under Persian control.
This empire is, in fact, the Middle East as we now know it, and it's what shapes the Middle East as we now know it.
It was the largest empire the world had known until then.
Much more important, it was the first multicultural, multifaith state on a huge scale.
And it had to be run in a quite new way.
It had to be run in different languages.
The fact that this decree is in Babylonian says one thing.
And it had to recognize their different habits, different peoples, different religions, different faiths.
All of those are respected by Cyrus.
Cyrus sets up a model of how you run a great multinational, multifaith, multicultural society.
And the result of that was an empire that included the areas you see on the screen, and which survived for 200 years of stability until it was shattered by Alexander.
It left a dream of the Middle East as a unit, and a unit where people of different faiths could live together.
The Greek invasions ended that.
And of course, Alexander couldn't sustain a government and it fragmented.
But what Cyrus represented remained absolutely central.
The Greek historian Xenophon wrote his book "Cyropaedia" promoting Cyrus as the great ruler.
And throughout European culture afterward,
Cyrus remained the model.
This is a 16th century image to show you how widespread his veneration actually was.
And Xenophon's book on Cyrus on how you ran a diverse society was one of the great textbooks that inspired the Founding Fathers of the American Revolution.
Jefferson was a great admirer -- the ideals of Cyrus obviously speaking to those 18th century ideals of how you create religious tolerance in a new state.
Meanwhile, back in Babylon, things had not been going well.
After Alexander, the other empires,
Babylon declines, falls into ruins, and all the traces of the great Babylonian empire are lost -- until 1879 when the cylinder is discovered by a British Museum exhibition digging in Babylon.
And it enters now another story.
It enters that great debate in the middle of the 19th century:
Are the scriptures reliable?
Can we trust them?
We only knew about the return of the Jews and the decree of Cyrus from the Hebrew scriptures.
No other evidence.
Suddenly, this appeared.
And great excitement to a world where those who believed in the scriptures had had their faith in creation shaken by evolution, by geology, here was evidence that the scriptures were historically true.
It's a great 19th century moment.
But -- and this, of course, is where it becomes complicated -- the facts were true, hurrah for archeology, but the interpretation was rather more complicated. Because the cylinder account and the Hebrew Bible account differ in one key respect.
The Babylonian cylinder is written by the priests of the great god of Bablyon, Marduk.
And, not surprisingly, they tell you that all this was done by Marduk.
"Marduk, we hold, called Cyrus by his name."
Marduk takes Cyrus by the hand, calls him to shepherd his people and gives him the rule of Babylon.
Marduk tells Cyrus that he will do these great, generous things of setting the people free.
And this is why we should all be grateful to and worship Marduk.
The Hebrew writers in the Old Testament, you will not be surprised to learn, take a rather different view of this.
For them, of course, it can't possibly by Marduk that made all this happen.
It can only be Jehovah.
And so in Isaiah, we have the wonderful texts giving all the credit of this, not to Marduk but to the Lord God of Israel -- the Lord God of Israel who also called Cyrus by name, also takes Cyrus by the hand and talks of him shepherding his people.
It's a remarkable example of two different priestly appropriations of the same event, two different religious takeovers of a political fact.
God, we know, is usually on the side of the big battalions.
The question is, which god was it?
And the debate unsettles everybody in the 19th century to realize that the Hebrew scriptures are part of a much wider world of religion.
And it's quite clear the cylinder is older than the text of Isaiah, and yet, Jehovah is speaking in words very similar to those used by Marduk.
And there's a slight sense that Isaiah knows this, because he says, this is God speaking, of course,
"I have called thee by thy name though thou hast not known me."
I think it's recognized that Cyrus doesn't realize that he's acting under orders from Jehovah.
And equally, he'd have been surprised that he was acting under orders from Marduk.
Because interestingly, of course,
Cyrus is a good Iranian with a totally different set of gods who are not mentioned in any of these texts.
(Laughter)
That's 1879.
40 years on and we're in 1917, and the cylinder enters a different world.
This time, the real politics of the contemporary world -- the year of the Balfour Declaration, the year when the new imperial power in the Middle East, Britain, decides that it will declare a Jewish national home, it will allow the Jews to return.
And the response to this by the Jewish population in Eastern Europe is rhapsodic.
And across Eastern Europe, Jews display pictures of Cyrus and of George V side by side -- the two great rulers who have allowed the return to Jerusalem.
And the Cyrus cylinder comes back into public view and the text of this as a demonstration of why what is going to happen after the war is over in 1918 is part of a divine plan.
You all know what happened.
The state of Israel is setup, and 50 years later, in the late 60s, it's clear that Britain's role as the imperial power is over.
And another story of the cylinder begins.
The region, the U.K. and the U.S. decide, has to be kept safe from communism, and the superpower that will be created to do this would be Iran, the Shah.
And so the Shah invents an Iranian history, or a return to Iranian history, that puts him in the center of a great tradition and produces coins showing himself with the Cyrus cylinder.
When he has his great celebrations in Persepolis, he summons the cylinder and the cylinder is lent by the British Museum, goes to Tehran, and is part of those great celebrations of the Pahlavi dynasty.
Cyrus cylinder: guarantor of the Shah.
10 years later, another story:
Iranian Revolution, 1979.
Islamic revolution, no more Cyrus; we're not interested in that history, we're interested in Islamic Iran -- until Iraq, the new superpower that we've all decided should be in the region, attacks.
Then another Iran-Iraq war.
And it becomes critical for the Iranians to remember their great past, their great past when they fought Iraq and won.
It becomes critical to find a symbol that will pull together all Iranians --
Muslims and non-Muslims, Christians, Zoroastrians, Jews living in Iran, people who are devout, not devout.
And the obvious emblem is Cyrus.
So when the British Museum and Tehran National Musuem cooperate and work together, as we've been doing, the Iranians ask for one thing only as a loan.
It's the only object they want.
They want to borrow the Cyrus cylinder.
And last year, the Cyrus cylinder went to Tehran for the second time.
It's shown being presented here, put into its case by the director of the National Museum of Tehran, one of the many women in Iran in very senior positions,
Mrs. Ardakani.
It was a huge event.
This is the other side of that same picture.
It's seen in Tehran by between one and two million people in the space of a few months.
This is beyond any blockbuster exhibition in the West.
And it's the subject of a huge debate about what this cylinder means, what Cyrus means, but above all, Cyrus as articulated through this cylinder --
Cyrus as the defender of the homeland, the champion, of course, of Iranian identity and of the Iranian peoples, tolerant of all faiths.
And in the current Iran, Zoroastrians and Christians have guaranteed places in the Iranian parliament, something to be very, very proud of.
To see this object in Tehran, thousands of Jews living in Iran came to Tehran to see it.
It became a great emblem, a great subject of debate about what Iran is at home and abroad.
Is Iran still to be the defender of the oppressed?
Will Iran set free the people that the tyrants have enslaved and expropriated?
This is heady national rhetoric, and it was all put together in a great pageant launching the return.
Here you see this out-sized Cyrus cylinder on the stage with great figures from Iranian history gathering to take their place in the heritage of Iran.
It was a narrative presented by the president himself.
And for me, to take this object to Iran, to be allowed to take this object to Iran was to be allowed to be part of an extraordinary debate led at the highest levels about what Iran is, what different Irans there are and how the different histories of Iran might shape the world today.
It's a debate that's still continuing, and it will continue to rumble, because this object is one of the great declarations of a human aspiration.
It stands with the American constitution.
It certainly says far more about real freedoms than Magna Carta.
It is a document that can mean so many things, for Iran and for the region.
A replica of this is at the United Nations.
In New York this autumn, it will be present when the great debates about the future of the Middle East take place.
And I want to finish by asking you what the next story will be in which this object figures.
It will appear, certainly, in many more Middle Eastern stories.
And what story of the Middle East, what story of the world, do you want to see reflecting what is said, what is expressed in this cylinder?
The right of peoples to live together in the same state, worshiping differently, freely -- a Middle East, a world, in which religion is not the subject of division or of debate.
In the world of the Middle East at the moment, the debates are, as you know, shrill.
But I think it's possible that the most powerful and the wisest voice of all of them may well be the voice of this mute thing, the Cyrus cylinder.
Thank you.
(Applause)
Let's do some examples dealing with equations of lines in standard form.
So, so far we've had two other forms. We've had slope-intercept, which is of the form, y is equal to mx plus b.
That's actually this right here.
This is in slope-intercept form.
We've seen point-slope form in the last video.
That's of the form, y minus some y-value on the line being equal to the slope times x minus some x-value on the line, when you have that y-value.
So the point x1, y1 is on the line.
This right here is an example of point-slope form.
And now we're going to talk about the standard form.
And the standard form-- let me write it here-- standard form is essentially putting all of the x and y terms onto the left-hand side of the equation.
So you get ax plus by is equal to c.
I want to really emphasize that all of these are just different ways of writing the same equation.
If you're given this, you can out algebraically manipulate it to get to that or to that.
If you're given that, you can get to that or that.
These are all different ways of writing the exact same relationship, the exact same line.
So here we have a line right here.
We have an equation written in slope-intercept form.
The slope is 3, the y-intercept is negative 8.
Let's put it into standard form.
So we just have to get the 3x onto the other side of the equation.
And the best way I can think of doing that-- let me rewrite the equation, y is equal to 3x minus 8-- let's some subtract 3x from both sides of the equation.
So if you subtract 3x from both sides-- so you subtract 3x, subtract 3x-- what do the left- and right-hand sides of the equation become?
The left-hand side becomes negative 3x plus y being equal to-- the 3x and the negative 3x cancel out-- being equal to negative 8.
We're done.
That's standard form right there.
Standard form, I guess people like it because it has both the coefficients on the left-hand side.
But it's kind of useless in trying to figure out slope and y-intercept.
I don't know what the slope and y-intercept is when I look at it in standard form.
Point-slope, easy to get to, and you can look at it and figure out the slope.
But y-intercept, you have to do a little bit of work to figure it out.
But anyway, let's go from this equation, which is written in point-slope form, and get it to the standard form.
So we want to get it to the standard form, to the same type of standard form.
So a good thing to do, let's just distribute things out. y minus 7 is equal to negative 5 times x, negative 5x, plus negative 5, times negative 12, which is positive 60.
Now, we want all of the variable terms on the left, all of the constant terms on the right.
So let's add 7 to both sides of this equation.
So plus 7 to both sides of this equation.
What does it become?
Well, the minus 7 disappears, because negative 7 plus 7.
So you're just left with a y being equal to negative 5x plus 67.
Now, if we want this x term on the left-hand side, we could add 5x to both sides.
So let's add 5x to both sides of this equation.
And we will get y plus 5x is equal to-- these cancel out-- 67.
Now, this is pretty much standard form.
If you really want to be a stickler for it, you can rearrange these two.
So it'd be 5x plus y is equal to 67.
And you are done.
Let's do one more of these.
So this is in neither point-slope nor in slope-intercept form.
This looks like some type of point-slope, but this looks like something different.
So it's really not point-slope.
Let's see if we can algebraically manipulate it to the standard form.
So we get 3y plus 5.
Let's distribute out this 4.
So it's equal to 4x minus 36.
Let's do exactly what we did in the last.
I'm using different notation on purpose, to expose you to different things.
So instead of doing it this way, I'm going to subtract 5 from both sides, but I'm going to do it on the same line.
So I'm going to subtract 5 from both sides.
And so the left-hand side of this equation becomes 3y, because these two guys cancel out, and that is equal to 4x.
And then what is minus 36 minus 5?
That's minus 41.
And now we want the x terms of the left-hand side.
So let's subtract 4x from both sides of this equation.
So negative 4x plus, and then minus 4x.
What does our equation become?
Well, the left-hand side just stays negative 4x plus 3y. And the right-hand, the reason why we subtracted 4x is so it cancels out with that.
You just have a negative 41.
And we're done.
We are in standard form.
Now, let's go the other way.
Let's start with some equations in standard form and figure out their slope and y-intercept.
And the best way I know to figure out the slope and y-intercept is to put it into slope-intercept form.
So we want to put these equations right here into the form, y is equal to mx plus b.
So we're essentially solving for y.
5x minus 2y is equal to 15.
Let's subtract 5x from both sides.
So minus 5x plus, you have a minus 5x.
These cancel out.
And so you're left with negative 2y is equal to 15 minus 5x.
If you divide everything by negative 2, what do we get?
The left-hand side just becomes a y. y is equal to-- 15 divided by negative 2 is negative 7.5.
And then negative 5 divided by negative 2-- you can imagine
I'm dividing both of these by negative 2.
So negative 5 divided by negative 2 is positive 2.5x.
And if you really wanted to put it in the slope-intercept form, you could say that y is equal to-- you could just rearrange these-- 2.5x minus 7.5.
You want the slope.
It's right here.
That is our slope.
You want the y-intercept.
It is right there.
It is negative 7.5.
That is the y-intercept.
And now this would be a form that's actually pretty straightforward to graph it in.
So once again, we just need to solve for y.
So let's subtract 3x from both sides.
So you get 6y is equal to 25 minus 3x.
And then you can divide both sides by 6.
So you're left with y is equal to 25 over 6 minus 3 over 6, or minus 1/2x.
If you really want it in this from, you just rearrange this. y is equal to negative 1/2x plus 25 over 6.
Where is the slope?
Here is the slope.
Negative 1/2, that is the slope.
Where is the y-intercept?
That's the y-intercept.
That is our b.
The point 0, 25 over 6 is on the line.
Let's do one more of these.
So we get 9x minus 9y is equal to 4.
Just for fun, let's just start off by dividing both sides of the equation by 9.
But this is kind of a fun way to do it, because the coefficients here will immediately become 1.
So if you divide both sides of the equation by 9, if you divide everything by 9, it becomes-- actually, well, let's divide everything.
Let's divide everything by negative 9, even better.
So this first term will become negative x.
The second term, you have a negative 9 divided by a negative 9, it will be a plus y.
And then this last term will just become a negative 4 over 9.
Negative 4 over 9.
I'm giving some space there.
Now, we want the x on the right-hand side, so let's add x to both sides of this equation.
And then the equation becomes y is equal to x minus 4/9.
Where is the slope?
The slope is the coefficient on the x term.
The slope is equal to 1.
Where is the y-intercept?
The y-intercept is right there.
It is negative 4/9.
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So we have f of x is equal to negative x plus 4, and f of x is graphed right here on our coordinate plane.
Let's try to figure out what the inverse of f is.
And to figure out the inverse, what I like to do is I set y, I set the variable y, equal to f of x, or we could write that y is equal to negative x plus 4.
Right now, we've solved for y in terms of x.
To solve for the inverse, we do the opposite. We solve for x in terms of y.
So let's subtract 4 from both sides. You get y minus 4 is equal to negative x.
And then to solve for x, we can multiply both sides of this equation times negative 1.
And so you get negative y plus 4 is equal to x.
Or just because we're always used to writing the dependent variable on the left-hand side, we could rewrite this as x is equal to negative y plus 4.
Or another way to write it is we could say that f inverse of y is equal to negative y plus 4.
So this is the inverse function right here, and we've written it as a function of y, but we can just rename the y as x so it's a function of x.
So if we just rename this y as x, we get f inverse of x is equal to the negative x plus 4.
These two functions are identical.
Here, we just used y as the independent variable, or as the input variable.
Here we just use x, but they are identical functions.
Now, just out of interest, let's graph the inverse function and see how it might relate to this one right over here.
It's a negative x plus 4.
It's the exact same function.
So let's see, if we have-- the y-intercept is 4, it's going to be the exact same thing.
The function is its own inverse.
And so, there's a couple of ways to think about it.
In the first inverse function video, I talked about how a function and their inverse-- they are the reflection over the line y equals x.
So where's the line y equals x here?
Well, line y equals x looks like this.
And negative x plus 4 is actually perpendicular to y is equal to x, so when you reflect it, you're just kind of flipping it over, but it's going to be the same line.
When we're dealing with the standard function right there, if you input a 2, it gets mapped to a 2.
If you input a 4, it gets mapped to 0.
What happens if you go the other way?
If you input a 2, well, 2 gets mapped to 2 either way, so that makes sense.
For the regular function, 4 gets mapped to 0.
For the inverse function, 0 gets mapped to 4.
For the regular function-- let me write it explicitly down.
Let's pick f of 5. f of 5 is equal to negative 1.
Or we could say, the function f maps us from 5 to negative 1.
Now, what does f inverse do?
What's f inverse of negative 1? f inverse of negative 1 is 5.
Or we could say that f maps us from negative 1 to 5.
So let's say that this is the domain of f, this is the range of f. f will take us from 5 to negative 1.
Let's do one more of these.
So here I have g of x is equal to negative 2x minus 1.
So just like the last problem, I like to set y equal to this.
So we say y is equal to g of x, which is equal to negative 2x minus 1.
Now we just solve for x. y plus 1 is equal to negative 2x.
Now we can divide both sides of this equation by negative 2, and so you get negative y over 2 minus 1/2 is equal to x, or we could write x is equal to negative y over 2 minus 1/2, or we could write f inverse as a function of y is equal to negative y over 2 minus 1/2, or we can just rename y as x.
And we could say that f inverse of-- oh, let me careful here.
The original function was g , so let me be clear.
That is g inverse of y is equal to negative y over 2 minus 1/2 because we started with a g of x, not an f of x.
Now, let's graph it.
Its y-intercept is negative 1/2.
Let's see, if we start at negative 1/2, if we move over to 1 in the positive direction, it will go down half.
If we move over 1 again, it will go down half again.
It'll just keep going, so it'll look something like that, and it'll keep going in both directions.
And now let's see if this really is a reflection over y equals x. y equals x looks like that, and you can see they are a reflection.
But the general idea, you literally just-- a function is originally expressed, is solved for y in terms of x.
Solve for x in terms of y, and that's essentially your inverse function as a function of y, but then you can rename it as a function of x.
We're asked to simplify 8 plus 5 times 4 minus, and then in parentheses, 6 plus 10 divided by 2 plus 44.
Whenever you see some type of crazy expression like this where you have parentheses and addition and subtraction and division, you always want to keep the order of operations in mind.
Let me write them down over here.
So when you're doing order of operations, or really when you're evaluating any expression, you should have this in the front of your brain that the top priority goes to parentheses.
Those are the parentheses right there.
That gets top priority.
Then after that, you want to worry about exponents.
There are no exponents in this expression, but I'll just write it down just for future reference: exponents.
One way I like to think about it is parentheses always takes top priority, but then after that, we go in descending order, or I guess we should say in-- well, yeah, in descending order of how fast that computation is.
When I say fast, how fast it grows.
When I take something to an exponent, when I'm taking something to a power, it grows really fast. Then it grows a
little bit slower or shrinks a little bit slower if I multiply or divide, so that comes next: multiply or divide.
Multiplication and division comes next, and then last of all comes addition and subtraction.
So these are kind of the slowest operations.
This is a little bit faster.
This is the fastest operation.
And then the parentheses, just no matter what, always take priority.
So let's apply it over here.
Let me rewrite this whole expression.
So it's 8 plus 5 times 4 minus, in parentheses, 6 plus 10 divided by 2 plus 44.
So we're going to want to do the parentheses first. We have parentheses there and there.
Now this parentheses is pretty straightforward.
Well, inside the parentheses is already evaluated, so we could really just view this as 5 times 4.
So let's just evaluate that right from the get go.
So this is going to result in 8 plus-- and really, when you're evaluating the parentheses, if your evaluate this parentheses, you literally just get 5, and you evaluate that parentheses, you literally just get 4, and then they're next to each other, so you multiply them.
So 5 times 4 is 20 minus-- let me stay consistent with the colors.
Now let me write the next parenthesis right there, and then inside of it, we'd evaluate this first.
Let me close the parenthesis right there.
And then we have plus 44.
So what is this thing right here evaluate to, this thing inside the parentheses?
Well, you might be tempted to say, well, let me just go left to right.
6 plus 10 is 16 and then divide by 2 and you would get 8.
But remember: order of operations.
Division takes priority over addition, so you actually want to do the division first, and we could actually write it here like this.
You could imagine putting some more parentheses.
Let me do it in that same purple.
You could imagine putting some more parentheses right here to really emphasize the fact that you're going to do the division first.
So 10 divided by 2 is 5, so this will result in 6, plus 10 divided by 2, is 5.
6 plus 5.
Well, we still have to evaluate this parentheses, so this results-- what's 6 plus 5?
Well, that's 11.
So we're left with the 20-- let me write it all down again.
We're left with 8 plus 20 minus 6 plus 5, which is 11, plus 44.
And now that we have everything at this level of operations, we can just go left to right.
So 8 plus 20 is 28, so you can view this as 28 minus 11 plus 44.
28 minus 11-- 28 minus 10 would be 18, so this is going to be 17.
It's going to be 17 plus 44.
And then 17 plus 44-- I'll scroll down a little bit.
7 plus 44 would be 51, so this is going to be 61.
So this is going to be equal to 61.
And we're done!
Find the range and the midrange of the following sets of numbers
So what the range tells us is essentially how spread apart these numbers are
And the way that you calculate it is
You just take the difference between the the largest of these numbers and the smallest of these numbers
And so if we look at the largest of these numbers I'll circle it in magenta, it looks like it is 94 94 is larger than every other number here So that's the largest of the numbers
And from that we want to subtract the smallest of the numbers
And the smallest of the numbers in our set right over here is 65 (Circled in green)
So you want to subtract 65 from 94 and this is equal to... if this was 95 minus 65, it would be 30 94 is one less than 95 so it is 29
So the larger this number is that means the more spread out the larger the difference between the largest and the smallest number the smaller this is, that means, the [tighter?] the range [just to use the word itself?] of the numbers actually are, so that's the range the midrange is one way of thinking to some degree of kind of central tendency, so midrange, midrange, and would you do with the midrange is to take the average of the largest number and the smallest number so, here we took the difference that's the range.
The midrange would be the average of this two numbers so 94 plus 65 when we talk about average and [talk about] arithmetic mean over 2 so this is going to be what... 90 plus 60 is 150, 150 plus... 4 plus 5 is 159, 159 divided by 2 is equal to 150 divided by 2, is 75, 9 divided by 2 is 4.5, so this would be 79.5 so is one kind [of way?] of thinking about the middle of these numbers, another way is obviously the arithmetical mean we [] to take [] obviously you can also look at things as the median and the mode so range and midrange
What I want to do in this video is give you at least a basic overview of 'probability' - a word that you've probably heard a lot.
But, hopefully, this will give you a little deeper understanding.
So let's say that I have a fair coin over here
And so, when I talk about a fair coin, I mean that it has an equal chance of landing on one side or another.
So you can maybe view it as the sides are equal - their weight is the same on either side.
So you have one side of this coin - (So this would be the heads, I guess.
I'm trying to draw George Washington.
I'll assume it's a quarter of some kind.)
And then on the other side, of course, is the tails.
So that is heads.
So, if I were to ask you, "What is the probability -
I'm going to flip a coin.
And I want to know, "What is the probability of getting heads?"
And I could write that like this:
WRlTING: The probability of getting heads.
And you probably, just based on that question, have a sense of what probability is asking.
It's asking for some type of way of getting your hands around an event that's fundamentally random.
We don't know whether it's heads or tails. But we can start to describe the chances of it being heads or tails.
And we'll talk about different ways of describing that.
So, one way to think about it - (And this is the way that probability tends to be introduced in textbooks.)
"So how many equally likely possibilities?"
So, number of equally - (Let me write 'equally.') - of equally likely possibilities.
And of the number of equally likely possibilities,
I care about the number that contain my event right here.
So, the number of possibilities that meet my constraint - that meet my conditions.
So, in the case of the probability of figuring out heads, what is the number of equally likely possibilities? Well, there are only two possibilities.
We're assuming that the coin can't land on its edge and remain standing straight up.
We're assuming it lands flat.
So, there are two possibilities here - two equally likely possibilities.
I encourage you to do it. if you take 100 or 200 quarters or pennies, and you stick them in a big box, and shake the box, so you are kind of simultaneously flipping all the coins, and then count how many of those are going to be heads, you're going to see that the larger the number of coins that you are doing, the more likely you are going to get something really close to 50%.
But there's always some chance that even if you flipped a coin a million times - there's some super-duper small chance that you get all tails.
But the more you do, the more likely that things are going to trend toward 50% of them being heads.
When you roll this, you could get a 1, a 2, a 3, a 4, a 5, or a 6.
And they are all equally likely.
So if I were to ask you, "What is the probability, given that I'm rolling a fair die" - (So the experiment is rolling this fair die.) "What is the probability of getting a 1?"
And I'm just talking about on one roll of the die.
Well, in any roll of the die, I can only get a 2 or a 3.
I'm not talking about taking two rolls of this die.
So in this situation, there are 6 possibilities, but none of these possibilities are a 2 AND a 3.
On one trial, you can't get a 2 and a 3 in the same experiment.
Getting a 2 and a 3 are mutually exclusive events. They cannot happen at the same time.
So the probability of this is actually 0.
There's no way to roll this normal die, and all of a sudden you get a 2 AND a 3.
And I don't want to confuse you with that, because it's abstract and impossible.
So let's cross this out right over here.
Now, what is the probability of getting an even number?
So, once again, I have 6 equally likely possibilities when I roll that die. And which of these possibilities meet my condition - the condition of being even?
So three of the possibilities meet my conditions - meet my constraints.
So this is 1/2.
If I roll a die, I have a 1/2 chance of getting an even number.
Four people earn $180 for working at an after-school program.
If they divide this money up equally, how much will each person receive?
So we want to divide $180 into four equal groups so that each of the four people can have the same amount.
So we want to divide 180 by 4.
We want to take 180 divided by 4.
Now, most of us don't know this off the top of our heads, so we need to solve for it.
We need to do a little bit of division.
So another way of writing this exact same expression is to write 4 divided into 180.
And when you write it like this, it's easier to do it if either of them actually has more than one digit, especially if the number we're dividing into has more than one or two or three or four digits.
So let's do it.
So the first thing you say is, well, does 4 go into 1?
Well, no, 4 does not go into 1.
It's larger than 1.
So you could put a 0 up here, but instead of doing that, let's just move on to the right and say, well, OK, it doesn't go into 1.
Does 4 go into 18?
Well, 4 times 4 is 16, so that goes into 18 at least four times.
4 times 5-- let me write this down.
4 times 4 is equal to 16, so that goes into 18.
4 times 5 is equal to 20, so that does not go into 18, so this is going to go into 18 four times.
4 times 4 is 16, and now we subtract.
We essentially find the remainder here.
18 minus 6 is 2.
Now we want to bring down this 0, because we really said 4 goes into 180 40 times, because it's in the tens place.
40 times 4 is 160.
180 minus 160 is 20.
That's why we bring down the 0.
But if you just think about the process, you say, OK, what's the smallest-- if I just go with the 1, 4 doesn't go into it, so let me move on.
Let me look at the 1 and the 8, 18.
4 goes into that four times.
4 times 4 is 16.
Subtract from 18, you get a 2, bring down the 0.
Now 4 goes into 20 how many times?
Well, we just wrote it over here.
4 times 5 is equal to 20.
So 4 goes into 20 five times.
5 times 4 is 20.
You subtract, and you have no remainder left over.
So 180 divided by 4 is equal to 45.
So if these four people were to split the money equally, they'll each get $45.
Let's do some more matrix multiplication examples, because I think it is all about seeing as many examples as possible.
So let's do what may seem to be a more difficult problem, and it might not be even clear that we can multiply these matrices.
And maybe that's the first thing we should think about.
So let's say I wanted to multiply the matrix-- I'll do it relatively small so we don't run out of space.
3, 1, 2, minus 2, 0, 5.
Let's say I want to multiply that times the matrix, minus 1, 0, 2, 3, 5, 5.
I'm just making up these numbers.
So the first thing you might be wondering is, well can I even multiply these matrices?
Because you know from the first video we did on matrices, that you can't add these two matrices.
This term corresponds to this one; this one corresponds to this one; but this term corresponds to nothing over here so you couldn't add or subtract these matrices.
So the question is, can I multiply these matrices?
Well, what did we learn about multiplying matrices?
We know that, for example, if this is going to result in some matrix--
However we don't know even what the dimensions are yet until we work through this example, although there is a quick way for figuring it out.
So this first term here, the upper left term, where does it get its row information from and where does it get its column information from? Well, it gets its row information from here.
So it is essentially this row times which column?
Times this column, right?
And we can actually take the dot product of this row vector and this column vector because they have the same length.
This is a column vector but it has a length of 3, right?
But it's a 3 by 1, it has three elements in it.
And this is a 1 by 3 row vector, but it also has three elements in it.
So we actually can take the dot product or we can multiply these two.
And similarly we can multiply this times this whole thing to get this term right here.
And we can multiply this thing times this thing to get this term, and then this thing times that term to get that term.
So it actually turns out that you can-- so what kind of a matrix is this?
Let's call it that this is matrix-- let me switch to
[UNlNTELLlGIBLE].
So this is matrix A.
And what are it's dimensions?
It has 2 rows, 1, 2, and 3 columns.
So it's a 2 by 3 matrix.
And what are B's dimensions? Well, it has 3 rows, 1, 2, 3.
So it is a 3 by-- and how many columns does it have?
1, 2-- 2 matrix.
So it turns out that we can multiply two matrices.
You can say that the number-- if, on the first matrix-- the number of columns is equal to the number of rows in the second matrix.
So here, 2 by 3 times 3 by 2, we can multiply.
For example, we could have multiplied, if this is matrix C.
I don't know if I take so much time to keep bolding these things.
And I don't care how many rows it has.
It can have n rows, n times a columns.
I can multiply it times matrix D, as long as matrix D has a rows.
As long as you can say these two inner numbers are the same, right?
This 3 is the same as 3.
And why does that matter, what was the logic?
Because this row will have 3 elements because there's 3 columns, and each column vector here will have 3 elements, because there's 3 rows.
That's where intuition comes from, but if you had to do it really quickly you say 2 by 3, 3 by 2, this number is equal to that number, I can multiply.
So let me clear up some space and let's do the multiplication.
Let's do some multiplication.
I'm debating where I should do it, actually I think I should do it down here maybe because I'll have more space.
So let me do it down there; I don't have to erase anything else.
So let me get some space ready.
OK, this will take up a lot of space.
So to get this row 1, column 1 element, what do I do?
I multiply this vector times this vector.
I take the dot product, right?
So it's 3 times negative 1-- I'm just going to write it all
-- 3 times minus 1, plus 1 times 0, plus 2 times 2.
So the second term here, what am I going to do?
I'm going to multiply that vector times that row vector times this column vector.
And I think you're getting the hang of this, and really the hardest part about this is staying focused and not making a careless mistake.
And not getting it confused with rows and columns and all that.
It just sends blood to your brain, but it's not that hard, I think.
So what do we do?
We multiply this row vector times this column vector to get row 1, column 2, right?
Because this row, row 1, column 2.
3 times 3, plus 1 times 5, plus 2 times 5, right.
We're just multiplying the corresponding terms, the third term times the third term, the second term times the second term, the first term times the first term.
Although, in this case they're going down, in this case they're going left and right.
Oh, we add them all up.
OK, so now we're in the second row, and we get our row information from the first vector-- and let me do a red that I never use because I think it's kind of tacky, this red right here.
So I'm going to multiply this row vector times this column vector.
So it's minus 2 times minus 1, plus 0 times 0, plus 5 times 2.
Let me see-- I don't like this color at all-- and now we're going to multiply this row, because we're in this bottom row, we're in row 2, column 2, to row 2, column 2.
So it's minus 2 times 3, plus 0 times 5, plus 5 times 5.
And then if we simplify, let's see, this is minus 3 plus 0, plus 4, so this-- if I have my math correct-- simplifies to 1.
9 plus 5 is 14, plus 10 is 24.
This is 1, 24, and then minus 2 times minus 1 is 2, plus 10, so this is 12.
And then minus 2 times 3 is minus 6, plus 10-- this is 0-- so minus 6 plus 10 is 4.
So that's interesting.
When I multiplied a 2 by 3 vector times a 3 by 2 vector, what did I get?
I got a 2 by 2 matrix.
A 2 by 3 matrix, a 2 by 3 times 3 by 2 matrix, I got a 2 by 2 matrix.
And where do you see a 2 by 2?
Well, it's like this got multiplied with this, and what we have left over is a 2 by 2 matrix.
So in general-- well actually, before I go into the general, let me ask you a question.
Could I have multiplied the matrices the other way?
Could I have multiplied-- so this right here that is A times B, or you can sometimes write this AB, and we'd bold it all up so we know it's matrices.
So could we have multiplied B times A?
Let me clear this down here and let's try.
Let's see if we can multiply B times A.
I think you can already suspect that, since I'm asking the question, maybe you cannot.
Let's clear up some space.
Let's try to do it the other way around, let's try to multiply B times A.
So B is minus 1, 0, 2, 3, 5, 5.
And A is-- I'm switching the order-- 3, 1, 2, minus 2, 0, 5.
And I tend to put brackets around my matrices.
Some people have these big parentheses.
It's just all notation; there's nothing particular about notation.
So let's see if you can multiply these.
So we learned that you get the row information from the first matrix and the column information from the second one.
So this term, in theory, should be that row times what?
Why?
Because this is a 3 by 2, and this is a 2 by 3, right?
So we're going to take that row times what?-- times this column to get the first term, right?
So what is it going to be?
It's going to be minus 1.
So I actually thought I was doing a counter example, but actually because this too is the same as this, or when you switch the row this is the same as this, you can multiply them.
So I wanted to do a counter example, but hey.
Let's just work through this because it never hurts to see another example.
And you can see that I just do this on the fly.
So let's do this.
And actually ahead of time, how large will this matrix be?
Well, this is interesting.
It's actually going to be a 3 by 3 matrix, a much bigger matrix.
Let's work it all out, and maybe you want to pause it and try it yourself.
This row times this column, so minus 1 times 3, it's minus 3, 3 times minus 2 is minus 6.
And then it's going to be this row times this column.
So it's minus 1 times 1 plus 3 times 0, so that's just minus 1, right?
Because 3 times 0 is 0.
And then, that was that one, then there's the middle one, and now we get the row 1, column 3.
So row 1, column 3.
So it's that row times this column.
You can tell, this is often better done by a computer.
Minus 1 times 2 is minus 2 plus 15-- 3 times 5-- so minus 2 plus 5 is 13.
Let's keep going.
So now we're going to take--
I'm sweating, this is so computationally intensive--
We're taking this row times each of these columns.
And actually we are going to learn later that there are multiple ways of actually thinking about how this multiplication happens, even multiple ways by computer, but this is the traditional way.
So this row times each of these columns, right?
So 0, 5, so 0 times 3 plus 5 times minus 2, that's minus 10, and it's 0 times 1 plus 5 times 0.
That's easy, that's 0.
0 times 2 plus 5 times 5 is 25-- almost there, almost done.
Now we're going to take this row and multiply it times each of these columns.
So 2 times 3, that's 6, plus minus 10, so that's minus 4, right?
2 times 3 plus 5 times minus 2.
Yes, that's minus 4, 6 minus 10, right?
We have 2 times 1 plus 5 times 0, that's 2.
Then you have 2 times 2 plus 5 times 5, so 4 plus 25 is 29.
And of course that first term, minus 3 minus 6, so this is minus 9.
So there you have it.
We multiplied the 3 by 2 matrix times a 2 by 3 matrix, and we got a 3 by 3 matrix.
And where did that 3 by 3 come from?
Because this 3 is the number of rows in the first matrix, and this 3 is the number of columns in the second matrix, which makes sense because we got our row information from the first matrix and our column information from the second matrix.
Now let me actually show you an example that you cannot multiply.
So what if I wanted to multiply a-- let me do a very simple example-- what if I wanted to multiply the matrix, 2, 1.
And really, all this is, is a row vector.
And let's say that I wanted to multiply this times-- I don't know, so this is a 2 by 1.
So then let me say I want to multiply this times-- so let me think of something-- 1, 2, 3, 4, 5, 6.
Now, can I multiply this?
Well, what do we have?
This is a 3 by 2 matrix.
Can I multiply these two matrices?
Well, what do we have to do?
We get our row information from here, and our column information from here--
Oh sorry, this isn't 2 by 1, this is 1 row, two columns.
This is a 1 by 2, right?
That's a 1 by 2 matrix.
So can you multiply the 1 by 2 times a 3 by 2 matrix?
So we get our row information from here, so we essentially have to multiply this by this times this column to get our first element, then this times this column to get our second element.
And I don't know what happens from there, but let me-- well, can we multiply?
Just the way we have defined our multiplication, or the dot product, can we multiply?
Let's see, 2 times 1 plus 1 times 2.
Then we don't have anything to do with the 3.
So the way that we've defined matrix multiplication, you cannot multiply these two matrices.
And you didn't have to go through that exercise.
You could've looked at the dimensions, 1 by 2, and this is a 3 by 2.
This 2 is not equal to this 3, the number of columns in the first are not equal to the number of rows in the second.
So you can not multiply those two matrices.
So that's something interesting to think about.
And they're actually examples, and it's a good exercise for you to think about it, where you can multiply A times B, but you can't multiply B times A.
So I want you think about examples where that happens.
But anyway, I'm pushing 15 minutes, and I will see you in the next video.
How beautiful, is this worldly life
But not a soul shall remain
We've all come into this world
Only to leave it one day
I can see that everything around me
Rises then fades away
Life is just a passing moment
Nothing is meant to stay, oh
This worldly life has an end
And it's then real life begins
A world where we will live forever
This beautiful worldly life has an end
It's just a bridge that must be crossed
To a life that will go on forever
So many years, quickly slipping by
Like the Sleepers of the Cave
Wake up and make a choice
Before we end up in our graves
O God!
You didn't put me here in vain
I know I'll be held accountable for what I do
This life is just a journey And it's taking me back to You
This worldly life has an end
And it's then real life begins
A world where we will live forever
This beautiful worldly life has an end
It's just a bridge that must be crossed
To a life that will go on forever
So many get caught in this beautiful web
Its gardens become an infatuation
But surely they'll understand at the final stop
That its gardens are meant for cultivation, oh
This worldly life has an end
And it's then real life begins
A world where we will live forever
This beautiful worldly life has an end
It's just a bridge that must be crossed
To a life that will go on forever
This worldly life has an end
And it's then real life begins
A world where we will live forever
This beautiful worldly life has an end
It's just a bridge that must be crossed
To a life that will go on forever
I think you're probably reasonably familiar with the idea of a square root, but I want to clarify some of the notation that at least, I always found a little bit ambiguous at first.
I want to make it very clear in your head.
If I write a 9 under a radical sign, I think you know you'll read this as the square root of 9.
But I want to make one clarification.
When you just see a number under a radical sign like this, this means the principal square root of 9.
And when I say the principal square root, I'm really saying the positive square root of 9.
So this statement right here is equal to 3.
And I'm being clear here because you might already know that 9 has two actual square roots.
By definition, a square root is something-- A square root of 9 is a number that, if you square it, equals 9.
3 is a square root, but so is negative 3.
Negative 3 is also a square root.
But if you just write a radical sign, you're actually referring to the positive square root, or the principal square root.
If you want to refer to the negative square root, you'd actually put a negative in front of the radical sign.
That is equal to negative 3.
Or if you wanted to refer to both the positive and the negative, both the principal and the negative square roots, you'll write a plus or a minus sign in front of the radical sign.
And of course, that's equal to plus or minus 3 right there.
So with that out of the way, what I want to talk about is the graph of the function, y is equal to the principal square root of x.
And see how it relates to the function y is equal to x-- Let me write it over here because I'll work on it.
See how it relates to y is equal to x squared.
And then, if we have some time, we'll shift them around a little bit and get a better understanding of what causes these functions to shift up down or left and right.
So let's make a little value table before we get out our graphing calculator.
So this is for y is equal to x squared.
So we have x and y values.
This is y is equal to the square root of x.
Once again, we have x and y values right there.
So let me just pick some arbitrary x values right here, and I'll stay in the positive x domain.
So let's say x is equal to 0, 1-- Let me make it color coded.
When x is equal to 0, what's y going to be equal to?
Well y is x squared.
0 squared is 0.
When x is 1, y is 1 squared, which is 1.
When x is 2, y is 2 squared, which is 4.
When x is 3, y is 3 squared, which is 9.
We've seen this before.
And I could keep going.
Let me add 4 here.
So when x is 4, y is 4 squared, or 16.
We've seen all of this.
We've graphed our parabolas.
This is all a bit of review.
Now let's see what happens when y is equal to the principal square root of x.
Let's see what happens.
And I'm going to pick some x values on purpose just to make it interesting.
When x is equal to 0, what's y going to be equal to?
The principal square root of 0?
Well it's 0.
0 squared is 0.
When x is equal to 1, the principal square root of x of 1 is just positive 1.
It has another square root that's negative 1, but we don't have a positive or negative written here.
We just have the principal square root.
When x is a 4, what is y?
Well, the principal square root of 4 is positive 2.
When x is equal to 9, what's y?
When x is equal to 9, the principal square root of 9 is 3.
Finally, when x is equal to 16, the principal square root of 16 is 4.
So I think you already see how these two are related.
We've essentially just swapped the x's and the y's.
Well, these are the same x and y's, but here you have x is 2, y is 4.
Here x is 4, y is 2.
3 comma 9, 9 comma 3.
4 comma 16, 16 comma 4.
And that makes complete sense.
If you were to square both sides of this equation, you would get y squared is equal to x right there.
And, of course, you would want to restrict the domain of y to positive y's because this can only take on positive values because this is a principal square root.
But the general idea, we just swapped the x's and y's between this function and this function right here, if you assume a domain of positive x's and positive y's.
Now, let's see what the graphs look like.
And I think you might already have a guess of-- Let me just graph them here.
Let me do them by hand because I think that's instructive sometimes before you take out the graphing calculator.
So I'm just going to stay in the positive, in the first quadrant here.
So let me graph this first.
So we have the point 0, 0, the point 1 comma 1, the point 2 comma 2, which I'm going to have to draw it a little bit smaller than that.
Let me mark this is 1, 2, 3.
Actually, let me do it like this.
Let me go 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16.
That's about how far I have to go.
And then I have 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16.
That's about how far I have to go in that direction as well.
And now let's graph it.
So we have 0, 0, 1, 1, 2 comma 1, 2, 3, 4.
2 comma 4 right there.
3 comma 9.
3 comma 5, 6, 7, 8, 9. 3 comma 9 is right about there.
And then we have 4 comma 16.
4 comma 16 is going to be right above there.
So the graph of y is equal to x squared, and we've seen this before.
It's going to look something like this.
We're just graphing it in the positive quadrant, so we get this upward opening u just like that.
Now let's graph y is equal to the principal square root of x.
So here, once again, we have 0, 0.
We have 1 comma 1.
We have 4 comma 2.
1, 2, 3, 4 comma 2.
We have 9 comma 3.
5, 6, 7, 8, 9 comma 3 right about there.
Then we have 16 comma 4.
16 comma 4 is right about there.
So this graph looks like that.
So notice, they look like they're kind of flipped around the axes.
This one opens along the y-axis, this one opens along the x-axis.
And once again, it makes complete sense because we've swapped the x's and the y's.
Especially if you just consider the first quadrant.
And actually, these are symmetric around the line, y is equal to x.
And we'll talk about things like inverses in the future that are symmetric around the line, y is equal to x.
And we can graph this better on a regular graphing calculator.
I found this on the web.
I just did a quick web search.
I want to give proper credit to the people whose resource I'm using.
So this is my.hrw.com/math06.
You could pause this video.
And hopefully, you should be able read this.
Especially if you're looking at it in HD.
But let's graph these different things.
Let's graph it a little bit cleaner than what I can do by hand.
And actually, let me have some of what I wrote there.
So that should give you-- OK.
So let's first just graph y is equal to x squared. And then in green, let me graph y is equal to the square root of x. They have some buttons here on the right, just so you know what I'm doing.
Look, if you just focus on the first quadrant right here, you see that you get the exact same result that I got over there, although mine is messier. Now, just for fun and, you know, I really didn't do this yet with the regular quadratics, let's see what happens.
I'm going to scale the graphs and I'm going to shift them. So that's x squared. So let's just focus on the x squared and see what happens when we scale it.
And then I'll do it with the radical sign as well. This will really work for anything.
Let's see what happens when you get 2 times-- no, not 2 squared --2 times x squared. And let's do another one that is 1.5 times our 0.-- I could just do 0.4 actually.
0.5 times x squared. Let's graph these right there. So x squared.
So that's how you kind of decide how wide or how narrow the opening of our parabola is. And then if you want to shift it to the left or the right, and I want you to think about why this is.
So that's x squared. Let's say I want to just take the graph of x squared and I want to shift it four to the right.
What I do is I say, x minus 4. x minus 4 squared.
And if I want to shift it two to the-- Let's say I want to shift it two to the left. x plus 2 squared, what do we get?
Notice it did exactly what I said. x minus 4 squared was shifted four to the right. x plus 2 squared, was shifted two to the left.
And it might be unintuitive at first, this shifting that I'm talking about.
But really think about what's happening.
Over here, the vertex is where x is equal to 0.
When you get 0 squared up here.
Now over here, the vertex is when x is equal to 4.
But when x is equal to 4, you stick 4 in here, you get 4 minus 4.
So you're still squaring 0.
4 minus 4 is 0 and that's what you're squaring.
Over here, when x is equal to negative 2-- negative 2 plus 2
--you are squaring 0.
So, in other words, whatever you're squaring, that 0 is equivalent to 4 here.
Or 4 is equivalent to 0.
And negative 2 is equivalent to 0 over there.
So I want you to think about it a little bit.
Another way you could think about it, when x is equal to 1, we're at this point of the red parabola.
But when x is equal to 5 on the green parabola, you have 5 minus 4.
Inside of the parentheses you have a 1, just like x is equal to 1 over here, up here.
So you're at the same point in the parabola.
So I want you to think about that a little bit.
It might be a little non-intuitive that you say minus 4 to shift to the right and plus 2 to shift to the left.
But it actually makes a lot of sense.
Now, the other interesting thing is to shift things up and down.
And that's actually pretty straightforward.
You want to shift this curve up.
Let's say we want to shift the red curve up a little bit.
You do x squared plus 1.
Notice it got shifted up.
If you want this green curve to be shifted down by 5, put a minus 5 right there.
And then you graph it and it got shifted down by 5.
If you want it to open up a little wider than that, maybe scale it down a little bit.
Scale it down and let's say 0.5 times that.
So now the green curve will be scaled down and it opens slower, it has a wider opening.
And the same idea can be done with the principal square roots.
So let me do that.
Let me do the same idea.
And the same idea actually, can be done with any function.
So let's do the square root of x.
And in green, let's do the square root of x.
Let's say, minus 5.
So we're shifting it over to the right by 5.
And then let's have the square root of x plus 4.
So we're going to shift it to the left by 4.
Let's shift it down by 3.
And so lets graph all of these.
The square root of x.
Then have the square root of x minus 5.
Notice it's the exact same thing as the square root of x, but I shifted it to the right by 5.
When x is equal to 5, I have a 0 under the radical sign.
Same thing as square root of 0.
So this point is equivalent to that point.
Now, when I have the square root of x plus 4, I've shifted it over to the left by 4.
When x is negative 4, I have a 0 under the radical sign.
So this point is equivalent to that point.
And then I subtracted 3, which also shifted it down 3.
So this is my starting point.
If I want this blue square root to open up slower, so it'll be a little bit narrower, I would scale it down.
So here, putting a low number will scale it down and make it more narrow because we're opening along the x-axis.
So let me to do that.
Let me make this green one-- Let me open up wider.
So let me say it's 3 times the square root of x minus 5.
So let's graph all of these.
So notice, this blue one now opens up more narrow and this green one now opens up a lot, I guess you could say, a lot faster.
It's scaled up.
Then we could shift that one up a little bit by 4.
And then we graph it and there you go.
And notice when we graph these, it's not a sideways parabola because we're talking about the principal square root.
And if you did the plus or minus square root, it actually wouldn't even be a valid function because you would have two y values for every x value.
So that's why we have to just use the principal square root.
Anyway, hopefully you found this little talk, I guess, about the relationships with parabolas, and/or with the x squared's and the principal square roots, useful.
And how to shift them.
And that will actually be really useful in the future when we talk about inverses and shifting functions.
CHAPTER ill.
Gregor's serious wound, from which he suffered for over a month--since no one ventured to remove the apple, it remained in his flesh as a visible reminder--seemed by itself to have reminded the father that, in spite of his present unhappy and hateful appearance, Gregor was a member of the family, something one should not treat as an enemy, and that it was, on the contrary, a requirement of family duty to suppress one's aversion and to endure--nothing else, just endure.
And if through his wound Gregor had now apparently lost for good his ability to move and for the time being needed many, many minutes to crawl across his room, like an aged invalid--so far as creeping up high was concerned, that was unimaginable-- nevertheless for this worsening of his condition, in his opinion, he did get completely satisfactory compensation, because every day towards evening the door to the living room, which he was in the habit of keeping a sharp eye on even one or two hours beforehand, was opened, so that he, lying down in the darkness of his room, invisible from the living room, could see the entire family at the illuminated table and listen to their conversation, to a certain extent with their common permission, a situation quite different from what had happened before.
Of course, it was no longer the animated social interaction of former times, which
Gregor in small hotel rooms had always thought about with a certain longing, when, tired out, he had had to throw himself into the damp bedclothes.
For the most part what went on now was very quiet.
After the evening meal, the father fell asleep quickly in his arm chair.
The mother and sister talked guardedly to each other in the stillness.
Bent far over, the mother sewed fine undergarments for a fashion shop.
The sister, who had taken on a job as a salesgirl, in the evening studied stenography and French, so as perhaps later to obtain a better position.
Sometimes the father woke up and, as if he was quite ignorant that he had been asleep, said to the mother "How long you have been sewing today?" and went right back to sleep, while the mother and the sister smiled tiredly to each other.
With a sort of stubbornness the father refused to take off his servant's uniform even at home, and while his sleeping gown hung unused on the coat hook, the father dozed completely dressed in his place, as if he was always ready for his responsibility and even here was waiting for the voice of his superior.
As a result, in spite of all the care of the mother and sister, his uniform, which even at the start was not new, grew dirty, and Gregor looked, often for the entire evening, at this clothing, with stains all over it and with its gold buttons always polished, in which the old man, although very uncomfortable, slept peacefully nonetheless.
As soon as the clock struck ten, the mother tried gently encouraging the father to wake up and then persuading him to go to bed, on the ground that he couldn't get a proper sleep here and that the father, who had to report for service at six o'clock, really needed a good sleep.
But in his stubbornness, which had gripped him since he had become a servant, he insisted always on staying even longer by the table, although he regularly fell asleep and then could only be prevailed upon with the greatest difficulty to trade his chair for the bed.
No matter how much the mother and sister might at that point work on him with small admonitions, for a quarter of an hour he would remain shaking his head slowly, his eyes closed, without standing up.
The mother would pull him by the sleeve and speak flattering words into his ear; the sister would leave her work to help her mother, but that would not have the desired effect on the father.
He would settle himself even more deeply in his arm chair.
Only when the two women grabbed him under the armpits would he throw his eyes open, look back and forth at the mother and sister, and habitually say "This is a life.
This is the peace and quiet of my old age."
And propped up by both women, he would heave himself up elaborately, as if for him it was the greatest trouble, allow himself to be led to the door by the women, wave them away there, and proceed on his own from there, while the mother quickly threw down her sewing implements and the sister her pen in order to run after the father and help him some more.
In this overworked and exhausted family who had time to worry any longer about Gregor more than was absolutely necessary?
The household was constantly getting smaller.
The servant girl was now let go.
A huge bony cleaning woman with white hair flying all over her head came in the morning and evening to do the heaviest work.
The mother took care of everything else in addition to her considerable sewing work.
It even happened that various pieces of family jewellery, which previously the mother and sister had been overjoyed to wear on social and festive occasions, were sold, as Gregor found out in the evening from the general discussion of the prices they had fetched.
But the greatest complaint was always that they could not leave this apartment, which was too big for their present means, since it was impossible to imagine how Gregor might be moved.
But Gregor fully recognized that it was not just consideration for him which was preventing a move, for he could have been transported easily in a suitable box with a few air holes.
The main thing holding the family back from a change in living quarters was far more their complete hopelessness and the idea that they had been struck by a misfortune like no one else in their entire circle of relatives and acquaintances.
What the world demands of poor people they now carried out to an extreme degree.
The father bought breakfast to the petty officials at the bank, the mother sacrificed herself for the undergarments of strangers, the sister behind her desk was at the beck and call of customers, but the family's energies did not extend any further.
And the wound in his back began to pain Gregor all over again, when now mother and sister, after they had escorted the father to bed, came back, let their work lie, moved close together, and sat cheek to cheek and when his mother would now say, pointing to Gregor's room, "Close the door,
Grete," and when Gregor was again in the darkness, while close by the women mingled their tears or, quite dry eyed, stared at the table.
Gregor spent his nights and days with hardly any sleep.
Sometimes he thought that the next time the door opened he would take over the family arrangements just as he had earlier.
In his imagination appeared again, after a long time, his employer and supervisor and the apprentices, the excessively spineless custodian, two or three friends from other businesses, a chambermaid from a hotel in the provinces, a loving fleeting memory, a female cashier from a hat shop, whom he had seriously but too slowly courted--they all appeared mixed in with strangers or people he had already forgotten, but instead of helping him and his family, they were all unapproachable, and he was happy to see them disappear.
But then he was in no mood to worry about his family.
He was filled with sheer anger over the wretched care he was getting, even though he couldn't imagine anything which he might have an appetite for.
Still, he made plans about how he could take from the larder what he at all account deserved, even if he wasn't hungry.
Without thinking any more about how they might be able to give Gregor special pleasure, the sister now kicked some food or other very quickly into his room in the morning and at noon, before she ran off to her shop, and in the evening, quite indifferent to whether the food had perhaps only been tasted or, what happened most frequently, remained entirely undisturbed, she whisked it out with one sweep of her broom.
The task of cleaning his room, which she now always carried out in the evening, could not be done any more quickly.
Streaks of dirt ran along the walls; here and there lay tangles of dust and garbage.
At first, when his sister arrived, Gregor positioned himself in a particularly filthy corner in order with this posture to make something of a protest.
But he could have well stayed there for weeks without his sister's changing her ways.
In fact, she perceived the dirt as much as he did, but she had decided just to let it stay.
In this business, with a touchiness which was quite new to her and which had generally taken over the entire family, she kept watch to see that the cleaning of
Gregor's room remained reserved for her.
Once his mother had undertaken a major cleaning of Gregor's room, which she had only completed successfully after using a few buckets of water.
But the extensive dampness made Gregor sick and he lay supine, embittered and immobile on the couch.
However, the mother's punishment was not delayed for long.
For in the evening the sister had hardly observed the change in Gregor's room before she ran into the living room mightily offended and, in spite of her mother's hand lifted high in entreaty, broke out in a fit of crying.
Her parents--the father had, of course, woken up with a start in his arm chair--at first looked at her astonished and helpless, until they started to get agitated.
Turning to his right, the father heaped reproaches on the mother that she was not to take over the cleaning of Gregor's room from the sister and, turning to his left, he shouted at the sister that she would no
longer be allowed to clean Gregor's room ever again, while the mother tried to pull the father, beside himself in his excitement, into the bed room.
The sister, shaken by her crying fit, pounded on the table with her tiny fists, and Gregor hissed at all this, angry that no one thought about shutting the door and sparing him the sight of this commotion.
But even when the sister, exhausted from her daily work, had grown tired of caring for Gregor as she had before, even then the mother did not have to come at all on her behalf.
And Gregor did not have to be neglected.
For now the cleaning woman was there.
This old widow, who in her long life must have managed to survive the worst with the help of her bony frame, had no real horror of Gregor.
Without being in the least curious, she had once by chance opened Gregor's door.
At the sight of Gregor, who, totally surprised, began to scamper here and there, although no one was chasing him, she remained standing with her hands folded across her stomach staring at him.
Since then she did not fail to open the door furtively a little every morning and evening to look in on Gregor.
At first, she also called him to her with words which she presumably thought were friendly, like "Come here for a bit, old dung beetle!" or "Hey, look at the old dung beetle!"
Addressed in such a manner, Gregor answered nothing, but remained motionless in his place, as if the door had not been opened at all.
If only, instead of allowing this cleaning woman to disturb him uselessly whenever she felt like it, they had given her orders to clean up his room every day!
One day in the early morning--a hard downpour, perhaps already a sign of the coming spring, struck the window panes-- when the cleaning woman started up once again with her usual conversation, Gregor was so bitter that he turned towards her, as if for an attack, although slowly and weakly.
But instead of being afraid of him, the cleaning woman merely lifted up a chair standing close by the door and, as she stood there with her mouth wide open, her intention was clear: she would close her mouth only when the chair in her hand had been thrown down on Gregor's back.
"This goes no further, all right?" she asked, as Gregor turned himself around again, and she placed the chair calmly back in the corner.
Gregor ate hardly anything any more.
Only when he chanced to move past the food which had been prepared did he, as a game, take a bit into his mouth, hold it there for hours, and generally spit it out again.
At first he thought it might be his sadness over the condition of his room which kept him from eating, but he very soon became reconciled to the alterations in his room.
People had grown accustomed to put into storage in his room things which they couldn't put anywhere else, and at this point there were many such things, now that they had rented one room of the apartment to three lodgers.
These solemn gentlemen--all three had full beards, as Gregor once found out through a crack in the door--were meticulously intent on tidiness, not only in their own room but, since they had now rented a room here, in the entire household, and particularly in the kitchen.
They simply did not tolerate any useless or shoddy stuff.
Moreover, for the most part they had brought with them their own pieces of furniture.
Thus, many items had become superfluous, and these were not really things one could sell or things people wanted to throw out.
All these items ended up in Gregor's room, even the box of ashes and the garbage pail from the kitchen.
The cleaning woman, always in a hurry, simply flung anything that was momentarily useless into Gregor's room.
Fortunately Gregor generally saw only the relevant object and the hand which held it.
The cleaning woman perhaps was intending, when time and opportunity allowed, to take the stuff out again or to throw everything out all at once, but in fact the things remained lying there, wherever they had ended up at the first throw, unless Gregor squirmed his way through the accumulation of junk and moved it.
At first he was forced to do this because otherwise there was no room for him to creep around, but later he did it with a growing pleasure, although after such movements, tired to death and feeling wretched, he didn't budge for hours.
Because the lodgers sometimes also took their evening meal at home in the common living room, the door to the living room stayed shut on many evenings.
But Gregor had no trouble at all going without the open door.
Already on many evenings when it was open he had not availed himself of it, but, without the family noticing, was stretched out in the darkest corner of his room.
However, once the cleaning woman had left the door to the living room slightly ajar, and it remained open even when the lodgers came in in the evening and the lights were put on.
They sat down at the head of the table, where in earlier days the mother, the father, and Gregor had eaten, unfolded their serviettes, and picked up their knives and forks.
The mother immediately appeared in the door with a dish of meat and right behind her the sister with a dish piled high with potatoes.
The food gave off a lot of steam.
The gentlemen lodgers bent over the plate set before them, as if they wanted to check it before eating, and in fact the one who sat in the middle--for the other two he seemed to serve as the authority--cut off a piece of meat still on the plate obviously to establish whether it was sufficiently tender and whether or not something should be shipped back to the kitchen.
He was satisfied, and mother and sister, who had looked on in suspense, began to breathe easily and to smile.
The family itself ate in the kitchen.
In spite of that, before the father went into the kitchen, he came into the room and with a single bow, cap in hand, made a tour of the table.
The lodgers rose up collectively and murmured something in their beards.
Then, when they were alone, they ate almost in complete silence.
It seemed odd to Gregor that, out of all the many different sorts of sounds of eating, what was always audible was their chewing teeth, as if by that Gregor should be shown that people needed their teeth to eat and that nothing could be done even with the most handsome toothless jawbone.
"I really do have an appetite," Gregor said to himself sorrowfully, "but not for these things.
How these lodgers stuff themselves, and I am dying."
On this very evening the violin sounded from the kitchen.
Gregor didn't remember hearing it all through this period.
The lodgers had already ended their night meal, the middle one had pulled out a newspaper and had given each of the other two a page, and they were now leaning back, reading and smoking.
When the violin started playing, they became attentive, got up, and went on tiptoe to the hall door, at which they remained standing pressed up against one another.
They must have been audible from the kitchen, because the father called out
"Perhaps the gentlemen don't like the playing?
It can be stopped at once."
"On the contrary," stated the lodger in the middle, "might the young woman not come into us and play in the room here, where it is really much more comfortable and cheerful?"
"Oh, thank you," cried out the father, as if he were the one playing the violin.
The men stepped back into the room and waited.
Soon the father came with the music stand, the mother with the sheet music, and the sister with the violin.
The sister calmly prepared everything for the recital.
The parents, who had never previously rented a room and therefore exaggerated their politeness to the lodgers, dared not sit on their own chairs.
The father leaned against the door, his right hand stuck between two buttons of his buttoned-up uniform.
The mother, however, accepted a chair offered by one lodger.
Since she left the chair sit where the gentleman had chanced to put it, she sat to one side in a corner.
The sister began to play.
The father and mother, one on each side, followed attentively the movements of her hands.
Attracted by the playing, Gregor had ventured to advance a little further forward and his head was already in the living room.
He scarcely wondered about the fact that recently he had had so little consideration for the others.
Earlier this consideration had been something he was proud of.
And for that very reason he would have had at this moment more reason to hide away, because as a result of the dust which lay all over his room and flew around with the slightest movement, he was totally covered in dirt.
On his back and his sides he carted around with him dust, threads, hair, and remnants of food.
His indifference to everything was much too great for him to lie on his back and scour himself on the carpet, as he often had done earlier during the day.
In spite of his condition he had no timidity about inching forward a bit on the spotless floor of the living room.
In any case, no one paid him any attention.
The family was all caught up in the violin playing.
The lodgers, by contrast, who for the moment had placed themselves, hands in their trouser pockets, behind the music stand much too close to the sister, so that they could all see the sheet music, something that must certainly bother the sister, soon drew back to the window conversing in low voices with bowed heads, where they then remained, worriedly observed by the father.
It now seemed really clear that, having assumed they were to hear a beautiful or entertaining violin recital, they were disappointed and were allowing their peace and quiet to be disturbed only out of politeness.
The way in which they all blew the smoke from their cigars out of their noses and mouths in particular led one to conclude that they were very irritated.
And yet his sister was playing so beautifully.
Her face was turned to the side, her gaze followed the score intently and sadly.
Gregor crept forward still a little further, keeping his head close against the floor in order to be able to catch her gaze if possible.
Was he an animal that music so captivated him?
For him it was as if the way to the unknown nourishment he craved was revealing itself.
He was determined to press forward right to his sister, to tug at her dress, and to indicate to her in this way that she might still come with her violin into his room, because here no one valued the recital as he wanted to value it.
He did not wish to let her go from his room any more, at least not as long as he lived.
His frightening appearance would for the first time become useful for him.
He wanted to be at all the doors of his room simultaneously and snarl back at the attackers.
However, his sister should not be compelled but would remain with him voluntarily.
She would sit next to him on the sofa, bend down her ear to him, and he would then confide in her that he firmly intended to send her to the conservatory and that, if his misfortune had not arrived in the interim, he would have declared all this last Christmas--had Christmas really already come and gone?--and would have brooked no argument.
After this explanation his sister would break out in tears of emotion, and Gregor would lift himself up to her armpit and kiss her throat, which she, from the time she started going to work, had left exposed without a band or a collar.
"Mr. Samsa," called out the middle lodger to the father and, without uttering a further word, pointed his index finger at Gregor as he was moving slowly forward.
The violin fell silent.
The middle lodger smiled, first shaking his head once at his friends, and then looked down at Gregor once more.
Rather than driving Gregor back again, the father seemed to consider it of prime importance to calm down the lodgers, although they were not at all upset and
Gregor seemed to entertain them more than the violin recital.
The father hurried over to them and with outstretched arms tried to push them into their own room and simultaneously to block their view of Gregor with his own body.
At this point they became really somewhat irritated, although one no longer knew whether that was because of the father's behaviour or because of knowledge they had just acquired that they had, without knowing it, a neighbour like Gregor.
They demanded explanations from his father, raised their arms to make their points, tugged agitatedly at their beards, and moved back towards their room quite slowly.
In the meantime, the isolation which had suddenly fallen upon his sister after the sudden breaking off of the recital had overwhelmed her.
She had held onto the violin and bow in her limp hands for a little while and had continued to look at the sheet music as if she was still playing.
All at once she pulled herself together, placed the instrument in her mother's lap-- the mother was still sitting in her chair having trouble breathing for her lungs were labouring--and had run into the next room, which the lodgers, pressured by the father, were already approaching more rapidly.
One could observe how under the sister's practiced hands the sheets and pillows on the beds were thrown on high and arranged.
Even before the lodgers had reached the room, she was finished fixing the beds and was slipping out.
The father seemed so gripped once again with his stubbornness that he forgot about the respect which he always owed to his renters.
He pressed on and on, until at the door of the room the middle gentleman stamped loudly with his foot and thus brought the father to a standstill.
"I hereby declare," the middle lodger said, raising his hand and casting his glance both on the mother and the sister, "that considering the disgraceful conditions prevailing in this apartment and family"-- with this he spat decisively on the floor-- "I immediately cancel my room.
I will, of course, pay nothing at all for the days which I have lived here; on the contrary I shall think about whether or not I will initiate some sort of action against you, something which--believe me--will be very easy to establish."
He fell silent and looked directly in front of him, as if he was waiting for something.
In fact, his two friends immediately joined in with their opinions, "We also give immediate notice."
At that he seized the door handle, banged the door shut, and locked it.
The father groped his way tottering to his chair and let himself fall in it.
It looked as if he was stretching out for his usual evening snooze, but the heavy nodding of his head, which looked as if it was without support, showed that he was not sleeping at all.
Gregor had lain motionless the entire time in the spot where the lodgers had caught him.
Disappointment with the collapse of his plan and perhaps also weakness brought on by his severe hunger made it impossible for him to move.
He was certainly afraid that a general disaster would break over him at any moment, and he waited.
He was not even startled when the violin fell from the mother's lap, out from under her trembling fingers, and gave off a reverberating tone.
"My dear parents," said the sister banging her hand on the table by way of an introduction, "things cannot go on any longer in this way.
Maybe if you don't understand that, well, I do.
I will not utter my brother's name in front of this monster, and thus I say only that we must try to get rid of it.
We have tried what is humanly possible to take care of it and to be patient.
I believe that no one can criticize us in the slightest."
"She is right in a thousand ways," said the father to himself.
The mother, who was still incapable of breathing properly, began to cough numbly with her hand held up over her mouth and a manic expression in her eyes.
The sister hurried over to her mother and held her forehead.
The sister's words seemed to have led the father to certain reflections.
He sat upright, played with his uniform hat among the plates, which still lay on the table from the lodgers' evening meal, and looked now and then at the motionless
Gregor.
"We must try to get rid of it," the sister now said decisively to the father, for the mother, in her coughing fit, was not listening to anything.
"It is killing you both.
I see it coming.
When people have to work as hard as we all do, they cannot also tolerate this endless torment at home.
I just can't go on any more."
And she broke out into such a crying fit that her tears flowed out down onto her mother's face.
She wiped them off her mother with mechanical motions of her hands.
"Child," said the father sympathetically and with obvious appreciation, "then what should we do?"
The sister only shrugged her shoulders as a sign of the perplexity which, in contrast to her previous confidence, had come over her while she was crying.
"If only he understood us," said the father in a semi-questioning tone.
The sister, in the midst of her sobbing, shook her hand energetically as a sign that there was no point thinking of that.
"If he only understood us," repeated the father and by shutting his eyes he absorbed the sister's conviction of the impossibility of this point, "then perhaps some compromise would be possible with him.
But as it is. . ." "It must be gotten rid of," cried the sister.
"That is the only way, father.
You must try to get rid of the idea that this is Gregor.
The fact that we have believed for so long, that is truly our real misfortune.
But how can it be Gregor?
If it were Gregor, he would have long ago realized that a communal life among human beings is not possible with such an animal and would have gone away voluntarily.
Then we would not have a brother, but we could go on living and honour his memory.
But this animal plagues us.
It drives away the lodgers, will obviously take over the entire apartment, and leave us to spend the night in the alley.
Just look, father," she suddenly cried out,
"he's already starting up again."
With a fright which was totally incomprehensible to Gregor, the sister even left the mother, pushed herself away from her chair, as if she would sooner sacrifice her mother than remain in Gregor's vicinity, and rushed behind her father who, excited merely by her behaviour, also stood up and half raised his arms in front of the sister as though to protect her.
But Gregor did not have any notion of wishing to create problems for anyone and certainly not for his sister.
He had just started to turn himself around in order to creep back into his room, quite a startling sight, since, as a result of his suffering condition, he had to guide himself through the difficulty of turning around with his head, in this process lifting and banging it against the floor several times.
He paused and looked around.
His good intentions seem to have been recognized.
Now they looked at him in silence and sorrow.
His mother lay in her chair, with her legs stretched out and pressed together; her eyes were almost shut from weariness.
The father and sister sat next to one another.
The sister had set her hands around the father's neck.
"Now perhaps I can actually turn myself around," thought Gregor and began the task again.
He couldn't stop puffing at the effort and had to rest now and then.
Besides, no one was urging him on.
It was all left to him on his own.
When he had completed turning around, he immediately began to wander straight back.
He was astonished at the great distance which separated him from his room and did not understand in the least how in his weakness he had covered the same distance a short time before, almost without noticing it.
Constantly intent only on creeping along quickly, he hardly paid any attention to the fact that no word or cry from his family interrupted him.
Only when he was already in the door did he turn his head, not completely, because he felt his neck growing stiff.
At any rate he still saw that behind him nothing had changed.
Only the sister was standing up.
His last glimpse brushed over the mother who was now completely asleep.
Hardly was he inside his room when the door was pushed shut very quickly, bolted fast, and barred.
Gregor was startled by the sudden commotion behind him, so much so that his little limbs bent double under him.
It was his sister who had been in such a hurry.
She had stood up right away, had waited, and had then sprung forward nimbly.
Gregor had not heard anything of her approach.
She cried out "Finally!" to her parents, as she turned the key in the lock.
Gregor asked himself and looked around him in the darkness.
He soon made the discovery that he could no longer move at all.
He was not surprised at that.
On the contrary, it struck him as unnatural that up to this point he had really been able up to move around with these thin little legs.
Besides he felt relatively content.
True, he had pains throughout his entire body, but it seemed to him that they were gradually becoming weaker and weaker and would finally go away completely.
He remembered his family with deep feelings of love.
In this business, his own thought that he had to disappear was, if possible, even more decisive than his sister's.
He remained in this state of empty and peaceful reflection until the tower clock struck three o'clock in the morning.
From the window he witnessed the beginning of the general dawning outside.
Then without willing it, his head sank all the way down, and from his nostrils flowed out weakly his last breath.
Early in the morning the cleaning woman came.
In her sheer energy and haste she banged all the doors--in precisely the way people had already asked her to avoid--so much so that once she arrived a quiet sleep was no longer possible anywhere in the entire apartment.
In her customarily brief visit to Gregor she at first found nothing special.
She thought he lay so immobile there because he wanted to play the offended party.
She gave him credit for as complete an understanding as possible.
Since she happened to be holding the long broom in her hand, she tried to tickle
Gregor with it from the door.
When that was quite unsuccessful, she became irritated and poked Gregor a little, and only when she had shoved him from his place without any resistance did she become attentive.
When she quickly realized the true state of affairs, her eyes grew large, she whistled to herself.
However, she didn't restrain herself for long.
She pulled open the door of the bedroom and yelled in a loud voice into the darkness,
"Come and look.
It's kicked the bucket.
It's lying there, totally snuffed!"
The Samsa married couple sat upright in their marriage bed and had to get over their fright at the cleaning woman before they managed to grasp her message.
But then Mr. and Mrs. Samsa climbed very quickly out of bed, one on either side.
Mr. Samsa threw the bedspread over his shoulders, Mrs. Samsa came out only in her night-shirt, and like this they stepped into Gregor's room.
Meanwhile, the door of the living room, in which Grete had slept since the lodgers had arrived on the scene, had also opened.
She was fully clothed, as if she had not slept at all; her white face also seem to indicate that.
"Dead?" said Mrs. Samsa and looked questioningly at the cleaning woman, although she could check everything on her own and even understand without a check.
"I should say so," said the cleaning woman and, by way of proof, poked Gregor's body with the broom a considerable distance more to the side.
Mrs. Samsa made a movement as if she wished to restrain the broom, but didn't do it.
"Well," said Mr. Samsa, "now we can give thanks to God."
He crossed himself, and the three women followed his example.
Grete, who did not take her eyes off the corpse, said, "Look how thin he was.
He had eaten nothing for such a long time.
The meals which came in here came out again exactly the same."
In fact, Gregor's body was completely flat and dry.
That was apparent really for the first time, now that he was no longer raised on his small limbs and nothing else distracted one's gaze.
"Grete, come into us for a moment," said Mrs. Samsa with a melancholy smile, and
Grete went, not without looking back at the corpse, behind her parents into the bed room.
The cleaning woman shut the door and opened the window wide.
In spite of the early morning, the fresh air was partly tinged with warmth.
It was already the end of March.
The three lodgers stepped out of their room and looked around for their breakfast, astonished that they had been forgotten.
"Where is the breakfast?" asked the middle one of the gentlemen grumpily to the cleaning woman.
However, she laid her finger to her lips and then quickly and silently indicated to the lodgers that they could come into Gregor's room.
So they came and stood in the room, which was already quite bright, around Gregor's corpse, their hands in the pockets of their somewhat worn jackets.
Then the door of the bed room opened, and Mr. Samsa appeared in his uniform, with his wife on one arm and his daughter on the other.
All were a little tear stained.
Now and then Grete pressed her face onto her father's arm.
"Get out of my apartment immediately," said Mr. Samsa and pulled open the door, without
"What do you mean?" said the middle lodger, somewhat dismayed and with a sugary smile.
The two others kept their hands behind them and constantly rubbed them against each other, as if in joyful anticipation of a great squabble which must end up in their favour.
"I mean exactly what I say," replied Mr. Samsa and went directly with his two female companions up to the lodger.
The latter at first stood there motionless and looked at the floor, as if matters were arranging themselves in a new way in his head.
"All right, then we'll go," he said and looked up at Mr. Samsa as if, suddenly overcome by humility, he was asking fresh permission for this decision.
Mr. Samsa merely nodded to him repeatedly with his eyes open wide.
Following that, the lodger actually went with long strides immediately out into the hall.
His two friends had already been listening for a while with their hands quite still, and now they hopped smartly after him, as if afraid that Mr. Samsa could step into the hall ahead of them and disturb their reunion with their leader.
In the hall all three of them took their hats from the coat rack, pulled their canes from the cane holder, bowed silently, and left the apartment.
In what turned out to be an entirely groundless mistrust, Mr. Samsa stepped with the two women out onto the landing, leaned against the railing, and looked over as the three lodgers slowly but steadily made their way down the long staircase, disappeared on each floor in a certain turn of the stairwell, and in a few seconds came out again.
The deeper they proceeded, the more the Samsa family lost interest in them, and when a butcher with a tray on his head come to meet them and then with a proud bearing ascended the stairs high above them, Mr.
Samsa., together with the women, left the banister, and they all returned, as if relieved, back into their apartment.
They decided to pass that day resting and going for a stroll.
Not only had they earned this break from work, but there was no question that they really needed it.
And so they sat down at the table and wrote three letters of apology:
Mr. Samsa to his supervisor, Mrs. Samsa to her client, and Grete to her proprietor.
During the writing the cleaning woman came in to say that she was going off, for her morning work was finished.
The three people writing at first merely nodded, without glancing up.
Only when the cleaning woman was still unwilling to depart, did they look up angrily.
"Well?" asked Mr. Samsa.
The cleaning woman stood smiling in the doorway, as if she had a great stroke of luck to report to the family but would only do it if she was asked directly.
The almost upright small ostrich feather in her hat, which had irritated Mr. Samsa during her entire service, swayed lightly in all directions.
"All right then, what do you really want?" asked Mrs. Samsa, whom the cleaning lady still usually respected.
"Well," answered the cleaning woman, smiling so happily she couldn't go on speaking right away, "about how that rubbish from the next room should be thrown out, you mustn't worry about it.
It's all taken care of."
Mrs. Samsa and Grete bent down to their letters, as though they wanted to go on writing.
Mr. Samsa, who noticed that the cleaning woman wanted to start describing everything in detail, decisively prevented her with an outstretched hand.
But since she was not allowed to explain, she remembered the great hurry she was in, and called out, clearly insulted, "Bye bye, everyone," turned around furiously and left the apartment with a fearful slamming of the door.
"This evening she'll be let go," said Mr. Samsa, but he got no answer from either his wife or from his daughter, because the cleaning woman seemed to have upset once again the tranquillity they had just attained.
They got up, went to the window, and remained there, with their arms about each other.
Mr. Samsa turned around in his chair in their direction and observed them quietly for a while.
Then he called out, "All right, come here then.
Let's finally get rid of old things.
And have a little consideration for me."
They rushed to him, caressed him, and quickly ended their letters.
Then all three left the apartment together, something they had not done for months now, and took the electric tram into the open air outside the city.
The car in which they were sitting by themselves was totally engulfed by the warm sun.
Leaning back comfortably in their seats, they talked to each other about future prospects, and they discovered that on closer observation these were not at all bad, for the three of them had employment, about which they had not really questioned each other at all, which was extremely favourable and with especially promising prospects.
The greatest improvement in their situation at this moment, of course, had to come from a change of dwelling.
Now they wanted to rent an apartment smaller and cheaper but better situated and generally more practical than the present one, which Gregor had found.
While they amused themselves in this way, it struck Mr. and Mrs. Samsa, almost at the same moment, how their daughter, who was getting more animated all the time, had blossomed recently, in spite of all the troubles which had made her cheeks pale, into a beautiful and voluptuous young woman.
Growing more silent and almost unconsciously understanding each other in their glances, they thought that the time was now at hand to seek out a good honest man for her.
And it was something of a confirmation of their new dreams and good intentions when at the end of their journey their daughter got up first and stretched her young body.
The goal of this video is to explore some of the concepts or formulas you might see in the traditional Physics class but even more importantly to see that they are really just common sense ideas.
So let's just start with a simple example.
Let's say that, and for the sake of this video just so I don't have to keep saying this is the magnitude of the velocity, this is the direction of the velocity, et cetera.
Let's just assume that if I have positive number that it means for example if I have a positive velocity it means that I am going to the right and let's say if I have a negative number which we won't see in this video, let's assume that I'm going to the left and that way I can just write a number down -we're only operating in one dimension- you know that it is specifying what the magnitude and the direction.
If I said that the velocity was 5 metres per second that means 5 metres per second to the right.
If I said it is negative 5 metres per second that means it's 5 metres per second to the left.
Now let's just say, just for simplicity, let's just say that if we start with an initial velocity, we start with an initial velocity of 5 meters per second
Once again I am specifying with a magnitude and the direction because of this convention here.
We know it is to the right and let's say that we have a constant acceleration we have a constant acceleration at play of 2 meters per second per second, or 2 m/s^2 and once again since this is positive, it is, to the right and let's say that we do this for a duration so my change in time is...let's say we do this for a duration of 4 s so s for this video is seconds
So what I want to do is think about how far how far do we travel?
Well there's two things here. How far or how fast are we going, after 4 seconds and how far have we traveled over the course of those 4 seconds
So let's draw ourselves a little bit of a diagram here so this is my velocity axis and this over here is my time axis (let me draw a straighter line than that) so that is my time axis
This is velocity, that is my velocity right over there and I'm starting off at 5 m/s this is 5 m/s right over here so V_i is equal to 5 m/s and then every second that goes by, I'm going 2 m/s faster because it's 2 meters per second per second! so every second that goes by so after 1 second...I'm going to go 2 m/s faster...so I'll be at 7
Or another way to think about it is the slope of this velocity line is my constant acceleration
I have a constant slope here So it might look something like that
So what has happened after 4 seconds? so 1...2...3...4...so this is my delta t
So my final velocity is going to be right over there (I'll write it down here because it's getting in the way of this word velocity)
And so this is V_f, this is my final velocity and what would it be?
Well I'm starting at 5 m/s, so I'm going to do it both ways... using the variables and using the concrete numbers
So I'm starting at some initial velocity the subscript i says i for initial
And then each second that goes by, I'm getting this much faster
So if I want to see how much faster have I gone I multiply the number of seconds that go by times my acceleration
And once again, this right here I just wrote the subscript c saying it's a constant acceleration
And so that will tell me how fast I've gone
If I start at this point, and I multiply the duration times my slope I will get this high, I will get to my final velocity and just to make it clear with the numbers These numbers really could be anything
I'm just picking these to make it concrete in your mind
You have 5 m/s plus 4 seconds (I'm going to do that in yellow) plus 4 seconds times our acceleration of 2 m/s^2
And what is this going to be equal to?
You have the seconds cancelling out with one of the seconds down here
You have 4 times, (so let me write it) So you have 5 meters per second, plus, 4 times 2 is 8 8, this seconds is gone so we're just left with m/s. or this is the same thing as 13 m/s which is going to be our final velocity. And i wanna take a pause here (and you can pause here and think about it yourself)
This hopefully should be intuitive We were starting at going 5 m/s Every second that goes by, we're going to go 2 m/s faster.
So after 1 second, we'll be at 7 m/s after 2 seconds we will be at 9 m/s. After, after 3 seconds we will be at 11 m/s. And then after 4 seconds we will be at 13 m/s.
So you multiply how much time passed times acceleration, this is how much faster we are going to be going.
We are already going 5 m/s, 5 plus how much faster, 13 m/s
So this right up here is 13 m/s.
So, I'll take a little pause here,hopefully that is intuitive. And the whole point of that is to show that this formula that you'll often see in many physics books It's not just something that randomly popped out of air.
Now the next thing I want to talk about is what is the total distance we would have traveled?
Now we know from the last video that distance is just the area under this curve right over here. So it's just the area under this curve.
Oh yea, you see this is kind of a strange shape right here, how do I calculate its area?
Now we can just use a little simple geometry to break it down into 2 different areas. That are very easy to calculate the areas.
Or 2 simple shapes, you can break it down into this blue part, this rectangle right over here.
Easy to figure out the area of a rectangle.
And we can break it down into this purple part, this triangle right here. Easy to figure out the area of a triangle.
And that will be the total distance we traveled.
And even this will hopefully make some intuition. Because this blue area is how far would we have traveled if we were not accelerating, If we just went 5 m/s, four 4 seconds.
So if you go 5 m/s times (so this is 1 second, 2 second, 3 second, 4 second)
So you're going from 0 sec.. time 0 from time 4
Your change in time is 4 seconds, so if you go 5 m/s for 4 seconds, you're going to go 20 meters.
This right here is 20 meters.
That is the area of this right here. 5 times 4.
This .. this.. this.. mag(enta).. I guess purple or magenta area tells you how further than this are you going because you are accelerating because you kept going faster and faster and faster.
It's pretty easy to calculate this area.
The base here is still 5 cause that's 5 seconds have gone by.
And what is the height here?
The height here is my final velocity minus my initial velocity.
Or it's the change in velocity due to the acceleration. And the change in velocity due to the acceleration 13 minus 5 is 8. Or it's this 8 right over here.
It is 8 m/s So this height right over here is 8 m/s.
The base right over here is 5... eh sorry, it's 4 seconds. That's the time that passed.
So what's the area of this triangle?
The area of a triangle is 1/2 times the base which is 4 seconds, times the height. which is 8 m/s, times 8 m/s. seconds cancel out, 1/2 times 4 is 2, times 8 is equal to 16 meters.
So the total distance we traveled is 20 plus 16, is 36 meters.
That is the total, or I could say total displacement. And, once again, it is to the right since it is positive.
This is our displacement.
Now, what I want to do is this exact same calculations, but keep it in variable form and that will give another formula that many people often memorize, but I want you to understand that it is a completely intuitive formula and it just comes out of the kind of the logical flow of reasoning that we went through this video.
Once again if we use it in the, (if we just think about the variables) well, the area of this rectangle right here is our initial velocity, times our change in time so that's the blue, this is the blue rectangle right over here.
We have the change in time, once again, we have the change in time.
Times this height, which is our final velocity minus our initial velocity (these are all vectors) (well, they're just positive telling us we're going to the right) and if we just multiply the base times the height, that would give us the area of this entire rectangle.
We have to take it by half because the triangle is only half of that rectangle.
So times 1/2, so this is the area, this is the purple area.
(That's not purple) this is the purple area right over here.
This is the area of this, this is the area of that
And let's simplify this a little bit.
Let's factor out a delta t
So if you factor out a delta t, you get delta t times a bunch of stuff. v sub i, so your initial velocity
We factor this out, plus this stuff. Plus this thing right over here And we can distribute the 1/2.
We factored, we factored the 1/2 (sorry) we factored the delta t's out. And let's multiply the 1/2 times each of these things.
So it's going to be plus 1/2 times Vf, our final velocity (That's not the right color, let me actually do it in the right color so that you actually understand what I'm doing.)
So this is the 1/2, so plus 1/2 times our final velocity minus 1/2 times our initial velocity (I want to do that in blue.
Sorry I'm having trouble changing colors today.)
Minus 1/2 times our initial velocity.
And now what does this simplify into?
We have something plus 1/2 times something else, minus 1/2 times that original something
So what is Vi minus 1/2 times Vi
So anything minus half of it, you're just going to have a positive half left.
So these two terms this term and this term will simplify to 1/2 Vi, 1/2 the initial velocity plus 1/2 times the final velocity. And all of that is being multiplied by our change in time, or the time that has gone by. And this tells us the distance that we traveled.
Or another way to think about it, let's factor out this 1/2.
You get distance is equal to change in time, times factoring out the 1/2.
Vi plus Vf (No that's not the right color)
So this is interesting, the distance we traveled is equal to 1/2 of the initial velocity plus the final velocity.
So this is really, if you just took this quantity right over here is just the arithmetic. (I always have trouble saying that word) is the arithmetic mean of these two numbers. So I'm going to define this as something new.
But we have to be very careful with this.
This right here is the average velocity. But the only reason why I can just take the starting velocity and the ending velocity and adding them together and then divide by two it's actually taking the average of these two things which would be some place over here. And I take that as the average velocity is because my acceleration is constant
If this was a curve, if the acceleration was changing, you could not do that. But what's useful about this, is if you want to figure out the distance that was traveled, you just need to know the initial velocity and the final velocity, average the two, and then multiply that times the time that goes by. So in this situation, our final velocity is 13 m/s,
Our initial velocity was 5 m/s. So you have 13 plus 5 is equal to 18.
You divide that by two. Your average velocity is 9 m/s if you take the average of 13 and 5.
And then 9 m/s times 4 seconds gives you 36 meters.
So hopefully that doesn't confuse you. I just wanna show you where some of these things that you'll see in your physics class Some of these formulas, why you shouldn't memorize them, and they can all be deduced.
Find the sum 3 1/8 + 3/4 + ( -2 1/6) Let's just do the first part first,
This is pretty straightforward. We have two positive numbers, let me draw a number line , we are going to start with 3 1/8, this is 0, then we have 1, 2, 3 and then you have 4.
3 1/8 is going to be right about there so let me just draw its absolute value 3 1/8, is going to be 3 1/8ths to the right of 0
So it is going to be exactly that distance from 0 to the right. The length of this arrow, you could view it as 3 1/8th.
Now, whenever I like to deal with fractions especially when I have different denominators i like to deal them with improper fractions, it makes the addition, and the subtraction, and actually the multiplication and divison a lot easier.
So 3 1/8 is the same thing as 8 times 3 is 24 plus one is 25 over 8.
To that we are going to add 3/4, we are going to move another 3/4
to the right, this length of this is 3/4
So plus 3/4.
Where does this put us, so both of these are positive intergers, so we can just add them, we just have to find the like denominators we have 25/8 + 3/4.
That's the same thing as, we have to find the common denominator here, the common denominator, or the least common multiple of 4 and 8 is 8, so it's going to be something over 8.
To get from 4 to 8, we multiplied by 2, so we have to multiply 3 by 2 as well. So we get 6, so 3/4 is the same thing as 6/8.
So we have 25/8, and we're adding 6/8 to that, that gives us 25 plus 6 is 31, over 8.
So this number right over here is 31/8 And it makes sense, because 32/8 will be 4, so it should be a litte bit less than 4
So this number right over here is 31/8 or the length of this arrow, the absolute value of that number is 31/8.
If you want to write it as a mixed number, it would be 3 7/8. Now to that we want to add a -2 1/6.
So we're going to add a negative number.
So think about what -2 1/6 is going to be like. Let me do this in a new color, do it in pink. -2 1/6.
So -2 1/6, we can literally draw it like this. -2 1/6, we can draw it with an arrow that looks something like that, so this is -2 1/6.
There are a couple of ways to think about it, we could just say, when you add this arrow, this thing is moving to the left. We could put it over here and you would get straight to -2 1/6. But we're adding this -2 1/6, it is same thing as subtracting a 2 1/6; we're moving 2 1/6 to the left.
This value right here, which is going to be the answer to our problem, is going to be the difference of 31/8 and 2 1/6. And it's a positive difference, because we're dealing with a positive number.
So we just take 31/8, and from that, we will subtract 2 1/6. So this orange value is going to be 31/8 minus 2 1/6. So 2 1/6 is the same thing as 6 times 2 is 12 plus 1 is 13.
-13/6, and this is equal to -- once again we're going to get the common denominator over here - and it looks like 24 will be the common denominator. This is the 31/8, and this is the 2 1/6.
So 31/8, over 24, you have to multiply by 3 to get the 24 over here, so we multiply by 3 on the 31, that gives us 93. And then to go from 6 to 24, you have to multiply by 4, I'll do that in another color, so you have to multiply by 4 up here as well.
3 minus 2 is 1, 9 minus 5 is 4.
So it is 41/24, positive. You can see that here, just by looking at the number line. This right here is 41/24, and it should be a little bit less than 2, because 2 would be 48/24.
So this would be 48/24, and it makes sense because we're are a little bit less than that.
Let me tell you something you already know. The world ain't all sunshine and rainbows. It's a very mean and nasty place and I don't care how tough you are.
Many people take their lives every day because of this taboo.
The Bible is a very dangerous text.
In the FPÖ [Austrian populist party] they said that homosexuality is a culture of death.
If it's not possible to sacrifice just a little bit of tradition in order to give teenagers the feeling that they live in a less threatening environment and they can therefore avoid taking their own lives, then you can not really talk about loving your neighbour.
The Bible is a very dangerous text.
There are several passages which incite homophobic hatred.
There is one, for example, that says that if two men sleep with each other, both of them must be killed.
It says exactly: "their blood shall be upon themselves". This is in Leviticus.
It is of course also in the Torah.
In the Qu'ran it doesn't say that they should be killed, but that they should be punished.
There are crazy and fanatic people everywhere.
The probability that someone opens those books and kills someone because of that is there as a result and will be always there, as long as these texts continue to be blessed as God's word.
There are many priests who speak in favour of homosexual marriage. but each one reads what he wants and interprets what suits him.
I think homosexuality is illegal in 71 countries and in eight of these countries it is punishable by death.
Acceptance of homosexuality is as low as two percent in some countries.
In India there are temples where you can see figures having homosexual intercourse, and of course those also having heterosexual intercourse.
In Japan and in China it was also like that, you can appreciate it in the arts, and in literature.
In Peru and in Ecuador there are lesbian teenagers who are committed into clinics where they are raped because their parents don't know what else to do with them.
The archbishop of Oaxaca, Mexico, said a short time ago that no clean and honest woman or man would like to be homosexual.
Some others spoke against our right to work as teachers.
Last year between 800 and 1000 rabbis; I don't know if only in the USA or worldwide; said that homosexuals are to blame for the earthquake in Haiti.
Berlusconi said, for example, that it's better to treat women the way he does, that it's better to treat women the way he does than to be gay, even though he sleeps with minors!
Not only right-wing politicians speak like that, but also for example, one left-wing politician,
Evo Morales from Bolivia said that the reason why there are so many homosexuals in Europe; which is of course nonsense because in Bolivia there are just as many as there are here and they just hide themselves more there because they cannot live as freely, exactly because of people like him who instigate homophobic ideas like that,
He said that the reason that there are so many homosexuals in Europe is that our food here is genetically altered.
When homosexual marriage got legalized last year in Argentina, the archbishop of Buenos Aires
Said it's a war of God.
Of course he found support in the Bible for that.
They say it's an anomaly and also something unnatural, but they don't know that homosexuality is documented in detail in 500 species and it was registered in 1500.
Homosexuality is observed especially between intelligent species, for example, between monkeys.
There was no homophobic behaviour found among animals.
The problem is that at school they speak a lot about racism, about acceptance of minorities, but they don't speak at all about homophobia.
They always leave that out.
Most frequent swear words in every school playground, according to the union of teachers of Germany, are "gay" and "faggot".
The teachers don't intervene and many of them even support that.
Excuse me!
Couldn't you do that at home?
It's disgusting!
"We'll play a joke.
Are you ready?" and they say "yes, of course".
For most teenagers it's not so easy because it takes a time till you accept it, since it's so frowned upon in society.
Children don't have contact with other homosexuals or they don't know that they do, and that's why the suicide rate among homosexual teenagers is much higher than among heterosexuals.
That's why it's very very dangerous to use the word "gay" in a negative sense.
Also lesbian teens suffer a lot because of that.
The Church always speaks against the marriage and says that the sense of marriage is reproduction.
This doesn't make a lot of sense because also other people who aren't able to reproduce are allowed to marry.
50 year old women, for example, can also get married and no one considers it a scandal. And it's also because of this tradition that homosexuals generally have very low self-confidence and that's why they don't talk about their rights in public. and unfortunately only the people who are really concerned are the ones who speak about it.
This was the same in the case of black people in the USA.
They were always black people who fought against racism.
In the case of homosexuals it's the same, but I don't completely agree with the way they speak out.
Only one time a year are there parades, in cities around the world, that for me are actually pointless they only make many people confirm the prejudices they have.
I think many of them mean it ironically.
They show exactly the characteristics society ascribes to us. and you laugh about yourself.
But most people don't understand it and think homosexuals are only those crazy people who walk half-naked on the street.
Many people don't know that we are exactly like others and that we don't always dress in such a strange and conspicuous way. and that the life we lead is not so different from that most people lead.
I wake up in the morning, have breakfast, I brush my teeth, I have a shower, I go then to the University or to work, after that I go back home and I don't lead an especially different life from most other people.
But people don't understand it because most of them hide themselves because they don't dare to be open about it
And because of the influence of Saudi Arabia they criminalized it...
Hello!
This is an interview.
You can take part if you want.
- Did you hear what he said?
- What?
- "Is this a karaoke show?"
Welcome to the presentation on BASlC ADDlTION. I know what you're thinking:
Hopefully, by the end of this presentation, or in a couple of weeks, it will seem basic.
So lets get started with, I guess we could say, some problems.
1 + 1
And I think you already know how to do this.
But, I'll kind of show you a way of doing this, in case you don't have this memorized, or you haven't already mastered this.
You say, well, if I have one (Let's call that an avocado.)
If I have 1 avocado, and then you were to give me another avocado, how many avocados do I now have?
Well, let's see.
I have 1 ... 2 avocados.
So 1 + 1 is equal to 2.
Now, I know what you are thinking: "That was too easy." So, let me give you something a little bit more difficult.
What is 3 + 4?
Well, let's stick with the avocados.
So, let's say I have 3 avocados.
1, 2, 3. Right? 1, 2, 3.
So let me put this 4 in yellow, so you know that these are the ones you're giving me.
1 2 3 4
That's 1, 2, 3, 4, 5, 6, 7 avocados.
So 3 + 4 is equal to 7.
And now I am going to introduce you to another way of thinking about this. It's called the number line.
And, actually, I think this is how I do it in my head, when I forget -- if I don't have it memorized.
So [on the] number line, I just write all the numbers in order, and I go high enough just so I can -- [so that] all the numbers I am using are, kind of, in it.
So, you know the first number is 0, which is nothing. Maybe you don't know; but now you know.
And then you go to 1 (one) 2 (two) 3 (three) 4 (four) 5 (five) 6 (six) 7 (seven) 8 (eight) 9 (nine) 10 (ten) It keeps going, 11 (eleven)
So, we're sayng 3 + 4. So let's start at 3. So I have 3 here.
And we're going to add 4 to that 3.
So all we do is we go up the number line, or we go to the right on the number line, 4 more.
So we go 1 ... 2 ... 3 ... 4.
Notice, all we did is we just increased it by 1, by 2, by 3, by 4. And then we ended up at 7.
We could do a couple of different ones. We could say, what is -- What if I asked you what 8 + 1 is?
Well, you might already know it. 8 + 1 is just the next number [after 8].
But if you look at the number line, you start at 8, and you add 1.
8 + 1 is equal to 9.
Let's do some harder problems.
And, just so you know, if you're a little daunted by this initially, you can always draw the circles, you can always do the number line, and, eventually over time, the more practice you do, you'll hopefully memorize these, and you'll do these problems in, like, half a second.
Let's say.... I want to draw the number line again.
Look at that. Look at that. That's amazing.
I'm gonna feel bad to erase it later on. So let me draw a number line.
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
And the reason why I say this is a hard problem is because the answer [is] more [than the] [number of fingers you have on your two hands].
So we start at the 5.
And we're gonna add 6 to it.
So we go:
We're at 11! So 5 + 6 is equal to 11.
Now I'm gonna ask you a question. What is 6 + 5?
Well, we're now going to see that, OK? Can you switch the two numbers and get the same answer?
Well, let's try that. I'm gonna try it in a different color, so we don't get all confused.
So let's start at 6. Right? Ignore the yellow for now and add 5 to it.
1 ... 2 ... 3 ... 4 ... 5.
Ah. We get to the same place.
And I think you might want to try this on a bunch of problems.
And you'll see it always works out -- that it doesn't matter in what order you --
"5 + 6" is the same thing as "6 + 5."
I'm gonna have 11 -- either way. Let's do a couple of --
What is -- What is 8 + 7?
Well, if you can still read this, 8 is right here. Right? We're gonna add 7 to it.
1 ... 2 ... 3 ... 4 ... 5 ... 6 ... 7.
We go to 15.
8 + 7 is 15.
So hopefully, that gives you a sense of how to do these types of problems.
But these types of problems are, when you're getting started off in mathematics, these kind of require the most practice.
And, to some degree, you have to start memorizing them.
But, over time, you know, when you look back,
If you don't know the answer to any of the addition problems, that we give you in the exercises, you can press the "Hints," and it'll draw circles, and then you can just count up the circles. Or, if you want to do it on your own, so you get the problem right, you could draw the circles, or you could draw a number line, -- like we did in this presentation.
I think you might be ready to tackle the addition problems.
Have fun!
I'm here with Dr. Laura Bachrack at Stanford Medical School and what are we going to talk about?
We are going to talk about normal and abnormal growth in children
Fascinating...so, this is an important concern...
Parents really worry if their child is growing normally and physicians worry about this too because the change in height is an important barometer of how the child is doing overall in terms of health
Right...so to begin to assess the child's growth pattern we have to think about what are the determinants of where the child should be on the growth curve
Right...the number one most important determinant, of course, is genetics.
Short parents are more likely to have short children and vice versa
And that's also true even when the child is young if...like...big, cause sometimes I've seen in the opposite so, you know....people who are petite have large children and all the rest but it is true even if someone is large or someone is large they're more like to have large children even in infants and toddlers...
You have hit upon a really important issue that is shown here in the slide.. the size of a baby at birth isn't necessarily going to reflect the genetics
There are babies that are born small because the mother didn't have pre-natal care...mother was a smoker... other factors that compromised the growth of the child and those can be born small for their gestational age.
During the first two to three years of life, they have a chance to catch up on the curve and reach what's called their genetic potential.
So, I want to make sure...I have seen these curves before...
I remember this when I used to visit the Paediatrician which I did, may be a little too long, but eh, so so this axis right over here is age, in months
In months...so this is right here at birth.
So if a baby born at, I don't know, uh, this is the weight right over here
So if the baby are born at 5 pounds, is this in pounds, this is in kilograms.
So this would be a baby born at 5 pounds.
And I'm talking more here during this growth lecture about the height or the length of the baby throughout childhood, but let say the baby were born light in weight and short in length
So maybe 18 inches here would be a short length.
And let's say that that baby were small because his mother had issues during pregnancy.
Is it always the case that the baby would be small because of issues or i mean...
No...the bottom line is the genetics plays less of a part in the size of the baby at birth and it will later on in childhood.
So it comes back to your point.
You'll meet parents whose baby seemed a bit larger or smaller than they are.
But by age 3, the child should be...
Hold on 1 second, let me just close this...OK.
By age 3, the child should be in his or her genetic group if you will.
So, there can be movement on the growth curve in the first 2 to 3 years of life.
Where you have a very big baby, let's say the mother had uncontrolled diabetes and the baby was born very large, that baby can have catch down growth to the 50%.
By the age of 3, certainly movement across percentile is considered to be abnormal and warrants an investigation.
So you really can predict someones even adult height based on where they are at 3?
The general rule of thumb is that by the age of 2 and a half to 3 the child is in their genetic growth. Really? Mhmmm...
So if a child in age of 3 or 4 is in the 25% of height, it is unlikely that they are gonna be in the NBA.
In general that's true there's a few exception there are late group of bloomers what we call a constitutional delay of growth but the general rule would be what percentile you are by the age of 2 or 3 is pretty much where you're gonna track if all things are going normally.
Wow..I never realize that's ahh...that's ahhh..
In genetics, it's an important determinant as they said. we can actually do a calculation of where we think the child should end up the so called mid-parental height I wish we're gonna talk about it later.
So, genetics is a critical factor but whether or not you reach your genetic potential means that the cards have to be lined up appropriately.
So the cards that are important for achieving your genetic potentials first of all, number one, normal amounts of hormones that are important for growing.
And those are thyroid and growth hormone to a large extent.
The second factor of course is adequate nutrition and we think worldwide of children who are under nourished who don't look anywhere near their age in terms of height because they're so under nourished.
And you see the reverse of that, I mean I was born here and my parents were the 1st or 2nd generation.. we see that people in my generation are much taller that their parents because their parents were probably malnourished in some way.
Certainly there can be a secular trend where the children get taller than their parents if the children have a different environment.
The other thing that we notice about nutrition in our country is the over nutrition of our children and what happens with obesity is that children may grow faster, in terms of weight and height for their age.. they don't end up taller in the long run but they move ahead more quickly through the maturation process
I see...like they accelerate.
Exactly.
I never realized that.
That's fascinating.
And then we think about psycho social factors, there literally a situation where infants can be deprived of parental love and support and you can see some dwarfing there.
In a teenager we see problems with eating disorder that's a cross between nutrition and a psychological problem.
It a psycho social factors.
So it's been seen that it's a noticeable changes in physical development based on attention in love and....
Yes, there's actually a syndrome called Psycho Social Dwarfism where you actually see them slow down in growing without adequate interpersonal support.
So, the issue is when do you need to worry about a child's growth pattern. In order to interpret that you really have to understand about the variability in growth.
In the first 2 to 3 years of life children grow much more quickly than they will later on..
By the age of three, until they hit puberty, children should grow 2 inches a year.
This is out of the toddler hood until they hit puberty.
Wow, so this is like the tree of puberty.
But when kids will hit puberty is going to be very long... and so that's an issue.
If the children are growing at a normal rate it's not necessary to memorize the inches per year
Children will track along the growth curve and if we could turn to the next slide or graph.
This is the graph that we use for older children.
After the age of 2 up until they're 18.
This is the curve that we use.
Now, beyond the age of 2, I told it is not normal for the children to necessarily cross percentiles.
So if for example you have a child who is tracking along the 5th percentile every year growing their 2 inches per year...
They're moving along steadily, steadily, steadily... that child has a more reassuring growth curve than one for example who as a 5 year old had been on the top of the curve and then the next year is on the 75th moving down the line and the year after is on the 50th percentile.
Now that point in time the child has theoretically a normal height because its within the curve, but there's something very abnormal about that rate of growing and that's the child is more worrisome than the shorter child.
I see...fascinating.
So bottom line when a child would come in to present to me because of the concern about growing, I first of all try to decide if they're short and if they're growing normally.
And those are 2 different questions.
The 1st question is are they short?
And are they short can be defined by looking at these curves. These are curves representing the spectrum of normal height for healthy American youth. And they go from the 5th to the 95th percentile.
So you can compare a child to the population as a whole but I also like to calculate what we call the mid-parental height.
This is where we take into account the heights of the parents. Because that's the most important determinant.
So how we calculate that is as follows.
We take the height of mom and dad and average them.
OK, let's do that.
So, I'm 5"9 if I'm wearing decent shoes.
And how tall is the mother of your children?
She's 5"6.
And are we trying to calculate your son or your daughter?
Let's do my son since he's little older, so he is plus 66 inches.
So we'd take the mid-point of that and we're gonna add 2 and a half inches.
OK, so that gets us exactly 70 inches.
Right, so that's the height prediction for your son.
Oh, very good.
Plus or minus...4 inches.
Oh, plus or minus 4 inches, that's a big difference.
It's a big difference but that's the nature of human variability.
OK, if these were your daughter, we would take the 67.5 inches and subtract 2 and a half inches.
Let's do that.
OK, so she would get 65...plus or minus 4 inches.
So that's something we do.
We then calculate, in fact let's plot that right on the curve, this is the boy's curve.
So let's plot the 70 inches.
70 inches is right over here, OK.
And then the range of 74 to 66.
Pretty broad range.
OK, but if we had a child who is growing well below the curve and we thought that mid-point she'd be about the 50th percentile, that child would be short for the family.
So we always like to take the family's height into account.
So, number 1 question is the child short?
It will depend on what the height prediction is.
I see.
So if my son was tracking down here at the 5%...that would be concerning.
Even if he's growing the 2 inches every year, it would still be concerning?
Well, it would raise some questions in our mind.
But more important factor is not just where they are on the curve at the moment, but are they growing at the normal rate.
And the child who is not growing at the normal rate raise more red flags than the child who is trotting up the curve.
Fascinating, it's interesting.
Wow!
So that's the issue and that's what we approach every day we want to look into the various causes, potentially for a growth slowdown we want to adjust treatment to the specific ideology
And ideology means....?
Well for example, if the child has a deficiency of thyroid hormone, we'd want to give the thyroid hormone back.
So ideology is like the cause of the...right, right, right..
So if the child isn't growing because he has a nutritional problem like Celiac disease, we want to put him on a special diet to address that issue.
Some parents think, well, what we wanna do..my child is healthy and normal and growing normally but I wanna give him growth hormone, that becomes a topic in itself.
Well, thank you for this.
This is super informative.
Multiply 6 times 1/4.
Simplify your answer and write it as a mixed number.
So let's just do the multiplication.
So at first when you try to multiply 6 times 1/4, you'll be like, well, gee, I know how to multiply a fraction times a fraction.
I know how to multiply a whole number times a whole number, but what about a whole number times a fraction?
And kind of the key insight you need here is that any whole number can be written as a fraction.
We can rewrite 6 as 6/1, right?
6 divided by 1 is 6.
6 ones is 6.
Depending how you think about it, this is exactly the same thing as 6.
So we just rewrote our whole number as a fraction.
You can do it for any number.
10 is the same thing as 10/1.
So this become 6/1 times 1/4, and then we just multiply the fraction.
We multiply the numerators, so this is equal to 6 times 1 as our numerator.
Let me do that in another color.
So this becomes 6 times 1 for our numerator and 1 times 4 for our denominator, for the number on the bottom.
And so this will become 6 over 4.
And right now, it's just as an improper fraction and it's also not in lowest terms.
You immediately see 6 and 4 are both divisible by 2, so let's divide them both by 2.
If you divide 6 by 2-- and I'll do it in a new color again.
If you divide 6 by 2, you get 3.
If you divide 4 by 2, you get 2, so this is equal to 3/2.
So it's still written as an improper fraction.
We now have to write it as a mixed a number.
And the process for writing it as a mixed number, you just divide the denominator into the numerator, so this just becomes 2 into 3.
Divide 2 into 3.
2 goes into 3 one time.
1 times 2 is 2.
You subtract.
You have a remainder of 1.
So this will become one whole and 1/2 left over.
So that's our right answer.
We've just simplified the answer and wrote it is a mixed number or we could simplify it at this stage.
We could say right here, well, look, we could divide what's eventually going to be in the numerator by 2 and get a 3 there, and divide what's eventually in the denominator by 2 and get a 2 there.
3 times 1 is 3.
1 times 2 is 2, so it's 3/2.
And you do this exact same process.
You say that 3/2 is the same thing as 1 and 1/2.
Either one of those will work.
Now let's think about why this makes sense.
Let's think about what 6 times 1/4 is.
Let me draw 1/4.
Let's say that that is 1/4 right there, and
let's do six of them.
So that's 1/4, that's 2/4 that's 3/4, that's 4/4, which would be a whole, and then you have 5/4, and then you have 6/4.
So this is 6 times 1/4.
This right here is 4 over 4, which is equal to a 1, so this is equal to 1.
And then this right here is two 1/4's, or this right here is 2/4.
You can imagine this is two out of a potential, if a whole has to have two more of them, has to have four of them. so this is 1 and-- let me do it in the same colors-- 1 and 1/2, right?
2 out of 4 is the same thing as 1/2, so this right here is one out of a possible one, and then two.
So this is 1 and 1/2, which is exactly what we got before.
Hello. I'm now going to use the actual Khan Academy website to do some more problems. And this time we're going to go the other way around.
So we have a-- well we don't know if it's a sine curve or a cosine curve, but I guess it's fair to say that it's one of the two. Actually, let's answer that question first. What do you think this is?
What is sine of 0? And it could be 0 degrees or 0 radians. Well if you remember from a couple of the other modules, or even if you want to use a calculator, sine of 0 is 0.
later with shifts we'll learn that it could be a shifted sine curve-- that this isn't a sine curve, that this is a cosine curve. And then you might ask, well Sal if this is a cosine curve why is f of 0 equal to 1 1/2, or 3/2, instead of 1? Because I just said here that cosine of 0 is 1.
Well that's because there must be some type of a coefficient here, let's call it A, that is changing the amplitude of this cosine curve. And if you remember from the last module, what do you think this A is?
Well that A is just literally the amplitude of the curve. And what's the amplitude of this curve? Well, the amplitude of this curve, if we just see how much it moves above and below the x-axis, well it's that 3/2, or that 1 1/2, we've been talking about.
See it moves up 3/2, and it moves down 3/2. So let me just write that. So we know that this is 3/2 cosine of, well, something x.
When I click hint-- there; drew the period. And you could have figured it out on your own. If you just go from any point and then follow the curve back to the same point again, you'll see how long it's period is.
All right. OK. This one's interesting.
So the last thing we have to figure out, we can either figure out the period or we could use the method that I just showed you where we say, well how many times does it cycle within 2pi radians? So let's do it that way. And then we immediately know the coefficient.
Let's do one more.
All right. So what's the amplitude here? Well, let's see.
OK. Hope I don't confuse you. So the amplitude, let's just call it Amplitude, is equal to 1/2.
And how many cycles does it complete within 2pi radians? Let's see. If we start here it looks like it completes only half a cycle.
So it's 1/2 sine of 1/2 x. Or we could use the formula f of x equals goes 1/2 sine of 2pi divided by the period x. Right?
Khan Academy website. Have fun.
[music]
Who taught you to hate the color of your skin?
Who taught you to hate the texture of your hair?
Who taught you to hate the shape of your nose, and the shape of your lips?
Who taught you to hate yourself, from the top of your head to the soles of your feet?
Who taught you to hate your own kind?
Who taught you to hate the race that you belong to
Before you come asking Mr. Muhammad does he teach hate, you should ask yourself who taught you to hate being what God made you.
You know.
Most of us, blacks, or negroes as he called us, really thought we were free, without being aware that in our subconscious, all those chains we thought had been struck off were still there
And there were many ways, where what really motivated us was our desire to be loved by the white man.
Malcolm meant to lance that sense of inferiority.
He knew it would be painful.
He knew that people could kill you because of it, but he dared to take that risk.
He was saying something, over and above that of any other leader of that day.
While the other leaders were begging for entry into the house of their oppressor, he was telling you to build your own house.
He expelled fear for African Americans.
He said "I will speak out loud what you've been thinking" and he said "You'll see, people will hear, and it will not do anything to us, necessarily, ok?
But I will not speak it for the masses of people."
When he said it in a very strong fashion, in this very manly fashion, in this fashion that says,
"I am not afraid to say what you've been thinking all these years," that's why we loved him.
He said it out loud, not behind closed doors,
He took on America for us.
And I, for one, as a Muslim believe that the white man is intelligent enough.
If he were made to realize how Black people really feel and how fed up we are without that old compromising sweet talk
Why, you're the one who make it hard for yourself.
The white man believes you when you go through with that old sweet talk It should catch on fire, and burn down... [applause]
Stop sweet talking him!
Tell him how you feel!
Tell him how, what kind of hell you've been catching, and let him know that if he's not ready to clean his house up, if he's not ready to clean his house up, he shouldn't have a house. [crowd:
That's right!]
[drums and music]
On these Harlem street corners, for most of this century, Black people have celebrated their culture, and argued the question of race in America.
It was here that Malcolm first joined the street orators who gave voice to Harlem's hope, and its anger.
I've taught nationalism, and that means that I want to go out of this white man's country, because integration will never happen
You will never, as long as you live, integrate into the white men's system
A hundred and twenty-fifth street and Seventh Avenue was the center of activity among the black street orators.
When Malcolm arrived, technically he had no corner.
So he established his base, you might say, in front of Elder Michaux's bookstore.
When Malcolm would ascent the little platform, he didn't, he couldn't talk for the first four, five minutes.
The people would be making such a praise-shout to him and he would stand there, taking his due. and then he would open his mouth.
They call Mr. Muhammad a hate-teacher because he makes you hate dope and alcohol.
They call Mr. Muhammad a black supremacist because he teaches you and me not only that we are as good as the white man, but better than the white man.
Yes, better than the white man.
You are better than the white man and that's not saying anything.
That's not saying, you know we're just as equal with him.
Who is he to be equal with?
You look at his skin
You can't compare your skin with his skin,
Why your skin look like gold beside his skin.
There was a time when we used to drool in the mouth over white people.
We thought they were pretty 'cause we were blind, we were dumb.
We couldn't see them as they are.
But since the honorable Elijah Muhammad has come and taught us the religion of Islam, which have cleaned us up, and made us so we can see for ourselves now we can see that old pale thing to look exactly as he look nothing but an old, pale thing.
I came away from that rally feeling that with him once you heard him speak, you never went back to where you were before.
You had to, even if you kept your position you had to rethink it.
We weren't accustomed to being told that we were devils and that we were oppressors up here in our wonderful northern cities.
He was speaking for a silent mass of black people and sang it out front on the devil's own airwaves, and that was an act of war.
When he came off the stage, I jumped off the island, walked up to him, and of course when I got to him the bodyguards, you know, moved in front, and he just pushed them away.
And I went in front of him and extended my hand, and said "I liked some of what you said.
I didn't agree with what, all that you said, but I liked some of what you said"
And he looked at me, held my hand in a very gentle fashion and says
"One day you will, Sister.
One day you will, Sister", and he smiled.
To make his message clear, Malcolm used his own life as a lesson for all black Americans.
He preached it in fables and parables and later, in writing his autobiography with Alex Haley, he sought some control over how his life would be interpreted in the future.
I would be rather taken by a statement he would make of himself
He would say "I am a part of all I have met" and by that he meant that all the things he had done in his earlier life had exposed him to things and taught him skills of one or another sort, all of which had synthesized into the Malcolm who became the spokesman for the Nation of Islam.
You were born in Omaha, is that right?
Yes sir
And you left, your familiy left Omaha when you were about one year old?
I imagine about a year old.
Why did they leave Omaha?
Well, to my understanding, the Ku Klux Klan burned down one of their homes in Omaha
There's a lot of Ku Klux Klan
They made your family feel very unhappy, I'm sure.
Well, insecure, if not unhappy.
So you must have a somewhat prejudiced point of view, a personally prejudiced point of view
In other words, you cannot look at this in a broad, academic sort of way, really, can you?
I think that's incorrect, because despite the fact that that happened in Omaha and then when we moved to Lansing, Michigan,our home was burned down again in fact my father was killed by the Ku Klux Klan, and despite all of that, no one was more thoroughly integrated with whites than I
No one has lived more so in the society of whites than I.
We were the only black children in the neighborhood but on the back of our property we had a wooded area, so the white kids would all come over to our house and they'd go back and play in the woods.
So Malcolm would say "Well let's go play Robin Hood"
Well, so we'd go back there to play Robin Wood
Robin Hood was Malcolm. and these white kids would go along with it.
Malcolm said he was the lightest skinned of the seven children born to Earl and Louise Little, a reminder, he said, of the white man who had raped his mother's mother.
In 1929, when Malcolm was four years old, his father, a carpenter and preacher, moved the family to Lansing, Michigan.
Lansing was a small town and the west side was the side of town that blacks lived on.
Malcolm and his family lived outside of the city and they had a four-acre parcel with a small house on it, so they were sort of considered as farmers.
Three months after the Littles moved in, white neighbors took legal action to evict them.
A county judge ruled that the farm property was restricted to whites only.
But Earl Little refused to move.
Here in Michigan, Ku Klux Klan membership was at least 70,000, five times more than in Mississippi.
For Malcolm's family, white hostility was a fact of life.
Everybody was asleep in our house and all of a sudden, we heard a big boom.
And when we woke up, fire was everywhere and everybody was running into the walls and into each other, you know.
Well, what I recall about that was my mother telling us to,
"Get up, get up, get up, the house is on fire," and to get out.
That's what I actually recall.
I could hear my mother yelling, I hear my father yelling.
And so they made sure they got us all rounded up and got us out.
The house burned down to the ground.
No firewagon came, nothing, and we were burned out.
Malcolm's father, Earl Little, accused local whites of setting the fire.
The police accused Earl and arrested him on suspicion of arson.
The charges were later dropped.
In the city where we grew up, whites could refer to us as "those uppity niggers," or,
"those smart niggers that live out south of town."
In those days, whenever a white person referred to you as a "smart nigger," that was their way of saying, "This is a nigger you have to watch because he's not dumb."
My father was independent.
He didn't want anybody to feed him.
He wanted to raise his own food.
He didn't want anybody to exercise authority over his children.
He wanted to exercise the authority, and he did.
Let's say we have the indefinite integral of the square root of 6x minus x squared minus 5. And obviously this is not some simple integral.
I don't have just, you know, this expression and its derivative lying around, so u-substitution won't work.
And so you can guess from just the title of this video that we're going to have to do something fancier. And we'll probably have to do some type of trig substitution.
But this immediately doesn't look kind of amenable to trig substitution.
I like to do trig substitution when I see kind of a 1 minus x squared under a radical sign, or maybe an x squared minus 1 under a radical sign, or maybe a x squared plus 1.
These are the type of things that get my brain thinking in terms of trig substitution. but that doesn't quite look like that just yet.
I have a radical sign.
I have some x squared, but it doesn't look like this form.
So let's if we can get it to be in this form.
Let me delete these guys right there real fast.
So let's see if we can maybe complete the square down here.
So let's see.
If this is equal to, let me rewrite this. And if this completing the square doesn't look familiar to you, I have a whole bunch of videos on that.
Let me rewrite this as equal to minus 5 minus-- I need more space up here-- minus 5 minus x squared.
Now there's a plus 6x, but I have a minus out here.
So minus 6 x, right?
A minus and a minus will becomes plus 6x.
And then, I want to make this into a perfect square.
So what number when I add it to itself will be minus 6?
Well, it's minus 3 and minus 3 squared.
So you take half of this number, you get minus 3, and you square it.
Then you put a 9 there.
Now, I can't just arbitrarily add nines. Or actually, I didn't add a 9 here.
What did I do?
I subtracted a 9. Because I threw a 9 there, but it's really a minus 9, because of this minus sign out there.
So in order to make this neutral to my 9 that I just threw in there, this is a minus 9.
I have to add a 9.
So let me add a 9.
So plus 9, right there.
If this doesn't make complete sense, what I just did, and obviously you have the dx right there, multiply this out.
You get minus x squared plus 6x, which are these two terms right there, minus 9, and then you'll have this plus 9, and these two will cancel out, and you'll just get exactly back to what we had before.
Because I want you to realize, I didn't change the equation.
This is a minus 9 because of this.
So I added a 9, so I really added 0 to it.
But what this does, it gets it into a form that I like.
Obviously this, right here, just becomes a 4, and then this term right here becomes, what?
That is x minus 3 squared. x minus 3 squared.
So my indefinite integral now becomes the integral, I'm just doing a little bit of algebra, the integral of the square root of 4 minus x minus 3 squared dx.
Now this is starting to look like a form that I like, but
I like to have a 1 here.
So let's factor a 4 out.
So this is equal to, I'll switch colors, that's equal to the integral of the radical, and we'll have the 4, times 1 minus x minus 3 squared over 4.
I just took a 4 out of both of these terms.
Bacteria are the oldest living organisms on the earth.
They've been here for billions of years, and what they are are single-celled microscopic organisms.
So they are one cell and they have this special property that they only have one piece of DNA.
They have very few genes, and genetic information to encode all of the traits that they carry out.
And the way bacteria make a living is that they consume nutrients from the environment, they grow to twice their size, they cut themselves down in the middle, and one cell becomes two, and so on and so on.
They just grow and divide, and grow and divide -- so a kind of boring life, except that what I would argue is that you have an amazing interaction with these critters.
I know you guys think of yourself as humans, and this is sort of how I think of you.
This man is supposed to represent a generic human being, and all of the circles in that man are all of the cells that make up your body.
There is about a trillion human cells that make each one of us who we are and able to do all the things that we do, but you have 10 trillion bacterial cells in you or on you at any moment in your life.
So, 10 times more bacterial cells than human cells on a human being.
And of course it's the DNA that counts, so here's all the A, T, Gs and Cs that make up your genetic code, and give you all your charming characteristics.
You have about 30,000 genes.
Well it turns out you have 100 times more bacterial genes playing a role in you or on you all of your life.
At the best, you're 10 percent human, but more likely about one percent human, depending on which of these metrics you like.
I know you think of yourself as human beings, but I think of you as 90 or 99 percent bacterial.
(Laughter)
These bacteria are not passive riders, these are incredibly important, they keep us alive.
They cover us in an invisible body armor that keeps environmental insults out so that we stay healthy.
They digest our food, they make our vitamins, they actually educate your immune system to keep bad microbes out.
So they do all these amazing things that help us and are vital for keeping us alive, and they never get any press for that.
But they get a lot of press because they do a lot of terrible things as well.
So, there's all kinds of bacteria on the Earth that have no business being in you or on you at any time, and if they are, they make you incredibly sick.
And so, the question for my lab is whether you want to think about all the good things that bacteria do, or all the bad things that bacteria do.
The question we had is how could they do anything at all?
I mean they're incredibly small, you have to have a microscope to see one.
They live this sort of boring life where they grow and divide, and they've always been considered to be these asocial reclusive organisms.
And so it seemed to us that they are just too small to have an impact on the environment if they simply act as individuals.
And so we wanted to think if there couldn't be a different way that bacteria live.
The clue to this came from another marine bacterium, and it's a bacterium called Vibrio fischeri.
What you're looking at on this slide is just a person from my lab holding a flask of a liquid culture of a bacterium, a harmless beautiful bacterium that comes from the ocean, named Vibrio fischeri.
This bacterium has the special property that it makes light, so it makes bioluminescence,
like fireflies make light.
We're not doing anything to the cells here.
We just took the picture by turning the lights off in the room, and this is what we see.
What was actually interesting to us was not that the bacteria made light, but when the bacteria made light.
What we noticed is when the bacteria were alone, so when they were in dilute suspension, they made no light.
But when they grew to a certain cell number all the bacteria turned on light simultaneously.
The question that we had is how can bacteria, these primitive organisms, tell the difference from times when they're alone, and times when they're in a community, and then all do something together.
What we've figured out is that the way that they do that is that they talk to each other, and they talk with a chemical language.
This is now supposed to be my bacterial cell.
When it's alone it doesn't make any light.
But what it does do is to make and secrete small molecules that you can think of like hormones, and these are the red triangles, and when the bacteria is alone the molecules just float away and so no light.
But when the bacteria grow and double and they're all participating in making these molecules, the molecule -- the extracellular amount of that molecule increases in proportion to cell number.
And when the molecule hits a certain amount that tells the bacteria how many neighbors there are, they recognize that molecule and all of the bacteria turn on light in synchrony.
That's how bioluminescence works -- they're talking with these chemical words.
The reason that Vibrio fischeri is doing that comes from the biology.
Again, another plug for the animals in the ocean,
Vibrio fischeri lives in this squid.
What you are looking at is the Hawaiian Bobtail Squid, and it's been turned on its back, and what I hope you can see are these two glowing lobes and these house the Vibrio fischeri cells, they live in there, at high cell number that molecule is there, and they're making light.
The reason the squid is willing to put up with these shenanigans is because it wants that light.
The way that this symbiosis works is that this little squid lives just off the coast of Hawaii, just in sort of shallow knee-deep water.
The squid is nocturnal, so during the day it buries itself in the sand and sleeps, but then at night it has to come out to hunt.
On bright nights when there is lots of starlight or moonlight that light can penetrate the depth of the water the squid lives in, since it's just in those couple feet of water.
What the squid has developed is a shutter that can open and close over this specialized light organ housing the bacteria.
Then it has detectors on its back so it can sense how much starlight or moonlight is hitting its back.
And it opens and closes the shutter so the amount of light coming out of the bottom -- which is made by the bacterium -- exactly matches how much light hits the squid's back, so the squid doesn't make a shadow.
It actually uses the light from the bacteria to counter-illuminate itself in an anti-predation device so predators can't see its shadow, calculate its trajectory, and eat it.
This is like the stealth bomber of the ocean. (Laughter)
But then if you think about it, the squid has this terrible problem because it's got this dying, thick culture of bacteria and it can't sustain that.
And so what happens is every morning when the sun comes up the squid goes back to sleep, it buries itself in the sand, and it's got a pump that's attached to its circadian rhythm, and when the sun comes up it pumps out like 95 percent of the bacteria.
Now the bacteria are dilute, that little hormone molecule is gone, so they're not making light -- but of course the squid doesn't care.
And as the day goes by the bacteria double, they release the molecule, and then light comes on at night, exactly when the squid wants it.
First we figured out how this bacterium does this, but then we brought the tools of molecular biology to this to figure out really what's the mechanism.
And what we found -- so this is now supposed to be, again, my bacterial cell -- is that Vibrio fischeri has a protein -- that's the red box -- it's an enzyme that makes that little hormone molecule, the red triangle.
And then as the cells grow, they're all releasing that molecule into the environment, so there's lots of molecule there.
And the bacteria also have a receptor on their cell surface that fits like a lock and key with that molecule.
These are just like the receptors on the surfaces of your cells.
When the molecule increases to a certain amount -- which says something about the number of cells -- it locks down into that receptor and information comes into the cells that tells the cells to turn on this collective behavior of making light.
Why this is interesting is because in the past decade we have found that this is not just some anomaly of this ridiculous, glow-in-the-dark bacterium that lives in the ocean -- all bacteria have systems like this.
So now what we understand is that all bacteria can talk to each other. They make chemical words, they recognize those words, and they turn on group behaviors that are only successful when all of the cells participate in unison. We have a fancy name for this: we call it quorum sensing.
They vote with these chemical votes, the vote gets counted, and then everybody responds to the vote.
What's important for today's talk is that we know that there are hundreds of behaviors that bacteria carry out in these collective fashions.
But the one that's probably the most important to you is virulence.
It's not like a couple bacteria get in you and they start secreting some toxins -- you're enormous, that would have no effect on you.
What they do, we now understand, is they get in you, they wait, they start growing, they count themselves with these little molecules, and they recognize when they have the right cell number that if all of the bacteria launch their virulence attack together, they are going to be successful at overcoming an enormous host.
Bacteria always control pathogenicity with quorum sensing.
That's how it works.
We also then went to look at what are these molecules -- these were the red triangles on my slides before.
This is the Vibrio fischeri molecule.
This is the word that it talks with.
So then we started to look at other bacteria, and these are just a smattering of the molecules that we've discovered.
What I hope you can see is that the molecules are related.
The left-hand part of the molecule is identical in every single species of bacteria. But the right-hand part of the molecule is a little bit different in every single species.
What that does is to confer exquisite species specificities to these languages.
Each molecule fits into its partner receptor and no other.
So these are private, secret conversations.
These conversations are for intraspecies communication.
Each bacteria uses a particular molecule that's its language that allows it to count its own siblings.
Once we got that far we thought we were starting to understand that bacteria have these social behaviors.
But what we were really thinking about is that most of the time bacteria don't live by themselves, they live in incredible mixtures, with hundreds or thousands of other species of bacteria.
And that's depicted on this slide.
This is your skin.
So this is just a picture -- a micrograph of your skin.
Anywhere on your body, it looks pretty much like this, and what I hope you can see is that there's all kinds of bacteria there.
And so we started to think if this really is about communication in bacteria, and it's about counting your neighbors, it's not enough to be able to only talk within your species.
There has to be a way to take a census of the rest of the bacteria in the population.
So we went back to molecular biology and started studying different bacteria, and what we've found now is that in fact, bacteria are multilingual.
They all have a species-specific system -- they have a molecule that says "me."
But then, running in parallel to that is a second system that we've discovered, that's generic.
So, they have a second enzyme that makes a second signal and it has its own receptor, and this molecule is the trade language of bacteria.
It's used by all different bacteria and it's the language of interspecies communication.
What happens is that bacteria are able to count how many of me and how many of you.
They take that information inside, and they decide what tasks to carry out depending on who's in the minority and who's in the majority of any given population.
Then again we turn to chemistry, and we figured out what this generic molecule is -- that was the pink ovals on my last slide, this is it.
It's a very small, five-carbon molecule.
What the important thing is that we learned is that every bacterium has exactly the same enzyme and makes exactly the same molecule.
So they're all using this molecule for interspecies communication.
This is the bacterial Esperanto.
(Laughter)
Once we got that far, we started to learn that bacteria can talk to each other with this chemical language.
But what we started to think is that maybe there is something practical that we can do here as well.
I've told you that bacteria do have all these social behaviors, they communicate with these molecules.
Of course, I've also told you that one of the important things they do is to initiate pathogenicity using quorum sensing.
We thought, what if we made these bacteria so they can't talk or they can't hear?
Couldn't these be new kinds of antibiotics?
Of course, you've just heard and you already know that we're running out of antibiotics.
Bacteria are incredibly multi-drug-resistant right now, and that's because all of the antibiotics that we use kill bacteria.
They either pop the bacterial membrane, they make the bacterium so it can't replicate its DNA.
We kill bacteria with traditional antibiotics and that selects for resistant mutants.
And so now of course we have this global problem in infectious diseases.
We thought, well what if we could sort of do behavior modifications, just make these bacteria so they can't talk, they can't count, and they don't know to launch virulence.
And so that's exactly what we've done, and we've sort of taken two strategies.
The first one is we've targeted the intraspecies communication system.
So we made molecules that look kind of like the real molecules -- which you saw -- but they're a little bit different.
And so they lock into those receptors, and they jam recognition of the real thing.
By targeting the red system, what we are able to do is to make species-specific, or disease-specific, anti-quorum sensing molecules.
We've also done the same thing with the pink system.
We've taken that universal molecule and turned it around a little bit so that we've made antagonists of the interspecies communication system.
The hope is that these will be used as broad-spectrum antibiotics that work against all bacteria.
To finish I'll just show you the strategy.
In this one I'm just using the interspecies molecule, but the logic is exactly the same.
What you know is that when that bacterium gets into the animal, in this case, a mouse, it doesn't initiate virulence right away.
It gets in, it starts growing, it starts secreting its quorum sensing molecules.
It recognizes when it has enough bacteria that now they're going to launch their attack, and the animal dies.
What we've been able to do is to give these virulent infections, but we give them in conjunction with our anti-quorum sensing molecules -- so these are molecules that look kind of like the real thing, but they're a little bit different which I've depicted on this slide.
What we now know is that if we treat the animal with a pathogenic bacterium -- a multi-drug-resistant pathogenic bacterium -- in the same time we give our anti-quorum sensing molecule, in fact, the animal lives.
We think that this is the next generation of antibiotics and it's going to get us around, at least initially, this big problem of resistance.
What I hope you think, is that bacteria can talk to each other, they use chemicals as their words, they have an incredibly complicated chemical lexicon that we're just now starting to learn about.
Of course what that allows bacteria to do is to be multicellular.
So in the spirit of TED they're doing things together because it makes a difference.
What happens is that bacteria have these collective behaviors, and they can carry out tasks that they could never accomplish if they simply acted as individuals.
What I would hope that I could further argue to you is that this is the invention of multicellularity.
Bacteria have been on the Earth for billions of years; humans, couple hundred thousand.
We think bacteria made the rules for how multicellular organization works.
We think, by studying bacteria, we're going to be able to have insight about multicellularity in the human body.
We know that the principles and the rules, if we can figure them out in these sort of primitive organisms, the hope is that they will be applied to other human diseases and human behaviors as well.
I hope that what you've learned is that bacteria can distinguish self from other.
By using these two molecules they can say "me" and they can say "you."
Again of course that's what we do, both in a molecular way, and also in an outward way, but I think about the molecular stuff.
This is exactly what happens in your body.
It's not like your heart cells and your kidney cells get all mixed up every day, and that's because there's all of this chemistry going on, these molecules that say who each of these groups of cells is, and what their tasks should be.
Again, we think that bacteria invented that, and you've just evolved a few more bells and whistles, but all of the ideas are in these simple systems that we can study.
The final thing is, again just to reiterate that there's this practical part, and so we've made these anti-quorum sensing molecules that are being developed as new kinds of therapeutics.
But then, to finish with a plug for all the good and miraculous bacteria that live on the Earth, we've also made pro-quorum sensing molecules.
So, we've targeted those systems to make the molecules work better.
Remember you have these 10 times or more bacterial cells in you or on you, keeping you healthy.
What we're also trying to do is to beef up the conversation of the bacteria that live as mutualists with you, in the hopes of making you more healthy, making those conversations better, so bacteria can do things that we want them to do better than they would be on their own.
Finally, I wanted to show you this is my gang at Princeton, New Jersey.
Everything I told you about was discovered by someone in that picture.
I hope when you learn things, like about how the natural world works -- I just want to say that whenever you read something in the newspaper or you get to hear some talk about something ridiculous in the natural world it was done by a child.
Science is done by that demographic.
All of those people are between 20 and 30 years old, and they are the engine that drives scientific discovery in this country.
It's a really lucky demographic to work with.
I keep getting older and older and they're always the same age, and it's just a crazy delightful job.
I want to thank you for inviting me here.
It's a big treat for me to get to come to this conference.
(Applause)
Thanks.
(Applause)
I think we're now ready to learn a little bit about the dark reactions.
But just to remember where we are in this whole scheme of photosynthesis, photons came in and excited electrons in chlorophyil in the light reactions. and as those photons went to lower and lower energy states-- we saw it over here in the last video-- as they went to lower and lower energy states, and all of this was going on in the thylakoid membrane right over here.
You can imagine-- Let me do it in a different color.
You can imagine it occurring right here.
As they went into lower and lower energy states, two things happened.
One, the release of energy was able to pump the hydrogens across this membrane.
And then when you had a high concentration of hydrogens here, those went back through the ATP synthase and drove that motor to produce ATP.
And then the final electron acceptor, or hydrogen acceptor, depending on how you want to view it. The whole hydrogen atom was NAD plus.
So the two byproducts, or the two byproducts that we're going to continue using in photosynthesis from our light cycle, from our light reactions I guess.
I shouldn't call it the light cycle-- were-- I wrote it up here-- ATP and NADPH.
And then the byproduct was that we needed the electron to replace that first excited electron.
So we take it away from water.
And so we also produce oxygen, which is a very valuable byproduct of this reaction.
But now that we have this ATP and this NADPH, we're ready to proceed into the dark reactions.
And I want to highlight again, even though it's called the dark reactions it doesn't mean that it happens at night.
It actually happens at the same time as light reactions.
It occurs while the sun is out.
The reason why they call it the dark reactions is that they're light independent.
They don't require photons.
They only require ATP, NADPH, and carbon dioxide.
So let's understand what's going on here a little bit better.
So let me go down to where I have some clean space down here.
So we had our light reactions.
And they produced-- I just reviewed this-- produced some ATP and produced some and NADPH.
And now we're going to take some carbon dioxide from the atmosphere.
And all of this will go into the-- I'll call it the light independent reactions. Because dark reactions is misleading.
So the light independent reactions, the actual mechanism is called the Calvin Cycle.
And that's what this video is really about.
It goes into the Calvin Cycle and out pops-- whether you want to call it PGAL-- we talked about it in the first video-- or G3P.
This is glyceraldehyde 3-phosphate.
This is phosphoglyceraldehyde They are the exact same molecule, just different names.
And you can imagine it as a 3-carbon chain with a phosphate group.
And then this can then be used to build other carbohydrates.
You put two of these together you can get a glucose.
You might remember in the first stage of glycolysis, or the first time we cut a glucose molecule we ended up with two phosphoglyceraldehyde molecules.
Glucose has six carbons.
This has three.
Let's study the Calvin Cycle in just a little bit more detail.
So let's say exiting the light reactions, let's say we have-- well let's start off with six carbon dioxides.
So this is independent of the light reactions.
And I'll show you why I'm using these numbers.
I don't have to use these exact numbers. So let's say I start off with six CO2s.
And I could write a CO2 because we really care about what's happening to the carbon.
We can just write it as a single carbon that has two oxygens on it, which I could draw.
But I'm not going to draw them right now. Because I want to really show you what happens to the carbons.
Maybe I should draw this in this yellow.
Just to show you only the carbons.
I'm not showing you the oxygens on here.
And what happens is the CO2, the six CO2s, essentially react with-- and I'll talk a little bit about this reaction in a second-- they react with six molecules-- and this is going to look a little bit strange to you-- of this molecule, you could call it RuBP.
That's short for ribulose biphosphate.
Sometimes called ribulose-1 5-biphosphate.
And the reason why it's called that is because it's a 5-carbon molecule.
So, three, four five.
And it has a phosphate on the 1 and 5 carbon.
So it's ribulose biphosphate. Or sometimes, ribulosee-1-- let me write this-- that's the first carbon.
5-biphosphate.
We have two phosphates.
So that's ribulose-1 5-biphosphate.
Fancy name, but it's just a 5-carbon chain with 2 phosphates on it.
These two react together.
And this is a simplification. These two react together.
There's a lot more going on here, but I want you to get the big picture. to form, 12 molecules of PGAL, of phosphoglyceraldehyde or glyceraldihyde 3-phosphate of PGAL, which you can view as a-- it has three carbons and then it has a phosphate group.
And just to make sure we're accounting for our carbons properly, let's think about what happens.
We have 12 of these guys.
You can think of it that we have-- 12 times 3-- we have 36 carbons.
Now did we start with 36 carbons?
Well we have 6 times 5 carbons. That's 30.
Plus another 6 here.
So, yes. We have 36 carbons.
They react with each other to form this PGAL.
The bonds or the electrons in this molecule are in a higher energy state than the electrons in this molecule.
So we have to add energy in order for this reaction to happen.
This won't happen spontaneously.
And the energy for this reaction, if we use the numbers 6 and 6 here, the energy from this reaction is going to come from 12 ATPs-- you could imagine 2 ATPs for every carbon and every ribulose biphosphate; and 12 NADPHs.
I don't want to get you confused with-- it's very similar to NADH, but I don't want to get you confused with what goes on in respiration.
And then these leave as 12 ADPs plus 12 phosphate groups.
And then you're going to have plus 12 NADP pluses.
And the reason why this is a source of energy is because the electrons in NADPH, or you could say the hydrogen with the electron in NADPH, is at a higher energy state.
So as it goes to lower energy state, it helps drive a reaction.
And of course ATPs, when they lose their phosphate groups, those electrons are in a very high energy state, they enter a lower energy state, help drive a reaction, help put energy into a reaction.
So then we have these 12 PGALs.
Now the reason why it's called a Calvin Cycle-- as you can imagine-- we studied the Kreb Cycle. Cycles start reusing things.
The reason why it's called the Calvin Cycle is because we do reuse, actually, most of these PGALs.
So of the 12 PGALs, we're going to use 10 of them to--
let me actually do it this way.
So we're going to have 10 PGALs. 10 phosphoglyceraldehydes 10 PGALs we're going to use to recreate the ribulose biphosphate.
And the counting works.
Because we have ten 3-carbon molecules. That's 30 carbons.
Then we have six 5-carbon molecules. 30 carbons.
But this, once again, is going to take energy. This is going to take the energy from six ATPs.
So you're going to have six ATPs essentially losing their phosphate group.
The electrons enter lower energy states, drive reactions.
And you're going to have six ADPs plus six phosphate groups that get released.
And so you see it as a cycle.
But the question is, well gee I used all of these.
What do I get out of it?
Well I only used 10 out of the 12.
So I have 2 PGALs left.
And these can then be used-- and the reason why I used 6 and 6 is so that I get 12 here.
And I get 2 here.
And the reason why I have 2 here is because 2 PGALs can be used to make a glucose. Which is a 6-carbon molecule.
It's formula, we've seen it before, is C6H12O6.
But it's important to remember that it doesn't have to just be glucose.
It can then go off and generate longer chained carbohydrates and starches, anything that has a carbon backbone.
So this is it.
This is the dark reaction.
We were able to take the byproducts of the light reactions, the ATP and the NADHs-- there's some more ATP there-- and use it to fix carbon.
This is called carbon fixation.
When you take carbon in a gaseous form and you put it into a solid structure, that is called carbon fixation.
So through this Calvin Cycle we were able to fix carbon and the energy comes from these molecules generated from the light reaction.
And of course, it's called a cycle because we generate these PGALs, some of them can be used to actually produce glucose or other carbohydrates while most of them continue on to be recycled into ribulose biphosphate, which once again reacts with carbon dioxide.
And then you get this cycle happening over and over again.
Now we said it doesn't happen in a vacuum.
Actually if you want to know the actual location where this is occurring, this is all occurring in the stroma.
In the fluid, inside the chloroplast but outside of your thylakoid.
So in your stroma, this is where your light independent reactions are actually occurring.
And it's not just happening with the ADP and the NADPH.
There's actually a fairly decent sized enzyme or protein that's facilitating it.
That's allowing the carbon dioxide to bond at certain points and the ribulose biphosphate and the ATP to react at certain points, to essentially drive these two guys to react together.
And that enzyme, sometimes it's called RuBisCo, I'll tell you why it's called RuBisCo.
So this is RuBisCo.
So rub-- let me get the capitalization right-- ribulose biphosphate rub-- bis-- co-- carboxylase.
And this is what it looks like.
So it's a pretty big protein enzyme molecule.
You can imagine that you have your ribulose biphosphate bonding at one point.
You have your carbon dioxide bonding at another point.
I don't know what points they are.
ATP bonds at another point.
It reacts.
That makes this thing twist and turn in certain ways to make the ribulose biphosphate react with the carbon dioxide.
NADPH might be reacting at other parts.
And that's what facilitates this entire Calvin Cycle.
And you might-- I told you over here-- that this R U B P, this is ribulose-1 5-biphosphate.
This RuBisCo, this is short for ribulose-1 5-biphosphate carboxylase.
I won't write it all out; you could look it up.
But it's just telling you, it's an enzyme that's used to react carbon and ribulose-1 5-biphophate.
But now we're done.
We're done with photosynthesis.
We were able to start off with photons and water to produce
ATP and NADPH because we had those excited electrons, we had the whole chemiosmosis to drive the-- that allowed the ATP synthase to produce ATP.
NADPH was the final electron acceptor.
These are then used as the fuel in the Calvin Cycle, in the dark reaction.
Which is badly named, it should be called the light independent reaction. Because it actually does happen in the light.
You take your fuel from the light reactions with some carbon dioxide and you can fix it using your-- I like to call it-- the RuBisCo enzyme in the Calvin Cycle.
And you end up with your phosphoglyceraldehyde which could also be called your glyceraldehyde 3-phosphate, which can then be used to generate glucose, which we all use to eat and fuel our bodies.
Or we learn in cellular respiration, that can then be converted into ATP when we need it.
500 years ago, trans-oceanic travel became a reality.
Since the end of the last Ice Age, farming societies have been absorbing their neighbors, making populations more similar within continents.
That when people began to cross oceans, in large numbers, the genetic and cultural differences between people from different continents also began to fade, though not disappear.
Many families relocated Willingly, or unwillingly to very distant lands.
Sometimes, they found unoccupied lands, and sometimes they found lands occupied, and wished they weren't.
And sometimes they found land and labor, and devised ways of exploiting both.
All over the world, people separated by thousands of kilometers for thousands of years began meeting once again and producing children.
Today, whole regions, like the Americas, are populated by people who can trace their ancestry back to multiple continents.
But some small groups are more geographically or culturally isolated, and remain genetically distinguishable.
As long distance transportation gets easier and easier, and individual societies become more diverse, languages are being lost, and genetic distinctions across the globe are fading.
But these genetic distinctions, are a relatively recent phenomenon in our history.
We haven't been separated for very long.
What expression can be used to show dividing 18 boxes into two equals stacks?
Find the expression three times using different ways to write division.
Find the value of the expression.
So let's just do this top part right here.
We have 18 boxes, and we want to divide them into two equals stacks, so we want to divide 18 by 2.
And the way we would write this, and we'll think a little bit more about what this means, we could write this as 18 over 2.
This means 18 divided by 2.
We could write it as 18 divided by 2, just like that, or we could write it as 18 divided by 2.
Now before we evaluate it, they say find the value of the expression.
Let's think about what this means.
We have 18 boxes and we want to divide them into two equal stacks.
Let me draw 18 boxes.
So I have 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12-- almost there-- 13, 14, 15, 16, 17, 18.
So those are my 18 boxes, and I divide them into two equals stacks or two equal groups.
So if I want to divide these into two different groups that have the same number of boxes, I could just eyeball it, and say, well, let's make these top ones one group.
Let's make that one of the groups, and let's making these bottom ones another group.
And these are equal groups.
How many do we have in each group?
Well, in the top one, we have one, two, three, four, five, six, seven, eight, nine, and in the bottom one we have one, two, three, four, five, six, seven, eight, nine.
So we've split it into two groups of nine.
So 18 divided into two equal groups is equal to 9, or 18 divided by 2 is equal to 9, or 2 goes into 18 nine times.
Welcome to the presentation on level two addition. Well I think we should get started with some problems, and hopefully as we work through them, you'll have an understanding of how to do these types of problems. Let's see...
You knew that, right? Right? You know that 1+4=5.
So if I had 11 balls -- 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11. That's 11, right? 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11.
Alright, I should do it like they do on Sesame Street, (singing) "1, 2, 3, 4, 5, 6, 7, 8, 9, 10-" Oh actually I think I messed up. It's 11.
15, and I don't recommend that you do this every time you do a problem because it'll take you a long time. But hey, if you ever get confused, it's better to take along time than to get it wrong. Let's think about another way of representing this, because I think different visual approaches appeal in different ways to different people.
8+7 -- I'll tell you, frankly, even to this day, I sometimes get confused with 8+7. So let's-- If you know the answer then you already know how to do this problem, you can just write whatever the answer is right here.
8+7. And this time I'm not going to start at 0, I'll start at like 5, because, you know, if you keep going you'll get to 0 eventually. So let's see you get 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, and so on
You put it up there. I think in a future presentation I'll explain why this works and maybe you might even kind of have an intuition because the 1 is in the ten's place, and this is the ten's place. I don't want to confuse you.
So you have that 1 and now you add it to the 2, and you get 35. Right? Because 1+2=3, right?
And you might ask, well, does that make sense that 28+7=35? And there's a couple of ways I'd like to think about this. Well, 8+7 we know is 15, right?
9+9 is equal to 18...so 9+9... and you put the 8 down here and you carry the 1. And now you just say 1+9. Well you know what 1+9 is.
1+ 9=10. And so there's nowhere to carry this 1, so you write the whole thing down here. So 99+9=108.
Well 6+7=13, right? If you get confused, draw out everything again. And then you get 1+5.
 We're told to solve for y, and we have this inequality that says that the absolute value of y plus 22 is less than or equal to 13 and 1/2 or 13.5. So a good place to start is maybe to just isolate the absolute value of y on the left-hand side of this inequality.
My brain imagines, or the way I process it is, I say, well--
I always like to put the larger number first-- I say that's the negative of 22 minus 13.5. And 22 minus 14 is 8, or the difference between 22 and 14 is 8, so the difference between 22 and 13 and 1/2 is going to be 1/2 more than that. So this is going to be 8.5.
So we get the absolute value of y is less than or equal to negative 8.5. Now, this should cause you some pause, because when you take the absolute value of anything, what do you know you're going to get? If I tell you that the absolute value of any number, oh, we'll just say the absolute value of a is equal to x.
Stop crying Stop with the tears
Don't cry Pick yourself up Stop with the emotions
Learning English: Subtitles done by Ryan Tunney
Lesson One With Misterduncan
Are you happy?
I hope so.
Welcome to the very first episode of my series of English teaching videos.
Before I begin we will take a look at some of the common questions that often arise when talking about learning the English language and more importantly learning it as a second language.
So, the first question must be:
"Why do we need to learn English?"
Of course one of the reasons why we need to be able to speak English nowadays is because the world is becoming smaller.
Thanks to the Internet and our developing global economy more and more people are using English as a common way to communicate with each other.
So now it has become unavoidable that companies and large businesses will need to employ people who can speak more than their own native language.
That is where English comes in...
It is now officially considered as an international language.
Of course learning anything is difficult and English is no exception.
However, there are ways to make the situation easier.
I have come up with my own list of general rules for learning English.
Do you want to hear them?
Do you want to know what they are?
Ok. Let's go!
Learning English takes time and patience.
It cannot be rushed.
Try to relax and take it easy.
The most important thing you need at the beginning is a good vocabulary.
Without words, you have nothing to work with.
You must start with a strong foundation or base and slowly build on it, day by day.
You must view English as a part of your body just as you would, an arm or a leg.
It must become a part of your everyday life.
Daily practice is very important.
Do not worry about making mistakes.
In fact the more mistakes you make the more you will learn from them.
Just like learning to ride a bike.
Sometimes you fall off.
So what do you do?
You get back on and try again.
Do not look at English as just another subject.
Your attitude to English and the way you view it will decide how well you progress.
Just as we say in English:
"No pain, no gain"
The two most important words to remember when learning English are
Practice and Confidence.
Practice English everyday and be confident.
You will find that the more you use English the better your English will become and the more confident you become then the more you will want to use it.
Make it a rule to tell yourself
I can do it!
I can do it!!
I can do it!!!
Please remember, my lessons are aimed at everyone so hopefully you will find something useful in each one.
Maybe you will find some of the words I use very easy.
But you will also see some words that may be new to you.
Remember!
My lessons are aimed at everyone.
Even teachers are very welcome to join in.
Learning English should be a fun experience and I hope with the help of my video lessons you will discover just how much fun it can be.
I hope you've enjoyed my first lesson.
This is Misterduncan in England saying
Thanks for watching and bye-bye for now!
Presented By Misterduncan
Thanks For Watching
 Where I left off in the last video, we talked about how the hemoglobin in red blood cells is what sops up all of the oxygen so that it increases the diffusion gradient-- or it increases the incentive, we could say, for the oxygen to go across the membrane.
We know that the oxygen molecules don't know that there's less oxygen here, but if you watch the video on diffusion you know how that process happens.
If there's less concentration here than there, the oxygen will diffuse across the membrane and there's less inside the plasma because the hemoglobin is sucking it all up like a sponge.
Now, one interesting question is, why does the hemoglobin even have to reside within the red blood cells?
Why aren't hemoglobin proteins just freely floating in the blood plasma?
That seems more efficient. You don't have to have things crossing through, in and out of, these red blood cell membranes.
You wouldn't have to make red blood cells.
What's the use of having these containers of hemoglobin?
It's actually a very interesting idea.
If you had all of the hemoglobin sitting in your blood plasma, it would actually hurt the flow of the blood. The blood would become more viscous or more thick.
I don't want to say like syrup, but it would become thicker than blood is right now-- and by packaging the hemoglobin inside these containers, inside the red blood cells, what it allows the blood to do is flow a lot better.
Imagine if you wanted to put syrup in water.
If you just put syrup straight into water, what's going to happen?
The water's going to become a little syrupy, a little bit more viscous and not flow as well.
So what's the solution if you wanted to transport syrup in water?
Well, you could put the syrup inside little containers or inside little beads and then let the beads flow in the water and then the water wouldn't be all gooey-- and that's exactly what's happening inside of our blood.
Instead of having the hemoglobin sit in the plasma and make it gooey, it sits inside these beads that we call red blood cells that allows the flow to still be non-viscous.
So I've been all zoomed in here on the alveolus and these capillaries, these pulmonary capillaries-- let's zoom out a little bit-- or zoom out a lot-- just to understand, how is the blood flowing? And get a better understanding of pulmonary arteries and veins relative to the other arteries and veins that are in the body.
So here-- I copied this from Wikipedia, this diagram of the human circulatory system-- and here in the back you can see the lungs.
Let me do it in a nice dark color.
So we have our lungs here.
You can see the heart is sitting right in the middle.
And what we learned in the last few videos is that we have our little alveoli and our lungs.
Remember, we get to them from our bronchioles, which are branching off of the bronchi, which branch off of the trachea, which connects to our larynx, which connects to our pharynx, which connects to our mouth and nose.
But anyway, we have our little alveoli right there and then we have the capillaries.
So when we go away from the heart-- and we're going to delve a little bit into the heart in this video as well-- so when blood travels away from the heart, it's de-oxygenated.
It's this blue color.
So this right here is blood.
This right here is blood traveling away from the heart.
It's going behind these two tubes right there.
So this is the blood going away from the heart.
So this blue that I've been highlighting just now, these are the pulmonary arteries and then they keep splitting into arterials and all of that and eventually we're in capillaries-- super, super small tubes.
They run right past the alveoli and then they become oxygenated and now we're going back to the heart.
So we're talking about pulmonary veins.
So we go back to the heart.
So these capillaries-- in the capillaries we get oxygen.
Now we're going to go back to the heart.
Hope you can see what I'm doing.
And we're going to enter the heart on this side.
You actually can't even see where we're entering the heart.
We're going to enter the heart right over here-- and I'm going to go into more detail on that.
Now we have oxygenated blood.
It's red.
And then that gets pumped out to the rest of the body.
Now this is the interesting thing.
When we're talking about pulmonary arteries and veins-- remember, the pulmonary artery was blue.
As we go away from the heart, we have de-oxygenated blood, but it's still an artery.
Then as we go towards the heart from the lungs, we have a vein, but it's oxygenated.
So that's this little loop here that we start and I'm going to keep going over the circulation pattern because the heart can get a little confusing, especially because of its three-dimensional nature.
But what we have is, the heart pumps de-oxygenated blood from the right ventricle.
You're saying, hey, why is it the right ventricle?
That looks like the left side of the drawing, but it's this dude's right-hand side, right?
This is this guy's right hand.
And this is this dude's left hand.
He's looking at us, right?
We don't care about our right or left.
We care about this guy's right and left. And he's looking at us. He's got some eyeballs and he's looking at us.
So this is his right ventricle.
Actually, let me just start off with the whole cycle.
So we have de-oxygenated blood coming from the rest of the body, right?
The name for this big pipe is called the inferior vena cava-- inferior because it's coming up below.
Actually, you have blood coming up from the arms and the head up here.
They're both meeting right here, in the right atrium.
Let me label that.
I'm going to do a big diagram of the heart in a second.
And why are they de-oxygenated?
Because this is blood returning from our legs if we're running, or returning from our brain, that had to use respiration-- or maybe we're working out and it's returning from our biceps, but it's de-oxygenated blood.
It shows up right here in the right atrium.
It's on our left, but this guy's right-hand side.
From the right atrium, it gets pumped into the right ventricle.
It actually passively flows into the right ventricle.
The ventricles do all the pumping, then the ventricle contracts and pumps this blood right here-- and you don't see it, but it's going behind this part right here.
It goes from here through this pipe.
So you don't see it.
I'm going to do a detailed diagram in a second-- into the pulmonary artery.
We're going away from the heart.
This was a vein, right?
This is a vein going to the heart.
This is a vein, inferior vena cava vein.
This is superior vena cava.
These are veins.
They're de-oxygenated.
Then I'm pumping this de-oxygenated blood away from the heart to the lungs.
Now this de-oxygenated blood, this is in an artery, right?
This is in the pulmonary artery.
It gets oxygenated and now it's a pulmonary vein.
And once it's oxygenated, it shows up here in the left-- let me do a better color than that-- it shows up right here in the left atrium.
Atrium, you can imagine-- it's kind of a room with a skylight or that's open to the outside and in both of these cases, things are entering from above-- not sunlight, but blood is entering from above.
On the right atrium, the blood is entering from above.
And in the left atrium, the blood is entering-- and remember, the left atrium is on the right-hand side from our point of view-- on the left atrium, the blood is entering from above from the lungs, from the pulmonary veins.
Veins go to the heart.
Then it goes into-- and I'll go into more detail-- into the left ventricle and then the left ventricle pumps that oxygenated blood to the rest of the body via the non-pulmonary arteries.
So everything pumps out.
Let me make it a nice dark, non-blue color.
So it pumps it out through there.
You don't see it right here, the way it's drawn.
It's a little bit of a strange drawing.
It's hard to visualize, but I'll show it in more detail and then it goes to the rest of the body.
Let me show you that detail right now.
So we said, we have de-oxygenated blood.
Let's label it right here.
This is the superior vena cava.
This is a vein from the upper part of our body from our arms and heads.
This is the inferior vena vaca.
This is veins from our abdomen and from our legs and the rest of our body.
So it it first enters the right atrium.
Remember, we call the right atrium because this is someone's heart facing us, even though this is on the left-hand side.
It enters through here.
It's de-oxygenated blood. It's coming from veins. the body used the oxygen.
Then it shows up in the right ventricle, right?
These are valves in our heart.
And it passively, once the right ventricle pumps and then releases, it has a vacuum and it pulls more blood from the right atrium.
It pumps again and then it pushes it through here.
Now this blood right here-- remember, this one still is de-oxygenated blood.
De-oxygenated blood goes to the lungs to become oxygenated.
So this right here is the pulmonary-- I'm using the word pulmonary because it's going to or from the lungs. It's dealing with the lungs.
And it's going away from the heart.
It's the pulmonary artery and it is de-oxygenated.
Then it goes to the heart, rubs up against some alveoli and then gets oxygenated and then it comes right back.
Now this right here, we're going to the heart.
So that's a vein.
It's in the loop with the lungs so it's a pulmonary vein and it rubbed up against the alveoli and got the oxygen diffused into it so it is oxygenated.
And then it flows into your left atrium.
Now, the left atrium, once again, from our point of view, is on the right-hand side, but from the dude looking at it, it's his left-hand side.
So it goes into the left atrium.
Now in the left ventricle, after it's done pumping, it expands and that oxygenated blood flows into the left ventricle.
Then the left ventricle-- the ventricles are what do all the pumping-- it squeezes and then it pumps the blood into the aorta.
This is an artery.
Why is it an artery?
Because we're going away from the heart.
Is it a pulmonary artery?
No, we're not dealing with the lungs anymore.
We dealt with the lungs when we went from the right ventricle, went to the lungs in a loop, back to the left atrium.
Now we're in the left ventricle. We pump into the aorta.
Now this is to go to the rest of the body.
This is an artery, a non-pulmonary artery-- and it is oxygenated.
So when we're dealing with non-pulmonary arteries, we're oxygenated, but a pulmonary artery has no oxygen.
It's going away from the heart to get the oxygen.
Pulmonary vein comes from the lungs to the heart with oxygen, but the rest of the veins go to the heart without oxygen because they want to go into that loop on the pulmonary loop right there.
So I'll leave you there.
Hopefully that gives-- actually, let's go back to that first diagram.
I think you have a sense of how the heart is dealing, but let's go look at the rest of the body and just get a sense of things.
You can look this up on Wikipedia if you like.
All of these different branching points have different names to them, but you can see right here you have kind of a branching off, a little bit below the heart.
This is actually the celiac trunk.
Celiac, if I remember correctly, kind of refers to an abdomen.
So this blood that-- your hepatic artery. Hepatic deals with the liver.
Your hepatic artery branches off of this to get blood flow to the liver.
It also gives blood flow to your stomach so it's very important in digestion and all that.
And then let's say this is the hepatic trunk.
Your liver is sitting like that.
Hepatic trunk-- it delivers oxygen to the liver.
The liver is doing respiration.
It takes up the oxygen and then it gives up carbon dioxide.
So it becomes de-oxygenated and then it flows back in and to the inferior vena cava, into the vein.
I want to make it clear-- it's a loop.
It's a big loop.
The blood doesn't just flow out someplace and then come back someplace else. This is just one big loop.
And if you want to know at any given point in time, depending on your size, there's about five liters of blood.
And I looked it up-- it takes the average red blood cell to go from one point in the circulatory system and go through the whole system and come back, 20 seconds.
That's an average because you can imagine there might be some red blood cells that get stuck someplace and take a little bit more time and some go through the completely perfect route.
Actually, the 20 seconds might be closer to the perfect route.
I've never timed it myself. But it's an interesting thing to look at and to think about what's connected to what.
You have these these arteries up here that they first branch off the arteries up here from the aorta into the head and the neck and the arm arteries and then later they go down and they flow blood to the rest of the body.
So anyway, this is a pretty interesting idea.
In the next video, what I want to do is talk about, how does the hemoglobin know when to dump the oxygen?
Or even better, where to dump the oxygen-- because maybe I'm running so I need a lot of oxygen in the capillaries around my thigh muscles. I don't need them necessarily in my hands.
How does the body optimize where the oxygen is actually delivering?
It's actually fascinating.
Dear Samsul,
I have written two letters to you but you never replied.
Hopefully, through this video letter, you will see your daughter and be moved to respond.
I brought this video letter from Bupul to Merauke so you could watch it.
Samsul, I still live in Bupul village with Mum and Dad.
The village is still like before.
The air is still fresh.
But to this day there is still no electricity and no telephone.
On the journey to Merauke we pass through many border security posts.
The TNI post that used to be near the Maro River bridge ... ... has been moved to near the Eligobel District office.
As you know, the trip from Bupul to Merauke is really tough ... ... usually between 4 and 5 hours.
Samsul, I miss you.
After you left me - when I was 5 months pregnant with our child ... ... life was difficult.
Many people ask who is the father of my child.
Those who know that her father is a TNI soldier call her an army brat.
Sometimes, when Yani is fussy and cranky,
Mum and Dad become emotional and say to her:
"Your father only knows how to make you, but he is irresponsible!'
I usually just stay quiet and accept these words from my parents.
Samsul, do you remember when we first met in 2008?
You were very polite and kind.
You used to visit our house often, bringing biscuits, cereal mix and milk.
You came by the house every day until we started dating.
I was still in high school at the time.
I thought we were going to get married.
But you left for Bandung in November 2008 when I was 5 months pregnant.
You promised to move to Merauke and asked me to take care of our daughter.
On 17 March 2009, our daughter, Anita Mariani, was born in the Bupul village.
I call her Yani.
Now Yani has grown big.
She's three years old.
She wants to go to school and become somebody useful for the nation.
Samsul, Mum and Dad have grown old.
They can no longer work to support our child.
I find it difficult to work because I have to take care of Yani constantly.
But I continue to fight to support our child.
If you come back to us, of course I will accept you with open arms.
I will continue to wait for you, Samsul.
I don't care what people say.
Love, from Bupul and Merauke, 21 November 2011.
Maria Goreti Mekiw
Let's add 249 to 383.
Now, the first thing you want to do with any type of addition problem, especially when you have multiple digits, is to write the two numbers above and below each other.
So we have 200-- let me write a little bigger than that-- 249 plus 383.
And you want to line them up so that we have the same places above and below each other.
So the 9 and the 3 are both in the ones place here, so we've lined them up.
The 4 and the 8 are both in the tens place, and the 2 and the 3 are both in the hundreds place.
If you had a thousands place in one of them and not in the other, it would just kind of be sitting out here by themselves.
The easiest thing is just to kind of both make them line up to the right, or the ones places.
Now I'll show you the process, but while we do the process, we'll think a little bit about why it makes sense.
So we start at the ones place, and we say what is 9 plus 3?
So we say 9 plus 3.
Well, that's equal to 12.
I'm writing the 1 in 12 in orange on purpose, because when you want to write the sum down here, you can't write a two-digit number.
You can only write a digit between 0 and 9.
So what we do is 9 plus 3 is 12, that's the equivalent of 10 plus 2.
So we write the 2 in the ones place, and the 1, which is really representing 10, we put in the tens place, which hopefully makes sense.
This now represents 10.
And now we want to add this 10 plus 40 plus 80.
It looks like we're adding a 1 to a 4 to an 8, but these are really in the tens place, so this is really a 10, a 40 and an 80.
But if you just think about the process, you just take your 1, you add it to your 4 and your 8-- plus 4 plus 8-- and what do you get?
1 plus 4 plus 8 is what?
5 plus 8, that is 13.
I'll write it like this.
Actually, this is in the tens place, so it actually represents 130, but you don't have to think about that.
The process is fairly straightforward.
You have 13.
You write the 3 down here, and we regroup the 1 or, you might have learned, you carry the 1, so then you carry the 1 up here.
Same process now in the hundreds place.
This 1 actually represent a hundred, because this was actually 130 because it was in the tens place.
So we have a 1 plus 2 plus 3, what is that?
Well, that's just 6, right?
1 plus 2 is 3 plus 3 is 6.
So that is equal to 6.
So we write it right over here.
So 249 plus 383 is 632.
What we're going to do in this video is graph some lines using the x- and y-intercepts of the line.
So first of all, a line is defined by two points.
If you find two points-- if you're able to plot two points on a line, then you can connect them and keep going in both directions.
And you will have drawn the line.
What I'm going to do in this video-- the two points I'm going to pick are the intercepts of the lines.
There's two of them.
There's the x-intercept and then there's the y-intercept.
These are the points where the lines intersect the x- and y-axes.
And just to make it clear, this right here is the x-axis on my graph paper.
That right there is my x-axis.
It just keeps going.
That's my x-axis.
This right here, in the middle, going up and down, is my y-axis.
That right there is my y-axis.
I don't think you can see what I just wrote.
That is the y-axis right there.
So let me show you what I mean by x- and y-intercepts.
So let's do part (a).
I'll do it in a different color, not the same color as my intercepts.
Part (a), we have the equation y is equal to 2x plus 3.
So first of all, let's think about what happens when x is equal to 0.
When x is equal to 0, what is y equal to? y is going to be equal to two times 0 plus 3.
Well, 2 times 0, that's just 0.
So y is equal to 0 plus 3 or y is equal to 3.
So the point x is equal to 0, y is equal to 3, that satisfies this equation.
Or it's on the line defined by this equation.
So the point 0, 3.
Let me plot that.
The point 0, 3.
Now notice, this point-- this is when x is equal to 0, this sits on our y-axis.
We call this right here a y-intercept.
It is when x is equal to 0.
But it's called a y-intercept because it sits on the y-axis.
This is where the line intercepts the y-axis.
Now let's do the same for the x-axis.
Let's set y equal to 0.
So if y is equal to 0, we have 0 is equal to 2x plus 3.
We could subtract 3 from both sides of that equation.
And you get negative 3 is equal to 2x.
We can divide both sides by 2.
And you get negative 3/2 is equal to x.
And negative 3/2, that's the same thing as negative 1 1/2.
So we know that the point negative 3/2, 0, right?
The second scenario, y is equal to 0.
We know that this set of values of x and y also satisfy this equation.
Or that this point also sits on the line.
So negative 3/2-- remember that's the same thing as negative 1 1/2.
That's right there. y is 0.
So that's that second point we just figured out.
When y is 0, we're dealing with our x-intercept.
We're intercepting the x-axis.
That is the x-intercept right there.
If I wanted to draw the line, it'll look like this.
Very roughly, I'll connect those points and then just keep going.
Keep going in both directions.
Keep going in both directions forever and then I will have drawn my line.
Let's do one more of these.
I don't want to make it too messy over here.
Let me clear all this stuff out of the way.
Let me clear this out of the way as well.
You could always pause it, if you want to gaze at it-- oh I shouldn't have done that, I got rid of my-- well you can see still the axes.
I'll redraw the axes.
I'll redraw it right there.
Good enough.
That's one, my x-axis.
That is my y-axis right over there.
Let me do part (b).
(b) looks like an interesting one right there.
