How can I link to a specific comment in a Trello card?

Question: As the activity on a card grows, specific comments can sometimes get lost in the clutter. Can I link to a specific comment?
Answer: Unfortunately, there seems to be no way to link to just an activity record inside a card.
The best way to keep a comment visible and near the top is to add the comment to the card description in addition to the activity records.
You can link to a card by using the link found in the "Show Card ID" button on the back of the card.


Database Files and Filegroups

Question: In my case wherein I have a file file_01.mdf and file_02.ndf under 1 filegroup, if ever file_01.mdf was already full (no autogrowth enabled), will it give me error on file_01.mdf if data is attempted to be added in it?
Comment: Comments like this are why I stopped answering questions on forums. Edgar asked a basic question that Dominique proved was able to be answered in a short statement. But instead of providing an answer a bunch of questions where asked that don't give any insight into the answer to the question.
Comment: Is this something you're having a hard time testing on your own?
Comment: yes. I am just a newbie DBA. What steps should I take to test this?. Also, I am not that familiar specifically in the behavior of files and filegroups.
Comment: I'll answer that with a question: what steps would you want someone else to take to answer your question?
Comment: step by step? instructional? an overview?
Comment: That's exactly how you should write your test! This sounds like a great learning process for a new DBA.
Answer: No, you won't get an error until both datafile are full.. The error is thrown when there is no more space in the filegroup (not for every file in it).
You can test it pretty easily by creating a database with 2 data file (one with the auto-growth enable) and inserting data in it until it fills the first data file.
You will see the the first file fills up to 100% and you won't get any error.
If you disable the auto-growth on the second file and continue inserting, we will get an error when both file will be filled.
Thanks.

Database Files and Filegroups


Is "I never saw him yesterday" grammatical?

Question: Is "I never saw him yesterday" grammatical, used to mean that "at no point in time in yesterday did I see him"? Does the sentence sound weird to a native speaker of AmE?
Comment: To this native AmE speaker it does not sound anything buy natural. It doesn't sound weird or anything else. But I would probably say it only to make a flat denial to someone who is asserting that I did see *him* yesterday (and *him* is not the one making the assertion).
Comment: sounds fine to me.
Comment: Note that this is almost certainly *spoken* not *written* English, and is very definitely *not formal*. It's a colloquialism, to be used in informal conversation.
Answer:
I didn't see him yesterday

is a more standard way to express the basic idea.

I never saw him yesterday.

We would normally use never saw in this way only when there is a special reason to do so.
As Adam and gnasher729 point out or suggest, the reason for doing so is to communicate contrast.
For example, many prior occasions contrasted with none

Although I saw him several or many times before yesterday, I saw him zero times yesterday.

Or a lengthy period in which I might have seen him or numerous opportunities to check or notice contrasted with zero sightings

I was here all day (or I looked for him many times) but in all that long period (or on all those many occasions) I didn't see him even once.
Answer: It may be grammatical but it is a sentence that makes one stumble. One reads "I never saw him" and is astonished to find it limited to "yesterday". Then one reads the sentence again to understand how you think, but it is an unusual formulation. "Never" is used without any limitation as in "He left and we never saw him again".
The normal way of saying it would be: I didn't see him yesterday.
Comment: But isn't "I didn't see him yesterday" talking about _some particular_ time in yesterday?
Comment: "Yesterday" refers to the whole day before today. If you you want to speak of a specific part of yesterday you have to say it, eg. I didn't see him yesterday evening. –  rogermue 4 hours ago
Comment: @user132181 In other words, "I didn't see him yesterday" is the negation of "I saw him yesterday". "I saw him yesterday" doesn't imply the full 24 hours, and would be correct if I saw him at any point in time on the day before today. The negation of that means there was no point in time on the day before today at which I saw him. (I realise this sounds awkward, but I'm trying to leave no room for misinterpretations.)
Answer: 'Never' puts an emphasis on the statement.
In the affirmative sentences we use 'did' to emphasise on what you are saying.
For example

I did see him at the party yesterday.

Here you affirmatively emphasized your point.
But what if in the same situation you want to say you didn't see him there. Then it'd be,

I didn't see him at the party yesterday.  (Here 'didn't' does not denote any emphasis on the statement. it is just a plain negative statement)

But what if when you want to emphasize the point that you did not see him at the party ?
So in these situations 'never' can be used
So you can say
I never saw him at the party yesterday.
So the meaning you quoted in your answer sounds correct to me.
Another example
I was waiting for him outside the office. But he didn't come.
I was waiting for him outside the office. But he never came.
Answer: (AmE)
Normally I would use "never saw" if there was an extended or repeated window when I might have seen someone or something.

Rick Astley used to play at a bar by my house each and every Wednesday, but I never saw him.  Now he is retired.
I lived in the Himalayas for twenty years.  People said there was a yeti nearby, but  I never saw him.

These concepts could apply to yesterday too.

The mailman normally drives by my house at 5.  I waited and waited, but I never saw him yesterday.
Everytime I hear a bird sing I jump to my window to try to catch a glimpse of the oriole.  Usually I catch a glimpse, but I never saw him yesterday.

People do occasionally use never saw simply to impart emphasis, but with a specific time in mind (e.g. "Accuse me all you want, but I never saw him at six o'clock last night" )  I don't, and it always sounds antiquated or uneducated to my ear. I think it is a matter of style, though, not grammar.
Comment: Oh yeah - the hills were crawling with yetesses.
Comment: But only if the Yeti was male? ;)
Answer: A situation where it would be reasonably natural: "I saw him three times on Monday, and six times on Tuesday, but I never saw him yesterday".


Getting from Victoria Falls airport to town

Question: What are my options for getting from Victoria Falls airport into town? All I have seen so far are taxis and pre-booked accommodation transfers.
Comment: I have another trick that worked for me when I tried it in Bangkok: If you can spot an Israeli backpackers in the airport ask them how they got there and how much they paid. Israeli backpackers always have tiny budgets (just got out of the army) and are very good hagglers (-:
Comment: Sometimes you can either ask or watch the local people. I did this in Hanoi, Vietnam four or five years ago. All the foreigners except me took expensive taxis or tourist buses. All the Vietnamese plus me took the local bus for a fraction of a fraction of the price and a much more memorable arrival (-:
Comment: Normally that's the sort of thing id do, but I have a relatively short time in Vic Falls and I want to pack a lot in so planning is going to be crucial.
Answer: There are a ton of taxis who come in to meet the planes.  Try and buddy up with another tourist if possible and save on cost, and be aware - you're a tourist, taxi drivers will sometimes ask 10x the normal price just to see if you'll take it - do ask a couple of drivers before accepting one.
Acceptable price is US$25, but if you're a good negotiator you can get this down to $20.  It is about 22km out of town.  Price is per taxi, so more people = less money for you ;)
And yes, they want US$, although may take Rand.
There are also airpor transfers, for around US$12 if you just want that, for more details you can email email@example.com to book a transfer.  There are several companies, but this address will do the dealing on your behalf, and someone will meet you at the airport.
As a final thought - check with your hotel - they may well offer airport pick-up, either free or as an optional add-on!
Comment: So if you don't book something there is a $30USD per head charge, there is only one taxi company that operates there.
Comment: returning to the airport its $30 a taxi not $30 a head. also a lot of accommodation offers shuttles to the airport but not from. the adventure lodge where I'm staying is charging $13 per head.
Comment: Didn't I say per taxi, not per head?
Comment: Sorry I was commenting on my comment. Last time I was airport to town this time I was the other way round.


blanch after vacuum seal?

Question: Since there's problems vacuum sealing after blanching due to excess water is there a problem sealing the fresh vegetables first and then boiling the package to get the same effect as blanching?
Comment: What specific problems with excess moisture are you having?  Is this for a particular application?  We may be able to provide a better answer if we know what exactly you're facing.
Answer: I don't think this will be such a good solution. You can try it, but it probably won't do what you want.
First, there is the problem of temperature control. In blanching, it is critically important that your vegetables heat up quickly, and then cool down just as quickly. If you insulate them with a plastic bag, you are building a thermal delay into the system, and this will reduce the quality of the blanched vegetables. They will be mushier and have worse color than when directly blanched.
The second problem is that you'll still get liquid inside the pouch. Blanching destroys the cell walls of the vegetables. The juices from inside the cells start leaking. And this will happen inside the vacuum bag too. So, you won't have dry vegetables in the bag, you'll have vegetables swimming in their own juice. Unlike the normal blanching scenario, it won't be diluted in water, but it's still probably not what you wanted.
This doesn't mean it's impossible to do it. You can try and see if you like your vegetables better that way. Just make sure that you choose bags which stand up to rapidly boiling water - it may be quite hard finding such bags.

blanch after vacuum seal?