(b) has 6 times x minus 1 is equal to 2 times y plus 3.
So let's look at the situation when x is equal to zero.
When x is equal to 0, that equation up there becomes 6 times negative 1. Right?
Because this is 0.
So 6 times negative 1 is negative 6 is equal to 2-- let me distribute this-- 2y plus 6.
I multiplied 2 times the y and times the 3.
And then we can subtract 6 from both sides, so that you get negative 12. Negative 12 is equal to 2y.
I subtracted 6 from both sides to essentially move this 6 on to the left-hand side.
You subtract 6 here, this disappears.
You subtract 6 from here, you get negative 12.
Divide both sides by 2, you get negative 6 is equal to y.
So our first point that we know is on the line is a point x is equal to 0, y is equal to negative 6.
That is our y-intercept.
Now let's see what happens when y is equal to 0.
Go back to the original equation.
We have-- let me write that a little bit different-- when y is equal to 0, we have 6 times x minus 1.
Let me just distribute that.
So 6x minus 6 is equal to 2 times y.
Well, y is just going to be 0.
So it's going to be 2 times 3.
This whole thing is going to be 3.
It's going to be equal to 6.
So let's subtract 6 from both sides-- or let's add 6 to both sides of this equation.
I want to get rid of that right there.
So I need to add 6 to make that 0.
So we get 6x is equal to-- you add 6 to the right-hand side, you get 12.
And you get x-- divide both sides by 6, you get x is equal to 2.
So our other intercept is x is equal to 2, y is equal to 0.
So we have x is equal to 2, y is equal to 0.
Right there.
That is our x-intercept.
And then our actual line, we just connect the dots.
It will look something like that.
Obviously, you have trouble drawing a straight line, but I think you got the idea.
Two points define a line.
Let me do one more of these.
I could probably do it up here, in this real estate up here.
Let's do part d.
You can do part c if you want extra practice.
So part d, we have x plus y is equal to 8.
This is actually very, very straightforward.
When x is equal to 0, what is y equal to?
If this is 0, all we have left is y is equal to 8.
And then when y is 0, what is x?
Well, you can just almost cover this up.
Then you just get x plus 0 is equal to 8. x is equal to 8.
So that was pretty straightforward right there.
So we have one point, 0, 8.
So 0, 8.
That is the y-intercept.
And then we have the point 8, 0.
8, 0.
That is the x-intercept.
And then we can connect the dots.
It looks something like that.
Now let's do this problem down here.
At a local grocery store, strawberries cost $3.00 per pound and bananas cost $1.00 per pound.
If I have $10 to spend between strawberries and bananas, draw a graph to show the combination of each I can buy and spend exactly $10.
Let me draw my axes.
Make sure that these are nice and filled in.
So that remember is my horizontal access.
But just for fun, instead of calling it the x-axis, I'm going to call it the strawberry-axis.
Actually let me call it s, the s-axis, where s is for strawberries.
Let s equal the number of strawberries.
I think you know where I'm going. b will be number of bananas.
Let me do my b-axis.
I'm going to plot the number bananas on the vertical axis.
So this right there, that is the b-axis. b for bananas.
Strawberries cost $3.00.
OK, this isn't the number of strawberries.
This is the number of pounds.
Let me clear that up.
This is pounds of strawberries.
We're not going by the number of strawberries.
We're going by pounds of strawberries.
This is pounds of bananas.
All right.
Strawberries cost $3.00 per pound, bananas cost $1.00 per pound.
So how much am I going to spend?
I'm going to spend $3.00 times the number of strawberries because they're $3.00.
All right, I'm going to spend $3.00 times the number pounds of strawberries because it's $3.00 per pound plus $1.00 times the number of pounds of bananas.
And they say I have $10.00 to spend on both.
So that's going to be equal to $10.
So 3 times the pounds of strawberries plus the pounds of bananas are going to be equal to 10.
1b, that's the same thing as b, so I can rewrite this as 3s plus b is equal to 10.
Now let's plot this.
Let's look at the situation where I get no strawberries.
So my pounds of strawberries are 0.
What does this equation become?
It becomes 3 times 0 plus b is equal to 10. That's just 0.
So b will be equal to 10.
So I would have the point 0 pounds of strawberries, I could get 10 pounds of bananas.
So if I get 0 pounds of strawberries, I can get 10 pounds, right there, of bananas.
Now what about the other scenario?
What about the scenario where I get no bananas?
I get 0 pounds of bananas.
Now let's substitute back here.
We have 3 times my pounds of strawberries plus 0 pounds of bananas will equal 10.
That's just a 0.
Divide both sides by 3.
I could-- if I get no bananas-- I can get 10/3 pounds of strawberries. Or this is equal to 3 1/3.
So it would have the point 3 1/3 pounds of strawberries, 0 pounds of bananas. So 3 1/3 pounds of strawberries, 0 pounds of bananas.
And then we can connect the line.
This whole line I'm going to draw, I am just going to draw it in the first quadrant.
Because I can't have negative bananas.
I'm not going to sell pounds of bananas.
And I can't have negative strawberries.
We're not talking about selling strawberries.
So I can only buy these things.
This is the amount that I'm buying.
So let me to connect the dots right there.
This is neat because this line shows all of the possible combinations of pounds of strawberries and bananas.
For example, this point right here-- I don't know if I'm drawing it exactly-- it looks like if I get about 5 pounds of bananas, I can get a little under 2 pounds of strawberries.
That's what that tells me.
If I get 3 pounds of strawberries, if I get exactly 3 pounds of strawberries, I can get 1 pound of bananas.
Every point here represents a combination that I can get for $10.
Today, the Court indicted the plaintiffs for criminal misconduct (by state officials) on the death of Imam Yapa Kaseng which consisted of the relatives of the deceased, to hear whether the court would try the case
Today, we are here at the court to hear the judgement
This is the case of my father, who died in custody of military officials, for which we filed a lawsuit
We filed against a total of 6 officials, 1 of whom is a police officer who is the Director of Rueso Police Station
The reason for the motion is that the police officer brought us to a news conference at Muaeng Narathiwat District Police Station, and locked us up in a police truck at Task Force 39, Suam Tham Temple, Rueso District
The other 5 officials were in the military, who tortured Father to death on that day
Today, the ruling of the Court came in 2 parts.
The first ruling is to dismiss the motion against the 6th defendent, the police officer. for whom the plaintiff attorney filed the motion that the police officer was involved in the crime which resulted in death during custody
Thus, acquittal would equal to non-involvement of the police in the crime
However, the attorney who wrote the complaint or the motion deemed that the role of the police officer, from the arrest to the press conference and returning to Task Force 39 and allowing the military officials to use the truck in the detainment for 2 days, and causing the death which should result in the police official also being responsible for the mentioned act
However, the Court did not concur, and the motion was dismissed
Therefore, at this moment, the co-offenders only include Defendent 1-5, all of whom are military officials
One more thing, in the court ruling, the judge also said that
"Although the act of the police might be the violation of rights in the Constitution, Section 39 on human dignity, etc.", the details of which would have to be provided by our lawyer
So the judge ruled that (on the police officer) there was violation of constitutional rights
But as this violation did not have any law or regulation that specified the sentense
It resulted in the Judge ruling that there was no role in the crime (by the police officer)
As for the 1st to 5th defendent, all of whom are military officials, by Thai Laws, these defendents would have to be tried by Court Martial
Today, we came here with the hope that justice would be on our side
The police officer must also take responsiblity for this case
But today, things did not turn out as we expected.
I think that the police officer should take responsiblity, but when I heard the court ruling, it turned out that the cop did not do anything wrong
I feel very unsatisfied, and very angry
As for my feeling, it was very unhappy with the ruling that the police officer did not play a role in the crime
We were thinking that a civilian court should be able to protect the rights of the people better than others
But when the court ruled as mentioned, we felt a bit despaired
People were affected, as severely as death, during custody (by officials)
And this is one of the first cases where the relatives seek justice in the judicial process
Yet the Court decided to drop the charge and did not grant motion
Which may cause the people to seek justice elsewhere
I think that the Court should be the best place or the last resort on which the people can rely
We will keep on fighting in order to see justice done. We will never back down
Even if we have to fight this case in court martial
Time is not an obstacle for us in continuing the search for the word "Justice". We will keep on fighting.
Say we have a right triangle.
Let me draw my right triangle just like that.
This is a right triangle. This is the 90 degree angle right here. And we're told that this side's length right here is 14.
This side's length right over here is 9. And we're told that this side is a.
And we need to find the length of a.
So as I mentioned already, this is a right triangle.
And we know that if we have a right triangle, if we know two of the sides, we can always figure out a third side using the Pythagorean theorem.
And what the Pythagorean theorem tells us is that the sum of the squares of the shorter sides is going to be equal to the square of the longer side, or the square of the hypotenuse.
And if you're not sure about that, you're probably thinking, hey Sal, how do I know that a is shorter than this side over here?
How do I know it's not 15 or 16?
And the way to tell is that the longest side in a right triangle, and this only applies to a right triangle, is the side opposite the 90 degree angle.
And in this case, 14 is opposite the 90 degrees.
This 90 degree angle kind of opens into this longest side. The side that we call the hypotenuse.
So now that we know that that's the longest side, let me color code it.
So this is the longest side.
This is one of the shorter sides.
And this is the other of the shorter sides.
The Pythagorean theorem tells us that the sum of the squares of the shorter sides, so a squared plus 9 squared is going to be equal to 14 squared.
And it's really important that you realize that it's not 9 squared plus 14 squared is going to be equal to a squared. a squared is one of the shorter sides.
The sum of the squares of these two sides are going to be equal to 14 squared, the hypotenuse squared.
And from here, we just have to solve for a.
So we get a squared plus 81 is equal to 14 squared.
In case we don't know what that is, let's just multiply it out.
14 times 14. 4 times 4 is 16. 4 times 1 is 4 plus 1 is 5.
Take a 0 there. 1 times 4 is 4.
1 times 1 is 1. 6 plus 0 is 6.
5 plus 4 is 9, bring down the 1.
It's 196.
So a squared plus 81 is equal to 14 squared, which is 196.
Then we could subtract 81 from both sides of this equation.
On the left-hand side, we're going to be left with just the a squared.
These two guys cancel out, the whole point of subtracting 81.
So we're left with a squared is equal to 196 minus 81.
What is that?
If you just subtract 1, it's 195.
If you subtract 80, it would be 115 if I'm doing that right.
And then to solve for a, we just take the square root of both sides, the principal square root, the positive square root of both sides of this equation.
So let's do that.
Because we're dealing with distances, you can't have a negative square root, or a negative distance here.
And we get a is equal to the square root of 115.
Let's see if we can break down 115 any further.
So let's see. It's clearly divisible by 5.
If you factor it out, it's 5, and then 5 goes in the 115 23 times.
So both of these are prime numbers. So we're done.
So you actually can't factor this anymore.
So a is just going to be equal to the square root of 115.
Now if you want to get a sense of roughly how large the square root of 115 is, if you think about it, the square root of 100 is equal to 10.
And the square root of 121 is equal to 11.
So this value right here is going to be someplace in between 10 and 11, which makes sense if you think about it visually.
Epah, how do you find the (Silent Riot) film earlier
I was shocked, because it was my first time watching that movie I never knew before this history of Sabah before this
Oh I was very shocked when I watched it! because it's Sabah's history... and I think although I'm considered old enough, but I never knew this part of Sabah's history because, although I know what is Sabah United Party (PBS), but that's only because through family
My dad is the one who told me about PBS, and about Pairin... is all I know is the fact that he is Pairin, that's all
But I never know anything behind the administration of Datu *Mustapha
So after the screening, now I know something about Sabah's past, it really opens my mind
I think.. I am still processing, because not because of my age but actually, I hate politics but actually, politics is necessary and we can't run away from it right its useless to close your ears and don't want to know anything about it
like the film just now, me too never know about that and if we were to talk about PBS or Pairin, I only know the surface only the only thing I kniw is Pairin won and then he becomes the Chief Minister, but then was shackled by the Federal that is all I know Epah, and I think I need to explore more bout our history ya same with me here, and in the film after old lady was saying
now I know that... there's a lot of Sabah's history which I discovered today especially when the video says the reason and how illegal immigrant came so all this while, the we realized that we're actually oppressed
All right, I have a problem here.
Jacob and Emily ride a ferris wheel at a carnival in Billings, Montana.
The wheel has a 16-meter diameter.
So let me draw the wheel.
It has a 16-meter diameter.
So let me draw it big.
Give me a lot of space.
So it has a 16-meter diameter, so what's its radius going to be?
Its radius is going to be half of that, right?
So if I were to draw its radius, just draw it like that.
It's a 16-meter diameter, so it's radius is going to be 8 meters with its lowest point above the ground-- oh, with its lowest point 1 meter above the ground.
So its lowest point is right here.
This is its lowest point, and that is 1 meter above the ground.
So this distance right here is 1 meter.
Fair enough.
Assume that Jacob and Emily's height h above the ground is a sinusoidal function of time where t equals 0 represents the
So this is at point t equals 0 right here. t equals 0 is the lowest point of the wheel.
Write an equation for h.
Oh, I think I forgot, so let me reread it.
Jacob and Emily ride a ferris wheel at a carnival in Billings, Montana.
The wheel has a 16-meter diameter-- we did that-- and turns at 3 revolutions per minute.
So it turns at 3 revolutions per minute with its lowest point 1 meter above the ground.
Assume that Jacob and Emily's height h above the ground is a sinusoidal function of time, where t equals 0.
So we need to write a function of h, their distance above the ground, as a function of time, and they're saying that time is given in seconds.
So, first of all, they're telling us 3 revolutions every minute, right?
So that's 3 revolutions per 60 seconds, and that's the same thing as 1 revolution per 20 seconds, right?
I just divide both sides of the per by 3 for 20 seconds.
And one revolution is how many degrees?
One revolution is 360 degrees.
So it's 360 degrees per 20 seconds.
And if you're going 360 degrees per 20 seconds, let's divide-- you know, the per you can just kind of use as an equal sign of the equation.
That means you're going to go what?
18 degrees, Just divide both sides by 20.
And we could have done it with a numerator and a denominator. 3 revs per-- you know, you could have said 3 revs over 60 seconds.
That's actually how I should have done it. 3 revs over 60 seconds is equal to 1 rev over 20 seconds, which is equal to 360 degrees over 20 seconds, which is equal to 18 degrees per second, right?
So we're going to travel 18 degrees per second.
So the total number of degrees we've traveled in t seconds is going to be-- so see, if we say the angle, that's the angle from our starting point.
So let's say we've traveled t seconds, and we're right there.
What is-- let's drop a little altitude right here.
What is this angle going to be, where this angle is right here?
What is this angle going to be?
How many degrees have we traveled?
Well, we say we traveled 18 degrees per second, so if we travel t seconds, this is going to be 18t degrees, right?
All right, so let's see if we can figure out how their height as a function of this-- well, as a function of t or as a function of this angle right here.
So what is this height right here?
Up here?
It's 1 meter plus the radius because this distance right here is 8.
So we could say that this is-- this point right here is h is equal to 9 at this point, right?
We could almost view that as the h axis.
So that's h is equal to 9.
So at this point, how high are they?
If this is h-- so right now, let me draw a little drop and go flat here.
So their height above the ground is this distance h, which is the same thing as this distance h.
So what is that distance?
Well, it's going to be-- well, if this distance is h, what is this distance going to be?
This distance is going to be 9 minus h.
How do I know this?
This whole distance is 9.
This distance is h, so-- let me do it in a better color-- so that this distance right here is 9 minus h.
So let's see what we can do.
What do we know?
We know this distance.
We know this angle is 18t degrees. And do we know this side?
Sure.
That's the radius.
That's 8. 8 meters. 9 minus h meters, 8 meters, and 18 degrees.
And what are these sides relative to this angle?
Well, if we were to draw a triangle here relative to this angle right here, the 9 minus h is adjacent, and the 8 meters is, of course, the hypotenuse, right?
So what trig function deals with adjacent and hypotenuse.
SOHCAHTOA.
CAH, cosine is adjacent over hypotenuse.
So we could say the cosine at 18 degrees, the cosine of 18t degrees, is equal to its adjacent side.
The adjacent side is 9 minus h.
It's equal to 9 minus h over the hypotenuse, over 8.
And now we can solve for h, and we'll have h as a function of t.
So we multiply both sides by 8.
You get 8 cosine of 18t is equal to 9 minus h.
Maybe we could subtract 9 from both sides.
So we get minus 9 plus 8 cosine of 18t is equal to minus h, and then multiply both sides by negative 1, and then you get 9-- positive 9, right-- minus 8 cosine of 18t is equals to h, or h is equal to 9 minus 8 cosine of 18t.
So there we have it.
We have expressed h as a function of t.
And in the next video, I'm actually going to graph this function.
See you soon.
Evet
Welcome to you
Alhamdulilahi Rabul 'alamin with the support of our Seyh, Allah SWT has granted us another week another Thursday, another Jummah, another zikr another chance for us to remember Him to remember Allah SWT don't think that the zikr that we have just done is something it is nothing it is not worth to be presented to the presence of Allah SWT it is not worth to be presented to the divine presence of our holy Prophet (S) but with the blessings of our Seyh, inshallah it will be accepted we are not those ones who are proud and arrogant and depending on our worship worship is an obligation, worship gives so much blessings... but we are not depending on the worship we are depending on Allah we are depending on holy Prophet ASWS His shafat, his intercession and we are hoping for the intercession of our Seyh - that is the most important thing
Man falls into this heedless and headless station because he is only depending on himself whereas, in reality he is only a prisoner between two breaths if Allah does not give permission, he can not take a breath in if Allah does not give the permission, he can not take the breath out if Allah does not give him the permission, he can not even enter into the bathroom and finish whatever it is that he has put into his body the most beautiful things that he has put into his body that takes hours, months, sometimes years to prepare... but it comes out form his body in the most dirty, smelly, poisonous way that no one can bare to look at or to smell understand what Man, if he is still stuck in the animal station and he has not reached to the level of perfection (the Insan-e-Kamil) station if he has not reached to the station where he came from (which is a Paradise station) that is what is going to happen may Allah make us to become Ahli Jannat here on Earth before we pass, inshallah with the shaffat of our Prophet and with the blessings of our Seyh
Auzubillahi minashaytan irRajeem
Bismillahir Rahmanir Rahim
Destur!
Medet ya Sahib al-Saif, Seyh Abdul Kerim al-Rabbani, Medet.
Bismillahir Rahmanir Rahim
Tarikatuna sohbet, fil khayri min jami'at
The pir of our tarikat, our way - Shah Naksibendi is saying, "Our way continues with association, and goodness comes from being in jamat" so many may say, "We want to break away from jamat." It's okay, you are free to do that for a certain time As you like.
We are not an authority on you... but Shah Naksibendi is saying goodness comes form the jamat, he did not say goodness comes from breaking away and being alone or independant or being rebellious and he is saying that because holy Prophet ASWS is saying, "Deen e nasihat"
"Our religion is advice."
Shah Naksibendi is saying, "We are not prophets, we don't give advice - we give sohbet, we form an association where one speaks and the rest listen."
One speaks who has been given an authority, one speaks who has given the knowledge
The knowledge does not come from him too, he has been granted that knowledge
That one - for today he may speak.
Tomorrow may be someone else. The next day may be someone else
Nobody in this way of Allah is indispensable we cannot claim that this way depends on us and if we stop this... if I stop this, or you, or whoever it is who thinks that they are indispensable, irreplaceable, unique, and special in their role because they say,
"If I don't do this everything is going to fall!" ...If I say, "If I don't do this everything is going to fall." my faith is in a big question mark because I am saying I am something, everything is depending on me then where is the faith in Allah? isn't this way Allah's way?
Isn't this way the holy Prophet's way?
Isn't our Seyh controlling us? Controlling everything that is happening here? Making things to continue with his blessings so what right do I, or you, or anyone have to say, "Well, I have to do this because I am the only one who can do this - nobody else can do this!"
No.
You have to learn faith that time
Listen to me - you have to understand.
Start from scratch again
Faith. Don't look at yourself as something, we are trying to be nothing
Yes, responsibility is given to us
Yes, we have to do but never we are going to say, "If I don't do this, then this way, this world, everything is going to fall"
That time you are discounting Allah, you are discounting the Prophet, you are discounting Awliyaullah and our Seyh's - the friends of Allah!
The saints of Allah, you are discounting them.
You are saying, "It's me!" Ego is saying, "It's me!" again...
"I am important!"
No. (laughs)
Billions came before you and me, billions may come after you or me and Allah SWT is saying, "If you can not carry what I have given you, I will raise a people that maybe you are going to be enemies and look down to them, but they are going to be better than you..."
"...and they are going to carry that better than you." so we must not thing that we are something, because this way is going to continue with me or without me, with you or without you don't think we are the only ones, don't think we are doing something we are not
If you say, "Yes we are, if I don't do this everything is going to fall, we are going to get into this trouble..." Then you completely don't understand how the tariqat is going to work You think tariqat came out only last century in America?
Tarikat has seen so many Americas, so many empires, so many sultans... so whatever is in our hands, that responsibility, we have to carry it we have to do as much as we can but doing that, we have to follow our role model we have to follow our guide. We are here following our guide, isn't it? Who is our guide?
Shaytan understands.
He has more knowledge that you or me or everyone put together so our role model is our Seyh, and to do things the way that he taught us to do things, to think, to walk, to sit, to stand, to take care of our children, to pray, to worship, to wash clothes, to cook, to do everything according to his way
Zahir and Batin, according to his way we are saying that we are trying to be like Sahab Kiram in the presence of the Holy Prophet ASWS
Did you ever any Sahabi Kiram after they met the Holy Prophet ASWS, and they say, "Well, I still love this one, this guide, teacher, or prophet that I had before."? Did you ever hear? In dunya people understand that very good, very well when it comes to nafs and the dunya they say, "Now you love me right?
"Even if you spent your whole life with that one, but that one just passed - you can not love that one, now you have to love me! I must be the only one" Isn't it? so how can it be when we're following that one who is teaching us life and love our guide, our role model
Hazrati Salman al-Farisi (QS) is saying that he followed so many teachers, so many holy people from different religions that he was following and they were following the Hanafi way, meaning the purified way (hanifs) but when he found Holy Prophet ASWS, did you ever see that he is still going back to the teachings of those ones?
No. because he found someone who is completing everything and in reality, he is the master of the beginning and the end (Sayyidul awwalin wa'al akhireen) what about us now? We know so much Islamic knowledge, mashallah.
We know so much seerah.
We know so much history.
We know to say we love Prophet, we know to say we love the Companions... but when it comes to their lifestyle, the way that they live, we say that we don't want that
There is one word for that, it is called being a hypocrite That word is not a small word in the presence of Allah that word is the heaviest word
Holy Prophet ASWS is saying the hypocrite is going to be in the Hell that is lower than the unbelievers so we need to check that hypocrisy that is in our hearts
Thats why we have a seyh, a guide, a teacher.
To pull out the hypocrisy we have in our hearts to teach us, "You think you had faith?
It is not faith.
You think you had this?
It is not that.
You think you have eman?
It is not eman."
Understand that is hypocrisy
Understand that it's just an excuse.
Understand that is arrogance. Understand that is anger.
Understand that you are just being ungrateful.
Understand you are just complaining.
Understand that you are just being a dragon...
Understand that you are saying and claiming that you are following a seyh for decades, but still when something touches you a little bit, you are ready to blow up the whole world then later to say, "Oh, i'm sorry.
I'm just venting, after that i'm okay now."
It's like someone coming when he is upset and shooting, killing people.
Then when his anger cools down because he shot people, because he's done damage to say, "Now i'm cool, okay i'm sorry.
Why is everyone so upset?"
"Why are you so upset with me?
What did I do?
I already said i'm sorry, right?"
That is how they teach America to be, isn't it? do as much damage as you want to yourself and to the whole world, then later say, "I'm sorry." Then get upset if people don't hug you after that.
Don't clean up your mess
No.
There is always a price to pay and the price to pay, to find out and to discover yourself, is your ego.
That is the price you have to pay because the ego is the one that is standing infront of us, preventing us from discovering who we are and preventing us from discovering and understanding our relationship to our Lord and from knowing our Lord and worshipping Him
Allah!
You can never discover Allah. but the drop that you may know of him, you may worship him that time.
All that, the key is form you too.
It is form inside of you but you can not do it by yourself.
Yes, you have to have a guide and that guide definitely is going to teach you something that you dont know definitely in this way, because this way is concentrating on the ego, is going to concentrate on your ego
He is not going to pet you on the back and say, "Mashallah, such nur coming out from your face!"
"Mashallah, yesterday I see such high stations that you are coming from"
"Mashallah, I see in a dream that you're here, you're there..."
He's not going to praise you.
That is not the way.
That is not this tarikat.
That is not the way that is the tarikat al-aliyya
That is not the way the way is to concentrate on the ego and for you to understand what kind of creature the ego is that Allah SWT has given power to the ego, and the ego is rebelling against Allah
Shaytan disobeyed Allah once, but the ego is continuous from the day that it was created, until the day that either you are going to control it... either you are going to step on it and it is going to give you that power either you are going to ride on it in this world or that ego is going to pull you to Jahannam. that time it's going to be completely under control by the other ones
You have no part to play in it, but because you did not control it when you had the chance you are going to pay a heavy price for it too because you identified yourself with the ego, you did not identify yourself with the spirit so you are going to go where the ego is, and the ego is to the Fire. so we are watching these days, Alhamdulilahi Rabbul alameen we are watching these days how different people are behaving.
How different people are thinking, walking, living, acting... in these days that our Seyh has passed
We are watching, we are not saying anything.
We are observing, we are taking lesson we take lesson either take lesson, or Allah is going to make you to become a lesson to others and we are noticing so many things, and it is an obligation to us to speak a couple things for those of us, myself included, i'm not saying it's just you, that may find some benefit in it.
That will take it, inshallah we are here to continue our Seyh Effendi's way.
We are here because we believe in him, because we took beyat with him we are not saying we are 100% very very good, best mureeds.
No. we know we don'y qualify for that, but we don't...
Inshallah, May Allah not put us through that test - we don't doubt that he is our Seyh
We are not taking from anyone else
Sultan al Awliya is Sultan al Awliya we have manners, we are not saying that we are mureeds of Sultan al Awliya our Seyh is his mureed just as everyone may belong to the king in a kingdom... but nobody can say, "Yes, i'm directly under the king and the king is giving me special attention because I am in his kingdom."
The king has vizirs, ministers, and it goes down from the ministers and top people all the way down...
That is how the protocol is working people understand that in dunya elections coming up, that is democracy, correct? democracy hypocrisy but you don't find that equality in your workplace - between you and your manager, or your boss you can not say now to your boss, "Well, we are living in a democracy and we are all supposed to be equal!
"You sit over here!
We are free!
You speak? I speak!
You give orders?
Let me give orders too!"
No.
People understand that it does not work in dunya.
Why do you think it's working in the way of Allah? why do you think it's working in religion and spiritulaity?
Hmm... wrong understanding. we have to turn our way back
We've taken a detour
We have to bring ourselves back to the main highway and the highway of our Seyh - Sahib al Saif
The main highway, not any other highways
Of course so many now, don't be surprised, you may hear people who have been with Seyh Effendi saying, "No, I did not give beyat to him, I gave beyat to Seyh Mawlana"
You may.
Well here it from me - I didn't give beyat to Seyh Mawlana.
Did anyone of you give Beyat to Seyh Mawlana?
We gave our beyat to Seyh Effendi
People may also say, "Well, it's not Seyh Mawlana, it's Seyh Sharafuddin, or Seyh Abdullah, or Salman al-Farisi, or Hazrati Abu Bakr, or..."
Why you don't say you gave beyat to Holy Prophet directly?
"Oh, because Seyh Effendi is connecting us to Seyh Mawlana - so Seyh Mawlana is my real shaykh"
They are also connecting you. They are connecting you so Seyh Abdullah, isn't it?
Why you don't say?
Maybe some are saying, I don't know...
Then Seyh Abdullah is connecting to Seyh Sharafuddin, Seyh Sharafuddin is connecting to 38 others all the way to the Holy Prophet ASWS
Why you don't say, "He is just connecting me.
All these ones - they are connecting ME!" 'me', meaning, "I am important!
They are working for ME!
They are connecting ME to the top ones!"
Why you don't say you are connected directly to the holy Prophet? Simple, that is the logic, isn't it? or to Allah?
Isn't that what Shaytan is saying?
"I'm connected only to you!
I refuse to bow down to Adam AS. To the authority that you have put on me..."
"What is he?
Who is that one?
He just came."
Who is that one?
He is made from inferior material.
Who is that one?"
Same understanding, same logic...
May Allah not put us in that situation, in that position these are very strange times, and as much as we are holding on to the rope of Allah we will find safety and the rope is our Seyh, no one else.
You are free, you may say you follow Seyh Mawlana.
There, you are free.
You may go.
You may say you are following Seyh Abdullah, you may say Holy Prophet ASWS - you may go.
Then this association... we are happy to be here, maybe you are not happy to be here you are such a high level person, then 'welcome to those that come, farewell to those that leave'
We welcome everyone, we never kick anyone out.
We don't say 'go!' but so many people don't feel uncomfortable and they leave definitely, because this is a holy association.
This is an association that is supported by the Holy Prophet ASWS
You are not going to find comfort here, impossible you are going to find comfort anywhere else in this world
Run!
Run anywhere you want to go!
People have forgotten, there are those who left too...
There are those who have forgotten how they left before and how Shaytan was circling around them and they could not even find peace to sleep at night and they are begging and crying for Seyh Effendi to welcome them back and Seyh Effendi went out on a limb to pull them back again, and now they left.
That is a sign of hypocrisy.
They feel uncomfortable.
They don't like a jamaat.
You see them coming here and they always put their head down.
They don't want to see anything.
They don't want to hear anything.
They are just being here because they are scared...
They don't want to form relationships or friendships jamaat is not just sitting and eating and talking together jamaat is having your lives together to watch out and to care for each other you see them not having that jamaat
"Tarikatuna sohbet fil khayri min jami'aah"
Yes, association.
Goodness and blessings come from the jamaat you dont like to be jamaat, you are free to go you don't like to stay in Paradise, you are free to go to any Hell that you want it's a big place out there strange days are upon us, strange days are upon this ummah the ummah is still not waking up this nation of the Holy Prophet ASWS is still not waking up we just passed the season of the Hajj we just passed the Kurban still Muslims are not waking up how are they going to wake up if their leaders are already sold? how are they going to wake up if the leaders are already bought? how are they going to wake up when their leaders, their scholars, those heads... they are the ones making fitna we are not taking about Muslims who are back biting now days so much mureeds are backbiting backbiting and gossiping, slandering and having bad intentions imagining illusion and delusion heaviness is going to fall on you more, definietly never you are going to find peace until you stop this backbiting and slandering, and lying and cheating and this entering into a imagination world where you are suspicious of everyone... never you are going to find peace.
Muslims just finished this holy season where you say, "Labayk, here I am, oh my Lord!"
Where you say, "Here I am to sacrifice for you"
"Here I am, I've left everything, and i'm going to your house as your guest wearing my funeral shroud..."
"...Leaving my family, leaving my wealth, leaving everything that I have an attachment to"
Yes, "Dropping my baby!"
Some take offense at that now
Holy Prophet ASWS is saying if Hazrati Mahdi takes the takbir and you are holding a baby - drop it. they misunderstand, of course, they want to.
Labayk, Allah humma labayk.
"Here I am, oh my Lord, here I am." "I've left everything for you.
You are my reason.
You are my Creator."
"My sons, my daughters, my father, my mother - they are related to me by blood, but you are their creator too"
"...and You are the creator of my father and mother.
They love me, but you love more than them!" "...Because you are the creator of love."
Allah is not love.
Allah is the creator of love.
"And You love me more than a mother loves her baby.
And here I am returning that love to you."
We just passed that we also passed a few weeks before that, when the whole world (Muslim world) is boiling because they played into the tricks of the enemies of Islam
Saying, on the one hand, Prophet is Prophet of mercy and Prophet of love and on the other hand, to show their love and their mercy, they are destroying... isn't it?
You get upset because some idiot just made a movie about the Holy Prophet ASWS - insulting him. Which is nothing that we've never heard before we've heard these same things for almost 1400 years.
Kafirs, they are always saying that
Definitely Christians are saying that, Jews are saying that...
Never you are going to find Muslims saying anything wrong, anything bad, about Hazrati Musa and Hazrati Isa we don't even say, 'Moses' or 'Jesus' because we love them, you don't love them! you don't even have respect for them we say Hazrati Musa, his holiness and his holiness, Jesus. we never say anything wrong about them, we never say anything bad about them we say these are all prophets, these are the highest level prophets
Prophets and Saints are ma'soom
They are protected, they are innocent
They dont even commit a sin - a wrong thing we dont even say prophets make a sin
You do. You run to kill your own prophets! You run and you insult your prophets in your own books!
You run on the one hand you say you love your prophet, but on the other hand you are doing the worse thing that your prophet is saying to you, "Don't do." but never are you going to find Muslims saying anything wrong about your Prophets 1400 years non-stop
Those ones who are unbelievers in the Jewish and Christian tradition, there are exceptions always, there are good ones in there... but non-stop for 1400 years always insulting and putting down, and saying the most horrible things about our Holy Prophet ASWS but never are you going to find Muslims retaliating the way that you do because dogs will bark at the caravan, always. We dont stop to bark at the dogs because we are humans.
But Muslims in the 21st century now...
Yes you got so upset, isn't it?
This is where we are
This is the lowest level of faith that we have.
How can we be proud of the worship that we just did?
We can not.
In fact, we should say astagfirullah more and say, "Ya Rabbi, that disaster that just passed us a few days ago..."
Muslims, forget about Muslims...
Mureeds they are not waking up, they are not understanding
They are not putting their heads together to become more awake, more aware, more serious...
They are not.
They are becoming more ghaflat, more arrogant
You can not be.
You shouldn't be.
You do that, you are dishonoring your Seyh, definitely these words are for me and for you, I'm in it too
If you think this is not for you, leave it.
I will take it.
But definitely, Allah is not happy
Prophet is not happy
Awliyaullah, they are not happy the Angels are not happy do you have to be a saint to understand this? do you have to be a genius to understand that even the earth is not happy with us?
This air is not happy, the water is not happy, the trees are not happy, the animals are not happy... because we made a mess of everything. Everything.
This whole system that we are living in now, this is a completely Shaytanic system the foods that we are putting into our mouth, we have messed up so much that it is not even natural and it is poisoning us and our children
The water that we are drinking, we put so much things in there, that it is becoming a poison to us and our children we have poisoned this earth, we have poisoned the water and intelligent man, the man who has faith is going to sit down and understand these things and ask himself, "Where am I in all of this?"
"Where am I?
What can I do?
What must I do?"
The man of faith will sit down and ask himself these questions...
Inshallah ar Rahman, we are saying...
Seyh Effendi is saying that we've pulled ourselves away from populated areas to be in the mountains away from populated areas because danger and disaster and the curse is raining down on those areas but don't bring your dirtiness to the mountains the mountains are clean, we are here to learn new things we are here to learn good things we are here to put away all the things that are part of our ignorant time, part of our jahiliyyah
Maybe you say, "I did not know that was wrong." But now you know better, change. You will only win for yourself
I'm not going to benefit, no one is going to benefit except for you.
We've pulled ourselves away from the populated areas to come to the mountains, to run away from the dunya
Don't make your own dunyas here.
That is the biggest mistake that you will ever do.
Even the angles are going to curse at you and say, "You disgusting creature.
You are taking the place of so many that are better than you..."
"You are running away from this dunya to come here, to live your life like a mureed, and you're bringing, you're making a dunya here?'
Don't make your dunya here.
We are here as a jamaat
These words are for you and for me
Wa min Allahu tawfiq
May Allah forgive me and bless all of you for the sake of our Seyh
May Allah SWT grant long life, and healthy life, strong life to our Grand Seyh (ameen)
May Allah SWT bless our Seyh, bring him to higher stations, and grant him more strength and more light, so that he can send to us more support to stay on this way strong and with faith and with intelligence (ameen)
May wrong things change
May those ones who have deviated come back to the sirat al-mustaqim
May the fitna and the wrong things be away from our association May we not be those ones who are causing fitna and confusion
Astagfirullah, Astagfirullah...
Fatiha
Ameen
Salam aleykum wa rahmatullah
Evet.
This is a question about peg solitaire.
In peg solitaire, a single player faces the following kind of board.
Initially, all pieces are occupied except for the center piece.
You can find more information on peg solitare at the following URL. [http://en.wikipedia.org/wiki/peg_solitaire]
I wish to know whether this game is partially observable,
Please say yes or no.
I wish to know whether it is stochastic.
Please say yes if it is and no if it's deterministic.
Let me know if it's continuous, yes or no, and let me know if it's adversarial, yes or no.
I now want to solve some inequalities that also have absolute values in them.
And if there's any topic in algebra that probably confuses people the most, it's this.
But if we kind of keep our head on straight about what absolute value really means, I think you will find that it's not that bad.
So let's start with a nice, fairly simple warm-up problem.
Let's start with the absolute value of x is less than 12.
So remember what I told you about the meaning of absolute value.
It means how far away you are from 0.
So one way to say this is, what are all of the x's that are less than 12 away from 0?
Let's draw a number line.
So if we have 0 here, and we want all the numbers that are less than 12 away from 0, well, you could go all the way to positive 12, and you could go all the way to negative 12.
Anything that's in between these two numbers is going to have an absolute value of less than 12.
It's going to be less than 12 away from 0.
So this, you could say, this could be all of the numbers where x is greater than negative 12.
Those are definitely going to have an absolute value less than 12, as long as they're also-- and, x has to be less than 12.
So if an x meets both of these constraints, its absolute value is definitely going to be less than 12.
You know, you take the absolute value of negative 6, that's only 6 away from 0.
The absolute value of negative 11, only 11 away from 0.
So something that meets both of these constraints will satisfy the equation.
And actually, we've solved it, because this is only a one-step equation there.
But I think it lays a good foundation for the next few problems.
And I could actually write it like this.
In interval notation, it would be everything between negative 12 and positive 12, and not including those numbers.
Or we could write it like this, x is less than 12, and is greater than negative 12.
That's the solution set right there.
Now let's do one that's a little bit more complicated, that allows us to think a little bit harder.
So let's say we have the absolute value of 7x is greater than or equal to 21.
So let's not even think about what's inside of the absolute value sign right now.
In order for the absolute value of anything to be greater than or equal to 21, what does it mean?
It means that whatever's inside of this absolute value sign, whatever that is inside of our absolute value sign, it must be 21 or more away from 0.
Let's draw our number line.
And you really should visualize a number line when you do this, and you'll never get confused then.
You shouldn't be memorizing any rules.
So let's draw 0 here.
Let's do positive 21, and let's do a negative 21 here.
So we want all of the numbers, so whatever this thing is, that are greater than or equal to 21.
They're more than 21 away from 0.
Their absolute value is more than 21.
Well, all of these negative numbers that are less than negative 21, when you take their absolute value, when you get rid of the negative sign, or when you find their distance from 0, they're all going to be greater than 21.
If you take the absolute value of negative 30, it's going to be greater than 21.
Likewise, up here, anything greater than positive 21 will also have an absolute value greater than 21.
So what we could say is 7x needs to be equal to one of these numbers, or 7x needs to be equal to one of these numbers out here.
So we could write 7x needs to be one of these numbers.
Well, what are these numbers?
These are all of the numbers that are less than or equal to negative 21, or 7x-- let me do a different color here-- or 7x has to be one of these numbers.
And that means that 7x has to be greater than or equal to positive 21.
I really want you to kind of internalize what's going on here.
If our absolute value is greater than or equal to 21, that means that what's inside the absolute value has to be either just straight up greater than the positive 21, or less than negative 21.
Because if it's less than negative 21, when you take its absolute value, it's going to be more than 21 away from 0.
Hopefully that make sense.
We'll do several of these practice problems, so it really gets ingrained in your brain.
But once you have this set up, and this just becomes a compound inequality, divide both sides of this equation by 7, you get x is less than or equal to negative 3.
Or you divide both sides of this by 7, you get x is greater than or equal to 3.
So I want to be very clear.
This, what I drew here, was not the solution set.
This is what 7x had to be equal to.
I just wanted you to visualize what it means to have the absolute value be greater than 21, to be more than 21 away from 0.
This is the solution set. x has to be greater than or equal to 3, or less than or equal to negative 3.
So the actual solution set to this equation-- let me draw a number line-- let's say that's 0, that's 3, that is negative 3. x has to be either greater than or equal to 3.
Or less than or equal to negative 3.
Let's do a couple more of these.
Because they are, I think, confusing, but if you really start to get the gist of what absolute value is saying, they become, I think, intuitive.
So let's say that we have the absolute value-- let me get a good one.
Let's say the absolute value of 5x plus 3 is less than 7.
So that's telling us that whatever's inside of our absolute value sign has to be less than 7 away from 0.
So the ways that we can be less than 7 away from 0-- let me draw a number line-- so the ways that you can be less than 7 away from 0, you could be less than 7, and greater than negative 7.
Right?
You have to be in this range.
So in order to satisfy this thing in this absolute value sign, it has to be-- so the thing in the absolute value sign, which is 5x plus 3-- it has to be greater than negative 7 and it has to be less than 7, in order for its absolute value to be less than 7.
If this thing, this 5x plus 3, evaluates anywhere over here, its absolute value, its distance from 0, will be less than 7.
And then we can just solve these.
You subtract 3 from both sides.
5x is greater than negative 10.
Divide both sides by 5. x is greater than negative 2.
Now over here, subtract 3 from both sides.
5x is less than 4.
Divide both sides by 5, you get x is less than 4/5.
And then we can draw the solution set.
We have to be greater than negative 2, not greater than or equal to, and less than 4/5.
So this might look like a coordinate, but this is also interval notation, if we're saying all of the x's between negative 2 and 4/5.
Or you could write it all of the x's that are greater than negative 2 and less than 4/5.
These are the x's that satisfy this equation.
And I really want you to internalize this visualization here.
Now, you might already be seeing a bit of a rule here.
And I don't want you to just memorize it, but I'll give it to you just in case you want it.
If you have something like f of x, the absolute value of f of x is less than, let's say, some number a.
Right?
So this was the situation.
We have some f of x less than a.
That means that the absolute value of f of x, or f of x has to be less than a away from 0.
So that means that f of x has to be less than positive a or greater than negative a.
That translates to that, which translates to f of x greater than negative a and f of x less than a.
But it comes from the same logic.
This has to evaluate to something that is less than a away from 0.
Now, if we go to the other side, if you have something of the form f of x is greater than a. That means that this thing has to evaluate to something that is further than a away from 0.
So that means that f of x is either just straight up greater than positive a, or f of x is less than negative a.
Right?
If it's less than negative a, maybe it's negative a minus another 1, or negative 5 plus negative a.
Then, when you take its absolute value, it'll become a plus 5.
So its absolute value is going to be greater than a.
So I just want to-- you could memorize this if you want, but I really want you to think about this is just saying, OK, this has to evaluate, be less than a away from 0, this has to be more than a away from 0.
Let's do one more, because I know this can be a little bit confusing.
And I encourage you to watch this video over and over and over again, if it helps.
Let's say we have the absolute value of 2x-- let me do another one over here.
Let's do a harder one.
Let's say the absolute value of 2x over 7 plus 9 is greater than 5/7.
So this thing has to evaluate to something that's more than 5/7 away from 0.
So this thing, 2x over 7 plus 9, it could just be straight up greater than 5/7.
Or it could be less than negative 5/7, because if it's less than negative 5/7, its absolute value is going to be greater than 5/7.
Or 2x over 7 plus 9 will be less than negative 5/7.
We're doing this case right here.
And then we just solve both of these equations.
See if we subtract-- let's just multiply everything by 7, just to get these denominators out of the way.
So if you multiply both sides by 7, you get 2x plus 9 times 7 is 63, is greater than 5.
Let's do it over here, too.
You'll get 2x plus 63 is less than negative 5.
Let's subtract 63 from both sides of this equation, and you get 2x-- let's see. 5 minus 63 is 58, 2x is greater than 58.
If you subtract 63 from both sides of this equation, you get 2x is less than negative 68.
Oh, I just realized I made a mistake here.
You subtract 63 from both sides of this, 5 minus 63 is negative 58.
I don't want to make a careless mistake there.
And then divide both sides by 2.
You get, in this case, x is greater than-- you don't have to swap the inequality, because we're dividing by a positive number-- negative 58 over 2 is negative 29, or, here, if you divide both sides by 2, or, x is less than negative 34.
68 divided by 2 is 34.
And so, on the number line, the solution set to that equation will look like this.
That's my number line.
I have negative 29.
I have negative 34.
So the solution is, I can either be greater than 29, not greater than or equal to, so greater than 29, that is that right there, or I could be less than negative 34.
So any of those are going to satisfy this absolute value inequality.
Pro Pakatan supporters want Selangor to take over Syabas
Long live!
Long live the people!
We have successfully handed over 5 memorandums to the Syabas management
Especially for YB Datuk Rosali who is the CEO of Syabas These 5 memorandums were submitted by <i>Angkatan Muda</i> and also the state government representative
I'm about to lose the battle and cross the line
I'm about to make another mistake
And even though I try to stay away
Everything around me keeps dragging me in
I can't help thinking to myself
What if my time would end today, today, today?
Can I guarantee that I will get another chance
Before it's too late, too late, too late
Forgive me... My heart is so full of regret
Forgive me... Now is the right time for me to repent, repent, repent..
Am I out of my mind?
What did I do?
Oh, I feel so bad!
And every time I try to start all over again
My shame comes back to haunt me
I'm trying hard to walk away
But temptation is surrounding me, surrounding me
I wish that I could find the strength to change my life
Before it's too late, too late, too late
Forgive me... My heart is so full of regret
Forgive me... Now is the right time for me to repent, repent, repent..
I know O Allah You're the Most-Forgiving
And that You've promised to
Always be there when I call upon You
So now I'm standing here
Ashamed of all the mistakes I've committed
Please don't turn me away
And hear my prayer when I ask You to
Forgive me... My heart is so full of regret
Forgive me... Now is the right time for me to repent, repent, repent..
Forgive me... My heart is so full of regret
Forgive me... Now is the right time for me to repent, repent, repent..
Forgive me... My heart is so full of regret
Forgive me... Now is the right time for me to repent, repent, repent..
Hi.
I am an architect.
I am the only architect in the world making buildings out of paper like this cardboard tube, and this exhibition is the first one I did using paper tubes.
1986, much, much longer before people started talking about ecological issues and environmental issues, I just started testing the paper tube in order to use this as a building structure.
It's very complicated to test the new material for the building, but this is much stronger than I expected, and also it's very easy to waterproof, and also, because it's industrial material, it's also possible to fireproof.
Then I built the temporary structure, 1990.
This is the first temporary building made out of paper.
There are 330 tubes, diameter 55 [centimeters], there are only 12 tubes with a diameter of 120 centimeters, or four feet, wide.
As you see it in the photo, inside is the toilet.
In case you're finished with toilet paper, you can tear off the inside of the wall.
So it's very useful.
Year 2000, there was a big expo in Germany.
I was asked to design the building, because the theme of the expo was environmental issues.
So I was chosen to build the pavilion out of paper tubes, recyclable paper.
My goal of the design is not when it's completed.
My goal was when the building was demolished, because each country makes a lot of pavilions but after half a year, we create a lot of industrial waste, so my building has to be reused or recycled.
After, the building was recycled.
So that was the goal of my design.
Then I was very lucky to win the competition to build the second Pompidou Center in France in the city of Metz.
Because I was so poor,
I wanted to rent an office in Paris, but I couldn't afford it, so I decided to bring my students to Paris to build our office on top of the Pompidou Center in Paris by ourselves.
So we brought the paper tubes and the wooden joints to complete the 35-meter-long office.
We stayed there for six years without paying any rent.
(Laughter) (Applause)
Thank you.
I had one big problem.
Because we were part of the exhibition, even if my friend wanted to see me, they had to buy a ticket to see me.
That was the problem.
Then I completed the Pompidou Center in Metz.
It's a very popular museum now, and I created a big monument for the government.
But then I was very disappointed at my profession as an architect, because we are not helping, we are not working for society, but we are working for privileged people, rich people, government, developers.
They have money and power.
Those are invisible.
So they hire us to visualize their power and money by making monumental architecture.
That is our profession, even historically it's the same, even now we are doing the same.
So I was very disappointed that we are not working for society, even though there are so many people who lost their houses by natural disasters.
But I must say they are no longer natural disasters.
For example, earthquakes never kill people, but collapse of the buildings kill people.
That's the responsibility of architects.
Then people need some temporary housing, but there are no architects working there because we are too busy working for privileged people.
So I thought, even as architects, we can be involved in the reconstruction of temporary housing.
We can make it better.
So that is why I started working in disaster areas.
1994, there was a big disaster in Rwanda, Africa.
Two tribes, Hutu and Tutsi, fought each other.
Over two million people became refugees.
But I was so surprised to see the shelter, refugee camp organized by the U.N.
They're so poor, and they are freezing with blankets during the rainy season,
In the shelters built by the U.N., they were just providing a plastic sheet, and the refugees had to cut the trees, and just like this.
But over two million people cut trees.
It just became big, heavy deforestation and an environmental problem.
That is why they started providing aluminum pipes, aluminum barracks.
Very expensive, they throw them out for money, then cutting trees again.
So I proposed my idea to improve the situation using these recycled paper tubes because this is so cheap and also so strong, but my budget is only 50 U.S. dollars per unit.
We built 50 units to do that as a monitoring test for the durability and moisture and termites, so on.
And then, year afterward, 1995, in Kobe, Japan, we had a big earthquake.
Nearly 7,000 people were killed, and the city like this Nagata district, all the city was burned in a fire after the earthquake.
And also I found out there's many Vietnamese refugees suffering and gathering at a Catholic church -- all the building was totally destroyed.
So I went there and also I proposed to the priests,
"Why don't we rebuild the church out of paper tubes?"
And he said, "Oh God, are you crazy?
After a fire, what are you proposing?"
So he never trusted me, but I didn't give up.
I started commuting to Kobe, and I met the society of Vietnamese people.
They were living like this with very poor plastic sheets in the park.
So I proposed to rebuild.
I raised -- did fundraising.
I made a paper tube shelter for them, and in order to make it easy to be built by students and also easy to demolish,
I asked the Kirin beer company to propose, because at that time, the Asahi beer company made their plastic beer crates red, which doesn't go with the color of the paper tubes.
The color coordination is very important.
And also I still remember, we were expecting to have a beer inside the plastic beer crate, but it came empty.
(Laughter)
So I remember it was so disappointing.
So during the summer with my students, we built over 50 units of the shelters.
Finally the priest, finally he trusted me to rebuild.
He said, "As long as you collect money by yourself, bring your students to build, you can do it."
So we spent five weeks rebuilding the church.
It was meant to stay there for three years, but actually it stayed there 10 years because people loved it.
Then, in Taiwan, they had a big earthquake, and we proposed to donate this church, so we dismantled them, we sent them over to be built by volunteer people.
It stayed there in Taiwan as a permanent church even now.
So this building became a permanent building.
Then I wonder, what is a permanent and what is a temporary building?
Even a building made in paper can be permanent as long as people love it.
Even a concrete building can be very temporary if that is made to make money.
In 1999, in Turkey, the big earthquake, I went there to use the local material to build a shelter.
2001, in West India, I built also a shelter.
In 2004, in Sri Lanka, after the Sumatra earthquake and tsunami, I rebuilt Islamic fishermen's villages.
And in 2008, in Chengdu, Sichuan area in China, nearly 70,000 people were killed, and also especially many of the schools were destroyed because of the corruption between the authority and the contractor.
I was asked to rebuild the temporary church.
I brought my Japanese students to work with the Chinese students.
In one month, we completed nine classrooms, over 500 square meters.
It's still used, even after the current earthquake in China.
In 2009, in Italy, L'Aquila, also they had a big earthquake.
And this is a very interesting photo: former Prime Minister Berlusconi and Japanese former former former former Prime Minister Mr. Aso -- you know, because we have to change the prime minister ever year.
And they are very kind, affording my model.
I proposed a big rebuilding, a temporary music hall, because L'Aquila is very famous for music and all the concert halls were destroyed, so musicians were moving out.
So I proposed to the mayor, I'd like to rebuild the temporary auditorium.
He said, "As long as you bring your money, you can do it."
And I was very lucky.
Mr. Berlusconi brought G8 summit, and our former prime minister came, so they helped us to collect money, and I got half a million euros from the Japanese government to rebuild this temporary auditorium.
Year 2010 in Haiti, there was a big earthquake, but it's impossible to fly over, so I went to Santo Domingo, next-door country, to drive six hours to get to Haiti with the local students in Santo Domingo to build 50 units of shelter out of local paper tubes.
This is what happened in Japan two years ago, in northern Japan.
After the earthquake and tsunami, people had to be evacuated in a big room like a gymnasium.
But look at this. There's no privacy.
People suffer mentally and physically.
So we went there to build partitions with all the student volunteers with paper tubes, just a very simple shelter out of the tube frame and the curtain.
However, some of the facility authority doesn't want us to do it, because, they said, simply, it's become more difficult to control them.
But it's really necessary to do it.
They don't have enough flat area to build standard government single-story housing like this one.
Look at this.
Even civil government is doing such poor construction of the temporary housing, so dense and so messy because there is no storage, nothing, water is leaking, so I thought, we have to make multi-story building because there's no land and also it's not very comfortable.
So I proposed to the mayor while I was making partitions.
Finally I met a very nice mayor in Onagawa village in Miyagi.
He asked me to build three-story housing on baseball [fields].
I used the shipping container and also the students helped us to make all the building furniture to make them comfortable, within the budget of the government but also the area of the house is exactly the same, but much more comfortable.
Many of the people want to stay here forever.
I was very happy to hear that.
Now I am working in New Zealand, Christchurch.
About 20 days before the Japanese earthquake happened, also they had a big earthquake, and many Japanese students were also killed, and the most important cathedral of the city, the symbol of Christchurch, was totally destroyed.
And I was asked to come to rebuild the temporary cathedral.
So this is under construction.
And I'd like to keep building monuments that are beloved by people.
Thank you very much.
(Applause)
Thank you.
(Applause)
Thank you very much.
(Applause)
A card game using 36 unique cards, four suits, diamonds, hearts, clubs and spades-- this should be spades, not spaces-- with cards numbered from 1 to 9 in each suit.
A hand is chosen.
A hand is a collection of 9 cards, which can be sorted however the player chooses.
Fair enough.
How many 9 card hands are possible?
So let's think about it.
There are 36 unique cards-- and I won't worry about, you know, there's nine numbers in each suit, and there are four suits, 4 times 9 is 36.
But let's just think of the cards as being 1 through 36, and we're going to pick nine of them.
So at first we'll say, well look, I have nine slots in my hand, right?
1, 2, 3, 4, 5, 6, 7, 8, 9.
Right?
I'm going to pick nine cards for my hand.
And so for the very first card, how many possible cards can I pick from?
Well, there's 36 unique cards, so for that first slot, there's 36.
But then that's now part of my hand.
Now for the second slot, how many will there be left to pick from?
Well, I've already picked one, so there will only be 35 to pick from. And then for the third slot, 34, and then it just keeps going. Then 33 to pick from, 32, 31, 30, 29, and 28.
So you might want to say that there are 36 times 35, times 34, times 33, times 32, times 31, times 30, times 29, times 28 possible hands.
Now, this would be true if order mattered.
This would be true if I have card 15 here.
Maybe I have a-- let me put it here-- maybe I have a 9 of spades here, and then I have a bunch of cards. And maybe I have-- and that's one hand.
And then I have another.
So then I have cards one, two, three, four, five, six, seven, eight.
I have eight other cards.
Or maybe another hand is I have the eight cards, 1, 2, 3, 4, 5, 6, 7, 8, and then I have the 9 of spades.
If we were thinking of these as two different hands, because we have the exact same cards, but they're in different order, then what I just calculated would make a lot of sense, because we did it based on order.
But they're telling us that the cards can be sorted however the player chooses, so order doesn't matter.
So we're overcounting.
We're counting all of the different ways that the same number of cards can be arranged.
So in order to not overcount, we have to divide this by the ways in which nine cards can be rearranged.
So we have to divide this by the way nine cards can be rearranged.
So how many ways can nine cards be rearranged?
If I have nine cards and I'm going to pick one of nine to be in the first slot, well, that means I have 9 ways to put something in the first slot.
Then in the second slot, I have 8 ways of putting a card in the second slot, because I took one to put it in the first, so I have 8 left.
Then 7, then 6, then 5, then 4, then 3, then 2, then 1.
That last slot, there's only going to be 1 card left to put in it.
So this number right here, where you take 9 times 8, times 7, times 6, times 5, times 4, times 3, times 2, times 1, or 9-- you start with 9 and then you multiply it by every number less than 9.
Every, I guess we could say, natural number less than 9.
This is called 9 factorial, and you express it as an exclamation mark.
So if we want to think about all of the different ways that we can have all of the different combinations for hands, this is the number of hands if we cared about the order, but then we want to divide by the number of ways we can order things so that we don't overcount.
And this will be an answer and this will be the correct answer.
Now this is a super, super duper large number.
Let's figure out how large of a number this is.
We have 36-- let me scroll to the left a little bit-- 36 times 35, times 34, times 33, times 32, times 31, times 30, times 29, times 28, divided by 9.
Well, I can do it this way.
I can put a parentheses-- divided by parentheses, 9 times 8, times 7, times 6, times 5, times 4, times 3, times 2, times 1.
Now, hopefully the calculator can handle this.
And it gave us this number, 94,143,280.
Let me put this on the side, so I can read it.
So this number right here gives us 94,143,280.
So that's the answer for this problem.
That there are 94,143,280 possible 9 card hands in this situation.
Now, we kind of just worked through it.
We reasoned our way through it. There is a formula for this that does essentially the exact same thing.
And the way that people denote this formula is to say, look, we have 36 things and we are going to choose 9 of them.
Right?
And we don't care about order, so sometimes it'll be written as n choose k.
Let me write it this way.
So what did we do here?
We have 36 things.
We chose 9.
So this numerator over here, this was 36 factorial.
But 36 factorial would go all the way down to 27, 26, 25.
It would just keep going.
But we stopped only nine away from 36.
So this is 36 factorial, so this part right here, that part right there, is not just 36 factorial.
It's 36 factorial divided by 36, minus 9 factorial.
What is 36 minus 9?
It's 27.
So 27 factorial-- so let's think about this-- 36 factorial, it'd be 36 times 35, you keep going all the way, times 28 times 27, going all the way down to 1.
That is 36 factorial.
Now what is 36 minus 9 factorial, that's 27 factorial.
So if you divide by 27 factorial, 27 factorial is 27 times 26, all the way down to 1.
Well, this and this are the exact same thing. This is 27 times 26, so that and that would cancel out.
So if you do 36 divided by 36, minus 9 factorial, you just get the first, the largest nine terms of 36 factorial, which is exactly what we have over there.
So that is that.
And then we divided it by 9 factorial.
And this right here is called 36 choose 9.
And sometimes you'll see this formula written like this, n choose k.
And they'll write the formula as equal to n factorial over n minus k factorial, and also in the denominator, k factorial.
And this is a general formula that if you have n things, and you want to find out all of the possible ways you can pick k things from those n things, and you don't care about the order.
All you care is about which k things you picked, you don't care about the order in which you picked those k things.
So that's what we did here.
ETYMOLOGY and EXTRACTS ETYMOLOGY.
(Supplied by a Late Consumptive Usher to a Grammar School)
The pale Usher--threadbare in coat, heart, body, and brain; I see him now.
He was ever dusting his old lexicons and grammars, with a queer handkerchief, mockingly embellished with all the gay flags of all the known nations of the world.
He loved to dust his old grammars; it somehow mildly reminded him of his mortality.
"While you take in hand to school others, and to teach them by what name a whale-fish is to be called in our tongue leaving out, through ignorance, the letter H, which almost alone maketh the signification of the word, you deliver that which is not true."
--HACKLUYT
"WHALE....Sw. and Dan.
HVAL.
This animal is named from roundness or rolling; for in
Dan.
HVALT is arched or vaulted." --WEBSTER'S DlCTlONARY
"WHALE....It is more immediately from the Dut. and Ger.
WALLEN; A.S. WALW-IAN, to roll, to wallow." --RlCHARDSON'S DlCTlONARY
KETOS,GREEK.
CETUS,LATlN.
WHOEL,ANGLO-SAXON.
HVALT,DANlSH.
WAL,DUTCH.
HWAL,SWEDlSH.
WHALE,ICELANDlC.
WHALE,ENGLlSH.
BALElNE,FRENCH.
BALLENA,SPANlSH.
PEKEE-NUEE-NUEE,FEGEE.
PEKEE-NUEE-NUEE,ERROMANGOAN.
EXTRACTS (Supplied by a Sub-Sub-Librarian).
It will be seen that this mere painstaking burrower and grub-worm of a poor devil of a
Sub-Sub appears to have gone through the long Vaticans and street-stalls of the earth, picking up whatever random allusions to whales he could anyways find in any book whatsoever, sacred or profane.
Therefore you must not, in every case at least, take the higgledy-piggledy whale statements, however authentic, in these extracts, for veritable gospel cetology.
Far from it.
As touching the ancient authors generally, as well as the poets here appearing, these extracts are solely valuable or entertaining, as affording a glancing bird's eye view of what has been promiscuously said, thought, fancied, and sung of Leviathan, by many nations and generations, including our own.
So fare thee well, poor devil of a Sub-Sub, whose commentator I am.
Thou belongest to that hopeless, sallow tribe which no wine of this world will ever warm; and for whom even Pale Sherry would be too rosy-strong; but with whom one sometimes loves to sit, and feel poor- devilish, too; and grow convivial upon tears; and say to them bluntly, with full eyes and empty glasses, and in not altogether unpleasant sadness--Give it up,
Sub-Subs!
For by how much the more pains ye take to please the world, by so much the more shall ye for ever go thankless!
Would that I could clear out Hampton Court and the Tuileries for ye!
But gulp down your tears and hie aloft to the royal-mast with your hearts; for your friends who have gone before are clearing out the seven-storied heavens, and making refugees of long-pampered Gabriel, Michael, and Raphael, against your coming.
Here ye strike but splintered hearts together--there, ye shall strike unsplinterable glasses!
EXTRACTS.
"And God created great whales."
--GENESlS.
"Leviathan maketh a path to shine after him; One would think the deep to be hoary."
--JOB.
"Now the Lord had prepared a great fish to swallow up Jonah."
--JONAH.
"There go the ships; there is that Leviathan whom thou hast made to play therein." --PSALMS.
"In that day, the Lord with his sore, and great, and strong sword, shall punish
Leviathan the piercing serpent, even Leviathan that crooked serpent; and he shall slay the dragon that is in the sea."
--ISAlAH
"And what thing soever besides cometh within the chaos of this monster's mouth, be it beast, boat, or stone, down it goes all incontinently that foul great swallow of his, and perisheth in the bottomless gulf of his paunch."
--HOLLAND'S PLUTARCH'S MORALS.
"The Indian Sea breedeth the most and the biggest fishes that are: among which the
Whales and Whirlpooles called Balaene, take up as much in length as four acres or arpens of land."
--HOLLAND'S PLlNY.
"Scarcely had we proceeded two days on the sea, when about sunrise a great many Whales and other monsters of the sea, appeared.
Among the former, one was of a most monstrous size....
This came towards us, open-mouthed, raising the waves on all sides, and beating the sea before him into a foam." --TOOKE'S LUClAN.
"THE TRUE HlSTORY."
"He visited this country also with a view of catching horse-whales, which had bones of very great value for their teeth, of which he brought some to the king....
The best whales were catched in his own country, of which some were forty-eight, some fifty yards long.
He said that he was one of six who had killed sixty in two days."
--OTHER OR OTHER'S VERBAL NARRATlVE TAKEN DOWN FROM HlS MOUTH BY KlNG ALFRED, A.D. 890.
"And whereas all the other things, whether beast or vessel, that enter into the dreadful gulf of this monster's (whale's) mouth, are immediately lost and swallowed up, the sea-gudgeon retires into it in great security, and there sleeps."
--MONTAlGNE.
--APOLOGY FOR RAlMOND SEBOND.
"Let us fly, let us fly!
Old Nick take me if is not Leviathan described by the noble prophet Moses in the life of patient Job."
--RABELAlS.
"This whale's liver was two cartloads." --STOWE'S ANNALS.
"The great Leviathan that maketh the seas to seethe like boiling pan."
--LORD BACON'S VERSlON OF THE PSALMS.
"Touching that monstrous bulk of the whale or ork we have received nothing certain.
They grow exceeding fat, insomuch that an incredible quantity of oil will be extracted out of one whale."
--IBlD.
"HlSTORY OF LlFE AND DEATH."
"The sovereignest thing on earth is parmacetti for an inward bruise."
--KlNG HENRY.
"Very like a whale." --HAMLET.
"Which to secure, no skill of leach's art Mote him availle, but to returne againe
To his wound's worker, that with lowly dart
Dinting his breast, had bred his restless paine,
Like as the wounded whale to shore flies thro' the maine."
--THE FAERlE QUEEN.
"Immense as whales, the motion of whose vast bodies can in a peaceful calm trouble the ocean til it boil."
--SlR WlLLlAM DAVENANT.
PREFACE TO GONDlBERT.
"What spermacetti is, men might justly doubt, since the learned Hosmannus in his work of thirty years, saith plainly, Nescio quid sit."
--SlR T. BROWNE.
OF SPERMA CETI AND THE SPERMA CETI WHALE.
VlDE HlS V. E.
"Like Spencer's Talus with his modern flail He threatens ruin with his ponderous tail.
Their fixed jav'lins in his side he wears, And on his back a grove of pikes appears."
--WALLER'S BATTLE OF THE SUMMER ISLANDS.
"By art is created that great Leviathan, called a Commonwealth or State--(in Latin,
Civitas) which is but an artificial man." --OPENlNG SENTENCE OF HOBBES'S LEVlATHAN.
"Silly Mansoul swallowed it without chewing, as if it had been a sprat in the mouth of a whale." --PlLGRlM'S PROGRESS.
"That sea beast Leviathan, which God of all his works Created hugest that swim the ocean stream." --PARADlSE LOST.
---"There Leviathan, Hugest of living creatures, in the deep Stretched like a promontory sleeps or swims, And seems a moving land; and at his gills Draws in, and at his breath spouts out a sea."
--IBlD.
"The mighty whales which swim in a sea of water, and have a sea of oil swimming in them." --FULLLER'S PROFANE AND HOLY STATE.
"So close behind some promontory lie The huge Leviathan to attend their prey,
And give no chance, but swallow in the fry, Which through their gaping jaws mistake the way." --DRYDEN'S ANNUS MlRABlLIS.
"While the whale is floating at the stern of the ship, they cut off his head, and tow it with a boat as near the shore as it will come; but it will be aground in twelve or thirteen feet water."
--THOMAS EDGE'S TEN VOYAGES TO SPlTZBERGEN, IN PURCHAS.
"In their way they saw many whales sporting in the ocean, and in wantonness fuzzing up the water through their pipes and vents, which nature has placed on their shoulders."
--SlR T. HERBERT'S VOYAGES INTO ASlA AND AFRlCA.
HARRlS COLL.
"Here they saw such huge troops of whales, that they were forced to proceed with a great deal of caution for fear they should run their ship upon them."
--SCHOUTEN'S SlXTH ClRCUMNAVlGATlON.
"We set sail from the Elbe, wind N.E. in the ship called The Jonas-in-the-Whale....
Some say the whale can't open his mouth, but that is a fable....
They frequently climb up the masts to see whether they can see a whale, for the first discoverer has a ducat for his pains....
I was told of a whale taken near Shetland, that had above a barrel of herrings in his belly....
One of our harpooneers told me that he caught once a whale in Spitzbergen that was white all over." --A VOYAGE TO GREENLAND, A.D. 1671 HARRlS
COLL.
"Several whales have come in upon this coast (Fife) Anno 1652, one eighty feet in length of the whale-bone kind came in, which (as I was informed), besides a vast quantity of oil, did afford 500 weight of baleen.
The jaws of it stand for a gate in the garden of Pitferren."
--SlBBALD'S FlFE AND KlNROSS.
"Myself have agreed to try whether I can master and kill this Sperma-ceti whale, for
I could never hear of any of that sort that was killed by any man, such is his fierceness and swiftness."
--RlCHARD STRAFFORD'S LETTER FROM THE BERMUDAS.
PHlL.
TRANS.
A.D. 1668.
"Whales in the sea God's voice obey." --N. E. PRlMER.
"We saw also abundance of large whales, there being more in those southern seas, as
I may say, by a hundred to one; than we have to the northward of us."
--CAPTAlN COWLEY'S VOYAGE ROUND THE GLOBE, A.D. 1729. "... and the breath of the whale is frequently attended with such an insupportable smell, as to bring on a disorder of the brain."
--ULLOA'S SOUTH AMERlCA.
"To fifty chosen sylphs of special note,
We trust the important charge, the petticoat.
Oft have we known that seven-fold fence to fail,
Tho' stuffed with hoops and armed with ribs of whale."
--RAPE OF THE LOCK.
"If we compare land animals in respect to magnitude, with those that take up their abode in the deep, we shall find they will appear contemptible in the comparison.
The whale is doubtless the largest animal in creation."
--GOLDSMlTH, NAT.
HlST.
"If you should write a fable for little fishes, you would make them speak like great wales." --GOLDSMlTH TO JOHNSON.
"In the afternoon we saw what was supposed to be a rock, but it was found to be a dead whale, which some Asiatics had killed, and were then towing ashore.
They seemed to endeavor to conceal themselves behind the whale, in order to avoid being seen by us." --COOK'S VOYAGES.
"The larger whales, they seldom venture to attack.
They stand in so great dread of some of them, that when out at sea they are afraid to mention even their names, and carry dung, lime-stone, juniper-wood, and some other articles of the same nature in their boats, in order to terrify and prevent their too near approach."
--UNO VON TROlL'S LETTERS ON BANKS'S AND SOLANDER'S VOYAGE TO ICELAND IN 1772.
"The Spermacetti Whale found by the Nantuckois, is an active, fierce animal, and requires vast address and boldness in the fishermen."
--THOMAS JEFFERSON'S WHALE MEMORlAL TO THE FRENCH MlNISTER IN 1778.
"And pray, sir, what in the world is equal to it?"
--EDMUND BURKE'S REFERENCE IN PARLlAMENT TO THE NANTUCKET WHALE-FlSHERY.
"Spain--a great whale stranded on the shores of Europe."
--EDMUND BURKE.
(SOMEWHERE.)
"A tenth branch of the king's ordinary revenue, said to be grounded on the consideration of his guarding and protecting the seas from pirates and robbers, is the right to royal fish, which are whale and sturgeon.
And these, when either thrown ashore or caught near the coast, are the property of the king."
--BLACKSTONE.
"Soon to the sport of death the crews repair:
Rodmond unerring o'er his head suspends The barbed steel, and every turn attends."
--FALCONER'S SHlPWRECK.
"Bright shone the roofs, the domes, the spires,
And rockets blew self driven, To hang their momentary fire
Around the vault of heaven.
"So fire with water to compare, The ocean serves on high,
Up-spouted by a whale in air, To express unwieldy joy."
--COWPER, ON THE QUEEN'S VlSIT TO LONDON.
"Ten or fifteen gallons of blood are thrown out of the heart at a stroke, with immense velocity." --JOHN HUNTER'S ACCOUNT OF THE DlSSECTlON
OF A WHALE.
(A SMALL SlZED ONE.)
"The aorta of a whale is larger in the bore than the main pipe of the water-works at
London Bridge, and the water roaring in its passage through that pipe is inferior in impetus and velocity to the blood gushing from the whale's heart."
--PALEY'S THEOLOGY.
"The whale is a mammiferous animal without hind feet."
--BARON CUVlER.
"In 40 degrees south, we saw Spermacetti Whales, but did not take any till the first of May, the sea being then covered with them."
--COLNETT'S VOYAGE FOR THE PURPOSE OF EXTENDlNG THE SPERMACETI WHALE FlSHERY.
"In the free element beneath me swam, Floundered and dived, in play, in chace, in battle, Fishes of every colour, form, and kind;
Which language cannot paint, and mariner Had never seen; from dread Leviathan
To insect millions peopling every wave:
Gather'd in shoals immense, like floating islands,
Led by mysterious instincts through that waste
And trackless region, though on every side Assaulted by voracious enemies,
Whales, sharks, and monsters, arm'd in front or jaw,
With swords, saws, spiral horns, or hooked fangs."
--MONTGOMERY'S WORLD BEFORE THE FLOOD.
"Io!
Paean!
Io! sing.
To the finny people's king.
Not a mightier whale than this In the vast Atlantic is;
Not a fatter fish than he, Flounders round the Polar Sea."
--CHARLES LAMB'S TRlUMPH OF THE WHALE.
"In the year 1690 some persons were on a high hill observing the whales spouting and sporting with each other, when one observed: there--pointing to the sea--is a green pasture where our children's grand- children will go for bread."
--OBED MACY'S HlSTORY OF NANTUCKET.
"I built a cottage for Susan and myself and made a gateway in the form of a Gothic
Arch, by setting up a whale's jaw bones." --HAWTHORNE'S TWlCE TOLD TALES.
"She came to bespeak a monument for her first love, who had been killed by a whale in the Pacific ocean, no less than forty years ago."
--IBlD.
"No, Sir, 'tis a Right Whale," answered Tom; "I saw his sprout; he threw up a pair of as pretty rainbows as a Christian would wish to look at.
He's a raal oil-butt, that fellow!"
--COOPER'S PlLOT.
"The papers were brought in, and we saw in the Berlin Gazette that whales had been introduced on the stage there." --ECKERMANN'S CONVERSATlONS WlTH GOETHE.
I answered, "we have been stove by a whale."
Mr. Chace, what is the matter?"
--"NARRATlVE OF THE SHlPWRECK OF THE WHALE SHlP ESSEX OF NANTUCKET, WHlCH WAS ATTACKED
AND FlNALLY DESTROYED BY A LARGE SPERM WHALE IN THE PAClFIC OCEAN."
BY OWEN CHACE OF NANTUCKET, FlRST MATE OF SAlD VESSEL.
NEW YORK, 1821.
"A mariner sat in the shrouds one night, The wind was piping free;
Now bright, now dimmed, was the moonlight pale,
And the phospher gleamed in the wake of the whale,
As it floundered in the sea."
--ELlZABETH OAKES SMlTH.
"The quantity of line withdrawn from the boats engaged in the capture of this one whale, amounted altogether to 10,440 yards or nearly six English miles....
"Sometimes the whale shakes its tremendous tail in the air, which, cracking like a whip, resounds to the distance of three or four miles."
--SCORESBY.
"Mad with the agonies he endures from these fresh attacks, the infuriated Sperm Whale rolls over and over; he rears his enormous head, and with wide expanded jaws snaps at everything around him; he rushes at the boats with his head; they are propelled before him with vast swiftness, and sometimes utterly destroyed....
It is a matter of great astonishment that the consideration of the habits of so interesting, and, in a commercial point of view, so important an animal (as the Sperm
Whale) should have been so entirely neglected, or should have excited so little curiosity among the numerous, and many of them competent observers, that of late years, must have possessed the most abundant and the most convenient opportunities of witnessing their habitudes."
--THOMAS BEALE'S HlSTORY OF THE SPERM WHALE, 1839.
"The Cachalot" (Sperm Whale) "is not only better armed than the True Whale" (Greenland or Right Whale) "in possessing a formidable weapon at either extremity of its body, but also more frequently displays a disposition to employ these weapons offensively and in manner at once so artful, bold, and mischievous, as to lead to its being regarded as the most dangerous to attack of all the known species of the whale tribe."
--FREDERlCK DEBELL BENNETT'S WHALlNG VOYAGE ROUND THE GLOBE, 1840.
October 13.
"There she blows," was sung out from the mast-head.
"Where away?" demanded the captain.
"Three points off the lee bow, sir."
"Raise up your wheel.
Steady!"
"Steady, sir." "Mast-head ahoy!
Do you see that whale now?"
"Ay ay, sir!
A shoal of Sperm Whales!
There she blows!
There she breaches!"
"Sing out! sing out every time!"
"Ay Ay, sir!
There she blows! there--there--THAR she blows--bowes--bo-o-os!" "How far off?"
"Two miles and a half."
"Thunder and lightning! so near!
Call all hands."
--J. ROSS BROWNE'S ETCHlNGS OF A WHALlNG CRUlZE.
1846.
"The Whale-ship Globe, on board of which vessel occurred the horrid transactions we are about to relate, belonged to the island of Nantucket."
--"NARRATlVE OF THE GLOBE," BY LAY AND HUSSEY SURVlVORS.
A.D. 1828.
Being once pursued by a whale which he had wounded, he parried the assault for some time with a lance; but the furious monster at length rushed on the boat; himself and comrades only being preserved by leaping into the water when they saw the onset was inevitable."
--MlSSlONARY JOURNAL OF TYERMAN AND BENNETT.
"Nantucket itself," said Mr. Webster, "is a very striking and peculiar portion of the
National interest.
There is a population of eight or nine thousand persons living here in the sea, adding largely every year to the National wealth by the boldest and most persevering industry."
--REPORT OF DANlEL WEBSTER'S SPEECH IN THE U. S. SENATE, ON THE APPLlCATlON FOR THE
ERECTlON OF A BREAKWATER AT NANTUCKET.
1828.
"The whale fell directly over him, and probably killed him in a moment."
--"THE WHALE AND HlS CAPTORS, OR THE WHALEMAN'S ADVENTURES AND THE WHALE'S
BlOGRAPHY, GATHERED ON THE HOMEWARD CRUlSE OF THE COMMODORE PREBLE." BY REV.
HENRY T.
CHEEVER.
"If you make the least damn bit of noise," replied Samuel, "I will send you to hell."
--LlFE OF SAMUEL COMSTOCK (THE MUTlNEER), BY HlS BROTHER, WlLLlAM COMSTOCK.
ANOTHER VERSlON OF THE WHALE-SHlP GLOBE NARRATlVE.
"The voyages of the Dutch and English to the Northern Ocean, in order, if possible, to discover a passage through it to India, though they failed of their main object, laid-open the haunts of the whale."
--MCCULLOCH'S COMMERClAL DlCTlONARY.
"These things are reciprocal; the ball rebounds, only to bound forward again; for now in laying open the haunts of the whale, the whalemen seem to have indirectly hit upon new clews to that same mystic North- West Passage."
--FROM "SOMETHlNG" UNPUBLlSHED.
"It is impossible to meet a whale-ship on the ocean without being struck by her near appearance.
The vessel under short sail, with look-outs at the mast-heads, eagerly scanning the wide expanse around them, has a totally different air from those engaged in regular voyage."
--CURRENTS AND WHALlNG.
U.S. EX.
EX.
"Pedestrians in the vicinity of London and elsewhere may recollect having seen large curved bones set upright in the earth, either to form arches over gateways, or entrances to alcoves, and they may perhaps have been told that these were the ribs of whales."
--TALES OF A WHALE VOYAGER TO THE ARCTlC OCEAN.
"It was not till the boats returned from the pursuit of these whales, that the whites saw their ship in bloody possession of the savages enrolled among the crew."
--NEWSPAPER ACCOUNT OF THE TAKlNG AND RETAKlNG OF THE WHALE-SHlP HOBOMACK.
"It is generally well known that out of the crews of Whaling vessels (American) few ever return in the ships on board of which they departed."
--CRUlSE IN A WHALE BOAT.
"Suddenly a mighty mass emerged from the water, and shot up perpendicularly into the air.
It was the while."
--MlRIAM COFFlN OR THE WHALE FlSHERMAN.
"The Whale is harpooned to be sure; but bethink you, how you would manage a powerful unbroken colt, with the mere appliance of a rope tied to the root of his tail."
--A CHAPTER ON WHALlNG IN RlBS AND TRUCKS.
"On one occasion I saw two of these monsters (whales) probably male and female, slowly swimming, one after the other, within less than a stone's throw of the shore" (Terra Del Fuego), "over which the beech tree extended its branches."
--DARWlN'S VOYAGE OF A NATURALlST. "'Stern all!' exclaimed the mate, as upon turning his head, he saw the distended jaws of a large Sperm Whale close to the head of the boat, threatening it with instant destruction;--'Stern all, for your lives!'"
--WHARTON THE WHALE KlLLER.
"So be cheery, my lads, let your hearts never fail, While the bold harpooneer is striking the whale!" --NANTUCKET SONG.
"Oh, the rare old Whale, mid storm and gale In his ocean home will be
A giant in might, where might is right, And King of the boundless sea."
--WHALE SONG. >
-Chapter 1.
Loomings.
Call me Ishmael.
Some years ago--never mind how long precisely--having little or no money in my purse, and nothing particular to interest me on shore, I thought I would sail about a little and see the watery part of the world.
It is a way I have of driving off the spleen and regulating the circulation.
Whenever I find myself growing grim about the mouth; whenever it is a damp, drizzly
November in my soul; whenever I find myself involuntarily pausing before coffin warehouses, and bringing up the rear of every funeral I meet; and especially whenever my hypos get such an upper hand of me, that it requires a strong moral principle to prevent me from deliberately stepping into the street, and methodically knocking people's hats off--then, I account it high time to get to sea as soon as I can.
This is my substitute for pistol and ball.
With a philosophical flourish Cato throws himself upon his sword; I quietly take to the ship.
There is nothing surprising in this.
If they but knew it, almost all men in their degree, some time or other, cherish very nearly the same feelings towards the ocean with me.
There now is your insular city of the Manhattoes, belted round by wharves as
Indian isles by coral reefs--commerce surrounds it with her surf.
Right and left, the streets take you waterward.
Its extreme downtown is the battery, where that noble mole is washed by waves, and cooled by breezes, which a few hours previous were out of sight of land.
Look at the crowds of water-gazers there.
Circumambulate the city of a dreamy Sabbath afternoon.
Go from Corlears Hook to Coenties Slip, and from thence, by Whitehall, northward.
What do you see?--Posted like silent sentinels all around the town, stand thousands upon thousands of mortal men fixed in ocean reveries.
Some leaning against the spiles; some seated upon the pier-heads; some looking over the bulwarks of ships from China; some high aloft in the rigging, as if striving to get a still better seaward peep.
But these are all landsmen; of week days pent up in lath and plaster--tied to counters, nailed to benches, clinched to desks.
How then is this?
Are the green fields gone?
What do they here?
But look! here come more crowds, pacing straight for the water, and seemingly bound for a dive.
Strange! Nothing will content them but the extremest limit of the land; loitering under the shady lee of yonder warehouses will not suffice.
No. They must get just as nigh the water as they possibly can without falling in.
And there they stand--miles of them-- leagues.
Inlanders all, they come from lanes and alleys, streets and avenues--north, east, south, and west.
Yet here they all unite.
Tell me, does the magnetic virtue of the needles of the compasses of all those ships attract them thither?
Once more.
Say you are in the country; in some high land of lakes.
Take almost any path you please, and ten to one it carries you down in a dale, and leaves you there by a pool in the stream.
There is magic in it.
Let the most absent-minded of men be plunged in his deepest reveries--stand that man on his legs, set his feet a-going, and he will infallibly lead you to water, if water there be in all that region.
Should you ever be athirst in the great American desert, try this experiment, if your caravan happen to be supplied with a metaphysical professor.
Yes, as every one knows, meditation and water are wedded for ever.
But here is an artist.
He desires to paint you the dreamiest, shadiest, quietest, most enchanting bit of romantic landscape in all the valley of the Saco.
What is the chief element he employs?
There stand his trees, each with a hollow trunk, as if a hermit and a crucifix were within; and here sleeps his meadow, and there sleep his cattle; and up from yonder cottage goes a sleepy smoke.
Deep into distant woodlands winds a mazy way, reaching to overlapping spurs of mountains bathed in their hill-side blue.
But though the picture lies thus tranced, and though this pine-tree shakes down its sighs like leaves upon this shepherd's head, yet all were vain, unless the shepherd's eye were fixed upon the magic stream before him.
Go visit the Prairies in June, when for scores on scores of miles you wade knee- deep among Tiger-lilies--what is the one charm wanting?--Water--there is not a drop of water there!
Were Niagara but a cataract of sand, would you travel your thousand miles to see it?
Why did the poor poet of Tennessee, upon suddenly receiving two handfuls of silver, deliberate whether to buy him a coat, which he sadly needed, or invest his money in a pedestrian trip to Rockaway Beach?
Why is almost every robust healthy boy with a robust healthy soul in him, at some time or other crazy to go to sea?
Why upon your first voyage as a passenger, did you yourself feel such a mystical vibration, when first told that you and your ship were now out of sight of land?
Why did the old Persians hold the sea holy?
Why did the Greeks give it a separate deity, and own brother of Jove?
Surely all this is not without meaning.
And still deeper the meaning of that story of Narcissus, who because he could not grasp the tormenting, mild image he saw in the fountain, plunged into it and was drowned.
But that same image, we ourselves see in all rivers and oceans.
It is the image of the ungraspable phantom of life; and this is the key to it all.
Now, when I say that I am in the habit of going to sea whenever I begin to grow hazy about the eyes, and begin to be over conscious of my lungs, I do not mean to have it inferred that I ever go to sea as a passenger.
For to go as a passenger you must needs have a purse, and a purse is but a rag unless you have something in it.
Besides, passengers get sea-sick--grow quarrelsome--don't sleep of nights--do not enjoy themselves much, as a general thing;- -no, I never go as a passenger; nor, though
I am something of a salt, do I ever go to sea as a Commodore, or a Captain, or a Cook.
I abandon the glory and distinction of such offices to those who like them.
For my part, I abominate all honourable respectable toils, trials, and tribulations of every kind whatsoever.
It is quite as much as I can do to take care of myself, without taking care of ships, barques, brigs, schooners, and what not.
And as for going as cook,--though I confess there is considerable glory in that, a cook being a sort of officer on ship-board--yet, somehow, I never fancied broiling fowls;-- though once broiled, judiciously buttered, and judgmatically salted and peppered, there is no one who will speak more respectfully, not to say reverentially, of a broiled fowl than I will.
It is out of the idolatrous dotings of the old Egyptians upon broiled ibis and roasted river horse, that you see the mummies of those creatures in their huge bake-houses the pyramids.
No, when I go to sea, I go as a simple sailor, right before the mast, plumb down into the forecastle, aloft there to the royal mast-head.
True, they rather order me about some, and make me jump from spar to spar, like a grasshopper in a May meadow.
And at first, this sort of thing is unpleasant enough.
It touches one's sense of honour, particularly if you come of an old established family in the land, the Van Rensselaers, or Randolphs, or Hardicanutes.
And more than all, if just previous to putting your hand into the tar-pot, you have been lording it as a country schoolmaster, making the tallest boys stand in awe of you.
The transition is a keen one, I assure you, from a schoolmaster to a sailor, and requires a strong decoction of Seneca and the Stoics to enable you to grin and bear it.
But even this wears off in time.
What of it, if some old hunks of a sea- captain orders me to get a broom and sweep down the decks?
What does that indignity amount to, weighed, I mean, in the scales of the New
Testament?
Do you think the archangel Gabriel thinks anything the less of me, because I promptly and respectfully obey that old hunks in that particular instance?
Who ain't a slave?
Tell me that.
Well, then, however the old sea-captains may order me about--however they may thump and punch me about, I have the satisfaction of knowing that it is all right; that everybody else is one way or other served in much the same way--either in a physical or metaphysical point of view, that is; and so the universal thump is passed round, and all hands should rub each other's shoulder- blades, and be content.
Again, I always go to sea as a sailor, because they make a point of paying me for my trouble, whereas they never pay passengers a single penny that I ever heard of.
On the contrary, passengers themselves must pay.
And there is all the difference in the world between paying and being paid.
The act of paying is perhaps the most uncomfortable infliction that the two orchard thieves entailed upon us.
But BElNG PAlD,--what will compare with it?
The urbane activity with which a man receives money is really marvellous, considering that we so earnestly believe money to be the root of all earthly ills, and that on no account can a monied man enter heaven.
Ah! how cheerfully we consign ourselves to perdition!
Finally, I always go to sea as a sailor, because of the wholesome exercise and pure air of the fore-castle deck.
For as in this world, head winds are far more prevalent than winds from astern (that is, if you never violate the Pythagorean maxim), so for the most part the Commodore on the quarter-deck gets his atmosphere at second hand from the sailors on the forecastle.
He thinks he breathes it first; but not so.
In much the same way do the commonalty lead their leaders in many other things, at the same time that the leaders little suspect it.
But wherefore it was that after having repeatedly smelt the sea as a merchant sailor, I should now take it into my head to go on a whaling voyage; this the invisible police officer of the Fates, who has the constant surveillance of me, and secretly dogs me, and influences me in some unaccountable way--he can better answer than any one else.
And, doubtless, my going on this whaling voyage, formed part of the grand programme of Providence that was drawn up a long time ago.
It came in as a sort of brief interlude and solo between more extensive performances.
I take it that this part of the bill must have run something like this:
"GRAND CONTESTED ELECTlON FOR THE PRESlDENCY OF THE UNlTED STATES.
"WHALlNG VOYAGE BY ONE ISHMAEL.
"BLOODY BATTLE IN AFFGHANlSTAN."
Though I cannot tell why it was exactly that those stage managers, the Fates, put me down for this shabby part of a whaling voyage, when others were set down for magnificent parts in high tragedies, and short and easy parts in genteel comedies, and jolly parts in farces--though I cannot tell why this was exactly; yet, now that I recall all the circumstances, I think I can see a little into the springs and motives which being cunningly presented to me under various disguises, induced me to set about performing the part I did, besides cajoling me into the delusion that it was a choice resulting from my own unbiased freewill and discriminating judgment.
Chief among these motives was the overwhelming idea of the great whale himself.
Such a portentous and mysterious monster roused all my curiosity.
Then the wild and distant seas where he rolled his island bulk; the undeliverable, nameless perils of the whale; these, with all the attending marvels of a thousand
Patagonian sights and sounds, helped to sway me to my wish.
With other men, perhaps, such things would not have been inducements; but as for me,
I am tormented with an everlasting itch for things remote.
I love to sail forbidden seas, and land on barbarous coasts.
Not ignoring what is good, I am quick to perceive a horror, and could still be social with it--would they let me--since it is but well to be on friendly terms with all the inmates of the place one lodges in.
By reason of these things, then, the whaling voyage was welcome; the great flood-gates of the wonder-world swung open, and in the wild conceits that swayed me to my purpose, two and two there floated into my inmost soul, endless processions of the whale, and, mid most of them all, one grand hooded phantom, like a snow hill in the air.
Chapter 2.
The Carpet-Bag.
I stuffed a shirt or two into my old carpet-bag, tucked it under my arm, and started for Cape Horn and the Pacific.
Quitting the good city of old Manhatto, I duly arrived in New Bedford.
It was a Saturday night in December.
Much was I disappointed upon learning that the little packet for Nantucket had already sailed, and that no way of reaching that place would offer, till the following
Monday.
As most young candidates for the pains and penalties of whaling stop at this same New
Bedford, thence to embark on their voyage, it may as well be related that I, for one, had no idea of so doing. For my mind was made up to sail in no other than a Nantucket craft, because there was a fine, boisterous something about everything connected with that famous old island, which amazingly pleased me.
Besides though New Bedford has of late been gradually monopolising the business of whaling, and though in this matter poor old Nantucket is now much behind her, yet
Nantucket was her great original--the Tyre of this Carthage;--the place where the first dead American whale was stranded.
Where else but from Nantucket did those aboriginal whalemen, the Red-Men, first sally out in canoes to give chase to the Leviathan?
And where but from Nantucket, too, did that first adventurous little sloop put forth, partly laden with imported cobblestones--so goes the story--to throw at the whales, in order to discover when they were nigh enough to risk a harpoon from the bowsprit?
Now having a night, a day, and still another night following before me in New
Bedford, ere I could embark for my destined port, it became a matter of concernment where I was to eat and sleep meanwhile.
It was a very dubious-looking, nay, a very dark and dismal night, bitingly cold and cheerless.
I knew no one in the place.
With anxious grapnels I had sounded my pocket, and only brought up a few pieces of silver,--So, wherever you go, Ishmael, said I to myself, as I stood in the middle of a dreary street shouldering my bag, and comparing the gloom towards the north with the darkness towards the south--wherever in your wisdom you may conclude to lodge for the night, my dear Ishmael, be sure to inquire the price, and don't be too particular.
With halting steps I paced the streets, and passed the sign of "The Crossed Harpoons"-- but it looked too expensive and jolly there.
Further on, from the bright red windows of the "Sword-Fish Inn," there came such fervent rays, that it seemed to have melted the packed snow and ice from before the house, for everywhere else the congealed frost lay ten inches thick in a hard, asphaltic pavement,--rather weary for me, when I struck my foot against the flinty projections, because from hard, remorseless service the soles of my boots were in a most miserable plight.
Too expensive and jolly, again thought I, pausing one moment to watch the broad glare in the street, and hear the sounds of the tinkling glasses within.
But go on, Ishmael, said I at last; don't you hear? get away from before the door; your patched boots are stopping the way.
So on I went.
I now by instinct followed the streets that took me waterward, for there, doubtless, were the cheapest, if not the cheeriest inns.
Such dreary streets! blocks of blackness, not houses, on either hand, and here and there a candle, like a candle moving about in a tomb.
At this hour of the night, of the last day of the week, that quarter of the town proved all but deserted.
But presently I came to a smoky light proceeding from a low, wide building, the door of which stood invitingly open.
It had a careless look, as if it were meant for the uses of the public; so, entering, the first thing I did was to stumble over an ash-box in the porch.
Ha! thought I, ha, as the flying particles almost choked me, are these ashes from that destroyed city, Gomorrah?
But "The Crossed Harpoons," and "The Sword- Fish?"--this, then must needs be the sign of "The Trap."
However, I picked myself up and hearing a loud voice within, pushed on and opened a second, interior door.
It seemed the great Black Parliament sitting in Tophet.
A hundred black faces turned round in their rows to peer; and beyond, a black Angel of
Doom was beating a book in a pulpit.
It was a negro church; and the preacher's text was about the blackness of darkness, and the weeping and wailing and teeth- gnashing there.
Ha, Ishmael, muttered I, backing out, Wretched entertainment at the sign of 'The
Trap!'
Moving on, I at last came to a dim sort of light not far from the docks, and heard a forlorn creaking in the air; and looking up, saw a swinging sign over the door with a white painting upon it, faintly representing a tall straight jet of misty spray, and these words underneath--"The
Spouter Inn:--Peter Coffin."
Coffin?--Spouter?--Rather ominous in that particular connexion, thought I.
But it is a common name in Nantucket, they say, and I suppose this Peter here is an emigrant from there.
As the light looked so dim, and the place, for the time, looked quiet enough, and the dilapidated little wooden house itself looked as if it might have been carted here from the ruins of some burnt district, and as the swinging sign had a poverty-stricken sort of creak to it, I thought that here was the very spot for cheap lodgings, and the best of pea coffee.
It was a queer sort of place--a gable-ended old house, one side palsied as it were, and leaning over sadly.
It stood on a sharp bleak corner, where that tempestuous wind Euroclydon kept up a worse howling than ever it did about poor Paul's tossed craft.
Euroclydon, nevertheless, is a mighty pleasant zephyr to any one in-doors, with his feet on the hob quietly toasting for bed.
"In judging of that tempestuous wind called Euroclydon," says an old writer--of whose works I possess the only copy extant--"it maketh a marvellous difference, whether thou lookest out at it from a glass window where the frost is all on the outside, or whether thou observest it from that sashless window, where the frost is on both sides, and of which the wight Death is the only glazier."
True enough, thought I, as this passage occurred to my mind--old black-letter, thou reasonest well.
Yes, these eyes are windows, and this body of mine is the house.
What a pity they didn't stop up the chinks and the crannies though, and thrust in a
little lint here and there.
But it's too late to make any improvements now.
The universe is finished; the copestone is on, and the chips were carted off a million years ago.
Poor Lazarus there, chattering his teeth against the curbstone for his pillow, and shaking off his tatters with his shiverings, he might plug up both ears with rags, and put a corn-cob into his mouth, and yet that would not keep out the tempestuous Euroclydon.
Euroclydon! says old Dives, in his red silken wrapper--(he had a redder one afterwards) pooh, pooh!
What a fine frosty night; how Orion glitters; what northern lights!
Let them talk of their oriental summer climes of everlasting conservatories; give me the privilege of making my own summer with my own coals.
But what thinks Lazarus?
Can he warm his blue hands by holding them up to the grand northern lights?
Would not Lazarus rather be in Sumatra than here?
Would he not far rather lay him down lengthwise along the line of the equator; yea, ye gods! go down to the fiery pit itself, in order to keep out this frost?
Now, that Lazarus should lie stranded there on the curbstone before the door of Dives, this is more wonderful than that an iceberg should be moored to one of the Moluccas.
Yet Dives himself, he too lives like a Czar in an ice palace made of frozen sighs, and being a president of a temperance society, he only drinks the tepid tears of orphans.
But no more of this blubbering now, we are going a-whaling, and there is plenty of that yet to come.
Let us scrape the ice from our frosted feet, and see what sort of a place this
"Spouter" may be. >
-Chapter 3.
The Spouter-Inn.
Entering that gable-ended Spouter-Inn, you found yourself in a wide, low, straggling entry with old-fashioned wainscots, reminding one of the bulwarks of some condemned old craft.
On one side hung a very large oilpainting so thoroughly besmoked, and every way defaced, that in the unequal crosslights by which you viewed it, it was only by diligent study and a series of systematic visits to it, and careful inquiry of the neighbors, that you could any way arrive at an understanding of its purpose.
Such unaccountable masses of shades and shadows, that at first you almost thought some ambitious young artist, in the time of the New England hags, had endeavored to delineate chaos bewitched.
But by dint of much and earnest contemplation, and oft repeated ponderings, and especially by throwing open the little window towards the back of the entry, you at last come to the conclusion that such an idea, however wild, might not be altogether unwarranted.
But what most puzzled and confounded you was a long, limber, portentous, black mass of something hovering in the centre of the picture over three blue, dim, perpendicular lines floating in a nameless yeast.
A boggy, soggy, squitchy picture truly, enough to drive a nervous man distracted.
Yet was there a sort of indefinite, half- attained, unimaginable sublimity about it that fairly froze you to it, till you involuntarily took an oath with yourself to find out what that marvellous painting meant.
Ever and anon a bright, but, alas, deceptive idea would dart you through.--
It's the Black Sea in a midnight gale.-- It's the unnatural combat of the four primal elements.--It's a blasted heath.--
It's a Hyperborean winter scene.--It's the breaking-up of the icebound stream of Time.
But at last all these fancies yielded to that one portentous something in the picture's midst.
THAT once found out, and all the rest were plain.
But stop; does it not bear a faint resemblance to a gigantic fish? even the great leviathan himself?
In fact, the artist's design seemed this: a final theory of my own, partly based upon the aggregated opinions of many aged persons with whom I conversed upon the subject.
The picture represents a Cape-Horner in a great hurricane; the half-foundered ship weltering there with its three dismantled masts alone visible; and an exasperated whale, purposing to spring clean over the craft, is in the enormous act of impaling himself upon the three mast-heads.
The opposite wall of this entry was hung all over with a heathenish array of monstrous clubs and spears.
Some were thickly set with glittering teeth resembling ivory saws; others were tufted with knots of human hair; and one was sickle-shaped, with a vast handle sweeping round like the segment made in the new-mown grass by a long-armed mower.
You shuddered as you gazed, and wondered what monstrous cannibal and savage could ever have gone a death-harvesting with such a hacking, horrifying implement.
Mixed with these were rusty old whaling lances and harpoons all broken and deformed.
Some were storied weapons.
With this once long lance, now wildly elbowed, fifty years ago did Nathan Swain kill fifteen whales between a sunrise and a sunset.
And that harpoon--so like a corkscrew now-- was flung in Javan seas, and run away with by a whale, years afterwards slain off the Cape of Blanco.
The original iron entered nigh the tail, and, like a restless needle sojourning in the body of a man, travelled full forty feet, and at last was found imbedded in the hump.
Crossing this dusky entry, and on through yon low-arched way--cut through what in old times must have been a great central chimney with fireplaces all round--you enter the public room.
A still duskier place is this, with such low ponderous beams above, and such old wrinkled planks beneath, that you would almost fancy you trod some old craft's cockpits, especially of such a howling night, when this corner-anchored old ark rocked so furiously.
On one side stood a long, low, shelf-like table covered with cracked glass cases, filled with dusty rarities gathered from this wide world's remotest nooks.
Projecting from the further angle of the room stands a dark-looking den--the bar--a rude attempt at a right whale's head.
Be that how it may, there stands the vast arched bone of the whale's jaw, so wide, a coach might almost drive beneath it.
Within are shabby shelves, ranged round with old decanters, bottles, flasks; and in those jaws of swift destruction, like another cursed Jonah (by which name indeed they called him), bustles a little withered old man, who, for their money, dearly sells the sailors deliriums and death.
Abominable are the tumblers into which he pours his poison.
Though true cylinders without--within, the villanous green goggling glasses deceitfully tapered downwards to a cheating bottom.
Parallel meridians rudely pecked into the glass, surround these footpads' goblets.
Fill to THlS mark, and your charge is but a penny; to THlS a penny more; and so on to the full glass--the Cape Horn measure, which you may gulp down for a shilling.
Upon entering the place I found a number of young seamen gathered about a table, examining by a dim light divers specimens of SKRlMSHANDER.
I sought the landlord, and telling him I desired to be accommodated with a room, received for answer that his house was full--not a bed unoccupied.
"But avast," he added, tapping his forehead, "you haint no objections to sharing a harpooneer's blanket, have ye?
I s'pose you are goin' a-whalin', so you'd better get used to that sort of thing."
I told him that I never liked to sleep two in a bed; that if I should ever do so, it would depend upon who the harpooneer might be, and that if he (the landlord) really had no other place for me, and the harpooneer was not decidedly objectionable, why rather than wander further about a strange town on so bitter a night, I would put up with the half of any decent man's blanket.
"I thought so.
All right; take a seat.
Supper?--you want supper?
Supper'll be ready directly."
I sat down on an old wooden settle, carved all over like a bench on the Battery.
At one end a ruminating tar was still further adorning it with his jack-knife, stooping over and diligently working away at the space between his legs.
He was trying his hand at a ship under full sail, but he didn't make much headway, I thought.
At last some four or five of us were summoned to our meal in an adjoining room.
It was cold as Iceland--no fire at all--the landlord said he couldn't afford it.
Nothing but two dismal tallow candles, each in a winding sheet.
We were fain to button up our monkey jackets, and hold to our lips cups of scalding tea with our half frozen fingers.
But the fare was of the most substantial kind--not only meat and potatoes, but dumplings; good heavens! dumplings for supper!
One young fellow in a green box coat, addressed himself to these dumplings in a most direful manner.
"My boy," said the landlord, "you'll have the nightmare to a dead sartainty."
"Landlord," I whispered, "that aint the harpooneer is it?"
"Oh, no," said he, looking a sort of diabolically funny, "the harpooneer is a dark complexioned chap.
He never eats dumplings, he don't--he eats nothing but steaks, and he likes 'em rare."
"The devil he does," says I. "Where is that harpooneer?
Is he here?"
"He'll be here afore long," was the answer.
I could not help it, but I began to feel suspicious of this "dark complexioned" harpooneer.
At any rate, I made up my mind that if it so turned out that we should sleep together, he must undress and get into bed before I did.
Supper over, the company went back to the bar-room, when, knowing not what else to do with myself, I resolved to spend the rest of the evening as a looker on.
Presently a rioting noise was heard without.
Starting up, the landlord cried, "That's the Grampus's crew.
I seed her reported in the offing this morning; a three years' voyage, and a full ship. Hurrah, boys; now we'll have the latest news from the Feegees."
A tramping of sea boots was heard in the entry; the door was flung open, and in rolled a wild set of mariners enough.
Enveloped in their shaggy watch coats, and with their heads muffled in woollen comforters, all bedarned and ragged, and their beards stiff with icicles, they seemed an eruption of bears from Labrador.
They had just landed from their boat, and this was the first house they entered.
No wonder, then, that they made a straight wake for the whale's mouth--the bar--when the wrinkled little old Jonah, there officiating, soon poured them out brimmers all round.
One complained of a bad cold in his head, upon which Jonah mixed him a pitch-like potion of gin and molasses, which he swore was a sovereign cure for all colds and catarrhs whatsoever, never mind of how long standing, or whether caught off the coast of Labrador, or on the weather side of an ice-island.
The liquor soon mounted into their heads, as it generally does even with the arrantest topers newly landed from sea, and they began capering about most obstreperously.
I observed, however, that one of them held somewhat aloof, and though he seemed desirous not to spoil the hilarity of his shipmates by his own sober face, yet upon the whole he refrained from making as much noise as the rest.
This man interested me at once; and since the sea-gods had ordained that he should soon become my shipmate (though but a sleeping-partner one, so far as this narrative is concerned), I will here venture upon a little description of him.
He stood full six feet in height, with noble shoulders, and a chest like a coffer- dam.
I have seldom seen such brawn in a man.
His face was deeply brown and burnt, making his white teeth dazzling by the contrast; while in the deep shadows of his eyes floated some reminiscences that did not seem to give him much joy.
His voice at once announced that he was a Southerner, and from his fine stature, I thought he must be one of those tall mountaineers from the Alleghanian Ridge in
Virginia.
When the revelry of his companions had mounted to its height, this man slipped away unobserved, and I saw no more of him till he became my comrade on the sea.
In a few minutes, however, he was missed by his shipmates, and being, it seems, for some reason a huge favourite with them, they raised a cry of "Bulkington!
Bulkington! where's Bulkington?" and darted out of the house in pursuit of him.
It was now about nine o'clock, and the room seeming almost supernaturally quiet after these orgies, I began to congratulate myself upon a little plan that had occurred to me just previous to the entrance of the seamen.
No man prefers to sleep two in a bed.
In fact, you would a good deal rather not sleep with your own brother.
I don't know how it is, but people like to be private when they are sleeping.
And when it comes to sleeping with an unknown stranger, in a strange inn, in a strange town, and that stranger a harpooneer, then your objections indefinitely multiply.
Nor was there any earthly reason why I as a sailor should sleep two in a bed, more than anybody else; for sailors no more sleep two in a bed at sea, than bachelor Kings do ashore.
To be sure they all sleep together in one apartment, but you have your own hammock, and cover yourself with your own blanket, and sleep in your own skin.
The more I pondered over this harpooneer, the more I abominated the thought of sleeping with him.
It was fair to presume that being a harpooneer, his linen or woollen, as the case might be, would not be of the tidiest, certainly none of the finest.
I began to twitch all over.
Besides, it was getting late, and my decent harpooneer ought to be home and going bedwards.
Suppose now, he should tumble in upon me at midnight--how could I tell from what vile hole he had been coming?
"Landlord!
I've changed my mind about that harpooneer.--I shan't sleep with him.
I'll try the bench here."
"Just as you please; I'm sorry I cant spare ye a tablecloth for a mattress, and it's a plaguy rough board here"--feeling of the knots and notches.
"But wait a bit, Skrimshander; I've got a carpenter's plane there in the bar--wait,
I say, and I'll make ye snug enough."
So saying he procured the plane; and with his old silk handkerchief first dusting the bench, vigorously set to planing away at my bed, the while grinning like an ape.
The shavings flew right and left; till at last the plane-iron came bump against an indestructible knot.
The landlord was near spraining his wrist, and I told him for heaven's sake to quit-- the bed was soft enough to suit me, and I did not know how all the planing in the world could make eider down of a pine plank.
So gathering up the shavings with another grin, and throwing them into the great stove in the middle of the room, he went about his business, and left me in a brown study.
I now took the measure of the bench, and found that it was a foot too short; but that could be mended with a chair.
But it was a foot too narrow, and the other bench in the room was about four inches higher than the planed one--so there was no yoking them.
I then placed the first bench lengthwise along the only clear space against the wall, leaving a little interval between, for my back to settle down in.
But I soon found that there came such a draught of cold air over me from under the sill of the window, that this plan would never do at all, especially as another current from the rickety door met the one from the window, and both together formed a series of small whirlwinds in the immediate vicinity of the spot where I had thought to spend the night.
The devil fetch that harpooneer, thought I, but stop, couldn't I steal a march on him-- bolt his door inside, and jump into his bed, not to be wakened by the most violent knockings?
It seemed no bad idea; but upon second thoughts I dismissed it.
For who could tell but what the next morning, so soon as I popped out of the room, the harpooneer might be standing in the entry, all ready to knock me down!
Still, looking round me again, and seeing no possible chance of spending a sufferable night unless in some other person's bed, I began to think that after all I might be cherishing unwarrantable prejudices against this unknown harpooneer.
Thinks I, I'll wait awhile; he must be dropping in before long.
I'll have a good look at him then, and perhaps we may become jolly good bedfellows after all--there's no telling.
But though the other boarders kept coming in by ones, twos, and threes, and going to bed, yet no sign of my harpooneer.
"Landlord!" said I, "what sort of a chap is he--does he always keep such late hours?"
It was now hard upon twelve o'clock.
The landlord chuckled again with his lean chuckle, and seemed to be mightily tickled at something beyond my comprehension.
"No," he answered, "generally he's an early bird--airley to bed and airley to rise-- yes, he's the bird what catches the worm.
But to-night he went out a peddling, you see, and I don't see what on airth keeps him so late, unless, may be, he can't sell his head."
"Can't sell his head?--What sort of a bamboozingly story is this you are telling me?" getting into a towering rage.
"Do you pretend to say, landlord, that this harpooneer is actually engaged this blessed
Saturday night, or rather Sunday morning, in peddling his head around this town?"
"That's precisely it," said the landlord, "and I told him he couldn't sell it here, the market's overstocked." "With what?" shouted I.
"With heads to be sure; ain't there too many heads in the world?"
"I tell you what it is, landlord," said I quite calmly, "you'd better stop spinning that yarn to me--I'm not green."
"May be not," taking out a stick and whittling a toothpick, "but I rayther guess you'll be done BROWN if that ere harpooneer hears you a slanderin' his head."
"I'll break it for him," said I, now flying into a passion again at this unaccountable farrago of the landlord's.
"It's broke a'ready," said he.
"Broke," said I--"BROKE, do you mean?"
"Sartain, and that's the very reason he can't sell it, I guess."
"Landlord," said I, going up to him as cool as Mt.
Hecla in a snow-storm--"landlord, stop whittling.
You and I must understand one another, and that too without delay.
I come to your house and want a bed; you tell me you can only give me half a one; that the other half belongs to a certain harpooneer.
And about this harpooneer, whom I have not yet seen, you persist in telling me the most mystifying and exasperating stories tending to beget in me an uncomfortable feeling towards the man whom you design for my bedfellow--a sort of connexion, landlord, which is an intimate and confidential one in the highest degree.
I now demand of you to speak out and tell me who and what this harpooneer is, and whether I shall be in all respects safe to spend the night with him.
And in the first place, you will be so good as to unsay that story about selling his head, which if true I take to be good evidence that this harpooneer is stark mad, and I've no idea of sleeping with a madman; and you, sir, YOU I mean, landlord, YOU, sir, by trying to induce me to do so knowingly, would thereby render yourself liable to a criminal prosecution."
"Wall," said the landlord, fetching a long breath, "that's a purty long sarmon for a chap that rips a little now and then.
But be easy, be easy, this here harpooneer I have been tellin' you of has just arrived from the south seas, where he bought up a lot of 'balmed New Zealand heads (great curios, you know), and he's sold all on 'em but one, and that one he's trying to sell to-night, cause to-morrow's Sunday, and it would not do to be sellin' human heads about the streets when folks is goin' to churches.
He wanted to, last Sunday, but I stopped him just as he was goin' out of the door with four heads strung on a string, for all the airth like a string of inions."
This account cleared up the otherwise unaccountable mystery, and showed that the landlord, after all, had had no idea of fooling me--but at the same time what could
I think of a harpooneer who stayed out of a
Saturday night clean into the holy Sabbath, engaged in such a cannibal business as selling the heads of dead idolators?
"Depend upon it, landlord, that harpooneer is a dangerous man."
"He pays reg'lar," was the rejoinder.
"But come, it's getting dreadful late, you had better be turning flukes--it's a nice bed; Sal and me slept in that ere bed the night we were spliced.
There's plenty of room for two to kick about in that bed; it's an almighty big bed that.
Why, afore we give it up, Sal used to put our Sam and little Johnny in the foot of it.
But I got a dreaming and sprawling about one night, and somehow, Sam got pitched on the floor, and came near breaking his arm.
Arter that, Sal said it wouldn't do.
Come along here, I'll give ye a glim in a jiffy;" and so saying he lighted a candle and held it towards me, offering to lead the way.
But I stood irresolute; when looking at a clock in the corner, he exclaimed "I vum it's Sunday--you won't see that harpooneer to-night; he's come to anchor somewhere-- come along then; DO come; WON'T ye come?"
I considered the matter a moment, and then up stairs we went, and I was ushered into a small room, cold as a clam, and furnished, sure enough, with a prodigious bed, almost big enough indeed for any four harpooneers to sleep abreast.
"There," said the landlord, placing the candle on a crazy old sea chest that did double duty as a wash-stand and centre table; "there, make yourself comfortable now, and good night to ye."
I turned round from eyeing the bed, but he had disappeared.
Folding back the counterpane, I stooped over the bed.
Though none of the most elegant, it yet stood the scrutiny tolerably well.
I then glanced round the room; and besides the bedstead and centre table, could see no other furniture belonging to the place, but a rude shelf, the four walls, and a papered fireboard representing a man striking a whale.
Of things not properly belonging to the room, there was a hammock lashed up, and thrown upon the floor in one corner; also a large seaman's bag, containing the harpooneer's wardrobe, no doubt in lieu of a land trunk.
Likewise, there was a parcel of outlandish bone fish hooks on the shelf over the fire- place, and a tall harpoon standing at the head of the bed.
But what is this on the chest?
I took it up, and held it close to the light, and felt it, and smelt it, and tried every way possible to arrive at some satisfactory conclusion concerning it.
I can compare it to nothing but a large door mat, ornamented at the edges with little tinkling tags something like the stained porcupine quills round an Indian moccasin.
There was a hole or slit in the middle of this mat, as you see the same in South
American ponchos.
But could it be possible that any sober harpooneer would get into a door mat, and parade the streets of any Christian town in that sort of guise?
I put it on, to try it, and it weighed me down like a hamper, being uncommonly shaggy and thick, and I thought a little damp, as though this mysterious harpooneer had been wearing it of a rainy day.
I went up in it to a bit of glass stuck against the wall, and I never saw such a sight in my life.
I tore myself out of it in such a hurry that I gave myself a kink in the neck.
I sat down on the side of the bed, and commenced thinking about this head-peddling harpooneer, and his door mat.
After thinking some time on the bed-side, I got up and took off my monkey jacket, and then stood in the middle of the room thinking.
I then took off my coat, and thought a little more in my shirt sleeves.
But beginning to feel very cold now, half undressed as I was, and remembering what the landlord said about the harpooneer's not coming home at all that night, it being so very late, I made no more ado, but jumped out of my pantaloons and boots, and then blowing out the light tumbled into bed, and commended myself to the care of heaven.
Whether that mattress was stuffed with corn-cobs or broken crockery, there is no telling, but I rolled about a good deal, and could not sleep for a long time.
At last I slid off into a light doze, and had pretty nearly made a good offing towards the land of Nod, when I heard a heavy footfall in the passage, and saw a glimmer of light come into the room from under the door.
Lord save me, thinks I, that must be the harpooneer, the infernal head-peddler.
But I lay perfectly still, and resolved not to say a word till spoken to.
Holding a light in one hand, and that identical New Zealand head in the other, the stranger entered the room, and without looking towards the bed, placed his candle a good way off from me on the floor in one corner, and then began working away at the knotted cords of the large bag I before spoke of as being in the room.
I was all eagerness to see his face, but he kept it averted for some time while employed in unlacing the bag's mouth.
This accomplished, however, he turned round--when, good heavens! what a sight!
Such a face!
It was of a dark, purplish, yellow colour, here and there stuck over with large blackish looking squares.
Yes, it's just as I thought, he's a terrible bedfellow; he's been in a fight, got dreadfully cut, and here he is, just from the surgeon.
But at that moment he chanced to turn his face so towards the light, that I plainly saw they could not be sticking-plasters at all, those black squares on his cheeks.
They were stains of some sort or other.
At first I knew not what to make of this; but soon an inkling of the truth occurred to me.
I remembered a story of a white man--a whaleman too--who, falling among the cannibals, had been tattooed by them.
I concluded that this harpooneer, in the course of his distant voyages, must have met with a similar adventure.
And what is it, thought I, after all!
It's only his outside; a man can be honest in any sort of skin.
But then, what to make of his unearthly complexion, that part of it, I mean, lying round about, and completely independent of the squares of tattooing.
To be sure, it might be nothing but a good coat of tropical tanning; but I never heard of a hot sun's tanning a white man into a purplish yellow one.
However, I had never been in the South Seas; and perhaps the sun there produced these extraordinary effects upon the skin.
Now, while all these ideas were passing through me like lightning, this harpooneer never noticed me at all.
But, after some difficulty having opened his bag, he commenced fumbling in it, and presently pulled out a sort of tomahawk, and a seal-skin wallet with the hair on.
Placing these on the old chest in the middle of the room, he then took the New
Zealand head--a ghastly thing enough--and crammed it down into the bag.
He now took off his hat--a new beaver hat-- when I came nigh singing out with fresh surprise.
There was no hair on his head--none to speak of at least--nothing but a small scalp-knot twisted up on his forehead.
His bald purplish head now looked for all the world like a mildewed skull.
Had not the stranger stood between me and the door, I would have bolted out of it quicker than ever I bolted a dinner.
Even as it was, I thought something of slipping out of the window, but it was the second floor back.
I am no coward, but what to make of this head-peddling purple rascal altogether passed my comprehension.
Ignorance is the parent of fear, and being completely nonplussed and confounded about the stranger, I confess I was now as much afraid of him as if it was the devil himself who had thus broken into my room at the dead of night.
In fact, I was so afraid of him that I was not game enough just then to address him, and demand a satisfactory answer concerning what seemed inexplicable in him.
Meanwhile, he continued the business of undressing, and at last showed his chest and arms.
As I live, these covered parts of him were checkered with the same squares as his face; his back, too, was all over the same dark squares; he seemed to have been in a
Thirty Years' War, and just escaped from it with a sticking-plaster shirt.
Still more, his very legs were marked, as if a parcel of dark green frogs were running up the trunks of young palms.
It was now quite plain that he must be some abominable savage or other shipped aboard of a whaleman in the South Seas, and so landed in this Christian country.
I quaked to think of it.
A peddler of heads too--perhaps the heads of his own brothers.
He might take a fancy to mine--heavens! look at that tomahawk!
But there was no time for shuddering, for now the savage went about something that completely fascinated my attention, and convinced me that he must indeed be a heathen.
Going to his heavy grego, or wrapall, or dreadnaught, which he had previously hung on a chair, he fumbled in the pockets, and produced at length a curious little deformed image with a hunch on its back, and exactly the colour of a three days' old Congo baby.
Remembering the embalmed head, at first I almost thought that this black manikin was a real baby preserved in some similar manner.
But seeing that it was not at all limber, and that it glistened a good deal like polished ebony, I concluded that it must be nothing but a wooden idol, which indeed it proved to be.
For now the savage goes up to the empty fire-place, and removing the papered fire- board, sets up this little hunch-backed image, like a tenpin, between the andirons.
The chimney jambs and all the bricks inside were very sooty, so that I thought this fire-place made a very appropriate little shrine or chapel for his Congo idol.
I now screwed my eyes hard towards the half hidden image, feeling but ill at ease meantime--to see what was next to follow.
First he takes about a double handful of shavings out of his grego pocket, and places them carefully before the idol; then laying a bit of ship biscuit on top and applying the flame from the lamp, he kindled the shavings into a sacrificial blaze.
Presently, after many hasty snatches into the fire, and still hastier withdrawals of his fingers (whereby he seemed to be scorching them badly), he at last succeeded in drawing out the biscuit; then blowing off the heat and ashes a little, he made a polite offer of it to the little negro.
But the little devil did not seem to fancy such dry sort of fare at all; he never moved his lips.
All these strange antics were accompanied by still stranger guttural noises from the devotee, who seemed to be praying in a sing-song or else singing some pagan psalmody or other, during which his face twitched about in the most unnatural manner.
At last extinguishing the fire, he took the idol up very unceremoniously, and bagged it again in his grego pocket as carelessly as if he were a sportsman bagging a dead woodcock.
All these queer proceedings increased my uncomfortableness, and seeing him now exhibiting strong symptoms of concluding his business operations, and jumping into bed with me, I thought it was high time, now or never, before the light was put out, to break the spell in which I had so long been bound.
But the interval I spent in deliberating what to say, was a fatal one.
Taking up his tomahawk from the table, he examined the head of it for an instant, and then holding it to the light, with his mouth at the handle, he puffed out great clouds of tobacco smoke.
The next moment the light was extinguished, and this wild cannibal, tomahawk between his teeth, sprang into bed with me.
I sang out, I could not help it now; and giving a sudden grunt of astonishment he began feeling me.
Stammering out something, I knew not what, I rolled away from him against the wall, and then conjured him, whoever or whatever he might be, to keep quiet, and let me get up and light the lamp again.
But his guttural responses satisfied me at once that he but ill comprehended my meaning.
"Who-e debel you?"--he at last said--"you no speak-e, dam-me, I kill-e."
And so saying the lighted tomahawk began flourishing about me in the dark.
"Landlord, for God's sake, Peter Coffin!" shouted I.
"Landlord!
Watch!
Coffin! Angels! save me!"
"Speak-e! tell-ee me who-ee be, or dam-me, I kill-e!" again growled the cannibal, while his horrid flourishings of the tomahawk scattered the hot tobacco ashes about me till I thought my linen would get on fire.
But thank heaven, at that moment the landlord came into the room light in hand, and leaping from the bed I ran up to him.
"Don't be afraid now," said he, grinning again, "Queequeg here wouldn't harm a hair of your head."
"Stop your grinning," shouted I, "and why didn't you tell me that that infernal harpooneer was a cannibal?"
"I thought ye know'd it;--didn't I tell ye, he was a peddlin' heads around town?--but turn flukes again and go to sleep.
Queequeg, look here--you sabbee me, I sabbee--you this man sleepe you--you sabbee?"
"Me sabbee plenty"--grunted Queequeg, puffing away at his pipe and sitting up in bed.
"You gettee in," he added, motioning to me with his tomahawk, and throwing the clothes to one side.
He really did this in not only a civil but a really kind and charitable way.
I stood looking at him a moment.
For all his tattooings he was on the whole a clean, comely looking cannibal.
What's all this fuss I have been making about, thought I to myself--the man's a human being just as I am: he has just as much reason to fear me, as I have to be afraid of him.
Better sleep with a sober cannibal than a drunken Christian.
"Landlord," said I, "tell him to stash his tomahawk there, or pipe, or whatever you call it; tell him to stop smoking, in short, and I will turn in with him.
But I don't fancy having a man smoking in bed with me.
It's dangerous.
Besides, I ain't insured."
This being told to Queequeg, he at once complied, and again politely motioned me to get into bed--rolling over to one side as much as to say--"I won't touch a leg of ye."
"Good night, landlord," said I, "you may go."
I turned in, and never slept better in my life. >
-Chapter 4.
The Counterpane.
Upon waking next morning about daylight, I found Queequeg's arm thrown over me in the most loving and affectionate manner.
You had almost thought I had been his wife.
The counterpane was of patchwork, full of odd little parti-coloured squares and triangles; and this arm of his tattooed all over with an interminable Cretan labyrinth of a figure, no two parts of which were of one precise shade--owing I suppose to his keeping his arm at sea unmethodically in sun and shade, his shirt sleeves irregularly rolled up at various times-- this same arm of his, I say, looked for all the world like a strip of that same patchwork quilt.
Indeed, partly lying on it as the arm did when I first awoke, I could hardly tell it from the quilt, they so blended their hues together; and it was only by the sense of weight and pressure that I could tell that Queequeg was hugging me.
My sensations were strange.
Let me try to explain them.
When I was a child, I well remember a somewhat similar circumstance that befell me; whether it was a reality or a dream, I never could entirely settle.
The circumstance was this.
I had been cutting up some caper or other-- I think it was trying to crawl up the chimney, as I had seen a little sweep do a few days previous; and my stepmother who, somehow or other, was all the time whipping me, or sending me to bed supperless,--my mother dragged me by the legs out of the chimney and packed me off to bed, though it was only two o'clock in the afternoon of the 21st June, the longest day in the year in our hemisphere.
I felt dreadfully.
But there was no help for it, so up stairs I went to my little room in the third floor, undressed myself as slowly as possible so as to kill time, and with a bitter sigh got between the sheets.
I lay there dismally calculating that sixteen entire hours must elapse before I could hope for a resurrection.
Sixteen hours in bed! the small of my back ached to think of it.
And it was so light too; the sun shining in at the window, and a great rattling of coaches in the streets, and the sound of gay voices all over the house.
I felt worse and worse--at last I got up, dressed, and softly going down in my stockinged feet, sought out my stepmother, and suddenly threw myself at her feet, beseeching her as a particular favour to give me a good slippering for my misbehaviour; anything indeed but condemning me to lie abed such an unendurable length of time.
But she was the best and most conscientious of stepmothers, and back I had to go to my room.
For several hours I lay there broad awake, feeling a great deal worse than I have ever done since, even from the greatest subsequent misfortunes.
At last I must have fallen into a troubled nightmare of a doze; and slowly waking from it--half steeped in dreams--I opened my eyes, and the before sun-lit room was now wrapped in outer darkness.
Instantly I felt a shock running through all my frame; nothing was to be seen, and nothing was to be heard; but a supernatural hand seemed placed in mine.
My arm hung over the counterpane, and the nameless, unimaginable, silent form or phantom, to which the hand belonged, seemed closely seated by my bed-side.
For what seemed ages piled on ages, I lay there, frozen with the most awful fears, not daring to drag away my hand; yet ever thinking that if I could but stir it one single inch, the horrid spell would be broken.
I knew not how this consciousness at last glided away from me; but waking in the morning, I shudderingly remembered it all, and for days and weeks and months afterwards I lost myself in confounding attempts to explain the mystery.
Nay, to this very hour, I often puzzle myself with it.
Now, take away the awful fear, and my sensations at feeling the supernatural hand in mine were very similar, in their strangeness, to those which I experienced on waking up and seeing Queequeg's pagan arm thrown round me.
But at length all the past night's events soberly recurred, one by one, in fixed reality, and then I lay only alive to the comical predicament.
For though I tried to move his arm--unlock his bridegroom clasp--yet, sleeping as he was, he still hugged me tightly, as though naught but death should part us twain.
I now strove to rouse him--"Queequeg!"--but his only answer was a snore.
I then rolled over, my neck feeling as if it were in a horse-collar; and suddenly felt a slight scratch.
Throwing aside the counterpane, there lay the tomahawk sleeping by the savage's side, as if it were a hatchet-faced baby.
A pretty pickle, truly, thought I; abed here in a strange house in the broad day, with a cannibal and a tomahawk!
"Queequeg!--in the name of goodness,
Queequeg, wake!"
At length, by dint of much wriggling, and loud and incessant expostulations upon the unbecomingness of his hugging a fellow male in that matrimonial sort of style, I succeeded in extracting a grunt; and presently, he drew back his arm, shook himself all over like a Newfoundland dog just from the water, and sat up in bed, stiff as a pike-staff, looking at me, and rubbing his eyes as if he did not altogether remember how I came to be there, though a dim consciousness of knowing something about me seemed slowly dawning over him.
Meanwhile, I lay quietly eyeing him, having no serious misgivings now, and bent upon narrowly observing so curious a creature.
When, at last, his mind seemed made up touching the character of his bedfellow, and he became, as it were, reconciled to the fact; he jumped out upon the floor, and by certain signs and sounds gave me to understand that, if it pleased me, he would dress first and then leave me to dress afterwards, leaving the whole apartment to myself.
Thinks I, Queequeg, under the circumstances, this is a very civilized overture; but, the truth is, these savages have an innate sense of delicacy, say what you will; it is marvellous how essentially polite they are.
I pay this particular compliment to Queequeg, because he treated me with so much civility and consideration, while I was guilty of great rudeness; staring at him from the bed, and watching all his toilette motions; for the time my curiosity getting the better of my breeding.
Nevertheless, a man like Queequeg you don't see every day, he and his ways were well worth unusual regarding.
He commenced dressing at top by donning his beaver hat, a very tall one, by the by, and then--still minus his trowsers--he hunted up his boots.
What under the heavens he did it for, I cannot tell, but his next movement was to crush himself--boots in hand, and hat on-- under the bed; when, from sundry violent gaspings and strainings, I inferred he was hard at work booting himself; though by no law of propriety that I ever heard of, is any man required to be private when putting on his boots.
But Queequeg, do you see, was a creature in the transition stage--neither caterpillar nor butterfly.
He was just enough civilized to show off his outlandishness in the strangest possible manners.
His education was not yet completed.
He was an undergraduate.
If he had not been a small degree civilized, he very probably would not have troubled himself with boots at all; but then, if he had not been still a savage, he never would have dreamt of getting under the bed to put them on.
At last, he emerged with his hat very much dented and crushed down over his eyes, and began creaking and limping about the room, as if, not being much accustomed to boots, his pair of damp, wrinkled cowhide ones-- probably not made to order either--rather pinched and tormented him at the first go off of a bitter cold morning.
Seeing, now, that there were no curtains to the window, and that the street being very narrow, the house opposite commanded a plain view into the room, and observing more and more the indecorous figure that
Queequeg made, staving about with little else but his hat and boots on; I begged him as well as I could, to accelerate his toilet somewhat, and particularly to get into his pantaloons as soon as possible.
He complied, and then proceeded to wash himself.
At that time in the morning any Christian would have washed his face; but Queequeg, to my amazement, contented himself with restricting his ablutions to his chest, arms, and hands.
He then donned his waistcoat, and taking up a piece of hard soap on the wash-stand centre table, dipped it into water and commenced lathering his face.
I was watching to see where he kept his razor, when lo and behold, he takes the harpoon from the bed corner, slips out the long wooden stock, unsheathes the head, whets it a little on his boot, and striding up to the bit of mirror against the wall, begins a vigorous scraping, or rather harpooning of his cheeks.
Thinks I, Queequeg, this is using Rogers's best cutlery with a vengeance.
Afterwards I wondered the less at this operation when I came to know of what fine steel the head of a harpoon is made, and how exceedingly sharp the long straight edges are always kept.
The rest of his toilet was soon achieved, and he proudly marched out of the room, wrapped up in his great pilot monkey jacket, and sporting his harpoon like a marshal's baton.
Chapter 5.
Breakfast.
I quickly followed suit, and descending into the bar-room accosted the grinning landlord very pleasantly.
I cherished no malice towards him, though he had been skylarking with me not a little in the matter of my bedfellow.
However, a good laugh is a mighty good thing, and rather too scarce a good thing; the more's the pity.
So, if any one man, in his own proper person, afford stuff for a good joke to anybody, let him not be backward, but let him cheerfully allow himself to spend and be spent in that way.
And the man that has anything bountifully laughable about him, be sure there is more in that man than you perhaps think for.
The bar-room was now full of the boarders who had been dropping in the night previous, and whom I had not as yet had a good look at.
They were nearly all whalemen; chief mates, and second mates, and third mates, and sea carpenters, and sea coopers, and sea blacksmiths, and harpooneers, and ship keepers; a brown and brawny company, with bosky beards; an unshorn, shaggy set, all wearing monkey jackets for morning gowns.
You could pretty plainly tell how long each one had been ashore.
This young fellow's healthy cheek is like a sun-toasted pear in hue, and would seem to smell almost as musky; he cannot have been three days landed from his Indian voyage.
That man next him looks a few shades lighter; you might say a touch of satin wood is in him.
In the complexion of a third still lingers a tropic tawn, but slightly bleached withal; HE doubtless has tarried whole weeks ashore.
But who could show a cheek like Queequeg? which, barred with various tints, seemed like the Andes' western slope, to show forth in one array, contrasting climates, zone by zone.
"Grub, ho!" now cried the landlord, flinging open a door, and in we went to breakfast.
They say that men who have seen the world, thereby become quite at ease in manner, quite self-possessed in company.
Not always, though:
Ledyard, the great New England traveller, and Mungo Park, the
Scotch one; of all men, they possessed the least assurance in the parlor.
But perhaps the mere crossing of Siberia in a sledge drawn by dogs as Ledyard did, or the taking a long solitary walk on an empty stomach, in the negro heart of Africa, which was the sum of poor Mungo's performances--this kind of travel, I say, may not be the very best mode of attaining a high social polish.
Still, for the most part, that sort of thing is to be had anywhere.
These reflections just here are occasioned by the circumstance that after we were all seated at the table, and I was preparing to hear some good stories about whaling; to my no small surprise, nearly every man maintained a profound silence.
And not only that, but they looked embarrassed.
Yes, here were a set of sea-dogs, many of whom without the slightest bashfulness had boarded great whales on the high seas-- entire strangers to them--and duelled them dead without winking; and yet, here they sat at a social breakfast table--all of the same calling, all of kindred tastes-- looking round as sheepishly at each other as though they had never been out of sight of some sheepfold among the Green Mountains.
A curious sight; these bashful bears, these timid warrior whalemen!
But as for Queequeg--why, Queequeg sat there among them--at the head of the table, too, it so chanced; as cool as an icicle. To be sure I cannot say much for his breeding.
His greatest admirer could not have cordially justified his bringing his harpoon into breakfast with him, and using it there without ceremony; reaching over the table with it, to the imminent jeopardy of many heads, and grappling the beefsteaks towards him.
But THAT was certainly very coolly done by him, and every one knows that in most people's estimation, to do anything coolly is to do it genteelly.
We will not speak of all Queequeg's peculiarities here; how he eschewed coffee and hot rolls, and applied his undivided attention to beefsteaks, done rare.
Enough, that when breakfast was over he withdrew like the rest into the public room, lighted his tomahawk-pipe, and was sitting there quietly digesting and smoking with his inseparable hat on, when I sallied out for a stroll.
Chapter 6.
The Street.
If I had been astonished at first catching a glimpse of so outlandish an individual as
Queequeg circulating among the polite society of a civilized town, that astonishment soon departed upon taking my first daylight stroll through the streets of New Bedford.
In thoroughfares nigh the docks, any considerable seaport will frequently offer to view the queerest looking nondescripts from foreign parts.
Even in Broadway and Chestnut streets, Mediterranean mariners will sometimes jostle the affrighted ladies.
Regent Street is not unknown to Lascars and Malays; and at Bombay, in the Apollo Green,
live Yankees have often scared the natives.
But New Bedford beats all Water Street and
Wapping.
In these last-mentioned haunts you see only sailors; but in New Bedford, actual cannibals stand chatting at street corners; savages outright; many of whom yet carry on their bones unholy flesh.
It makes a stranger stare.
But, besides the Feegeeans, Tongatobooarrs, Erromanggoans, Pannangians, and
Brighggians, and, besides the wild specimens of the whaling-craft which unheeded reel about the streets, you will see other sights still more curious, certainly more comical.
There weekly arrive in this town scores of green Vermonters and New Hampshire men, all athirst for gain and glory in the fishery.
They are mostly young, of stalwart frames; fellows who have felled forests, and now seek to drop the axe and snatch the whale- lance.
Many are as green as the Green Mountains whence they came.
In some things you would think them but a few hours old.
Look there! that chap strutting round the corner.
He wears a beaver hat and swallow-tailed coat, girdled with a sailor-belt and sheath-knife.
Here comes another with a sou'-wester and a bombazine cloak.
No town-bred dandy will compare with a country-bred one--I mean a downright bumpkin dandy--a fellow that, in the dog- days, will mow his two acres in buckskin gloves for fear of tanning his hands.
Now when a country dandy like this takes it into his head to make a distinguished reputation, and joins the great whale- fishery, you should see the comical things he does upon reaching the seaport.
In bespeaking his sea-outfit, he orders bell-buttons to his waistcoats; straps to his canvas trowsers.
Ah, poor Hay-Seed! how bitterly will burst those straps in the first howling gale, when thou art driven, straps, buttons, and all, down the throat of the tempest.
But think not that this famous town has only harpooneers, cannibals, and bumpkins to show her visitors.
Not at all.
Still New Bedford is a queer place.
Had it not been for us whalemen, that tract of land would this day perhaps have been in as howling condition as the coast of Labrador.
As it is, parts of her back country are enough to frighten one, they look so bony.
The town itself is perhaps the dearest place to live in, in all New England.
It is a land of oil, true enough: but not like Canaan; a land, also, of corn and wine.
The streets do not run with milk; nor in the spring-time do they pave them with fresh eggs.
Yet, in spite of this, nowhere in all America will you find more patrician-like houses; parks and gardens more opulent, than in New Bedford.
Whence came they? how planted upon this once scraggy scoria of a country?
Go and gaze upon the iron emblematical harpoons round yonder lofty mansion, and your question will be answered.
Yes; all these brave houses and flowery gardens came from the Atlantic, Pacific, and Indian oceans.
One and all, they were harpooned and dragged up hither from the bottom of the sea. Can Herr Alexander perform a feat like that?
In New Bedford, fathers, they say, give whales for dowers to their daughters, and portion off their nieces with a few porpoises a-piece.
You must go to New Bedford to see a brilliant wedding; for, they say, they have reservoirs of oil in every house, and every night recklessly burn their lengths in spermaceti candles.
In summer time, the town is sweet to see; full of fine maples--long avenues of green and gold.
And in August, high in air, the beautiful and bountiful horse-chestnuts, candelabra- wise, proffer the passer-by their tapering upright cones of congregated blossoms.
So omnipotent is art; which in many a district of New Bedford has superinduced bright terraces of flowers upon the barren refuse rocks thrown aside at creation's final day.
And the women of New Bedford, they bloom like their own red roses.
But roses only bloom in summer; whereas the fine carnation of their cheeks is perennial as sunlight in the seventh heavens.
Elsewhere match that bloom of theirs, ye cannot, save in Salem, where they tell me the young girls breathe such musk, their sailor sweethearts smell them miles off shore, as though they were drawing nigh the odorous Moluccas instead of the Puritanic sands.
Chapter 7.
The Chapel.
In this same New Bedford there stands a Whaleman's Chapel, and few are the moody fishermen, shortly bound for the Indian Ocean or Pacific, who fail to make a Sunday visit to the spot.
I am sure that I did not.
Returning from my first morning stroll, I again sallied out upon this special errand.
The sky had changed from clear, sunny cold, to driving sleet and mist.
Wrapping myself in my shaggy jacket of the cloth called bearskin, I fought my way against the stubborn storm.
Entering, I found a small scattered congregation of sailors, and sailors' wives and widows.
A muffled silence reigned, only broken at times by the shrieks of the storm.
Each silent worshipper seemed purposely sitting apart from the other, as if each silent grief were insular and incommunicable.
The chaplain had not yet arrived; and there these silent islands of men and women sat steadfastly eyeing several marble tablets, with black borders, masoned into the wall on either side the pulpit.
Three of them ran something like the following, but I do not pretend to quote:--
SACRED TO THE MEMORY OF JOHN TALBOT, Who, at the age of eighteen, was lost overboard,
Near the Isle of Desolation, off Patagonia, November 1st, 1836.
THlS TABLET Is erected to his Memory BY HlS SlSTER.
SACRED TO THE MEMORY OF ROBERT LONG, WlLLlS ELLERY, NATHAN COLEMAN, WALTER CANNY, SETH
MACY, AND SAMUEL GLElG, Forming one of the boats' crews OF THE SHlP ELlZA Who were towed out of sight by a Whale, On the Off- shore Ground in the PAClFIC, December 31st, 1839.
THlS MARBLE Is here placed by their surviving SHlPMATES.
SACRED TO THE MEMORY OF The late CAPTAlN EZEKlEL HARDY, Who in the bows of his boat was killed by a Sperm Whale on the coast of Japan, AUGUST 3d, 1833.
THlS TABLET Is erected to his Memory BY HlS WlDOW.
Shaking off the sleet from my ice-glazed hat and jacket, I seated myself near the door, and turning sideways was surprised to see Queequeg near me.
Affected by the solemnity of the scene, there was a wondering gaze of incredulous curiosity in his countenance.
This savage was the only person present who seemed to notice my entrance; because he was the only one who could not read, and, therefore, was not reading those frigid inscriptions on the wall.
Whether any of the relatives of the seamen whose names appeared there were now among the congregation, I knew not; but so many are the unrecorded accidents in the fishery, and so plainly did several women present wear the countenance if not the trappings of some unceasing grief, that I feel sure that here before me were assembled those, in whose unhealing hearts the sight of those bleak tablets sympathetically caused the old wounds to bleed afresh.
Oh! ye whose dead lie buried beneath the green grass; who standing among flowers can say--here, HERE lies my beloved; ye know not the desolation that broods in bosoms like these.
What bitter blanks in those black-bordered marbles which cover no ashes!
What despair in those immovable inscriptions!
What deadly voids and unbidden infidelities in the lines that seem to gnaw upon all
Faith, and refuse resurrections to the beings who have placelessly perished without a grave.
As well might those tablets stand in the cave of Elephanta as here.
In what census of living creatures, the dead of mankind are included; why it is that a universal proverb says of them, that they tell no tales, though containing more secrets than the Goodwin Sands; how it is that to his name who yesterday departed for the other world, we prefix so significant and infidel a word, and yet do not thus entitle him, if he but embarks for the remotest Indies of this living earth; why the Life Insurance Companies pay death- forfeitures upon immortals; in what eternal, unstirring paralysis, and deadly, hopeless trance, yet lies antique Adam who died sixty round centuries ago; how it is that we still refuse to be comforted for those who we nevertheless maintain are dwelling in unspeakable bliss; why all the living so strive to hush all the dead; wherefore but the rumor of a knocking in a tomb will terrify a whole city.
All these things are not without their meanings.
But Faith, like a jackal, feeds among the tombs, and even from these dead doubts she gathers her most vital hope.
It needs scarcely to be told, with what feelings, on the eve of a Nantucket voyage,
I regarded those marble tablets, and by the murky light of that darkened, doleful day read the fate of the whalemen who had gone before me.
Yes, Ishmael, the same fate may be thine.
But somehow I grew merry again.
Delightful inducements to embark, fine chance for promotion, it seems--aye, a stove boat will make me an immortal by brevet.
Yes, there is death in this business of whaling--a speechlessly quick chaotic bundling of a man into Eternity.
But what then?
Methinks we have hugely mistaken this matter of Life and Death.
Methinks that what they call my shadow here on earth is my true substance.
Methinks that in looking at things spiritual, we are too much like oysters observing the sun through the water, and thinking that thick water the thinnest of air.
Methinks my body is but the lees of my better being.
In fact take my body who will, take it I say, it is not me.
And therefore three cheers for Nantucket; and come a stove boat and stove body when they will, for stave my soul, Jove himself cannot. >
-Chapter 8.
The Pulpit.
I had not been seated very long ere a man of a certain venerable robustness entered; immediately as the storm-pelted door flew back upon admitting him, a quick regardful eyeing of him by all the congregation, sufficiently attested that this fine old man was the chaplain.
Yes, it was the famous Father Mapple, so called by the whalemen, among whom he was a very great favourite.
He had been a sailor and a harpooneer in his youth, but for many years past had dedicated his life to the ministry.
At the time I now write of, Father Mapple was in the hardy winter of a healthy old age; that sort of old age which seems merging into a second flowering youth, for among all the fissures of his wrinkles, there shone certain mild gleams of a newly developing bloom--the spring verdure peeping forth even beneath February's snow.
No one having previously heard his history, could for the first time behold Father
Mapple without the utmost interest, because there were certain engrafted clerical peculiarities about him, imputable to that adventurous maritime life he had led.
When he entered I observed that he carried no umbrella, and certainly had not come in his carriage, for his tarpaulin hat ran down with melting sleet, and his great pilot cloth jacket seemed almost to drag him to the floor with the weight of the water it had absorbed.
However, hat and coat and overshoes were one by one removed, and hung up in a little space in an adjacent corner; when, arrayed in a decent suit, he quietly approached the pulpit.
Like most old fashioned pulpits, it was a very lofty one, and since a regular stairs to such a height would, by its long angle with the floor, seriously contract the already small area of the chapel, the architect, it seemed, had acted upon the hint of Father Mapple, and finished the pulpit without a stairs, substituting a perpendicular side ladder, like those used in mounting a ship from a boat at sea.
The wife of a whaling captain had provided the chapel with a handsome pair of red worsted man-ropes for this ladder, which, being itself nicely headed, and stained with a mahogany colour, the whole contrivance, considering what manner of chapel it was, seemed by no means in bad taste.
Halting for an instant at the foot of the ladder, and with both hands grasping the ornamental knobs of the man-ropes, Father Mapple cast a look upwards, and then with a truly sailor-like but still reverential dexterity, hand over hand, mounted the steps as if ascending the main-top of his vessel.
The perpendicular parts of this side ladder, as is usually the case with swinging ones, were of cloth-covered rope, only the rounds were of wood, so that at every step there was a joint.
At my first glimpse of the pulpit, it had not escaped me that however convenient for a ship, these joints in the present instance seemed unnecessary.
For I was not prepared to see Father Mapple after gaining the height, slowly turn round, and stooping over the pulpit, deliberately drag up the ladder step by step, till the whole was deposited within,
I pondered some time without fully comprehending the reason for this.
Father Mapple enjoyed such a wide reputation for sincerity and sanctity, that
I could not suspect him of courting notoriety by any mere tricks of the stage.
No, thought I, there must be some sober reason for this thing; furthermore, it must symbolize something unseen.
Can it be, then, that by that act of physical isolation, he signifies his spiritual withdrawal for the time, from all outward worldly ties and connexions?
Yes, for replenished with the meat and wine of the word, to the faithful man of God, this pulpit, I see, is a self-containing stronghold--a lofty Ehrenbreitstein, with a perennial well of water within the walls.
But the side ladder was not the only strange feature of the place, borrowed from the chaplain's former sea-farings.
Between the marble cenotaphs on either hand of the pulpit, the wall which formed its back was adorned with a large painting representing a gallant ship beating against a terrible storm off a lee coast of black rocks and snowy breakers.
But high above the flying scud and dark- rolling clouds, there floated a little isle of sunlight, from which beamed forth an angel's face; and this bright face shed a distinct spot of radiance upon the ship's tossed deck, something like that silver plate now inserted into the Victory's plank where Nelson fell.
"Ah, noble ship," the angel seemed to say, "beat on, beat on, thou noble ship, and bear a hardy helm; for lo! the sun is breaking through; the clouds are rolling off--serenest azure is at hand."
Nor was the pulpit itself without a trace of the same sea-taste that had achieved the ladder and the picture.
Its panelled front was in the likeness of a ship's bluff bows, and the Holy Bible rested on a projecting piece of scroll work, fashioned after a ship's fiddle- headed beak.
What could be more full of meaning?--for the pulpit is ever this earth's foremost part; all the rest comes in its rear; the pulpit leads the world.
From thence it is the storm of God's quick wrath is first descried, and the bow must bear the earliest brunt.
From thence it is the God of breezes fair or foul is first invoked for favourable winds.
Yes, the world's a ship on its passage out, and not a voyage complete; and the pulpit is its prow.
Chapter 9.
The Sermon.
Father Mapple rose, and in a mild voice of unassuming authority ordered the scattered people to condense.
"Starboard gangway, there! side away to
larboard--larboard gangway to starboard!
Midships! midships!"
There was a low rumbling of heavy sea-boots among the benches, and a still slighter shuffling of women's shoes, and all was quiet again, and every eye on the preacher.
He paused a little; then kneeling in the pulpit's bows, folded his large brown hands across his chest, uplifted his closed eyes, and offered a prayer so deeply devout that he seemed kneeling and praying at the bottom of the sea.
This ended, in prolonged solemn tones, like the continual tolling of a bell in a ship that is foundering at sea in a fog--in such tones he commenced reading the following hymn; but changing his manner towards the concluding stanzas, burst forth with a pealing exultation and joy--
"The ribs and terrors in the whale, Arched over me a dismal gloom,
While all God's sun-lit waves rolled by, And lift me deepening down to doom.
"I saw the opening maw of hell, With endless pains and sorrows there;
Which none but they that feel can tell-- Oh, I was plunging to despair.
"In black distress, I called my God, When I could scarce believe him mine,
He bowed his ear to my complaints-- No more the whale did me confine.
"With speed he flew to my relief, As on a radiant dolphin borne;
Awful, yet bright, as lightning shone The face of my Deliverer God.
"My song for ever shall record That terrible, that joyful hour;
I give the glory to my God, His all the mercy and the power."
Nearly all joined in singing this hymn, which swelled high above the howling of the storm.
A brief pause ensued; the preacher slowly turned over the leaves of the Bible, and at last, folding his hand down upon the proper page, said: "Beloved shipmates, clinch the
'And God had prepared a great fish to swallow up Jonah.'"
"Shipmates, this book, containing only four chapters--four yarns--is one of the smallest strands in the mighty cable of the Scriptures.
Yet what depths of the soul does Jonah's deep sealine sound! what a pregnant lesson to us is this prophet!
What a noble thing is that canticle in the fish's belly!
How billow-like and boisterously grand!
We feel the floods surging over us; we sound with him to the kelpy bottom of the waters; sea-weed and all the slime of the sea is about us!
But WHAT is this lesson that the book of Jonah teaches?
Shipmates, it is a two-stranded lesson; a lesson to us all as sinful men, and a lesson to me as a pilot of the living God.
As sinful men, it is a lesson to us all, because it is a story of the sin, hard- heartedness, suddenly awakened fears, the swift punishment, repentance, prayers, and finally the deliverance and joy of Jonah.
As with all sinners among men, the sin of this son of Amittai was in his wilful disobedience of the command of God--never mind now what that command was, or how conveyed--which he found a hard command.
But all the things that God would have us do are hard for us to do--remember that-- and hence, he oftener commands us than endeavors to persuade.
And if we obey God, we must disobey ourselves; and it is in this disobeying ourselves, wherein the hardness of obeying God consists.
"With this sin of disobedience in him, Jonah still further flouts at God, by seeking to flee from Him.
He thinks that a ship made by men will carry him into countries where God does not reign, but only the Captains of this earth.
He skulks about the wharves of Joppa, and seeks a ship that's bound for Tarshish.
There lurks, perhaps, a hitherto unheeded meaning here.
By all accounts Tarshish could have been no other city than the modern Cadiz.
That's the opinion of learned men.
And where is Cadiz, shipmates?
Cadiz is in Spain; as far by water, from
Joppa, as Jonah could possibly have sailed in those ancient days, when the Atlantic was an almost unknown sea.
Because Joppa, the modern Jaffa, shipmates, is on the most easterly coast of the
Mediterranean, the Syrian; and Tarshish or Cadiz more than two thousand miles to the westward from that, just outside the Straits of Gibraltar.
See ye not then, shipmates, that Jonah sought to flee world-wide from God?
Miserable man!
Oh! most contemptible and worthy of all scorn; with slouched hat and guilty eye, skulking from his God; prowling among the shipping like a vile burglar hastening to cross the seas.
So disordered, self-condemning is his look, that had there been policemen in those days, Jonah, on the mere suspicion of something wrong, had been arrested ere he touched a deck.
How plainly he's a fugitive! no baggage, not a hat-box, valise, or carpet-bag,--no friends accompany him to the wharf with their adieux.
At last, after much dodging search, he finds the Tarshish ship receiving the last items of her cargo; and as he steps on board to see its Captain in the cabin, all the sailors for the moment desist from hoisting in the goods, to mark the stranger's evil eye.
Jonah sees this; but in vain he tries to look all ease and confidence; in vain essays his wretched smile.
Strong intuitions of the man assure the mariners he can be no innocent.
In their gamesome but still serious way, one whispers to the other--"Jack, he's robbed a widow;" or, "Joe, do you mark him; he's a bigamist;" or, "Harry lad, I guess he's the adulterer that broke jail in old
Gomorrah, or belike, one of the missing murderers from Sodom."
Another runs to read the bill that's stuck against the spile upon the wharf to which the ship is moored, offering five hundred gold coins for the apprehension of a parricide, and containing a description of his person.
He reads, and looks from Jonah to the bill; while all his sympathetic shipmates now crowd round Jonah, prepared to lay their hands upon him.
Frighted Jonah trembles, and summoning all his boldness to his face, only looks so much the more a coward.
He will not confess himself suspected; but that itself is strong suspicion.
So he makes the best of it; and when the sailors find him not to be the man that is advertised, they let him pass, and he descends into the cabin. "'Who's there?' cries the Captain at his busy desk, hurriedly making out his papers for the Customs--'Who's there?'
Oh! how that harmless question mangles
Jonah!
For the instant he almost turns to flee again.
'I seek a passage in this ship to Tarshish; how soon sail ye, sir?'
Thus far the busy Captain had not looked up to Jonah, though the man now stands before him; but no sooner does he hear that hollow voice, than he darts a scrutinizing glance.
'We sail with the next coming tide,' at last he slowly answered, still intently eyeing him.
'No sooner, sir?'--'Soon enough for any honest man that goes a passenger.'
Ha!
Jonah, that's another stab.
But he swiftly calls away the Captain from that scent.
'I'll sail with ye,'--he says,--'the passage money how much is that?--I'll pay now.'
For it is particularly written, shipmates, as if it were a thing not to be overlooked in this history, 'that he paid the fare thereof' ere the craft did sail.
And taken with the context, this is full of meaning.
"Now Jonah's Captain, shipmates, was one whose discernment detects crime in any, but whose cupidity exposes it only in the penniless.
In this world, shipmates, sin that pays its way can travel freely, and without a passport; whereas Virtue, if a pauper, is stopped at all frontiers.
So Jonah's Captain prepares to test the length of Jonah's purse, ere he judge him openly.
He charges him thrice the usual sum; and it's assented to.
Then the Captain knows that Jonah is a fugitive; but at the same time resolves to help a flight that paves its rear with gold.
Yet when Jonah fairly takes out his purse, prudent suspicions still molest the
Captain.
He rings every coin to find a counterfeit.
Not a forger, any way, he mutters; and Jonah is put down for his passage.
'Point out my state-room, Sir,' says Jonah now, 'I'm travel-weary; I need sleep.'
'Thou lookest like it,' says the Captain, 'there's thy room.'
Jonah enters, and would lock the door, but the lock contains no key.
Hearing him foolishly fumbling there, the Captain laughs lowly to himself, and mutters something about the doors of convicts' cells being never allowed to be locked within.
All dressed and dusty as he is, Jonah throws himself into his berth, and finds the little state-room ceiling almost resting on his forehead.
The air is close, and Jonah gasps.
Then, in that contracted hole, sunk, too, beneath the ship's water-line, Jonah feels the heralding presentiment of that stifling hour, when the whale shall hold him in the smallest of his bowels' wards.
"Screwed at its axis against the side, a swinging lamp slightly oscillates in
Jonah's room; and the ship, heeling over towards the wharf with the weight of the
last bales received, the lamp, flame and all, though in slight motion, still maintains a permanent obliquity with reference to the room; though, in truth, infallibly straight itself, it but made obvious the false, lying levels among which it hung.
The lamp alarms and frightens Jonah; as lying in his berth his tormented eyes roll round the place, and this thus far successful fugitive finds no refuge for his restless glance.
But that contradiction in the lamp more and more appals him.
The floor, the ceiling, and the side, are all awry.
'Oh! so my conscience hangs in me!' he groans, 'straight upwards, so it burns; but the chambers of my soul are all in crookedness!'
"Like one who after a night of drunken revelry hies to his bed, still reeling, but with conscience yet pricking him, as the plungings of the Roman race-horse but so much the more strike his steel tags into him; as one who in that miserable plight still turns and turns in giddy anguish, praying God for annihilation until the fit be passed; and at last amid the whirl of woe he feels, a deep stupor steals over him, as over the man who bleeds to death, for conscience is the wound, and there's naught to staunch it; so, after sore wrestlings in his berth, Jonah's prodigy of ponderous misery drags him drowning down to sleep.
"And now the time of tide has come; the ship casts off her cables; and from the deserted wharf the uncheered ship for Tarshish, all careening, glides to sea.
That ship, my friends, was the first of recorded smugglers! the contraband was
Jonah.
But the sea rebels; he will not bear the wicked burden.
A dreadful storm comes on, the ship is like to break.
But now when the boatswain calls all hands to lighten her; when boxes, bales, and jars are clattering overboard; when the wind is shrieking, and the men are yelling, and every plank thunders with trampling feet right over Jonah's head; in all this raging tumult, Jonah sleeps his hideous sleep.
He sees no black sky and raging sea, feels not the reeling timbers, and little hears he or heeds he the far rush of the mighty whale, which even now with open mouth is cleaving the seas after him.
Aye, shipmates, Jonah was gone down into the sides of the ship--a berth in the cabin as I have taken it, and was fast asleep.
But the frightened master comes to him, and shrieks in his dead ear, 'What meanest thou, O, sleeper! arise!'
Startled from his lethargy by that direful cry, Jonah staggers to his feet, and stumbling to the deck, grasps a shroud, to look out upon the sea.
But at that moment he is sprung upon by a panther billow leaping over the bulwarks.
Wave after wave thus leaps into the ship, and finding no speedy vent runs roaring fore and aft, till the mariners come nigh to drowning while yet afloat.
And ever, as the white moon shows her affrighted face from the steep gullies in the blackness overhead, aghast Jonah sees the rearing bowsprit pointing high upward, but soon beat downward again towards the tormented deep.
"Terrors upon terrors run shouting through his soul.
In all his cringing attitudes, the God- fugitive is now too plainly known.
The sailors mark him; more and more certain grow their suspicions of him, and at last, fully to test the truth, by referring the whole matter to high Heaven, they fall to casting lots, to see for whose cause this great tempest was upon them.
The lot is Jonah's; that discovered, then how furiously they mob him with their questions.
'What is thine occupation?
Whence comest thou?
Thy country?
What people?
But mark now, my shipmates, the behavior of poor Jonah.
The eager mariners but ask him who he is, and where from; whereas, they not only receive an answer to those questions, but likewise another answer to a question not put by them, but the unsolicited answer is forced from Jonah by the hard hand of God that is upon him. "'I am a Hebrew,' he cries--and then--'I fear the Lord the God of Heaven who hath made the sea and the dry land!'
Fear him, O Jonah?
Aye, well mightest thou fear the Lord God
THEN!
Straightway, he now goes on to make a full confession; whereupon the mariners became more and more appalled, but still are pitiful.
For when Jonah, not yet supplicating God for mercy, since he but too well knew the darkness of his deserts,--when wretched Jonah cries out to them to take him and cast him forth into the sea, for he knew that for HlS sake this great tempest was upon them; they mercifully turn from him, and seek by other means to save the ship.
But all in vain; the indignant gale howls louder; then, with one hand raised invokingly to God, with the other they not unreluctantly lay hold of Jonah.
"And now behold Jonah taken up as an anchor and dropped into the sea; when instantly an oily calmness floats out from the east, and the sea is still, as Jonah carries down the gale with him, leaving smooth water behind.
He goes down in the whirling heart of such a masterless commotion that he scarce heeds the moment when he drops seething into the yawning jaws awaiting him; and the whale shoots-to all his ivory teeth, like so many white bolts, upon his prison.
Then Jonah prayed unto the Lord out of the fish's belly.
But observe his prayer, and learn a weighty lesson.
For sinful as he is, Jonah does not weep and wail for direct deliverance.
He feels that his dreadful punishment is just.
He leaves all his deliverance to God, contenting himself with this, that spite of all his pains and pangs, he will still look towards His holy temple.
And here, shipmates, is true and faithful repentance; not clamorous for pardon, but grateful for punishment.
And how pleasing to God was this conduct in Jonah, is shown in the eventual deliverance of him from the sea and the whale.
Shipmates, I do not place Jonah before you to be copied for his sin but I do place him before you as a model for repentance.
Sin not; but if you do, take heed to repent of it like Jonah."
While he was speaking these words, the howling of the shrieking, slanting storm without seemed to add new power to the preacher, who, when describing Jonah's sea- storm, seemed tossed by a storm himself.
His deep chest heaved as with a ground- swell; his tossed arms seemed the warring elements at work; and the thunders that rolled away from off his swarthy brow, and the light leaping from his eye, made all his simple hearers look on him with a quick fear that was strange to them.
There now came a lull in his look, as he silently turned over the leaves of the Book once more; and, at last, standing motionless, with closed eyes, for the moment, seemed communing with God and himself.
But again he leaned over towards the people, and bowing his head lowly, with an aspect of the deepest yet manliest humility, he spake these words:
"Shipmates, God has laid but one hand upon you; both his hands press upon me.
I have read ye by what murky light may be mine the lesson that Jonah teaches to all sinners; and therefore to ye, and still more to me, for I am a greater sinner than ye.
And now how gladly would I come down from this mast-head and sit on the hatches there where you sit, and listen as you listen, while some one of you reads ME that other and more awful lesson which Jonah teaches to ME, as a pilot of the living God.
How being an anointed pilot-prophet, or speaker of true things, and bidden by the
Lord to sound those unwelcome truths in the ears of a wicked Nineveh, Jonah, appalled at the hostility he should raise, fled from his mission, and sought to escape his duty and his God by taking ship at Joppa.
But God is everywhere; Tarshish he never reached.
As we have seen, God came upon him in the whale, and swallowed him down to living gulfs of doom, and with swift slantings tore him along 'into the midst of the seas,' where the eddying depths sucked him ten thousand fathoms down, and 'the weeds were wrapped about his head,' and all the watery world of woe bowled over him.
Yet even then beyond the reach of any plummet--'out of the belly of hell'--when the whale grounded upon the ocean's utmost bones, even then, God heard the engulphed, repenting prophet when he cried.
Then God spake unto the fish; and from the shuddering cold and blackness of the sea, the whale came breeching up towards the warm and pleasant sun, and all the delights of air and earth; and 'vomited out Jonah upon the dry land;' when the word of the Lord came a second time; and Jonah, bruised and beaten--his ears, like two sea-shells, still multitudinously murmuring of the ocean--Jonah did the Almighty's bidding.
And what was that, shipmates?
To preach the Truth to the face of
Falsehood!
That was it!
"This, shipmates, this is that other lesson; and woe to that pilot of the living
God who slights it.
Woe to him whom this world charms from
Gospel duty!
Woe to him who seeks to pour oil upon the waters when God has brewed them into a gale!
Woe to him who seeks to please rather than to appal!
Woe to him whose good name is more to him than goodness!
Woe to him who, in this world, courts not dishonour!
Woe to him who would not be true, even though to be false were salvation!
Yea, woe to him who, as the great Pilot Paul has it, while preaching to others is himself a castaway!"
He dropped and fell away from himself for a moment; then lifting his face to them again, showed a deep joy in his eyes, as he cried out with a heavenly enthusiasm,--"But oh! shipmates! on the starboard hand of every woe, there is a sure delight; and higher the top of that delight, than the bottom of the woe is deep.
Is not the main-truck higher than the kelson is low?
Delight is to him--a far, far upward, and inward delight--who against the proud gods and commodores of this earth, ever stands forth his own inexorable self.
Delight is to him whose strong arms yet support him, when the ship of this base treacherous world has gone down beneath him.
Delight is to him, who gives no quarter in the truth, and kills, burns, and destroys all sin though he pluck it out from under the robes of Senators and Judges.
Delight,--top-gallant delight is to him, who acknowledges no law or lord, but the
Lord his God, and is only a patriot to heaven.
Delight is to him, whom all the waves of the billows of the seas of the boisterous mob can never shake from this sure Keel of the Ages.
And eternal delight and deliciousness will be his, who coming to lay him down, can say with his final breath--O Father!--chiefly known to me by Thy rod--mortal or immortal, here I die.
I have striven to be Thine, more than to be this world's, or mine own.
I leave eternity to Thee; for what is man that he should live out the lifetime of his God?"
He said no more, but slowly waving a benediction, covered his face with his hands, and so remained kneeling, till all the people had departed, and he was left alone in the place. >
Well, I hope the first lecture convinced you that arguments really matter.
Of course, they're not the only thing that matters,
There's more to life than reason and arguments.
But, they are something that matters, and they matter a lot. So, we need to understand arguments.
And the first step in understanding arguments is to figure out what arguments are.
And the first step in understanding what arguments are is to figure out what arguments are not because we want to distinguish arguments from all those things that don't count as arguing.
And the best source of information about what arguments are not is, of course,
Monty Python.
Well, that was pretty silly wasn't it?
But it in the midst of all that silliness, we find some truth because, after all, many members of the Monty Python troupe were philosophy majors.
So, each room represents a kind of thing that we need to distinguish from arguments.
Save heritage, menahankan warisan
Its Wilayah Day and it is a day that we chose to conduct this city tour this city tour is going to go through Jalan Sultan for us to advocate a very important message that is to advocate the importance of preservation of heritage and culture and history of a city we all know that Kuala Lumpur is like any city in other part of the world,
Kuala Lumpur has its own character, history and cultural background we wanted the Malaysians especially and the world to understand how Kuala Lumpur was established and came to today as a developed city it is very important as part of the history of Malaysians to know that the establishment and development of Kuala Lumpur is through the effort put together by all the races, all races that stay in this country
It is a concerted effort of all races that upbring Kuala Lumpur until today,
Today MRT wishes to construct an underground tunnel, going to cost RM40 billion through Jalan Sultan, to us this is very unwise.
It is unwise because the construction even though they use the latest best methods available in the world it is not able to guarantee the stability of the old buildings along Jalan Sultan and along Jalan Petaling.
We therefore have a strong desire to keep the development of Kuala Lumpur going on at the same time maintain, keep the character of Kuala Lumpur city as it is.
We wish MRT to consider realignment.
Today we have to conduct this city tour because through the last four months we have requested MRT to sit down with us to have a dialogue to understand the people's voice but four months effort have brought us to nowhere.
Asalaam Alaykum Wa Rahmatullah Wa Barakatuhu
Happy Birthday to our Shaykh
Happy Birthday to our Grand Shaykh
Happy Birthday to our Prophet (ASWS)
Everyday is a new day
We are asking support from our Shaykh, Sahibul Saif, Shaykh Abdul Kerim el-Kibrisi el-Rabbani to be with us, to make us to be with him to make us to unveil our hearts
InshAllah, the murids, they will rise from the ghaflat stations that they are always in we are asking that the murids, the Muslims, the believers their hearts, one day, will be unveiled to understand how much this world is blessed by his physical presence how much this mankind, how much this Ummat is blessed because of him, that he came 55 years ago
Hello.
I'm a toy developer.
With a dream of creating new toys that have never been seen before, I began working at a toy company nine years ago.
When I first started working there, I proposed many new ideas to my boss everyday.
However, my boss always asked if I had the data to prove it would sell, and to think of product development after analyzing market data.
Data, data, data...
So, I analyzed the market data before thinking of a product.
However, I was unable to think of anything new at that moment.
(Laughter)
My ideas were unoriginal.
I wasn't getting any new ideas and I grew tired of thinking,
It was so hard that I became this skinny.
(Laughter)
It's true. (Applause)
You've all probably had similar experience and felt this way too.
Your boss was being difficult. The data was difficult. You become sick of thinking.
Now, I throw out the data.
It's my dream to create new toys.
And now, instead of data, I'm using a game called "shiritori" to come up with new ideas.
I would like to introduce this method today.
What is "shiritori"? Take apple, elephant, and trumpet, for example. It's a game where you take turns saying words that start with the last letter of the previous word.
It's the same in Japanese and English.
You can play "shiritori" as you like. "neKO, KOra, RAibu, BUrashi," etc, etc. (cat, cola, concert, brush)
Many random words will come out.
You force those words to connect to what you want to think of and form ideas.
In my case, for example, since I want to think of toys, what could a toy cat be?
A cat that lands after doing a somersault from a high place? How about a toy with cola?
A toy gun where you shoot cola and get someone soaking wet?
(Laughter) Ridiculous ideas are okay.
The key is to keep them flowing.
The more ideas you produce, you're sure to come up with some good ones, too.
Can we make a toothbrush into a toy?
We could combine a toothbrush with a guitar and -- "Strum! Strum!
Strum!" -- you've got a toy you can play with while brushing your teeth. (Laughter) (Applause)
Kids who don't like to brush their teeth might begin to like it.
Can we make a hat into a toy?
How about something like Russian Roulette, where you try the hat on one by one, and then, when someone puts it on, a scary alien breaks through the top screaming, "Aaahh!!"
I wonder if there would be a demand for this at parties?