How thick to pour slab over existing brick patio

Question: I have an old brick patio, cracked in some places. I want to pour concrete over it and stamp the concrete with a texture. What is the thinnest I can go? 1 inch? 2 inch? I have 5000 square feet and need to save as much on materials as possible.
Comment: Considering that we know nothing about what's under the brick we have to assume a self-supporting slab that will accommodate settling and movement. (Concrete doesn't usually work as an overlay, especially when over an unstable substrate.) 4" with rebar on a 24" grid is my answer. I don't imagine that's helpful. Perhaps you're asking the wrong question.
Comment: I had a professional pour a slab over dirt and they only used 4 inches,
Answer: You can go with whatever thickness you like, however, if you want it to last, you need to determine if the brick will continue to settle and crack. If so, thicker is better or your cracks will eventually show up in your slab. 4" would be the best, with expansion joints. You might be able to get away with 3" with more joints, but you'd be pushing it and possibly inviting cracking. A standard sidewalk is 4" thick, and even they crack from settling. 1" is just a skim coat and will definitely crack. You can't make up 4" by using your 2" brick, plus 2" slab. The brick below will continue to move and seperate from the slab, causing more cracking. Your best bet....remove the brick and level, grade, gravel and then pour a new slab, 4" minimum with proper expansion joints. Not cheap however.
What will this slab hold? Heavy weights like a vehicle? If so, you will want 6" minimum.


What to recite for asking forgiveness?

Question: There is a Hadith in Abu dawood that says, "If anyone continually asks pardon, Allah will appoint for him a way out of every distress, and a relief from every anxiety, and will provide for him from where he did not reckon."
My question is, in what way one should ask pardon? By reciting what exactly? Did our prophet (sa) suggested in what way we should seek pardon in this Hadith?
Answer: The first and simple way is just be ashamed and regretful. Say sorry from your heart to god. Cry and be sorry. Then promise to don't do that bad work ever never. And try to do good things for compensate.
Actually god is very kind and generous. So just be ashamed, cry and say sorry then promised and compensate. :-) Be optimistic :-)

What to recite for asking forgiveness?


Is "am going" a verb phrase?

Question: What part of a sentence is the phrase "am going", as in "I am going to pray"?
Comment: I can read that in two different ways. "I will pray", or I am going (somewhere presumably) to pray. I think that makes a difference in what parse results you get. "be going to" can be substituted for "will" in many cases. So again, I can read it as "I will pray" or I am going (to church) so that I may pray (because praying in a church is the only place I pray) (or for the reason that I might pray).
Answer: It's the first person singular of the present tense indicative of the auxiliary verb 'be', followed by the '-ing' form of the main verb 'go'. Together they express progressive aspect, which typically describes an action taking place at the time of speaking. In this example, however, 'go' carries no sense of actual movement. The construction is one of the ways in which English, in the absence of a future tense, expresses the future. It indicates the intention to do the action described by the following verb, 'pray'.
In terms of immediate constituent analysis, 'I' is a Noun Phrase and the whole of the rest of the sentence is a Verb Phrase.
Answer: The Berkeley parser says:

The meaning of these tags is here.
"am" is treated as the head-word here, just as it is in "I am green", "I am hungry" or "I am the president". "am going" is not treated as a phrasal unit in English. It could be a phrasal unit in some other language where the concept of "am going" is represented (with morphology) with just one word.
Comment: One of the few responses which actually answers the question. Many of them ignore the question, and give additional information which the OP may or may not want.
Answer: The present continuous (present progressive) tense is formed by using the auxiliary verb to be in front of the main action verb.
I go -- present simple
I am going -- present continuous
Answer: OP's use of am going to is a semi-auxiliary modal (as opposed to the 'fully auxiliary' modal will) used to express what would be the future tense in other languages.
English doesn't really have a future tense - we just use the present tense plus those 'helper' auxiliaries. Will and be going to are pretty much interchangeable for this purpose, but will stays unchanged, whereas be going to conjugates as normal (I am going to. You are going to...)
Note that this usage is not the same as, for example, I am going to London. Although this may have a 'future' sense, it can also be present tense (you could say it to a traffic cop who stopped you en route and asked what you were doing).
The 'primary' verb in my example is to go, but in OP's it's to pray. This is more obvious in the alternative/equivalent future tense I will pray.
Answer: The way the sentence breaks down is as follows:
I [subject] am [helping verb] going [verb] to pray [infinitive].
Generally a helping verb is followed by another verb and a linking verb is followed by a noun or noun phrase.
Answer: "Be going to" and "will" are English's way of expressing something that will take place in the future.  It doesn't matter when it will happen. It could be in two seconds or in two decades.
"Will" is a modal verb.
"Am going to" does the same job as "will"
I am going to pray.
I will pray.
Comment: A useful distinction is that "going to" often implies a preconceived intention, whereas "will" is used at the point of making a decision. Example: Would you like a drink? Yes, I'll have a beer, please. "I am going to .." would not work here.
Comment: I think we're on the same page here. I've been racking my brains trying to think of a case where *will* and *be going to* aren't interchangeable when used to form the future tense. The best I can come up with is Mommie's response to child asking for a treat, where it doesn't really work for me if she says *"We're going to see"* instead of *"We'll see"*.
Comment: @Shoe: Conversely, if somebody asks "Why did you come into town today?" you could answer "I'm going to have a beer with John," but "I will have a beer with John" wouldn't work.

Is "am going" a verb phrase?


What details should I be recording during my research?

Question: I have only recently become interested in my family tree. I am using PAF and am aware of GEDCOM. In addition to the details that PAF and GEDCOM support, what other information should I be recording?
Comment: Welcome Joel. You have asked a question so BIG that it might not get you useful answers. Unless of course, you are happy with the suggestion to record everything you find. I suggest that you read through the questions already on the site then pick a narrower topic that interests you and ask a more focused question; perhaps about a type of record or a place  or a period of time. Then other users of the site can offer you some really practical advice.
Comment: Hi Joel. Welcome to genealogy (and to genealogy.se). You are going to love it. It is a big question, but you may have something specific to add that would help us understand the context of your question. I've added an answer below and so has Duncan. You can let us all know if we are on the right track by editing your question and providing more direction. Thanks again for supporting genealogy.se.
Answer: Most importantly, record your sources.  Put down the kind of source, author, title or description, location of the source, and any other information that would be needed for anyone (including yourself) to find the item of data again.  This is the most vital item that beginners often overlook.  PAF, like other genealogy programs, has a mechanism for recording sources, use it!
As for what personal data to record (beyond what simply interests you), the guiding principle is to record information that will help identify the person and their relatives, and help resolve ambiguities with other people.  So obviously birth & death dates and places as you find them out, but also dates and places of marriage, residence, educational milestones, and other life incidents.  For people living in recent decades, much more may well be available than you need to seek out for identification, but as you get back in time items will be scarcer and you will want to search out more obscure data such as property deeds.  You will want to record a person's siblings and children because knowing these close relatives can be essential to identifying earlier generations.
Answer: Ummm. How about anything and everything that may be relevant or interesting to you.
Genealogy is not just defined by the fields that are in your genealogy software. There is the ever-present "note" field that allows what you record to be open ended. And don't forget the "objects" (pictures, videos and sound files).
Genealogy is more enriching when you extend it to more than just the names, events and facts. When you get into the family stories and family history, then you'll really enjoy it.
Comment: I was thinking along the lines of details to look for and record that may be interesting to those that follow. I have no real understanding of additional items to include and was looking at some sort of predefined list that I could compare to. Then I would know what to keep if I stumbled across it or even better, what additional things to search for. I am happy to use another software product or other techniques, I just would like it to be a useful compilation.
Comment: @Joel: When you stumble across something good, you'll know it! I don't know of any such lists. Why don't you start your own?
Comment: @Joel: If you organize everything you find into a structured compendium of information, with your opinions about each item as to what it provides and whether or not you found it useful in any of your conclusions , then this will be helpful to others who want to follow up on the same lines. But if you "just" record everything, then it won't help much.
Comment: So if I were to record everything I find, you are saying this would be beneficial to people in the future?
Answer: Alot depends on what you want to get out of your genealogy research. Start with what you know. Add how you know it (sources). If you record your sources, you'll appreciate it later when you are looking for it again.
Are you interested in a particular ancestor and his/her descendents? Or are you interested in fanning out your ancestor tree? Is there a particular family reunion coming up that you are interested in the ancestors of that particular branch of the tree? Are you interested in joining lineage (descended from a particular person) or heritage (descended from a collective of people, eg fought in the US War of 1812) society?
Another whole area is DNA. Males have the advantage we each carry the Y-chromosome of our father, father's father, etc. Both males and females carry the mitochondrial DNA of their mother, mother's mother, etc. So those two particular lines are of particular interest to research.
One strong recommendation I have is to sit down with your older relatives and ask them questions, preferably recording it. You'll find you'll be really glad you did this later. I suspect you'll also discover some things right away you didn't realize. Don't just ask about relatives, ask about conditions when they grew up, major events, etc. It blew me away when my late father mentioned mentioned that when he was a kid, the 'vets in the parade' were Civil War veterans instead of the WWII veterans in today's parades.
One decision you'll have to make is how much you'll be wanting to share what you know and how much you want to co-operate with others. I find the pando (one big tree) at werelate.org useful. It's particularly useful the farther back you go (ie it's unlikely anyone has entered your grandfather yet, but entirely possible they've entered your 10x grandfather). One of the reasons I find it useful is that it's pando of sources as well.
Another thing you'll have to decide is your budget - both time and money. Some sites (eg this site, werelate, findagrave) are free, some societies (eg New England Historical Genealogy Society) cost money to use their resources, and some commercial sites (eg ancestry.com, myheritage.com, etc) exist with you as their target customer. You've already discovered this stackexchange site. It's still in beta (just starting up) but hopefully will be useful to you. Spend some time looking thru the questions already here to get a feel. It might also give you other avenues to explore you hadn't thought of yet.
Most of the websites mentioned here and elsewhere on genealogy.stackechange will have 'getting started' help. There are also many blogs, podcasts, and courses (both online and classroom). Read thru many of them and form your own consensus based on what you want to do. Note many of the commercial sites have an obvious incentive for you to join their site and pay them. Look at several and decide what's best for you.
Answer: Reading genealogy journals, articles and blogs is a great way to discover the way others relate to their research and their historical families. Perhaps the structure of a genealogical biography, in the spirit of Register and Quarterly style, provide a little direction. All too abbreviated here, a biography can be broken down into three sections:

Genealogical Summary Paragraph: This identifies the subject, his/her birth and death and parents. Also his/her marriage(s), including each spouse's birth/death and parents.
Life Story: This is about the subject's life--the different places he/she moved, his/her education, military or voluntary services, vocations ...  What were the events that impacted on this person's life (and how)?
Child List: This is a list of the children in the household--they may have been born to the subject or one of the spouses; they may have been adopted or otherwise considered a child of that household.

To learn more about genealogical biographies, see Lynn Betlock's blog, "The Daily Genealogist, Writing in Register Style," 21 Sept 2012, or check out

Michael Leclerc and Henry Hoff, editors, Genealogical Writing in the 21st Century: A Guide to Register Style and More, 2nd ed. (Boston, Mass.: New England Historic Genealogical Society, 2006).
Joan F. Curran, Madilyn C. Crane, and John H. Wray, authors, edited by Elizabeth Shown Mills, Numbering Your Genealogy: Basic Systems, Complex Families, and International Kin, rev.ed. (Washington: NGS,2008).

Separately, as you are developing your own approach to "what" you want to record, consider starting a research journal or a research log.
Learning about my family history has been progressive and changeable. There is a good chance that what I thought I might have known yesterday will change based on what I learn tomorrow.
Below is a snippet from one of the research journals kept by Bernice McKarns (1911-2005). She is no longer with us, but her records are as valuable to us today as they likely were to her when she made them.

Bernice used spiral notebooks. My journal combines the characteristics of a research log and a research journal. I've always used a text editor or word processor. A few entries to my 1997 log appear below.

Some opt for more traditional research logs, and some genealogy software programs incorporate research logs or features that are similar. The FamilySearch Wiki has several pages dedicated to logs: "Research Logs," "Keeping a Research Log," "Prepare a Research Log,," "Describe the Records on a Research Log." You can read more about research logs on genealogy.SE. See the answers linked below or search the site.

https://genealogy.stackexchange.com/a/1536/7
https://genealogy.stackexchange.com/a/1526/7
https://genealogy.stackexchange.com/a/1559/7

Remember to have fun!


Is the binomial theorem actually more efficient than just distributing

Question: Is the binomial theorem actually more efficient than just distributing a given binomial. I believe it is more confusing for me to remember and work out using the binomial theorem as a guide, than to just distribute when given a problem like: $$(x-4)^6$$
I think distributing that would be equally as painful as using the binomial theorem. Am I alone or is there actually a reason to practice the painful procedures?
Comment: Well if you distribute without adding equal terms, you will end up with $2^6$ terms, while the theorem gives you the right $6$ terms.
Comment: @Phicar $7$ terms, not $6$.
Comment: What about $(x-1)^{10}$? Binomial theorem gives it by hand in under a minute. How long would you take to expand that by hand? The theorem is also much more conducive to algorithms, meaning it's strength in both computation and proof is far greater than direct distribution.
Comment: @Nij Actually the OP's method of repeatedly multiplying can be more efficient than the binomial theorem for large polynomials of certain types. There is much symbolic computation literature on this topic, e.g.see R. J. Fateman, [Polynomial Multiplication, Powers and Asymptotic Analysis: Some Comments,](http://dx.doi.org/10.1137/0203016) SIAM J. Comput., 3(3),(1974),196–213.
Comment: What about using Pascal's triangle to compute the binomial coefficients?
Comment: @Nij There is no "huge trend". Intuition based on hand computations will lead you astray. Read the paper and chase its citations to learn about these results. They are used in all the major symbolic computation systems (Macsyma, Maple, Mathematica, etc).
Comment: Mathematical beauty?
Comment: What algorithm do the calculators use?
Comment: I have practiced using the theorem. I came to agree that it is more efficient. I'm getting better at realizing the methods while solving such problems, rather than just remembering and plugging in variables. Thanks to all.
Comment: How did you learn the binomial theorem?  For any exponent after 2, I can't see how distributing could even hope to be more efficient or less confusing than the binomial theorem.
Comment: I learned it from my preCalculus class originally, but it was explained horribly. I'm now refreshing my skills on my own for the upcoming semester using Stewart Calculus Early Transcendentals 8th edition. I have practiced and understood why as of now so I agree with what you are saying. It was all in my head from my past horrible learning experience. @Teepeemm
Comment: Special cases don't defeat a huge trend; BinThm remains much better much more often. Interesting paper though, I'll have a look anyway. @BillDubuque
Answer: The binomial theorem
allows you to
write out the expansion
of your polynomial immediately.
It also allows you
to answer such questions as
"What is the coefficient
of $x^{20}$ in
$(1+x)^{100}$?"
Its generalisation to
non-integer exponents
allows you to
get the expansion of
$(1-x)^{-1/2}$.
It is a good thing.
Comment: (+1) And needing "just one term" isn't an idle exercise, either: anyone having taken calculus should recognize the importance of: "What's the coefficient of $x^{n - 1}$ in $(x + h)^n - x^n$?"
Comment: *"It is a good thing"* - Well said! :) (+1)
Answer: There are all sorts of reasons.  First of all, you'll learn when you've moved forward a bit that the binomial theorem can actually be applied in cases of non-integer exponents, by defining $\binom{n}{k} = \dfrac{n^{\underline{k}}}{k!}$, where the underline represents a falling power (i.e., $n(n-1)(n-2)\cdots$).  Another that comes to mind immediately is the series expansion of $e$...
$$e^x = \lim_{n\to\infty}\left(1+\frac{x}{n}\right)^n = \lim_{n\to\infty}\left(1 + n\frac{x}{n} + \frac{n^\underline{2}}{2!}\frac{x^2}{n^2} + \frac{n^\underline{3}}{3!}\frac{x^3}{n^3} + \cdots + \frac{x^n}{n^n}\right)$$
As $n$ gets very large, for fixed $k$, $n^\underline{k}$ approaches $n^k$, and $\frac{x^n}{n^n}$ vanishes since $x$ is fixed, so you end up with the familiar series...
$$e^x = 1 + x + \frac{x^2}{2} + \frac{x^3}{6} + \frac{x^4}{24} + \cdots$$
Comment: Very nice link to expansion for $e^x$. (+1)
Comment: @6005 You're right, done. [Here](http://meta.math.stackexchange.com/q/25614/2582)'s the discussion.
Comment: Weird. I don't see the underline in the definition of $\binom nk$. Am I the only one with this problem? I'm on Chromium 55.0.2883.87 (64-bit).
Comment: @rubik I had the same problem -- edited the post to make it displaystyle so it would show up. I think we should bring up this on meta as a bug with mathjax, would you like to do it or should I?
Comment: The frac displays fine in my mobile Chrome (both with dfrac and frac).
Comment: Putting in the last term of the falling power would be useful for the definition. As its written it could imply an infinite number of terms.
Answer: If you're not seeing the utility of the binomial theorem, then I think you're missing an important observation:
The coefficients of every term can be calculated extremely efficiently (your example of $(x-4)^6$ is easy to expand by hand with the binomial theorem, without, it's doable but very tedious).
A useful shorthand for lower powers of the exponent is to remember the first few rows of Pascal's Triangle along with the rule for adding more if you need them. Example of first few rows:
$$1$$
$$1\qquad 1$$
$$1\qquad 2\qquad 1$$
$$1\qquad 3\qquad 3\qquad 1$$
$$1\qquad 4\qquad 6\qquad 4\qquad 1$$
$$1\qquad 5\qquad 10\qquad 10\qquad 5\qquad 1$$
$$1\qquad 6\qquad 15\qquad 20\qquad 15\qquad 6\qquad 1$$
The last row gives the coefficients of $x^k\cdot(-4)^{(6-k)}$ for $k$ running from $0$ to $6$. Computing $(-4)^{(6-k)}$ is easy enough by hand, and multiplying it by the relevant entry in the last row above is also fairly easy (give it a try).
One more thing: The binomial theorem admits an interesting generalization to powers of general polynomials of a given length sometimes called the multinomial theorem. (Challenge: try investigating the coefficients of the first few powers of $(x+y+z)^n$ and perhaps you can figure out the pattern for trinomials? How does it relate to the pattern for binomials? Can you generalize it to general polynomials?)
Answer: Marty Cohen and Phicar answered your question correctly. In mathematics, as we always use small numbers, It could be feasible to think this. Why learn the binomial theorem to compute $(a+b)^2$? But what can you say about $(3a+5b)^{987658}$? The binomial theorem is way more efficient in this case and the actual number of cases in which it wouldn't be efficient is very small.
The binomial theorem gives you a powerful tool: The computation for any exponent in - perhaps - the fastest way possible in which it is only not effective for a finite amount of exponents, but its the best possible for an endless amount of exponents.
This is one trap in mathematics: We implicitly assume that the mathematical tools are created to treat familiar cases, but they are created to treat all cases in the neatest way possible, they will be cumbersome for some simple cases (Example: Integrating $f(x)=mx$ in the interval $[0,a]$. This is just a triangle, there is no need for integral calculus here). I remember of me asking about why we need analysis if calculus seems to work well, but I was supposing (without realizing) that calculus is used only on familiar cases, but we want to be useful also for very imaginative cases!
Comment: Just a small note to support the statement that it's as fast as it gets: using the recursion ${n\choose k+1} = {n\choose k}\frac{n-k}{k+1}$ with ${n\choose 0} = 1$ and the symmetry ${n\choose k} = {n\choose n-k}$ then we can compute all the $n$ binomial coefficients ${n\choose k}$ for $k=1,2,\ldots,n$ with only $n$ operations (multiplications and divisions). That is hard to beat! This can be compared with $\mathcal{O}(2^n)$ operations needed to distribute $(a+b)^n$.
Comment: Excelent addendum, @Winther!
Answer: To add to other answers, in higher-level math it's important to be able to generalize the behavior of $(a + b)^n$ when $n$ is a variable. The work that you're doing now is mostly just training exercises for being familiar with, and having intuition for, the general binomial theorem.
For example, there's a really key moment early on in calculus when it's critical to understand that, for all $n$: $(x + h)^n = x^n + nx^{n-1}h....$ plus a bunch of other stuff with higher powers of $h$ in it, but whose exact numerical coefficients we can ignore.