Ideas that didn't come out while you stare at the data will start to come out.
Actually, this bubble wrap, which is used to pack fragile objects, combined with a toy, made "Mugen Pop Pop," a toy where you can pop the bubbles as much as you like.
It was a big hit when it reached stores.
Data had nothing to do with its success.
Although it's only popping bubbles but it's a great way to kill time, so please pass this around amongst yourselves today and play with it.
(Applause)
Anyway, you continue to come up with useless ideas.
Think up many trivial ideas, everyone.
If you base your ideas on data analysis and know what you're aiming for, you'll end up trying too hard, and you can't produce new ideas.
Even if you know what your aim is, think of ideas as freely as if you were throwing darts with your eyes closed.
If you do this, you surely will hit somewhere near the center.
At least one will.
That's the one you should choose.
If you do so, that idea will be in demand and, moreover, it will be brand new.
That is how I think of new ideas.
It doesn't have to be "shiritori"; there are many different methods.
You just have to choose words at random.
You can flip through a dictionary and choose words at random.
For example, you could look up two random letters and gather the results or go to the store and connect product names with what you want to think of.
The point is to gather random words, not information from the category you're thinking for.
If you do this, the ingredients for the association of ideas are collected and form connections that will produce many ideas.
The greatest advantage to this method is the continuous flow of images.
Because you're thinking of one word after another, the image of the previous word is still with you.
That image will automatically be related with future words.
Unconsciously, a concert will be connected to a brush and a roulette will be connected to a hat.
You would't even realize it. You can come up with ideas that you wouldn't have thought otherwise.
This method is, of course, not just for toys.
You can collect ideas for books, apps, events, and many other projects.
I hope you all try this method.
There are futures that are born from data.
However, using this silly game called "shiritori," I look forward to exciting future you will create, a future you couldn't even imagine.
Thank you very much. (Applause)
Blood flows everywhere everyday people lie dead ... blazed by guns swished by bullets, wounded or dead
Blood flows everywhere everyday people lie dead ... blazed by guns swished by bullets, wounded or dead
The news never stopped in the media at first people were scared, then they just don't care the sign of conscience, before it dies the sign of conscience, before it dies the sign of conscience, before it dies
 Determine whether the ordered pairs 3 comma 5 and 1 comma negative 7 are solutions to the inequality 5x minus 3y is greater than or equal to 25.
So again, let me just try each of these ordered pairs.
We could try what happens when x is equal to 3 and y is equal to 5 in this inequality and see if it satisfies it. And then we could try it for 1 and negative 7. So let's do that first.
Let's do it first for 3 and 5.
So when x is 3, y is 5.
Let's see if this actually gets satisfied. So we get 5 times 3. Let me color code it.
So this is 5-- I didn't want to do it in that color-- 5 times 3 minus 3 times 5.
Let's see if this is greater than or equal to 25.
So 5 times 3 is 15. And then from that, we're going to subtract 15, and let's see if that is greater than or equal to 25. Put that question mark there because we don't know.
And 15 minus 15, that is 0.
So we get the expression 0 is greater than or equal to 25.
This is not true.
0 is less than 25.
So this is not true. This is not true.
So this ordered pair is not a solution to the inequality.
So this is not a solution.
You put in x is 3, y is 5, you get 0 is greater than or equal to 25, which is absolutely not true.
Now let's try it with 1 and negative 7.
So we have 5 times 1 minus 3 times negative 7 needs to be greater than or equal to 25.
5 times 1 is 5, and then minus 3 times negative 7 is negative 21.
So it becomes minus negative 21 is to be greater than or equal to 25.
This is the same thing as 5 plus 21-- subtracting a negative same thing as adding the positive-- is greater than or equal to 25.
And 5 plus 21 is 26 is indeed greater than or equal to 25.
So this works out. So this is a solution.
And just to see if we can visualize this a little bit better, I'm going to graph this inequality.
I'm not going to show you exactly how I do it this time, but I'm going to show you where these points lie relative to this solution.
So we have 5x-- that's not a new color.
Having trouble switching colors today.
We have 5x minus 3y is greater than or equal to 25.
Let me write this inequality in kind of our slope-intercept form. So this would be the same thing.
If we subtract 5x from both sides, we get negative 3y is greater than or equal to negative 5x plus 25. I just subtracted 5x from both sides. So that gets eliminated, and you have a negative 5x over here.
Now let's divide both sides of this equation, or I should say this inequality, by negative 3. And when you divide both sides of an inequality by a negative number, multiply or divide by a negative number, it swaps the inequality.
So if you divide both sides by negative 3, you get y is less than or equal to negative 5 divided by negative 3 is 5 over 3x.
And then 25 divided by negative 3 is minus 25/3.
So this is now the expression or the inequality, y is less than or equal to 5/3 x minus 25/3.
So if I wanted to graph this-- I'll try to draw a relatively rough graph here, but really just so that we can visualize this.
That's the same thing as negative 8 and 1/3.
So that's 1, 2, 3, 4, 5, 6, 7, 8, and a little bit more than 8.
So our y-intercept is negative 8 and 1/3 like that. And it has a slope of 5/3.
So that means for every 3 it goes to the right, it rises 5. So it goes 1, 2, 3, it rises 5.
So the line is going to look something like this.
I'm drawing a very rough version of it.
So the line will look something like that, this line over here.
That's if it was a y is equal to 5/3 x minus 25/3.
But here we have an inequality. It's y is less than or equal to.
So for any x, the y's that satisfy it are the y's that equals 5/3 x minus 25/3-- that would be on the line, so it would be that point there-- and all the y's less than it.
So the solution is this whole area right over here.
Since it's less than or equal to, we can include the line.
The equal to allows us to include the line, and the less than tells us we're going to go below the line. And we can verify that by looking at these two points over here. We saw that 3 comma 5 is not part of the solution.
So 3 comma 5 is 1, 2-- it's right about there and then up 5.
So 3 comma 5 is right above here.
It's in this region above the line, and notice not part of the solution.
And then 1 comma negative 7 is going to be right over here. It's almost on the line. So 1 comma negative 7 is going to be right over there.
So hopefully that gives you a little bit more sense of how to visualize these things. And we'll cover this in more detail in future videos.
A microbiologist has 1,256 microbes growing in culture.
When he checks again after fifteen minutes, there are 2,283 microbes in the same culture, so they're growing pretty fast.
Estimate the difference between the number of microbes at each check by rounding each number to the nearest ten.
So what they want us to do, they want us to round each number to the nearest ten, and then with the rounded numbers, find the difference between the two checks.
So let's round each of these numbers.
So we started with 1,256 microbes.
So how do we round this to the nearest ten?
That's what they want us to do.
So you look at the tens place.
The tens place is that 5 right there.
So if we round it up, it would go to a 6.
If we round it down, it would stay at a 5.
If we round it up, this would be 60.
If we round it down, this will be 50.
And the rule for rounding is you look at the place one below that.
You go to the ones place in this case, and you see if that is 5 or more, or 5 or greater, and it is.
It's 6, which is definitely 5 or greater, so we want to round up.
So we want to round up, and we're rounding up to the nearest ten.
So this will be go from 56 to 60, so it'll be 1,260.
We've rounded up.
Now, when we wait fifteen minutes, we check and we see that there are 2,283 microbes.
Once again, let's look at the tens place.
That's the 8 right there.
Let me do that in a different color.
That is the 8 right there.
And you look at the place one below that. If that's 5 or greater, you round up.
Otherwise, you round down.
This right here, 3 is less than 5 so you want to round down.
We want to round down, so we're going to be left with 2,200, and instead of 83, we're just going to have 80. 2,280.
Now, they want us to estimate the difference between the number of microbes at each check by rounding each number to the nearest ten, so we've done that part.
We've rounded each number to the nearest ten.
Now we have to find the difference.
So let's subtract the first check from the second check.
That's how we get a positive number.
So let's do that.
So if we subtract this 1,260-- let me just copy and paste it.
So we want to subtract this-- copy it and paste it.
We want to subtract that from the 2,280 to figure out the difference.
So we're going to subtract here.
Let me put the subtraction sign, and let's do some subtraction.
So you go first to the ones place.
0 minus 0.
Well, that's just going to be 0.
8 minus 6 in the tens place, it's really 80 minus 60.
That's going to be 2, but since it's in the tens place, it's 20, or you could just do 80 minus 60 is 20, so everything makes sense so far.
2 minus 2 is 0, and then 2 minus 1 is 1.
So when we rounded each number to the nearest ten and then took the difference, our estimated difference is 1,020.
"Google began as a research project in 1996."
"This is a look at how search has evolved."
Gomes:
Our goal is actually to make improvements to Search that just answer the user's information need.
Get them to their answer faster and faster.
So that there's almost a seamless connection between their thoughts and their information needs and the search results that they find.
Singhal:
Well, Google was started based upon algorithms that Larry and Sergey developed in Stanford called the PageRank algorithm.
And they used that algorithm to indeed build a very novel way of searching the web.
Gomes:
What was happening at that point was there was this huge explosion of content in the web, a bigger explosion of information than had ever happened before.
And it was getting increasingly hard to find the piece of content you wanted.
"Adwords"
Mayer:
In the beginning, we didn't have any advertisements at all.
And as we went to add advertisements, it was very important to us that those ads be as relevant to the search as the search results themselves.
It was also very important to us that they be distinguished from the search results.
There was a clear separation between ads and Search from the very earliest times.
Search had one goal and one goal alone, to provide the most relevant information for the user in the fastest time possible.
"Universal Results"
Mayer:
In 1999 and 2000, we had a search engine that worked wonderfully, and it worked wonderfully for web pages.
One of the things we saw was, as Google got better and better, users expected more and more from it.
They didn't want just web pages.
They wanted the best possible information available, be that a picture or a book.
And so we started looking at how we could search new and other forms of content.
And Image Search was the first of those because we know that a picture is worth 1,000 words, and there were a lot of times when people would say, you know, what is turquoise?
You know, we got a search, "what is turquoise?"
And there's no way to answer that question without a picture.
When September 11th happened, we as Google were failing our users.
Our users were searching for "New York Twin Towers," and our results had nothing relevant, nothing related to the sad events of the day because our index was crawled a month earlier, and, of course, there was no news in that index.
So we placed links to all the news organizations like CNN right on our front page saying please visit those sites to get the news of the day, because our search is failing you.
My friend Krishna and I were attending a conference at the time, and Krishna started thinking about the problem, saying, "If we could crawl news quickly,
"and we can provide multiple points of view
"about the same story to our users, wouldn't it be amazing?"
That was the birth of Google News specialized search service.
Well, in 2002, one of the trends we started to see was that the web had become a lot more rich.
More images, more video, different kinds of content.
And we started to realize that our users expected Google to be able to find something if it existed on the web.
They didn't care if it was text or a web page or news, they wanted it all in one place.
And so we came up with this notion of Universal Search, the idea that you could just go to Google, and no matter what type of content it was, we could find it.
One of the challenges that came up in Universal Search is that we were really comparing apples and oranges.
You can imagine these apples are web pages, and you can imagine an orange would be an image.
When we look at ranking images, we know what the aspect ratio of an image is, how big is the image, how many pixels this image is.
Is it a black and white image or a color image?
And all these signals are only relevant to images, but are not relevant to web pages.
And that's why Universal Search was such a hard task when we did it, because the science was not fully developed.
Mayer: We basically ended up putting things either on the top of the page, on the bottom of the page, or somewhere in the middle because we didn't have a finer-grained way of looking at the relevance, especially across different media types.
And over the years, we developed our science tremendously, and today we are beginning to place several kinds of information in multiple positions on our result page as our algorithms get better and better.
"Quick Answers"
Our goal is to make it so that the improvement we make is so much what you wanted and fits so cleanly into the flow of what you are looking for that you almost don't notice that it's happened.
And looking back at it, it seems obvious that that's the way it should have always been in the first place.
Menzel:
When you do need a specific bit of information,
Google tries to provide you exactly that using our Quick Answers.
For example, take sport scores.
You kind of want to know what the score is right now.
You want to know how tall is the Empire State Building?
Wright: We want users to come to Google and get their information as quickly as they possibly can.
And with Instant, you don't even have to type in your full thought.
You don't have to hit enter.
You can type in something like, "bike h," and we'll just show you the results right there before you've even finished your thoughts.
"The Future of Search"
We are pushing the boundaries of how you actually fundamentally interact with the search engine itself.
With Search by Image, you can actually use that image as an input for the search.
The truth is that our users need much more complex answers.
My dream has always been to build the "Star Trek" computer.
And in my ideal world,
I would be able to walk up to a computer and say,
"Hey, what is the best time for me to sow seeds in India, given that monsoon was early this year?"
And once we can answer that question, which we don't today, people will be looking for answers to even more complex questions.
These are all genuine information needs.
Genuine questions that, if we, Google, can answer, our users would become more knowledgeable, and they would be more satisfied in their quest for knowledge.
Multiply, expressing the product in scientific notation.
So let's multiply first, and then let's get what we have into scientific notation.
Actually, before we do that, let's remember what it means to be in scientific notation.
So, to be in scientific notation, and actually, each of these numbers right here are in scientific notation, it's going to be the form
"a" times ten to some power, where "a" can be greater than or equal to one, and it is going to be less than ten.
So both of these numbers are greater than or equal to one, and less than ten, and they are being multiplied by some power of ten.
Let's see how we can multiply this.
So this over her is just the exact same thing as (I do this part in magenta) is the same as 9.1 times 10 to the sixth times ... (let me write it all out with a dot notation... make it a little more straight forward)
So this is equal to 9.1 times 10 to the sixth times (in green) 3.2 times ten to the negative fifth power.
Now, in multiplication, this comes from the associative property, which allows us to essentially remove these parentheses.
It says, hey, you can multiply like that first, or you can actually multiply these guys first, you can re-associate them.
And the commutative property tells us that we can rearrange this thing here.
And what I want to rearrange is,
I want to multiply the 9.1 times the 3.2 first, and then multiply that by 10 to the sixth times 10 to the negative five.
So I'm just going to rearrange this using the commutative property.
So this is the same thing as 9.1 times 3.2, and then I'm going to re-associate, so I'm going to do these first.
And then that times 10 to the 6th times 10 to the negative 5.
And the reason this is useful, is that this is really easy to multiply.
We have the same base here, base 10, so we can, and we're taking the product, so we can add the exponents.
So this part right over here, 10 to the 6th times 10 to the negative 5, that's going to be 10 to the 6 minus 5 power, so we're essentially just 10 to the first power, which is really just equal to ten. and that is going to be multiplied by 9.1 times 3.2
Let me do that over here.
9.1 times 3.2.
So first, I'm going to ignore the decimal.
I'm just going to treat it like 91 times 32.
So I have 2 times 1 is 2.
2 times 9 is 18.
Take a zero her because I'm in the tenths place now,
I'm really multiplying by 30, that's why my zero is there.
I multiply 3 by 1 to get 3.
And then 3 times 9 is 27.
And so it is 2, (I'm adding here), 8 plus 3 is 11, carry/regroup the one, 1 plus 1 is two, 2 plus 7 is 9, and then I have a two here. 91 times 32 is 2912, but I didn't multiply 91 by 32 here,
I multiplied 9.1 times 3.2.
So I want to count the number of digits behind the decimal point.
And I have one, two digits behind the decimal point.
And so I'll have to have two digits behind the decimal point in the answer.
I'll stick the decimal right over there.
So this part right over here, comes out to be 29.12.
You might say, might feel like we're done.
This kind of looks like scientific notation.
I have a number times a power of ten.
But remember, this number has to be greater than or equal to one, which it is, AND less than ten!
But this number is not less than ten.
Therefore, it is not scientific notation.
So what we can do is, let's just write this number in scientific notation, and then we can use the multiply by ten part to multiply by this power of ten.
So 29.12, this is the same thing as 2.912, notice, what did I do to get from there to there?
I just moved the decimal to the left.
Or, another way to think about it; if I wanted to go from here to there, what could I do to this?
I would multiply by ten.
I would move the decimal to the right;
It would go from 2.912 to 29.12.
So if I want to write this value, this is just this [2.912] times ten.
29.12 is the same thing as 2.912 times 10.
And now, this is in scientific notation, but that's just this part.
We still have to multiply it by another 10.
So, times another ten.
And so, to finish up this problem, we get 2.912 times 10 times 10, or 10 to the first times 10 to the first.
Well, what's that?
Well, that's just going to be 10 squared.
So it is 2.912 times 10 to the second power.
And we are done.
Thanks You Sal!
You are awesome! :)
So, I'll start with this: a couple years ago, an event planner called me because I was going to do a speaking event.
And she called, and she said,
"I'm really struggling with how to write about you on the little flyer."
And I thought, "Well, what's the struggle?"
And she said, "Well, I saw you speak, and I'm going to call you a researcher, I think, but I'm afraid if I call you a researcher, no one will come, because they'll think you're boring and irrelevant."
(Laughter) And I was like, "Okay."
And she said, "But the thing I liked about your talk is you're a storyteller.
So I think what I'll do is just call you a storyteller."
And of course, the academic, insecure part of me was like, "You're going to call me a what?"
And she said, "I'm going to call you a storyteller."
And I was like, "Why not 'magic pixie'?"
(Laughter)
I was like, "Let me think about this for a second."
I tried to call deep on my courage. And I thought, you know, I am a storyteller.
I'm a qualitative researcher.
I collect stories; that's what I do.
And maybe stories are just data with a soul.
And maybe I'm just a storyteller.
And so I said, "You know what? Why don't you just say I'm a researcher-storyteller."
And she went, "Ha ha.
There's no such thing."
(Laughter)
So I'm a researcher-storyteller, and I'm going to talk to you today -- we're talking about expanding perception -- and so I want to talk to you and tell some stories about a piece of my research that fundamentally expanded my perception and really actually changed the way that I live and love and work and parent.
And this is where my story starts.
When I was a young researcher, doctoral student, my first year, I had a research professor who said to us, "Here's the thing, if you cannot measure it, it does not exist."
And I thought he was just sweet-talking me.
I was like, "Really?" and he was like, "Absolutely."
And so you have to understand that I have a bachelor's and a master's in social work, and I was getting my Ph.D. in social work, so my entire academic career was surrounded by people who kind of believed in the "life's messy, love it."
And I'm more of the, "life's messy, clean it up, organize it and put it into a bento box."
(Laughter)
And so to think that I had found my way, to found a career that takes me -- really, one of the big sayings in social work is,
"Lean into the discomfort of the work."
And I'm like, knock discomfort upside the head and move it over and get all A's.
That was my mantra.
So I was very excited about this.
And so I thought, you know what, this is the career for me, because I am interested in some messy topics.
But I want to be able to make them not messy.
I want to understand them. I want to hack into these things that I know are important and lay the code out for everyone to see.
So where I started was with connection.
Because, by the time you're a social worker for 10 years, what you realize is that connection is why we're here.
It's what gives purpose and meaning to our lives.
This is what it's all about.
It doesn't matter whether you talk to people who work in social justice, mental health and abuse and neglect, what we know is that connection, the ability to feel connected, is -- neurobiologically that's how we're wired -- it's why we're here.
So I thought, you know what, I'm going to start with connection.
Well, you know that situation where you get an evaluation from your boss, and she tells you 37 things that you do really awesome, and one "opportunity for growth?"
(Laughter)
And all you can think about is that opportunity for growth, right?
Well, apparently this is the way my work went as well, because, when you ask people about love, they tell you about heartbreak.
When you ask people about belonging, they'll tell you their most excruciating experiences of being excluded.
And when you ask people about connection, the stories they told me were about disconnection.
So very quickly -- really about six weeks into this research -- I ran into this unnamed thing that absolutely unraveled connection in a way that I didn't understand or had never seen.
And so I pulled back out of the research and thought, I need to figure out what this is.
And it turned out to be shame.
And shame is really easily understood as the fear of disconnection:
Is there something about me that, if other people know it or see it, that I won't be worthy of connection?
The things I can tell you about it: It's universal; we all have it.
The only people who don't experience shame have no capacity for human empathy or connection.
No one wants to talk about it, and the less you talk about it, the more you have it.
What underpinned this shame, this "I'm not good enough," -- which, we all know that feeling:
"I'm not blank enough.
I'm not thin enough, rich enough, beautiful enough, smart enough, promoted enough."
The thing that underpinned this was excruciating vulnerability.
This idea of, in order for connection to happen, we have to allow ourselves to be seen, really seen.
And you know how I feel about vulnerability.
I hate vulnerability.
And so I thought, this is my chance to beat it back with my measuring stick. I'm going in, I'm going to figure this stuff out, I'm going to spend a year, I'm going to totally deconstruct shame,
So I was ready, and I was really excited.
As you know, it's not going to turn out well.
(Laughter)
You know this. So, I could tell you a lot about shame, but I'd have to borrow everyone else's time.
But here's what I can tell you that it boils down to -- and this may be one of the most important things that I've ever learned in the decade of doing this research.
My one year turned into six years: Thousands of stories, hundreds of long interviews, focus groups.
At one point, people were sending me journal pages and sending me their stories -- thousands of pieces of data in six years.
And I kind of got a handle on it.
I kind of understood, this is what shame is, this is how it works.
I wrote a book, I published a theory, but something was not okay -- and what it was is that, if I roughly took the people I interviewed and divided them into people who really have a sense of worthiness -- that's what this comes down to, a sense of worthiness -- they have a strong sense of love and belonging -- and folks who struggle for it, and folks who are always wondering if they're good enough.
There was only one variable that separated the people who have a strong sense of love and belonging and the people who really struggle for it.
And that was, the people who have a strong sense of love and belonging believe they're worthy of love and belonging. That's it.
They believe they're worthy.
And to me, the hard part of the one thing that keeps us out of connection is our fear that we're not worthy of connection, was something that, personally and professionally, I felt like I needed to understand better.
So what I did is I took all of the interviews where I saw worthiness, where I saw people living that way, and just looked at those.
What do these people have in common?
I have a slight office supply addiction, but that's another talk.
So I had a manila folder, and I had a Sharpie, and I was like, what am I going to call this research?
And the first words that came to my mind were "whole-hearted."
These are whole-hearted people, living from this deep sense of worthiness.
So I wrote at the top of the manila folder, and I started looking at the data.
In fact, I did it first in a four-day, very intensive data analysis, where I went back, pulled the interviews, the stories, pulled the incidents.
What's the theme?
What's the pattern?
My husband left town with the kids because I always go into this Jackson Pollock crazy thing, where I'm just writing and in my researcher mode.
And so here's what I found.
What they had in common was a sense of courage.
And I want to separate courage and bravery for you for a minute.
Courage, the original definition of courage, when it first came into the English language -- it's from the Latin word "cor," meaning "heart" -- and the original definition was to tell the story of who you are with your whole heart.
And so these folks had, very simply, the courage to be imperfect.
They had the compassion to be kind to themselves first and then to others, because, as it turns out, we can't practice compassion with other people if we can't treat ourselves kindly.
And the last was they had connection, and -- this was the hard part -- as a result of authenticity, they were willing to let go of who they thought they should be in order to be who they were, which you have to absolutely do that for connection.
The other thing that they had in common was this:
They fully embraced vulnerability.
They believed that what made them vulnerable made them beautiful.
They didn't talk about vulnerability being comfortable, nor did they really talk about it being excruciating -- as I had heard it earlier in the shame interviewing.
They just talked about it being necessary.
They talked about the willingness to say, "I love you" first ... the willingness to do something where there are no guarantees ... the willingness to breathe through waiting for the doctor to call after your mammogram.
They're willing to invest in a relationship that may or may not work out.
They thought this was fundamental.
I personally thought it was betrayal.
I could not believe I had pledged allegiance to research, where our job -- you know, the definition of research is to control and predict, to study phenomena for the explicit reason to control and predict.
And now my mission to control and predict had turned up the answer that the way to live is with vulnerability and to stop controlling and predicting.
This led to a little breakdown -- (Laughter)
-- which actually looked more like this.
(Laughter)
And it did.
I call it a breakdown; my therapist calls it a spiritual awakening.
(Laughter) A spiritual awakening sounds better than breakdown, but I assure you, it was a breakdown.
And I had to put my data away and go find a therapist.
Let me tell you something: you know who you are when you call your friends and say, "I think I need to see somebody.
Do you have any recommendations?"
Because about five of my friends were like,
"Wooo, I wouldn't want to be your therapist."
(Laughter)
I was like, "What does that mean?"
And they're like, "I'm just saying, you know. Don't bring your measuring stick."
(Laughter)
So I found a therapist.
My first meeting with her, Diana --
I brought in my list of the way the whole-hearted live, and I sat down.
And she said, "How are you?"
And I said, "I'm great.
I'm okay."
She said, "What's going on?"
And this is a therapist who sees therapists, because we have to go to those, because their B.S. meters are good.
(Laughter)
And so I said, "Here's the thing, I'm struggling."
And she said, "What's the struggle?"
And I said, "Well, I have a vulnerability issue.
And I know that vulnerability is the core of shame and fear and our struggle for worthiness, but it appears that it's also the birthplace of joy, of creativity, of belonging, of love.
And I think I have a problem, and I need some help."
And I said, "But here's the thing: no family stuff, no childhood shit."
(Laughter)
"I just need some strategies."
(Laughter) (Applause)
Thank you.
So she goes like this.
(Laughter)
And then I said, "It's bad, right?"
And she said, "It's neither good nor bad."
(Laughter)
"It just is what it is."
And I said, "Oh my God, this is going to suck."
(Laughter)
And it did, and it didn't.
And it took about a year.
And you know how there are people that, when they realize that vulnerability and tenderness are important, that they surrender and walk into it.
A: that's not me, and B:
I don't even hang out with people like that. (Laughter)
For me, it was a yearlong street fight.
It was a slugfest.
Vulnerability pushed, I pushed back.
I lost the fight, but probably won my life back.
And so then I went back into the research and spent the next couple of years really trying to understand what they, the whole-hearted, what choices they were making, and what we are doing with vulnerability.
Why do we struggle with it so much?
Am I alone in struggling with vulnerability? No.
So this is what I learned.
We numb vulnerability -- when we're waiting for the call.
It was funny, I sent something out on Twitter and on Facebook that says, "How would you define vulnerability?
What makes you feel vulnerable?" And within an hour and a half, I had 150 responses.
Because I wanted to know what's out there.
Having to ask my husband for help because I'm sick, and we're newly married; initiating sex with my husband; initiating sex with my wife; being turned down; asking someone out; waiting for the doctor to call back; getting laid off; laying off people. This is the world we live in.
We live in a vulnerable world.
And one of the ways we deal with it is we numb vulnerability.
And I think there's evidence -- and it's not the only reason this evidence exists, but I think it's a huge cause -- We are the most in-debt ... obese ... addicted and medicated adult cohort in U.S. history.
The problem is -- and I learned this from the research -- that you cannot selectively numb emotion.
You can't say, here's the bad stuff.
Here's vulnerability, here's grief, here's shame, here's fear, here's disappointment.
I don't want to feel these.
I'm going to have a couple of beers and a banana nut muffin.
(Laughter)
I don't want to feel these.
And I know that's knowing laughter.
I hack into your lives for a living.
God.
(Laughter)
You can't numb those hard feelings without numbing the other affects, our emotions.
You cannot selectively numb. So when we numb those, we numb joy, we numb gratitude, we numb happiness.
And then, we are miserable, and we are looking for purpose and meaning, and then we feel vulnerable, so then we have a couple of beers and a banana nut muffin.
And it becomes this dangerous cycle.
One of the things that I think we need to think about is why and how we numb.
And it doesn't just have to be addiction.
The other thing we do is we make everything that's uncertain certain.
Religion has gone from a belief in faith and mystery to certainty.
"I'm right, you're wrong. Shut up."
That's it.
Just certain.
The more afraid we are, the more vulnerable we are, the more afraid we are.
This is what politics looks like today.
There's no discourse anymore.
There's no conversation.
There's just blame.
You know how blame is described in the research?
A way to discharge pain and discomfort.
We perfect.
If there's anyone who wants their life to look like this, it would be me, but it doesn't work.
Because what we do is we take fat from our butts and put it in our cheeks.
(Laughter)
Which just, I hope in 100 years, people will look back and go, "Wow."
(Laughter)
And we perfect, most dangerously, our children.
Let me tell you what we think about children.
They're hardwired for struggle when they get here.
And when you hold those perfect little babies in your hand, our job is not to say, "Look at her, she's perfect.
My job is just to keep her perfect -- make sure she makes the tennis team by fifth grade and Yale by seventh."
That's not our job.
Our job is to look and say,
"You know what?
You're imperfect, and you're wired for struggle, but you are worthy of love and belonging." That's our job.
Show me a generation of kids raised like that, and we'll end the problems, I think, that we see today.
We pretend that what we do doesn't have an effect on people.
We do that in our personal lives.
We do that corporate -- whether it's a bailout, an oil spill ... a recall. We pretend like what we're doing doesn't have a huge impact on other people.
I would say to companies, this is not our first rodeo, people.
We just need you to be authentic and real and say ...
"We're sorry.
We'll fix it."
But there's another way, and I'll leave you with this.
This is what I have found: To let ourselves be seen, deeply seen, vulnerably seen ... to love with our whole hearts, even though there's no guarantee -- and that's really hard, and I can tell you as a parent, that's excruciatingly difficult -- to practice gratitude and joy in those moments of terror, when we're wondering, "Can I love you this much?
Can I believe in this this passionately?
Can I be this fierce about this?" just to be able to stop and, instead of catastrophizing what might happen, to say, "I'm just so grateful, because to feel this vulnerable means I'm alive."
And the last, which I think is probably the most important, is to believe that we're enough.
Because when we work from a place, I believe, that says, "I'm enough" ... then we stop screaming and start listening, we're kinder and gentler to the people around us, and we're kinder and gentler to ourselves.
That's all I have.
Thank you.
We're now going to learn how to go from mixed numbers to improper fractions and vice versa.
So first a little bit of terminology.
What is a mixed number?
Well, you've probably seen someone write, let's say, two and one half.
This is a mixed number.
So you're saying why is it a mixed number?
Well, because we're including a whole number and a fraction.
So that's why it's a mixed number.
It's a whole number mixed with a fraction.
So two and one half.
And I think you have a sense of what two and one half is.
It's some place halfway between two and three.
And what's an improper fraction?
Well an improper fraction is a fraction where the numerator is larger than the denominator.
So let's give an example of an improper fraction.
I'm just going to pick some random numbers.
Let's say I had twenty-three over five.
This is an improper fraction.
Why?
Because twenty-three is larger than five.
It's that simple.
It turns out that you can convert an improper fraction into a mixed number or a mixed number into an improper fraction.
So let's start with the latter.
Let's learn how to do a mixed number into an improper fraction.
So first I'll just show you kind of just the basic systematic way of doing it.
It'll always give you the right answer, and then hopefully I'll give you a little intuition for why it works.
So if I wanted to convert two and one half into an improper fraction, or I want to unmix it you could say, all I do is I take the denominator in the fraction part, multiply it by the whole number, and add the numerator.
So let's do that.
I think if we do enough examples, you'll get the pattern.
So two times two is four plus one is five.
So let's write that. It's two times two plus one, and that's going to be the new numerator.
And it's going to be all of that over the old denominator.
So that equals five halves.
So two and one half is equal to five halves.
Let's do another one.
Let's say I had four and two thirds.
This is equal to -- so this is going to be all over three.
We keep the denominator the same.
And the new numerator is going to be three times four plus two.
So it's going to be three times four, and then you're going to add two.
Well that equals three times four-- order of operations, you always do multiplication first, and that's actually the way I taught it-- how to convert this, anyway. three times four is twelve plus two is fourteen.
So that equals fourteen over three.
Let's do another one.
Let's say I had six and seventeen eighteenths.
I gave myself a hard problem.
Well, we just keep the denominator the same.
And then new numerator is going to be eighteen times six or six times eighteen, plus seventeen.
Well six times eighteen.
Let's see, that's sixty plus forty-eight it's one hundred eight, so that equals one hundred eight plus seventeen.
All that over eighteen.
One hundred eight plus seventeen is equal to one hundred twenty-five over eighteen.
So, six and seventeen eighteenths is equal to one hundred twenty-five over eighteen.
Let's do a couple more.
And in a couple minutes I'm going to teach you how to go the other way, how to go from an improper fraction to a mixed number.
And this one I'm going to try to give you a little bit of intuition for why what I'm teaching you actually works.
So let's say two and one fourth.
If we use the-- I guess you'd call it a system that I just showed you-- that equals four times two plus one over four.
Well that equals, four times two is eight plus one is nine.
Nine over four.
I want to give you an intuition for why this actually works.
So two and one fourth, let's actually draw that, see what it looks like.
So let's put this back into kind of the pie analogy.
So that's equal to one pie.
Two pies.
And then let's say, one fourth of a pie.
One fourth is like this.
A fourth of a pie, right?
Two and one fourth, and ignore this, this is nothing.
It's not a decimal point-- actually, let me erase it so it doesn't confuse you even more.
So go back to the pieces of the pie.
So there's two and one fourth pieces of pie.
And we want to rewrite this as just, how many fourths of pie are there total?
Well if we take each of these pies-- oh, whoops!
I need to change the color-- if we take each of these pies, and we divide it into fourths, we can now say how many total fourths of pie do we have?
Well we have one, two, three, four, five, six, seven, eight, nine fourths.
Makes sense, right?
Two and one fourth is the same thing as nine fourths.
And this will work with any fraction.
So let's go the other way.
Let's figure out how to go from an improper fraction to a mixed number.
Let's say I had twenty-three over five.
So here we go in the opposite direction.
We actually take the denominator, we say how many times does it go into the numerator?
And then we figure out the remainder.
So let's say five goes into twenty-three-- well, five goes into twenty-three four times.
Four times five is twenty.
And the remainder is three.
So twenty-three over five, we can say that's equal to four, and in the remainder, three over five.
So it's four and three fifths.
Let's review what we just did.
We just took the denominator and divided it into the numerator.
So five goes into twenty-three four times.
And what's left over is three.
So, five goes into twenty-three four and three fifths times.
Or another way of saying that is twenty-three over five is four and three fifths.
Let's do another example like that.
Let's say, seventeen over eight.
What does that equal as a mixed number?
You can actually do this in your head, but I'll write it out just so you don't get confused.
Eight goes into seventeen two times.
Two times eight is sixteen. Seventeen minus sixteen is one.
Remainder, one.
So, seventeen over eight is equal to two-- that's this two-- and one eighth.
Right? Because we have one eight left over.
Let me show you kind of a visual way of representing this too, so it actually makes sense how this conversion is working.
Let's say I had five halves, right?
So that literally means I have five halves, or if we go back to the pizza or the pie analogy, let's draw my five halves of pizza.
So let's say I have one half of pizza here, and let's say I have another half of pizza here.
I just flipped it over.
So that's two.
So it's one half, two halves.
So that's three halves.
And then I have a fourth half here.
These are halves of pizza, and then I have a fifth half here, right? So that's five halves.
Well, if we look at this, if we combine these two halves, this is equal to one piece, I have another piece, and then I have half of a piece, right?
So that is equal to two and one half pizzas.
Hopefully that doesn't confuse you too much.
And if we wanted to do this the systematic way, we could have said two goes into five-- well, two goes into five two times, and that two is right here.
And then two times two is four.
Five minus four is one, so the remainder is one, and that's what we use here.
And of course, we keep the denominator the same.
So five halves equals two and one half.
Hopefully that gives you a sense of how to go from a mixed number to an improper fraction, and vice versa, from an improper fraction to a mixed number.
If you're still confused let me know, and I might make some more modules.
Have fun with the exercises!
What we're doing in this video is study a proof of the Pythagorean theorem, that was first discovered,as far as we know by James Garfield in 1876.
What's exciting about this is that he was not a professional mathematician.
You might know James Garfield as the twentieth president of the United States.
He was elected president in 1880, and then he became president in 1881.
And he did this proof while he was a sitting member of the United States House of Representatives.
What's exciting about that is is it shows that Abraham Lincoln was not the only US politician or the only US president who was into geometry.
And what Garfield realised is that we can construct a right triangle-
Let's say this side over here is length 'b'(blue) and this side is length 'a'(red), and let's say this side, the hypotenuse of my right triangle, has length 'c'.
And let me make it clear -- it is a right triangle.
He essentially flipped and rotated this triangle to construct another one that is congruent to the first one.
So let me construct that.
So we're going to have length 'b.'
And it's colinear with length 'a', It's along the same line as length 'a.' They don't overlap with each other.
So this is a side of length 'b.' And then you have your side of length 'a' at a right angle. And then you have your side of length 'c.'
So the first thing we need to think about is, "What's the angle between these two sides?"
What's this mystery angle going to be?
Well, it looks like something, but let's see if we can prove to ourselves it really is what we think it looks like.
If we look at this original triangle, and we call this angle 'theta,' what's this angle over here, the angle that's between the sides of length a and c. what's the measure of this angle going to be?
Well, theta plus this angle has to add up to 90, because when you add those two together, they add up to the 90.
So 90 and 90 you get 180 degrees for the interior angles of this triangle.
So if these two angles together is 90, then this angle is '90 minus theta'.
Well if this angle up here is congruent -- (And we've constructed it so it is congruent.) the angle corresponding to theta is also going to be theta, And this angle right over here is also going to be 90 - theta.
So given that this is theta and this is 90 - theta, what is our angle going to be?
Well they all, collectively, add up to 180 degrees.
So you have theta + (90-theta) + our mystery angle is going to be equal to 180 degrees.
The thetas cancel out (theta - theta), and you have 90 + our mystery angle is a 180 degrees,
We subtract 90 from both sides.) - and you are left with your mystery angle equalling 90 degrees. So that all worked out well.
So let me make that clear. That's going to be useful for us.
So now we can say definitively that this is 90 degrees.
This is a right angle.
Now what we are going to do, is we are going to construct a trapezoid.
This side 'a' is parallel to side 'b' down here the way its been constructed and this is just one side right over here, this goes straight up and now let's just connect these two sides right over there.
So there's a couple of ways to think about the area of this trapezoid.
One is we can just think of it as a trapezoid and come up with its area, And then we could think about it as the sum of the areas of its components.
So let's just first think of it as trapezoid.
So, what do we know about the area of the trapezoid?
The area of a trapezoid,is gonna be the height of the trapezoid, which is (a+b) times, the way I think of it, the mean or average of the top and the bottom. So, ar(trapezoid) = (a+b) x 1/2(a+b)
In the intuition there you are taking the height times the average of the bottom and the top, gives you the area of the trapezoid.
Now, how can we also figure out the area with its component parts?
So as far as we do the correct things, we should come up with the same result. so how else can we come up with this area?
Well, we could say it's the area of the two right triangles.
The area of each of them is one half of a times b.
But there's two of them, Let me do that say in blue colour, But there's two of these right triangles, so let's multiply them by two.
So 2 times half ab, that takes into consideration this bottom right triangle, and this top one. and what's the area of this large one, that I'll colour in green
Well that's pretty straightforward, it's just one half c times c.
So, plus one half c times c, which is one half c square.
Now , let's simplify this thing and see what we come up with and you might guess where all of this is going.
So, we can rearrange this.
So this one half times (a+b) squared is going to be equal to two times one half, well that's just going to be one, so its gonna be equal to a times b plus one half c squared.
I don't like these one halves lying around, so let's multiply both sides, this equation, by 2.
I'm just gonna multiply both sides by two.
So, on the left hand side, I'm just left with (a+b) squared, and on the right hand side, I'm left with 2ab and then two times one half c squared, i.e., plus c squared.
What happens if you multiply out (a+b) times (a+b)?
We get (a+b) squared.
That is a sq. + 2ab+ b sq. = 2ab + c sq.
Subtracting 2ab from both sides, we are left with, a sq. + b sq. = c sq. i.e. the Pythagorean theorem.
Brought to you by the PKer team @ www.Viki Episode 5
What are you doing?
Like a thief.
That's not it.
I had to look for something.
Do you expect me to believe that?
When there is nobody but us home, you suddenly had something to find?
No.
Really.
Are they busy?
Seems like they're sleeping.
Why are you like this?
What do you mean why am I like this?
Didn't you come in here wanting this?
What?
No!
So what?
We're the only ones in the house.
Seung Jo, why are you like this?
Seung Jo ssi!
Aigoo!
First... ...let's soundly date.
Soundly?
When was that word ever used?
Soundly.
Oh.
You came.
What the...
What's wrong with Oh Ha Ni?
Her face is really red.
Really?
I wonder what's wrong.
Stupid jerk.
Always playing around with me.
Am I really dumb?
After this (the love letter being graded)...
Doongi ah.
Is it supposed to be like this?
My heart... ...it isn't doing what I want it to do.
- Hey, what about Oh Ha Ni?
- She must not be on here.
- Did Oh Ha Ni's grades drop?
- What happened?
Why isn't she on here?
So it was because of Baek Seung Jo's help.
After going to the Special Study Hall, I found out it wasn't that great.
The kids there are weird too.
Anyway...
Out of all those colleges, isn't there one we can go to?
There will be one.
A college that will accept you... There will be one.
Let's try for a special circumstance admission.
A special circumstance admission?
In truth, for an exceptional admission you need to have many letters of recommendation and awards or trophies as well.
Anyway, you have to be really good at something.
This...
Even though one may not be doing that well now, they choose those who they think will do well in the future.
Ah!
Latent potential!
That's right!
Here, let's look for a place that'll match us.
By any chance, was your grandfather a patriot?
It's okay if it's the grandfather on the mother's side.
Really?
Ha Ni.
Your grandfather (maternal)... ...was a shutter man (opens and closes the shop shutter, i.e., while his wife works, he plays).
Ah, he was ahead of his time...
Okay.
Uhhh...
Was your father a special agent?
Special missions? Well...
There is something special in making noodles.
Ha Ni, it will work if you're the female householder.
Ha Ni...
Your dad...
Should I just move out?
It's unlikely... ...but you're not from a multicultural heritage, are you?
Multicultural heritage?
Think about it, Dad.
Did Mom possibly speak Thai or anything like that?
She didn't do that?
Thai?
Tom Yam Koong! (a kind of Thai food called sour soup)
Does this mean that there's not a single one out of all of these?
I'm worrying!
Stop doing that!
Blood donation?
You can have it.
There's a lot at home.
Do you donate a lot of blood?
Once every two months.
I donate more through money.
You should have said something earlier!
It says that giving blood once equals ten hours of service!
Really?!
Then, if it's ten times... 100 hours?!
Yeah!
I found it.
The "Giving Back to the Community" option.
Social Science.
Parang University?
Yeah.
Min Ah, you're also going to Parang University, right?
Yeah, as an animation major.
Our teacher said to try it once.
Wow, then are you both going to Parang University?
If we get in that is.
Even if the application goes through, I heard the interview process is very picky.
I have a skill examination as well.
How come our teacher didn't say anything to me about Parang University?
What are you doing?!
Look at you.
Stop eating.
I'm getting angry so give it to me.
Ju Ri.
I was wondering why we hadn't seen you around, especially since Oh Ha Ni is here.
What?
Did you put some kind of tracker on her?
How did you just pop out of nowhere like a ghost?
You guys still don't know?
Ha Ni is my life's navigation system.
She tells me where I need to go, location, direction, speed.
Navigation my butt.
Hey, where are all your little friends and why did you come alone?
They went to an audition.
They practice for auditions after all.
Really?
Oh my, I thought they were audition applicants since they go to auditions all the time.
What are you saying, girl?
What?
What?
Isn't that Baek Seung Jo?
I think you should go to a school with lots of history and tradition... ...a university that has produced many great scholars.
Or the American Ivy Leagues...
Who's the guy in front of him?
What are they talking about? Brought to you by the PKer team @ www.Viki
[Student Personal Information Form]
Special skill?
Specialty?
Specialty?!
Specialty?!
Specialty?!
You're working hard.
Of course.
Do you think I'm a teacher who plays around like a certain someone?
Me?
When...have I ever played around that makes you say that?
Vice principal.
Please give me what you told me about a while ago.
What was it?
Ah!
The Principal's recommendation?
How can I do that?!
How can I give a Principal's recommendation to the bottom ranked students?
Oh Ha Ni went up from the bottom ranks to the top fifty in one week.
If that's not potential, then what is?
The special case admissions look at potential.
Yes, that is so.
Look at the kids who got into college last year.
70% were ranked 1st, 2nd, or 3rd class.
Just because a person has passion, does that make them a good teacher?
They have to be able to teach the kids about looking into reality properly.
If Oh Ha Ni gets into Parang University... ...then I am Teacher Song's child.
Always passionate...
Excuse me...
This.
It's vitamin C.
You should dissolve it in water.
This is the first time, you seem like a person.
You're head over heels for me, aren't you?!
It's done!
Uh... Self introduction.
I was born August 11th...
Okay.
Okay, so now...
I just have to register...
What!
What's wrong with this?
Why isn't it opening?!
What?
Error Report?
"Please click here."
Click.
"What you were working on..." "...will be lost."
Is it going well?
Why did you have so many useless tabs open?
I didn't!
What do I do?
What do I do?!
What to do?!
It's going to be okay, Ha Ni.
It couldn't have all been erased.
In a little bit, it will close.
Urgh, shut up!
I can't think straight.
It's fixed!
Really?
What about the written application?
It's there!
Really?
It's not gone?
Yes, he found it!
Oh, thank you. Stop fooling around and quickly get the receipt.
Yes.
Oh, it's a relief.
Hurry and go downstairs to have dinner.
Let's go, Eun Jo.
Let's go down.
What's wrong?
Thank you.
Parang University undergraduate course?
Yes.
Actually, there aren't a lot of possibilities for me.
My grades are really bad.
You went that crazy when you don't even really have a chance?
Still, I have to try doing what I can.
Why are you going to college?
Huh?
Why do you ask?
Well, to study and...
Having nothing you're good at, nor a field you're interested in... ...why are you still doing this?
If not to study, then I can find my purpose in life.
Find out about what I like or what I'm good at.
How would you know if you like something?
Of course you would know!
Your heart starts beating fast.
If you find something you like, it'll beat fast here.
My dad... When he smells noodles drying, his heart still beats fast.
I'd like to experience it too, that kind of feeling.
Ah, hurry!
I wonder why I'm going to college?
I've never worried about it before.
After all, geniuses must have their own worries.
Did he show me a little of his feelings?
Ah!
[Acceptance Letter]
[Acceptance Letter]
Did you have to print them out?
It feels good.
Well, there are always those one or two mysteries.
Yes, there are.
But, please, it would be nice if they weren't from Class 7.
Then, if you pass the interview you can go to Parang University?
They said they chose a lot.
The competition isn't a joke.
They only picked a multiple of five.
But, what will they ask at the interviews?
I'm not really good with speaking.
I still have the skills exam too.
There is no way my Ha Ni can fail that interview.
Even if she does fail, at least she got it.
My Ha Ni is really good, isn't she?!
Ha Ni sunbae, do you have some kind of backing?
Backing?
Yeah.
The heavens must've helped me.
The 11th typhoon, "La Na Nim", is blowing through Korea.
Ha Ni!
Dad! What is this?!
The subway is going to be safe.
Ha Ni, will you be okay?
Of course! After all, it's just raining.
It's not just raining!
There's a typhoon out there.
Right!
Just don't...
How about giving up the interview?
Why!
You think I don't have a chance of getting in?
You don't believe in me, Dad?!
Th...that's not it!
Just look at the weather!
This is the only place that will accept me despite my grades.
Even if it's only because I'm grateful, I have to go.
Dad, don't worry.
I'll be going now!
Bye!
Right!
Right!
- Be careful!
- I'll see you later.
- But just wait. - I don't wanna!
Nothing's going easily.
You're right.
A typhoon coming so suddenly.
Because the tracks are filled with water, the subway will not continue to run.
All passengers are asked to leave the train at the next stop, and find other means of transportation to reach their destinations.
Seoul, Kyung Gi schools have already closed today because of the typhoon.
Typhoon warning:
Schools in the central district of Seoul will be closed.
All companies will open late. Forecast for Seoul: there will be heavy rain from today until tomorrow. High winds expected with major flooding.
Student, you didn't have a lot of trouble getting here?
My house is nearby.
That's a relief.
You can leave this way.
Only a small number of students have arrived.
Excuse me...
Many students were not able to make it.
Wouldn't it be best if we postpone the interviews?
How many typhoons will come in one's lifetime?
Eh?
Whenever that happens, should we postpone and end it here?
Send in the next one.
Next student, please come in. Brought to you by the PKer team @ www.Viki
Eun Jo, what are you doing?
Alright! I'm not going to school because of the typhoon.
Aigoo, Ha Ni going to an interview in this kind of weather...
I hope the results are good.
This is interesting.
Well then, what are you most interested in?
Oh, that.
It's Baek Seung Jo!
Um, what I meant to say was... ...a person.
Oh, you have an interest in people?
Yes! That's right, people!
Recently, I've been thinking... ...if we were to get to know other people, how much time would it take to get to know them?
In our lifetime, could we fully understand... ...even one person?
I don't think I could ever understand Baek Seung Jo.
Why must we choose you?
Excuse me?
Your teacher's letter of recommendation... ...is almost at the level of a pledge in blood.
Even so...
In a week, you were able to raise your grades from the 90th place to the 50th.
However, on the very next test, you dropped back down again.
And since last year, every two months... ...you've donated blood.
That is all. How could you possibly have passed the first round?
She got a high score for her personal introduction.
Her confidence is high and her community service is amazing.
We're not picking just any miscellaneous writer.
If there is any reason why we must choose you, Oh Ha Ni, then please do tell!
There's one minute left.
Uh.
That...
Okay. If you don't have any, you don't have to say anything.
Nice job.
Next participant.
Yes. Excuse me.
You were right.
You saw through me.
I really don't have anything that I do well.
Passing the first round was a miracle for me.
So, in truth, I'm really thankful.
However, I think I could say this...
If it's not me, and you picked another student with good grades and lots of awards...
Anyway, if you picked such a stellar student, but if that student is lazy, and doesn't work hard!
When it's rainy and windy, he gives up.
So, then if you guys think that person isn't right for your college, if that happens, then choose me!
I'm slower than other people, but I never give up.
I always do everything till the end. That's why my nickname is "Noah's Snail."
Try having a snail as a pet.
I don't think I'm going to make it.
I knew... Ah well, the results haven't come yet.
Yeah, that's right. You can study and go together with Seung Jo.
I'm not going to take the exam.
What?
I'm saying that I don't want to take the exam.
I'm not going to college.
Yeah, but why?
Because there isn't anything I want to do.
And I don't want to go anywhere either.
Huh.
Then, what will you do after graduating?
Well, I could work part time.
Baek Seung Jo!
Is your life a joke!?
Do you live life however you feel like living it?
Well, then do you want to do business with your mom?
What about running an internet shopping mall?
Then, how am I supposed to live?
What?
Because I don't know how to live... ...is why I say I won't go.
Because I don't want to live like other people, without any motives.
How should I live?
Aye... Tec... That's...
You can study and take over your father's company.
You know that I'm selfish, right? A business that doesn't fit my liking...
I don't have any plans of working there.
Don't expect anything from me.
Baek Seung Jo!
I'm done eating.
Really... That punk...
Aish.
He's only saying that; it's not like he won't take it. Don't worry.
Y-y-yeah, right.
No matter what he does, he can do it with ease, that must be why he doesn't feel any motivation.
He has to find a field of interest soon.
I'd really like to experience it too. That feeling.
Min Ah's.
- We'll enjoy the meal!
- We'll enjoy the meal!
Here... I made these for you guys on such a special occasion.
The name is Bul Nak porridge.
Bul Nak porridge?
It's written right here. Bul means "not," Nak means "fail". Never fail.
- Ahhh.
- It's really written. What did you write this with?
You don't know? They're sesame seeds.
So, it means that if you eat this, you guys will never fail.
Oh really!?
Then I'll just have to eat everything here.
Hey, Jung Ju Ri.
Stop it. Is this all yours?
What?
"Ah, is this all yours?" Is he speaking Japanese?
Jung Ju Ri, just stop it.
Are all these yours?
Yeah.
She's right right right!
Yes, eat up.
Ha Ni, you aren't eating?
I'm eating.
Ha Ni.
What?
Are you getting nervous?
There's no need!
Just eat up all this that your dad made for you.
Then just walk down proudly!
Right?
Yeah, you too.
Ah.
Father.
This recipe is just killer!
Is this octopus?
Aigoo, you know well.
Father, I told you last time.
My taste buds are really sensitive.
I can't let it go.
Well, eat a lot! And do well on the test tomorrow.
Like the octopus, stick to (get into) a college.
Yes.
Dad.
Yes?
Could you pack one more of this porridge?
Are you sleeping?
Baek Seung Jo.
You're going to take that test tomorrow, right?
Everyone is worried about you.
Especially your father.
He keeps worrying about you and he doesn't laugh very often.
First you could take the test, then later you can make a decision on college.
If you don't take the test, but suddenly you figure out what you want to do, then what will you do?
Open the door for a moment.
You can do anything.
So, you have to use your head for the sake of other people.
I believe that people who have a lot need to share what they have.
Even though I want to share everything, I don't have anything, so I can't.
This... I'll just leave it here.
Eat it before it cools.
Also...
See you tomorrow.
Is it a cold?
Do you have a cold?
Maybe...
I... I have medicine.
Just a sec...
This one is very effective.
It's the best!
Here's some water!
Thank you.
This doesn't cause drowsiness, right?
What?!
What?!
"Do not use in case of driving or activities that require concentration."
Oh!
It causes drowsiness!!
What to do?!
Spit it out.
Hey, what are you doing?!
Everything you do is like this anyway.
It'll be alright, since you're strong!
Wait!
You guys have to take your packed lunches.
Filled with nutritious food I have... ...especially made "Exam Pass" lunches.
Thank you very much.
Thanks, Dad!
Thanks, man.
When did you prepare something like this?
That's right... Thank you very much.
Oh, it was no sweat.
Wise choice. Good luck!
Yes.
FlGHTlNG!!
You thought well.
Everyone likes it (the decision to take the test).
Nice boy.
Stop joking around.
Ah, fork...
Do you think I'm you?
Why would I spear a random answer?
Ah, that's right. I measured your corn by my own bushel.
- How far are you going to follow me!?
- Huh?
You're that way.
That's right...
It's the opposite direction...
Go ahead.
I see... So our paths separate here.
Yeah...
Baek Seung Jo needs to go on his own path.
Good luck on your test!
FlGHTlNG!
Aigoo, even so he went.
Yeah...
He's not my son, he's really a godsend... A godsend!
Up until yesterday, he was being stubborn and saying he wouldn't take it... ...why all of the sudden...?
I feel uneasy...
Something just makes me uneasy.
STUDENT!
STUDENT!
There are only fifteen minutes left.
You haven't marked anything yet.
I took some cold medicine this morning... Brought to you by the PKer team @ www.Viki
It was totally scary!
The people didn't even smile.
"Why must we accept you?"
Ahh... She was like a witch.
Did you do well on the exam?
- I don't know...
I just took it.
- Aigoo. I think I screwed up the entrance exam...
What do I do!
Ha Ni, exams are already over so why are you complaining?
We don't even have class!
What have you been doing right now?
TADA!
You were putting on makeup?
Don't I totally look like Ga-In? (Brown Eyed Girls member) Ireoda naega michyeo yeoriyeori chak... (singing Brown Eyed Girls' hit song, "Abracadabra")
Oh, here...
You even have fake eyelashes?
Would you like me to put them on for you?
Sit down! Sit down!
Ha Ni, even though you don't have double eyelids, your eyes are really big.
Close your eyes.
If you put some eyelashes on like this...
Wow!
You look very pretty!
Here, look in the mirror.
Jackpot.
Hey, Dok Go Min Ah, look.
Her eyes look ten times bigger, don't they? If they were ten times bigger, she would be a monster.
Should I put it on the other side too?
Here.
Close your eyes.
Like this.
Hello!
Are you putting on makeup?
It's not makeup...
You have the guts to put on makeup after ruining someone else's life?
Huh?
I heard you gave Seung Jo Oppa sleeping pills on the morning of the college entrance exam.
What?!
What do you mean?
I heard you gave him cold medicine this morning.
After taking those, he fell asleep and had to fill in all the answers right before the test was over.
What are you going to do about it?
How are you going to take responsibility for what you've done?
Hey, Hong Jang Mi!!
Because of that, he might not be able to go to college, but you seem to only care about yourself.
Even like that, you still dare to say that you like him?
Right?
I'm asking you!
It's okay, right?
You did well, right?
You're the Baek Seung Jo.
No way... Just because of the medicine?
Tell me it isn't so, please.
That there was nothing wrong.
Jae Eun Jung.
Relax.
Kim Su Ahn.
We still have time.
Be strong.
Kids, in the next four days your scores will be out.
Yes.
Wherever you go, make sure you have your phones.
Yes.
Bong Joon Gu!
Oh.
Don't have that sad look on your face, okay?
I already have something planned for my life.
Really? Yes.
So, Ha Ni, even if your scores don't come out that good...don't worry.
I'll take care of you forever.
HUUUUUUUU...
Bong Joon Gu, that's enough.
She has Baek Seung Jo.
What did you say?
Who did you say she has?
That cowardly guy can't make a girl happy.
Then what about you?
What can you do for Ha Ni?
What?
An axe comb?
What did you just say?
An axe comb?
Ah, be quiet!
That's enough.
Ha Ni...
Fighting!
Be strong!
Why?
Nothing.
After seeing this, I'm wondering if I really am a genius.
What's wrong, Seung Jo?
You're scaring me.
You still have the interview, so you just have to do that.
Ah, should we drop the curtains for you?
For getting into Tae San University with the highest score?
But honestly, with your skills, going to Tae San University seems like a waste.
You should be going to some place like Harvard.
Anyway, you did well!
Seung Jo, great job!
Hurray!
He did it!
Oh Ha Ni, even after getting those scores, you say "hurray"?
But how do I stop myself from being so happy!?
Baek Seung Jo HURRAY!
Korea HURRAY!
Ring... Ring...
Please... Ring...
It will ring. It will ring.
Please, help me.
It will ring.
Hello?
Yes.
This isn't the roast duck restaurant.
The number is 0292, but... ...this isn't the roast duck place.
Hello?
Yes.
Yes, I am Oh Ha Ni.
Oh my!
Parang University?!
Is it right?
Really?
Wow, thank you!
Thank you.
What?
Oh!
I applied for the social sciences major.
Not the apple department?
Huh?
Apple department?
There's something like that...
Surprise!
Baek Eun Jo!
Oh Ha Ni dummy!
Aiyoo!
Baek Seung Jo is going to Tae San University with the highest score...
What am I going to do if I don't get into college at all?
Oh, Min Ah.
I got into Parang University.
Really?
Did they call you?
Just now.
Wow, congratulations!
And you, Ha Ni?
Not yet.
The call will come.
Yes.
Thank you.
Just wait.
Let's hang up.
Okay. Ah, Min Ah.
Once again, super super congratulations.
You did well.
Why?
Someone like me doesn't have the right to eat.
Eat, eat!
Everything will be alright.
It's over.
Today's the last day for acceptances to be revealed.
It's already 10:00.
I already knew I wouldn't make it.
That witch...
No, that scary professor has no reason to accept me.
But, I was still thinking I could possibly get in.
Hey, you can still go with the SATs.
You can still get into a couple of places with that.
My scores aren't that good.
Hello!
Yes, it is me.
Parang University?
Hey, this...
It's you again, Baek Eun Jo!
What?
Why did you call my name?
Oh my!
Hello.
Yes.
Yes, it is me.
I'm sorry, I thought it was a prank call.
Just now, another person gave up their enrollment.
Student Oh Ha Ni, you passed as an additional acceptance.
Yes yes yes yes yes yes yes! I will go, I will go, I will go!
Ah, hurray!
I think I really have good luck.
Because of the typhoon, kids couldn't go.
That's why I got the chance.
What would I have done if the typhoon hadn't come?
Yeah.
That's not it!
It's because of my Bul Nak porridge.
That's right. Correct.
Here's a present.
Ahjusshi (Seung Jo's father) picked it out.
It's nothing big.
Wow!
It's really beautiful.
Thank you!
Thank you.
For what?
And this is my present.
There's another one?
These are musical tickets.
I've never seen a musical before.
It's this Saturday. Let's meet in front of the theater at 2:30.
You hold on to the tickets.
You can't forget.
What do you mean forget?
Thank you.
Where are you?
Oh Ha Ni, you're in front of the theater, right?
What should I do?
There's so much traffic.
There's no traffic!
Because it's Saturday...
Why don't you go on ahead and leave one ticket at the booth.
Yes, I'll do that.
Hello.
Could I leave one ticket with you?
Ah... Yes.
The idol of every Korean girl, the Crown Prince...
Together with him, a new dream world of the 21st century opens up to you now!
So, 1996.
Ah, really!
I'm sorry. > >
Pass! I don't remember from when it was. When I started to keep thinking about you.
Ah...it hurts.
Why? You want me to pinch them for you?
But, how did you come?
How do you think I came?
How?
Eun Jo, your mom is a really good actress, huh?
You heard me on the phone right? "I'm in front of the theater, and I got stood up."
I have no one to see it with.
So, he said he got it and would come, that great Baek Seung Jo.
Should I just be an actress?
Was it really... ...just because of your acting?
Huh?
Excuse me.
You're going to do the interview for Tae San University, right?
Why are you being like that too?
I don't get why people keep saying college, college, college.
You're smart because you have something to offer.
It has to be that way.
Well, if I say "find your dream," it sounds huge, but... ...just have fun living.
Have fun.
Fun?
My grandma used to say that all the time.
"Ha Ni, have fun living, fun."
"You have fun and make others happy."
She said it'd be fine as long as I live like that.
Fun?
If you come to Parang University, I'll make it fun for you.
Oh, it's so nervewracking.
Just a bit more.
No, no.
This way, this way.
To the left.
Just a bit, just a bit.
Straight.
It's good, it's good!
You got it!
You got it!
You got it!
Aren't you going to take it?
Would I have gotten it so I could play with it?
Ha Ni! Ha Ni!
Come here!
Come here!
What are you doing?
You guys went to a musical?
Think I'll go crazy.
Ha Ni, did he make a move on you?
Make a move?
I mean like while you guys were eating popcorn, doing hand motions like this or...
When watching a musical, you don't eat popcorn.
Oh, really?
Then what do you eat?
Oh!
Did you buy a doll? Wow, it even talks.
This... Seung Jo got it for me, from that doll vending machine.
What?
He gave it to me as a congratulatory gift for getting into college.
Congratulatory gift?
He gave you such cheap trash? Hey, Baek Seung Jo, are you making fun of Ha Ni?
What's wrong with this? And he got it himself.
Hey! You know how difficult doll vending machines are.
Ha Ni, what's hard about that?
Stuff like that, anyone can do it.
Really?
This was my first time seeing it.
Wow.
Hey! Hey, did you see it!? It was totally cool!
Here... Here... Watch this.
Hey!
Where are you going?
Look at this!
Look at this!
Urgh really!
Such a bother.
Here. Look, look, look, look!
Urgh!!
Let me go, let me go, let me go.
Hey look! That's not how it's done.
Ah!
Is this what I see a lot in movies?
Look at me.
Look in my eyes.
In my eyes and in my heart, there is only you.
No.
I can't have both feelings in my heart.
Then I have no choice. Whether it's by using love or using strength, I have to make you love me.
Leave her alone.
No, please don't.
If you do, I will be scared for you.
A coward can die many times, but a real man can only die once.
If I die for you, that is not my death... ...it is love.
No!
Un Deux, Un Deux, Un Deux (One, Two).
What?
Son, do well! Fighting!
Even if someone is rude to you, just let it be.
Do...do your best.
Good luck, Hyung.
Fighting!
Right.
After making me upset over going and not going, it's all over now.
Ah, this is so sad! Why must they go through all of this at such a beautiful age?
You got married at that age. Why are they going on and on about college? I just don't get it.
Ha Ni!
Where are you going?
This isn't going to work.
My heart won't stop racing.
I'll just keep an eye on him until he goes into the exam hall.
This is worrisome.
Worrisome.
Hey, did you see that? That car totally hit someone!
It looks like it hit a girl.
She's waking up.
Ha Ni!
Aigoo!
My daughter!
Aigoo!
Dad.
Where is this place?
It's the hospital.
You were in a traffic accident.
Don't you remember?
You pooong...
I remember.
What about Seung Jo?
He went to take the test, of course.
That's a relief.
You came? Brought to you by the PKer team @ www.Viki Is Ha Ni still being like that?
Can you please teach me? Please, Father... It was fun.
What could happen today... So? Baek Seung Jo?!
That brat.
He's going to make noodles. Why do you like someone like that? Oh Ha Ni!
That hurts! When I go to college I'll find someone else... Then try to forget me.
As, shall we say, a mature citizen, I have lived in Singapore when we were a British colony; and then, under self-government; as a Malaysian; and, in the last 47 years, a proud Singaporean.
We've come a long way.
Last year, was an exciting time, with more changes to come.
I look forward to the time ahead: a Singapore for Singaporeans; a future for us all.
Growing up in our cherished republic, being a part of our nation-building, our 47th birthday is, for me, a time to celebrate.
And remember.
To thank the old folks for their contribution.
To join the children in preparing for the next 47 years.
For an open, democratic and free Singapore.
My grandfather came to Singapore with little.
Through his hard work, he built our family.
And helped to build our nation.
I'm proud of my roots.
And just as proud of my Singapore.
But as I look into the future, I see challenges. The challenge to build the economy of the future.
An economy we can all be proud of.
And share.
So that no one goes hungry. Or homeless.
Truly a community.
I was born in 1994.
I never saw the fight for independence.
I never met the heroes of our freedom.
I didn't know that by the time I was born more than a thousand people had been jailed under the ISA for serving their fellow Singaporeans.
Some for ten, twenty, even thirty years.
I wonder if we would also serve our nation so selflessly.
Because it sometimes doesn't feel like our Singapore to fight for anymore.
So, on this National Day, I hope for a future that makes us Singaporeans again.
A Singapore to live and die for.
One year after I was born, the new millennium was born.
When I was born, Singapore was still a young lady like me.
Now, she is middle-aged like my parents.
I'm so grateful for what our parents did to build our country.
And I want to do the same: to make our island a home for all of us, rich and poor, able and disabled, young and old.
I know we have to work hard so that Singapore cares for all our brothers and sisters, uncles and aunties.
It's the Singapore I want to live in.
Happy 47th birthday, Singapore!
And a happy National Day to you all from the Singapore Democratic Party.
Love Letter to the Soldier
Dear Samsul,
I have written two letters to you but you never replied.
Hopefully, through this video letter, you will see your daughter and be moved to respond.
I brought this video letter from Bupul to Merauke so you could watch it.
Samsul, I still live in Bupul village with Mum and Dad.
The village is still like before. The air is still fresh.
But to this day there is still no electricity and no telephone.
On the journey to Merauke we pass through many border security posts. The TNI post that used to be near the Maro River bridge ... ... has been moved to near the Eligobel District office.
Samsul, I still keep the mobile phone, clothes, blanket and matress you left for me.
Samsul, I miss you.
After you left me - when I was 5 months pregnant with our child ... ... life was difficult.
Many people ask who is the father of my child.
Those who know that her father is a TNI soldier call her an army brat.
Sometimes, when Yani is fussy and cranky,
Mum and Dad become emotional and say to her:
"Your father only knows how to make you, but he is irresponsible!'
Samsul, do you remember when we first met in 2008?
You were very polite and kind.
You used to visit our house often, bringing biscuits, cereal mix and milk.
You came by the house every day until we started dating.
I was still in high school at the time.
I thought we were going to get married.
But you left for Bandung in November 2008 when I was 5 months pregnant.
You promised to move to Merauke and asked me to take care of our daughter.
On 17 March 2009, our daughter, Anita Mariani, was born in the Bupul village.
I call her Yani.
Now Yani has grown big. She's three years old.
She wants to go to school and become somebody useful for the nation.
Samsul, Mum and Dad have grown old.
They can no longer work to support our child.
I find it difficult to work because I have to take care of Yani constantly.
But I continue to fight to support our child.
If you come back to us, of course I will accept you with open arms.
I will continue to wait for you, Samsul. I don't care what people say.
Love, from Bupul and Merauke, 21 November 2011.
Maria Goreti Mekiw
The Catholic Church group JPlC MSC recorded at least 19 cases of sexual misconduct by the Indonesian Armed Forces (TNl) Border Security in the Bupul Village, Merauke from 1992 to 2009.
Women were courted, impregnated and abandoned.
So the answer to this one was 16.
See you in the next video.
Ride of Silence untuk keselamatan di jalan raya
Hari ini, kita anjurkan Ride of Silence
Edisi Penang, Malaysia
Ini adalah acara pertama yang diadakan di Penang, Malaysia
Dan di anjurkan oleh G-Club
Acara ini dilancarkan sepuluh tahun lalu oleh sekumpulan kawan di Dallas
The answer is: these 2 characters here appear only in these 2 locations corresponding to the words corn cream which appear only in these locations in the English text.
Again, we're not 100% sure that's the right answer, but it looks like a strong correlation.
Now, 1 more question.
Tell me what character or characters in Chinese correspond to the English word soup.
My question is when you speak about freedom of religion, are you actually applying to the Malays as well?
Thanks.
There's no compulsion in religion.
Even Dr Farouk quoted that verse in the Quran.
How can you ask me or anyone; how could anyone really say, sorry this only applies to non-Malays.
It has to apply equally.
In the Quran, there's no specific term for the Malays, this is how it should be done.
So I'm tied of course, you know with the prevailing views but I will say that.
So what you want is most is in terms of quality.
You believe so strongly in your faith that even me ...
That question, to Nurul Izzah Anwar at a Novermber 3rd 2012 forum and her subsequent response put the opposition politician in a tight spot.
Condemnation came from all sides of the political divide as politicians exploited her views for political gain.
Nurul Izzah seemed to have come to that point of view from a section of the Surah AlBaqarah, paragraph 256 but is this paragraph relevant as source to conclude that Islam does allow o
The first point this sentence has no relevance to apostasy actually.
As is the current issue.
But this sentence tells the story of how we can become a Muslim of quality.
Because this sentence came down when the Prophet pbuh had migrated to Medina.
When he was in Mecca, a dilemma came about when Muslims were forced to convert to the religion of the Quresh. and there were those who were tortured and killed.
When the Prophet went on his pilgrimage to Medina, this sentence was sent to him; there is no compulsion in religion. to distinguish between truth and falsehood, to illustrate that force is a tool of non-believers as Islam in not a religion that forces people to adopt it, as was the practice of the non-believers in Mecca at that time.
Secondly this sentence, cannot be read part way.
It has to be read in toto. "there is truth over falsehood".
This is to inform us that Muslims with quality do not just know the truth, but must also know that which is false.
So there this 'la ikra ha fiddeen' has not relevance to the issue of apostasy.
But there are other paragraphs in the Ayat Surah Al-Baqarah that deals with apostasy.
"Those who have left Islam, when he/she dies as an infidel (kafir), his practices as a Muslim is 'cancelled' in this life and in the next."
The views of Muslims on whether Muslims can leave the religion, are divided
From an outright 'No!' to a call for the death penalty to a view that it is better to have a true Muslims in their midst than a false one. a 'munafik' or hypocrit.
Islam celebrates freedom of religion.
The freedom that is understood is that Islam does not force people to embrace it.
But when someone leaves the religion of Islam in Islam this is a crime.
And there is punishment for that crime is death.
But the punishment of death for an apostate is not because of his/her apostasy, but the punishment of death is because it is considered at act of war.
And this is why that if a person wants to leave Islam and does so quietly (without a declaration) no form of punishment will befall the person.
But can a Muslim leave Islam in Malaysia? and what is the penalty?
My answer is that there is no law that prohibits a person from leaving Islam.
How can a person be an apostate?
When that person from being a Muslim makes a declaration.
But current laws do not say directly 'if you leave Islam this will be the punishments'
Currently if a person and this seems common with all State enactments if the person declares being a non-Muslim to escape being charged for a Syariah crime
For instance, if a person is eating during the fasting month of Ramadhan and if he is caught, he declares that he is not a Muslim (but it is state that his religion is Islam in his Identity Card), then that is a crime.
But if a person goes through the process (Syariah) of application to leave Islam, he will not be subjected to any punishment.
He will not be charged for leaving Islam (i.e. it is not a punishable crime).
That in the din created by hardline Muslims calling for the death penalty for those wanting to leave Islam, there is in fact no Syriah law preventing anyone applying to do so.
But the religious authorities will not make it easy for the applicant subjecting the person to counselling, investigations and a trial before deciding to allow or dis-allow the application.
So in principle, there is no compulsion for Muslims to remain in Islam as the law stands
But in reality it is difficult to leave.
Let's do a couple of examples dealing with angles between parallel lines and transversals.
So let's say that these two lines are a parallel, so I can a label them as being parallel.
That tells us that they will never intersect; that they're sitting in the same plane.
And let's say I have a transversal right here, which is just a line that will intersect both of those parallel lines, and I were to tell you that this angle right there is 60 degrees and then I were to ask you what is this angle right over there?
You might say, oh, that's very difficult; that's on a different line.
But you just have to remember, and the one thing I always remember, is that corresponding angles are always equivalent.
And so if you look at this angle up here on this top line where the transversal intersects the top line, what is the corresponding angle to where the transversal intersects this bottom line?
Well this is kind of the bottom right angle; you could see that there's one, two, three, four angles.
So this is on the bottom and kind of to the right a little bit.
Or maybe you could kind of view it as the southeast angle if we're thinking in directions that way.
And so the corresponding angle is right over here.
So this right here is 60 degrees.
Now if this angle is 60 degrees, what is the question mark angle?
Well the question mark angle-- let's call it x --the question mark angle plus the 60 degree angle, they go halfway around the circle.
They are supplementary; They will add up to 180 degrees.
So we could write x plus 60 degrees is equal to 180 degrees.
And if you subtract 60 from both sides of this equation you get x is equal to 120 degrees.
You could actually figure out every angle formed between the transversals and the parallel lines.
If this is 120 degrees, then the angle opposite to it is also 120 degrees.
If this angle is 60 degrees, then this one right here is also 60 degrees.
If this is 60, then its opposite angle is 60 degrees.
And then you could either say that, hey, this has to be supplementary to either this 60 degree or this 60 degree.
Or you could say that this angle corresponds to this 120 degrees, so it is also 120, and make the same exact argument.
This angle is the same as this angle, so it is also 120 degrees.
Let's do another one.
Let's say I have two lines.
Let me do that in purple and let me do the other line in a different shade of purple.
Let me darken that other one a little bit more.
So you have that purple line and the other one that's another line.
That's blue or something like that.
And then I have a line that intersects both of them; we draw that a little bit straighter.
And let's say that this angle right here is 50 degrees.
And let's say that I were also to tell you that this angle right here is 120 degrees.
Now the question I want to ask here is, are these two lines parallel?
Is this magenta line and this blue line parallel?
So the way to think about is what would have happened if they were parallel?
If they were parallel, then this and this would be corresponding angles, and so then this would be 50 degrees.
This would have to be 50 degrees.
We don't know, so maybe I should put a little asterisk there to say, we're not sure whether that's 50 degrees.
Maybe put a question mark.
This would be 50 degrees if they were parallel, but this and this would have to be supplementary; they would have to add up to 180 degrees.
Actually, regardless of whether the lines are parallel, if I just take any line and I have something intersecting, if this angle is 50 and whatever this angle would be, they would have to add up to 180 degrees.
But we see right here that this will not add up to 180 degrees.
50 plus 120 adds up to 170.
So these lines aren't parallel.
Another way you could have thought about it-- I guess this would have maybe been a more exact way to think about it
--is if this is 120 degrees, this angle right here has to be supplementary to that; it has to add up to 180.
So this angle-- do it in this screen --this angle right here has to be 60 degrees.
Now this angle corresponds to that angle, but they're not equal.
The corresponding angles are not equal, so these
I spent the best part of last year working on a documentary about my own happiness -- trying to see if I can actually train my mind in a particular way, like I can train my body, so I can end up with an improved feeling of overall well-being.
Then this January, my mother died, and pursuing a film like that just seemed the last thing that was interesting to me.
So in a very typical, silly designer fashion, after years worth of work, pretty much all I have to show for it are the titles for the film.
(Music)
They were still done when I was on sabbatical with my company in Indonesia.
We can see the first part here was designed here by pigs.
It was a little bit too funky, and we wanted a more feminine point of view and employed a duck who did it in a much more fitting way -- fashion.
My studio in Bali was only 10 minutes away from a monkey forest, and monkeys, of course, are supposed to be the happiest of all animals.
So we trained them to be able to do three separate words, to lay out them properly.
You can see, there still is a little bit of a legibility problem there. The serif is not really in place.
So of course, what you don't do properly yourself is never deemed done really.
So this is us climbing onto the trees and putting it up over the Sayan Valley in Indonesia.
In that year, what I did do a lot was look at all sorts of surveys, looking at a lot of data on this subject.
And it turns out that men and women report very, very similar levels of happiness.
This is a very quick overview of all the studies that I looked at.
That climate plays no role.
That if you live in the best climate, in San Diego in the United States, or in the shittiest climate, in Buffalo, New York, you are going to be just as happy in either place.
If you make more than 50,000 bucks a year in the U.S., any salary increase you're going to experience will have only a tiny, tiny influence on your overall well-being.
Black people are just as happy as white people are.
If you're old or young it doesn't really make a difference. If you're ugly or if you're really, really good-looking it makes no difference whatsoever.
You will adapt to it and get used to it.
If you have manageable health problems it doesn't really matter.
Now this does matter.
So now the woman on the right is actually much happier than the guy on the left -- meaning that, if you have a lot of friends, and you have meaningful friendships, that does make a lot of difference.
As well as being married -- you are likely to be much happier than if you are single.
A fellow TED speaker, Jonathan Haidt, came up with this beautiful little analogy between the conscious and the unconscious mind.
He says that the conscious mind is this tiny rider on this giant elephant, the unconscious. And the rider thinks that he can tell the elephant what to do, but the elephant really has his own ideas.
If I look at my own life,
I'm born in 1962 in Austria.
If I would have been born a hundred years earlier, the big decisions in my life would have been made for me -- meaning I would have stayed in the town that I was born in;
I would have very much likely entered the same profession that my dad did; and I would have very much likely married a woman that my mom had selected.
I, of course, and all of us, are very much in charge of these big decisions in our lives.
We live where we want to be -- at least in the West.
We become what we really are interested in.
We choose our own profession, and we choose our own partners.
And so it's quite surprising that many of us let our unconscious influence those decisions in ways that we are not quite aware of.
If you look at the statistics and you see that the guy called George, when he decides on where he wants to live -- is it Florida or North Dakota? -- he goes and lives in Georgia.
And if you look at a guy called Dennis, when he decides what to become -- is it a lawyer, or does he want to become a doctor or a teacher? -- best chance is that he wants to become a dentist.
And if Paula decides should she marry Joe or Jack, somehow Paul sounds the most interesting.
And so even if we make those very important decisions for very silly reasons, it remains statistically true that there are more Georges living in Georgia and there are more Dennises becoming dentists and there are more Paulas who are married to Paul than statistically viable.
(Laughter)
Now I, of course, thought, "Well this is American data," and I thought, "Well, those silly Americans.
They get influenced by things that they're not aware of.
This is just completely ridiculous."
Then, of course, I looked at my mom and my dad -- (Laughter)
Karolina and Karl, and grandmom and granddad,
Josefine and Josef.
So I am looking still for a Stephanie.
I'll figure something out.
If I make this whole thing a little bit more personal and see what makes me happy as a designer, the easiest answer, of course, is do more of the stuff that I like to do and much less of the stuff that I don't like to do -- for which it would be helpful to know what it is that I actually do like to do.
I'm a big list maker, so I came up with a list. One of them is to think without pressure.
This is a project we're working on right now with a very healthy deadline.
It's a book on culture, and, as you can see, culture is rapidly drifting around.
Doing things like I'm doing right now -- traveling to Cannes.
The example I have here is a chair that came out of the year in Bali -- clearly influenced by local manufacturing and culture, not being stuck behind a single computer screen all day long and be here and there.
Quite consciously, design projects that need an incredible amount of various techniques, just basically to fight straightforward adaptation.
Being close to the content -- that's the content really is close to my heart.
This is a bus, or vehicle, for a charity, for an NGO that wants to double the education budget in the United States -- carefully designed, so, by two inches, it still clears highway overpasses.
Having end results -- things that come back from the printer well, like this little business card for an animation company called Sideshow on lenticular foils.
Working on projects that actually have visible impacts, like a book for a deceased German artist whose widow came to us with the requirement to make her late husband famous.
It just came out six months ago, and it's getting unbelievable traction right now in Germany. And I think that his widow is going to be very successful on her quest.
And lately, to be involved in projects where I know about 50 percent of the project technique-wise and the other 50 percent would be new.
So in this case, it's an outside projection for Singapore on these giant Times Square-like screens.
And I of course knew stuff, as a designer, about typography, even though we worked with those animals not so successfully.
But I didn't quite know all that much about movement or film.
And from that point of view we turned it into a lovely project.
But also because the content was very close.
In this case, "Keeping a Diary Supports Personal Development" --
I've been keeping a diary since I was 12. And I've found that it influenced my life and work in a very intriguing way.
In this case also because it's part of one of the many sentiments that we build the whole series on -- that all the sentiments originally had come out of the diary.
Thank you so much.
(Applause)
Now that we hopefully have a conceptual understanding... ...of what a surface integral like this COULD represent, ...I want to think about how we can actually construct... ...a unit vector... ...a unit normal vector, at any point on the surface.
In this video we're going to get introduced to the Pythagorean theorem, which is fun on its own.
But you'll see as you learn more and more mathematics it's one of those cornerstone theorems of really all of math. It's useful in geometry, it's kind of the backbone of trigonometry. You're also going to use it to calculate distances between points.
So let's say I have a triangle that looks like that. Let me draw it a little bit nicer. So let's say I have a triangle that looks like that.
The C squared is the hypotenuse squared. So you could say 12 is equal to C. And then we could say that these sides, it doesn't matter whether you call one of them A or one of them B.
A squared, which is 6 squared, plus the unknown B squared is equal to the hypotenuse squared-- is equal to C squared.
Is equal to 12 squared. And now we can solve for B. And notice the difference here.
So this is going to be 108. So that's what B squared is, and now we want to take the principal root, or the positive root, of both sides.
Now let's see if we can simplify this a little bit. The square root of 108. And what we could do is we could take the prime factorization of 108 and see how we can simplify this radical.
2 times 2 is 4. 4 times 9, this is 36. So this is the square root of 36 times the square root of 3.
Hey, Welcome to Twitter
Let's quickly go over some basics at the heart of Twitter there are small bursts of information called Tweets quick updates like a text message but a Tweet can be more than just text it can include a photo uploaded to Twitter a video you can watch inside the Tweet or a link to great content on the web the stream of of Tweets is your Twitter and you create it by following accounts that are interesting to you when you first join, your Twitter is empty but during the signup we'll help you find great accounts that match your interests.
Just pick categories you like such as entertainment, news, sports, or enter your favorite hobby and then we will show you some recommended accounts in those areas when you click on the Follow button you'll start seeing
Tweets from that account on your Twitter clicking on someone's name or picture will tell you more about the account
It will also give you the option to follow or unfollow them
Following is not permanent, you can always unfollow accounts that you're not that into or search for accounts that you may have missed after you're done signing up
It's important to know that you don't need to Tweet to enjoy Twitter many use it just to listen, rather than share
Once you finish your Twitter profile by uploading a picture and completing your bio consider downloading the app to take Twitter with you on your smartphone
It's a great way to stay up to date with everything you care about while you're on the go
So there you have it!
Just click the Next button below and we'll take you through the rest
In the completing the square video I kept saying that all the quadratic equation is completing the square as kind of a short cut of completing square.
And I was under the impression that I had done this proof already but now I realize that I haven't.
So let me prove the quadratic equation to you, by completing the square.
So let's say I have a quadratic equation.
I guess a quadratic equation is actually what you're trying to solve, and what a lot of people call the quadratic equation is actually the quadratic formula.
But anyway I don't want to get caught up in terminology.
But let's say that I have a quadratic equation that says ax squared plus bx plus c is equal to 0.
And let's just complete the square here.
So how do we do that?
Well let's subtract c from both sides so we get ax squared plus the bx is equal to minus c.
And just like I said in the completing the square video I don't like having this a coefficient here.
I like just having one coefficient on my x squared term so let me divide everything by a.
So I get x squared plus b/a x is equal to-- you have to divide both sides by a --minus c/a.
What was completing the square?
Well it's somehow adding something to this expression so it has the form of something that is the square of an expression.
What do i mean by that?
Well, I'll do a little aside here. if I told you that x plus a squared, that equals x squared plus two ax plus a squared, right?
So if I can add something here so that this left hand side this expression looks like this, then I could go the other way.
I can say this is going to be x plus something squared.
So what do I have to add on both sides?
If you watched the completing the square video this should be hopefully intuitive for you.
What you do is you say well this b/a, this corresponds to the 2a term, so a is going to be half of this, is going to be half of this coefficient.
That would be the a.
And then what I need to add is a squared.
So I need to take half of this and then square it and then add it to both sides.
Let me do that in a different color.
Do it in this magenta.
So I'm going to take half of this-- I'm just completing square, that's all I'm doing, no magic here --so plus half of this.
Well half of that is b/2a right?
You just multiply by 1/2.
And I have to square it.
Well if I did it to the left hand side of the equation, I have to do it to the right hand side.
So plus b/2a squared.
And now I have this left hand side of the equation in the form that it is the square of an expression that is x plus something.
And what is it?
Well that's equal to-- let me switch colors again --what's the left hand side of this equation equal to?
And you can just use this pattern and go to the left.
It's x plus what?
Well we said a, you can do one of two ways. a is 1/2 of this coefficient or a is the square root of this coefficient or since we didn't even square it we know that this is a. b/2a is a.
So this is the same thing as x plus b over 2a everything squared, and then that equals-- let's see if we can simplify this or make this a little bit cleaner --that equals--
See, if I were to have a common denominator-- I'm just doing a little bit of algebra here --see, when I square this it's going to be 4a squared-- let me let me write this.
This is equal to b squared over 4a squared.
Right?
And so if I have to add these two fractions, let me make this equal to 4a squared.
Right?
And if the denominator is 4a squared, what does the minus c/a become?
I See if I multiply the denominator by 4a, I have to multiply the numerator by 4a.
So this becomes minus 4ac, right?
And then b squared over 4a squared, well that's just still b squared.
I'm just doing a little bit of algrebra.
Hopefully I'm not confusing you.
I just expanded this.
I just took the square of this, b squared over 4a squared.
And then I added this to this, I got a common denominator.
And minus c/a is the same thing as minus 4ac over 4a squared.
And now we can take the square root of both sides of this equation.
And this should hopefully start to look a little bit familiar to you now.
So let's see, so we get x.
So if we take the square root of both sides of this equation we get x plus b/2a is equal to the square root of this-- let's take the square root of the numerator and the demoninator.
So the numerator is-- I'm going to put the b squared first, I'm just going to switch this order, it doesn't matter --the square root of b squared minus 4ac, right?
That's just the numerator.
I just the square root of it, and we have to get the square root of the denominator too.
What's the square roof of 4a squared?
Well it's just 2a, right?
2a.
And now what do we do?
Oh, it's very important!
When we're taking the square root, it's not just the positive square root.
It's the positive or minus square root.
We saw that couple of times when we did the-- and you could say it's a plus or minus here too, but if you look plus or minus on the top and a plus or minus on the bottom, you can just write it once on the top.
I'll let you think about why you only have to write it once.
If you had a negative an a plus, or negative and a plus sometimes cancel out, or a negative and a negative, that's the same thing as just having a plus on top.
Anyway, I think you get that.
And now we just have to subtract b/2a from both sides. and we get, we get-- and this is the exciting part --we get x is equal to minus be over to 2a plus or minus this thing, so minus b squared minus 4ac, all of that over 2a.
And we already have a common denominator, so we can just add the fractions.
So we got --and I'm going to do this in a vibrant bold-- I don't know maybe not so much bold, well green color --so we get x is equal to, numerator, negative b plus or minus square root of b squared minus 4ac, all of that over 2a.
And that is the famous quadratic formula.
So, there we go we proved it.
And we proved it just from completing the square.
I hope you found that vaguely interesting.
See in the next Video.
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BORN INTO MAFlA
Directed by Vitaliy Versace
Singer..Don't speak to me, Is so hard to resist when you talk to me
Don't reach for me I know that you care, but when it comes up to loving, you are unaware Don't you know you are a perfect drug
Inside drives me blind with one look from you
Hi Dad.
Hi son, you're here.
I told you I will be here.
Is that the same woman that I saw at our house last night?
Yes, That's her.
She thinks she's in love with me.
Don't you know you are the perfect drug.
Are you serious?
Isn't she to young for you dad?
That's enough Ivan.
I did not asked you here for that.
And what that would be?
If you stop with the sarcasm, we can get to the point. there are two things I need you to do for me.
What is it?
Ivan, I don't know what got into you in the last few months.
You are totally different person, and is not good.
I have this friend and i want you to go talk with her.
Maybe she can help.
You are sending me to a shrink?
She is not a shrink, she is a very educated woman.
She is the best pshichologist in Moscow.
She is very good.
But I don't have any problems.
Why would I need a shrink?
Oh yes you do.
I need you to stay focused.
Not to do things that are below your station.
Fine I will go and see your highly recommended shrink.
You need to act like it.
It won't change anything.
What else do you want from me?
I won't do it! Yes you are!
(applause) Hi honey.
What is wrong?
You look worried.
It is Ivan.
He is changing by the minute.
I don't know what to do about it.
He does not seem like he cares.
I'm worried about him.
Oh, I wish I could help.
He is a story
Enough with my words.
Tell me how have you been doing?
Oh, I don't have enough words to tell you. It's
I'm so grateful for everything that you did for me Alex.
It is also wonderful.
I didn't even dream that one day I will be sitting in one of the most expensive restaurants.
My pleasure.
Give my beautiful lady a drink.
Yes Sir, What can I get you madam?
Same thing like Alex is having.
Yes madam, I'll get it right away.
Thank You.
You are welcome.
Hi Ivan.
Have a sit.
How are you doing today?
Good.
Thank You.
Ivan, I worked with a lot of people that worked with your father.
They all have problems.
They all can't sleep and they come to me because they have problems.
Whatever I have said in this room, Whatever they said in this room, stays in this room.
So don't be afraid to open up and tell me what is bothering you.
Oh, I'm not afraid.
Ivan.
Your father told me you are believing in God and you talk to God?
Do you want to tell me a little bit about it?
What's so hard to understand that i believe in God.
What's wrong with you people?
Are you feeling angry Ivan?
No. I'm not angry.
Do you want to talk about your feelings?
Oh, do you want to know how I feel?
I feel like I want to run.
I want to run away and never come back.
Ivan.
You have everything.
Everything that a kid can wish for.
Maybe you are right.
I have everything, except that I don't have love.
My father is killing people, you know that, and you feel so calm.
Let's make appointment for next week.
I'm moving to United States.
I want to start a new life.
Hey, hey Ivan Here is the book you are looking for man.
Thank you Sergei.
You are a good friend Sergei.
Of course man.
Friends forever.
Forever man.
We know each other since we were kids man.
Yeah, that's why I have to tell you something.
Something important.
Tell me what.
I'm tired of this Mafia.
Is not for me.
So what are you gonna do?
How are you gone get out of this?
I'm moving to United States.
Are you crazy?
Your father won't let you do this in a million years.
If he is not gonna allow me, I'm just gonna run.
I wonder if you can pull this off.
You know,
I was wondering about the same thing too.
Come with me then.
Let's go together to America.
That would be so great.
Move to America.
Get a new place.
Florida maybe!
I have something better!
What?
Hollywood.
Wow, Sunny California! maybe we can see some movie stars there too.
I have friends there, we can stay at Jacob's house.
Who is Jacob?
He is a kid I have met online.
He is a good guy.
He invited me over at his house.
You know what man?
Let's do it.
Let's do it.
I asked you to take care of that situation for you and you let me down.
I'm not like you.
I can't just pull the trigger and kill somebody for $5000, I'm not going to do it.
I built up this whole business, my whole life for you.
For you!
And you are just gonna live me like this?
I did not ask for.
Because of your business, mom is dead.
I don't have a mom.
I just have a dad who's too busy killing people, not hug his son or
love his family. I'm sick of this. I don't want to do this.
Why are you bringing up this old stuff.
This is got nothing to do with anything.
I sent you to the best schools in Moscow.
I gave you the best education you could possibly get.
You've done everything you wanted.
You've done everything you wanted to to.
All I asked is to help me out in a situation but you wouldn't even do that.
Is not the help, is just to shoot somebody, come on.
I know you do this for whole your life, I just can't go and shoot somebody.
Is just crazy.
You know two years ago I found God.
I'm going every Sunday to Church.
I'm praying.
I'm happy.
Why do you want me to kill somebody.
This is crazy.
You use keep doing your thing if you think is right.
I'm just gonna.. just do your business I'm not gonna do this.
I'm gonna stay away from this.
This business is taking you to Los Angeles.
From where do you think you get all the money from?
Do you think it just grows on trees?
I did not ask for this.
I did not ask for you, I did not ask for mom, I'm your son and .. is just crazy, it just happened this.
My mother died because of this shit and rest of the stuff, you know?
I can't deal with this, you know?
Mom told me, I never told you this, but Mom told me before when I was a kid.
I still remember when I was 10 years old.
She told me, she was praying with me one night and she told me.
"I hope you are not gonna grow up like your Dad." I'm not gonna be like you.
I'll be something different like a Doctor or a Lawyer.
Something that people used to
look up to and say: "That's a good man, he is helping people.
Not shooting people." Unbelievable.
This business is our life.
You were groomed to take over the family business.
I don't have anybody else I can come on.
I can't count on my brother. i don't trust him too.
He is doing some crazy stuff behind your back.
I see him with different people from different groups of the town. Your competitors in this thing. i don't like him too.
I don't like what you guys do, but I'm not gonna mix in this and not gonna tell you what to do.
Is just You know who to trust, just don't count on me. I'm not gonna do it.
I can not trust my brother.
You are the only one I can trust.
This is when i need you most. I ned you now.
I don't need you in Los Angeles.
I'm not gonna do it Dad, If you want to pull the gun and shoot me right here.
I'm not gonna do it.
Bible and God said DON"T KlLL.
I'm not gonna kill anybody for money.
Is not good.
My brother, he is a scumbag.
Is nobody I can trust but you.
I need you watching my back.
Do you know how many times a day somebody tries to kill me?
Dad, that's why i told you to live this business and start something else, retire and give up this.
He has been with you 15 years in this business.
Twenty, I don't even know.
He doesn't have a problem to shoot somebody.
You need that kind of people.
You don't need somebody like me who can't even shoot a guy. Retire!
You don't just retire.
You don't just get out of this, just say "I'm done and that's it." It doesn't work like that.
That's why I don't want to jump in.
Because if I jump in, there is no way out.
I want normal family, I want normal life.
I want to have wife, children, drive safe.
Not thinking somebody is going to kill me.
But you are already in. You can't get out.
You can't back out now.
You are past that point of no return.
This is it.
Ivan!
This is it!
This is the life.
This is what you were born into.
This is what i groomed you for all these years.
You can do this.
I need you. Please.
Tell me you will stay.
Dad.
I'm just gonna run away from Russia, just go somewhere and start a new life.
Hopefully nobody is gonna find me somewhere and I'm gonna be happy and not hear again about this Mafia thing.
Stop the car.
I'I walk from here.
Are you sure?
Yeah, I'm sure.
I'll call you sometimes.
Tom, LA.
Tom, how are you?
Listen.
My son is flying to LA tomorrow.
Can you look after him?
Thank you.
I knew I can count on you.
Sergei!
Sergei YOU ARE NOT GOlNG TO AMERlCA
Told you not to bother me.
I need some time alone.
I know Sir.
It's your brother.
He is here to see you.
What do you want Demitry?
I'm not exactly in the mood to talk with you right now.
Would you like something?
Ivan plane just took off.
I know that.
Is there anything else?
Actually no.
How could you?!
What?
Do you want Ivan to take over your place?
He is my son.
What did you expect?
I work for you for over 15 years and this is how you repay?
Oh, please.
You really didn't expect me to give you my empire, did you?
But Ivan he couldn't even kill a fly.
Why do you expect him to take over your business?
Huh?
He is a coward.
Don't you see that?
Don't talk about my son like that, or I'll kill you!
That's why I'm here.
This! -screaming-
Don't be stupid guys.
I'm in charge here now.
Hey, do you want to go to the airport?
Why, what's at the airport?
Do you remember the russian guy I've met, like, two months ago on the internet?
Yeah, what about him?
He is coming into town.
What is your mom going to say about this?
Hey, she is cool.
She said he can move with us.
Dog, are you coming or what?
Ok, allright.
Let's go.
So where is this russian friend of yours anyway?
Just be cool. He will be here any minute.
So we are just gonna stand here and wait all day or what?
He is coming, just be cool.
Why do you have to be like that?
Dude?
You have such an attitude.
Sorry man.
Here he comes, right there.
Nice to meet you.
So how is the LA.
It is awesome.
Look at the weather.
So we get your luggage?
I don't have a luggage.
A russian with no luggage.
What are the chances of that.
Hold on second. I see somebody who
Hello Ivan, my name is Tom.
Your father called me and ask me to help you out for a few days.
I'm sorry I couldn't get you a car in such short notice.
Here are the keys to my car.
You can use it for a few days.
There are enough money in the trunk to cover all the expenses.
So who is that guy?
I don't know.
All right, thanks.
You got it.
Hey guys, I've got a car.
Are you going to get your car?
I'm just gonna live my car here man.
Are you sure?
Let's go.
So drive .. watch the stuff!. there are people in there man!
Mrs Marshal.
Mom, this is Ivan.
Oh, Hi Ivan.
Welcome to America.
I know you are going to enjoy staying in our home.
Let's all have some tea.
I'll get the tea.
Demitry, is jake.
Yeah.
LA. I know.
I understand Sir.
We're doing the best we can.
How was your flight?
That was pretty long huh?
Yeah, it was 14 hours long.
Is it cold out here all the time.
No man, it is not just like in the movies.
Is same thing like in USA, you know.
We have winter, we have four seasons basically.
Yeah.
What's the temperature?
Well, right now is cold man, it's i think 20 degrees below zero.
Basically where I grew up is same thing like in New York city.
Wow, I only have spring clothes and summer clothes so yeah Somebody has to take you shopping, maybe my son Hehehehe I understand. You don't need to come here.
I'll handle this.
I want to be a part of the family.
I can handle this.
We don't know where Ivan is yet.
Do you have a sister or something?
No man, I'm the only son.
My mom died when I was ten.
My dad has his own crazy business and I'm not into supporting so I kinda of walked away.
I did not know your mother died.
Yeah, she died man.
I was ten years old.
That sucks.
But we are working ..
We have a lead You don't need to come out here Sir, I understand.
I unders..
I'll
That's why I'm kid of jealous man.
You have a good mom and is cool.
You don't have to be jealous!
There is enough of me to go around.
Thank you.
All my friends come one, hang out, kick it.
Thank you for letting him.. let me stay here with you guys.
I appreciate that.
I know I met you just for two months online and it was really col. i was basically having a bad day, and i went online two months ago and I've met Jacob. We had a short online conversation, he told me about Hollywood, LA.
It's just I had to run away from all this and start a new life.
I admire you for your courage.
Thank You.
I did not have a clue.
I'd probably, no
I would've not had the courage to come so far by myself.
But, you know.
I'll pick you up at the airpot Sir.
Until you get here I'll.
Hello?
I couldn't imagine, like, leaving the United
States to go live in another country, it's just like, near, No You now me like not knowing what the area is, or is kind of scary.
Yeah, I took english in school so, I know a little bit.
I speak little bit english.
Is my first day in LA, in United States, It's cool.
I'm glad that I understand you guys.
If I would start speaking Russian, nobody would probably understand anything.
In school do you have to learn english?
Or is it like, you can take other language like Spanish or something like that?
Same thing.
You have a choice, German, French or English.
I took English so, I just took English.
Did they encourage you to select English?
Yeah, because English is first language in the world.
I was in a private school.
My father has a lot of money and connections. so I was
I just jot tied of that.
I had the best education basically.
Is not about that.
After my mom died, I missed love.
It was not enough love from my dad, he was always busy and that kind of stuff, so.
He got you that fat car?
That's my uncles.
That's actually Tom's car.
He knows my father.
They used to do a lot of business together, so.
He is kind of, kind of like my dad so I don't want anything from them
But for first days, couple days, I'll take their help, but then I just wanna be independent.
I don't want anything of this, I just run away from this but is keep following me.
Well, as long as you are in my household, you've got a cool mom.
I told you she was cool.
Let me show you your room.
Thank You, the tea is good.
Smells good.
Oh, That's my home made vegetable soup.
Come on.
Look at that shit, he is getting her number.
He's been in LA for 5 hours, I've been here for 5 months and I can't get a girl. That's sad. ha ha ha ha Dude she is hot!
That's crazy!
He is one lucky son of a gun, that's all I know.
I'll call you.
Got her number.
What's her name?
Celine.
Do you have to look at the paper?
Yeah.
Come on dude. It just happen two seconds ago.
She's hot.
Let' go.
I've got to call her.
Do you guys got a dollar?
Dude. Get a job.
What did he just say to you?
He mistakend me with somebody else.
Hi Celine.
This is Ivan.
Remember me? Yes.
From Russia.
I would like to take you out.
Tomorrow, at 11.
That is perfect.
I'll see you tomorrow.
Thank You Bye Bye.
YES!
I'm sorry I'm late.
Thank you for going out with me.
You look beautiful.
Thank You.
I see something special in you.
I see something special in your too.
Good, I like that.
So What did you use to do in Paris?
I used to model.
For how long have you been in LA?
Six months.
What brought you to LA?
I just wanted to turn the page.
Start a new life.
That's funny, because that is why I came to LA.
That's good.
Why do you think I'm so special?
like nobody else I know. Beautiful, smart.
Thank You.
I'm just very happy that I've met you.
Me too.
Happy for us.
I had a good day.
Thank You. Me too.
I'm happy that you enjoyed.
In long time I did not had such a good day.
Me too.
I enjoy you.
Thank You.
That means a lot to me.
Oh, My, God
Hey, it is the guy from the airport.
Hey guys, where is Ivan at?
He is out on a date or something.
Oh shit!
What's going on?
His uncle killed his father so he can take over the family business.
Now he wants Ivan dead too.
What's the family business?
He never mentioned it to you?
His father is the head of the Russian Mob.
What?!
He never mentioned the Mafia!
I knew there was something fishy about him.
He did not say anything to me.
Did he say anything to you?
No, he didn't.
Look, we do not have time for this.
We need to find Ivan and we need to find him now.
He is in trouble.
What kind of trouble.
I don't understand.
What is going on?
Let's find Ivan, let's find him now.
What are you talking Russian Mafia?
Man, I just want to play basketball.
Don't get me involved in this crap.
I'm not getting you involved.
I made a promise to his father a while back
I'll watch for him, and that's what I'm gonna do.
Well, I don't know how that involves me, so find Ivan yourself.
Look, Ivan's problem can become your problem, real quick.
We need to really help him now.
Don't be like this.
He is our friend.
The next time we see Ivan, he could be dead.
We need to find him now.
Get out of here.
I'll keep them busy!
Call the police!
Looking for me?
Get your ass up!
Demitry, welcome to the States!
Don't screw around.
This guy is crazy.
He is here to kill his nephew.
Do you think he's got a problem killing you?
I've made arrangements to get your clothes and your choice of transportation.
Why do I have to come out here and take care of things myself?
Tony, get in the car!
Not in the front sit.
Get in the back!
Where the hell do you find these guys?
What's wrong with you?
He is too dumb to pay him it any less.
Yes...
So what's your plan?
My plan is Well first of all I want to explain myself to you.
We had a problem catching Ivan because Tom was protecting him.
By who?
Tom.
I understand that you are upset but we took care of Tom.
Tom was protecting them, hiding them all over the city.
We have a guy in the back right here, that might know where Ivan might be.
But he is not giving us the information.
Let's tell him we don't have to friendly either and let's get some information out of him.
All right.
Let's go.
Have this stab on side.
Tony, give me your gun.
My gun?
Yes, your gun.
You are ready.
Please, today.
Let's go.
By all means you came so far.
Show me how the russians do it.
Wakey, wakee.
Do you know who we are.
Do you know what we're doing here.
Do you remember me?
I guess.
Listen to me.
We are not playing around.
Listen to him!
Listen to me.
We're here about your friend Ivan.
Where is he?
I don't know!
You don't know?
Your friend Ivan.
Where is he.
We saw you plying basketball with him where is he?
I don't know.
Tony.
One more time.
Do you see this gun at your throat?
The last thing you are going to hear is me pulling the trigger.
Where is he? Your friend Ivan, you know what I'm talking about!
Do you like the air?
Do you like the air to clean up your brain?
Do you hear me know?
A minute ago you did not know what is all about, now you know.
Look at that man right there.
Do you see him?
See him?
He came over all the way from Russia to find you.
Now listen, I've seen you in the neighborhood and I don't want to hurt you
Are you trying to say something to me?
I don't.
You don't what?
Point the gun?
Look at Him!
See that man right there.
I didn't do anythin
He's from Moscow, he came here to find you, but you want to talk with me.
Look at me.
You're not gonna talk are you?
Demitry!
I tried to save you kid but you don't want to listen.
Just let me go.
So you're gonna tell us where Ivan is?
What's gonna be kid?
Do you want to get out of here alive?
He's staying at Jacob's, he's staying at Jacob's!
At Jacob's?
Yes.
Oh, why you just didn't say so.
So he's at jacob's huh?
Nice knowing you kid.
Wait, I thought you are going to let me go!
So do you know where to find this Jacob kid, right?
The one he got away?
Yeah.
Where is he?
Well, we have to find him.
Find him!
I gave you the responsibility of the address book.
Where is he?
I don't know where he is.
It is very important as soon as you know where
Ivan is, I need to take care of it.
This is personal.
Right?
All right man.
Go on the phone, call who you need.
We need to find that kid right now.
Listen, when we spoke on the phone last fall you were suppose to be the man in LA.
Take care of everything. Every time you have a problem, I can't come from Moscow all the way here to make sure it is all OK.
You need to be in charge of that.
Alright, I'll take care of it.
I promised you, that you are going to have a shot at it and I'm gonna keep my word.
But every time you have a little problem, you need to be the man who solves these things out.
OK.
Thank You.
Tony.
I missed you so much.
Thank you for coming.
You did not change yet.
What happened.
No, I did not change yet.
I didn't go home.
Listen, I know we didn't know each other that long but i fell in love with you.
I feel like you are very special person.
I'm very happy that I've met you.
Last night I was thinking about you.
How beautiful you are, how good you smell and beautiful lips and eyes and.. perfect, you are perfect.
I fell in love with you and i have something for you.
I hope this is not gonna be a shock, but, would you marry me? Wow!
This is a big surprise.
I don't know what to say, I mean, I love you too but I barely met you.
I'll take that as a yes.
This is a beautiful ring.
It is a big surprise.
I love you.
I love you too.
Trying to run from me?
I got you now Jacob!
Nice work!
What's wrong man?
What were my instructions?
What were my instructions?!
We were suppose to get information and shoot his ass.
What information did you get?
He wasn't gonna talk anyways.
He never had a chance because you put a bullet in his brain before he had a chance to say anything!
Just tell him something else happened alright.
We'll tell him that he tried something so we had to put a bullet in his ass.
It's done.
We can't go back.
It's over.
You gonna want me to tell Demitry that?
You are going to tell him.
Fine. If I'll have to, I'll tell him
It is just It takes like wow I was expecting to come here, I was alone, no friends and suddenly I've met you.
You are a great man and you know, I feel for you and it's happy.
It's something amazing what happened to me.
I think, I think we are going to be very happy family.
We can have a good time together.
I think so too.
I'm so happy.
Where do you think we will live?
I don't know.
We will talk.
As long as we are happy, that's important.
I'm agreeing with you.
It is just, you know.
I'm new here and everything is crazy.
And you know, I have to get used to everything.
Get it step by step.
You know.
Me too.
I've been in Los Angeles for two days, but we're i think this is the best.
You came from Paris, I came from Moscow and we met and it is very cool.
Isn't that strange that we've met after you know, you came more that 12 hours in the plane, get here wow!
It is something amazing.
It is the best thing, you know.
People are suppose to meet each other.
Suppose to meet people they love. It just happened to us.
Surprised.
You kind of remind me of my mom.
You look beautiful and you are an awesome person.
I've never met anybody like you, so open.
We've got good time and is awesome.
This is the most important.
I think is great.
I would like to meet your family, maybe they will come here.
Because you know, if we wanna marry.
You know.
Then.
I would like to know the members of your family, most of your family.
I think is important.
Yeah, met too.
I don't have much family.
My mom died when I was ten and I have...
I have my dad left and he is in Moscow.
Maybe he will come.
I think he will come when he will find out I'm getting married.
I think he is gonna love you.
He is very busy with his job.
I don't approve what he is doing with his job.
I think he is gonna love you, as a daughter.
I'm the only one son in the family so to have a daughter.
He is gonna have a daughter. Beautiful.
Thank You.
I'm sorry what happened to your mom.
You had to grow up alone with your father.
You don't have your grandma helping you.
I don't know, is just...
I'm sad when I hear that because, it wasn't easy for you.
Yeah, you are right it wasn't easy. Maybe this is why I've made this move so fast just to get married because, I missed us for the last 11 years.
I'm 21 and you are 20 and we are happy.
So is really cool.
I just have basically, like I've got my mom back.
I've got with the person that I'll spend my life with.
That is more than mom.
I'e got the person that I will spend my life with it.
Well, we are both young and hopefully we will get along together well, because we need more experience.
But I'm so happy to be here, I have only you here.
It is amazing.
You are amazing.
That's what happened to me.
I'm gonna pray to God that our marriage is gonna last forever and we are going to spend to death and die in the same day.
Wow!
I hope so too, in the dame day!
I promise you.
I'll treat you like a queen.
Uncle!
Ivan, are you alright?
Your father asked me if you are OK.
I'm OK, I'm gonna just use the restroom.
I'll ask Jacob's mom to make us some tea.
I don't think she is in any condition to fix us tea.
Ivan what are you doing?
Come back!
I just want to talk with you.
Celine!
Hey baby.
I had a nightmare.
I'm sorry. I dreamed that my uncle came from Moscow and killed all my friends and killed you and we've got married and...
It is not that is just all my friends died, and you...
I've got a call.
That's from Moscow.
Take it.
Hello.
What?
What happened?
Somebody called me from Moscow.
One of my uncles said that my dad got shot two days ago
What! I'm so sorry.
Oh, poor you.
When I've got the news that my father died is like my dream became alive.
Where is Tony?
Who's Tony?
The guy from the airport.
That guy.
He took the Escalade to the shop.
Had to get fixed.
Can he handle that?
I don't know.
He's gonna probably crush the damn thing.
I'm out.
Demitry, What did you got?
Full house.
Nobody is that lucky.
OK boys, that's enough.
Don't we have anything else to do?
Demitry, a little bit more poker won't kill you.
A little bit?
We're playing for one or two hours!
What else we're gonna do?
We have people to kill.
Let't get to work.
Work?
We don't work.
We don't have jobs.
Our only job, is you.
Don't you ever speak to me like that.
Or what?
You are messing with the wrong person.
You are going to come to our country, my city, and tell me what to do?
You guy, think I would give you a loaded gun?
Do you believe this guy?
Call Tony.
Tony!
Yeah.
Come on in. We have a mess to clean.
Thank you Jake for not betraying me and taking care of Demitry.
Demitry thought he can come here and tell us what to do?
It was fun.
But he was wrong.
Now I can see I can trust you Jake.
I'm gonna let you run the area that you wanted so bad.
So you are going to put me in charge of LA?
After Demitry took out Alexander, we became independent.
Now nobody can tell us what to do.
Except for me.
Are you having a good time?
Yes, I am Jacob.
Baby, do you know what day is today?
It is our anniversary!
I can't believe I forgot about it.
I've got you something.
Oh, That is so sweet.
I love you baby.
Thank You for Watching BORN INTO MAFlA
Subtitle Translation and Adaptation
ANTON PlCTURES
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 Let's think about what functions really do, and then we'll think about the idea of an inverse of a function. So let's start with a pretty straightforward function.
And in that domain, 2 is sitting there, you have 3 over there, pretty much you could input any real number into this function.
So this is going to be all real, but we're making it a nice contained set here just to help you visualize it. Now, when you apply the function, let's think about it means to take f of 2.
We're inputting a number, 2, and then the function is outputting the number 8.
It is mapping us from 2 to 8.
So let's make another set here of all of the possible values that my function can take on.
There are more formal ways to talk about this, and there's a much more rigorous discussion of this later on, especially in the linear algebra playlist, but this is all the different values I can take on.
So if I take the number 2 from our domain, I input it into the function, we're getting mapped to the number 8. So let's let me draw that out. So we're going from 2 to the number 8 right there.
The function is doing that mapping.
That function is mapping us from 2 to 8. This right here, that is equal to f of 2. Same idea.
You start with 3, 3 is being mapped by the function to 10.
It's creating an association.
The function is mapping us from 3 to 10.
Now, this raises an interesting question.
Is there a way to get back from 8 to the 2, or is there a way to go back from the 10 to the 3?
Or is there some other function?
Is there some other function, we can call that the inverse of f, that'll take us back?
Is there some other function that'll take us from 10 back to 3?
We'll call that the inverse of f, and we'll use that as notation, and it'll take us back from 10 to 3.
Is there a way to do that?
Will that same inverse of f, will it take us back from-- if we apply 8 to it-- will that take us back to 2?
What you'll find is it's actually very easy to solve for this inverse of f, and I think once we solve for it, it'll make it clear what I'm talking about.
That the function takes you from 2 to 8, the inverse will take us back from 8 to 2.
So to think about that, let's just define-- let's just say y is equal to f of x.
So y is equal to f of x, is equal to 2x plus 4.
So I can write just y is equal to 2x plus 4, and this once again, this is our function.
You give me an x, it'll give me a y.
But we want to go the other way around.
We want to give you a y and get an x.
So all we have to do is solve for x in terms of y.
So let's do that.
If we subtract 4 from both sides of this equation-- let me switch colors-- if we subtract 4 from both sides of this equation, we get y minus 4 is equal to 2x, and then if we divide both sides of this equation by 2, we get y over 2 minus 2-- 4 divided by 2 is 2-- is equal to x.
Or if we just want to write it that way, we can just swap the sides, we get x is equal to 1/2y-- same thing as y over 2-- minus 2.
So what we have here is a function of y that gives us an x, which is exactly what we wanted.
We want a function of these values that map back to an x. So we can call this-- we could say that this is equal to--
I'll do it in the same color-- this is equal to f inverse as a function of y. Or let me just write it a little bit cleaner.
We could say f inverse as a function of y-- so we can have 10 or 8-- so now the range is now the domain for f inverse. f inverse as a function of y is equal to 1/2y minus 2.
So all we did is we started with our original function, y is equal to 2x plus 4, we solved for-- over here, we've solved for y in terms of x-- then we just do a little bit of algebra, solve for x in terms of y, and we say that that is our inverse as a function of y. Which is right over here.
And then, if we, you know, you can say this is-- you could replace the y with an a, a b, an x, whatever you want to do, so then we can just rename the y as x.
So if you put an x into this function, you would get f inverse of x is equal to 1/2x minus 2.
So all you do, you solve for x, and then you swap the y and the x, if you want to do it that way.
That's the easiest way to think about it.
And one thing I want to point out is what happens when you graph the function and the inverse.
So let me just do a little quick and dirty graph right here.
And then I'll do a bunch of examples of actually solving for inverses, but I really just wanted to give you the general idea.
Function takes you from the domain to the range, the inverse will take you from that point back to the original value, if it exists.
So if I were to graph these-- just let me draw a little coordinate axis right here, draw a little bit of a coordinate axis right there.
This first function, 2x plus 4, its y intercept is going to be 1, 2, 3, 4, just like that, and then its slope will look like this.
It has a slope of 2, so it will look something like-- its graph will look-- let me make it a little bit neater than that-- it'll look something like that.
That's what that function looks like.
What does this function look like? What does the inverse function look like, as a function of x?
Remember we solved for x, and then we swapped the x and the y, essentially.
We could say now that y is equal to f inverse of x.
So we have a y-intercept of negative 2, 1, 2, and now the slope is 1/2.
The slope looks like this. Let me see if I can draw it.
The slope looks-- or the line looks something like that.
And what's the relationship here?
I mean, you know, these look kind of related, it looks like they're reflected about something.
It'll be a little bit more clear what they're reflected about if we draw the line y is equal to x.
So the line y equals x looks like that.
I'll do it as a dotted line.
And you could see, you have the function and its inverse, they're reflected about the line y is equal to x.
And hopefully, that makes sense here.
Because over here, on this line, let's take an easy example.
Our function, when you take 0-- so f of 0 is equal to 4.
Our function is mapping 0 to 4. The inverse function, if you take f inverse of 4, f inverse of 4 is equal to 0. Or the inverse function is mapping us from 4 to 0.
Which is exactly what we expected.
The function takes us from the x to the y world, and then we swap it, we were swapping the x and the y.
We would take the inverse.
And that's why it's reflected around y equals x.
So this example that I just showed you right here, function takes you from 0 to 4-- maybe I should do that in the function color-- so the function takes you from 0 to 4, that's the function f of 0 is 4, you see that right there, so it goes from 0 to 4, and then the inverse takes us back from 4 to 0.
So f inverse takes us back from 4 to 0.
You saw that right there.
When you evaluate 4 here, 1/2 times 4 minus 2 is 0.
The next couple of videos we'll do a bunch of examples so you really understand how to solve these and are able to do the exercises on our application for this.
We are asked to find the cube root of -512
Or another way to think about it is if I have some number and it is equal to the cube root of -512
This just means if I take that number and I raise it to the to the third power then I get -512.
And if doesn't jump out at you immediately what this is the cube of or what we have to raise to the third power to get -512 the best thing to do, is just to do a prime factorization of it. And before we do a prime factorization of it and to see which of these factors show up at least 3 times,
lets at least think about the negative part a little bit.
So negative 512 thats the same thing, so let me re-write the expression this is the same thing as the cube root of negative 1 times 512.
Which is the same thing as the cube root, which is the same thing as the cube root of -1 times the cube root of 512 and this one is pretty straight forward to answer.
What number, when I raise it to the third power, do I get -1?
Well I get -1! This right here is -1
-1 to the third power is equal to -1 time-1 times -1, which is equal to -1
So the cube root of -1 is -1
So it becomes -1 times, times this business right here Times the cube root, cube root of 512 and lets think of what this might be
So, so lets do the prime factorization
So 512 is 2 times 256 256 is 2 times 128 128 is 2 times 64
We already see a 2 three times 64 is 2 times 32 32 is 2 times 16
We're getting a lot of twos here 16 is 2 times 8 8 is 2 times 4
So essentially if you multiply two 1, 2, 3, 4, 5, 6, 7, 8, 9 times You are going to get 512
Or 2 to the 9th power is 512
But can we find 3 groups of 2
So that's 2 times 2 is 4 2 times 2 is 4
So definitely 4 multiplied by itself 3 times is divisible into this
But even better it looks like we can get three groups of three twos
So one group, two groups and three groups
So each of these groups 2 times 2 times 2, that's 8
And this is 2 times 2 times 2, thats eight And this is also 2 times 2 times 2 So that's 8
So we could write 512 as being equal to 8 times 8 times 8
And so we can re-write this expression right over here As the cube root of 8 times 8 times 8
Or I'll just put a negitave sign here -1 times the cube root, the cube root of 8 times 8 times 8
What number can we multiply by itself 3 times Or to the third power to get 512 Which is the same thing as 8 times 8 times 8
And so our answer to this The cube root of -512 is -8
And we are done
And you can verify this
Multiply -8 times itself 3 times
-8 times -8 times -8 -8 times -8 is positive 64 You multiply that times negative 8
A town had a population of 11,256 in 1995.
By 2010, the population in that town had increased by 4,312.
Estimate the town's population in 2010 by first rounding these two numbers to the nearest hundred.
So we could figure out the exact population just by adding these two, but they want us to round to the nearest hundred first and get an estimate, and then add, so it'll be an estimate of the town's population.
So first we have this 11,256.
That's the population in 1995.
11,256.
We need to round to the nearest hundred, so let's look at the hundreds place here.
So this is either going to go down to 200 or go up to 300, depending on what the next place is or the next lowest place.
So we go down to the tens place, we see a 5.
5 is 5 or greater, so we want to round this number up.
We are going to round up.
So if you round up to the nearest hundred, you get 11,000.
Instead of having 256, we're rounding up to 300.
300 is closer to 256 than 200 is.
That's why we're rounding up to that.
That's why it's to the nearest hundred.
Now, we added 4,312 people, so 4,312.
Now once again, we look at the hundreds place.
We go one spot below that.
The question we're trying to answer:
Do we go down to 4,300 or do we go up to 4,400?
Which one is closer?
Well, we see we only have a 1 here.
1 is definitely less than 5, so we want to round down.
So 312 is closer to 300.
We round down to just a 3 here and these get zeroed out.
So 4,300.
And now we're ready to add our rounded numbers.
0 plus 0 is 0.
0 plus 0 is 0.
3 plus 3 is 6.
Let's put a comma here so it's easy to read every third digit.
1 plus 4 is 5, and then 1 plus-- we have nothing here, so we just bring down that 1.
We could have written that addition there.
We're adding those two numbers.
So our estimate of the town's population in 2010 is 15,600.
 Hadi Calvin döngüsünü biraz gözden geçirelim.
Bu sefer diğer videodan biraz daha detaylı inceleyebiliriz. -
Böylece fotosolunum yapan bütün fotosentetik bitkilerde oluşan verimsizliği fark edebiliriz. - -
Calvin döngüsünü incelemeye karbondioksit ile başlayacağız. -
Geçen videoda, 6 molekül CO2 ve 6 molekül ribüloz difosfatım vardı. -
Ama şimdi, size sadece bir önceki döngüyü ikiye bölebileceğimi göstermek için göstermek için, 3 molekül CO2 3 molekül ribüloz difosfat alarak başlayacağım -
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Eğer ribüloz difosfatın ne olduğunu hatırlamıyorsanız hatırlatayım; Ribüloz difosfat, üzerinde iki fosfat olan, beş karbonlu bir molekül. -
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Buraya biraz daha detay ekleyeceğim. Bildiğiniz gibi karbondioksitte sadece bir karbon var. -
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Önceki videoda bu ikisini reaksiyona uğramış şekilde görmüştük. -
Bu ikisi, Ribüloz bifosfat karboksilaz enziminin varlığında tepkimeye girdiler. İşte bu enzim.
Size geçen videoda gösterdiğim büyük protein işte.
Ve kısaca RuBisCo diye adlandırılır.
Bütün döngünün ortasına RuBisCo yazıyorum, çünkü bütün döngü RuBisCo enzimiyle gerçekleşir -
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Bu moleküiler RuBisCo enzimine katılır ve ATP ile NADH'ler farklı bölgelerde reaksiyon verirler.
Ve aslında bütün reaksiyonun gerçekleşmesi bu şekilde sağlanır.
Yani, bütün olay şu büyük RuBisCo enziminin başının altından çıkıyor.
Ve RuBisCo da, Ribüloz Bifosfat Karboksil anlamına geliyor. -
Yani size bir karbonun ribuloz bifosfatın üzerine kaynaştığını anlatıyor. -
Önceki videoda, bu konuya sadece uzaktan baktık, çok fazla detaya girmedik. -
Ama size bu durumda 6 ATP ve 6 NADH kullanarak reaksiyonu sonlandırırsanız, oluşacak ürünün Gliserat 3-fosfat olduğunu gösterdim.
Ya da namındeğer G3P.
Ya da fotofosfogliseraldehit, yani PGAL şeklinde de yazılabilir.
Ama onu bir fosfatı olan 3 karbon zinciri olarak tanımlamak çok daha kolay. -
Son videoda 6 karbondioksitle ve 6 Ribuloz bifosfatla başladığımda Bunlardan 12 tanesini elde etmiştim.
Ama şimdi elimde ikisinden de 3'er tane var.
Yani bundan 6 tane elde edeceğim.
Yani, 6 tane G3P'm olacak.
Matematik işe yarıyor, değil mi? Üç karbonum ve üç kere beş karbonum var:
Yani 18 tane.
Bu da 6 tane üç karbon yapar. Ya da 18 karbon.
Bu da size geçen videoda gösterdiğim şeyin aynısı. Ancak Birkaç ara adım daha var.
Örneğin, oluşan ilk madde aslında 3-fosfogliserat.
Bu detayı size göstermemin tek sebebiyse Eğer bu kadar detaylı bir biyoloji dersi alıyorsanız, Ara adım bu maddenin
Sonuç olarak 3-fosfogliserat elde ediyoruz. O da zaten üç karbonlu bir zincir.
Ancak bizim istediğimiz değil.
Bu glükoz elde etmek için uygun değil.
Ama yine de bunu 3 karbonlu ve fosfat gruplu bir zincir olarak hayal edebilirsiniz.
Sonunda, bunlardan altı tane üretmiş olacağız. Sadece bütün karbonların kullanıldığından emin olmak için.
İki tarafta da toplam 18 tane karbon olmalı.
Yani elinizde bunlardan altı tane 3 fosfogliserat üretilmiş olacak.
Ve her biri ATP'den birer fosfat alacak.
Yani altı tane ATP reaksiyona girecek.
Bu ATP'lerin tilakoid zarda gerçekleşen ışığa bağımlı reaksiyonlarda üretildiğini unutmayın.
Her neyse, bu ATP'ler geldi. Elimizde altı tane var.
Ve her biri ADP'ye dönüşecek. Yani, aslında her bir ATP bir fosfat grubundan oldu.
Her biri bir fosfat grubunu Elimizdeki altı 3-fosfogliserata verdi.
Ve bu şekilde sonlanacak. Hiç yerim kalmadı.
Belki yeterince titiz davranmadım. Ama ortaya bu üç karbon zinciri çıkacak. Ya da üç karbonlu bileşik.
Yani iki fosfatı olacak.
Ve bu, ismini bilirsiniz: Bu 1 3-bifosfogliserat.
İlki sadece 3-fosfogliserattı, yani Sadece üçüncü karbonun üzerinde bir tane fosfor grubu vardı.
Ama şimdi, 1 3-difosfogliseratımız var.
1. karbon ve 3. karbon üzerinde birer fosfat grubu var.
Ve bunlardan ikişer tane var.
Yani difosfogliserat.
Şimdilik olanlar böyle. Yani 1 3-difosfogliserat elde etmek için Elimizde 6 tane şunlardan olmalı.
6 tane şu, 6 tane buna dönüşüyor yani. Ve bu altı 1 3-fosfogliseratı Üç gliseraldehite fosfata ya da fosfogliseraldehite çeviriyoruz.
Burası aynı zamanda NADPH'i oksitleyeceğimiz yer.
Oksitlenmenin elektronları, yani hidrojenleri sahip oldukları elektronlarla beraber kaybetmek olduğunu hatırlayın.
Yani bu adımda, aynı anda iki şey gerçekleşecek.
Altı tane NADPH altı tane NADP artıya dönüşecek.
Yani NADPH'ler hidrojen ve dolayısıyla elektron kaybedecekler.
Ve aynı zamanda her bir molekülden birer fosfat ayrılacak.
Sonrasında elinizde ekstradan altı tane fosfat grup oluşacak.
Fosfat grupları burada kaybolmuyorlar. Buradaki moleküilere eklenecekler.
Ve altıncı G3P'yle reaksiyon sonlanır. Bir önceki videoda öğrendiğimiz gibi G3P, yakıt, glükoz ya da diğer karbonhidratların üretiminde kullanılır.
Bu olayın Calvin Döngüsü olarak adlandırıldığını da öğrendik.
Yani tamamı gerçek glükoz ya da diğer karbonhidratların üretiminde kullanılmaz.
Çoğu, bu altılının içinde, yani beş tanesi üç ribüloz difosfat yapımında kullanılır.
Şu şekilde yapmama izin verin.
Bu yönde giden beş tane G3P var.
Yani üretilen her altı G3P'in beşi döngüye geri döner ve bir tanesi döngüyü terk eder.
Bunu geçen videoda gördük. Geçen videoda 12 tane vardı, yanı 10 tanesi bu yönde, diğer ikisi de bu yönde gitti.
Bu videoyla her şeyi ikiye bölüyorum.
Bunun asıl nedeni, geçen videoda her şeyi ikiyle çarpmam. Çünkü iki tane bu yönde giden molekül, en azından bir tane Glükoz üretebilir.
Ama bizim iki taneye sahip olmamız gerekmez.
İki tane elde etmek için aynı döngüden iki tane yaplır da diyebiliriz.
Her neyse, en sonda oluşan bir tane gliseraldehit 3-fosfatım var.
Ve diğer beş gliseraldehit 3-fosfat da Döngünün içinde kalıyor.
Bunların sadece fosfat grubu olan 3-karbon olduğunu hatırlayın.
Şuraya önceden çizmiştim.
Daha sona üç tane ATP kullanacaklar.
Yani üç tane ADP'miz var.
Fosfat grupları da döngünün tekrar gerçekleşebilmesi için Ribüloz difosfata gelirler ve tekrar kullanıma uygun hale getirilirler.
Bu reaksiyonların büyük bir enzimin yüzeyinde gerçekleştiğini hayal edebileceğinizi hatırlayın.
Bu enzim de ribüloz difosfat karboksilazdır.
Aslında, biraz terminolojiye girmek gerekirse, Bu tip bir fotosentez C3 fotosentezi olarak adlandırılır.
C3 fotosentezi olarak adlandırılmasının sebebiyse, karbondioksitle reaksiyona girildiğinde elde edilen ilk madde, karbondioksiti fixlediğinizde
- Bunun karbondioksiti gaz halinden molekül haline getirmek olduğunu hatırlayın-
Kullanılan ilk karbon molekülü 3-karbon molekülü şeklinde fixlenir.
Yani fosfoogliserat.
Size arada göstermemin sebebi buydu.
Çünkü burası C3'ün içindeki fotosentezin geldiği yer.
Şimdi yaptığım her şey geçen videoda yaptığım şeylerin bir tekrarı gibi oldu.
Belki biraz daha detaylısı.
Ve size 6'ya 6 moleküile başlamak zorunda olmadığınızı da söyledim.
Üçe üç başlayabilirsiniz ve ikiye katlamak yerine beşi buraya, diğeri şuraya gidebilir.
Ama şimfi bitkilerde oluşan verimsizliği göstermek istiyorum.
This RuBisCo doesn't necessarily just fix carbon dioxide.
It can also react with oxygen.
And actually, its name is ribulose bisphosphate carboxylase oxygenase, which means it can react with carbon or oxygen.
And this mechanism-- so let's say you have your ribulose bisphosphate hanging around.
You know we're in the stroma of our chloroplast.
So let's say we have our five ribulose bisphosphates.
And instead of reacting with carbon it can actually react with oxygen.
So instead of having carbon dioxide here, I can have O2 coming in here. We have oxygen coming in here.
And all of this, once again, is occurring on the surface or with the assistance of the RuBisCo.
The exact same, the RuBisCo enzyme.
Ribulose bisphosphate carboxylase oxygenase.
That's why. Because it can also fix oxygen.
And when these two things react, you don't get useful things that can be used for fuel and all of that.
You end up with-- and my drawing is a little messy-- you end up with-- well when these two guys react-- you'll end up with five molecules of this guy right here.
Five molecules of this 3-phosphoglycerate right there.
Remember here we ended up with six of them.
But now we're only going to end up with five phosphoglycerates.
I know the names are all very confusing.
But the basic idea is to remember that what's happening here is if carbon dioxide isn't getting fixed, oxygen can get fixed.
And you end up with five phosphoglycerates.
And you actually also end up with five-- this is called phosphoglycolate.
I know these are very daunting names.
Phosphoglycolate, which is a 2-carbon molecule.
Which makes sense because we only have five carbons to start with.
This thing right here is a 3-carbon molecule.
That's a 3-carbon molecule and this right here is a 2-carbon molecule.
So this right here is going to be a 2-carbon molecule and it has a phosphate group.
So as you can imagine, in this situation we're not going to be able to keep going forward and produce our glyceraldehyde 3-phosphate, which we can then use to make up carbohydrates.
We're stuck.
We just have these five phosphoglycerates.
These can go on and some percentage of them, but the ratios are all getting messed up.
But everything doesn't necessarily happen this cleanly in the cell.
These things can go on, but we have one less being produced.
And this thing right here, it's actually using up some of our carbon from our ribulose bisphosphate.
And if this thing kept going up, all of our ribulose bisphosphate is going to get eaten up.
We're not going to be able to continue on into this cycle over and over again.
And actually this is kind of a waste product.
Right here this is a waste product.
Or we think it's a waste product.
And this actually has to exit your chloroplast and actually get processed by other organelles in the plant cells.
And these are called, these waste processing organelles in your cells, these are peroxisomes I know there's a
lot of complicated terminology here.
But the important thing to remember, when RuBisCo fixes oxygen, this is actually called photorespiration.
That's an important word to know.
Photorespiration.
All of a sudden, instead of being able to carry forward with your Calvin cycle and produce a lot of sugar, instead you are depleting your RuBisCo.
So this is a very bad process.
This is going to get in the way of your Calvin cycle.
And remember how important each of these G3Ps are.
Because for every turn of the Calvin cycle, or at least the way I did it, we only produce one G3P that actually gets used for something useful.
The other five G3Ps have to go back to produce ribulose bisphosphate.
RuBisCo of course is the enzyme.
So in this situation we only have five phosphoglycerates to begin with.
Maybe if we have our ATP or an NADH, we can convert these five-- and it doesn't have to go in this direction-- but maybe we can convert these five phosphoglycerates into five glyceraldehyde 3-phosphates.
G3Ps.
Then all of these are going to be used back to produce our ribulose bisphosphate.
So to go from here to here, we actually had to use up ATP and NADH.
And then to go from here to here, we have to use more ATP.
But we went through this whole cycle and we didn't produce anything, in terms of useful things that can be used to-- essentially sugars or carbohydrates that can be used to fuel or provide structure for the plant in any way.
So this is a completely-- or we think-- this is a wasteful process.
So people wonder, when you look a lot of biological systems you don't see wasteful processes all the time.
You would say, well wouldn't natural selection have selected against this?
And some people believe that this is just a remnant from our evolutionary past, or our plants' evolutionary past, where there wasn't a lot of oxygen in the atmosphere.
And if there wasn't a lot of oxygen in the atmosphere, this was not that likely of an occurrence.
But there's some people who actually believe that no, this might actually have been selected for in natural selection.
Because if there is a lot of oxygen hanging around in the cell, more than you need, that oxygen might actually react with your ATP and create other harmful compounds in the cell.
And this might be a way of sopping up the harmful oxygen that's actually hanging around the cell.
So who knows?
But it's interesting idea.
That you have this one enzyme that can react with ribulose bisphosphate and carbon dioxide.
And if that happens, we just get our regular Calvin cycle.
Or it can react with ribulose bisphosphate and oxygen and actually fix oxygen into these two molecules.
Especially the phosphoglycolate which we think is a waste compound.
And if you just went on and on in the Calvin cycle in this way, you will not produce any useful sugars.
So in the next video, what I want to do is study some plants that have been able to get by this photorespiration problem.
And you could imagine, photorespiration could be a really big deal or it could be very harmful in situations where, one, it's very important for a plant to be very productive of sugars.
And it can also, we'll see, it can be a problem-- it's definitely a problem if there's a huge amount of oxygen content.
But in the next video I'm going to show you plants that have gotten around this problem by, instead of performing C-3 photosynthesis, which is the classic Calvin cycle that I just showed you, they perform C-4 photosynthesis.
And I'll show you what that means in the next video.
CHAPTER 1 LEAVE IT TO JEEVES
Jeeves--my man, you know--is really a most extraordinary chap.
So capable. Honestly, I shouldn't know what to do without him.
On broader lines he's like those chappies who sit peering sadly over the marble battlements at the Pennsylvania Station in the place marked "Inquiries."
You know the Johnnies I mean.
You go up to them and say:
"When's the next train for Melonsquashville, Tennessee?" and they reply, without stopping to think, "Two-forty-three, track ten, change at San
Francisco."
And they're right every time.
Well, Jeeves gives you just the same impression of omniscience.
As an instance of what I mean, I remember meeting Monty Byng in Bond Street one morning, looking the last word in a grey check suit, and I felt I should never be happy till I had one like it.
I dug the address of the tailors out of him, and had them working on the thing inside the hour.
"Jeeves," I said that evening.
"I'm getting a check suit like that one of Mr. Byng's."
"Injudicious, sir," he said firmly.
"It will not become you."
"What absolute rot!
It's the soundest thing I've struck for years."
"Unsuitable for you, sir."
Well, the long and the short of it was that the confounded thing came home, and I put it on, and when I caught sight of myself in the glass I nearly swooned.
Jeeves was perfectly right.
I looked a cross between a music-hall comedian and a cheap bookie.
Yet Monty had looked fine in absolutely the same stuff.
These things are just Life's mysteries, and that's all there is to it.
But it isn't only that Jeeves's judgment about clothes is infallible, though, of course, that's really the main thing.
The man knows everything.
There was the matter of that tip on the
"Lincolnshire." I forget now how I got it, but it had the aspect of being the real, red-hot tabasco.
"Jeeves," I said, for I'm fond of the man, and like to do him a good turn when I can,
"if you want to make a bit of money have something on Wonderchild for the
'Lincolnshire.'"
He shook his head.
"I'd rather not, sir."
"But it's the straight goods.
I'm going to put my shirt on him."
"I do not recommend it, sir.
The animal is not intended to win.
Second place is what the stable is after."
How the deuce could Jeeves know anything about it?
Still, you know what happened.
Wonderchild led till he was breathing on the wire, and then Banana Fritter came along and nosed him out.
I went straight home and rang for Jeeves.
"After this," I said, "not another step for me without your advice.
From now on consider yourself the brains of the establishment."
"Very good, sir.
I shall endeavour to give satisfaction." And he has, by Jove!
I'm a bit short on brain myself; the old bean would appear to have been constructed more for ornament than for use, don't you know; but give me five minutes to talk the thing over with Jeeves, and I'm game to advise any one about anything.
And that's why, when Bruce Corcoran came to me with his troubles, my first act was to ring the bell and put it up to the lad with the bulging forehead.
"Leave it to Jeeves," I said.
I first got to know Corky when I came to New York.
He was a pal of my cousin Gussie, who was in with a lot of people down Washington
Square way.
I don't know if I ever told you about it, but the reason why I left England was because I was sent over by my Aunt Agatha to try to stop young Gussie marrying a girl on the vaudeville stage, and I got the whole thing so mixed up that I decided that it would be a sound scheme for me to stop on in America for a bit instead of going back and having long cosy chats about the thing with aunt.
So I sent Jeeves out to find a decent apartment, and settled down for a bit of exile.
I'm bound to say that New York's a topping place to be exiled in.
Everybody was awfully good to me, and there seemed to be plenty of things going on, and
I'm a wealthy bird, so everything was fine.
Chappies introduced me to other chappies, and so on and so forth, and it wasn't long before I knew squads of the right sort, some who rolled in dollars in houses up by the Park, and others who lived with the gas turned down mostly around Washington Square--artists and writers and so forth.
Brainy coves.
Corky was one of the artists.
A portrait-painter, he called himself, but he hadn't painted any portraits.
He was sitting on the side-lines with a blanket over his shoulders, waiting for a chance to get into the game.
You see, the catch about portrait-painting- -I've looked into the thing a bit--is that you can't start painting portraits till people come along and ask you to, and they won't come and ask you to until you've painted a lot first.
This makes it kind of difficult for a chappie.
Corky managed to get along by drawing an occasional picture for the comic papers--he had rather a gift for funny stuff when he got a good idea--and doing bedsteads and chairs and things for the advertisements.
His principal source of income, however, was derived from biting the ear of a rich uncle--one Alexander Worple, who was in the jute business.
I'm a bit foggy as to what jute is, but it's apparently something the populace is pretty keen on, for Mr. Worple had made quite an indecently large stack out of it.
Now, a great many fellows think that having a rich uncle is a pretty soft snap: but, according to Corky, such is not the case.
Corky's uncle was a robust sort of cove, who looked like living for ever.
He was fifty-one, and it seemed as if he might go to par.
It was not this, however, that distressed poor old Corky, for he was not bigoted and had no objection to the man going on living.
What Corky kicked at was the way the above Worple used to harry him.
Corky's uncle, you see, didn't want him to be an artist.
He didn't think he had any talent in that direction.
He was always urging him to chuck Art and go into the jute business and start at the bottom and work his way up.
Jute had apparently become a sort of obsession with him.
He seemed to attach almost a spiritual importance to it.
And what Corky said was that, while he didn't know what they did at the bottom of the jute business, instinct told him that it was something too beastly for words.
Corky, moreover, believed in his future as an artist.
Some day, he said, he was going to make a hit.
Meanwhile, by using the utmost tact and persuasiveness, he was inducing his uncle to cough up very grudgingly a small quarterly allowance.
He wouldn't have got this if his uncle hadn't had a hobby.
Mr. Worple was peculiar in this respect.
As a rule, from what I've observed, the American captain of industry doesn't do anything out of business hours.
When he has put the cat out and locked up the office for the night, he just relapses into a state of coma from which he emerges only to start being a captain of industry again.
But Mr. Worple in his spare time was what is known as an ornithologist.
He had written a book called American Birds, and was writing another, to be called More American Birds.
When he had finished that, the presumption was that he would begin a third, and keep on till the supply of American birds gave out.
Corky used to go to him about once every three months and let him talk about
American birds.
Apparently you could do what you liked with old Worple if you gave him his head first on his pet subject, so these little chats used to make Corky's allowance all right for the time being.
But it was pretty rotten for the poor chap.
There was the frightful suspense, you see, and, apart from that, birds, except when broiled and in the society of a cold bottle, bored him stiff.
To complete the character-study of Mr. Worple, he was a man of extremely uncertain temper, and his general tendency was to think that Corky was a poor chump and that whatever step he took in any direction on his own account, was just another proof of his innate idiocy.
I should imagine Jeeves feels very much the same about me.
So when Corky trickled into my apartment one afternoon, shooing a girl in front of him, and said, "Bertie, I want you to meet my fiancee, Miss Singer," the aspect of the matter which hit me first was precisely the one which he had come to consult me about.
The very first words I spoke were, "Corky, how about your uncle?"
The poor chap gave one of those mirthless laughs.
He was looking anxious and worried, like a man who has done the murder all right but can't think what the deuce to do with the body.
"We're so scared, Mr. Wooster," said the girl.
"We were hoping that you might suggest a way of breaking it to him."
Muriel Singer was one of those very quiet, appealing girls who have a way of looking at you with their big eyes as if they thought you were the greatest thing on earth and wondered that you hadn't got on to it yet yourself.
She sat there in a sort of shrinking way, looking at me as if she were saying to herself, "Oh, I do hope this great strong man isn't going to hurt me."
She gave a fellow a protective kind of feeling, made him want to stroke her hand and say, "There, there, little one!" or words to that effect.
She made me feel that there was nothing I wouldn't do for her.
She was rather like one of those innocent- tasting American drinks which creep imperceptibly into your system so that, before you know what you're doing, you're starting out to reform the world by force if necessary and pausing on your way to tell the large man in the corner that, if he looks at you like that, you will knock his head off.
What I mean is, she made me feel alert and dashing, like a jolly old knight-errant or something of that kind. I felt that I was with her in this thing to the limit.
"I don't see why your uncle shouldn't be most awfully bucked," I said to Corky.
"He will think Miss Singer the ideal wife for you."
Corky declined to cheer up.
"You don't know him.
Even if he did like Muriel he wouldn't admit it.
That's the sort of pig-headed guy he is.
It would be a matter of principle with him to kick.
All he would consider would be that I had gone and taken an important step without asking his advice, and he would raise Cain automatically.
He's always done it."
I strained the old bean to meet this emergency.
"You want to work it so that he makes Miss Singer's acquaintance without knowing that you know her.
Then you come along----" "But how can I work it that way?"
I saw his point.
That was the catch.
"There's only one thing to do," I said.
"What's that?" "Leave it to Jeeves."
"Sir?" said Jeeves, kind of manifesting himself.
One of the rummy things about Jeeves is that, unless you watch like a hawk, you very seldom see him come into a room.
He's like one of those weird chappies in India who dissolve themselves into thin air and nip through space in a sort of disembodied way and assemble the parts again just where they want them.
I've got a cousin who's what they call a Theosophist, and he says he's often nearly worked the thing himself, but couldn't quite bring it off, probably owing to having fed in his boyhood on the flesh of animals slain in anger and pie.
The moment I saw the man standing there, registering respectful attention, a weight seemed to roll off my mind.
I felt like a lost child who spots his father in the offing.
There was something about him that gave me confidence.
Jeeves is a tallish man, with one of those dark, shrewd faces.
His eye gleams with the light of pure intelligence.
"Jeeves, we want your advice."
"Very good, sir." I boiled down Corky's painful case into a few well-chosen words.
"So you see what it amount to, Jeeves.
We want you to suggest some way by which Mr. Worple can make Miss Singer's acquaintance without getting on to the fact that Mr. Corcoran already knows her.
Understand?"
"Perfectly, sir." "Well, try to think of something."
"I have thought of something already, sir." "You have!"
"The scheme I would suggest cannot fail of success, but it has what may seem to you a drawback, sir, in that it requires a certain financial outlay."
"He means," I translated to Corky, "that he has got a pippin of an idea, but it's going to cost a bit." Naturally the poor chap's face dropped, for this seemed to dish the whole thing.
But I was still under the influence of the girl's melting gaze, and I saw that this was where I started in as a knight-errant.
"You can count on me for all that sort of thing, Corky," I said.
"Only too glad.
Carry on, Jeeves."
"I would suggest, sir, that Mr. Corcoran take advantage of Mr. Worple's attachment to ornithology."
"How on earth did you know that he was fond of birds?"
"It is the way these New York apartments are constructed, sir.
Quite unlike our London houses.
The partitions between the rooms are of the flimsiest nature.
With no wish to overhear, I have sometimes heard Mr. Corcoran expressing himself with a generous strength on the subject I have mentioned."
"Oh!
Well?" "Why should not the young lady write a small volume, to be entitled--let us say-- The Children's Book of American Birds, and dedicate it to Mr. Worple!
A limited edition could be published at your expense, sir, and a great deal of the book would, of course, be given over to eulogistic remarks concerning Mr. Worple's own larger treatise on the same subject.
I should recommend the dispatching of a presentation copy to Mr. Worple, immediately on publication, accompanied by a letter in which the young lady asks to be allowed to make the acquaintance of one to whom she owes so much.
This would, I fancy, produce the desired result, but as I say, the expense involved would be considerable."
I felt like the proprietor of a performing dog on the vaudeville stage when the tyke has just pulled off his trick without a hitch.
I had betted on Jeeves all along, and I had known that he wouldn't let me down.
It beats me sometimes why a man with his genius is satisfied to hang around pressing my clothes and whatnot.
If I had half Jeeves's brain, I should have a stab, at being Prime Minister or something.
"Jeeves," I said, "that is absolutely ripping!
One of your very best efforts." "Thank you, sir."
The girl made an objection. "But I'm sure I couldn't write a book about anything.
I can't even write good letters." "Muriel's talents," said Corky, with a little cough "lie more in the direction of the drama, Bertie.
I didn't mention it before, but one of our reasons for being a trifle nervous as to how Uncle Alexander will receive the news is that Muriel is in the chorus of that show Choose your Exit at the Manhattan.
It's absurdly unreasonable, but we both feel that that fact might increase Uncle
Alexander's natural tendency to kick like a steer."
I saw what he meant.
Goodness knows there was fuss enough in our family when I tried to marry into musical comedy a few years ago.
And the recollection of my Aunt Agatha's attitude in the matter of Gussie and the vaudeville girl was still fresh in my mind.
I don't know why it is--one of these psychology sharps could explain it, I suppose--but uncles and aunts, as a class, are always dead against the drama, legitimate or otherwise.
They don't seem able to stick it at any price.
But Jeeves had a solution, of course.
"I fancy it would be a simple matter, sir, to find some impecunious author who would be glad to do the actual composition of the volume for a small fee.
It is only necessary that the young lady's name should appear on the title page."
"That's true," said Corky.
He writes a novelette, three short stories, and ten thousand words of a serial for one of the all-fiction magazines under different names every month.
A little thing like this would be nothing to him.
I'll get after him right away." "Fine!"
"Will that be all, sir?" said Jeeves.
"Very good, sir.
Thank you, sir."
I always used to think that publishers had to be devilish intelligent fellows, loaded down with the grey matter; but I've got their number now.
All a publisher has to do is to write cheques at intervals, while a lot of deserving and industrious chappies rally round and do the real work.
I know, because I've been one myself.
I simply sat tight in the old apartment with a fountain-pen, and in due season a topping, shiny book came along.
I happened to be down at Corky's place when the first copies of The Children's Book of
American Birds bobbed up.
Muriel Singer was there, and we were talking of things in general when there was a bang at the door and the parcel was delivered.
It was certainly some book.
It had a red cover with a fowl of some species on it, and underneath the girl's name in gold letters.
I opened a copy at random.
"Often of a spring morning," it said at the top of page twenty-one, "as you wander through the fields, you will hear the sweet-toned, carelessly flowing warble of the purple finch linnet.
When you are older you must read all about him in Mr. Alexander Worple's wonderful book--American Birds." You see.
A boost for the uncle right away.
And only a few pages later there he was in the limelight again in connection with the yellow-billed cuckoo. It was great stuff. I didn't see how the uncle could fail to drop.
You can't call a chap the world's greatest authority on the yellow-billed cuckoo without rousing a certain disposition towards chumminess in him.
"It's a cert!"
I said.
"An absolute cinch!" said Corky.
And a day or two later he meandered up the Avenue to my apartment to tell me that all was well.
The uncle had written Muriel a letter so dripping with the milk of human kindness that if he hadn't known Mr. Worple's handwriting Corky would have refused to believe him the author of it.
Any time it suited Miss Singer to call, said the uncle, he would be delighted to make her acquaintance.
Shortly after this I had to go out of town.
Divers sound sportsmen had invited me to pay visits to their country places, and it wasn't for several months that I settled down in the city again.
I had been wondering a lot, of course, about Corky, whether it all turned out right, and so forth, and my first evening in New York, happening to pop into a quiet sort of little restaurant which I go to when I don't feel inclined for the bright lights, I found Muriel Singer there, sitting by herself at a table near the door.
Corky, I took it, was out telephoning.
I went up and passed the time of day.
"Well, well, well, what?"
I said.
"Why, Mr. Wooster!
How do you do?"
"Corky around?" "I beg your pardon?"
"You're waiting for Corky, aren't you?" "Oh, I didn't understand.
No, I'm not waiting for him."
It seemed to roe that there was a sort of something in her voice, a kind of thingummy, you know.
"I say, you haven't had a row with Corky, have you?"
"A row?" "A spat, don't you know--little misunderstanding--faults on both sides--er- -and all that sort of thing."
"Why, whatever makes you think that?"
"Oh, well, as it were, what?
What I mean is--I thought you usually dined with him before you went to the theatre." "I've left the stage now."
Suddenly the whole thing dawned on me.
I had forgotten what a long time I had been away.
"Why, of course, I see now!
You're married!"
"Yes."
"How perfectly topping!
I wish you all kinds of happiness."
"Thank you, so much.
Oh Alexander," she said, looking past me,
"this is a friend of mine--Mr. Wooster."
I spun round.
A chappie with a lot of stiff grey hair and a red sort of healthy face was standing there.
Rather a formidable Johnnie, he looked, though quite peaceful at the moment.
"I want you to meet my husband, Mr. Wooster.
Mr. Wooster is a friend of Bruce's, Alexander."
The old boy grasped my hand warmly, and that was all that kept me from hitting the floor in a heap.
The place was rocking.
Absolutely.
"So you know my nephew, Mr. Wooster," I heard him say.
"I wish you would try to knock a little sense into him and make him quit this playing at painting.
But I have an idea that he is steadying down.
I noticed it first that night he came to dinner with us, my dear, to be introduced to you. He seemed altogether quieter and more serious.
Something seemed to have sobered him.
Perhaps you will give us the pleasure of your company at dinner to-night, Mr. Wooster?
Or have you dined?"
I said I had.
What I needed then was air, not dinner.
I felt that I wanted to get into the open and think this thing out.
When I reached my apartment I heard Jeeves moving about in his lair.
I called him.
"Jeeves," I said, "now is the time for all good men to come to the aid of the party.
A stiff b.-and-s. first of all, and then I've a bit of news for you."
He came back with a tray and a long glass.
"Better have one yourself, Jeeves.
You'll need it."
"Later on, perhaps, thank you, sir." "All right.
Please yourself.
But you're going to get a shock.
You remember my friend, Mr. Corcoran?"
"Yes, sir." "And the girl who was to slide gracefully into his uncle's esteem by writing the book on birds?"
"Perfectly, sir."
"Well, she's slid.
She's married the uncle."
He took it without blinking.
You can't rattle Jeeves.
"That was always a development to be feared, sir."
"You don't mean to tell me that you were expecting it?"
"It crossed my mind as a possibility."
"Did it, by Jove! Well, I think, you might have warned us!"
"I hardly liked to take the liberty, sir."
Of course, as I saw after I had had a bite to eat and was in a calmer frame of mind, what had happened wasn't my fault, if you come down to it.
I couldn't be expected to foresee that the scheme, in itself a cracker-jack, would skid into the ditch as it had done; but all the same I'm bound to admit that I didn't relish the idea of meeting Corky again until time, the great healer, had been able to get in a bit of soothing work.
I cut Washington Square out absolutely for the next few months.
I gave it the complete miss-in-baulk.
And then, just when I was beginning to think I might safely pop down in that direction and gather up the dropped threads, so to speak, time, instead of working the healing wheeze, went and pulled the most awful bone and put the lid on it.
Opening the paper one morning, I read that Mrs. Alexander Worple had presented her husband with a son and heir.
I was so darned sorry for poor old Corky that I hadn't the heart to touch my breakfast.
I told Jeeves to drink it himself.
I was bowled over.
Absolutely.
It was the limit.
I hardly knew what to do.
I wanted, of course, to rush down to Washington Square and grip the poor blighter silently by the hand; and then, thinking it over, I hadn't the nerve.
Absent treatment seemed the touch.
I gave it him in waves.
But after a month or so I began to hesitate again.
It struck me that it was playing it a bit low-down on the poor chap, avoiding him like this just when he probably wanted his pals to surge round him most.
I pictured him sitting in his lonely studio with no company but his bitter thoughts, and the pathos of it got me to such an extent that I bounded straight into a taxi and told the driver to go all out for the studio.
I rushed in, and there was Corky, hunched up at the easel, painting away, while on the model throne sat a severe-looking female of middle age, holding a baby.
A fellow has to be ready for that sort of thing.
"Oh, ah!" I said, and started to back out.
Corky looked over his shoulder.
"Halloa, Bertie.
Don't go.
We're just finishing for the day.
That will be all this afternoon," he said to the nurse, who got up with the baby and decanted it into a perambulator which was standing in the fairway.
"At the same hour to-morrow, Mr. Corcoran?"
"Yes, please." "Good afternoon."
"Good afternoon."
Corky stood there, looking at the door, and then he turned to me and began to get it off his chest.
Fortunately, he seemed to take it for granted that I knew all about what had happened, so it wasn't as awkward as it might have been.
"It's my uncle's idea," he said.
"Muriel doesn't know about it yet.
The portrait's to be a surprise for her on her birthday.
The nurse takes the kid out ostensibly to get a breather, and they beat it down here.
If you want an instance of the irony of fate, Bertie, get acquainted with this.
Here's the first commission I have ever had to paint a portrait, and the sitter is that human poached egg that has butted in and bounced me out of my inheritance.
Can you beat it!
I call it rubbing the thing in to expect me to spend my afternoons gazing into the ugly face of a little brat who to all intents and purposes has hit me behind the ear with a blackjack and swiped all I possess.
I can't refuse to paint the portrait because if I did my uncle would stop my allowance; yet every time I look up and catch that kid's vacant eye, I suffer agonies.
I tell you, Bertie, sometimes when he gives me a patronizing glance and then turns away and is sick, as if it revolted him to look at me, I come within an ace of occupying the entire front page of the evening papers as the latest murder sensation.
There are moments when I can almost see the headlines:
'Promising Young Artist Beans
Baby With Axe.'"
My sympathy for the poor old scout was too deep for words.
I kept away from the studio for some time after that, because it didn't seem right to me to intrude on the poor chappie's sorrow.
Besides, I'm bound to say that nurse intimidated me.
She reminded me so infernally of Aunt Agatha.
She was the same gimlet-eyed type.
But one afternoon Corky called me on the
'phone.
"Bertie." "Halloa?"
"Are you doing anything this afternoon?" "Nothing special."
"You couldn't come down here, could you?"
"What's the trouble?
Anything up?"
"I've finished the portrait." "Good boy!
Stout work!"
"Yes." His voice sounded rather doubtful.
"The fact is, Bertie, it doesn't look quite right to me.
There's something about it--My uncle's coming in half an hour to inspect it, and--
I don't know why it is, but I kind of feel I'd like your moral support!"
I began to see that I was letting myself in for something.
The sympathetic co-operation of Jeeves seemed to me to be indicated.
"You think he'll cut up rough?"
"He may." I threw my mind back to the red-faced chappie I had met at the restaurant, and tried to picture him cutting up rough.
It was only too easy.
I spoke to Corky firmly on the telephone.
"I'll come," I said.
"Good!" "But only if I may bring Jeeves!"
"Why Jeeves?
What's Jeeves got to do with it?
Who wants Jeeves?
Jeeves is the fool who suggested the scheme that has led----"
"Listen, Corky, old top!
If you think I am going to face that uncle of yours without Jeeves's support, you're mistaken. I'd sooner go into a den of wild beasts and bite a lion on the back of the neck."
"Oh, all right," said Corky. Not cordially, but he said it; so I rang for Jeeves, and explained the situation.
"Very good, sir," said Jeeves.
That's the sort of chap he is.
You can't rattle him.
We found Corky near the door, looking at the picture, with one hand up in a defensive sort of way, as if he thought it might swing on him.
"Stand right where you are, Bertie," he said, without moving.
"Now, tell me honestly, how does it strike you?"
The light from the big window fell right on the picture.
I took a good look at it.
Then I shifted a bit nearer and took another look.
Then I went back to where I had been at first, because it hadn't seemed quite so bad from there. "Well?" said Corky, anxiously.
I hesitated a bit.
"Of course, old man, I only saw the kid once, and then only for a moment, but--but it was an ugly sort of kid, wasn't it, if I remember rightly?"
"As ugly as that?"
I looked again, and honesty compelled me to be frank.
"I don't see how it could have been, old chap."
Poor old Corky ran his fingers through his hair in a temperamental sort of way.
He groaned.
"You're right quite, Bertie.
Something's gone wrong with the darned thing.
My private impression is that, without knowing it, I've worked that stunt that
Sargent and those fellows pull--painting the soul of the sitter.
I've got through the mere outward appearance, and have put the child's soul on canvas." "But could a child of that age have a soul like that?
I don't see how he could have managed it in the time.
What do you think, Jeeves?" "I doubt it, sir."
"It--it sorts of leers at you, doesn't it?"
"You've noticed that, too?" said Corky.
"I don't see how one could help noticing."
"All I tried to do was to give the little brute a cheerful expression.
But, as it worked out, he looks positively dissipated."
"Just what I was going to suggest, old man.
He looks as if he were in the middle of a colossal spree, and enjoying every minute of it.
Don't you think so, Jeeves?"
"He has a decidedly inebriated air, sir."
Corky was starting to say something when the door opened, and the uncle came in.
For about three seconds all was joy, jollity, and goodwill.
The old boy shook hands with me, slapped Corky on the back, said that he didn't think he had ever seen such a fine day, and whacked his leg with his stick.
Jeeves had projected himself into the background, and he didn't notice him.
"Well, Bruce, my boy; so the portrait is really finished, is it--really finished?
Well, bring it out.
This will be a wonderful surprise for your aunt.
Where is it?
Let's----"
And then he got it--suddenly, when he wasn't set for the punch; and he rocked back on his heels.
"Oosh!" he exclaimed.
And for perhaps a minute there was one of the scaliest silences I've ever run up against.
"Is this a practical joke?" he said at last, in a way that set about sixteen draughts cutting through the room at once.
I thought it was up to me to rally round old Corky.
"You want to stand a bit farther away from it," I said.
"You're perfectly right!" he snorted.
"I do!
I want to stand so far away from it that I can't see the thing with a telescope!"
He turned on Corky like an untamed tiger of the jungle who has just located a chunk of meat.
"And this--this--is what you have been wasting your time and my money for all these years!
A painter!
I wouldn't let you paint a house of mine!
I gave you this commission, thinking that you were a competent worker, and this-- this--this extract from a comic coloured supplement is the result!"
He swung towards the door, lashing his tail and growling to himself.
"This ends it!
If you wish to continue this foolery of pretending to be an artist because you want an excuse for idleness, please yourself.
But let me tell you this.
Unless you report at my office on Monday morning, prepared to abandon all this idiocy and start in at the bottom of the business to work your way up, as you should have done half a dozen years ago, not another cent--not another cent--not another--Boosh!"
Then the door closed, and he was no longer with us.
And I crawled out of the bombproof shelter.
"Corky, old top!" I whispered faintly.
Corky was standing staring at the picture.
His face was set.
There was a hunted look in his eye.
"Well, that finishes it!" he muttered brokenly.
"What are you going to do?" "Do?
What can I do?
I can't stick on here if he cuts off supplies.
You heard what he said.
I shall have to go to the office on
Monday."
I couldn't think of a thing to say.
I knew exactly how he felt about the office.
I don't know when I've been so infernally uncomfortable.
It was like hanging round trying to make conversation to a pal who's just been sentenced to twenty years in quod.
And then a soothing voice broke the silence.
"If I might make a suggestion, sir!" It was Jeeves.
He had slid from the shadows and was gazing gravely at the picture.
Upon my word, I can't give you a better idea of the shattering effect of Corky's uncle Alexander when in action than by saying that he had absolutely made me forget for the moment that Jeeves was there.
"I wonder if I have ever happened to mention to you, sir, a Mr. Digby
Thistleton, with whom I was once in service?
Perhaps you have met him?
He was a financier.
He is now Lord Bridgnorth.
It was a favourite saying of his that there is always a way.
The first time I heard him use the expression was after the failure of a patent depilatory which he promoted." "Jeeves," I said, "what on earth are you talking about?"
"I mentioned Mr. Thistleton, sir, because his was in some respects a parallel case to the present one.
His depilatory failed, but he did not despair.
He put it on the market again under the name of Hair-o, guaranteed to produce a full crop of hair in a few months.
It was advertised, if you remember, sir, by a humorous picture of a billiard-ball, before and after taking, and made such a substantial fortune that Mr. Thistleton was soon afterwards elevated to the peerage for services to his Party.
It seems to me that, if Mr. Corcoran looks into the matter, he will find, like Mr.
Thistleton, that there is always a way.
Mr. Worple himself suggested the solution of the difficulty.
In the heat of the moment he compared the portrait to an extract from a coloured comic supplement.
I consider the suggestion a very valuable one, sir.
Mr. Corcoran's portrait may not have pleased Mr. Worple as a likeness of his only child, but I have no doubt that editors would gladly consider it as a foundation for a series of humorous drawings.
If Mr. Corcoran will allow me to make the suggestion, his talent has always been for the humorous.
There is something about this picture-- something bold and vigorous, which arrests the attention.
I feel sure it would be highly popular."
Corky was glaring at the picture, and making a sort of dry, sucking noise with his mouth.
He seemed completely overwrought.
And then suddenly he began to laugh in a wild way.
"Corky, old man!" I said, massaging him tenderly.
I feared the poor blighter was hysterical.
He began to stagger about all over the floor.
"He's right!
The man's absolutely right!
Jeeves, you're a life-saver!
You've hit on the greatest idea of the age!
Report at the office on Monday!
Start at the bottom of the business!
I'll buy the business if I feel like it.
I know the man who runs the comic section of the Sunday Star.
He'll eat this thing.
He was telling me only the other day how hard it was to get a good new series.
He'll give me anything I ask for a real winner like this.
I've got a gold-mine.
Where's my hat?
I've got an income for life!
Where's that confounded hat?
Lend me a fiver, Bertie.
I want to take a taxi down to Park Row!" Jeeves smiled paternally.
Or, rather, he had a kind of paternal muscular spasm about the mouth, which is the nearest he ever gets to smiling.
"If I might make the suggestion, Mr. Corcoran--for a title of the series which you have in mind--'The Adventures of Baby Blobbs.'"
Corky and I looked at the picture, then at each other in an awed way.
Jeeves was right.
There could be no other title.
"Jeeves," I said.
It was a few weeks later, and I had just finished looking at the comic section of the Sunday Star.
"I'm an optimist.
I always have been.
The older I get, the more I agree with Shakespeare and those poet Johnnies about it always being darkest before the dawn and there's a silver lining and what you lose on the swings you make up on the roundabouts.
Look at Mr. Corcoran, for instance.
There was a fellow, one would have said, clear up to the eyebrows in the soup.
To all appearances he had got it right in the neck.
Yet look at him now.
Have you seen these pictures?"
"I took the liberty of glancing at them before bringing them to you, sir.
Extremely diverting." "They have made a big hit, you know."
"I anticipated it, sir."
I leaned back against the pillows.
"You know, Jeeves, you're a genius.
You ought to be drawing a commission on these things."
"I have nothing to complain of in that respect, sir.
Mr. Corcoran has been most generous.
I am putting out the brown suit, sir."
"No, I think I'll wear the blue with the faint red stripe."
"Not the blue with the faint red stripe, sir."
"But I rather fancy myself in it."
"Not the blue with the faint red stripe, sir."
"Oh, all right, have it your own way." "Very good, sir.
Thank you, sir."
Of course, I know it's as bad as being henpecked; but then Jeeves is always right.
You've got to consider that, you know.
What? >
CHAPTER 2 JEEVES AND THE UNBlDDEN GUEST
I'm not absolutely certain of my facts, but I rather fancy it's Shakespeare--or, if not, it's some equally brainy lad--who says that it's always just when a chappie is feeling particularly top-hole, and more than usually braced with things in general that Fate sneaks up behind him with a bit of lead piping.
There's no doubt the man's right.
It's absolutely that way with me.
Take, for instance, the fairly rummy matter of Lady Malvern and her son Wilmot.
A moment before they turned up, I was just thinking how thoroughly all right everything was.
It was one of those topping mornings, and I had just climbed out from under the cold shower, feeling like a two-year-old.
As a matter of fact, I was especially bucked just then because the day before I had asserted myself with Jeeves--absolutely asserted myself, don't you know.
You see, the way things had been going on I was rapidly becoming a dashed serf.
The man had jolly well oppressed me.
I didn't so much mind when he made me give up one of my new suits, because, Jeeves's judgment about suits is sound.
But I as near as a toucher rebelled when he wouldn't let me wear a pair of cloth-topped boots which I loved like a couple of brothers.
And when he tried to tread on me like a worm in the matter of a hat, I jolly well put my foot down and showed him who was who.
It's a long story, and I haven't time to tell you now, but the point is that he wanted me to wear the Longacre--as worn by John Drew--when I had set my heart on the
Country Gentleman--as worn by another famous actor chappie--and the end of the matter was that, after a rather painful scene, I bought the Country Gentleman.
So that's how things stood on this particular morning, and I was feeling kind of manly and independent. Well, I was in the bathroom, wondering what there was going to be for breakfast while I massaged the good old spine with a rough towel and sang slightly, when there was a tap at the door.
I stopped singing and opened the door an inch.
"What ho without there!" "Lady Malvern wishes to see you, sir," said
Jeeves.
"Eh?" "Lady Malvern, sir.
She is waiting in the sitting-room."
"Pull yourself together, Jeeves, my man," I said, rather severely, for I bar practical jokes before breakfast.
"You know perfectly well there's no one waiting for me in the sitting-room.
How could there be when it's barely ten o'clock yet?"
"I gathered from her ladyship, sir, that she had landed from an ocean liner at an early hour this morning."
This made the thing a bit more plausible.
I remembered that when I had arrived in America about a year before, the proceedings had begun at some ghastly hour like six, and that I had been shot out on to a foreign shore considerably before eight.
"Who the deuce is Lady Malvern, Jeeves?" "Her ladyship did not confide in me, sir."
"Is she alone?"
"Her ladyship is accompanied by a Lord Pershore, sir.