How do you explain to a very sociable 5 year old about strangers?

Question: I have a 5 year old that is very very very sociable.  I am being a generous here.  I have tried to explain to him in simple terms that not everyone is good and that he can't go up to everyone he sees and start a conversation like he is a little adult, but it confuses him.  He think that everyone is good and no one is bad or can do bad things.  So when I explain to him about strangers, he usually doesn't listen to me, but if he does, he does a complete 360 and now everyone is a stranger and I don't want him to feel that he either has to say talk to trust/talk to everyone or trust in no one.  How can I better explain to him about strangers and how to be more careful.  As a parent, I have my eagle eyes on him all the time because I know how he is, but I also want him to be aware of these things even if it is start.
Answer: The thing to do is not teach him to be wary of people, but of behaviors.  Most of the bad things that happen to children are perpetrated by people they know.  Children and adults both benefit from interactions with each other.  It's a shame that this rich source of learning is so often stifled.
What we teach our children to watch out for is adults who:

Want to touch your private parts.
Tell you to keep a secret from your parents.
Tell you to do things your parents said not to do.
Ask you to go somewhere without telling your parents.
This includes adults you know.

With those rules in mind, we actually encourage our children to interact with strangers, and they are more adept at it than most children.  I think that will help them more easily recognize the bad types of encounters compared to children who have no experience interacting with strangers.
Answer: It is a tricky balance at 5, or 30 for that matter.
When he is about that age I would start by saying that he should not approach people that he has not been introduced to by you and should immediately come get you if someone he has never seen before starts talking to him. You don't have to get too detailed, just explain that you want to make sure you know people he talks to first.
As he gets older it will get easier for him to understand and navigate, teach him to use his common sense (which shows that you trust him) and that most people are good but never to put himself in a situation where he is no longer in control.
It is scary, but it is the best that you can do. You do not want to give him either a false sense of security or a false sense that people are out to get him.
If it is any help, problems stemming from malicious adults are very rare, that does not mean that it does not happen or that it is not terrible when it does, but the likelihood of running into trouble, especially while using common sense is very low.


Spotted a moving star-like object

Question: So a couple days ago, my husband and I spotted a moving object in the sky just like a star. I know it wasn't a plane or a drone, and it was way up in the sky just a star. It just moved smoothly across the skies and than disappeared. I love to observe the sky so that was priceless for me and my husband.
Comment: I think it was probably an airplane, with its navigation lights turned on. It may have been an atypical meteor, too (the typical meteor moves quickly, it is visible only for some seconds, it makes a stripe, and it moves always linear), but I think a plane is the most probable.
Answer: Based on your description, that might be the International Space Station:

The ISS is visible to the naked eye as a slow-moving, bright white dot because of reflected sunlight, and can be seen in the hours after sunset and before sunrise, when the station remains sunlit but the ground and sky are dark.

So if what you saw was not long after sunset, and if the object was quite bright and moving slowly across the sky, that might be the answer.
If you want to check for yourself, you can input your location on this webpage and change the search period to see if the ISS passed above your heads on that day.
Other possibilities include other satellites (not very bright but also moving smoothly in the sky), or—more rarely—particularly large shooting stars.

Spotted a moving star-like object


RockShox Psylo oil replacement

Question: I have a Specialized bike that I haven't been using that I want to give to my sister. It's been sitting in my basement for about 5 years stored upside down. When I brought it up to my shop to do some maintenance I noticed the shock (RockShox Psylo) was leaking oil. I googled around to see how hard of a job this is to do myself and it looked pretty straight forward as there weren't any special tools. I did read that some shocks have specific specs for oil and this shock is a bit old so I don't know yet if I will be able to dig those specs up. Should I attempt to fix or should I have a tech do it?
Comment: Search for "Rockshox Psylo oil".... https://sram-cdn-pull-zone-gsdesign.netdna-ssl.com/cdn/farfuture/yCV4_rHIL_OCKnPaTIArUGdVtqflfS9qXYVgzI6__6c/mtime:1372788192/sites/default/files/techdocs/02_04PsyloandDukeUTurn.pdf.   Needs 140cc of 5WT oil (for this model - what year is yours).
Comment: We can't tell you what a fork service will cost at your LBS, better to ring them and ask.   Assuming it was stored properly, and not ridden hard then put away dirty then it should be simple rebuild.  If it has drained all the oil then you might have a bigger job.
Comment: Sorry for the late reply guys. I'm unsure what model I have. I will need to try to find the model year of the bike and will report back. The bike has never had a fork service before but it also wasn't ridden very often. I stored it in my basement for a long time upside down.
Comment: @JohnDrach The question is 5 months old - how did you get on with the fork?  Feel free to add and accept your own answer.
Answer: Rebuild manuals seem available (see link in comments). Figure out what year the fork is and google for the appropriate document. If you can't find it contact RockShox, they should be able to provide you with what you need.
Assuming the bike has not been ridden to the point where seals etc need replacing you should be able to just do a oil change.
If you have the tools and are confident you can do what the manual describes, go for it. If you mess up you can take it to the LSB.
Comment: I may give it a try
Comment: If it is leaking oil the seals may be shot. I wouldn't be surprised given the age of the fork. Changing the seals does require a special tool.
Comment: I've found a large socket or piece of PVC pipe perfect for installing fork seals.

RockShox Psylo oil replacement


Is it he or him that is the correct sentence?

Question: His parents didn't want him to go. This is how I would write it, but when trying to translate it (to swedish) it seems he would be the correct word to use. I would never have thought twice about using him if it wasn't for the fact I have to explain why him not he. Please help me out!
Answer:
His parents didn't want him /* he to go.

"He" is impossible her. The pronoun is the syntactic object of the verb "want", and hence takes accusative case "him".
The pronoun is also the understood subject of the subordinate clause "to go", and pronoun subjects of infinitival clauses always take accusative form.
Answer:
His parents didn't want him to go.

This sentence is correct. "him" in this sentence is the object.
If you use "he", it will be incorrect since the word "he" must only be used as the subject of a sentence.
Let me give you some examples that are similar to this.

Her parents didn't want her to go.
My parents didn't want me to go.
Our parents didn't want us to go.
Their parents didn't want them to go.
Your parents didn't want you to go.

Therefore, the translation that you translate that sentence in English into Swedish might be wrong.
Comment: As I thought, but great with some clarifications!!


Is my printer over extruding?

Question:

I'm getting some slight pooling on the end of straight lines on my Ender-3
Is this due to over extruding? Or some other issue?
Comment: Please do post some of the slicer settings like temperature, speed, filament type, which slicer (Slic3r?), etc.
Comment: Welcome to 3DPrinting.SE!
Comment: Is the result similar if you print at a lower speed?
Answer: It looks like you some of your layers are printing with 100% infill.
If you are noticing plastic still coming out at the end of lines then I think your pressure in the nozzle is high when it is getting to the end of those lines and that pressure is pushing out the extra plastic.
That could be because your over extruding, but if it is only happening on layers where you are printing with 100% infill it could also be because lines are too close together and so when your trying to push out plastic to fill all the gaps in the model the pressure is building up in the nozzle because the gaps in the infill are to small for the amount of plastic the printer is trying to push into them.
I would see if it is happening on all your lines or is it worse on layers where the printer is printing 100% infill. Then maybe try adjusting the amount the printer is extruding and see how it changes the print.
Adjusting the speed could also make a difference. And some slicers have a setting to tell the printer to coast at the end of a line so the printer will stop extruding just before finishing a line as well. If you think the other setting are all tuned as good as you can get them then trying the coast setting might help for the model you are trying to print.
Comment: What do you mean by "layers of 100 % infill", to me this looks like an aborted print where you look at the bottom layers and some of the infill of about 20 % layers. The bottom layers are 100 % infill as it is the base of the print object.
Answer: The extruded filament is very inconsistent in deposited line width, so this is potentially over-extrusion. It is advised to check and calibrate the extruder, see "How do I calibrate the extruder of my printer?".
It looks as though the positional accuracy is off (without knowing the actual print object; some lines are not touching), please check your belt tension.

Is my printer over extruding?


Alternative to Backspace Parameter

Question: I asked this question some time back and it worked, however I don't see the backspace parameter listed in the docs now, nor do I see in the change log that it was removed. I tried it anyway and it doesn't work. Is there another way to remove the last comma from a list of tags? Thanks
Comment: What version of Tag and EE are you using? Can you show your template code for completeness?
Answer: backspace="" also takes newlines and extra spaces into account. So if you have
{exp:tag:tags backspace="2"}
   {tag_name},

{/exp:tag:tags}

...this will remove the last two linebreaks, leaving the last comma intact. Instead try removing these non-printing characters:
{exp:tag:tags backspace="2"}{tag_name}, {/exp:tag:tags}

This can happen not only with Tag, but with other add-on and native EE tags as well.
Comment: Got it working using backspace and incrementally increasing the value until the comma disappeared. Thanks.

Alternative to Backspace Parameter


Need a brief analysis of Karna. Is he representative of anything in Indian mythology?

Question: Can someone please give me a brief analysis of who Karna was and what legacy he left behind?
Is he representative of anything (i.e., any symbolism attached to him) in Indian mythology?
Comment: Do you think you could edit the title of this post? The title and the actual question are unrelated and I was very confused.
Comment: He is known for his generosity..hence people call him **Daanveer**...
Answer: KARNA is one of the most fascinating characters of MAHABHARAT, the longest Sanskrit epic written two millennium ago.  Besides being an invincible warrior he was known for his generosity.
Story behind Karna's Birth:-
Karna was the son of Surya (a solar deity) and Kunti. He was born to Kunti before her marriage with Pandu. The story is that Kunti, while still very young, had occasion to serve Rishi (sage) Durvasha. She looked after him with great dedication. Durvasha was highly pleased. He gave Kunti a mantra(chant) and said that whichever God she would think of after reciting the mantra, would appear before her and bless her with a son endowed with his own godly qualities.
Kunti got scared and wanted the Sun God to go away, but he pleaded his helplessness against the power of mantra. Surya however assured Kunti that even after being blessed with a son, she would still remain a virgin and would not have to suffer any opprobrium. And so Karna was born with kavach and kundal (armor which would make him invincible).
Nurturing of Karna:-
Kunti was nevertheless afraid of social stigma and therefore she abandoned the child. She put Karna in a basket and placed the same in the Ganges river, the basket was seen by Adhirath, a charioteer, who had no issues. He picked up the baby and brought him up. That is why Karna is also sometimes referred to as Sarathiputra.
Education:-
Karna was keen to acquire the Brahmastra mantra from the great teacher Parshuram.  However, he knew that Parshuram gave instructions to Brahmins (the priestly tribe)  only.  So he disguised as a Brahmin and beseeched  Parshuram to accept him as a shishya(disciple).  Parshuram accepted him as such and started giving him instructions.  One day when Parshuram was resting in Karnas lap, it so happened that a bee stung Karna on the lower portion of his thigh.  It was very painful and he started bleeding.  However, fearing that if he moved his legs, he would awaken Parshuram, he did not move at all and continued to suffer.  When Parshuram woke up, he saw Karna bleeding.  He asked, Son, tell me truthfully who you are? A Brahmin cannot suffer so much physical pain.  Only a kshattriya (the warrior tribe) can endure so much discomfort.  Karna was obliged to disclose his identity.  Parshuram was greatly annoyed because he was a sworn enemy of Kshattriyas.  He therefore cursed Karna that as he had learnt through deceit, he shall forget the vidya (skill) which Parshuram had taught him at the crucial juncture.
Ultimate warrior:-
Arjuna had killed Karna's son, Vrishasena, in order to make Karna experience the pain that he himself had borne when Abhimanyu was brutally executed. But Karna refused to grieve his son's death and continued to fight Arjuna in order to keep his word and fulfill Duryodhana's destiny.
Finally when Karna and Arjuna came face to face, a serpent called Naga Ashwasena secretly entered Karna's quiver. This serpent was the one whose mother was relentlessly burnt when Arjuna had set Khandava-prastha ablaze. Ashwasena, being in his mother's womb at that time, was able to save himself from getting charred. Destined to avenge his mother's death by killing Arjuna, he transformed himself into an arrow and waited his turn. Karna unknowingly released Naga Ashwasena at Arjuna. Realizing that this was no ordinary arrow, Lord Krishna, Arjuna's charioteer, in his bid to save Arjuna's life, sunk the wheel of his chariot in the ground by pressing his feet against its floor. This made the Naga, who was speedily advancing like a thunderbolt, missed his target and hit Arjuna's crown instead, causing it to fall on the ground. Disheartened, Naga Ashwasena returned to Karna and asked him to fire him towards Arjuna once again, this time making a promise that he would definitely not miss his target. After hearing Ashwasena's words, this is what the mighty AngaRaj said to him:
"It is beneath my stature as a warrior to shoot the same arrow twice. Find some other way to avenge your family's death."
Saddened by Karna's words, Ashwasena tried to kill Arjuna on his own but failed miserably. Arjuna was able to finish him off in a single stroke.
Who knows what would have happened had Karna released Ashwasena for the second time. He even might have killed Arjuna or at least would have injured him. But he upheld his principles and did not use the presented opportunity. Such was the character of AngaRaj. He was the man of his words and the epitome of morality. He was the ultimate warrior.
Greatest DaanVeer ever:-
Duryodhan, in fact, built him up as a counterweight to Arjuna.  On the eve of the famous Mahabharata battle, Lord Indra, the rain God and king of heavens,  disguised as an old Brahmin went to Karna and asked for his Kavach and Kundal in daan (donation).  Indra was apprehensive that Karna, by virtue of his phenomenal skills as a warrior,  may be able to overwhelm Arjuna.  He  therefore asked for this gift so as to reduce his strength.  Karna had been cautioned by the Sun God that Lord Indra was going to make some such move. But Karna was so large hearted that he could not refuse anyone.  Knowing fully well, that Indra was playing a trick on him disguised as a Brahmin, he yet parted with his Kavach and Kundal, which were parts of his body since birth and which made him invincible.  Lord Indra was taken aback at Karna's capacity to give away anything asked for.  He said, Karna, what you have done today, no ordinary mortal could have done.  I am immensely pleased with your generosity.  You can ask for any vardaan.   Karna said, If you are really pleased with me, then you may kindly give me your weapon Shakti which has the potential to destroy any enemy.  Lord Indra gave Shakti to Karna with the proviso however that he could use it only once and that thereafter the weapon shall return to him (Lord Indra).
One more story about his charity:-
When Karna was on his death bed, Krishna came to test him. He disguised himself as a Brahmin saint , and asked Karna for some offering in the name of Dharma.Karna cited his debilitated condition and asked Krishna, "O Lord Brahmin, what can i offer you in this capitulated condition". Krishna teased him ,"I thought you were the greatest philanthropist on earth, are you not going to offer anything to this old brahmin?"
Karna thought for a while and then grabbed a stone from his macabre surroundings. He then thwarted the stone into his mouth and although his brutally beaten frame was cursing every movement he was afflicting upon himself, he kept doing that continuously. Meanwhile Krishna was surprised as well as awed by courage of this great warrior. After many strong blows, Karna was able to break two golden teeth he had, and offered them to the disguised Krishna.Krishna being extremely impressed by the valor of this great warrior , did not show any visible emotions. Instead he cursed Karna(to test him again) on how he was offering such saliva ridden teeth to such a pious brahmin. Karna deeply engraved by this statement, tried to crawl up to his bow and arrow. His bow was in tatters and the thread supporting it was nowhere to be seen. He cursed himself upon the defeat he faced to Arjuna in the earlier part of the day, and kept crawling to find an auxiliary thread to support his bow. Luckily he found one a few feet away from him. Every inch that he crawled made his wounds even more blood stained, and he was slowly losing his consciousness.
But he kept crawling as the legend of Karna will not have an apt ending if this saint would not be satiated by him. Finally having reached the supporting thread he drew the thread in his bow. Meanwhile his hand continued to bleed profusely, and his nerves were  on the verge of bursting up.He finally launched the final assault on his body and caressed the final arrow of his life into the ground. Subsequently, a stream of water came bursting out of the ground. He washed those saliva and blood stained teeth in  this pristine stream of water and offered them to the disguised saint. Krishna embarrassed and visibly taken aback, gave up his disguised identity and came in his original form.    Bowing to the great warrior he said, "Karna, if you want i can make you alive at this moment and make the world bow at your feet, Until you are there at the face of this earth , i am assured that Adharma shall never ever reign on this planet".Karna replied. "O Lord Krishna ,you are the creator and are omnipresent everywhere. Don't insult me by bowing in front of me. I have had enough of travails and hardships in my life, so much  so that even the most ebullient luxuries are not able to lure me back into this life again. Let me die in peace and assure me that the legend of Karna may inspire generations to come. I beg forgiveness for all the wrongs that i have done unintentionally. Let the world turn into a righteous place, where the reign of Dharma shall ensure prosperity to everyone irrespective of their not caste and their not so noble beginnings". Krishna silently nodded in agreement and blessed the warrior prince.
In short HE WAS REAL HERO.
More reading resources:-