I fancy that his lordship would be her ladyship's son."
"Oh, well, put out rich raiment of sorts, and I'll be dressing."
"Our heather-mixture lounge is in readiness, sir."
"Then lead me to it."
While I was dressing I kept trying to think who on earth Lady Malvern could be.
It wasn't till I had climbed through the top of my shirt and was reaching out for the studs that I remembered.
"I've placed her, Jeeves.
She's a pal of my Aunt Agatha."
"Indeed, sir?" "Yes.
I met her at lunch one Sunday before I left London.
A very vicious specimen.
Writes books.
She wrote a book on social conditions in India when she came back from the Durbar."
"Yes, sir?
Pardon me, sir, but not that tie!"
"Eh?"
"Not that tie with the heather-mixture lounge, sir!"
It was a shock to me.
I thought I had quelled the fellow.
It was rather a solemn moment.
What I mean is, if I weakened now, all my good work the night before would be thrown away.
I braced myself.
"What's wrong with this tie?
I've seen you give it a nasty look before.
Speak out like a man!
What's the matter with it?" "Too ornate, sir."
"Nonsense!
A cheerful pink.
Nothing more."
"Unsuitable, sir." "Jeeves, this is the tie I wear!"
"Very good, sir."
Dashed unpleasant.
I could see that the man was wounded.
But I was firm.
I tied the tie, got into the coat and waistcoat, and went into the sitting-room.
"Halloa!
Halloa!
Halloa!" I said.
"What?"
"Ah!
How do you do, Mr. Wooster?
You have never met my son, Wilmot, I think?
Motty, darling, this is Mr. Wooster."
Lady Malvern was a hearty, happy, healthy, overpowering sort of dashed female, not so very tall but making up for it by measuring about six feet from the O.P. to the Prompt
Side.
She fitted into my biggest arm-chair as if it had been built round her by someone who knew they were wearing arm-chairs tight about the hips that season.
She had bright, bulging eyes and a lot of yellow hair, and when she spoke she showed about fifty-seven front teeth. She was one of those women who kind of numb a fellow's faculties.
She made me feel as if I were ten years old and had been brought into the drawing-room in my Sunday clothes to say how-d'you-do.
Altogether by no means the sort of thing a chappie would wish to find in his sitting- room before breakfast.
Motty, the son, was about twenty-three, tall and thin and meek-looking.
He had the same yellow hair as his mother, but he wore it plastered down and parted in the middle.
His eyes bulged, too, but they weren't bright.
They were a dull grey with pink rims.
His chin gave up the struggle about half- way down, and he didn't appear to have any eyelashes.
A mild, furtive, sheepish sort of blighter, in short.
"Awfully glad to see you," I said.
"So you've popped over, eh?
Making a long stay in America?" Your aunt gave me your address and told me to be sure and call on you."
I was glad to hear this, as it showed that Aunt Agatha was beginning to come round a bit.
There had been some unpleasantness a year before, when she had sent me over to New
York to disentangle my Cousin Gussie from the clutches of a girl on the music-hall stage.
When I tell you that by the time I had finished my operations, Gussie had not only married the girl but had gone on the stage himself, and was doing well, you'll understand that Aunt Agatha was upset to no small extent.
I simply hadn't dared go back and face her, and it was a relief to find that time had healed the wound and all that sort of thing enough to make her tell her pals to look me up.
What I mean is, much as I liked America, I didn't want to have England barred to me for the rest of my natural; and, believe me, England is a jolly sight too small for anyone to live in with Aunt Agatha, if she's really on the warpath.
So I braced on hearing these kind words and smiled genially on the assemblage.
"Your aunt said that you would do anything that was in your power to be of assistance to us." "Rather?
Oh, rather!
Absolutely!" "Thank you so much.
I want you to put dear Motty up for a little while."
I didn't get this for a moment.
"Put him up?
For my clubs?"
"No, no!
Darling Motty is essentially a home bird.
Aren't you, Motty darling?"
Motty, who was sucking the knob of his stick, uncorked himself.
"Yes, mother," he said, and corked himself up again.
"I should not like him to belong to clubs.
I mean put him up here.
Have him to live with you while I am away."
These frightful words trickled out of her like honey.
The woman simply didn't seem to understand the ghastly nature of her proposal.
I gave Motty the swift east-to-west.
He was sitting with his mouth nuzzling the stick, blinking at the wall.
The thought of having this planted on me for an indefinite period appalled me.
Absolutely appalled me, don't you know.
I was just starting to say that the shot wasn't on the board at any price, and that the first sign Motty gave of trying to nestle into my little home I would yell for the police, when she went on, rolling placidly over me, as it were.
There was something about this woman that sapped a chappie's will-power.
"I am leaving New York by the midday train, as I have to pay a visit to Sing-Sing prison.
I am extremely interested in prison conditions in America.
After that I work my way gradually across to the coast, visiting the points of interest on the journey.
You see, Mr. Wooster, I am in America principally on business.
No doubt you read my book, India and the Indians?
My publishers are anxious for me to write a companion volume on the United States.
I shall not be able to spend more than a month in the country, as I have to get back for the season, but a month should be ample.
I was less than a month in India, and my dear friend Sir Roger Cremorne wrote his
America from Within after a stay of only two weeks.
I should love to take dear Motty with me, but the poor boy gets so sick when he travels by train.
I shall have to pick him up on my return."
From where I sat I could see Jeeves in the dining-room, laying the breakfast-table.
I wished I could have had a minute with him alone.
I felt certain that he would have been able to think of some way of putting a stop to this woman.
"It will be such a relief to know that
Motty is safe with you, Mr. Wooster.
I know what the temptations of a great city are.
Hitherto dear Motty has been sheltered from them.
He has lived quietly with me in the country.
I know that you will look after him carefully, Mr. Wooster.
He will give very little trouble."
She talked about the poor blighter as if he wasn't there.
Not that Motty seemed to mind.
He had stopped chewing his walking-stick and was sitting there with his mouth open.
"He is a vegetarian and a teetotaller and is devoted to reading.
Give him a nice book and he will be quite contented."
She got up.
"Thank you so much, Mr. Wooster!
I don't know what I should have done without your help. Come, Motty!
We have just time to see a few of the sights before my train goes.
But I shall have to rely on you for most of my information about New York, darling.
Be sure to keep your eyes open and take notes of your impressions!
It will be such a help.
Good-bye, Mr. Wooster.
I will send Motty back early in the afternoon."
They went out, and I howled for Jeeves.
"Jeeves!
What about it?"
"Sir?" "What's to be done?
You heard it all, didn't you?
You were in the dining-room most of the time.
That pill is coming to stay here." "Pill, sir?"
"The excrescence." "I beg your pardon, sir?"
I looked at Jeeves sharply.
It was as if he were deliberately trying to give me the pip.
Then I understood.
The man was really upset about that tie.
He was trying to get his own back.
"Lord Pershore will be staying here from to-night, Jeeves," I said coldly.
"Very good, sir.
Breakfast is ready, sir."
I could have sobbed into the bacon and eggs.
That there wasn't any sympathy to be got out of Jeeves was what put the lid on it.
For a moment I almost weakened and told him to destroy the hat and tie if he didn't like them, but I pulled myself together again.
I was dashed if I was going to let Jeeves treat me like a bally one-man chain-gang!
But, what with brooding on Jeeves and brooding on Motty, I was in a pretty reduced sort of state.
The more I examined the situation, the more blighted it became.
There was nothing I could do.
If I slung Motty out, he would report to his mother, and she would pass it on to
Aunt Agatha, and I didn't like to think what would happen then.
Sooner or later, I should be wanting to go back to England, and I didn't want to get there and find Aunt Agatha waiting on the quay for me with a stuffed eelskin.
There was absolutely nothing for it but to put the fellow up and make the best of it.
About midday Motty's luggage arrived, and soon afterward a large parcel of what I took to be nice books.
I brightened up a little when I saw it.
It was one of those massive parcels and looked as if it had enough in it to keep the chappie busy for a year.
I felt a trifle more cheerful, and I got my Country Gentleman hat and stuck it on my head, and gave the pink tie a twist, and reeled out to take a bite of lunch with one or two of the lads at a neighbouring hostelry; and what with excellent browsing and sluicing and cheery conversation and what-not, the afternoon passed quite happily.
By dinner-time I had almost forgotten blighted Motty's existence.
I dined at the club and looked in at a show afterward, and it wasn't till fairly late that I got back to the flat.
There were no signs of Motty, and I took it that he had gone to bed.
It seemed rummy to me, though, that the parcel of nice books was still there with the string and paper on it.
It looked as if Motty, after seeing mother off at the station, had decided to call it a day.
Jeeves came in with the nightly whisky-and- soda.
I could tell by the chappie's manner that he was still upset.
"Lord Pershore gone to bed, Jeeves?" I asked, with reserved hauteur and what- not.
"No, sir.
His lordship has not yet returned."
"Not returned?
What do you mean?"
"His lordship came in shortly after six- thirty, and, having dressed, went out again."
At this moment there was a noise outside the front door, a sort of scrabbling noise, as if somebody were trying to paw his way through the woodwork.
Then a sort of thud.
"Better go and see what that is, Jeeves." "Very good, sir."
He went out and came back again.
"If you would not mind stepping this way, sir, I think we might be able to carry him in." "Carry him in?"
"His lordship is lying on the mat, sir."
I went to the front door.
The man was right.
There was Motty huddled up outside on the floor.
He was moaning a bit.
"He's had some sort of dashed fit," I said.
I took another look.
"Jeeves!
Someone's been feeding him meat!"
"Sir?"
"He's a vegetarian, you know.
He must have been digging into a steak or something.
Call up a doctor!"
"I hardly think it will be necessary, sir.
If you would take his lordship's legs, while I----"
"Great Scot, Jeeves!
You don't think--he can't be----"
"I am inclined to think so, sir."
And, by Jove, he was right!
Once on the right track, you couldn't mistake it.
Motty was under the surface.
It was the deuce of a shock.
"You never can tell, Jeeves!" "Very seldom, sir."
"Remove the eye of authority and where are you?"
"Precisely, sir."
"Where is my wandering boy to-night and all that sort of thing, what?"
"It would seem so, sir." "Well, we had better bring him in, eh?"
"Yes, sir."
So we lugged him in, and Jeeves put him to bed, and I lit a cigarette and sat down to think the thing over.
I had a kind of foreboding.
It seemed to me that I had let myself in for something pretty rocky.
Next morning, after I had sucked down a thoughtful cup of tea, I went into Motty's room to investigate.
I expected to find the fellow a wreck, but there he was, sitting up in bed, quite chirpy, reading Gingery stories.
"What ho!"
I said.
"What ho!" said Motty.
"What ho!
What ho!" "What ho!
What ho!
What ho!" After that it seemed rather difficult to go on with the conversation.
I asked.
"Topping!" replied Motty, blithely and with abandon.
"I say, you know, that fellow of yours-- Jeeves, you know--is a corker.
I had a most frightful headache when I woke up, and he brought me a sort of rummy dark drink, and it put me right again at once.
Said it was his own invention.
I must see more of that lad.
He seems to me distinctly one of the ones!" I couldn't believe that this was the same blighter who had sat and sucked his stick the day before.
"You ate something that disagreed with you last night, didn't you?"
I said, by way of giving him a chance to slide out of it if he wanted to.
But he wouldn't have it, at any price.
"No!" he replied firmly.
"I didn't do anything of the kind.
I drank too much!
Much too much.
Lots and lots too much!
And, what's more, I'm going to do it again!
I'm going to do it every night.
If ever you see me sober, old top," he said, with a kind of holy exaltation, "tap me on the shoulder and say, 'Tut!
Tut!' and I'll apologize and remedy the defect."
"But I say, you know, what about me?" "What about you?"
"Well, I'm so to speak, as it were, kind of responsible for you.
What I mean to say is, if you go doing this sort of thing I'm apt to get in the soup somewhat."
"I can't help your troubles," said Motty firmly.
"Listen to me, old thing: this is the first time in my life that I've had a real chance to yield to the temptations of a great city.
What's the use of a great city having temptations if fellows don't yield to them?
Makes it so bally discouraging for a great city.
Besides, mother told me to keep my eyes open and collect impressions."
I sat on the edge of the bed.
I felt dizzy.
"I know just how you feel, old dear," said Motty consolingly.
"And, if my principles would permit it, I would simmer down for your sake.
But duty first!
This is the first time I've been let out alone, and I mean to make the most of it.
We're only young once.
Why interfere with life's morning?
Young man, rejoice in thy youth!
Tra-la!
What ho!"
Put like that, it did seem reasonable.
"All my bally life, dear boy," Motty went on, "I've been cooped up in the ancestral home at Much Middlefold, in Shropshire, and till you've been cooped up in Much
Middlefold you don't know what cooping is! When that happens, we talk about it for days.
I've got about a month of New York, and I mean to store up a few happy memories for the long winter evenings.
This is my only chance to collect a past, and I'm going to do it.
Now tell me, old sport, as man to man, how does one get in touch with that very decent chappie Jeeves?
Does one ring a bell or shout a bit?
I should like to discuss the subject of a good stiff b.-and-s. with him!"
I had had a sort of vague idea, don't you know, that if I stuck close to Motty and went about the place with him, I might act as a bit of a damper on the gaiety.
What I mean is, I thought that if, when he was being the life and soul of the party, he were to catch my reproving eye he might ease up a trifle on the revelry.
So the next night I took him along to supper with me.
It was the last time.
I'm a quiet, peaceful sort of chappie who has lived all his life in London, and I can't stand the pace these swift sportsmen from the rural districts set.
What I mean to say is this, I'm all for rational enjoyment and so forth, but I think a chappie makes himself conspicuous when he throws soft-boiled eggs at the electric fan.
And decent mirth and all that sort of thing are all right, but I do bar dancing on tables and having to dash all over the place dodging waiters, managers, and chuckers-out, just when you want to sit still and digest.
Directly I managed to tear myself away that night and get home, I made up my mind that this was jolly well the last time that I went about with Motty.
The only time I met him late at night after that was once when I passed the door of a fairly low-down sort of restaurant and had to step aside to dodge him as he sailed through the air en route for the opposite pavement, with a muscular sort of looking chappie peering out after him with a kind of gloomy satisfaction.
In a way, I couldn't help sympathizing with the fellow.
He had about four weeks to have the good time that ought to have been spread over about ten years, and I didn't wonder at his wanting to be pretty busy.
I should have been just the same in his place.
Still, there was no denying that it was a bit thick.
If it hadn't been for the thought of Lady Malvern and Aunt Agatha in the background,
I should have regarded Motty's rapid work with an indulgent smile.
But I couldn't get rid of the feeling that, sooner or later, I was the lad who was scheduled to get it behind the ear.
And what with brooding on this prospect, and sitting up in the old flat waiting for the familiar footstep, and putting it to bed when it got there, and stealing into the sick-chamber next morning to contemplate the wreckage, I was beginning to lose weight.
Absolutely becoming the good old shadow, I give you my honest word.
Starting at sudden noises and what-not.
And no sympathy from Jeeves.
That was what cut me to the quick.
The man was still thoroughly pipped about the hat and tie, and simply wouldn't rally round.
One morning I wanted comforting so much that I sank the pride of the Woosters and appealed to the fellow direct. "Jeeves," I said, "this is getting a bit thick!"
"Sir?" Business and cold respectfulness.
"You know what I mean.
This lad seems to have chucked all the principles of a well-spent boyhood.
He has got it up his nose!" "Yes, sir."
"Well, I shall get blamed, don't you know.
You know what my Aunt Agatha is!"
"Yes, sir."
"Very well, then." I waited a moment, but he wouldn't unbend.
"Jeeves," I said, "haven't you any scheme up your sleeve for coping with this blighter?"
"No, sir." And he shimmered off to his lair.
Obstinate devil!
So dashed absurd, don't you know.
It wasn't as if there was anything wrong with that Country Gentleman hat.
It was a remarkably priceless effort, and much admired by the lads.
But, just because he preferred the Longacre, he left me flat.
It was shortly after this that young Motty got the idea of bringing pals back in the small hours to continue the gay revels in the home.
This was where I began to crack under the strain.
You see, the part of town where I was living wasn't the right place for that sort of thing.
I knew lots of chappies down Washington Square way who started the evening at about 2 a.m.--artists and writers and what-not, who frolicked considerably till checked by the arrival of the morning milk.
That was all right.
They like that sort of thing down there.
The neighbours can't get to sleep unless there's someone dancing Hawaiian dances over their heads.
But on Fifty-seventh Street the atmosphere wasn't right, and when Motty turned up at three in the morning with a collection of hearty lads, who only stopped singing their college song when they started singing "The
Old Oaken Bucket," there was a marked peevishness among the old settlers in the flats.
The management was extremely terse over the telephone at breakfast-time, and took a lot of soothing.
The next night I came home early, after a lonely dinner at a place which I'd chosen because there didn't seem any chance of meeting Motty there.
The sitting-room was quite dark, and I was just moving to switch on the light, when there was a sort of explosion and something collared hold of my trouser-leg.
Living with Motty had reduced me to such an extent that I was simply unable to cope with this thing.
I jumped backward with a loud yell of anguish, and tumbled out into the hall just as Jeeves came out of his den to see what the matter was.
"Did you call, sir?"
There's something in there that grabs you by the leg!" "That would be Rollo, sir."
"Eh?"
"I would have warned you of his presence, but I did not hear you come in.
His temper is a little uncertain at present, as he has not yet settled down."
"Who the deuce is Rollo?"
"His lordship's bull-terrier, sir. His lordship won him in a raffle, and tied him to the leg of the table. If you will allow me, sir, I will go in and switch on the light."
There really is nobody like Jeeves.
He walked straight into the sitting-room, the biggest feat since Daniel and the lions' den, without a quiver.
What's more, his magnetism or whatever they call it was such that the dashed animal, instead of pinning him by the leg, calmed down as if he had had a bromide, and rolled over on his back with all his paws in the air.
If Jeeves had been his rich uncle he couldn't have been more chummy.
Yet directly he caught sight of me again, he got all worked up and seemed to have only one idea in life--to start chewing me where he had left off.
"Rollo is not used to you yet, sir," said Jeeves, regarding the bally quadruped in an admiring sort of way.
"He is an excellent watchdog."
"I don't want a watchdog to keep me out of my rooms."
"No, sir." "Well, what am I to do?"
"No doubt in time the animal will learn to discriminate, sir.
He will learn to distinguish your peculiar scent."
"What do you mean--my peculiar scent?
Correct the impression that I intend to hang about in the hall while life slips by, in the hope that one of these days that dashed animal will decide that I smell all right."
I thought for a bit.
"Jeeves!"
"Sir?" "I'm going away--to-morrow morning by the first train.
I shall go and stop with Mr. Todd in the country."
"Do you wish me to accompany you, sir?" "No."
"Very good, sir."
"I don't know when I shall be back.
Forward my letters."
"Yes, sir." As a matter of fact, I was back within the week.
Rocky Todd, the pal I went to stay with, is a rummy sort of a chap who lives all alone in the wilds of Long Island, and likes it; but a little of that sort of thing goes a long way with me.
Dear old Rocky is one of the best, but after a few days in his cottage in the woods, miles away from anywhere, New York, even with Motty on the premises, began to look pretty good to me.
The days down on Long Island have forty- eight hours in them; you can't get to sleep at night because of the bellowing of the crickets; and you have to walk two miles for a drink and six for an evening paper.
I thanked Rocky for his kind hospitality, and caught the only train they have down in those parts.
It landed me in New York about dinner-time.
I went straight to the old flat.
Jeeves came out of his lair.
I looked round cautiously for Rollo.
"Where's that dog, Jeeves?
Have you got him tied up?"
"The animal is no longer here, sir.
His lordship gave him to the porter, who sold him.
His lordship took a prejudice against the animal on account of being bitten by him in the calf of the leg."
I don't think I've ever been so bucked by a bit of news.
I felt I had misjudged Rollo.
Evidently, when you got to know him better, he had a lot of intelligence in him.
"Ripping!" I said.
"Is Lord Pershore in, Jeeves?" "No, sir."
"Do you expect him back to dinner?"
"No, sir." "Where is he?"
"In prison, sir." Have you ever trodden on a rake and had the handle jump up and hit you?
That's how I felt then.
"In prison!"
"Yes, sir." "You don't mean--in prison?"
"Yes, sir."
I lowered myself into a chair.
"Why?"
I said.
"He assaulted a constable, sir."
"Lord Pershore assaulted a constable!"
"Yes, sir." I digested this.
"But, Jeeves, I say!
This is frightful!"
"Sir?"
"What will Lady Malvern say when she finds out?"
"I do not fancy that her ladyship will find out, sir."
"But she'll come back and want to know where he is."
"I rather fancy, sir, that his lordship's bit of time will have run out by then."
"But supposing it hasn't?"
"In that event, sir, it may be judicious to prevaricate a little."
"How?"
"If I might make the suggestion, sir, I should inform her ladyship that his lordship has left for a short visit to Boston."
"Why Boston?"
"Very interesting and respectable centre, sir."
"Jeeves, I believe you've hit it." "I fancy so, sir."
"Why, this is really the best thing that could have happened.
If this hadn't turned up to prevent him, young Motty would have been in a sanatorium by the time Lady Malvern got back."
"Exactly, sir." The more I looked at it in that way, the sounder this prison wheeze seemed to me.
There was no doubt in the world that prison was just what the doctor ordered for Motty.
It was the only thing that could have pulled him up.
I was sorry for the poor blighter, but, after all, I reflected, a chappie who had lived all his life with Lady Malvern, in a small village in the interior of
Shropshire, wouldn't have much to kick at in a prison.
Altogether, I began to feel absolutely braced again.
Life became like what the poet Johnnie says--one grand, sweet song.
Things went on so comfortably and peacefully for a couple of weeks that I give you my word that I'd almost forgotten such a person as Motty existed.
The only flaw in the scheme of things was that Jeeves was still pained and distant.
It wasn't anything he said or did, mind you, but there was a rummy something about him all the time.
Once when I was tying the pink tie I caught sight of him in the looking-glass.
There was a kind of grieved look in his eye.
And then Lady Malvern came back, a good bit ahead of schedule.
I'd forgotten how time had been slipping along.
She turned up one morning while I was still in bed sipping tea and thinking of this and that.
I draped a few garments round me and went in.
There she was, sitting in the same arm- chair, looking as massive as ever.
The only difference was that she didn't uncover the teeth, as she had done the first time.
"Good morning," I said.
"So you've got back, what?"
"I have got back."
There was something sort of bleak about her tone, rather as if she had swallowed an east wind.
This I took to be due to the fact that she probably hadn't breakfasted.
It's only after a bit of breakfast that I'm able to regard the world with that sunny cheeriness which makes a fellow the universal favourite.
I'm never much of a lad till I've engulfed an egg or two and a beaker of coffee.
"I suppose you haven't breakfasted?" "I have not yet breakfasted."
"Won't you have an egg or something?
Or a sausage or something?
Or something?"
"No, thank you."
She spoke as if she belonged to an anti- sausage society or a league for the suppression of eggs.
There was a bit of a silence.
"I called on you last night," she said, "but you were out."
"Awfully sorry!
Had a pleasant trip?"
"Extremely, thank you."
"See everything?
Niag'ra Falls, Yellowstone Park, and the jolly old Grand Canyon, and what-not?" "I saw a great deal."
There was another slightly frappe silence.
Jeeves floated silently into the dining- room and began to lay the breakfast-table.
"I hope Wilmot was not in your way, Mr. Wooster?"
I had been wondering when she was going to mention Motty.
"Rather not!
Great pals!
Hit it off splendidly."
"You were his constant companion, then?" "Absolutely!
We were always together.
Saw all the sights, don't you know.
We'd take in the Museum of Art in the morning, and have a bit of lunch at some good vegetarian place, and then toddle along to a sacred concert in the afternoon, and home to an early dinner.
We usually played dominoes after dinner.
And then the early bed and the refreshing sleep.
We had a great time.
I was awfully sorry when he went away to Boston."
"Oh!
Wilmot is in Boston?"
"Yes.
I ought to have let you know, but of course we didn't know where you were.
You were dodging all over the place like a snipe--I mean, don't you know, dodging all over the place, and we couldn't get at you.
Yes, Motty went off to Boston." "You're sure he went to Boston?"
"Oh, absolutely."
I called out to Jeeves, who was now messing about in the next room with forks and so forth:
"Jeeves, Lord Pershore didn't change his mind about going to Boston, did he?"
"No, sir."
"I thought I was right.
Yes, Motty went to Boston."
"Then how do you account, Mr. Wooster, for the fact that when I went yesterday afternoon to Blackwell's Island prison, to secure material for my book, I saw poor, dear Wilmot there, dressed in a striped suit, seated beside a pile of stones with a hammer in his hands?"
I tried to think of something to say, but nothing came.
A chappie has to be a lot broader about the forehead than I am to handle a jolt like this.
I strained the old bean till it creaked, but between the collar and the hair parting nothing stirred.
I was dumb.
Which was lucky, because I wouldn't have had a chance to get any persiflage out of my system.
Lady Malvern collared the conversation.
She had been bottling it up, and now it came out with a rush:
"So this is how you have looked after my poor, dear boy, Mr. Wooster!
So this is how you have abused my trust!
I left him in your charge, thinking that I could rely on you to shield him from evil.
He came to you innocent, unversed in the ways of the world, confiding, unused to the temptations of a large city, and you led him astray!"
I hadn't any remarks to make.
All I could think of was the picture of Aunt Agatha drinking all this in and reaching out to sharpen the hatchet against my return.
"You deliberately----"
Far away in the misty distance a soft voice spoke:
"If I might explain, your ladyship." Jeeves had projected himself in from the dining-room and materialized on the rug.
Lady Malvern tried to freeze him with a look, but you can't do that sort of thing to Jeeves.
He is look-proof.
"I fancy, your ladyship, that you have misunderstood Mr. Wooster, and that he may have given you the impression that he was in New York when his lordship--was removed.
When Mr. Wooster informed your ladyship that his lordship had gone to Boston, he was relying on the version I had given him of his lordship's movements.
Mr. Wooster was away, visiting a friend in the country, at the time, and knew nothing of the matter till your ladyship informed him."
Lady Malvern gave a kind of grunt.
It didn't rattle Jeeves.
"I feared Mr. Wooster might be disturbed if he knew the truth, as he is so attached to his lordship and has taken such pains to look after him, so I took the liberty of telling him that his lordship had gone away for a visit.
It might have been hard for Mr. Wooster to believe that his lordship had gone to prison voluntarily and from the best motives, but your ladyship, knowing him better, will readily understand."
"What!" Lady Malvern goggled at him.
"Did you say that Lord Pershore went to prison voluntarily?"
"If I might explain, your ladyship.
I think that your ladyship's parting words made a deep impression on his lordship.
I have frequently heard him speak to Mr. Wooster of his desire to do something to follow your ladyship's instructions and collect material for your ladyship's book on America.
Mr. Wooster will bear me out when I say that his lordship was frequently extremely depressed at the thought that he was doing so little to help."
"Absolutely, by Jove!
Quite pipped about it!" I said.
"The idea of making a personal examination into the prison system of the country--from within--occurred to his lordship very suddenly one night.
He embraced it eagerly.
There was no restraining him." Lady Malvern looked at Jeeves, then at me, then at Jeeves again.
I could see her struggling with the thing.
"Surely, your ladyship," said Jeeves, "it is more reasonable to suppose that a gentleman of his lordship's character went to prison of his own volition than that he committed some breach of the law which necessitated his arrest?"
Lady Malvern blinked.
Then she got up.
"Mr. Wooster," she said, "I apologize.
I have done you an injustice.
I should have known Wilmot better.
I should have had more faith in his pure, fine spirit."
"Absolutely!"
I said.
"Your breakfast is ready, sir," said
I sat down and dallied in a dazed sort of way with a poached egg.
"Jeeves," I said, "you are certainly a life-saver!"
"Thank you, sir."
"Nothing would have convinced my Aunt Agatha that I hadn't lured that blighter into riotous living." "I fancy you are right, sir."
I champed my egg for a bit.
I was most awfully moved, don't you know, by the way Jeeves had rallied round.
Something seemed to tell me that this was an occasion that called for rich rewards.
For a moment I hesitated.
Then I made up my mind.
"Jeeves!"
"Sir?" "That pink tie!"
"Yes, sir?"
"Burn it!" "Thank you, sir."
"And, Jeeves!" "Yes, sir?"
"Take a taxi and get me that Longacre hat, as worn by John Drew!"
"Thank you very much, sir." I felt most awfully braced.
I felt as if the clouds had rolled away and all was as it used to be.
I felt like one of those chappies in the novels who calls off the fight with his wife in the last chapter and decides to forget and forgive.
I felt I wanted to do all sorts of other things to show Jeeves that I appreciated him.
"Jeeves," I said, "it isn't enough.
Is there anything else you would like?"
"Yes, sir. If I may make the suggestion--fifty dollars." "Fifty dollars?"
"It will enable me to pay a debt of honour, sir.
I owe it to his lordship." "You owe Lord Pershore fifty dollars?"
"Yes, sir.
I happened to meet him in the street the night his lordship was arrested.
I had been thinking a good deal about the most suitable method of inducing him to abandon his mode of living, sir.
His lordship was a little over-excited at the time and I fancy that he mistook me for a friend of his.
At any rate when I took the liberty of wagering him fifty dollars that he would not punch a passing policeman in the eye, he accepted the bet very cordially and won it."
I produced my pocket-book and counted out a hundred.
"Take this, Jeeves," I said; "fifty isn't enough.
Do you know, Jeeves, you're--well, you absolutely stand alone!"
"I endeavour to give satisfaction, sir," said Jeeves. >
CHAPTER 3 JEEVES AND THE HARD-BOlLED EGG
Sometimes of a morning, as I've sat in bed sucking down the early cup of tea and watched my man Jeeves flitting about the room and putting out the raiment for the day, I've wondered what the deuce I should do if the fellow ever took it into his head to leave me.
It's not so bad now I'm in New York, but in London the anxiety was frightful.
There used to be all sorts of attempts on the part of low blighters to sneak him away from me.
Young Reggie Foljambe to my certain knowledge offered him double what I was giving him, and Alistair Bingham-Reeves, who's got a valet who had been known to press his trousers sideways, used to look at him, when he came to see me, with a kind of glittering hungry eye which disturbed me deucedly.
Bally pirates!
The thing, you see, is that Jeeves is so dashed competent.
You can spot it even in the way he shoves studs into a shirt.
I rely on him absolutely in every crisis, and he never lets me down.
And, what's more, he can always be counted on to extend himself on behalf of any pal of mine who happens to be to all appearances knee-deep in the bouillon.
Take the rather rummy case, for instance, of dear old Bicky and his uncle, the hard- boiled egg.
It happened after I had been in America for a few months.
I got back to the flat latish one night, and when Jeeves brought me the final drink he said:
"Mr. Bickersteth called to see you this evening, sir, while you were out."
"Oh?" I said.
"Twice, sir.
He appeared a trifle agitated."
"What, pipped?"
"He gave that impression, sir." I sipped the whisky.
I was sorry if Bicky was in trouble, but, as a matter of fact, I was rather glad to have something I could discuss freely with Jeeves just then, because things had been a bit strained between us for some time, and it had been rather difficult to hit on anything to talk about that wasn't apt to take a personal turn.
You see, I had decided--rightly or wrongly- -to grow a moustache and this had cut
Jeeves to the quick.
He couldn't stick the thing at any price, and I had been living ever since in an atmosphere of bally disapproval till I was getting jolly well fed up with it.
What I mean is, while there's no doubt that in certain matters of dress Jeeves's judgment is absolutely sound and should be followed, it seemed to me that it was getting a bit too thick if he was going to edit my face as well as my costume.
No one can call me an unreasonable chappie, and many's the time I've given in like a lamb when Jeeves has voted against one of my pet suits or ties; but when it comes to a valet's staking out a claim on your upper
"He said that he would call again later, sir."
"Something must be up, Jeeves." "Yes, sir."
I gave the moustache a thoughtful twirl. It seemed to hurt Jeeves a good deal, so I chucked it.
"I see by the paper, sir, that Mr. Bickersteth's uncle is arriving on the
Carmantic." "Yes?"
"His Grace the Duke of Chiswick, sir."
This was news to me, that Bicky's uncle was a duke.
Rum, how little one knows about one's pals!
I had met Bicky for the first time at a species of beano or jamboree down in
Washington Square, not long after my arrival in New York.
I suppose I was a bit homesick at the time, and I rather took to Bicky when I found that he was an Englishman and had, in fact, been up at Oxford with me.
Besides, he was a frightful chump, so we naturally drifted together; and while we were taking a quiet snort in a corner that wasn't all cluttered up with artists and sculptors and what-not, he furthermore endeared himself to me by a most extraordinarily gifted imitation of a bull- terrier chasing a cat up a tree.
But, though we had subsequently become extremely pally, all I really knew about him was that he was generally hard up, and had an uncle who relieved the strain a bit from time to time by sending him monthly remittances.
"If the Duke of Chiswick is his uncle," I said, "why hasn't he a title?
Why isn't he Lord What-Not?"
"Mr. Bickersteth is the son of his grace's late sister, sir, who married Captain Rollo
Bickersteth of the Coldstream Guards." Jeeves knows everything.
"Is Mr. Bickersteth's father dead, too?"
"Yes, sir." "Leave any money?"
"No, sir." I began to understand why poor old Bicky was always more or less on the rocks.
To the casual and irreflective observer, if you know what I mean, it may sound a pretty good wheeze having a duke for an uncle, but the trouble about old Chiswick was that, though an extremely wealthy old buster, owning half London and about five counties up north, he was notoriously the most prudent spender in England.
He was what American chappies would call a hard-boiled egg.
If Bicky's people hadn't left him anything and he depended on what he could prise out of the old duke, he was in a pretty bad way.
Not that that explained why he was hunting me like this, because he was a chap who never borrowed money.
He said he wanted to keep his pals, so never bit any one's ear on principle.
Mr. Wooster has just returned," I heard him say.
And Bicky came trickling in, looking pretty sorry for himself.
"Halloa, Bicky!" I said.
"Jeeves told me you had been trying to get me.
Jeeves, bring another glass, and let the revels commence.
What's the trouble, Bicky?"
"I'm in a hole, Bertie.
I want your advice."
"Say on, old lad!" "My uncle's turning up to-morrow, Bertie."
"So Jeeves told me."
"The Duke of Chiswick, you know." "So Jeeves told me."
Bicky seemed a bit surprised.
"Jeeves seems to know everything."
"Rather rummily, that's exactly what I was thinking just now myself."
"Well, I wish," said Bicky gloomily, "that he knew a way to get me out of the hole I'm in."
Jeeves shimmered in with the glass, and stuck it competently on the table. "Mr. Bickersteth is in a bit of a hole, Jeeves," I said, "and wants you to rally round."
"Very good, sir." Bicky looked a bit doubtful. "Well, of course, you know, Bertie, this thing is by way of being a bit private and all that."
"I shouldn't worry about that, old top.
I bet Jeeves knows all about it already.
Don't you, Jeeves?" "Yes, sir."
"Eh!" said Bicky, rattled.
"I am open to correction, sir, but is not your dilemma due to the fact that you are at a loss to explain to his grace why you are in New York instead of in Colorado?"
Bicky rocked like a jelly in a high wind.
"How the deuce do you know anything about it?"
"I chanced to meet his grace's butler before we left England.
He informed me that he happened to overhear his grace speaking to you on the matter, sir, as he passed the library door." Bicky gave a hollow sort of laugh.
"Well, as everybody seems to know all about it, there's no need to try to keep it dark.
The old boy turfed me out, Bertie, because he said I was a brainless nincompoop.
The idea was that he would give me a remittance on condition that I dashed out to some blighted locality of the name of Colorado and learned farming or ranching, or whatever they call it, at some bally ranch or farm or whatever it's called.
I didn't fancy the idea a bit.
I should have had to ride horses and pursue cows, and so forth.
I hate horses.
They bite at you.
I was all against the scheme.
At the same time, don't you know, I had to have that remittance."
"I get you absolutely, dear boy." "Well, when I got to New York it looked a decent sort of place to me, so I thought it would be a pretty sound notion to stop here.
So I cabled to my uncle telling him that I had dropped into a good business wheeze in the city and wanted to chuck the ranch idea.
He wrote back that it was all right, and here I've been ever since.
He thinks I'm doing well at something or other over here.
I never dreamed, don't you know, that he would ever come out here.
What on earth am I to do?" "Jeeves," I said, "what on earth is Mr.
Bickersteth to do?"
"You see," said Bicky, "I had a wireless from him to say that he was coming to stay with me--to save hotel bills, I suppose.
I've always given him the impression that I was living in pretty good style.
I can't have him to stay at my boarding- house."
"Thought of anything, Jeeves?" I said.
"To what extent, sir, if the question is not a delicate one, are you prepared to assist Mr. Bickersteth?" "I'll do anything I can for you, of course,
Bicky, old man."
"Then, if I might make the suggestion, sir, you might lend Mr. Bickersteth----"
"No, by Jove!" said Bicky firmly.
"I never have touched you, Bertie, and I'm not going to start now.
I may be a chump, but it's my boast that I don't owe a penny to a single soul--not counting tradesmen, of course." "I was about to suggest, sir, that you might lend Mr. Bickersteth this flat.
Mr. Bickersteth could give his grace the impression that he was the owner of it.
With your permission I could convey the notion that I was in Mr. Bickersteth's employment, and not in yours.
You would be residing here temporarily as Mr. Bickersteth's guest.
His grace would occupy the second spare bedroom.
I fancy that you would find this answer satisfactorily, sir."
Bicky had stopped rocking himself and was staring at Jeeves in an awed sort of way.
"I would advocate the dispatching of a wireless message to his grace on board the vessel, notifying him of the change of address.
Mr. Bickersteth could meet his grace at the dock and proceed directly here.
Will that meet the situation, sir?" "Absolutely."
"Thank you, sir."
Bicky followed him with his eye till the door closed.
"How does he do it, Bertie?" he said.
"I'll tell you what I think it is.
I believe it's something to do with the shape of his head.
Have you ever noticed his head, Bertie, old man?
It sort of sticks out at the back!"
I hopped out of bed early next morning, so as to be among those present when the old boy should arrive.
I knew from experience that these ocean liners fetch up at the dock at a deucedly ungodly hour.
It wasn't much after nine by the time I'd dressed and had my morning tea and was leaning out of the window, watching the street for Bicky and his uncle.
It was one of those jolly, peaceful mornings that make a chappie wish he'd got a soul or something, and I was just brooding on life in general when I became aware of the dickens of a spate in progress down below.
A taxi had driven up, and an old boy in a top hat had got out and was kicking up a frightful row about the fare.
As far as I could make out, he was trying to get the cab chappie to switch from New
York to London prices, and the cab chappie had apparently never heard of London before, and didn't seem to think a lot of it now.
The old boy said that in London the trip would have set him back eightpence; and the cabby said he should worry.
I called to Jeeves.
"The duke has arrived, Jeeves."
"Yes, sir?" "That'll be him at the door now."
Jeeves made a long arm and opened the front door, and the old boy crawled in, looking licked to a splinter.
"How do you do, sir?"
I said, bustling up and being the ray of sunshine.
"Your nephew went down to the dock to meet you, but you must have missed him.
My name's Wooster, don't you know.
Great pal of Bicky's, and all that sort of thing.
I'm staying with him, you know.
Would you like a cup of tea?
Jeeves, bring a cup of tea."
Old Chiswick had sunk into an arm-chair and was looking about the room.
"Does this luxurious flat belong to my nephew Francis?"
"Absolutely."
"It must be terribly expensive." "Pretty well, of course.
Everything costs a lot over here, you know."
He moaned.
Jeeves filtered in with the tea.
Old Chiswick took a stab at it to restore his tissues, and nodded.
"A terrible country, Mr. Wooster!
A terrible country!
Nearly eight shillings for a short cab- drive!
Iniquitous!" He took another look round the room.
It seemed to fascinate him.
"Have you any idea how much my nephew pays for this flat, Mr. Wooster?"
"About two hundred dollars a month, I believe."
"What!
Forty pounds a month!" I began to see that, unless I made the thing a bit more plausible, the scheme might turn out a frost.
I could guess what the old boy was thinking.
He was trying to square all this prosperity with what he knew of poor old Bicky.
And one had to admit that it took a lot of squaring, for dear old Bicky, though a stout fellow and absolutely unrivalled as an imitator of bull-terriers and cats, was in many ways one of the most pronounced fatheads that ever pulled on a suit of gent's underwear.
"I suppose it seems rummy to you," I said, "but the fact is New York often bucks chappies up and makes them show a flash of speed that you wouldn't have imagined them capable of.
It sort of develops them.
Something in the air, don't you know.
I imagine that Bicky in the past, when you knew him, may have been something of a chump, but it's quite different now.
Devilish efficient sort of chappie, and looked on in commercial circles as quite the nib!" "I am amazed!
What is the nature of my nephew's business, Mr. Wooster?"
"Oh, just business, don't you know.
The same sort of thing Carnegie and Rockefeller and all these coves do, you know." I slid for the door.
"Awfully sorry to leave you, but I've got to meet some of the lads elsewhere."
Coming out of the lift I met Bicky bustling in from the street.
"Halloa, Bertie!
I missed him.
Has he turned up?"
"He's upstairs now, having some tea." "What does he think of it all?"
"He's absolutely rattled."
"Ripping!
I'll be toddling up, then.
Toodle-oo, Bertie, old man.
See you later."
"Pip-pip, Bicky, dear boy."
He trotted off, full of merriment and good cheer, and I went off to the club to sit in the window and watch the traffic coming up one way and going down the other.
It was latish in the evening when I looked in at the flat to dress for dinner.
"Where's everybody, Jeeves?" I said, finding no little feet pattering about the place.
"Gone out?" "His grace desired to see some of the sights of the city, sir.
Mr. Bickersteth is acting as his escort.
I fancy their immediate objective was Grant's Tomb."
"I suppose Mr. Bickersteth is a bit braced at the way things are going--what?"
"Sir?"
"I say, I take it that Mr. Bickersteth is tolerably full of beans."
"Not altogether, sir." "What's his trouble now?"
"The scheme which I took the liberty of suggesting to Mr. Bickersteth and yourself has, unfortunately, not answered entirely satisfactorily, sir."
"Surely the duke believes that Mr. Bickersteth is doing well in business, and all that sort of thing?" "Exactly, sir.
With the result that he has decided to cancel Mr. Bickersteth's monthly allowance, on the ground that, as Mr. Bickersteth is doing so well on his own account, he no
longer requires pecuniary assistance."
"Great Scot, Jeeves!
This is awful."
"Somewhat disturbing, sir." "I never expected anything like this!"
"I confess I scarcely anticipated the contingency myself, sir."
"I suppose it bowled the poor blighter over absolutely?"
"Mr. Bickersteth appeared somewhat taken aback, sir."
My heart bled for Bicky.
"We must do something, Jeeves."
"Yes, sir."
"Can you think of anything?" "Not at the moment, sir."
"There must be something we can do."
"It was a maxim of one of my former employers, sir--as I believe I mentioned to you once before--the present Lord Bridgnorth, that there is always a way.
I remember his lordship using the expression on the occasion--he was then a business gentleman and had not yet received his title--when a patent hair-restorer which he chanced to be promoting failed to attract the public.
He put it on the market under another name as a depilatory, and amassed a substantial fortune.
I have generally found his lordship's aphorism based on sound foundations.
No doubt we shall be able to discover some solution of Mr. Bickersteth's difficulty, sir."
"Well, have a stab at it, Jeeves!" "I will spare no pains, sir."
I went and dressed sadly.
It will show you pretty well how pipped I was when I tell you that I near as a toucher put on a white tie with a dinner- jacket.
I sallied out for a bit of food more to pass the time than because I wanted it.
It seemed brutal to be wading into the bill of fare with poor old Bicky headed for the breadline.
When I got back old Chiswick had gone to bed, but Bicky was there, hunched up in an arm-chair, brooding pretty tensely, with a cigarette hanging out of the corner of his mouth and a more or less glassy stare in his eyes.
He had the aspect of one who had been soaked with what the newspaper chappies call "some blunt instrument."
"This is a bit thick, old thing--what!" I said.
He picked up his glass and drained it feverishly, overlooking the fact that it hadn't anything in it.
"I'm done, Bertie!" he said.
He had another go at the glass.
It didn't seem to do him any good.
"If only this had happened a week later,
Bertie!
My next month's money was due to roll in on Saturday.
I could have worked a wheeze I've been reading about in the magazine advertisements.
It seems that you can make a dashed amount of money if you can only collect a few dollars and start a chicken-farm.
Jolly sound scheme, Bertie!
Say you buy a hen--call it one hen for the sake of argument. You sell the eggs seven for twenty-five cents.
Keep of hen costs nothing.
Profit practically twenty-five cents on every seven eggs.
Or look at it another way:
Suppose you have a dozen eggs.
Each of the hens has a dozen chickens.
Why, in no time you'd have the place covered knee-deep in hens, all laying eggs, at twenty-five cents for every seven.
You'd make a fortune.
Jolly life, too, keeping hens!"
He had begun to get quite worked up at the thought of it, but he slopped back in his chair at this juncture with a good deal of gloom.
"But, of course, it's no good," he said, "because I haven't the cash."
"You've only to say the word, you know, Bicky, old top."
"Thanks awfully, Bertie, but I'm not going to sponge on you."
That's always the way in this world.
The chappies you'd like to lend money to won't let you, whereas the chappies you don't want to lend it to will do everything except actually stand you on your head and lift the specie out of your pockets.
As a lad who has always rolled tolerably free in the right stuff, I've had lots of experience of the second class.
Many's the time, back in London, I've hurried along Piccadilly and felt the hot breath of the toucher on the back of my neck and heard his sharp, excited yapping as he closed in on me.
I've simply spent my life scattering largesse to blighters I didn't care a hang for; yet here was I now, dripping doubloons and pieces of eight and longing to hand them over, and Bicky, poor fish, absolutely on his uppers, not taking any at any price.
"Well, there's only one hope, then." "What's that?"
"Jeeves."
"Sir?" There was Jeeves, standing behind me, full of zeal.
In this matter of shimmering into rooms the chappie is rummy to a degree.
You're sitting in the old armchair, thinking of this and that, and then suddenly you look up, and there he is.
He moves from point to point with as little uproar as a jelly fish.
The thing startled poor old Bicky considerably.
He rose from his seat like a rocketing pheasant.
I'm used to Jeeves now, but often in the days when he first came to me I've bitten my tongue freely on finding him unexpectedly in my midst.
"Did you call, sir?"
"Oh, there you are, Jeeves!" "Precisely, sir."
"Jeeves, Mr. Bickersteth is still up the pole.
Any ideas?"
"Why, yes, sir.
Since we had our recent conversation I fancy I have found what may prove a solution.
I do not wish to appear to be taking a liberty, sir, but I think that we have overlooked his grace's potentialities as a source of revenue."
Bicky laughed, what I have sometimes seen described as a hollow, mocking laugh, a sort of bitter cackle from the back of the throat, rather like a gargle.
"I do not allude, sir," explained Jeeves, "to the possibility of inducing his grace to part with money.
I am taking the liberty of regarding his grace in the light of an at present--if I may say so--useless property, which is capable of being developed."
Bicky looked at me in a helpless kind of way.
I'm bound to say I didn't get it myself.
"Couldn't you make it a bit easier,
Jeeves!"
"In a nutshell, sir, what I mean is this: His grace is, in a sense, a prominent personage.
The inhabitants of this country, as no doubt you are aware, sir, are peculiarly addicted to shaking hands with prominent personages.
It occurred to me that Mr. Bickersteth or yourself might know of persons who would be willing to pay a small fee--let us say two dollars or three--for the privilege of an introduction, including handshake, to his grace."
Bicky didn't seem to think much of it.
"Do you mean to say that anyone would be mug enough to part with solid cash just to shake hands with my uncle?"
"I have an aunt, sir, who paid five shillings to a young fellow for bringing a moving-picture actor to tea at her house one Sunday.
It gave her social standing among the neighbours."
Bicky wavered.
"If you think it could be done----"
"I feel convinced of it, sir."
"What do you think, Bertie?" "I'm for it, old boy, absolutely.
A very brainy wheeze." "Thank you, sir.
Will there be anything further?
Good night, sir." And he floated out, leaving us to discuss details.
I had never realized what a perfectly foul time those Stock Exchange chappies must have when the public isn't biting freely.
Nowadays I read that bit they put in the financial reports about "The market opened quietly" with a sympathetic eye, for, by Jove, it certainly opened quietly for us!
You'd hardly believe how difficult it was to interest the public and make them take a flutter on the old boy.
By the end of the week the only name we had on our list was a delicatessen-store keeper down in Bicky's part of the town, and as he wanted us to take it out in sliced ham instead of cash that didn't help much.
There was a gleam of light when the brother of Bicky's pawnbroker offered ten dollars, money down, for an introduction to old Chiswick, but the deal fell through, owing to its turning out that the chap was an anarchist and intended to kick the old boy instead of shaking hands with him.
At that, it took me the deuce of a time to persuade Bicky not to grab the cash and let things take their course.
He seemed to regard the pawnbroker's brother rather as a sportsman and benefactor of his species than otherwise.
The whole thing, I'm inclined to think, would have been off if it hadn't been for
There is no doubt that Jeeves is in a class of his own.
In the matter of brain and resource I don't think I have ever met a chappie so supremely like mother made.
He trickled into my room one morning with a good old cup of tea, and intimated that there was something doing.
"Might I speak to you with regard to that matter of his grace, sir?"
"It's all off.
We've decided to chuck it."
"Sir?" "It won't work.
We can't get anybody to come."
"I fancy I can arrange that aspect of the matter, sir."
"Do you mean to say you've managed to get anybody?"
"Yes, sir.
Eighty-seven gentlemen from Birdsburg, sir."
I sat up in bed and spilt the tea.
"Birdsburg?"
"Birdsburg, Missouri, sir."
"How did you get them?"
"I happened last night, sir, as you had intimated that you would be absent from home, to attend a theatrical performance, and entered into conversation between the acts with the occupant of the adjoining seat.
I had observed that he was wearing a somewhat ornate decoration in his buttonhole, sir--a large blue button with the words 'Boost for Birdsburg' upon it in red letters, scarcely a judicious addition to a gentleman's evening costume.
To my surprise I noticed that the auditorium was full of persons similarly decorated.
I ventured to inquire the explanation, and was informed that these gentlemen, forming a party of eighty-seven, are a convention from a town of the name if Birdsburg, in the State of Missouri.
Their visit, I gathered, was purely of a social and pleasurable nature, and my informant spoke at some length of the entertainments arranged for their stay in the city.
It was when he related with a considerable amount of satisfaction and pride, that a deputation of their number had been introduced to and had shaken hands with a well-known prizefighter, that it occurred to me to broach the subject of his grace.
To make a long story short, sir, I have arranged, subject to your approval, that the entire convention shall be presented to his grace to-morrow afternoon."
I was amazed.
This chappie was a Napoleon.
"Eighty-seven, Jeeves.
At how much a head?" "I was obliged to agree to a reduction for quantity, sir.
The terms finally arrived at were one hundred and fifty dollars for the party."
I thought a bit.
"Payable in advance?"
"No, sir.
I endeavoured to obtain payment in advance, but was not successful."
"Well, any way, when we get it I'll make it up to five hundred.
Bicky'll never know.
Do you suspect Mr. Bickersteth would suspect anything, Jeeves, if I made it up to five hundred?" "I fancy not, sir.
Mr. Bickersteth is an agreeable gentleman, but not bright."
After breakfast run down to the bank and get me some money."
"Yes, sir." "You know, you're a bit of a marvel,
Jeeves." "Thank you, sir."
"Right-o!"
"Very good, sir." When I took dear old Bicky aside in the course of the morning and told him what had happened he nearly broke down.
He tottered into the sitting-room and buttonholed old Chiswick, who was reading the comic section of the morning paper with a kind of grim resolution.
"Uncle," he said, "are you doing anything special to-morrow afternoon?
I mean to say, I've asked a few of my pals in to meet you, don't you know."
The old boy cocked a speculative eye at him.
"There will be no reporters among them?" "Reporters?
Rather not!
Why?" "I refuse to be badgered by reporters.
There were a number of adhesive young men who endeavoured to elicit from me my views on America while the boat was approaching the dock.
I will not be subjected to this persecution again."
"That'll be absolutely all right, uncle.
There won't be a newspaper-man in the place."
"In that case I shall be glad to make the acquaintance of your friends."
"You'll shake hands with them and so forth?"
"I shall naturally order my behaviour according to the accepted rules of civilized intercourse."
Bicky thanked him heartily and came off to lunch with me at the club, where he babbled freely of hens, incubators, and other rotten things.
After mature consideration we had decided to unleash the Birdsburg contingent on the old boy ten at a time.
Jeeves brought his theatre pal round to see us, and we arranged the whole thing with him.
A very decent chappie, but rather inclined to collar the conversation and turn it in the direction of his home-town's new water- supply system.
We settled that, as an hour was about all he would be likely to stand, each gang should consider itself entitled to seven minutes of the duke's society by Jeeves's stop-watch, and that when their time was up
Jeeves should slide into the room and cough meaningly.
Then we parted with what I believe are called mutual expressions of goodwill, the
Birdsburg chappie extending a cordial invitation to us all to pop out some day and take a look at the new water-supply system, for which we thanked him.
Next day the deputation rolled in.
The first shift consisted of the cove we had met and nine others almost exactly like him in every respect.
They all looked deuced keen and businesslike, as if from youth up they had been working in the office and catching the boss's eye and what-not.
They shook hands with the old boy with a good deal of apparent satisfaction--all except one chappie, who seemed to be brooding about something--and then they stood off and became chatty.
"What message have you for Birdsburg, Duke?" asked our pal.
The old boy seemed a bit rattled.
"I have never been to Birdsburg."
The chappie seemed pained.
"The most rapidly-growing city in the country.
Boost for Birdsburg!"
"Boost for Birdsburg!" said the other chappies reverently.
The chappie who had been brooding suddenly gave tongue.
"Say!"
He was a stout sort of well-fed cove with one of those determined chins and a cold eye.
The assemblage looked at him.
"As a matter of business," said the chappie--"mind you, I'm not questioning anybody's good faith, but, as a matter of strict business--I think this gentleman here ought to put himself on record before witnesses as stating that he really is a duke."
"What do you mean, sir?" cried the old boy, getting purple.
"No offence, simply business.
I'm not saying anything, mind you, but there's one thing that seems kind of funny to me.
This gentleman here says his name's Mr.
Bickersteth, as I understand it.
Well, if you're the Duke of Chiswick, why isn't he Lord Percy Something?
I've read English novels, and I know all about it."
"This is monstrous!"
"Now don't get hot under the collar.
I'm only asking.
I've a right to know.
You're going to take our money, so it's only fair that we should see that we get our money's worth." The water-supply cove chipped in:
"You're quite right, Simms.
I overlooked that when making the agreement.
You see, gentlemen, as business men we've a right to reasonable guarantees of good faith.
We are paying Mr. Bickersteth here a hundred and fifty dollars for this reception, and we naturally want to know--- -"
Old Chiswick gave Bicky a searching look; then he turned to the water-supply chappie.
He was frightfully calm.
"I can assure you that I know nothing of this," he said, quite politely.
"I should be grateful if you would explain."
"Well, we arranged with Mr. Bickersteth that eighty-seven citizens of Birdsburg should have the privilege of meeting and shaking hands with you for a financial consideration mutually arranged, and what my friend Simms here means--and I'm with him--is that we have only Mr. Bickersteth's word for it--and he is a stranger to us-- that you are the Duke of Chiswick at all."
Old Chiswick gulped.
"Allow me to assure you, sir," he said, in a rummy kind of voice, "that I am the Duke of Chiswick." "Then that's all right," said the chappie heartily.
"That was all we wanted to know.
Let the thing go on."
"I am sorry to say," said old Chiswick, "that it cannot go on.
I am feeling a little tired.
I fear I must ask to be excused." "But there are seventy-seven of the boys waiting round the corner at this moment, Duke, to be introduced to you."
"I fear I must disappoint them."
"But in that case the deal would have to be off."
"That is a matter for you and my nephew to discuss."
The chappie seemed troubled.
"You really won't meet the rest of them?" "No!" "Well, then, I guess we'll be going." They went out, and there was a pretty solid silence.
Then old Chiswick turned to Bicky: "Well?"
Bicky didn't seem to have anything to say.
"Was it true what that man said?"
"Yes, uncle."
"What do you mean by playing this trick?" Bicky seemed pretty well knocked out, so I put in a word.
"I think you'd better explain the whole thing, Bicky, old top."
Bicky's Adam's-apple jumped about a bit; then he started:
"You see, you had cut off my allowance, uncle, and I wanted a bit of money to start a chicken farm.
I mean to say it's an absolute cert if you once get a bit of capital.
You buy a hen, and it lays an egg every day of the week, and you sell the eggs, say, seven for twenty-five cents.
"Keep of hens cost nothing.
Profit practically----"
"What is all this nonsense about hens?
You led me to suppose you were a substantial business man."
"Old Bicky rather exaggerated, sir," I said, helping the chappie out.
"The fact is, the poor old lad is absolutely dependent on that remittance of yours, and when you cut it off, don't you know, he was pretty solidly in the soup, and had to think of some way of closing in on a bit of the ready pretty quick.
That's why we thought of this handshaking scheme."
Old Chiswick foamed at the mouth.
"So you have lied to me!
You have deliberately deceived me as to your financial status!" "Poor old Bicky didn't want to go to that ranch," I explained.
"He doesn't like cows and horses, but he rather thinks he would be hot stuff among the hens.
All he wants is a bit of capital.
Don't you think it would be rather a wheeze if you were to----"
"After what has happened?
After this--this deceit and foolery?
Not a penny!"
"But----" "Not a penny!"
There was a respectful cough in the background.
"If I might make a suggestion, sir?"
Jeeves was standing on the horizon, looking devilish brainy.
"Go ahead, Jeeves!" I said.
"I would merely suggest, sir, that if Mr. Bickersteth is in need of a little ready money, and is at a loss to obtain it elsewhere, he might secure the sum he requires by describing the occurrences of this afternoon for the Sunday issue of one of the more spirited and enterprising newspapers." "By Jove!"
I said.
"By George!" said Bicky.
"Great heavens!" said old Chiswick.
"Very good, sir," said Jeeves.
Bicky turned to old Chiswick with a gleaming eye.
"Jeeves is right.
I'll do it!
The Chronicle would jump at it.
They eat that sort of stuff."
Old Chiswick gave a kind of moaning howl.
"I absolutely forbid you, Francis, to do this thing!"
"That's all very well," said Bicky, wonderfully braced, "but if I can't get the money any other way----"
"Wait!
Er--wait, my boy!
You are so impetuous!
We might arrange something."
"I won't go to that bally ranch."
"No, no!
No, no, my boy!
I would not suggest it.
I would not for a moment suggest it.
I--I think----"
He seemed to have a bit of a struggle with himself.
"I--I think that, on the whole, it would be best if you returned with me to England.
I--I might--in fact, I think I see my way to doing--to--I might be able to utilize your services in some secretarial position."
"I shouldn't mind that."
"I should not be able to offer you a salary, but, as you know, in English political life the unpaid secretary is a recognized figure----"
"The only figure I'll recognize," said Bicky firmly, "is five hundred quid a year, paid quarterly." "My dear boy!"
"Absolutely!"
"But your recompense, my dear Francis, would consist in the unrivalled opportunities you would have, as my secretary, to gain experience, to accustom yourself to the intricacies of political life, to--in fact, you would be in an exceedingly advantageous position."
"Five hundred a year!" said Bicky, rolling it round his tongue.
"Why, that would be nothing to what I could make if I started a chicken farm.
It stands to reason.
Suppose you have a dozen hens.
Each of the hens has a dozen chickens.
After a bit the chickens grow up and have a dozen chickens each themselves, and then they all start laying eggs!
There's a fortune in it.
You can get anything you like for eggs in America.
Chappies keep them on ice for years and years, and don't sell them till they fetch about a dollar a whirl.
You don't think I'm going to chuck a future like this for anything under five hundred o' goblins a year--what?"
A look of anguish passed over old Chiswick's face, then he seemed to be resigned to it.
"Very well, my boy," he said.
"What-o!" said Bicky.
"All right, then." "Jeeves," I said.
Bicky had taken the old boy off to dinner to celebrate, and we were alone.
"Jeeves, this has been one of your best efforts."
"Thank you, sir." "It beats me how you do it."
"Yes, sir."
"The only trouble is you haven't got much out of it--what!"
"I fancy Mr. Bickersteth intends--I judge from his remarks--to signify his appreciation of anything I have been fortunate enough to do to assist him, at some later date when he is in a more favourable position to do so."
"It isn't enough, Jeeves!" "Sir?"
It was a wrench, but I felt it was the only possible thing to be done.
"Bring my shaving things." A gleam of hope shone in the chappie's eye, mixed with doubt.
"You mean, sir?" "And shave off my moustache."
There was a moment's silence.
I could see the fellow was deeply moved.
"Thank you very much indeed, sir," he said, in a low voice, and popped off. >
CHAPTER 4 ABSENT TREATMENT
I want to tell you all about dear old Bobbie Cardew.
It's a most interesting story.
I can't put in any literary style and all that; but I don't have to, don't you know, because it goes on its Moral Lesson.
If you're a man you mustn't miss it, because it'll be a warning to you; and if you're a woman you won't want to, because it's all about how a girl made a man feel pretty well fed up with things.
If you're a recent acquaintance of Bobbie's, you'll probably be surprised to hear that there was a time when he was more remarkable for the weakness of his memory than anything else.
Dozens of fellows, who have only met Bobbie since the change took place, have been surprised when I told them that.
Yet it's true.
Believe me.
In the days when I first knew him Bobbie Cardew was about the most pronounced young rotter inside the four-mile radius.
People have called me a silly ass, but I was never in the same class with Bobbie.
When it came to being a silly ass, he was a plus-four man, while my handicap was about six.
Why, if I wanted him to dine with me, I used to post him a letter at the beginning of the week, and then the day before send him a telegram and a phone-call on the day itself, and--half an hour before the time we'd fixed--a messenger in a taxi, whose business it was to see that he got in and that the chauffeur had the address all correct.
By doing this I generally managed to get him, unless he had left town before my messenger arrived.
The funny thing was that he wasn't altogether a fool in other ways.
Deep down in him there was a kind of stratum of sense.
I had known him, once or twice, show an almost human intelligence.
But to reach that stratum, mind you, you needed dynamite.
At least, that's what I thought.
But there was another way which hadn't occurred to me.
Marriage, I mean.
Marriage, the dynamite of the soul; that was what hit Bobbie.
He married.
Have you ever seen a bull-pup chasing a bee?
The pup sees the bee.
It looks good to him.
But he still doesn't know what's at the end of it till he gets there.
It was like that with Bobbie.
He fell in love, got married--with a sort of whoop, as if it were the greatest fun in the world--and then began to find out things.
She wasn't the sort of girl you would have expected Bobbie to rave about.
And yet, I don't know.
What I mean is, she worked for her living; and to a fellow who has never done a hand's turn in his life there's undoubtedly a sort of fascination, a kind of romance, about a girl who works for her living.
Her name was Anthony.
Mary Anthony.
She was about five feet six; she had a ton and a half of red-gold hair, grey eyes, and one of those determined chins.
She was a hospital nurse.
When Bobbie smashed himself up at polo, she was told off by the authorities to smooth his brow and rally round with cooling unguents and all that; and the old boy hadn't been up and about again for more than a week before they popped off to the registrar's and fixed it up.
Quite the romance.
Bobbie broke the news to me at the club one evening, and next day he introduced me to her.
I admired her.
I've never worked myself--my name's Pepper, by the way.
Almost forgot to mention it.
Reggie Pepper.
My uncle Edward was Pepper, Wells, and Co., the Colliery people.
He left me a sizable chunk of bullion--I say I've never worked myself, but I admire any one who earns a living under difficulties, especially a girl.
And this girl had had a rather unusually tough time of it, being an orphan and all that, and having had to do everything off her own bat for years.
Mary and I got along together splendidly.
We don't now, but we'll come to that later.
I'm speaking of the past.
She seemed to think Bobbie the greatest thing on earth, judging by the way she looked at him when she thought I wasn't noticing.
And Bobbie seemed to think the same about her.
So that I came to the conclusion that, if only dear old Bobbie didn't forget to go to the wedding, they had a sporting chance of being quite happy. Well, let's brisk up a bit here, and jump a year.
The story doesn't really start till then.
They took a flat and settled down.
I was in and out of the place quite a good deal.
I kept my eyes open, and everything seemed to me to be running along as smoothly as you could want.
If this was marriage, I thought, I couldn't see why fellows were so frightened of it.
There were a lot of worse things that could happen to a man.
But we now come to the incident of the quiet Dinner, and it's just here that love's young dream hits a snag, and things begin to occur.
I happened to meet Bobbie in Piccadilly, and he asked me to come back to dinner at the flat.
And, like a fool, instead of bolting and putting myself under police protection, I went.
When we got to the flat, there was Mrs. Bobbie looking--well, I tell you, it staggered me.
Her gold hair was all piled up in waves and crinkles and things, with a what-d'-you- call-it of diamonds in it.
And she was wearing the most perfectly ripping dress.
I couldn't begin to describe it.
I can only say it was the limit.
It struck me that if this was how she was in the habit of looking every night when they were dining quietly at home together, it was no wonder that Bobbie liked domesticity.
"Here's old Reggie, dear," said Bobbie.
"I've brought him home to have a bit of dinner. I'll phone down to the kitchen and ask them to send it up now--what?"
She stared at him as if she had never seen him before.
Then she turned scarlet.
Then she turned as white as a sheet.
Then she gave a little laugh.
It was most interesting to watch.
Made me wish I was up a tree about eight hundred miles away.
Then she recovered herself.
"I am so glad you were able to come, Mr. Pepper," she said, smiling at me.
And after that she was all right.
At least, you would have said so.
She talked a lot at dinner, and chaffed Bobbie, and played us ragtime on the piano afterwards, as if she hadn't a care in the world.
Quite a jolly little party it was--not.
I'm no lynx-eyed sleuth, and all that sort of thing, but I had seen her face at the beginning, and I knew that she was working the whole time and working hard, to keep herself in hand, and that she would have given that diamond what's-its-name in her hair and everything else she possessed to have one good scream--just one.
I've sat through some pretty thick evenings in my time, but that one had the rest beaten in a canter.
At the very earliest moment I grabbed my hat and got away.
Having seen what I did, I wasn't particularly surprised to meet Bobbie at the club next day looking about as merry and bright as a lonely gum-drop at an
Eskimo tea-party.
He started in straightway.
He seemed glad to have someone to talk to about it.
"Do you know how long I've been married?" he said.
I didn't exactly.
"About a year, isn't it?"
"Not about a year," he said sadly.
"Exactly a year--yesterday!"
Then I understood.
I saw light--a regular flash of light.
"Yesterday was----?"
"The anniversary of the wedding.
I'd arranged to take Mary to the Savoy, and on to Covent Garden.
She particularly wanted to hear Caruso.
I had the ticket for the box in my pocket.
Do you know, all through dinner I had a kind of rummy idea that there was something
I'd forgotten, but I couldn't think what?"
"Till your wife mentioned it?" He nodded----
"She--mentioned it," he said thoughtfully.
I didn't ask for details.
Women with hair and chins like Mary's may be angels most of the time, but, when they take off their wings for a bit, they aren't half-hearted about it.
"To be absolutely frank, old top," said poor old Bobbie, in a broken sort of way,
"my stock's pretty low at home." There didn't seem much to be done.
I just lit a cigarette and sat there.
He didn't want to talk.
Presently he went out.
I stood at the window of our upper smoking- room, which looks out on to Piccadilly, and watched him.
He walked slowly along for a few yards, stopped, then walked on again, and finally turned into a jeweller's.
Which was an instance of what I meant when I said that deep down in him there was a certain stratum of sense.
It was from now on that I began to be really interested in this problem of
Bobbie's married life.
Of course, one's always mildly interested in one's friends' marriages, hoping they'll turn out well and all that; but this was different.
The average man isn't like Bobbie, and the average girl isn't like Mary.
It was that old business of the immovable mass and the irresistible force.
There was Bobbie, ambling gently through life, a dear old chap in a hundred ways, but undoubtedly a chump of the first water.
And there was Mary, determined that he shouldn't be a chump.
And Nature, mind you, on Bobbie's side.
When Nature makes a chump like dear old
Bobbie, she's proud of him, and doesn't want her handiwork disturbed.
She gives him a sort of natural armour to protect him against outside interference.
And that armour is shortness of memory.
Shortness of memory keeps a man a chump, when, but for it, he might cease to be one.
Take my case, for instance.
I'm a chump.
Well, if I had remembered half the things people have tried to teach me during my life, my size in hats would be about number nine.
But I didn't.
I forgot them.
And it was just the same with Bobbie.
For about a week, perhaps a bit more, the recollection of that quiet little domestic evening bucked him up like a tonic.
Elephants, I read somewhere, are champions at the memory business, but they were fools to Bobbie during that week.
But, bless you, the shock wasn't nearly big enough.
It had dinted the armour, but it hadn't made a hole in it.
Pretty soon he was back at the old game.
It was pathetic, don't you know.
The poor girl loved him, and she was frightened.
It was the thin edge of the wedge, you see, and she knew it.
A man who forgets what day he was married, when he's been married one year, will forget, at about the end of the fourth, that he's married at all.
If she meant to get him in hand at all, she had got to do it now, before he began to drift away.
I saw that clearly enough, and I tried to make Bobbie see it, when he was by way of pouring out his troubles to me one afternoon.
I can't remember what it was that he had forgotten the day before, but it was something she had asked him to bring home for her--it may have been a book.
"It's such a little thing to make a fuss about," said Bobbie.
"And she knows that it's simply because I've got such an infernal memory about everything.
I can't remember anything.
Never could."
He talked on for a while, and, just as he was going, he pulled out a couple of sovereigns.
"Oh, by the way," he said.
"What's this for?"
I asked, though I knew.
"I owe it you."
"How's that?"
I said.
"Why, that bet on Tuesday.
In the billiard-room.
Murray and Brown were playing a hundred up, and I gave you two to one that Brown would win, and Murray beat him by twenty odd." "So you do remember some things?"
I said.
He got quite excited.
Said that if I thought he was the sort of rotter who forgot to pay when he lost a bet, it was pretty rotten of me after knowing him all these years, and a lot more like that.
"Subside, laddie," I said.
Then I spoke to him like a father.
"What you've got to do, my old college chum," I said, "is to pull yourself together, and jolly quick, too.
As things are shaping, you're due for a nasty knock before you know what's hit you.
You've got to make an effort.
Don't say you can't.
This two quid business shows that, even if your memory is rocky, you can remember some things.
What you've got to do is to see that wedding anniversaries and so on are included in the list.
It may be a brainstrain, but you can't get out of it."
"I suppose you're right," said Bobbie.
"But it beats me why she thinks such a lot of these rotten little dates.
What's it matter if I forgot what day we were married on or what day she was born on or what day the cat had the measles?
She knows I love her just as much as if I were a memorizing freak at the halls."
"That's not enough for a woman," I said.
"They want to be shown.
Bear that in mind, and you're all right.
Forget it, and there'll be trouble."
He chewed the knob of his stick.
"Women are frightfully rummy," he said gloomily.
"You should have thought of that before you married one," I said.
I don't see that I could have done any more.
I had put the whole thing in a nutshell for him.
You would have thought he'd have seen the point, and that it would have made him brace up and get a hold on himself.
But no.
Off he went again in the same old way.
I gave up arguing with him.
I had a good deal of time on my hands, but not enough to amount to anything when it was a question of reforming dear old Bobbie by argument.
If you see a man asking for trouble, and insisting on getting it, the only thing to do is to stand by and wait till it comes to him.
After that you may get a chance.
But till then there's nothing to be done.
But I thought a lot about him.
Bobbie didn't get into the soup all at once.
Weeks went by, and months, and still nothing happened.
Now and then he'd come into the club with a kind of cloud on his shining morning face, and I'd know that there had been doings in the home; but it wasn't till well on in the spring that he got the thunderbolt just where he had been asking for it--in the thorax.
I was smoking a quiet cigarette one morning in the window looking out over Piccadilly, and watching the buses and motors going up one way and down the other--most interesting it is; I often do it--when in rushed Bobbie, with his eyes bulging and his face the colour of an oyster, waving a piece of paper in his hand.
"Reggie," he said.
"Reggie, old top, she's gone!"
"Gone!" I said.
"Who?" "Mary, of course!
Gone!
Left me!
Gone!"
"Where?" I said.
Anyhow, dear old Bobbie nearly foamed at the mouth.
Perhaps you're right.
"Where?
How should I know where?
Here, read this." He pushed the paper into my hand.
It was a letter.
"Go on," said Bobbie.
"Read it."
So I did.
It certainly was quite a letter.
There was not much of it, but it was all to the point.
This is what it said:
"MY DEAR BOBBlE,--I am going away.
When you care enough about me to remember to wish me many happy returns on my birthday, I will come back.
My address will be Box 341, London Morning News."
I read it twice, then I said, "Well, why don't you?"
"Why don't I what?"
"Why don't you wish her many happy returns?
It doesn't seem much to ask."
"But she says on her birthday." "Well, when is her birthday?"
"Can't you understand?" said Bobbie.
"I've forgotten." "Forgotten!"
I said.
"Yes," said Bobbie.
"Forgotten."
"How do you mean, forgotten?" I said.
"Forgotten whether it's the twentieth or the twenty-first, or what?
How near do you get to it?"
"I know it came somewhere between the first of January and the thirty-first of
December.
That's how near I get to it."
"Think."
"Think?
What's the use of saying 'Think'?
Think I haven't thought?
I've been knocking sparks out of my brain ever since I opened that letter."
"And you can't remember?" "No."
I rang the bell and ordered restoratives.
"Well, Bobbie," I said, "it's a pretty hard case to spring on an untrained amateur like me.
Suppose someone had come to Sherlock Holmes and said, 'Mr.
When is my wife's birthday?'
Wouldn't that have given Sherlock a jolt?
However, I know enough about the game to understand that a fellow can't shoot off his deductive theories unless you start him with a clue, so rouse yourself out of that pop-eyed trance and come across with two or three.
For instance, can't you remember the last time she had a birthday?
What sort of weather was it?
That might fix the month." Bobbie shook his head.
"It was just ordinary weather, as near as I can recollect."
"Warm?"
"Warmish." "Or cold?"
"Well, fairly cold, perhaps.
I can't remember."
I ordered two more of the same.
They seemed indicated in the Young Detective's Manual.
"You're a great help, Bobbie," I said.
"An invaluable assistant.
One of those indispensable adjuncts without which no home is complete."
Bobbie seemed to be thinking.
"I've got it," he said suddenly.
"Look here.
I gave her a present on her last birthday.
All we have to do is to go to the shop, hunt up the date when it was bought, and the thing's done."
"Absolutely.
What did you give her?" He sagged.
"I can't remember," he said.
Getting ideas is like golf.
Some days you're right off, others it's as easy as falling off a log.
I don't suppose dear old Bobbie had ever had two ideas in the same morning before in his life; but now he did it without an effort.
He just loosed another dry Martini into the undergrowth, and before you could turn round it had flushed quite a brain-wave.
Do you know those little books called When were you Born?
There's one for each month.
They tell you your character, your talents, your strong points, and your weak points at fourpence halfpenny a go.
Bobbie's idea was to buy the whole twelve, and go through them till we found out which month hit off Mary's character.
That would give us the month, and narrow it down a whole lot.
A pretty hot idea for a non-thinker like dear old Bobbie.
We sallied out at once. He took half and I took half, and we settled down to work.
As I say, it sounded good.
But when we came to go into the thing, we saw that there was a flaw.
There was plenty of information all right, but there wasn't a single month that didn't have something that exactly hit off Mary.
For instance, in the December book it said, "December people are apt to keep their own secrets.
They are extensive travellers."
Well, Mary had certainly kept her secret, and she had travelled quite extensively enough for Bobbie's needs.
Then, October people were "born with original ideas" and "loved moving."
You couldn't have summed up Mary's little jaunt more neatly.
February people had "wonderful memories"-- Mary's speciality.
We took a bit of a rest, then had another go at the thing.
Bobbie was all for May, because the book said that women born in that month were
"inclined to be capricious, which is always a barrier to a happy married life"; but I plumped for February, because February women "are unusually determined to have their own way, are very earnest, and expect a full return in their companion or mates." Which he owned was about as like Mary as anything could be.
In the end he tore the books up, stamped on them, burnt them, and went home.
It was wonderful what a change the next few days made in dear old Bobbie.
Have you ever seen that picture, "The Soul's Awakening"?
It represents a flapper of sorts gazing in a startled sort of way into the middle distance with a look in her eyes that seems to say, "Surely that is George's step I hear on the mat!
Can this be love?" Well, Bobbie had a soul's awakening too.
I don't suppose he had ever troubled to think in his life before--not really think.
But now he was wearing his brain to the bone.
It was painful in a way, of course, to see a fellow human being so thoroughly in the soup, but I felt strongly that it was all for the best.
I could see as plainly as possible that all these brainstorms were improving Bobbie out of knowledge.
When it was all over he might possibly become a rotter again of a sort, but it would only be a pale reflection of the rotter he had been.
It bore out the idea I had always had that what he needed was a real good jolt.
I saw a great deal of him these days. I was his best friend, and he came to me for sympathy.
I gave it him, too, with both hands, but I never failed to hand him the Moral Lesson when I had him weak. He looked happier than he had done in weeks.
"Reggie," he said, "I'm on the trail.
This time I'm convinced that I shall pull it off.
I've remembered something of vital importance."
"Yes?" I said.
"I remember distinctly," he said, "that on Mary's last birthday we went together to the Coliseum.
How does that hit you?" "It's a fine bit of memorizing," I said;
"but how does it help?" "Why, they change the programme every week there."
"Ah!" I said.
"Now you are talking." "And the week we went one of the turns was
Professor Some One's Terpsichorean Cats.
I recollect them distinctly.
Now, are we narrowing it down, or aren't we?
Reggie, I'm going round to the Coliseum this minute, and I'm going to dig the date of those Terpsichorean Cats out of them, if I have to use a crowbar."
So that got him within six days; for the management treated us like brothers; brought out the archives, and ran agile fingers over the pages till they treed the cats in the middle of May.
"I told you it was May," said Bobbie.
"Maybe you'll listen to me another time."
"If you've any sense," I said, "there won't be another time."
And Bobbie said that there wouldn't.
Once you get your money on the run, it parts as if it enjoyed doing it.
I had just got off to sleep that night when my telephone-bell rang.
It was Bobbie, of course.
He didn't apologize.
"Reggie," he said, "I've got it now for certain.
It's just come to me.
We saw those Terpsichorean Cats at a matinee, old man."
"Yes?" I said.
"Well, don't you see that that brings it down to two days?
It must have been either Wednesday the seventh or Saturday the tenth."
"Yes," I said, "if they didn't have daily matinees at the Coliseum."
I heard him give a sort of howl.
"Bobbie," I said.
My feet were freezing, but I was fond of him. "Well?" "I've remembered something too.
It's this.
The day you went to the Coliseum I lunched with you both at the Ritz.
You had forgotten to bring any money with you, so you wrote a cheque."
"But I'm always writing cheques."
But this was for a tenner, and made out to the hotel.
Hunt up your cheque-book and see how many cheques for ten pounds payable to the Ritz
Hotel you wrote out between May the fifth and May the tenth."
He gave a kind of gulp.
"Reggie," he said, "you're a genius.
I've always said so.
I believe you've got it. Hold the line."
Presently he came back again.
"Halloa!" he said.
"I'm here," I said.
"It was the eighth.
Reggie, old man, I----"
"Topping," I said.
"Good night." It was working along into the small hours now, but I thought I might as well make a night of it and finish the thing up, so I rang up an hotel near the Strand.
"Put me through to Mrs. Cardew," I said.
"It's late," said the man at the other end.
"And getting later every minute," I said.
"Buck along, laddie."
I waited patiently.
I had missed my beauty-sleep, and my feet had frozen hard, but I was past regrets.
"What is the matter?" said Mary's voice.
"My feet are cold," I said.
"But I didn't call you up to tell you that particularly.
I've just been chatting with Bobbie, Mrs. Cardew."
"Oh! is that Mr. Pepper?"
"Yes.
He's remembered it, Mrs. Cardew."
She gave a sort of scream.
I've often thought how interesting it must be to be one of those Exchange girls.
The things they must hear, don't you know.
Bobbie's howl and gulp and Mrs. Bobbie's scream and all about my feet and all that.
Most interesting it must be.
"He's remembered it!" she gasped.
"Did you tell him?" "No."
Well, I hadn't.
"Mr. Pepper."
"Yes?"
"Was he--has he been--was he very worried?" I chuckled.
This was where I was billed to be the life and soul of the party.
"Worried!
He was about the most worried man between here and Edinburgh.
He has been worrying as if he was paid to do it by the nation.
He has started out to worry after breakfast, and----"
Oh, well, you can never tell with women.
My idea was that we should pass the rest of the night slapping each other on the back across the wire, and telling each other what bally brainy conspirators we were, don't you know, and all that.
But I'd got just as far as this, when she bit at me.
Absolutely!
I heard the snap.
And then she said "Oh!" in that choked kind of way.
And when a woman says "Oh!" like that, it means all the bad words she'd love to say if she only knew them.
And then she began.
"What brutes men are!
What horrid brutes!
How you could stand by and see poor dear Bobbie worrying himself into a fever, when a word from you would have put everything right, I can't----"
"But----"
"And you call yourself his friend!
His friend!"
(Metallic laugh, most unpleasant.) "It shows how one can be deceived.
I used to think you a kind-hearted man."
"But, I say, when I suggested the thing, you thought it perfectly----"
"I thought it hateful, abominable." "But you said it was absolutely top----"
"I said nothing of the kind.
And if I did, I didn't mean it.
I don't wish to be unjust, Mr. Pepper, but I must say that to me there seems to be something positively fiendish in a man who can go out of his way to separate a husband from his wife, simply in order to amuse himself by gloating over his agony----"
"But----!" "When one single word would have----"
"But you made me promise not to----" I bleated.
"And if I did, do you suppose I didn't expect you to have the sense to break your promise?"
I had finished.
I had no further observations to make.
I hung up the receiver, and crawled into bed.
I still see Bobbie when he comes to the club, but I do not visit the old homestead.
He is friendly, but he stops short of issuing invitations.
I ran across Mary at the Academy last week, and her eyes went through me like a couple of bullets through a pat of butter.
And as they came out the other side, and I limped off to piece myself together again, there occurred to me the simple epitaph which, when I am no more, I intend to have inscribed on my tombstone.
It was this:
"He was a man who acted from the best motives.
There is one born every minute." >
Well, I'm involved in other things, besides physics.
In fact, mostly now in other things.
One thing is distant relationships among human languages.
And the professional, historical linguists in the U.S. and in Western Europe mostly try to stay away from any long-distance relationships, big groupings, groupings that go back a long time,
longer than the familiar families.
They don't like that. They think it's crank. I don't think it's crank.
And there are some brilliant linguists, mostly Russians, who are working on that, at Santa Fe Institute and in Moscow, and I would love to see where that leads.
Does it really lead to a single ancestor some 20, 25,000 years ago?
And what if we go back beyond that single ancestor, when there was presumably a competition among many languages?
How far back does that go?
How far back does modern language go?
How many tens of thousands of years does it go back?
Chris Anderson:
Do you have a hunch or a hope for what the answer to that is?
Well, I would guess that modern language must be older than the cave paintings and cave engravings and cave sculptures and dance steps in the soft clay in the caves in Western Europe, in the Aurignacian Period some 35,000 years ago, or earlier.
I can't believe they did all those things and didn't also have a modern language.
So, I would guess that the actual origin goes back at least that far and maybe further.
But that doesn't mean that all, or many, or most of today's attested languages couldn't descend perhaps from one that's much younger than that, like say 20,000 years, or something of that kind.
It's what we call a bottleneck.
CA:
Well, Philip Anderson may have been right.
You may just know more about everything than anyone.
So, it's been an honor.
Thank you Murray Gell-Mann.
(Applause)
Determine whether the points on this graph represent a function.
Now, just as a refresher, a function, is really just an association between members of a set that we call the domain, and members of a set that we call a range.
So, if I take any member of the domain, let's call that x, and I give it to the function, the function should tell me, what member of my range is that associated with it?
So, it should point to some other value.
This is a function.
It would not be a function if it says, well, it could point to y or, or it could point to z, or maybe it could point to e.
Or whatever else, this would not be a function, because over here, so this right over here, not a function.
Not a function, because it's not clear if you input x, what member of the range you're going to get.
In order for it to be a function, it has to be very clear, for any, for any input into the function, you have to be very clear that you're only going to get one output.
Now, that out of the way, let's think about this function that is defined graphically.
So, the ranges, or as I should say, the domains, the valid inputs, are the x values where this function is defined.
So for example, it tells us that if x is equal to negative 1, if we assume that this over here is the x-axis, and this is a y-axis.
It tells us, when x is equal to negative 1, we should output or out, or y is going to be equal to 3.
So one way to write that mapping is you could say, you could say x when you input it, or let me write it this way, negative 1.
If you take negative 1, and you input it into our function.
I'll put it a little f box right over there. You will get, you will get the number 3.
This is our x, and this is our y, so that seems reasonable.
Negative 1, very clear that you get to 3.
If you put 2 into the function, when x is 2, y is negative 2.
Once again, when x is 2, the function associates 2, and, if, for x, which is a member of the domain, it's defined for 2.
It's not defined for 1.
We don't know what our function is equal to at 1, so it's not defined there.
So, 1 isn't part of the domain.
2 is, it tells us when x is 2, then y is going to be equal to negative 2.
So it maps it or associates it with negative 2, that doesn't seem too troublesome just yet.
Our function is also defined at x is equal to 3.
It associates 3, our function associates or maps 3, to the value y is equal to 2.
Y is equal to 2.
And then we get 2x is equal to 4, where it seems like this thing that could be a function, it, it is def, it is somewhat defined, it does try to associate 4 with things, but what's interesting here is it tries to associate 4 with two different things, all of a sudden.
In this thing that we think might have been a function, but it looks like it might not be.
Do we associate 4 with 5?
Do we associate with 5?
Or, do we associate it, with negative 1?
So, this thing right over here is actually a relation.
You can have, you can have one member of the domain, being related to multiple members of the range.
So, once again, because of this, this is not, not a function.
It's not clear that when you input x, when you input 4 into it, should you output 5, or should you output negative 1?
And sometimes, there's something called the vertical line test, that tells you whether something is a function.
When it's graphically defined like this, you literally say, okay, when x is 4, if I draw a vertical line, do I intersect the function at two places?
Or more, it could be two or more places.
And if you do, that means that there's two or more values that are related to that, that value in the domain.
There's two or more outputs for the input 4.
And if there are two or more outputs for that one input, then you're not dealing with a function.
You're just dealing with a relation.
A function is a special case of a relation, or you could view it as a well-behaved relation.
So we're given the following equation, that 5 times the absolute value of x plus 3 minus 3 is equal to 7.
It's always a little daunting to see an equation with an absolute value sign.
And when you only have one of them, like this, what I like to do is isolate it, and just kind of think it through from that point.
So let's try to isolate the absolute value of x plus 3 here.
Let's try to isolate that part of our equation.
So the first thing we might want to do is add 3 to both sides of the equation.
That'll get rid of this minus 3, or this negative 3, on the left-hand side.
So let's add 3 to both sides of this equation.
And this'll turn the equation into-- do it in that same pink color --the left-hand side will still be 5 times the absolute value of x plus 3.
The minus 3, or the negative 3 plus the 3, those will cancel out.
That'll just be 0.
And then that will be equal to 7 plus 3, which is 10.
Now, we have 5 times the thing we want to isolate.
The best way to isolate it completely is to divide both sides of this equation by 5.
So if you divide that side by 5, and then the right-hand side by 5.
We divide it by 5 so that these guys will cancel out. 5 times something divided by 5 is just that something.
So these cancel out.
That's 2.
So we're left with the absolute value of x plus 3 is equal to 10 divided by 5, which is 2.
So we've simplified the equation a good bit, now we just have to put our thinking caps on a little bit.
If the absolute value of something is 2, what does it mean that that something is?
What are the two numbers that, if I were take it's absolute value, I could get 2.
I'll do a little thing on the side here.
We know that the absolute value of 2 is equal to 2.
So maybe this thing was equal to 2.
So maybe x plus 3 is equal to 2.
If x plus 3 is equal to 2, and you take its absolute value, you're going to get 2 again.
But we also know that the absolute value of negative 2 is also equal to 2.
So maybe x plus 3 is equal to negative 2.
Because if x plus 3 is equal to negative 2, and we take its absolute value, then we're going to get 2 again.
So we could also write or x plus 3 could be equal to negative 2.
That's what I mean about thinking about it a little bit.
Another way to think about it-- I've said this in other videos --is absolute value means distance from 0.
So if we were to draw a number line here, that is 0, this is saying that, whatever this quantity is inside the absolute value sign, its distance from 0 is 2.
So what numbers are 2 away from 0?
Well, you have positive 2.
I'll write a positive there explicitly.
And you also have a negative 2.
So this thing here could be a positive 2, or it could be a negative 2.
Either way you take the absolute value of a positive 2 or a negative 2, you're going to get a 2.
So let's solve these.
So over here we can subtract 3 from both sides of this equation.
So if you subtract 3 from both sides, you get-- The left-hand side, you're just left with an x. These 3's cancel out.
That's the whole point of subtracting the 3. x will be equal to 2 minus 3 is negative 1.
So that is one solution to our absolute value equation.
And what's our other solution?
Well here, once again, let's subtract 3 from both sides.
So you subtract 3 from both sides.
The left-hand side just becomes an x.
The right-hand side, negative 2 minus 3 is negative 5.
So this is our other solution.
And let's verify that they both work.
So if x is equal to negative 1, what does this equation become?
We have 5 times the absolute value of negative 1 plus 3 minus 3.
And if this really is a solution, then this should be equal to positive 7.
So let's see.
This is 5 times negative 1 plus 3 is 2.
So it's 5 times the absolute value of 2 minus 3.
The absolute value of 2 is just 2.
So this is 5 times 2 minus 3. 5 times 2 is 10 minus 3, which is, indeed, equal to 7.
So this is definitely a solution.
Let's try the other one out. x is equal to negative 5.
Running out of some real estate, but I could clear some up right here.
If x is equal to negative 5, same drill.
5 times the absolute value of negative 5 plus 3 minus 3.
This again should be equal to 7.
Negative 5 plus 3 is negative 2.
Since there's 5 times the absolute value of negative 2 minus 3, the absolute value of negative 2 is positive 2.
So this is 5 times 2 minus 3, which is 10 minus 3, which is again equal to 7.
And notice, in this situation, the thing in the absolute value sign became a negative 2, because we said, oh, x plus 3 could be equal to negative 2.
In the magenta situation, the thing in the absolute value sign was positive 2, because this was a situation where we assumed that the thing in the absolute value sign was a positive 2.
Now if we were to graph these solutions on the number line, if we were to graph the two solutions on a number line--
I'll draw a new number line here.
Let me draw a new number line, just like that.
Both of these are less than 0, so I'll put 0 all the way over here.
Maybe 0, 1, 2.
Let's go negative, negative 1, negative 2, negative 3, negative 4, negative 5, negative 6.
This solution right here-- x is equal to negative 1 --we could plot on the number line right over there.
And then the other solution-- x is equal to negative 5 --we can plot it right over there.
Hopefully you found that enjoyable.
What I wanna do this video is prove that the opposite angles of a parallelogram are congruent So, for example, we wanna prove that CAB is congruent to BDC So, that angle is equal to that angle and that ABD, which is this angle is congruent to DCA which is that angle over here
So, let's say, let's start right here at angle BDC
Angle BDC over here, it is an alternate interior angle with this angle right over here with that angle right over there And actually we can extend this point over here I could call that point E if I want
by alternate interior angles This is a transversal, these two lines are parallel
AB or AE is parallel to CD Fair enough Now, if we kinda change our thinking a little bit and instead we now view BD and AC as the parallel line and now view AB as the transversal, then we see that angle EBD is going to be congruent to angle BAC because they're corresponding angles
We are told that the formula for finding the perimeter of a rectangle is P is equal to 2l plus 2w, where P is the perimeter, I is the length, and w is the width. And just to visualize what they're saying, and you might already be familiar with this, let me draw a rectangle. That looks like a rectangle.
And so, that distance is going to be this w plus this I, plus this w-- or that width-- plus this length. And if you have 1 w and you add it to another w, that's going to give you 2 w's. So that's 2 w's.
They want us to write it so it's, this w, right here, they want it to be w is equal to a bunch of stuff with I's and
P's in it, and maybe some numbers there. So let's think about how we can do this. So they tell us that P is equal to 2 times l, plus 2 times w.
And remember, an equation says P is equal to that, so if you do anything to that, you have to do it to P. So if you subtract 2l from this, you're going to have to subtract 2l from P in order for the equality to keep being true. So the left-hand side is going to be P minus 2l, and then that is going to be equal to-- well, 2l minus 2l, the whole reason why we subtracted 2l is because these are going to cancel out.
And then the left-hand side, you're going to have, it could be a negative I plus P over 2, or you could just change the order, and you can write this as P over 2 minus l. And this is also an equally legitimate answer. And you're probably saying, hey Sal, wait.
P minus 2l over 2, that looks different than P over 2 minus l. And they're not. Think about this.
We could rewrite this as P-- let me do this with the same colors-- this over here is the same thing as P over 2 minus 2l over 2. Right? If I have a minus b and they're both being divided by 2, I can just separate-- you can imagine I'm distributing the division by 2 right over here.
Let's do some example problems dealing with functions and their domains and ranges.
Just as a review, a function is just an operator-- let's say this function is f; that tends to be the most typical
letter for functions-- that operates on some input, in this case, the input is x, and it produces some output y.
Or you could view it as you take some input x, put it into your function box f, and it's going to operate on it and produce some y.
And the set of values that x can take on is the domain.
The set of values that f can legitimately operate on, that's the domain.
And the set of values y that f can produce, that is the range.
Now, with that in mind, let's figure out, one, the function definitions for each of these problems here, these example problems, and then figure out the domains and the ranges.
So here we have Dustin charges $10.00 per hour-- so let me write that down-- $10.00 per hour for mowing lawns.
So how much does he charge as a function of hours?
So let's say Dustin charges, so the function, I'll call it d for Dustin.
Dustin charges as a function of hours.
It depends on hours.
The input into our box is going to be hours that he worked.
It's going to be equal to the number of hours times 10.
It's going to be 10 times-- I won't write the times there.
Maybe I can just write 10h.
And, of course, he can't work negative hours, so we could write h is going to be greater than or equal to 0.
That's our function definition.
If you say, hey, how much is he going to charge for working half an hour?
You put 1/2 in here, which essentially substitutes this h with a 1/2. You do 10 times 1/2.
Let me write that down on the side here.
So Dustin's going to charge for 1/2 hour.
He's going to charge 10-- wherever you see the h, replace it with 1/2-- times 1/2, which is equal to $5.00.
That's our function definition.
I was just showing you an example of applying it.
Now, let's figure out the domain and the range.
This number, this function, is not defined if h is less than 0.
And we could say real numbers, which it could be everything including pi and e and all of that. But you can't legitimately charge someone 10 times pi dollars.
That's not a legitimate amount that one can charge someone in the real world, because at the end of the day, you have to round to the penny.
So any number that he charges is going to be a rational number. It can be expressed as a fraction.
So we can kind of take out numbers like e and pi.
So if we want to be really cute about it, we would say non-negative. rational numbers.
And these are just numbers that can be expressed as a fraction, which are most numbers, just not these numbers that just keep not repeating and all of that.
So non-negative rational numbers is what he can input in here. And then the range, which is the valid-- once again, whatever number you put in for h, remember, you can only put in non-negative values for h, non-negative rational values for h, so whatever numbers you put in for h, you're going to get positive values for how much he charges for 10h, for the value of the function.
So once again it's going to be non-negative, and if you put a rational number here and it's being expressed as a fraction and you multiply it by 10, it's still going to be a rational number.
I think you get the idea.
Let's do more problems.
All right.
Here we have Maria doing some tutoring.
Maria charges $25.00 per hour for tutoring math with a minimum charge of $15.00. So Maria charges as a function of hours. So she's going to charge $15.00 if you don't get enough hours in.
So if her hours are less than 3/5 and greater than or equal to 0, she's going to charge $15.00.
Because if she only worked 1/5 of an hour, the bill would have been $5.00, but she says she has a minimum charge of $15.00.
So she's going to charge $15.00 up until 3/5 of an hour, or 36 minutes. And then after that, for h greater than 3/5, she's going to charge $25.00 an hour.
She's going to charge 25 times h. So that's her function definition right there. Now, what is the domain, the domain for
Maria's billing function?
And by the same logic we used here, we got a little cute.
We said, oh, she really can't charge e hours or pi hours. That's not realistic for her to measure. Everything's going to be expressible as a fraction.
No matter what, she's going to charge $15.00, so it's going to be $15.00 or more.
So it's going to be rational numbers greater than or equal to $15.00. There's no situation in which she will charge $14.00.
There's no situation in which she would charge negative $1.00.
Everything's going to be greater than or equal to 15.
So now we have these more abstract function definitions, so now can stick really any number in it.
Well, I can stick any real number x in here and I'm just going to multiply it by 15 and then subtract 12. I could put pi there. I could put the square of 2 there.
Any real number I put in for x, I'm going to get a legitimate output.
Well, once again, this can take on any value out there. I can get to any negative value if I make x negative enough. I'm going to subtract 12 from it, but I could get to any negative value.
Because no matter what number I put here, this value right here is going to be greater than zero.
Even if you put a really negative number here, you're going to square it, so it's going to become a really positive number when you square it. So this expression right here is going to be non-negative. So if you take a non-negative number and you add it to 5, you're always going to get something greater than or equal to 5.
Problem 5.
They have f of x is equal to 1 over x. So, once again, our domain. Well, we could put any value in for x.
Oh, actually, let me be very, very careful.
This is not defined for x is equal to 0. All real that are not equal to zero. If I put zero here, I'm going to get 1/0.
Problem 6. What is the range of the function y is equal to x squared minus 5 when the domain is-- so they're defining the domain. They're restricting it.
Well, the range is all of the functions, all the values that f of x can take on. So the range is going to be the set of values that we get when we put in all of these different x's. So let's try this first one: negative 2.
 Եկեք մի փոքր խոսենք բջջի կառուցվածքի մասին
Ես շատ տեսհոլովակներ եմ պատրաստել, որտեղ առնչություն եմ ունեցել այս թեմայի մասին, բայց երբեք չեմ խոսել ամբողջ կառուցվածքի մասին:
Շատ լավ ժամանակ է սկսել--եկեք գծեմ թաղանթ
Շատ լավ է քննարկումը սկսել բջջային թաղանթից հենց սրա շնորհից է բջիջը բաժանվում արտաքին աշխարհից, հիմնականում թաղանթն է նկարագրում բջիջը
Նկարագրում է այս շատ փոքրիկ բաժանմունքը այդտեղից էլ բջիջ բառն է առաջացել:
Եկեք դա նշեմ բջջային թաղանթ
Եվ բոլոր բջիջները ունեն բջջային թաղանթ
Եթե մտածենք ամենակարևորը բանը ինչ սահմանում է բջիջը, դու հավանաբար տեսել եք ԴՆԹ-ի տեսահոլովակներում և մենք կխոսենք տրանսիլացիայի և տրանսկրիպցիայի մասին ու այն ամենը: Ինչն է սահմանում կենդանի օրգանիզմը, իր ԴՆԹ-ն է:
Այսպիսով բոլոր բջիջներն ունեն իրենց ԴՆԹ:
Ես շատ չեմ խորանա, թե ինչպես է ԴՆԹ-ն սահմանվում ինչ է կենդանի օրգանիզմը:
ԴՆԹ-ի տեսահոլովակում խոսել եմ այդ ամենի մասին:
Բայց բոլոր բջիջներն ունեն ԴՆԹ:
Սա ավելի շատ ԴՆԹ-ի անատոմիա է , քան ֆունկցիան, բայց մենք կանդրադառնանք ֆունկցիային, քանի որ մենք կարիք ունենք իմանալու առանձին մասերի գործունեությունը
Եվ այսպես, աջ կողմում, ԴՆԹ-ն է
Եվ այստեղ քրոմատին է առաջանում
Այստեղ նաև կան փոքրիկ սպիտակուցներ Ոչ բոլոր կենդանի օրգանիզմներում, բայց մենք ավելի շատ կենտրոնանալու ենք էուկարիոտներին, և մի փոքր խոսելու են էուկարիոտ և պրոկարիոտ բջիջների տարբերությունը
Բայց մենք ունենք ԴՆԹ
Ահա իմ նկարած բջիջը, հիմնականում բոլոր բջիջները, ցանկացած կենդանի կամ բույսի կամ ցանկացած թագավորության այսպիսի տեսք ունեն
Ես շատ մանրամասն չեմ նկարել:
Ես նոր նկարեցի ԴՆԹ-ն և բջջային թաղանթը
Ահա, այստեղ տեղի է ունենում հիմնական բաժանումը կենդանի աշխարհում, դիտելով մեր տեսանկյունից, կամ դա թվում է սովորական, որ որոշ բջիջներ ունեն թաղանթ ԴՆԹ-ի շուրջ
Այսպիսով նրանք ունեն թաղանթ ԴՆԹ-ի շուրջ, որը առանձնացնում է
ԴՆԹ-ն և քրոմատինը և ամեն բան ինչ կապված է ԴՆԹ-ի հետ, առանձնացված է բջջի այլ մասերից և կոչվում է կորիզ
Սա կոչվում է կորիզ:
Եվ ես ասացի, որ սա հիմնականում բաժանումն է, քանի որ երբ որոշ մարդիկ նայում են որոշ բջիջներին և տեսնում են կորիզ և մեկ այլ բջիջներ ու չեն տեսնում կորիզը, նրանք ասում են, թե սա լավ միջոց է դասակարգելու օրգանիզմները:
Այսպիսով նրանք անվանեցին որոշներին, ովքեր ունեն կորզիներ, էուկարիոտներ
Սա ունի բջիջ պրոկարիորտ առանց կորիզի
Եվ պրոկարիոտի օրինակներն են, երկու մեծ խմբի են բաժանվում Բակտերիաներ և Արքեաներ
Ահա, արքեաները շատ հետաքրքիր են մենք շատ քիչ գիտենք նրանց մասին
Կարծիք կա, որ նրանք բակտերիաներից են առաջացել, բայց հիմա մարդիկ հասկանում են, որ գոյություն ունի ընդհանրապես առանձին այլ խումբ, և մենք հայտանաբերել ենք դրա շատ փոքր մասը նրանց ենթատեսակը, ահա, սա շատ հետաքրքիր խումբ է
Եվ իրականում պարզվում է, էվոլուցիոն տեսանկյունից , որ կարիք չկա բաժանումներ անել. Դա իրականում Դա ավելի կիրառելի էուկարիոտ բջիջների տեսակները բաժանել, ես ուղղակի գրեմ Էուկարիոտ, բակտերիա և արքեա
Դու չես ցանկանում կատարել այս երեք բաժանումները.
Այստեղ իրականում երեք առանձին խմբեր կան որոնցից կսկսենք
Այս ամենի մասին կխոսենք հետագա վիդեոներում
Բայց եթե ուզում ես հարցնես, ինչը ունի կորիզ
Լավ, սահմանումից ելնելով էուկարիոտները ունեն կորիզ
Ինչը չունի կորիզ
Լավ, բակտերիաները և արքեաները չունեն կորիզ ընհամենը այդքանը
Բայց ես կենտրոնանալու եմ էուկարիոտների վրա, քանի որ նրանք մի փոքր ավելի բարդ կառուցվածք ունեն Նրանք ավելի մեծ են
Հիմնականում ինչի մասին խոսում ենք, ամենաքիչը մեր վիդեոներում վերաբերում են էուկարիոտներին
Էուկարիոտներ են բույսերը, կենդանիները: Մենք կենդանիներ են, հենց օրինակ ես: Կենդանիները և սնկերը, և կան նաև այլ խմբեր էուկարիոտիների մեջ, բայց սրանք այն հիմնական խմբերն են որոնք հետ առնչվում ենք մեր առօրյա կյանքում:
Բայց եկեք նորից խոսենք բջջի անատոմիայի մասին:
Ահա մենք ունենք ԴՆԹ:
Մենք գիտենք, որ այն փոխակերպվում է ի-ՌՆԹ-ի, այդ ի-ՌՆԹ-ն լքում է կորիզը և փոխակերպվում է սպիտակուցների ռիբոսոմի մեջ:
Ահա ռիբոսոմները այս փոքրիկ կոմպլեքսներն են, որոնք կարող պտտվել բջջի շուրջը, և մենք կտեսնենք նաև, որ նրանք նաև կարող ենք կցված լինել այլ կառուցվածքների թաղանթներին.
Ահա սա ռիբոսոմ է:
Եվ եթե այս ամբողջ խոսակցությունը ԴՆԹ-ի փոխակերպումը ի-ՌՆԹ-ի և ի-ՌՆԹ-ի լքումը կորիզից և տեղափոխումը ռիբոսոմներ սպիտակուցի վերածվելու համար որևէ կերպ օգտակար չեղավ, այստեղ կան վիդեոներ, որոնց մասին ավելի մանրամասն կխոսեմ:
Բայց ես ցանկանում եմ կենտրոնանալ տարբեր parts to kind of give a big picture of things.
Այսպիսով ռիբոսոմը այն վայրն է, որտեղ ի-ՌՆԹ-ն, որը գրառվել էր կորիզում ԴՆԹ-ից, փոխակերպվում է սպիտակուցի:
Այսպիսով դու կարող ես նրանց դիտել մի վայլ, որտեղ ինֆորմացիան փոխակերպվում է սպիտակուցի, որը կարող է կիրառվել բջջի տարբեր մասերում:
Եվ այս ռիբոսոմները կազմված կազմված են սպիտակուցներից, և իրականում նրանք կազմվել են ՌՆԹ-ից:
Մեկ հարց է առաջանում, որտեղ են ռիբոսոմները կազմվում
Որոշները կազմված են սպիտակուցներից, որոնք հավանաբար կազմվել են այլ ռիբոսոմներում:
Բայց նրանց մի մասը, ի-ՌՆԹ-ն, ռիբոսոմները, դու նրանց կարող ես դիտել, որպես մի մեծ խառնափնթորիկ, եթե դու նրանց ուսումնասիրես մանրամասնորեն:
Այստեղ որոշ սպիտակուցներ կան:
Եվ ես նրանց չեմ նկարում իրական տեսքով, բայց հետո դու կունենաս ի-ՌՆԹ կապված սպիտակուցի հետ, և ի-ՌՆԹ-ն իրականում չի օգտագործվում տեղեկատվական նպատակի համար normally is when it goes from DNA to the ribosome.
Ռիբոսոմի մեջ, ռիբոսոմային ՌՆԹ-ն իրականում օգտագործում է որպես կառուցվածքի մաս:
Իրականում այն օգնում է ռիբոսոմին գործել որպես ռիբոսոմ:
Այն իրականում ռիբոսոմի մաս է կազմում:
Եվ նրանք բոլորը ստեղծվում են կորիզի մեջ գտնվող կորիզակում:
Եկեք գրեմ այդ բառը:
Ահա աջ կողմում, հետաքրքիր է ահա այստեղ:
Սա կորիզակ է կամ nucleole
Եվ սա առանձին օրգան չէ, և թաղանթով առանձնացված չէ, բայց մանրադիտակով տեսանելի է:
Երբ մարդիկ առաջին անգամ տեսան կորիզակ, ասացին, լսեք, այստեղ ինչ-որ կապոց կա:
Դա հավանաբար պետք է լինի բջջի միջուկը կամ նմանատիպ բան:
Բայց ինչ պարզվեց, որ շատ խիտ փաթեթավորված է ինչպես ԴՆԹ և ՌՆԹ իրավիճակում, դա իրականում ռիբոսոմային ՌՆԹ է, հումք, որտեղ կազմվում են ռիբոսոմներ, ավելի ճիշտ արտադրվում:
Բայց դա այնքան խիտ էր երևում մանրադիտակով, որի պատճառով մարդիկ որոշեցին մեկ այլ անվանում տալ:
Բայց դա թաղանթային սահման չէ:
Դա օրգանոիդ չէ օրգանոիդի մեջ:
Դա պարզապես քիչ պաթաթված սպիտակուցներ են և ռիբոսոմային ՌՆԹ և սա այն տեղն է, որտեղ արտադրվում է ռիբոսոմային ՌՆԹ-ն:
Ինչևէ, մենք կանգնեցինք ռիմոբոսմների վրա:
Սա այն վայրն է, որտեղ սպիտակուցներ են արտադրվում:
Բայց ռիբոսոմները ուղղակի պտտվում են, եթե նրանք ազատ ռիբոսոմներ են, հետո այդ սպիտակուցները, որոնք արտադրվեցին ռիբոսոմի վրա, կպտտվեն այստեղ բջջի հեղուկ մասսայում դա մենք կոչում ենք ցիտոպլազմա
Իսկ եթե մենք ցանկանանք սպիտակուց արտադրել, որոնք ենթադրենք մինչև, երևի բջջի թաղանթը, կամ կամ ենթադրենք բջջից դուրս
Բջիջները արտադրում են մասնիկներ, որոնք օգտագործվում են այլ բջիջների կողմիվ, որոնք օգտագործվում են մարմնի այլ մասերի համար
Եվ այստեղ մենք պետք է գնանք դեպի սպիտակուց, որոնք կցված են թաղանթին այս թաղանթին
Կարող ես դիտել սա որպես թունելների փունջ
Տեսնենք ինչպես կստացվի իմ նկարը Ես պատրաստվում եմ այն շատ վատ նկարել:
Դու ունես այսպիսի բաներ, որոնք կոչվում են էնդոպլազմային ցանց:
Էնդոպլազմային ցանց:
Կարող ես նրանց դիտել որպես խողովակների խուրց:
Էնդոպլազմային ցանց:
Եվ որոնք ի վերջո տանում են դեպի Գոլջիի ապարատ: Ի պատից պարոն Գոլջիի:
Ահա, էնդոպլազմային ցանցը կանեմ դեղինով և Գոլջիի ապարատը կանաչով, այ այսպես
Հետո կբացարտեմ ինչ են իրենցից ներկայացնում: Այսպիսով, ինչ է տեղի ունենում:
Սա ինչ-որ մեծ կույտ է կամ կարող ես տեսնել սա փաթաթված թաղանթների կույտ է:
Եվ որոշ ռիբոսոմներ կցված են նրա վրա, ինչը ես կկոչեմ էնդոպլազմային ցանց:
Ահա մենք ունեն կցված ռիբոսոմներ:
Որոշները ազատ են, որոշնեը կցված:
Եկեք իմ նշանները գրեմ:
Ահա այստեղ, աջ կողմում, և մենք օգտագործում ենք տարածությունը այստեղ, այս մեծ փաթաթված թաղանթի եզրի, սա էնդոպլազմային ցանցն է: ծիծաղելի է ասել: էնդոպլազմային ցանց
Հավանաբար երաժշտական խմբի լավ անուն կլիներ
Էնդոպլազմային ցանց և այն մասերը, և այն մասերը որոնք կցված են ողորկ էնդոպլազմային ցանցին:
Հավանաբար խմբի համար ավելի լավ անուն:
Ահա այստեղ, որտեղ ես կցեցի ռիբոսոմներին, ահա այս ռիբոսոմները կցված են այստեղ, սա ողորկ էնդոպլազմային ցանցն է կամ հավանաբար ողորկ ԷՑ
Ողորկ ԷՑ, ԷՑ որպես էնդոպլազմային ցանց
Եվ որտեղ, որ ռիբոսոմներ կցված են կոչվում է հարթ էնդոպլազմային ցանց
Ահա այստեղ, սա հարց էնդոպլազմային ցանցն է:
Եվ ես հիմա պատրաստվում եմ ձեզ պատմել, թե ինչ է դա, բայց մենք կարող ենք շարունակել քննարկել թաղանթների մասին
Ի վերջո հասանք Գոլջիի ապարատին
Եվ ինչ է տեղի ունենում, ակնարկեցի մեր ազատ ռիբոսոմներում, ի-ՌՆԹ-ն հասնում է, վերածվում է սպիտակուցի, և սպիտակուցները հետո ուղղակի պտտվում են ցիտոպլազմայի շուրջ:
Բայց ինչ կլինի, եթե մենք ուզում ենք սպիտակուցները լինեն թաղանթում կամ բջջից դուրս:
Եվ ահա այստեղ են էնդոպլազմային ցանցն ու գոլջիի ապարատը դեր խաղում:
Որովհետև հիմա մենք ինչ կարող ենք անել, մենք ունենք ունենք ի-ՌՆԹ, որը կորիզից դուրս է գալիս, և նա կարող կպնել ռիբոսոմներին կամ կարող է թարգմանվել ռիբոսոմների կողմից ողորկ ԷՑ
Եվ ինչ է պատահում, այստեղ քո ի-ՌՆԹ գալիս է այստեղ և getting-- and I drew that arrow very small-- it's թարգմանվում է էնդոպլազմային ցանցից դուրս, բայց որպես սպիտակուց արտադրվում է, ինքը մղվում է էնդոպլազմային ցանցի մեջ
Եվ երբ ես ասում եմ էնդոպլազմային ցանցի մեջ, ես խոսում եմ տարածության մասին
Ես գունավորում եմ:
Սա էնդոպլազմային ցանցի ներսն է:
Եվ ահա սպիտակուցները կմղվեն ներս դեպի էնդոպլազմային ցանց
Նրանք, որոնք պիտի օգտագործվեն բջջից դուրս բջջից դուրս կամ բջջի թաղանթի համար
Ահա սպիտակուցները կկանգնեն այստեղ
Ահա ինչու են ռիբոսոմները թաղանթի վրա, քանի որ նրանք կարող են թարգմանել մասնիկներ ԷՑ-ից դուրս բայց երբ սպիտակուցները արտադրվում են, ամինաթթվի շղթան վերջանում է ներսը:
Եկեք ձեզ մի քիչ զարմացնեմ, կարծում եմ դա օգտակար կլինի
Ահա եկեք գծեմ- ենթադրենք սա էնդոպլազմային ցանցի թաղանթն է և դու ունես նրան կցված ռիբոսոմներ
Ասենք սա ռիբոսոմ է էնդոպլազմային ցանցի վրա
And is this is going to be the rough endoplasmic reticulum.
And what you can have is mRNA coming into one side of it. mRNA can kind of come in through here.
Միգուցե այս ուղղությամբ գնա
Սա թարգմանվում է սպիտակուցի
Բայց հետո սպիտակուցը, որպես ամինաթթվի շղթա կառուցվում է դուրս է մղվում այս թաղանթի վերջում
Հիշեք, սա մեր էնդոպլազմային ցանցի թաղանթն է
Even though իՌՆԹ-ն դրսում է, որովհետև ռիբոսոմները կցված են նրան, սպիտակուցները կարող են երևալ ներսը
Հենց սպիտակուցը արտադրվում է, հավանաբար հետո պաթաթվում է գիտես, սպիտակուցը դա պարզապես պաթեթավորված սպիտակուցներ է դա կարող է անցնել ԷՑ-ի միջով
Եվ նա անցնում է դրա միջով
Անցնում է հարթ ԷՑ-ի միջով այնպես, որ հասնի Գոլջիի ապարատ
Եվ այլ տարբեր տեսակի բաներ են պատահում
Սա շատ պարզվեցված է, բայց ցանկանում է պատկերացում կազմեք, թե ինչից ենք խոսում:
Եվ երբ սպիտակուցները անցնում են դեպի Գոլջիի ապարատ և պատրաստվում են բջջից դուրս գալ կամ անցնել բջջի թաղանթ, նրանք իրականում դուրս է պրծնում Գոլջիի ապարատից: այս նույն սպիտակուցը, որը գնում է գոլջիի ապարատ, հիշիր սա գոլջիի ապարատի ներսն է նկարեմ այստեղ գոլջիի ապարատի թաղանթը
Սպիտակուցը կարող է վերջանալ այստեղ
Սա պարզապես ամինաթթվի երկար շղթա է
Եվ հետո դուրս կբողբոջի
Լավ եկեք ասենք, որ սա ունի այսպիսի տեսք և հավանաբար հաջորդ քայլում կունենա այսպիսի տեսք
Կունենա այսպիսի տեսք
Եվ հաջորդ քայլում դու կարող ես պատկերացնեմ, կունենա այսպիսի տեսք, որտեղ իրականում ամբողջությամբ բողբոջված է
It's popped out a little of the membrane of the Golgi body with it.
Ահա հիմա սպիտակուցը շրջապատված է իր փոքրիկ թաղանթով
Եկեք մտածենք ինչ եղավ մենք ունենք ԴՆԹ գրառված իՌՆԹ-ի իՌՆԹ գնում է ռիբոսոմ, կցվում է էնդոպլազմային ցանցին թարգմանվում է սպիտակուցի, որը անցնում է էնդոպլազմային ցանցի միջով
Սկզբում, ողորկը, որտեղ բոլոր ռիբոսոմներն են հետո հարթը
Հարթը ունի այլ ֆունկցիաներ
Օգնում է արտադրել հորմոններ և այլ ճարպային միացություններ, բայց ես չեմ մանրամասնի ուղղակի անցնում է
Կապում է գոլջիի ապարատին
Հետո Գոլջիի ապարատը, սպիտակուցները դուրս են գալիս և մի փոքր մեմբրանից են վերցնում.
Եվ թաղանթով շրջապատված լինելու գաղափարը և բջջում ճանափարհորդումը, երևի սպիտակուցը այսպիսի տեսք ունի խոշորացնեմ
Երևի սպիտակուցը այստեղ է և հետո մի փոքր վերցնում է գորլջիի ապարատի թաղանթից
Սա կոչվում է բշտիկ:
Եվ ահա այստեղ, եկեք ավելացնեմ մեկ ուրիշը այստեղ
Անում եմ, որպեսզի նշեմ Սա կոչվում է բշտիկ
Եվ բշտիկը իրականում հիմնական պայմանն է ամեն ինչի, փոքրիկ մասնիկներ, հիմնականում սպիտակուցներ, բջջում , որը ուղղակի պտտվում է , որոնք շրջապատված են իրենց փոքրիկ թաղանթներով
Եվ պատճառը, որ այս փոքրիկ մինի-թաղանթները օգտակար են, որ այս սպիտակուցները կարող են պտվվել ու բջջի թաղանթից դուրս գալ
Այն կարող է պտտվել բջջի այլ մասեր
Կատարեմ պարզեցում
Եվ հետո այն կարող ձուլվել բջջի թաղանթը կամ կարող է օգտագործել թաղանթը, այս փոքրիկ բշտիկը, բջջից դուրս գալու համար
Դու կարող ես պատկերացնել, գիտես այս բանը- ենթադրենք բջջի արտաքին թաղանթը
Եվ կանեմ խառը պարզեցում
Ես անգամ չեմ նկարում ... մասը
Սակայն ուղղակի ունենալու տեսողական տպավորում, թե ինչ տեսք կարող է ունենալ բշտիկը , փոքրիկ սպիտակուցը իր ներսը, և մոտենում է ավելի ու ավելի մոտ թաղանթին, և հետո միանում է թաղանթին քանի որ կազմված է նույն նյութից: միանում է թաղանթին, քո սպիտակուցը ներսում պատահական փոխեցի գույները
Բայց հիմա, հանկարծակի, հենց ձուլվում է թաղանթի հետ սպիտակուցը արդեն կարող հիմնական բջջից, կամ իրականում կարող է իրեն միաձուլել թաղանթին, արտաքին բջջային թաղանթին, որը կնկարեմ շատ բարակ, բայց ունի երկու շերտ
Եվ հիմա մենք կխոսենք ավելի շատ դրա մասին
Եվ ես կարող էի հավանաբար պատրաստել մի ամբողջ այս թեմայով
Ահա սրանք- մենք արդեն բավական անցել ենք ցույց են տալիս բջջի անատոմիան
Այնտեղ որոշ փոքր բաներ կան, որոնք մասին կարելի էր խոսալ կան լիզոսոմներ, որոնք գտնվում են կենդական բջջում, որոնք իրենց մեջ պարունակում են ֆերմենտներ, որոնք օգնում են մարսել այլ բաներ:
Ահա եթե լիզոսոմը կցվում է մեկ այլ բանի և ունակ է փոխել իր ֆերմենտներին, իրականում սպանել իրականում մարսում է
Ահա, թե ինչ է անում լիզոսոմը
Բույսերում, մենք ունենք լուծվող վակուոլներ, և իրականում գրեթե նույն ֆունկցիան ունեն ինչ լիզոսոմը նրանք շատ մեծ բշտիկներ են
Փաստացի, իրականում վակուոլը ուղղակի մեծ բշտիկ է
Ուղղակի ընդհանուր տերմին է բոլոր մեծ թաղանթով շրջապտված օրգանոիդների
Վակուոլ.
Եվ նորից, ինչ է օրգանոիդը
Եկեք գրեմ այդ բառը
Օրգանոիդ.
Սա ուղղակի թաղանթով շրջապտված բջջի ենթամիավոր է
Օրինակ իմ լյարդը ենթամիավոր է Սալ-ի և դա օրգան է, օրգանոիդը բջջի ենթամիավոր է
Վակուոլը ուղղակի ընդհանուր պայման է թաղանթով շրջապատված օրգանոիդի, որը կուտակում է ինչ-որ բաներ մեր բջջի ներսում
Ահա լուծվող վակուոլը կլինի վակուոլ բուսական բջջում, որը կուտակում է տարբեր տեսակի ֆերմենտներ և եթե կցված է մեկ այլ բանի, կլուծվի, եթե ունակ է հանել իր սպիտակուցները մեկ այլ բաների
Հիմա, կան որոշ օրգանոիդներ, որոնք մասին խոսել ենք բջջային շնչառության և ֆոտոսինթեզի տեսանկյունից, և կմանրամասնեմ այս տեսանյութում
Բայց մենք միտքոնդրիում կոչվածներ
Միտքոնդրիան բջիջներ
Եվ նրանք ունեն ներքին և արտաքին թաղանթներ և սա այն տեղն է, որտեղ մենք արտադրում ենք էներգիա, որտեղ շաքարները վերածվում են ԱԵՖ-ի
Ես բավական մանրամասնեցի այս տեսանյութում
Նրան ունեն իրենց ԴՆԹ-ն, և անգամ ինքնուրույն են բազմանում, որը ստիպում է մարդկանց հավատալ, որ նրանց նախնիները եղել են անկախ պրոկարիոտ օրգանիզմենր, և ինչ-որ պահից սկսած մտածին, թե ինչու չապրել այլ օրգանիզմի մեջ և այսպես ասած ապրել սիմբիոզի մեջ
Միտոքոնդրիումները օրգաններ են, որոնց նախնինները մի ժամանակ եղել են անկախ պրոկարիոտներ
Միտոքոնդրիում
Այստեղ տեղի է ունենում բջջային շնչառությունը, և մենք կմանրասնենք
Եվ հետո բուսական բջջում, մենակ--- հաստատ ոչ կենդական բջջում-- դու ունես քլորոպլաստներ որոնք ենթամիավոր են այսպես կոչված պլաստիդների, բայց ամենահայտնին քլորոպլաստներն են
Ես երևի պետք է անեի դա կանաչով
Ահա մենք ունենք քլորոպլաստ
Եվ մենք գիտենք, որ նրանք ունեն թիլակոիդնր այնտեղ
Սա այն տեղն է, որտեղ ֆոտոսինթեզն է տեղի ունենում:
Դու ունես քո գրանան և ամեն ինչը
Եվ ես կմանրամասնեմ ֆոտոսինթեզի տեսանյութում, բայց լավ է իմանալ սրանք այլ օրգանոիդներ են
Եվ միտքոնդրիումի նման նրանք ունեն իրենց ԴՆԹ-ն և իրենց ռիբոսոմները
Եվ համոզմունք կա, որ նրանք անկախ պրոկարիոտներ են եղել, որոնք սիմբիոզով ապրել են ավելի մեծ էուկարիոտ բջիջներում:
Մենք հիմանկանում վերջացրել ենք բջջի կառուցվածքի թեման
Այստեղ այլ բաներ կա, որ կարող ենք խոսել
Եթե մենք գործ ունենք բուսական կամ ոչկենդանական բջջի հետ մենք ունենք այսպես կոչված բջջապատ, որ տալիս է բջջին որոշակի ամրություն
Դու կարող ես նրան դիտել այդպես կամ տալ որոշակի ամրությոն .
Ահա դու ունես մասնիկներ' բջջապատ անունով, և անպայմանորեն ամուր չեն
Դու նրանց կարող ես դիտել որպես փուչիկներ, որոնք մի փոքր ավելի ամուր են
Օրինակ փայտը ունի կրկնակի բջջապատ, որը շատ ամուր է
Ահա սա բջջապատն է ոչ-կենդանական է բույսերում կազմված է ցելուլոզից, ոչ թե ցելուլիտից ժամանակին շփոթվում էի
Սա տալիս է լրացուցիչ ամրություն, որպեսզի կազմի բջջային թաղանթ
Եվ հետո տա բջջին իր իրական չափերը, դու ունես այս բաները, որոնք կոչվում են միկրոխողովակներ, կամ երբմեն ակտին թելիկներ, սրանք այն փոքրիկ խողովակներ են , որոնք անցնում են ամբողջ բջջով
Սա իրականում օգնում է բջջին ստանալ իր իրական չափսերը և իրականում կարող է մասնակցվել այն բաների մեջ, որոնք շարժվում է բջջի մեջ կամ անգամ ինքն իր շուրջը պտտվող բջջի
Եվ որպեսզի լինի ամբողջական և համոզված լինենք, որ ամեն բան արել ենք, եթե դու նայես միտոզի և մեյոզի վիդեոն , դու ունես այսպես կոչված ցենտրիոլներ
Ես ավելի մանրամասնեմ
Ցենտրիոլները, որոնք կորիզից դուրս են
Երկու ցենտրիոլներ, որոնք ուղղահայաց են իրար նկատմամբ կազմում են ցենտրոսոմ, և նրանք այսպես ասած ղեկավարում են միկրոխողովակներին, երբ մենք սկսենք բաժանել բջիջը մեյոզի ու միտոզի
Ես հիմա չեմ մանրամասնի Ես շատ տեսանյութեր եմ պատրաստել այդ թեմայով
Բայց հիմա, այսքանը բավարար է իմանալ շատ լավ է, որպես առաջին նյութը բջջի կառուցվածքի մասին
Եվ մեկ տեսանյութում, մենք վերջապես ամեն բան բերեցինք մեկ տեղում այսքանը բավարար է-- ես չեմ շատ մանրամասնել ամեն բան- հիմանական մասերը բջջի
Հուսով եմ, ունեցար ավելի մեծ պատկերացում,թե ինչպես է ամեն բան կազմակերպված իր ներսը
Patani students campaign for peace on the International Day of Peace.
On the international Day of Peace this is a small campaign by members of Thailand's Federation of Southern Students.
We will display our cards of words.
To let people suggest what peace means for each of them.
I've seen what the students do today, of their activities for peace.
They suggest peaceful solution to the conflict and violence in the three southern provinces
I myself have joined a campaign group for peace in the south.
This is therefor something I'd like to see students participate.
Because part of the problem comes from some young people and students.
If they join this campaign, it will offer us the best way-out.
Peace for me means no problem.
But of course, there's no society without problem.
What we have to do is to try to reduce the problem as best we can. When it happens, peace begins. It begins when we respect each others.
Peace begins when we understand each others.
I think this is good, that we let people express themselves.
They can tell us how they think of peace.
When we don't have a chance like this, we could forget peace or that such word exists.
Today is the International Day of Peace.
I am one of those people who want global peace.
Especially in the three southern provinces. May God protect us and give us, people in the south, peace, which we've been deprived of for many years.
The government should understand that we are under the law which is not by international standard.
I'd like the government to consider this as well as peace.
Patani wants peace.
Welcome back.
In this presentation, I actually want to show you how we can use the antiderivative to figure out the area under a curve.
Actually I'm going to focus more a little bit more on the intuition.
So let actually use an example from physics.
I'll use distance and velocity.
And actually this could be a good review for derivatives, or actually an application of derivatives.
So let's say that I described the position of something moving.
Let's say it's s.
Let's say that s is equal to, I don't know, 16t squared.
So s is distance.
Let me write this in the corner.
I don't know why the convention is to use s as the variable for distance.
So s is equal to distance, and then t is equal to time.
So this is just a formula that tells us the position, kind of how far has something gone, after x many, let's say, seconds, right?
So after like, 4 seconds, we would have gone, let's say the distance is in feet, this is in seconds.
After 4 seconds, we would have gone 256 feet.
And let me graph that as well.
So this curve will essentially just be a parabola, right?
The object, every second you go, it's going a little bit further, right?
So it's actually accelerating.
And so what if we wanted to figure out what the velocity of this object, right?
This is, let's see, this is d, this is t, right?
And this is, I don't know if it's clear, but this is kind of 1/2 a parabola.
So this is the distance function.
What would the velocity be?
It's distance divided by time, right?
And since this velocity is always changing, we want to figure out the instantaneous velocity.
And that's actually one of the initial uses of what made derivatives so useful.
So we want to find the change, the instantaneous change with respect to time of this formula, right?
Because this is the distance formula.
So if we know the instant rate of change of distance with respect to time, we'll know the velocity, right?
So ds, dt, is equal to?
So what's the derivative here?
It's 32t, right?
And this is the velocity.
Maybe I should switch back to, let me write that, v equals velocity.
So let's graph this function.
This will actually be a fairly straightforward graph to draw.
OK.
So this, I'll draw it in red, this is this going to be a line, right?
32t it's a line with slope 32.
So it's actually a pretty steep line.
So this is the velocity.
This is that graph, and this is distance, right?
So in case you hadn't learned already, and maybe I'll do a whole presentation on kind of using calculus for physics, and using derivatives for physics.
But if you have to distance formula, it's derivative is just velocity.
And I guess if you view it the other way, if you have the velocity, it's antiderivative is distance.
Although you won't know where, at what position, the object started.
In this case, the object started at position of 0, but it could be, you know, at any constant, right?
You could have started here and then curved up.
But anyway, let's just assume we started at 0.
So the derivative of distance is velocity, the antiderivative of velocity is distance.
Let's assume that we were only given this graph.
And we said, you know, this is the graph of the velocity of some object.
And we want to figure out what the distance is after, you know, t seconds, right?
So this is the t-axis, this is the velocity axis, right?
So let's say we were only given this, and let's say we didn't know that the antiderivative of the velocity function is the distance function.
How would we figure out, how would we figure out what the distance would be at any given time?
If we have a constant, this red is kind of bloody.
If we have, over any small period of time, right, or if we have a constant velocity, when you have a constant velocity, distance is just velocity times time, right?
So let's say we had a very small time fragment here, right?
I'll draw it big, but let's say this time fragment it is really small.
And let's called this very small time fragment, let call this delta t, or dt actually.
So it's like almost instantaneous, but not quite.
Or you can actually view it as instantaneous.
So this is how much time goes by.
You can kind of view this as a very small change in time.
So if we have a very small change of time, and over that very small change in time, we have a roughly constant velocity, let's say the roughly constant velocity is this.
Right, this is the velocity, so say we had over this very small change in time, we have this roughly constant velocity that's on this graph.
So the distance that the object travels over the small time would be the small time times the velocity, right?
It would be whatever the value of this red line is, times the width of this distance, right?
So what's another way?
Visually I kind of did it ahead of time, but what's happening here?
If I take this change in time, right, which is kind of the base of this rectangle, and I multiply it times the velocity which is really just the height of this rectangle, what have I figured out?
Well I figured out the area of this rectangle, right?
Right, the velocity this moment, times the change in time at this moment, is nothing but the area of this very skinny rectangle.
It's almost infinitely skinny, but it's, we're assuming for these purposes it has some very notional amount of width.
So there we figured out the area of this column, right?
Well, if we wanted to figure out the distance that you travel after, let's say, you know, I don't know, let's say t, let's say t sub nought, right?
After t sub nought seconds, right?
Well then, all we would have to do is, we would have to just figure, we would just do a bunch of dt's, right?
You'd do another one here, you'd figure out the area of this column, you'd figure out the area of this column, the area of this column, right?
So if you wanted to know how far you traveled after t sub zero seconds, you'd essentially get, or an approximation would be, the sum of all of these areas.
And as you got more and more, as you made the dt's smaller and smaller, skinnier, skinnier, skinnier.
And you had more and more and more and more of these rectangles, then your approximation will get pretty close to, well, two things.
It'll get pretty close to, as you can imagine, the area under this curve, or in this case a line.
But it would also get you pretty much the exact amount of distance you've traveled after t sub nought seconds.
So I think I'm running into the ten minute wall, so I'm just going to pause here, and I'm going to continue this in the next presentation.
What I wanna do in this video is give an overview of quadrilaterals.
And you can imagine from this prefix, or I guess you could say from the beginning of this word - quad
This involves four of something.
And quadrilaterals, as you can imagine, are, are shapes.
And we're gonna be talking about two-dimensional shapes that have four sides, and four vertices, and four angles.
So, for example, one, two, three, four.
That is a quadrilateral.
Although that last side didn't look too straight.
That is a quadrilateral.
One, two, three, four. These are all quadrilaterals.
They all have four sides, four vertices, and clearly four angles. One angle, two angles, three angles, and four angles.
Here you can measure.
Here actually let me draw this one a little bit bigger 'cause it's interesting.
So in this one right over here you have one angle, two angles, three angles and then you have this really big angle right over there.
If you look at the, if you look at the interior angles of this quadrilateral.
Now quadrilaterals, as you can imagine, can be subdivided into other groups based on the properties of the quadrilaterals.
And the main subdivision of quadrilaterals is between concave and convex quadrilaterals
So you have concave, and you have convex.
And the way I remember concave quadrilaterals, or really concave polygons of any number of shapes is that it looks like something has caved in.
So, for example, this is a concave quadrilateral
It looks like this side has been caved in.
And one way to define concave quadrilaterals, so let me draw it a little bit bigger, so this right over here is a concave quadrilateral, is that it has an interior angle, it has an interior angle that is larger than 180 degrees.
So, for example, this interior angle right over here is larger, is larger than 180 degrees.
It's an interesting proof, maybe I'll do a video, it's actually a pretty simple proof, to show that if you have a concave quadrilateral if at least one of the interior angles has a measure larger than 180 degrees that none of the sides can be parallel to each other.
The other type of quadrilateral, you can imagine, is when all of the interior angles are less than 180 degrees. And you might say, "Well, what happens at 180 degrees?"
Well, if this angle was 180 degrees then these wouldn't be two different sides it would just be one side and that would look like a triangle.
But if all of the interior angles are less than 180 degrees, then you are dealing with a convex quadrilateral.
So this convex quadrilateral would involve that one and that one over there.
So this right over here is what a convex quadrilateral, this is what a convex quadrilateral could look like. Four points.
Four sides.
Four angles.
Now within convex quadrilaterals there are some other interesting categorizations.
So now we're just gonna focus on convex quadrilaterals so that's gonna be all of this space over here.
So one type of convex quadrilateral is a trapezoid.
A trapezoid. And a trapezoid is a convex quadrilateral and sometimes the definition here is a little bit, different people will use different definitions, so some people will say a trapezoid is a quadrilateral that has exactly two sides that are parallel to each other
So, for example, they would say that this right over here this right over here is a trapezoid, where this side is parallel to that side.
If I give it some letters here, if I call this trapezoid A, B, C, D, we could say that segment AB is parallel to segment DC and because of that we know that this is, that this is a trapezoid
Now I said that the definition is a little fuzzy because some people say you can have exactly one pair of parallel sides but some people say at least one pair of parallel sides.
So if you say, if you use the original definition, and that's the kind of thing that most people are referring to when they say a trapezoid, exactly one pair of parallel sides, it might be something like this, but if you use a broader definition of at least one pair of parallel sides, then maybe this could also be considered a trapezoid.
So you have one pair of parallel sides.
Like that.
And then you have another pair of parallel sides. Like that.
So this is a question mark where it comes to a trapezoid.
A trapezoid is definitely this thing here, where you have one pair of parallel sides.
Depending on people's definition, this may or may not be a trapezoid.
If you say it's exactly one pair of parallel sides, this is not a trapezoid because it has two pairs.
If you say at least one pair of parallel sides, then this is a trapezoid.
So I'll put that as a little question mark there.
But there is a name for this regardless of your definition of what a trapezoid is.
If you have a quadrilateral with two pairs of parallel sides, you are then dealing with a parallelogram.
So the one thing that you definitely can call this is a parallelogram.
Parallelo, parallelo parallelogram Parallelogram.
And I'll just draw it a little bit bigger.
So it's a quadrilateral.
If I have a quadrilateral, and if I have two pairs of parallel sides
So two of the opposite sides are parallel.
So that side is parallel to that side and then this side is parallel to that side there
You're dealing with a parallelogram.
And then parallelograms can be subdivided even further.
They can be subdivided even further if the four angles in a parallelogram are all right angles, you're dealing with a rectangle.
So let me draw one like that.
So if the four sides, so from parallelograms, these are, this is all in the parallelogram universe.
What I'm drawing right over here, that is all the parallelogram universe.
This parallelogram tells me that opposite sides are parallel.
And if we know that all four angles are 90 degrees and we've proven in previous videos how to figure out the sum of the interior angles of any polygon and using that same method, you could say that the sum of the interior angles of a rectangle, or of any, of any quadril, of any quadrilateral, is actually a hund- is actually 360 degrees, and you see that in this special case as well, but maybe we'll prove it in a separate video.
But this right over here we would call a rectangle a parallelogram, opposite sides parallel, and we have four right angles.
Now if we have a parallelogram, where we don't necessarily have four right angles, but we do have, where we do have the length of all the sides be equal, then we're dealing with a rhombus.
So let me draw it like that.
So it's a parallelogram. This is a parallelogram.
So that side is parallel to that side.
This side is parallel to that side.
And we also know that all four sides have equal lengths.
So this side's length is equal to that side's length.
Which is equal to that side's length, which is equal to that side's length.
Then we are dealing with a rhombus.
So one way to view it, all rhombi are parallelograms
All rectangles are parallelograms
All parallelograms you cannot assume to be rectangles.
All parallelograms you cannot assume to be rhombi.
Now, something can be both a rectangle and a rhombus.
So let's say this is the universe of rectangles
So the universe of rectangles.
Drawing a little of a venn diagram here.
Is that set of shapes, and the universe of rhombi is this set of shapes right over here.
So what would it look like?
Well, you would have four right angles, and they would all have the same length.
So, it would look like this.
So it would definitely be a parallelogram.
It would be a parallelogram.
Four right angles. Four right angles, and all the sides would have the same length.
And you probably. This is probably the first of the shapes that you learned, or one of the first shapes.
This is clearly a square.
So all squares are both rhombi, are are members of the, they can also be considered a rhombus and they can also be considered a rectangle, and they could also be considered a parallelogram.
But clearly, not all rectangles are squares and not all rhombi are squares and definitely not all parallelograms are squares.
This one, clearly, right over here is neither a rectangle, nor a rhombi nor a square.
So that's an overview, just gives you a little bit of taxonomy of quadrilaterals. And then in the next few videos, we can start to explore them and find their interesting properties Or just do interesting problems involving them.
We are asked to solve the proportion and we have 8/36 = 10/?
Now there is a bunch of different ways to solve this.
And I will explore all of them.
So one way to think about it is these two need to be equivalent fractions.
So whatever happened to the numerator also has to happen to the denominator.
So what do you have to multiply 8 by to get 10?
You could multiply 8 * 10/8 will definitely give you 10.
So we're multiplying by 10/8 over here.
Or another way to write 10/8 is the same thing as 5/4.
So we're multiplying by 5/4 to get from 8 to 10.
If we did that to the numerator in order to have an equivalent fraction you have to do the same thing to the denominator.
You have to multiply it times 5/4.
And so we can say that this n is going to be equal to 36 * 5/4.
Or you could say that this is going to be equal to 36*5 divided by 4.
And now 36 divided by 4, we know what that is.
We can divide both the numerator and denominator by 4.
You divide the numerator by 4, you get 9.
Divide the denominator by 4, you get 1.
You get 45.
So that's one way to think about it.
8/36 = 10/45.
Another way to think about it is, what do we have to multiply 8 by to get its denominator?
How much larger is the denominator 36 than 8?
Let's just divide 36 over 8.
So 36/8 is the same thing as-- so we can simplify, dividing the numerator and denominator by 4.
That's their greatest common divisor.
That's the same thing as 9/2.
If you multiply the numerator by 9/2, you get the denominator.
Then we'll have to do the same thing over here.
If 36 is 9/2 times 8, let me write this.
8 * 9/2 = 36.
That's how we go from the numerator to the denominator.
Then to figure out what the denominator here is, if we want the same fraction, we'll have to multiply by 9/2 again.
So then we'll get 10 * 9/2 = n, is going to be equal to this denominator.
And so this is the same thing as saying 10*9 / 2, divide the numerator and denominator by 2, you get 5/1 which is 45.
So 45 = n.
Once again we got the same way, completely legitimate way to solve it.
Now sometimes when you see a proportion like this, sometimes you'll say oh you could cross multiply.
And you can cross multiply and I'll teach you how to do that.
And that's sometimes the quick way to do it.
But I don't like teaching it the first time you look at proportions because it's really just something mechanical.
You really don't understand what you're doing and it really comes out of a little bit of algebra.
And I'll show you the algebra as well.
But if you don't understand it and if it doesn't make as much sense to you at this point, don't worry too much about it.
So we have 8/36 = 10/n.
When you cross multiply you're saying that the numerator here times the denominator over here is going to be equal to, so 8*n is going to be equal to the denominator over here-- let me do this in a different colour-- the denominator over here times the numerator over here.
This is what it means to cross multiply.
So this is going to be equal to 36*10.
Or you could say, let me do this in a neutral colour now, you could say that 8n = 360.
And so you're saying 8 times what is equal to 360.
Or to figure out what that times what is, you divide 360 divided by 8.
So we can divide, and this is a little bit of algebra here, we're dividing both sides of the equation by 8, and we're getting n= 360/8.
And you know, you can do that without thinking in strict algebraic terms.
You say 8 times what is 360?
Well, 8 times 360/8.
If I write 8 x ? = 360, well ? could definitely be 360/8.
If I multiply these out, this guy and that guy cancel out and it's definitely 360.
And that's why it's 360/8.
But then we want to actually divide this to actually get our right answer or a simplified answer.
8 goes into 360.
8 goes into 36 4 times.
4 times 8 is 32.
You have a remainder of 4.
Bring down the 0.
8 goes into 40 5 times.
5 times 8 is 40.
And then you have no remainder.
And you're done.
Once again we got n=45.
Now the last way I am going to show you involves a little bit of algebra.
If any of the ways before this worked, that's fine.
And where this is sitting in the playlist you're not expected to know the algebra.
But I want to show you the algebra just because I want to show you that this cross-multiplication isn't some magic.
That using algebra we will get this exact same thing.
But you could stop watching this, if you find this part confusing.
So let's rewrite our proportion.
8/36 = 10/n.
And we want to solve for n.
The easiest way to solve for n is maybe multiply both-- this thing on the left is equal to this thing on the right.
So we can multiply them both by the same thing and the equality will still hold.
So we can multiply both of them by n.
On the right hand side, the n's cancel out.
On the left hand side we have 8/36 * n = 10.
Now if we want to solve for n, we can literally multiply if we want just an n here, we would want to multiply this side times 36- I'll do that in a different colour- we would want to multiply this side times 36 times 8.
Because if you multiply these guys out, you get 1 and you just have an n.
But since we're doing it to the left hand side, we also have to do it to the right hand side.
So times 36/8.
These guys cancel out and we're left with n= 10 * 36 is 360/8.
And notice we're getting the exact same value that we got with cross multiplying.
And with cross multiplying, you're actually doing 2 steps.
You're actually doing an extra step here.
You're multiplying both sides by n so that you get 8n.
And then you're multiplying both sides by 36 so that you get your 36 on both sides and you get this value here.
But at the end when you simplify it, you'll get the exact same answer.
Those are all different ways to solve this proportion.
Probably the most obvious way or the easiest way to do it in your head was either just looking at what you have to multiply the numerator by and then doing the same thing to the denominator or maybe by cross multiplication.
In Oxford in the 1950s, there was a fantastic doctor, who was very unusual, named Alice Stewart.
And Alice was unusual partly because, of course, she was a woman, which was pretty rare in the 1950s.
And she was brilliant, she was one of the, at the time, the youngest Fellow to be elected to the Royal College of Physicians.
She was unusual too because she continued to work after she got married, after she had kids, and even after she got divorced and was a single parent, she continued her medical work.
And she was unusual because she was really interested in a new science, the emerging field of epidemiology, the study of patterns in disease.
But like every scientist, she appreciated that to make her mark, what she needed to do was find a hard problem and solve it.
The hard problem that Alice chose was the rising incidence of childhood cancers.
Most disease is correlated with poverty, but in the case of childhood cancers, the children who were dying seemed mostly to come from affluent families.
So, what, she wanted to know, could explain this anomaly?
Now, Alice had trouble getting funding for her research.
In the end, she got just 1,000 pounds from the Lady Tata Memorial prize.
And that meant she knew she only had one shot at collecting her data.
Now, she had no idea what to look for.
This really was a needle in a haystack sort of search, so she asked everything she could think of.
Had the children eaten boiled sweets?
Had they consumed colored drinks?
Did they eat fish and chips?
Did they have indoor or outdoor plumbing?
What time of life had they started school?
And when her carbon copied questionnaire started to come back, one thing and one thing only jumped out with the statistical clarity of a kind that most scientists can only dream of.
By a rate of two to one, the children who had died had had mothers who had been X-rayed when pregnant.
Now that finding flew in the face of conventional wisdom.
Conventional wisdom held that everything was safe up to a point, a threshold.
It flew in the face of conventional wisdom, which was huge enthusiasm for the cool new technology of that age, which was the X-ray machine.
And it flew in the face of doctors' idea of themselves, which was as people who helped patients, they didn't harm them.
Nevertheless, Alice Stewart rushed to publish her preliminary findings in The Lancet in 1956.
People got very excited, there was talk of the Nobel Prize, and Alice really was in a big hurry to try to study all the cases of childhood cancer she could find before they disappeared.
In fact, she need not have hurried. It was fully 25 years before the British and medical --
British and American medical establishments abandoned the practice of X-raying pregnant women.
The data was out there, it was open, it was freely available, but nobody wanted to know.
A child a week was dying, but nothing changed.
Openness alone can't drive change.
So for 25 years Alice Stewart had a very big fight on her hands.
So, how did she know that she was right?
Well, she had a fantastic model for thinking.
She worked with a statistician named George Kneale, and George was pretty much everything that Alice wasn't.
So, Alice was very outgoing and sociable, and George was a recluse.
Alice was very warm, very empathetic with her patients.
George frankly preferred numbers to people.
But he said this fantastic thing about their working relationship.
He said, "My job is to prove Dr. Stewart wrong."
He actively sought disconfirmation.
Different ways of looking at her models, at her statistics, different ways of crunching the data in order to disprove her.
He saw his job as creating conflict around her theories.
Because it was only by not being able to prove that she was wrong, that George could give Alice the confidence she needed to know that she was right.
It's a fantastic model of collaboration -- thinking partners who aren't echo chambers.
I wonder how many of us have, or dare to have, such collaborators.
Alice and George were very good at conflict.
They saw it as thinking.
So what does that kind of constructive conflict require?
Well, first of all, it requires that we find people who are very different from ourselves.
That means we have to resist the neurobiological drive, which means that we really prefer people mostly like ourselves, and it means we have to seek out people with different backgrounds, different disciplines, different ways of thinking and different experience, and find ways to engage with them.
That requires a lot of patience and a lot of energy.
And the more I've thought about this, the more I think, really, that that's a kind of love.
Because you simply won't commit that kind of energy and time if you don't really care.
And it also means that we have to be prepared to change our minds.
Alice's daughter told me that every time Alice went head-to-head with a fellow scientist, they made her think and think and think again.
"My mother," she said, "My mother didn't enjoy a fight, but she was really good at them."
So it's one thing to do that in a one-to-one relationship.
But it strikes me that the biggest problems we face, many of the biggest disasters that we've experienced, mostly haven't come from individuals, they've come from organizations, some of them bigger than countries, many of them capable of affecting hundreds, thousands, even millions of lives.
So how do organizations think?
Well, for the most part, they don't.
And that isn't because they don't want to, it's really because they can't.
And they can't because the people inside of them are too afraid of conflict.
In surveys of European and American executives, fully 85 percent of them acknowledged that they had issues or concerns at work that they were afraid to raise.
Afraid of the conflict that that would provoke, afraid to get embroiled in arguments that they did not know how to manage, and felt that they were bound to lose.
Eighty-five percent is a really big number.
It means that organizations mostly can't do what George and Alice so triumphantly did.
They can't think together.
And it means that people like many of us, who have run organizations, and gone out of our way to try to find the very best people we can, mostly fail to get the best out of them.
So how do we develop the skills that we need?
Because it does take skill and practice, too.
If we aren't going to be afraid of conflict, we have to see it as thinking, and then we have to get really good at it.
So, recently, I worked with an executive named Joe, and Joe worked for a medical device company.
And Joe was very worried about the device that he was working on.
He thought that it was too complicated and he thought that its complexity created margins of error that could really hurt people.
He was afraid of doing damage to the patients he was trying to help.
But when he looked around his organization, nobody else seemed to be at all worried.
So, he didn't really want to say anything.
After all, maybe they knew something he didn't.
Maybe he'd look stupid.
But he kept worrying about it, and he worried about it so much that he got to the point where he thought the only thing he could do was leave a job he loved.
In the end, Joe and I found a way for him to raise his concerns.
And what happened then is what almost always happens in this situation.
It turned out everybody had exactly the same questions and doubts.
So now Joe had allies.
They could think together.
And yes, there was a lot of conflict and debate and argument, but that allowed everyone around the table to be creative, to solve the problem, and to change the device.
Joe was what a lot of people might think of as a whistle-blower, except that like almost all whistle-blowers, he wasn't a crank at all, he was passionately devoted to the organization and the higher purposes that that organization served.
But he had been so afraid of conflict, until finally he became more afraid of the silence.
And when he dared to speak, he discovered much more inside himself and much more give in the system than he had ever imagined.
And his colleagues don't think of him as a crank.
They think of him as a leader.
So, how do we have these conversations more easily and more often?
Well, the University of Delft requires that its PhD students have to submit five statements that they're prepared to defend.
It doesn't really matter what the statements are about, what matters is that the candidates are willing and able to stand up to authority.
I think it's a fantastic system, but I think leaving it to PhD candidates is far too few people, and way too late in life.
I think we need to be teaching these skills to kids and adults at every stage of their development, if we want to have thinking organizations and a thinking society.
The fact is that most of the biggest catastrophes that we've witnessed rarely come from information that is secret or hidden.
It comes from information that is freely available and out there, but that we are willfully blind to, because we can't handle, don't want to handle, the conflict that it provokes.
But when we dare to break that silence, or when we dare to see, and we create conflict, we enable ourselves and the people around us to do our very best thinking.
Open information is fantastic, open networks are essential.
But the truth won't set us free until we develop the skills and the habit and the talent and the moral courage to use it.
Openness isn't the end.
It's the beginning.
(Applause)
We need to add 7.056 to 605.7 to 5.67.
Now when you're adding any number, you always want to make sure you line up numbers in the same place.
And especially when you're dealing with decimals, the easiest way to do that is to just line up the decimals.
So let's do that.
So the first number right here is 7,056.
This second number right here is 605.7.
And then this last number is 5.67.
So now we have everything lined up.
Everything that's in the ones place is below or above everything else in the ones place.
Everything in the tenths place is below or above everything else in the tenths place, and so on and so forth.
So we can add.
So let's add it.
So you want to start off in the smallest place.
So you start off here.
This is the tenths, hundredths, thousandths place.
This is literally 6 thousandths, and you want to add it to the other thousandths.
There aren't any other thousandths.
So you can view it two ways. You can just bring in this 6 down, or you could view this 605.7 as the same thing as 605.700.
You can add as many zeroes to the right of this decimal, to the right of the 7, as you want, since we're sitting on the right side of the decimal, without changing its value.
You can also do it here.
This 5.67, you can write it as 5.670.
When you write it like this, and you have 6 plus 0 plus 0 is 6.
And you keep going.
5 plus 0 plus 7 is 12.
You write the 2 in the hundredths place, and carry the 1.
1 plus 0 plus 7 is 8, plus 6 is 14.
Write the 4, regroup the 1 into the ones place.
1 plus 7 is 8.
8 plus 5 is 13.
13 plus 5 is 18.
This is 18.
Carry or regroup the 1.
1 plus 0 is just 1.
And then finally.
You have the 6 in the hundreds place.
Nothing gets added to it, so you can just bring down that 6 and it's right there.
And you don't want to forget the decimal.
And so when you add the numbers you get 618.426, or 618 and 426 thousandths.
And we're done.
How many cups are in 3 and 1/2 gallons?
So before even addressing this question, let's just think about how large a cup is.
Actually, I'll give you a little bit of overview of how many cups there are in a pint, how many pints in a quart, and how many quarts in a gallon.
Let me just draw a cube here, and let's imagine that this is a gallon.
The most common time we see a gallon is when you see a gallon of milk.
So let's say that that whole thing is a gallon.
You can imagine if it had a handle, it would be kind of a big gallon of milk.
Now, there are 4 quarts per gallon.
Let me write this over here.
There are 4 quarts per gallon.
So if I were to draw the quarts here, I could divide this gallon into 4 quarts, and then each of these sections would be a quart.
So you would have 4 quarts.
So this right here that I've just drawn in blue would be exactly 1 quart.
And obviously, there's 4 of them in this entire gallon.
Now, you can divide the quarts into pints.
You have 2 pints per quart.
So this quart that I drew here, I can divide it into 2, like that, and this little section that I'm highlighting in magenta is a pint.
That is a pint right over there.
And then finally, there are 2 cups per pint.
So this pint right here, I can divide it into 2, and each of these will be a cup.
So this section right here will be a cup.
Now, we can go straight and figure out exactly how many cups there are per gallon.
Actually, that might be an interesting way to think about it.
If you have 4 quarts-- let's multiply it right here.
So you have 4 quarts per gallon times 2 pints per quart.
What does this give you?
This gives you 4 times 2 is equal to 8.
And then the quarts cancel out, and you have 8 pints per gallon.
And that makes complete sense because we had 4 quarts in this gallon, and then each of those quarts have 2 pints in them.
So 4 times 2.
So 8 pints per gallon.
And then we can multiply that times 2 cups per pint.
So I could just copy and paste this right here.
Actually, I should've cut and paste.
Let me select it again.
I want to do that so I get that real estate back.
So edit, cut, edit, paste.
There you go.
So now you multiply this times 2 cups per pint.
And the reason why this will work is because you have pints in the numerator.
It cancels out with the pints in the denominator.
And you will be left with-- I'll go back to the yellow-- 8 times 2 is 16.
In the numerator, we have cups per gallon.
Now, we just figured how many cups there are per gallon.
That makes sense.
This section right here is exactly 1/16 of this entire cube, this entire gallon.
But we haven't even answered our question.
We want to figure out how many cups there are in 3 and 1/2 gallons.
So let's write it over here.
So we're concerned with 3 and 1/2 gallons.
I don't like working with mixed numbers.
I like to turn them into improper fractions. 3 and 1/2 is the same thing as 2 times 3 is 6, plus 1 is 7.
This is the same thing as 7/2.
If you divided 7 by 2, you would get 3 with a remainder of 1, or this would be 3 and 1/2, so this is the exact same thing.
So we want to know how many cups are in 7/2 gallons.
So what we want to do is end up with cups, and we want the gallons to cancel out.
So we have gallons in the numerator right here.
It's definitely not in the denominator.
And so we want to divide by gallons.
And then we're going to have a numerator.
We have cups in the numerator.
And how many cups are there per gallon?
Well, we just figured that out.
There are 16 cups per gallon.
When you multiply these two quantities, the gallons will cancel out, and you'll just be left with cups, and that's what we wanted.
So it's going to be 7/2 times 16.
So this is going to be 7 times 16/2 cups.
You could divide 16 by 2 to get 8. 2 divided by 2 is 1.
So it just becomes 7 times 8 divided by 1, or just 7 times 8, which is 56.
So this is equal to 56 cups.
And this should make sense.
This should be a much larger number because cups are a much smaller unit.
So if you have 3 and 1/2 gallons, you will have many, many, many more cups in that 3 and 1/2 gallons, so this makes sense.
Now we've had an introduction to Al.
We've heard about some of the properties of environments, and we've seen some possible architecture for agents.
I'd like next to show you some examples of AI in practice.
And Sebastian and I have some experience personally in things we have done at Google, at NASA, and at Stanford.
And I want to tell you a little bit about some of those.
One of the best successes of AI technology at Google has been the machine translation system.
Here we see an example of an article in Italian automatically translated into English.
Now, these systems are built for 50 different languages, and we can translate from any of the languages into any of the other languages.
So, that's over 2,500 different systems, and we've done this all using machine learning techniques, using AI techniques, rather than trying to build them by hand.
And the way it works is that we go out and collect examples of text that's a line between the 2 languages.
So we find, say, a newspaper that publishes 2 editions, an Italian edition and an English edition, and now we have examples of translations.
And if anybody ever asked us for exactly the translation of this one particular article, then we could just look it up and say "We already know that."
But of course, we aren't often going to be asked that.
Rather, we're going to be asked parts of this.
Here are some words that we've seen before, and we have to figure out which words in this article correspond to which words in the translation article.
And when we do that by examining many, many millions of words of text in the 2 languages and making the correspondence, and then we can put that all together.
And then when we see a new example of text that we haven't seen before, we can just look up what we've seen in the past for that correspondence.
So, the task is really two parts.
Off-line, before we see an example of text we want to translate, we first build our translation model.
We do that by examining all of the different examples and figuring out which part aligns to which.
Now, when we're given a text to translate, we use that model, and we go through and find the most probable translation.
So, what does it look like?
Well, let's look at it in some example text.
And rather than look at news articles, I'm going to look at something simpler.
I'm going to switch from Italian to Chinese.
Here's a bilingual text.
Now, for a large-scale machine translation, examples are found on the Web.
This example was found in a Chinese restaurant by Adam Lopez.
Now, it's given, for a text of this form, that a line in Chinese corresponds to a line in English, and that's true for each of the individual lines.
But to learn from this text, what we really want to discover is what individual words in Chinese correspond to individual words or small phrases in English.
I've started that process by highlighting the word "wonton" in English.
It appears 3 times throughout the text.
Now, in each of those lines, there's a character that appears, and that's the only place in the Chinese text where that character appears.
So, that seems like it's a high probability that this character in Chinese corresponds to the word "wonton" in English.
Let's see if we can go farther.
My question for you is what word or what character or characters in Chinese correspond to the word "chicken" in English?
And here we see "chicken" appears in these locations.
Click on the character or characters in Chinese that corresponds to "chicken."
Round 9.564, or nine and five hundred sixty-four thousandths, to the nearest tenth.
So let me write it a little bit larger, 9.564.
And we need to round to the nearest tenth.
So what's the tenth place?
The tenths place is right here.
This right here represents 5 tenths.
This is the ones place, this is the tenths place, this is the hundredths place, and this is the thousandths place right here.
So we need to round to the nearest tenth.
So if we round up, this will be 9.6.
If we round down, this will be 9.5.
And just like regular rounding, when we're not dealing with decimals, you move to one spot, or you look at one place to the right or one place lower, I guess, and you say is that 5 or larger?
If it is, you round up, if it isn't, you round down.
6 is definitely 5 or larger, so we want to round up.
So this 9.564 becomes 9.6, or we can call this nine and six tenths.
And then we're done!
1 year ago
Home isn't the same without you
Hey Dad, at the apartment now.
Can you talk?
Sure I'm ready
Dad
Dad, is that mold?
Thanks for all your help dad
Happy birthday Sis!
Honey are you there?
We miss you.
Tomorrow we're gonna go shopping and try to find some...
Who is that?
His name is David
I don't like him
Maybe we should meet him first
Ok.
Nervous...
Hi
Not so bad after all!
Um, guys, are you around...
Sure, we're here honey?
Me too
Is that...
It is!
We're on our way
Thanks for today guys.
It was amazing!
Conversations that last, with the people you love
Long time ago, we just issue a statement but this is not enough
And that's the reason why we have many colleagues who were attacked all this while.
And I think it's the time for us to stand up, voice out that's why we handed over the memorandum to the police
This is what we are trying to do and we choose black color because it is very sad and it is very serious. We cannot tolerate anymore. So, instead of issuing a statement and press release we choose to stand up and voice out, for our rights, for our friends, for what is right.
Original Story by Suzuki Yumiko Forget about him.
And coming here every week won't change your fate.
If that were the case, I'd be making a fortune.
But it's not.
Should I tell you again?
You've had a tough life, and you will.
And you don't stand a chance with this man.
I wish otherwise, but it's the truth.
Don't tell me it's written on my face.
It is.
But you never know.
Then why try to find out?
I'll write you an amulet.
Look at your hair.
When'd you wash it?
Have him carry this.
I can't guarantee anything.
Free of charge.
Take it and leave.
What? Let me bow to you.
You don't need to.
To show my gratitude.
No, just go.
Thank you.
Way to go, girl.
Keep it up.
I'm so curious. What are you good at?
Hit me with a belt. produced by PARK Moo-seung, WON Dong-yeon Why do I do this? You don't need the look for this job.
And I need to make lots of money. For my dad. - Tell me your body size.
- That's it for today. Tell me your body size.
It's a secret. Please!
You'll be amazed.
Yes... Tell me.
Waist is 24, and hip is 36. What is it?
Bang! Answer the phone. My wife is in the shower.
I'm so scared.
- Honey. - Yes? starring by JOO Jin-mo She's just taking a shower. - You think?
- Calm down.
Should I sing you your favorite song?
KlM A-joong Should I sing you your favorite song? Should I sing you your favorite song?
Jesus blessed me with... Most of my customers have been emotionally hurt.
Honey, cheer up.
I'll help you through this.
Okay, I'll take them off. What? Here we go.
Sang-jun!
Hanna?
- Damn it! - Chorus, take over!
Hanna?
Hanna?
Can you hear me?
Hanna? Hanna? Can you hear me?
- Sang-jun, I'm fine.
- Okay. Ammy, at the count of 3.
Three! Two! One!
Good job. Encore my ass!
What's wrong?
It was a good show.
Thanks.
Tired?
Don't you ever dance.
You almost blew it.
I dance along with you to make it seem real.
Are you performing?
Wear a sweat shirt.
There isn't any that fits me.
Sang-jun?
Why'd the stage collapse?
Sang-jun?
Good job.
Great job.
You okay?
They built the stage poorly.
I was worried sick.
Okay.
I need to assess the situation.
So he's interested in you?
It's the feeling.
He's very nice to me.
Save it.
There are 3 types of women for men.
Look.
Pretty ones. They're a treasure.
The average ones.
We're a present. You? A reject!
Get it now? Don't eat the fat.
Listen.
I have a woman's intuition.
It's your illusion.
Intuition is from experience.
Have you ever been in love? - Tell me. - Have I been in love?
Yes, I have. My first love.
Sweetie?
Did I ask you to buy diet pills from me?
What am I?
A guy who sells you diet pills costing 3 grand?
Don't say that.
Your business is slow.
I just wanted to help.
It is. And you're not helping.
You made me feel so miserable.
I'm sorry.
I'm warning you. Don't do it again.
Give pills to Jung-min.
You're as pretty as you are.
Try to lose weight, and we're through.
Okay? These are checks.
- Okay.
- Endorse them.
Just do the first one.
If you do this again, we're done. It was the last of him I saw. I'm sorry.
I'll pray for you to meet someone better than me. Amen. That day, I decided not to eat.
And to lose some weight. Move.
This requires a skill.
Grab that end.
Lift her at the count of 3.
One, two, three.
Lift her.
I said at the count of 3.
You lifted at 2.
Hey! Yes?
Lift at 3, okay?
We need to work together.
Grab it.
At 3, okay?
One, two, three!
Bring that bed.
Put them together.
We'll roll her over.
I'll do it.
Excuse me?
I'll roll over.
Why didn't you wake her? I learned that night. I'm not cut out for love and diet.
It's Hakuna Matata.
Africans believe it grants them their wishes.
Oh! Nicely done.
Are you hung over?
Give it some feelings.
God!
It's a vital part.
Try to feel the rhythm.
It's taking forever.
She's trying hard?
Is trying hard enough?
Everyone does that.
Doing well is what counts.
Like you.
Keep up the good work.
Why does my hope get higher? Thanks for the ride.
You're welcome.
Who are you visiting?
Someone that I love.
Who's he?
Check me out.
Sorry!
Bye. Wait. I'm having a birthday party tomorrow.
Don't miss it.
What do I mean? Darling, how's Hanna?
I told you.
She's become a singer.
And she's in love.
Darling? Why do you get heavier by the day?
Let's keep on dancing.
A delivery for you.
"Hanna, I'm so grateful for your hard work." "Wear this dress to my birthday party."
"HAN Sang-jun" HAN Sang-jun?
It's a dress?
What's this?
A strap on the bus?
I'm not so sure.
Hi! Hi.
Hanna, sit here.
Come on. Pass around drinks.
Excuse me.
Excuse me. Sorry.
You could've come around.
Thanks.
Just come!
Thanks.
I got you something.
You shouldn't have.
Oh, I love this.
Thanks.
Take off your coat.
It's so heavy.
Aren't you hot?
Make yourself comfortable.
Yes.
Go ahead.
You sent it.
So I'm wearing it.
Yeah? Yeah, Hanna.
Wear a dress like that more often.
I'm totally fine with that.
Right?
I love the design.
She's here.
Is she the Queen? You don't need to announce her.
Let her in.
Where are you going?
I feel like dancing.
Let her through. - Hold on. - What?
They're cleaning.
Use the other restroom.
You're so funny.
How stupid can you get?
I'd never know.
I wanna live with style.
But you're not helping.
That's a problem for me.
Miss backup dancer days?
The bitch gets on my nerves.
If so, you sing.
You think I like her?
You don't have to remind her what a turnoff she is.
Leave her be.
Be grateful she's come to us.
I'll teach her a lesson.
Give me back the keys to the house and the car.
Then teach her a lesson.
Why are you crying?
Why? Hanna is the one to be crying.
She's talented, but ugly and fat.
You're untalented, but gorgeous and sexy.
You got it all going.
She exists for you.
Listen.
We're just using her.
Understood? Be nice to her.
If she walks, it's over. I couldn't be happier dreaming about you. Even if it didn't last long...
Thanks for making me happy. Thank you so much. My wife is showering again.
Pick up the phone. What a story!
Don't tell me you made it up.
Can you make it happen?
Your willpower can.
All I do is to remove a scar from your hurt soul.
How much will it cost?
I'm a doctor, not a businessman.
Is it expensive?
All the things you want done with 30% discount... I'll pay you every penny with interest.
Can I do it on credit? - Ms. KlM? - Yes?
Will you show this lady out?
Don't validate parking.
Jesus protects me How blessed I am Don't you recognize my voice?
Shall we go to the injection room?
And tear up stockings?
Right.
Did you make love last night after she showered?
Who did the eye job on that patient yesterday?
It was horrible.
And what's up with meals for patients?
They complained to me.
Get out! Leave!
Who are you?
I know you're a good person.
You've given your wife a full body makeover.
Now you dread laying your hands on her.
You must know how I feel.
I've done crazy things during phone sex.
You say they don't respect plastic surgeons.
That's because they don't deal with lives.
I'm doing this so I can live a life.
Not to satisfy my vanity.
It's the right cause you've been looking for.
Right? Did you memorize all that?
You could die from all these.
I died yesterday.
Go ahead.
I knew you'd do that so I made a copy.
You'll put it on the net?
You can't blackmail me!
My life is in your hands.
You can end it.
Or save it.
- Yes? - Get me my operation schedule.
These eyes.
What about a nose?
Okay, this.
Without a mole.
Pick the face shape from these actresses.
Which one? Kate Moss!
Meet a skinny, pretty master and live happily.
Okay? Love... I love you!
Here we go.
Count backwards from ten.
Ten, eleven, twelve... Backwards!
Nine, eight, seven... Ammy's 2nd album postponed You call yourself an agent?
Call me now, or I'll report you missing. Years of suffering is over.
Make peace with yourself and enjoy freedom.
What was once you... It's gone forever.
We'll redo the nose.
You bought me this saying that I'd be as pretty.
Remember?
I'll be pretty soon.
That... That's me?
Sir, it's flawless.
That's the only flaw.
It's too natural.
I even cry prettily.
Hey! Take it easy.
Your jawbone will drop.
- Hi.
- Hi. Nurse Locker Room
# I'm a beautiful girl So beautiful
# Beauty is my weapon
# I'm a beautiful girl
# So beautiful Everybody loves me
# I'm a beautiful girl Line up, please.
What a surprise to see you at a signing event.
I love your sitcom.
Rating is 5%?
That's hard to achieve.
5%!
Give me those songs you're not using.
For Pink.
Bye. Smile, dude.
Miss?
That's for your eyes.
I don't wanna do the sitcom.
It cost me a fortune to get you in it.
Get in the car.
Sure.
Sir?
Are you okay?
God, it must hurt.
What a waste!
Were you delivering? Or... You got a cut here.
I'm sorry.
Dude, are you okay?
- Are you okay? - Yes.
An automatic transmission with full options.
You're into speed?
What?
How much is this?
I wouldn't recommend it.
It has a lot of miles on it, and the brakes are bad.
No air conditioning?
What do you expect for 5 grand?
It's pretty bad.
Who would buy this?
- I'm sorry. - It's okay.
It's okay. It's okay.
This can be a good practice car... ...for novice drivers.
Check out something else.
I'd be happy to get rid of this junk.
But my conscience won't allow me.
Bye.
Come on.
You know what?
You're gorgeous.
Don't mind me saying this.
You're beautiful.
I made the right decision.
I needed a car.
The seatbelt?
It's only 5 grand.
No problem. "You're gorgeous." "You're beautiful."
It's a bad business day. And you've added insult to injury.
Get out of the car.
Get out!
I'll bill you for a year's treatment.
I can't believe this is happening.
See what she's done?
Damn!
What'd you honk for?
Get the hell up, asshole.
What?
Fucking lunatic. No name calling, asshole!
Bring it on, fuckface!
Yeah, run!
What a moron!
Can you believe this?
She has no conscience.
Damn!
Sir... If you can't drive, don't!
The road is so wide.
Why crash into me?
I live from hand to mouth, and you ruined...
- You okay?
- What?
You look familiar.
Ever been in my taxi?
You're blocking the traffic!
Direct the traffic. Move it.
We have an accident here.
You okay?
Yes.
Not hurt? No, I'm totally fine.
God!
Hey, you're bleeding.
Are you okay?
Absolutely.
But...
It doesn't hurt. This is embarrassing.
I'm really okay.
The damage to your car is bad.
Know any garage?
I know a good one.
What's your cell number?
What?
I saw the whole thing.
You cut in front of her.
Didn't I?
What was I thinking?
Check her license.
She might not have one.
Are you a cop?
Check her license!
Can I see it?
Here.
There's nothing to worry.
If your friend confirms your ID, we'll let you go.
I knew she didn't have a license.
How convenient.
Plastic surgery?
Which hospital is it?
I should get it done, too.
Ma'am?
Her friend is coming.
We don't need her, do we?
Right.
Hanna?
Hanna?
Pork.
I want some... Pork.
Why didn't you feed her?
We sure did!
You should've fed her 3 portions at a meal.
Let's get out of here and eat some pork.
God, you've lost so much weight.
When'd you get a perm?
Jung-min?
Do I know you?
Hanna?
You...
It's really you! What?
The silicon might slip out of place.
Look at you!
What? Go where?
I shouldn't?
They'll recognize you.
You disappeared a year ago.
They've been looking all over for you.
You ruined Ammy's 2nd album.
They're looking hard for your replacement.
I can be the replacement.
They'll like me since I have the same voice.
No? If they find out, you're done.
You didn't recognize me until I told you.
No way!
I hate myself I know I'm fool But, I can't stop loving you It hurts me You're hurting my ears.
See you later.
I'm just so nervous.
Give me another shot.
Get out!
Okay.
Excuse me? Here.
A Korean-American?
Yes.
Send her in.
Jenny?
It says here you're fluent in Korean.
A little bit.
Lose those shades.
Face us, will you?
Hit it.
# The wind knocks on the window
# Over the room as small as me
# Twinkling stars so beautiful Filling the room with love
# Don't be hurt
# Caressing my wound gently
# Embracing me to sleep
# Too hurt for my legs to walk
# Eyes so blurry with tears
# Before love Never meant for me
# I will keep on smiling She's a slugger.
Look at her, man.
She's far from a slut.
# Like those stars embroidered in my eyes
# I will love you forever I think it's over.
Wait outside, please.
Okay.
We're good now!
We're good!
Sang-jun, congratulations.
Putting out my album now?
Leave us alone.
Leave. Ammy, let's go.
Look.
Can't you see who she is?
Huh?
You know me, don't you?
I think I know you.
You can tell?
You can, can't you?
Of course I can.
Why can't you be honest?
Thought you could fool me?
I'm sorry.
I'm so sorry.
Listen. I just... You're no different.
Why lie to me?
I'm sorry. I'm so sorry.
The department store, the used car market... You followed me?
Thought I wouldn't know?
You told her I'm the best producer in the business?
Yes, I am.
Why couldn't you face me... ...and tell me you wanna be a singer?
Yes, I do.
I want to be a singer.
Right? Yes, she'll be awesome.
A top singer.
Let's go!
What's wrong with you?
Bye.
She's a dog.
Why the tears?
Look what you did.
You made her cry.
By the way... Let's get your face fixed up.
Slit your eyes bigger and get your nosed raised.
No! No way.
You know what?
I'm too scared to go under a knife.
Plastic surgery?
I would never do it.
It's for those who lack confidence in themselves.
What?
Wait.
Are you telling me I'm not pretty enough?
No, I'm not.
A natural beauty?
I love it! Good for building your image.
Right, Sang-jun?
So you're all natural?
I surely am.
Let's sign a contract.
Take a good look at her.
Think about it, Dad.
Jenny has a quality that you can't find... ...in any other girls today.
What's so special about her?
She looks a bit awkward.
Personally, I prefer Ammy.
An image of innocence.
A natural beauty.
It's what money can't buy.
Right. That's what it is.
You're sleeping her, aren't you?
She's not a tramp.
She has a special quality that money can't buy.
Can't you see that?
You're a hound dog.
Look who's talking.
Dad?
Come on! We don't need his help.
Let's just do it.
Don't disappoint me.
It'll speed up things.
I can't kiss his ass anymore.
Come on!
What?
This isn't so like you.
What's your good quality?
Perseverance!
Why trashing it now?
I'm counting on you.
Big brother. You trust me, don't you?
Don't call me that.
I'm only 13 months older.
Let's do this, okay?
God damn it!
You're bad!
Dad, please... Dad!
Okay, that's it.
Just like that.
That's good.
Good!
Okay!
Ammy!
Drag it out at the end.
They'll go crazy.
Pee...
Pee...
Pee is coming.
Excuse me? Nurse!
What's new isn't always good.
That's not it.
You're making me sick of what I had before. You want me to walk?
You'll be sorry.
I never look for a dog that's run.
I always find my dog, no matter what.
Watch me. I'll find Hanna.
Don't bring Hanna up!
Stop talking about her. More coming. If she was worried about her father... ...she would've showed up long ago.
You're wasting your time.
Focus on the sitcom.
Memorize your lines.
I'm a singer.
You realized that now?
Hello?
I'm a singer. A singer!
I want to be a singer!
A singer!
God is the only one who can do everything.
We humans do what we're capable of.
Jung-min, look at him.
He's been waving at me.
What took you so long?
I've been admiring you.
What are we doing today?
We're making you happy.
How does that sound?
That's right.
I'm THE Jenny.
Put suntan oil on me.
Why should I?
You have nice boobs.
Of course.
They're natural, right?
You're a natural beauty, aren't you?
Of course!
It's done so naturally.
I'm natural.
Turn around.
Come on. Good.
Hey, you're so fair-skinned. You're from California, right?
Yes.
Did you live in the basement?
You look like a bean curd.
So tacky. Never got a tanning?
Never been to a tanning saloon?
So? You covered your breasts for 3 hours?
You thought they'd pop inside the tanning machine?
That's a load of bullshit.
She got a boob job, too.
You're talking about one on that sitcom, right?
She has bags of saline solution for boobs.
They hurt when touched.
And they don't feel good to touch.
That's why I put silicone bags in you.
Right?
Not because they're cheaper.
Right? Please, tell me.
I'm sad. So sad.
Do you know what it is?
It's lack of confidence.
Didn't I tell you?
Unless you act confidently, you can't win his heart.
Beauty is attitude, okay?
This is an engine.
No way I'm doing that.
# Here we go again
# Make it hot, Baby
# Oh.
Don't be afraid
# High in the sky
# The sun shines the way
# Oh.
Don't you stop, Baby
# Maria... Let's call it a day.
What do you say?
The video quality is good.
What cam did you use?
Not that.
What do you feel from her song?
Her song carries her heart... ...for someone that she loves.
I think. No?
Can't you sing like her?
You care too much about how you look.
Come on, she's ugly.
You must've been embarrassed seen with her.
Stop it!
She was special to me.
You're here, thanks to her.
Still... You're no half of her.
Why are you crying?
Are you nuts?
So you'll confess to him?
After all this?
You've committed a fraud.
So I should do it before it's too late.
He'll understand.
Remember 3 types of women I told you about?
I'm a pretty one now.
No, it doesn't apply.
You know why?
Those with plastic surgery aren't women. But monsters.
Jung-min...
What are you, an expert in relationships?
You sound like you have tons of experience.
More than you.
At least, my love isn't one-way.
Oh, you're in a crazy love?
With whom? This guy?
Is he in love with you, too?
Or trying to sell you stuff?
You ransacked my bag?
You didn't empty the pockets after wearing my clothes.
Whatever it is... Don't buy anything from him.
I'm not like you.
I know.
Like I did. No, like the old Hanna.
Don't do everything his way like a fool.
At the end of the day, you get the same thing. "We're too different." He'll never say you're ugly and fat.
Like the old saying, nothing beats experience.
Confess to him.
What are you doing here?
That video... Should we study it more?
Come in.
Mr. CHOI once told me.
Do many Korean girls do plastic surgery?
I'm just asking.
What do you think about it?
Didn't you tell me you didn't understand?
What are you doing?
You said it was for those who lack confidence.
I think the same.
Stop it.
Come here.
Sorry. Let's go.
We're doing the concert.
It's been a while.
Love!
How'd you end up here?
What happened?
I'm sorry.
It's my bad. Love!
You feed her raw fish?
Why am I yawning?
She loves raw fish.
Anyway, we're on the same page about plastic surgery.
Go away.
Then again... Desire to become pretty isn't a bad thing.
Men who are only after pretty women are bad.
And these days...
Okay, okay. And these days...
Hey.
Bang!
And it's like cosmetics today.
Why do they hide it then?
They hate revealing it.
It's a lame self-justification.
Can't you see?
That's why you stand out in this business.
This is fresh.
Eat some.
About plastic surgery... I've thought about it.
I think I can understand.
Only if it's not my girl.
I absolutely hate it.
But I understand.
Let's go.
Go, Natural beauty!
Goodnight.
Jenny!
Out of the way!
Hi.
What's wrong?
You shot a film here.
How long has it been?
Who put you up to this?
Put it out.
Nobody did.
I just like her so much.
Aren't you that delivery man?
That's right.
You remember me.
I understand, but... Why laughing?
It tickles.
If this gets out, it's the violation of publicity.
I like her so much, and... You like her so much... ...but didn't care how she feels being watched?
Documenting her private life is a crime.
No, it was for myself.
Stop laughing.
This is what stalkers do.
Aren't you ashamed of yourself?
Wait.
Don't be too harsh.
Give him a break.
He did it out of liking me.
What's the big deal?
What's a person to do when all they can do is... ...watch from afar?
Do you have any idea what it feels like... ...not being able to confess one's love?
Excuse me.
How do you know so well how I feel?
This is what you had to say, right?
Daddy...
Ammy!
Let go of me. Let go. Becoming someone new?
I even sweat pretty. Maria.
Ave maria, a~ maria~ mari
Practicing at the sauna will help.
Tell me.
Do you have to sing?
Of course! Singers sing.
You kidding me?
No. All I'm saying is...
Do what you can.
You'd be God if you did everything you want.
What?
It's what my dad says.
God is the only one who can do everything.
We humans do what we're capable of. You're a phony Is this van a phony?
Jenny, it's your phone.
Hello? What?
Jung-min did? To a hospital? Why?
Jung-min tried to kill herself.
It's your first TV show.
You can't screw it up.
My friend is more important!
We were quiet worried.
But we found nothing in her stomach.
It'd been digested.
30 sleeping pills can be lethal for others.
So she's in a coma?
She's just sleeping.
Like a bear hibernating.
It can't be explained medically.
She was lucky.
30 sleeping pills could kill an elephant.
What's this?
She bought this?
A home sauna?
Jenny?
I've been calling you, Babe.
What's going on?
Think of what you want for lunch.
Hey, Su-jin.
How are you?
Su-jung! I meant Su-jung.
Wanna go swimming?
Excuse me.
I'll call you back.
Did you dump her because you loved her?
Why so fast?
You should've waited to see what a home sauna can do.
Did you tell her not to go on a diet? "I'll be upset if you lose weight." You told her so?
Why didn't you be a man and tell her the truth?
And you were desperate... ...to sell your products.
If you loved her... Why'd you have to dump her?
You bastard!
Wait! What's wrong?
You don't know?
Is it a crime to be ugly?
We're not charity cases.
I have so much to say, but... Wait! Who are you?
Damn!
What's going on?
Who's this?
Who are you?
Oh, you're in this together.
Calm down!
Hey! You two are dead.
Stay right here.
I'll call the cops.
You okay?
My nose...
What'd I tell you?
That miniskirt is an invitation to a rapist.
Look what happened.
Sorry. What if I was late? Let's go.
Get her dress!
She's here.
1 minute to go.
Standby.
What happened?
How much time?
Look who's here.
Isn't this Sang-jun?
What's that?
Is that her concept?
Sang-jun, this concept doesn't appeal to me.
Hurry!
Don't worry.
They'll love your voice.
This is it.
Show them what you got.
We can't lose to them.
Right.
Can you do it?
Okay. I believe in you.
No matter what...
Get a room! Get out there!
Okay, Jenny.
They're not a couple.
Trust me.
Here is Jenny!
"Maria"
# Here we go again
# Make it hot, Baby
# Oh, don't be afraid
# High in the sky The sun shines the way
# Oh, don't you stop, Baby
# Maria Ave maria
# Fly and catch those clouds
# Maria Ave maria
# Strong against violent waves She's pretty good.
# Maria Ave maria She's good.
# Fly and catch those clouds
# Maria Ave maria
# Strong against violent waves What's her concept?
It's singing.
What's yours?
Strawberry milk?
# Maria Ave maria
# Flay and catch those clouds
# Maria Ave maria
# Strong against the violent waves
# Maria~ This sauna thing is okay. You're a phony
Spit out the gum. "Jenny" "New star comes up!"
I'm drunk. God, this is awkward.
He'll know they're fake if he touches them.
Not there.
Not there, either.
Should I sing for you?
You wanna work now?
This way.
What?
Come on.
Jenny?
Answer it.
Answer it, will you?
I know it all.
You even watch porn.
What are we doing?
What type do you want?
A nurse, a high school girl, a secretary?
What? A nurse?
Okay, it's a favorite pick.
A nurse it is.
Jenny, open the door.
This isn't it.
Just try to relax.
It'll help.
What should I do with it?
Should I rip it?
See? There you go.
You can wear it over your head.
Hakuna Matata. The African symbol has granted me my wish.
Do many Korean girls do plastic surgery?
Do you know how it feels hiding your love? You wrote this song? Yes.
What are you doing?
Watching porn again?
About last night... It never happened, okay?
Last night...
Hello?
Damn, she's almost naked.
I'll be back.
Hey.
Hey!
Congrats! Your fan is here.
Someone dying to see you.
I can't hear you.
What?
I brought this for you. - Here.
- What are you doing?
What are you doing?
Take it.
You know him?
Just... A fan of mine, I hear.
Who brought him?
Did you?
Take him back home.
He's your fan.
Why didn't you take the doll?
Jung-min... Let's go.
Still here?
Go to bed early for the concert tomorrow.
I know that old man.
I know.
He's your fan.
No. I mean he is... Stop it.
KANG Hanna.
What'd you just call me?
Don't worry.
Nobody else knows.
I didn't, either.
When'd you find out?
Is that important?
You're Jenny now.
And it's Jenny's first concert tomorrow.
How... You knew he was my dad?
I gave both Hanna and Jenny a chance.
It's scary.
So I'm only a product.
Hanna is worthless, but Jenny is worth a fortune.
Is that it?
Because of you... That I've been deceiving you... It's been so hard.
Now I see I was a big fool.
Why'd you take my dog?
As a hostage?
That's enough.
You find me repulsive with plastic surgery?
I said enough! Stop it.
So you avoided me.
Watch your voice.
I'll do the concert.
They're repulsive and scary.
I'm fine.
It doesn't hurt.
It's nothing, compared to what I went through. I cut off my bone and skin.
Laying on the table... You know whom I thought of?
I never knew... I thought that was painful.
But this is worse.
You broke my heart.
Tissue won't fix it.
Now you cut yourself?
You should be able to fix something simple like this.
Give it a shot, okay?
Thanks, Doc.
That ticket is expensive.
Please, come.
I want money, not a concert ticket.
God damn it!
It's complimentary!
What's wrong?
Aren't you going to the concert?
Someone sent this.
I'm sorry.
I'll take the responsibility.
You will?
Okay then.
Cancel the concert.
I can't do that.
Dad, that's unnecessary.
I will quit.
Stay out. If we don't, this will go to the press.
That she was a singer for Ammy.
It isn't just about the label.
What about cosmetics?
You'll eat them all?
You know the contract inside and out.
Unless you'll pay penalty, do as I say.
Put out her nude album.
Do it before it's too late.
We'll squeeze out of her whatever we can.
Dad!
You're grown old.
And scared.
Son of a bitch, I made you who you are!
Company's stock price... You forgot who helped it rise?
I know who's behind this.
I'll handle it.
We're doing the concert.
And it'll be a success.
Let's go.
We have a concert to do.
Get up.
Damn, he messed it up.
I made it worse.
You said it didn't hurt.
But it does.
Don't worry about it.
I'll handle Ammy.
Jung-min, last night... I'm sorry.
About what?
You brought my dad?
Your dad?
Oh, that old man?
He slept at my place.
Cause he was locked out of the hospital.
And, doesn't he have to see your concert?
If you got a problem, tell me.
Then again, he means nothing to you.
Jenny!
Jenny!
Jenny!
Jenny!
Why can't you do it?
I said it was okay.
Don't you get it?
This isn't for me nor Ammy.
It's your show.
Do it for yourself.
For nobody else, but yourself.
Stop!
I can't do this.
I really can't.
I'm sorry.
I'm really sorry.
I'm not Jenny.
I'm Hanna.
KANG Hanna.
I was an ugly, fat girl.
So... I sang for someone else hiding in the back.
Then I got plastic surgery.
From head to toe... Everything.
Now that I'm pretty... I can sing.
I've been in love.
I was so happy being Jenny.
But I'm sorry.
I ruined it.
I've deserted my friend.
My dad.
And myself.
I don't know who I am anymore.
I can't remember what I looked like.
I miss you, Hanna.
Hanna... That's me.
KANG Hanna.
It's okay.
It's okay. It's okay.
It's okay.
Dad!
Jenny isn't here.
But if you wanna hear... ...that fat, ugly girl sing... Please, listen to me sing once for all.
# Crawling to me like a dream
# My little star up high Dazzling my eyes
# Shining brightly
# Falling on my shoulders
# Don't be sad anymore
# Holding my hands tightly Caressing my wound
# It embraces me warmly
# Too hurt for my legs to walk
# Eyes so blurry with tears
# Before love Never meant for me
# I will keep on smiling
# Dear moments with you
# Buried deep in my heart
# Like those stars embroidered in my eyes
Look at you.
Your undershirt shows.
Can you tell?
No.
No, you can't.
Dad, I really didn't know.
Sang-jun, I love this.
# Like those stars embroidered in my eyes
# I will love you forever "A Shocking Confession Jenny was a fake!" Jenny went down like that.
Lower it a bit.
Make it lower.
That's nice.
It's cool, isn't it?
Leave!
It's cool. She's got more fans now. More anti-fans, too.
Hey! "A pig"? I'll kill you!
Stay away from me! I don't think she likes me anymore.
I'm doing my best.
Your best isn't enough.
Doing well is what counts. I don't wanna admit it... ...but people say I like her more now.
What do you like about her?
I don't know.
Because she's pretty?
Assholes like you would say so.
Because she's innocent?
Assholes like me would say so.
I'm the famous Dr. Lee, known as Hand of God.
I might win the next Nobel Prize.
What do you want fixed?
My whole body.
Your whole body?
Every time I close my eyes I see you in front of me
I still can hear your voice calling out my name
And I remember all the stories you told me
I miss the time you were around
But I'm so grateful for every moment I spent with you
'Cause I know life won't last forever
You went so soon, so soon
You left so soon, so soon
I have to move on 'cause I know it's been too long
I've got to stop the tears, keep my faith and be strong
I'll try to take it all, even though it's so hard
I see you in my dreams but when I wake up you are gone
Gone so soon
Night and day, I still feel you are close to me
And I remember you in every prayer that I make
Every single day may you be shaded by His mercy
But life is not the same, and it will never be the same
But I'm so thankful for every memory I shared with you
'Cause I know this life is not forever
You went so soon, so soon
You left so soon, so soon
I have to move on 'cause I know it's been too long
I've got to stop the tears, keep my faith and be strong
I'll try to take it all, even though it's so hard
I see you in my dreams but when I wake up you are gone
Oh, there were days when I had no strength to go on
I felt so weak and I just couldn't help asking:
"Why?"
Oh, but I got through all the pain when I truly accepted
That to God we all belong, and to Him we'll return, oh
You went so soon, so soon
You left so soon, so soon
I have to move on 'cause I know it's been too long
I've got to stop the tears, keep my faith and be strong
I'll try to take it all, even though it's so hard
I see you in my dreams but when I wake up you are gone
Gone so soon
So soon
Now, I want to start with a question:
When was the last time you were called "childish"?
For kids like me, being called childish can be a frequent occurrence.
Every time we make irrational demands, exhibit irresponsible behavior, or display any other signs of being normal American citizens, we are called childish. Which really bothers me.
After all, take a look at these events:
Imperialism and colonization, world wars, George W. Bush.
Ask yourself, who's responsible?
Adults.
Now, what have kids done?
Well, Anne Frank touched millions with her powerful account of the Holocaust.
Ruby Bridges helped to end segregation in the United States. And, most recently,
Charlie Simpson helped to raise 120,000 pounds for Haiti, on his little bike.
So as you can see evidenced by such examples, age has absolutely nothing to do with it.
The traits the word "childish" addresses are seen so often in adults, that we should abolish this age-discriminatory word, when it comes to criticizing behavior associated with irresponsibility and irrational thinking.
(Applause)
Thank you.
Then again, who's to say that certain types of irrational thinking aren't exactly what the world needs?
Maybe you've had grand plans before, but stopped yourself, thinking, "That's impossible," or "That costs too much," or "That won't benefit me."
For better or worse, we kids aren't hampered as much when it comes to thinking about reasons why not to do things.
Kids can be full of inspiring aspirations and hopeful thinking, like my wish that no one went hungry, or that everything were free, a kind of utopia.
How many of you still dream like that, and believe in the possibilities?
Sometimes a knowledge of history and the past failures of Utopian ideals can be a burden, because you know that if everything were free, then the food stocks would become depleted and scarce and lead to chaos.
On the other hand, we kids still dream about perfection. And that's a good thing, because in order to make anything a reality, you have to dream about it first.
In many ways, our audacity to imagine helps push the boundaries of possibility.
For instance, the Museum of Glass in Tacoma, Washington, my home state -- yoohoo, Washington!
(Applause) has a program called Kids Design Glass, and kids draw their own ideas for glass art. The resident artist said they got some of their best ideas from the program, because kids don't think about the limitations of how hard it can be to blow glass into certain shapes, they just think of good ideas.
Now, when you think of glass, you might think of colorful Chihuly designs, or maybe Italian vases, but kids challenge glass artists to go beyond that, into the realm of brokenhearted snakes and bacon boys, who you can see has meat vision. (Laughter)
Now, our inherent wisdom doesn't have to be insider's knowledge.
Kids already do a lot of learning from adults, and we have a lot to share.
I think that adults should start learning from kids.
Now, I do most of my speaking in front of an education crowd -- teachers and students, and I like this analogy:
It shouldn't be a teacher at the head of the class, telling students, "Do this, do that."
The students should teach their teachers. Learning between grown-ups and kids should be reciprocal.
The reality, unfortunately, is a little different, and it has a lot to do with trust, or a lack of it.
Now, if you don't trust someone, you place restrictions on them, right?
If I doubt my older sister's ability to pay back the 10 percent interest I established on her last loan,
I'm going to withhold her ability to get more money from me, until she pays it back. (Laughter)
True story, by the way.
Now, adults seem to have a prevalently restrictive attitude towards kids, from every "Don't do that, don't do this" in the school handbook, to restrictions on school Internet use.
As history points out, regimes become oppressive when they're fearful about keeping control.
And although adults may not be quite at the level of totalitarian regimes, kids have no or very little say in making the rules, when really, the attitude should be reciprocal, meaning that the adult population should learn and take into account the wishes of the younger population.
Now, what's even worse than restriction, is that adults often underestimate kids' abilities.
We love challenges, but when expectations are low, trust me, we will sink to them.
My own parents had anything but low expectations for me and my sister.
Okay, so they didn't tell us to become doctors or lawyers or anything like that, but my dad did read to us about Aristotle and pioneer germ-fighters, when lots of other kids were hearing
"The Wheels on the Bus Go Round and Round."
Well, we heard that one too, but "Pioneer Germ Fighters" totally rules. (Laughter)
I loved to write from the age of four, and when I was six, my mom bought me my own laptop equipped with Microsoft Word.
Thank you, Bill Gates, and thank you, Ma.
I wrote over 300 short stories on that little laptop, and I wanted to get published.
Instead of just scoffing at this heresy that a kid wanted to get published, or saying wait until you're older, my parents were really supportive.
Many publishers were not quite so encouraging.
One large children's publisher ironically said that they didn't work with children.
Children's publisher not working with children?
I don't know, you're kind of alienating a large client there.
(Laughter)
One publisher, Action Publishing, was willing to take that leap and trust me, and to listen to what I had to say.
They published my first book, "Flying Fingers," you see it here. And from there on, it's gone to speaking at hundreds of schools, keynoting to thousands of educators, and finally, today, speaking to you.
I appreciate your attention today, because to show that you truly care, you listen. But there's a problem with this rosy picture of kids being so much better than adults.
Kids grow up and become adults just like you.
(Laughter)
Or just like you? Really?
The goal is not to turn kids into your kind of adult, but rather, better adults than you have been, which may be a little challenging, considering your guys' credentials. (Laughter) But the way progress happens, is because new generations and new eras grow and develop and become better than the previous ones.
It's the reason we're not in the Dark Ages anymore.
No matter your position or place in life, it is imperative to create opportunities for children, so that we can grow up to blow you away.
(Laughter)
Adults and fellow TEDsters, you need to listen and learn from kids, and trust us and expect more from us.
You must lend an ear today, because we are the leaders of tomorrow, which means we're going to take care of you when you're old and senile.
No, just kidding.
(Laughter) No, really, we are going to be the next generation, the ones who will bring this world forward.
And in case you don't think that this really has meaning for you, remember that cloning is possible, and that involves going through childhood again, in which case you'll want to be heard, just like my generation.
Now, the world needs opportunities for new leaders and new ideas.
Kids need opportunities to lead and succeed.
Are you ready to make the match?
Because the world's problems shouldn't be the human family's heirloom.
Thank you.
(Applause)
Thank you.
Thank you.
Welcome to the video on 'basic subtraction.'
Let's do a little bit a review of 'basic addition' first.
If I said '4 plus 3' (4 + 3), what would this mean?
What did that equal?
Well, there are a couple of ways we could have viewed this.
We could have said, "I had 4 of something."
Let's say I had 4 circles - or, I don't know -
I had 4 lemons for breakfast.
So 1, 2, 3, 4 lemons for breakfast.
And let's say I had another 3 lemons for lunch.
1, 2, 3.
"How many total lemons did I have?"
I'm adding 3 to 4.
So how many total did I have?
Well, it's (COUNTlNG:
1, 2, 3, 4, 5, 6) 7.
So I had a total of 7 lemons.
Another way we could have viewed that is we could have drawn our 'number line.'
(And I'll draw it in yellow because we're -
So let's say that's our number line.
And if I start at the number - (Let me draw all of the numbers.) 0, 1, 2, 3, 4, 5, 6, 7.
We start at the number 4. Right? (That's this number 4.)
So we'll increase along the number line by 3.
So we'll go 1, 2, 3 - and you end up at 7.
So you could say,
Or, "If I increase 4 by 3, I also get 7."
So what's 'subtraction' now?
So let's take the example of 4 minus 3 (4 - 3).
What is that equal to?
So what is 4 - 3 equal to?
Subtraction - or 'minus' - is the opposite of addition.
So in addition, you're doing something more.
I had 4 lemons, and then I had 3 more.
In 'subtraction,' you're taking away.
So in this example, if I started with 4 lemons -
If I'm subtracting 3 - If I'm saying minus 3, Instead of adding these 3 here, and getting 7,
So to take away 3 from this 4 - Let's say this one goes away. This one goes away.
How many lemons would we have left?
Well, this is the only one that I haven't crossed out. So we would have 1 lemon left.
Another way to view that - (Let's draw the same lemon colored number line.)
Let's say that this is the number line, right here.
And I'll draw all the same numbers.
So that's 0, 1, 2, 3, 4, 5, 6, 7.
Of course, the number line keeps going.
So that's why we draw that arrow there. I could never draw the entire number line.
So we're starting at 4 lemons, right?
When we added 3 - plus 3 - We went to the right 4 spaces on the number line.
And that's because the right is increasing value.
So we went from 4 to 5. That was 1 more.
5 to 6 was 2 more.
Now we're taking away from 4.
So what do we do?
What would you think we do?
Well, since we're taking away, we're going to decrease the total number of lemons we have. Right?
So if we take away 1 - we get to 3.
Take away 2 - get to 2.
Take away 3. We took away 3, right?
So we'll go back [to the left] 1, 2, 3 along the number line.
And we'll end up at 1.
So, just to review, addition is when you're getting more of something.
Subtraction is when you are taking something away.
If you think about it on the number line, addition is increasing along the number line by that amount.
So, in this case, we increased along the number line by 3.
And so we went from 4 to 7.
In the subtraction case, we decrease back [to the left] on the number line. So we decrease by the amount that you're subtracting.
So, in this case, we decreased by 3.
So we went back [to the left]
And the other way to view it - if I have 4 of something - if I give 3 away - or if I ate 3 of them -
If I lost 3 of them I would have 1 left.
Now let me show you some interesting things about subtraction.
So we know that 4 minus 3 is equal to 1.
What is 4 minus 1?
Let's say I had 1, 2, 3, 4.
Let's say I had 4 apples.
And I were to eat one of them.
So one of them were to go away.
How many apples would I have left?
Well, 3-- 1, 2, 3.
So 4 minus 1 is equal to 3.
And if we did it on the number line, if we started at 4 and we subtracted 1-- we took 1 away.
So we're going to become one smaller.
We go back one, we get 3.
Either way works.
4 minus 3 is equal to 1 and 4 minus 1 is equal to 3.
But I'll show you another interesting thing.
What is 3 plus 1? 3 plus 1 is equal to what?
Well, that's easy.
You know that from basic addition.
You can start on the number line at 3 and add 1 do it.
You end up at 4.
3 plus 1 is equal to 4.
Or you could have started at 1 on the number line and added 3.
1, 2, 3 and you would have also ended up at 4.
So we also know that you could have switch this either way.
Both of those are equal to 4.
What do you see here?
Well, there's a bunch of things I've written here and they all kind of relate to each other.
1 plus 3 is equal to 4.
3 plus 1 is equal to 4.
4 minus 1 is 3.
Essentially, 4 minus 1 and getting 3 is the exact same-- you're saying the same thing as 3 plus 1 is equal to 4.
This statement says if I add 1 to 3 I get 4.
This is saying if I take away 1 from 4 I get 3.
Hopefully that gives you a little bit of intuition about what subtraction is.
In the next video I'll just do as many basic subtraction problems I can do in 10 minutes.
And then you'll be ready to do the exercises.
See you soon.
This is really a two-hour presentation I give to high school students, cut down to three minutes.
And it all started one day on a plane, on my way to TED, seven years ago.
And in the seat next to me was a high school student, a teenager, and she came from a really poor family.
And she wanted to make something of her life, and she asked me a simple little question.
She said, "What leads to success?" And I felt really badly, because I couldn't give her a good answer.
So I get off the plane, and I come to TED.
And I think, jeez, I'm in the middle of a room of successful people!
So why don't I ask them what helped them succeed, and pass it on to kids?
So here we are, seven years, 500 interviews later, and I'm going to tell you what really leads to success and makes TEDsters tick.
And the first thing is passion.
Freeman Thomas says, "I'm driven by my passion."
TEDsters do it for love; they don't do it for money.
Carol Coletta says, "I would pay someone to do what I do."
And the interesting thing is: if you do it for love, the money comes anyway.
Work! Rupert Murdoch said to me, "It's all hard work.
Nothing comes easily.
But I have a lot of fun."
Did he say fun?
Rupert?
Yes!
(Laughter) TEDsters do have fun working.
And they work hard.
I figured, they're not workaholics.
They're workafrolics.
(Laughter)
Alex Garden says, "To be successful, put your nose down in something and get damn good at it."
There's no magic; it's practice, practice, practice.
And it's focus. Norman Jewison said to me,
"I think it all has to do with focusing yourself on one thing."
And push!
David Gallo says, "Push yourself.
Physically, mentally, you've got to push, push, push."
You've got to push through shyness and self-doubt.
Goldie Hawn says, "I always had self-doubts.
I wasn't good enough; I wasn't smart enough.
I didn't think I'd make it."
Now it's not always easy to push yourself, and that's why they invented mothers.
(Laughter) (Applause)
Frank Gehry said to me,
"My mother pushed me."
(Laughter)
Serve! Sherwin Nuland says, "It was a privilege to serve as a doctor."
A lot of kids want to be millionaires.
The first thing I say is:
"OK, well you can't serve yourself; you've got to serve others something of value.
Because that's the way people really get rich."
Ideas!
TEDster Bill Gates says, "I had an idea: founding the first micro-computer software company."
I'd say it was a pretty good idea.
And there's no magic to creativity in coming up with ideas -- it's just doing some very simple things.
And I give lots of evidence.
Persist!
Joe Kraus says,
"Persistence is the number one reason for our success."
You've got to persist through failure.
You've got to persist through crap!
Which of course means "Criticism, Rejection, Assholes and Pressure."
(Laughter)
So, the answer to this question is simple:
Pay 4,000 bucks and come to TED.
(Laughter) Or failing that, do the eight things -- and trust me, these are the big eight things that lead to success.
Thank you TEDsters for all your interviews!
I am back.
Where were we?
We were saying that we know that velocity, or kind of a change in velocity, is acceleration times time.
I just wrote that a little bit more formally, really kind of incorporating the change in velocity. Right?
The final velocity is equal to the initial velocity plus acceleration times time.
I actually could have written it like this:
I could have written vf minus vi is equal to acceleration times time, and this is the change in velocity.
Actually, that's the way I should be doing it.
As you can tell, I kind of do some of this stuff on the fly, but I do that for a reason-- it's because I want you to get the same intuition that I hopefully have, instead of just kind of doing it in a very formal way in a book, and sometimes the book doesn't necessarily make the connections in the most natural way.
This is going straight from my brain to this video, and hopefully into your brain.
These are all ways of saying the same thing, and I actually should write this as change in velocity-- that triangle, or delta, just means change.
The final velocity, my initial velocity, is equal to acceleration times time.
The average velocity, you could just figure-- you take the final, and you take the initial, and you average the two, and it's equal to this.
Then I said, we know what the final velocity is-- this is the final velocity, and the average velocity is this.
We substitute it for the final velocity, and then we came to this equation for average velocity.
Then before I almost ran out of time, I said I'm going to take this formula for the average velocity-- and I really encourage you to just play around with these formulas yourself and derive it yourself, because it's going to pay huge rewards later on when you forget the formulas on your exam, but you can work it out anyway.
We have this formula for average velocity, and let's substitute it back into this, so we can say that distance is equal to the average velocity, and that's this: vi plus at over 2 times time.
If we just distributed that t, we have the initial velocity times time, plus acceleration times time squared over 2.
So, distance is equal to the initial velocity-- let me draw a line here, so we don't confuse things-- distance is equal to the initial velocity times time plus acceleration times time squared divided by 2.
Sometimes the physics teacher might just teach at squared 2-- that's sometimes what people memorize, and that's because in a lot of these projectile motion problems, your initial velocity is 0, especially when you're dropping a rock.
If your initial velocity is 0, this term would cancel out.
If you do that last problem that we just did using this example, you'll get the same answer.
I said we're accelerating with gravity, so a is equal to 10 meters per second squared, then time is equal to 2 seconds, and then initial velocity is equal to 0, and
The initial velocity is 0-- so this term just cancels out-- plus acceleration, 10 meters per second squared times time squared.
You have 10 meters per second squared times time squared, time is two seconds, so it's 4.
Since we've squared the number, we should also square the units, so it's 4 seconds squared, and all of that is over 2.
Like we learned before-- 10 times 4 divided 2 is 20, and we have seconds squared the denominator and we have seconds squared in the numerator here.
They cancel out, and we're just left with meters.
Actually, I'm going to leave it there for now, and in the next presentation, I'll explore some of these mechanics even further.
I'll see you soon.
We are asked to solve log of x plus log of 3 is equal to 2 log of 4 minus log of 2.
So we have the log of x plus the log of 3 is equal to 2 times log of 4 minus log of 2.
And this is reminder: whenever you see logarithm written without a base, the implicit base is 10.
So we could write 10 here, here, here and here.
But for the rest of this example, I'll just skip writing 10 just cause it'll save a little bit time.
But remember it only means log base 10.
So this expression right over here is the power I have to raise 10 to get x.
Power I have to raise 10 to get 3.
Now that out of the way, let's see what logarithm properties we can use.
So we know -- and these are all the same base -- we know that if we have log base a of b plus log base a of c that this is the same thing as log base a of bc.
And we also know -- so let me write all of the logarithm properties that we know, over here.
We also know that if we have a logarithm --
let me write it this way actually b times log base a of c this is equal to log base a of c to the b-th power.
And we also know -- and this is derived really straight from both of these, is: that log base a of b minus log base a of c that this is equal to
And this is really straight derived from these two right over here.
So right over here we have -- all of the logs are the same base -- we have logarithm of x plus logarithm of 3, so by this property right over here -- the sum of the logarithms of the same base this is going to be equal to log base 10 of 3 times x of 3x.
Then based on this property right over here this thing can be rewritten, this is going to be equal to this can be written as log base 10 of 4 to the second power, which is really just 16. and then we still have minus logarithm base 10 of 2.
And now using this last property -- we know we have one logarithm minus another logarithm.
This is going to be equal to log base 10 of 16 over 2, 16 divided by 2, which is the same thing as 8.
So right-hand side simplifies to log base 10 of 8 the left-hand side is log base 10 of 3x.
So if 10 to some power is going to be equal 3x, 10 to the same power is going to be equal to 8.
So 3x must be equal to 8.
3x is equal to 8.
And then we can divide both sides by 3.
You get x is equal to 8 over 3.
One way this little step here I said: look this is an exponent.
If I raise 10 to this exponent I get 3x, 10 to this exponent I get 8.
So 8 and 3x must be the same thing.
let's take 10 to this power on both sides.
So you could say 10 to this power and then 10 to this power over here.
If I raise 10 to the power that I need to raise 10 to get 3x well I'm just going to get 3x!
If I raise 10 to the power that I need to raise 10 to get 8
I'm just going to get 8.
So once again you get 3x is equal to 8.
And you can simplify,you get x is equal to 8/3.
 I'm sure many of y'all have already heard of the molecule DNA, and it stands for deoxyribonucleic acid.
I wrote it out ahead of time to spare you the pain of watching me spell this in real time.
But it is-- and I think you already have an idea. This is the basic unit of heredity, or it's what codes all of our genetic information.
And what I want to do in this video-- because I think that's kind of common knowledge.
That's popular knowledge that, oh, everything that makes my hair black or my eyes blue or whatever, that's all somehow encoded in our DNA.
But what I want to do in this video is give you an idea of how something like DNA, a molecule, can actually code for what we are.
How does the information, one, get stored in this type of a molecule, then how does that actually turn into the proteins that make up our enzymes and our organs and our brain cells and everything else that really make us us?
So this is a computer graphics representation of DNA, and I'm sure many of y'all have heard of the double helix.
And that's in reference to the structure that DNA takes.
And you can see here it's a double helix.
As you can see here, you have two of these lines, and they're intertwined with each other.
You see there, that's one of them, and then you see another one intertwined like that.
And then they're connected by-- you can almost view it as like these bridges between the two helixes, and they twist around each other.
I think you get the idea. So the double helix just describes the structure, the shape that DNA takes, and it leads to all sorts of interesting repercussions in terms of how heredity takes place and how natural selection and variation might take place as well.
And actually, in the future, I do want to actually read with you Watson and Crick's paper on the double helix where they essentially talk about their discovery.
The best thing about that paper, besides the fact that it was probably one of the biggest discoveries in the history of mankind, is that the paper is only a page and a half long, and it goes to my general view that if you have something good to say, it shouldn't take you that long to say it.
But with that said, let's think a little bit about how this can actually generate the proteins and whatever else that make up all of us.
So right here this is a zoomed-up version of that graphic that I just showed you a little bit earlier, and this is each of the helixes.
So if this is the magenta side, if you unwound this helix-- right now it shows it in its wound state, but if I unwind this helix, one side would maybe be this magenta side of our helix and then one side is this green side, right?
And if you twist it up, you get back to this drawing up here.
And then these bridges that you see in this drawing in the double helix, those are these connections right here.
These are the bridges.
Now, what allows us to code information is that the blocks that make up the bridges are made of different molecules.
And the four different molecules that are made up in DNA are adenine-- and it's written here on this little chart.
I got all of this from Wikipedia, so if you want more information I encourage you to go there.
Adenine, that's up here.
This is the molecular structure of adenine.
It's connected to a sugar right here, ribose.
I won't go into a deoxyribose. And then you have your phosphate group.
But these kind of form the backbone of the DNA: the sugar and the phosphate groups.
And I'm not going to go into the microbiology of it, because that's not important right now to understanding just how does this intuitively code for what we are.
So along the backbone, which is identical, and we'll talk about it. They run in different directions.
It's called antiparallel, so they label the ends.
And I'm not going to go into detail there, but the important thing are these bases here.
So you have adenine, and adenine pairs with thymine, and you see that up here.
If you have an adenine molecule here, an adenine base here, it'll pair with thymine, and this is called the base pair.
Adenine and thymine pair with each other.
If you have thymine, it's going to pair with adenine.
And then you have guanine and it pairs with cytosine.
And the names of these, you should know these names, just because they are almost-- well, if you ever enter any discussion about DNA and base pairs, this is expected knowledge.
But the names of the molecules and how they're structured, not important just yet. But what's important is the fact that there are four of them and that they essentially code information.
So you can view one of these strands in kind of a simplified way.
You can just view it as a strand of-- so this one, if it has an adenine and then it has a cytosine, then it has a guanine.
That's a guanine.
They did it in purple.
And then it has a-- oh, no, it has a thymine, not a guanine.
So it has a thymine in purple, and then in blue, it has a guanine.
So this strand right here codes ACTG.
And if you were to code the opposite side of the strand, you could immediately-- I don't even have to look here.
I can look at this side and say, OK, adenine will pair with thymine, cytosine pairs with guanine, thymine pairs with adenine, and guanine pairs with cytosine.
So they're complementary strands.
So if you think about it, they're really coding the same thing.
If you have one of them, you have all of the information for the other.
Now, in our DNA, in a human's DNA, you might say, hey, Sal, how do I go from these little chains of these molecules? How does that turn into me?
How does that turn into this complex organism?
And the simple answer is, well, the human genome has three billion of these base pairs.
And that's actually just in half of your chromosomes.
And I'll tell you, maybe in this video or a future video, why we only consider half of your chromosomes, and that's because essentially you have a pair of every chromosome.
I'll talk in more detail about that.
And this number, to some people, they might say, it only takes three billion base pairs to describe who I am?
And some people would say, wow, it takes three billion base pairs to describe who I am.
I never thought I was that complex.
So depending on your point of view, this is either a large or small number.
But when you take these three billion base pairs, you're actually encoding all of the information that it takes to make in this case a human being.
And actually it turns out a lot of primates don't have that many different base pairs than human beings.
The amazing thing is even things like roundworms and fruit flies also number in a surprisingly large fraction of the base pairs of a human being.
Maybe I'll do another video where I go into comparative biology.
But how do these base pairs actually lead to proteins?
I mean, it's fair enough. That's information.
It's like you can view these as ones and zeroes in some type of computer language, but really they're not just ones and zeroes, because they can take on four different values.
They can take on an A, a T, a C or a G, so you could think of them as zero, ones, twos and threes, but I won't go into that whole aspect of it just now.
So how does that actually code information?
So DNA when it actually transcribes something-- the process is called transcription, and I'm going to do a pretty gross simplification of it, but I think it'll give you the gist of how it codes for proteins.
So what happens when transcription happens is that these two strands split up, and one of the strands-- let me just take one of them.
Let's say it looks like this.
I'll do it all in one color.
Let's say it's just ATGGACG-- I'm just making up stuff-- TA.
Let's say that that's the strand that got split up.
And what happens is it transcribes-- and I won't say itself.
There's a whole bunch of enzymes and proteins and a whole bunch of chemical reactions that have to happen, but this DNA essentially transcribes a complementary mRNA.
And I'll introduce RNA.
It's essentially the exact same thing as-- well, the word is ribonucleic acid, so it's literally-- you get rid of the deoxy, so you can kind of say it's got its oxy, and it's ribonucleic acid, but it's very similar to DNA.
It codes in the exact same way.
The only difference between RNA, instead of a thymine, it has something called a uracil.
So every place where you would have expected a thymine, you would have expected a T, you'll now see a U.
So, for example, if this is the DNA strand, then an RNA, an mRNA, in a messenger RNA strand, will be built complementary to this.
So it'll be built-- let's see. With A, you'd normally have thymine when you're talking
DNA, but now we're talking RNA, so it'll be a uracil, then an adenine, cytosine, cytosine, uracil, then we got a guanine, a cytosine, an adenine, and then we'll have a uracil.
So this is the mRNA strand here.
And all of this is occurring inside the nucleus of your cells.
And we'll do a whole series of videos in the future about the structure of our cells, but I think most of us know that our cells-- and I'll talk more about eukaryotic and prokaryotic organisms in the future, but most complex organisms, they have a cell nucleus where we have all of our chromosomes that contain all of our DNA.
And so this mRNA then detaches itself from the DNA that it was transcribed from, and then it leaves the nucleus, and it goes to these structures called ribosomes.
I'm oversimplifying it a little bit, but at the ribosomes, this mRNA is translated into proteins.
So let me do that.
So let's say this is the mRNA.
It was transcribed from that DNA, so let me get rid of that DNA now. I got rid of the DNA.
This is the mRNA that we were able to transcribe from that DNA, and they have these other things called tRNA or transfer RNA.
And what these are-- and this is the really interesting part.
So you may or may not know that pretty much everything we are is made up of proteins.
And these proteins, the building blocks of proteins are amino acids.
And for those of you who like to lift weights, I'm sure you've seen ads for amino acid supplements and things of the like.
And the reason why they talk about amino acids is because those are the building blocks of proteins.
My son actually has an allergy to milk protein, so we had to get him a formula that was just pure amino acids, just all of the milk proteins broken down.
So if you look at a protein, it's actually a chain of these amino acids and usually a fairly long chain.
We'll look at some protein structures in the very near future, just to give you an idea of things.
It's a very long chain of these amino acids, and there are actually 20 different amino acids.
Twenty different amino acids are pretty much the structure of all of our proteins.
Let me write that.
So a very obvious question is how can these things code for 20 different amino acids?
I can only have four different things in this little bucket right here.
And then you just have to go back to your combinatorics, or if you can't go back to it to watch the playlist on probability and combinatorics, and say, OK, there's only four ways that I can have for each of these bases. There's only four different bases that I can have here, either an adenine guanine, cytosine or, depending on whether we're talking about DNA or RNA, a uracil or a thymine.
But how can we increase the combinations?
Well, if we include two of them, if we include two bases, then how many combinations can we have?
Well, we have four possibilities here, then we'd have four possibilities here, so we'd have 16 possibilities.
But that's still not enough. That's still not enough to code for one of 20 amino acids to say, hey, this is going to code for amino acid number five, and we'll talk more about their actual names.
So what do we have to do?
Well, we have to use three of them.
So three of them, there's actually four times four times four possibilities here, so they could code for 64 different things.
They could take on 64 different combinations or permutations, this UAC right here.
So if we have three of these bases, we can actually code for an amino acid.
Actually, it's overkill, because we can actually have 64 combinations here, and there are only 20 amino acids, so we can even have redundant combinations code for different amino acids.
For example, we might say that, and this isn't the actual code, but maybe UAC, and I should look these up. This codes for amino acid number 1.
And if it was AAU, then this codes for amino acid number 2.
And if I have-- I mean, I think you get the idea.
If I have GGG, this codes for amino acid number 10.
And what happens is when this messenger RNA leaves the nucleus, it goes to the ribosomes, and at the ribosomes-- we're going to look at that diagram in a few seconds-- but at the ribosomes-- let me take my same mRNA molecule.
And they're much longer than what I'm showing here.
This is just a fraction of an mRNA molecule.
So I'll take my mRNA molecule, and what they do is they essentially act as a template for tRNA molecules.
And tRNA molecules are these molecules that are attached to the-- they're almost like the trucks for the amino acids.
So let's say I have some amino acid right here, and then I have another amino acid that's right here like that, and then I have another amino acid that's like that.
They'll be attached to tRNA molecules.
So let's say that this tRNA molecule has on it-- so this amino acid is attached to a tRNA molecule that has the code on it A-- let me do it in a darker color.
It has the code AUG.
This one right here has the code-- let me pick another one.
Let's say it has GAC.
So what's going to happen?
When you're in the ribosome, and it's a complex situation, but actually what's happening isn't too fancy. This tRNA, it wants to bond to this part of the mRNA.
Why?
Because adenine bonds with uracil, uracil bonds with adenine, and guanine bonds with cyotsine, so it'll pull up right here.
It'll pull up right next to this thing, and actually, I should probably-- well, I don't know if I can rotate it.
But it'll just pull up right here and attach to this mRNA molecule.
And this right here is tRNA.
This is mRNA.
And the names don't matter. I really just want to give you the big picture idea of how the proteins are actually formed.
And this is an amino acid.
I don't know, let's call it amino acid 1, amino acid 5, amino acid 20.
This guy, he's going to pull up right here.
The guanine is attracted to the cytosine, and if you watch the chemistry videos, these are actually hydrogen bonds that form the base pairs.
Adenine, wants to pull up to uracil, cytosine to guanine, and so on and so forth.
And so once all of these guys have pulled up-- let me do that.
So once you've pulled up, let's say that this is-- I could do it up here.
This is my mRNA molecule. I'm not going to draw the specifics right there.
My little tRNA's pull up, pull up next to it, and they each hold a payload, right?
So this first one holds this payload right here of this amino acid.
The second one holds this payload of this amino acid and so forth and so on.
And so it might keep going, and there's another green amino acid here. They really don't have those colors, but I'm just-- just for the sake of simplicity like that.
And then the amino acids bond to each other when they're held like that close to each other.
This doesn't happen all by itself. The ribosome serves a purpose, and there are enzymes that facilitate this process, but once these guys bond together, the tRNA detaches, and you have this chain of amino acids.
And then the chain of amino acids starts to bend around so they have all of these-- and it's actually a fascinating-- I mean, people spend their lives studying how proteins fold, and that's actually where they get most of their structural properties.
It's not just the chain of the amino acids, but what's more important is how these amino acids actually fold.
So once you fold them, they form these really ultracomplex patterns based on what amino acid is attracted to what other amino acid in these very intricate three-dimensional shapes.
And what I took here from Wikipedia is these are some amino acids.
And just to be able to relate this to the DNA, this right here is insulin.
It's key in our ability to process glucose in our body.
So this right here is insulin.
It's a hormone.
So sometimes you hear people talk about your immune system.
Sometimes you hear people talking about your endocrine system and hormones, sometimes your digestive system.
This is hemoglobin, what essentially transports our oxygen in our blood.
But all of these things are proteins, and all these
little, little folds you see, these are all little amino-- I mean, they're just little dots of amino acids.
Some of these are multiple chains of amino acids kind of fitting together like a big puzzle, but some of them or just single chains of amino acids.
For insulin right here, this is 50 amino acids.
And then once the chain forms, it all bundles together and forms this little blob like you see, but the shape of that blob is super important for insulin being able to perform the function that it needs to perform in our systems.
But this right here is approximately 50-- I forgot the exact number-- amino acids.
This right here, this immunoglobulin G, which is part of our immune system, this is roughly 1,500 amino acids.
So how much DNA or how many base pairs had to code for this?
Well, three times as much, right?
Because you have to have three base pairs that code for one amino acid, and actually, three base pairs, this is called a codon, because it codes for amino acids.
So three base pairs make a codon.
So if you have 50 amino acids that make up insulin, that means you're going to have to have 50 codons, which means you have to have 150 bases or 150 of these
A's and G's and T's.
If you have 1,500 amino acids, that means you're going to have to have 1,500 codons, which means you're going to have roughly 4,500 of these base pairs that code for it.
Now, there are some notions that get confused a lot, so I went to kind of the smallest level of our DNA right here, and this is the level at which-- well, this is RNA that I'm pointing to right there, but this is the smallest level of DNA, and that's the level at which the information is actually coded.
But how does that relate to things like genes and chromosomes and things that you might talk about in other contexts?
So let's say the 150 base pairs that coded for insulin, these make up a gene.
And these 4,500 base pairs make up another gene.
Now, all of the genes don't make proteins, but all of the proteins are made by genes.
So let's say I have just a bunch of-- I'll just make another A, G, and it goes down, down, down, and you have a T and then a C and a C, and let's say I have 4,500 of these.
These could code for a protein.
These could code for protein, or they could have all of these other kind of regulatory functions telling what other parts of the DNA should and should not be coded and how the DNA behaves, so it becomes super, super complex.
But this kind of section of our DNA, this is what we refer to as a gene, and a gene can have anywhere from a couple of hundreds of these base pairs or these bases to several thousand of these base pairs.
Now, a gene is that part of our chromosome that codes for a particular protein or serves a certain function.
Now, there are different versions of genes.
It's a gross oversimplification, but let me say this is the gene for insulin.
Now, there might be slight variations in how insulin can be coded for, and I'm kind of going out of my domain right here, because I don't know if that's true.
And maybe I shouldn't just speak specifically about insulin, but it's coding for some protein, but there's maybe multiple different ways that that protein can be coded.
Maybe instead of a T here, sometimes there's a C there.
It still codes for the same protein.
It doesn't change it quite enough, but that protein acts just a little bit different.
It's a slight variant. I'll use that word.
Now, each variant of this gene is called an allele.
It's a specific variant of your gene.
Now, if you take this DNA chain, and this chain over here-- let's see.
This is one base pair.
This might be like one base. This is another base.
Maybe this is an adenine and then this would be a thymine over here in green.
This is an adenine and this would be a thymine.
If right here this is a guanine, then right here would be a cytosine.
This would be just a very small section.
If I were to like zoom out, and let's say we have a big chain of DNA where each of these little dots are a base pair that I'm drawing here, maybe this section codes for gene 1.
And then there's some noise or things that we haven't fully understood yet.
Now, I want to be clear. Just with a simple discussion of DNA, we're already kind of approaching the frontiers of what we know and what we don't know, because DNA is hugely complex, and there's all of these feedback structures, and certain genes tell you to code for other genes and not to code for other genes and to code under certain circumstances, hugely complex. So there's huge sections of DNA that we still don't understand what exactly they do.
But then maybe they'll have another section here that codes for gene 2.
Maybe gene 2 is a little bit longer.
Maybe it's 1,000 base pairs.
But when you take all of these and you turn it into a-- it kind of winds in on itself like this.
Let me do it.
So it'll wind up, winding in on itself like this and do all sorts of crazy things.
Remember, it completely bundles itself up, and then it looks something like that.
Then you get a chromosome.
And just to get an idea of how large a chromosome is compared to the actual base pairs, chromosome number one in the human genome-- so we have 23 pairs.
If you look at it inside of a nucleus-- so let's say that's the nucleus.
Let's say this is the cell.
The cell is much bigger than what I'm showing.
But we have 23 pairs of chromosomes.
I won't do all of them.
You can actually see chromosomes in a not-too-expensive microscope, so we're already getting to a scale that we can start to look at.
But the largest chromosome, which is chromosome number one in the human genome, just to give an idea of how much information it's packing, that thing right there has 220 million base pairs.
Sometimes people talk about chromosomes and genetics and genes and base pairs interchangeably, but it's very important to kind of get an idea of scale.
These chromosomes are a super-long strand of DNA that's all configured and bundled up, and it contains 220 million base pairs.
So the actual elements that are coding for the information are unbelievably small relative to the chromosome itself.
But now that we understand a little bit, and actually I want to take a look back at this, because this kind of blows my mind, that if you just take those little combinations of those amino acids, you can form these very intricate, very advanced structures that we're still fully understanding how they actually interact with each other and regulate how all of our biological processes work.
And what's even more amazing is that this scheme that I've talked about in this video about DNA to mRNA to tRNA to these molecules, this is true for all of life on our planet, so we all share this same mechanism.
Me and this plant, we share that common root that we all have DNA.
As different as me and that roach that I might not like to be in the same room, we all share that same common root of DNA and that all of it codes to proteins in this exact same way, that there's this commonality amongst all life.
That, to me, is mind blowing.
Then even more mind blowing is how these very complex shapes are formed by the DNA.
And this isn't speculation.
This is observed behavior.
This is a fascinating structure right here, but it's just based on 20 amino acid-- you can almost view the amino acid as the LEGOS, and you put the LEGOS together, and just the chemical interactions form these fairly impressive structures right here.
So now that we know a little bit about DNA and how it codes into protein, we can take a little jump back and talk a little bit more about how variation is actually introduced into a population.
Let's try to learn a thing or two about ratios.
So ratios are just expressions that compare quantities.
So that might just be a fancy way-- let me just --of saying something that you may or may not understand.
So let me give you actual examples.
If I have ten horses and I have five dogs.
And someone were to come to me and say Sal, what is the ratio is of horses to dogs?
So I want to know how many horses do I have for some number of dogs.
So I could say I have ten horses for every five dogs.
So I could say the ratio of horses to dogs is ten:five.
Or I could also write that as a fraction.
I could say the ratio of horses to dogs is ten / five.
Or I could just write it out.
I could say it is ten to five.
These all are saying the same thing.
And the thing I write first, or the thing that I write on top, is the number of horses.
So this is the number of horses right there.
If I wanted to talk about the number of dogs, this is the number of dogs, that's the number of dogs, or that's the number of dogs.
I'm just-- These are all just expressions that are comparing two quantities.
Now, I just said I have ten horses for every five dogs.
But what does that mean?
That means I have five horses for every one dog.
Sorry.
Not five horses for every one dog.
It means I have two horses for every one dog, right?
If for five dogs I have ten, that means that for every one of these dogs, there are two horses.
For every one of-- every two of these horses, there's one dog.
I just kind of reasoned through that.
So this is-- I have two horses for every one dog.
But how do you get there?
How do you get from ten:five to two:one?
Well you can think of what's the biggest number that divides into both of these numbers?
What's their greatest common divisor?
I have a whole video on that.
The biggest number that divides into both of these guys is five.
So you divide both of them by five and you can kind of get this ratio into a reduced form.
And if I write it here, it would be the same thing as two / one or two to one.
And so what's interesting about ratios, it isn't literally, or doesn't always have to be literally, the number of horses and the numbers of dogs you have.
What a ratio tells you is how many horses do I have for every dog.
Or how many dogs do I have for every horse.
Now, just to make things clear, what if someone asked me what is the ratio of dogs to horses?
So what's the difference in these two statements?
Here I said horses to dogs.
Here I'm saying dogs to horses.
So, since I've switched the ratio-- What I'm looking for--
I'm looking for the ratio of dogs to horses, I switch the numbers.
So dogs-- For every five dogs, I have ten horses.
Or if I divide both of these by five, for every one dog, I have five horses.
So the ratio of dogs to horses is five:ten or one:five.
Or you could write it this way. one to-- I can write it-- Let me write it down here. one / five.
Or I could write one to five.
And the general convention-- This wouldn't be necessarily incorrect.
That's not wrong.
But the general convention is to get your ratio or your fraction, if you want to call it that, into the simplest form or into this reduced form right there.
Let's just do a couple of other examples.
Let's say I have twenty apples.
Let's say I have forty oranges.
And let's say that I have sixty strawberries.
Now what is the ratio of apples to oranges to strawberries?
I could write it like this.
I could write what is the ratio of-- I'll write it like this
--apples:oranges:strawberries?
Well I can start off by literally saying, well for sixty strawberries-- for every sixty strawberries, I have forty oranges and I have twenty apples.
And this would be legitimate.
You could say the ratio of apples to oranges to strawberries are twenty:forty-- Sorry. twenty:forty:sixty.
And that wouldn't be wrong.
But we saw before, we could put into reduced form.
So we think of what's the largest number that divides into all three of these?
We can't just do it into two of these now because now my ratio has three actual quantities.
Well the largest number that divides into all of these guys is twenty.
If we divide all of them by twenty, we can then say for every one apple, I now have-- you divide this guy by twenty --I have two oranges, and I have three strawberries.
So the ratio of apples to oranges to strawberries is one:two:three.
And I got that, in every case, by just dividing these guys all by twenty.
I divided by twenty.
I think you get the general idea.
If someone were to ask you what's the ratio of-- Let me just write it down because it never hurts to have a little bit more clarification.
If someone wanted to know the ratio of strawberries to oranges-- Let me get into my orange color.
Strawberries to oranges to apples.
I thought I was going to do that in yellow. To apples.
What is this ratio going to be?
Well for every three strawberries, I have two oranges and I have one apple.
So then it would be three:two:one.
The general idea is whatever order someone asks you for the different items, you put-- the ratio is going to be in that same exact order.
Now, in all of the examples so far I gave you the number of quantity-- the quantity of things we had and I-- we figured out the ratio.
What if it went the other way?
What if I told you a ratio?
What if I said the ratio of boys to girls in a classroom is-- Let's say the ratio of boys to girls is two / three.
Which I could've also written as two:three just like that.
So for every two boys, I have three girls or for every three girls, I have two boys.
And let's say that there are forty students in the classroom.
And then someone were to ask you how many girls are there?
How many girls are in the classroom?
So this seems a little bit more convoluted than what we did before.
We know the total number of students and we know the ratio.
But how many girls are in the room?
So let's think about it this way.
The fact that the ratio of boys to girls-- I'll write it like this.
Boys-- Maybe I'll be stereotypical with the colors.
The ratio of boys to girls is equal to two:three.
Hate to be so stereotypical, but it doesn't hurt. two:three.
The ratio of boys to girls is two:three.
So this stands for every three girls, there's two boys.
For every two boys, there's three girls.
But what does it also say?
It also says for every five students, there are what?
There are two boys and three girls.
Now why is this statement helpful?
Well how many groups of five students do I have?
I have forty students in my class right there, right?
I have forty students in my class.
And for every five students, there are two boys and three girls.
So how many groups of five students do I have?
So I have a total of forty students.
Let me do it in this purple color.
I have forty students and then there are five students per group.
And I figured out that group just by looking at the ratio.
For every five students, I have two boys and three girls.
How many groups of five students do I have?
So that means that I have eight groups-- forty divided by five --I have eight groups of five students.
Now we're wondering how many girls there are.
So each group is going to have three girls.
So how many girls do I have?
I have eight groups, each of them have three girls.
So I have eight groups times three girls per group is equal to twenty-four girls in the classroom.
And you could do the same exercise with boys.
How many boys are there?
There's a couple of ways you could do it.
You could say for every group, there are two boys.
There's eight groups.
There's sixteen boys.
Or you could say there's forty students. twenty-four of them are girls. forty minus twenty-four is sixteen.
So either way you get to sixteen boys.
And if you want to pick up a fast way to do it.
It would be identical.
You'd say look, two plus three is five.
For every five students, two boys, three girls.
How many groups are there?
You say forty divided by five is equal to eight groups.
Every group has three girls.
So you do eight times three is equal to twenty-four girls.
Let's do one that's a little bit harder than that.
Let's do one where I say that the ratio of let's say--
Well let's go back to the farm example.
The ratio of sheep-- I'll do sheep in white.
The ratio of sheep to-- I don't know --chickens to-- I don't know.
What's another farm animal? --to pigs.
The ratio of sheep to chicken to pigs-- Maybe I should just say chicken right there.
The ratio of sheep to chicken to pigs-- Or chickens.
I should say chickens. Is-- Let's say the ratio is two:five:ten.
And notice, I can't reduce this anymore.
There's no number that divides into all of these.
So this is the ratio if sheep to chickens to pigs.
And let's say that I have a total of fifty-one animals.
And I want to know how many chickens do I have.
Well we do the same idea.
For every two sheep, I have five chickens and I have ten pigs.
That tells me for every seventeen animals-- So every group of seventeen animals, what do I have?
And where did I get seventeen from?
I just added two plus five plus ten.
For every seventeen animals, I'm going to have-- Let me pick a new color.
I'm going to have two sheep, five chickens, and ten pigs.
Now, how many groups of seventeen animals do I have?
I have a total of fifty-one animals.
So if there's seventeen animals per group, fifty-one animals divided by seventeen animals per group.
I have three groups of seventeen animals.
Now I want to know how many chickens.
Every group has five chickens.
We already know that.
And I have three groups.
So I have three groups.
Every group has five chickens.
So I'm going to have three times five chickens, which is equal to fifteen chickens. Not too bad.
All I did is add these up and say for every seventeen animals, I've got five chickens.
I've got three groups of seventeen.
So for each of those groups, I have five chickens. three times five is fifteen chicken.
You could use the same process to figure out the number sheep or pigs you might have.
Round 1,585 to the nearest ten.
Let me rewrite the number. 1,585 to the nearest ten.
So we want to focus on the tens place.
If we were to round it up, we would go to 1,500-- let me color code it.
We would round up to 1,590.
The 8 would round up to a 9.
And 90, if we were to round down, we would go to 1,500, and we would round down to 80.
So these are our two choices.
Now we've seen the last two examples. If the place to the right of it is 5 or greater, we round up.
Well, the place to the right of it is definitely 5 or greater.
It is 5, so we round up.
So it is 1,590.
And we're done!
Welcome back.
I'll now do a couple of more momentum problems.
So this first problem, I have this ice skater and she's on an ice skating rink.
And what she's doing is she's holding a ball.
And this ball-- let me draw the ball-- this is a 0.15 kilogram ball.
Let's just say she throws it directly straight forward in front of her, although she's staring at us.
She's actually forward for her body.
So she throws it exactly straight forward.
And I understand it is hard to throw something straight forward, but let's assume that she can.
So she throws it exactly straight forward with a speed-- or since we're going to give the direction as well, it's a velocity, right, cause speed is just a magnitude while a velocity is a magnitude and a direction-- so she throws the ball at 35 meters per second, and this ball is 0.15 kilograms.
Now, what the problem says is that their combined mass, her plus the ball, is 50 kilograms.
So they're both stationary before she does anything, and then she throws this ball, and the question is, after throwing this ball, what is her recoil velocity?
Or essentially, well how much, by throwing the ball, does she push herself backwards?
So what is her velocity in the backward direction?
And if you're not familiar with the term recoil, it's often applied to when someone, I guess, not that we want to think about violent things, but if you shoot a gun, your shoulder recoils back, because once again momentum is conserved.
So there's a certain amount of momentum going into that bullet, which is very light and fast going forward.
But since momentum is conserved, your shoulder has velocity backwards.
But we'll do another problem with that.
So let's get back to this problem.
So like I just said, momentum is conserved.
So what's the momentum at the start of the problem, the initial momentum? Let me do a different color.
So this is the initial momentum.
Initially, the mass is 50 kilograms, right, cause her and the ball combined are 50 kilograms, times the velocity.
Well the velocity is 0. So initially, there is 0 velocity in the system.
So the momentum is 0. The P initial is equal to 0.
And since we start with a net 0 momentum, we have to finish with a net 0 momentum.
So what's momentum later? Well we have a ball moving at 35 meters per second and the ball has a mass of 0.15 kilograms.
I'll ignore the units for now just to save space. Times the velocity of the ball. Times 35 meters per second.
So this is the momentum of the ball plus the new momentum of the figure skater.
So what's her mass?
Well her mass is going to be 50 minus this.
It actually won't matter a ton, but let's say it's 49-- what is that-- 49.85 kilograms, times her new velocity.
Times velocity. Let's call that the velocity of the skater.
So let me get my trusty calculator out.
OK, so let's see. 0.15 times 35 is equal to 5.25. So that equals 5.25. plus 49.85 times the skater's velocity, the final velocity.
And of course, this equals 0 because the initial velocity was 0.
So let's, I don't know, subtract 5.25 from both sides and then the equation becomes minus 5.25 is equal to 49.85 times the velocity of the skater.
So we're essentially saying that the momentum of just the ball is 5.25.
And since the combined system has to have 0 net momentum, we're saying that the momentum of the skater has to be 5.25 in the other direction, going backwards, or has a momentum of minus 5.25.
And to figure out the velocity, we just divide her momentum by her mass.
And so divide both sides by 49.85 and you get the velocity of the skater. So let's see. Let's make this a negative number divided by 49.85 equals minus 0.105.
When she throws this ball out at 35 meters per second, which is pretty fast, she will recoil back at about 10 centimeters, yeah, roughly 10 centimeters per second.
So she will recoil a lot slower, although she will move back.
And if you think about it, this is a form of propulsion. This is how rockets work.
They eject something that maybe has less mass, but super fast.
And that, since we have a conservation of momentum, it makes the rocket move in the other direction.
Well anyway, let's see if we could fit another problem in.
Actually, it's probably better to leave this problem done and then I'll have more time for the next problem, which will be slightly more difficult.
See you soon.
<i>Brought to you by the PKer team @ www.viikii.net</i> <i>Episode 6
I'm sorry...
I'm really sorry.
I know how hard it was arranging to take this test.
Everyone was looking forward to it... But...
Because of me...
All because I needlesly tagged along.
You should have just left me and went on.
I should have, shouldn't I?
What you're saying is right.
I really am an obstacle in your life.
No!
Even that word doesn't describe it.
I'm a disaster.
Oh, it's here.
Where?
Oh, Ha Ni!
Ha Ni!
Aigoo!
What's happening here?!
What!?
You even have a cast!?
Aigoo!
What to do...
Oh, Baek Seung Jo!
You agai...
Joon Gu, drop it.
Hey! Whenever you're around Ha Ni, she's always prone to accidents!
I told you to drop it!
Oh?
Ha... Ha Ni...
Just go.
Ha Ni...
I want to be alone now.
Hey, Ha Ni... Are you alright?
Come on, let go of me!
Ha Ni, is there anything you want to eat?
I'll go buy it and come back.
Ha Ni! Let go of me, will you?
Should I leave as well?
Go...
Go and get some rest.
I'm really sorry.
I'm at a loss for words, Jae Su (sister-in-law) (He's referring to Seung Jo's dad as his brother)
Not at all...
That's right.
After dropping her off at the hospital, he still had plenty of time to go, but he chose not to.
But still... He was reluctant to take the test before and now he was going to...
He must have something in mind.
Don't worry...
After all, a youth who doesn't rebel is not a youth.
It's just a child.
Thanks, Unni.
Alright, now let's get to work!
The customers should be rolling on in soon.
- Yes.
- Yes.
Hey, Ha Ni, our family must have a knack for speedy recoveries.
Even the doctor said that there wasn't such a case like yours, where a patient left the hospital so early.
Dad...
Yeah?
Shouldn't we leave Seung Jo's house?
Why?
Do you feel like we're being senseless?
There's no need to!
Everyone is worrying about you more than they are for Seung Jo.
That's why it bothers me even more.
Why am I always like this?
Oh, welcome!
Hey, a customer came in now, so come on and get up.
I'll drop you off.
Is Ha Ni still sulking?
She won't move an inch from her room and she'll barely eat anything.
When everyone's asleep, she comes out and starts to walk around.
In the middle of the night, I was startled because I thought she was a ghost!
Baek Seung Jo.
You should treat her well.
Just a kind word from you will solve things. Why are you causing her so much grief!
I did tell her!
Really?
What did you say?
Thanks for not letting me do the interview.
Is that some sort of condolence?
That's like slapping the face of a crying kid.
You don't get to eat either until Ha Ni starts eating again. <i>I heard you gave Seung Jo some sleeping pills on the morning of the test.<i> <i>Even like this, do you think you still have any right to say that you like him?<i>
Good luck on your test!
FlGHTlNG!
I'm feeling uneasy so I'm going to at least make sure he goes inside of the building.
[From:
Ha Ni For: Mother, Father... I'm sorry...]
Long time no see.
Are you leaving?
Is it because I didn't get into Tae Sung University?
That, too, but also because of the cough medicine incident.
I keep trying to do well, but I keep...
No matter how hard I think about it, I don't think I should be by your side.
I don't know what might happen because of me.
Don't hold me back.
I don't have any thought like that.
Huh?
Should I help you?
It seems heavy.
It's okay.
Alright then.
Take care!
Ah.
Is it for me?
Parang University?
Oh... Enrollment fee?
Eh, zero won?
The enrollment fee is zero won!
Undecided major?
Ah, this must be a mistake.
It isn't for me.
It's addressed to "Baek Seung Jo".
Baek Seung Jo...?
Baek Seung Jo?! <i>Oh my...
Really?
You're really going to Parang University?
Why?
Who knows?
Because they begged me to go?
What?! <i>If you would enroll at our school, <i>we would offer everything and anything.
They're going to pay for me to study abroad, as well as combined masters and doctorate degrees.
If I stay within the school, they said they would even give me a tenured position there.
For me, they were really pissed asking why they should pick me.
But, even if it's Parang University, isn't priority admission the same for every university?
Through all of my life up until now,
I think I was the angriest last year.
I was anxious and pissed wondering what's going to happen today.
It was a complete mess.
Sorry.
But it was fun.
Falling asleep while taking the exam was fun.
Wondering what my score would be after taking the exam, that was new too.
Thanks to you, I experienced a lot of new things.
It was pretty exciting and fun.
So...
So?
So you're saying...
You're going because of me? To Parang University?
It's not because of you, but because of me!
Just until I figure out what I want to do.
I want to live an exciting life until then.
I thought your grandmother said to live a fun life!
Right.
Well then...
See you.
Wait!
Then...
Does that mean I can stay here longer?
I won't be a pain anymore!
You won't?
Sure you won't.
I guess so... ...but I'll try!
I promise your life will be fun and exciting!
Thanks.
But...
So you've been feigning ignorance this whole time even knowing about Parang University?!
Even after seeing how I was dying of guilt?
Why?!
Because it was fun.
What?! You don't like it?
If you don't like it, I can cancel it right now...
No, no, no!
I like it.
I'm happy.
I know.
See, I told you he had something in mind.
Parang University?
When did he apply here?
I'm sorry.
If my Ha Ni hadn't gotten into that accident, he would have just gone to Tae San University.
What's so great about Tae San University?
It's probably full of kids like Seung Jo.
Ha Ni and Seung Jo at the same university...
No matter how you see it, don't you think those two are a match made in heaven?
Match made in heaven...
Welcome!
Hello, Father!
I came again!
Oh, let me do it, I'll do it!
It's fine!
Look here, look here!
What chef does chores like this?!
Chef?
If it's what I think you came here to say, then just go on your way.
Oh no, today I came to give you this.
What's this?
Oh yes, it's safflower seeds.
Safflower seeds?
I hear this is the best for healing broken bones!
Even after one has taken off the cast, stuff like this needs to be eaten like crazy!
Please mix it with some water and feed it to Ha Ni.
Thanks.
Chef!
What are you doing?
Please don't be like this!
Can't you just take me in?!
Sixty years of tradition, So Pal Bok Noodles!
That tradition can't come to end, right?!
How many times do I have to tell you?
Do something you want to do.
Don't decide because of my Ha Ni!
What I want to do is this!
When I first ate your noodles... ...my heart felt like it was sinking!
Let go.
Father!
- Let go! - Please, please!
Excuse me!
Yes, welcome!
Oh yes.
Is this... ...the place that sells some porridge that helps people get accepted into university?
It's just that I hear that... ...eating your porridge helps even the 90th place students get into Parang University.
By any chance, do you mean Bul Nak porridge?
Yes, that's right!
This is it, this is the place! Come in, come in!
- Oh, this is wonderful!
- Oh, yes, welcome!
So this is where it was!
Hey, hurry and get up!
No sir!
I will not budge from this spot today, not until you take me in!
You little...
Your act is an obstruction of business!
Obstruction?
Oh, that won't do.
Excuse me, can we get some warm water here?
- Oh, yes, yes!
- Yes, yes!
It's fine, I'll do it!
Can we see a few menus?
Oh, yes!
Menu, menu, menu!
Oh, here they are!
Here you go.
You look so hardworking.
There's even pine mushroom and oyster chopped noodles!
This is the best time for oysters, you know.
The aroma of the ocean is embedded in them!
Such a youngster, but you're great at business.
- Then I'll have the oyster noodles.
- I want the Bul Nak porridge.
Alright, then one order of oyster noodles, and three Bul Nak porridges?
Got it!
Please wait just a bit!
One Chopped Noodles and three Bul Nak porridges!
Are you looking for something in particular?
I was just...
Where are the mp3s and digital cameras?
They're in that corner.
How nifty! <i>Brought to you by the PKer team @ www.viikii.net
There are so many things I want to buy for him.
It looks so nice.
It'll probably look really good on Seung Jo.
Thank you, boss!
I'll give it my all!
Do your best from now on.
Yes! I'll do my best!
I'll be right there!
This tastes really good.
It's 6,200 Won.
($6.20)
Gosh.
Oh, you're here?
I'm home.
Oh good.
She's constantly late these days.
She's probably lazing around now that she's been accepted into university!
Where did you learn to talk in such a way!? <i>Brought to you by the PKer team @ www.viikii.net</i>
Oh Ha Ni!
You've been staying out late these days.
Why?
Were you worried?
Worried?
Don't you know that my mom stays up late every day so that she can open the door for you?
I know.
But I have no choice.
What? Rice balls...
If it's 3,800 won (per hour) for 7 hours... ...it's 26,600 won.
It's 7,000 won.
I've received 10,000 won.
Your change is 3,000 won.
Come again.
Welcom...
How much is it?
It's 1,200 won.
Here.
Hey... Customer...
How much did you give me just now?
10,000 won.
I've received 10,000 won.
Excuse me...
Customer...
From here...
Please take 8,800 won.
What?
8,800 won?
Ah... Yes.
Goodbye.
Manager!
What?
Please take 8,800 won?!
Out of all those other convenience stores, why did he have to come to this one?
Well, it must be our destiny.
Anyways...
Where could I make money?
It shouldn't be too late either.
Yes!
[Tae Yang Chicken]
Ha Ni!
What to do?
You're going to have to go on a delivery again.
It's okay! As long as you pay me, then it's fine.
It is here.
Ah good.
Ah stupid.
Why didn't I know while I was coming here?
Yes.
No...
I came already.
Yes, i am in front of the house.
Yes.
Who is it?
Hello, i am the chicken...
I am really busy now.
I'll just leave this here.
So could you bring it in?
Huh?
What about the money?
That's right!
The money!
You need to give it to me, the money.
Ah, what do i do!
Out of all those chicken places, why did he have to order from this one?
Our destiny must not be just some regular destiny.
Ah, Min Ah!
I can't get a hold of Joo Ri.
They said she left really early in the morning and her phone has been off all day.
Actually, after she found out we both got into Parang University, I haven't been able to talk or to get a hold of her.
So, that's why I came alone when you got in the accident.
Joo Ri, where are you?
Min Ah!
Yes.
Where did she go?
Where have we not gone yet?
- At school!
- At school!
She is not here.
Let's go.
Hey!
Jong Joo Ri!
Oh my gosh!
I thought I was about to drop my liver!
(saying for when you get surprised)
What's up with you Jung Joo Ri?
And your phone is off too.
What are you doing here alone?
You are busy...
Since you guys are college students.
Not yet.
We haven't graduated.
Sorry!
My mind was everywhere.
It is alright.
I said I was going to go to the academy (cram school) this morning and left.
I didn't want to.
But there wasn't anywhere for me to go but school.
You're going to retake your SATs?
My parents are telling me to retake them and try to get into even a 2 year college.
What will I do if I go to college?
It's just a waste of money.
Why don't they know their daughter?
Then, tell them that you're going to do what you want to do.
I have to know how to do something in order for me to tell them.
Why would you not (have something you know how to do)?
What is there?
You're the one that made me this hairstyle.
You are right!
You always tie my hair and pin it too.
That's right.
Our teacher did also recognize it.
- Of course!
- Right?
The best.
Okay.
I'm not going to retake them!
I'm not retaking the SATs!
It is also the end of the annoying stuff.
Colleges that are concerned only with names, this dirty world!
You dirty world that only makes it easy for the pretty girls!
Jung Joo Ri is beautiful.
Dok Go Min Ah is pretty too!
Anyways, congratulations to you both on going to college.
Ah embarrassing!
This isn't my style.
We know, we know!
So strange of you!
Don't do it. <i>What's the deal about life.
You're filled with so many worries. <i>Change up that frustration. <i>A completely empty wallet. <i>You're drenched in despair. <i>I know how that feels. <i>But with your... <i>Heart afire! <i>Sometimes you have to face it head on. <i>Sometimes you've got to cry, that is youth. <i>Just kick it out. <i>Sometimes you have to face it head on. <i>Sometimes you've got to cry, that is youth. <i>That's what it is!
I'm not going to university.
Even if you wanted to, you couldn't go! <i> <i>
Ha Ni!
Baek Seung Jo, hurry and come down!
You know...
What?
Here!
What is it?
Just because I feel bad for a lot of things...
And I'm thankful for a lot of things too.
You could call it a graduation gift too.
You're going to do an all-in-one, is it?
Want to see?
What the hell is this?
It's a head massager.
It seems like you're constantly talking about how your head hurts.
Where did you buy something like this?
Definitely a gift like Oh Ha Ni.
You don't like it?
Want me to exchange it for something else?
You're going to be late to your graduation? Why aren't you two coming down?
Oh my, what's this?
Is it a helmet?
It's a head massager.
Since Seung Jo uses his head a lot.
Oh this works as a neck massager as well.
It's a gift for Seung Jo?
Oh godness, you're so thoughtful.
Try it on Seung Jo!
I don't want to!
Who in the world wears things like this!
He's so mean.
Goodness, this looks expensive.
Where did you get the money?
I took on a part-time job.
So that's why you were late these days.
Oh my.
Mic test.
1.
2.
What are you going to do if you're freaking out already?
Guys, I can't breathe very well.
I've never been up on stage!
Oh gosh.
Our homeroom teacher put on a real show in order to have you accept on behalf of our class.
- Really? - That's right.
Class 1's representative is Baek Seung Jo, and Class 7's is Oh Ha Ni.
So do a good job!
Don't go up there and fall over! Crashing all over the place!
Don't say such negative things.
Be careful.
Hey Baek Seung Jo.
I hear you got into Parang University.
Speak up.
What kind of intentions do you have?
Intentions?
That's right. There are hundreds of universities.
But I hear you've got the skills to get into Taesan University even if you took the exams with your eyes closed.
So why the hell are you going to Parang University?
So I could see you react like this.
What? You little! Till the very end I see!
Can everyone hear?
We will now be commencing with
Parang High School's graduation ceremony.
Ha Ni and Seung Jo?
Though there were SAT mysteries every year...
This year,
There were 2 events that were so absurd you couldn't really call it a mystery.
One of them is...
Class 7's Oh Ha Ni getting into Parang University.
The other one is that Class 1's Baek Seung Jo is also attending Parang University.
Does this make any sense?!
It doesn't make any sense!
Next is the speech from the representative of the graduating class.
Class 1's Baek Seung Jo.
Oliver Wendell Holmes once said this.
The great thing in the world...
Is not so much where we stand,
As in what direction we are moving.
Today we graduate.
After 3 years, this is how far we have come.
Once this chapter of your life ends, where will all of you go?
To the Chinese restaurant?
Family restaurants?
Though I joke about it,
Even I didn't know which direction I was supposed to go. Actually no, I've still yet to find it.
But I found something out.
It's thanks to a grandmother whose face I've never even seen.
She said that I just need to have fun, and others need to be happy.
She said that's how to live life.
But as you all know, I don't have the personality to make others happy?
So for the time being, I'm planning on at least living a fun life.
Though I still don't know how to yet.
I hope for all of you out there, despite which direction your life is headed...
I hope that road is filled with fun.
Thank you. <i>Just have a fun life. <i>Have fun. <i>Fun? <i>My grandmother used to say it all the time. <i>Ha Ni, enjoy your life, have fun. <i>You have fun, and make sure others are happy. <i>She said living life like that is fine. <i>Fun?
Oh Ha Ni!
What?
Is Class 7's Oh Ha Ni not here?
Here!
I'm here!
It's Ha Ni!
Along with Class 1's Baek Seung Jo...
Class 7's Oh Ha Ni...
They will be accepting the diplomas,
On behalf of the graduating seniors of Parang High School.
Please come up to the podium.
Do you, Baek Seung Jo, take Oh Ha Ni to be your lawfully wedded wife,
Despite rain, snow, wind, and flowers?
Do you vow to love and cherish her?
I do.
Do you, Oh Ha Ni, take Baek Seung Jo to be your lawfully wedded husband,
Despite...
Yes, I do!
Ha Ni, I promise too!
You're the only one for me!
I'm going to look onto just you until my dying days!
Who says?!
I'm against it!
I'm totally against it!
Hey Seung Jo, you say something too!
Tell him that you're totally against it too!
Is that Baek Seung Jo's mom?
Baek Seung Jo's got it rough too.
There's Oh Ha Ni, and his mom.
What are you doing?
Hurry and come down!
Oh gosh, Oh Ha Ni.
You were so funny today.
Seriously!
I told you, you were going to fall.
Oh goodness Ha Ni, I'm sorry.
I was just so worked up earlier on.
It's fine.
Did Eun Jo leave too?
Yeah. He said I'm too embarassing.
What does it matter? Right?
What's it matter?
It was totally like you, Oh Ha Ni.
- You think so?
- That's right, if nothing happened you wouldn't be Oh Ha Ni.
Oh yea, but where is Seung Jo?
I told him I wanted to take pictures.
I want to start school again
And wear a school uniform like this.
Really? We're so tired of them.
Oh! <i>Brought to you by the PKer team @ www.viikii.net </i>
That's so cool!
That's what I'm talking about!
That's what high school graduation is all about.
Oh, where is Seung Jo? Hurry up and find him.
Oh, he's over there.
Excuse me,
Looks like they want to take pictures.
See you later.
Aw, poor things.
Ha!
It's Hong Jang Mi.
Seung Jo Oppa, let's take a picture.
Teacher, Wait a moment please.
Hurry!
Ready?
1, 2, 3.
Hey, Ha Ni.
Go over there, let's take a picture quickly!
Yes?
I don't want to.
I'm scared.
Scared?
I'm just saying you should show her how it's done.
Baek Seung Jo!
Hurry.
What?
You want to take a picture too?
Yeah.
Are you saying that you want me to take a picture with you now?
No.
It doesn't.
Sorry.
Oh Ha Ni.
Come here.
Is this good enough?
It's fine.
Stay like that.
Ah, so pretty!
Thank you.
I'm going to take it now!
Customer, how much money have you given me?
2,
Please take 8,800 won from here.
3!
That's right Ha Ni!
Today I'll make a night you'll never be able to forget.
Aigoo! Come on in! Please come this way!
Ah what's this?! Why are class 7 here?
I really hate this!
We hate you too!
Ah Ahjushi! How could you do this?
You're from the same school so it's okay if you have fun together!
Have a great time!
We don't get along with them!
Even on graduation day... Hurry, hurry! Ha Ni.
These are my feeling for you.
Do you understand?
Listen well.
Hey Baek Seung Jo! Why are you here?
It seems like they got everything ready, so let's just stay here.
Okay!
Great!
Oh, oh, oh!
Urgh! Doing as he pleases!
Urgh!
There is nothing we can do! Let's just start.
Don't you look at us! <i> You are my life's navigation
Bong Joon Gu! <i>You guide me through the road I have to take. <i> Please let me know about life's directions, speed <i> and locations. <i> If it gets too hard and I start shedding tears, <i> please hold me tightly. <i> if I get tired and fall, <i> Please reach out to me and hold my hand. <i> I love you, I love you, you are the one I love, I love you! <i> My life's navigation. Boong Joon Gu <i>BulNak porridge for the examinees.
Good-bye!
Sir!
Aigoo! Congratulations!
Okay, right away!
Wait a moment!
I'm coming!
Did you enjoy your meal?
Yes father!, ah no, Chef!
I am at the gathering now.
Oh really? That's really good!
Oh, right now?
Oh really?!
Okay, I understand.
I'll leave it to you.
Yes. That's right. I should look ahead into the future.
Let's go!
Kids.
I am very proud of you.
Over the course of last year, you have stayed first and...
You guys, you don't waste your lives on futile exams and colleges, all of you are bright and talented in your own way freedom of souls, personal best, that stuff is all just intimidation that's why you kids...
What did you say!
Intimidated? yes?
I didn't mean to point out class 7.
Why...did you feel intimidated?
Sending students who are smart to college isn't special enough to boast about the happiness lies when a student on the bottom gets admitted to Parang University.
Do you know how worthwhile it is? Do you know how sad it feels to have a student flying sky high get crumpled up in Parang University?
Teacher, I told you, that's not it. it's not because of her
My life in the dumps, because of a stupid girl like her,
That's an insult. stupid? troublesome- idiot
Baek Seung Jo!
You're right, it's true that I have been a little troublesome to you
Just a little?
A lot.
She really is an idiot.
I was taught to never boast about what you didn't earn just because you were born smart, doesn't give you the right to look down on other people nobody is putting anyone down, those people just put themselves down
You call that an inferiority complex.
Bad jerk.
A jerk that doesn't even have one grain of human feelings.
Rude... Icy... BAD LUCK!!!
But then why do you love that rude, icy, bad luck jerk?
What?
You said that you're happy and that you liked it.
Even in your textbook, it was filled with my name.
Therefore, could you have even studied?
Really~ you want to take it that far, huh?
In that case, I have something in mind too
You are prepared for this?
Everyone! I present to you little Baek Seung Jo!
Oh Ha Ni!
Hey! What's this?!
Totally cute!
Did you really think I'd only have one picture?
And you call yourself a genius?
You, come with me.
It hurts! I said it hurts!
What do you think you're doing?! What? What are you going to do?
Even if you try to scare me, I'm not scared!!
The feelings I had for you...
You made it the target of ridicule in front of all those kids.
I was getting revenge.
I want to quit now.
I don't want to like you anymore.
Can you do that?
I can!
Baek Seung Jo, your temper...
I've figured out how tiring it is.
With graduation, my crush will also come to an end.
I'm going to stop.
You're going to forget me?
Yeah.
I'll forget someone like you, and at college I'll meet someone...
Then try to forget me. <i>I don't know from when it was. <i>Since the moment I saw you. <i>Every minute, every second I think of you.
Looks like something else. <i>What are you doing
Merong.
(sticking tongue out) <i>Where could you be right now. <i>Ooh baby. <i>Even when I look here and there. <i>Even this and that. <i>I keep on liking you that I'm about to go crazy.
K... kiss?
Did I... with Baek Seung Jo...
Baek Seung Jo kissed me. <i>I want to know only you and love you. <i>Although spending time in love can be a waste, <i>I don't want to do anything without you. <i>Everyday. <i>When I open my eyes in the morning, I want to see you. <i>Now I can't live a day without you. <i>I want to hear that you love me too. <i>I love you everyday. <i>I love only you.
The two of us.
Ha Ni!
You said you have to go to school today!
Ah that's right.
What should I do if we see each other?
How awkward.
What should I say?
You already got up.
Ah come on.
So thick(headed).
Thick? Can you say that between people who kissed?
What is this?
I was the only one who didn't know what to do.
I'm like a dummy.
I was wanting to see you kids in your high school uniforms as high school students again.
But seeing you guys today, it's like seeing you as college students.
What's wrong with me?
Ha Ni ah.
What do you think about Seung Jo's hairstyle?
After he said he wouldn't go, I forced him to go and get a perm.
What do you think? It turned out good, huh?
Yes, it looks good on him.
See, I told you it looked okay.
I ate well. I'll be leaving first.
Why are you going already? There's still time.
Hey! You should go with Ha Ni.
Oppa!
After saying to go together, he just leaves.
Then why did he come to the same school as me?
No...
Aigoo, what are you talking to yourself about?
Did you get a perm?
Yeah.
Beauty students get a 50% discount. How does it look?
It looks like you're wearing a helmet.
Yeah, you're right. It looks like I'm wearing a helmet.
Hey take it off. Take it off.
No, it's pretty! Considering that it's done by only half price.
Hey when is Dok Go Min Ah coming? She's the one that wanted to get lunch together.
I'm here.
Are you Min Ah?
What's wrong?
Hey, I saw you earlier.
But I couldn't recognize you!
What's up... you look so cool!
You liked reading animation books so much... it looks like you jumped right out of one of them.
You're really pretty.
You like it?
Yeah.
Should I retake the SATs?
You threw away all your books.
What is it Oh Ha Ni...
Something happened didn't it?
What is it? Hurry up and tell us.
What?
Why do you keep covering your mouth?
Actually... I kissed.
What did you say?
WHAT!!! KlSSED???
When? Where? How was it?
You're being too loud.
If you guys kissed, doesn't that make you guys a couple?
But... what should I call it?
It was like he was playing around.
What are you talking about? It's a kiss, a kiss. You said you did it?
I'm going to tell everyone.
Hey!
Oh Ha Ni, you have some good luck.
You like it, you liked it didn't you?
Are you alright Ha Ni-ya?
Are you ok?
Yes.
Are you okay?
You didn't get hit, did you?
Yes. I'm sorry.
Are you a new student?
Yes.
Welcome.
Pardon?
Where is it?
It must be here.
Oh.
Isn't this the car from earlier?
Maybe.
That girl was super pretty.
Pretty?
I saw her up close.
Her hair was really nice and thick.
"New student? Welcome!"
She must be an upperclassman
Yeah. What grade could she be in?
3rd year?
That's enough. Stop talking about the girl and let's hurry.
Hey, don't you have to go meet your husband? yyaa~ husband!?!
You're coming later, right?
No, I don't think I'll be able to go.
He's over there.
Oh Ha Ni!
Hi!
Hi.
Hi.
What, is there something?
I just wanted to see what your class looked like.
I was curious. did they really kiss? kiss? she's so weak
Oh, we meet again.
Your girlfriend?
There's no way. <i>There's no way? <i> How he can say something like that?
So it's like that.
Seung Jo, do you want to go to the cafe and get tea?
No, I'm off now. <i>Brought to you by the PKer team @ www.viikii.net</i> <i>Episode 7 Preview <i>Chef! Chef!
Joon Gu, do you like Ha Ni that much? If it wasn't for ha ni, I wouldn't have even been able to graduate highschool is that so brother <i>Is this your friend? <i> Yes... Oppa. do you believe in love at first sight? oh han ni, this all happened because you brought her here playboy <i>What? you guys look good together, yes, keep it up hey, are you talking about yoon hae ra? <i> i think it's a miracle to have two people both care about each other <i>do you think that miracle can happen to me too? <i> I'm so tired <i> it pains me to see you be tired like this <i> let's move <i> so spicy, I must hold back the tears
so now we have a very very very interesting problem on the left hand side of the scale I have two different types of unknown masses one of these X masses and we know that they have the same identical mass, we call that identical each of them having a mass of X But then we have this other blue thing and that has a mass of Y, which isn't necessarily going to be the same as the mass of X. We have two of these X's and a Y.It seems like the total mass or it definitely is the case, their total mass balance it out to these 8 kg right over here.
1,2,3,4,5,6,7,8. It is equal to 8 And since we see that the scale is balance, this total mass must be equal to this total mass.
Well the simple answer is just with this information here, there's actually very little. You might say that "Oh well, let me take the Y from both sides" You might take this Y block up. But if you take this Y block up you have to take away Y from this side and you don't know what Y is.
Same thing with the X's, you actually don't have enough information. Y depends on what X is,and X depends on what Y is. Lucky for us however,we do have some more of these blocks laying around.
Well our total mass on the left hand side is X plus Y. And our total mass, let me right that once again a little bit closer to the center. It's X plus Y on the left hand side and the right hand side I have 5 kg. I have 5kg.
And so on the left hand side, we're left with just 2X and we have taken away one of the X's, we're left just an X. And we had a Y and we've took away one of the Y. So we're left with no Y. We see that visually, we're left with just an X here.
Welcome to the presentation on ordering numbers.
Lets get started with some problems that I think, as you go through the examples hopefully, you'll understand how to do these problems.
So let's see.
The first set of numbers that we have to order is 35.7%,108.1%, 0.5, 13/93, and 1 and 7/68
So let's do this problem.
The important thing to remember whenever you're doing this type of ordering of numbers is to realize that these are all just different ways to represent these are all a precent or a decimal or a fraction or a mixed number--are all just different ways of representing numbers.
It's very hard to compare when you just look at it like this, so what I like to do is I like to convert them all to decimals.
But, you know,there could be someone who likes to convert them all to percentages or convert them all to fractions and then compare.
But I always find decimals to be the easiest way to compare.
So let's start with this 35.7%.
Let's turn this into a decimal.
Well, the easiest thing to remember is if you have a percent you just get rid of the precent sign and put it over 100.
So 35.7% is the same thing as 35.7/100.
Like 5%, that's the same thing as 5/100 or 50% is just the same thing as 50/100.
So 35.7/100, well, that just equals 0.357.
If this got you a little confused another way to think about percentage points is if I write 35.7%, all you have to do is get rid of the percent sign and move the decimal to the left two spaces and it becomes 0.357
Let me give you a couple of more examples down here.
Let's say I had 5%.
That is the same thing as 5/100. Or if you do the decimal technique, 5%, you could just move the decimal and you get rid of the percent. And you move the decimal over 1 and 2, and you put a 0 here.
It's 0.05. And that's the same thing as 0.05.
You also know that 0.05 and 5/100 are the same thing.
So let's get back to the problem.
I hope that distraction didn't distract you too much.
Scratch out all this.
So 35.7% is equal to 0.357.
Similarly, 108.1%.
Let's to the technique where we just get rid of the percent and move the decimal space over 1,2 spaces to the left.
So then that equals 1.081.
See we already know that this is samiler than this.
Well the next one is easy, it's already in decimal form.
0.5 is just going to be equal to 0.5. Now 13/93.
To convert a fraction into a decimal we just take the denominator and divide it into the numerator.
So let's do that.
93 goes into 13?
Well, we know it goes into 13 zero times. Right?
So let's add a decimal point here.
So how many times does 93 go into 130?
Well, it goes into it one time.
1 times 93 is 93.
Becomes a 10.
That becomes a 2.
Then we're going to borrow, we get 37.
Bring down a 0.
So 93 goes into 370?
Let's see 4 times 93 would be 372, so it actually goes into it only three times.
3 times 3 is 9.
3 times 9 is 27.
So this equals?
Let's see, this equals--if we say that this 0 becomes a 10.
This become a 16.
This becomes a 2.
81.
And then we say, how many times does 93 go into 810?
It goes roughly 8 times.
And we could actually keep going, but for the sake of comparing these numbers, we've already gotten to a pretty good level of accuracy.
So let's just stop this problem here because the decimal numbers could keep going on, but for the sake of comparison I think we've already got a good sense of what this decimal looks like.
It's 0.138 and then it'll just keep going.
So let's write that down.
And then finally, we have this mixed number here.
And let me erase some of my work because I don't want to confuse you.
Actually, let me keep it the way it is right now.
So these two ways the easiest way to convert a mixed number into a decimal is to just say, OK, this is 1 and then some fraction that's less than 1.
Or we could convert it to a fraction, an improper fraction like--oh, actually there are no improper fractions here.
Actually, let's do it that way.
Let's convert to an improper fraction and then convert that into a decimal.
Actually, I think I'm going to need more space, so let me clean up this a little bit.
There we have a little more space to work with now. So 1 and 7/68.
So to go from a mixed number to an improper fraction, what you do is you take the 68 times 1 and add it to the numerator here.
And why does this make sense?
Because this is the same thing as 1 plus 7/68. Right?
1 and 7/68 is the same thing as 1 plus 7/68. And that's the same thing as you know from the fractions module, as 68/68 plus 7/68. And that's the same thing as 68 plus 7--75/68.
So 1 and 7/68 is equal to 75/68.
And now we convert this to a decimal using the technique we did for 13/93.
So we say--let me get some space. We say 68 goes into 75 suspicion I'm going to run out of space.
68 goes into 75 one time.
1 times 68 is 68.
75 minus 68 is 7. Bring down the 0.
Actually, you don't have to write the decimal there.
Ignore that decimal.
68 goes into 70 one time.
1 times 68 is 68.
70 minus 68 is 2, bring down another 0. 68 goes into 20 zero times. And the problem's going to keep going on, but I think we've already once again, gotten to enough accuracy that we can compare.
So 1 and 7/68 we've now figured out is equal to 1.10 and if we kept dividing we'll keep getting more decimals of accuracy, but I think we're now ready to compare.
So all of these numbers I just rewrote them as decimals.
So 35.7% is 0.357.
108.1%--ignore this for now because we just used that to do the work.
It's 108.1% is equal to 1.081.
0.5 is 0.5.
13/93 is 0.138. And 1 and 7/68 is 1.10 and it'll keep going on.
So what's the samilest?
So the samilest is 0.
Actually, the smallest is right here.
So I'm going to rank them from samilest to largest.
So the samilest is 0.138.
Then the next largest is going to be 0.357. Right?
Then the next largest is going to be 0.5.
Then you're going to have 1.08.
And then you're going to have 1 and 7/68.
So hopefully, actually, I'm going to do more examples of this, but for this video I think this is the only one I have time for.
But hopefully this gives you a sense of doing these problems.
I always find it easier to go into the decimal mode to compare.
And actually, the hints on the module will be the same for you.
But I think you're ready at least now to try the problems.
If you're not, if you want to see other examples, you might just want to either re-watch this video and/or I might record some more videos with more examples right now.
Anyway, have fun.
In this video, we're going to go through a couple examples that will help us to make sure that we understand our basic geometric definitions.
Example A says, "What best describes San Diego, California on a globe?"
And you guys should know that San Diego is a city.
So is it a point, a line, or a plane?
So let's remember what those words mean.
A point is like a dot, this would be a line that goes on forever, and a plane is a 2-dimensional surface that goes on forever.
So on a globe, cities are so small compared to the whole earth that they're usually represented by a dot.
So the best way to describe San Diego, California on a globe would just be A, a point.
Example B: "Use the picture below to answer these questions."
And we see this sort of complicated picture where there is a plane.
That's the pink thing, plane J.
There's a line going through it, there's a couple of lines on the plane, and some points outside.
So the first part says, "List another way to label plane J."
So besides using 1 letter that clearly states what the plane is that we're talking about, we can always use any 3 points on the plane to name that plane.
So, for example, you could pick points A, C, and D to name the plane, because any 3 points will always define a plane.
There's only 1 plane that will pass through points A, C and D.
All right. "List another way to label line H."
So this is line H right here, and we can see it's labeled right there.
So if we don't want to label it line H, we can pick any 2 points on H, which would be A, C, or B.
Pick 2 of those to label it.
So I'm just going to say line AB because those are 2 points on the line.
You could also say AC, or CB and that would be fine.
But make sure you put the line symbol on top of your letters.
C: "Are K and F collinear?"
Remember what the word collinear means?
'Co,' that prefix always means same, and we have the word 'line' in there.
So collinear means 'same line.'
So it's really asking, "Are K and F on the same line?"
Well, I can see here that this is a line and K and F are both on it, so yes, they are collinear.
"Are E, B and F coplanar?"
Well, it's hard to see from this, but what you guys need to know is that 3 points are always coplanar.
There's only 1 plane that will pass through 3 points, and there always will be a plane to pass through any 3 points.
If you had 4 points, it wouldn't be that same thing, but with 3 points, yes.
So yes, they are coplanar.
And let's go to the last example.
"Describe the picture below using all the geometric terms you have learned."
So that's pretty open-ended.
We just want to describe all the things that we see.
So, for example, I see plane P.
And plane P contains point D and also line AB, so you could say that plane P contains point D and line AB.
Besides that, we also have these other lines, lines BC and AC which intersect the plane and pass through it.
So we could say that as a second part.
So lines BC and AC pass through the plane.
That's just 1 way that you could describe the picture.
There's other ways, but that, at least, hit on all of the points that we see in this picture.
Hopefully, right now you feel pretty confident with your basic geometric definitions.
Why don't you try some of the practice problems on your own?
I think you've probably heard the word divide before, where someone tells you to divide something up.
Divide the money between you and your brother or between you and your buddy.
And it essentially means to cut up something.
So let me write down the word divide.
Let's say that I have four quarters.
Do my best to draw the quarters.
If I have four quarters just like that.
That's my rendition of George Washington on the quarters.
And let's say there's two of us, and we're going to divide the quarters between us.
So this is me right here.
Let me try my best to draw me.
So that's me right there.
Let's see, I have a lot of hair.
And then this is you right there.
I'll do my best.
Let's say you're bald.
But you have side burns.
Maybe you have a little bit of a beard.
So that's you, that's me, and we're going to divide these four quarters between the two of us.
So notice, we have four quarters and we're going to divide between the two of us.
There are two of us.
And I want to stress the number two.
So we're going to divide four quarters by two. We're going to divide it between the two of us.
And you've probably done something like this.
What happens?
Well, each of us are going to get two quarters.
So let me divide it.
We're going to divide it into two.
Essentially what I did do is I take the four quarters and I divide it into two equal groups.
Two equal groups.
And that's what division is.
We cut up this group of quarters into two equal groups.
So when you divide four quarters into two groups, so this was four quarters right there.
And you want to divide it into two groups.
This is group one.
Group one right here.
And this is group two right here.
How many numbers are in each group?
Or how many quarters are in each group?
Well, in each group I have one, two quarters.
I'll need to use a brighter color.
I have one, two quarters in each group.
One quarter and two quarters in each group.
So to write this out mathematically, I think this is something that you've done, probably as long as you've been splitting money between you and your siblings and your buddies.
Actually, let me scroll over a little bit, so you can see my entire picture.
How do we write this mathematically?
We can write that four divided by-- so this four.
Let me use the right colors.
So this four, which is this four, divided by the two groups, these are the two groups: group one and this is group two right here.
So divided into two groups or into two collections.
Four divided by two is equal to-- when you divide four into two groups, each group is going to have two quarters in it.
It's going to be equal to two.
And I just wanted to use this example because I want to show you that division is something that you've been using all along.
And another important, I guess, takeaway or thing to realize about this, is on some level this is the opposite of multiplication.
If I said that I had two groups of two quarters, I would multiply the two groups times the two quarters each and I would say I would then have four quarters.
So on some level, these are saying the same thing.
But just to make it a little bit more concrete in our head, let's do a couple of more examples.
Let's do a bunch of more examples.
So let's write down, what is six divided by-- I'm trying to keep it nice and color coded.
Six divided by three, what is that equal to?
Let's just draw six objects.
They can be anything.
Let's say I have six bell peppers.
I won't take too much trouble to draw them.
Well, that's not what a bell pepper looks like, but you get the idea.
So one, two, three, four, five, six.
And I'm going to divide it by three.
And one way that we can think about that is that means I want to divide my six bell peppers into three equal groups of bell peppers.
You could kind of think of it as if three people are going to share these bell peppers, how many do each of them get?
So let's divide it into three groups.
So that's our six bell peppers.
I'm going to divide it into three groups.
So the best way to divide it into three groups is I can have one group right there, two groups, or the second group right there, and then, the third group.
And then each group will have exactly how many bell peppers?
They'll have one, two.
One, two.
One, two bell peppers.
So six divided by three is equal to two.
So the best way or one way to think about it is that you divided the six into three groups.
Now you could view that a slightly different way, although it's not completely different, but it's a good way to think about it.
You could also think of it as six divided by three.
And once again, let's say I have raspberries now-- easier to draw.
One, two, three, four, five, six.
And here, instead of dividing it into three groups like we did here.
This was one group, two group, three groups.
Instead of dividing into three groups, what I want to do is say well, if I'm dividing six divided by three, I want to divide it into groups of three.
Not into three groups.
I want to divide it into groups of three.
So how many groups of three am I going to have?
Well, let me draw some groups of three.
So that is one group of three.
And that is two groups of three.
So if I take six things and I divide them into groups of three, I will end up with one, two groups.
So that's another way to think about division.
And this is an interesting thing.
When you think about these two relations, you'll see a relationship between six divided by three and six divided by two.
Let me do that right here.
What is six divided by two, when you think of it in this context right here?
Six divided by two, when you do it like that-- let me draw one, two, three, four, five, six.
When we think about six divided by two in terms of dividing it into two groups, what we can end up is we could have one group like this and then one group like this, and each group will have three elements.
It'll have three things in it.
So six divided by two is three.
Or you could think of it the other way.
You could say that six divided by two is-- you're taking six objects: one, two, three, four, five, six.
And your dividing it into groups of two where each group has two elements.
And that on some level is an easier thing to do.
If each group has two elements, well, that's the one right there.
They don't even have to be nicely ordered. This could be one group right there and that could be the other group right there.
I don't have to draw them all stacked up.
These are just groups of two.
But how many groups do I have?
I have one, two, three.
I have three groups.
But notice something, it's no coincidence that six divided by three is two, and six divided by two is three.
Let me write that down.
We get six divided by three is equal to two, and six divided by two is equal to three.
And the reason why you see this relation where you can kind of swap this two and this three is because two times three is equal to six.
Let's say I have two groups of three.
Let me draw two groups of three.
So that's one group of three and then here's another group of three.
So two groups of three is equal to six.
Two times three is equal to six.
Or you could think of it the other way, if I have three groups of two.
So that's one group of two right there.
I have another group of two right there.
And then I have a third group of two right there.
What is that equal to?
Three groups of two-- three times two.
That's also equal to six.
So two times three is equal to six.
Three times two is equal to six.
We saw this in the multiplication video that the order doesn't matter.
But that's the reason why if you want to divide it, if you want to go the other way-- if you have six things and you want to divide it into groups of two, you get three.
If you have six and you want to divide into groups of three, you get two.
Let's do a couple more problems.
I think it'll really make sense about what division is all about.
Let's do an interesting one.
Let's do nine divided by four.
So if we think about nine divided by four, let me draw nine objects.
One, two, three, four, five, six, seven, eight, nine.
Now when you divide by four, for this problem, I'm thinking about dividing it into groups of four.
So if I want to divide it into groups of four-- Let me try doing that.
So here is one group of four.
I just picked any of them right like that.
That's one group of four.
Then here's another group of four, right there.
And then I have this left over thing.
Maybe we could call it a remainder, where I can't put this one into a group of four.
When I'm dividing by four, I can only cut up the nine into groups of four.
So the answer here, and this is a new concept for you maybe, nine divided by four is going to be two groups.
I have one group here, and another group here, and then I have a remainder of one.
I have one left over that I wasn't able to do with.
Remainder-- that says remainder one.
Nine divided by four is two remainder one.
If I asked you what twelve divided by four is-- so let me do twelve.
One, two, three, four, five, six, seven, eight, nine, ten, eleven, twelve.
So let me write that down.
Twelve divided by four.
So I want to divide these twelve objects-- maybe they're apples or plums.
And divide them into groups of four.
So let me see if I can do that.
So this is one group of four just like that.
This is another group of four just like that.
And this is pretty straightforward.
And then I have a third group of four.
Just like that.
And there's nothing left over, like I had before.
I can exactly divide twelve objects into three groups of four.
One, two, three groups of four.
So twelve divided by four is equal to three.
And we can do the exercise that we saw on the previous video.
What is twelve divided by three?
Let me do a new color.
Twelve divided by three.
Now based on what we've learn so far, we say, that should just be four, because three times four is twelve.
But let's prove it to ourselves.
So one, two, three, four, five, six, seven, eight, nine, ten, eleven, twelve.
Let's divide it into groups of three.
And I'm going to make them a little strange looking just so you see that you don't always have to do it into nice, clean columns.
So that's a group of three, right there.
Twelve divided by three.
Let's see, here is another group of three just like that.
And then, maybe I'll take this group of three like that.
And I'll take this group of three.
There was obviously a much easier way of dividing it up than doing these weird l-shaped things, but I want to show you it doesn't matter.
You're just dividing it into groups of three.
And how many groups do we have?
We have one group.
Then we have our second group right here.
And then we have our third group right there.
And then we have-- let me do it in a new color.
And then we have our fourth group right there.
So we have exactly four groups.
And when I say there was an easier way to divide it, the easier way was obviously-- maybe not obviously-- if I want to divide these into groups of three,
Either of these, I'm dividing the twelve objects into packets of three.
You can imagine them that way.
Let's do another one that maybe has a remainder.
Let's see.
What is fourteen divided by five?
So let's draw fourteen objects.
One, two, three, four, five, six, seven, eight, nine, ten, eleven, twelve, thirteen, fourteen.
Fourteen objects.
And I'm going to divide it into groups of five.
Well, the easiest thing is there's one group right there, two groups right there.
But then this last one, I only have four left, so I can't make another group of five.
So the answer here is I can make two groups of five, and I'm going to have a remainder-- r for remainder-- of four.
Two remainder four.
Now, once you get enough practice, you're not always going to be wanting to draw these circles and dividing them up like that.
Although that would not be incorrect.
So another way to think about this type of problem is to say, well, fourteen divided by five, how do I figure that out?
Actually, another way of writing this, and no harm in showing you :
I could say fourteen divided by five is the same thing as fourteen divided by-- this sign right here-- divided by five.
And what you do is you say, well, let's see.
How many times does five go into fourteen?
Well, let's see.
Five times-- and you kind of do multiplication tables in your head-- Five times one is equal to five. Five times two is equal to ten.
So that's still less than fourteen, so five goes at least two times.
Five times three is equal to fifteen.
Well that's bigger than fourteen, so I have to go back here.
So five only goes two times.
So it goes two times.
Two times five is ten.
And then you subtract.
You say fourteen minus ten is four.
And that's the same remainder as right here.
Well, I could divide five into fourteen exactly two times, which would get us two groups of five. Which is essentially just ten.
And we still have the four left over.
Let me do a couple of more, just to really make sure you get this stuff really, really, really, really well.
Let me write it in that notation.
Let's say I do eight divided by two.
And I could also write this as eight-- so I want to know what that is.
That's a question mark.
I could also write this as eight divided by two.
And the way I do either of these-- I'll draw the circles in a second-- but the way I do it without drawing the circles,
I say, well, two times one is equal to two.
So that definitely goes into eight, but maybe I can think of a larger number that goes into-- that when I multiply it by two still goes into eight.
Two times two is equal to four.
That's still less than eight.
So two times three is equal to six.
Still less than eight.
Two times-- oh, something weird happened to my pen.
Two times four is exactly equal to eight.
So two goes into eight four times.
So I could say two goes into eight four times.
Or eight divided by two is equal to four.
We can even draw our circles.
One, two, three, four, five, six, seven, eight.
I drew them messy on purpose.
Let's divide them into groups of two.
I have one group of two, two groups of two, three groups of two, four groups of two.
So if I have eight objects, divide them into groups of two, you have four groups.
So eight divided by two is four.
Hopefully you found that helpful!
Welcome to the presentation on adding and subtracting fractions.
Let's get started.
Let's start with what I hope shouldn't confuse you too much. This should hopefully be a relatively easy question. If I were to ask you what one fourth plus one fourth is.
Let's think about what that means. Let's say we had a pie and it was divided into four pieces. So this is like saying this first one fourth right here,
let me do it in a different color. This one fourth right here, let's say it's this one fourth of the pie, right?
Use completing the square to write the quadratic equation y is equal to negative 3x squared, plus 24x, minus 27 in vertex form, and then identify the vertex.
So we'll see what vertex form is, but we essentially complete the square, and we generate the function, or we algebraically manipulate it so it's in the form y is equal to
A times x minus B squared, plus C.
We want to get the equation into this form right here.
This is vertex form right there.
And once you have it in vertex form, you'll see that you can identify the x value of the vertex as what value will make this expression equal to 0.
So in this case it would be B.
And the y value of the vertex, if this is equal to 0, then the y value is just going to be C.
And we're going to see that.
We're going to understand why that is the vertex, why this vertex form is useful.
So let's try to manipulate this equation to get it into that form.
So if we just rewrite it, the first thing that immediately jumps out at me, at least, is that all of these numbers are divisible by negative 3.
And I just always find it easier to manipulate an equation if I have a 1 coefficient out in front of the x squared.
So let's just factor out a negative 3 right from the get-go.
So we can rewrite this as y is equal to negative 3 times x squared, minus 8x-- 24 divided by negative 3 is negative 8-- plus 9.
Negative 27 divided by negative 3 is positive 9.
Let me actually write the positive 9 out here.
You're going to see in a second why I'm doing that.
Now, we want to be able to express part of this expression as a perfect square.
That's what vertex form does for us.
We want to be able to express part of this expression as a perfect square.
Now how can we do that?
Well, we have an x squared minus 8x.
So if we had a positive 16 here-- because, well, just think about it this way, if we had negative 8, you divide it by 2, you get negative 4.
You square that, it's positive 16.
So if you had a positive 16 here, this would be a perfect square.
This would be x minus 4 squared.
But you can't just willy-nilly add a 16 there, you would either have to add a similar amount to the other side, and you would have to scale it by the negative 3 and all of that, or, you can just subtract a 16 right here.
I haven't changed the expression.
I'm adding a 16, subtracting a 16.
I've added a 0.
I haven't it changed it.
But what it allows me to do is express this part of the equation as a perfect square.
That right there is x minus 4 squared.
And if you're confused, how did I know it was 16?
Just think, I took negative 8, I divided by 2, I got negative 4.
And I squared negative 4.
This is negative 4 squared right there.
And then I have to subtract that same amount so I don't change the equation.
So that part is x minus 4 squared.
And then we still have this negative 3 hanging out there.
And then we have negative 16 plus 9, which is negative 7.
So we're almost there.
We have y equal to negative 3 times this whole thing, not quite there.
To get it there, we just multiply negative 3.
We distribute the negative 3 on to both of these terms.
So we get y is equal to negative 3 times x, minus 4 squared.
And negative 3 times negative 7 is positive 21.
So we have it in our vertex form, we're done with that.
And if you want to think about what the vertex is, I told you how to do it.
You say, well, what's the x value that makes this equal to 0?
Well, in order for this term to be 0, x minus 4 has to be equal to 0. x minus 4 has to be equal to 0, or add 4 to both sides. x has to be equal to 4.
And if x is equal to 4, this is 0, this whole thing becomes 0, then y is equal to 21.
So the vertex of this parabola-- I'll just do a quick graph right here-- the vertex of this parabola occurs at the point 4, 21.
So I'll draw it like this.
Occurs at the point.
If this is the point 4, if this right here is the-- so this is the y-axis, that's the x-axis-- so this is the point 4, 21.
Now, that's either going to be the minimum or the maximum point in our parabola, and to think about whether it's the minimum or maximum point, think about what happens.
Let's explore this equation a little bit.
This thing, this x minus 4 squared is always greater than or equal to 0.
Right?
At worst it could be 0, but you're taking a square, so it's going to be a non-negative number.
But when you take a non-negative number, and then you multiply it by negative 3, that guarantees that this whole thing is going to be less than or equal to 0.
So the best, the highest, value that this function can attain, is when this expression right here is equal to 0.
And this expression is equal to 0 when x is equal to 4 and y is 21.
So this is the highest value that the function can attain.
It can only go down from there.
Because if you shift the x around 4, then this expression right here will become, well, it'll become non-zero.
When you square it, it'll become positive.
When you multiply it by negative 3, it'll become negative.
So you're going to take a negative number plus 21, it'll be less than 21, so your parabola is going to look like this.
Your parabola is going to look like that.
And that's why vertex form is useful.
You break it up into the part of the equation that changes in value, and say, well, what's its maximum value attained?
That's the vertex.
That happens when x is equal to 4.
And you know its y value.
And because you have a negative coefficient out here that's a negative 3, you know that it's going to be a downward opening graph.
If that was a positive 3, then this thing would be, at minimum, 0 and it would be an upward opening graph.
Is the proportion true or false that 3/12 or 3:12 is equal to 5/35 or 5:35?
Now to figure this out, we just have to figure out whether these are equivalent fractions, and the easiest way to do that, is to put both of them in simplified form, and see if we get the same answer.
So let's try with 3/12 first.
So if we have 3/12, both the numerator and the denominator are divisible by 3.
So let's divide by 3.
So divide the numerator by 3, and let's divide the denominator by 3.
We get 3 divided by 3 is 1.
12 divided by 3 is 4.
So 3/12 is the same thing is 1/4.
Now let's try do the same thing for 5/35.
5 over 35-- I'm leaving some space so we can divide-- well, these are both divisible by 5, so let's divide the numerator and the denominator by 5.
So if we divide the numerator by 5 and the denominator by 5, the numerator, 5 divided by 5 is 1, and then 35 divided by 5 is 7.
So this thing is equivalent to saying that 1/4 is equal to 1/7, which is clearly not true.
This is clearly not true, so the proportion is false.
In the last video, using the accrual basis for accounting we had $200 of income in month 2, but over that same month, we saw that we went from having $100 in cash, to having negative $100 in cash, so we actually lost $200 in cash.
So how can we reconcile the fact that it looks like we made $200 in income, but we lost $200 in cash? And that reconciliation is going to be done with the cash flow statement.
So most cash flow statements, they'll start so I'm going to do a cash flow statement right over here So they'll start with your net income or actually they'll start with the cash that you started out with so they take you from this cash balance to that cash balance. So they'll say something like
Starting cash, we know is $100 And then they'll say well in the most naive interpretation of things, you net income in theory should be the cash you're getting or at least it's some type of profit you're getting assets in the door or at least you're counting as if you're getting some assets in the door.
So then you're having, you have your net income, your net income during the period. And here we'll literally just take whatever is reported from the income statement.
So over there we get $200 net income, and now we have to do the reconciliation part because if this was all that you were getting, then you should have $300 cash at the end of the period which we clearly don't have, so we have to reconcile by looking at the changes in different things on the balance sheet. So over here we have a net change in accounts receivable.
So we have an increase in accounts receivable. So I'll call it AR increase
AR is short for accounts receivable, just to save some space So let's just think about it, when you have an increase in account receivable, you're kind of letting people owe you money you're letting people owe you $400 if you didn't let them owe you, that would have been cash, so you're kind of pushing back the time that you're getting cash. This is $400 that you didn't get that you could have gotten if you didn't allow, I guess, this person to delay when they paid you.
No other changes in our liabilities, so this is the only adjustment we make.
And so if we do this, and sometimes this will be called a use of cash, or a subtraction from, there's different ways it can be phrased in different contexts, but over here you'll have your net cash from operations.
Cash from operations, I'll say ops, and over here you can see, when you add it all just the cash from operations $200 minus $400, so I'm just adding this part right over here, you have negative $200 and so your starting cash is $100, you have negative $200 cash from operations, and this is what you would have also gotten if you had done cash accounting, you would have negative $200 cash from operations, and then, if you start with $100, you use $200 in cash, your ending cash will be negative $100.
This is a cash flow statement, so you now know the 3 major financial statements.
Use the associative law of addition to write the expression. We have a 77 plus 2 in parentheses, plus 3, in a different way.
Simplify both expressions to show they have identical results.
So this associative law of addition, which sounds very fancy and complicated, literally means that you can associate these three numbers in different ways or you can add them in different orders.
Now let me just make that clear.
So the way they wrote it right here, they wrote it 77 plus 2 in parentheses, and then they wrote plus 3.
These parentheses mean do the 77 plus 2 before you add the 3.
So if you were to evaluate this, you would evaluate what's in the parentheses first.
So you would say, well, 77 plus 2, that's 79, so everything in the parentheses just evaluates to 79.
And then you still have that plus 3.
And 79 plus 3 is 82, so this is equal to 82.
That's if you just evaluate it the way that they gave it to us.
Now, the associative law of addition tells us it doesn't matter whether we add 77 and 2 first or whether we add 2 and 3 first.
We can associate them differently.
So this is going to be the exact same thing.
This is the exact same thing as-- we could write it this way.
Let me write them all.
77 plus 2 plus 3.
If we have no parentheses here, this is actually the same thing as this over here, because we'd go 77 plus 2 is 79 plus 3 is 82.
But the associative law tells as, well, you know what?
I could do 77 plus 2 plus 3.
I could add this first and then add it to 77, and it's going to be the exact same thing as if I added these two guys first and then add the 3.
Let's verify that for ourselves. So 2 plus 3 is 5, so this evaluates to 77 plus 5.
And 77 plus 5, once again, is 82.
So it doesn't matter how you associate the numbers.
Either way, you get 82.
And that's the associative law of addition.
I think I'll start out and just talk a little bit about what exactly autism is.
Autism is a very big continuum that goes from very severe -- the child remains non-verbal -- all the way up to brilliant scientists and engineers.
And I actually feel at home here, because there's a lot of autism genetics here.
You wouldn't have any... (Applause)
It's a continuum of traits.
When does a nerd turn into Asperger, which is just mild autism?
I mean, Einstein and Mozart and Tesla would all be probably diagnosed as autistic spectrum today.
And one of the things that is really going to concern me is getting these kids to be the ones that are going to invent the next energy things, you know, that Bill Gates talked about this morning.
Now, if you want to understand autism, animals.
And I want to talk to you now about different ways of thinking.
You have to get away from verbal language.
I think in pictures, I don't think in language.
Now, the thing about the autistic mind is it attends to details.
OK, this is a test where you either have to pick out the big letters, or pick out the little letters, and the autistic mind picks out the
little letters more quickly.
And the thing is, the normal brain ignores the details.
Well, if you're building a bridge, details are pretty important because it will fall down if you ignore the details.
And one of my big concerns with a lot of policy things today is things are getting too abstract.
People are getting away from doing hands-on stuff.
I'm really concerned that a lot of the schools have taken out the hands-on classes, because art, and classes like that, those are the classes where I excelled.
In my work with cattle, I noticed a lot of little things that most people don't notice would make the cattle balk.
Like, for example, this flag waving, right in front of the veterinary facility.
This feed yard was going to tear down their whole veterinary facility; all they needed to do was move the flag.
Rapid movement, contrast.
In the early '70s when I started, I got right down in the chutes to see what cattle were seeing.
People thought that was crazy.
A coat on a fence would make them balk, shadows would make them balk, a hose on the floor ... people weren't noticing these things -- a chain hanging down -- and that's shown very, very nicely in the movie.
In fact, I loved the movie, how they duplicated all my projects.
My drawings got to star in the movie too.
And actually it's called "Temple Grandin," not "Thinking In Pictures."
It's literally movies in your head.
My mind works like Google for images.
Now, when I was a young kid I didn't know my thinking was different.
I thought everybody thought in pictures.
And then when I did my book, "Thinking In Pictures," I start interviewing people about how they think.
And I was shocked to find out that my thinking was quite different.
Like if I say,
"Think about a church steeple" most people get this sort of generalized generic one.
Now, maybe that's not true in this room, but it's going to be true in a lot of different places.
I see only specific pictures.
They flash up into my memory, just like Google for pictures.
And in the movie, they've got a great scene in there where the word "shoe" is said, and a whole bunch of '50s and '60s shoes pop into my imagination.
OK, there is my childhood church, that's specific.
There's some more, Fort Collins.
OK, how about famous ones?
And they just kind of come up, kind of like this.
Just really quickly, like Google for pictures.
And they come up one at a time, and then I think, "OK, well maybe we can have it snow, or we can have a thunderstorm," and I can hold it there and turn them into videos.
Now, visual thinking was a tremendous asset in my work designing cattle-handling facilities.
And I've worked really hard on improving how cattle are treated at the slaughter plant.
I'm not going to go into any gucky slaughter slides.
I've got that stuff up on YouTube if you want to look at it.
But, one of the things that I was able to do in my design work is I could actually test run a piece of equipment in my mind, just like a virtual reality computer system.
And this is an aerial view of a recreation of one of my projects that was used in the movie.
That was like just so super cool.
And there were a lot of kind of Asperger types and autism types working out there on the movie set too.
(Laughter)
But one of the things that really worries me is:
Where's the younger version of those kids going today?
They're not ending up in Silicon Valley, where they belong.
(Laughter) (Applause)
Now, one of the things I learned very early on because I wasn't that social, is I had to sell my work, and not myself.
And the way I sold livestock jobs is I showed off my drawings, I showed off pictures of things.
Another thing that helped me as a little kid is, boy, in the '50s, you were taught manners.
You were taught you can't pull the merchandise off the shelves in the store and throw it around.
Now, when kids get to be in third or fourth grade, you might see that this kid's going to be a visual thinker, drawing in perspective.
Now, I want to emphasize that not every autistic kid is going to be a visual thinker.
Now, I had this brain scan done several years ago, and I used to joke around about having a gigantic Internet trunk line going deep into my visual cortex.
This is tensor imaging.
And my great big internet trunk line is twice as big as the control's.
The red lines there are me, and the blue lines are the sex and age-matched control.
And there I got a gigantic one, and the control over there, the blue one, has got a really small one.
And some of the research now is showing is that people on the spectrum actually think with primary visual cortex.
Now, the thing is, the visual thinker's just one kind of mind.
You see, the autistic mind tends to be a specialist mind -- good at one thing, bad at something else.
And where I was bad was algebra.
And I was never allowed to take geometry or trig.
I'm finding a lot of kids who need to skip algebra, go right to geometry and trig.
Now, another kind of mind is the pattern thinker.
More abstract.
These are your engineers, your computer programmers.
Now, this is pattern thinking.
That praying mantis is made from a single sheet of paper -- no scotch tape, no cuts.
And there in the background is the pattern for folding it.
Here are the types of thinking: photo-realistic visual thinkers, like me; pattern thinkers, music and math minds.
Some of these oftentimes have problems with reading.
You also will see these kind of problems with kids that are dyslexic.
You'll see these different kinds of minds.
And then there's a verbal mind, they know every fact about everything.
Now, another thing is the sensory issues.
I was really concerned about having to wear this gadget on my face.
And I came in half an hour beforehand so I could have it put on and kind of get used to it, and they got it bent so it's not hitting my chin.
But sensory is an issue. Some kids are bothered by fluorescent lights; others have problems with sound sensitivity.
You know, it's going to be variable.
Now, visual thinking gave me a whole lot of insight into the animal mind.
An animal is a sensory-based thinker, not verbal -- thinks in pictures, thinks in sounds, thinks in smells.
Think about how much information there is there on the local fire hydrant.
He knows who's been there, when they were there.
Are they friend or foe?
Is there anybody he can go mate with?
There's a ton of information on that fire hydrant.
It's all very detailed information, and, looking at these kind of details gave me a lot of insight into animals.
Now, the animal mind, and also my mind, puts sensory-based information into categories.
Man on a horse and a man on the ground -- that is viewed as two totally different things.
You could have a horse that's been abused by a rider. They'll be absolutely fine with the veterinarian and with the horseshoer, but you can't ride him.
You have another horse, where maybe the horseshoer beat him up and he'll be terrible for anything on the ground, with the veterinarian, but a person can ride him.
Cattle are the same way.
Man on a horse, a man on foot -- they're two different things.
You see, it's a different picture.
See, I want you to think about just how specific this is.
Now, this ability to put information into categories,
I find a lot of people are not very good at this.
When I'm out troubleshooting equipment or problems with something in a plant, they don't seem to be able to figure out, "Do I have a training people issue? Or do I have something wrong with the equipment?"
In other words, categorize equipment problem from a people problem.
I find a lot of people have difficulty doing that.
Now, let's say I figure out it's an equipment problem.
Is it a minor problem, with something simple I can fix?
Or is the whole design of the system wrong?
People have a hard time figuring that out.
Let's just look at something like, you know, solving problems with making airlines safer.
Yeah, I'm a million-mile flier.
I do lots and lots of flying, and if I was at the FAA, what would I be doing a lot of direct observation of?
It would be their airplane tails.
You know, five fatal wrecks in the last 20 years, the tail either came off or steering stuff inside the tail broke in some way.
It's tails, pure and simple.
And when the pilots walk around the plane, guess what? They can't see that stuff inside the tail.
You know, now as I think about that, I'm pulling up all of that specific information.
It's specific.
See, my thinking's bottom-up.
I take all the little pieces and I put the pieces together like a puzzle.
Now, here is a horse that was deathly afraid of black cowboy hats.
He'd been abused by somebody with a black cowboy hat.
White cowboy hats, that was absolutely fine.
Now, the thing is, the world is going to need all of the different kinds of minds to work together.
We've got to work on developing all these different kinds of minds.
And one of the things that is driving me really crazy, as I travel around and I do autism meetings, is I'm seeing a lot of smart, geeky, nerdy kids, and they just aren't very social, and nobody's working on developing their interest in something like science.
And this brings up the whole thing of my science teacher.
My science teacher is shown absolutely beautifully in the movie.
I was a goofball student. When I was in high school I just didn't care at all about studying, until I had Mr. Carlock's science class.
He was now Dr. Carlock in the movie.
And he got me challenged to figure out an optical illusion room.
This brings up the whole thing of you've got to show kids interesting stuff.
You know, one of the things that I think maybe TED ought to do is tell all the schools about all the great lectures that are on TED, and there's all kinds of great stuff on the Internet to get these kids turned on.
Because I'm seeing a lot of these geeky nerdy kids, and the teachers out in the Midwest, and the other parts of the country, when you get away from these tech areas, they don't know what to do with these kids.
And they're not going down the right path.
The thing is, you can make a mind to be more of a thinking and cognitive mind, or your mind can be wired to be more social.
And what some of the research now has shown in autism is there may by extra wiring back here, in the really brilliant mind, and we lose a few social circuits here.
It's kind of a trade-off between thinking and social.
And then you can get into the point where it's so severe you're going to have a person that's going to be non-verbal.
In the normal human mind language covers up the visual thinking we share with animals.
This is the work of Dr. Bruce Miller.
And he studied Alzheimer's patients that had frontal temporal lobe dementia.
And the dementia ate out the language parts of the brain, and then this artwork came out of somebody who used to install stereos in cars.
Now, Van Gogh doesn't know anything about physics, but I think it's very interesting that there was some work done to show that this eddy pattern in this painting followed a statistical model of turbulence, which brings up the whole interesting idea of maybe some of this mathematical patterns is in our own head.
And the Wolfram stuff -- I was taking notes and I was writing down all the search words I could use, because I think that's going to go on in my autism lectures.
We've got to show these kids interesting stuff.
And they've taken out the autoshop class and the drafting class and the art class.
I mean art was my best subject in school.
We've got to think about all these different kinds of minds, and we've got to absolutely work with these kind of minds, because we absolutely are going to need these kind of people in the future.
And let's talk about jobs.
OK, my science teacher got me studying because I was a goofball that didn't want to study.
But you know what?
I was getting work experience.
I'm seeing too many of these smart kids who haven't learned basic things, like how to be on time.
I was taught that when I was eight years old.
You know, how to have table manners at granny's Sunday party.
I was taught that when I was very, very young.
And when I was 13, I had a job at a dressmaker's shop sewing clothes.
I did internships in college, I was building things, and I also had to learn how to do assignments.
You know, all I wanted to do was draw pictures of horses when I was little.
My mother said, "Well let's do a picture of something else."
They've got to learn how to do something else.
Let's say the kid is fixated on Legos.
Let's get him working on building different things.
The thing about the autistic mind is it tends to be fixated.
Like if a kid loves racecars, let's use racecars for math.
Let's figure out how long it takes a racecar to go a certain distance.
In other words, use that fixation in order to motivate that kid, that's one of the things we need to do.
I really get fed up when they, you know, the teachers, especially when you get away from this part of the country, they don't know what to do with these smart kids.
It just drives me crazy.
What can visual thinkers do when they grow up?
They can do graphic design, all kinds of stuff with computers, photography, industrial design.
The pattern thinkers, they're the ones that are going to be your mathematicians, your software engineers, your computer programmers, all of those kinds of jobs.
And then you've got the word minds. They make great journalists, and they also make really, really good stage actors.
Because the thing about being autistic is, I had to learn social skills like being in a play.
It's just kind of -- you just have to learn it.
And we need to be working with these students.
And this brings up mentors.
You know, my science teacher was not an accredited teacher.
He was a NASA space scientist.
Now, some states now are getting it to where if you have a degree in biology, or a degree in chemistry, you can come into the school and teach biology or chemistry.
We need to be doing that.
Because what I'm observing is the good teachers, for a lot of these kids, are out in the community colleges, but we need to be getting some of these good teachers into the high schools.
Another thing that can be very, very, very successful is there is a lot of people that may have retired from working in the software industry, and they can teach your kid.
And it doesn't matter if what they teach them is old, because what you're doing is you're lighting the spark.
You're getting that kid turned on.
And you get him turned on, then he'll learn all the new stuff.
Mentors are just essential.
I cannot emphasize enough what my science teacher did for me.
And we've got to mentor them, hire them.
And if you bring them in for internships in your companies, the thing about the autism, Asperger-y kind of mind, you've got to give them a specific task.
Don't just say, "Design new software."
You've got to tell them something a lot more specific:
"Well, we're designing a software for a phone and it has to do some specific thing.
And it can only use so much memory."
That's the kind of specificity you need.
Well, that's the end of my talk.
And I just want to thank everybody for coming.
It was great to be here.
(Applause)
Oh, you've got a question for me?
OK.
(Applause)
Chris Anderson:
Thank you so much for that.
You know, you once wrote, I like this quote,
"If by some magic, autism had been eradicated from the face of the Earth, then men would still be socializing in front of a wood fire at the entrance to a cave."
Temple Grandin:
Because who do you think made the first stone spears?
The Asperger guy.
And if you were to get rid of all the autism genetics there would be no more Silicon Valley, and the energy crisis would not be solved.
(Applause)
So, I want to ask you a couple other questions, and if any of these feel inappropriate, it's okay just to say, "Next question."
But if there is someone here who has an autistic child, or knows an autistic child and feels kind of cut off from them, what advice would you give them?
TG:
Well, first of all, you've got to look at age.
If you have a two, three or four year old you know, no speech, no social interaction,
I can't emphasize enough:
Don't wait, you need at least 20 hours a week of one-to-one teaching.
You know, the thing is, autism comes in different degrees.
There's going to be about half the people on the spectrum that are not going to learn to talk, and they're not going to be working Silicon Valley, that would not be a reasonable thing for them to do.
But then you get the smart, geeky kids that have a touch of autism, and that's where you've got to get them turned on with doing interesting things.
I got social interaction through shared interest.
I rode horses with other kids, I made model rockets with other kids, did electronics lab with other kids, and in the '60s, it was gluing mirrors onto a rubber membrane on a speaker to make a light show.
That was like, we considered that super cool.
CA:
TG:
Well let me tell you, that child will be loyal, and if your house is burning down, they're going to get you out of it.
CA:
So, most people, if you ask them what are they most passionate about, they'd say things like,
"My kids" or "My lover."
What are you most passionate about?
TG:
I'm passionate about that the things I do are going to make the world a better place.
When I have a mother of an autistic child say,
"My kid went to college because of your book, or one of your lectures," that makes me happy.
You know, the slaughter plants, I've worked with them in the '80s; they were absolutely awful.
I developed a really simple scoring system for slaughter plants where you just measure outcomes: How many cattle fell down?
How many cattle got poked with the prodder?
How many cattle are mooing their heads off?
And it's very, very simple.
You directly observe a few simple things.
I get satisfaction out of seeing stuff that makes real change in the real world.
We need a lot more of that, and a lot less abstract stuff.
(Applause)
When we were talking on the phone, one of the things you said that really astonished me was you said one thing you were passionate about was server farms.
Well the reason why I got really excited when I read about that, it contains knowledge.
It's libraries.
And to me, knowledge is something that is extremely valuable.
So, maybe, over 10 years ago now our library got flooded.
And this is before the Internet got really big.
And I was really upset about all the books being wrecked, because it was knowledge being destroyed.
And server farms, or data centers are great libraries of knowledge.
CA:
Temple, can I just say it's an absolute delight to have you at TED.
TG:
Well thank you so much. Thank you.
(Applause)
78 is 15% of what number?
So there's some unknown number out there, and if we take 15% of that number, we will get 78.
So let's just call that unknown number x.
And we know that if we take 15% of x, so multiply x by 15%, we will get 78.
And now we just literally have to solve for x.
Now, 15% mathematically, you can deal directly with percentages, but it's much easier if it's written as a decimal.
And we know that 15% is the same thing as 15 per 100.
That's literally per cent.
Cent means 100, which is the same thing as 0.15.
This is literally 15 hundredths.
So we could rewrite this as 0.15 times some unknown number, times x, is equal to 78.
And now we can divide both sides of this equation by 0.15 to solve for x.
So you divide the left side by 0.15, and I'm literally picking 0.15 to divide both sides because that's what I have out here in front of the x.
So if I'm multiplying something by 0.15 and then I divided by 0.15, I'll just be left with an x here.
That's the whole motivation.
If I do it to the left-hand side, I have to do it to the right-hand side.
These cancel out, and I get x is equal to 78 divided by 0.15.
Now, we have to figure out what that is.
If we had a calculator, pretty straightforward, but let's actually work it out.
So we have 78 divided by, and it's going to be some decimal number.
It's going to be larger than 78.
But let's figure out what it ends up being, so let's throw some zeroes out there.
It's not going to be a whole number.
And we're dividing it by 0.15.
Now, to simplify things, let's multiply both this numerator and this denominator by 100, and that's so that 0.15 becomes 15.
So 0.15 times 100 is 15.
We're just moving the decimal to the right.
Let me put that in a new color.
Right there, that's where our decimals goes.
Let me erase the other one, so we don't get confused.
If we did that for the 15, we also have to do that for the 78.
So if you move the decimal two to the right, one, two, it becomes 7,800.
So one way to think about it, 78 divided by 0.15 is the same thing as 7,800 divided by 15, multiplying the numerator and the denominator by 100.
So let's figure out what this is.
15 does not go into 7, So you could do it zero times and you can do all that, or you can just say, OK, that's not going to give us anything.
So then how many times does 15 go into 78?
So let's think about it.
15 goes into 60 four times.
15 times 5 is 75.
That looks about right, so we say five times.
5 times 15.
5 times 5 is 25.
Put the 2 up there.
5 times 1 is 5, plus 2 is 7.
75, you subtract.
78 minus 75 five is 3.
Bring down a zero.
15 goes into 30 exactly two times.
2 times 15 is 30.
Subtract.
No remainder.
Bring down the next zero.
We're still to the left of the decimal point.
The decimal point is right over here.
If we write it up here, which we should, it's right over there, so we have one more place to go.
So we bring down this next zero.
15 goes into 0 zero times.
0 times 15 is 0.
Subtract.
No remainder.
So 78 divided by 0.15 is exactly 520.
So x is equal to 520.
So 78 is 15% of 520.
And if we want to use some of the terminology that you might see in a math class, the 15% is obviously the percent.
520, or what number before we figured out it was 520, that's what we're taking the percentage of.
This is sometimes referred to as the base.
And then when you take some percentage of the base, you get what's sometimes referred to as the amount.
So in this circumstance, 78 would be the amount.
You could view it as the amount is the percentage of the base, but we were able to figure that out.
It's nice to know those, if that's the terminology you use in your class.
But the important thing is to be able just answer this question.
And it makes sense, because 15% is a very small percentage.
If 78 is a small percentage of some number, that means that number has to be pretty big, and our answer gels with that.
This looks about right.
78 is exactly 15% of 520.
What I want to do in this video is order these fractions from least to greatest And, the easiest way--and the way that people are sure to get the right answer-- is to find a common denominator, because if we can't find a common denominator, these fractions are difficult to compare:
4/9 v. 3/4 v. 4/5, 11/12, 13/15.
You can try to estimate them, but you'll be able to directly compare them if they all have the same denominator.
So, the trick here is to first find the common denominator.
And there is many ways to do it, you could just pick one of these numbers, and take all of its multiples until you find a multiple that is divisible by all of the rest.
Another way to do it is to look at the prime factorization of each of these numbers. and then the 'least common multiple' of them would have each of those prime numbers in it.
Let's do it that second way, and then verify it.
So, 9 is 33, so our LCM is going to have at least one 33 in it.
And then 4 is the same thing as 2*2.
So, we will also have 2*2 in our prime factorization (LCM).
5 is a prime number, so we'll put 5 right there.
And then, 12 is the same thing as 26, and 6 = 23.
So, in our LCM, we have to have two 2's, but we already have two 2's, and we already have one 3.
Another way to think about it, is that something that is divisible by both 9 and 4 is going to be divisible by 12.
And then finally, we need it to be divisible by 15's prime factors.
15 is the same thing as 3*5.
So once again, we already have 3 and 5.
So, this is our least common multiple (LCM).
So, LCM is going to be equal to 33225 =180
So, our LCM is 180.
So, we want to rewrite all of these fractions with 180 in the denominator.
So, our first fraction, 4/9, is what over 180?
To go from 9 to 180, we have to multiple 9 by 20.
So, to get the denominator to equal 180, we multiple by 20.
Since we don't want to change the value of the fraction, we should also multiple by the 4 by 20.
4*20 = 80.
So, 4/9 is the same thing as 80/180.
Now, let's do 3/4.
What do we have to multiple the denominator by to equal 180?
You can divide 4 into 180 (180/4 = x) to figure that out.
4*45 = 180.
Now, you also have to multiple the numerator by 45.
3*45 = 135.
So, 3/4 equals 135/180.
Now let's do 4/5.
To get 180 from 5, multiple 5 by 36.
Have to multiple numerator by same number, 36.
So, 144/180.
And then we have only two more to do.
180/12 = 15. Same for numerator, 15.
So, 11/12 = 165/180.
And then finally, we have 13/15.
To get 180 from 15, multiply 15 by 12--1510 = 150, 30 remaining for 180. 152 = 30. So, 15*12 = 180.
Multiple numerator by same number, 13.
We know 12*12 = 144, so just add one more 12 = 156.
So, we've rewritten each of these fractions with the new common denominator.
Now, it is very easy to compare them. We only have to look at their numerators.
Foe example, the smallest numerator is 80, so 4/9 is the least of these numbers.
The next smallest number looks like 135, which was 3/4.
And then the next one is going to be the 144/180, which was 4/5.
Next is 156/180, which was 13/15.
Finally, we have 165/180, which was 11/12.
And, we're done! We have finished our ordering.
In this video I want to do a bunch of examples of factoring a second degree polynomial, which is often called a quadratic.
Sometimes a quadratic polynomial, or just a quadratic itself, or quadratic expression, but all it means is a second degree polynomial.
So something that's going to have a variable raised to the second power.
In this case, in all of the examples we'll do, it'll be x.
So let's say I have the quadratic expression, x squared plus 10x, plus 9.
And I want to factor it into the product of two binomials.
How do we do that? Well, let's just think about what happens if we were to take x plus a, and multiply that by x plus b.
If we were to multiply these two things, what happens?
Well, we have a little bit of experience doing this.
This will be x times x, which is x squared, plus x times b, which is bx, plus a times x, plus a times b-- plus ab.
Or if we want to add these two in the middle right here, because they're both coefficients of x.
We could right this as x squared plus-- I can write it as b plus a, or a plus b, x, plus ab.
So in general, if we assume that this is the product of two binomials, we see that this middle coefficient on the x term, or you could say the first degree coefficient there, that's going to be the sum of our a and b.
And then the constant term is going to be the product of our a and b.
Notice, this would map to this, and this would map to this.
And, of course, this is the same thing as this.
So can we somehow pattern match this to that?
Is there some a and b where a plus b is equal to 10?
And a times b is equal to 9? Well, let's just think about it a little bit.
What are the factors of 9?
What are the things that a and b could be equal to?
And we're assuming that everything is an integer.
And normally when we're factoring, especially when we're beginning to factor, we're dealing with integer numbers.
So what are the factors of 9?
They're 1, 3, and 9.
So this could be a 3 and a 3, or it could be a 1 and a 9.
Now, if it's a 3 and a 3, then you'll have 3 plus 3-- that doesn't equal 10.
But if it's a 1 and a 9, 1 times 9 is 9.
1 plus 9 is 10.
So it does work.
So a could be equal to 1, and b could be equal to 9.
So we could factor this as being x plus 1, times x plus 9.
And if you multiply these two out, using the skills we developed in the last few videos, you'll see that it is indeed x squared plus 10x, plus 9.
So when you see something like this, when the coefficient on the x squared term, or the leading coefficient on this quadratic is a 1, you can just say, all right, what two numbers add up to this coefficient right here?
And those same two numbers, when you take their product, have to be equal to 9.
And of course, this has to be in standard form.
Or if it's not in standard form, you should put it in that form, so that you can always say, OK, whatever's on the first degree coefficient, my a and b have to add to that.
Whatever's my constant term, my a times b, the product has to be that.
Let's do several more examples.
I think the more examples we do the more sense this'll make.
Let's say we had x squared plus 10x, plus-- well, I already did 10x, let's do a different number-- x squared plus 15x, plus 50.
And we want to factor this.
Well, same drill.
We have an x squared term.
We have a first degree term.
This right here should be the sum of two numbers.
And then this term, the constant term right here, should be the product of two numbers.
So we need to think of two numbers that, when I multiply them I get 50, and when I add them, I get 15.
And this is going to be a bit of an art that you're going to develop, but the more practice you do, you're going to see that it'll start to come naturally.
So what could a and b be?
Let's think about the factors of 50.
It could be 1 times 50.
2 times 25.
Let's see, 4 doesn't go into 50.
It could be 5 times 10.
I think that's all of them.
Let's try out these numbers, and see if any of these add up to 15.
So 1 plus 50 does not add up to 15.
2 plus 25 does not add up to 15.
But 5 plus 10 does add up to 15.
So this could be 5 plus 10, and this could be 5 times 10.
So if we were to factor this, this would be equal to x plus 5, times x plus 10.
And multiply it out.
I encourage you to multiply this out, and see that this is indeed x squared plus 15x, plus 10.
In fact, let's do it. x times x, x squared. x times 10, plus 10x.
5 times x, plus 5x.
5 times 10, plus 50.
Notice, the 5 times 10 gave us the 50.
The 5x plus the 10x is giving us the 15x in between.
So it's x squared plus 15x, plus 50.
Let's up the stakes a little bit, introduce some negative signs in here.
Let's say I had x squared minus 11x, plus 24.
Now, it's the exact same principle.
I need to think of two numbers, that when I add them, need to be equal to negative 11. a plus b need to be equal to negative 11.
And a times b need to be equal to 24.
Now, there's something for you to think about.
When I multiply both of these numbers, I'm getting a positive number.
I'm getting a 24.
That means that both of these need to be positive, or both of these need to be negative.
That's the only way I'm going to get a positive number here.
Now, if when I add them, I get a negative number, if these were positive, there's no way I can add two positive numbers and get a negative number, so the fact that their sum is negative, and the fact that their product is positive, tells me that both a and b are negative. a and b have to be negative.
Remember, one can't be negative and the other one can't be positive, because the product would be negative.
And they both can't be positive, because when you add them it would get you a positive number.
So let's just think about what a and b can be.
So two negative numbers.
So let's think about the factors of 24.
And we'll kind of have to think of the negative factors.
But let me see, it could be 1 times 24, 2 times 11, 3 times 8, or 4 times 6.
Now, which of these when I multiply these-- well, obviously when I multiply 1 times 24, I get 24.
When I get 2 times 11-- sorry, this is 2 times 12.
I get 24.
So we know that all these, the products are 24.
But which two of these, which two factors, when I add them, should I get 11?
And then we could say, let's take the negative of both of those.
So when you look at these, 3 and 8 jump out.
3 times 8 is equal to 24.
3 plus 8 is equal to 11.
But that doesn't quite work out, right?
Because we have a negative 11 here.
But what if we did negative 3 and negative 8?
Negative 3 times negative 8 is equal to positive 24.
Negative 3 plus negative 8 is equal to negative 11.
So negative 3 and negative 8 work.
So if we factor this, x squared minus 11x, plus 24 is going to be equal to x minus 3, times x minus 8.
Let's do another one like that.
Actually, let's mix it up a little bit.
Let's say I had x squared plus 5x, minus 14.
So here we have a different situation.
The product of my two numbers is negative, right? a times b is equal to negative 14.
My product is negative.
That tells me that one of them is positive, and one of them is negative.
And when I add the two, a plus b, it'd be equal to 5.
So let's think about the factors of 14.
And what combinations of them, when I add them, if one is positive and one is negative, or I'm really kind of taking the difference of the two, do I get 5?
So if I take 1 and 14-- I'm just going to try out things-- 1 and 14, negative 1 plus 14 is negative 13.
Negative 1 plus 14 is 13.
So let me write all of the combinations that I could do.
And eventually your brain will just zone in on it.
So you've got negative 1 plus 14 is equal to 13.
And 1 plus negative 14 is equal to negative 13.
So those don't work.
That doesn't equal 5.
Now what about 2 and 7?
If I do negative 2-- let me do this in a different color-- if
I do negative 2 plus 7, that is equal to 5.
We're done!
That worked!
I mean, we could have tried 2 plus negative 7, but that'd be equal to negative 5, so that wouldn't have worked.
But negative 2 plus 7 works.
And negative 2 times 7 is negative 14.
So there we have it.
We know it's x minus 2, times x plus 7.
That's pretty neat.
Negative 2 times 7 is negative 14.
Negative 2 plus 7 is positive 5.
Let's do several more of these, just to really get well honed this skill.
So let's say we have x squared minus x, minus 56.
So the product of the two numbers have to be minus 56, have to be negative 56.
And their difference, because one is going to be positive, and one is going to be negative, right?
Their difference has to be negative 1.
And the numbers that immediately jump out in my brain-- and I don't know if they jump out in your brain, we just learned this in the times tables-- 56 is 8 times 7.
I mean, there's other numbers.
It's also 28 times 2.
It's all sorts of things.
But 8 times 7 really jumped out into my brain, because they're very close to each other.
And we need numbers that are very close to each other.
And one of these has to be positive, and one of these has to be negative.
Now, the fact that when their sum is negative, tells me that the larger of these two should probably be negative.
So if we take negative 8 times 7, that's equal to negative 56.
And then if we take negative 8 plus 7, that is equal to negative 1, which is exactly the coefficient right there.
So when I factor this, this is going to be x minus 8, times x plus 7.
This is often one of the hardest concepts people learn in algebra, because it is a bit of an art.
You have to look at all of the factors here, play with the positive and negative signs, see which of those factors when one is positive, one is negative, add up to the coefficient on the x term.
But as you do more and more practice, you'll see that it'll become a bit of second nature.
Now let's step up the stakes a little bit more.
Let's say we had negative x squared-- everything we've done so far had a positive coefficient, a positive 1 coefficient on the x squared term.
But let's say we had a negative x squared minus 5x, plus 24.
How do we do this?
Well, the easiest way I can think of doing it is factor out a negative 1, and then it becomes just like the problems we've been doing before.
So this is the same thing as negative 1 times positive x squared, plus 5x, minus 24.
Right?
I just factored a negative 1 out.
You can multiply negative 1 times all of these, and you'll see it becomes this.
Or you could factor the negative 1 out and divide all of these by negative 1.
And you get that right there.
Now, same game as before.
I need two numbers, that when I take their product I get negative 24.
So one will be positive, one will be negative.
So let's think about 24 is 1 and 24.
Let's see, if this is negative 1 and 24, it'd be positive 23, if it was the other way around, it'd be negative 23.
Doesn't work.
What about 2 and 12? Well, if this is negative-- remember, one of these has to be negative.
If the 2 is negative, their sum would be 10.
If the 12 is negative, their sum would be negative 10.
Still doesn't work.
3 and 8.
If the 3 is negative, their sum will be 5.
So it works!
So if we pick negative 3 and 8, negative 3 and 8 work.
Because negative 3 plus 8 is 5.
Negative 3 times 8 is negative 24.
So this is going to be equal to-- can't forget that negative 1 out front, and then we factor the inside.
Negative 1 times x minus 3, times x plus 8.
And if you really wanted to, you could multiply the negative 1 times this, you would get 3 minus x if you did.
Or you don't have to.
The more practice, the better, I think.
All right, let's say I had negative x squared plus 18x, minus 72.
So once again, I like to factor out the negative 1.
So this is equal to negative 1 times x squared, minus 18x, plus 72.
Now we just have to think of two numbers, that when I multiply them I get positive 72.
So they have to be the same sign.
And that makes it easier in our head, at least in my head.
When I multiply them, I get positive 72.
When I add them, I get negative 18.
So they're the same sign, and their sum is a negative number, they both must be negative.
But the one that springs up, maybe you think of 8 times 9, but 8 times 9, or negative 8 minus 9, or negative 8 plus negative 9, doesn't work.
That turns into 17.
That was close.
Let me show you that.
Negative 9 plus negative 8, that is equal to negative 17.
Close, but no cigar.
So what other ones are there?
We have 6 and 12.
That actually seems pretty good.
If we have negative 6 plus negative 12, that is equal to negative 18.
Notice, it's a bit of an art.
You have to try the different factors here.
So this will become negative 1-- don't want to forget that-- times x minus 6, times x minus 12.
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Solve using the elimination method and they tell us the sum of two numbers is 70
Their difference is 24. What are the two numbers? So let's use this first sentence.
Let's construct an equation from this first sentence.
Lets construct an constraint. The sum of two numbers, lets call them x and y.
So their sum, x + y is equal to 70. That's what this first sentence tells us.
The second sentence tells us their difference is 24. So that means that x minus y is equal to 24.
We're going to assume that x is the larger of the two numbers and y is the smaller one.
So when you take a difference like this you get a positive 24.
So you have system of two equations with two unknowns and they want us to solve it using the elimination method so let's do that.
So we can literally just add these two questions.
On the left side we would have a positive y and a negative y over here, and they would just cancel out.
So if we were to just add these equations, they would cancel out, so if we were able to just add these two equations we would be able to eliminate the y's.
Well the plus y and the minus y cancel out and you're left with x plus an x which is 2x.
And that is going to be equal to 70 plus 24. 70 plus 24 is equal to 94.
And I want to make it clear.
This is nothing new, we're really just adding the same thing to both side of this equation. You could say we're adding 24 to both sides of t this equation.
Over here we're explicitly adding 24 to the 70. And over here you could say we could add 24 to x plus y.
But the second constraint tells us that x minus y is the same thing as 24. So we're adding the same thing to both sides.
Here we're calling it 24, here we're calling it x minus y.
So we get 2x is equal to 94 now we can divide both sides by 2.
And we are left with x is equal to 47.
And now we can substitute back into either one of these equations to solve for y.
So let's try this first one over here. So we have 47 plus y is equal to 70.
We can subtract 47 from both sides of this equation.
So we subtract 47 and we are left with y is equal to 23.
And you can verify that this works.
If you add the two numbers 47 plus 23 you definitely get 70.
If you take 47 minus 23 you definitely get 24.
So it definitely meets both constraints.
Identify 15 eights, or 15 over 8, as a proper or an improper fraction. or an improper fraction.
So this is actually just a good review of proper and improper fractions. And there's a pretty easy way to identify them.
You have a proper fraction if your numerator -- so this right here is your numerator -- the number on top. if your numerator ... Let me just label them numerator and denominator ... de nom in a tor
You have a proper fraction if your numerator if your numerator is less than your denominator if your numerator is less than your denominator and if you don't have a proper fraction you have an improper fraction.
Improper fraction is if your numerator is greater than or equal to your denominator And over here, actually, all the numbers are positive,
But if you had some negative numbers here, you would actually say the absolute value of numerator is lesser than the absolute value of the denominator, for a proper fraction
And the absolute value of numerator is greater than or equal to the absolute value of the denominator for an improper fraction
Anyway, let's go back to this problem 15 is clearly greater than or equal to 8
So 15 is greater than or equal to 8, so we are dealing with an improper fraction.
The Aquino administration's K+12 program added two more years to the basic education cycle.
When we are all together, oh such happiness...
When there is laughter all around, oh such happiness...
Life is carefree with merry singing.
When we are all together, oh such happiness...
Children, you are good Filipino citizens, right?
Yes.
Let's talk about how you will be of help to our country's progress particularly when you grow up.
When I grow up I want to be a .
When I grow up, I want to be a meat packer in Canada.
When I grow up, I want to work in a call centre.
When I grow up, I want to sew clothes for export.
When I grow up, I want to be a saleslady.
When I grow up, I want to be a domestic helper in Singapore.
When I grow up, I will be a driver in Korea.
When I grow up, I want to be a nurse in the United States.
As the most forward deployed citizens of the planet at this moment and the first expedition crew aboard Space Station Alpha
We are well started on our journey of exploration and discovery building a foothold for men and women who will voyage and live in places far away from our home planet.
We are opening a Gateway to Space for all humankind.
As we orbit planet every 90 minutes we see a world without borders and send our wish that all nations will work towards peace and harmony.
Our world has changed dramatically, still the ISS is the physical proof that nations can work together in harmony and should promote peace and global cooperation, and rich goals that are simply out of this world.
On this night, we would like to share with all our good fortune on this space adventure our wonder and excitement as we gaze on the Earth's splendor and our strong sense that the human spirit to do, to explore, to discover has no limit.
Times are hard all over the world but this is a time when we can all think about being together and treasuring our planet and we have a pretty nice view of it up here.
Thank God If he were to sit with you for one minute, what would you tell him?
This is very hard.
I wish....
I wish he would just take me away from this life Those who preserved the blessing were so many. Prophet Muhammad and servants.
Okay.
♫ Strolling along in Central Park ♫ ♫ Everyone's out today ♫ ♫ The daisies and dogwoods are all in bloom ♫ ♫ Oh, what a glorious day ♫ ♫ For picnics and Frisbees and roller skaters, ♫ ♫ Friends and lovers and lonely sunbathers ♫ ♫ Everyone's out in merry Manhattan in January ♫ (Laughter) (Applause) ♫ I brought the iced tea; ♫ ♫ Did you bring the bug spray? ♫ ♫ The flies are the size of your head ♫ ♫ Next to the palm tree, ♫ ♫ Did you see the 'gators ♫ ♫ Looking happy and well fed? ♫ ♫ Everyone's out in merry Manhattan in January ♫
(Whistling)
Everyone!
(Whistling) (Laughter) ♫ My preacher said, ♫ ♫ Don't you worry ♫ ♫ The scientists have it all wrong ♫ ♫ And so, who cares it's winter here? ♫ ♫ And I have my halter-top on ♫ ♫ I have my halter-top on ♫ ♫ Everyone's out in merry Manhattan in January. ♫ (Applause)
Chris Anderson:
Jill Sobule!
Considering that I have a cold right now I can't imagine a more appropriate topic to make a video on than a virus Don't make it that thick. A virus, or viruses.
S's in front of it. Let's say they are talking about double stranded DNA, they'll put a ds in front of it. But the general idea-- and viruses can come in all of these forms-- is that they have some genetic information, some chain of nucleic acids.
Either as single or double stranded RNA or single or double stranded DNA. And it's just contained inside some type of protein structure, which is called the capsid. And kind of the classic drawing is kind of an icosahedron type looking thing.
Sometimes it can essentially fuse-- I don't want to complicate the issue-- but sometimes viruses have their own little membranes. And we'll talk about in a second where it gets their membranes. So a virus might have its own membrane like that.
And these sides will eventually merge. And then the cell and the virus will go into it. This is called endocytosis.
And then in cases where the cell in question-- for example in the situation with bacteria-- if the cell has a very hard shell-- let me do it in a good color. So let's say that this is a bacteria right here. And it has a hard shell.
That's the nucleus of the cell and it normally has the DNA in it like that. Maybe I'll do the DNA in a different color.
But DNA gets transcribed into RNA, normally. So normally, the cell, this a normal working cell, the RNA exits the nucleus, it goes to the ribosomes, and then you have the RNA in conjunction with the tRNA and it produces these proteins.
The RNA codes for different proteins. And I talk about that in a different video. So these proteins get formed and eventually, they can form the different structures in a cell.
This RNA will essentially go and do what the cell's own RNA would have done. And it starts coding for its own proteins. Obviously it's not going to code for the same things there.
Everything I talk about, these are specific ways that a virus might work. But viruses really kind of explore-- well different types of viruses do almost every different combination you could imagine of replicating and coding for proteins and escaping from cells. Some of them just bud.
And you could imagine why that would be useful thing to have with you. Because now that you have this membrane, you kind of look like this cell.
And if you don't think that this is creepy-crawly enough, that you're hijacking the DNA of an organism, viruses can actually change the DNA an organism. And actually one of the most common examples is HlV virus. Let me write that down.
HlV, which is a type of retrovirus, which is fascinating. Because what they do is, so they have RNA in them.
And when they enter into a cell, let's say that they got into the cell. So it's inside of the cell like this.
They actually bring along with them a protein. And every time you say, where do they get this protein? All of this stuff came from a different cell.
DNA of the host cell. Let's say the yellow is the DNA of the host cell. And this is its nucleus.
I mean I can't imagine a more intimate way to become part of an organism than to become part of its DNA.
I can't imagine any other way to actually define an organism. And if this by itself is not eerie enough, and just so you know, this notion right here, when a virus becomes part of an organism's DNA, this is called a provirus.
But if this isn't eerie enough, they estimate-- so if this infects a cell in my nose or in my arm, as this cell experiences mitosis, all of its offspring-- but its offspring are genetically identical-- are going to have this viral DNA.
And that might be fine, but at least my children won't get it. You know, at least it won't become part of my species. But it doesn't have to just infect somatic cells, it could infect a germ cell.
It's all a guess. I mean people are doing it based on just looking at the
DNA and how similar it is to DNA in other organisms. But the estimate is 5-8% of the human genome is from viruses, is from ancient retroviruses that incorporated themselves into the human germ line. So into the human DNA.
Which is mind blowing to me, because it's not just saying these things are along for the ride or that they might help us or hurt us. It's saying that we are-- 5-8% of our DNA actually comes from viruses. And this is another thing that speaks to just genetic variation.
And you could imagine, as a virus goes from one species to the next, as it goes from Species A to B, if it mutates to be able to infiltrate these cells, it might take some-- it'll take the DNA that it already has, that makes it, it with it. But sometimes, when it starts coding for some of these other guys, so let's say that this is a provirus right here. Where the blue part is the original virus.
So maybe most of it was the viral DNA, but it might have, when it transcribed and translated itself, it might have taken a little bit-- or at least when it translated or replicated itself-- it might take a little bit of the organism's previous DNA. So it's actually cutting parts of DNA from one organism and bringing it to another organism. Taking it from one member of a species to another member of the species.
And infect that DNA into the next organism. So you actually have this DNA, this jumping, from organism to organism. So it kind of unifies all DNA-based life.
But there's a whole-- we could talk all about the different classes of viruses. But just so you're familiar with some of the terminology, when a virus attacks bacteria, which they often do. And we study these the most because this might be a good alternative to antibiotics.
And I've already talked to you about how they have their DNA.
But since bacteria have hard walls, they will just inject the DNA inside of the bacteria. And when you talk about DNA, this idea of a provirus. So when a virus lyses it like this, this is called the lytic cycle.
Normally when people talk about the lysogenic cycle, they're talking about viral DNA laying dormant in the DNA of bacteria. Or bacteriophage DNA laying dormant in the DNA of bacteria. But just to kind of give you an idea of what this, quote unquote, looks like, right here.
These little green dots you see right here all over the surface, this big thing you see here, this is a white blood cell. Part of the human immune system. This is a white blood cell.