Wikipedia
The spiritual scientist-part-1
The spiritual scientist-part-2
The spiritual scientist-part-3
Comment: Hello and welcome to Hinduism.SE. We ecourage the users of this site to write the answers on their own and not just copy paste from Wikipedia or similar resources. It is great if you provide Wikipedia links as a reference/proof to support your claims but avoid copy pasting the answers. Will give you time to write in your own words, if failed, then I'll be deleting your answer. For more information refer to [this meta post](http://meta.hinduism.stackexchange.com/questions/253/).
Comment: edited my answer with more information
Answer: Here is basic info about karna:

KARNA is one of the most fascinating characters of MAHABHARAT, the
longest Sanskrit epic written two millennium ago. Besides being an invincible warrior he   was known for his generosity.
Karna was the son of Kunti from the Sun God.
Karna was born with kavach and kundal (armor which would make him invincible).
Karna was keen to acquire the Brahmastra mantra from the great teacher  Parashuram. he disguised as a Brahmin and beseeched  Parshuram to accept him as a shishya.
After lot of events happened within his relations.
Finally he died in Kurukshetra war.

For more information GOOGLE it.


What is the reason why we use natural logarithm (ln) rather than log to base 10 in specifying function in econometrics?

Question: What is the reason why we use natural logarithm (ln) rather than log to base 10 in specifying functions in econometrics?
Comment: Check this for details
https://www.youtube.com/watch?v=IXhucU6214M&feature=youtu.be this will tell why natural logs are calculated with reasons and references of the renowned authors
Answer: In the context of linear regression in the social sciences, Gelman and Hill write[1]:

We prefer natural logs (that is, logarithms base $e$) because, as
  described above, coefficients on the natural-log scale are directly
  interpretable as approximate proportional differences: with a
  coefficient of 0.06, a difference of 1 in $x$ corresponds to an
  approximate 6% difference in $y$, and so forth.

[1] Andrew Gelman and Jennifer Hill (2007). Data Analysis using Regression and Multilevel/Hierarchical Models. Cambridge University Press: Cambridge; New York, pp. 60-61.
Comment: +1: For concrete reason to prefer the natural logarithm.
Comment: More generally, the exponential function is the only continuous function that is equal to its derivative.
Comment: @cs0815 if you apply the Taylor expansion around the point b

$$f(x) = \sum_{n=0}^{\infty} \frac{f^{(n)}(b)}{n!}(x-b)^n$$

to the exponential function $f(x)=a^x$, with $f^{(n)}(x) = ln(a)^n a^x$ then you get for the first two terms:

$$f(b+x) = f(b) + ln(a)f(b)x + \mathcal{O}(x^2)$$

and the $ln(a)$ term becomes 1 for $a=e$ such that you can use $f(b+x) \sim f(b) (1+x)$, which is however only true for small x. *Also you can simply try it out exp(1.06)/exp(1) = 1.0618 and 10^1.06/10^1=1.1418154*
Comment: would this not apply if we apply log10 to the dependent and the independent variable(s)?
Comment: Expanding on @SextusEmpiricus. "small" x are definitely within [-0.5, 0.5] which yields 0.64 (an error of 0.14). See a plot of the relationship between x and the error here: https://stats.stackexchange.com/a/244237/17459.
Comment: Can someone explain why "with a coefficient of 0.06, a difference of 1 in x corresponds to an approximate 6% difference in y" ?    $0.06\ln\left(50\right)-0.06\ln\left(49\right) = 0.00121216243905$  , which is far from a 6% difference from $0.06\ln\left(50\right)$.
Answer: There is no very strong reason for preferring natural logarithms.  Suppose we are estimating the model:
ln Y = a + b ln X

The relation between natural (ln) and base 10 (log) logarithms is ln X = 2.303 log X (source).  Hence the model is equivalent to:
2.303 log Y = a + 2.303b log X

or, putting a / 2.303 = a*:
log Y = a* + b log X

Either form of the model could be estimated, with equivalent results.
A slight advantage of natural logarithms is that their first differential is simpler: d(ln X)/dX = 1/X,  while d(log X)/dX = 1 / ((ln 10)X) (source).
For a source in an econometrics textbook saying that either form of logarithms could be used, see Gujarati, Essentials of Econometrics 3rd edition 2006 p 288.
Comment: The natural log is also useful in a semi-log time series regression since the estimated coefficients can be interpreted as continuously compounded growth rates.
Answer: I think that the natural logarithm is used because the exponential is often used when doing interest/growth calculation.
If you are in continuous time and that you are compounding interests, you will end up having a future value of a certain sum equal to $F(t)=N.e^{rt}$ (where r is the interest rate and N the nominal amount of the sum).
Since you end up with exponential in the calculus, the best way to get rid of it is by using the natural logarithm and if you do the inverse operation, the natural log will give you the time needed to reach a certain growth.
Also, the good thing about logarithms (be it natural or not) is the fact that you can turn multiplications into additions.
As for mathematical explanations of why we end up using an exponential when compounding interest, you can find it here:http://en.wikipedia.org/wiki/Continuously_compounded_interest#Periodic_compounding
Basically, you need to take the limit to have an infinite number of interest rate payment, which ends up being the definition of exponential
Even thought, continuous time is not widely used in real life (you pay your mortgages with monthly payments, not every seconds..), that kind of calculation is often used by quantitative analysts.
Comment: I probably would have given an answer like this.  The point that it doesn't matter in modeling is a good one too. We could just as easily use base 2.  The difference is only a constant factor
Comment: Surely, you could write it $Nr^t$ (more intuitively), and so are you arguing that the base doesn't matter as Adam Bailey does?
Answer: An additional reason why economists like to use regressions with logarithmic functional forms is an economic one: Coefficients can be understood as elasticities of a Cobb-Douglas function. This function is probably the most common one used among economists to analyze issues regarding microeconomic behaviour (consumers´preferences, technology, production functions) and macroeconomic issues (economic growth). The elasticity term is used to describe the degree of response of a change of a variable with respect to another.
Answer: The only reason is that the Taylor expansion, gives an intuitive interpretation of the result.
Let's look at a typical variable used in econometrics a lot, the log difference of GDP:
$$\Delta \ln Y_t=\ln Y_t-\ln Y_{t-1}=\ln\frac{Y_{t}}{Y_{t-1}}=\ln\left(1+\frac{\Delta Y_t}{Y_{t-1}}\right)$$
, where $\frac{\Delta Y_t}{Y_{t-1}}$ is GDP growth rate now.
Let's apply Taylor expansion of the log:
$$\Delta\ln Y_t\approx\frac{\Delta Y_t}{Y_{t-1}}-\frac 1 2 \left(\frac{\Delta Y_t}{Y_{t-1}}\right)^2+\dots$$
Since, GDP growth rate is usually small, e.g. for USA around 2% lately, we can drop all the higher order terms then we get:
$$\Delta\ln Y_t\approx\frac{\Delta Y_t}{Y_{t-1}}$$
So, if you're using the log differences of GDP in the right hand side of the equation, e.g. as an explanatory variable in the regression you may have the following:
$$\dots=\dots+\beta\times\Delta\ln Y_t$$
which can be interpreted as "$\beta$ times percentage change in GDP."
Economists like the variables that can be interpreted easily. If you plugged the different log base then the interpretability is weaker. For example, see what happens to the log base 10:
$$\dots=\dots+\beta\times\Delta\log_{10} Y_t\\
\approx\dots+\beta\times\frac 1 {\ln(10)}\frac{\Delta Y_t}{Y_{t-1}}$$
This still works, but now you need to divide $\beta$ by some unintuitive number to get the "percentage change" effect interpretation.
Answer: Is this unique to economics? The standard normal distribution features an $e^{-{1\over2}x^2}$ in it, and the normal distribution is only one of the large family of exponential distributions that cover a huge swath of statistics. (See GLM's.) It seems like the natural log would be useful in these cases.
Comment: Yes, but the variance term of the normal distribution is equivalent to a change of base of the exponent.  Even the way you've drawn it, the base could be $(\sqrt{e})^{-x^2}$
Answer: There is a good reason to use the log transformation of the variable if you think that the inverse function of logarithm is the exponential function which is a continuous version of conpounding. The economic variable which is growing around 10% at a time can be transformed to the variable with its mean around 10 (plus a constant). You cannot do that with the transformation of logarithm of different base.
Answer: Not only in econometrics, using base $e$ is more "natural" in almost every domain, including computer science, where dominated by $0,1$ (where $\log_2$ may be natural).
I would like to use some experiments to show the base $e$ is very natural.

Consider following three functions $f_1(x)=2^x$, $f_{2}(x)=10^x$, $f_3(x)=e^x$, which one seems more natural? Many people may say first two seems better, because $2$ and $10$ are small integers, and $e$ is an irrational number.
However, consider following experiment, we want to investigate the relationship between the function's derivative at $x_0$ and the function value at $x_0$.
We pick two random points, say $1.23$ and $2.34$ and we will use $f_1$ as example.
Here are some facts:
$f_1'(1.23)=1.625894, ~f_1'(2.34)= 3.509423$
$f_1(1.23)=2.34567, ~f_1(2.34)=5.063026$
We see there are some patterns: if we calculate $f_1'(x_0)/f_1(x_0)$, it is a constant: $0.6931472 = \log(2)$.
For another function $f_2$, this constant is $2.302585 = \log(10)$. (I will attach the code for some fun experiments)
So, the natural question to ask is when we can get a simplified results, that do not need to scale with this constant (or this constant is equal to $1.0$)?
The answer is when the base is $e$. Where $f_3'(x)=f_3(x)$. Now, we may think base $e$ is more natural?

some code for fun experiments
# suppose we have some exponential functions
# because 2 and 10 are small integers f1, f2 seems pretty natural
f1 <- function(x) 2^x
# f2 <- function(x) 10^x

# simple code to calculate numeric gradient
simpleNumDiff <- function(f, x0){
  (f(x0+1e-8)-f(x0))/1e-8
}

# we try to investigate derv value and function value pattern
# note, they are not equal but have very strong pattern
a1 = simpleNumDiff(f1,1.23)
b1 = f1(1.23)
a2 = simpleNumDiff(f1,2.34)
b2 = f1(2.34)
c(a1/b1,a2/b2) # log(2)

Comment: very nice explain of e in a specific area (computer science)! I mention that in ODE, the equation y'=a y is called one of natural growth rate.


Algorithm for checking unambiguity in the derivation of a string

Question: It is known that given a Context Free Grammar $G$, checking that it is ambiguous or not is undecidable. But, if I have a string $s \in L(G)$, does there exist an algorithm to check whether $s$ particularly can be derived unambiguously in $G$?
Comment: I suppose Earley's algorithm would easily find all derivations, except you'd have problems if there are too many. Finding that there are at least two derivations would be about as simple as finding there is at least one.
Comment: I imagine that most parsing algorithms can be adapted to keep track of this information.
Answer: gnasher's comment more or less answers this. A sketch of an algorithm would be:

enumerate all derivations of the grammar that do not generate strings longer than $s$. This can be done, because CFGs do not have deleting rules (or if yours do, they can be converted for example to Chomsky Normal Form)
check how many of the strings generated are equal to $s$.

This takes a long time, of course. But I doubt that there is a fundamentally better way.
Comment: Nice answer!  This is a clean way to see that the problem is decidable.  Incidentally, while the question didn't ask for it, there is even an efficient algorithm for the problem; see my answer.  (This is exponential time; my answer sketches how to do it polynomial time.)
Answer: The CYK algorithm can be modified in a straightforward way to solve this problem.  In particular, the problem is not only decidable -- there is a reasonably efficient algorithm to solve it.
The standard CYK algorithm uses dynamic programming to compute $P[i,j,X]$, a boolean that indicates whether $s[i..j]$ is a member of $L(X)$, for each pair of indices $i,j$ and each non-terminal $X$.  I suggest you also compute $Q[i,j,X]$, which indicates whether $s[i..j]$ can be derived unambiguously from $X$.  It is easy to adjust the recursion to compute both $P$ and $Q$ simultaneously.
This achieves a $O(n^3 \cdot |G|)$ running time, i.e., polynomial time.
You can probably do the same with Earley parsing or any method of GLR parsing.


Just what is unhealthy in the water in Mexico?

Question: I've looked everywhere from guidebooks to the CDC website, but haven't been able to find out what is in the water in Mexico that makes it unhealthy to drink. I'm asking because my backpacking water filter takes care of bacteria and protozoa, but not viruses, and I'm wondering if that will cover me. We'll be backpacking around the Sian Ka'an Reserve in Quintana Roo.
Comment: The answer is going to vary depending on where you are. Some places in Mexico the water is fine to drink. Can you be more specific about the location(s) you'll be visiting?
Comment: I recall hearing in Mexico that one problem is that the pipes for both water and sewage are in such poor condition that there is some cross contamination. I don't know if this is actually true though. Mexico is a big country!
Answer: You can probably look at Index Mundi as a starting point, which lists potential food and waterborne diseases like:

food or waterborne diseases acquired through eating or drinking on the local economy:
Hepatitis A - viral disease that interferes with the functioning of the liver; spread through consumption of food or water contaminated with fecal matter, principally in areas of poor sanitation; victims exhibit fever, jaundice, and diarrhea; 15% of victims will experience prolonged symptoms over 6-9 months; vaccine available.
Hepatitis E - water-borne viral disease that interferes with the functioning of the liver; most commonly spread through fecal contamination of drinking water; victims exhibit jaundice, fatigue, abdominal pain, and dark colored urine.
Typhoid fever - bacterial disease spread through contact with food or water contaminated by fecal matter or sewage; victims exhibit sustained high fevers; left untreated, mortality rates can reach 20%.

What else could potentially be in the water might depend on the region and industry such as potentially pesticides or other chemicals.
Comment: That's a good site. Looks like I'll be bringing a wee bottle of diluted bleach as well, to kill viruses. Thank you!
Answer: This came up in a microbio class I took in college. Apparently Giardia is a major player in the problem with Mexico's water. It is a parasite that is very easily spread, especially when water municipalities aren't up to par. I did a quick search for some more in depth info on Giardia so I didn't have to type it all out again. I would say your water filter should help as far as drinking water is concerned, but you also have to be careful about contaminated food, pools, other people, etc.
http://www.mayoclinic.org/diseases-conditions/giardia-infection/basics/definition/CON-20024686


What is a layman's term for internet-enabled or web-enabled?