And what you see emerging from the surface, essentially budding from the surface of this white blood cell-- and this gives you a sense of scale too-- these are HlV-1 viruses. And so you're familiar with the terminology, the HlV is a virus that infects white blood cells.
AlDS is the syndrome you get once your immune system is weakened to the point. And then many people suffer infections that people with a strong immune system normally won't suffer from. But this is creepy.
These things went inside this huge cell, they used the cell's own mechanism to reproduce its own DNA or its own RNA and these protein capsids. And then they bud from the cell and take a little bit of the membrane with it.
And they can even leave some of their DNA behind in this cell's own DNA.
So they really change what the cell is all about. This is another creepy picture. These are bacteriaphages.
And these show you what I said before. This is a bacteria right here. This is its cell wall.
So it's hard to just emerge into it.
Or you can't just merge, fuse membranes with it. So they hang out on the outside of this bacteria. And they are essentially injecting their genetic material into the bacteria itself.
And these are much less than 1/100 of this cell we're talking about. And they're extremely hard to filter for. To kind of keep out.
If you think that these are exotic things that exist for things like HlV or Ebola , which they do cause, or SARS, you're right.
But they're also common things. I mean, I said at the beginning of this video that I have a cold. And I have a cold because some viruses have infected the tissue in my nasal passage.
Are we these things that contain DNA or are we just transport mechanisms for the DNA? And these are kind of the more important things. And these viral infections are just battles between different forms of DNA and RNA and whatnot.
The question we're given asks us, how many students attended Einstein School in 2006?
And in this little table, they tell us how many attended in 2001, 150 students, and in 2002, 225, 2003, we had 300 students, but they don't tell us 2006.
So what I think they want us to do is to see the pattern and how many students the population of students grew by every year, and just assume that that pattern continues through 2006.
So we need to figure out what the pattern is from one year to the next, and then we're going to figure out 2004, 2005, and then 2006.
So the assumption that we're making in this problem, and I think that the problem wants us to make, is that whatever the pattern of growth was in these three years, that they continue all the way to 2006.
So let's see what's happening here.
When we go the first year, what happens to our student population?
We go from 150 to 225 students.
And the easiest pattern to think about is, well just how much are we increasing by every year?
So how much do we have to go to from 150 to 225?
Well, if you increase by 50, you get to 200, so we increased another 25.
So we increased by 75 students.
And then they go from 225 to 300, how many did we increase by?
Looks like 75 again.
75 plus 225 is 300.
So it looks like we increased by another 75.
So the pattern here is that each year, 75 more students attend the Einstein School.
So let's just continue that pattern.
So let's add another 75.
Let's add another 75 to the 300 in 2003, and we'll get 375.
In 2004, if we assume the pattern continues, let's add another 75.
And then what will that give us?
That'll give us 450 students in 2005, if we assume the pattern continues.
And we're almost there.
Let's add a final 75, 75 plus 450.
If you add 50, you get to 500, so it's another 25, so it's 525.
So that would be the answer to our question, if we assume the pattern continued, that 525 students attended Einstein
School in 2006.
Let's start with a warm-up problem to avoid getting any mental cramps as we learn new things. So this is a problem that hopefully, if you understood what we did in the last video, you can kind of understand what we're about to do right now. And I'm going to escalate it even more.
Four times nine is equal to thirty-six. Right? Eighteen times two.
You can even think of it as order of operations, but you just should know that you do the multiplication first. So four times two is eight. Plus three is equal to eleven.
Put this one down here and put the one ten and eleven up there. Then you got four times three. Four times three.
Four times six is twenty-four. Plus one is twenty-five.
Put the five down here. There's no where to put the two-- there's no more multiplications to do-- so we just put the two down there. So sixty-four thousand three hundred twenty-nine times four is two hundred fifty-seven thousand three hundred sixteen.
Now let's do a bunch of digits times a two-digit number. So let's say we want to multiply thirty-six times-- instead of putting a one-digit number here, I'm going to put a two-digit number.
You can kind of ignore the two for a little bit. So three times six is equal to eighteen. So you just put the eight here, put the ten there, or the one there because it's ten plus eight.
So you put the ten there. There's nothing left.
You put the zero there. There's nothing left to put the one over, so you put the ten there. So you essentially have solved the problem that thirty-six--
We put the one up here and we have to be very careful because we had this one from our previous problem, which doesn't apply anymore. So we could erase it or that one we could get rid of. If you have an eraser get rid of it, or you can just keep track in your head that the one you're about to write is a different one.
Put the two here.
Put the one up here. And I got rid of the previous one because that would've just messed me up. Now I have two times three.
But then I have this plus one up here, so I have to add plus one. So I get seven. So that is equal to seven.
So this seven hundred twenty we just solved, that's literally-- let me write that down. What is that?
Eight hundred twenty-eight? Is that what we got? We got eight hundred twenty-eight.
Put the four up here. Seven times seven, well, that's forty-nine. Plus four is fifty-three.
There's no where to put the five, so we put it down here. Seven times seven is forty-nine. Plus four is fifty-three.
Put a four there. Seven times seven is forty-nine. Plus four, which is fifty-three.
Nine plus zero is nine. Three plus nine is twelve. Carry the one.
We now know what a probability distribution is.
It could be a discrete probability distribution or a continuous one, and we learned that that's a probability density function.
Now let's study a couple of the more common ones.
So let's say I have a coin, and it's a fair coin, and I'm going to flip it five times.
And I'm going to define my random variable,
X, I'll define it.
I'll make it a capital X.
It equals the number of heads I get after 5 flips.
Maybe I flip them all at once.
Maybe I have 5 coins and I flip them all at once and I just count the heads.
Or I could have one coin and I could flip it five times and see the number of heads.
It actually doesn't matter.
But let's say I have 1 coin and I flip it five times, just so we have no ambiguity.
So this is my definition of my random variable.
As we know, a random variable, it's a little different than a regular variable, it's more of a function.
It assigns a number with an experiment and this one's pretty easy.
We just count the number of heads we got after 5 flips and that's our random variable, X.
Let's think a little bit of what are the different probabilities of getting different numbers here?
So what is the probability that X, big capital X, is equal to 0?
So what's the probability that you get no heads after 5 flips?
Well, that's essentially the same thing as the probability of getting all tails.
This is a bit of a review of probability.
You have to get all tails.
And what's the probably of each of these tails?
Well, it's 1/2.
So it'd have to be 1/2 times 1/2 times 1/2 times 1/2 times 1/2.
So it'd have to be 1/2 to the fifth power.
1 to the fifth is 1 over 2 to the fifth is 32.
Fair enough.
Now what's the probability-- I'm going through a little bit of a probability review.
Just because I think it's important just to get the intuition of where we're going now and how you actually form a discrete probably distribution.
Now what's the probability that you get exactly 1 head?
Well, that could just be the first head.
It could be heads, then tails, tails, tails, tails, tails.
Or it could be the second head.
It could be the probability of tails, heads, tail, tails, tails and so forth.
This one head that you get, it could be in any of the 5 spots.
So what's the probability of each of these situations?
Well the probability that you get a head is 1/2.
Then the probability you get tails is 1/2 times 1/2 times 1/2 times 1/2.
So the probability of each of these situations is 1/32.
Just like the probability of this particular situation.
In fact, the probability of any particular order of heads and tails is going to be 1 out of 32.
There's actually 32 possible scenarios.
So the probability of this is 1 out of 32.
The probability of this is 1 out of 32.
And there's situations like this because the heads could be in any of the 5 spots.
So the probability that we have exactly one head is equal to 5 times 1/32, which is equal to 5/32.
Fair enough.
Now it gets interesting.
What is the probability-- I'll do each of these in a different color.
What is the probability that my random variable is equal to 2?
So I flip the coin five times, what is the probability that I get exactly 2 heads?
Now it becomes a little bit interesting.
So what are all the situations?
I could have heads, heads, tails, tails, tails.
I could have a head, tails, heads, tails, tails.
And if you think about it there's these two heads and they can go in a bunch of different places, and it starts to get a little bit confusing.
You can't just think of it in kind of the scenario analysis like we did here.
You can, but it becomes a little bit confusing.
You have to realize one thing.
Each of the scenarios, there's a 1 out of 32 probability.
1/2 times 1/2 times 1/2 times 1/2 times 1/2.
So that's a 1 out of 32 probability-- each of those.
Welcome to the presentation on dividing decimals.
Let's get started with a problem. If I were to say, how many times does point two eight go into twenty-three point eight two eight? So you're going to see that these dividing decimal problems are actually just like the level four division problems.
And if I want to, let me see if I could-- well, I won't erase the old decimal because if you were doing it with a pen you would kind of have the same problem I have.
So now we do it just like a level four division problem. So we say, how many times does twenty-eight go into two? Well, no times.
So eight was the largest number of times that the twenty-eight could go into two hundred and thirty-eight without being larger. So now I bring down this two. Once again, you recognize this is just purely a level two division problem-- a level four division problem.
So yeah, I'll take a guess and I'll say let's say it goes into it four times. I could be wrong, but let's see if it works out.
Let me get rid of this old six. Four times eight is thirty-two. And four times two is eight.
And otherwise, you raise or lower the number accordingly. So let me erase that four. I'm going to try not to mess up.
I probably should have tried it out on the side first before doing all this and I wouldn't have had to go back and erase it.
And then let me get back to what I was doing. So when I went into it four times the remainder was too large, so let me try five now. Five times eight is forty.
Two is less than twenty-eight. This five is correct. Now I just bring down the eight.
Let's do three point three goes into forty-three point two three. That's a three. So first thing we want to do is move the decimal.
Put the decimal right up here. And now it's just a level four division problem. Thirty-three goes into four zero times.
YouTube puts a limit on this stuff. So let's say two point five goes into point three three five zero how many times? Well once again, let's move the decimal point over one here.
Put the decimal here. So how many times does twenty-five go into three? Well zero.
I'm a savant, or more precisely, a high-functioning autistic savant.
It's a rare condition.
And rarer still when accompanied, as in my case, by self-awareness and a mastery of language.
Very often when I meet someone and they learn this about me, there's a certain kind of awkwardness.
I can see it in their eyes. They want to ask me something.
And in the end, quite often, the urge is stronger than they are and they blurt it out:
"If I give you my date of birth, can you tell me what day of the week I was born on?"
(Laughter)
Or they mention cube roots or ask me to recite a long number or long text.
I hope you'll forgive me if I don't perform a kind of one-man savant show for you today.
I'm going to talk instead about something far more interesting than dates of birth or cube roots -- a little deeper and a lot closer, to my mind, than work.
I want to talk to you briefly about perception.
When he was writing the plays and the short stories that would make his name,
Anton Chekhov kept a notebook in which he noted down his observations of the world around him -- little details that other people seem to miss.
Every time I read Chekhov and his unique vision of human life, I'm reminded of why I too became a writer.
In my books, I explore the nature of perception and how different kinds of perceiving create different kinds of knowing and understanding.
Here are three questions drawn from my work.
Rather than try to figure them out, I'm going to ask you to consider for a moment the intuitions and the gut instincts that are going through your head and your heart as you look at them.
For example, the calculation: can you feel where on the number line the solution is likely to fall?
Or look at the foreign word and the sounds: can you get a sense of the range of meanings that it's pointing you towards?
And in terms of the line of poetry, why does the poet use the word hare rather than rabbit?
I'm asking you to do this because I believe our personal perceptions, you see, are at the heart of how we acquire knowledge.
Aesthetic judgments, rather than abstract reasoning, guide and shape the process by which we all come to know what we know.
I'm an extreme example of this.
My worlds of words and numbers blur with color, emotion and personality.
As Juan said, it's the condition that scientists call synesthesia, an unusual cross-talk between the senses.
Here are the numbers one to 12 as I see them -- every number with its own shape and character.
One is a flash of white light.
Six is a tiny and very sad black hole.
The sketches are in black and white here, but in my mind they have colors.
Three is green.
Four is blue.
Five is yellow.
I paint as well.
And here is one of my paintings.
It's a multiplication of two prime numbers.
Three-dimensional shapes and the space they create in the middle creates a new shape, the answer to the sum.
What about bigger numbers?
Well you can't get much bigger than Pi, the mathematical constant.
It's an infinite number -- literally goes on forever.
In this painting that I made of the first 20 decimals of Pi, I take the colors and the emotions and the textures and I pull them all together into a kind of rolling numerical landscape.
But it's not only numbers that I see in colors.
Words too, for me, have colors and emotions and textures.
And this is an opening phrase from the novel "Lolita."
And Nabokov was himself synesthetic.
And you can see here how my perception of the sound L helps the alliteration to jump right out.
Another example: a little bit more mathematical.
And I wonder if some of you will notice the construction of the sentence from "The Great Gatsby."
There is a procession of syilables -- wheat, one; prairies, two; lost Swede towns, three -- one, two, three.
And this effect is very pleasant on the mind, and it helps the sentence to feel right.
Let's go back to the questions I posed you a moment ago.
64 multiplied by 75.
If some of you play chess, you'll know that 64 is a square number, and that's why chessboards, eight by eight, have 64 squares.
So that gives us a form that we can picture, that we can perceive.
What about 75?
Well if 100, if we think of 100 as being like a square, 75 would look like this.
So what we need to do now is put those two pictures together in our mind -- something like this.
64 becomes 6,400.
And in the right-hand corner, you don't have to calculate anything.
Four across, four up and down -- it's 16.
So what the sum is actually asking you to do is 16, 16, 16.
That's a lot easier than the way that the school taught you to do math, I'm sure.
It's 16, 16, 16, 48, 4,800 -- 4,800, the answer to the sum.
Easy when you know how.
(Laughter)
The second question was an Icelandic word.
I'm assuming there are not many people here who speak Icelandic.
So let me narrow the choices down to two.
Hnugginn: is it a happy word, or a sad word?
What do you say?
Okay.
Some people say it's happy.
Most people, a majority of people, say sad.
And it actually means sad.
(Laughter)
Why do, statistically, a majority of people say that a word is sad, in this case, heavy in other cases?
In my theory, language evolves in such a way that sounds match, correspond with, the subjective, with the personal, intuitive experience of the listener.
Let's have a look at the third question.
It's a line from a poem by John Keats.
Words, like numbers, express fundamental relationships between objects and events and forces that constitute our world.
It stands to reason that we, existing in this world, should in the course of our lives absorb intuitively those relationships.
And poets, like other artists, play with those intuitive understandings.
In the case of hare, it's an ambiguous sound in English.
It can also mean the fibers that grow from a head.
And if we think of that -- let me put the picture up -- the fibers represent vulnerability.
They yield to the slightest movement or motion or emotion.
So what you have is an atmosphere of vulnerability and tension.
The hare itself, the animal -- not a cat, not a dog, a hare -- why a hare?
Because think of the picture -- not the word, the picture.
The overlong ears, the overlarge feet, helps us to picture, to feel intuitively, what it means to limp and to tremble.
So in these few minutes, I hope I've been able to share a little bit of my vision of things and to show you that words can have colors and emotions, numbers, shapes and personalities.
The world is richer, vaster than it too often seems to be.
I hope that I've given you the desire to learn to see the world with new eyes.
Thank you.
(Applause)
Let's now talk about what is easily one of the most famous theorems in all of mathematics.
And that's the Pythagorean theorem.
So a right triangle is a triangle that has a 90 degree angle in it.
So the way I drew it right here, this is our 90 degree angle.
If you've never seen a 90 degree angle before, the way to think about it is, if this side goes straight left to right, this side goes straight up and down.
These sides are perpendicular, or the angle between them is 90 degrees, or it is a right angle.
And the Pythagorean theorem tells us that if we're dealing with a right triangle-- let me write that down-- if we're dealing with a right triangle-- not a wrong triangle-- if we're dealing with a right triangle, which is a triangle that has a right angle, or a 90 degree angle in it, then the relationship between their sides is this.
So this side is a, this side is b, and this side is c.
And remember, the c that we're dealing with right here is the side opposite the 90 degree angle.
It's important to keep track of which side is which.
The Pythagorean theorem tells us that if and only if this is a right triangle, then a squared plus b squared is going to be equal to c squared.
And we can use this information.
If we know two of these, we can then use this theorem, this formula to solve for the third.
And I'll give you one more piece of terminology here.
This long side, the side that is the longest side of our right triangle, the side that is opposite of our right angle, this right here-- it's c in this example-- this is called a hypotenuse.
A very fancy word for a very simple idea.
The longest side of a right triangle, the side that is opposite the 90 degree angle, is called the hypotentuse.
Now that we know the Pythagorean theorem, let's actually use it.
Because it's one thing to know something, but it's a lot more fun to use it.
So let's say I have the following right triangle.
Let me draw it a little bit neater than that.
This side over here has length 9.
This side over here has length 7.
And my question is, what is this side over here?
Maybe we can call that-- we'll call that c.
Well, c, in this case, once again, it is the hypotenuse.
It is the longest side.
So we know that the sum of the squares of the other side is going to be equal to c squared.
So by the Pythagorean theorem, 9 squared plus 7 squared is going to be equal to c squared.
9 squared is 81, plus 7 squared is 49. 80 plus 40 is 120.
Then we're going to have the 1 plus the 9, that's another 10, so this is going to be equal to 130.
So let me write it this way.
The left-hand side is going to be equal to 130, and that is equal to c squared.
So what's c going to be equal to? Let me rewrite it over here. c squared is equal to 130, or we could say that c is equal to the square root of 130.
And notice, I'm only taking the principal root here, because c has to be positive.
We're dealing with a distance, so we can't take the negative square root.
So we'll only take the principal square root right here.
And if we want to simplify this a little bit, we know how to simplify our radicals.
130 is 2 times 65, which is 5 times 13. Well, these are all prime numbers, so that's about as simple as I can get. c is equal to the square root of 130.
Let's do another one of these.
Maybe I want to keep this Pythagorean theorem right there, just so we always remember what we're referring to.
So let's say I have a triangle that looks like this.
Let's see.
Let's say it looks like that.
And this is the right angle, up here.
Let's say that this side, I'm going to call it a.
The side, it's going to have length 21.
And this side right here is going to be of length 35.
So your instinct to solve for a, might say, hey, 21 squared plus 35 squared is going to be equal to a squared.
But notice, in this situation, 35 is a hypotenuse.
35 is our c.
It's the longest side of our right triangle.
So what the Pythagorean theorem tells us is that a squared plus the other non-longest side-- the other non-hypotenuse squared-- so a squared plus 21 squared is going to be equal to 35 squared.
You always have to remember, the c squared right here, the c that we're talking about, is always going to be the longest side of your right triangle.
The side that is opposite of our right angle.
This is the side that's opposite of the right angle.
So a squared plus 21 squared is equal to 35 squared. And what do we have here?
So 21 squared-- I'm tempted to use a calculator, but I won't.
So 21 times 21: 1 times 21 is 21, 2 times 21 is 42. It is 441.
Once again, I'm tempted to use a calculator, but I won't.
35 times 35: 5 times 5 is 25. Carry the 2.
Put a 0 here, get rid of that thing.
3 times 5 is 15.
3 times 3 is 9, plus 1 is 10.
So it is 11-- let me do it in order-- 5 plus 0 is 5, 7 plus 5 is 12, 1 plus 1 is 2, bring down the 1.
1225.
So this tells us that a squared plus 441 is going to be equal to 35 squared, which is 1225.
Now, we could subtract 441 from both sides of this equation.
The right-hand side, what do we get?
We get 5 minus 1 is 4.
We want to-- let me write this a little bit neater here.
So the left-hand side, once again, they cancel out. a squared is equal to-- and then on the right-hand side, what do we have to do?
That's larger than that, but 2 is not larger than 4, so we're going to have to borrow.
So that becomes a 12, or regrouped, depending on how you want to view it. That becomes a 1.
1 is not greater than 4, so we're going to have to borrow again.
Get rid of that.
And then this becomes an 11.
5 minus 1 is 4.
12 minus 4 is 8.
11 minus 4 is 7. So a squared is equal to 784.
And we could write, then, that a is equal to the square root of 784.
And once again, I'm very tempted to use a calculator, but let's, well, let's not.
Let's not use it.
So this is 2 times, what?
392.
And then this-- 390 times 2 is 78, yeah.
And then this is 2 times, what?
This is 2 times 196.
That's right.
190 times 2 is-- yeah, that's 2 times 196. 196 is 2 times-- I want to make sure I don't make a careless mistake.
196 is 2 times 98.
Let's keep going down here. 98 is 2 times 49.
And, of course, we know what that is.
So notice, we have 2 times 2, times 2, times 2.
So this is 2 to the fourth power. So it's 16 times 49.
So a is equal to the square root of 16 times 49.
I picked those numbers because they're both perfect squares.
So this is equal to the square root of 16 is 4, times the square root of 49 is 7.
It's equal to 28.
So this side right here is going to be equal to 28, by the Pythagorean theorem.
Let's do one more of these.
Can never get enough practice.
So let's say I have another triangle.
I'll draw this one big. There you go.
That's my triangle.
That is the right angle.
This side is 24.
This side is 12.
We'll call this side right here b.
Now, once again, always identify the hypotenuse.
That's the longest side, the side opposite the 90 degree angle.
You might say, hey, I don't know that's the longest side. I don't know what b is yet.
How do I know this is longest? And there, in that situation, you say, well, it's the side opposite the 90 degree angle.
So if that's the hypotenuse, then this squared plus that squared is going to be equal to 24 squared.
So the Pythagorean theorem-- b squared plus 12 squared is equal to 24 squared.
Or we could subtract 12 squared from both sides.
We say, b squared is equal to 24 squared minus 12 squared, which we know is 144, and that b is equal to the square root of 24 squared minus 12 squared.
Now I'm tempted to use a calculator, and I'll give into the temptation.
So let's do it.
The last one was so painful, I'm still recovering. So 24 squared minus 12 squared is equal to 24.78.
So this actually turns into-- let me do it without a-- well, I'll do it halfway.
24 squared minus 12 squared is equal to 432. So b is equal to the square root of 432.
And let's factor this again.
We saw what the answer is, but maybe we can write it in kind of a simplified radical form. So this is 2 times 216.
216, I believe, is a-- let me see.
I believe that's a perfect square.
So let me take the square root of 216.
Nope, not a perfect square.
So 216, let's just keep going. 216 is 2 times 108.
108 is, we could say, 4 times what?
25 plus another 2-- 4 times 27, which is 9 times 3.
So what do we have here?
We have 2 times 2, times 4, so this right here is a 16.
16 times 9 times 3.
Is that right?
I'm using a different calculator.
16 times 9 times 3 is equal to 432.
So this is going to be equal to-- b is equal to the square root of 16 times 9, times 3, which is equal to the square root of 16, which is 4 times the square root of 9, which is 3, times the square root of 3, which is equal to 12 roots of 3.
So b is 12 times the square root of 3.
Hopefully you found that useful.
Write 2.75 as a simplified fraction.
So once you get some practice here. You're going to find it pretty straightforward to do.
But we're really going to think through it and get the intuition for why this makes sense.
So if we were to write this down, the 2, that literally just represents two 1's, I'll just write it down like that.
Then we have the 7. Let me do that in another color.
We have a 7 one place to the right of the decimal.
It's in the tenths place, with a T-H-S at the end.
So it literally represents 7 over 10.
And then finally, we have the 5 in the hundredths place, so it represents 5 over 100.
Now, if I want to write this as a simplified fraction, or or really as a mixed number, I have to merge these fraction parts right here.
And to add two fractions, you have to have a common denominator.
And to figure out the common denominator, you just have to think about the least common multiple of 10 and 100.
And that's 100.
100 is divisible by both 100 and 10.
So let's get this 10 to be a 100.
So we can do that by multiplying it by 10.
So when you multiply something by 10, you add a zero at the end of it.
But you can't just do that to the denominator.
We also have to do that to the numerator.
So we multiplied the denominator by 10.
Let's also multiply the numerator by 10.
7 times 10 is 70, or 70 over 100.
It's the exact same thing as 7/10.
Now we can add these two.
What is 70 plus 5?
70 plus 5 is 75.
And our denominator is 100, so this can be rewritten as 2 and 75/100.
And we saw that in the last video, you would read this as two and seventy-five hundredths.
Now, we aren't in a completely simplified fraction yet because 75 and 100 have common factors.
And the largest number that goes into both, if you're familiar with quarters, is 25.
Three quarters is $0.75, four quarters is 100 cents, or four quarters is $1.00.
So you divide both of them by 25.
So 75 divided by 25 is 3, and 100 divided by 25 is 4.
So as a simplified mixed number, this becomes 2 and 3/4.
And after you do a lot of practice here, and you just see a lot of numbers like this, it will be almost second nature for you to say, oh, 2.75 is the same thing as 2 and 75/100, is the same thing as 2 and 3/4.
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Find the perimeter of this hexagon.
So the perimeter just means the distance around the object, or if you add up all of the lengths of the sides of the object, so we're going to add up all of the lengths of sides of this hexagon, and a hexagon is just a six-sided geometrical shape like this.
So to find the perimeter, we just need to find the distance around the hexagon, which is going to be the sum of all of the lengths of the sides.
So the perimeter is going to be 24-- so how many of these do we have?
We have one, two, three, four, five, six 24's, which makes sense, because a hexagon has six sides.
So we're going to have-- let me write this a little bit bigger-- 24 plus 24 plus 24 plus 24 plus 24-- and that's five 24's-- plus 24.
So let's add them all at the same time.
We could've done it piece by piece, but let's just go straight ahead.
So let's go first to the ones place.
So 4 plus 4 is 8, 8 plus 4 is 12, 12 plus 4 is 16, 16 plus 4 is 20, 20 plus 4 is 24.
And now we're in the tens place.
2 plus 2 is 4 plus 2 is 6 plus 2 is 8 plus 2 is 10 plus 2 is 12 plus 2 is 14.
So the sum of these six 24's is 144.
That is the perimeter.
And when we learn multiplication, if you haven't learned it already, you could've down this simpler.
You just say you have six 24's, so this would actually be a multiplication problem of 6 times 24.
If you don't know how to do that just yet, don't worry about it.
You can just add them all up.
You get 144.
My talk today is about something maybe a couple of you have already heard about.
It's called the Arab Spring.
Anyone heard of it?
(Applause)
So in 2011, power shifted, from the few to the many, from oval offices to central squares, from carefully guarded airwaves to open-source networks.
But before Tahrir was a global symbol of liberation, there were representative surveys already giving people a voice in quieter but still powerful ways.
I study Muslim societies around the world at Gallup.
Since 2001, we've interviewed hundreds of thousands of people -- young and old, men and women, educated and illiterate.
My talk today draws on this research to reveal why Arabs rose up and what they want now.
Now this region's very diverse, and every country is unique.
But those who revolted shared a common set of grievances and have similar demands today.
I'm going to focus a lot of my talk on Egypt.
It has nothing to do with the fact that I was born there, of course.
But it's the largest Arab country and it's also one with a great deal of influence.
But I'm going to end by widening the lens to the entire region to look at the mundane topics of Arab views of religion and politics and how this impacts women, revealing some surprises along the way.
So after analyzing mounds of data, what we discovered was this:
Unemployment and poverty alone did not lead to the Arab revolts of 2011.
If an act of desperation by a Tunisian fruit vendor sparked these revolutions, it was the difference between what Arabs experienced and what they expected that provided the fuel.
To tell you what I mean, consider this trend in Egypt.
On paper the country was doing great.
In fact, it attracted accolades from multinational organizations because of its economic growth.
But under the surface was a very different reality.
In 2010, right before the revolution, even though GDP per capita had been growing at five percent for several years, Egyptians had never felt worse about their lives.
Now this is very unusual, because globally we find that, not surprisingly, people feel better as their country gets richer.
And that's because they have better job opportunities and their state offers better social services.
But it was exactly the opposite in Egypt.
As the country got more well-off, unemployment actually rose and people's satisfaction with things like housing and education plummeted.
But it wasn't just anger at economic injustice.
It was also people's deep longing for freedom.
Contrary to the clash of civilizations theory, Arabs didn't despise Western liberty, they desired it.
As early as 2001, we asked Arabs, and Muslims in general around the world, what they admired most about the West.
Among the most frequent responses was liberty and justice.
In their own words to an open-ended question we heard, "Their political system is transparent and it's following democracy in its true sense."
Another said it was "liberty and freedom and being open-minded with each other."
Majorities as high as 90 percent and greater in Egypt, Indonesia and Iran told us in 2005 that if they were to write a new constitution for a theoretical new country that they would guarantee freedom of speech as a fundamental right, especially in Egypt.
Eighty-eight percent said moving toward greater democracy would help Muslims progress -- the highest percentage of any country we surveyed.
But pressed up against these democratic aspirations was a very different day-to-day experience, especially in Egypt.
While aspiring to democracy the most, they were the least likely population in the world to say that they had actually voiced their opinion to a public official in the last month -- at only four percent.
So while economic development made a few people rich, it left many more worse off.
As people felt less and less free, they also felt less and less provided for.
So rather than viewing their former regimes as generous if overprotective fathers, they viewed them as essentially prison wardens.
So now that Egyptians have ended Mubarak's 30-year rule, they potentially could be an example for the region.
If Egypt is to succeed at building a society based on the rule of law, it could be a model.
If, however, the core issues that propelled the revolution aren't addressed, the consequences could be catastrophic -- not just for Egypt, but for the entire region.
The signs don't look good, some have said.
Islamists, not the young liberals that sparked the revolution, won the majority in Parliament.
The military council has cracked down on civil society and protests and the country's economy continues to suffer.
Evaluating Egypt on this basis alone, however, ignores the real revolution.
Because Egyptians are more optimistic than they have been in years, far less divided on religious-secular lines than we would think and poised for the demands of democracy.
Whether they support Islamists or liberals,
Egyptians' priorities for this government are identical, and they are jobs, stability and education, not moral policing.
But most of all, for the first time in decades, they expect to be active participants, not spectators, in the affairs of their country.
I was meeting with a group of newly-elected parliamentarians from Egypt and Tunisia a couple of weeks ago.
And what really struck me about them was that they weren't only optimistic, but they kind of struck me as nervous, for lack of a better word.
One said to me,
"Our people used to gather in cafes to watch football" -- or soccer, as we say in America --
"and now they gather to watch Parliament."
(Laughter)
"They're really watching us, and we can't help but worry that we're not going to live up to their expectations."
And what really struck me is that less than 24 months ago, it was the people that were nervous about being watched by their government.
And the reason that they're expecting a lot is because they have a new-found hope for the future.
So right before the revolution we said that Egyptians had never felt worse about their lives, but not only that, they thought their future would be no better.
What really changed after the ouster of Mubarak wasn't that life got easier.
It actually got harder.
But people's expectations for their future went up significantly.
And this hope, this optimism, endured a year of turbulent transition.
One reason that there's this optimism is because, contrary to what many people have said, most Egyptians think things really have changed in many ways.
So while Egyptians were known for their single-digit turnout in elections before the revolution, the last election had around 70 percent voter turnout -- men and women.
Where scarcely a quarter believed in the honesty of elections in 2010 --
I'm surprised it was a quarter -- 90 percent thought that this last election was honest.
Now why this matters is because we discovered a link between people's faith in their democratic process and their faith that oppressed people can change their situation through peaceful means alone.
(Applause)
Now I know what some of you are thinking.
The Egyptian people, and many other Arabs who've revolted and are in transition, have very high expectations of the government.
They're just victims of a long-time autocracy, expecting a paternal state to solve all their problems.
But this conclusion would ignore a tectonic shift taking place in Egypt far from the cameras in Tahrir Square.
And that is Egyptians' elevated expectations are placed first on themselves.
In the country once known for its passive resignation, where, as bad as things got, only four percent expressed their opinion to a public official, today 90 percent tell us that if there's a problem in their community, it's up to them to fix it.
(Applause) And three-fourths believe they not only have the responsibility, but the power to make change.
And this empowerment also applies to women, whose role in the revolts cannot be underestimated.
They were doctors and dissidents, artists and organizers.
A full third of those who braved tanks and tear gas to ask or to demand liberty and justice in Egypt were women.
(Applause)
Now people have raised some real concerns about what the rise of Islamist parties means for women.
What we've found about the role of religion in law and the role of religion in society is that there's no female consensus.
We found that women in one country look more like the men in that country than their female counterparts across the border.
Now what this suggests is that how women view religion's role in society is shaped more by their own country's culture and context than one monolithic view that religion is simply bad for women.
Where women agree, however, is on their own role, and that it must be central and active.
And here is where we see the greatest gender difference within a country -- on the issue of women's rights.
Now how men feel about women's rights matters to the future of this region.
Because we discovered a link between men's support for women's employment and how many women are actually employed in professional fields in that country.
So the question becomes,
What drives men's support for women's rights?
What about men's views of religion and law?
[Does] a man's opinion of the role of religion in politics shape their view of women's rights?
The answer is no.
We found absolutely no correlation, no impact whatsoever, between these two variables.
What drives men's support for women's employment is men's employment, their level of education as well as a high score on their country's U.N. Human Development Index.
What this means is that human development, not secularization, is what's key to women's empowerment in the transforming Middle East.
And the transformation continues.
From Wall Street to Mohammed Mahmoud Street, it has never been more important to understand the aspirations of ordinary people.
Thank you.
(Applause)
Welcome to this presentation on logarithm properties.
If you don't believe that one of these properties are true and you want them proved, I've made three or four videos that actually prove these properties.
So let's just do a little bit of a review of just what a logarithm is.
Let's say I say that a-- Let me start over. a to the b is equal to c.
So if we-- a to the b power is equal to c.
So another way to write this exact same relationship instead of writing the exponent, is to write it as a logarithm.
So we can say that the logarithm base a of c is equal to b.
So this are essentially saying the same thing, they just have different kind of results.
In one, you know a and b and you're kind of getting c.
And the second one, you know a and you know that when you raise it to some power you get c.
And then you figure out what b is.
So they're the exact same relationship, just stated in a different way.
Now I will introduce you to some interesting logarithm properties.
So the first is that the logarithm-- Let me do a more cheerful color.
The logarithm, let's say, of any base-- So let's just call the base-- Let's say b for base.
Logarithm base b of a plus logarithm base b of c-- and this only works if we have the same bases.
That equals the logarithm of base b of a times c.
Now what does this mean and how can we use it?
So let's say logarithm of base two of-- I don't know --of eight plus logarithm base two of-- I don't know let's say --thirty-two.
So, in theory, this should equal, if we believe this property, this should equal logarithm base two of what?
So log-- So this is-- We just used our property.
This little property that I presented to you. And let's just see if it works out.
So log base two of eight. two to what power is equal to eight?
Well two to the third power is equal to eight, right?
So this term right here, that equals three, right?
Log base two of eight is equal to three. two to what power is equal to thirty-two?
Let's see. two to the fourth power is sixteen. two to the fifth power is thirty-two.
And two to the what power is equal to two hundred and fifty-six?
So it's two to the eighth power.
But this is eight.
And for those of you who it might seem a little obvious, you're probably thinking, well two to the third times two to the fifth is equal to two to the three plus five, right?
And that equals two to eight, two to the eighth.
On this side, we had two the third times two to fifth essentially, and on this side you have them added to each other.
But this should hopefully give you an tuition for why this property holds, right?
Because when you multiply two numbers of the same base, right? Two exponential expressions of the same base, you can add their exponents.
Similarly, when you have the log of two numbers multiplied by each other, that's equivalent to the log of each of the numbers added to each other.
This is the same property.
So let's do a-- Let me show you another log property.
So this is log base b of a minus log base b of c is equal to log base b of-- well I ran out. I'm running out of space --a divided by c.
Let's say log base three of-- I don't know --log base three of-- well you know, let's make it interesting --log base three of one / nine minus log base three of eighty-one.
So this property tells us-- This is the same thing as--
Log base three of one / nine divided by eighty-one.
So that's the same thing as one / nine times one / eighty-one.
So let's see. nine times eight is seven hundred and twenty, right? nine times-- Right. nine times eight is seven hundred and twenty.
So this is one / seven hundred and twenty-nine. So this is log base three over one / seven hundred and twenty-nine.
So three-- So we know that if three squared is equal to nine, then we
know that three to the negative two is equal to one / nine, right?
So this is equal to negative two, right?
And then minus-- three to what power is equal eighty-one? three to the third power is twenty-seven.
So three to the fourth power.
So we have minus two minus four is equal to-- Well, we could do it a couple of ways.
Minus two minus four is equal to minus six.
And now we just have to confirm that three to the minus sixth power is equal to one / seven hundred and twenty-nine.
Is three to the minus sixth power, is that equal to seven-- one / seven hundred and twenty-nine?
Well that's the same thing as saying three to sixth power is equal to seven hundred and twenty-nine, because that's all the negative exponent does is inverts it.
But let's see. three to the third power-- This would be three to the third power times three to the third power is equal to twenty-seven times twenty-seven.
You can confirm it with a calculator if you don't believe me.
Anyway, that's all the time I have in this video.
In the next video, I'll introduce you to the last two logarithm properties. And, if we have time, maybe I'll do examples with the leftover time.
Use the associative law of multiplication to write-- and here they have 12 times 3 in parentheses, and then they want us to multiply that times 10-- in a different way.
Simplify both expressions to show they have identical results.
So the way that they wrote it is-- let me just rewrite it.
So they have 12 times 3 in parentheses, and then they multiply that times 10.
Now whenever something is in parentheses, that means do that first. So this literally says let's do the 12 times 3 first.
Now, what is 12 times 3?
It's 36.
So this evaluates to 36, and then we still have that times 10 over there.
And we know the trick.
Whenever we multiply something times a power of ten, we just add the number of zeroes that we have at the back of it, so this is going to be 360.
This is going to be equal to 360.
Now, the associative law of multiplication, once again, it sounds like a very fancy thing.
All that means is it doesn't matter how we associate the multiplication or it doesn't matter how we put the parentheses, we're going to get the same answer, so let me write it down again.
If we were to do 12 times 3 times 10, if we just wrote it like this without parentheses, if we just went left to right, that would essentially be exactly what we just did here on the left.
But the associative law of multiplication says, you know what?
We can multiply the 3 times 10 first and then multiply the 12, and we're going to get the exact same answer as if we multiplied the 12 times the 3 and then the 10.
So let's just verify it for ourselves.
So 3 times 10 is 30, and we still want to multiply the 12 times that.
Now, what's 12 times 30?
And we've seen this several times before.
You can view it as a 12 times 3, which is 36, but we still have this 0 here.
So that is also equal to 360.
So it didn't matter how we associated the multiplication.
You can do the 12 times 3 first or you can do the 3 times 10 first.
Either way, they both evaluated to 360.
A Visit from Saint Nicholos by Clement Clarke Moore
Twas the night before Christmas, when all through the house
Not a creature was stirring, not even a mouse;
The stockings were hung by the chimney with care,
In hopes that St. Nicholas soon would be there;
The children were nestled all snug in their beds,
While visions of sugar-plums danced in their heads;
And mamma in her kerchief, and I in my cap,
Had just settled our brains for a long winter's nap--
When out on the lawn there rose such a clatter,
I sprang from my bed to see what was the matter,
Away to the window I flew like a flash,
Tore open the shutters and threw up the sash.
The moon, on the breast of the new-fallen snow,
Gave a lustre of mid-day to objects below;
When, what to my wondering eyes should appear,
But a miniature sleigh, and eight tiny rein-deer,
With a little old driver, so lively and quick,
I knew in a moment it must be St. Nick.
More rapid than eagles his coursers they came,
And he whistled, and shouted, and called them by name;
"Now, Dasher! now, Dancer! now, Prancer and Vixen!
On!
Comet, on!
Cupid, on!
Dunder and Blitzen--
To the top of the porch, to the top of the wall!
Now, dash away, dash away, dash away all!"
As dry leaves that before the wild hurricane fly,
When they meet with an obstacle, mount to the sky,
So, up to the house-top the coursers they flew,
With a sleigh full of toys--and St. Nicholas too.
And then in a twinkling I heard on the roof,
The prancing and pawing of each little hoof.
As I drew in my head, and was turning around,
Down the chimney St. Nicholas came with a bound.
He was dressed all in fur from his head to his foot,
And his clothes were all tarnished with ashes and soot;
A bundle of toys he had flung on his back,
And he looked like a peddler just opening his pack;
His eyes how they twinkled! his dimples how merry!
His cheeks were like roses, his nose like a cherry;
His droll little mouth was drawn up like a bow,
And the beard on his chin was as white as the snow;
The stump of a pipe he held tight in his teeth,
And the smoke, it encircled his head like a wreath.
He had a broad face, and a little round belly
That shook when he laughed, like a bowl full of jelly.
He was chubby and plump--a right jolly old elf;
And I laughed when I saw him in spite of myself.
A wink of his eye, and a twist of his head,
Soon gave me to know I had nothing to dread.
He spoke not a word, but went straight to his work,
And filled all the stockings; then turned with a jerk,
And laying his finger aside of his nose,
And giving a nod, up the chimney he rose.
He sprang to his sleigh, to his team gave a whistle,
And away they all flew like the down of a thistle;
But I heard him exclaim, ere he drove out of sight,
"Merry Christmas to all, and to all a good night!"
One last logarithm property to show you.
So let's say that just, I don't know, x to the n is equal to a.
Well, that's just another way of saying that log base x of a is equal to n, right?
That's the exact same -- this is just the exact same way of writing the exact same thing.
One's a logarithm, one's an exponent, right?
But what we can do is, if n is actually equal to this expression, we can, like I did a couple of videos ago, you could just substitute this for n.
So we could write x to this thing, log base x a.
And we could set that as equal to what? a.
So now what I'm going to do and, actually, this is going to get pretty messy is, I'm going to raise -- actually, let me write this a little more space.
So, if I set x to the log base x of a, that equals -- and you'll see why I'm giving you so much space right now.
Now, what I want to do is, I want to raise both sides of this equation to 1 over this exponent.
So I'm going to raise that to 1 over log base x of a.
If I do something to one side of the equation, I have to do it to the other.
So that's also, that's equal to a, to 1 over log base x to a.
This expression is just another way of writing this expression.
And I substitut it for n.
And now I'm raising both to this exponent.
Well, if you're raising something to an the exponent and then you're raising that to an exponent, you just multiply the two, right?
Because this will be the numerator.
And this'll be the denominator.
So that gets us to this. x to the 1 power, right?
Because log base x of a over log base x of a is equal to 1.
So that's the same thing as x is equal to a to the 1 over log base x of a.
So, we could also just replace a with another variable, right?
I could also write x is also equal to b to the 1 over log base x of b, right?
The same exact thing I did with a, I could do with a.
The same thing I did with a, I could do with b.
So I've written these two expressions. I said x is equal to both of these things.
So let's set them equal to each other.
So, we know that a to 1 over log base x of a, is equal to b to the 1 over log base x of b.
So, what can we do now?
I said that, because I need a lot of space for what I plan to do.
So, I said, a to the 1 over log base x of a -- well, that equals b to the 1 over log base x of b.
Now, let's raise both of these sides to the log base x of b power.
Now, hopefully you'll see why I'm doing this.
On this side they'll cancel out, right? Because this becomes a numerator, that's the denominator.
And on this side, you get a to the -- this becomes the numerator, right, because we just multiply the exponents.
Log base x, that little dot is an x.
Of b over log base x of a.
And what does that equal?
Well, that equals just b, right? Because this over this is 1.
This b to the 1.
That equals b. Now let's write this entire thing as a logarithm. a to this thing is equal to b.
That's the exact same thing as saying that the logarithm base a of b is equal to this thing.
Is equal to the log base x of b divided by the log base x of a. This might seem confusing, it might seem daunting, but we're actually going to do a lot of examples with this.
And this is probably the single most useful identity, I guess you could call it, if you're using a calculator.
Why?
Because your calculator only has two bases.
It either has log base, you know base 10, or base e, right?
And most of them, when you press the log button on your calculator, it assumes log base 10. So if I gave you a problem where I wanted to know what is the log base 7 of 3, right?
And there's no easy way, on most calculators, to do this.
Well, you can use this identity. That this is the same thing as the log base 10 of 3, divided by the log base 10 of 7.
And these are very easy to calculate on your calculator.
You just type 3 and press log.
It'll give you this number. And you press 7 and click on log, it'll give you this number.
And then you're done.
So hopefully you're satisfied that this is true and you have a little bit of an intuition of how to use it. And I'll make a bunch of videos now, on actually how you can use these logarithm properties.
I just wanted to get it out of the way so that you're satisfied that they are true.
Let's do some order of operations problems, and for the sake of time I'll do every other problem. So let's start with 1b. 1b right there.
So you could view this as being equivalent to-- So we're going to do our multiplication before we do any addition or subtraction, and we're going to do our division before doing any addition or subtraction. Problem 1b is exactly equivalent to this, the parentheses are just-- I'm reinforcing the notion that
So 7 times 11 is 77, and then 12 divided by 3 is 4. And the rest of the problem was 2 plus this thing, which is 77, minus this thing.
2 plus 77 is 79 minus 4, which is equal to 75. So 1b is equal to 75. Let's do 1d.
Closing two parentheses, all of that over 4 minus 6 plus 2 minus 3 minus 5. Let's see if we can simplify this a little bit. As we said, parentheses take our priority.
2 minus 1. 2 minus 1 is just 1. 3 minus 5.
So this whole thing simplifies to 8 divided by negative 4 is negative 2 plus 2.
So it equals 0. So this big, hairy thing simplified to 0. Now let's do 2b.
Evaluate the following expressions involving variables. Fair enough. So they wrote 2y squared, and they're saying that x is equal to 1, which is irrelevant because there is no x here, and y is equal to 5.
And if you look at the order of operations, exponents take priority over multiplication. That's why in my head I just automatically put those parentheses. We're going to do the exponent first.
They're giving us y squared minus x, whole thing squared. x is equal to 2 and y is equal to 1. Well, we just substitute. Where we see a y we put a 1.
Evaluate the following expressions involving variables. All right. Same idea.
We have z squared over x plus y plus x squared over x minus y. And they're telling us that x is equal to 1, y is equal to negative 2, and z is equal to 4.
So let's just do our substitutions first. So z squared, that's the same thing as-- I'll do it in a different color --4 squared over x, 1, plus y, negative 2, plus x squared, that's 1 squared, over x, which is 1, minus y. y is negative 2. So this is going to be equal to 4 squared is 16 over 1 plus negative 2, that's 1 minus 2-- it's just a negative 1 --plus 1 squared, which is 1, over 1 minus negative 2.
Negative 16 is the same thing as minus 48 over 3, or negative 48 over 3. If you take 48 divided by 3 you'll get 16, and I'm just keeping the negative sign. And then you add that plus 1/3.
Negative 48 plus 1 is negative 47. So our answer is negative 47 over 3.
Same type of situation. x squared minus z squared over xz minus 2x times z minus x. x is equal to negative 1, z is equal to 3.
Let's do our substitutions. So this is x squared. That's minus 1 squared.
Minus z squared, so minus 3 squared.
All of that over x times z. x times z is minus 1 times 3, minus 2 times x, x is negative 1, times z minus x, times 3 minus x. x is negative 1 minus x.
Wherever we saw an x we put a minus 1. So this is going to be equal to-- Remember, you do your exponents first. Well, parentheses first, then exponents.
Negative 1 times 3 is negative 3. And then let's go to our parentheses here. We have 3 minus negative 1, that's the same thing as 3 plus plus 1.
Problem 4: insert parentheses in each expression to make it a true equation. Fascinating. So 4b.
So if did 12 divided by 4 first, and we would get 3. So let me just do this in yellow. So if we did regular order of operations this would be a 3.
So we really just have to do regular order of operations. So it already looks like a true equation. So if you do 12 divided by 4 plus 10 minus 3 times 3 plus 7, I think it turns out right.
12 divided by 4 is 3 plus 10 minus 3 times 3 is 9 plus 7. This is equal to 13 minus 9, which is equal to-- So all of this is equal to 13 minus 9 is equal to 4 plus 7 is, indeed, equal to 11. So that one wasn't too bad.
12 minus 8 minus 4 times 5 is equal to minus 8. So first let's just see what happens if we did traditional order of operations. If we did traditional order of operations we would do this 4 times 5 first, which would give us 20 over there.
[Thrun]
The correct answer is intelligent agent.
Let's talk about intelligent agents.
Here is my intelligent agent, and it gets to interact with an environment.
The agent can perceive the state of the environment through its sensors, and it can affect its state through its actuators.
The big question of artificial intelligence is the function that maps sensors to actuators.
That is called the control policy for the agent.
So all of this class will deal with how does an agent make decisions that it can carry out with its actuators based on past sensor data.
Those decisions take place many, many times, and the loop of environment feedback to sensors, agent decision, actuator interaction with the environment and so on is called perception action cycle.
So here is my very first quiz for you.
Artificial intelligence, Al, has successfully been used in finance, robotics, games, medicine, and the Web.
Check any or all of those that apply. And if none of them applies, check the box down here that says none of them.
We have the inequality 2/3 is greater than negative 4y minus 8 and 1/3.
Now, the first thing I want to do here, just because mixed numbers bother me-- they're actually hard to deal with mathematically.
They're easy to think about-- oh, it's a little bit more than 8.
Let's convert this to an improper fraction.
So 8 and 1/3 is equal to-- the denominator's going to be 3.
3 times 8 is 24, plus 1 is 25.
So this thing over here is the same thing as 25 over 3.
Let me just rewrite the whole thing. So it's 2/3 is greater than negative 4y minus 25 over 3.
Now, the next thing I want to do, just because dealing with fractions are a bit of a pain, is multiply both sides of this inequality by some quantity that'll eliminate the fractions.
And the easiest one I can think of is multiply both sides by 3.
That'll get rid of the 3's in the denominator.
So let's multiply both sides of this equation by 3.
That's the left-hand side.
And then I'm going to multiply the right-hand side.
3, I'll put it in parentheses like that.
Well, one point that I want to point out is that I did not have to swap the inequality sign, because I multiplied both sides by a positive number.
If the 3 was a negative number, if I multiplied both sides by negative 3, or negative 1, or negative whatever, I would have had to swap the inequality sign.
Anyway, let's simplify this. So the left-hand side, we have 3 times 2/3, which is just 2.
2 is greater than.
And then we can distribute this 3.
3 times negative 4y is negative 12y.
And then 3 times negative 25 over 3 is just negative 25.
Now, we want to get all of our constant terms on one side of the inequality and all of our variable terms-- the only variable here is y on the other side-- the y is already sitting here, so let's just get this 25 on the other side of the inequality.
And we can do that by adding 25 to both sides of this equation.
So let's add 25 to both sides of this equation. --Adding 25--
And with the left-hand side, 2 plus 25 is 27 and we're going to get 27 is greater than.
The right-hand side of the inequality is negative 12y.
And then negative 25 plus 25, those cancel out, that was the whole point, so we're left with 27 is greater than negative 12y.
Now, to isolate the y, you can either multiply both sides by negative 1/12 or you could say let's just divide both sides by negative 12.
Now, because I'm multiplying or dividing by a negative number here, I'm going to need to swap the inequality.
So let me write this.
If I divide both sides of this equation by negative 12, then it becomes 27 over negative 12 is less than-- I'm swapping the inequality, let me do this in a different color-- is less than negative 12y over negative 12.
Notice, when I divide both sides of the inequality by a negative number, I swap the inequality, the greater than becomes a less than.
When it was positive, I didn't have to swap it.
So 27 divided by negative 12, well, they're both divisible by 3.
So we're going to get, if we divide the numerator and the denominator by 3, we get negative 9 over 4 is less than-- these cancel out-- y. So y is greater than negative 9/4, or negative 9/4 is less than y.
And if you wanted to write that-- just let me write this-- our answer is y is greater than negative 9/4.
I just swapped the order, you could say negative 9/4 is less than y.
Or if you want to visualize that a little bit better, 9/4 is 2 and 1/4, so we could also say y is greater than negative 2 and 1/4 if we want to put it as a mixed number.
And if we wanted to graph it on the number line-- let me draw a number line right here, a real simple one.
Maybe this is 0.
Negative 2 is right over, let's say negative 1, negative 2, then say negative 3 is right there.
Negative 2 and 1/4 is going to be right here, and it's greater than, so we're not going to include that in the solution set.
So we're going to make an open circle right there.
And everything larger than that is a valid y, is a y that will satisfy the inequality.
An abstract artist wants to create two proportional painting
The dimensions of one painting are shown And that's this top one right over here
How long should the two missing sides be in the second painting?
So there're two proportional triangular paintings Or one way to think about it is gonna be two triangles that are similar
And actually we know based on how these triangles are marked up
That they are similar triangles you have this angle,
This angle with these 2 arcs right over here has the same measure As that angle right over there
This angle with the 3 arcs has the same measures
This angle right over there
And that this angle let me do it in new color
With the one arc has the same measure as this angle right over there
If the corresponding angles are have the same measures Of the corresponding angles are congruent
Then we know that these are similar triangles
The other thing tells you about similar triangles
Or if you know that two triangles are similar that means That the ratio between corresponding sides is going to be the same
So let's look at the corresponding sides and then let's try figure out
That same ratio or use that same ratio
So we can figure out the missing side right over here
So the first thing if you look at the side that's opposite this blue angle
This one arc angle side XY over here
That's going to correspond to the side opposite
That's opposite this blue angle over here so side AB
These are corresponding side you can also view it as A side between the orange and the magenta The side between the orange and the magenta
That's opposite the orange the double arc angle is going to correspond To this side that's opposite the orange the double arc angle
Or you could view it as a side That's between the magenta and the blue angle
And then finally let me use a we have this side
Which is opposite the magenta angle, it's opposite the magenta angle
It's between the blue and the orange angles is going To correspond to this side which is opposite the magenta angle
And between the blue and the orange angles
So what this tells us is that the ratio we know since they are similar
The ratio between corresponding sides is going to be the same
So the ratio between these two sides AB to XY
The ratio between the length of side AB and length of side XY is going
To be equal to the ratio between the length of side BC
And the length of side YZ
Which going to be equal to the ratio of AC, AC to XZ
And they tell us what some of these lengths are
They tell us AB is equal to 5, they tell us that XY is equal to 2
They tell us that BC is equal to 9
And YZ is one of the things we're going to have to solve for
But they also tells us that AC is equal to 10 right?
No I cannot use the magenta
AC is equal to 10 and we also have to solve for XC
So we can actually get this you know this triple equality
We can actually create two separate equations
Each of which have one unknown and then we could solve for that unknown
So the first is you have 5 halves is equal to 9 over YZ
Is equal to 9 9 over YZ
And to solve for YZ was bunch of ways that you could do it
But you could just let's see we can multiply YZ times both sides
You could multiply YZ times both sides Multiply YZ times both sides actually I won't well you could And then we could multiply both sides by two fifths
But let's just do one step at a time
So then you get YZ, YZ times 5 halves Times 5 halves is equal to 9 is equal to 9
And then you could multiply both sides' times the reciprocal of 5 halves
So you multiply both sides times 2 fifths
And we're doing that so that we could isolate the YZ
And then this right over here these cancel out on the left hand side
We're left with just YZ and on the right hand side we are left
With 9 times 2 is 18 over 5 and we can turn that
This is the same thing if we write it as a mix number 5 goes into 18 3 times with a remainder of 3
So it's 3 and 3 fifths which is the same thing as 3.6
So YZ over here is going to be 3.6
So we've done one of the sides
Now we have to figure out what XZ is and so here we know that five halves
We know that five halves is going to be equal to 10 over XZ Is going to be equal to 10 over XZ
And once again we're going to multiply
There's multiple ways you could do it
You could flip both sides of this equation
So you could say and so this is a slightly different way Than we did it that way just so there's multiple ways to solve this
You could say 2 over 5 is equal to XZ over 10
So I'm just taking the reciprocal of both sides
And then multiply both sides of this equation by 10
Multiply both sides by 10
So you're left with XZ is equal to 10 times 2 is 20 divided by 5
So this is going to be 4 so XZ ends up being 4 that is 4
And we're done the smaller painting has dimensions 2 3.6 and 4
<i>Brought to you by the PKer team @ www.viikii.net</i>
Episode 2
- <i>Baek Seung Jo, why aren't you coming in? <i>Ha Ni, come in quickly.
Why did you come out of that house?
Because it's my house.
- You said it's your...
Should I carry that?
Ah, I remember now.
Even if you're homeless, you don't want my help.
Oh Seung Jo, come here.
- Hello. - He's our eldest.
I've heard so much already.
I feel like we've been together for so long.
After watching the news, she's the one who wanted to look for you guys. So we could live together.
That's why we called the broadcasting studio immediately.
Oh, really?
Thank you.
He would always tell me that he was indebted to you and that he had to pay you back some day.
Oh, there's no need to...
But, what took you so long?
Don't you two know each other?
Both of you are in the same year.
Ah well, he's already pretty well known.
I guess.
He is pretty good at studying.
But, the others don't like him, do they?
What?
His personality is a little weird.
Always arrogant and looking down.
Look at him now.
He doesn't have any girls, does he? Well...
Oh.
Baek Eun Jo, you haven't slept yet?
I was studying.
Why?
Then you might become like your brother.
Say hello.
He's our second child.
A bit young, isn't he?
He's in fourth grade.
Hello, I am Baek Eun Jo.
He's quite good looking.
He must've got it from his mother.
You must be so lucky.
Really?
Say hello to noona, too.
Ha Ni Noona.
Oh Ha Ni.
Hi.
You're not greeting her?
I don't want to.
Why?
She looks dumb.
I'm sorry.
He must be going through puberty.
No, it's okay.
Why would she be dumb?
She's very good at studying.
Really?
Then...
What does that mean?
It's Chinese.
I see you're studying Chinese characters.
Let's see.
This is for sixth grade.
Oh.
"Han Woo Choong Dong."
You don't know what it means?
That's right.
"Han Woo Choong Dong."
The meaning of this... <I>What? <i>What?
So,
"Han Woo" (Korean beef).
You know how Korean beef is tasty, but is really expensive?
So, you have no money... you have no pocket money, but...
"Choong Dong." (urge)
You have an urge to eat Korean beef.
So in other words, you want something beyond your means.
That's it.
Is that true?
It means you have the urge to eat Korean beef? "Han" means sweaty. "Woo" means cow.
То make an ox sweat by pulling the wagon with the books, or to fill a house to the rafters with books.
In other words, it means "an immense number of books." Aren't you stupid?
Baek Eun Jo, you have no manners.
I hate stupid people the most. <i>I've been rejected by both siblings.
I don't want to.
I won't.
Tada!
I decorated it according to my taste, but I don't know if you will like it.
Oh my...
You did all of this for me?
Yes.
Why?
You don't like it?
No.
It's so pretty.
It's like a princess' bedroom.
Right?
This is also a princess' bed.
Hurry and try it out.
You know, I had so much fun decorating this room!
I really wanted to have a daughter so badly.
Decorating a room like this together and sharing pretty things.
And when she's older, to travel together.
However, I could only give birth to boys, so it's been really boring.
Let's go shopping and watch movies together.
Okay?
Yes.
It's going to be so much fun!
Ah, also...
Here, a gift.
Since you lost your house, you must have no shoes left.
Am I right?
Try them on.
It's pretty...
I'm causing you so much trouble that I don't know what to do.
Eh!
What trouble?
I was very happy to buy this.
Is the size a bit too big?
No, it's very comfortable.
I really like it.
Thank you.
Even the words you say are pretty!
Just become my daughter.
Oh!
You brought it?
Good.
Now, you must be very tired.
Have a good rest, okay?
Yes...
I'm very grateful for everything.
I'll see you tomorrow morning!
Yes...
Good night!
Yes.
Seung Jo, good night.
This room was originally... ...Eun Jo's room.
Ah...
But thanks to someone here...
Eun Jo's bed and desk...
My room is so crammed.
I'm sorry.
If you're sorry... ...won't you stop it now?
You've been annoying these past few days.
- I'm telling you not to make a big fuss at school.
- Make a big fuss?
Don't worry.
If the news of us living together gets out, I'll be more affected by it than you.
What do you mean "living together"?
Weren't you the one who came to live in my house?
I'm going to wash up first.
You're dead.
You made me bleed.
I regret it.
I didn't think of going so far.
However, I can't help it either.
Ahhh!
That stupid jerk!
Damn it, damn it!
I really hate smart guys like you!
Really?
So embarrassing!
Ah!
Why did he show up right then!
The toilet seat is warm.
What do I do?
To be so close we're using the same bathroom!
Did he hear me?
He's right next door.
Ah my tummy hurts!
I can't even poop because I'm scared I might make a sound.
They seem really close!
Aigoo, Oh Ha Ni.
You're still not back to your senses?
He said he doesn't like you.
He told you not to bother him.
Ah, yes. <i>I can't believe it! <i>I'm having breakfast with Baek Seung Jo! <i>So he's having toast and jam? <i>Geniuses eat jam. <i>This is so surreal. <i>By any chance, could this be a dream? <i>He won't be looking anymore, right?
Aigoo!
You must have choked on your food.
Here, drink water.
Are you alright?
Yes, I'm fine.
She's dumb just like I expected.
- Baek Eun Jo! - Watch it!
Hey, Ha Ni, are you okay?
Hey, give me some more soup. It's so delicious!
It's really good.
Your Guksu (noodles) restaurant is doing well, isn't it?
You have a lot of costumers, right?
Ah, yes... A lot of regular customers come over.
But you know, starting tomorrow you should sleep more, you go to work late anyway.
I'm done eating.
I'll be getting up first.
Dear, how can you do that?
Ha Ni has to go with you.
Hey!
She doesn't even know her way to school.
Me too.
Hey!
Why are you leaving already?
Eat some more.
Hey, Ha Ni!
Hurry!
Ah, yes!
I'll be going to school now!
- Bye!
- Bye!
Slow down!
How could you just stop so suddenly?
It's just for today.
What?
Walking to school together.
If someone sees us... ...it would end up being bothersome again.
I got it.
Don't tell anyone about it.
I won't!
At school, act like you don't even know me.
I said I got it!
Let's walk separately.
Stupid jerk!
STUPlD JERK!
To think that I've liked a jerk like him for three years!
What a waste of my tears. <i>Brought to you by the PKer team @ www.viki.com</i>
What are you daydreaming about?
None of your business.
What?
Why are you waiting for me, when you told me to walk separately?
Who's waiting?
You go in the front.
Why?
Ah!
What!?
Why do you keep changing your mind?
Because you're short.
Isn't it hard to follow me around?
Don't blame me when you get to school late, and just go in front of me. I'll just follow you from behind.
Let's see here...
This one.
What the heck?
Why are you all swollen?
Where's the syilabus for the next midterm exam?
Would we have any reason to know anything about that?
Will you not say "we"?
Do you know it?
No, I don't.
Don't worry.
I'll study really hard, so that our pride, will be restored.
- You're looking up the word "pride", right? - Yeah.
Let's see.
Ha Ni!
Good morning.
Bong Joon Gu. Greet us too.
Did you sleep well last night?
How did you like your father's friend's house?
Huh?
Yeah, it's great.
Oh, where is it?
Huh?
Huh?
Is it far?
No...
Two subway stops away.
No, about three subway stops away.
I got it! Let's go together later.
Why?
Does it make sense that a guy doesn't know where his girl lives?
Ah!
Was that a punch or a kick?!
Why? Do you want to be kicked too?
Hey!
Hey!
Move!
Ha!
Jung Ju Ri... You again?
I told you that if you're going to do people's hair, do it at home!
Is school a hair salon to you?
I'm sorry, Teacher.
Dryer, pins, perm roll...
You were just totally prepared.
What about your books?
I put all my books in my locker.
I'm sorry... I'll never bring them again.
Did you just cut her hair?
Yes, ma'am.
Just on the back.
Here...
Do something about this here, or just curl it.
Yes.
Oh my, oh my, teacher. Your hair is half curly.
Oh my, how'd you know?
I straightened it myself.
Ah, Teach, you can tell by your temples.
Where?
Here?
Yes, if you look here, it's slightly curly.
After washing your hair you should do it just a little bit towards the inside. - Like this?
- Yes.
Ahh!
Just the inside.
TEACHER SONG GANG Yl!
I don't even know what it is that I don't know. <i>[Special Study Hall]
One... two...
Three!
Wow, that study hall must be really good.
The air conditioner is pretty strong.
Huh!
And it even has soundproof walls! <i>[Just Being Alive is Happiness]
If you're not going to study, why are you even there?
Seung Jo.
Seung Jo.
Aigoo, aigoo.
What a flirt!
Thank you!
I'm envious.
She's pretty and smart. 1... 2... 3...
Three steps.
Is it far?
It's far...
Are you studying here?
That's right!
Why?
Are you scared?
If you're going to carry me, you better start working out.
Your study hall... ...looked very nice.
With the computers and soundproof walls... What cheapskates.
Even if you say that, it doesn't sound like the truth.
What's he talking about?
It sounds like an inferiority complex.
Aren't you going home?
What!?
You're saying you want to go together?
Ha Ni!
Oh...but!
Wait (downstairs).
You were here?
I looked for you for a long time.
Oh!?
Did that guy say something again?
Huh?
No, oh hey, give me my backpack.
Oh no, it's okay.
This is for guys to carry.
Let's go!
Hey!
Ha Ni, sit here.
Aren't you hungry?
Should we get off and eat something?
Come on, let's go eat something, alright?
We're almost at our stop.
I said it's okay. I'll just keeping carrying it.
Give it, it looks embarassing.
Oh, it's really okay...
Oh! I have to get off.
Ha Ni!
Oh Joon Gu, what do I do? I'm sorry!
Have a safe trip!
Thank you!
Take care.
Why didn't you guys come back together?
I'm sure she'll be here soon.
She's not very familar with the place yet.
Recently, there's been strange people around this neighborhood.
Oh Ha Ni is the strangest person here.
You come over here!
Hm! Come over here, you need a spanking!
Hey! Baek Eun Jo.
Man, what a bother!
That cheapskate...
He left even though I told him to wait for me.
I even took a taxi.
Man, I should've just asked the taxi driver to drive me all the way home.
Made me spend all my allowance.
Don't do it!
Don't do it!
If you open it, I won't look!
I'm going to close my eyes.
Then it wouldn't matter.
Aye... Pervert! Pervert!
No, you can't!
That was a present.
Mister!
Hurry up and give it to me!
I said that was a present!
It's not like you're going to wear it!
Just have a look!
Then I'll give it back to you!
Man, I'm really tired. I don't want to!!!
How far are you going to go?
Just once!
I beg you, please.
Without closing your eyes!
It's only going to take a second!
Really it's just once, right?
Really just once.
Then you'll give me my shoe back?
Of course, I'll return it. How would I use this?
Fine.
Fine?...
You said you're fine with it?
Since you asked nicely... ...but you MUST return the shoe to me.
Of course, very well. I'm a person who keeps his promises.
You... ...you can't close your eyes because then that's cheating.
Okay.
I'm a person who keeps her promises too.
Alright.
Wait a second!
What?
Let me prepare myself.
Fine. Then prepare yourself.
Go ahead.
Preparing for that long isn't good.
Let's do it!
1... 2... 3...
Sir, forgive me!
Just this once?
Please forgive me, just this once?
I just started doing this.
I've registered on a forum and it's only my second time on the field.
Please don't report me, I have a family... ...and I have a kid.
Just this once, if you forgive me I swear it will never happen again. Sir, eh?
Then go straight home right now.
Thank you, sir!
What the?
What?
You shouldn't take this with you.
You're right.
Goodbye.
Were you looking for me?
Because you were worried?
As if!
I bought this.
But how did you come right on time?
It was because of my bad luck.
Anyway, you...
In a situation like that, people would give up the shoe. How could...
Because they were a present from your mom.
Today was the first time I wore them!
Yeah, but still...
What did you buy?
Ah! It looks good.
Can I have some?
My throat is parched from the run.
It's melted.
Is it cause of the heat?
Hey! Is that the Big Dipper? One, two...
Hey, can you hear those crickets crying?
They're not crying.
Stupid girls... ...even if they have good taste,
I hate them.
Come to your senses, Oh Ha Ni.
Don't you have any pride?
Right.
Let's study!
Let's study and show them how it's done.
Math.
Let's start with math.
Okay...
It's the global age, so let's start with English.
Aigoo!
Let's start with our native language (Korean).
Ugh! What is this talking about?
I don't get it!
I don't know!
I've learned all of this?
There's no way...
Yes?
Here.
Have this to eat.
Thank you!
Come on in.
You're studying hard. Hehe. I'm just sitting around.
Make sure you take breaks in between. I've always wanted to do something like this.
Making late night snacks and saying that you should take breaks while studying.
Now I feel like the mother of a high school senior.
Seung Jo doesn't eat late night snacks?
It's not that, but rather Seung Jo doesn't study at all.
He doesn't study?
He's already sleeping.
But he always gets perfect scores.
He must be a real genius.
Is that so?
What's the use of getting perfect scores?
He's no fun at all.
Do you have a blog?
Of course! I'm a power blogger.
Ehh! You have 160 comments!
Oh! It's Eun Jo!
Eun Jo is lacking in manners, isn't he?
He likes his older brother so much that he takes after him.
Still, he's cute.
He looks a lot like Seung Jo.
I think you probably looked pretty when you were a child as well.
Don't you have an album? Aw, come on, let's see.
I don't have a lot of pictures.
Aww, how pretty!
Aww!
Your mom?
Oh, she's gorgeous.
That's why you're pretty.
To tell you the truth, I don't really remember her.
They say she passed away when I was four years old.
That's why I look at this sometimes, so I don't forget her.
There's a comment on every picture.
Hey, this is interesting.
"Summer. Maybe because we didn't have an air conditioner, it was even cooler."
Hey, you are so witty.
Did you write this?
- Yes. - Aww!
"Bbomi is really light."
"Even something light becomes heavy after holding it for a while."
"Everything in life seems to be the same way."
Aww, you're cute.
Seung Jo was also cute, right?
When he was little?
Yeah, well...
Ah!
Ha Ni!
Would you like me to show you something fun?
Aww! She's so cute, she's so pretty!
Who is this?
She looks a lot like Seung Jo.
Really?
Yes.
Like this here... it's exactly the same.
It's Seung Jo.
What!?
This is Seung Jo.
Wait a minute.
Where was it?
Hold on.
Look here.
When I was pregnant with Seung Jo, he was very calm inside my belly.
He only wanted to eat watermelon, strawberries, and grapes.
So I really thought it was a girl.
That's why the shoes, clothes, and toys that I bought were all for a girl.
But it was a boy.
So what to do?
Do I throw it all away?
That's true, but...
And didn't I tell you... ...that I really wanted a girl?
That's why I raised him as a girl for just a little while. But...
We went to the swimming pool and he was exposed.
He must have have been scarred at that time.
That's why I wonder if he's become so cold as a result of that.
Seung Jo thinks I burnt all of this. But what can I do, when I have the photo negatives right here?
When you look at it this way, he's not even a genius.
Hey!
What is this? Why do you keep laughing? (ooseo = laugh)
Me?!
I'm scary?
(mooseo)
Yeah! Scary.
Really? I wonder why?
It's not a reaction from constipation?
Oh! Baek Seung Jo?
- What's he doing here?
Who are you looking for?
Oh Ha Ni, get your P.E. uniform and come with me.
P.E. uniform?!
Why?
Okay.
Hey! What's going on? Why was Baek Seung Jo looking for you?
P.E. uniform?
It looks like they're exchanging something.
Isn't it the P.E. uniform?
Ahhh, this is really annoying!
Why? You could have just worn it.
What?!
So what if you wear girls' clothing? You're already familiar with it.
Hey! Where did you find this?! Give it to me!
What are they doing?
What is this?!
Oh Ha Ni.
What going on?! What are they doing?!
What's going on? Ha?
Oh! Seriously, that jerk!
Aah! Let go! Ha Ni!
Hey! Aren't you gonna give it to me?!
Hey!
Hey!
Wait a second, I'll give it to you.
I have a condition.
Condition?
What condition?
Help me with my studies.
What?
Help me raise my grades on the next exam.
You're saying this knowing there's only one week until the exam?
Of course I know.
Please help me.
Please help me get into the study hall.
Do you see me as someone who can create miracles?
I'm not a god!
I understand.
Guys!
Hey!
Oh Ha Ni!
You're trickier than I thought you were.
I said that if you get into the study hall, I'd carry you on my back.
Now you want me to help you study, and give you a piggyback ride too?
If you help me, that becomes void.
Do you think I'm that petty?
Don't worry! I don't have any feelings for you anymore.
Not even this little.
Really?
Hey!
Heeeeey! <i>Brought to you by the PKer team @ www.viki.com
Ahh.
This is so good.
Thanks to you, we ate so well.
I just brought over what was left at the restaurant.
But this! This!
It's really delicious!
Kkotjeon? (griddle cake of gluttinous rice shaped like a flower)
Hapkkotjeon.
The scent of the clam is very nice.
Ahh, yes. Thank you.
Ha Ni, what would you like for your late night snack?
Eh?
Ha Ni.
Are you going to study?
Starting today, please prepare for two.
Oh, why?
No way!
Are you going to study too?
It can't be anything too greasy or too sweet.
It'll be bad for her memory.
Wheat bread and olive oil should be enough.
And egg yolk too.
Oh. Okay.
I'll get up first.
Hyung! Teach m­­--- You do it with me.
I'll get going.
Hey!
Oh Ha Ni!
You don't even know this?
Why don't you just give up school?
What are you doing?
Baby Baek Seung Jo!
Oh Ha Ni!
Fine!
Then I'll start by explaining the basics completely, so listen well.
First, use "x" as the number you want to determine.
What is "x" here? Huh?
What is "x" here?
Alphabet!
I don't know.
What is it?
That's right!
It's the number that we don't know.
"X" is the unknown number.
What do we call an unsolved case?
X-file?
That's right.
What did we call the younger generation when we were kids?
Generation X!
Yup.
The difficult to understand generation.
The unsolved case.
It was decided that "x" is used for unknown numbers.
But, why is it "x"... ...when there's "w" and "h"?
What's the use of discussing the "what ifs"?
It's already been decided.
Here,
X equals 2 to the 30th power times 10 to the negative 7th power.
log(x) = log (2^30 * 10^-7)
log(x) = 30log2 - 7log10 log(x)=30*0.3-7
log(x) = 2.
So, x = 100.
But since we're supposed to write this as a binary number, what is it?
What is 100 as a binary number?
Calculate it.
What does that mean?
I feel like I'm going to explode. Yah!
Omo!
That Oh Ha Ni, so stupid and dumb.
Do you know what the decimal system is?
Yeah.
10<BR><BR>20<BR><BR>30
Then how about the binary numeral system?
It's a way to express a number using only 0 and 1.
But why?
What's the use of that?
The computer. Computer?
In 1974, from the Arecibo Observatory, a message was sent to outer space.
If there were real aliens out there, they would receive the message and respond.
But in what language could the message be sent?
In English?
In Korean?
We don't know what the level of intelligence of the aliens could be, so in order for them to decipher the message by simply knowing 0 and 1, the message was sent in binary code.
In order to communicate with aliens, I should learn the binary system.
This is a must learn. Put a star next to this.
Then, what is the way to change 100 to the binary numeral system?
Then, did we receive a response from the aliens?
So far, not yet.
But then again, the universe is so huge.
Right?
That's right!
Because the universe is so big, the log system was developed.
Really?
Log was made to express really big things.
Why don't you just give up?
Why?
It's fun.
How can there be so many things you don't know?
Do you know everything?
Who are these people?
Si Won, Kang In, Shin Dong, Kyuhyun, Han Kyung, Ki Bum...
Sung Min, Hee Chul, Ye Sung, Eun Hyuk, Dong Hae, Lee Teuk, Ryeowook (all 13 Super Junior members)!
We just have different fields of interest. So, what about logarithms?
As shown in my electroencephalogram, even when I'm sleeping, my alpha waves are moving.
I can read 7000 words per minute; I also have an excellent memory.
When you breathe, put strength on your belly button and inhale slowly... ...and slowly exhale. <Br>Your eyes should be focused on the dot.
Not the wall!
The dot!
Focus!
Until you can only see the dot.
Move.
You must move your body as you memorize, in order to retain better.
"At" for objects.
"With" for people.
1592 Imjin invasion.
Ha Ni! 1592 Imjin invasion! Oh!
What's wrong?!
Dark circles?
Ha Ni, tell us the truth.
What?
How are you doing at that place you're staying at?
I'm doing well.
Do you call this doing well?
Something's not right.
You heard it too, right?
Last time when I said I'd walk her home, she ran away.
Ha Ni,
Ha Ni, today let's...
Where did she go?
She went home.
She said she needs to study.
See, see, see! What kind of studying would she do?
In my opinion...
Surely...
Surely?
They're working her to death without letting her sleep.
You saw her face, right?
I think I, Bong Joon Gu, need to intervene.
Hyung.
How do I solve this?
Oh, Eun Jo.
Hyung needs to do this.
Ask Mom.
Yah!<BR><BR> Oh Ha Ni!
You stupid, idiotic moron.
Because of you, I can't study and my brother can't sleep.
Who the heck are you?
Go home!
Oh!
You came?
Oh.
Just forget it.
Here.
What is this?
Read that for today and go to bed early.
Tomorrow's the exam.
What is this?
I came up with potential exam questions.
Wow!
When did you make all this?
I'm totally touched!
Yah!
I told you to hurry and look through it.
Stop talking nonsense!
I got it. Why get mad?
It'd be nice if all the questions came out of this.
He's sleeping.
Then again, he hasn't slept much because of me.
The Almighty Baek Seung Jo sleeps like this.
Thank you.
Kids!
Oh my gosh!
Jackpot!
Let me get the camera!
I'm dying.
Oh my.
It's tiring. Oh gosh.
Good luck.
Punk!
What's with the cool act?
Is this good?
Wait...
A little higher. - Baek Seung Jo got a perfect score again. <i> Wow, he got a perfect score again. <i>When he couldn't even sleep much lately because of me. <i>What a relief!
You got a perfect score again!
You're amazing!
Congrats!
Of course, I studied for the first time in my life.
How could I <i>not</i> get a perfect score?
You too. Huh?
You didn't see it yet?
Me?
Me? [50th - Oh Ha Ni]
Oh Ha Ni.
You saw?
I did it!
Thank you!
Thank you so, so much!
It's all thanks to you!
Most of the exam questions were what you predicted!
What are you doing?
That thing.
Ahh.
This?
Don't just take it out any place!
Seung Jo!
Thank you!
Really!
Thank you so much!
Stop!
Yes.
Me?
Yes, you.<BR>Baek Seung Jo.
How can you leave just like that when there are so many witnesses?
Huh?
You promised to give her a piggyback ride around the school if our Ha Ni got into the Special Study Hall. No, teacher. We decided to void that.
What are you talking about?
This kind of miracle may never happen again!
But...that....
No, we can't!
When you said you were going to study hard, I just dismissed it.
As a teacher, I couldn't even help you.
I'm so proud of you, Ha Ni! You saved my pride!
But...
What the heck are you... Did you lie?
No, teacher.
No.
Carry her!
Carry her!
Carry her! <i>Brought to you by the PKer team @ www.viikii.net</i>
What do you mean it's okay? Get on!
What are you doing?
It's you again?
Yeah, why?
Hey, come here.
But...
Cheers!
Baek Seung Jo...
I don't like him.
"Honestly, I call you the Spirit of the Forest."
Yah!
It's amazing. It's a lot more serious than I thought.
Yah!
One, two.
Good job!
What's that?
It looks like socks.
No!
Mom is always the troublemaker in our house.
Done. Something fell. What is it?
What is it?
Welcome to the presentation on level 4 subtraction. Let's get started with some problems. First problem I have here is 33,220 minus 399.
10 is larger than 9, 11 is larger than 9, 11 is larger than 3, 2 is larger than nothing, 3 is larger than nothing.
So now we're ready to subtract. This is the easy part.
10 minus 9 is 1. 11 minus 9 is 2. 11 minus 3 is 8.
3 minus nothing is 3. So we get 32,821. The only thing that makes this harder than just normal subtraction is that you have to know how to do the borrowing.
The 0 becomes a 10 because we got this 1 right here. We got this 1 from this 2 and this 2 became a 1. I think you might see the pattern if we do a couple of more problems.
13 is now larger than 8, but 2 is now smaller than 7. So we have to borrow again.
This 2 becomes a 12. And this 6 will become a 5. 13 is larger than 8, 12 is larger than 7, 5 is the same as 5, so you can actually do the subtraction.
Because 5 minus 5 is 0. As long as the top number's not smaller than the number below it. And then obviously this 5 is larger than this 0 and this 2 is larger than this nothing here.
13 minus 8 is 5. 12 minus 7 is 5. 5 minus 5 is 0.
Right, it's 699. So that 700 becomes 699. Cross all of this out.
12 is larger than 5, nine is larger than 5, 9 is larger than 1 6 is larger than nothing, and 3 is larger than nothing, so we're ready to subtract.
12 minus 5 is 7. 9 minus 5 is 4. 9 minus 1 is 8.
Same drill. 1 is less than 2, so we have to borrow. Turn that into an 11.
This becomes a 19. so,lets check again 11 is greater than 2. Check.
9 is greater than 0. Check. Uh-oh.
1 is not greater than 5. So we have to borrow again.
This 1 becomes an 11. We borrowed from this 3, which becomes a 2.
11 is greater than 2, 9 is greater than 0, 11 is greater than 5 2 is obviously greater than nothing below it.
11 minus 2 is 9. 9 minus 0 is 9. 11 minus 5 is 6.
And 2 minus nothing is 2. So 3,201 minus 502 is equal to 2,699. I think you're now ready to try some of the level 4 subtraction problems.
Arguably, one of the most important molecules in all of biology is ATP.
ATP, which stands for adenosine triphosphate.
Which sounds very fancy.
But all you need to remember, or any time you see ATP hanging around in some type of biochemical reaction, something in your brain should say, hey, we're dealing with biological energy.
Or another way to think of ATP is the currency-- I'll put that in quotes-- of biological energy.
So how is it a currency of energy?
Well ATP stores energy in its bonds.
And I'll explain what that means in a second.
And before we learn what an adenosine group or a 3-phosphate group looks like, you can just take a bit of a leap of faith, that you could imagine ATP as being made up of something called-- let me do it in a nice color-- an adenosine group right there.
And then attached to it you'll have three phosphates.
Not might, you will.
You'll have three phosphates attached to it just like that.
And this is ATP.
Adenosine triphosphate.
Tri- meaning three phosphate groups.
Now if you take adenosine triphosphate and you hydrolyze this bond, which means if you take this in the presence of water.
So let me just throw some water in here.
Let's say I have H2O.
Then one of these phosphate groups will break off.
Essentially part of this water joins to this phosphate group, and then part of it joins to this phosphate group right there.
And I'll show you that in a little bit more detail.
But I want to give you the big picture first.
What you're left with is an adenosine group that now has two phosphates on it.
And this is called adenosine diphosphate or ADP.
Before we had triphosphate, which means three phosphates.
Now we have diphosphate, adenosine triphosphate, so instead of a tri here we just write a di.
Which means you have two phosphate groups.
And so the ATP has been hydrolyzed, or you have broken off one of these phosphate groups.
And so now you're left with ADP and then an extra phosphate group right here.
And-- and this is the whole key to everything that we talk about when we're dealing with ATP-- and you have some energy.
And so when I talk about ATP being the currency of biological energy, this is why.
Is that if you have ATP, and if you were to-- through some chemical reaction-- you pop off this phosphate right here.
It's going to generate energy.
That energy can be used for just general heat.
Or you could couple this reaction with other reactions that require energy.
And then those reactions will be able to move forward.
So, I draw these circles. Adenosine and phosphates.
And really, this is all you need to know.
Already, what I've shown you right here is really all you need to know to operationally think of how ATP operates in most biological systems.
And if you want to go the other way. If you have energy and you want to generate ATP, the reaction will just go this way.
Energy plus a phosphate group plus some ADP, you can go back to ATP.
And so this is stored energy.
So this side of the equation is stored energy.
And this side of the equation is used energy.
And this is really all you--well this is 95% of what you need to know to really understand the function of ATP in biological systems.
It's just a store of energy when you-- ATP has energy.
When you break a phosphate off, it generates energy.
And then if you want to go from ADP and a phosphate back to ATP, you have to use energy up again.
So if you have ATP, that's a source of energy.
If you have ADP and you want ATP, you need to use energy.
And so far I've just drawn a circle with an A around it and said that's an adenosine.
But sometimes I think it's satisfying to see what the molecule actually looks like.
So I cut and pasted this from Wikipedia.
And the reason why I didn't show this to you initially is because this looks very complicated.
While the conceptual reason why ATP is the currency of energy, I think is fairly straightforward.
When it has three phosphates, one phosphate can break off.
And then that'll result with some energy being put into the system.
Or if you want to attach that phosphate you have to use up energy.
That's just the basic principle of ATP.
But this is its actual structure.
But even here we can break it down and see that it's really not too bad.
We said adenosine.
Let me draw the adenosine group.
We have adenosine.
This right here is adenosine.
This part of the molecule right there. That is adenosine.
And for those of you that have really paid attention to some of the other videos, you might recognize that this part of adenosine-- so this is called adenosine, but this part right here-- is adenine.
Which is the same adenine that makes up the nucleotides that are the backbone of DNA.
So some of these molecules in biological systems have more than one use.
This is the same adenine where we talk about adenine and guanine.
This is a purine.
And there's also the pyrimidines, but I won't go into that much.
But that's the same molecule.
So that's just an interesting thing.
The same thing that makes up DNA is also part of what makes up these energy currency molecules.
So the adenine makes part of the adenosine part of ATP.
And then the other part right here is ribose.
Which you might also recognize from RNA, ribonucleic acid.
That's because you have ribose dealing in the whole situation.
But I won't go into that much.
But ribose is just a 5-carbon sugar.
When they don't draw the molecule, it's implied that it's a carbon.
So this is one carbon right there, two carbons, three carbons, four carbons, five carbons.
And that's just nice to know. It's nice to know that they share parts of their molecules with DNA.
And these are familiar building blocks that we see over and over again.
But I want to emphasize that knowing this, or memorizing this, in no way will help you understand the simpler understanding of ATP just being what drives biological reactions.
And then here I drew 3-phosphate groups, and this is their actual molecular structure.
Their Lewis structures right here.
That's one phosphate group.
This is the second phosphate group.
And this is a third phosphate group.
Just like that.
When I first learned this, my first question was, OK I can take this as a leap of faith that if you take one of these phosphate groups off or if this bond is hydrolyzed, that somehow that releases energy.
And then I kind of went on and answered all the questions that I had to answer.
But why does it release energy?
What is it about this bond that releases energy?
Remember all bonds are are electrons being shared with different atoms.
So the best way you could think about it is right here. These electrons that are being shared right across this bond, or this electron that's being shared right across this bond, and it's coming from the phosphate.
I won't draw the Periodic Table right now.
But you know the phosphate has five electrons to share.
It's less electronegative than oxygen, so oxygen will kind of hog the electron.
But this electron is very uncomfortable.
There's a couple of reasons why it is uncomfortable.
It's in a high energy state.
One reason why is, you have all these negative oxygens here.
So they kind of want to push away from each other.
So these electrons in this bond really can't kind of get close to the nucleus.
They'll go into kind of a low energy state.
All of this is more of an analogy than the reality.
We all know that electrons can get quite complex.
And there's a whole quantum mechanical world.
But that's a good way to think of it.
That these molecules want to be away from each other.
But you have these bonds, so this electron, it's kind of in a high energy state.
It's further from the nucleuses of these two atoms than it might want to be.
And when you pop this phosphate group off, all of a sudden these electrons can enter into a lower energy state.
And that generates energy.
So this energy right here is always-- in fact in any chemical reaction where they say energy is generated, it's always from electrons going to a lower energy state.
That's what it's all about.
And later in future videos when we do cellular respiration and glycolysis and all that, whenever we show energy, it's really from electrons going from uncomfortable states to more comfortable states.
And in the process they generate energy.
If I'm in a plane or I'm jumping out of a plane, I have a lot of potential energy right when I jump out of the plane.
And you can view that as an uncomfortable state.
And then when I'm sitting on my couch watching football, I have a lot less potential energy, so that's a very comfortable state.
And I could have generated a lot of energy falling to my couch.
But I don't knows.
My analogies always break down at some point.
Now, the last thing I want to go over for you is exactly how this reaction happens.
So far you could turn off this video and you could already deal with ATP as it is used in 95% of biology, especially AP Bio.
But I want you to understand how this reaction actually happens.
So to do that, what I'm going to do is copy and paste parts of these.
So I already told you that this guy right here is going to break off of the ATP.
So that's the phosphate group that breaks off.
And then you have the rest of it.
You have the ADP that's left over.
So this is the ADP.
I don't even have to copy and paste all of this stuff.
You can just accept that that's the adenosine group.
Just like that.
So we've already said that this thing gets hydrolyzed off, or gets cut off and that generates energy.
But what I want to do is actually show you the mechanism.
A little bit of hand-wavy mechanism of how this actually happens.
So I said this reaction occurs in the presence of water.
So let me draw some water here.
So I have an oxygen and a hydrogen.
And then I have another hydrogen.
That's water right there.
So hydrolysis is just a reaction where you say, hey, this guy here, he wants to bond with something or he wants to share someone else's electrons.
So maybe this hydrogen right here goes down here and shares its electron with this oxygen right here.
And then this phosphorus, it has an extra electron that it needs to share.
Remember it has five valence electrons; it wants to share them with oxygen.
It has one, two, three, four being shared right now.
Well, if this hydrogen goes to this guy, then you're left with this blue OH right here.
And this guy can share one of the phosphorus' extra electrons.
So you get the OH just like that.
So that's the actual process that happens.
And it could go the other way as well.
I could've cleaved it here.
I could have cleaved the whole thing here.
And so this guy would have kept the oxygen and the hydrogen would have gone to him.
And then this guy would have taken the OH.
It could happen in either order.
And so either order would be fine.
And there's one other point I want to make.
And this is a little bit more complex.
And I was even wondering whether I wanted to make it.
My whole reason why you're kind of in a lower energy state is, once you break apart--actually let me go down here-- is because I said, hey, this electron is happier when it's-- so let's say this electron that was part of this phosphorus is happier now.
It's in a lower energy state because it's not being stretched.
It's not having to spend time between that guy and that guy because this molecule and this molecule want to spread apart because they have negative charges.
That's part of the reason.
The other reason why, and we'll talk about this in a lot more detail when we learn more about organic chemistry, is that this has more resonance.
More resonance structures or resonance configurations.
And all that means is that these electrons, these extra electrons here, they can kind of move about between the different atoms.
And that makes it even more stable.
So if you imagine that this oxygen right here has an extra electron with it.
So that extra electron right there, it could come down here and then form a double bond with the phosphorus.
And then this electron right here can then jump back up to that oxygen.
And then that could happen on this side and on that side.
And I won't go into the details, but that's another reason why it makes it more stable.
If you've already taken organic chemistry, you can kind of appreciate that more.
But I don't want to get all into the weeds.
The most important thing to remember about ATP is that when you cleave off a phosphate group it generates energy that can drive all sorts of biological functions, like growth and movement, muscle movement, muscle contraction, electrical impulses in nerves and the brain.
So this is the main battery or currency of energy in biological systems.
That's the main thing that you really just need to remember about ATP.
You'll see the water shoals on the island side... while the deep soundings run to the mainland.
Have any of you seen the captain today? - No.
He wasn't down for dinner. - No, and he wasn't down for lunch.
He hasn't left the bridge since you decided to come through the channel.
What are you driving at? Ever since you gave him those orders yesterday to cut through these waters... he's had the jitters.
There's something wrong. I... Hey, I'm getting nervous myself.
Doc, what do you recommend for nerves? - Give him a shot of scotch.
- Give the whole bottle. - No!
I've got nerves too.
- Here you are, Doc. Just what you need.
- Well, maybe you're right.
- And how, boy. - Good evening, Captain.
- Good evening, sir.
- May I speak with you?
- Why, certainly.
Go ahead.
We're heading straight for the channel between Branca Island and the mainland.
- Good.
- But the lights are just a bit off, according to the chart.
The charts are never up to date in this part of the Pacific.
You know that. I know, sir, but...
Doesn't Branca Island mean anything to you?
- Well, not a lot. - Perhaps if I spoke with Mr. Rainsford...
Bob's not a sailor.
He's a hunter. He's made many of these trips.
He's young, but he has judgment.
I'll call him.
- Oh, Bob. Bob!
- What is it?
- Come up here, will ya? - Just a minute. What's bothering you, Captain?
There are no more coral-reefed, shark-infested waters in the whole world than these.
Boy! Just take a look at these.
You didn't turn out so hot as a hunter, Doc, but oh, what a photographer.
If we'd had you to take pictures on the Sumatran trip... they might have believed my book.
If you'd had me on the Sumatran trip, you'd have never had me on this one.
Say, here's a swell one of the ship, Skipper.
What's the matter?
These old sea dogs tell yarns to kid each other... and end up believing it all themselves.
I think that Mr. Rainsford should know... that the channel lights aren't just in the position given on the charts.
Oh. Well, what do you think, fellas?
I think we should turn back and take the outside course.
We'll go ahead. Very well, sir.
It's your ship.
"It was the schooner 'Hesperus,' and she sailed the wintry sea. "
Let's talk this over.
- There's no use taking any chances. - Chances? That's fine talk... coming from a fella who just got through slapping tigers in the face.
Get an eyeful of this.
And he talks about taking chances. Here's the doc charging the enemy with an unloaded camera.
Get the expression on Doc's face, Bill.
He looks more frightened than the tiger. - He is.
- What'd you have on your mind, Doc? I'll tell you what I had on my mind.
I was thinking of the inconsistency of civilization.
The beast of the jungle killing just for his existence is called savage.
The man, killing just for sport, is called civilized.
- Hear! Hear! - It's a bit contradictory, isn't it?
Now, just a minute.
What makes you think... it isn't just as much sport for the animal as it is for the man?
Take that fellow right there, for instance.
There never was a time when he couldn't have gotten away.
He didn't want to.
He got interested in hunting me.
He didn't hate me for stalking him... any more than I hated him for trying to charge me.
As a matter of fact, we admired each other.
Perhaps, but would you change places with the tiger?
- Well, not now. - Mm-mm!
Here comes that bad-luck lady again.
Third time tonight. - Here. Let me shuffle them.
Don't evade the issue. - Yeah, speak up. - I asked you a question.
- You did? I forgot.
- Oh, no, you didn't.
I asked you if there'd be as much sport in the game... if you were the tiger instead of the hunter.
- Come on. - What's your answer now, Bob?
That's something I'll never have to decide.
Listen here, you fellows. This world's divided into two kinds of people... the hunter and the hunted.
Luckily, I'm a hunter. Nothing can ever change that.
Hang on!
Hello!
Hello, down there!
Hello, Engine Room!
- The panel is flooded!
- If the water hits those hot boilers...
Help!
Help!
You trying to drown me? Where are the others? See anybody?
Nobody left but us two and... that fella.
Doc! Help! - Look!
Ohh!
It got me!
Don't you understand any English?
Lvan does not speak any language. He has the misfortune to be dumb. Oh, hello.
Welcome to my poor fortress. - Fortress? - It once was.
Built by the Portuguese, centuries ago.
I have had the ruins restored to make my home here. I am Count Zaroff.
My name's Robert Rainsford. Glad to meet you.
Very glad.
Lvan is a Cossack. I am afraid, like all my fellow countrymen, he is a bit of a savage.
Smile, Ivan.
I was trying to make him understand there'd been a shipwreck in the channel.
But how appalling!
And you mean to say that you are the only survivor?
Yes, I'm afraid I am.
You're certain? I'd have never left the spot if I hadn't been.
The swellest crowd on Earth... my best friends.
- It's incredible. - Such things are always incredible.
Death is for others, not for ourselves.
That is how most of my other guests have felt. Your other guests?
You mean this has happened before? My fellow, we have several survivors from the last wreck still in the house. It would seem that this island were cursed.
Only he thought it was uninhabited. We Cossacks find our inspiration in solitude.
- Well, it's a break for me, anyway.
- My house is yours. Oh, by the way.
You'll want to change those wet rags immediately. Yes. They look about the way I feel.
Yes.
I have some loose hunting clothes which I keep for my guests... that you can possibly get into.
Lvan will show you to your room.
- Thank you.
- You'll find a stiff drink there also.
Thanks a lot.
All pleasure is mine.
Come in.
- Ready, Rainsford? - All set.
I'm afraid we have finished dinner.
But I have ordered something for you.
Thanks. I don't feel like eating, though. Oh.
Well, perhaps later.
Now, then, what do you say to coffee... and most charming company? It is hard to forget your comrades' fate, I know... but our feminine guest is easily perturbed. If I could beg you to put a good face upon the matter.
- Thank you. Miss Trowbridge, may I present Mr. Robert Rainsford. - Miss Eve Trowbridge.
- How do you do? - And her brother, Mr. Martin Trowbridge. How are you, old chap?
Pretty well shaken up, I guess, huh?
- Coming out of it now, thanks. - We know how it feels, don't we, Eve?
Indeed we do.
Perhaps Mr. Rainsford would like some hot coffee.
Oh, yes, of course.
Mr. Rainsford, please sit here. Vodka, that's the stuff! One shot'll dry you out quicker than all the coffee in Java.
Like this. Now, Martin, you don't have to drink it all tonight, do you? Don't be ridiculous, sis.
Same as Mr. Rainsford. And if anyone has a right to his liquor, it's a victim of circumstance.
- Isn't that so, Count? - Of course, yes.
- You were in a shipwreck too? - Yes.
Our lifeboat was the only one saved... my brother and I and two sailors.
The count found us on the beach with nothing but the clothes on our backs.
Those channel lights must have been shifted. - I wonder it hasn't been reported.
- Well, we'll report 'em... just as soon as we get back to the mainland.
You see, the count has only one launch... and that's under repair.
Russians are not the best mechanics.
I'm afraid we'll have to be patient a few days longer.
It's all right with me. I feel as if I were living on borrowed time right now.
Speaking of that, perhaps now you'll tell us... a little bit about who you are.
Just sketchily, you know... born, married, why I left my last job.
No, no, no, no. One moment, please.
Mr. Rainsford need never explain who he is in my house.
We entertain a celebrity, Miss Trowbridge.
Wait a minute, wait a minute.
Don't tell me.
Let me guess. I know.
Flagpole sitter.
- I know. He wrote some books. - No, he lived some books.
If I am not mistaken, this is Mr. Robert Rainsford... who hunts big game so adventurously.
Yeah? Here's to ya.
- I've lugged a gun around a little. - "I've lugged a gun around a little. "
No, I have read your books. I read all books on hunting. - A papiroso?
Only in yours have I found a sane point of view. - What do you mean, "sane"? - Cigarette?
- Hmm? Yeah. Thanks.
- You do not excuse what needs no excuse. Let me see.
How did you put it?
"Hunting is as much a game as stud poker... only the limits are higher. " - You have put our case perfectly.
- Then you're a hunter yourself?
We are kindred spirits.
It is my one passion.
He sleeps all day and hunts all night.
And what's more, Rainsford, he'll have you doing the same thing.
We'll have capital sport together, I hope.
Don't encourage him.
He's had our two sailors so busy... chasing around the woods after flora and fauna... that we haven't seen them for three days.
But what do you hunt here?
I'll tell you.
You will be amused, I know.
I have done a rare thing.
I have invented a new sensation.
Yeah, and is he stingy with it.
What is this sensation, Count?
Mr. Rainsford, God made some men poets.
Some He made kings, some beggars.
Me, He made a hunter.
My hand was made for the trigger, my father told me.
He was a very rich man... with a quarter of a million acres in the Crimea, and an ardent sportsman.
When I was only still up high he gave me my first gun.
- Good for him. - My life has been one glorious hunt.
It would be impossible for me to tell you how many animals I have killed.
- But when the revolution... - Look out.
Oh, I'm so sorry. Count Zaroff was so interesting...
I didn't realize the danger. Oh, it's all right now.
What were you saying about the revolution, Count?
Oh, merely that I escaped with most of my fortune.
Naturally, I continued to hunt all over the world.
It was in Africa that the Cape buffalo gave me this.
That must have been a close call. Yes.
It still bothers me sometimes.
However, in two months I was on my way to the Amazon.
I'd heard that the jaguars there were unusually cunning. No, no, no. No sport at all.
Well, conditions are bad everywhere these days.
One night, as I lay in my tent with this... this head of mine... a terrible thought crept like a snake into my brain.
Hunting was beginning to bore me.
Is that such a terrible thought, Count? It is, my dear lady, when hunting has been the whip for all other passions.
When I lost my love of hunting...
I lost my love of life... of love.
Well, you seem to have stood it pretty well.
I even tried to sink myself to the level of the savage.
I made myself perfect in the use of the Tartar war bow. Tartar which?
Tartar war bow...
That one up there.
It's cute.
Even to this day I prefer to hunt with it... but alas, even that was too deadly.
What I needed was not a new weapon... but a new animal.
- A new animal?
- Exactly so. You found one? Yes.
Here on my island...
I hunt the most dangerous game.
"The most dangerous game"? You mean tigers? Tigers?
No.
The tiger has nothing but his claws and his fangs.
I heard some queer beast howling back there along the water.
Was that it? It's no use, Rainsford.
He won't tell.
He won't even let you see his trophy room... till he gets ready to take you on a hunt of the great whatsit.
I keep it as a surprise for my guests... against the rainy day of boredom.
You let me in on that game... and I'll bet you I go for it. You know, Rainsford, he hasn't failed yet.
If he says a thing is good, it is good.
He's a judge of liquor, wizard at contract... plays the piano... anything you want.
He's a good host and a good scholar, eh, Count?
Yes, yes. You want me to go hunting?
You just say the word. We're pals. We'll have a big party, get cockeyed and go hunting.
A completely civilized point of view.
I tell you what you do.
You come to my place in the Adirondacks, see.
We'll have a private car, liquor and gals on the trip... and the guides will make the deers behave.
I think we'd better change the subject. All right. Change the subject.
If you wish. Good idea. Play the piano.
Leave it to me, and I'll fix everything.
Perhaps the count doesn't want to play.
There you go, sis, throwing cold water. Leave me alone. I know where the piano is.
I'm perfectly sober.
Charming simplicity. "Completely civilized," did you say?
He talks of wine and women as a prelude to the hunt.
We barbarians know that it is after the chase... and then only that man revels.
It does seem a bit like cocktails before breakfast.
Of course, yes. You know the saying of the Ugandi chieftains... "Hunt first the enemy, then the woman. "
That's the savages' idea everywhere. It is the natural instinct.
What is woman... even such a woman as this... until the blood is quickened by the kill?
- Oh, I don't know.
- "Oh, I don't know. " You Americans.
One passion builds upon another.
Kill! Then love. When you have known that... you will have known ecstasy.
Oh, Martin!
Here you see Zaroff, the keyboard king... in his Branca Island hour.
Come on, Count. Now, you show them.
- What do you suggest? - Oh, just a good tune. But not highbrow, like last night.
- Just a good tune, see?
- I see.
Oh, his hunting dogs.
Keep your voice low and listen.
It isn't true about the launch needing repairs.
I heard it leave the boathouse last night. It returned this morning. You mean he's keeping you from returning to the mainland?
Yes.
Well, perhaps he enjoys the company of two very charming people.
There were four of us a week ago.
- The other two have disappeared.
- What do you mean?
One night after dinner, the count took one of our sailors... down to see his trophy room... at the foot of those stone steps.
- That iron door? - Yes.
Two nights later he took the other there. Neither has been seen since. Have you asked him about them?
He says they've gone hunting.
Oh, be careful. He's watching us.
Will you smile, as if I'd said something funny?
Now look here. You must be mistaken. Not now.
I'm afraid we have failed to hold the full attention of our audience. Well, I expect it's rather difficult for Mr. Rainsford... to concentrate on anything after all he's been through.
My dear lady, you are pleading for yourself.
I can see the drooping of those lovely eyes.
Excuse me.
You know, the count's worse than a family governess.
Every night he sends us off to bed like naughty children.
Oh, no, my dear. No.
Charming children.
There, you hear that, sis?
Now trot along upstairs and don't bother us grownups anymore.
Well, after that I guess... I guess I'll have to go. - Good night, Mr. Rainsford.
We'll be seeing each other at breakfast. - Good night.
- Good night.
Good night, sis.
We won't be seeing each other at breakfast.
Oh, my dear Rainsford, I have been most inconsiderate.
You must be feeling the need of sleep too.
- Yes, I am just about all in.
- Then Ivan will show you to your room.
Oh, Martin, turn in early, please?
Don't worry.
The count'll take care of me, all right.
Indeed I shall.
- Well, good night. - Good night, sir.
Sleep well.
Oh, uh, well, here's to long life.
A long life.
Tell me, Mr. Trowbridge... are you also fatigued? Tired?
Me? You know I'm not.
You know, Rainsford, we two are just alike.
Up all night and sleep all day.
Well, good night.
Well, what are we gonna do, huh?
What's the big idea?
I thought that perhaps... tonight you would like to see my trophy room?
Your trophy room?
I'm sure you will find it most... interesting.
Say, that's a great idea. Ho-ho. Now we're pals.
No more secrets now, huh? - We'll make a night of it. - I hope so, Mr. Trowbridge.
Attaboy, County, old boy, old boy, County.
Please let me come in.
I'm sorry to disturb you, but I'm frightened. - What was it? Those dogs?
I've just gone to his room. He isn't there!
- He's probably somewhere with the count. - That's just what I'm afraid of. Count Zaroff is planning something... about my brother and me.
You don't really think anything has happened to your brother?
Oh, I don't know, but we've got to find him. Won't you help me? Why, of course I'll help you.
- Where do you think he's gone?
- Where did the others go?
The iron door.
I'll meet you downstairs in five minutes.
Thank you.
That's queer.
It's unlocked.
Zaroff! He's coming down.
Back here, quick!
Where is my brother? You killed him!
You killed my brother! You! Why, you...
You and I, we are hunters.
So that's your most dangerous game.
Yes. My dear fellow, I intended to tell you last night... but you know, Miss Trowbridge... You hunted him like an animal.
An hour with my trophies... and they usually do their best to keep away from me. Where do you get these poor devils? Providence provided my island with dangerous reefs.
- You shifted them. - Precisely right.
Too bad your yacht should have suffered... but at least it brought us together.
You take half-drowned men from ships you've wrecked... and drive them out to be hunted.
I give them every consideration... good food, exercise... everything to get them in splendid shape. - To be shot down in cold blood. - Oh, no, no.
I even wait until midnight to give them the full advantage the dark.
And if one eludes me only till sunrise... he wins the game.
Suppose he refuses to be hunted.
Ivan is such an artist with these.
Invariably, Mr. Rainsford, invariably they choose to hunt.
And when they win?
To date I have not lost.
Oh, Rainsford, you'll find this game worth playing. When the next ship arrives, we'll have gorgeous sport together.
You murdering rat! I'm a hunter not an assassin. Come, Rainsford.
Say you will hunt with me. Hunt men?
Say you will hunt with me!
No? What do you think I am?
One, I fear, who dare not follow his own convictions... to their logical conclusion.
I'm afraid in this instance, Mr. Rainsford... you may have to follow them.
What do you mean? I shall not wait for the next ship.
Four o'clock. The sun is just rising.
Come, Mr. Rainsford.
Let us not waste time.
Ivan.
Your fangs and claws, Mr. Rainsford.
Bob!
Bob! Lvan. Bob!
Bob, what are they going to do? - I'm going to be hunted.
- Oh, no. No, Miss Trowbridge. Outdoor chess.
His brain against mine.
His good craft against mine.
- And the prize?
- The prize?
You may recall what I said last evening.
Only after the kill... does man know the true ecstasy of love.
If I do not...
What shall I say?..
Find you... between midnight and sunrise tomorrow, freedom for both of you.
- I'm going with you. - No.
He'll kill you too. Not at all.
One does not kill a female animal. If you lose, I can easily recapture her alive. All right.
I'll take her with me then.
We'll set him a trail he'll remember.
It's only fair to advise you against Fog Hollow.
Outdoor chess, Mr. Rainsford.
We'll beat this thing. - The others didn't.
- We will.
Come on.
Let's get going.
It seems as though we've come miles.
Yeah, but three hours doesn't take you far in this jungle.
Come on. Let's keep going.
Come on.
Just a little more of this, then easy downhill going.
We'll soon be safe.
No wonder he was so sure.
This island is no bigger than a deer park.
Oh, Bob! Come on, now. What are we going to do?
And leave you here with that savage?
Not a chance.
Now we've got to think of something to worry him. You'd never get near him. He'd shoot on sight.
Weapons aren't everything in the jungle. Say, did you notice that leaning tree down there?
- The one we just passed? - Yes. I want to show you something.
You see? If that supporting branch were cut away... this fallen tree would make a perfect Malay deadfall. A Malay deadfall?
We'll cut some strong vines.
There. Almost ready.
This bracelet of yours makes a fine guide ring for my necktie.
He'll have been on his way almost an hour now. Look out! Don't touch that trip line.
- Jungle wood's as heavy as iron. - Will it really work? I've never known a living thing to get by one yet.
Look here. You touch that trip line... it'll pull that trigger free. Once that's loose, there's nothing to keep the log from coming down.
We're ready.
Let him come.
Give me that knife.
Come out, Rainsford.
Why prolong it? I'll not bungle this shot.
You'll never even feel it.
But surely you don't think that anyone who has hunted leopards... would follow you into that ambush?
Oh, very well. If you choose to play the leopard...
I shall hunt you like a leopard.
Wait.
Maybe it's a trick.
Eve. Why did he go? He's playing with us... like a cat with a mouse.
- The swamp where he caught the others.
We haven't a chance of keeping ahead of him there.
- But there's no place else to run. - That's just what he's counting on. We've got two hours till dawn.
We've got to use our brains instead of our legs. But he'll have his rifle. And we'll have a man trap.
It makes me dizzy.
Cover this over. When Mr. Zaroff falls down there, he'll be all through hunting. Quick.
Gather some leaves and grass.
I'll cut some branches.
Yes.
Very good, Rainsford.
Very good. You have not won yet.
Look at your watch. Are you looking at it? Still half an hour till sunrise.
Swamp or no swamp, we can keep ahead of him that long.
As you are doubtless saying, the odds are against me.
You have made my rifle useless in the fog.
You cannot blame me if I overcome that obstacle.
Those animals I cornered... now I know how they felt.
Achmed, Miss Trowbridge... bring her here. Now! My dear Rainsford, I congratulate you.
No!
The boat!
Quick!
Impossible.
Subtitles By Captions, Inc. Los Angeles
Alright, now we have a very interesting situation. On both sides of the scale, we have our mystery mass and now I'm calling the mystery mass having a mass of Y. Just to show you that it doesn't always have to be X.
A Y is the same thing as 1Y. So I have the Y kilograms right there. And I have seven of these, right?
1,2,3,4,5,6,7. Yup, seven of these. So I have Y plus 7 kilograms on the right-hand side.
Now the next thing to do is, what are some reasonable next steps? How can we start to simplify this a little bit? You know, once again, I'll give you a few seconds to think about that.
But I will ask you, what can we do from this point? What can we do from this point to simplify it further or so, even better, think of it so we could isolate the, these Ys on the left-hand side. And I'll give you a few seconds to think about that.
These 3 minus 3 is 0, and you see that here. We're just left with 2Ys right over here, and on the right-hand side, we got rid of 3 of the blocks. So we only have 4 of them left.
Well, let's calculate it. We have 2 right, right over here, this is 2 kilograms, I'll do that in purple color,so this is a 2, this is a 2, this is a 2. So we had 6 kilograms plus these 3, we had 9 kilograms on the left-hand side.
We're on 41.
Lea made two candles in the shape of right rectangular prisms.
So I'm assuming when they say right rectangular prisms, they mean a kind of three dimensional rectangular shape.
The first candle is 15 centimeters height, 8 centimeters long and 8 centimeters wide.
So let's see, it's 15 centimeters high.
So that's 15.
8 centimeters long.
So maybe that's 8.
And 8 centimeters wide.
So maybe it goes back 8.
So it looks something like that.
That's candle number one.
The second candle is 5 centimeters higher, but the same length and width.
So the second candle is just 5 centimeters higher.
So it looks something like this.
Where this is still 8 and 8.
But the height is 5 more than 15, so it's 20.
Fair enough.
How much additional wax was needed to make the taller candle?
So if you think about it, we just have to think about how much incremental volume did we create by making that section five centimeters higher?
So this candle, you can kind of view it as going up to here.
It's 15 centimeters high.
And then we added 5 right here.
So what's the volume of this volume right there?
So it's 8 by 8 by 5.
So 5 times 8 times 8.
5 times 8 is 40 times 8 is 320.
So we have to add 320 cubic centimeters more of wax to make the taller candle.
Problem 42.
Two angles of a triangle have measures of 55 and 65.
Which of the following could not be a measure of an exterior angle of the triangle?
So I think this is a good time to introduce what an exterior angle even is.
So if I draw any polygon, and I'll draw a triangle since that's what this question is about.
So let's say that that's my triangle. An exterior angle of one of the vertices is, you essentially extend one of the lines of the vertices out.
So this is an interior angle right here.
The exterior angle is if you extend this line out, so if I were to draw a dotted line that extends out this bottom line.
This is the exterior angle right here.
As you can see, it's going to be the supplement to this interior angle.
And we could have extended the line out there.
Or we could have extended this line this way.
And we could have used this one.
But we wouldn't add these two if we wanted to find all of the exterior angles.
The exterior angle of this vertex right here is either this one or this one.
And they are the same because both of these are supplements of this angle.
This angle plus either of this angle or that one will add up to 180 degrees.
So that's what an exterior angle is.
So let's go back to the question.
Two angles of a triangle have measures of 55 and 65.
So let's say this is 55 and this is 65.
Which of the following could not be a measure of an exterior angle of the triangle?
Well we can figure out all of the exterior angles.
So first of all what's this third interior angle going to be?
Well they all have to add up to 180.
So let's call that x.
So we know that x plus 65 plus 55 is equal to 180. 65 plus 55 is 120.
120 is equal to 180. So x is equal to 60 degrees.
So this angle right here, I'll do it in another color, this is 60 degrees.
So what are all the possible exterior angles.
So if I extended this line out like I did in the example of when I defined what an exterior angle is, this exterior angle would be 120 degrees.
If were to do it here, if I would extend this out right here, what would this exterior angle be?
Let's see, this plus 65 is 180.
What's 180 minus 65.
180 minus 60 is 120, so this would have to be 115.
So that exterior angle is 115. And then this one, let's see if I extend it out.
One of the two lines that form the vertex.
This is going to be supplementary to 55.
So 180 minus 55 is 125.
180 minus 60 would be 120, and then it's only 55 so 125.
So the three supplementary, or the three exterior angles of this triangle are 125. And they want to know what could not be a measure.
So 125 is a measure of an exterior angle.
So is 115.
And so is 120.
So our answer is D.
None of the exterior angles are equal to 130 degrees.
Problem 43.
OK, they say the sum of the interior angles of a polygon is the same as the sum of its exterior angles, what type of polygon is it?
And this is an interesting question.
And it's something to experiment with for yourself.
But I want you to draw random polygons with angle measures, because you know what the angles all have to add up to in a polyogon.
And I think you'll find, that no matter what polygon you draw, all of the exterior angles are going to add up to 360 degrees.
In fact, in that example we just did, what were they they were, for that triangle.
If I remember, it's 115, 125, and 120.
This was for a triangle.
If you added them up, you get 5 plus 5, 10. And then that's 6.
360 degrees.
For that triangle, which had kind of strange angles.
It wasn't like an equilateral triangle or anything beautiful.
And it's also the same if I were to draw a rectangle.
Well let me not draw a solid rectangle.
So if I have a rectangle like that.
What are the exterior angles here?
Well, I can continue this line right here.
This angle right here is going to be 90.
I could go either way, I could continue this up, but you can only do it once though for each of the vertices.
Well that exterior angle is 90.
I could go like that, that exterior angle is 90.
I could go like that.
That exterior angle is 90.
So once again, 90 plus 90 plus 90 plus 90 that's 360 degrees.
So it's a good thing to know that the sum of the exterior angles of any polygon is actually 360 degrees.
And maybe we'll prove that in another video for a polygon with n sides.
But now that we know that, so they say that the sum of the interior angles of a polygon is the same as the sum of its exterior angles, this is the same as saying the sum of the interior angles is equal to 360.
Because this is always going to be 360 degrees no matter what the polygon is.
So they're essentially saying what polygon's interior angles add up to 360 degrees. And that of course is a quadrilateral.
My mouth got ahead of me.
And if you think in a quadrilateral you have 90, 90, 90, 90 and they add up to 360 degrees.
Next question.
Let me copy and paste a couple of them so I don't have to keep doing this.
OK.
All right.
What is a measure of angle x.
So this is an exterior angle to the vertex B.
So how do we figure this out?
Well there's kind of a fast way and a slow way.
And the slow way is to figure out this angle.
Because you know that the sum of the angles add up to 180.
And you say oh, x is going to be 180 minus that.
Let's just do it the slow way and I think you'll see the intuition of a slightly faster way you could have done it.
This plus 60 plus 25 is 85 degrees.
Let's call this angle y.
So we know that y plus 85 degrees is equal to 180.
I got this 85 just by adding 60 to 25. So this is just saying that the interior angles of a triangle add up to 180 degrees. And we could figure out y right now.
Two weeks ago,
I was sitting at the kitchen table with my wife Katya, and we were talking about what I was going to talk about today.
We have an 11-year-old son; his name is Lincoln.
He was sitting at the same table, doing his math homework.
And during a pause in my conversation with Katya, I looked over at Lincoln and I was suddenly thunderstruck by a recollection of a client of mine.
My client was a guy named Will.
He was from North Texas.
He never knew his father very well, because his father left his mom while she was pregnant with him.
And so, he was destined to be raised by a single mom, which might have been all right except that this particular single mom was a paranoid schizophrenic, and when Will was five years old, she tried to kill him with a butcher knife.
She was taken away by authorities and placed in a psychiatric hospital, and so for the next several years Will lived with his older brother, until he committed suicide by shooting himself through the heart.
And after that Will bounced around from one family member to another, until, by the time he was nine years old, he was essentially living on his own.
That morning that I was sitting with Katya and Lincoln, I looked at my son, and I realized that when my client, Will, was his age, he'd been living by himself for two years.
Will eventually joined a gang and committed a number of very serious crimes, including, most seriously of all, a horrible, tragic murder.
And Will was ultimately executed as punishment for that crime.
But I don't want to talk today about the morality of capital punishment.
I certainly think that my client shouldn't have been executed, but what I would like to do today instead is talk about the death penalty in a way I've never done before, in a way that is entirely noncontroversial.
I think that's possible, because there is a corner of the death penalty debate -- maybe the most important corner -- where everybody agrees, where the most ardent death penalty supporters and the most vociferous abolitionists are on exactly the same page.
That's the corner I want to explore.
Before I do that, though, I want to spend a couple of minutes telling you how a death penalty case unfolds, and then I want to tell you two lessons that I have learned over the last 20 years as a death penalty lawyer from watching well more than a hundred cases unfold in this way.
You can think of a death penalty case as a story that has four chapters.
The first chapter of every case is exactly the same, and it is tragic.
It begins with the murder of an innocent human being, and it's followed by a trial where the murderer is convicted and sent to death row, and that death sentence is ultimately upheld by the state appellate court.
The second chapter consists of a complicated legal proceeding known as a state habeas corpus appeal.
The third chapter is an even more complicated legal proceeding known as a federal habeas corpus proceeding.
And the fourth chapter is one where a variety of things can happen.
The lawyers might file a clemency petition, they might initiate even more complex litigation, or they might not do anything at all.
But that fourth chapter always ends with an execution.
When I started representing death row inmates more than 20 years ago, people on death row did not have a right to a lawyer in either the second or the fourth chapter of this story.
They were on their own.
In fact, it wasn't until the late 1980s that they acquired a right to a lawyer during the third chapter of the story.
So what all of these death row inmates had to do was rely on volunteer lawyers to handle their legal proceedings.
The problem is that there were way more guys on death row than there were lawyers who had both the interest and the expertise to work on these cases.
And so inevitably, lawyers drifted to cases that were already in chapter four -- that makes sense, of course. Those are the cases that are most urgent; those are the guys who are closest to being executed.
Some of these lawyers were successful; they managed to get new trials for their clients.
Others of them managed to extend the lives of their clients, sometimes by years, sometimes by months.
But the one thing that didn't happen was that there was never a serious and sustained decline in the number of annual executions in Texas.
In fact, as you can see from this graph, from the time that the Texas execution apparatus got efficient in the mid- to late 1990s, there have only been a couple of years where the number of annual executions dipped below 20.
In a typical year in Texas, we're averaging about two people a month.
In some years in Texas, we've executed close to 40 people, and this number has never significantly declined over the last 15 years.
And yet, at the same time that we continue to execute about the same number of people every year, the number of people who we're sentencing to death on an annual basis has dropped rather steeply.
So we have this paradox, which is that the number of annual executions has remained high but the number of new death sentences has gone down.
Why is that?
It can't be attributed to a decline in the murder rate, because the murder rate has not declined nearly so steeply as the red line on that graph has gone down.
What has happened instead is that juries have started to sentence more and more people to prison for the rest of their lives without the possibility of parole, rather than sending them to the execution chamber.
Why has that happened? It hasn't happened because of a dissolution of popular support for the death penalty.
Death penalty opponents take great solace in the fact that death penalty support in Texas is at an all-time low.
Do you know what all-time low in Texas means?
It means that it's in the low 60 percent.
Now, that's really good compared to the mid-1980s, when it was in excess of 80 percent, but we can't explain the decline in death sentences and the affinity for life without the possibility of parole by an erosion of support for the death penalty, because people still support the death penalty.
What's happened to cause this phenomenon?
What's happened is that lawyers who represent death row inmates have shifted their focus to earlier and earlier chapters of the death penalty story.
So 25 years ago, they focused on chapter four.
And they went from chapter four 25 years ago to chapter three in the late 1980s.
And they went from chapter three in the late 1980s to chapter two in the mid-1990s.
And beginning in the mid- to late 1990s, they began to focus on chapter one of the story.
Now, you might think that this decline in death sentences and the increase in the number of life sentences is a good thing or a bad thing.
I don't want to have a conversation about that today.
All that I want to tell you is that the reason that this has happened is because death penalty lawyers have understood that the earlier you intervene in a case, the greater the likelihood that you're going to save your client's life.
That's the first thing I've learned.
Here's the second thing I learned:
My client Will was not the exception to the rule; he was the rule.
I sometimes say, if you tell me the name of a death row inmate -- doesn't matter what state he's in, doesn't matter if I've ever met him before --
I'll write his biography for you.
And eight out of 10 times, the details of that biography will be more or less accurate.
And the reason for that is that 80 percent of the people on death row are people who came from the same sort of dysfunctional family that Will did.
Eighty percent of the people on death row are people who had exposure to the juvenile justice system.
That's the second lesson that I've learned.
Now we're right on the cusp of that corner where everybody's going to agree.
People in this room might disagree about whether Will should have been executed, but I think everybody would agree that the best possible version of his story would be a story where no murder ever occurs. How do we do that?
When our son Lincoln was working on that math problem two weeks ago, it was a big, gnarly problem.
And he was learning how, when you have a big old gnarly problem, sometimes the solution is to slice it into smaller problems.
That's what we do for most problems -- in math, in physics, even in social policy -- we slice them into smaller, more manageable problems.
But every once in a while, as Dwight Eisenhower said, the way you solve a problem is to make it bigger.
The way we solve this problem is to make the issue of the death penalty bigger.
We have to say, all right.
We have these four chapters of a death penalty story, but what happens before that story begins?
How can we intervene in the life of a murderer before he's a murderer?
What options do we have to nudge that person off of the path that is going to lead to a result that everybody -- death penalty supporters and death penalty opponents -- still think is a bad result: the murder of an innocent human being?
You know, sometimes people say that something isn't rocket science.
And by that, what they mean is rocket science is really complicated and this problem that we're talking about now is really simple.
Well that's rocket science; that's the mathematical expression for the thrust created by a rocket.
What we're talking about today is just as complicated.
What we're talking about today is also rocket science.
My client Will and 80 percent of the people on death row had five chapters in their lives that came before the four chapters of the death penalty story.
I think of these five chapters as points of intervention, places in their lives when our society could've intervened in their lives and nudged them off of the path that they were on that created a consequence that we all -- death penalty supporters or death penalty opponents -- say was a bad result.
Now, during each of these five chapters: when his mother was pregnant with him; in his early childhood years; when he was in elementary school; when he was in middle school and then high school; and when he was in the juvenile justice system -- during each of those five chapters, there were a wide variety of things that society could have done.
In fact, if we just imagine that there are five different modes of intervention, the way that society could intervene in each of those five chapters, and we could mix and match them any way we want, there are 3,000 -- more than 3,000 -- possible strategies that we could embrace in order to nudge kids like Will off of the path that they're on.
So I'm not standing here today with the solution.
But the fact that we still have a lot to learn, that doesn't mean that we don't know a lot already.
We know from experience in other states that there are a wide variety of modes of intervention that we could be using in Texas, and in every other state that isn't using them, in order to prevent a consequence that we all agree is bad. I'll just mention a few.
I won't talk today about reforming the legal system.
That's probably a topic that is best reserved for a room full of lawyers and judges.
Instead, let me talk about a couple of modes of intervention that we can all help accomplish, because they are modes of intervention that will come about when legislators and policymakers, when taxpayers and citizens, agree that that's what we ought to be doing and that's how we ought to be spending our money.
We could be providing early childhood care for economically disadvantaged and otherwise troubled kids, and we could be doing it for free.
And we could be nudging kids like Will off of the path that we're on.
There are other states that do that, but we don't.
We could be providing special schools, at both the high school level and the middle school level, but even in K-5, that target economically and otherwise disadvantaged kids, and particularly kids who have had exposure to the juvenile justice system.
There are a handful of states that do that; Texas doesn't.
There's one other thing we can be doing -- well, there are a bunch of other things -- there's one other thing that I'm going to mention, and this is going to be the only controversial thing that I say today.
We could be intervening much more aggressively into dangerously dysfunctional homes, and getting kids out of them before their moms pick up butcher knives and threaten to kill them.
If we're going to do that, we need a place to put them.
Even if we do all of those things, some kids are going to fall through the cracks and they're going to end up in that last chapter before the murder story begins, they're going to end up in the juvenile justice system.
And even if that happens, it's not yet too late.
There's still time to nudge them, if we think about nudging them rather than just punishing them.
There are two professors in the Northeast -- one at Yale and one at Maryland -- they set up a school that is attached to a juvenile prison.
And the kids are in prison, but they go to school from eight in the morning until four in the afternoon.
Now, it was logistically difficult.
They had to recruit teachers who wanted to teach inside a prison, they had to establish strict separation between the people who work at the school and the prison authorities, and most dauntingly of all, they needed to invent a new curriculum because you know what?
People don't come into and out of prison on a semester basis. (Laughter)
But they did all those things.
Now, what do all of these things have in common?
What all of these things have in common is that they cost money.
Some of the people in the room might be old enough to remember the guy on the old oil filter commercial.
He used to say, "Well, you can pay me now or you can pay me later."
What we're doing in the death penalty system is we're paying later.
But the thing is that for every 15,000 dollars that we spend intervening in the lives of economically and otherwise disadvantaged kids in those earlier chapters, we save 80,000 dollars in crime-related costs down the road.
Even if you don't agree that there's a moral imperative that we do it, it just makes economic sense.
I want to tell you about the last conversation that I had with Will.
It was the day that he was going to be executed, and we were just talking.
There was nothing left to do in his case.
And we were talking about his life.
And he was talking first about his dad, who he hardly knew, who had died, and then about his mom, who he did know, who was still alive. And I said to him,
"I know the story.
I've read the records.
I know that she tried to kill you."
I said, "But I've always wondered whether you really actually remember that."
I said, "I don't remember anything from when I was five years old.
Maybe you just remember somebody telling you."
And he looked at me and he leaned forward, and he said, "Professor," -- he'd known me for 12 years, he still called me Professor.
He said, "Professor, I don't mean any disrespect by this, but when your mama picks up a butcher knife that looks bigger than you are, and chases you through the house screaming she's going to kill you, and you have to lock yourself in the bathroom and lean against the door and holler for help until the police get there," he looked at me and he said,
"that's something you don't forget."
I hope there's one thing you all won't forget:
In between the time you arrived here this morning and the time we break for lunch, there are going to be four homicides in the United States.
We're going to devote enormous social resources to punishing the people who commit those crimes, and that's appropriate because we should punish people who do bad things.
But three of those crimes are preventable.
If we make the picture bigger and devote our attention to the earlier chapters, then we're never going to write the first sentence that begins the death penalty story.
Thank you.
(Applause)
Google Translate is a free tool that enables you to translate sentences, documents and even whole websites instantly.
But how exactly does it work?
While it may seem like we have a room full of bilingual elves working for us, in fact all of our translations come from computers.
These computers use a process called "statistical machine translation" -- which is just a fancy way to say that our computers generate translations based on patterns found in large amounts of text.
But let's take a step back.
If you want to teach someone a new language you might start by teaching them vocabulary words and grammatical rules that explain how to construct sentences.
A computer can learn a foreign language the same way - by referring to vocabulary and a set of rules.
But languages are complicated and, as any language learner can tell you, there are exceptions to almost any rule.
When you try to capture all of these exceptions, and exceptions to the exceptions, in a computer program, the translation quality begins to break down.
Google Translate takes a different approach.
Instead of trying to teach our computers all the rules of a language, we let our computers discover the rules for themselves.
They do this by analyzing millions and millions of documents that have already been translated by human translators.
These translated texts come from books, organizations like the UN and websites from all around the world.
Our computers scan these texts looking for statistically significant patterns--that is to say, patterns between the translation and the original text that are unlikely to occur by chance.
Once the computer finds a pattern, it can use this pattern to translate similar texts in the future.
When you repeat this process billions of times you end up with billions of patterns and one very smart computer program.
For some languages however we have fewer translated documents available and therefore fewer patterns that our software has detected. This is why our translation quality will vary by language and language pair.
We know our translations aren't always perfect but by constantly providing new translated texts we can make our computers smarter and our translations better.
So next time you translate a sentence or webpage with Google Translate, think about those millions of documents and billions of patterns that ultimately led to your translation - and all of it happening in the blink of an eye.
Pretty cool, isn't it?
Give it a try at translate.google.com.
Use the change of base formula to find log base 5 of 100, to the nearest thousandth.
So the change of the base formula is a useful formula, especially when you're going to use a calculator, because most calculators don't allow you to arbitrarily change the base of your logarithm.
They have functions for log base e, which is a natural logarithm.
And log base 10.
So you generally need to change your base.
And if we have time, I'll tell you why it makes a lot of sense or how we can derive it.
So the change of the base formula just tells us that -- and let me do some colors here -- log of base a of b is the same thing as log base x, where x is arbitrary base of b over log base x over a.
The reason why this is useful is that we can change our base.
Here our base is a and we can change it to base x.
So if our calculator has a certain base x function we can convert to that base, it's usually e or base 10.
Base 10 is an easy way to go.
And in general if you just see someone write a logarithm like this.
If they just write log of x -- they're implying, this implies log base 10 of x.
If someone writes natural log of x, they're implying log base e of x.
And e is obviously the number 2.71...keeps going on and on forever.
Now, let's apply it to this problem.
We have logarithm -- I'll use colors -- base 5 of 100.
So this property, this change of base formula tells us that this is exact same thing as log -- I'll make x = 10 -- log base 10 of 100 divided by log base 10 of 5.
And actually we don't even need a calculator to evaluate this top part. log base 10 of 100 -- what power I have to rise 10 to get to 100?
The second power.
So this enumerator is just equal to 2.
So this simplifies to 2 over log base 10 of 5.
We can now use our calculator, because log function on the calculator is log base 10.
So let's get our calculator out.
And we're going to get, we want -- let me clear this -- 2 divided by, when someone just writes log, they mean base 10.
They press ln, they mean base e.
So log without any other information is log base 10.
So it is log base 10 of 5 is equal to, and they want us to round to the nearest thousandth, so 2.861.
So this is approximately equal to 2.861.
And we can verify it, because in theory if I raise 5 to this power I should get 100.
And it kinda makes sense, cause 5 to the 2nd power is 25, 5 to the 3rd power is 125.
And this is in between the two and it's closer to the third power than it is to the second power and this number is closer to three than it is to 2.
But let's verify it, so if I take 5 to that power.
5 to the 2.861, so I'm not putting in all of the digits.
What do I get?
I get 99.94. if I'd put all of those digits in, it should get pretty close to 100.
So that's what make you feel good that this is the power you have to raise 5 to get to 100.
Now that out of the way, let's actually think about why this property, why this thing right over here makes sense?
So if I write log base a, I'm trying to be fair to the colors, log base a of b, let's say I said that to be equal to some number, let's call that's equal to c.
So that means a to c-th power is equal to b.
This is an exponential way of writing this truth.
This is a logarithmic way of writing this truth. ... is equal to b.
Now we can take the logarithm of any base of both sides of this.
Anything you do... if you say 10 to the what power is equal this.
10 to the same power will be equal to this, cause those two things are equal to each other.
So let's take the same logarithm of both sides of this.
So logarithm with the same base.
And I actually will do log base x, to prove the general case here.
So I'm going to take log base x of both sides of this.
So this is log base x of a to the c-th power.
Is equal to log base x of b.
And we know from out logarithm properties:
log of a to the c is the same thing as c times the logarithm of whatever base we are of a.
And of course this going to be equal to log base x of b.
Let me put b right over there. and if we want to solve for the c, you just divide both sides by log base x of a.
So you get c is equal to and I'll stick to the color -- so it's log base x of b over log base x of a. And this is what c was, c was logarithm base a of b. ... is equal to log base a of b.
So c is equal to log base x of b over -- let me scroll down a little bit -- over log base x -- dividing both sides by that -- of a.
This is also equal to c.
This is also equal to c.
And we're done. We've proven the change of the base formula.
Log of base a of b is equal to log base x of b divided by log base x of a.
And in this example: a was 5, b is 100 and base we switched to is 10 -- x is 10.
Estimate the solution to 582,205 plus 610,859, rounding these two numbers to the nearest thousand.
So we going to round each of these numbers to the nearest thousand and then add them, and that'll give us an estimate to this solution.
So let's do each of these numbers.
So if we start off with 582,205, we want to round to the nearest thousand.
So you go to the thousands place, and you go one place below that.
If that's 5 or greater, round up.
If it's less than 5, round down.
This is less than 5.
The 2 here is less than 5, so we want round down.
We are going to round it down, so it's going to be 582,000.
We're just going to round it down to 2,000.
We're going to get rid of all of this 205 here.
582,000 when we rounded it down to the nearest thousand.
Now, we have 610,859.
Same drill.
Go to the thousands place.
That's the 0 right there.
Look one place below the thousands place.
This is that 8 right there.
If this is 5 or greater, you round up.
Less than 5, round down.
It is 5 or greater.
8 is greater than 5.
Or it could even be 5 and we'd still around up, so we're going to round up in this situation.
We're going to round up, so we end up with 600, and instead of 610,000, we're rounding up to 611,000.
We've rounded the two numbers to the nearest thousand.
Now we're ready to add.
So let's add them.
Let's add the two numbers.
0 plus 0 is 0.
0 plus 0 is 0.
0 plus 0 is 0.
2 plus 1 is 3.
8 plus 1 is 9.
5 plus 6 is 11.
If there were more places here, we would carry the 1 in the tens place.
But there isn't, so you can just write an 11 here.
And so we are left with-- put a comma every third digit-- 1,193,000, which is our estimate.
And the whole reason why this is useful is if someone were to give these numbers to you and you had to do it in your head, it's hard to add these whole numbers, but you might be able to do 582 plus 611, knowing everything is in thousands.
So it allows you to do things in your head a little bit easier when you round, and then you estimate the sum of the rounded numbers.
A local hospital recently conducted a blood drive where they collected a total of 80 pints of blood from donors.
The hospital was hoping to collect a total of 8 gallons of blood from the drive.
Did they meet their goal?
How much more or less than their goal did the hospital collect?
So really, they collected 80 pints.
We just need to figure out how many gallons that is, and then say, well, is that going to be more or less than 8 gallons?
So we start with 80 pints.
And we can take it step by step.
You may or may not know how many pints there are per gallon, so let's just go straight to quarts first, and then from quarts we can go to gallons.
But if you know right from the get go how many pints there are per gallon, you could go there.
So let's convert this to quarts.
So we have 80 pints, so what are we going to multiply or divide by to get quarts?
Well, one way to think about it, you're going from a smaller unit, pints, to a larger unit, so you're going to have less of that larger unit.
So you're going to divide.
This number's going to be smaller when it goes into quarts.
And it's going to be smaller by a factor of 2 because you have 2 pints per quart.
You're not going to multiply by 2.
You're not going to have more quarts.
You're going to divide by 2.
So you could say, times 1/2.
We have one quart for every 2 pints, or you can view this as 2 pints per quart or 1/2 of a quart per pint.
Either way, the units work out, and you're essentially taking 80 and dividing by 2, or multiplying by 1/2, and you get 40 quarts.
And I want to make sure that your brain does it both ways.
Because when you're just doing it, you don't have paper, you don't have the units around, you should just think, hey, 80 pints, there's 2 pints per quart.
I'm going to have 40 quarts.
But when problems get a little bit more complicated, it is nice to make sure that the units cancel out in this way, so that you know, OK, 1 quart is 2 pints. Pints in the denominator, pints in the numerator, cancel them out, and I'm just left with quarts, and 80 times 1/2, which is 40.
So we have 40 quarts now, and now we can convert this to gallons.
We know that there are 4 quarts per gallon or that 1 gallon has 4 quarts.
And once again, we're going to go from a smaller unit to a larger unit, to gallons.
Since you're going to a larger unit, your brain should say, hey, I'm going to divide by 4.
I'm going to have a factor 4 fewer gallons because it's a larger unit.
And to make sure that units work out, you just remember, well, we have quarts up here in the numerator, you're going to want quarts down here in the denominator.
And we care about converting into gallons, and 1 gallon is 4 quarts.
The quarts will cancel out.
And notice, you're also dividing by 4.
40 times 1/4 is the exact same thing as 40 divided by 4, which makes sense.
We're going to a larger unit.
So 40 times 1/4 is 10, and the units left are gallons.
So the 80 pints of blood that the hospital collected is 10 gallons.
Their goal was only 8 gallons.
Yes, they met their goal!
How much more or less than their goal did the hospital collect?
Well, their goal was 8, they collected 10.
I want to review a little bit of what we did in the last video. And maybe draw a larger, more spread-out diagram.
Because I think in the last video I started to cram things on the right-hand side here.
And this is a very important concept, so I want to do it nice and spread-out in a way that we can breathe.
And maybe in the process I can fill in some more blanks.
So let's go back and draw the membrane of a thylakoid that's sitting inside of a chloroplast.
I'm going to draw this same membrane here.
So let me draw it nice and spread out.
So let me draw a nice big membrane like that.
That's the inside of the membrane.
So you can imagine that this loops around and that would form the thylakoid.
On this side of the membrane we have the lumen.
And on the outside of the membrane we have the stroma, where all the fluid that fills up the choloroplast.
So this is the stroma right there.
And this is just a kind of standard membrane that we see in a lot of organelles.
But this is actually a membrane within an organelle.
And then maybe there will be a phospho-bilipid layer.
And I just say that, or I'm pointing that out because I want to think a little bit about, in this video, how protons can actually get across this thing. How do we use the energy from these electrons going to lower energy states to actually pump protons across this membrane.
So you know when you have these bilipid layers, your outside is hydrophilic.
And of course, it's hydrophilic because it operates well in a polar environment.
And then the insides are non-polar or they're hydrophobic and you have these tales.
So I could draw the whole membrane like that, but I won't do that.
It will take me forever.
But let me draw some of the components that I did in the last video.
So we have these complexes that span across this membrane.
And the place we started off with was the photosystem II complex.
And then later on we have the photosystem I complex.
And let me draw the ATP synthase right here.
So ATP synthase also spans across it.
Then it has little motor part of it.
And the hydrogens go through and it spins the motor and it crams the phosphate groups into the ADP to make ATP.
I'll talk about that in a second.
But the first thing I want to point out is, as I said in the last video, the first place where the electrons get excited is in the chlorophyil and photosystem Il.
And then it gets less and less and less excited, it gets headed off from one complex to another complex. And eventually ends up in photosystem I.
It gets excited again.
Then it gets handed off, handed off, the whole time that energy is being used to transfer hydrogen protons from the stroma into the lumen .
But the first question that I would ask is, why is this called photosystem Il, while this is called photosystem I when we're starting over here?
And the reason is, this was discovered first. Even though in the light reaction it actually comes into use, or it comes into play, second.
This was discovered first.
That's why they call it photosystem I.
But the reality is photosystem II is where everything starts from.
Now in some textbooks you'll also see this written as P680. And you'll see photosystem I written as P700.
And these numbers come from the wavelength of light that is best absorbed by the chlorophyil in these photosystems.
So 680 corresponds to 680 nanometers.
That's the wavelength of light that this absorbs the best.
700 corresponds to 700 nanometers.
That's the wavelength of light it absorbs best.
Now what I want to do here is draw a little diagram below here to kind of talk more about the electron energy states.
I just kind of handwaved it a little bit in the last video.
So I'm going to draw a little diagram here.
And over here I'm going to write the different things that the electron can be a part of.
So right now the electrons can be part of H2O.
It could be part of chlorophyil A.
It could be a part of-- I'll talk more about this in a little bit-- pheophytin And then you have all of the molecules or the complexes it can become a part of.
I'll actually write them down here.
So let me write.
I don't want to take up too much space.
Plastoquinone and then there's a cytochrome B6F complex.
I'll just write B6F.
Then you have plastocyanin .
I'll just write as PC.
You don't have to memorize these.
You'll forget them in a week if you do.
But unless you're studying photosynthesis, then it might make sense to memorize them.
And this is in photosystem Il.
Then you have chlorophyil in photosystem I.
And then you have some other, you know you have ferredoxin
I'll just write FD for ferredoxin Some other molecules, you keep going and then you have your eventual electron acceptor NADP plus. Which, once it accepts the electron, becomes NADPH.
Now, electrons are very-- so this is, if we go up that's a high energy state, down it's a low energy state.
So electrons are already very comfortable. in water.
And in chlorophyil A they're even more comfortable.
At least this is how I view it.
But left to its own devices, this electron will never leave chlorophyil A. But we know what happens.
A photon comes in from 93 million miles away.
You could imagine photons as little light packets or you could view it as a light wave.
And it excites-- not necessarily directly the chlorophyil A. It might excite other antenna chlorophyil or other pigment molecules.
And then through resonance energy, you can imagine them vibrating, and it eventually will excite the photophorylation A directly. Or excite the electrons in chlorophyil A directly.
And this dude right here gets excited.
Let me do that in a brighter color.
So it goes to a high energy state.
So the electron here is in a high energy state.
Ignore that lumen right there. It has nothing to do with this electron.
And then it goes-- and actually when it goes to the high energy state, maybe I should draw it like this, it actually shows up in pheophytin.
That is the primary electron acceptor.
And it's actually a chlorophyil A molecule.
Actually, let me show you what a chlorophyil A molecule looks like.
This is what a chlorophyil A molecule looks like.
In general, it has a hydrocarbon tail.
You see that right here.
And it has a porphyrin ring. Or porphyrin head, I guess you could call it.
This little group right here is called a porphyrin.
And right in the center of it, you have a magnesium.
That green right there, that's a magnesium ion.
And when the photon comes in or when the resonance energy comes in from some of the antenna molecules, electrons in the double bond sitting here in the porphyrin head get excited.
Those are the electrons that we're talking about.
And they get excited.
And the first electron acceptor is this pheophytin that I just talked about.
Pheophytin.
It actually looks just like a chlorophyil, but it has no magnesium ion in the middle.
And maybe I'm getting a little bit into the weeds a little bit too much. But the pheophytin, you actually see in this diagram right here.
It's part of this photosystem complex.
So the electron, you can imagine, jumping from the chlorophyil to the pheophytin that does not have that magnesium in the center.
And when it sits in the pheophytin it's at a very, very, very, very, high energy state.
And then it keeps being transferred from the pheophytin.
It goes to the plastoquinone So maybe we go to a slightly lower energy state here.
We keep using the electron in green.
Then it keeps going to a slightly lower energy state in the cytochrome B6F complex.
And then you have the plastocyanin complex, lower energy state.
And then eventually it goes into photosystem I at an even lower energy state.
Maybe slightly higher than the energy state that it was originally in the chlorophyil A molecule in photosystem Il.
Another photon or another set of photons comes and hits photosystem I.
Maybe its antenna molecules, through resonance energy, that excites the electron.
It might directly hit the chlorophyil in photosystem in its reaction center.
And then this gets excited again.
And so once again we have an electron with a high potential that can keep going to, from one molecule to another as it gets more and more comfortable.
And this releases energy that can drive the proton pump.
And it eventually ends up in the NADPH. At a fairly high level of energy still.
This electron can still be transferred to other things and release energy.
And we'll see that when we talk about the light independent reactions.
Now the whole point of me showing you this is, I wanted to kind of depict graphically that the electron is starting off at a pretty low energy state.
And the only way this happens is by energy from light.
This would not happen on its own. Going from a low energy state to a higher energy state.
And I touched on in the last video, you have this electron going here and it gets transferred from one molecule to another.
Gets excited again, then keeps going all the way, eventually being accepted by the NAD plus to become NADPH.
And you're like, where did that H come from?
You could say, well that H is a proton.
It gets that electron and then they merge together and you have NADPH. But either way.
But the question is, what replaces this electron?
And that's where that amazing thing that I talked about in the last video happens.
Water gets oxidized.
Oxidizing is losing electrons.
OlL RlG.
So water gets oxidized by the water oxidation on photosystem Il.
And that electron ends up and replaces the electron in the chlorophyil.
So once again, that's an amazing idea, that you're oxidizing oxygen.
So the net effect of what happens is, is you're using energy, using this photon energy right here, to essentially strip electrons off of water.
And as you know, when it's on water it's spending most of its time on the oxygen.
So it essentially strips electrons off of oxygen and put them in a higher energy state and have them end up on NADPH.
And in the process, it had gone to an even higher energy state.
And then as it goes down to NADPH, you are pumping protons across the membrane.
We learned in the last video, through chemiosmosis, eventually goes through the ATP synthase channel, turns around this part of this protein complex or enzyme complex and actually generates ATP.
ATP from ADP and phosphate groups.
And in the electron transport chain video, when I talk about cellular respiration, I give a visual concept of how this actually might happen.
How you could, as these go through, you actually can jam together the ATP and the ADP.
So that's another question in my head is, we talk about these electrons going from one molecule to another. But how does that actually pump hydrogen through?
And I'm just going to do a very gross oversimplification.
I'm sure it's much more complicated in actual plant cells.
But you could imagine that we have our pheophytin right here that has that electron on it right there.
Maybe it has its electron right there.
This is a gross oversimplification.
And then you have your plastoquinone right here.
That's the next acceptor.
Now maybe on this protein complex right there, the point that wants to accept the electron is right there.
And let's say that there's another point on it that can accept a hydrogen.
Maybe it accepts a hydrogen proton there.
So you can imagine when it's on this side of the membrane, a hydrogen can become attached right there.
And this guy will want to be attracted to that.
So he'll rotate around.
So you can imagine this-- if this is kind of a wheel-- this attraction. Because the electron wants to go into a lower energy state right here.
It'll rotate around.
That'll allow, essentially, this hydrogen as it rotates. As this molecule, as this protein rotates around this hydrogen will be able to cross the barrier.
And then once this guy and that guy meet, then the hydrogen will be on the other side.
And so it can freely go away again.
So that's, at least in my head, how I imagine the electrons going from a high energy state to a lower energy state, how that can actually drive a reaction.
Remember, the electrons want to do this.
So they'll attract the different parts of the molecules together.
And as those molecules turn and rotate and move, that can help facilitate hydrogen going from the stroma, the outside of the thylakoid, to the inside of the thylakoid.
That will drive the chemiosmosis later on.
Now there's one other point I want to touch on here.
Everything I've described so far, we started with an electron in water.
And obviously when water loses its hydrogens, it loses both the hydrogen protons and electrons associated with it.
You end up with just water.
So you start off with hydrogens and then you end up with just O2.
And then the hydrogen protons-- the electron got taken up by the chlorophyil.
When you start off with that, we've seen already that you end up with the electron sitting in NADPH.
The electron sitting out here in NADPH.
At some point you have NAD as the final acceptor.
Let me do it in the right color.
You have NAD plus as the final acceptor. And it becomes NADPH.
You can imagine it accepts maybe a hydrogen proton from out here.
It accepts the electron from this electron transport chain in photosynthesis.
And it becomes NADPH and that travels in the stroma, which is where the dark reactions occur that actually produce the carbohydrate.
But this idea of an electron going from water to NADPH, this is called non-cyclic photophosphorylation And it's called non-cyclic because you're not reusing the same electrons over and over again.
The electrons start off, and depending how you view it, in the chlorophyil or the water. And they end up in the NADPH.
Now there's another type of photophosphorylation and you might guess what it's called.
It's called cyclic.
Cyclic photophosphorylation We'll see when we study the dark cycles or the Calvin cycle or the dark reactions or the light independent reactions, that it uses a lot of ATP.
Actually ATP in disproportion to the amount of NADPH it uses.
It uses both, but it uses a ton of ATP.
So cyclic phosphorylation only produces ATP and actually does not oxidize water.
So what happens in that situation is this electron, after it gets activated or after it gets excited in photosystem I, it's the electron, it eventually ends up-- instead of at NADPH, it ends up at photosystem Il.
So instead of this guy having to be replaced by electrons from water, this guy, in cyclic photophosphorylation ends up-- well, maybe I should do it from here-- ends up getting replaced by the original electrons.
It gets excited here.
It goes from molecule to molecule, lower energy states, hydrogen gets pumped into the lumen.
Gets excited again in photosystem I and it enters lower and lower energy states.
But then ends up again in photosystem Il.
That is cyclic photophosphorylation.
So you can imagine in this situation, since the electron never ends up at NAD plus, you don't end up producing NADPH.
And since you're replacing this electron from the photosynthesis or from the electron transport chain directly, you don't have to strip the electrons off of the water.
So you're not going to produce your oxygen.
So, in this situation-- so this non-cyclic phosphorylation, which is kind of what most photophosphorylation, is what most people associate with photophosphorylation, this produces O2 and NADPH.
And of course it produces ATP.
While cyclic photophosphorylation, because it doesn't have to strip electrons off of water and the electrons don't end up at NADPH, only produces ATP.
So I think we now have a very good understanding, hopefully, of the light reactions in photosynthesis.
We're now ready to take the products of this.
Now let's remember what the products were.
Well, the oxygen just gets eliminated.
We don't need the oxygen anymore.
But that goes into the atmosphere and you and I can breathe that and we can use that for cellular respiration.
But in the photosynthesis context, we've now generated a bunch of ATP.
And now we have a bunch of NADPH.
And we can use that in conjunction with carbon dioxide to produce actual carbohydrates in the stroma. Outside the thylakoids, but we're still inside of the chloroplast.
And I'll cover that in the next video.
A thermometer in a science lab displays the temperature in both Celsius and Fahrenheit.
If the mercury in the thermometer rises to 56 degrees Fahrenheit, what is the corresponding Celsius termperature?
And then they give us the two formulas - if we know the Celsius temperature, how do we figure out the Fahrenheit temperature, or if we know the Fahrenheit temperature how do we figure out the Celsius temperature.
And these are actually derived from each other, and you'll learn more about that when you do algebra, and we also - maybe in another video - will explain how you do derive them, and this is kind of interesting, involves a little bit of algebra.
But they gave us the formula, so they really just want us to apply it, and, maybe, make sure we understand which one we should apply.
Well, they're giving us the Fahrenheit temperature here, so F is equal to 56, and they're asking us for the Celsius temperature, so we need to figure out what the Celsius temperature is.
Well, in this one over here, if you know the Fahrenheit temperature you can solve for the Celsius termperature.
So let's use this, right over here.
Our Celsius temperature is going to be (5 / 9) times the Fahrenheit temperature. - the Fahrenheit temperature is 56 degrees Fahrenheit - minus 32.
Well 56 minus 32 is 24, so this is going to be equal to (5 / 9) times 24, and this is the same thing as 5 times 24, all over 9.
And before multiplying out 5 times 24 we can divide the numerator and the denominator by 3, so lets do that.
If we divide the numerator and denominator by 3 we're not changing the value.
24 divided by 3 is 8, 9 divided by 3 is 3.
So it becomes 5 times 8, which is 40, over 3, degrees.
And if we want to write this as a number which makes a little bit more sense, in terms of temperature, lets divide 3 into 40 to get the number of degrees we have.
3 goes into 4 one time, with a remainder of 1, carry the 1 down and bring down the zero.
3 goes into 10 three times, with a remainder of 1, carry the 1 again, then you could bring down another zero - we now have a decimal point over here.
3 goes into ten 3 times, so this 3 is going to repeat forever.
So you could view this as equal 13.333... - it'll just keep repeating, this line on top means repeating - degrees Celsius.
Or, you could say that 3 goes into 40 13 times with a remainder of 1.
So you could say that this is also equal to 13, remainder 1.
So 13 and one third degrees Celsius.
Either way it works, but that's our Celsius temperature when our Fahrenheit temperature is 56 degrees.
In this video we are gonna talk a little bit about order of operations.
And I want you to pay close attention because, really, EVERYTHlNG else that you are gonna do in mathematics is going to be based on your having a solid grounding in Order of Operations.
So, what are we even talk...mean, when we say Order of Operations?
So let me give you an example.
The whole point, is so we have one way to interpret a mathematical statment.
So let's say I have the mathematical statement:
7 plus 3, times 5.
Now if we didn't all agree on Order of Operations, there would be 2 ways of interpreting this statement.
You could just read it left-to-right.
So you could say "well, let me just take 7 + 3."
You could say 7 + 3 and then multiply that times 5 - and 7+3 is 10. and then you multiply that by 5.
10 x 5, it would get you 50.
So, that's one way you would interpret it if we didn't agree on an order of operations - maybe it's a natural way - you just go left-to-right.
Another way you could interpret it -- you say
"oh, I like to do multiplication before I do addition" so you might interpret it as - I'll try to color code it - 7+ ... and you do the 3x5 first 7 + 3x5 which would be 7+ 3x5 is 15 ... and 7+15 is 22.
So notice we interpreted this statement in two different ways this was just straight left-to-right, doing the addition, then the multiplication.
This way, we did the multiplication first, then the addition. We get 2 different answers.
That's just not cool in mathematics.
So this is just completely unacceptable, and that's why we have to have an agreed upon Order of Operations. an agreed upon way to interpret this statement.
So, the agreed upon order of operations is to do parentheses first.
-- let me write it over here --
'parentheses' first. then do exponents.
If you don't know what exponents are, don't worry about it right now.
In this video we're not going to have exponents in our examples. So you don't really have to worry about it for this video.
Then you do multiplication -
Then you do multiplication and division next. they kind of have the same level of priority.
And then finally you do addition and subtraction.
Let me label it - this right here is, that is the agreed upon order of operations and if we follow these order of operations we should always get to the same answer for a given statement.
What is the best way to interpret this up here?
Well, we have no parentheses - parentheses look like that, these little curly things around numbers.
We don't have any parentheses here - I'll do some examples that do have parentheses.
We don't have any exponents here, but we do have some multiplication and division or we actually just have some multiplication.
So the order of operations say
'do the multiplication and division first'.
So it says do the multiplication first - that's a multiplication.
It gets priority over addition or subtraction.
So if we do this first, we get the three times five, which is fifteen, and then we add the seven.
The addition or subtraction - I'll do it here we just have addition - just like that.
So we do the multiplication first, get 15, then add the 7 ... 22
So based upon the agreed order of operations, this right here is the correct answer - the correct way to interpret this statement.
Let's do another example.
I think it'll make things a little bit more clear.
And I'll do the example in pink.
So let's say I have 7+3
- put some parentheses there - x 4 divided by 2 - 5 x 6. So there's all sorts of crazy things here, but if you just follow the Order of Operations, you'll simplify it in a very clean way and hopefully we'll all get the same answer.
So let's just follow the order of operations.
The first thing we have to do is look for parentheses.
Are there parentheses here?
Yes, there are!
There's parentheses around the 7+3.
So it says, "lets do that first". So 7+3 is 10.
So this we can simplify - just looking at this order of operations - to 10 times all of that. Let me copy and paste that, so I don't have to keep rewriting it.
So, let me copy. Let me paste it.
So that simplifies to ten times all of that - we did our parentheses first.
There are no more parentheses in this expression.
Then we should do exponents.
I don't see any exponents here. and just so if you are curious what exponents would look like an exponent would look like
You'd see these little small numbers up in the top right.
We don't have any exponents here, so we don't have to worry about it.
Then it says to do multiplication and division next.
So where do we see multiplication - we have a multiplication, a division, a multiplication again.
Now, when you have multiple operations at the same level and in our order of operations, multiplication and division are at the same level - then you do left-to-right.
So in this situation, you're going to multiply by 4 and then divide by 2. You won't multiply by 4 divided by 2.
Then we'll do the 5 times 6 before we do the subtraction, right here.
So let's figure out what this is.
So we'll do this multiplication first.
We'll do that multiplication first - we could simultaneously do this multiplication cause it's not going to change things, but I'll do things one step at a time.
So the next step we're going to do is this 10x4.
10x4 is 40
Then you have 40 divided by 2 - let me copy and paste all of that again -
Then it simplifies to that right there.
Remember multiplication and division, they are at the exact same level - so we're going to do it left-to-right.
You xould also express this as multiplying by one-half and then it wouldn't matter the order.
But for simplicity multiplication / division go left-to-right.
So then you have 40 divided by 2 minus 5 times 6.
So, division - you just have 1 division here -
You want to do that. This is going to take...
You have this division and this multiplication.
They are not together.
So you can actually kind of do them simultaneously.
And to make it clear that you do this before you do the subtraction, because multiplication/division take priority over addition/subtraction we can put parentheses around them.
Just say "look, we're gonna do that and that first, BEFORE I do that subtraction" because multiplication / division have priority.
So 40 divided by 2 is 20.
We're going to have that minus sign.
-5 times 6 is 30.
20 minus 30 is equal to negative 10.
And that is the correct interpretation of that.
So I want to make something very, very, very clear: if you have things at the same level so if you have 1 + 2 - 3 + 4 - 1 so addition and subtraction are at the same level in order of operations - you should go left-to-right.
You should interpret this as 1+2 is 3.
So this is the same thing as 3 - 3 + 4 - 1.
Then you do 3 - 3 is 0, + 4, - 1.
OR this is the same thing as 4 - 1 which is the same thing as 3 - you just go left to right.
Same thing if you have multiplication and division all on the same level.
So if you have 4x2, divided by 3, times 2, you do 4x2 is 8, divided by 3, times 2 and you say 8 divided by 3 is - well you get a fraction there - it would be 8/3.
So this would be 8/3 times 2.
And 8/3 times 2 is equal to 16/3.
THAT's how you interpret it - you don't do this multiplication first, and then divide the 2 by that, and all of that.
Now the one time you can be loosey-goosey with order of operations is if you have ALL addition or ALL multiplication.
So if you have 1+5+7+3+2 does not matter what order you do it in.
You could do the two plus three; you could go from the right to the left; you could go from the left to the right; you could start some place in between - if it's ONLY all addition - and the same thing is true if you have ALL mutliplication - if it's 1 times 5 , times 7, times 3, times 2 does not matter what order you are doing it in.
That's only with all multiplication OR all addition.
If there's some division in here or some subtraction in here, you're best off just going left-to-right.
By the end of this year, there'll be nearly a billion people on this planet that actively use social networking sites.
The one thing that all of them have in common is that they're going to die.
While that might be a somewhat morbid thought,
I think it has some really profound implications that are worth exploring.
What first got me thinking about this was a blog post authored earlier this year by Derek K. Miller, who was a science and technology journalist who died of cancer.
And what Miller did was have his family and friends write a post that went out shortly after he died.
Here's what he wrote in starting that out.
He said, "Here it is.
I'm dead, and this is my last post to my blog.
In advance, I asked that once my body finally shut down from the punishments of my cancer, then my family and friends publish this prepared message I wrote -- the first part of the process of turning this from an active website to an archive."
Now, while as a journalist, Miller's archive may have been better written and more carefully curated than most, the fact of the matter is that all of us today are creating an archive that's something completely different than anything that's been created by any previous generation.
Consider a few stats for a moment.
Right now there are 48 hours of video being uploaded to YouTube every single minute.
There are 200 million Tweets being posted every day.
And the average Facebook user is creating 90 pieces of content each month.
So when you think about your parents or your grandparents, at best they may have created some photos or home videos, or a diary that lives in a box somewhere.
But today we're all creating this incredibly rich digital archive that's going to live in the cloud indefinitely, years after we're gone.
And I think that's going to create some incredibly intriguing opportunities for technologists.
Now to be clear, I'm a journalist and not a technologist, so what I'd like to do briefly is paint a picture of what the present and the future are going to look like.
Now we're already seeing some services that are designed to let us decide what happens to our online profile and our social media accounts after we die.
One of them actually, fittingly enough, found me when I checked into a deli at a restaurant in New York on foursquare.
(Recording) Adam Ostrow:
Hello.
Death:
Adam?
Death can catch you anywhere, anytime, even at the Organic.
AO:
Who is this?
Death: Go to ifidie.net before it's too late.
(Laughter)
Adam Ostrow:
Kind of creepy, right?
So what that service does, quite simply, is let you create a message or a video that can be posted to Facebook after you die.
Another service right now is called 1,000 Memories.
And what this lets you do is create an online tribute to your loved ones, complete with photos and videos and stories that they can post after you die.
But what I think comes next is far more interesting.
Now a lot of you are probably familiar with Deb Roy who, back in March, demonstrated how he was able to analyze more than 90,000 hours of home video.
I think as machines' ability to understand human language and process vast amounts of data continues to improve, it's going to become possible to analyze an entire life's worth of content -- the Tweets, the photos, the videos, the blog posts -- that we're producing in such massive numbers.
And I think as that happens, it's going to become possible for our digital personas to continue to interact in the real world long after we're gone thanks to the vastness of the amount of content we're creating and technology's ability to make sense of it all.
Now we're already starting to see some experiments here.
One service called My Next Tweet analyzes your entire Twitter stream, everything you've posted onto Twitter, to make some predictions as to what you might say next.
Well right now, as you can see, the results can be somewhat comical.
You can imagine what something like this might look like five, 10 or 20 years from now as our technical capabilities improve.
Taking it a step further, MlT's media lab is working on robots that can interact more like humans.
But what if those robots were able to interact based on the unique characteristics of a specific person based on the hundreds of thousands of pieces of content that person produces in their lifetime?
Finally, think back to this famous scene from election night 2008 back in the United States, where CNN beamed a live hologram of hip hop artist will.i.am into their studio for an interview with Anderson Cooper.
What if we were able to use that same type of technology to beam a representation of our loved ones into our living rooms -- interacting in a very lifelike way based on all the content they created while they were alive?
I think that's going to become completely possible as the amount of data we're producing and technology's ability to understand it both expand exponentially.
Now in closing, I think what we all need to be thinking about is if we want that to become our reality -- and if so, what it means for a definition of life and everything that comes after it.
Thank you very much.
(Applause)
The point of math is to understand math so you can actually apply it in life later on and not have to relearn everything every time.
So the next logarithm property is, if I have A times the logarithm base B of C, if I have A times this whole thing, then that equals logarithm base B of C to the A power.
Fascinating. So let's see if this works out.
So let's say if I have three times logarithm base two of eight.
So this property tells us that this is going to be the same thing as logarithm base two of eight to the third power.
And that's the same thing.
Well, that's the same thing as-- we could figure it out.
So let's see what this is. three times log base-- what's log base two of eight?
What is this? two to the what power is eight? two to the third power is eight, right?
So that's three.
We have this three here, so three times three.
So this thing right here should equal nine.
If this equals nine, then we know that this property works at least for this example. You don't know if it works for all examples, and for that maybe you'd want to look at the proof we have in the other videos.
But the important thing first is just to understand how to use it.
Let's see, what is two to the ninth power?
Well it's going to be some large number.
Actually, I know what it is-- it's two hundred and fifty-six.
So two to the ninth should be five hundred and twelve. So two to the ninth should be five hundred and twelve. So if eight to the third is also five hundred and twelve then we are correct, right?
Because log base two of five hundred and twelve is going to be equal to nine.
What's eight to the third?
It's sixty-four-- right. eight squared is sixty-four, so eight cubed-- let's see. four times eight. so, it's two and three. six times eight-- looks like it's five hundred and twelve.
Correct. And there's other ways you could have done it.
Because you could have said eight to the third is the same thing as two to the ninth. How do we know that?
Well, eight to the third is equal to two to the third to the third, right?
I just rewrote eight.
And we know from our exponent rules that two to the third to the third is the same thing as two to the ninth.
And actually it's this exponent property, where you can multiply-- when you take something to exponent and then take that to an exponent, and you can essentially just multiply the exponents-- that's the exponent property that actually leads to this logarithm property.
But I'm not going to dwell on that too much in this presentation.
The next logarithm property I'm going to show you-- and then I'll review everything and maybe do some examples.
This is probably the single most useful logarithm property if you are a calculator addict.
And I'll show you why.
So let's say I have log base B of A is equal to log base C of A divided by log base C of B.
Now why is this a useful property if you are calculator addict?
Well, let's say you go class, and there's a quiz.
The teacher says, you can use your calculator, and using your calculator I want you to figure out the log base seventeen of three hundred and fifty-seven.
And you will scramble and look for the log base seventeen button on your calculator, and not find it.
Because there is no log base seventeen button on your calculator. You'll probably either have a log button or you'll have an ln button.
And just so you know, the log button on your calculator is probably base ten.
And your ln button on your calculator is going to be base e.
For those you who aren't familiar with e, don't worry about it but it's 2.71 something something.
It's an amazing number, but we'll talk more about that in a future presentation.
But so there's only two bases you have on your calculator.
So if you want to figure out another base logarithm, you use this property.
So if you're given this on an exam, you can very confidently say, oh, well that is just the same thing as-- you'd have to switch to your yellow color in order to act with confidence-- log base-- we could do either e or ten.
We could say that's the same thing as log base ten of three hundred and fifty-seven divided by log base ten of seventeen.
So you literally could just type in three hundred and fifty-seven in your calculator and press the log button and you're going to get blah blah blah.
Then, you know, you can clear it, or if you know how to use the parentheses on your calculator, you could do that.
But then you type seventeen on your calculator, press the log button, you get blah blah blah. And then you just divide them, and you get your answer.
So this is a super useful property for calculator addicts.
And once again, I'm not going to go into a lot of depth.
This one, to me it's the most useful, but it doesn't completely-- it does fall out of, obviously, the exponent properties.
But it's hard for me to describe the intuition simply, so you probably want to watch the proof on it, if you don't believe why this happens.
But anyway, with all of those aside, and this is probably the one you're going to be using the most in everyday life.
Just so you know logarithms are useful.
Let's do some examples.
Let's just rewrite a bunch of things in simpler forms.
So if I wanted to write the log base two of the square root of-- let me think of something. Of thirty-two divided by the cube-- no, I'll just take the square root.
This is the same thing, this is equal to--
I'll move vertically.
This is the same thing as the log base two of thirty-two over the square root of eight to the one half power, right?
And we know from our logarithm properties, the third one we learned, that that is the same thing as one half times the logarithm of thirty-two divided by the square root of eight, right?
I just took the exponent and made that the coefficient on the entire thing.
And we learned that in the beginning of this video.
And now we have a little quotient here, right?
Logarithm of thirty-two divided by logarithm of square root of eight.
Well, we can use our other logarithm--
let's keep the one half out.
That's going to equal, parentheses, logarithm-- oh, I forgot my base.
Logarithm base two of thirty-two minus, right?
Because this is in a quotient.
Minus the logarithm base two of the square root of eight.
Well here once again we have a square root here, so we could say this is equal to one half times log base two of thirty-two.
Minus this eight to the one half, which is the same thing as one half log base two of eight.
We learned that property in the beginning of this presentation.
And then if we want, we can distribute this original one half.
This equals one half log base two of thirty-two minus one fourth-- because we have to distribute that one half-- minus one fourth log base two of eight.
This is five halves minus, this is three. three times one fourth minus three fourths.
Or ten fourths minus three fourths is equal to seven fourths.
I probably made some arithmetic errors, but you get the point.
See you soon!
Identify complementary and supplementary angles in the image below
So, just as a reminder:
Complementary angles are two angles that add up to 90 degrees, and supplementary angles add up to 180 degrees.
So let's look at this diagram
First let's look for the complementary angles so angles that add up to 90 degrees.
And so they drew this right angle over here so we know that angle FAH is a right angle because of this half box right over there. And it's made up of two adjacent angles. And these two adjacent angles make up a 90 degree angle so they must add up to 90 degrees.
So the two angles, angle FAC, and angle CAH are complementary because the measures of these two angles must add up to 180 degrees, oh sorry... must add up to this 90 degrees, right over here.
And I think that's all the complementary angles, just these two.
They add up to this right angle - to this 90 degrees.
Now let's think about the supplementary angles. so supplementary angles
So you have angle FAC, or we could call it CAF- its the same angle
So angle CAF and then this angle out here
FAB, they're adjacent to each other and they clearly form a straight angle, which is 180 degrees when you add their two measures.
So these two are clearly supplementary. and angle FAB.
CAF and FAB together definitely add up to 180 degrees so they're supplementary.
And the other one: we could do angle CAH, which is this right over here that plus HAB clearly add up they're adjacent, they form a straight angle so they're clearly adding up to 180 degrees.
So they're also supplementary.
CAH and angle HAB.
And we're done!
These two angles add up to 90 these two add up to 180, these two also add up to 180.
There is a classic story out there that has a character named Jack.
You may have heard this story, but I'm sure that there's a part of that story that you have not heard.
And so I'm actually gonna try to fill in those parts so that you get a complete a idea of what happened.
Now, Jack came across, a long time ago, a famous, now famous, beanstalk.
So this beanstalk has been growing and growing and have these huge leaves.
And actually Jack used these leaves to make his way up this beanstalk.
So, this is how this beanstalk became very famous because it basically allowed Jack to use it like a ladder.
Now, the part that we don't hear about is, what was going on between Jack and the beanstalk?
He was exercising, right?
He was actually making a lot of carbon dioxide.
He is making a lot of this gas, this carbon dioxide gas, as kind of a waste product, as he was running, scampering up the beanstalk.
And the beanstalk was helping him physically, but also actually providing him with a very precious oxygen.
In fact, if the beanstalk didn't do that, he may not have even made it.
And we also... We don't know for sure but we think that perhaps some of the story may have taken place during the day.
And in fact, we know that sunlight is quite important for this process and we think that this process... the name that we give it, for the beanstalk anyway, is photosynthesis.
And so, what is really happening? I'm actually kind of gonna write it out here, between Jack and the bean stock? And really, between all plants and animals?
What is this process between them?
We know that on the one hand, you have beanstalk doing photosynthesis, and on the other hand, you have folks like Jack doing cellular respiration, right?
This is really kind of interesting simbiosis.
And by that, I just mean that the two are kind of relying on each other to really work, right?
So you kind of need both of them to work well.
And so, let's actually take a moment to write out these processes that are happening between Jack and the beanstalk.
So let's start with the process of photosynthesis, the beanstalk.
So on the one hand, you've got water, 'cause of course the beanstalk needs water.
And you've got carbon dioxide.
I'm gonna do carbon dioxide in orange.
So it's taking in water and carbon dioxide.
And it's going to put out, it's going to take these ingredients, if you want to think of it as it's kind of cooking, it's gonna take these ingredients and it's gonna put out oxygen and glucose.
I'll put glucose at top and oxygen down below.
So these are the inputs and outputs of photosynthesis, right?
And on the other side, you've got something very similar.
You've got inputs, you've got glucose and oxygen going in.
You're gonna see some serious similarities here.
You've got glucose and oxygen going in.
So, Jack is taking in those two things.
And he's again, of course, processing them.
And he's putting out water and carbon dioxide.
So, this looks really really nice, it looks perfect actually because everything is nice and balance, and you can see how it makes perfect sense that not only did Jack need the beanstalk, but actually it sounds like the beanstalk needed Jack, based on how I've drawn it.
Now remember, none of this would even happen if there was no sunlight.
So we actually need light energy.
In fact, that's the whole purpose of this, right?
Getting energy.
So you have to have some light energy.
I'm gonna put a big plus sign, I might even circle it because it's so important, I don't you lose track of it.
And on the other side, of course, Jack is getting something as well.
He's getting chemical energy.
In fact, he's using the chemical energy to help him climb the beanstalk.
And so the chemical energy comes in the form of what we call ATP, which is just a molecule of high energy.
And so, Jack is basically, or Jack is actually going from light energy to chemical energy, using these two equations.
Now here's the part that people don't always appreciate.
And I'm actually gonna take just a moment to show you that this isn't the full story, there's actually something else going on as well.
And that is that, there is actually some cellular respiration happening on the plant side.
So remember, not only does the human or Jack need energy, but so does the plant, right, the plant needs energy as well, and in fact, if it takes in light energy right here, it needs to find a way to eventually get some chemical energy itself so that it can do all the things it needs to do.
You know, it doesn't need to run because plants don't move in that sense, but it might need to make new roots, it might need to make a flower and all these things take energy.
So actually, photosynthesis is happening during the day, but at all times, plants are also capable of doing cellular respiration, just like humans are, so humans and plants have actually more in common than you might think.
So, this brings up an obvious question:
Why in the world would a plant sends its glucose and oxygen this way where it needs it itself?
You know, why would it actually get rid of it?
Well the truth is that, the glucose ends up often times in fruits and vegetables that we can eat, but as far as the oxygen goes, it makes an excess of oxygen, so there is actually enough oxygen to go both to us or to Jack, and to be used by itself, so it actually has an excess of oxygen that it's making.
So that's actually kind of interesting, good to know.
Now if you think about it, if I was to...
Let's say sketch out a planet.
Let's draw a little, a planet over here.
And ask you the question, you know, if this was your planet Earth, and you've got thousands, instead of just one Jack.
Let's say now you have thousands of Jacks and thousands of beanstalks.
In fact, not even thousands, let's say, billions, because really, that's what we have, right?
We have a planet full of humans, and full of other animals and full of plants.
What would the atmosphere look like?
This is the atmosphere.
What would the atmosphere look like?
Well, you guess, that the atmosphere is, you know, gas.
What would those gases be? ???
It looks like I've got lots of oxygen and lots of carbon dioxide. So well,
I guess there must be, I don't know, maybe 50-50 carbon dioxide and oxygen, based on what we know so far.
And the truth is, that's actually not true.
If you actually look at air, you actually kind of break down the atmosphere or air.
I'm gonna write "air" here, you actually break it down.
It turns out that the ratio is actually a little different, so for example, oxygen makes up about 21% of our air.
This is our air breakdown.
Air.
And carbon dioxide makes up about less than 1%.
So, that leaves you wondering what the heck is making up all that other parts of the air? What does it made of?
And it turns out about 78% is nitrogen.
Now you know, you've got nitrogen in your protein, we've got nitrogen in our DNA; so nitrogen is part of us, part of, you know, many many living things.
But nitrogen gas specifically is actually N2.
And N2, this nitrogen gas, really, it's not too reactive.
It kinds of just hangs out by itself.
It does not like to react with things.
So, looking at our little atmosphere graph, you'll now think about it, knowing that we've got very little carbon dioxide and you know, about 21% oxygen.
You could think of oxgyen kind of being, let's say something like that, well then, relative to that, nitrogen would be you know, much more, right?
You have much more nitrogen hanging out.
And so, this is really what our atmosphere looks like.
It looks more filled with nitrogen than anything else.
And, it turns out that carbon dioxide, it's just got a little ??? maybe right there, that could be carbon dioxide, maybe even less than that.
So, this is really what our atmosphere looks like visually.
And the nitrogen again, it's making up the majority.
And if you actually kind of wonder where all that nitrogen is coming from.
'Cause it's not mentioned in any of the equations, right?
Most of the nitrogen has been around...
Scientists think since the beginning of... When Earth even had an atmosphere.
And that nitrogen was just kind of carrying with us at all times and that's why it just kind of remains at 78%.
It will probably remain there for many many years to come.
 Graph the inequality y minus 4x is less than negative 3.
So the first thing we could do is we could kind of put this in mx plus b form, or slope-intercept form, but as an inequality.
So we're starting with y minus 4x is less than negative 3.
We can add 4x to both sides of this inequality. So let's add 4x to both sides of this inequality, and then we'll just have a y on the left-hand side. These guys cancel out.
So you have y is less than 4x minus 3. We could have had negative 3 plus 4x, but we want to write the 4x first just because that's a form that we're more familiar with.
So it's less than 4x minus 3. And now we can attempt to graph it. But before I graph it, I want to be a little bit careful here.
So this is the x-axis, and is that is the y-axis. And we want to be careful, because this says y is less than 4x minus 3, not less than or equal to 4x minus 3, or not y is equal to 4x minus 3.
So what we want to do is kind of create a boundary at y is equal to 4x minus 3, and the solution to this inequality will be all of the area below that, all of the y values
less than that. So let's try to do it.
So the boundary line would look like-- so let me write it over here-- so we have a boundary at y is equal to 4x minus 3.
Notice this isn't part of the solution. This isn't less than or equal. It's just less than.
But this will at least help us draw, essentially, the boundary. So we could do it two ways.
If you know slope and y-intercept, you know that 4 is our slope and that negative 3 is our y-intercept.
Or you can literally just take two points, and that'll help you define a line here. So you could say, well, when x is equal to 0, what is y?
You get 4 times 0 minus 3, you get y is equal to negative 3.
And we knew that because it was the y-intercept.
So you have 0, and then you have 1, 2, 0, and negative 3.
And then you have the point, let's say, when x is equal to-- I don't know--
let's say when x is equal to 2. When x is equal to 2, what is y?
We have 4 times 2 is 8 minus 3, y is then going to be equal to 5.
So then you go 1, 2, and you go 1, 2, 3, 4, 5.
And so you have that point there as well.
And then we can just connect the dots.
Or you could say, look, there's a slope of 4. So every time we move over 1, every time we move 1 in the x direction, we move up 4 in the y direction. So we could draw it like that.
So the line will look something like this.
And I'm just going to draw it in a dotted line because, remember, this isn't part of the solution.
Actually, let me draw it a little bit neater because that point should be right about there, and this point should be right about there. And then this boundary line I'm going to draw as a dotted line.
So it's going to look something like that. I draw it a dotted line to show that it's not part of the solution.
Our solution has the y's less than that. So for any x, so you pick an x here, if you took 4x minus 3, you're going to end up on the line.
But we don't want the y's that are equal to that line.
We want for that particular x, the y's that are less than the line. So it's going to be all of this area over here.
We're less than the line, and we're not including the line, and that's why I put a dotted line here.
You can also try values out.
You can say, well, this line is dividing our coordinate axes into, essentially, the region above it and the region below it, and you can test it out.
Let's take the point 0, 0 and see if that satisfies our inequality.
If we have y is 0 is less than 0 minus 3, or we get 0 is less than negative 3.
This is definitely not the case. This is not true.
And it makes sense because that 0, 0 is not part of the solution.
Now, we could go on the other side of our boundary line. And we could take the point, I don't know, let's take the point 3 comma 0.
So let's say that this is the point-- well, that's right. There's a point 2 comma 0. Let's take the point 3 comma 0 right over here.
This should work because it's in the region less than. But let's verify it for ourselves. So we have y is 0.
0 is less than 4 times 3 minus 3.
0 is less than 12 minus 3.
0 Is less than 9, which is definitely true.
So that point does satisfy the inequality.
So in general, you want to kind of look at this as an equal to draw the boundary line. We did it.
But we drew it as a dotted line because we don't want to include it because this isn't less than or equal to. It's just less than. And then our solution to the inequality will be the region below it, all the y's
less than the line for x minus 3.
Hello, I'm Hank Green and I want to teach you Chemistry.
Please do not run away screaming.
If you give me five minutes to try to convince you that chemistry is not torture but instead the amazing and beautiful science of stuff and if you give it a chance it will not only blow you mind but also give you a deeper understanding of your world.
This is just my opinion here but I think that understanding the world leads to a greater ability to enjoy the world and there's nothing that helps you understand the world better than Chemistry.
Chemistry holds the secrets to how life first formed, how cancers are cured, how iPhones have bigger hard drives than 5 year old laptops, and how life on this planet might just be able to continue thriving, even ours, if we play our cards right. Chemistry is the science of how 3 tiny particles, the proton, the neutron and the electron, came together in trillions of combinations to form, get this, everything. Now chemistry is a peculiar science, sometimes talked about as a bridge to the ultra-abstract world of particle physics and the more visible sciences like biology.
In this video, I'm going to do several examples of quadratic equations that are really of a special form, and it's really a bit of warm-up for the next video that we're going to do on completing the square.
So let me show you what I'm talking about.
So let's say I have 4x plus 1 squared, minus 8 is equal to 0.
Now, based on everything we've done so far, you might be tempted to multiply this out, then subtract 8 from the constant you get out here, and then try to factor it.
And then you're going to have x minus something, times x minus something else is equal to 0.
And you're going to say, oh, one of these must be equal to 0, so x could be that or that.
We're not going to do that this time, because you might see something interesting here.
We can solve this without factoring it.
And how do we do that?
Well, what happens if we add 8 to both sides of this equation?
Then the left-hand side of the equation becomes 4x plus 1 squared, and these 8's cancel out.
The right-hand becomes just a positive 8.
Now, what can we do to both sides of this equation?
And this is just kind of straight, vanilla equation-solving.
This isn't any kind of fancy factoring.
We can take the square root of both sides of this equation.
We could take the square root.
So 4x plus 1-- I'm just taking the square root of both sides.
You take the square root of both sides, and, of course, you want to take the positive and the negative square root, because 4x plus 1 could be the positive square root of 8, or it could be the negative square root of 8.
So 4x plus 1 is equal to the positive or negative square root of 8.
Instead of 8, let me write 8 as 4 times 2.
We all know that's what 8 is, and obviously the square root of 4x plus 1 squared is 4x plus 1.
So we get 4x plus 1 is equal to-- we can factor out the 4, or the square root of 4, which is 2-- is equal to the plus or minus times 2 times the square root of 2, right?
Square root of 4 times square root of 2 is the same thing as square root of 4 times the square root of 2, plus or minus the square root of 4 is that 2 right there.
Now, it might look like a really bizarro equation, with this plus or minus 2 times the square of 2, but it really isn't.
These are actually two numbers here, and we're actually simultaneously solving two equations.
We could write this as 4x plus 1 is equal to the positive 2, square root of 2, or 4x plus 1 is equal to negative 2 times the square root of 2.
This one statement is equivalent to this right here, because we have this plus or minus here, this or statement.
Let me solve all of these simultaneously.
So if I subtract 1 from both sides of this equation, what do I have?
On the left-hand side, I'm just left with 4x.
On the right-hand side, I have-- you can't really mathematically, I mean, you could do them if you had a calculator, but I'll just leave it as negative 1 plus or minus the square root, or 2 times the square root of 2.
That's what 4x is equal to.
If we did it here, as two separate equations, same idea.
Subtract 1 from both sides of this equation, you get 4x is equal to negative 1 plus 2, times the square root of 2.
This equation, subtract 1 from both sides. 4x is equal to negative 1 minus 2, times the square root of 2.
This statement right here is completely equivalent to these two statements.
Now, last step, we just have to divide both sides by 4, so you divide both sides by 4, and you get x is equal to negative 1 plus or minus 2, times the square root of 2, over 4.
Now, this statement is completely equivalent to dividing each of these by 4, and you get x is equal to negative 1 plus 2, times the square root 2, over 4.
This is one solution.
And then the other solution is x is equal to negative 1 minus 2 roots of 2, all of that over 4.
That statement and these two statements are equivalent.
And if you want, I encourage you to-- let's substitute one of these back in, just so you feel confident that something as bizarro as one of these expressions can be a solution to a nice, vanilla-looking equation like this.
So let's substitute it back in. 4 times x, or 4 times negative 1, plus 2 root 2, over 4, plus 1 squared, minus 8 is equal to 0.
Now, these 4's cancel out, so you're left with negative 1 plus 2 roots 2, plus 1, squared, minus 8 is equal to 0.
This negative 1 and this positive 1 cancel out, so you're left with 2 roots of 2 squared, minus 8 is equal to 0.
And then what are you going to have here?
So when you square this, you get 4 times 2, minus 8 is equal to 0, which is true. 8 minus 8 is equal to 0.
And if you try this one out, you're going to get the exact same answer.
Let's do another one like this.
And remember, these are special forms where we have squares of binomials in our expression.
And we're going to see that the entire quadratic formula is actually derived from a notion like this, because you can actually turn any, you can turn any, quadratic equation into a perfect square equalling something else.
We'll see that two videos from now. But let's get a little warmed up just seeing this type of thing.
So the Awesome story:
It begins about 40 years ago, when my mom and my dad came to Canada.
My mom left Nairobi, Kenya.
My dad left a small village outside of Amritsar, India.
And they got here in the late 1960s.
They settled in a shady suburb about an hour east of Toronto, and they settled into a new life.
They saw their first dentist, they ate their first hamburger, and they had their first kids.
My sister and I grew up here, and we had quiet, happy childhoods.
We had close family, good friends, a quiet street.
We grew up taking for granted a lot of the things that my parents couldn't take for granted when they grew up -- things like power always on in our houses, things like schools across the street and hospitals down the road and popsicles in the backyard.
We grew up, and we grew older.
I went to high school.
I graduated.
I moved out of the house, I got a job, I found a girl, I settled down -- and I realize it sounds like a bad sitcom or a Cat Stevens' song -- (Laughter) but life was pretty good.
Life was pretty good.
2006 was a great year.
Under clear blue skies in July in the wine region of Ontario, I got married, surrounded by 150 family and friends.
2007 was a great year.
I graduated from school, and I went on a road trip with two of my closest friends.
Here's a picture of me and my friend, Chris, on the coast of the Pacific Ocean.
We actually saw seals out of our car window, and we pulled over to take a quick picture of them and then blocked them with our giant heads.
(Laughter)
So you can't actually see them, but it was breathtaking, believe me.
(Laughter) 2008 and 2009 were a little tougher.
I know that they were tougher for a lot of people, not just me.
First of all, the news was so heavy.
It's still heavy now, and it was heavy before that, but when you flipped open a newspaper, when you turned on the TV, it was about ice caps melting, wars going on around the world, earthquakes, hurricanes and an economy that was wobbling on the brink of collapse, and then eventually did collapse, and so many of us losing our homes, or our jobs, or our retirements, or our livelihoods.
2008, 2009 were heavy years for me for another reason, too.
I was going through a lot of personal problems at the time.
My marriage wasn't going well, and we just were growing further and further apart.
One day my wife came home from work and summoned the courage, through a lot of tears, to have a very honest conversation.
And she said, "I don't love you anymore," and it was one of the most painful things I'd ever heard and certainly the most heartbreaking thing I'd ever heard, until only a month later, when I heard something even more heartbreaking.
My friend Chris, who I just showed you a picture of, had been battling mental illness for some time.
And for those of you whose lives have been touched by mental illness, you know how challenging it can be.
I spoke to him on the phone at 10:30 p.m. on a Sunday night.
We talked about the TV show we watched that evening.
And Monday morning, I found out that he disappeared.
Very sadly, he took his own life.
And it was a really heavy time.
And as these dark clouds were circling me, and I was finding it really, really difficult to think of anything good, I said to myself that I really needed a way to focus on the positive somehow.
So I came home from work one night, and I logged onto the computer, and I started up a tiny website called 1000awesomethings.com.
I was trying to remind myself of the simple, universal, little pleasures that we all love, but we just don't talk about enough -- things like waiters and waitresses who bring you free refills without asking, being the first table to get called up to the dinner buffet at a wedding, wearing warm underwear from just out of the dryer, or when cashiers open up a new check-out lane at the grocery store and you get to be first in line -- even if you were last at the other line, swoop right in there. (Laughter)
And slowly over time, I started putting myself in a better mood.
I mean, 50,000 blogs are started a day, and so my blog was just one of those 50,000.
And nobody read it except for my mom.
Although I should say that my traffic did skyrocket and go up by 100 percent when she forwarded it to my dad.
(Laughter)
And then I got excited when it started getting tens of hits, and then I started getting excited when it started getting dozens and then hundreds and then thousands and then millions.
It started getting bigger and bigger and bigger.
And then I got a phone call, and the voice at the other end of the line said,
"You've just won the Best Blog In the World award."
I was like, that sounds totally fake.
(Laughter) (Applause)
Which African country do you want me to wire all my money to?
(Laughter)
But it turns out, I jumped on a plane, and I ended up walking a red carpet between Sarah Silverman and Jimmy Fallon and Martha Stewart.
And I went onstage to accept a Webby award for Best Blog.
And the surprise and just the amazement of that was only overshadowed by my return to Toronto, when, in my inbox, 10 literary agents were waiting for me to talk about putting this into a book.
Flash-forward to the next year and "The Book of Awesome" has now been number one on the bestseller list for 20 straight weeks.
(Applause)
But look, I said I wanted to do three things with you today.
I said I wanted to tell you the Awesome story,
I wanted to share with you the three As of Awesome, and I wanted to leave you with a closing thought.
So let's talk about those three As.
Over the last few years, I haven't had that much time to really think.
But lately I have had the opportunity to take a step back and ask myself:
"What is it over the last few years that helped me grow my website, but also grow myself?"
And I've summarized those things, for me personally, as three As. They are Attitude, Awareness and Authenticity.
I'd love to just talk about each one briefly.
So Attitude:
Look, we're all going to get lumps, and we're all going to get bumps.
None of us can predict the future, but we do know one thing about it and that's that it ain't gonna go according to plan.
We will all have high highs and big days and proud moments of smiles on graduation stages, father-daughter dances at weddings and healthy babies screeching in the delivery room, but between those high highs, we may also have some lumps and some bumps too.
It's sad, and it's not pleasant to talk about, but your husband might leave you, your girlfriend could cheat, your headaches might be more serious than you thought, or your dog could get hit by a car on the street.
It's not a happy thought, but your kids could get mixed up in gangs or bad scenes.
Your mom could get cancer, your dad could get mean.
And there are times in life when you will be tossed in the well, too, with twists in your stomach and with holes in your heart, and when that bad news washes over you, and when that pain sponges and soaks in,
One, you can swirl and twirl and gloom and doom forever, or two, you can grieve and then face the future with newly sober eyes.
Having a great attitude is about choosing option number two, and choosing, no matter how difficult it is, no matter what pain hits you, choosing to move forward and move on and take baby steps into the future.
The second "A" is Awareness.
I love hanging out with three year-olds.
I love the way that they see the world, because they're seeing the world for the first time.
I love the way that they can stare at a bug crossing the sidewalk.
I love the way that they'll stare slack-jawed at their first baseball game with wide eyes and a mitt on their hand, soaking in the crack of the bat and the crunch of the peanuts and the smell of the hotdogs.
I love the way that they'll spend hours picking dandelions in the backyard and putting them into a nice centerpiece for Thanksgiving dinner.
I love the way that they see the world, because they're seeing the world for the first time.
Having a sense of awareness is just about embracing your inner three year-old.
Because you all used to be three years old.
That three-year-old boy is still part of you.
That three-year-old girl is still part of you.
They're in there.
And being aware is just about remembering that you saw everything you've seen for the first time once, too.
So there was a time when it was your first time ever hitting a string of green lights on the way home from work.
There was the first time you walked by the open door of a bakery and smelt the bakery air, or the first time you pulled a 20-dollar bill out of your old jacket pocket and said, "Found money."
The last "A" is Authenticity.
And for this one, I want to tell you a quick story.
Let's go all the way back to 1932 when, on a peanut farm in Georgia, a little baby boy named Roosevelt Grier was born.
Roosevelt Grier, or Rosey Grier, as people used to call him, grew up and grew into a 300-pound, six-foot-five linebacker in the NFL.
He's number 76 in the picture.
Here he is pictured with the "fearsome foursome."
These were four guys on the L.A. Rams in the 1960s you did not want to go up against.
They were tough football players doing what they love, which was crushing skulls and separating shoulders on the football field.
But Rosey Grier also had another passion.
In his deeply authentic self, he also loved needlepoint. (Laughter)
He loved knitting.
He said that it calmed him down, it relaxed him, it took away his fear of flying and helped him meet chicks.
That's what he said.
I mean, he loved it so much that, after he retired from the NFL, he started joining clubs.
And he even put out a book called "Rosey Grier's Needlepoint for Men."
(Laughter) (Applause)
It's a great cover.
If you notice, he's actually needlepointing his own face.
(Laughter)
And so what I love about this story is that Rosey Grier is just such an authentic person, and that's what authenticity is all about.
It's just about being you and being cool with that.
And I think when you're authentic, you end up following your heart, and you put yourself in places and situations and in conversations that you love and that you enjoy.
You meet people that you like talking to.
You go places you've dreamt about.
And you end you end up following your heart and feeling very fulfilled.
So those are the three A's.
For the closing thought, I want to take you all the way back to my parents coming to Canada.
I don't know what it would feel like coming to a new country when you're in your mid-20s.
I don't know, because I never did it, but I would imagine that it would take a great attitude.
I would imagine that you'd have to be pretty aware of your surroundings and appreciating the small wonders that you're starting to see in your new world.
And I think you'd have to be really authentic, you'd have to be really true to yourself in order to get through what you're being exposed to.
I'd like to pause my TEDTalk for about 10 seconds right now, because you don't get many opportunities in life to do something like this, and my parents are sitting in the front row.
So I wanted to ask them to, if they don't mind, stand up.
And I just wanted to say thank you to you guys.
(Applause)
When I was growing up, my dad used to love telling the story of his first day in Canada.
And it's a great story, because what happened was he got off the plane at the Toronto airport, and he was welcomed by a non-profit group, which I'm sure someone in this room runs.
(Laughter)
And this non-profit group had a big welcoming lunch for all the new immigrants to Canada.
And my dad says he got off the plane and he went to this lunch and there was this huge spread.
There was bread, there was those little, mini dill pickles, there was olives, those little white onions.
There was rolled up turkey cold cuts, rolled up ham cold cuts, rolled up roast beef cold cuts and little cubes of cheese.
There was tuna salad sandwiches and egg salad sandwiches and salmon salad sandwiches.
There was lasagna, there was casseroles, there was brownies, there was butter tarts, and there was pies, lots and lots of pies.
And when my dad tells the story, he says,
"The craziest thing was, I'd never seen any of that before, except bread.
(Laughter)
I didn't know what was meat, what was vegetarian.
I was eating olives with pie.
(Laughter)
I just couldn't believe how many things you can get here."
(Laughter)
When I was five years old, my dad used to take me grocery shopping, and he would stare in wonder at the little stickers that are on the fruits and vegetables.
He would say, "Look, can you believe they have a mango here from Mexico?
They've got an apple here from South Africa.
Can you believe they've got a date from Morocco?"
He's like, "Do you know where Morocco even is?"
And I'd say, "I'm five.
I don't even know where I am.
Is this A&P?"
And he'd say, "I don't know where Morocco is either, but let's find out."
And so we'd buy the date, and we'd go home.
And we'd actually take an atlas off the shelf, and we'd flip through until we found this mysterious country.
And when we did, my dad would say,
"Can you believe someone climbed a tree over there, picked this thing off it, put it in a truck, drove it all the way to the docks and then sailed it all the way across the Atlantic Ocean and then put it in another truck and drove that all the way to a tiny grocery store just outside our house, so they could sell it to us for 25 cents?"
And I'd say, "I don't believe that."
And he's like, "I don't believe it either.
Things are amazing.
There's just so many things to be happy about."
When I stop to think about it, he's absolutely right. There are so many things to be happy about.
We are the only species on the only life-giving rock in the entire universe that we've ever seen, capable of experiencing so many of these things.
I mean, we're the only ones with architecture and agriculture.
We're the only ones with jewelry and democracy.
We've got airplanes, highway lanes, interior design and horoscope signs.
We've got fashion magazines, house party scenes.
You can watch a horror movie with monsters.
You can go to a concert and hear guitars jamming.
We've got books, buffets and radio waves, wedding brides and rollercoaster rides.
You can sleep in clean sheets.
You can go to the movies and get good seats.
You can smell bakery air, walk around with rain hair, pop bubble wrap or take an illegal nap.
We've got all that, but we've only got 100 years to enjoy it.
And that's the sad part.
The cashiers at your grocery store, the foreman at your plant, the guy tailgating you home on the highway, the telemarketer calling you during dinner, every teacher you've ever had, everyone that's ever woken up beside you, every politician in every country, every actor in every movie, every single person in your family, everyone you love, everyone in this room and you will be dead in a hundred years.
Life is so great that we only get such a short time to experience and enjoy all those tiny little moments that make it so sweet.
And that moment is right now, and those moments are counting down, and those moments are always, always, always fleeting.
You will never be as young as you are right now.
And that's why I believe that if you live your life with a great attitude, choosing to move forward and move on whenever life deals you a blow, living with a sense of awareness of the world around you, embracing your inner three year-old and seeing the tiny joys that make life so sweet and being authentic to yourself, being you and being cool with that, letting your heart lead you and putting yourself in experiences that satisfy you, then I think you'll live a life that is rich and is satisfying, and I think you'll live a life that is truly awesome.
Thank you.
First, a video.
Yes, it is a scrambled egg.
But as you look at it, I hope you'll begin to feel just slightly uneasy. Because you may notice that what's actually happening is that the egg is unscrambling itself.
And you'll now see the yolk and the white have separated.
And now they're going to be poured back into the egg.
And we all know in our heart of hearts that this is not the way the universe works.
A scrambled egg is mush -- tasty mush -- but it's mush.
An egg is a beautiful, sophisticated thing that can create even more sophisticated things, such as chickens.
And we know in our heart of hearts that the universe does not travel from mush to complexity.
In fact, this gut instinct is reflected in one of the most fundamental laws of physics, the second law of thermodynamics, or the law of entropy.
What that says basically is that the general tendency of the universe is to move from order and structure to lack of order, lack of structure -- in fact, to mush.
And that's why that video feels a bit strange.
And yet, look around us.
What we see around us is staggering complexity.
Eric Beinhocker estimates that in New York City alone, there are some 10 billion SKUs, or distinct commodities, being traded.
That's hundreds of times as many species as there are on Earth.
And they're being traded by a species of almost seven billion individuals, who are linked by trade, travel, and the Internet into a global system of stupendous complexity.
So here's a great puzzle: in a universe ruled by the second law of thermodynamics, how is it possible to generate the sort of complexity I've described, the sort of complexity represented by you and me and the convention center?
Well, the answer seems to be, the universe can create complexity, but with great difficulty.
In pockets, there appear what my colleague, Fred Spier, calls "Goldilocks conditions" -- not too hot, not too cold, just right for the creation of complexity.
And slightly more complex things appear.
And where you have slightly more complex things, you can get slightly more complex things.
And in this way, complexity builds stage by stage.
Each stage is magical because it creates the impression of something utterly new appearing almost out of nowhere in the universe.
We refer in big history to these moments as threshold moments.
And at each threshold, the going gets tougher.
The complex things get more fragile, more vulnerable; the Goldilocks conditions get more stringent, and it's more difficult to create complexity.
Now, we, as extremely complex creatures, desperately need to know this story of how the universe creates complexity despite the second law, and why complexity means vulnerability and fragility.
And that's the story that we tell in big history.
But to do it, you have do something that may, at first sight, seem completely impossible.
You have to survey the whole history of the universe.
So let's do it.
(Laughter)
Let's begin by winding the timeline back 13.7 billion years, to the beginning of time.
Around us, there's nothing.
There's not even time or space.
Imagine the darkest, emptiest thing you can and cube it a gazillion times and that's where we are.
And then suddenly, bang!
A universe appears, an entire universe.
And we've crossed our first threshold.
The universe is tiny; it's smaller than an atom.
It's incredibly hot.
It contains everything that's in today's universe, so you can imagine, it's busting.
And it's expanding at incredible speed.
And at first, it's just a blur, but very quickly distinct things begin to appear in that blur.
Within the first second, energy itself shatters into distinct forces including electromagnetism and gravity.
And energy does something else quite magical: it congeals to form matter -- quarks that will create protons and leptons that include electrons.
And all of that happens in the first second.
Now we move forward 380,000 years.
That's twice as long as humans have been on this planet.
And now simple atoms appear of hydrogen and helium.
Now I want to pause for a moment, 380,000 years after the origins of the universe, because we actually know quite a lot about the universe at this stage.
We know above all that it was extremely simple.
It consisted of huge clouds of hydrogen and helium atoms, and they have no structure.
They're really a sort of cosmic mush.
But that's not completely true.
Recent studies by satellites such as the WMAP satellite have shown that, in fact, there are just tiny differences in that background.
What you see here, the blue areas are about a thousandth of a degree cooler than the red areas.
These are tiny differences, but it was enough for the universe to move on to the next stage of building complexity.
And this is how it works.
Gravity is more powerful where there's more stuff.
So where you get slightly denser areas, gravity starts compacting clouds of hydrogen and helium atoms.
So we can imagine the early universe breaking up into a billion clouds.
And each cloud is compacted, gravity gets more powerful as density increases, the temperature begins to rise at the center of each cloud, and then, at the center, the temperature crosses the threshold temperature of 10 million degrees, protons start to fuse, there's a huge release of energy, and -- bam!
We have our first stars.
From about 200 million years after the Big Bang, stars begin to appear all through the universe, billions of them.
And the universe is now significantly more interesting and more complex.
Stars will create the Goldilocks conditions for crossing two new thresholds.
When very large stars die, they create temperatures so high that protons begin to fuse in all sorts of exotic combinations, to form all the elements of the periodic table.
If, like me, you're wearing a gold ring, it was forged in a supernova explosion.
So now the universe is chemically more complex.
And in a chemically more complex universe, it's possible to make more things.
And what starts happening is that, around young suns, young stars, all these elements combine, they swirl around, the energy of the star stirs them around, they form particles, they form snowflakes, they form little dust motes, they form rocks, they form asteroids, and eventually, they form planets and moons.
And that is how our solar system was formed, four and a half billion years ago.
Rocky planets like our Earth are significantly more complex than stars because they contain a much greater diversity of materials.
So we've crossed a fourth threshold of complexity.
Now, the going gets tougher.
The next stage introduces entities that are significantly more fragile, significantly more vulnerable, but they're also much more creative and much more capable of generating further complexity.
I'm talking, of course, about living organisms.
Living organisms are created by chemistry.
We are huge packages of chemicals.
So, chemistry is dominated by the electromagnetic force.
That operates over smaller scales than gravity, which explains why you and I are smaller than stars or planets.
Now, what are the ideal conditions for chemistry?
What are the Goldilocks conditions?
Well, first, you need energy, but not too much.
In the center of a star, there's so much energy that any atoms that combine will just get busted apart again.
But not too little.
In intergalactic space, there's so little energy that atoms can't combine.
What you want is just the right amount, and planets, it turns out, are just right, because they're close to stars, but not too close.
You also need a great diversity of chemical elements, and you need liquids, such as water.
Why?
Well, in gases, atoms move past each other so fast that they can't hitch up.
In solids, atoms are stuck together, they can't move.
In liquids, they can cruise and cuddle and link up to form molecules.
Now, where do you find such Goldilocks conditions?
Well, planets are great, and our early Earth was almost perfect.
It was just the right distance from its star to contain huge oceans of liquid water.
And deep beneath those oceans, at cracks in the Earth's crust, you've got heat seeping up from inside the Earth, and you've got a great diversity of elements.
So at those deep oceanic vents, fantastic chemistry began to happen, and atoms combined in all sorts of exotic combinations.
But of course, life is more than just exotic chemistry.
How do you stabilize those huge molecules that seem to be viable?
Well, it's here that life introduces an entirely new trick.
You don't stabilize the individual; you stabilize the template, the thing that carries information, and you allow the template to copy itself.
And DNA, of course, is the beautiful molecule that contains that information.
You'll be familiar with the double helix of DNA.
Each rung contains information.
So, DNA contains information about how to make living organisms.
And DNA also copies itself.
So, it copies itself and scatters the templates through the ocean.
So the information spreads.
Notice that information has become part of our story.
The real beauty of DNA though is in its imperfections.
As it copies itself, once in every billion rungs, there tends to be an error.
And what that means is that DNA is, in effect, learning.
It's accumulating new ways of making living organisms because some of those errors work.
So DNA's learning and it's building greater diversity and greater complexity.
And we can see this happening over the last four billion years.
For most of that time of life on Earth,
living organisms have been relatively simple -- single cells.
But they had great diversity, and, inside, great complexity.
Then from about 600 to 800 million years ago, multi-celled organisms appear.
You get fungi, you get fish, you get plants, you get amphibia, you get reptiles, and then, of course, you get the dinosaurs.
And occasionally, there are disasters.
Sixty-five million years ago, an asteroid landed on Earth near the Yucatan Peninsula, creating conditions equivalent to those of a nuclear war, and the dinosaurs were wiped out.
Terrible news for the dinosaurs, but great news for our mammalian ancestors, who flourished in the niches left empty by the dinosaurs.
And we human beings are part of that creative evolutionary pulse that began 65 million years ago with the landing of an asteroid.
Humans appeared about 200,000 years ago.
And I believe we count as a threshold in this great story.
Let me explain why.
We've seen that DNA learns in a sense, it accumulates information.
But it is so slow.
DNA accumulates information through random errors, some of which just happen to work.
But DNA had actually generated a faster way of learning: it had produced organisms with brains, and those organisms can learn in real time.
They accumulate information, they learn.
The sad thing is, when they die, the information dies with them.
Now what makes humans different is human language.
We are blessed with a language, a system of communication, so powerful and so precise that we can share what we've learned with such precision that it can accumulate in the collective memory.
And that means it can outlast the individuals who learned that information, and it can accumulate from generation to generation.
And that's why, as a species, we're so creative and so powerful, and that's why we have a history.
We seem to be the only species in four billion years to have this gift.
I call this ability collective learning.
It's what makes us different.
We can see it at work in the earliest stages of human history.
We evolved as a species in the savanna lands of Africa, but then you see humans migrating into new environments, into desert lands, into jungles, into the Ice Age tundra of Siberia -- tough, tough environment -- into the Americas, into Australasia.
Each migration involved learning -- learning new ways of exploiting the environment, new ways of dealing with their surroundings.
Then 10,000 years ago, exploiting a sudden change in global climate with the end of the last ice age, humans learned to farm.
Farming was an energy bonanza.
And exploiting that energy, human populations multiplied.
Human societies got larger, denser, more interconnected.
And then from about 500 years ago, humans began to link up globally through shipping, through trains, through telegraph, through the Internet, until now we seem to form a single global brain of almost seven billion individuals.
And that brain is learning at warp speed.
And in the last 200 years, something else has happened. We've stumbled on another energy bonanza in fossil fuels.
So fossil fuels and collective learning together explain the staggering complexity we see around us.
So -- Here we are, back at the convention center.
We've been on a journey, a return journey, of 13.7 billion years.
I hope you agree this is a powerful story.
And it's a story in which humans play an astonishing and creative role.
But it also contains warnings.
Collective learning is a very, very powerful force, and it's not clear that we humans are in charge of it.
I remember very vividly as a child growing up in England, living through the Cuban Missile Crisis.
For a few days, the entire biosphere seemed to be on the verge of destruction.
And the same weapons are still here, and they are still armed.
If we avoid that trap, others are waiting for us.
We're burning fossil fuels at such a rate that we seem to be undermining the Goldilocks conditions that made it possible for human civilizations to flourish over the last 10,000 years.
So what big history can do is show us the nature of our complexity and fragility and the dangers that face us, but it can also show us our power with collective learning.
And now, finally -- this is what I want.
I want my grandson, Daniel, and his friends and his generation, throughout the world, to know the story of big history, and to know it so well that they understand both the challenges that face us and the opportunities that face us.
And that's why a group of us are building a free, online syilabus in big history for high-school students throughout the world.
We believe that big history will be a vital intellectual tool for them, as Daniel and his generation face the huge challenges and also the huge opportunities ahead of them at this threshold moment in the history of our beautiful planet.
I thank you for your attention.
(Applause)
We're all used to the traditional operators like addition and subtraction and multiplication and division, and we've seen there's multiple ways to represent this but what we are going to do in this video is a little bit of fun.
We are actually going to define our own operators.
And what's neat about this it kind of shows how broad mathematics can be.
And in a more practical sense it is something that you actually might see on some standardized test.
And the reason why they do that is so that you can appreciate that these are not the only operators out there, plus exponentiation and all those, that in mathematics you can define whole new set of operators.
Let's just do that.
So let me just define x diamond x diamond y and I'm going to define that as
I'm just gonna define that as 5x minus y.
So you could view this kind of defining a function but we are defining it using an operator so if i have x diamond y by definition we've defined this operator, that means that's going to be equal to 5x minus y.
So given that definition, what would-what would 7 diamond 11 be?
Well, you just go to the definition.
7 diamond 11 for instead of a x we have 7, so it's going to be 5 times 7.
Just let me do 5 times 7 minus, and instead of a y, we have an 11.
So one way to think about it is every--in our definition every place you saw a x you can replace with 7 and every place you saw y, you replace with 11.
So you have minus 11 over here. So this is the 7 This 7 is this 7 and this 11--this 11 is this 11 right over here.
And then we just evaluate that.
So 5 times 7 is 35,
So this is equal to 35, minus 11, which is equal to 24
So 7 star--or not, this isn't a star--7 diamond 11 is equal to 24.
We can define other things.
We can define something crazy like--let me define a--well I mentioned a star, let me use a star a star-- a -- write it this way a star b--let's say that is the same thing as-- I don't know a over a plus b.
What would, 5 star --5 star 6 be?
Well you go back to the definition.
By definition every place you see a you would now replace with 5 every time you'd see b, you'd now replace with 6 this is going to be equal to 5 over 5 plus 6 a plus b a is 5, b is 6 over 5 plus 6 so this would be 5/11 5/11.
And then you can compound them.
We haven't defined and order of operations for these particular operations we just have defined.
So we are going to be careful to use parentheses when we do, when we put some of these together.
But you could do something like, something interesting
like -1 diamond--negative 1 diamond 0 star--0 star 5 and once again we just focus on parentheses, because that is the only thing that is telling us what to start on first because we haven't, we haven't figured out we haven't defined whether diamond takes precedence over star or star takes precedence over diamond.
The way we have that thing saying hey, you do multiplication before you do addition we haven't defined it for those operations.
But that's what parentheses help us do.
So we want to evaluate the parentheses first.
0 star 5, that is 0, because so now this you can zero as the a and the 5 as the b this is going to be 0 over 0 plus 5.
Over 0 plus 5. which is just going to be 0. So this is just goes to 0.
So this whole expression simplifies to negative 1 diamond this diamond right over here diamond 0.
Well that's five times first, the first number in our operator. The first term we are giving the operator I guess you can think of it that way.
So 5 times that, so that will be 5 times negative 1 x is negative 1 minus y.
Well y here is the zero.
Minus 0
So 5 times negative 1. 5 times negative 1 is negative 5
And you will see and the idea is just to make you feel comfortable defining new operators like this, and not feel being daunted if you all of a sudden see a diamond.
And they are defined the diamond for you and you are like you never saw a diamond. They are actually defining it for you
So you shouldn't say I never saw a diamond.
You'll just say, oh well they have defined diamond for me this is how I use that operator.
And sometimes you'll see even wackier things.
You'll see things like, let me draw
So they'll define. So this is, I don't know if you'd even consider this as an operator. By definiton, if somebody writes a symbol like this and they put an a b c--let me write this way a, b, c, d.
They'll say this is the same thing as ad minus b, all of that over c.
And once again, this is just a definition.
They have this weird symbolic way of representing these variables but they are just defining how (do) you evaluate this crazy expression.
And so if someone were to give you, say evaluate this diamond evaluate this diamond--let me evaluate the diamond so evaluate the diamond where in my little sections of the diamond I have a negative 1, a five, a three and a two.
And we would just use the definition of how we evaluate the diamond.
And we'd say every time we see an a, we say that's negative 1 so we have negative 1 times d, well d.
Well d is whatever is in the bottom right section of this diamond or this kite. So d is going to be 2.
Let me write this this way.
This is a.
This is b.
This is c. and this is d.
So this is going to be negative 1 times 2, minus b
Well b is 5 minus five all of that over c, which is 3.
So this is going to be equal to negative 2 minus 5.
So that is negative 7. Negative 7 over 3.
And you can go crazy like this. And it might be a fun thing actually if you have some spare time.
Define your own operators and see how creative you can be with those operators.
Show 109% by shading.
So just as a bit of review, 109% if we were to write it out, would literally be 109 percent, which is the same thing as 109 per-- and I could write cent again, but that's getting old.
If you had 100 per 100, you're dealing with the whole, but now we have more than a whole.
We have 109 per 100.
We can actually write this as a ratio, or as a fraction.
This is the same thing as 109 per 100.
It's the the same thing as 109/100.
So let's shade that in.
So we have a whole here, so we could consider this square a whole.
In the last video, we counted.
This is a 10 by 10 square.
It is cut up into 100 pieces.
So if we want 109 of those 100 pieces, what are we talking about?
That means we're going to shade in all of the 100 right over here.
Let me do that in a new color.
So we'll shade in all of this.
That would be 100/100, or 100 per 100, or 100%.
I think you're getting the meaning of all of this.
I don't just want you just memorize this stuff.
This really just means 100 out of 100, or a whole.
And you can see that this is the whole square.
That's 100 out of 100 right there.
The question is saying show us 109% by shading.
We already did 100 per 100, but we need to do another 9, so let's shade in another 9.
So now we have one, two, three, four, five, six, seven, eight, nine.
So this piece right here, you could almost view that is-- well, that is!
That is 9% of an entire square.
This is 100% of an entire square.
If you considered this whole thing plus this blue area right over here, you are talking about 109% of one whole square.
Hopefully, that made sense.
In this video, I really wanted to introduce you to some terminology for some basic angle types and terminology.
I wanted to introduce you to are acute angles, right angles, and obtuse angles.
I think when we go through these, it will be pretty self-explanatory.
And an acute angle is an angle -- let me just draw them first then you might, you might, it might start to make sense.
So an acute angle will look something like that.
I draw two rays coming from a common point.
I could also -- so the acute angle could be this angle right over here.
I could also draw an acute angle; maybe an angle that is formed from an intersection of two lines, so this angle would be acute, and so will this angle.
They're both acute angles.
We are going to see acute angles as ones that are -- that since I haven't defined right angles yet.
They are narrower, so we are going to see that they are smaller than right angles.
Right angles are when the rays or the lines are going, oh I guess, I don't want to use the word "right" in my definition.
They are kind of if one is going horizontal then the other one will be going vertical. so let me draw with rays first so the right angle this one is going from the left to the right and the other ray is going from the bottom to the top this angle right over here is a right angle and I could label it like that but as a traditional angle but the general, the general convention for labeling right angles is to put a little, a kind of a half of a box over there.
That tells me that this is a right angle or, that if this is going left to right this is going perfectly top to bottom that this is a no way kind of that this is a completely, I guess the best way to think about it why it's called right is that this ray is completely upright compared to this ray over here let me draw with some lines if I have one line like this and I have another line like that a right angle over here actually all of these would have to be right angles it would mean that this line is completely, if this line were the ground, this line is completely upright relative to this line over here. so either these, so that is what a right angle means so now that we defined right angle
I can give you another definition for acute angle so an acute angle has a measure or it's smaller than a right angle so you learn about radients and degrees which are different ways to measure angles so you'll see that a right angle can be measured as 90 degrees this over here is less than 90 degrees so this is less than 90 degrees. and one way to conceptualize this is that this angle, it's opening is smaller it's more narrow, it's lines are, you would have to rotate one line less to get to the other line then you would over here. here, you would have to move all the way over there here you only have to move it a little bit so the acute angle is less than a right angle so you might imagine already what an obtuse angle is it is greater than a right angle so let me draw a couple of examples of obtuse angles so an obtuse angle might look like let me get it a little clearer might look like that if it was a right angle, then this line over here would be, would look something like that it would be completely upright relative to this, if this were the ground. but we don't see that this orange ray over here is actually opened out wider it's opened up wider so it is obtuse. it is obtuse so this kind of comes from the actual everyday meaning acute means very sharp or very sensitive obtuse means not very sharp or not very sensitive. you could imagine this looks like a sharp point or it's, it's not opening up much. so maybe it's more sensitive to you know, relative to other things
It won't be able to notice things that are small or maybe that is not an appropriate analogy but one way to think about it it's kind of open up wider, or it's bigger than a right angle it's larger than 90 degrees
larger than 90 degrees if you measure it you would have to rotate this ray more to get to this other ray than you would if you had right angles and definitively a lot more if they were acute angles.
If I were to draw this with lines, which of the angles are obtuse and which are acute?
Well the way I drawn them right over here, these two over here are acute are acute and then these over here are going to be obtuse so this one and this one these are both obtuse angles and I actually drew them up here as well.
This one and this one are going to be obtuse so very simple idea if one line or if one ray is relative to the other one is straight up and down versus left to the right or is completely upright then we're talking about a right angle if they are closer to each other if you had to rotate them less you're talking about a acute angle if you had to rotate them more you are talking about an obtuse angle and I think if you look at them visually it's pretty easy to pick out
We are told that triangle ABC has perimeter p and inradius r and then they want us to find the area of ABC in terms of p and r so we know that perimeters are just the sum of the sides of the triangle or how long of length will have to be if you wanna to go around the triangle and let's just remind ourselves what the inradius is if we take the angle bisectors of each of these vertexes each of these angles right over here so bisectors that right over there and then bisector that right over there this angle is going to be equal to that angle this angle is going to be equal to that angle and then this angle is going to be equal to that angle there and the point where those angle bisectors intersect that right over there is our incenter and it is equal distant from all of the three sides and the distance from those sides that's the inradius so let me draw the inradius so when you find the distance between the point and the line you wanna drop a perpendicular so this length right over here is the inradius this length right over here is the inradius and this length right over here is the inradius and if you want you could draw a incircle here with the center at the incenter and with the radius r and that circle would look something like this we don't have to actually draw for this problem so you could draw a circle that looks something like that then we call that the incircle so let's think about how we can find the area here especially in terms of this inradius well the cool thing about the inradius is this it looks like the altitude well this looks like the altitude for this triangle right over here triangle A let's label the center let's call it I for incenter so r is this r right over here is the altitude of triangle AlC this r is the altitude of triangle BlC and this r which we didn't label that r right over there is the altitude of triangle AlB and so we could find the area of each of those triangles in terms of both r and their basis maybe if we sum up the area of all the triangles we can get something in terms of our perimeter and our inradius so let's just try to do this so the area of the entire triangle the area of ABC is going to be equal to and I will color code this this is going to be equal to the area of AlC so that's what I am shading here in magenta is going to be euqal to the area of AlC plus the area of BlC which is this triangle right over here
I will show you that in a different color I have already used blue so let me do that in orange plus the area of BlC so that's this area right over here so plus the area of BlC and then finally plus the area
I will do this in let's see I will use this pink color plus the area of AlB that is the area AlB take the sum of the areas of these three triangles you've got the area of the larger triangle
Now AlC the area of AlC is going to be equal to one half base times height so this is going to be one half the basis of the length of AC one half AC times the height times this altitude right over here which is just going to be r times r that's the area of AlC and then the area of BlC is going to be one half the base which is BC times a height which is r and then plus the area of AlB this one right over here is going to be one half the base which is the length of the side AB
AB times a height which is oneeagain r and over here we can fetch out one half r for all of these terms and you get one half r times AC plus BC plus AB and I think you see where this is going plus that's the different shade of pink plus AB
Now what is AC plus BC plus AB well that's going to be the perimeter p if you just take the sum of the sides that is the perimeter of p and it looks like we are done the area of our triangle of ABC is equal to one half times r times the perimeter which is kind of a neat result one half times the inradius times the perimeter of the triangle or sometimes we will see it written like this is equal to r times p over s oh sorry p over 2 and this term right over here the perimeter divided by 2 is sometimes called semi perimeter and sometimes it is denoted by s so sometimes you will see the area is equal to r times s where s is the semi perimeter it's the perimeter divided by 2
I firstly like this way a little bit more because I remember that p is the perimeter this is useful because obviously now if someone gives you inradius and a perimeter you can figure out the area of a triangle or someone gives you the area of the triangle and the perimeter you can get the inradius of it if given any two of these variables you can always get the third so for example if someone if this was a triangle right over here which is the most famous of the right triangles if I have a triangle that has length 3 4 and 5 we know this is a right triangle you can verify this from the pythagorean theorem and someone says what is the inradius of this triangle right over here well we can figure out the area pretty easily we know that this is a right triangle 3 squared plus 4 squared is equal to 5 squared so the area is going to be equal to 3 times 4 times one half so 3 times 4 times one half is 6 and the perimeter here is going to be equal to 3 plus 4 which is 7 plus 5 is 12 and so we have the area so let's write this the area is equal to one half times the inradius times the perimeter so here we have 12 is equal to one half times the inradius times the perimeter so we have oh sorry we have 6 let me write this the area 6 6 is equal to one half times the inradius times 12 and so in this situation one half times 12 is 6 6 is equal to 6r divide both sides by 6 you get r is equal to 1 so if you want to draw the inradius for this one which is kind of a neat result so let me draw some angle bisectors here this 3-4-5 right triangle has inradius of 1 so this distance equals this distance which is equal to this distance which is equal to 1 just kind of a neat result
We're asked to add 4/9 and 11/12 and to write our answer as a mixed number, and then simplify and write our answer as a mixed number.
So here we have two fractions we're adding together, but we have different denominators.
So whenever you add fractions, the first thing you have to do is check the denominators.
If they're the same, you can add, but if they're different
like this, you have to make them have the same denominator.
So what we have to do is find a number that both 9 and 12 will divide into, and that will be our common denominator, and you'll see why both 9 and 12 have to divide into it.
So let's think about what that number is, and there's two ways of coming up with that what we could call a least common multiple, the smallest multiple of both 9 and 12 that is common.
One way is just to kind of look at the multiples of 9 and see if any of them are divisible by 12.
So if you start with 9-- we can do it over here. So you have 9, that's not divisible by 12.
18 isn't divisible by 12.
27 isn't divisible by 12.
36, well, that is divisible by 12.
That is 12 times 3.
So 9 goes into 36 and 12 goes into 36.
So what we want to do is write a common denominator.
So we're going to write 4/9 as something over 36, and we're going to write 11/12 as something over 36.
Now, to turn your 9 into a 36, you have to multiply it by 4, right?
9 times 4 is equal to 36.
Now, you can't just multiply the denominator by 4.
You also have to multiply the numerator by the same thing.
So if you multiply the numerator by 4, you get 4 times 4 is 16.
So 4/9 is the exact same thing as 16/36.
If you wanted to simplify this one to 4/9, you divide the numerator and the denominator by 4.
Now, we do the same thing over here.
36, 12 times 3, so we're multiplying 12 by 3 to get 36.
Well, if we did that to the denominator, we also have to do that to the numerator, so 11 times 3 is 33.
And just like that, we've now rewritten each of the fractions so that they have the same denominator.
Both of their denominators is 36.
So now we're ready to add.
If you add these two things, we'll have 36, because we're considering kind of parts of 36 or fractions of 36, and then we have 16 plus 33 in the numerator.
Let me write that down.
16 plus 33 in the numerator.
And 16 plus 33 is what?
6 plus 33 would be 39 and then you have another 10, so it's 49.
So it's equal to 49/36.
Now, can we simplify this?
49, it's 7 squared, so it has 1, 7 and 49 as factors.
This has 1-- it has a bunch of numbers, but it's not divisible by 7, so this is actually in simplest form, but this is an improper fraction.
The numerator is larger than the denominator.
So let's write it as a proper fraction.
To do that, we divide 36 into 49.
36 goes into 49 how many times?
Well, it only goes one time, so it equals 1.
And how much will be left over?
If I divide 36 into 49 one time, or 1 times 36 is 36, then I have 13 left over to get to 49.
So it's 1 and 13/36.
And you can do that manually, if you like you.
You'd say 36 into 49.
36 goes into 49 one time.
1 times 36 is 36, and then you subtract.
9 minus 6 is 3.
4 minus 3 is 1.
You have a remainder of 13.
So that's our answer:
1 and 13/36.
Up until now, I haven't heard, I've never known what is Frog.
All I know was Frog is "katak" (malay translation of frog).
On November 2012, we were invited to attend the Frog VLE training at the Teachers Activity Center.
It only took me 3 days to create and complete the school dashboard.
We were also invited to attend another Frog training.
I have thought about having an in-school Frog VLE training, and the first thing we did was, we printed out the students
IDs and their parents' IDs and as well as the teachers'.
In March, we have held another in-school training, specially for the trainers.
Moving forward, these trainers will hold another training for the teachers in their respective departments.
When the teachers adapted to Frog VLE, they will then continue to train the students on how to use it.
In the school dashboard, I have created different tabs, for example the main page, administration and also the external links.
The thing I like about Frog is, it is very user friendly.
It is very easy to use, when I'm giving out tasks to my students, the widget I like to use the most is 'Text Activity'.
It is very easy for me to check, and I don't need to be carrying a bunch of activity books around.
For the school admins out there, happy Froggying!
Don't be afraid when you are called to attend the Frog VLE training.
Use the Frog VLE as much as you can.
If we can explore our Facebook everyday, why don't we explore the Frog VLE as well.
We're asked to sort the following units of measurement into two categories: U.S. customary units and metric units.
So these are just two different systems.
You'll get more and more familiar with them.
Then indicate whether each unit measures length, weight, mass, or volume.
So the liter is a metric unit.
You would use it in the metric system.
A gallon is a U.S. customary unit.
We've been dealing with that. If you fill your gasoline in Europe, you're going to be filling it in terms of liters.
In the U.S., you're going to be filling it in terms of gallons.
And we're going to talk about whether they're units of volume and whatnot in a little bit.
Decigram, that is metric system.
In general, whenever you see these prefixes, deci, centi, kilo, you're dealing with the metric system.
Same thing, millimeter. This is metric system.
A gram is metric system.
Meter is metric system.
The foot is a U.S. customary unit.
We'll talk about whether it's distance or any of that in a little bit.
Kilogram, once again, it is metric units.
In case you haven't gotten what I'm doing here, blue for metric, red for U.S. customary units, or I guess magenta.
Centiliter, that is metric.
Centimeter, meters are metric.
And notice we have the prefix in both cases.
Centi means 1/100.
Cup, that is U.S. customary units.
Cup, U.S. customary units.
Meter, that is the metric system.
Pound, U.S. customary units.
Inch, same thing, that's what we use in the U.S. Ounce, we use that in the U.S. And then the yard, we also use that in the U.S.
Now we've divided them up.
All the magenta ones are used in the U.S. All of the blue ones are used really in the rest of the world, and actually some places in the U.S. as well.
I think a lot of the world is frustrated that the U.S., that we're not all converted to this because the metric system is actually a little bit more logical.
It's easy to just figure out what it's saying, and we'll deal with that in more detail in the future.
Now the next thing we to figure out is whether something is a measure of length, weight/mass-- and they're not exactly the same thing.
Mass is how much of a substance you have.
Weight is how much force with which gravity is pulling on that mass.
And it would change depending on what planet you're on.
And then you have volume, or how much space something takes up.
So this is distance.
This is moving in one dimension.
Mass is how much stuff there is.
Weight is how much the force that stuff is pulled on, on a planet, by gravity, or I guess a star anywhere.
And volume is how much space does that stuff take up.
Now let's think about it.
Liter is volume.
This right here is volume.
How much space do you take up.
Gallon is also volume.
That's in the U.S. and in Europe, or in the metric system, it would be a liter.
That's a gram.
Gram is a unit of mass.
So decigram just means 1/10 of a gram.
Millimeter.
Meter is a unit.
Meter right here, that is the unit of distance or of length.
Millimeter, milli means 1/1,000 of a meter.
Foot, that is also a unit of length.
Kilogram, that just means 1,000 grams.
Kilo means a thousand.
Gram, we already said, is a unit of mass.
Centiliter, that means 1/100 of a liter.
Liter, we already figured out, is a unit of volume.
Centimeter, we already figured out.
Meter is a unit of length.
Centimeter means 1/100 of a meter.
So this is a unit of length.
Cup, we've seen multiple times already.
It is a unit of volume, how much space does something take up.
Meter, that is length.
Pound, that is actually a unit of weight.
An inch is a unit of length.
An ounce-- you have to be careful here-- if someone just has an ounce, that is 1/16 of a pound.
It as a unit of weight.
If it was written fluid ounce, then we'd be talking about 1/16 of a pint, and then it would be a unit of volume.
But since it's just ounce, it's a unit of weight, 1/16 of a pound.
And then finally, a yard is a unit of length.
And we are done.
Let's work through another few senarios involving displacement, velocity and time or distance, rate and time. So over here we have Ben is running at a constant velocity of 3m/s to the east, three meters per second to the east and this is a review, this is a vector quanity they are giving us the magnitude and the direction, if they just said three meters per second then that would just be speed, this is the magnitude its 3m/s and it is to the east and they are giving us the direction so this is a vector quantity that's why it's velocity instead of speed.
I will do it both with the vector version and maybe they should say how long it will take it to travel 720 meters to the east. Make sure that I make it clear that it is a vector quantity because displacement suppose to distance We will do it both ways.
Some time people will write a triangle or delta there for change in time. That\'s explicitly ment when you just write over time like that.
So rate or speed is equal to distance divided by time, now if you know they're giving us in this problem, they're giving us the rate, if we think about the scaler part of it they're giving us the rate, they're telling us that is 3m/s they're also telling us the time, or sorry they're not telling us the time, they're telling us the distance and they want us to figure out the time.
So we have, if we just do the scalar version we're not dealing with velocity and displacement, we're dealing with rate or speed and distance.
So we can algebracially manipulate this, we muiltiply both sides by time right over there.
And then we could take this once step at a time, so 3m/s times time is equal to 720 meters.
And that makes sense at least units wise because time is going to be in seconds and it cancels out with the seconds in the denominator so you will just get meters so that just makes sense there.
So if you want to solve for time you can divide both sides by 3m/s and then on the left side they cancel out on the right hand side this is going to be equal to720 divided by 3 times meters then m/s of the denominator, if you bring it out to the numerator you take the inverse of it so that's m, meters was on top, so 720 meters and now you're dividing by m/s and that's the same thing as multiplying by the inverse times s/m and so what you're going to get here the meters are going to get 720 divided by three seconds so what is that, 720 divided by 3, 72 divided by 3 is 24, so this is going to 240 this part riight over is going to be 240. It's going to be 240 seconds, that's the only unit we're left with.
On the left hand side we just had the time, so the time is 240 seconds.
Sometimes you'll see it and just to show you know in some physics classes they show all these formulas, one thing i really want you to understand as we go through this this journey together is that all those formulas are really algebraic minupulations of each other.
You really shouldn't memorize any of them you should always, hey that's just manipulating one of those other formulas that i got before.
One of those, even these formulas are only reasonably common sense. So you can start from very common sense things rate as distance divided by time and then just manipulate it to get other common sense things so we could've done it here.
We could've multiplied both sides by time before we
So, checkers is an interesting game.
Here's the typical board of the game of checkers.
Your pieces might look like this, and your opponent's pieces might look like this.
And apart from some very cryptic rules in checkers, which I won't really discuss here, the board basically tells you everything there is to know about checkers, so it's clearly fully observable.
It is deterministic because your move and your opponent's move very clearly affect the state of the board in ways that have absolutely no stochasticity.
It is also discrete because there's finitely many action choices and finitely many board positions, and obviously, it is adversarial, since your opponent is out to get you.
Use the quadratic formula to solve the equation, negative x squared plus 8x is equal to 1.
Now, in order to really use the quadratic equation, or to figure out what our a's, b's and c's are, we have to have our equation in the form, ax squared plus bx plus c is equal to 0.
And then, if we know our a's, b's, and c's, we will say that the solutions to this equation are x is equal to negative b plus or minus the square root of b squared minus 4ac-- all of that over 2a.
So the first thing we have to do for this equation right here is to put it in this form.
And on one side of this equation, we have a negative x squared plus 8x, so that looks like the first two terms.
But our constant is on the other side.
So let's get the constant on the left hand side and get a 0 here on the right hand side.
So let's subtract 1 from both sides of this equation.
The left hand side of the equation will become negative x squared plus 8x minus 1.
And then the right hand side, 1 minus 1 is 0.
Now we have it in that form.
We have ax squared a is negative 1.
Negative x squared is the same thing as negative 1x squared. b is equal to 8.
So b is equal to 8, that's the 8 right there.
And c is equal to negative 1.
So now we can just apply the quadratic formula.
The solutions to this equation are x is equal to negative b.
Plus or minus the square root of b squared, of 8 squared, minus 4ac-- let me do it in that green color --minus 4, the green is the part of the formula.
The colored parts are the things that we're substituting into the formula.
Minus 4 times a, which is negative 1, times negative 1, times c, which is also negative 1.
And then all of that-- let me extend the square root sign a
little bit further --all of that is going to be over 2 times a.
In this case a is negative 1.
So let's simplify this.
So this becomes negative 8, this is negative 8, plus or minus the square root of 8 squared is 64.
And then you have a negative 1 times a negative 1, these just cancel out just to be a 1.
So it's 64 minus is 4.
That's just that 4 over there.
All of that over negative 2.
So this is equal to negative 8 plus or minus the square root of 60.
And let's see if we can simplify the radical expression here, the square root of 60.
Let's see, 60 is equal to 2 times 30.
30 is equal to 2 times 15.
And then 15 is 3 times 5.
So we do have a perfect square here.
It is 2 times 2 times 15, or 4 times 15.
So we could write, the square root of 60 is equal to the square root of 4 times the square root of 15, right?
The square root of 4 times the square root of 15, that's what 60 is.
4 times 15.
And so this is equal to-- square root of 4 is 2 times the square of 15.
So we can rewrite this expression, right here, as being equal to negative 8 plus or minus 2 times the square root of 15, all of that over negative 2.
So we have negative 8 divided by negative 2, which is positive 4.
So let me write it over here.
Negative 8 divided by negative 2 is positive 4.
Plus or minus 2 divided by negative 2.
And really what we have here is 2 expressions.
But if we're plus 2 and we divide by negative 2, it will be negative 1.
And if we take negative 2 and divide by negative 2, we're going to have positive 1.
Minus or plus 2 times the square root of 15.
Or another way to view it is that the two solutions here are 4 minus two roots of 15, and 4 plus two roots of 15.
These are both values of x that'll satisfy this equation.
And if this confuses you, what I did, turning a plus or minus into minus plus.
I could write this expression up here as two expressions.
That's what the plus or minus really is.
There's a negative 8 plus 2 roots of 15 over negative 2.
And then there's a negative 8 minus 2 roots of 15 over negative 2.
This one simplifies to-- negative 8 divided by negative 2 is 4.
2 divided by negative 2 is negative 1.
2 times a 4 minus the square root of 15.
And then over here you have negative 8 divided by negative 2, which is 4.
And then negative 2 divided by negative 2, which is plus the square of 15.
And I just realized I made a mistake up here.
When we're dividing a 2 divided by negative 2, we don't have this 2 over here.
This is just a plus or minus the root of 15.
So this is minus the square root of 15. And this is plus the square root of 15.
The two solutions could be 4 minus the square root of 15, or x, or and, x could be 4 plus the square root of 15.
Either of those values of x will satisfy this original quadratic equation.
Migrant Worker Exploitation
My name is Cuseti.
I used to be a migrant worker.
I had worked in Jordan and Taiwan.
I went to Jordan in 2006 and came back home at the end of 2008.
I worked in Jordan for two years, where I was working 24 hours a day.
Actually, there was document forgery before I went (to Jordan).
Because I was still under-aged, my age was falsified.
The sponsor (agent) took care of that.
Then I left for Jordan.
Thank God everything went well, because at that time the regulation was not as strict.
There were a lot of violations by the government.
So, it was not hard to forge documents.
I was working in Amman, Jordan for two years.
I was taking care of a baby, cleaning the house and also cooking.
Working in Saudi, just like in other Middle Eastern countries, we had to standby for 24 hours a day.
It's a common practice there.
I could say that I did not have the freedom to communicate with my family while I was there.
My salary was only $100, or equal to 900 thousand Rupiah at that time.
Come to think about it, I just succumbed rather than being abused.
I was tired from begging for mercy.
I wasn't being treated as human being.
But as a slave instead.
So I thought it would be better for me to go home rather than stay (in Jordan) and get abused.
Finally, after two years I went back home.
My boss said because they have to take in another maid, I had to pay for my own expenses to return home.
I paid for my own ticket and it cost me my five months salary.
But well, it was better than feeling the way I felt.
I could not take it anymore.
The work was just too much.
I had to take care of everything, the house and the kid.
And the kids there, unlike kids in here, they didn't want to listen to us.
So after two years of working, I went back home. Took some time off at home and then signed up to go to Taiwan.
I was working as domestic worker too, but I took care of an old woman.
That was my main job.
But after I finished taking care of the old woman, I did the house chores and cooked.
In Taiwan, I worked from 5:30 am to 7 pm.
Even If there were guests coming at 7 pm, I did not have to do anything.
Work was done by 7 pm, but I did not go anywhere.
I did not have a place to stay outside the house.
I stayed (in the boss's house) and took care of the grandmother.
The Struggle of a Mother
What was your experience working abroad as migrant worker?
I worked in Saudi Arabia, in Riyadh.
I worked there for 14 months.
Then I got sick.
I asked to go home.
When I told my boss, they asked me:
"Why don't you want to work?"
I replied:
'I am sick."
Then I was taken to the hospital.
The doctor said I should rest.
But I could not rest well.
So, I got sick again.
I asked my boss to send me home.
"I want to go home."
"If you don't have money to pay for my ticket, I'll use my own money."
I also asked to be sent back to the (sponsor/agent) office.
Then my boss's female relative came with her husband
I insisted to go home.
But he (the boss' relative) also insisted I stay.
When I was going to the toilet,
He pulled me.
He dragged me.
He strangled my neck.
He dragged me down the stairs.
My whole body hurt and my clothes were ripped.
I begged for help from my boss.
And my boss said:
"Stop, don't do that to her."
"She'll die," my boss said.
But the person who was torturing me said:
"Stay away. Let her die."
Then I was slapped in the face.
After that, I was taken to Mubaroqh's (boss' relative) house.
When we got there, he stripped me naked.
All my clothes were taken off and he asked:
"What do you bring?
What do you bring?"
I replied, " I haven't brought anything.
I've only brought the clothes I am wearing."
And he let me wear my clothes again.
For two months I was wearing ripped clothes.
And for two weeks I was not allowed to drink clean water.
I worked as a migrant worker driven by economic factors.
I had a dream of sending my kids to school.
And because I did not have money, and there was no job opportunities here.
I also only finished Elementary School.
So, I had no other choice than to be a migrant worker.
Yes.
Because I saw that my neighbors who went abroad they all returned successful.
So it struck my mind to try my luck.
Who knows, that if by becoming a migrant worker I could be as successful as they were?
But in reality, my fate was different from that of my neighbors.
My fate was unfortunate,
and full of difficulty How did you deal with your problems when working abroad?
At that time, I tried to report to the Indonesian Embassy. And I also insisted to go home.
And if they refused to send me home, I would have still gone home
And I would have still filed a report
So finally my boss allowed me to go home.
I also kept resisting.
I said to my boss that I am also a human being.
I did not want to be treated like an animal.
I chose to go home rather than to be treated like an animal.
I didn't care whether I could bring money home or not.
I just wanted to go home.
The most important thing was for me to be free from the abuse Do you still have the desire to work abroad?
No, because I don't want to experience what I experienced before.
I am trying to open a small business here, making cassava chips.
Besides making cassava chips I also want to run a small stall.
Hopefully in the future I could expand my business bit by bit.
And hopefully I can send my kids to school like any other kids.
The love of a mother... to me... unconditionally till the end of time... only giving... without expecting anything in return... like the sun lighting the whole world...
we're used to seeing things from a particular point of view that is from a particular frame of reference and things look different to us under different circumstances at the moment
you look to queue here you're upside down you're the ones upside down no europe turns out well not he's the one that's upside down his name well let's talk for a
hi you lose people want to really up that that you better come into my frame of reference now
frame of reference was inverted from what it usually is that view of things would be normal for me if i normally walk to my friends this represents a frame of reference just three route that together so that peace is at right angles to the other two now i'm going to move in this direction if either plane at the same spot on your screen but you know i'm moving that way because you see the wall moving that way behind me but how do you know that i'm not that i think bill and the wall moving workable now the wallet that the pier and you have no way of telling whether imovie or not but now you know that i'm moving the point of it is that all motions it's relative in both cases i was moving relative to the wall and the wall with moving relative to me all motion is relative but we tend to think of one thing is being fixed and the other thing has been moving we usually think of the earth inspect and walls are usually pick to beer so perhaps you were the part of the first time when it was the wallet was moving and not doctor whom a frame of reference text of the earth is the most common frame of reference in which to observe the motion of other things that is the frame of reference that you're used to the framers baton to the table the table is bolted to the floor the florida anchored in the building and the building at firmly attached to the earth of course the reason for having three rods if the position uh... any object such as this fall can be specified using these three reference line this reference line points in the direction which we called up two different directions here than it is on the other side of the air and these two reference lines specify a plane which we call horizontal or level in this film we're going to look at the motion of object in this third frame of reference and other frames of reference moving in different ways relative to the other frame well let's look at a motion this field ball can be held are by the electra mode no i'm going to open the switch and you watch the motions of the ball the ball is accelerated straight down by gravity along the line parallel to this vertical reference blood as you can see the electromagnetic mounted on the cockpit can move i'm going to do exactly the same experiment the doc resume did but this time while a cart is moving at a constant velocity is pulled along by spring which is longer on this photograph turntable and that hold that with a constant velocity when the car passes this line be lol this week that you can see i'm going to start the cart down at the end of the table so that by the time it gets to this point by can be sure it's moving with a constant velocity i want you to watch right here so that you will see the ball falling
i think you can see that the ball landed in exactly the same position of the did before when doctor whom did the experiment with the car text but this time the ball could not have fallen straight down let me show you off the ball was released at that point if it had fallen straight down because the cart moves on in the time to take the fall would have landed back here somewhere but it didn't wanted to do the experiment again best time i'm going to let you watch the motion through slow-motion camera which is fixed the cart moves by the ball will fall and you can watch a missile which the camera
how true this again first-time there'll be a line on the film so if you can see the fat repeatedly complete but the problem all to the ground all of this has been in a frame of reference fixed to the year all of this motion locked in a frame of reference which was moving along with the car frame of reference like that well so that you can see what it looks like i'm going through solution camera so that it was with the car permittivity experiment again incidently i started and the number to stand here when the ball for all of you will have something which is fixed as a reference point
in their moving frame of reference i think you can see but the problem all as a political straight line it looks exactly the same as the day before when doctor whom did the experiment with the car etc if we were moving along in this frame of reference and we couldn't see the surroundings then we wouldn't be able to tell by this experiment that we were moving at a constant velocity as a matter of fact we wouldn't be able to tell by any experiment that we were moving at a constant velocity i'm gonna do the experiment once more and this time i'm not going to stand here behind the ball at the fall so that you won't have any fixed repertoire
as far as you're concerned that time the karke wasn't necessarily moving at all that time when you couldn't see the background then i think perhaps it was harder for you to realize that you were in moving frame of reference important thing to realize here all frames of reference moving at constant velocity with respect to one another are equivalent doctor ivy showed you but the motion of the ball that was released from the moving karte
looked like in the current frame of reference and in the car frame the motion looks simpler from a car now i want you to watch the motion white spot would probably be the clock moving out circle
but that is what it's practiced actually like in the hurt of reference this is your normal frame of reference you father thought moving in the circle because you're high moved along with the car you put yourself in the frame of reference of the moving truck so if it isn't always true that we view motion from the third frame of reference when the motion is simpler from the moving frame you automatically put yourself and not moving frame now we're going to do another experiment on a relative motion to show how the compare the block today of an object in one printer records to explore all serbian another frame of reference forgiveness drive a spark a certain stark it moves a straight across the table with a speed which is essentially constant because the forces of friction of the made very small this is just the law of inertia an object moves the constant velocity unless an unbalanced force acts on it how you get the same start backwards uh... dougherty and gives it the same started moves back in this direction with the same philosophy now we're on a car here a car which can move in which were you going to move in this direction and we're going to repeat the experiment all right let's go
if we were making measurements here then we would observe the same but lots of these that is the same experimental results that we did before and so would you because you are observing this experiment through with the camera which is fast into this car added you were in the moving frame of reference but now we're going to do the experiment again and this time you watched through a camera which is fixed in the poor frame of reference or concentrate on watching the clock to lecture i follow us i think you'll see that in a move faster that way and not so bad this way relative to u_n_ relative to the wall husband
here the car which was moving along in this direction with the velocity we were thinking on the card at a table here i am over on the side and uh... doctor doom was on the side and we were pushing back-and-forth on the table well i pushed it and went into this direction with the velocity v when doctor didn't want to do when in this direction the same velocity v but this is the velocity relative to the car what about the velocity relative to an observer on the ground in the picture brain well if it was pushed in this direction it's velocity to you plot being if it's in this direction it will also be used u minded b this is all very reasonable is nothing very hard to understand here the surprising thing about this expression is that it is not actor in all circumstances at very high speed by high speed i mean speeds close to the velocity of light expression breakdown at these very high speed we have to use the ideas about relative motion developed by a albert einstein in his special theory of relativity for all the speed of the we're ever likely to run into this expression you plus or minus the is completely adequate so far we've been talking about frames of reference moving at a constant velocity relative to one another now i'm going to do the experiment with the dropping ball again only that time the karte will be accelerated relative to the earth frame these weight will fall and give the cart a constant acceleration first of all out and then i'll really put the motion is very fast and i want you to watch at the point where the ball is released from the pic camera i don't know whether you thought that are not at the top of the vault with the things that was before for either prime it landed in a different spots this is because the cart kept on accelerating in this direction as the ball was falling now i'm going to let you see it again with the slow-motion camera fixed on to the car
this time you saw the bull moving off to one side falling down the vertical reference line as it did in the constant velocity case but suppose you were in the six telerate a frame of reference how could you explain this gravity is the only force acting on this fall so it should fall straight down but at the law of inertia is to hold there must be a farce pushing sideways on the ball in this direction accorded to deviate from the vertical path but what kind of a force is it it is not gravitational or an electric or nuclear force in fact it is in the force at all as we know what story left to conclude but it gets sensor is no force that could be pushing in this direction on the ball but the law governorship just does not hold this is a strange frame of reference we call a frame of reference in which the law of inertia holes and inertial the law how the nurse or holds in the third frame of reference so it is an inertial frame the car moving at constant velocity relative to the earth is an inertial frame but the car which is expel a rated is not an inertial frame because the frame of reference that we're used to living in is one in which the law of inertia holds when we go into a non inertial
what's happening this time why doesn't the talking straight across the table i did it before how you can see it doesn't if we believe in the law of inertia but we must believe that there is an unbalanced force to change the velocity of the pot but this pope is nearly friction locks so what can be exerting this unbalanced correspondent though that you watched the motion this time through a camera which is fixed in the earth's frame of reference
i think if you concentrate on watching dot papa you can't be that it is a warning is a great time and that therefore there is no i'm not quite acting on it
now we're going to stop this rotation but i can talk to you about what is happening here i don't know about you but i'm busy in d fixed fame of reference there was no one balanced force within the frame of reference for taking in this turntable there was and unbalanced because the velocity kept changing was with the fictitious part rotating plane is unknown inertial or accelerated fame just as the accelerated frame of the karte the doctor humes showed you you know that every object which is moving in a circle has an acceleration toward the center of the circle this is the exploration of has a special namely and capital acceleration now you will this puck for a while workstudy while the turntable is rotating i'll get off theoretic i'm ready but the rotation
you concede that now the park isn't moving in a circle dr humans exerting a force to keep it moving in the circle and you can see this from the fact that the rubber ring is extended heat is exerting the center of the billboards and this is the only horizontal force acting on the part but not let's look at it again from his point of view in the rotating system he is exerting a force towards the center of the table and yet the puck is standing still produced more or less taylor some vibration how he believes in a lot of inertia so he thinks there's and equal parts on the part away from the center of the table so that there is no unbalanced boring this outward force in the pocket the fictitious sports in this case sometimes it's called the centrifugal force in the pics reference frame there is no award boris on the path now suppose the doctor doom stops exerting a barge watch the pot in the picture frame of reference the puck moves off in a straight line there's no no unbalanced boris acting on it now let's look at it again from his point of view in the rotating system when he releases the proc which to him was everest it mood the force away from the sender is now on unbalanced part on the talked to him the outward course on the part is fictitious in our food frame of reference it doesn't think that's but the doctor whom in the accelerated frame of reference it's a perfectly real force i hope by now doctor i do not have convinced you the rotating frame of reference is not in their shel frame for you've all been told that the hurt it's rotating abode of taxes and that also it travels in a nearly circular orbit around the time why then do we find in a frame of reference attached securely to the earth but the law of inertia seems to hold why don't we observed fictitious forces the five of the fictitious forces which we have to introduce in a non initial frame depends upon the acceleration of the frame these smaller the acceleration is v smaller the fictitious forces that we introduced here's a frame of reference attached to the equator of the car the acceleration of this frame is really very small because bearded spinning about it axis it has an acceleration directly inward app three d_ one hundred of a major per second square on they one kilogram at the equator their is the fictitious for us directly upwards out three one hundred but this is not by gravity which is a port downward of nine point eight new so the net downward force is smaller than that of gravity alone if i've dropped av one kilogram at the equator the acceleration would be slightly smaller than that due to gravity alone very much now the acceleration of the car in its orbit is even smaller still and produces even smaller affect in our frame of reference mike said that the earth was rotating abode faxes how do we know but this is slow well if you take a time exposure photograph of the stars they seem to be moving in circles a both p pole star but all motion is relative is there any way of telling which is moving or the stars the fact that it is because which is rotating can be demonstrated by means of the pendulum if i've got a pendulum swinging its wings back-and-forth in a plane though it turns out is this pendulum with the north pole of the art the plane of swing would remain fixed relative to the stars but would rotate relative now i'll have to show you what i need this pendulum is epicenter how this turntable which will represent europe no i was about the cable turning around in this direction i'll put a black arrow on so that you'll remember but the rotation the pendulum is that the north pole of the earth annuals motion as you ordinarily do standing on the earth the playing of swing rotates in the opposite direction from the rotation of the turntable and that exactly the same rate now look at it from the fixed cabral which will represent the frame of the stars the turntable the alert rotate but the plane of the pendulum remain specs a pendulum used for this purpose because approval pendulum use tommy dot wong at the beginning of this film
let's look back again now the focal pendulum dropped slammed as its wings i think you can see the paint line where the planned trail began the amplitude upswing is decreasing the famed trail is not long now but the important thing to speak is that the plane upswing has been rotating during the half hour that we've been talking to you an inertial frame of reference is one in which the alarm inner cities without all frames of reference moving at a constant velocity with respect to an inertial frame are also inertial frame we use the word as an inertial frame of reference but it is only approximately one a small acceleration with respect to the stars for example the frame of reference other stars is the best we can do when we look for a frame of reference which is for all practical purposes bextra accelerated frame of reference is not a member shall frame and when we are in an accelerated frame we have to introduce forces which we called fictitious forces in order that the law of inertia and the other laws of physics don't change
DARUS (Abandoned Widowers)
I had a small business before.
Making bread, sponge cakes and donuts.
I had people who sold my products.
I also had some employees.
Aside from that, I also worked as an administrative staff at SMP (Junior High School) 2, which now has become SMP 2 Balongan.
Tempted with the offer of being granted a visa, right away I went to Al-Masjid al-Ḥarām (The Grand Mosque).
I had imagined what Al-Masjid al-Ḥarām looks like.
I finally signed up by paying a lump sum from selling my land and rice field.
I also left my job at the school.
I signed up in Jakarta and was going back and forth for almost a year.
It cost me a lot of money.
But then the sponsor (agent) ran away.
During that year I was going back and forth between Jakarta and Indramayu.
But the sponsor (agent) disappeared and I was deserted in the (migrant workers) compound with 3-4 other people.
In that uncertain situation with the sponsor disappearing, we all went back home.
Back to the village.
When I got home, I was deeply in debt.
I sold my rice field and borrowed money.
My wife and I discussed about it.
Half-heartedly, my wife had to go abroad (to become a migrant worker) to pay off our debt, that I used to sign up (to go to the Al-Masjid al-Ḥarām).
Also to pay off our previous debts, we pawned off our rice field, borrowed money for my business, borrowed money for our daily needs and for our children's school tuition.
So that they could stay in school.
I failed twice.
First, the plan to go to Al-Masjid al-Ḥarām, and second, to Malaysia.
When I got back home, I had so much burden in my mind.
Then I thought of forming a Depok (traditional cultural) group.
I gathered friends who were left by their wives abroad.
I named it DARUS, which stands for "Duda nggak ada yang ngurus" (Abandoned Widowers).
That's the group's name.
To gather friends who felt left behind (by their wives), we practiced every afternoon.
That was the beginning.
When it started to go well, I changed the name into Putra Millenium.
Thank God for every performance we could get even though I don't have much capital to start the business.
But I can create job opportunities for friends, even if it's only seasonal.
Usually during harvest time.
How many personnel I can bring depends on the request.
Some clients ask for 30 people, some ask for 40 people to perform.
It's dangdut music with someone wearing a large lion costume and 4 people carrying it.
The daughter of the person who hold the celebration sits on top of the lion.
They would go round and round.
One lion needs four men to carry, so if there are four lions, it means we need 16 men.
Not to mention we need men to push the carriage and the singer on the stage.
This is what we call Depok Lion, with the kids of those who hold the celebration, or the neighbors or family members sit on top.
One lion needs four men to carry, so five lions needs 20 men.
The lions would be carried around the neighborhood.
The singer and musicians are on the carriage as well.
Being pushed by some men.
The sound system is put in here.
Around 15 people are on the carriage. We need at least 4-5 men to push the carriage.
This man is one of the managers. The 25 personnel includes the musicians who are in the carriage.
We go around the neighborhood and stop right before the afternoon prayer time.
We stop at the celebration venue around 12 pm, and start again at 1 pm.
But at 1 pm we don't go around anymore, we perform at the venue.
We play different kind of songs, Javanese songs, and also dangdut songs. Many people come and watch. (The fee) depends on how far the location is.
If it is far, in Indramayu for instance, it could be around 2,5 - 3 million Rupiah ($250 - $300).
But if it is only around here, we charge around 2 million Rupiah ($200).
It can provide job opportunity to friends to earn more money.
At least each person get 25 - 30 thousand Rupiah ($2,5 - $3).
If get saweran (donation) from people who watch, then we get more money.
The audience gives money.
Sometimes we can get around 700 thousand - 1 million Rupiah ($70 - $100), and we divide the money equally between all personnel.
Most of the singers are also former migrant workers.
And the personnel are mostly men whose wives have left abroad to be migrant workers.
Quadrilateral ABCD is a rhombus
What they want us to prove is that their diagonals are perpendicular, that AC is perpendicular to BD
Let's think about everything we know about a rhombus
First of all, a rhombus is a special case of a parallelogram
In a parallelogram, the opposite sides are parallel
That side is parallel to that side These 2 sides are parallel
In a rhombus, not only are the opposite sides parallel, but also all the sides have equal length
This side is equal to this side, which is equal to that side, which is equal to that side right over there
There's other interesting things we know about the diagonals of a parallelogram, which we know all rhombi are parallelograms
The other way around is not necessarily true
We know that for any parallelogram, and a rhombus is a parallelogram, that the diagonals bisect each other
For example, let me label this point in the center, point E
We know that AE is going to be equal to EC,
I'll put 2 slashes right over there
We also know that EB is going to be equal to ED
This is all of what we know, when someone just says that ABCD is a rhombus, based on other things that we've proven to ourselves
Now we're gonna prove that AC is perpendicular to BD
An interesting way to prove it, and you can look at it just by eyeballing it, is if we can show that this triangle is congruent to this triangle and that these 2 angles right over here correspond to each other then they have to be the same and they'll be supplementary and they'll be 90 degrees so let's just prove it to ourselves
The first thing we see is we have a side, a side, and a side A side a side and a side
So we can see that triangle, let me write here with a new color,
ABE is congruent to triangle CBE
Once we know that, we know that all the corresponding angles are congruent
In particular, we know that angle AEB is going to be congruent to angle CEB because they are corresponding angles of congruent triangles
This angle right over here is going to be equal to that angle over there
We also that they're supplementary
Let me write it this way
They're congruent and they are supplementary These 2 are gonna have the same measure and they need to add up to 180 degrees
If I have 2 things that are the same thing and add up to 180 degrees, what does that tell me?
That tells me that the measure of angle AEB is equal to the measure of angle CEB which must be equal to 90 degrees
They're the same measure and they're supplementary
This is a right angle and then, this is a right angle
Obviously, this is a right angle
This angle down here is a vertical angle, that's gonna be a right angle
This is a right angle this over here is gonna be a vertical angle
You see the diagonals intersect at a 90 degree angle so we've just proved
This is interesting
A parallelogram, the diagonals bisect each other
For a rhombus, where all the sides are equal, we've shown that not only do they bisect each other but they're perpendicular bisectors of each other
<i>Brought to you by the PKer team @ www.viikii.net</i>
Episode 7
Oh. We meet again.
Is she your girlfriend?
There's no way.
Of course.
Seung Jo, want to come have some tea at the cafe?
No.
I'll go ahead first.
You're home?
Hey.
What?
That girl I saw in front of the classroom earlier...
Yoon Hae Ra?
Her name is Hae Ra?
Is she your senior?
Senior?
Does she look like someone above us?
Then again she is called the Goddess of the freshmen.
Goddess?
Wait, she's the same year as us?!
She entered as the second best in Parang University,
And you were the top student in the whole school.
Someone so amazing...
Why did she come to our school?
Are you being jealous now?
No way!
Jealous?
Why would I be jealous?
Of course you would be,
After all, we did kiss.
Kiss? <i> Ho!
Perhaps, is this going to be the 2nd kiss?
This is just too good to be seen by myself.
I was played again.
To that person, the kiss we had that day meant nothing at all.
It was just a prank!
Come join us! Please join our club!
So what?
You're not really going out with Seung Jo.
Maybe you should just attack him.
What if he hates her even more.
That's hard.
It sure is.
Oh, my! I have to go.
You're not eating with us?
To be honest, I got a job.
A job?
Parang Beauty salon.
The one In front of school.
Really?!
That's great!
That's great.
I don't really know if it's really great or not.
They said I have to crawl up, but I'm trying it out.
So it seems it will be hard for me to keep having lunch with you guys.
I've got to eat up lunch when there aren't any customers around.
You should come over too when you have time.
Yeah.
Then, I'll go off first.
I'm going. Bye.
Have fun!
Fighting!
I can't have lunch with you either.
Why?
The seniors from our major invited the freshmen to lunch.
Then do I have to eat alone?
Sorry.
Oh. I'm coming now.
Yeah.
Go.
I'm sorry Ha Ni.
Sorry.
I'm going.
What's up with this?!
I hate eating alone!
Ah.
Seung Jo, did you eat lunch?
Seung Jo, do you perhaps have no one to eat lunch with?
I'll have chicken cutlet.
Wang Donkas, Chicken Cutlets, Hamburger steak...
You can't think if you don't say it out loud?
You came?
Even if you didn't, I was about to ask you if you wanted to have lunch together.
What are you going to eat?
Donkas?
Hamburger steak please.
Me too.
Can I get a lot of vegetables?
Me too.
Excuse me!
Hasn't there been a mistake?
Yes??
What is the problem??
Hey, Mr. Prodigy, you sure are brave in going against my fair distribution of foods.
Bong Joon Gu?
Ha Ni!
It's been a long time, right?
You, why are you here?
Weren't you working at my father's restaurant?
That's right.
I work there in the evening, and here during the day.
I'm earning this much money, so you can come marry me any time you want!
I've prepared everything.
Knowing you're going to the same school as this jerk, you thought I would do nothing about it?
So Baek Seung Jo, how is it?
You were really surprised, right?
Right.
I was REALLY surprised!
How could you allow yourself to trail alongside the skirt of some girl?
The skirt of some girl?
That's called love, love.
You don't know what love is?
Hey!
Excuse me, please remake this.
Oh my, how come you only gave him half a serving?
Youngster Bong, is this how you're going to do your job?
Lady, this is more than enough for this fool!
Eat well.
Eat up Ha Ni!
This seat is empty ...
Hi!
Ha Ni. uhm... you go first
Omg, I finally found you all my life, I was waiting.
I've been looking forever!
Oh Sunbae, long time no see.
"Long time no see"?
Since you're the new student here, shouldn't you have been the one to look for me?
That saddens me.
Is that so?
"Is that so?" Look at this kid acting so gentle!
Well then, I'll get straight to the point.
Have you joined any school club? <i>School club?</i>
I haven't thought of that.
You can't just enter a club without thinking.
Just forget about that, and come join our club.
If you're with us , we can go to Nationals this time.
Nationals?
I don't want to, and it's been a long time since I last played.
Yeah.
Seung Jo, who was the person that got you the "Red Shoes" series when you were a sophomore?
-Don't remember?
Then when you were a junior, who downloaded those really hot-- -Alright, alright.
You're saying okay?
You're okay with it?
Thank you Seung Jo.
You are such a nice boy.
After your classes are over, come find me in the club room, okay?
Yes.
Alright, then you better come later!
I'll see you later, alright?!
School club?
Hi.
You don't have class?
You sure are following me all around.
What kind of club is it?
Who said I would follow you? <i>Brought to you by the PKer team @ www.viikii.net
Why?
You're going to follow me if I do.
Follow you?
Would you like something?
Hi!
Hello~!
-So everyone is here.
-This is the list of members.
Why isn't she coming?
Come.
So you followed me.
What are you doing?!
Come here.
Omo, we meet again. What is this? If I didn't follow then there would be trouble.
You play Tennis well?
I can't play it.
Of course I don't since I've never tried it before.
You shouldn't have come if you've never played.
You obviously think lightly of clubs.
What do you mean?
That person said that I can join even if I can't play.
He said I just have to want to play and be sincere about it.
That person?
Let her be.
She's normally pretty mindless.
OK.
It seems like it.
Alright now.
Attention, attention.
Let us begin.
Today it seems to be a little awkward Since you still don't know each other,
I'm just going to do a brief intro, and we will begin our official training starting Thursday.
So you should bring along your rackets.
Pleased to meet you.
I am the club vice-president, Wang Kyung Soo.
Second year student.
Second year?
Yeah.
21 years old.
21 years old?!
I apologize.
No.
It's fine, it's fine.
Sometimes, even my mother talks to me formally,
Well it's good, since our beginning is light hearted and fun like this.
Then I will continue to get into the details.
This year our Top Spin club has been blessed with the entry of some very talented freshmen.
The winner of last year's high school tennis nationals.
First place, first place.
Right, Baek Seung jo.
Also, she was in the same tournament,
I present to you the girl's division winner.
Yoon Hae Ra.
Nice to meet you all.
Ah!
I don't really know why, but as of last year, no new female students have joined our club.
However, a female student who cares greatly about our club and genuinely wants to join came today.
Her name is...
Her nam...
It's Oh Ha Ni.
Oh Ha Ni.
Hello everyone.
I am Oh Ha Ni from the social studies department.
Excuse me, but how long have you been playing Tennis?
I have never held a racket.
But I've played badminton!
Ah!
Applause, applause.
Are you okay?
Yeah I'm okay.
Yah, that was pretty powerful.
You just need a little more practice and you'll be fine.
I'm sorry.
I said it was okay, so keep playing.
Oh, Pretty!
You look pretty.
For real?
Yeah, really pretty.
It's perfect!
It's really pretty.
Oh you bought brand new clothes from head to toe.
Well, I have to go get ready...
"This is the first time in my life that I am playing tennis ," So you appear.
It's normally the kids that can't study that buy pencils before they even take an exam.
Right!
And all different kinds.
By the way, you look to be getting along well with Kyung Soo Sunbae.
Yeah, I like Wang Sunbae.
He's exactly like Tofu.
Tofu?
Yeah.
He's smooth, and very kind.
His words are very nice too.
Very different from a certain someone.
You're really clueless.
Let's go.
Okay, now.
Kyung Soo.
Since it's your first day, we're going to have an ability test.
Go to the back and stay the way you are right now, and just get the balls.
Kyung Soo will be serving the balls.
Please don't feel burdened.
Today we will be testing to see what skill level everyone is.
Don't be nervous.
I'm going to serve 5 balls.
Don't force yourselves, and only do what you can.
Don't over do it, or else, you can get hurt.
You play even when it's raining?
Of course, whether it's raining or snowing, we play.
So get ready everyone.
We're going to start.
HEY!
Hurry up and move it!
Those pieces of junk!
Electronics major, Han Ha Shik.
Fighting!
Fighting!
Oh, startled me!
What the hell are you doing?!
Hit the ball! The ball, damn it! Again.
Open your eyes WlDE!
Go!
What are you doing, punk?
Here!
At least get one you punks!
I told you to Get it!
Next.
Get it right!
Get it RlGHT!
Hit it correctly!
Hit it!
Please hit it, damn it!
Undecided major, Yoon Hae Ra.
Sunbae, what are you doing?
Serve the ball correctly.
Next.
Undecided major, Baek Seung Jo. <i>Brought to you by the PKer team @ www.viikii.net</i>
Oh!
Baek Seung Jo, nice to meet you.
I've been waiting for the day to go 1 on 1 with you, like this.
Please take care of me.
Hey, I've been going easy since you said you haven't played for awhile, but I don't think I need to.
No, please go easy on me.
That was just a coincidence.
Cocky fool.
Okay, that's it.
Good job.
This isn't good, Wang Sunbae is totally pissed.
I know, the next person is dead now.
Last one, Oh Ha Ni.
Oh Ha Ni!
Where are you hiding?
Come here.
Come here!
Go on over, he's calling you.
It's all your fault!
Come here quickly!
Excuse me...
Stand up straight!
I'm sorry, but this is the first time I'm playing in my entire life!
Please be gentle...
Shut up!
What's up with all the talk!
Are you playing dodgeball?
Why are you avoiding the balls!
Don't you dare avoid the balls again.
Don't you dare!
-Hey!
Hey!
Ha Ni!
-Are you alright?
-I think she fainted!
-Ha Ni get up!
She's got a bloody nose!
It's a bloody nose!
That's right, this is what it's about!
This is the kind of will power I'm talking about!
The need to hit the ball even if it means to faint!
That's right Oh Ha Ni!
Cheers!
Cheers!
Are you okay?
That fool is typically really well mannered, but once he picks up a racket he turns into a different person.
Really?
Yeah.
He feels so bad he's not even able to come over here right now.
You two, how the hell do both of you look so good, study so well, and even play tennis that great?
Isn't that just a bit too unfair?
You guys were really popular in high school too, right?
Not really.
Whatever, Hye Ra looks like she dated quite a lot.
I wasn't at all interested in dating.
Why?
Other people and I, have a hostile relationship, but I need other people. Because I want to be acknowledged as independent through the mere independence of the other person.
And in so we begin to begin a process called dating.
And the meaning of independence here?
The ability to transcend all situations with my own will and ambition.
And when we respect the other person's independence...
That is Love.
That is what is said.
What? Does it hurt your head?
This is where it get's really important.
Eventually ...
Eventually love is to throw away one's own independence, which becomes the posession of the other person.
The feelings that one feels at that point, is what's called hatred.
Therefore love can only fail.
What the hell is this?
My head hurts!
Are you interested in Sartre?
Not really Sartre, but I'm more interested in the relationship between Sartre and Beauvoir.
Oh Sartre and Beauvoir.
Even I know who they are.
Oh, now that I think about it, you two are simliar to them.
Didn't those two meet because they both placed 1st and 2nd place for the state exams?
That's right.
Really?
That's crazy.
She's totally a girl version of Baek Seung Jo.
Seriously.
You better be on your toes.
You followed your significant other to play tennis, which you have no clue about, and came back with a damaged nose.
What about it, Oh Ha Ni?
And here I thought you were on a roll this Spring, but look at you now.
Seriously, you went from winter back to winter.
No, there's still hope.
To be honest I do feel a bit uneasy about the club, but there is still one area of hope left.
What is it?
You were here.
What a coincidence that we're in the same lecture?
What a relief, because I heard this lecture was hard.
Since you're here. <i>This is it!
Listening to a lecture along with Seung Jo. <i>I could have never imagined this in high school. <i>I knew it!
Oh Ha Ni's spring has arrived!
The guy sitting behind you came along too?
Huh?
Ha Ni!
What are you doing here?
What is it?
Can I not be here?
I just really miss the old days of studying!
Did you like to study so much that you miss it?
Fool, it's because of you that I got out of the cafeteria during it's busiest hours!
Was the cafeteria that slow?
Of course I feel bad towards the cafeteria lady.
But it can't be helped!
Is that seat taken?
What a real coincidence?
We're sitting in another lecture together.
What do you usually eat for breakfast?
I really don't know.
Ha Ni!
Ha Ni!
Do you understand?
Joon Gu, shhh!
Pardon me.
Oh.
Why do you have a bandaid on?
Did you hurt yourself?
Huh?
Me?
What did he say?
I am sorry.
I'm be quiet!
Oh, shut the mouth!
Shut the mouth?
What, why are you guys laughing!?
She's doing good!
And... who are you?
Me?
Me?
You don't have any books.
Did you originally take this class or...?
Oh.
What?
Huh?
Hey man!
I'm sorry.
But I am coding!
Yes I'm coding!
Coding?
What does that mean?
Are you trying to say you're a high school student?
Not that, but that I just have a high school diploma.
That I don't attend this school.
He doesn't go to school here.
He just works at the school cafeteria.
I guess...
He likes Ha Ni. That's why, he's here.
Oh.
I see.
What the hell is this hag talking about?
What did you say?
Hey, why are you acting so high and mighty when I didn't even ask you to!?
Everyone is sitting here after paying the expensive tuition.
Stop being a nuisance and why don't you just leave now?
What?
A nuisance?!
If you're stupid, the least you could be is modest.
Gosh, I absolutely hate stupid guys.
You're like a bug!
You don't have class today?
After going to university...
It really is no joke.
What?
Did something happen?
That's not it...
I think there are so many kids that are super smart and super pretty.
Seung Jo as well, probably likes the pretty, smart, and skinny ones.
He probably likes girls like that right?
Hey!
Did a girl like that appear before him?!
Hey, Ha Ni.
I may look this young, but I am an adult.
I can tell just looking at you two.
You two can only be perfect when together.
Huh?
You're meant to be.
Like this.
I don't know how great that girl may be, but it can't be helped if she's not his other half.
See?
See, it can't be helped if it doesn't fit.
So don't you worry.
Alright?
Yes.
That's right. Now stop wiping that, you're going to put a hole in it!
Oh.
Baek Eun Jo.
What is it?
Your caligraphy supplies?
Yeah.
The ink stone...
And rice paper?
What are you looking at that you don't even hear me when I call?
Oh.
What is it, Oh Ha Ni?
Why did you come to someone else's school?
Uhjjoo (Look at you)!
I brought your materials...
I'm going to take it back.
Ah give it to me.
What are you watching?
I got it.
It's her.
Am I right?
Ohh.
She's pretty.
Actually, they're all prettier than you.
This...
Here.
Thank you! <i>Brought to you by the PKer team @ www.viikii.net
I don't want to do this anymore.
Ah. Is that so?
Then, eat this
I'll get fat!
Where do you have fat?
Then do you want to play Omok (Korean game)?
Boring...
Ah, he has to make her have fun.
I want to leave.
My mom's making some food.
Hyung!
Is this your friend?
Yes.
Oh, you did a good job making this.
Eun Jo's pretty smart.
This
Like this.
Wow.
Could I stay for dinner?
Sarah, should I give you more?
No thank you.
I ate well.
Aigoo, so clever.
Seung Jo, oppa!
Huh?
Oppa, do you believe in love at first sight?
Hmm, I'm not sure.
I never thought about it.
I used to not believe it.
I thought adults were just saying things, but i think it's real.
Earlier, when you came into the room, the background behind Oppa really became white and
I couldn't see anyone but oppa.
Oppa, just wait 7 years.
Eun Jo, you... since Sarah likes your hyung are you here because you're sad?
Our Eun Jo is so cool though,right?
Eun Jo ahh.
I don't know.
Aigoo what's wrong?
Eun Jo, you're cool too!
Ah.
Where's Eun Jo?
Are you even worried?
What?
Why are you being like that to me?
Cheater (relationship-wise).
What?
You act like you're not, while you're managing(?) it.
I see it all.
Manage?
Yeah.
Manage.
Whenever I want to throw away my feelings because I think it just must not be, you laugh for me once in awhile.
Whether it's real or you're playing around, you make people confused and make them dumb.
What are you talking about?
You're right.
You did well.
You two look good together. Mean.
Hey, are you talking about Yoon Hae Ra right now?
Not talking about Eun Jo?
Ah, it's the same thing.
How did it go?
Go away, Oh Ha Ni!
I don't want to see you! It's all your fault!
Just go!
I'm sorry.
You brought her here and it ended up like this.
Did I ask you for that favor?
You're right.
I went overboard again.
Well, that's just like me.
I'm really sorry.
I know that I can't say anything to make you feel better...
What do you know?
What do you know?
I know.
In this world, I probably know it the best.
The person I like doesn't look at me but looks at someone else.
Smiles/laughs for someone else.
I really know what that feels like.
And I can't be truthfully jealous either.
Are you talking about my brother?
Eun Jo.
I think... if two people mutually like each other...
It's almost a miracle.
Someday, will that miracle come true for me too?
I don't know.
Don't do that.
Stop it.
Should I get another house?
Chef.
Chef.
Take a look at this.
Okay.
Hey hey, why is this so watery? When you made the dough... Did you mix in one direction?
Ah that's right.
I did it that way.
Aigoo.
Oh?
The seasoning is good.
Yes.
But it's really interesting!
How can it have that salty taste? Yet it also tastes sweet!
Ah.
That's right.
If you leave it for a couple hours, you don't need to add MSG.
Someone will hear. The way...
Hey, go make the batter again.
Oh, then what should I do with this?
In the refridgerator, there should be batter.
Mix this with both halves of that.
Yes.
I understand.
Here.
When am I going to make noodles out of this. i need to hurry up and make a bowl for Ha Ni to eat.
Joon Gu.
Yes.
Chef.
What do you like about Ha Ni?
Oh.
Chef.
Since you ask me like that, I'm a little embarrassed.
If it wasn't for Ha Ni, I wouldn't have been able to graduate.
I used to get in trouble everyday and the kids used to avoid me.
Ha Ni became my friend, and I was able to graduate.
Ah. Is that so?
Yes.
Chef.
This is correct, right?
Like this, like this.
So it is true that you live under one roof.
Hyung.
Oh. Eun Jo.
We've got to look for some documents for a joint assignment.
I'm sorry, but do you think you could take your work to the study?
What kind of assignment?
It's a general ed class based on Western studies, but we had to partner up and complete the assignment.
Your brother?
Yes.
Eun Jo.
Hello.
Come on.
She's so pretty.
Seems like none of the adults are home?
Yeah, father is late all the time and it seems mother has gone out.
What are we going to do about the assignment?
Do you know a bit about Nietzsche?
I've read some of his works, but I don't know if I could say I know it.
Then again...
It's Nietzsche, do you think that's what I meant?
Oh it's nice here!
The view is so much better!
I hear Western guys think that when a girl innocently follows them home, it means that the girl is okay with spending the night with the guy.
What should we do?
Let's each organize the documents and then make a conclusion.
Sounds good.
Since we can't look at all of them in this short amount of time.
What's our theme going to be?
Nietzsche may have said God is dead, but in the end he wasn't denying God but praising him.
What do you think is the core of Nietzsche's words?
Well...
The word joy keeps coming to mind.
Hwan Hee = Joy
What?!
Did he say Ha Ni?
Joy.
That's a good one!
Overcoming denial and changing into joy!
How about we turn in a video file instead of a report.
A video?
Like using clay animation or something.
We can show the process of extinction to formation.
So we'll show the notion of joy via a video file.
You have a camera at home right?
You're home?
I'm going to use the camera.
Camera?!
Hyung is working on an assignment with a friend.
It's a 2 person assignment.
Really?!
But the friend he came with is a girl.
She's so pretty.
What?
A girl?
Yes.
The professor assigned the partners, so don't be mistaken.
I'm going to use this.
I'll put it back after I'm done.
Eun Jo, I need something from some of your supplies.
I'm going to use it.
Goodnight, Father.
Alright.
Don't leave the door open because you have to go somewhere or anything.
Don't worry!
-Goodnight!
-Thank you!
-Thank you for the hard work!
-Good luck!
Others have all gone to university.
They're doing well with clubs and listening to lectures.
Bong Joon Gu.
You're so pathetic.
But what can you do.
Hurry and learn the trade and become a top chef, so you can proudly propose to Ha Ni.
Ha Ni, what are you doing right now?
Should I call her?
I've never called her this late.
Man, now that I'm going to call her, it's a bit nerve wrecking.
Pretty good.
It's unfortunate I can't be a bit more detailed, but this isn't an art project so...
Let's film it.
Seung Jo can you spread out the petals?
Like this?
Yes
Your mother?
She's my friend.
Hello.
Yes. So you're working on an assignment together?
Yes
We should have asked permission before hand.
Barging in without contacting you...
I'm sorry.
Yes.
Where is Ha Ni?
Probably in her room.
Where did she go?
I heard she came home.
Oh. She left her handphone.
Ha Ni isn't in her room.
Is that so?
She must have gone some where.
Ha Ni.
Ha Ni.
Oh, what's this?
It's awesome once something living is on it.
Oh it is.
Where did this guy come from? <i>It's the first time I've seen him so happy.</i>
Is Seung Jo...
Having a taste of joy right now?
It's done.
Do you think you can grab me a glass of water?
Oh then again we haven't had anything to eat this whole time.
Hold on a second. <I>What should I do? <I>Should I jump down? <i>If she sees me here, <i>I'm better off dying!
Yes.
No I'm out.
I'm at a friend's house because of a school assignment.
We're done.
I'll call once I leave. <i>Brought to you by the PKer team @ www.viikii.net
You should quickly be able to play on the courts.
You can't just shag balls everyday until graduation.
But still, you're trying your best.
Even when Seung Jo is not here, you still come.
Why isn't he coming?
Omo, you didn't know?
Seung Jo is a special member. He joined the club on the condition to come and play whenever he feels like it.
You're living together, but you don't even know about that?
Wait a moment.
So your relationship is at that level?
Great.
Not getting anxious... is a little boring.
She's so mature.
We're the same age, but why do I seem like a kid?
Baek Seung Jo can come when he feels like it?
Then why did I join here?
Why I am gathering those?
Oh, dad.
What?
It's going to be spicy.
I like it spicy.
Tennis?
Is it fun?
It's hard...
Really?
Why did you call me?
Put a little bit more radish juice in it.
I asked you why you called me!
Yeah.
Let's move out.
In the end, we can't just keep living there forever.
But...<Br><Br> However I'm... usually out here because I'm working, but
It seems like you're having a real hard time so my heart is unsettled.
Let's move out.
I'll take care of a place for us to temporarily reside at.
Ar... Are you alright?
Oh, it's spicy.
I might have put too much horseradish
I'm starting to tear up.
So, why did you put a lot?
I'm against it.
Thinking that Ha Ni will be gone!
I don't want to.
I'm against this.
Honey, be a little thoughtful.
He's saying that Ha Ni will go away!
Ah... Really.
Ki Dong, you really don't have to be concerned about it.
We really want you to live with us.
It's not like you're just staying here for nothing, you're paying the monthly rent.<Br><Br> Thanks for the offer but we've been here too long.
We've been bothering Seung Jo and Eun Jo.
And our Ha Ni,
Will be able to give up Seung Jo quickly.
About that...
How can I?
It's alright, Jae Su-Shi
No, it's not.
Anyhow, this problem should be dealt with by the the 2 who are concerned.
Seung Jo doesn't have any interest in Ha Ni, and... What should I do?!
If Ha Ni marries into our family that won't be a problem anymore right?
Oh, I really love that bright personality And that cuteness of hers.
Even Seung Jo, will come to like her .
Aigoo! Our Ha...Ha Ni
Is a happy child. for you adoring her like this.
Stop crying already.
Hyung.
Oh Ha Ni is moving out.
She's moving back with her father to their house.
Isn't that great?
Ever since she moved in, she has only been a pain to you and me.
You're moving out?
Yeah...
Are you disappointed?
Well, it's a relief since my life can finally go back to normal.
Right.
Yea...That's what I hope too.
I have to go pack now.
Goodnight.
Ha Ni we have to go now. They're all waiting downstairs.
Is that all?
Dad...
Jae Su-Shi.
Aigoo
Seung Jo, Eun Jo. We've brought you much trouble. Really sorry.
Oh right.
You should come by our house sometimes.
Ha Ni, say goodbye.
For taking care of us, I'm very grateful.
For making delicious meals everyday,
On the day of the sports competition, you brought us Pizza and took pictures with us.
Even taking my friends with me
And even took my friends with us to the beach. and threw me a congratulation party for passing the exam.
To me everything is a pleasant memory.
Everything that happened when I lived here, really...
Ha Ni...
I'm sorry for being a bother to you this far.
Ha Ni...
Mother!
My life with you....
If you're like this then it'll make Ha Ni awkward.
Stay well.
Okay.
Come back and visit.
Ha Ni, let's go now.
Yes...
Good bye.
Well, then.
Put on your seat belt.
Ha Ni...
Assa! Now I can have my room back.
Baek Eun Jo, You!
Mother! Aren't you going to feed us?
This is all your fault, Seung Jo. <i>Brought to you by the PKer team @ www.viikii.net <i>Are you okay? Nothing is wrong with you? <i>I... really gave up on Baek Seung Jo. <i>What? <i>I'm really trying my best to let go of that guy. <i>Whenever I see Oh Ha Ni, she's amazing. <i>You should definitely remember, <i>I am your home.
A home that will always be there for you no matter what. <i>You might not like it, but I'm interested in Seung Jo. <i>I like you. <i>And you? <i>Goodbye... Baek Seung Jo.
Jin Se Ryeong is in the room next to Tae Ik's?
That's what I said.
She brought in a lot of furniture as she pleased.
Her personality is like that.
She does everything as she pleases.
And, I've felt this from earlier.
It doesn't seem like you and Jin Se Ryeong are on good terms.
I... don't like people who are like watermelons.
Watermelon?
They are green on the outside... and red on the inside.
Moreover, they have seeds, which are cumbersome.
I don't like her!
I don't like!
I...
Someone like Man Ok...
Man Ok, stand up for a second.
Okay.
I like someone whose outside and inside are white.
What does that mean?
Oh, Man Ok, you look just like that.
That!
Excuse me? ♫ Round eyes, and a small nose. ♫ ♫ A cute little bear that wears white fur clothes. ♫ ♫ I will always look at you. ♫ ♫ And say a small wish. ♫ -♫ When I am next to you... -Yes, that! ♫ I am always happy. ♫ ♫ Whatever secret it may be.♫ ♫ I can say it. ♫ ♫ On the small little black nose, ♫ ♫ If you press your lips on it. ♫ ♫ Your face turns red because you are shy, pretty little baby bear. ♫
Are you blushing?
Man Ok, your face really became red!
Chaton!
Chaton.
Chaton, your mother's face became red.
Mother?
Yeah. I'm the father.
You don't want to?
Then, should I make it older sister and older brother?
Um, Kang Won-nim, our Chaton is male.
Really?
You aren't a girl?
What difference does it make if it's a girl or a boy?
As long as she's pretty.
Aren't I right?
Hey, Jang Man!
What is this?
It seems like he is into it.
What is it?
If you start working, you should finish it.
Who did you expect would finish the job that you threw aside like this?
From here, Jang Man, you do all of it.
Do you have time tonight?
Why are you asking if I have time suddenly?
There is somebody who wants to meet you, President.
Me?
Who?
Someone who will give you power.
If you meet the person, you will know.
How does 8 p.m. at Hotel H sound?
Let's make it at 9 o'clock.
I will make the arrangement accordingly then.
Hwa Ming?
It's Se Ryeong.
I told him about you and he wants to see you tonight.
Is 9 o'clock okay with you?
All right.
We'll be there. See you then.
Did you say you would invest in us?
Yes.
I have become interested in your company.
Why would an international designer invest in entertainment?
Can I ask the reason why?
Instead of a reason, I will give you one condition.
Please reinstate Won Kang Hwi into the entertainment world.
That is my one condition for investing.
Kang Hwi?
We are about to launch our brand in Korea at this time.
We want to use Won Kang Hwi as the new face of our brand, Win.
You may know, but reinstating Won Kang Hwi in the entertainment world is not such an easy thing.
In Korea, getting ousted is fatal.
That's why I am giving you so much investment money.
Your talent at destroying someone is first class.
I believe that your reconstruction will be fast, too.
That is why I came to see you, President.
Can I ask you why it has to be Won Kang Hwi?
Won Kang Hwi is my muse.
If you don't want to do it, I will look for another entertainment company.
Okay.
I will accept your condition.
As I have heard, your decisions are quick.
About the details of this business, I will contact you shortly as soon it is arranged.
Ah, right...
We should have a dinner together with Se Ryeong.
Se Ryeong was asked to speak for me as an invester and she arranged the introduction.
I will organize a meeting.
I am looking forward to it.
What about Kang Hwi's whereabouts?
I'm sorry, not yet.
By fair means or foul, find out as quickly as possible!
Yes.
There is definitely a hole somewhere to get in.
At this rate, how am I supposed to find the recording?
Why did they suddenly begin construction!
Should you be roaming around like that?
What are you going to do if you get caught?
What are you doing in someone else's room?
I have something to say.
I don't.
Chaton, come here!
Aigo!
My baby!
Hwa Ming.
You know her, right?
The creator of the brand, "Win."
You've heard her name before, haven't you?
That unni's taste is weird.
She said she's your fan.
I have a lot of fans.
Won Kang Hwi, the best in the universe, don't you know?
I got to know her by being in a couple of her shows in the States.
She's in Seoul right now.
If it's with Hwa Ming's power, couldn't she save you from this beggar-like place?
What do you want to say?
If you want, I can introduce you to Hwa Ming.
Why would you?
You wouldn't want me to be successful.
I don't like you here.
What did I ever do to you?
You know, there is something like that.
While living, there are people whose existence you just hate for no reason.
You are like that. As it is, you are a eye-sore. <br />And, you are even more so by being next to Tae Ik.
Are you jealous?
I'm not jealous.
I said that you're just cumbersome.
I am cumbersome because I see right through that bad heart of yours.
If I'm not here, you think everything will go well with Tae Ik?
Well, that's about right.
You seem to have forgotten...
Tae Ik got engaged.
Jang Man Ok?
She doesn't worry me at all.
After seeing the news about Tae Ik's engagement,<br />it's true that I was a little worried...
But, after looking at Jang Man Ok's face, that worry went away completely.
There's no way Tae Ik would like such a plain woman.
It'll be best if you leave this house as quickly as possible.
I also don't know until when my lips will be silent.
You're still the same, Jin Se Ryeong.
But, when did she get to know Hwa Ming?
Ah!
It's rice again?
I don't like it.
What is this?
Don't you know about giving preference to the patient?
Forget it!
This is my house.
Ah!
Seriously!
Man Ok, bring mine to the basement!
Set mine separately in the future.
If you don't eat now, there will be no food later.
So just know that!
Do you really think of me as a cook?
This is all because of you!
You be quiet!
Ah!
The soup is slightly salty. How can you...?
What is it?
Huh?
Ah!
It's nothing.
Jang Man Ok, it seems you take more care of Kang Hwi than your fiancé.
That is because... Kang Hwi is sick.
Did you also hurt your hand?
Hey!
What is it to you where I am hurt?
Man Ok, I'm sorry, but I will get up first.
I was just worried about him... Jesus!
Jang Man Ok!
Don't you take care of your skin?
What?
How can your skin be like that?
It has become dark.
You look like someone who was farming.
You are, after all, the fiancée of a top singer.
This is a little extreme.
Why?
Why don't you eat some more?
I lost my appetite.
With food is like this is why you have no appetite.
Jang Man Ok, isn't there anything fresh?
Uh...
Like a tofu salad?
Hey!
Jang Man!
Are you a social service worker?
Are you a domestic assistant?
Why do you serve food to just anyone?
You are my fiancée!
You are the fiancée of a top singer!
You needn't worry about weird dregs like them.
Just make my food in the future.
I am strong when I am on your shoulder
You raise me up... to more than I can be
You raise me up... To more than I can be
I am a lecturer in Taylor's College Canadian Pre University Program
I am the founder, I guess , of the Everyone has hope project which basically started after I saw a movie, Born in a brothel where a photographer taught children photography and liberate them and make them feel better about their situation
So that was how it started and here we are today
We have been working very closely with the Burmese refugees from the Alliance of Chin refugee school for the past two years and for the past 9 months we have been working with the second batch of students and they are really talented and exemplary
It has been a great experience working with them
My name is Molly and I am 14 years old.
I come from Chin state, I live in Malaysia for 2 years
My name is Simon, I come from Myanmar, a part of Chin state
I have been here 4 years, I am 15 years old
My family also with me in Malaysia we live in Pudu
My name is Jonah, I am 16 years old
I come from Myanmar Chin state
My name is Elijah I am 15 years old
I come from Chin state I have been in Malaysia 4 years
My name is Phillip, I am 15 years old
I come from Myanmar Chin state
I live in Malaysia for 2 years
My name in Tien Hui, I am 16 years old
I am from Myanmar
I am in Malaysia 3 years
And I must say I am very very impressed by these photographs
It goes to show that it's not about having, you know 10 years of training and having all the technical skills
It's about having an eye and a heart and there are opportunities to express yourself, That really brings out some of the most beautiful images that I have seen here.
In fact I have already chosen one, I am buying one
And the big thing is, of course they are kids, and if Malaysia, which Malaysia has, they have agreed to the Convention of refugee child it means all children in this country should have their basic rights
And one of these rights is the right to education these children aren't allowed into public schools that doesn't compute for me
So we have a situation where there are, you know a ballpark figure probably about 50,000 kids who can't attend school
When a kid can't go to school the kid doesn't develop in the way that child should
This is a key opportunity for Malaysia to take a step in making these kids" lives better and ultimately making Malaysia better
Let's do a little bit of probability with playing cards
For the sake of this video we're going to assume that our deck has no jokers in it.
You could do the same problems with the joker, you'll just get slightly different numbers.
So with that out of the way
Let's first just think about how many cards we have in a standard playing deck? so you have four suits and the suits are: the spades, the diamonds, the clubs and the hearts.
You have four suits and then in each of those suits you have thirteen different types of cards or sometimes it's called the rank.
So each suit has thirteen types of cards
You have the ace, then you have the two, the three, the four, the five, the six, seven, eight, nine, ten and then you have the jack, the king and the queen.
And that is thirteen cards
So you can have for each suit you can have any of these, for any of these you can have any of the suits
So you can a jack of diamonds, a jack of clubs a jack of spades or a jack of hearts.
So if you just multiply these two things you could take a deck of playing cards and actually count them, take up the jokers and count them.
But if you just multiply this, you have four suits each of those suits has thirteen types so you're gonna have 4 times 13 cards or you gonna have 52 cards in a standard playing deck.
Another way you can say it is like: look, there is thirteen of these ranks or types and each of those come in four different suits, 13 times 4 once again you'd have gotten 52 cards.
Now that out of the way, let's think about the probabilities of different events.
So let's say I shuffled that deck,
I shuffled it really, really well.
And then I randomly picked a card from that deck.
And I want to think about what is the probability that I pick what is the probability that I pick a jack?
Well, how many equally likely events are there?
Well, I can pick anyone of those 52 cards, so there's 52 possibilities for when I pick that card.
And how many of those 52 possibilities are jacks?
Well, you have the jack of spades, the jack of diamonds the jack of clubs and the jack of hearts.
There's four jacks
There's four jacks in that deck.
So it is 4 over 52, these are both divisible by four
Four divided by four is one 52 divided by 4 is 13.
Now let's think about the probability, so I will, you know, we're gonna start over
I'm gonna put that jack back in, I'm gonna reshuffle the deck
So once again I still have 52 cards.
So what's the probability that I get a hearts?
What's the probability that I randomly picked a card from a shuffled deck and it is a hearts?
Its suit is a heart.
Well once again, there's 52 possible cards I could pick from 52 possible, equally likely events that we're dealing with
And how many of those have our hearts?
Well, essentially thirteen of them are hearts.
For each of those suits you have thirteen types so there's thirteen hearts in that deck, there thirteen diamonds in that deck there thirteen spades in that deck, there thirteen clubs in that deck.
So the 13 of the 52 would result in hearts.
And both of those are divisible by 13, this is the same thing as one forth.
One in four times I'll pick it out or I'll have one forth probability of getting a hearts when I go to that, when I randomly pick a card from that shuffled deck.
Now let's do some things a little bit more interesting or maybe it's a little obvious: what's the probability that I pick something that is a jack and it is a hearts?
Well, if you're reasonably familiar with cards, you'll know that there's actually one card that is both jack and a heart
It is literally jack of hearts.
So we're saying what is the probability we picked exactly the card jack of hearts?
Well, there's only one event, one card that meets these criteria right over here and there's 52 possible cards.
So there's a 1 in 52 chance that I pick the jack of hearts something that is both a jack and it's a heart.
Now let's do something a little more interesting.
What is the probability, you may want to pause this and think about this a little bit before I give you the answer, what is the probability of, so I once again have a deck of 52 cards, I shuffle it randomly pick a card from that deck, what is the probability that that card I picked from that deck is jack or a heart?
So it could be the jack of hearts or it could be the jack of diamonds or could be the jack of spades or it could be the queen of hearts or it could be two of hearts.
So what is the probability of this?
And this is a little bit more of an interesting thing, because it's we know first of all that there are 52 possibilities but how many of those possibilities meet the criteria meet these conditions, that it is a jack or a heart.
And to understand that I'll draw a Venn diagram.
Sounds kind of fancy, but nothing fancy here.
So imagine that this rectangle I'm drawing here represents all of the outcomes.
So if you want you can imagine it has area of 52.
So this is 52 possible outcomes, now how many of those outcomes result in a jack?
So we already learned this, one out of thirteen of those outcomes result in a jack.
So I can draw a little circle here with that area and I'm approximating that represents the probability of a jack.
So that should be roughly 1/13 or 4/52 of this area right over here.
So I'll just draw it like this.
So this right over here is probability of a jack.
It is four, there's four possible cards out of the fifty two.
So that's 4/52 or 1/13.
Now what's the probability of getting a hearts?
Well, I'll draw another circle here, that represents that.
13 out of 52, 13 out of these 52 cards represent a heart.
And actually one of them represents both a heart and a jack.
So I'll actually overlap them and hopefully this will make sense in a second.
So there's actually thirteen cards that are heart.
So this is the number of hearts.
And actually let me right that top thing that way as well.
It makes it a little bit clear, we were actually looking at -- clear that
-- so the number of jacks. And of course this overlap right here is the number of jacks and hearts. The number of items out of this 52 that are both a jack and a heart.
It is in both sets here it is in this green circle and it is in this orange circle.
So this right over here I'm going to do that in yellow since I did that problem in yellow.
This right over here is a number of jack and hearts so let me draw a little arrow there. It's getting a little cluttered
I've actually should've drawn it little bit bigger.
The number of jacks and hearts.
And that's an overlap over there, so what's the probability of getting a jack or a heart?
So if you think about it the probability is going to be the number of events that meet this conditions over the total number of events.
Yeah, we already know the total number of events are 52.
But how many meet this conditions?
So it's going to be the number, it's going to be you could say: well look, the green circle right there says the number that gives us the jack and the orange circle tells us the number that gives us a heart.
So you might wanna say well, why don't we add up the green and the orange, but if you did that you'd be double-counting.
Cause if you add it up, if just did four plus thirteen what are we saying?
We're saying that there are four jacks and we're saying that there thirteen hearts.
But in both of these we're, in both when we're doing it this way in both cases we're counting the jack of hearts.
We're putting jack of hearts here and we're putting a jack of hearts here
So we're counting jack of hearts twice, even though there's only one card there.
So you'd have to subtract out where they're common.
You'd have to subtract out the item that is both the jack and a heart.
So you'd subtract out a one.
Another way to think about it is
You really want to figure out the total area here.
Let me zoom in.
I'll generalize it a little bit.
So if you have one circle like that and then you have another overlapping circle like that.
And you want to figure the total area of both of the circles combined.
You'll look at the area of this circle and then you could add it to the area of this circle.
But when you do that, you'll see that when you add the two areas you're counting this area twice.
So in order to only count that area once, you have to subtract that area from the sum.
So if this area, if this is, if this area has A, this area is B And the intersection, where they overlap is C the combined area is going to be A plus B minus where they overlap minus C.
So that's the same thing over here.
We're counting all the jacks and that includes the jack of hearts we're counting all the hearts and that includes the jack of hearts.
So we counted the jack of hearts twice, so we have to subtract one out of that.
So it's going to be four plus thirteen minus one.
And both of those things are divisible by four.
So this is going to be the same thing as if I divided sixteen by four you get four, fifty two divided by four is thirteen.
So this is, there's 4/13 chance that you get a jack or a hearts.
Use the commutative law of addition-- let me underline that-- the commutative law of addition to write the expression 5 plus 8 plus 5 in a different way and then find the sum.
Now, this commutative law of addition sounds like a very fancy thing, but all it means is if you're just adding a bunch of numbers, it doesn't matter what order you add the numbers in.
So we could add it as 5 plus 8 plus 5.
We could order it as 5 plus 5 plus 8.
We could order it 8 plus 5 plus 5.
These are all going to add up to the same things, and it makes sense.
If I have 5 of something and then I add 8 more and then I add 5 more, I'm going to get the same thing as if I had took 5 of something, then added the 5, then added the 8.
You could try all of these out.
You'll get the same thing.
Now, they say in a different way, and then find the sum.
The easiest one to find the sum of-- actually, let's do all of them.
But the easiest one, just because a lot of people immediately know that 5 plus 5 is 10, is to maybe start with the 5 plus 5.
So if you have 5 plus 5, that's 10, plus 8 is equal to 18.
Now, let's verify that these two are the same exact thing.
Up here, 5 plus 8 is 13.
13 plus 5 is also 18.
That is also 18.
If we go down here, 8 plus 5 is 13.
13 plus 5 is also equal to 18.
So no matter how you do it and no matter what order you do it in-- and that's the commutative law of addition.
It sounds very fancy, but it just means that order doesn't matter if you're adding a bunch of things.
Tell me not to do it.
Tell me not to go!!
Miss JaeKyung is looking for Miss Geum JanDi. It seems the groom is running way too late...
The groom is entering.
The bride is entering.
Starting now, the ceremony for the union of Goo JunPyo and Ha JaeKyung will begin.
To this couple comes marriage and the union of the bride and groom.
If anyone objects, please speak now, or forever hold your peace.
The Lord . . .
What are you doing right now?
I...
I object to this wedding.
Miss JaeKyung!
JaeKyung, what are you doing?!
I, bride Ha JaeKyung, object to this wedding.
Wh-What?
Aren't there any others who object?
I also object.
I also object.
Me too.
Me too.
I also object.
Miss JaeKyung.
This joke seems a little overboard.
Having fun is fine, but...
Madam Chairman, also Mom and Dad;
This isn't a joke.
I can't go along with this marriage to Goo JunPyo.
No matter how much I think about it, marriage just doesn't suit me right now.
I'm sorry.
Because of my conduct, I've caused a lot of trouble.
Dad.
Because this is all my fault, please don't take it out on Shinhwa Group.
Madam Chairman. and
Goo JunPyo,
I'm sincerely sorry.
Please forgive me.
Unbelievable.
What happened?
I'm usually a pretty cool girl.
Unni!
Oh yeah, Chen...
Chen, how's it going?
We're bringing her there right now.
Goo JunPyo!
JanDi.
Until when are you going to keep crying?
If someone saw, I would look like the bad guy.
Where can you find something more than a beautiful happy ending?
JaeKyung unni is so cool.
That day...
You asked why I didn't go, didn't you?
I... don't believe in happy endings.
Are you ok ?
This is why I always tell you to be careful all the time!
Sorry.
I'm okay..
You have guests, so I'll get going.
Weren't you waiting because you had something to tell me?
I have a favor to ask.
JanDi...
I can't let her go.
Even though I always make things hard for her.
I've sometimes thought it might be better to let her go to you.
I didn't even want to think about it, but if I had to
I thought you should be the one.
It can't be anyone else but you, JiHoo.
Goo JunPyo.
Even so, I don't think I can.
This lawn (JanDi) is the same as usual.
I missed it.
Don't you regret it?
I do.
I've been regretting the moment I let Goo JunPyo go.
JiHoo, I was supporting you, but . . .
It's now a waste since I gave up.
So I can't even do that.
Not long ago,
I asked JunPyo:
"Between friendship and love, If you were to pick only one,
What would you choose?".
He said he wouldn't give up either
They say people get as much as they are greedy for.
Neither you nor I have enough greed.
I'm leaving for New York tomorrow.
Can you give this to JanDi for me?
That J J
You have no idea how much I hoped it meant JiHoo and JanDi.
JiHoo, you probably don't know.
Good luck!
Take care.
Miss prepared this so that you can be comfortable.
Excuse me.
Please give this message to JaeKyung unni.
If it's okay with her, nothing has changed with our sister relationship.
Eat.
Miss Geum JanDi.
Would you like to dance with me?
I can't dance.
There's something I've been wanting to ask you from the beginning.
What is it?
Why was it me?
Me, I'm not pretty, I don' t have money or anything.
Why do you even like me?
Because I have everything. What?
Because I have money, status, and looks.
I have all that.
I don't need anything.
Geum JanDi, all you need to be is Geum JanDi.
It's really pretty.
Do you see the brightest star right there?
Yeah.
It's a star called Sirius in the Orion Constellation.
The brightest star in the winter sky.
You could say its existence looks like Goo JunPyo. How? Then I'm that one.
I want to be that one.
You sure do have taste.
Thats the second brightest star, Procyon.
That's it, benevolence at someone else's expense.
You're always so outgoing and obnoxious
It suits you perfectly. What?
But...
How did you get to like stars?
When I was little, my Dad sent me a telescope for my birthday.
He wrote in the card: study the stars well and we'll go look at them together.
So you went around looking at stars with your dad.
No.
I never went, not even once.
Why not?
Believing in that promise, I studied enough to go to major in astronomy, but do you know what I got for Christmas a few years later?
A telescope.
It was then that I realized it wasn't my Father sending those gifts, but his secretary.
Do you know what my dream is?
In the future, going to see the stars with your son.
How lame!
Not making promises I can't keep.
JanDi.
I'm sorry for hurting you.
JanDi.
What now?
I love you.
Look at this bliss.
When did you arrive?
JanDi!
GaEul!
It's a relief.
What is?
That you're smiling.
Here.
This...
I don't know why she had it, but she told me to give it to you.
Where is she right now?
She's about to depart.
Miss, it's time to go in.
Unni! JaeKyung unni!
Hey, monkey!
JanDi!
Goo JoonPyo!
How did you get here?
How can you just leave like this?
You weren't going to say goodbye to your little sis?
What kind of unni does that?
Sorry!
I'm really weak when it comes to saying goodbye.
Even the fierce Ha JaeKyung had a weak point?
That's right.
Have a safe journey.
And...
Thanks.
If you guys break up, I'll die from the injustice of it.
So, if you want to break up, come report to me and get permission.
Got it?
Unni...
Let me hug you once, my little sis, Jandi.
I'm leaving.
Have an enjoyable flight.
This is mine.
I picked it though.
I had dibs on it first.
Hurry, let go!
What are you?
Hey!
Hurry up and apologize, you jerk!
Get down!
Apologize!
Hurry!
I know this also, originally belonged to JanDi.
But, just this one thing, this one thing, give it to me, please.
Don't you think I should have at least one special memory to treasure?
Shinhwa Group and JK's merger has become uncertain, and the stock market and the government are watching Shinhwa's movements.
Shinhwa Group had planned to become in-laws with the American-based JK.
Now due to the broken engagement, Shinhwa is...
Hey. Open the door.
Hey!
Open the door!
Hey!
I said open the door!
Hey. Can't you hear me?
I said open the door!
This time, shouldn't you just come to my house?
What's the point of getting another house?
Who's to know whether that Evil Witch might tear down your house or kick you out in the middle of the night?
I should probably pack my belongings right away.
I'm really in trouble.
There's no need for that.
I knew you were something else, but
I didn't see you as someone who could pretend to be innocent, yet run around doing these kind of sly things behind people's backs.
It really is unbelievable.
It was my fault that I couldn't completely take care of things, but
I didn't know I would regret it so much.
Excuse me!
Why are you treating JanDi like this?
JanDi did nothing, but actually helped the two of them so they could work out.
If you have eyes, look at it.
Because of a worthless thing like you, do you know how huge a problem has been created?
A child like you couldn't even imagine the amount of damage that you've caused.
Look at what you have done to our household!
I'm not going to just sit back and suffer anymore.
It'd be best if you don't think I'll let things go like I have been.
I will make sure that you realize and understand and come to regret how monstrous a problem you've created. isn't this what you wanted?
Hey there!
It seems you're going a bit too far in the way you're talking to the child.
Grandpa!
Sir, how did you come to be here?
It's been a while, Shi Su.
Or do I need to call you Chairwoman Kang now?
You've changed a lot.
Let's talk about us later.
Let's talk about her first.
How do you know that child?
She's going to be my granddaughter-in-law.
What do you mean?
She's the girl I picked just for JiHoo.
Grandfather!
Are you serious?
Until now, I just kept an eye on her, but now, she's no different than family.
I would appreciate it if you didn't treat her so carelessly in the future.
JanDi, what are you doing?
Get your bags and follow me!
Y-Y-Yes.
Sunbae.
Starting today, she's going to be living with us.
What?
JiHoo, what are you doing?
You should be showing her to her room.
I came because Grandfather dragged me here, but
I can go to GaEul's tomorrow.
You kids!
Who said you two, all grown up boy and girl, could be in the same room together with the door closed?
Grandfather, I'm sorry and I'm grateful.
I'll spend the night here today.
Don't think about running away, and there's nothing to be grateful for.
You're the person that forced me into this house with that kid.
I brought you here to punish you.
What?
Do you know how hard it is for me to walk on eggshells around that grandson of mine?
Grandfather and Sunbae are . . . and I'm-
If you have caused trouble, then you should take the blame for it and accept your punishment.
JanDi might feel uncomfortable here.
It's not you who's uncomfortable?
I don't know anything about young people and their feelings being such and such.
I suppose things will happen as fate wills it to.
But that child has no place under heaven to go.
I want to become a guardian for that child.
There's nothing to like or be uncomfortable about.
But for like a child like Jandi to be paired with someone as stoic as you...
I'm against it, my boy.
When I think about it,
That was the first time EunJae asked for a favor.
That day, do you know what I was doing?
I have a favor to ask.
Favor?
Tomorrow morning, by 7 come here to this place.
Don't ask me for a reason.
Cha EunJae.
What is this?
I'm leaving.
YiJung!
I really hope that you'll come out. <i>Mother
What is it now?
A farewell trip?
And if I get him for you?
What's the use?
Mom.
Can't you just let him go now?
Please.
I said to give up now!
Please get in.
To be honest, I have a favor to ask of you, Miss Jandi.
A favor?
Whenever you have spare time, as a part-time job, Can you come visit this person?
Me?
You can tell him stories or you can just show your face once in a while.
Who is this person?
To me, he's like an older brother.
He's the same as family.
But why did you ask me to do this?
Because what this person needs the most...is warmth.
If I tell you that among the people I've met, Jandi, you seem to be the warmest person, would that be an answer?
Of course, you will be adequately compensated.
Oh, no!
If it is something I can help with, then of course, I'll do it.
This is a personal favor; neither the young master nor the Chairwoman must find out.
Okay.
Okay.
Hello. It's nice to meet you.
My name is Geum JanDi.
Though I'm lacking in much, I'll be a good friend to you.
Starting today, let's get along with each other.
Fighting!
Young Master.
What happened to JanDi?
Is she okay?
Dr. Yoon took her to his house.
To JiHoo's house?
Right now, that is the safest place she can be.
Lend me your cell phone.
I feel assured since she's at your house.
JoonPyo.
But why am I feeling so anxious?
My heart keeps feeling anguished. <i> Goo JunPyo
Jan Di.
WooBin Sunbae.
These days feel like death warmed over.
YiJung is acting like an invalid.
JoonPyo's under house arrest.
It's so stressful.
Look!
Even my skin is a mess.
Don't worry too much.
It's nothing big.
He's just not allowed to go out.
He destroyed a wedding in front of that important figure.
It'd be even weirder if nothing happened.
In any case, I was planning on going to see JoonPyo.
Do you have any message you want me to pass on to him?
JanDi, are you okay?
Ah!
As for me, well, I'm doing really well.
What?
Why are you looking at me like that?
Just because.
Living at JiHoo's house, both you and JiHoo look comfortable.
Geum JanDi, Goo JoonPyo, Yoon JiHoo.
You three.
Whatever kind of fate it is... it sure is complicated.
I'm just saying that's how it is.
Be strong, Geum JanDi.
And thanks.
For what?
JiHoo.
I don't think I've ever seen him so comfortable-looking.
And about finding his grandfather.
It's all thanks to you.
It's not.
No, lately I'm the one that is being a burden.
Here.
I'll clean your hands.
It feels refreshing, doesn't it? The worst kind of encounter is the fish meeting, because meeting leaves a horrible fishy smell. The encounter one must be most careful with is the flower meeting.
I really like this phrase, a handkerchief-like meeting.
Sir, how was it with you?
It would be great if I could be like a handkerchief to you.
Don't you think?
Isn't that right, sir?
Then, I'll read you something different next.
Do you want me to do it?
It's all right.
If I leave you to yourself,
I don't think you'll be able to go to school tomorrow.
You can't right there!
You can't cut the hair in the back!
I'll help you.
It's okay.
I'll do it myself.
You have to let me pay you back for trimming my hair. It's a car wash!
I wanted to tell you. That...
I love you.
I wanted to say it out loud like that.
That is all.
Are you quitting?
Are you really going to run away like this?
Do you think that this is what that person wants?
It doesn't matter anymore.
It matters to me.
In order to make your heart strong so that it isn't easily broken you said I needed to be molded, and shaped and burned in fiery oven; to endure that.
So that you don't have any regrets. You said that.
It was all nonsense.
It's not over yet.
You haven't done everything yet.
I can't give up like this.
I'm going to make this hand move again.
I just need to get in.
Go over there.
Thank you.
Take care.
Hey, GaEul.
What's wrong?
Are you okay?
Hey!
What are you doing these days?
You haven't been sleeping and you've been coming out before the crack of dawn.
Tell me.
What's wrong?
Is it something I can help you with?
Don't worry.
I only have a little more to do before it's over.
Are you ready?
Yeah. Okay.
Let's move out.
One. Two. Three.
I'm going out with my friend.
Whether you decide to follow or not, do whatever you want.
Then we shall go as well.
Manager Lee, you're ready, right?
Catch them! <BR> Hey! You almost caused an accident.
Don't worry and do whatever you need.
I'll take good care of him.
Mom will be right back.
Have fun with Noona.
Please take care of him.
Say "Bye, Mom." Bye, Mom.
Take care.
Let's have fun.
Gu JunPyo!
Are you okay?
Right now?
I'm tired.
What is it?
This isn't an 'it', it's a kid.
We haven't seen each other in forever, why on earth would you bring a little leech with you?
Did you adopt him from somewhere?
Noona, let's go here.
Okay, let's go.
I was wondering why you asked to meet at a zoo.
Is that little leech more important than I am?
If you don't want to be a leech yourself, then stop whining and follow me.
Let's go.
Let's go together.
We are asked, what number set does the number 8 belong to?
So this is actually a good review of the different sets of numbers that we often talk about.
So the first set under consideration is the natural numbers.
And these are essentially the counting numbers, and you're not counting 0.
So just if you were actually to count objects, and you have at least one of them, we're talking about the natural numbers. So that would be 1, 2, 3, so on and so forth.
So clearly, 8 is a natural number.
You can count up to 8 here. You could count 8 objects.
So 8 is a member of the natural numbers.
The next one we should consider, let's consider the whole numbers right over here.
And I should say natural numbers.
So let's consider the whole numbers.
The whole numbers are essentially the same thing as the natural numbers, but we're now going to include 0.
So this is 0, 1, 2, 3, so on and so forth.
So clearly, 8 is one of these as well.
You could eventually increment your way to 8,
like you're just counting all of the whole numbers.
Another way to view this is the non-negative numbers.
So 8 clearly belongs to this as well.
So let's expand our set a little bit. Let's think about integers.
Now these are all the numbers starting with, well you could keep counting down, all the way up to negative 3, negative 2, negative 1, 0, 1, 2, 3, and you could just keep going there.
Now clearly, 8 is one of these as well. You can just keep counting to 8. In fact, let me just put our check box there.
In general, you have your integers that contain both the positive and the negative numbers and 0, depending on whether you consider that positive or negative, or neither.
So that's the integers, right over here.
And then the whole numbers is a subset of the integers.
So I'll draw it like this.
The whole numbers are right over here, that is the whole numbers.
We've now excluded all of the negative numbers.
So these are all the non-negative numbers. All the non-negative integers, I should say. So these are the whole numbers.
And then the natural numbers are a subset of that. It's essentially everything. So the only thing that's in whole numbers that's not in the natural numbers is just the number 0.
So let me make it clear.
This circle is the whole numbers, and then I have the natural numbers, which is a subset of that.
Obviously this isn't drawn to scale.
The natural numbers is a subset of that.
8 is a member of all of them. 8 is sitting right over here.
So it's a member of the natural numbers, whole numbers, and the integers.
Now let's keep expanding things. Let's talk about rational numbers.
Now these are numbers that can be expressed in the form p over q, where both p and q are integers.
So can 8 be expressed this way?
Well, you can express 8 as 8 over 1. Or actually 16 over 2.
Or you could just keep going, 32 over 4, you can express it as a bunch of p's over q's, where both the p and q are integers.
So it's definitely a rational number.
And in fact, all of these things over here are rational numbers.
So let me draw.
So this is all a subset of rational numbers.
So 8 is definitely a member of that as well.
Rational numbers, so let me put the check box over here.
Now what about irrational numbers?
Irrational numbers.
Well, by definition, these are numbers that are not rational. These are numbers that cannot be expressed in this form, where p and q are integers.
So if something is rational, it just cannot be irrational.
So 8 is not a member of the irrational numbers.
The irrational numbers are just a completely separate set over here.
So I would draw it like this. This area right over here, this would be the irrational numbers.
Irrational.
Rational is not a subset of irrational, they are exclusive. You can't be in both sets.
So that's irrational right over there. And then finally let's ask, is 8 a member of the real numbers?
Now the real numbers are essentially all of these. It's combining both the rational and the irrational.
So the real numbers is all of this right over here.
And so 8 is clearly a member of the real.
It's a member of the real, and within the real, you either can be rational or irrational, 8 it is rational.
It's an integer. It's a whole number. And it is a natural number.
So it's definitely a member of the reals.
And just to give you might be saying, hey well, what is an irrational number then?
Can't almost every number be represented like this?
Or every number you can think of be represented like this? And an example of maybe the most famous example of an irrational number is pi.
Pi is equal to 3.14159, and people devote their lives to memorizing the digits of pi.
But what makes this irrational is you can't represent it as a ratio, or as a rational expression, of integers, the way you can for rational numbers.
And this right here is non-repeating.
And if it was repeating, you actually could express it as a ratio of integers, and we do that in other videos.
It is non-repeating and non terminating, so you never run out digits to the right of the decimal point.
So this would be an example of an irrational number.
So pi would sit here in the irrationals. Anyway, hopefully you found that helpful.
Rewrite 5 plus 5 plus 5 plus 5 plus 5 plus 5 plus 5 as a multiplication expression.
And then they want us to write the expression three times using different ways to write multiplication.
So let's do the first part.
Let's write it as a multiplication expression.
So how many times have we added 5 here?
Well, we've got it at one, two, three, four, five, six, seven.
So one way to think of it, if I just said what is here?
How many 5's are there?
You'd say, well, I added 5 to itself seven times, right?
You could literally say this is 7 times 5.
We could literally write, this is 7 times 5, or you could view it as 5 seven times.
I'm not even writing it mathematically yet.
I'm just saying, look, if I saw seven of something, you would literally say, if these were apples, you would say apples seven times, or you'd say seven times the apple, whatever it is.
Now, in this case, we're actually adding the number to each other, and we could figure out what that is, and why don't we?
But the way we would write this mathematically, we would say this is 7 times 5.
We could also write it like this.
We could write it 7 dot 5.
This and this mean the exact same thing.
It means we're multiplying 7 times 5 or 5 times 7.
You can actually switch the order, and you get the exact same value.
You could actually write it 5 times 7.
So you could interpret this as 7 five times or 5 seven times, however you like to do it, or 5 seven times.
I don't want to confuse you.
I just want to show you that these are all equivalent.
This is also equivalent.
5 times 7.
Same thing.
You could write them in parentheses.
You could write it like this.
This all means the same thing. That's 7 times 5, and so is this.
These all evaluate to the same thing:
5 times 7.
So these are all equivalent, and since we've worked with it so much, let's just figure out the answer.
So if we add up 5 to itself seven times, what do we get?
Well, 5 plus 5 is 10.
10 plus 5 is 15, plus 5 is 20, plus 5 is 25, plus 5 is 30, plus 5 is 35.
So all of these evaluate to 35, just so you see that they're the same thing.
These are all equivalent to 35.
And just something to think about, this is also the exact same thing, depending on how you want to interpret this, as 7 five times.
They didn't ask us to do it, but I thought I would point it out to you.
7 five times would look like this:
7 plus 7 plus 7 plus 7 plus 7, right?
I have 7 five times.
I added it to itself five different times.
There's five 7's here added to each other.
And when you add these up, you'll also get 35.
And that's why 5 times 7 and 7 times 5 is the same thing.
Today I have just one request.
Please don't tell me I'm normal.
Now I'd like to introduce you to my brothers.
Remi is 22, tall and very handsome.
He's speechless, but he communicates joy in a way that some of the best orators cannot.
Remi knows what love is.
He shares it unconditionally and he shares it regardless.
He's not greedy.
He doesn't see skin color.
He doesn't care about religious differences, and get this: He has never told a lie.
When he sings songs from our childhood, attempting words that not even I could remember, he reminds me of one thing: how little we know about the mind, and how wonderful the unknown must be.
Samuel is 16.
He's tall.
He's very handsome.
He has the most impeccable memory. He has a selective one, though.
He doesn't remember if he stole my chocolate bar, but he remembers the year of release for every song on my iPod, conversations we had when he was four, weeing on my arm on the first ever episode of Teletubbies, and Lady Gaga's birthday.
Don't they sound incredible?
But most people don't agree.
And in fact, because their minds don't fit into society's version of normal, they're often bypassed and misunderstood.
But what lifted my heart and strengthened my soul was that even though this was the case, although they were not seen as ordinary, this could only mean one thing: that they were extraordinary -- autistic and extraordinary.
Now, for you who may be less familiar with the term "autism," it's a complex brain disorder that affects social communication, learning and sometimes physical skills.
It manifests in each individual differently, hence why Remi is so different from Sam.
And across the world, every 20 minutes, one new person is diagnosed with autism, and although it's one of the fastest-growing developmental disorders in the world, there is no known cause or cure.
And I cannot remember the first moment I encountered autism, but I cannot recall a day without it.
I was just three years old when my brother came along, and I was so excited that
I had a new being in my life.
And after a few months went by, I realized that he was different.
He screamed a lot.
He didn't want to play like the other babies did, and in fact, he didn't seem very interested in me whatsoever.
Remi lived and reigned in his own world, with his own rules, and he found pleasure in the smallest things,
like lining up cars around the room and staring at the washing machine and eating anything that came in between.
And as he grew older, he grew more different, and the differences became more obvious.
Yet beyond the tantrums and the frustration and the never-ending hyperactivity was something really unique: a pure and innocent nature, a boy who saw the world without prejudice, a human who had never lied.
Extraordinary.
Now, I cannot deny that there have been some challenging moments in my family, moments where I've wished that they were just like me.
But I cast my mind back to the things that they've taught me about individuality and communication and love, and I realize that these are things that I wouldn't want to change with normality.
Normality overlooks the beauty that differences give us, and the fact that we are different doesn't mean that one of us is wrong.
It just means that there's a different kind of right.
And if I could communicate just one thing to Remi and to Sam and to you, it would be that you don't have to be normal.
You can be extraordinary.
Because autistic or not, the differences that we have --
We've got a gift!
Everyone's got a gift inside of us, and in all honesty, the pursuit of normality is the ultimate sacrifice of potential.
The chance for greatness, for progress and for change dies the moment we try to be like someone else.
Please -- don't tell me I'm normal.
Thank you. (Applause) (Applause)
If you've practiced and hopefully, memorized your multiplication tables, you'll now find out that you're prepared to do most any multiplication problem. You just have to understand, I guess for lack of a better word, the system of how to do it.
Nine times one is equal to nine. Anything times one is equal to itself. But we have this five sitting up here, so nine times one, we have to add that five.
And so what do we get?
So nine times one plus five is nine plus five, which is fourteen. Let me write it right there. Fourteen.
And to explain that I'm just going to rewrite these numbers. I can rewrite sixteen as ten-- let me do it right here. Ten plus six.
Nine times ten. Well, you've memorized this. And anything times ten is just that anything with a zero.
Same exercise. First, you start with the eight. Eight times five.
So let's say I had seventy-eight times-- let's do it times seven. Eight times seven. Eight times seven is fifty-six.
Well, that's fifty-four. So seven times seven is forty-nine. Plus five is fifty-four.
Three times nine is equal to twenty-seven.
Put the seven in the ones place. Put the two up here in the tens place, because it's twenty plus seven. Two tens is twenty.
So six times three is eighteen, plus five is twenty-three. Just to be clear, we didn't multiply six times three and add five. We actually, if you looked at where we are in our place on the problem, this is actually a thirty.
This is equal to twenty-three. We can put the three in the tens place and then put this two up here. Now we're almost done, one multiplication left.
Nine times two is eighteen. Eighteen. Then we do nine times six.
Nine times three is twenty-seven-- if we have that memorized. And then twenty-seven plus five is thirty-two.
Thirty-two. And then you have nine times seven. That's sixty-three, but we have this three hanging out there.
Welcome back.
In the last presentation, I showed you how to essentially reverse the chain rule when you're doing an integral.
And you could also do this by integral, it's called integration by substitution.
And I'll show you why.
And this is essentially just a reverse of the chain rule.
The last problem we did in that last video, I said, sine of x to the third power times cosine of x, and I took the integral of the whole thing.
So we see the derivative of the sine x here, right, which is cosine of x, so we can just treat sine of x like a variable and take its integral.
And I said that that is equal to sine of x to the fourth, times 1/4.
And the reason why we could just treat the sine of x like it's just like kind of a variable instead of a function, is because we had its derivative sitting right here.
And if you keep doing it back and forth between the chain rule and what I just did, I think it'll make a lot of sense.
So this might have been a little confusing.
So I'll show you a technique called integration by substitution, which is essentially the exact same thing.
We say, well, we have a function and its derivative, so let me let u equal the function that we have the derivative of.
Right? u is equal to sine of x, right? u is sine of x.
Well, what's the derivative of u? du, dx.
Well, we know what du dx is, right? du of dx is equal to cosine of x.
We memorized that, and maybe in a future presentation I'll actually prove it to you.
So what we can now do is substitute these 2 things into this integral.
So the integral now becomes, instead of writing sine of x to the third power, we can write u to the third power.
Well, we just showed, cosine of x is just du dx, right?
So it's times du dx, and then we have times dx, right?
So this dx and this dx actually do cancel out, and you're left with, that this is equal to the integral of u to the third du.
The only thing different than what you might have seen recently is that instead of an x, we have a u here.
And while we know that the answer of this integral, this is equal to 1/4 u to the fourth, and then, of course, we should add the plus c.
So u is the sine of x.
1/4 sine of x to the fourth, plus c.
Actually, this might be an easier way to think about these type of integrals than what I did in the last presentation.
Let's do a couple more problems like this.
Let's take the integral of 2x plus 3 times x squared plus 3x plus 15 to the fifth power dx.
That looks complicated to you, doesn't it?
Well, just like we said, this is a pattern, like we saw in the previous examples.
We have this expression here, x squared plus 3x plus 15, and well, what's the derivative of this? x squared plus 3x plus 15? Well, it's 2x plus 3, right?
So let's make the substitution.
Because we have a u that we can use, and then we have its derivative, right?
So we can say u is equal to x squared plus 3x plus 15, and we can say then, the derivative of u, we know the derivative of u is 2x plus 3, right?
So now we can make our substitutions.
I'm just going to switch the orders of these two around, no different.
So this is just u to the fifth, right?
So this is just u to the fifth.
And then this is du dx times du dx, right?
I just switched the orders.
And then I multiply that times dx.
And these cancel.
And I know you're not completely comfortable yet with even this integration notation, why is this dx sitting there in the first place, but when we do the definite integrals it will make more sense.
But this is just equal to the integral of u to the fifth du.
And the integral of this, well, this is easy.
This is just equal to 1/6 u to the sixth, right, plus c.
This is just equal to 1/6 times u, which is this right here, right, we just set u to equal this expression, 1/6 x squared plus 3x plus 15.
All of this to the sixth power, plus c.
Let's do one more.
Let's take the integral of e to the x times e to the x to the fifth.
Let's say to the minus third power. dx.
Well, once again, we have this expression e to the x, and what's the derivative of e to the x?
Well, the derivative of e to the x, as we learned, which is one of these things that amazes me, is e to the x. Actually, that's one definition for e, is number which, when it's raised to the x power, it's the derivative of the same expression.
But we can say then that u is equal to e to the x, and we know that du dx is equal to e to the x as well, which is, once again, mind blowing.
So if we rewrite this top integral, this is just equal to, I won't switch this time.
So this is du dx, right? du dx times u to the minus 3 dx.
Well, du dx is e to the x. u is also e to the x.
Why didn't I say that this one is u, and why didn't I say this one is du dx to the minus 3?
Because then I can't multiply it times a dx, and it gets all confusing.
So this, as we see, simplifies to the integral of u to the minus 3 du, and that that equals, let's see.
You raise exponent 1 minus 1/2 u to the minus two, and that's the same thing as minus 1/2 e to the x to the minus 2, or we could view that as minus 1/2 e to the minus 2x, and of course, plus c at the end.
Well, I could have simplified this before even doing the substitution, right?
I could have said that that's the same thing as the integral of e to the x times e to the minus three x dx, which is the same thing as the integral of e to the minus 2x dx.
But anyway, that's integration by substitution.
I might do another presentation where I do slightly harder problems, using this same technique.
I'll see you soon.
I have here three equations of four unknowns.
You can already guess, or you already know, that if you have more unknowns than equations, you are probably not constraining it enough.
You actually are going to have an infinite number of solutions.
Those infinite number of solutions could still be constrained.
Let's say we're in four dimensions, in this case, because we have four variables.
Maybe we were constrained into a plane in four dimensions, or if we were in three dimensions, maybe we're constrained to a line.
A line is an infinite number of solutions, but it's a more constrained set.
Let's solve this set of linear equations.
We've done this by elimination in the past. What I want to do is I want to introduce the idea of matrices.
The matrices are really just arrays of numbers that are shorthand for this system of equations.
Let me create a matrix here.
I could just create a coefficient matrix, where the coefficient matrix would just be, let me write it neatly, the coefficient matrix would just be the coefficients on the left hand side of these linear equations.
The coefficient there is 1.
The coefficient there is 1.
The coefficient there is 2.
You have 2, 2, 4.
2, 2, 4.
1, 2, 0.
1, 2, there is no coefficient the x3 term here, because there is no x3 term there.
We'll say the coefficient on the x3 term there is 0.
And then we have 1, minus 1, and 6.
Now if I just did this right there, that would be the coefficient matrix for this system of equations right there.
What I want to do is I want to augment it, I want to augment it with what these equations need to be equal to.
Let me augment it.
What I am going to do is I'm going to just draw a little line here, and write the 7, the 12, and the 4.
I think you can see that this is just another way of writing this.
And just by the position, we know that these are the coefficients on the x1 terms.
We know that these are the coefficients on the x2 terms.
And what this does, it really just saves us from having to write x1 and x2 every time.
We can essentially do the same operations on this that we otherwise would have done on that.
What we can do is, we can replace any equation with that equation times some scalar multiple, plus another equation.
We can divide an equation, or multiply an equation by a scalar.
We can subtract them from each other.
We can swap them.
Let's do that in an attempt to solve this equation.
The first thing I want to do, just like I've done in the past, I want to get this equation into the form of, where if I can, I have a 1.
My leading coefficient in any of my rows is a 1.
And that every other entry in that column is a 0.
In the past, I made sure that every other entry below it is a 0.
That's what I was doing in some of the previous videos, when we tried to figure out of things were linearly independent, or not.
Now I'm going to make sure that if there is a 1, if there is a leading 1 in any of my rows, that everything else in that column is a 0.
That form I'm doing is called reduced row echelon form.
Let me write that.
Reduced row echelon form.
If we call this augmented matrix, matrix A, then I want to get it into the reduced row echelon form of matrix A.
And matrices, the convention is, just like vectors, you make them nice and bold, but use capital letters, instead of lowercase letters.
We'll talk more about how matrices relate to vectors in the future.
Let's just solve this system of equations.
The first thing I want to do is, in an ideal world I would get all of these guys right here to be 0.
Let me replace this guy with that guy, with the first entry minus the second entry.
Let me do that.
The first row isn't going to change.
It's going to be 1, 2, 1, 1.
And then I get a 7 right there.
That's my first row.
Now the second row, I'm going to replace it with the first row minus the second row.
So what do I get.
1 minus 1 is 0.
2 minus 2 is 0.
1 minus 2 is minus 1. And then 1 minus minus 1 is 2.
That's 1 plus 1.
And then 7 minus 12 is minus 5.
Now I want to get rid of this row here.
I don't want to get rid of it.
I want to get rid of this 2 right here.
I want to turn it into a 0.
Let's replace this row with this row minus 2 times that row.
What I'm going to do is, this row minus 2 times the first row.
I'm going to replace this row with that.
2 minus 2 times 1 is 0.
That was the whole point.
4 minus 2 times 2 is 0.
0 minus 2 times 1 is minus 2.
6 minus 2 times 1 is 6 minus 2, which is 4.
4 minus 2 times 7, is 4 minus 14, which is minus 10.
Now what can I do next.
You can kind of see that this row, well talk more about what this row means.
When all of a sudden it's all been zeroed out, there's nothing here.
If I had non-zero term here, then I'd want to zero this guy out, although it's already zeroed out.
I'm just going to move over to this row.
The first thing I want to do is I want to make this leading coefficient here a 1.
What I want to do is, I'm going to multiply this entire row by minus 1.
If I multiply this entire row times minus 1.
I don't even have to rewrite the matrix.
This becomes plus 1, minus 2, plus 5.
I think you can accept that.
Now what can we do?
Well, let's turn this right here into a 0.
Let me rewrite my augmented matrix in the new form that I have.
I'm going to keep the middle row the same this time.
so Michele Thompson she has been diagnosed with something known as persistent sexual arousal syndrome, that sounds devastating right well she has up to three hundred orgasms a day alright okay so first we start off with persistent sexual arousal syndrome and that sounds pretty good right? three hundred orgasms yeah it became a really really serious problem for her it effected her relationships a lot of men couldn't keep up with her, I would imagine so so you know she would date guys for a couple months and they would you know get super tired of her, literally and they would leave her, so she thought she was never going to find her knight in shining armor yeah hold up before we get to him she had to leave a job at a factory because the vibrations of a machine sent her into an orgasmic epileptic fit you know she's like wha ha ha ha ha wha right and they're like hey hey just bring it down for a second I mean three hundred a day do you have any idea how much that is no that's insane that's insanity by the way she was working sorry she was working at a biscuit factory so you better get it right, biscuit factory aka cookie factory but um so yeah the machines out in the factory were setting her off man she's sensitive alright so we get to the man riding in for the rescue right his name is Andrew Carr he's a thirty two year old and they've been dating for the past six months she says that they have sex up to ten times a day and that he's doing a great job at um playing into her sexual arousal syndrome gez'um lord mercy ten times a day I didn't think anyone else was doing that, that's not even, I don't even, look, that kind of makes me think the story might be untrue, why is that? what kind of guy can have sex ten times a day? that's like physically impossible. yeah, there's something fishy going on here. because I mean, she's probably embellishing her sex life with him, I don't know but look but on the other hand, she did get, the other guys didn't make it right. and this guy did make it so obviously something's working right so she's happy with him maybe it's not ten maybe it's eight maybe it's four or maybe it's five I don't know four sounds superhuman but maybe he's a super generous guy and they're not only having coital relations maybe he's also you know giving her a little licky lick that's the first time we've ever come up with that I've hear of sippy sip but licky lick okay that's what the direction you decided to go with this? alright what you could of done is he's helping a sister out yes, in a couple of different ways and my guess is you're exactly right he's probably going downtown you know a little this a little that little this you know he's mixing it up right giving her a little boom boom pow here and there a little spinning the records as it were. so uh but they had a video with this which you know is probably copyrighted so you know
I don't want to get into it but that dude the whole time she's talking about how many orgasms he's given her he's got the biggest shit eating grin you've ever seen in your life he's like okay and i'm like dude I don't know that I'm bragging you know yeah at the same time she's getting orgasms at a cookie factory yeah I mean that's what I'm talking about
I mean a biscuit sends her into a canipsion right so you're like you know what I'm saying while on the other hand if the brother's actually putting out ten times a day that is pretty impressive so I'm split on this story but it reminded me of another story when i was in a brothel obviously, in turkey, in turkey the turkey brothel? yeah, you remember this story so I'm a kid and a friend of mine, kid teenagers right friend of mine takes me and another friend of mine from the states, the states that's what he called it uh to a turkish brothel uh the least sexually appealing place in the world, okay and it was perfect because you go there and you go oh no I'm done with brothels, not interested, right and one, there's one disaster after another okay it's like Amsterdamn but the road is closed off and you walk down the road and you see the women in the houses right and it's like oh no, oh no please please right, and so guy goes into the most disastrous of the options I mean this woman is gigantic she's old and okay, nothing wrong except she's in her lingerie or whatever I guess that was lingerie
I mean it was unreal right and he picks her he's back out in two minutes okay and he's on top of the world he's got his button he's got his shirt buttoned down to here and he's like this, yeah and he comes out and he's like who's next he tells his friend, you wanna be next?
And I'm like ew, ew
I'm like number one she was one of the most unattractive women I've ever seen in my life number two you paid for her, number three you were done in ninety seconds, okay and number for you're like hey, telling your guy buddy you wanna be next?
I'm like there's nothing I would desire less than being your friend, that's what I thought, now that's not the guy I knew, that's not the guy who took me the other guy took me but god what a parade of horrors that was anyway that guy now I'm being a little unfair here but he reminds me of this guy with his grin in the background like ha ha ten times a day, and I'm like okay okay but she's going off on biscuits, exactly, yeah but it's a fascinating thing man
I want to tell you all about a piece of American history that is so secret, that nobody has done anything about it for 167 years, until right now.
And the way that we're going to uncover this vestigial organ of America past is by asking this question: Why?
As we all know -- (Laughter) we are in the middle of another presidential election, hotly contested, as you can see.
(Laughter) But what you may not know is that American voter turnout ranks near the bottom of all countries in the entire world, 138th of 172 nations.
This is the world's most famous democracy.
So ... Why do we vote on Tuesday?
Does anybody know?
And as a matter of fact, Michigan and Arizona are voting today.
Here's the answer: Absolutely no good reason whatsoever.
(Laughter)
I'm not joking.
You will not find the answer in the Declaration of Independence, nor will you find it in the Constitution.
It is just a stupid law from 1845.
(Laughter)
In 1845, Americans traveled by horse and buggy.
As did I, evidently.
It took a day to get to the county seat to vote, a day to get back, and you couldn't travel on the Sabbath, so, Tuesday it was.
I don't often travel by horse and buggy, I would imagine most of you don't, so when I found out about this, I was fascinated.
I linked up with a group called, what else -- "Why Tuesday?" to go and ask our nation's most prominent elected leaders if they knew the answer to the question,
"Why do we vote on Tuesday?"
(Video) Rick Santorum: Anybody knows? OK, I'm going to be stumped on this.
Anybody knows why we vote on Tuesdays? Jacob Soboroff:
Do you happen to know?
Ron Paul: On Tuesdays? JS:
The day after the first Monday in November. RP: I don't know how that originated.
JS: Do you know why we do vote on Tuesday?
Newt Gingrich:
No. Dick Lugar: No, I don't.
Dianne Feinstein: I don't.
Darrell Issa: No.
In truth, really, I'm not sure why.
JS: OK, thanks very much.
(Laughter)
JS: These are people that live for election day, yet they don't know why we vote on that very day.
(Laughter) Chris Rock said, "They don't want you to vote.
If they did, we wouldn't vote on a Tuesday in November.
Have you ever thrown a party on a Tuesday?
(Laughter)
No, of course not.
Nobody would show up."
(Laughter)
Here's the cool part.
Because we asked this question, "Why Tuesday?" there is now this bill, the Weekend Voting Act in the Congress of the United States of America.
It would move election day from Tuesday to the weekend, so that -- duh -- more people can vote.
(Applause)
It has only taken 167 years, but finally, we are on the verge of changing American history.
Thank you very much.
(Applause)
Thanks a lot.
What I want to do in this video is a fairly straightforward primer on perimeter and area.
And I'll do perimeter here on the left, and I'll do area here on the right. And you're probably pretty familiar with these concepts, but we'll revisit it just in case you are not.
Perimeter is essentially the distance to go around something or if you were to put a fence around something or if you were to measure-- if you were to put a tape around a figure, how
long that tape would be. So for example, let's say I have a rectangle.
And a rectangle is a figure that has 4 sides and 4 right angles. So this is a rectangle right here. I have 1, 2, 3, 4 right angles.
And maybe I'll label the points A, B, C, and D.
And let's say we know the following.
And we know that AB is equal to 7, and we know that BC is equal to 5.
And we want to know, what is the perimeter of ABCD? So let me write it down. The perimeter of rectangle ABCD is just going to be equal to the sum of the lengths of the sides.
If I were to build a fence, if this was like a plot of land,
I would just have to measure-- how long is this side right over here? Well, we already know that's 7 in this color.
So it's that side right over there is of length 7. So it'll be 7 plus this length over here, which is going to be 5. They tell us that.
BC is 5. Plus 5. Plus DC is going to be the same length is AB, which is going to be 7 again.
So you have 7 plus 5 is 12 plus 7 plus 5 is 12 again.
So you're going to have a perimeter of 24. And you could go the other way around. Let's say that you have a square, which is a special case of a rectangle.
So this is A, B, C, D. And we're going to tell ourselves that this right here is a square. And let's say that this square has a perimeter. So square has a perimeter of 36.
So given that, what is the length of each of the sides? Well, all the sides are going to have the same length.
Let's call them x.
If AB is x, then BC is x, then DC is x, and AD is x. All of the sides are congruent.
All of these segments are congruent. They all have the same measure, and we call that x.
So if we want to figure out the perimeter here, it'll just be x plus x plus x plus x, or 4x. Let me write that. x plus x plus x plus x, which is equal to 4x, which is going to be equal to 36. They gave us that in the problem.
So this is a 9 by 9 square. This width is 9. This is 9, and then the height right over here is also 9.
Area is kind of a measure of how much space does this thing take up in two dimensions?
And one way to think about area is if I have a 1-by-1 square, so this is a 1-by-1 square-- and when I say 1-by-1, it means you only have to specify two dimensions for a square or a rectangle because the other two are going to be the same.
So for example, you could call this a 5 by 7 rectangle because that immediately tells you, OK, this side is 5 and that side is 5. This side is 7, and that side is 7. And for a square, you could say it's a 1-by-1 square because that specifies all of the sides.
You could really say, for a square, a square where on one side is 1, then really all the sides are going to be 1. So this is a 1-by-1 square.
And so you can view the area of any figure as how many 1-by-1 squares can you fit on that figure?
So for example, if we were going back to this rectangle right here, and I wanted to find out the area of this rectangle-- and the notation we can use for area is put something in brackets.
So the area of rectangle ABCD is equal to the number of 1-by-1 squares we can fit on this rectangle. So let's try to do that just manually.
I think you already might get a sense of how to do it a little bit quicker. But let's put a bunch of 1-by-1. So let's see.
So going along one of the sides, if we just go along one of the sides like this, you could put 7 just along one side just like that. And then over here, how many can we see? We see that's 1 row.
Then we have 3 rows and then 4 rows and then 5 rows. 1, 2, 3, 4, 5. And that makes sense because this is 1, 1, 1, 1, 1.
These are 1, 1, 1, 1, 1, 1, 1. Should add up to 7. Yup, there's 7.
So this is 5 by 7. And then you could actually count these, and this is kind of straight forward multiplication. If you want to know the total number of cubes here, you could count it, or you can say, well, I've got 5 rows, 7 columns.
I'm going to have 35-- did I say cube-- squares. I have 5 squares in this direction, 7 in this direction. So I'm going to have 35 total squares.
So the area of this figure right over here is 35.
And so the general method, you could just say, well, I'm just going to take one of the dimensions and multiply it by the other dimension.
So if I have a rectangle, let's say the rectangle is 1/2 by 1/2 by 2.
Those are its dimensions. Well, you could just multiply it. You say 1/2 times 2.
And you might say, well, what does 1/2 mean? Well, it means, in this dimension, I could only fit 1/2 of a 1-by-1 square.
And so when you add this guy and this guy together, you are going to get a whole one.
Now what about area of a square?
Well, a square is just a special case where the length and the width are the same.
So if I have a square-- let me draw a square here. And let's call that XYZ-- I don't know, let's make this S.
And let's say I wanted to find the area and let's say I know one side over here is 2. So XS is equal to 2, and I want to find the area of XYZS. So once again, I use the brackets to specify the area of this figure, of this polygon right here, this square.
We know all the sides are equal.
Well, it's a special case of a rectangle where we would multiply the length times the width. We know that they're the same thing.
If this is 2, then this is going to be 2. So you just multiply 2 times 2.
Or if you want to think of it, you square it, which is where the word comes from-- squaring something. So you multiply 2 times 2, which is equal to 2 squared.
Welcome to the presentation on averages.
Averages is probably a concept that you've already used before, maybe not in a mathematical way.
But people will talk in terms of, the average voter wants a politician to do this, or the average student in a class wants to get out early.
So you're probably already familiar with the concept of an average.
And you probably already intuitively knew that an average is just a number that represents the different values that a group could have.
But it can represent that as one number as opposed to giving all the different values.
And let's give a couple of examples of how to compute an average, and you might already know how to do this.
So let's say I had the numbers 1, 3, 5, and 20.
And I asked you, what is the average of these four numbers?
Well, what we do is, we literally just add up the numbers.
And then divide by the number of numbers we have.
So we say 1 plus 3 is 4.
So let me write that.
1 plus 3 plus 5 plus 20 equals, let's see, 1 plus 3 is 4.
4 plus 5 is 9.
9 plus 20 is 29.
And we had 4 numbers; one, two, three, four.
So 4 goes into 29.
And it goes, 7, 7, 28.
And then we have 10, I didn't have to do that decimal there, oh well.
2, 8, 25.
34 00:01:36,91 --> 00:01:40,88 So 4 goes into 29 7.25 times.
So the average of these four numbers is equal to 7.25.
And we can kind of view this, 7.25, as one way to represent these four numbers without having to list these four numbers.
There are other representations you'll learn later on.
Like the mode.
You'll also the mean, which we'll talk about later, is actually the same thing as the average.
So let's do some problems which I think are going to be close to your heart.
Let's say on the first four tests of an exam, I got a-- let's see, I got an 80, an 81. An 87, and an 88.
What's my average in the class so far?
Well, all I have to do is add up these four numbers.
So I say, 80 plus 81 plus 87 plus 88. Well, zero plus 1 is 1. 1 plus 7 is 8.
And, 4/8, so that's 32. Plus 1 is 33.
62 00:03:16,95 --> 00:03:20,75 And now we divide this number by 4.
4 goes into 336.
67 00:03:31,85 --> 00:03:34 33 minus 32 is 1, 16.
So the average is equal to 84.
So, so far my average after the first four exams is an 84.
Now let's make this a little bit more difficult.
We know that the average after four exams, at four exams, is equal to 84.
If I were to ask you what do I have to get on the next test to average an 88, to average an 88 in the class. 78 00:04:20,31 --> 00:04:23,49 So let's say that x is what I get on the next test.
80 00:04:28,18 --> 00:04:31,99 So now what we can say is, is that the first four exams, I
could either list out the first four exams that I took. Or I already know what the average is.
So I know the sum of the first four exams is going to 4 times 84.
And now I want to add the, what I get on the 5th exam, x.
And I'm going to divide that by all five exams.
So in other words, this number is the average of my first five exams.
We just figured out the average of the first four exams.
But now, we sum up the first four exams here. We add what I got on the fifth exam, and then we divide it by 5, because now we're averaging five exams.
And I said that I need to get in an 88 in the class.
And now we solve for x.
5 times 80 is 400, so it's 440.
440 equals 4 times 84, we just saw that, is 320 plus 16 is 336.
336 plus x is equal to 440.
Well, it turns out if you subtract 336 from both sides, you get x is equal to 104.
So unless you have a exam that has some bonus problems on it, it's probably impossible for you to get ah an 88 average in the class after just the next exam.
And let's just look at what we just did.
We said, after 4 exams we had an 84.
What do I have to get on that next exam to average an 88 in the class after 5 exams?
And that's what we solved for when we got x.
Now, let's ask another question.
I said after four exams, after four exams, I had an 84 average.
highest score I could get on an exam is 100, what is the highest average I can finish in the class if I were to really study hard and get 100 on the next 2 exams?
Well, once again, what we'll want to do is assume we get 100 on the next 2 exams and then take the average.
So we'll have to solve all 6 exams.
So we're going to have the average of 6, so in the
exams times the 84 average.
Plus, and there's going to be 2 more exams, right?
Because there's 6 exams in the class.
And I'm going to get 100 in each.
So that's 200.
And what's this average?
Well, 4 times 84, we already said, is 336.
Plus 200 over 6.
So that's 536 over 6. 6 goes into 5 36.
But 6 goes into 53, 8 times.
48. 56. 9 times.
9 times 6 is 54. 6 minus is 20 6 goes into-- so we'll see it's actually 89.333333, goes on forever.
So no matter how hard I try in this class, the best I can do. Because I only have two exams left, even if I were to get 100 on the next two exams.
I can finish the class with an 89.333 average.
You already had kind of a sense of what an average is.
I think it's important [that] people look at art, because we live in a visual world.
And understanding, and looking at, and thinking about the way images communicate - in all kinds of ways - is important to being alive today.
If one has heightened visual acumen - which you get from spending time looking at things - whether it's looking at newspaper photos closely or looking at works in a museum or looking at your surroundings - or birds - more closely, that sort of attention to an environment makes you a better person.
You are existing in a more aware, alert, present space.
Sometimes people think that the only way of looking at art is going to museum constantly - at places like that.
But, maybe sometimes, art is everywhere - in the street - if you look at architecture, places, or everything.
So, you really don't need to go to a museum to see art.
It could be anywhere - in a park, or looking at buildings, or going to the movies.
So I think that [art's] in everyday life.
It's all about noticing, for me.
It's all about trying to see beyond the first impression.
People look at art and they say,
"I like this.
I don't like this." And they move on.
They have predetermined notions.
But if you can stop, and take a breath, and look a little deeper at something, you can really start to notice some kind of detail that you might have not noticed before.
And I think that that skill applies to so many things in life - aside from art. About being able just to slow down and be aware of where, actually - where you're standing - and just even stop talking.
And just, maybe, open up your ears, for example.
There's so much detail around that you can absorb, if you really just take a moment and just let it come in - and listen.
Lets say i run some type of sheep farm or some type of wool producing business and in year one i go out there and buy a bunch of sheep and i put them on some land and i go and buy the sheep for one million dollars and i buy the land for 1.2 million dollars so we have 2.2 million dollars in assets.
Nothing confusing there .Now lets go to year two and think about how we want to account for the sheep and the land so one way we could say this the sheep are still there the land is still there i paid a million dollars for the sheep and they are all still there so ill put on my books that the sheep are still one million dollars and i paid 1.2 million dollars for the land so ill put on my books that the landis one .two million dollars so in this situation i have accounted for the sheep and the land based on their historical cost, so let me write this down this is based on historical cost .Now another and this is a legitimate way to account for things especially if theres no other way to really think about what my sheep or my land are worth .Look this is what i paid for them now lets say there is an active market in sheep and you can get a sheep apraiser to come over to your farm to come and tell you how much you sheep are worth andyour sheep appriaser comes and says wow your sheep are looking good but theresbeen a big, id dont know,sheep epidemic in another part of the country so there's a sheep shortage so your sheep are actually worth a lot more that they were last year and they say i think you sheep are now worth 2 million dollars .so you say Hey wow! the market value of my sheep is two million so you could say instead of putting one million there let me put two million dollars for my sheep and
lets say the land is also appreciated the highways gone by and someone wants to build a development nearby so theres the fair value of you land is also going up maybe its also two million dollars. so both of theses so this is two million and this is two mililion so this right over here you could view the market value or the fair value of your sheep.
Now either one of these is legititmate ways of accounting but its good to know the difference
This is historical cost accounting ,this is fair value accounting in general most accounting standard board want people to report the fair value to market value as frequently as possible so its very easy to do if there is kind of a market in that or you cannot get a apppraiser that can give you a pretty good estimate of what these things are worth if that isnt around or if its just inefficient to do it then you probably want to do the historical cost method so thats all the difference .Historial cost- how much yu paid for it
Fair value-whats the current market value today so it sound like very fancy words but its a pretty simple idea
say "Hey, this is going to be a 2".
But what we'll do in this video is to think How to troubleshoot these problems systematically.
Because what we'll find is that as more and more complicated are these equations, you will not be able to simply think about them and do them in your head
So it is very important that you first understand how manipulate these equations, but even more important is understand what they really represent
This literally just says 7 times x equals fourteen
In algebra, do not write "times" ali
When you write two numbers side-by-side or a number close a variable like this, that means you are multiplying
It is just a shorthand, a notion of shorthand
And usually we do not use the multiplication sign because He is confused, because x is the most common variable used in algebra
And if I had to write 7 times x equals 14, if I write my sign of "times" or my x so a bit strange, it may seem as xx "or" times "times"
So usually when you're dealing with equations, especially when one of the variables is an x, you would not use the traditional sign of multiplication
You can use something like this--you can use the point to represent the multiplication
Then you can have 7 times is equal to 14
But this is still a little unusual
If you have something multiplied by a variable you just going to write 7 x
This literally means 7 times x
Now, to understand how you can manipulate this equation to solve it, let's see a thing Then 7 times x, what is this?
This is the same as--so I'll just rewrite this equation, but I'll rewrite it in visual form
Soon, 7 times x
Soon this literally means x added yourself 7 times
This is the definition of multiplication So that's literally x x x x more more more more x--let's see, This is 5 x 's--more x more x
Soon this right there is literally 7 x's
This is 7 x, right there
Let me rewrite it
This right here is 7 x
Now, this equation tells us that equals 7 x 14
Then, just assuming this is equal to 14
Let me draw 14 objects here So let me say I have 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14
So literally we're talking 7 x equals 14 things
Now, the reason why I drew it that way is to you really understand what we will do when we We divide both sides by 7
So let me erase it right here
Then, the default step every time--I didn't want to do this,
Let me do this, let me draw this last circle
- a coefficient is only one number by multiplying the variable
So, some number by multiplying the variable or we can call the coefficient times the variable is equal to something
What you want to do is just divide both sides by 7 in this case, or divide both sides by the coefficient
So if you divide both sides by 7, what do you have?
7 times something divided by 7 is only
This original thing 7 's if void and 14 divided by 7 is 2
Then your solution is x equals 2
But just to make this very tangible in your head, what is happening here is that when we divide both sides of the the equation by 7, we literally we divide both sides by 7
This is an equation
If you are saying that this is equal to it
Anything I do on the left I will have to do on the right
If they started being equal, I can't just do an operation on the one hand and in doing so continue being equal
They were the same thing
So if I split the left side by 7, so let me break it in seven groups
Soon there are seven x's here, so that's one, two, three, four, five, six, seven
So that's one, two, three, four, five, six, seven groups
Now, if I divide it into seven groups, I also want to divide the right side into seven groups
One, two, three, four, five, six, seven
So, if this whole thing is equal to this whole thing, so each one of these small pieces that break, these seven pieces, shall be equivalent
So that piece, we can say, is equal to that piece This piece is equal to this piece--they are all pieces are equivalent
There are seven pieces here, seven pieces here
Soon, every x must be equal to two of these objects
Soon, we have x is equal to, in this case--in this case We had the drawn objects where there are two of them. x is equal to 2
Now, let's just use two other examples here only for really get into your mind that we are dealing with an equation, and any operation that you make on one side of the equation You must be on the other side
So let me turn down a bit more
So let's say that I have, I say, I have 3 x equals 15
Now, once again, you may be able to do it in your head
You're saying this is saying 3 times some number is equal to 15
You can use your multiplication table 3 and figure out
But if you just wanted to do this systematically, and that
It is good to understand systematically, you say OK, this thing on the left is equal to this thing in the right
What should I do with this thing on the left to have only one x there?
Well, to have only the x, I need to divide it by 3 and my motivation to do this and that ' 3 times anything divided by 3, 3 's Cancel and I stay with only the x now, 3 x 15 was equal to
If I am splitting the left side by 3, for equality be satisfied, I need to divide the right side by 3.
What this in '?
The left side, the left side only an x, then we have just the x and the right side, and ' 15 divided by 3?
This and ' 5.
Now you could have done this equacao slightly different, even though they are equivalent
If you start with 3 x equals 15, then we can say that instead of dividing by 3, I can just see me free to 3 I can stick with the left side only equal to x, if I multiply both sides by the equacao by 1/3 then if I multiply that estimate the equacao on both sides by 1/3
This also works you say, 1/3 of 3 and 1.
When we multiply this part, 1/3 times 3, this and ' x 1 x e ' equal to 15 times 1/3 and ' equal to 5 and a 1 time x and ' the same as x, and this is the same thing where x is equal to 5 and these two forms are equivalent to solve this
If we divide both sides by 3, this and ' equivalent to multiply both side of equacao by 1/3
Now let's do one more and I'll make it a little more complicated
I'll modify the ftminword_len a little
Let's say I have more 4y 2y = 18 now, suddenly it's a little harder and to make this twin
We are saying that something twice over 4 times that thing and ' equal to 18 and ' harder to think that number is this
You can try
Let's say we have 1 is 2 times 4 times 1, 1 more and it does not work but let's consider systematically solve this
You can try to guess and you can reach the answer, but how do we do it systematically?
Let's show
If two y's terms, what does that mean?
This means literally that I have two y's summed up with one another
IE and ' y y more and so I'm adding 4 y's that I am joining 4 y 's, who literally are four y's added with one another
logo and ' y y y y more more more and that has to be equal to 18 and that and ' equal to 18 now, how many y's I have on the left?
How many y's I have?
I have one, two, three, four, five, six y's
Thus we can simplify this as 6y and ' equal to 18 and if you think about it, this makes sense so this here, the more 4 y and 2y ' 6y then more 4y 2y and ' 6y, and this makes sense
If we have two more litters 4 stretchers, I'll have 6 stretchers
If I have more y 2y's 4 ' s, I'll have 6 y's and this is equal to 18 and now, we know how to do this
If I have 6 times something equal to 18, if we divide the two sides the equacao by 6, do I solve the equacao then divide the left by 6, and divide the so I figur by law 6
and we then y equals 3 and you can try
This and ' and ' cool about a equacao
You can always check if you got the right answer
Let's see if this works 2 times 3 times 3 and 4 more ' to that?
2 times 3, this and ' equal to 6 and then 4 times 3 and ' equal to 12 6 more ' equal to 12 and 18 soon this works
From Migrant Worker to Activist
[Talking on the phone]:
It was caused by over contract. The contract expired.
When coming home, it would be a problem if she doesn't get her rights.
She should come home bringing what she's entitled to, like her salary and others.
Hety was a migrant worker who faced abuses from her boss. She had returned home and is now actively giving counseling and education to potential migrant workers in the village she resides.
She works in the Middle East and now she is asking for the help from SBMC (Migrant Workers Solidarity in Cianjur).
We asked her to write the chronology of her case.
After that we can meet up in the City of Cianjur.
If there is problem, such as her salary not being given, we will call the boss, to ask for her to be sent home.
Aside being sent home, she should also be entitled to her rights, like her salary.
If she comes home without bringing her salary, it would not be good.
Right?
They have been working for three years.
In Saudi Arabia.
Both husband and wife.
She's coming home tomorrow.
She flew out yesterday at 4 pm.
The first time it was only two months, and then she left again.
It has been three years now and she doesn't want to come home.
It might also be because her husband had passed away.
So she extended her contract for another two months.
Thank God, she becomes a successful migrant worker.
Once or twice a week, her father comes to clean the house.
Ah, she's already in Jakarta this afternoon.
That means she will be here tonight.
Ah, early morning tomorrow.
Those two houses belong to sisters.
That one belongs to the older sister whose husband passed away.
The one below is the younger sister's.
Both are migrant workers.
And thank God she is also a successful migrant worker.
So she could afford a house and send her kids to school.
But too bad her husband passed away.
They could not enjoy the result of their work together.
This is Mrs. Aad, and her daughter, Lusni.
(Lusni) was a migrant worker from 2004 to 2007.
Then she went again in 2009 and came back in 2011.
Come and talk to us.
Ah, we're on camera.
Yes.
Thank God, she didn't have any problem when working as a migrant worker.
She brought home money and her salary was fully paid.
I work at home now.
I want to work if there is any job for me.
But there is no job.
I was married once, but it was short-lived.
Now, I am not married.
So I was trained to become a gymnast for two years in Hunan, China in the 1970s.
When I was in the first grade, the government wanted to transfer me to a school for athletes, all expenses paid.
But my tiger mother said, "No."
My parents wanted me to become an engineer like them.
After surviving the Cultural Revolution, they firmly believed there's only one sure way to happiness: a safe and well-paid job.
It is not important if I like the job or not.
But my dream was to become a Chinese opera singer.
That is me playing my imaginary piano.
An opera singer must start training young to learn acrobatics, so I tried everything I could to go to opera school.
I even wrote to the school principal and the host of a radio show.
But no adults liked the idea.
No adults believed I was serious.
Only my friends supported me, but they were kids, just as powerless as I was.
So at age 15, I knew I was too old to be trained.
My dream would never come true.
I was afraid that for the rest of my life some second-class happiness would be the best I could hope for.
But that's so unfair.
So I was determined to find another calling.
Nobody around to teach me?
Fine.
I turned to books.
I satisfied my hunger for parental advice from this book by a family of writers and musicians.["Correspondence in the Family of Fou Lei"]
I found my role model of an independent woman when Confucian tradition requires obedience.["Jane Eyre"]
And I learned to be efficient from this book.["Cheaper by the Dozen"]
And I was inspired to study abroad after reading these. ["Complete Works of Sanmao" (aka Echo Chan)] ["Lessons From History" by Nan Huaijin]
I came to the U.S. in 1995, so which books did I read here first?
Books banned in China, of course.
"The Good Earth" is about Chinese peasant life.
That's just not convenient for propaganda.
Got it.
The Bible is interesting, but strange.
(Laughter)
That's a topic for a different day.
But the fifth commandment gave me an epiphany:
"You shall honor your father and mother."
"Honor," I said.
"That's so different, and better, than obey."
So it becomes my tool to climb out of this Confucian guilt trap and to restart my relationship with my parents.
Encountering a new culture also started my habit of comparative reading.
It offers many insights.
For example, I found this map out of place at first because this is what Chinese students grew up with.
It had never occurred to me,
China doesn't have to be at the center of the world.
A map actually carries somebody's view.
Comparative reading actually is nothing new.
It's a standard practice in the academic world.
There are even research fields such as comparative religion and comparative literature.
Compare and contrast gives scholars a more complete understanding of a topic.
So I thought, well, if comparative reading works for research, why not do it in daily life too?
So I started reading books in pairs.
["John Adams" by David McCullough] -- who are involved in the same event, or friends with shared experiences.
["Personal History" by Katharine Graham] ["The Snowball:
Warren Buffett and the Business of Life," by Alice Schroeder]
I also compare the same stories in different genres -- (Laughter)
[Holy Bible:
["Lamb" by Chrisopher Moore] -- or similar stories from different cultures, as Joseph Campbell did in his wonderful book.["The Power of Myth" by Joseph Campbell]
For example, both the Christ and the Buddha went through three temptations.
For the Christ, the temptations are economic, political and spiritual.
For the Buddha, they are all psychological: lust, fear and social duty -- interesting.
So if you know a foreign language, it's also fun to read your favorite books in two languages.
["The Way of Chuang Tzu" Thomas Merton] ["Tao:
The Watercourse Way" Alan Watts]
Instead of lost in translation, I found there is much to gain.
For example, it's through translation that I realized "happiness" in Chinese literally means "fast joy." Huh!
"Bride" in Chinese literally means "new mother." Uh-oh.
(Laughter)
Books have given me a magic portal to connect with people of the past and the present.
I know I shall never feel lonely or powerless again.
Having a dream shattered really is nothing compared to what many others have suffered.
I have come to believe that coming true is not the only purpose of a dream.
Its most important purpose is to get us in touch with where dreams come from, where passion comes from, where happiness comes from.
Even a shattered dream can do that for you.
So because of books, I'm here today, happy, living again with a purpose and a clarity, most of the time.
So may books be always with you.
Thank you.
(Applause)
Thank you.
(Applause)
Thank you.
(Applause)
Welcome to the presentation on radians and degrees. So you all are probably already reasonably familiar with the concept of degrees. I think in our angles models we actually drill you through a bunch of problems.
So what is a radian? So I'll start with the definition and I think this might give you a little intuition for why it's even called radian.
This is a radius of length r. A radian is the angle that subtends an arc.
And all subtend means is if this is angle, and this is the arc, this angle subtends this arc and this arc subtends this angle.
So a radian -- one radian -- is the angle that subtends an arc that's the length of the radius. So the length of this is also r. And this angle is one radian. i think that's messy.
And let's say that this radius is a length r and that this arc right here is also length r. Then this angle, what's called theta, is equal to one radian. And now it makes sense that they call it a radian.
It's 2 pi r, right? You know that from the basic geometry module. So if the radian is the angle that sub tends an arc of r, then the angle that subtends an arc of 2 pi r is 2 pi radians.
If you're still confused, think of it this way. An angle of 2 pi radians going all the way around subtends an arc of 2 pi radiuses. Or radii.
I just want to one, give you an intuition for why it's called a radian and kind of how it relates to a circle. And then given that there 2 pi radians in a circle, we can now figure out a relationship between radians and degrees. Let me delete this.
And how many degrees are there in a circle?
Well that's equal to 360 degrees.
We have an equation that sets up a conversion between radians and degrees. So one radian is equal to 360 over 2 pi degrees. I just divided both sides by 2 pi.
1 degree is equal to 2 pi over 360 radians.
Which equals pi over 180 radians. So then we have a conversion:
1 radian equals 180 over pi degrees and 1 degree equals pi over 180 radians. Amd if you ever forget these, it doesn't hurt to to memorize this. But if you ever forget it, I always go back to this.
And that's also equal to pi radians. So pi radians equal 180 degrees and we can get to see the math. 1 radian equals 180 over pi degrees or 1 degree is equal to pi over 180 radians.
Well, we know that 1 degree os pi over 180 radians. So 45 degrees is equal to 45 times pi over 180 radians. And let's see, 45 divided by 180.
Let's do a couple of other examples. Just always remember: this 1 radian equals 180 over pi degrees. 1 degree equals pi over 180 radians.
Well I already forgot what I had just written so I just remind myself that pi radians is equal to 180 degrees.
But we know that pi radians is equal to 180 degrees, right? So one radian is equal to 180 over -- that's one radian -- is equal to 180 over pi degrees.
So pi over 2 radians is equal to pi over 2 times 180 over pi degrees.
Let's say 30 degrees.
Once again, I forgot the formula so I just remember that pi radians is equal to 180 degrees. So 1 degree is equal to pi over 180 radians. So 30 degrees is equal to 30 times pi over 180 radians which equals -- 30 goes into 180 six times.
Welcome to Level Four multiplication. Let's do some problems. Let's say we had two hundred thirty-five times--
Write 15:25 as a fraction in simplest form.
So 15 to 25 is just a ratio, and we can write it.
So they've given us 15 to 25.
And you can write this ratio as a fraction, as 15 over 25.
And if we want to put this in simplest form, we just have to think about what is the largest number that divides into both 15 and 25?
Or what is their greatest common factor?
When you just eyeball it, you say, well, 5 goes into both of them, and I'm pretty sure that's the largest number that divides into both, so let's divide both by 5.
If there is a larger number, then we might be able to see it once we've simplified it a little bit more.
So let's divide the numerator and the denominator by 5 and see what we get.
So now we get 15 divided by 5 is equal to 3.
And 25 divided by 5 is equal to 5, and now we have 3/5.
3 and 5 don't share any common factors greater than 1, so it is in simplest form.
So we've done what they asked.
We've written it as a fraction in simplest form.
We could also write this, if we want to write it in this type of notation, as 3:5.
The Internet is one of the United States' most robust and growing industries.
It enables free and open communication among billions, and it's been the backbone for protests around the world.
But a new bill proposes to give the power to censor the Internet to the entertainment industry.
It's called PROTECT IP, and here's how it works.
Private corporations want the ability to shut down unauthorized sites where people download movies, TV shows, and music.
Since most of these sites are outside US jurisdiction,
PROTECT IP uses a couple different tactics within American borders.
Firstly, it gives the government the power to make US Internet providers block access to infringing domain names.
They can also sue US-based search engines, directories, or even blogs and forums, to have links to these sites removed.
Secondly, PROTECT IP gives corporations and the government the ability to cut off funds to infringing websites by having US-based advertisers and payment services cancel those accounts.
In a nutshell, that's what PROTECT IP will try to do.
But in all likelihood, it'll do something else altogether.
For starters, it won't stop downloaders.
You'll still be able to access a blocked site just by entering its IP address instead of its name.
What PROTECT IP will do is cripple new startups because it also lets companies sue any site they feel isn't doing their filtering well enough.
These lawsuits could easily bankrupt new search engines and social media sites.
And PROTECT IP's wording is ambiguous enough that important social media sites could become targets.
Lots of trailblazing websites could look like piracy heavens to the wrong judge.
Tumblr, SoundCloud, an early YouTube, wherever people express themselves, make art, broadcast news or organize protests, there's plenty of TV footage, movie clips, and copyrighted music mixed in.
And even if you trust the US government not to abuse their new power to censor the Net, what about the countries that follow in our path and pass similar laws?
People around the world will have very different
Internets, and unscrupulous governments will have powerful tools to hinder free expression.
But perhaps most dangerously, PROTECT IP will meddle with the inner workings of the Net.
Experts believe by fiddling with the web's registry of domain names, the result will be less security, and less stability.
In short, PROTECT IP won't stop piracy, but it will introduce vast potential for censorship and abuse, while making the web less safe and less reliable.
This is the Internet we're talking about!
It's a vital and vibrant medium.
And our government is tampering with its basic structure, so people will maybe buy more Hollywood movies.
But Hollywood movies don't get grassroots candidates elected.
They don't overthrow corrupt regimes, and the entire entertainment industry doesn't even contribute that much to our economy.
The Internet does all these, and more.
Corporations already have tools to fight piracy.
They have the power to take down specific content, to sue peer-to-peer software companies out of existence, and to sue journalists just for talking about how to copy a DVD.
They have a history of stretching and abusing their powers.
They tried to take a baby video off YouTube, just for the music playing in the background.
They even sued to ban the VCR and the first MP3 players.
So the question is, "How far will they take all this?"
The answer at this point, is obvious.
As far as we'll let them.
So the type of magic I like, and I'm a magician, is magic that uses technology to create illusions.
So I would like to show you something I've been working on.
It's an application that I think will be useful for artists -- multimedia artists in particular.
It synchronizes videos across multiple screens of mobile devices.
I borrowed these three iPods from people here in the audience to show you what I mean.
And I'm going to use them to tell you a little bit about my favorite subject: deception.
(Music)
One of my favorite magicians is Karl Germain.
He had this wonderful trick where a rosebush would bloom right in front of your eyes.
But it was his production of a butterfly that was the most beautiful.
(Recording) Announcer: Ladies and gentlemen, the creation of life.
(Applause) (Music)
Announcer: Magic is the only honest profession.
A magician promises to deceive you -- and he does.
Now I feel bad about that.
But people lie every day.
(Ringing) Hold on.
Phone:
Hey, where are you? MT:
Stuck in traffic.
I'll be there soon. You've all done it.
(Laughter) (Music)
Right: I'll be ready in just a minute, darling.
Center:
It's just what I've always wanted.
Left:
You were great.
MT:
Deception, it's a fundamental part of life.
Now polls show that men tell twice as many lies as women -- assuming the women they asked told the truth.
(Laughing)
We deceive to gain advantage and to hide our weaknesses.
The Chinese general Sun Tzu said that all war was based on deception.
Oscar Wilde said the same thing of romance.
Some people deceive for money.
Let's play a game.
Three cards, three chances.
Announcer: One five will get you 10, 10 will get you 20.
Now, where's the lady?
Where is the queen?
MT: This one?
Sorry.
You lose. Well, I didn't deceive you.
You deceived yourself.
Self-deception.
That's when we convince ourselves that a lie is the truth.
Sometimes it's hard to tell the two apart.
Compulsive gamblers are experts at self-deception.
(Slot machine)
They believe they can win.
They forget the times they lose.
The brain is very good at forgetting.
Bad experiences are quickly forgotten.
Bad experiences quickly disappear.
Which is why in this vast and lonely cosmos, we are so wonderfully optimistic.
Our self-deception becomes a positive illusion -- why movies are able to take us onto extraordinary adventures; why we believe Romeo when he says he loves Juliet; and why single notes of music, when played together, become a sonata and conjure up meaning.
That's "Clair De lune."
Its composer, called Debussy, said that art was the greatest deception of all.
Art is a deception that creates real emotions -- a lie that creates a truth.
And when you give yourself over to that deception, it becomes magic.
(Music fades slowly) (Applause) Thank you.
Thank you very much.
Khan Academy is most known for its collection of videos, so before I go any further, let me show you a little bit of a montage.
(Video) Salman Khan:
So the hypotenuse is now going to be five.
This animal's fossils are only found in this area of South America -- a nice clean band here -- and this part of Africa.
We can integrate over the surface, and the notation usually is a capital sigma.
National Assembly: They create the Committee of Public Safety, which sounds like a very nice committee.
Notice, this is an aldehyde, and it's an alcohol.
Start differentiating into effector and memory cells.
A galaxy. Hey!
There's another galaxy.
Oh, look! There's another galaxy.
And for dollars, is their 30 million, plus the 20 million dollars from the American manufacturer.
If this does not blow your mind, then you have no emotion.
(Laughter) (Applause) (Live) SK:
We now have on the order of 2,200 videos, covering everything from basic arithmetic, all the way to vector calculus, and some of the stuff that you saw up there.
We have a million students a month using the site, watching on the order of 100 to 200,000 videos a day.
But what we're going to talk about in this is how we're going to the next level.
But before I do that, I want to talk a little bit about really just how I got started.
And some of you all might know, about five years ago, I was an analyst at a hedge fund, and I was in Boston, and I was tutoring my cousins in New Orleans, remotely.
And I started putting the first YouTube videos up, really just as a kind of nice-to-have, just kind of a supplement for my cousins, something that might give them a refresher or something.
And as soon as I put those first YouTube videos up, something interesting happened. Actually, a bunch of interesting things happened.
The first was the feedback from my cousins.
They told me that they preferred me on YouTube than in person.
(Laughter)
And once you get over the backhanded nature of that, there was actually something very profound there.
They were saying that they preferred the automated version of their cousin to their cousin.
At first it's very unintuitive, but when you think about it from their point of view, it makes a ton of sense.
You have this situation where now they can pause and repeat their cousin, without feeling like they're wasting my time.
If they have to review something that they should have learned a couple of weeks ago, or maybe a couple of years ago, they don't have to be embarrassed and ask their cousin.
They can just watch those videos; if they're bored, they can go ahead.
They can watch at their own time and pace. Probably the least-appreciated aspect of this is the notion that the very first time that you're trying to get your brain around a new concept, the very last thing you need is another human being saying, "Do you understand this?"
And that's what was happening with the interaction with my cousins before, and now they can just do it in the intimacy of their own room.
The other thing that happened is --
I put them on YouTube just --
I saw no reason to make it private, so I let other people watch it, and then people started stumbling on it, and I started getting some comments and some letters and all sorts of feedback from random people around the world.
These are just a few.
This is actually from one of the original calculus videos.
Someone wrote it on YouTube, it was a YouTube comment:
"First time I smiled doing a derivative."
(Laughter)
Let's pause here.
This person did a derivative, and then they smiled. (Laughter)
In response to that same comment -- this is on the thread, you can go on YouTube and look at the comments -- someone else wrote:
"Same thing here.
I actually got a natural high and a good mood for the entire day, since I remember seeing all of this matrix text in class, and here I'm all like, 'I know kung fu.'" (Laughter)
We get a lot of feedback along those lines.
This clearly was helping people.
But then, as the viewership kept growing and kept growing,
I started getting letters from people, and it was starting to become clear that it was more than just a nice-to-have.
This is just an excerpt from one of those letters:
"My 12 year-old son has autism, and has had a terrible time with math.
We have tried everything, viewed everything, bought everything.
We stumbled on your video on decimals, and it got through.
Then we went on to the dreaded fractions.
Again, he got it. We could not believe it.
He is so excited."
And so you can imagine, here I was, an analyst at a hedge fund -- it was very strange for me to do something of social value.
(Laughter) (Applause)
But I was excited, so I kept going.
And then a few other things started to dawn on me; that not only would it help my cousins right now, or these people who were sending letters, but that this content will never grow old, that it could help their kids or their grandkids.
If Isaac Newton had done YouTube videos on calculus, I wouldn't have to.
(Laughter)
Assuming he was good.
We don't know.
(Laughter)
The other thing that happened -- and even at this point, I said,
"OK, maybe it's a good supplement.
It's good for motivated students. It's good for maybe home-schoolers."
But I didn't think it would somehow penetrate the classroom.
Then I started getting letters from teachers, and the teachers would write, saying,
"We've used your videos to flip the classroom.
You've given the lectures, so now what we do --"
And this could happen in every classroom in America tomorrow --
"what I do is I assign the lectures for homework, and what used to be homework, I now have the students doing in the classroom."
And I want to pause here -- (Applause)
I want to pause here, because there's a couple of interesting things.
One, when those teachers are doing that, there's the obvious benefit -- the benefit that now their students can enjoy the videos in the way that my cousins did, they can pause, repeat at their own pace, at their own time.
But the more interesting thing -- and this is the unintuitive thing when you talk about technology in the classroom -- by removing the one-size-fits-all lecture from the classroom, and letting students have a self-paced lecture at home, then when you go to the classroom, letting them do work, having the teacher walk around, having the peers actually be able to interact with each other, these teachers have used technology to humanize the classroom.
They took a fundamentally dehumanizing experience -- 30 kids with their fingers on their lips, not allowed to interact with each other.
A teacher, no matter how good, has to give this one-size-fits-all lecture to 30 students -- blank faces, slightly antagonistic -- and now it's a human experience, now they're actually interacting with each other.
So once the Khan Academy --
I quit my job, and we turned into a real organization -- we're a not-for-profit -- the question is, how do we take this to the next level?
How do we take what those teachers were doing to its natural conclusion?
And so, what I'm showing over here, these are actual exercises that I started writing for my cousins.
The ones I started were much more primitive.
This is a more competent version of it.
But the paradigm here is, we'll generate as many questions as you need, until you get that concept, until you get 10 in a row.
And the Khan Academy videos are there.
You get hints, the actual steps for that problem, if you don't know how to do it.
The paradigm here seems like a very simple thing:
10 in a row, you move on.
But it's fundamentally different than what's happening in classrooms right now.
In a traditional classroom, you have homework, lecture, homework, lecture, and then you have a snapshot exam.
And that exam, whether you get a 70 percent, an 80 percent, a 90 percent or a 95 percent, the class moves on to the next topic.
And even that 95 percent student -- what was the five percent they didn't know?
Maybe they didn't know what happens when you raise something to the zeroth power.
Then you build on that in the next concept.
That's analogous to -- imagine learning to ride a bicycle.
Maybe I give you a lecture ahead of time, and I give you a bicycle for two weeks, then I come back after two weeks, and say, "Well, let's see.
You're having trouble taking left turns.
You can't quite stop.
You're an 80 percent bicyclist." So I put a big "C" stamp on your forehead -- (Laughter) and then I say, "Here's a unicycle."
(Laughter)
But as ridiculous as that sounds, that's exactly what's happening in our classrooms right now.
And the idea is you fast forward and good students start failing algebra all of the sudden, and start failing calculus all of the sudden, despite being smart, despite having good teachers, and it's usually because they have these Swiss cheese gaps that kept building throughout their foundation.
So our model is: learn math the way you'd learn anything,
like riding a bicycle. Stay on that bicycle.
Fall off that bicycle.
Do it as long as necessary, until you have mastery.
The traditional model, it penalizes you for experimentation and failure, but it does not expect mastery.
We encourage you to experiment.
We encourage you to fail. But we do expect mastery.
This is just another one of the modules.
This is trigonometry.
This is shifting and reflecting functions.
And they all fit together.
We have about 90 of these right now.
You can go to the site right now, it's all free, not trying to sell anything.
But the general idea is that they all fit into this knowledge map.
That top node right there, that's literally single-digit addition, it's like one plus one is equal to two.
The paradigm is, once you get 10 in a row on that, it keeps forwarding you to more and more advanced modules.
Further down the knowledge map, we're getting into more advanced arithmetic.
Further down, you start getting into pre-algebra and early algebra.
Further down, you start getting into algebra one, algebra two, a little bit of precalculus.
And the idea is, from this we can actually teach everything -- well, everything that can be taught in this type of a framework.
So you can imagine -- and this is what we are working on -- from this knowledge map, you have logic, you have computer programming, you have grammar, you have genetics, all based off of that core of, if you know this and that, now you're ready for this next concept.
Now that can work well for an individual learner, and I encourage you to do it with your kids, but I also encourage everyone in the audience to do it yourself.
It'll change what happens at the dinner table.
But what we want to do is use the natural conclusion of the flipping of the classroom that those early teachers had emailed me about.
And so what I'm showing you here, this is data from a pilot in the Los Altos school district, where they took two fifth-grade classes and two seventh-grade classes, and completely gutted their old math curriculum.
These kids aren't using textbooks, or getting one-size-fits-all lectures.
They're doing Khan Academy, that software, for roughly half of their math class.
I want to be clear: we don't view this as a complete math education.
What it does is -- this is what's happening in Los Altos -- it frees up time -- it's the blocking and tackling, making sure you know how to move through a system of equations, and it frees up time for the simulations, for the games, for the mechanics, for the robot-building, for the estimating how high that hill is based on its shadow.
And so the paradigm is the teacher walks in every day, every kid works at their own pace -- this is actually a live dashboard from the Los Altos school district -- and they look at this dashboard.
Every row is a student.
Every column is one of those concepts.
Green means the student's already proficient.
Blue means they're working on it -- no need to worry.
Red means they're stuck.
And what the teacher does is literally just say,
"Let me intervene on the red kids."
Or even better, "Let me get one of the green kids, who are already proficient in that concept, to be the first line of attack, and actually tutor their peer."
(Applause)
Now, I come from a very data-centric reality, so we don't want that teacher to even go and intervene and have to ask the kid awkward questions:
"What don't you understand?
What do you understand?" and all the rest.
So our paradigm is to arm teachers with as much data as possible -- data that, in any other field, is expected, in finance, marketing, manufacturing -- so the teachers can diagnose what's wrong with the students so they can make their interaction as productive as possible.
Now teachers know exactly what the students have been up to, how long they've spent each day, what videos they've watched, when did they pause the videos, what did they stop watching, what exercises are they using, what have they focused on?
The outer circle shows what exercises they were focused on.
The inner circle shows the videos they're focused on.
The data gets pretty granular, so you can see the exact problems the student got right or wrong.
Red is wrong, blue is right.
The leftmost question is the first one the student attempted.
They watched the video over there. And you can see, eventually they were able to get 10 in a row.
It's almost like you can see them learning over those last 10 problems.
They also got faster -- the height is how long it took them.
When you talk about self-paced learning, it makes sense for everyone -- in education-speak, "differentiated learning" -- but it's kind of crazy, what happens when you see it in a classroom.
Because every time we've done this, in every classroom we've done, over and over again, if you go five days into it, there's a group of kids who've raced ahead and a group who are a little bit slower.
In a traditional model, in a snapshot assessment, you say, "These are the gifted kids, these are the slow kids.
Maybe they should be tracked differently.
Maybe we should put them in different classes."
But when you let students work at their own pace -- we see it over and over again -- you see students who took a little bit extra time on one concept or the other, but once they get through that concept, they just race ahead.
And so the same kids that you thought were slow six weeks ago, you now would think are gifted.
And we're seeing it over and over again.
It makes you really wonder how much all of the labels maybe a lot of us have benefited from were really just due to a coincidence of time.
Now as valuable as something like this is in a district like Los Altos, our goal is to use technology to humanize, not just in Los Altos, but on a global scale, what's happening in education.
And that brings up an interesting point.
A lot of the effort in humanizing the classroom is focused on student-to-teacher ratios.
In our mind, the relevant metric is: student-to-valuable-human-time- with-the-teacher ratio.
So in a traditional model, most of the teacher's time is spent doing lectures and grading and whatnot.
Maybe five percent of their time is sitting next to students and working with them.
Now, 100 percent of their time is.
So once again, using technology, not just flipping the classroom, you're humanizing the classroom, I'd argue, by a factor of five or 10.
As valuable as that is in Los Altos, imagine what it does to the adult learner, who's embarrassed to go back and learn stuff they should have known before going back to college.
Imagine what it does to a street kid in Calcutta, who has to help his family during the day, and that's the reason he or she can't go to school.
Now they can spend two hours a day and remediate, or get up to speed and not feel embarrassed about what they do or don't know.
Now imagine what happens where -- we talked about the peers teaching each other inside of a classroom.
But this is all one system.
There's no reason why you can't have that peer-to-peer tutoring beyond that one classroom.
Imagine what happens if that student in Calcutta all of the sudden can tutor your son, or your son can tutor that kid in Calcutta.
And I think what you'll see emerging is this notion of a global one-world classroom.
And that's essentially what we're trying to build.
Thank you.
(Applause) Bill Gates: I'll ask about two or three questions.
(Applause ends) I've seen some things you're doing in the system, that have to do with motivation and feedback -- energy points, merit badges.
Tell me what you're thinking there.
SK:
Oh yeah. No, we have an awesome team working on it.
I have to be clear, it's not just me anymore.
I'm still doing all the videos, but we have a rock-star team doing the software.
We've put a bunch of game mechanics in there, where you get badges, we're going to start having leader boards by area, you get points.
It's actually been pretty interesting.
Just the wording of the badging, or how many points you get for doing something, we see on a system-wide basis, like tens of thousands of fifth-graders or sixth-graders going one direction or another, depending what badge you give them.
And the collaboration you're doing with Los Altos, how did that come about?
SK:
Los Altos, it was kind of crazy.
Once again, I didn't expect it to be used in classrooms.
Someone from their board came and said,
"What would you do if you had carte Blanche in a classroom?"
I said, "Well, every student would work at their own pace, on something like this, we'd give a dashboard."
They said, "This is kind of radical.
We have to think about it." Me and the rest of the team were like, "They're never going to want to do this."
But literally the next day they were like, "Can you start in two weeks?"
(Laughter)
BG: So fifth-grade math is where that's going on right now?
SK: It's two fifth-grade classes and two seventh-grade classes.
They're doing it at the district level.
I think what they're excited about is they can follow these kids, not only in school; on Christmas, we saw some of the kids were doing it.
We can track everything, track them as they go through the entire district.
Through the summers, as they go from one teacher to the next, you have this continuity of data that even at the district level, they can see.
BG:
So some of those views we saw were for the teacher to go in and track actually what's going on with those kids.
So you're getting feedback on those teacher views to see what they think they need? SK:
Oh yeah.
Most of those were specs by the teachers.
We made some of those for students so they could see their data, but we have a very tight design loop with the teachers themselves.
And they're saying, "Hey, this is nice, but --"
Like that focus graph, a lot of the teachers said,
"I have a feeling a lot of the kids are jumping around and not focusing on one topic."
So we made that focus diagram. So it's all been teacher-driven.
It's been pretty crazy. BG:
Is this ready for prime time?
Do you think a lot of classes next school year should try this thing out?
SK:
Yeah, it's ready.
We've got a million people on the site already, so we can handle a few more.
(Laughter)
No, no reason why it really can't happen in every classroom in America tomorrow.
And the vision of the tutoring thing. The idea there is, if I'm confused about a topic, somehow right in the user interface, I'd find people who are volunteering, maybe see their reputation, and I could schedule and connect up with those people?
SK:
Absolutely.
And this is something I recommend everyone in this audience do.
Those dashboards the teachers have, you can go log in right now and you can essentially become a coach for your kids, your nephews, your cousins, or maybe some kids at the Boys and Girls Club.
And yeah, you can start becoming a mentor, a tutor, really immediately.
But yeah, it's all there. BG:
Well, it's amazing.
I think you just got a glimpse of the future of education.
BG: Thank you.
SK:
Thank you.
So we need to figure out what 46 plus 43 is.
Let me write it down again and I'll write it like this:
46 plus 43.
What we do here is we just first look at the ones place
We literally have 6 ones plus 3 ones or you could say 6 and 3, and 6 plus 3 is just 9.
6 plus 3 is 9, so we have 9 ones.
And then you go to the tens place and there's two ways to think about it.
You could view this as 4 plus 4 is equal to 8 but really, the reality of what we're doing since we're operating in the tens place this is really 40 plus 40 is equal to 80.
And we could do the same problem expanded out.
This is the same thing as 40 plus 6.
We've seen this before, right?
That's what 46 is.
And then 43 is the same thing as 40 plus 3.
We've expanded these out before.
And so when you add them when you add a 6 plus a 3, you get a 9.
When you add a 40 plus a 40, you get an 80.
So you get 80 plus 9, which is 89.
And the whole reason why I did this is I wanted to show you that when you're adding 4's in the tens place you're really adding 40's.
The fact that it's in the tens place represents-- or the fact that the 4 is in the tens place shows that it represents 40.
The fact that the 8's there shows that it represents 80.
Divide and write the answer as a mixed number.
And we have 3/5 divided by 1/2.
Now, whenever you're dividing any fractions, you just have to remember that dividing by a fraction is the same thing as multiplying by its reciprocal.
So this thing right here is the same thing as 3/5 times-- so this is our 3/5 right here, and instead of a division sign, you want a multiplication sign, and instead of a 1/2, you want to take the reciprocal of 1/2, which would be 2/1-- so times 2/1.
So dividing by 1/2 is the exact same thing as multiplying by 2/1.
And we just do this as a straightforward multiplication problem now.
3 times 2 is 6, so our new numerator is 6.
5 times 1 is 5.
So 3/5 divided by 1/2 as an improper fraction is 6/5.
Now, they want us to write it as at mixed number.
So we divide the 5 into the 6, figure out how many times it goes.
That'll be the whole number part of the mixed number. And then whatever's left over will be the remaining numerator over 5.
So what we'll do is take 5 into 6.
5 goes into 6 one time.
1 times 5 is 5.
Subtract.
You have a remainder of 1.
So 6/5 is equal to one whole, or 5/5, and 1/5.
And now we're done!
3/5 divided by 1/2 is 1 and 1/5.
Now, the one thing that's not obvious is why did this work?
Why is dividing by 1/2 the same thing as multiplying essentially by 2.
2/1 is the same thing as 2.
And to do that, I'll do a little side-- fairly simple-- example, but hopefully, it gets the point across.
Let me take four objects.
So we have four objects: one, two, three, four.
So I have four objects, and if I were to divide into groups of two, so I want to divide it into groups of two.
So that is one group of two and then that is another group of two, how many groups do I have?
Well, 4 divided by 2, I have two groups of two, so that is equal to 2.
Now, what if I took those same four objects: one, two, three, four.
So I'm taking those same four objects.
Instead of dividing them into groups of two, I want to divide them into groups of 1/2, which means each group will have half of an object in it.
So let's say that would be one group right there.
That is a second group.
That is a third group.
I think you see each group has half of a circle in it.
That is the fourth.
That's the fifth.
That's the sixth.
That's the seventh, and then that's the eighth.
You have eight groups of 1/2, so this is equal to 8.
And notice, now each of the objects became two groups.
So you could say how many groups do you have?
Well, you have four objects and each of them became two groups.
I'm looking for a different color.
Each of them became two groups, and so you also have eight.
So dividing by 1/2 is the same thing as multiplying by 2.
And you could think about it with other numbers, but hopefully, that gives you a little bit of an intuition.
The perimeter of a rectangular fence measures 0.72 kilometers. The length of the fenced area is 160 meters.
What is its width?
Now the first thing that jumps out is that they're giving us different units.
They're giving us the perimeter in terms of kilometers and the length in terms of meters.
I am assuming that they want the width in meters because that's what they're giving us the length in.
Convert the perimeter into meters.
So we have the perimeter P is equal to 0.72 kilometers which I'll write km for short.
Kilometers.
1000 meters.
That's what the prefix "kilo" means.
And so we can say that for every 1 kilometer we have a 1000 meters.
And you might say so how do you know to multiply it by a 1000 instead of divide by a 1000?
One way to think about it and this is probably the best way to think about it is a kilometer is a huge bunch of meters, its actually 1000 meters.
So if I am converting kilometers into meters I should have a much larger number whatever my number is in kilometers it should be a much larger number in meters.
And also if you care about Dimensional Analysis, the dimensions cancel out here too.
We have km in the numerator, km in the denominator.
So you multiply it, you have 0.72 times a 1000 m and to multiply anything times a 1000 or any power of 10 if I multiply it by 10 I'll move the decimal to the right one space that would be multiplying it by 10 , it would be 7.2, multiplying it by a 100 would give us 72.
If we are multiplying by a 1000 that would give us 720.
So this is going to be equal to 720 m.
So that is the perimeter.
Now let's remind ourselves what the perimeter even is then hopefully we can figure out the width.
And they tell us that the length is 160 m.
So let's say that that's this dimension over here.
The length (l) is 160 m.
Its a rectangle so these sides are both the same length.
And our width is what we need to solve for so that's our width (w) and this is also our width.
And the perimeter is the measure going around it.
So the perimeter is going to be this length plus this width plus that same length again plus that width over there.
Or the perimeter (P) is equal to the length (l) plus the width (w) plus the length (l) plus the width (w)
We know what the length is so then the perimeter would be equal to 160 m plus w plus 160 m plus w.
And then we know what the perimeter is.
That's actually 720 m.
So 720 m is equal to 160 m plus w plus 160 m plus w.
Now there's a bunch of different ways to solve for w.
One way is to just add the width plus the length once, that's going to add up to half of the perimeter.
So if I just go half way around the rectangle that's going to add up to half the perimeter.
So w plus 160 m should be equal to one half of the perimeter which is one half times 720 m.
Or w plus 160 m is equal to 720 divided by 2 which is 360 m.
And so now you have w plus 160 m is 360 m.
So we could now subtract 160 from both sides to solve for it.
Something plus 160 is 360, you could in your head say, well, that something must be 200.
200 plus 160 is 360.
Or if you want to do it a little bit more formally you subtract 160 m from both sides of this equation and you are left with the width (w) is equal to 200 m.
We've solved the problem.
The other way is you could actually go straight from this equation.
So we get 720 is 160 plus 160 (320) and width (w) plus width (w) or 2 times the width (2w).
Anything plus itself is just 2 times that anything. Now if this plus 320 is equal to 720, what plus 320 is 720?
Well this thing must be equal to 400.
Or, formally, subtract 320 from both sides of this.
And you would get 400 is equal to 2w.
So if 2 times something is equal to 400 that something must be 200.
Or you can divide both sides of this equation by 2.
Either way you will get the width is equal to 200 m.
Janelle is training for a road race.
Her pedometer tracks how far she runs every day.
Here are the pedometer readings for the past four days: on Saturday, she went 3.89 miles; Sunday, 5.1;
Monday, 10.21; Tuesday, 3.35.
Estimate the total distance she ran over the four days, and then calculate the exact amount.
Let's estimate first.
So I'm just going to round them to the nearest mile.
So 3.89, let's round it up to 4 miles.
And I'm doing that because in the tenths place, we have an 8, which is 5 or greater.
So let's just make that roughly 4 miles.
Let's make this 5.1.
We round that down because this 1 is less than 5.
So let's make this 5 miles.
10.21, let's make that 10 miles because 2 would round down.
It's less than 5.
And 3.35, let's make that 3 miles, because 3 is less than 5, so we'd round down.
So that is 3 miles.
And if we were to add them up, 4 plus 5 is 9.
9 plus 10 is 19.
19 plus 3 is 22.
So my estimate is that she ran 22 miles over the four days.
That's my estimate.
Now let's figure out the exact amount that she ran.
Let me scroll down a little bit.
So we're going to have to add 3.89 to 5.1-- and remember, when you're adding decimals, you want to line up the decimal-- 10.21 and then finally 3.35.
And let's add all of these up.
Now we'll start in the hundredths place.
There's nothing here, so 9 plus nothing plus 1 is 10, plus 5 is 15.
So let's write the 5, and then carry, or regroup, the 1.
Let me do this in another color.
1 plus 8 is 9.
9 plus 1 is 10.
10 plus 2 is 12.
12 plus 3 is 15.
Put the 5 down.
Carry, or regroup, the 1.
1 plus 3 is 4.
4 plus 5 is 9.
9 plus 0 is still 9.
9 plus 3 is 12.
Write the 2.
Regroup this 1 right here.
I'll do it out here just so it's not part of any of these numbers, and then 1 plus 1 is 2.
And then we have to remember the decimal sitting right over there.
So the exact distance she ran was 22.55 miles.
So our estimate wasn't too bad.
It was 22 miles.
We got reasonably close, within about little over a half a mile.
The government is monitoring private phone calls your children and my children's private phone calls and tracking who their associates are.
This June we learned that out private lives are no longer private.
The US government is secretly tracking the emails purchases, text messages, location and phone calls of people all over the world.
Ed Rooney, Ed?
This is George Peterson...
With code names like PRlSM and XKEYSCORE, this network of monitoring programs is just one part of largest surveillance system in history.
This open-ended surveillance system is illegal and operates in total secrecy.
Under the system, the government can know where you've been, where you are, and where you're going.
The program was only exposed when former NSA contractor Edward Snowden leaked documents detailing the extensive data collection.
I've got information man, new shit is come to light.
The president, the NSA and their lawyers have tried to deflect the public outrage by distorting the facts and misleading the public about the process.
US courts have never allowed the government to run a spying program of this scale.
So how did this happen? Well, lets take a step back, for a minute. America's founders hated oppressive British surveillance and unreasonable search and seizure. the issue here is independence.
Welcome to the presentation on finding sums of integers.
You're probably wondering why are we doing this within the context of averages.
Well, if you think about it, all an average is is you take a sum of a bunch of numbers and then you divide by the number of numbers you have.
What we're going to do here is do a couple of algebra problems that involve just the sum parts first, and actually they can carry over into average problems as well.
Let's get started with a problem.
Let's say I told you that I had the sum of five consecutive integers is equal to 200.
-- what is the smallest of the five integers?
Well there's a couple of ways to do this, but I guess the most straightforward way is just to do it algebraically,
So let's say that x is the smallest of the integers, right, so x is actually what we're going to want to figure out.
Well if x is the smallest, what are the other four going to be?
We have a total of five.
Well, they're consecutive.
Consecutive just means that they follow each other, like 5, 6, 7, 8, 9, 10.
All of those are consecutive integers, right?
And if you remember, integers are just whole numbers, so it can't be a fraction or a decimal.
So if x is the smallest, so then the next integer is going to be x plus 1.
And the one after that's going to be x plus 2. And the one after that's going to be x plus 3.
And the one after that's going to be x plus 4, right?
It might seem confusing I'm writing all of these x's.
But if you think about it, if x was 5, then this would be 6, this would be 7, this would be 8, and this would be 9.
So these would be, assuming that x is the smallest of the integers, the five integers would be x, x+1, x+2, x+3, and x+4.
And we know that the sum of these five consecutive integers is 200.
What is the sum of these five, I guess we could say, numbers or expressions?
Well let's see, we have five x's -- 1, 2, 3, 4, 5. So x plus x plus x plus x plus x is equal to just 5x.
And then that's plus 1 plus 2 is 3, 3 plus 3 is 6, 6 plus 4 is 10.
So the sum of these five integers is going to be 5x plus 10, and all I did is add up the x's and added up the constants.
And we know that that is going to equal 200.
We can just solve for x.
So we get 5x is equal to 190 -- I just subtracted 10 from both sides, right?
And then x is equal to -- let me divide 5 into 190.
5 goes into 19 three times, 3 times 5 is 15. 9 minus 5 is 4, bring down the 0. 5 goes into 40, eight times.
So x is equal to 38.
Pretty straightforward problem, don't you think?
Now what if I were to ask you what is the average of the five consecutive numbers?
Well now, there's two ways of doing this.
Now that we already know that x is 38, we know that the other numbers are going to be -- well this is 38, 39, 40, 41, 42.
Well we could just average these four numbers.
You could just say 38 plus 39 plus 40 plus 41 plus 42.
And well we already know what those -- I don't even have to do the math.
You already know that they average up, they sum up to 200 and then we divide the sum by 5, because there are 5 numbers.
So the average is 40.
There are a couple ways you could think about that.
One, you see 40's just a middle number so that makes sense.
If we had a number that was much smaller than 40 or something, you couldn't just necessarily pick the middle number.
But in this case these are consecutive and makes sense.
Another way we could have done this problem, if you were, say, taking the SAT and they were to ask you the sum of five numbers is 200, what's the average of the numbers?
Well you say, well, all I have to do is divide that 200 by 5 and I'll get 40.
Let's do another problem and I'll make it a little bit harder.
Let's say the sum of seven odd numbers, and let me make up a good -- I hope this one works, I'm going to try to do it in my head -- is 217, what is the largest number?
I shouldn't say number -- seven odd integers.
Actually it becomes a much harder problem if it was just seven odd -- well actually, the only thing that could be odd are integers anyway, so you could almost assume it.
But the sum of seven odd integers is 217.
What is the largest of the integers?
So let's do this problem.
Let's say that x is the largest.
Then what would the number right below x be?
Would it be x minus 1?
Well, if x is an odd number, x minus 1 would be an even number.
So in order to get the number right below it, we have to do x minus 2 to get another odd number.
My apologies -- it should say the sum of seven consecutive odd.
The sum of seven consecutive odd integers is 217.
What is the largest of the integers?
So if x is the largest, then to next smallest one would be x minus 2, right, because it's consecutive odd numbers, not just consecutive.
So consecutive odd numbers are like 1, 3, 5, 7 -- you're skipping the evens, right?
So the next one down would be x minus 2, then we'll have x minus 4, x minus 6, x minus 8, x minus 10, x minus 12.
I think that's it.
One, two, three, four, five, six, seven, right.
Those are seven numbers.
They're separated by two.
X is the largest of them, right?
So what is the sum of these seven numbers?
Well the seven x's just add up to 7x.
And then let's see, 2 and 4 is 6, 6 and 6 is 12, 12 and 8 is 20, 20 and 10 is 30, 30 and 12 is 32.
So 7x minus 32 is equal to 217.
We just solved for x. 7x is equal to -- let's see, if we add 32 to both sides of this equation we get 249.
Let's see, 7 goes into 249 -- is that right?
Right.
So 7 goes into 249 -- did I do this addition properly?
I want to make sure.
2 plus 4 is 6, 6 plus 6 is 12, 12 plus 8 is 20, 20 plus 10 is 30, 30 plus 12 is 42.
Oh, here you go.
So that's 7x minus 42.
So if we add 42 to both sides it's 7x is equal to 259.
259.
So 7 goes into 259 -- let's see, 7 goes into 25 three times, 3 times 7 is 21, 49 -- it goes into it 37 times.
So we get x is equal to 37 and we're done.
The question was the sum of seven consecutive odd integers is 217.
What is the largest of the integers?
I said x is the largest, and then if x is the largest, the next smaller one will x minus 2.
So if x is 37, which is what we solved for, then x minus 2 is 35, this is 33, this is 31, this is 29, this is 27, this is 25.
And then we just added up all the x's and I'll add up all the constants and said, well they add up to 217.
And then we just solved for x.
I think you're now ready to try some of these problems.
Have fun.
Write 7/8 as a decimal.
And so the main realization here is that 7/8 is the same thing as 7 divided by 8, which is the same thing as 7 divided by 8.
These are all different ways of writing the same thing.
So let's actually divide 8 into 7.
And I'll do it down here just so I have some more real estate to work with.
I'm going to divide 8 into 7.
And I'm going to add a decimal point here, just because we know that this value is going to be less than 1.
7/8 is less than 1.
We're going to have some digits to the right of the decimal point.
And let me put the decimal point right up here, right above the decimal point in 7.
And then we start dividing.
And now this really turns into a long division problem. And we just have to make sure we keep track of the decimal sign.
So 8 goes into-- it doesn't go into 7 at all, but it does go into 70.
So 8 goes into 70 eight times. So it goes into 70 eight times.
8 times 8 is 64.
And then you subtract. 70 minus 64 is 6.
And then bring down another 0 because we still have a remainder.
We want to get to the point that we have no remainders. Assuming that this thing doesn't repeat forever.
And there's other ways we can deal with that.
8 goes into 60? Well, let's see. It doesn't go into it eight times because that's 64.
7 times 8 is 56.
60 minus 56 is 4. And now, we can bring down another 0 right over here.
And 8 goes into 40? Well, it goes into 40 exactly five times. 5 times 8 is 40.
And we have nothing. We have nothing left over.
And so we're done. 7 divided by 8 or 7/8 is equal to 7 divided by 8, which is equal to 0.875.
But I'll put a leading 0 here just so it makes it clear that this is where the decimal is.
0.875.
In this video, I want to do a couple more word problems dealing with graphs of lines.
So here we have a gym is offering a deal to new members.
Customers can sign up by paying a registration fee of $200 and then a monthly fee of $39.
This is registration.
Find the sum of -15 + (-46) + (-29)
To do this, let's just first visualize what each of these numbers look like.
So I'm going to draw a number line for each of them.
-15 might look something like this.
If this is 0, and let's say this is -15.
I can represent -15 as an arrow that points from 0 to -15.
The length of the arrow is the absolute value of this.
It's the distance from 0.
So the length here is 15 and the negative says we are pointing to the left.
So the absolute value is 15.
That's the length of that arrow.
Let's do the same thing for -46.
Once again let me draw my number line.
Put 0 is going to be right over there. and -46 is going to be someplace over here.
Notice the same exact idea
The distance between -46 and 0 or another way to think that is the absolute value of -46.
This distance right over here is going to be 46. And its direction is to the left.
That's why we get to the number -46.
The negative really tells you wether you're to the left or the right of 0.
The absolute value says how far you are to the left or the right of 0.
Finally let me do the same thing for -29.
So once again, let me draw my number line.
Use the yellow again. So got to draw my number line.
Say this is 0, -29 is going to be roughly over here.
Once again -29 is exactly 29 away from 0.
So this length right over here is 29 and it is to the left that is why it is -29.
If it was +29, it would be 29 to the right of 0.
So we have represented all of these numbers and you can see what their absolute values are like.
And now let's think what happens if you add them.
One way to think about adding these numbers is as if you added these arrows.
If you put this arrow on top of this arrow or to the left of this arrow
If you started with this arrow leaves off, then you put this green arrow. And then you put the orange arrow.
So let's do that. Let's draw that.
It's going to be a longer arrow now.
So we are going to start at 0.
First we have -15.
So we are going to move 15 spaces to the left, to get us to -15.
Then we are going to go 46 spaces to the left, to get us to -15 + (-46)
Let me draw that. Then we are going to go... We are going to figure out what that number is in a second.
Then we're going to go 46 to the left. That's about that far.
It's really just this arrow. I am now placing it.
I am starting off where the -15 started or where the -15 left off. and then I am putting that arrow after that.
And we don't know yet what number this gets us to.
We are going to have to do a little math here. That's actually the point of this problem.
But we know the length of this arrow is 46.
It is 46 to the left.
We know the length of this magenta arrow is 15.
Then finally we have this orange arrow which we know has a length of 29, although it's 29 to the left.
It has a length of 29.
So when all is said and done, where are we? Where do we end up on our number line?
Well, the total length that we are to the left, is going to be 15+46+29.
But it's going to be to the left. So it's going to be negative.
So we can really view this as Since all of these have the same sign
Look this is the same thing as abs(-15)+abs(-46)+abs(-29) But then take the negative value of it.
Let's just add that.
15+46+29 is equal to...let's see.
2+1 is 3.
3+4 is 7.
7+2 is 9.
So you get 90.
So this entire length here is 90.
If you add up the arrows, you get a 90.
But it is not 90 to the right.
If it was 90 to the right, this would all be positive.
Then we'll just get positive 90.
But this is 90 to the left.
So when you add these guys up, you don't get to positive 90. You get to negative 90.
So one way to think about it is, these are all the same sign. So this is going to be equal to the -( abs(-15)+abs(-46)+abs(-29)) and the reason why we are writing this. this might look fancy but this is really just the length of this purple arrow.
This absolute value of 46, that's really just the length of the green arrow, 46.
This is just the length of the orange arrow.
So this is 15+46+29, gives us 90.
But it's to the left.
So that is why it is -90.
Growing up in Taiwan as the daughter of a calligrapher, one of my most treasured memories was my mother showing me the beauty, the shape and the form of Chinese characters.
Ever since then, I was fascinated by this incredible language.
But to an outsider, it seems to be as impenetrable as the Great Wall of China.
Over the past few years, I've been wondering if I can break down this wall, so anyone who wants to understand and appreciate the beauty of this sophisticated language could do so.
I started thinking about how a new, fast method of learning Chinese might be useful.
Since the age of five, I started to learn how to draw every single stroke for each character in the correct sequence.
I learned new characters every day during the course of the next 15 years.
Since we only have five minutes, it's better that we have a fast and simpler way.
A Chinese scholar would understand 20,000 characters.
You only need 1,000 to understand the basic literacy.
The top 200 will allow you to comprehend 40 percent of basic literature -- enough to read road signs, restaurant menus, to understand the basic idea of the web pages or the newspapers.
Today I'm going to start with eight to show you how the method works.
You are ready?
Open your mouth as wide as possible until it's square.
You get a mouth.
This is a person going for a walk.
Person.
If the shape of the fire is a person with two arms on both sides, as if she was yelling frantically,
"Help!
I'm on fire!" --
This symbol actually is originally from the shape of the flame, but I like to think that way. Whichever works for you.
This is a tree.
Tree.
This is a mountain.
The sun.
The moon.
The symbol of the door looks like a pair of saloon doors in the wild west.
I call these eight characters radicals.
They are the building blocks for you to create lots more characters.
A person.
If someone walks behind, that is "to follow."
As the old saying goes, two is company, three is a crowd.
If a person stretched their arms wide, this person is saying, "It was this big."
The person inside the mouth, the person is trapped.
He's a prisoner, just like Jonah inside the whale.
One tree is a tree.
Two trees together, we have the woods.
Three trees together, we create the forest.
Put a plank underneath the tree, we have the foundation.
Put a mouth on the top of the tree, that's "idiot." (Laughter)
Easy to remember, since a talking tree is pretty idiotic.
Remember fire?
Two fires together, I get really hot.
Three fires together, that's a lot of flames.
Set the fire underneath the two trees, it's burning.
For us, the sun is the source of prosperity.
Two suns together, prosperous.
Three together, that's sparkles.
Put the sun and the moon shining together, it's brightness.
It also means tomorrow, after a day and a night.
The sun is coming up above the horizon.
Sunrise.
Put a plank inside the door, it's a door bolt.
Put a mouth inside the door, asking questions.
Knock knock.
Is anyone home?
This person is sneaking out of a door, escaping, evading.
On the left, we have a woman.
Two women together, they have an argument.
(Laughter) Three women together, be careful, it's adultery.
So we have gone through almost 30 characters.
By using this method, the first eight radicals will allow you to build 32.
The next group of eight characters will build an extra 32.
So with very little effort, you will be able to learn a couple hundred characters, which is the same as a Chinese eight-year-old.
So after we know the characters, we start building phrases.
For example, the mountain and the fire together, we have fire mountain. It's a volcano.
We know Japan is the land of the rising sun.
This is a sun placed with the origin, because Japan lies to the east of China.
So a sun, origin together, we build Japan.
A person behind Japan, what do we get?
A Japanese person.
The character on the left is two mountains stacked on top of each other.
In ancient China, that means in exile, because Chinese emperors, they put their political enemies in exile beyond mountains.
Nowadays, exile has turned into getting out.
A mouth which tells you where to get out is an exit.
This is a slide to remind me that I should stop talking and get off of the stage.
(Applause)
The officers put a cloth over my face and spun me around to make me dizzy.
Then they dragged and threw me into a 200-litre oil drum.
They lit a fire around the oil drum.
I tried to crawl out, but they hit me with the butt of a rifle.
Finally, I faked fainting. Then they let me crawl out.
Once I was out, they all ganged up and beat me.
They kicked my face, hit my mouth and knocked out two of my teeth.
They also tortured me by lighting a candle and burning my body.
They put ice in a large cylinder, and then they put me inside the cylinder.
They dunked my head under the water several times.
At last I ran out of patience.
So I stood up and fought them by pushing them away.
But they punched me and broke my eye socket.
In the Deep South, many people have told us that they have had experiences like this.
But the person who told us this story was a minor. He was only 16 years old when he was arrested.
Throughout the 7 years of the southern unrest
Young people have come under suspicion of being involved in the insurgency and they must face the same fate as adults.
In another case, there was a minor who was 16 years old when he became a suspect in a bombing case.
I was at school
Before I arrived home, a friend came to tell me that there were soldiers surrounding my house
My mom said that the soldiers wanted to see me
They asked me to go to the Army Task Force.
My mom had to wait outside.
I was interrogated there alone with the officer.
The officers told my mom that they would take me to Inkhayuth Army Camp.
I was shocked and then I cried. I didn't want to go.
According to the law and judicial process in general, youths should be given special treatment as they have not yet reached the age of majority.
They are considered to be incapable of taking full responsibility for their actions.
Generally, during investigation and proceedings, the minor's parent or guardian is required to be present, even during interrogation.
Whatever it takes to result in the minimal impact possible.
To ensure that youth do not feel ashamed or embarrassed and suffer subsequent mental impacts.
Physical action against youth are out of the question.
No force should be used on minors.
Even the use of restraints is prohibited
The application of chains, hand restraints, or handcuffs is prohibited.
The Muslim Attorney Center has never received any information from the parents or guardians that during the investigation process, there was a psychologist present to question the child and an interrogator taking notes.
All we have heard is that the interrogating officials directly questioned them.
The statistics of the Muslim Attorney Center on complaints received from the villagers shows that
In the Deep South, the number of youths arrested and prosecuted is 55 individuals in 31 cases.
But there is no information that suggests
They have received treatment as juveniles as outlined in the principles of special care for children and youths.
In addition to not receiving special treatment, they have also been abused.
Human rights activists indicated that this was partly due to the fact that state officials used their authority according to the special laws that have been declared in the area
The problem is with the power specified in the two special laws, which are the Emergency .Decree and Martial Law.
There's a lot of power and far-reaching authority.
The system of checks and balances to limit the wide-ranging powers was, however, designed in a way that does not limit abuses.
Therefore, the use of power under both laws
lacks the proper checks and balances
This leads to the illegitimate use of power in the form of torture.
On the issue of special treatment for children and youths
No clear answer could be obtained from state officials on whether they realize that this problem exists.
Regarding the issue of torture,
Responsible state officials, such as the military, insisted that there was very little torture.
As for state officials breaking the law beating people, violating human rights, during the time that I have been here, there have not been many cases.
Those cases that have come up are now going through the criminal justice process.
Therefore, regarding state officials beating and torturing those who they arrest,
I maintain that it does not exist.
If state officials do it, they must be severely punished.
This is became the Deep South is a special area, where we are trying to solve the problems using special means
Therefore, there can be little or no chance of human rights violations being committed.
If they do occur, then it is a case of an individuals.
But in terms of policy, the policy is to prevent it and use other methods.
Whether or not this is true, for those who have experienced it ,the attorneys say that they still have a way to fight and to demand justice.
If the question is: "Under what sort of authority did the officials act?"
I can answer that they have no authority to do so.
If the villagers are to bring a case against the officials, they can do so since the act is considered to be a deprivation of freedom and the officials have no authority to detain them.
Martial Laws allows for no more than 7 days of detention.
After 7 days, if further detention is necessary, a request must be made to the court for an arrest warrant according to the Emergency Decree.
This is the issue about which we have received a lot of complaints from the villagers including on not being notified of where the suspect would be taken, detaining suspects for more than 7 days and not detaining them officially under the Emergency Decree.
But the problem that attorneys themselves admit is that in many cases, the villagers do not dare to bring a case against state officials.
Human rights activists raise as a concern the issue that these violations then create frustration within the minds of individuals who experience them, particularly for the youth themselves.
I feel very sad that my son was beaten
It's not that I'm not hurt. I am really hurt.
I want to beg the officials to stop doing this.
I feel really sad that there is nothing we can do.
They are the mighty people, while we are just the small ones.
When officers arrest and detain children based only on suspicion, how are the villagers supposed to put their hope in the officials?
When something like this is done to the people, there will be a feeling of mistrust towards the officials and anger that the officials treat them this way.
Even today, there is anger, but it is hidden inside.
It cannot be vented out
It's hidden in our minds, and we would not dare take vengeance
But instead feel sorry and angry that the officials treated us like this.
Many experts have studied and looked for ways to solve the problems of affected youth.
Even though most are not ready to provide information nearly all have expressed concern about the long-term consequences.
If the child is not guilty but is accused of being guilty, they will be at risk of being persuaded from the opposite side, and more easily than other children.
Political scientists also commented that this issue will have long-term consequences on solving the conflict in the area, as by their own admission, the Melayu in the Deep South are already suspicious and afraid of state officials.
Let's do a couple of warm up problems converting fractions to percentages and then converting percentages to fractions. And then we can do some actual word problems. So on our first warm up, let's convert 5/24 to a percentage.
24 goes into 200-- let's see, eight times?
No it'd be eight times, I believe.
8 times 4 is 32. 8 times 2 is 16 plus 3 is 19.
200 minus 192, that's 8. That is 8.
24 goes into 80 three times.
3 times 4 is 12. Carry the 1. 3 times 2 is 6.
And we're going to have another 80. Well once again, 24 is going to go into that three times.
So 5 over 24-- let me write this down. 5 over 24-- I want you to understand why it keeps repeating. Every time we do this now, we're going to get a 3.
This decimal 0.2083 repeating is the same thing as 20.83 repeating over 100. This is how many we have per 100%. Or you could say that this is equal to 20.83%: per 100.
So 16 over 100. Put that in the lowest-- let's see, you can divide the numerator and the denominator by 4. We get 4 over 25.
You get 195 times 20 divided by 13 is equal to $300.
So $195 is actually divisible by 13. I should be able to do that without a calculator. Anyway, so the original price was $300.
So 9.50 times 1.12. 2 times 0 is 0. 2 times 5 is 10.
Let's do one more. Store A and store B both sell bikes. And both buy bikes from the same supplier at the same price.
Store B has a permanent sale, and always will sell at 60% off those prices.
Which store has a better deal? So let's say that they're both buying the bikes, so x is equal to the price from supplier.
So that's the price that both bike stores buy their bicycles at. They both buy bikes from the supplier at the same price.
Now lets do the scenario of store A. What does store A sell their bike for? They sell the bike for x plus 40% of x, which is equal to 1.4 times x.
So the real selling price is going to be 3.5 times the price from the supplier minus 0.6. Minus 0.6. Minus 60% of this price.
You might, eventually, do this in your head-- immediately say, oh, 60% off is the same thing as selling at 40%, or selling at 0.4 of the price. 3.5x. And let's multiply that out.
Let's say I go to a store and I have fifty dollars in my pocket. fifty dollars in my wallet.
And at the store that day they say it is a twenty-five percent off marked price sale.
So twenty-five percent off marked price means that if the marked price is one hundred dollars the price I'm going to pay is going to be twenty-five percent less than $one hundred.
So my question to you is if I have $fifty, what is the highest marked price I can afford?
Because I need to know that before I go finding something that I might like.
So let's do a little bit of algebra.
So let x be the highest marked price that I can afford.
So if the sale is twenty-five percent off of x, we could say that the new price, the sale price will be x minus twenty-five percent of x is equal to the sale price.
And I'm assuming that I'm in a state without sales tax.
Whatever the sale price is, is what I have to pay in cash.
So x minus twenty-five percent x is equal to the sale price.
The discount is going to be twenty-five percent of x.
But we know that this is the same thing as x minus 0.25x.
And we know that that's the same thing as-- well, because we know this is onex, x is the same thing is onex.
1x minus 0.25x.
Well, that means that 0.75x is equal to the sale price, right?
All I did is I rewrote x minus 25% of x as 1x minus 0.25x.
And that's the same thing as 0.75x.
Because 1 minus 0.25 is 0.75. So 0.75x is going to be the sale price.
Well, what's the sale price that I can afford?
Well, the sale price I can afford is $fifty.
So 0.75x is going to equal $50.
If x is any larger number than the number I'm solving for, then the sale price is going to be more than $fifty and I won't be able to afford it.
So that's how we set the-- the highest I can pay is $fifty and that's the sale price.
So going back to how we did these problems before.
We just divide both sides by 0.75.
And we say that the highest marked price that I can afford is $50 divided by 0.75.
And let's figure out what that is.
0.75 goes into 50-- let's add some 0's in the back.
If I take this decimal two to the right.
Take this decimal, move it two to the right, goes right there.
So 0.75 goes into 50 the same number of times that seventy-five goes into five thousand.
So let's do this. seventy-five goes into fifty zero times. seventy-five goes into five hundred-- so let me think about that.
I think it goes into it six times.
Because seven times is going to be too much.
So it goes into it six times. six times five is thirty. six times seven is forty-two.
Plus three is forty-five.
So the remainder is fifty.
I see a pattern.
Bring down the zero.
Well, same thing again. seventy-five goes into five hundred six times. six times seventy-five is going to be four hundred and fifty again.
We're going to keep having that same pattern over and over and over again.
It's actually 66.666-- I hope you don't think I'm an evil person because of this number that happened to show up.
But anyway, so the highest sale price that I can afford or the highest marked price I can afford is $sixty-six dollars.
And if I were to around up, and $0.67 if I were to round to the nearest penny.
If I were to write this kind of as a repeating decimal, I could write this as 66.66 repeating.
Or I also know that 0.6666 going on forever is the same thing as two / three.
So it's sixty-six and two / three.
But since we're working with money and we're working with dollars, we should just round to the nearest penny. So the highest marked price that I can afford is $66.67.
So if I go and I see a nice pair of shoes for $fifty-five, I can afford it.
If I see a nice tie for $seventy, I can't afford it with the $fifty in my pocket.
So hopefully not only will this teach you a little bit of math, but it'll help you do a little bit of shopping.
So let me ask you another problem, a very interesting problem.
Let's say I start with an arbitrary-- let's put a fixed number on it.
Let's say I start with $one hundred.
And after one year it grows by twenty-five percent.
And then the next year, let's call that year two, it shrinks by twenty-five percent.
So this could have happened in the stock market.
The first year I have a good year, my portfolio grows by twenty-five percent. The second year I have a bad year and my portfolio shrinks by twenty-five percent.
So my question is how much money do I have at the end of the two years?
Well a lot of people might say, oh, this is easy, Sal.
If I grow by twenty-five percent and then I shrink by twenty-five percent I'll end up with the same amount of money.
But I'll show you it's actually not that simple because the twenty-five percent in either case or in both cases is actually a different amount of money.
So let's figure this out.
If I start with $one hundred and I grow it by twenty-five percent-- twenty-five percent of $one hundred is $twenty-five.
So I grew it by $twenty-five.
So I go to $one hundred and twenty-five.
So after one year of growing by twenty-five percent I end up with $one hundred and twenty-five.
And now this $one hundred and twenty-five is going to shrink by twenty-five$.
So if something shrinks by twenty-five percent, that means it's just going to be 0.75 or 75% of what it was before, right? one minus twenty-five percent.
0.75 times $125.
So let's work that out here. $125 times 0.75.
And just in case you're confused, I don't want to repeat it too much, but if something shrinks by twenty-five percent it is now seventy-five percent of its original value.
So if $125 shrinks by 25% it's now 75% of $125 or 0.75.
Let's do the math. five times five is twenty-five. two times five is ten plus two is twelve. one times five-- seven. seven times five is thirty-five. seven times two is fourteen.
Plus three is seventeen.
Sorry. seven times one is seven.
Plus one is eight.
So it's five, seven, and then this is seven actually. fourteen. nine.
94.75, right?
Two decimal points.
94.75.
So it's interesting.
If I start with $one hundred and it grows by twenty-five percent, and then it shrinks by twenty-five percent I end up with less than I started with.
And I want you to think about why that happens.
Because twenty-five percent on $one hundred is the amount that I'm gaining.
That's a smaller number than the amount that I'm losing.
I'm losing twenty-five percent on $one hundred and twenty-five.
That's pretty interesting, don't you think?
That's actually very interesting when a lot of people compare-- well, actually I won't go into stock returns and things.
But I think that should be a pretty interesting thing.
You should try that out with other examples.
Another interesting thing is for any percentage gain, you should think about how much you would have to lose-- what percentage you would have to lose to end up where you started.
That's another interesting project.
Maybe I'll do that in a future presentation.
Anyway, I think you're now ready to do some of those percent madness problems.
Hope you have fun.
Bye.
The Shinwha group has selected as one of the biggest sponsors for the 2012 olympics ..
In the middle of a global financial crisis . .
Since the start of the Korean economic development. a single company has been holding the highest ranking continuing with its ever continuous growth.
Shinhwa has finally been established in the international market as a world-class company. ...And that company is Shinhwa.
From electronics...oil refining and automobiles... to delivery...and telecommunications, and even if you're a Korean who doesn't know the President's name, you would have definitely have come across the words "ShinHwa."
It is a massive empire; a model of Korean conglomerate.
The day ShinHwa achieved an unprecedented $10 billion in export....
Instead of accepting a medal of honor, the founder was invited to the Blue House, and it was there that he said,
"Mr. President...please let me build a school for my grandchildren."
Incorporated Association, ShinHwa Academy.... The school is the first of its kind to be seen in the history of Korean education it was During a time when economic development was more important than equal opportunities in education the president even spared every expense and even passed special laws to make his school a reality.
Now there's even a saying that a family won't get anywhere without a ShinHwa graduate..
ShinHwa is based on built by the top 1% of Korean society, for the top 1% of society.
Also, Enrollment is so competitive that even most upper class children would be unable to receive acceptance even if they were to apply for registration the moment after their birth.
However, once enrolled, students can attend ShinHwa from elementary, middle and high school all the way to university.
For all the Korean students and parents frustrated by college entrance exams, ShinHwa is both the object of their hatred and envy of every citizen.
However, in this school for the chosen sons and daughters of God.. something beyond anyone's imagination is happening..
Oh, poor MinHa...what shall we do about this?
You bastard!
Aish.Damn it! Get him! Get him!
How may I help you?
I have a delivery from JanDi's Dry Cleaning Service....
Okay, you may go in.
Thank you!
Ahh this isn't it
Find him!!!
There!!
There he is! Get him! wahh..Is this really a school?
Hey, he's on the rooftop!
Lee Min Ha is going to jump! whoah..Are you serious?
Is he putting on a show?
No, this is for real!!
Really?
Are you for real??
Lee MinHa??? oh!!! Lee MinHa!
I was right, huh?
He couldn't even last a week.
But he did survive three days.
It wasn't even three days.
Exactly speaking . . .
This is what you guys wanted... right?
Fine,....
I'll do as you guys wish.
Hey!
Hey!
Wait a moment, Lee Min Ah!!!!
Oh no,...what a customer!!
Who are you???
Me?
Oh, hehhh. i'm . . . i have a delivery for you!
JanDi Cleaners.
It is $30.
Oh ,my God! This is funny!!
OK, OK, $25.!
The gym suit is free.
In return, you should be a patron..
After I die, settle it with my family...
Oh!
Don't be like that...
D-d-die??!?
Are you going to die right now??
Why??
I mean..come on..
You attend such a great school!
This isnt a school...
This is hell..
Excuse me!!
The real hell is out there. ..
Have you ever heard about the hell of college entrance exams??
Have you ever heard of F4???
F..F.. what?
F4?? ....What is that???
Once you get their red card, you become the target of all the students in school...
Just like me...
So are you gonna just sit back and take it??
Losers like that always move around in large groups doing cruel things..
If it was my school, I would catch them and kick all of their asses!!
How lucky... your friends are....
Huh??
Your friends, they're lucky to have a friend like you..
Not really. hahaha.
NOOOO!!
At the cradle of privileged education...ShinHwa High School, saving an ostracized student was.. neither a son of chaebol nor of honorable family.. but an ordinary girl who was there to deliver laundry.!
The sons of God who are exempt from college entrance by way of wealth!!
If you guys have nothing to do...you should try taking the SAT!!
If such a thing should come from privilege, it deserves capital punishment! ShinHwa group.. should blow itself up!
As a parent, I can't forgive them.
I refuse to continue shopping at ShinHwa Mart.!!
ShinHwa Group, give us an explanation!
Give us an explanation!
Give us an explanation!!
ShinHwa Group, give us an explanation!
Give us an explanation!
Give us an explanation!!!
Abolish the elite education system!!!
I amm here now where people are protesting against the Shinhwa Group and they request to have Shinhwa elitist educational system.
Now, let's hear from one of the protesters.
Hello, what brought you out here today??
My friend was also heavily bullied and he dropped out of school...
That sort of thing can happen because of the unbearable stress of the entrance exams, but at a place like this they shouldn't have to suffer those kinds of hardships.
JanDi, do you know what your nickname is?
Common hero, Wonder Girl, you are our generation's true Wonder Woman.
Geum JanDi Laundry, fighting!
Send the Wonder Girl to ShinHwa High school!
Stop it!
Cool.
By the way, the Flower 4 . . .
Fly 4 makes more sense, four dung flies.
I wish I could see them up close in person.
Flower 4?
What flower 4?
Miss Jandi, please look over here!
Miss, please say something.
Excuse me!
Look here!
Smile!
Is that school for gifted people?
It's neither a science school nor a foreign language school.
It's literally a school for the rich.
Doesn't Korea pursue a fair society?
That bourgeoisie school is . . .
I'm sorry, Ma'am.
The group PR department and related companies are trying their best to extinguish the public opinion.
Extinguish?
Do you think this is being extinguished?
How do you let the reporters dare?!
Dare to mention JoonPyo's name?
I'm deeply ashamed.
Do you know why public opinion is something to be wary of?
Because it is ignorant.
Once it goes berserk, it's unmanageable.
Reason or common sense doesn't work any more.
The one who set the fire should extinguish it.
Madam Chairman, the prime minister is on the line.
Yes, sir.
Yes,
It's getting interesting.
I was never cut out for hiding from the paparazzi!
What a tough delivery!
Shoot!
I'm really sick and tired of this ShinHwa school or F 4 something.
I'm ho . . .
She's here!
JanDi!
Say hello to him.
He came from the ShinHwa Chairman's office.
So I finally meet the famous wonder girl.
Nice to meet you.
I didn't push him.
Really, I didn't.
F4 or something, they did it.
That's not it.
JanDi, my daughter, calm down and just listen.
Starting tomorrow, you will attend ShinHwa High .
You're in!
What the heck are you . . .
To tell the truth . . .
The Chairman has come to admire you, and she decided to accept you as a special scholarship student!
SHE DEClDED TO ACCEPT YOU!
Scholarship student?
Why me?
We would like you, Geum JanDi . . .
Noona, you know how you used to swim back in middle school?
She wants you to swim again!
SWlM AGAlN!
I don't want to!
What?
And why not?
Noona, are you crazy?
I like the way things are now.
I wouldn't fit into the school and I don't want to go to that school either.
You should probably go.
JanDi, why don't you think about it a litt-
There's no need to think about anything.
She will be there tomorrow.
Shut up!
JanDi: Why not?
Mom: Shut up!
Then, I'll see you at school tomorrow.
Yes, even if I have to drag her by the neck, I will make sure she's at school tomorrow.
Okay then.
Mr. Secretary, you are aware of the phrase "Nak Jang Bool Ip."?
"What's done cannot be undone.", right?
MOM!
Be quiet and just take a look at this!
ShinHwa High!
ShinHwa High!
ShinHwa High!
Sister,
I really didn't think this day would come in my lifetime.
For the first time in my life, I am proud to be your brother.
Dad!
Wooooohhh!
How can the words, "I'm not going" even come out of your mouth?
Do you even know how much the tuition is?
No. I still don't want to.
I still don't want to go. Mom, I really don't want to. Oh my!
Others study hard, have the money, and they still aren't able to get in .
Why wouldn't you want to go?
Wasn't it you who's always saying those people only know how to brag about their wealth?
It, it, it was jealousy.
The truth is, it's like winning the lottery.
Who wouldn't be happy?
I don't care.
I have a bad feeling about this.
Just to let you know, regardless of what you say, I'm not going.
But, you like to swim.
You said you wanted to go to a school with a swimming pool.
Are you trying to get me to go to that school by saying they have a swimming pool?
I"m not going. I don't want to.
I'll never go!
Wait!
Just wait a minute, miss!
I'll go and come back. (A Korean saying when they leave the house etc.)
Geum Jan Di, Fight!
Go on
Dry cleaning is here, dryyyy cleaningggg!
JanDi dryyyyyy cleaningggg!
Dry cleaning is hereeee! JanDi dryyyyyy cleaningggg!
Isn't it pretty?
Yeah, it is.
There were only two made imported from Japan.
I got myself one, guess who bought the other?
Who?
Goo JoonPyo.
That's really cool!
Don't you think my style is a lot better?
Hey, let me borrow it.
Hey, me too, me too!
Just where is it?
Uhhmm, do you know where the swimming pool is?
Oh, that way?
Thank you.
I'm so sorry for interrupting. You can continue on.
Goodbye!
AH!
It's F4!
AHHHH!
Move it!
Is something wrong?
I will give you to a count of three.
What?
What for?
Three . . .
Two . . .
One.
Hey, WooBin, do you have some juice left?
Yeah, you want it?
Hey, are you okay?
What kind of crazy person is that?!
How can they just stand there? oh my god
Watch your mouth.
Who are you guys?
Us?
By the way, sorry for the late greeting.
We are Ginger!
Sunny!
Miranda!
We are the Jin, Sun, Mi (the true, the good and the beautiful) of ShinHwa High School.
What you were saying before, it wasn't regarding the F4 was it transfer student?
F, F what?
So that guy who made a scene is a member of the notorious F4? notorious?
You mean famous.
If you're not careful with what you say, you'll be in big trouble!
I hear your family owns a laundry shop..
It's not a laundromat. It's a dry cleaners.
So, what?
This is my first time seeing a dry cleaner's daughter.
It's very fascinating.
Look all you want, I won't charge you.
Since this is your first day of school and you're a commoner who knows nothing of the world, I'll let you off this time.
What?
For the things you said about the F4!
What?
Are they that remarkable?
Hey transfer student, you really don't know a thing about the F4 do you?
No, I don't.
Girls, let's go.
Song WooBin, the son of Il Sim Construction, also know as the blue-chip stock of the construction industry.
They are real estate tycoons.
People say half of Jejudo belongs to Il-Sim.
The head family of Il-Sim-Pa, an organization(gang) of 50 years history.
They still have quite a few high-class clubs and saloons.
When it comes to cash mobilization, they are valued as King Wang Jjang.
So YiJung is a genius ceramic artist who debuted at Biennale at the age of 16 as the youngest artist.
He is one of the young artists to be selected by UNESCO.
There is at least one who made it on his own.
Cast away the prejudice that genius would be poor.
You know the cultural assets independence fighter, So YoonHe, in Korean History textbooks?
He is the owner of WooSong Museum and the grandfather of F4 So YiJung.
WooSong Museum?
Do you mean it's his family's?
How rich are they?
Don't imagine.
You'll hurt yourself.
That's a picture of the old president (of Korea).
Look at this kid sitting next to him.
He is F4's very own Yoon Ji Hoo.
The son and daughter-in-law of Yoon SeokYoung president died in a mysterious traffic accident.
The only survivor was his five year-old grandson.
You mean Yoon JiHoo is the grandson of President Yoon SeokYoung?
You know SooAm Art Center where Jang YoungJoo played?
He owns the SooAm Art Foundation, a soccer team in Europe and a Major League baseball team.
I envy him most in the world.
You know him without my explanation, right?
This man is the F4 leader, Goo JoonPyo, the successor of the great ShinHwa group, whom even 3 year-old Korean kids know.
F4 are those sort of guys?
No way!
Goo JoongPyo, you are Goo JoongMool (sewage)!
F4, you flies!
If you were born with a silver spoon in your mouth, you should be thankful and be nice to people!
It's annoying that someone like you is the successor of ShinHwa group!
You better hope the two of us never come face to face.
The day I have to call you "senior", I will dive from the rooftop!
Ahhhh!
Yoon JiHoo!
How noisy.
It's so loud, I can't even sleep.
I'm so sorry.
I thought no one was here.
Is that really true?
Eh?
That you will dive?
So, the thing is . . .
So you heard everything?
About what?
I mean . . .
Goo JungMool (sewage)? Or flies?
Oh right, JoonPyo
Huh?
It's "Goo JoonPyo," not "Goo JoongPyo".
Remembering the right name is the least thing to do when you hate someone, right?
Rice balls!
You like them?
What the heck are rice balls?
It looks so pretty and delicious!
What's that smell?
It completely stinks!
Oh, here it is.
Oh my god!
Terrible!
Hey, transfer student, why are you eating such low grade food when there's an expensive spread over there?
What?
Then?
Over $50 for one meal is a nuisance in my home.
So, you're planning to keep eating these stinky lunch boxes?
Yes I am.
God!
Good!
It's F4!
AH!
MiSook, come on!
I'm going crazy!
Can I . . . try that?
Welcome!
Thank You!
Is she from Germany?
Yeah, she looks really pretty. I thought she was a doll or something.
Anyway, it's great that you made a friend already.
I was worried you might be a loner.
I am a loner.
What?
I'm an outcast.
But I'm thankful that I don't get noticed.
I'll stay a loner until the day I graduate.
Who are you?
What happened to our JanDi?
The one who protected me from that wicked kindergarten owner's son, the one who fought against the gangs in junior high.
So what's wrong?
What can I do?
I'd sooner get into it with my mother before causing trouble and being expelled from school.
You!
Ah!
Do you think, do you think I'm wasting cucumbers?!
Your father wanted to eat cucumber kimchi but I'm investing it in your face.
What kind of investment are you doing with cucumbers?
Won't this treatment give you beautiful skin?
Even the worst boy in your school is the super A plus when it comes to marriage material.
It seems we've hit the jackpot.
Don't you think so, honey?
Don't disturb me.
I'm artistically sharpening the edge.
Mom, stop this!
Look at you, look at you! Don't be so ungrateful!
And why are you ironing that?
Your arms'll hurt because of ironing all day long.
15 years in the dry cleaning business and never once before have I seen such fine clothing.
Ordinary people would be lucky to wear such cloth even on their wedding day.
Oh, boy!
Sister, let me borrow it to wear on Sunday.
JanDi, when it comes to clothes like this, you must treat them as kindly as your boss.
Be careful when you sit and stand up.
Take good care of it and avoid any stains. Understand?
I'm ironing this beautiful thing for my daughter.
There's no way my arms would hurt from that.
No, daddy's totally fine.
Oh my!
That girl!
Honey, you should iron the lining too, right?
Justice Girl Geum Jan Di hasn't died yet.
Outcast in this way, outcast in that way, and thrown about anyway!
I will say what's on my mind!
F4, from tomorrow, you're all dead!
It's F4!
JoonPyo senior, I baked this myself for you.
Please accept my heart.
Our JoonPyo only eats cakes made by a top-notch patissier.
Who are you?
You have something to say?
Yeah, I have something to say!
I have a lot to say!
You!
Do you have absolutely no respect for people?
I don't even expect you to have humility as a rich person.
If you didn't want to eat it, then you could have rejected it nicely or . . .
Will it kill you to accept it by thinking of that person's effort?
What are you going to do if she says she'll jump off the roof, you bastard!
Who are you?
You have something to say?
No.
Why are you swimming so hard?
You'll become exhausted and faint.
It's punishment.
Punishment?
What did you do that was so bad?
It's the punishment that the Justice Girl inflicts upon the super obsequious.
So, do you feel better?
Yes.
All of the reasons why I'm going to this school are right here.
What are they?
The swimming pool and Oh MinJi.
Senior!
I'm so sorry, JoonPyo senior.
Sorry?
If apologizing solved everything there wouldn't be laws and police officers.
But it was an accident.
I'll buy you the same exact shoes right away!
You, are you richer than me?
Pardon?
Even if you had more money, it would be impossible.
These shoes were made by a craftsman in Firenze, how could you possibly buy me the exact same ones immediately?
I'm really sorry.
I'll do anything I can do to fix it.
Anything?
Yes!
Lick it.
Pardon?
I said to lick it.
Senior.
Didn't you say you'd do anything?
Isn't that enough?
You!
You think she fell because she wanted to?
Apologizing is enough, don't you think?
Who's this nosy person?
I'm guessing it hasn't been long since you returned (to Korea), but . . . you shouldn't try to use the American style here.
Why so informal?
Oh, so you're the famous "Wonder Girl"?
People were saying Wonder Woman and stuff, so I expected at least an "S" line and a "D" cup.
How homely!
So sorry to dissappoint you.
Is it comon for you to ignore your status and be so nosy?
Why are you butting into other people's business?
She' is my business.
She's my friend.
I guess in rich people's dictionaries, there are no words like "friend" or "friendship"?
Friendship?
Let's see this great friendship you speak about.
Lick it.
What?!
I'll forget all about this if you lick it instead.
Hey!
What's up with you?
Does she have more money than you?
Did you yourself earn all of that money?
What?
Is it common for me to be so nosy?
It's common for me not to overlook rich bastards who think it's okay to act out because they wealthy families to bail them out.
Why?!
At our place, it's $2.50, but I calculated it by Kangnam standards, ok?
If the stain still doesn't come out, then bring it by. [JanDi Cleaners, 300-5648]
What the hell is that piece of crap?!
What's the matter with JoonPyo?
I think he's still shocked from what happened today.
He just keeps throwing darts.
What's with that serious face?
Don't bother me.
Can't you hear the wheels turning in my head?
I'm thinking of the best way to completely crush that little weed.
Why are you even bothering to think about her?
Just handle things the way you always do.
Man!
You really are smart!
JanDi Cleaners, you're dead now.
Look, look!
Geum JanDi of second year Class B drew an F4 red card!
What is this, a soccer field?
What are they talking about a red card?
(What?)
Hello. Hello, Crazy!
I guess your desk isn't here.
How can you study with us when you're a commoner?
Why did you even come to school?
My book.
Hey, move over.
Get out of here!
Annoying!
Die! Go screw!
Lick my froth!
You're dead today. [Fuck off! Screw you!]
Who did this?
If you have something to say, then then say it to my face!
Who did it?
JanDi, when it comes to this kind of clothing, you must treat it as kindly as your boss.
Be careful with it at all times.
This great suit is my daughter's.
Why would my arms hurt?
Daddy will be just fine.
Throw more!
Throw more!
Just try and throw more!
Hey, hey, hey.
Someone bring some oil.
All we have to do now is to fry her.
What wil she be then?
A pan fried pumpkin?
Do more!
Just try and do more!
Isn't it over now?
What do you mean over?
It'll be over when that commoner kneels before me.
So, that's why they say not to bother a sleeping wolf.
Don't you mean a lion?
It seems this time it won't even last a week.
1 week?
I say three days.
Yi Jung, you, if I win, then I get that traditional pot from your last show.
For a fool that can't tell a pot from a water bottle, what's the sudden interest?
My baby is a fan of the potter, So YiJung.
Okay.
If I win, then I get the number of the Super Girls.
Deal!
Hey guys shut up.
It's almost time for her to show up.
Alright.
5, 4, 3, 2, 1.
Ah, that's right.
She's probably embarrassed to show up in front of me in that disastrous state.
Yep, I was a bit hasty.
What's wrong with you guys?
Did you do it right?
Then, why isn't she here?
Where the hell did that chick go?
Surrender?
You wish!
I say JanDi, and you think it's grass for you to walk all over?
You picked on the wrong person!
Have you guys ever eaten dough soup that has been cooked with tears?
Have you ever seen a free pass to the public bath house?
Commoners are nothing if not unyielding and persevering!
You should know that!
How many eggs did they just throw away?
Those idiots don't even know how precious flour is.
What's wrong with them?!
So wasteful . . .
How many pancakes could they have made with these?!
Seriously!
Oh my!
Who's there?
You're really noisy every time I see you.
Do you know how to make pancakes?
What?
Pancakes.
All you have to do is mix flour, eggs, milk, and sugar and fry it.
Just like Bindeadduk (korean pancake).
That's simple.
Your handkerchief . . .
I don't need it.
I'll return it to you next time.
I won't be here again.
It's no longer quiet, thanks to someone.
I'm sorry, JanDi.
Forgive me for being a coward.
I think it'll be at least $30.
Wow, I know the actual price.
That's not fair.
The express service is a little bit more expensive.
Also, look at the condition of these clothes.
I've already given you quite the discount only because it's a school uniform.
Come on, really.
I'm a junior of the dry cleaning business.
If you don't like the price, forget it.
Next door is JanDi Dry Cleaner. Go there.
Cmon, Mister.
Alright . . . $25!
Bon apetit !
Yo, yo, yo! What's up, man?!
They only accept one group per week here, so . . .
I made reservations a month ago and I'm still waiting, so. . .
How did you do it?
This one is better.
You're right.
It's a beauty.
Enough to make your cuisine even finer.
And just who told you that I was a chef?
Your . . . delicious-looking hands.
Do players know things just by looking at a woman's hand?
You need at least to know she's a chef at Michelin in order to be a player.
Of course. My bro, yo!
Yeah.
Are you doing what I told you to do?
Don't make a mistake and do it correctly.
Understand?
Let's eat.
Alright. Cheers!
Hey!!
Mom!
Everyone is dying to lose weight, but, here you are stuffing your face?!
Will you be happy if I die doing such a worthless thing?
Hey! You need to diet and at least have a killer body so the rich boys will notice you!
Really! We're not rich nor do we have a good family background nor are we smart!
What are you talking about?
Dieting is worthless?!
Give me the rice container!
No, I can't.
Right now, surviving is more important than dieting to me.
Hey! In this day and age, even swimmers must be skinny to become stars!
Haven't you seen Kim YuNa?
You're a young girl, how can you not know the trends?
Give me the rice container!
(Mom!
I said, I don't want to!)
Give it to me!
Hey, you!
Mom, Kim YuNa is a figure skater.
Kim Yuna is a figure skater, not a swimmer!
Stop!
You!
Hey!
Give up the rice container!
Hey!
JanDi?
JanDi?
The rice container . . . JanDi?
Has my stomach gotten bigger?
A little bit.
I'm sorry. I haven't been able to take care of you.
I'm only putting up with this because of the swimming pool.
If I had attended this kind of school from the get-go, there's no doubt I would have been in the Olympics.
No doubt at all.
What the? What is this?
Goo Joon Pyo!
Hey!
What's going on?
You keep on smiling to yourself.
She's probably really pissed right about now.
Who?
Perhaps, the laundry girl?
Still?
Wait a minute, how long has it been?
It's been over a week.
Okay, hand them over, the girls' phone numbers.
She's really something.
Wait, isn't she the first girl to really face off with the F4?
What are you saying?
It's only because I'm going easy on her.
But, how come JiHoo's not here again?
He's probably sleeping somewhere.
Let go!
Be quiet!
Let go of me!
The officers put a cloth over my face and spun me around to make me dizzy.
Then they dragged and threw me into a 200-liter oil drum.
They lit a fire around the oil drum.
I tried to crawl out, but they hit me with the butt of a rifle.
Finally, I faked fainting. Then they let me crawl out.
Once I was out, they all ganged up and beat me.
They kicked my face, hit my mouth and knocked out two of my teeth.
They also tortured me by lighting a candle and burning my body.
They put ice in a large cylinder, and then they put me inside the cylinder.
They dunked my head under the water several times.
At last I ran out of patience.
So I stood up and fought them by pushing them away.
But they punched me and broke my eye socket.
In the Deep South, many people have told us that they have had experiences like this
But the person who told us this story was a minor. He was only 16 years old when he was arrested.
Throughout the 7 years of the southern unrest
Young people have come under suspicion of being involved in the insurgency00:02:05:24 00:02:10:24 and they must face the same fate as adults.
In another case, there was a minor who was 16 years old when he became a suspect in a bombing case.
I was at school
Before I arrived home, a friend came to tell me that there were soldiers surrounding my house
My mom said that the soldiers wanted to see me
They asked me to go to the Army Task Force.
My mom had to wait outside.
I was interrogated there alone with the officer
The officers told my mom that they would take me to Inkhayuth Army Camp.
I was shocked and then I cried. I didn't want to go.
According to the law and judicial process in general, youths should be given special treatment as they have not yet reached the age of majority.
They are considered to be incapable of taking full responsibility for their actions.
Generally, during investigation and proceedings, the minor's parent or guardian is required to be present, even during interrogation.
Whatever it takes to result in the minimal impact possible.
To ensure that youth do not feel ashamed or embarassed. and suffer subsequent mental impacts.
Physical action against youth are out of the question.
No force should be used on minors.
Even the use of restraints is prohibited
The application of chains, hand restraints, or handcuffs is prohibited.
The Muslim Attorney Center has never received any information from the parents or guardians that during the investigation process, there was a psychologist present to question the child and an interrogator taking notes.
All we have heard is that the interrogating officials directly questioned them.
The statistics of the Muslim Attorney Center on complaints received from the villagers shows that
In the Deep South, the number of youths arrested and prosecuted is 55 individuals in 31 cases.
But there is no information that suggests They have received treatment as juveniles as outlined in the principles of special care for children and youths.
In addition to not receiving special treatment, they have also been abused.
Human rights activists indicated that this was partly due to the fact that state officials used their authority according to the special laws that have been declared in the area
The problem is with the power specified in the two special laws, which are the Emergency .Decree and Martial Law.
There's a lot of power and far-reaching authority.
The system of checks and balances to limit the wide-ranging powers was, however, designed in a way that does not limit abuses.
Therefore, the use of power under both laws lacks the proper checks and balances
This leads to the illegitimate use of power in the form of torture.
On the issue of special treatment for children and youths No clear answer could be obtained from state officials on whether they realize that this problem exists.
Regarding the issue of torture, Responsible state officials, such as the military, insisted that there was very little torture.
As for state officials breaking the law beating people, violating human rights, during the time that I have been here, there have not been many cases.
Those cases that have come up are now going through the criminal justice process.
Therefore, regarding state officials beating and torturing those who they arrest, I maintain that it does not exist.
If state officials do it, they must be severely punished.
This is became the Deep South is a special area, where we are trying to solve the problems using special means
Therefore, there can be little or no chance of human rights violations being committed.
If they do occur, then it is a case of an individuals.
But in terms of policy, the policy is to prevent it and use other methods.
Whether or not this is true, for those who have experienced it ,the attorneys say that they still have a way to fight and to demand justice.
If the question is: "Under what sort of authority did the officials act?"
I can answer that they have no authority to do so.
If the villagers are to bring a case against the officials, they can do so since the act is considered to be a deprivation of freedom and the officials have no authority to detain them.
After 7 days, if further detention is necessary, a request must be made to the court for an arrest warrant according to the Emergency Decree.
This is the issue about which we have received a lot of complaints from the villagers including on not being notified of where the suspect would be taken, detaining suspects for more than 7 days and not detaining them officially under the Emergency Decree.
But the problem that attorneys themselves admit is that in many cases, the villagers do not dare to bring a case against state officials.
Human rights activists raise as a concern the issue that these violations then create frustration within the minds of individuals who experience them, particularly for the youth themselves.
I feel very sad that my son was beaten
It's not that I'm not hurt.
I am really hurt.
I want to beg the officials to stop doing this.
I feel really sad that there is nothing we can do.
They are the mighty people, while we are just the small ones.
When officers arrest and detain children based only on suspicion, how are the villagers supposed to put their hope in the officials?
When something like this is done to the people, there will be a feeling of mistrust towards the officials and anger that the officials treat them this way.
Even today, there is anger, but it is hidden inside.
It cannot be vented out It's hidden in our minds, and we would not dare take vengeance
But instead feel sorry and angry that the officials treated us like this.
Many experts have studied and looked for ways to solve the problems of affected youth.
Even though most are not ready to provide information nearly all have expressed concern about the long-term consequences.
If the child is not guilty but is accused of being guilty, they will be at risk of being persuaded from the opposite side, and more easily than other children.
Political scientists also commented that this issue will have long-term consequences on solving the conflict in the area, as by their own admission, the Melayu in the Deep South are already suspicious and afraid of state officials.
It is a long-existing feeling and has been passed on until today.
Today, children and youth have been directly affected and thus the feeling of uneasiness and dislike is likely to mount up.
At present, I feel that the effect on children who experience this is that it may facilitate, partially, persuade or push them to act in another manner that it may cause them to take actions against the state it may only create further certainty that what they have done was correct.
Because no matter what state officials do, it will not be fair anyways
This will be be embedded and make it harder to solve the problem
One approach to solve the problem suggested by the attorneys and human rights activists is that the state should change their working method to take special care of youth.
This does not mean not taking legal action against them, but there should be a process in which these individuals receive special care.
I would like to ask security agencies to write a manual outlining policy on the treatment of youths, children, and women.
It should deal with is the method of arrest, the method of searching, the method of detaining, the conditions of the place of detention, method of interrogation while being detained by military units under martial law, the method of interrogation while being detained under the Emergency Decree, and the conditions of the place of detention.
In addition, children and youths should be given the right to have social workers or psychologists and their parents present during interrogation by officials, as we have to accept the fact that children and youth have different way of thinking than adults.
If the person interrogating the child is a soldier, the soldier should have received training on children's rights and training on the psychology of interrogating children
The judicial process for children and minors who have committed crimes, has the objective of rehabilitating juvenile offenders so that they can return to join society, and in which the child will feel remorse for their crime and grow in strength to an adequate extent that they will not re-commit the crime
Therefore, a just and fair criminal justice process for children and youth is important and should be made a reality.
We're on problem 32. What are the solutions to the equation 1 plus 1 over x squared is equal to 3 over x? So at first.
Then we'll get x squared times 1 is x squared, x squared times 1 over x squared, that's just 1.
Then x squared times 3 over x, that's 3x squared over x. x squared divided by x is just x, so that is equal to 3x. We can subtract 3x from both sides and you get x squared minus 3x plus 1 is equal to 0.
This is a simple quadratic.
It's not obvious that you can factor it. In fact, two numbers when you multiply them equal 1, and then when you add them equal minus 3.
So let's use the quadratic equation. When in doubt, use the quadratic equation. So minus B, this is B right?
B is this 3 right there, negative 3.
B is negative 3. So minus B is going to be plus 3, plus or minus the square root of B squared.
Minus 3 squared is 9, minus 4 times A, which is 1, times C which is 1. So it's minus 4, all of that over 2A.
A is 1 so it's just over 2. That is equal to 3/2 plus or minus the square root of 5 over 2. I just separated these out because I'm looking at the choices and it seems like they did that.
Then I've pasted it for you.
So there's two numbers with the following properties. The second number is 3 more than the first number. So let's say S for second number and F for first number.
So if we substitute for these S's, we get F plus 3 times F is equal to 9 plus F plus 3, right, instead of an S, F plus 3 and then plus F. Let's see if we can simplify this.
F times F is F squared plus 3F is equal to 9 plus 3 is 12 plus 2F.
Subtract 2F from both sides, you get F squared plus F is equal to 12. Subtract 12, you get F squared plus F minus 12 is equal to 0. This one looks factorable.
Let's see, this is F plus 4 times F minus 3, right? Because when you multiply those, you get negative 12. When you add those, you get plus 1, so that is equal to 0.
If F minus 3 is equal to 0, then that says that F could be 3.
So F could be minus 4 or 3. Now, S is F plus 3, so if we're dealing with the minus 4 scenario, if F is equal to minus 4, then what is S?
Then S is going to be minus 4 plus 3, and S is going to be equal to minus 1.
Then if F is equal to 3, than S is equal to 6.
Minus 4, minus 1, that's choice B.
Excellent. All right, problem 34. Let me see, maybe I should copy and paste these word problems so we can see how we parse the problems.
Jenny is solving the equation x squared minus 8x equals 9 by completing the square. What number should be added to both sides of the equation to complete the square? So x squared minus 8x is equal to 9.
When you're completing the square, you're trying to turn the left-hand side of this equation into some type of a perfect square. So if it's a perfect square, I have two numbers. It's the same number that when you add them together, you get minus 8, and when you square them, you should get something else, right?
So minus 4 squared is 16. So if I add 16 to both sides, I'm all set. Why did that work?
Remember the whole logic here, and I've done a few videos on completing the squares, is what number do I add here to make this a perfect square?
You say, OK, I have a minus 8x, so I take half of this number, because the same number added to itself twice is going to become minus 8. I take half of that number, then I squared it. So half of minus 8 is minus 4.
You can actually solve for this. x minus 4 is plus or minus 5. You keep going. That's actually where the quadratic equation comes from.
I'm going to copy and paste this entire problem here.
OK, which of the following most accurately describes the translation of the graph y is equal to x plus 3 squared minus 2 to the graph y equals x minus 2 squared plus 2? So the y translation tends to be pretty easy to figure out.
So if I had the graph x squared, the graph x squared looks something like this. Let's see if I can draw it.
So we're definitely going to be shifting from minus 2 to 2. So it's up 4. It's either going to be choice A or choice D.
So this graph will just get shifted to the right by 3.
That's x minus 3 shifts to the right by 3. x plus three would go in the other direction, because when x is minus 3, that's when it would equal to zero.
I haven't written that down. So let's think about this. We're going from x plus 3, so if this is x squared, x plus 3 would look something-- let me do it in a different color. x plus 3 is actually shifted to the left.
So the actual graph x plus 3 squared minus 2 is going to be here. Then to go here, you have a plus 2, so you're shifting the graph up by 4, and then you're going to x minus 2. So this graph right here is going to be up here.
Have you ever come home to a note that made life just a little bit easier?
A tip from someone you trust that helps you find the things you care about.
When you have lots of options in front of you, it's easy to find yourself wishing for a bit of advice.
That's why we're introducing the +1 -- a way for you and your friends to help each other find great things in Google search.
When you click +1, you're telling your friends, your family, and the rest of the world: "this is something you should check out."
Since people will find your recommendations right when they'll looking for them, you can +1 things you might not send an email or post an update about.
And the next time you're searching, you might see +1s from your friends and contacts, both on Google search and search ads.
So picking the right coffee maker, news article or chocolate chip cookie recipe could get a little easier.
And soon you'll be able to +1 more than just search results.
You'll also find the +1 button on sites across the web, making it easy to +1 pages after you've visited them. The web's a big place.
Sometimes it helps to have a tour guide.
So if you think something's cool, +1!
Use substitution to solve for x and y and we have a system of equations here.
The first equation is 2y=x+7 and the second equation here is x=y-4.
So what we want to do when we say substitution is we want to substitute one of the variables with an expression so that we have an equation in only one variable then we can solve for it.
So let me show you what I'm talking about.
Let me write this first degree equation.
2y=x+7. And we have the second equation over her, that x=y-4. So if we are looking for an x and y that satisfy both constraints, what we can see is, well look, if the x and the y's have to satisfy both restraints, both of these restraints have to be true.
So x must be equal to y-4. So anywhere in this top equation where we see an x we say, "Well look, that x by the second constraint has to be equal to y-4.
So everywhere we see an x, we can substitute it by a y-4.
So let's do that.
So if we substitute y-4 for x in this top equation, the top equation becomes 2y is equal to-- instead of an x, the second constraint tells us that x needs to be equal to y-4. So instead of an x, we'll have a y-4.
And then we have a plus seven. All I did here was I substituted y-4 for x.
The second constraint tells us that we need to do it. y-4 needs to be equal to x, or x needs to be equal to y-4.
The value here is now we have an equation.
One equation with one variable; we can just solve for y.
So we get 2y=y, and then we have minus 4 plus 7 so y+3, we can subtract y from both sides of this equation.
The left hand side -- 2y-y is just y. y is equal to-- these cancel out; y is equal to three.
And then we can go back and substitute into either of these equations and solve for x.
This is easier right over here, so let's substitute right over here. x needs to be equal to y-4.
So we can say that x is equal to 3-4, which is equal to -1.
So the solution to this system is x=-1, and y=3.
And you can verify that this works in this top equation right over here.
2*3 is 6, which is indeed equal to -1+7.
Now I want to show you that over here we substituted.
We had an expression or we had an equation that explicitly solved for x so we were able to substitute the x's.
What I want to show you is that we could have done it the other way around.
We could have solved for y and then substituted for the y's.
So let's do that.
We could have substituted from one constraint into the other constraint or vice-versa.
Either way, we would have gotten the same exact answer. So instead of saying that x=y-4, in that second equation, if we add 4 to both sides of this equation, we get x+4=y.
This and this is the exact same constraint.
I just added four to both sides to get this constraint over here.
And now since we've solved the equation explicitly for y, we can use the first constraint-- the first equation-- and everywhere we see y, we can substitute it with x+4. So it's 2 times--instead of 2 times y-- we can write 2(x+4). 2(x+4)=x+7.
We can distribute this two, so we get 2x+8=x+7.
We can subtract x from both sides of this equation, and we can subtract 8 from both sides of this equation. Subtract 8. The left hand side, that cancels out.
On the right hand side, that cancels out, and we are left with a -1.
Then, we can substitute back over here.
We have y=x+4, or so y=-1+4, which is equal to 3.
So once again we got the same answer, even though this time we substituted for y instead of substituting for x.
Hopefully you find that interesting.
Welcome to the presentation on why, not how, borrowing works. And I think this is very important because a lot of people who even know math fairly well or have an advanced degree still aren't completely sure on why borrowing works.
That's the focus of this presentation.
Let's say I have the subtraction problem 1,000-- that's a 0.
1,005 minus 616.
What I'm going to do is I'm going to write the same problem in a slightly different way.
We could call this the expanded form.
1,005-- what I'm going to do is I'm going to separate the digits out into their respective places.
So that is equal to 1,000 plus let's say zero 100's plus zero 10's plus 5.
1,005 is just 1,000 plus 0 plus 0 plus 5.
And then that's minus 616.
So that's minus 600 minus 10 minus 6.
616 could be rewritten as 600 plus 10 plus 6.
And I put a minus there because we're subtracting the whole thing.
So let's do this problem.
Well, if you're familiar with how you borrow is, this 5 is less than this 6, so we have to somehow make this 5 a bigger number so that we could subtract the 6 from it.
Well, we know from traditional borrowing that we have to borrow 1 from someplace and make this it into a 15.
But what I want to see actually, is understand where that 1 or actually where that 10 comes from.
Because if you're turning this 5 into a 15 you actually have to add 10 to it.
Well, if we look at this top number, the only place that a 10 could come from is here, is from this 1,000.
But what we're going to do since this is the 1,000's place, instead of borrowing 10 from here, which would make it kind of a very messy problem, I'm going to borrow 1,000 from here.
I'm going to get rid of this 1,000.
And I have a 1,000 that I took from this 1,000.
I have 1,000 now that I can distribute into these 3 buckets.
Into the 100's, 10's and 1's buckets.
Well, we need 10 here, so let's put 10 here.
So it's 10 plus 5 is equal to 15.
We got our 15.
If we took 10 from the 1,000 then we have 990 left.
So we could put 900 here and 90 here.
Notice, we just said-- so we had 1,000 and we just rewrote it as 900 plus 90 plus 10.
And we added this 10 to this 5.
And now we could do this subtraction just how we would do a normal problem.
15 minus 6 is 9.
90 minus 10 is 80.
900 minus 600 is 300.
So 300 plus 80 plus 9 is 389.
And let's see how we would have done it traditionally and make sure that it would have kind of translated into the same way.
Well, the way I teach it and I don't know if this is actually the traditional way of teaching borrowing, is I say, OK, I need to turn this 5 into a 15.
So I have to borrow a 1 from someplace.
Well, we know from this side of the problem that we actually borrowed a 10 because that's why it turned to 15.
If we're going to borrow 1, I'd say, well, can I borrow the 1 from the 0?
No.
Can I borrow the 1 from this 0?
No.
I could borrow it from here, but I'm borrowing it from 100, right?
So 100 minus 1 is 99.
So that's the how I do it.
And I say 15 minus 6 is 9.
9 minus 1 is 8. And 9 minus 6 is 300.
So this way that I just did it is clearly faster and, I guess you could say it's easier, but a lot of people might say, well Sal, that looks like a little bit of magic.
You just took that 5, put a 1 on it, and then you borrowed a 1 from this 100 here.
But really, what I did is right here.
I took 1,000 from this 1 and I redistributed that 1,000 amongst the 100's, 10's, and 1's place.
Let me do another example.
I think it might make it a little bit more clearer of why borrowing works.
Let me do a simpler problem.
I actually started off with a problem that tends to confuse the most number of people.
Let's say I had 732 minus-- Let me do a fairly simple one.
Minus 23.
Sometimes those 3's just come out weird.
Well, we just learned that's the same thing as 700 plus 30 plus 2 minus 20 minus 3.
Well, we see this 2, 2 is less than 3, so we can't subtract.
Wouldn't it be great if we could get a 10 from someplace?
We could get a 10 from here.
We make this into 20 and add the 10 to the 2 and we get 12.
And notice, 700 plus 20 plus 12 is still 732.
So we really didn't change the number up top at all.
We just redistributed its quantity amongst the different places. And now we're ready to subtract.
12 minus 3 is 9.
20 minus 20 is 0 and then you just bring down the 700.
You get 700 plus 0 plus 9, which is the same thing as 709.
And that's the reason why this borrowing will work.
Well, we say, oh, let's borrow 1 from the 3. Makes it a 2.
This becomes a 12.
And then we subtract. 9 0 7.
Let's do another problem, one last one.
And once again, you don't have to do it this way.
You don't have to every time you do a subtraction problem do it this way.
Although if you ever get confused, you can do it this way and you won't make a mistake, and you'll actually understand what you're doing.
But if you're on a test and you have to do things really fast you should do it the conventional way.
But it takes a lot of practice to make sure you never are doing something improper.
And that's the problem.
People learn just the rules, and then they forget the rules, and then they forgot how to do it.
If you learn what you're doing, you'll never really forget it because it should make some sense to you.
Let's do another one.
If I had 512 minus 38
Well, let's keep doing it that way I just showed you.
That's the same thing as 500 plus 10 plus 2 minus 30 minus 8.
Well, 2 is less than 8.
I need a 10 from someplace.
Well, one option we can do is we can just get the 10 from here.
So then that becomes 0.
And then this will become a 12.
Notice that 500 plus 0 plus 12, same thing as 512 still.
So we could subtract.
12 minus 8 is 4.
But here we see this 0 is less than 30, so we can't subtract.
But we can borrow from the 500.
Well, all we need is 100, so if we turn this into 100 then we took the 100 from the 500.
This becomes 400.
I just rewrote 500 as 400 plus 100.
Now I can subtract.
100 minus 30 is 70.
Bring down the 400. And this is the same thing as 474.
And the way you learn how to do it in school is you say, oh, well, 2 is less than 8, so let me borrow the 1.
It becomes 12.
This becomes a 0.
0 is less than 3, so let me borrow 1 from this 5.
Make this 4.
This becomes 10.
So then you say 12 minus 8 is 4.
10 minus 3 is 7 and you bring down the 4.
Hopefully what I've done here will give you an intuition of why borrowing works.
And this is something that actually I didn't quite understand until a while after I learned how to borrow.
And if you learned this, you'll realize that what you're doing here isn't really magic.
And hopefully, you'll never forget what you're actually doing and you can always kind of think about what's fundamentally happening to the numbers when you borrow.
I hope you found that useful.
Talk to later.
Bye.
My question is when you speak about freedom of religion, are you actually applying to the Malays as well?
Thanks.
There's no compulsion in religion.
Even Dr Farouk quoted that verse in the Quran.
How can you ask me or anyone; how could anyone really say, sorry this only applies to non-Malays.
It has to apply equally.
In the Quran, there's no specific term for the Malays, this is how it should be done.
So I'm tied of course, you know with the prevailing views but I will say that.
So what you want is most is in terms of quality.
You believe so strongly in your faith that even me ...
That question, to Nurul Izzah Anwar at a Novermber 3rd 2012 forum and her subsequent response put the opposition politician in a tight spot.
Condemnation came from all sides of the political divide as politicians exploited her views for political gain.
Nurul Izzah seemed to have come to that point of view from a section of the Surah AlBaqarah, paragraph 256 but is this paragraph relevant as source to conclude that Islam does allow o
The first point this sentence has no relevance to apostasy actually.
As is the current issue.
But this sentence tells the story of how we can become a Muslim of quality.
Because this sentence came down when the Prophet pbuh had migrated to Medina.
When he was in Mecca, a dilemma came about when Muslims were forced to convert to the religion of the Quresh. and there were those who were tortured and killed.
When the Prophet went on his pilgrimage to Medina, this sentence was sent to him; there is no compulsion in religion. to distinguish between truth and falsehood, to illustrate that force is a tool of non-believers as Islam in not a religion that forces people to adopt it, as was the practice of the non-believers in Mecca at that time.
Secondly this sentence, cannot be read part way.
It has to be read in toto. "there is truth over falsehood".
This is to inform us that Muslims with quality do not just know the truth, but must also know that which is false.
So there this 'la ikra ha fiddeen' has not relevance to the issue of apostasy.
But there are other paragraphs in the Ayat Surah Al-Baqarah that deals with apostasy.
"Those who have left Islam, when he/she dies as an infidel (kafir), his practices as a Muslim is 'cancelled' in this life and in the next."
The views of Muslims on whether Muslims can leave the religion, are divided
From an outright 'No!' to a call for the death penalty to a view that it is better to have a true Muslims in their midst than a false one. a 'munafik' or hypocrit.
Islam celebrates freedom of religion.
The freedom that is understood is that Islam does not force people to embrace it.
But when someone leaves the religion of Islam in Islam this is a crime.
And there is punishment for that crime is death.
But the punishment of death for an apostate is not because of his/her apostasy, but the punishment of death is because it is considered at act of war.
And this is why that if a person wants to leave Islam and does so quietly (without a declaration) no form of punishment will befall the person.
But can a Muslim leave Islam in Malaysia? and what is the penalty?
My answer is that there is no law that prohibits a person from leaving Islam.
How can a person be an apostate?
When that person from being a Muslim makes a declaration.
But current laws do not say directly 'if you leave Islam this will be the punishments'
Currently if a person and this seems common with all State enactments if the person declares being a non-Muslim to escape being charged for a Syariah crime
For instance, if a person is eating during the fasting month of Ramadhan and if he is caught, he declares that he is not a Muslim (but it is state that his religion is Islam in his Identity Card), then that is a crime.
But if a person goes through the process (Syariah) of application to leave Islam, he will not be subjected to any punishment.
He will not be charged for leaving Islam (i.e. it is not a punishable crime).
That in the din created by hardline Muslims calling for the death penalty for those wanting to leave Islam, there is in fact no Syriah law preventing anyone applying to do so.
But the religious authorities will not make it easy for the applicant subjecting the person to counselling, investigations and a trial before deciding to allow or dis-allow the application.
So in principle, there is no compulsion for Muslims to remain in Islam as the law stands
But in reality it is difficult to leave.
A ticket agent sells 42 tickets to a play.
The tickets cost $29 each.
Use rounding to estimate the total dollars taken in from the sale of the tickets.
Now if we wanted the exact number, we could say 42 times 29, and we could work out the multiplication, but they essentially want us to be able to do it in our head.
We want to round the numbers first and then multiply.
So if we want to round, and really we just have two places here, so if we're going to round anything, it's going to be to the nearest ten because that's the largest place we have.
So if we round 42 to the nearest ten-- we've done this drill many times-- 2 in the ones place is the less than 5, so we're going to round down.
The nearest ten is 40.
We're going to round down to 40.
29, if we round to the nearest ten, 9 in the ones place is greater than or equal to 5, so we round up.
And another way to think about it.
Just say, well, you know, 42, that's pretty close to 40.
29 is pretty close to 30.
Those are literally the nearest multiples of ten that I can figure out, so now I can multiply.
And here, once again, we can use-- you could call it a trick, but hopefully, you understand why it works.
But 30 times 40, instead of you saying, well, this is going to be the same thing as 3 times 4, but we're going to put two zeroes at the end of it.
30 times 40 is the same thing as 3 times 4 with two zeroes, so let's do that.
So you have 3 times 4 is 12, which we know, and then we have two zeroes.
We got that zero, so let's stick that zero there, and then we got that blue zero there, so let's put that over there.
So they're going to have roughly $1,200 taken it from sales of the tickets.
That is our estimate.
Your personal ancestry story begins with a shared story of our human ancestry.
You and your distant cousin, the chimpanzee, had a common ancestor, which lived about 6 and 1/2 million years ago.
We can learn about this common ancestor by noting what makes us similar to chimps.
But many things also distinguish us from chimpanzees,
like our big brains, which enable abstract reasoning and the development of complex languages, and our anatomy, adapted to upright walking.
These human traits developed gradually over millions of years.
The fossil record reveals a long and eventful parade of human ancestors.
Doing some periods, several of our ancestors coexisted.
Gradually, they became more efficient upright walkers.
And later, developed skulls with larger brain cases, devoted more time thinking and less to chewing.
Our knowledge of the exact relationships between these ancestors is incomplete and often is revised because of new fossil finds.
Some of them were our direct ancestors. Some of them were distant cousins, who became evolutionary dead-ends.
But by 200,000 years ago, we're on firmer ground.
We find the bones of people in Africa, who looked something
like us, not exactly like us, but close.
They built fires and flaked stone into spearheads, knives, and scrapers.
They were physically strong and still depended on their muscles, not their technology, for much of their survival.
Here, in addition to fossils, we have genetics to help us find our prehistoric kin.
All of us living today inherited our DNA from this small group of ancient people in Africa.
Over time, they began to look more and more like us.
And by 100,000 years ago, their skeletons weren't so different from ours. But these early homo sapiens shared the planet with two of their distant cousins.
By this time, as a result of previous migrations,
Homo erectus was living across Asia, and had been for 2 million years.
Homo erectus had a big brain. Some made hand axes, some built fires, and some may even have worn clothing.
At the same time, Neanderthals lived across Europe and Western and Central Asia.
They had even bigger brains.
They made spears and stone tools similar to those found in Africa. And we suspect they had strong social relationships.
They cared for their sick and infirmed and buried their dead, not so very different culturally from early Homo sapiens.
It seems that our human anatomy developed before our complex human culture.
But things were about to change.
Today, we live in all climates all over the world, and are unique in our dependence on our culture for survival.
How we got from there, to here, forms the next chapters in our human story.
So I've been requested to do the proof of the derivative of the square root of x, so I thought I would do a quick video on the proof of the derivative of the square root of x.
So we know from the definition of a derivative that the derivative of the function square root of x, that is equal to-- let me switch colors, just for a variety-- that's equal to the limit as delta x approaches 0.
In this video I want to give you an example of what it means to fit data to a line.
Instead of doing my traditional video using my little pen tablet, I'm going to do it straight on Excel so you could see how to do this for yourself, so if you have
Excel or some other type of a spreadsheet program.
We're not going to go into the math of it.
I really just want you to get the conceptual understanding of what it means to fit data with line, or do a linear regression.
So here, let's just read the problem.
The following table shows the median California income-- remember median is the middle, the middle California income
--from 1995 to 2002 as reported by the U.S. Census Bureau.
Draw a scatter plot and find the equation.
What would you expect the median annual income of a California family to be in the year 2010?
What are the meanings of the slope and the y-intercept of this problem?
So the first thing you'd want to do-- I just copied and pasted this image --we have to get the data in a form that the spreadsheet can understand it.
So let's make some tables here.
Let's say years since 1995.
Let's make that one column.
Let me make this a little bit wider.
Then let me put median income.
This is the median income in California for a family.
So we start off with 1 year, or 0 years since 1995, 0, 1, 2, 3, 4.
Actually if you want, it'll figure out the trend if you just keep going down.
It'll figure out you're just incrementing by 1.
Then the income, I'll just copy in these numbers right there.
So that's $53,807, $55,217, $55,209, $55,415 $63,100, $63,206, $63,761, and then we have $65,766.
So I don't need these over here.
So I'm going to get rid of them.
I can clear them.
So let me make sure I have enough entries.
This is 1, 2, 3, 4, 5, 6, 7, 8, and I have 1, 2, 3, 4, 5, 6, 7, 8 entries.
I want to make sure I got my data right. $53,807, $55,217, $55,209, 415, 100, 206, 761, 766.
OK, there we go.
Now you're going to find that in Excel this is incredibly easy if you know what to click on.
One, plot this data, create a scatter plot, and then even better, create a regression of that data.
So all you have to do is you select the data.
Then you go to insert, and I'm going to insert a scatter plot.
Then you can pick the different types of scatter plots.
I just want to plot the data.
There you go.
It plotted the data for me.
There you go.
If you go by this is the actual income, and this is by year since 1995.
So this is 1995.
It was $53,807.
In 1996 it's $55,217.
So it plotted all the data.
Now what I want to do is fit a line.
So this isn't exactly a line.
But let's see, if we assume that a line can model this data well, I'm going to get Excel to fit a line for me.
So what I can do is I have all of these options up here for different ways to fit a line, all of these different options.
I'm going to pick this one here.
You might not be able to see it.
It looks like it has a line between dots.
It also has fx which tells me going to tell me the equation of the line.
So if I click on that, there you go.
It not only fit, it replotted that same data on a different graph.
Let me make it a little bit bigger.
No, I don't want to that.
Let me make it a little bit bigger.
We can cover up the data now, just because I think we know what's going on.
So let me cover it up right like that.
So not only did it plot the various data points, it actually fit a line to that data and it gave me the equation of that line.
Let me see if I can make this a little bit bigger.
I'll move it out of the way so you can read it at least.
So it tells me right here, that the equation for this line is y is equal to 1,882.3x plus 52,847.
So if you remember what we know about slope and y-intercept, the y-intercept is 52,847, which is, if you use this line as your measure, where this line intersects at year 0, or in 1995.
So if you use this line as a model, in 1995 the line would say that you're going to make $52,847.
The actual data was a little bit off of that.
It was a little bit higher, $53,807.
So it was a little bit higher.
But we're trying to get a line that gets as close as possible to all of this data.
It's actually trying to minimize the distance, the square of the distance, between each of these points in the line.
We won't go into the math there.
But it gave us this nice equation.
Now we can use this nice equation to predict things.
If we say that this is a good a model for the data-- let me bring this down a little bit --let's try to answer our question.
So we drew a scatter plot-- really Excel did it for us.
We found the equation right there.
They say, what would you expect the median annual income of a California family to be in the year 2010?
So here, we can just use the equation they gave us.
This right here, was 2002.
So I could write down the year.
This was the year of 2002.
So the year 2010 is 8 more years.
Let me make a little column here.
So this is the year, 1995, 1996.
Then Excel will be able to figure out if I select those, and I go to this little bottom right square and I scroll down, Excel will actually figure out that I want to increment by 1 year every time.
If I say years since 1995, once again I can just continue this trend right here.
So 2010 would be 15 years.
So we can just apply this equation.
We could say it's going to be equal to, according to this line-- I'm just going to type it in, hopefully you can read what I'm saying --1,882.3 times x. x here is the year since 1995.
I could just select this cell, or I could type in the number 15.
That means times this cell, times 15.
Then plus 52,847, plus that right there.
Click enter and it predicts $81,081.50.
So if you just continue this line for another 8 or so years, it predicts that the median income in California for a family will be $81,000.
Anyway, hopefully you found that interesting.
Spreadsheets are very useful tools for manipulating data.
It'll give you a sense of why linear models are interesting, why lines are interesting, and how you can actually use these tools to interpret data and maybe even extrapolate some type of a prediction.
This right here, is an extrapolation using this linear regression.
Let's graph ourselves some inequalities. So let's say I had the inequality y is less than or equal to 4x plus 3.
On our xy coordinate plane, we want to show all the x and y points that satisfy this condition right here.
So a good starting point might be to break up this less than or equal to, because we know how to graph y is equal to 4x plus 3.
So this thing is the same thing as y could be less than 4x plus 3, or y could be equal to 4x plus 3.
That's what less than or equal means.
It could be less than or equal.
And the reason why I did that on this first example problem is because we know how to graph that.
So let's graph that.
Try to draw a little bit neater than that.
So that is-- no, that's not good.
So that is my vertical axis, my y-axis.
This is my x-axis, right there.
And then we know the y-intercept, the y-intercept is 3.
So the point 0, 3-- 1, 2, 3-- is on the line.
And we know we have a slope of 4.
Which means if we go 1 in the x-direction, we're going to go up 4 in the y. So 1, 2, 3, 4.
So it's going to be right here.
And that's enough to draw a line.
We could even go back in the x-direction.
If we go 1 back in the x-direction, we're going to go down 4.
1, 2, 3, 4.
So that's also going to be a point on the line.
So my best attempt at drawing this line is going to look something like-- this is the hardest part.
It's going to look something like that.
That is a line.
It should be straight.
I think you get the idea.
That right there is the graph of y is equal to 4x plus 3.
So let's think about what it means to be less than.
So all of these points satisfy this inequality, but we have more.
This is just these points over here.
What about all these where y ix less than 4x plus 3?
So let's think about what this means.
Let's pick up some values for x.
When x is equal to 0, what does this say?
When x is equal to 0, then that means y is going to be less than 0 plus 3. y is less than 3.
When x is equal to negative 1, what is this telling us?
4 times negative 1 is negative 4, plus 3 is negative 1. y would be less than negative 1.
When x is equal to 1, what is this telling us?
4 times 1 is 4, plus 3 is 7.
So y is going to be less than 7.
So let's at least try to plot these.
So when x is equal to-- let's plot this one first.
When x is equal to 0, y is less than 3.
So it's all of these points here-- that I'm shading in in green-- satisfy that right there.
If I were to look at this one over here, when x is negative 1, y is less than negative 1.
So y has to be all of these points down here.
When x is equal to 1, y is less than 7.
So it's all of these points down here.
And in general, you take any point x-- let's say you take this point x right there.
If you evaluate 4x plus 3, you're going to get the point on the line.
That is that x times 4 plus 3.
Now the y's that satisfy it, it could be equal to that point on the line, or it could be less than.
So it's going to go below the line.
So if you were to do this for all the possible x's, you would not only get all the points on this line which we've drawn, you would get all the points below the line.
So now we have graphed this inequality.
It's essentially this line, 4x plus 3, with all of the area below it shaded.
Now, if this was just a less than, not less than or equal sign, we would not include the actual line.
And the convention to do that is to actually make the line a dashed line.
This is the situation if we were dealing with just less than 4x plus 3.
Because in that situation, this wouldn't apply, and we would just have that.
So the line itself wouldn't have satisfied it, just the area below it.
Let's do one like that.
So let's say we have y is greater than negative x over 2 minus 6.
So a good way to start-- the way I like to start these problems-- is to just graph this equation right here.
So let me just graph-- just for fun-- let me graph y is equal to-- this is the same thing as negative 1/2 minus 6.
So if we were to graph it, that is my vertical axis, that is my horizontal axis.
And our y-intercept is negative 6.
So 1, 2, 3, 4, 5, 6.
So that's my y-intercept.
And my slope is negative 1/2.
Oh, that should be an x there, negative 1/2 x minus 6.
So my slope is negative 1/2, which means when I go 2 to the right, I go down 1.
So if I go 2 to the right, I'm going to go down 1.
If I go 2 to the left, if I go negative 2, I'm going to go up 1.
So negative 2, up 1.
So my line is going to look like this.
My line is going to look like that.
That's my best attempt at drawing the line.
So that's the line of y is equal to negative 1/2 x minus 6.
Now, our inequality is not greater than or equal, it's just greater than negative x over 2 minus 6, or greater than negative 1/2 x minus 6.
So using the same logic as before, for any x-- so if you take any x, let's say that's our particular x we want to pick-- if you evaluate negative x over 2 minus 6, you're going to get that point right there.
You're going to get the point on the line.
But the y's that satisfy this inequality are the y's greater than that.
So it's going to be not that point-- in fact, you draw an open circle there-- because you can't include the point of negative 1/2 x minus 6.
But it's going to be all the y's greater than that.
That'd be true for any x.
You take this x.
You evaluate negative 1/2 or negative x over 2 minus 6, you're going to get this point over here. The y's that satisfy it are all the y's above that.
So all of the y's that satisfy this equation, or all of the coordinates that satisfy this equation, is this entire area above the line.
And we're not going to include the line.
So the convention is to make this line into a dashed line.
And let me draw-- I'm trying my best to turn it into a dashed line.
I'll just erase sections of the line, and hopefully it will look dashed to you.
So I'm turning that solid line into a dashed line to show that it's just a boundary, but it's not included in the coordinates that satisfy our inequality.
The coordinates that satisfy our equality are all of this yellow stuff that I'm shading above the line.
Anyway, hopefully you found that helpful.
What I want to do in this video is think about the idea of fraction.
And for the sake of this video, as we learn what a fraction is, you can think of it as a part of a whole. Later on we will think of it in even more ways.
What do I mean by a "part of a whole"?
Let's imagine we have a pizza,
and let's say I divide it into 4 equal parts.
So there is a total of 4 equal slices of pizza.
And let's say on 3 of these slices I have cheese, only cheese.
And in the fourth slice I have cheese and olives.
So we can ask ourselves what fraction of this pizza has olives on it?
Well, we have 4 total slices, all equal sections, and 1 of those has olives.
So we can say 1/4 of this pizza has olives on it, 1 out of the 4.
Well, this slice has cheese but also olives, so we don't count that, but we have 3 of this 4 slices with only cheese.
So, 3/4 of the pizza has only cheese. Let's do a couple more examples, because this is probably one of the most important and useful idea you can have in your brain.
Let's imagine instead we were looking at some fruit,
let's say that I have an orange, a banana, a lemon, an apple and some grapes.
If I were to ask you what fraction of the fruit
I have is, let's say, yellow?
Well, we could say we have a total of 5 pieces of fruit.
What fraction of those pieces of fruit are yellow?
Well, I have 2 yellow pieces right over here, so let's say 2/5 of the fruit is yellow.
Let me do one more example, just to make the point clear.
Let me draw a candy bar, so that's all food-related.
Let's say I have a candy bar, just like that, and let me divide it into 5 equal pieces. Let's assume these are all equal pieces, and I'm hungry, so I eat this piece and this piece, so they essentially go away.
So, what fraction of these pieces have I eaten?
Well, I have a total of 5 pieces, and I ate 2 of them, so 2/5 of this bar have been eaten.
So I'll leave you there, maybe I'll make another video that doesn't have as many food analogies, but this is a super useful concept and I encourage you to think about it as much as possible and then try the exercises here on Khan Academy.
Today, the Court indicted the plaintiffs for criminal misconduct (by state officials) on the death of Imam Yapa Kaseng which consisted of the relatives of the deceased, to hear whether the court would try the case
Today, we are here at the court to hear the judgement
This is the case of my father, who died in custody of military officials, for which we filed a lawsuit
We filed against a total of 6 officials, 1 of whom is a police officer who is the Director of Rueso Police Station
The reason for the motion is that the police officer brought us to a news conference at Muaeng Narathiwat District Police Station, and locked us up in a police truck at Task Force 39, Suam Tham Temple, Rueso District
The other 5 officials were in the military, who tortured Father to death on that day
Today, the ruling of the Court came in 2 parts.
The first ruling is to dismiss the motion against the 6th defendent, the police officer. for whom the plaintiff attorney filed the motion that the police officer was involved in the crime which resulted in death during custody
Thus, acquittal would equal to non-involvement of the police in the crime
However, the attorney who wrote the complaint or the motion deemed that the role of the police officer, from the arrest to the press conference and returning to Task Force 39 and allowing the military officials to use the truck in the detainment for 2 days, and causing the death which should result in the police official also being responsible for the mentioned act
However, the Court did not concur, and the motion was dismissed
Therefore, at this moment, the co-offenders only include Defendent 1-5, all of whom are military officials
One more thing, in the court ruling, the judge also said that
"Although the act of the police might be the violation of rights in the Constitution, Section 39 on human dignity, etc.", the details of which would have to be provided by our lawyer
So the judge ruled that (on the police officer) there was violation of constitutional rights
But as this violation did not have any law or regulation that specified the sentense
It resulted in the Judge ruling that there was no role in the crime (by the police officer)
As for the 1st to 5th defendent, all of whom are military officials, by Thai Laws, these defendents would have to be tried by Court Martial
Today, we came here with the hope that justice would be on our side
The police officer must also take responsiblity for this case
But today, things did not turn out as we expected.
I think that the police officer should take responsiblity, but when I heard the court ruling, it turned out that the cop did not do anything wrong
I feel very unsatisfied, and very angry
As for my feeling, it was very unhappy with the ruling that the police officer did not play a role in the crime
We were thinking that a civilian court should be able to protect the rights of the people better than others
But when the court ruled as mentioned, we felt a bit despaired
People were affected, as severely as death, during custody (by officials)
And this is one of the first cases where the relatives seek justice in the judicial process
Yet the Court decided to drop the charge and did not grant motion
Which may cause the people to seek justice elsewhere
I think that the Court should be the best place or the last resort on which the people can rely
We will keep on fighting in order to see justice done. We will never back down
Even if we have to fight this case in court martial
Time is not an obstacle for us in continuing the search for the word "Justice". We will keep on fighting.
Convert 51.8 decimeters to kilometers.
So let's just think about what decimeters means in terms of meters, and then we can think about what kilometers mean in terms of meters, and then convert them.
So we're going to start with 51.8 decimeters.
Now, as a starting point, just to keep things simple, we're going to convert them into meters, because this prefix tells us a lot about how many meters this is.
So if we want to convert it into meters, our units are going to have to be meters per decimeter.
And we need this because this decimeter and that decimeter are going to cancel out, and we're going to be just left with meters.
Now 1 meter is how many decimeters?
Well, the prefix deci means 1/10.
So 1 decimeter is 1/10 of a meter.
Or another way of thinking about it is there are 10 decimeters for every meter.
This is a smaller unit. 10 of these make up 1 of these, or 1/10 of a meter per decimeter, which is exactly what that is telling you. 1/10 of a meter.
Now if you multiply these two things, what do we get?
Well, the decimeters cancel out, and we divide 51.8 by 10.
Multiplying by 1/10 is the same thing as dividing by 10.
So this is going to be equal to 51.8 divided by 10.
The decimal's just going to move to the left.
It's going to be 5.18.
So this is going to be 5.18 meters.
And you should always do a reality check.
Did it make sense?
Does it make sense that 51 decimeters are equal to 5 meters?
Well, sure.
It should go down.
We're going from a smaller unit to a larger unit, so we should have fewer of that larger unit to make the same distance in this case.
A meter is a unit of length.
Now, we're at 5.18 meters, and we want to now convert it to kilometers.
So we're going to want meters in the denominator and kilometers in the numerator.
Why?
Because this meter and that meter will cancel out.
Now, how many meters make up a kilometer?
The kilo tells us 1,000.
That is 1,000 meters.
So 1,000 meters are equal to 1 kilometer.
So if we were to multiply this, the meters cancel out and we'll just be left with kilometers.
And multiplying something by 1/1,000 is the exact same thing as dividing by 1,000, and that makes sense.
We should get a smaller number here because we're going from a smaller unit to a larger unit.
So we're going to need a much smaller amount of the larger unit.
So this is going to be equal to 5.18/1,000 kilometers.
Now, the easy way to do this, if we take 5.18/10 is equal to-- we just move the decimal one to the left.
It's going to be equal to 0.518.
If we take 5.18 and divide it by 100, we're going to take the decimal two to the left.
So one, two, we're going to have to add a zero here.
So it's going to be 0.0518.
And if we take 5.18 and we divide by 1,000, we're going to move the decimal three to the left.
So we'll just do it.
So if we start with 5.18-- the decimal started here-- we're going to go one, two, so that's one zero, and then three.
And that's where the decimal is going to sit there.
So this is Or another way, this is a little over 5/1,000.
This right here is 5/1,000.
It's a little bit more than that.
So our final answer:
51.8 decimeters is equal to 0.00518 kilometers.
And always do a reality check.
Does that make sense?
Well, sure.
We're going from a really small unit here, a bunch of a small unit, to a very small amount of a large unit.
It makes sense.
It makes sense that this number goes down while the actual unit becomes larger.
This video is 30 seconds long what's that?
It's 30 seconds long
We don't have time to get along because it's 30 seconds long
You all have many things to do That's why I'm being short with you
So I've decided not to bore you
By being 30 seconds long
Yes, this is 30 seconds long
We don't have time to wear a thong Or smoke a bong Or play ping pong
It's all fornot because you see the limitations that I'm in for being 30 seconds long
I was born and raised in North Korea.
Although my family constantly struggled against poverty, I was always loved and cared for first, because I was the only son and the youngest of two in the family.
But then the great famine began in 1994.
I was four years old.
My sister and I would go searching for firewood starting at 5 in the morning and come back after midnight.
I would wander the streets searching for food, and I remember seeing a small child tied to a mother's back eating chips, and wanting to steal them from him.
Hunger is humiliation.
Hunger is hopelessness.
For a hungry child, politics and freedom are not even thought of.
On my ninth birthday, my parents couldn't give me any food to eat.
But even as a child, I could feel the heaviness in their hearts.
Over a million North Koreans died of starvation in that time, and in 2003, when I was 13 years old, my father became one of them.
I saw my father wither away and die.
In the same year, my mother disappeared one day, and then my sister told me that she was going to China to earn money, but that she would return with money and food soon.
Since we had never been separated, and I thought we would be together forever, I didn't even give her a hug when she left.
It was the biggest mistake I have ever made in my life.
But again, I didn't know it was going to be a long goodbye.
I have not seen my mom or my sister since then.
Suddenly, I became an orphan and homeless.
My daily life became very hard, but very simple.
My goal was to find a dusty piece of bread in the trash.
But that is no way to survive.
I started to realize, begging would not be the solution.
So I started to steal from food carts in illegal markets.
Sometimes, I found small jobs in exchange for food.
Once, I even spent two months in the winter working in a coal mine, 33 meters underground without any protection for up to 16 hours a day.
I was not uncommon.
Many other orphans survived this way, or worse.
When I could not fall asleep from bitter cold or hunger pains,
I hoped that, the next morning, my sister would come back to wake me up with my favorite food.
That hope kept me alive.
I don't mean big, grand hope.
I mean the kind of hope that made me believe that the next trash can had bread, even though it usually didn't.
But if I didn't believe it, I wouldn't even try, and then I would die.
Hope kept me alive.
Every day, I told myself, no matter how hard things got, still I must live.
After three years of waiting for my sister's return, I decided to go to China to look for her myself.
I realized I couldn't survive much longer this way.
I knew the journey would be risky, but I would be risking my life either way.
I could die of starvation like my father in North Korea, or at least I could try for a better life by escaping to China.
I had learned that many people tried to cross the border to China in the nighttime to avoid being seen.
North Korean border guards often shoot and kill people trying to cross the border without permission.
Chinese soldiers will catch and send back North Koreans, where they face severe punishment.
I decided to cross during the day, first because I was still a kid and scared of the dark, second because I knew I was already taking a risk, and since not many people tried to cross during the day,
I thought I might be able to cross without being seen by anyone.
I made it to China on February 15, 2006.
I was 16 years old.
I thought things in China would be easier, since there was more food.
I thought more people would help me.
But it was harder than living in North Korea, because I was not free.
I was always worried about being caught and sent back.
By a miracle, some months later,
I met someone who was running an underground shelter for North Koreans, and was allowed to live there and eat regular meals for the first time in many years.
Later that year, an activist helped me escape China and go to the United States as a refugee.
I went to America without knowing a word of English, yet my social worker told me that I had to go to high school.
Even in North Korea, I was an F student.
(Laughter)
And I barely finished elementary school.
And I remember I fought in school more than once a day.
Textbooks and the library were not my playground.
My father tried very hard to motivate me into studying, but it didn't work.
At one point, my father gave up on me.
He said, "You're not my son anymore."
I was only 11 or 12, but it hurt me deeply.
But nevertheless, my level of motivation still didn't change before he died.
So in America, it was kind of ridiculous that they said I should go to high school.
I didn't even go to middle school.
I decided to go, just because they told me to, without trying much.
But one day, I came home and my foster mother had made chicken wings for dinner.
And during dinner, I wanted to have one more wing, but I realized there were not enough for everyone, so I decided against it.
When I looked down at my plate, I saw the last chicken wing, that my foster father had given me his.
I was so happy.
I looked at him sitting next to me.
He just looked back at me very warmly, but said no words.
Suddenly I remembered my biological father.
My foster father's small act of love reminded me of my father, who would love to share his food with me when he was hungry, even if he was starving.
I felt so suffocated that I had so much food in America, yet my father died of starvation.
My only wish that night was to cook a meal for him, and that night I also thought of what else I could do to honor him.
And my answer was to promise to myself that I would study hard and get the best education in America to honor his sacrifice.
I took school seriously, and for the first time ever in my life, I received an academic award for excellence, and made dean's list from the first semester in high school.
(Applause)
That chicken wing changed my life.
(Laughter)
Hope is personal.
Hope is something that no one can give to you.
You have to choose to believe in hope.
You have to make it yourself.
In North Korea, I made it myself.
Hope brought me to America.
But in America, I didn't know what to do, because I had this overwhelming freedom.
My foster father at that dinner gave me a direction, and he motivated me and gave me a purpose to live in America.
I did not come here by myself.
I had hope, but hope by itself is not enough.
Many people helped me along the way to get here.
North Koreans are fighting hard to survive.
They have to force themselves to survive, have hope to survive, but they cannot make it without help.
This is my message to you.
Have hope for yourself, but also help each other.
Life can be hard for everyone, wherever you live.
My foster father didn't intend to change my life.
In the same way, you may also change someone's life with even the smallest act of love.
A piece of bread can satisfy your hunger, and having the hope will bring you bread to keep you alive.
But I confidently believe that your act of love and caring can also save another Joseph's life and change thousands of other Josephs who are still having hope to survive.
Thank you.
(Applause)
Adrian Hong:
Joseph, thank you for sharing that very personal and special story with us.
I know you haven't seen your sister for, you said, it was almost exactly a decade, and in the off chance that she may be able to see this, we wanted to give you an opportunity to send her a message.
Joseph Kim: In Korean?
AH:
You can do English, then Korean as well.
(Laughter) Okay, I'm not going to make it any longer in Korean because I don't think I can make it without tearing up.
Nuna, it has been already 10 years that I haven't seen you.
I just wanted to say that I miss you, and I love you, and please come back to me and stay alive.
And I -- oh, gosh.
I still haven't given up my hope to see you.
I will live my life happily and study hard until I see you, and I promise I will not cry again.
(Laughter)
Yes, I'm just looking forward to seeing you, and if you can't find me, I will also look for you, and I hope to see you one day.
And can I also make a small message to my mom?
AH:
Sure, please.
I haven't spent much time with you, but I know that you still love me, and you probably still pray for me and think about me.
I just wanted to say thank you for letting me be in this world.
Thank you.
(Applause)
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New report -- Arrested Development
The Long Term Impact of Israel's Separation Barrier in the West Bank.
Why grow homes?
Because we can.
Right now, America is in an unremitting state of trauma.
And there's a cause for that, all right.
We've got McPeople, McCars, McHouses.
As an architect, I have to confront something like this.
So what's a technology that will allow us to make ginormous houses?
Well, it's been around for 2,500 years.
It's called pleaching, or grafting trees together, or grafting inosculate matter into one contiguous, vascular system.
And we do something different than what we did in the past; we add kind of a modicum of intelligence to that.
We use CNC to make scaffolding to train semi-epithetic matter, plants, into a specific geometry that makes a home that we call a Fab Tree Hab.
It fits into the environment.
It is the environment.
It is the landscape, right?
And you can have a hundred million of these homes, and it's great because they suck carbon.
They're perfect.
You can have 100 million families, or take things out of the suburbs, because these are homes that are a part of the environment.
Imagine pre-growing a village -- it takes about seven to 10 years -- and everything is green.
So not only do we do the veggie house, we also do the in-vitro meat habitat, or homes that we're doing research on now in Brooklyn, where, as an architecture office, we're for the first of its kind to put in a molecular cell biology lab and start experimenting with regenerative medicine and tissue engineering and start thinking about what the future would be if architecture and biology became one.
So we've been doing this for a couple of years, and that's our lab.
And what we do is we grow extracellular matrix from pigs.
We use a modified inkjet printer, and we print geometry.
We print geometry where we can make industrial design objects like, you know, shoes, leather belts, handbags, etc., where no sentient creature is harmed.
It's victimless.
It's meat from a test tube.
So our theory is that eventually we should be doing this with homes.
So here is a typical stud wall, an architectural construction, and this is a section of our proposal for a meat house, where you can see we use fatty cells as insulation, cilia for dealing with wind loads and sphincter muscles for the doors and windows.
(Laughter)
And we know it's incredibly ugly.
It could have been an English Tudor or Spanish Colonial, but we kind of chose this shape.
And there it is kind of grown, at least one particular section of it.
We had a big show in Prague, and we decided to put it in front of the cathedral so religion can confront the house of meat.
That's why we grow homes.
Thanks very much.
(Applause)
It is 10.45 am infront of the Parliment House in KL
More than 300 members of Malaysian Trade Union Congress have gathered here peacefully to protest amendments to the Employment Act
Earlier today, the President of the Congress, Mohd Khalid Atan have met the Minister of Human Resource S.Subramaniam to convey the Congress rejection of the proposed amendments which erode the workers rights
Khalid Atan is appealing to the Prime Minister, Najib Razak to intervene into this matter
We are asked to identify the percent amount and base in this problem.
They ask us 150 is 25% of what number?
So another way to think about it is 25% times some number, so I will do 25% in yellow.
And 25% times some number is equal to 150.
So the percent is pretty easy to spot. We have a 25% right over here.
So, this is going to be the percent.
That is the percent.
And we are multiplying the percent times some base number.
So this right over here is the base and we have percent times the base is equal to some amount.
And you can try to solve this in your head.
This is essentially saying 25% times some number is equal to 150.
If it helps, we can rewrite this as 0.25 (which is the same thing as 25%) 0.25 times some number is equal to 150.
And one interesting thing to think about is "should this number be larger or smaller than 150"?
Well, if we only take 25% of that number, if we only take 25/100 of that number
If we only take 1/4th of that number, because that's what 25% is, we get 150.
So this number needs to be larger than 150.
If fact, it has to be larger than 150 by 4.
And to actually figure out what this number is we can actually multiply, since what is on the left hand side is equal to what is on the right hand side.
If we want to solve this, we can multiply both sides by 4.
If we say, look, we have some value over here and we're going to multiply it by 4 in order for it to still be equal we would have to multiply 150 times 4.
4 times 0.25 (or 4 times 25% or times 1/4th), this is just going to be 1.
And we are going to get our number is equal to 150 times 4.
Or equal to 600.
And that makes sense. 25% of 600 is 150.
1/4th of 600 is 150.
What I want to do in this video is talk a little bit about compounding interest and then have a little bit of a discussion of a way to quickly, kind of an approximate way, to figure out how quickly something compounds.
Then we'll actually see how good of an approximation this really is.
Just as a review, let's say I'm running some type of a bank and I tell you that I am offering 10% interest that compounds annually.
That's usually not the case in a real bank; you would probably compound continuously, but I'm just going to keep it a simple example, compounding annually.
There are other videos on compounding continuously.
All that means is that let's say today you deposit $100 in that bank account.
If we wait one year, and you just keep that in the bank account, then you'll have your $100 plus 10% on your $100 deposit.
10% of 100 is going to be another $10.
After a year you're going to have $110.
You can just say I added 10% to the 100.
After two years, or a year after that first year, after two years, you're going to get 10% not just on the $100, you're going to get 10% on the $110.
10% on 110 is you're going to get another $11, so 10% on 110 is $11, so you're going to get 110 ...
That was, you can imagine, your deposit entering your second year, then you get plus 10% on that, not 10% on your initial deposit.
That's why we say it compounds.
You get interest on the interest from previous years.
So 110 plus now $11.
Every year the amount of interest we're getting, if we don't withdraw anything, goes up.
Now we have $121.
I could just keep doing that.
The general way to figure out how much you have after let's say n years is you multiply it. I'll use a little bit of algebra here.
Let's say this is my original deposit, or my principle, however you want to view it.
After x years, so after one year you would just multiply it ...
To get to this number right here you multiply it by 1.1.
Actually, let me do it this way.
I don't want to be too abstract.
Just to get the math here, to get to this number right here, we just multiplied that number right there is 100 times 1 plus 10%, or you could say 1.1.
This number right here is going to be, this 110 times 1.1 again.
It's this, it's the 100 times 1.1 which was this number right there.
Now we're going to multiply that times 1.1 again.
Remember, where does the 1.1 come from?
1.1 is the same thing as 100% plus another 10%.
That's what we're getting.
We have 100% of our original deposit plus another 10%, so we're multiplying by 1.1.
Here, we're doing that twice.
We multiply it by 1.1 twice.
After three years, how much money do we have?
It's going to be, after three years, we're going to have 100 times 1.1 to the 3rd power, after n years.
We're getting a little abstract here.
We're going to have 100 times 1.1 to the nth power.
You can imagine this is not easy to calculate.
This was all the situation where we're dealing with 10%.
If we were dealing in a world with let's say it's 7%.
Let's say this is a different reality here.
We have 7% compounding annual interest.
Then after one year we would have 100 times, instead of 1.1, it would be 100% plus 7%, or 1.07.
Let's go to 3 years.
After 3 years, I could do 2 in between, it would be 100 times 1.07 to the 3rd power, or 1.07 times itself 3 times. After n years it would be 1.07 to the nth power.
I think you get the sense here that although the idea's reasonably simple, to actually calculate compounding interest is actually pretty difficult.
Even more, let's say I were to ask you how long does it take to double your money?
If you were to just use this math right here, you'd have to say, gee, to double my money
I would have to start with $100.
I'm going to multiply that times, let's say whatever, let's say it's a 10% interest, 1.1 or 1.10 depending on how you want to view it, to the x is equal to ...
Well, I'm going to double my money so it's going to have to equal to $200.
Now I'm going to have to solve for x and I'm going to have to do some logarithms here.
You can divide both sides by 100.
You get 1.1 to the x is equal to 2.
I just divided both sides by 100.
Then you could take the logarithm of both sides base 1.1, and you get x.
I'm showing you that this is complicated on purpose.
I know this is confusing.
There's multiple videos on how to solve these.
You get x is equal to log base 1.1 of 2.
Most of us cannot do this in our heads.
Although the idea's simple, how long will it take for me to double my money, to actually solve it to get the exact answer, is not an easy thing to do.
You can just keep, if you have a simple calculator, you can keep incrementing the number of years until you get a number that's close, but no straightforward way to do it.
This is with 10%.
If we're doing it with 9.3%, it just becomes even more difficult.
What I'm going to do in the next video is I'm going to explain something called the Rule of 72, which is an approximate way to figure out how long, to answer this question, how long does it take to double your money?
We'll see how good of an approximation it is in that next video.
What is the most astounding fact you can share with us about the Universe?
The most astounding fact is the knowledge that the atoms that comprise life on Earth the atoms that make up the human body are traceable to the crucibles that cooked light elements into heavy elements in their core under extreme temperatures and pressures
These stars, the high mass ones among them went unstable in their later years they collapsed and then exploded scattering their enriched guts across the galaxy guts made of carbon, nitrogen, oxygen and all the fundamental ingredients of life itself
These ingredients become part of gas cloud that condense, collapse, form the next generation of solar systems stars with orbiting planets, and those planets now have the ingredients for life itself
So that when I look up at the night sky and I know that yes, we are part of this universe we are in this universe, but perhaps more important than both of those facts is that the Universe is in us.
When I reflect on that fact, I look up- many people feel small because they're small and the Universe is big- but I feel big, because my atoms came from those stars.
There's a level of connectivity.
That's really what you want in life, you want to feel connected, you want to feel relevant you want to feel like a participant in the goings on of activities and events around you
That's precisely what we are, just by being alive...