Question: I need a better term for internet-enabled or web-enabled that a non-technical person would understand includes their smartphone, tablet, laptop, desktop, smartTV, etc.
Comment: I would think that either of _internet-enabled_ or _web-enabled_ is fine if what you want to say is what they mean.
Comment: VTC: This question seems likely to solicit a large number of two-to-three word responses.
Comment: "Online"...?  "Online devices"/"The thneed is online"...
Comment: Perhaps "with internet access"?
Comment: @3nafish Is this neccesarily a bad thing? A rated list of easy-to-understand phrasings of the term internet-enabled is a useful artifact left for the internet and future visitors. The answer below, though good, is not more useful than a short version of the same answer in my opinion.
Answer: For one, I think @Dan D. is correct in saying that those terms by themselves should be pretty clear.
If you're looking for something that a very un-tech-savvy (surely that's a word) crowd could understand, I'd say swapping the word "enabled" with "connected" could work, even though it wouldn't be ideal.
Perhaps "always online"?
That'd be the only thing I can think of, short of changing it into a sentence like "devices that are connected to the internet" or @Kristoffer Nolgren's "with internet access".


Does the EXIF data "DateTimeOriginal" get recorded at the start or end of the exposure?

Question: I am working to determine the orbit of a satellite based on a long exposure photograph, and need precise observations.
Comment: have you tried an experiment?
Comment: My d90 shows the beginning of the exposure so I support the comment  by @ths . I'm not sure if I fully got your question, however out of curiosity, what satellite are you tracking? because almost all nearby satellites I know aren't visible nor have the same intensity in their orbit and these precise data are available online. so again, If again I understand correctly the exiff data just would be fine for a later reference if camera date/time synced to your local place of observation.
Comment: It was from a photo my mum took - and she was curious which satellite it was.  I didn't have access to the camera. I ended up just looking up what was around on Calsky (it was an old Falcon booster)
Answer: The EXIF standard describes the DateTimeOriginal tag simply as "the date and time when the original image data was generated."  It gives no guidance about what event (e.g., shutter released, shutter open, shutter closed, sensor read, post processing) should be used to determine the value.
As mentioned in a comment, the best way to find out how your camera defines it is through experimentation.  Synchronize its clock to one you can observe, record the start and end times of a long exposure and see which one ends up in the EXIF.  Note that the result you get will only be valid for that one camera with whatever firmware it was running.
Comment: @DavidWilson The standard doesn't make it clear enough for that to be a safe assumption.  I just did the experiment with two Nikon bodies and neither behaved as you described.
Comment: Rather than using an external clock, just "take 1/100s photo, take 30s photo, take 1/100s photo" should do.
Comment: @RichardBarber Without access to the sources for camera firmware, don't know that.  I can think of one reason for generating the EXIF data early:  it can be done while the shutter is open and the firmware is otherwise idle.  It's time that doesn't have to be spent post-exposure, which means you can get to shooting the next frame sooner.
Comment: @RichardBarber The camera needs to know most of the settings in the metadata, like shutter speed, ISO, flash, before the image acquisition begins, so the argument would be to fill out the metadata in advance.
Comment: I would assume then that the time recorded is at the point after the exposure has ended and the file is generated.
Comment: @birfl To be honest, I've never delved deeply into exif data, but perhaps the OP should do some comparisons between DateTimeOriginal and DateTimeDigitized.
Answer: Experimentally (on my EOS 70D), this is the beginning of the exposure, and not the end.
But:

this seems truncated to the second
it depends how accurate is the time of the camera (before doing this I carefully set the time on my camera, but I doubt I can do better than half a second)
... not speaking of clock drift if it hasn't been set recently

IMHO a better method is to trigger the picture from an external device than can have a really accurate clock (Raspberry with NTP clock, for instance)
Comment: Do you mind expanding, or giving a link, ton how to use an external device to help?
Comment: A Raspberry Pi is a Linux computer which can connect to the Internet and get accurate time over NTP. An RPi can control the wires and plug into a camera's remote trigger port. Hence, you could make an RPi command a camera to take a photo at exactly 01:23:45.6 UTC if that's what you wanted.
Comment: The [Rpi](https://en.wikipedia.org/wiki/Raspberry_Pi) is credit-card size computer that typically runs Linux (though there is also a Windows version for it) and can be used for [advanced control applications](https://www.theregister.co.uk/2014/07/08/cat_o_bolt/).
Answer: Just did a bulb exposure with a Nikon D850 of over a minute and a half (to make sure that time, during the exposure, chaged the time not just in seconds but also at least in a minute).
In this camera, at least for bulb, the recorded date time is the initial moment the shutter pressed, when exposure start, not when it's released and the exposure ends.
For other models and makers it may vary.


Has any NHL team ever won a game after being down 0-5?

Question: Has any NHL team ever won a game after being down 0-5? It would clearly be quite difficult and arguably miraculous.
Comment: Evidently, it is not arguable.
Answer: This has happened six times in NHL history so is not as uncommon as you suspect:

1982-04-10, Edmonton vs Los Angeles (playoffs)
1987-01-26, Calgary vs Toronto
1999-03-03, Colorado vs Florida
2000-11-29, St. Louis vs Toronto
2008-02-19, New York Rangers vs Montreal
2009-10-12, Calgary vs Chicago
Comment: @Joe There are [4 more instances between 1983 and 1989 where teams came back from a 5 goal deficit if not 5-0 to win](https://en.wikipedia.org/wiki/Comeback_(sports)#Regular_season_2). More modern overtime rules I suspect also play a part - e.g. the Canadiens win in 2008 was in a shootout which would have been a tie under old rules.
Comment: For perspective, about 60k NHL games have been played to date, making about 0.01% of games a 0-5 comeback. Of course, the vast majority of games never get to 0-5, so the likelihood of coming back if that deficit is actually reached will be quite a bit higher than that. Agree we're likely out of "miracle" territory, which could be benchmarked with the 1000:1 odds (0.1% chance) of 1980's Miracle on Ice. It would be miraculous for a random game to result in a 0-5 comeback, but seeing a comeback in a 0-5 game might not be.
Comment: Intriguing to me is that only the first two were in the "high scoring" era; the last four were in the more mundane modern era of actual defense, where 5 goals at all was fairly unusual.
Comment: That's a good point - so would the playoff game in 1982 had it been in the regular season!  And then of course you have the Colorado game where they came back and won 7-5 in regulation, because the 1999 Avs were just that good...  that game also had the rare double hat trick (Bure and Forsberg).
Comment: Maybe also show us how to find the answer?
Comment: @NikeDattani I would think you could ask a question about that (how to find answers like this more generally, at least) - it would be on topic here in my opinion, and also might be on topic on [opendata.se], but check there as I'm not sure exactly what they would consider on topic in this area.  Here only the sports-related side of things would be on topic, but I don't see why it wouldn't be.
Answer: Wayne Gretzky probably doesn't want to remember this one, but the Oilers lost to the Kings 6-5 in 1982 in the playoffs (Game 3 of the Smythe division semi-finals that year) after leading 5-0 after 2 periods. Not only did the Kings come back from down 5-0, but they came back entirely in the 3rd period and OT, scoring their last 3 goals of regulation in less than six minutes, and the tying goal on the power play with only 5 seconds remaining in regulation.
Contributing to the demise were a ton of penalties in the second half of the third period - this was not super uncommon back then, but there was a ton of offsetting penalties leading to quite a long time of 4-on-4 play, which undoubtedly simplified things, plus the high-stick major by Gary Unger at exactly 15:00 that meant that the Kings were able to play two men up after pulling their goalie for the last three minutes.  That plus some shenanigans with goaltenders that gave the Kings a breather allowed them to finally score at nearly the last second.


Duplicate transactions in blockchain

Question: Can someone explain what does this mean:

As i see: 2 transactions are having SAME txid and differ just by address. Is this normal behavior? Should I get both transactions in such cases?
Answer: Transactions can have multiple outputs. What you show are two outputs created by the same transaction.
The output positions are enumerated with the vout field. As the first one is vout = 0, the two that you show are the third and fourth output.
Comment: @0x49D1: If both of those addresses belong to you, which is what seems to be the case, then you've received two UTXO with the balances of 0.0874 and 0.103 BTC.
Comment: So its legit: i have 2 incomes?
Comment: Can one transaction have two of the same output address, maybe from different senders? Edit: Yes: https://bitcoin.stackexchange.com/questions/22295/how-can-there-be-multiple-outputs-with-same-address-in-the-same-transaction

Duplicate transactions in blockchain


Can't Resize Ext4 Partition through Gparted on Ubuntu Live USB

Question: I would like to increase my Linux Mint partition (/dev/sda3) with Gparted through a live Ubuntu session. However, Gparted doesn't increase my Linux Mint partition even though it's not mounted and has swap off. I can increase my Windows partition (/dev/sda1) which is formatted as ntfs through Gparted. Is it possible to resize the Linux Mint partition through Gparted or will I need to use terminal commands?
Picture of my Partitions
Picture showing that /dev/sda3 can't be resized
Answer: I'm guessing you'd be increasing the partition using some "empty" space on your partition? If you are resizing your windows partition, and it's right beside a linux one (/ or /home), you'd be in essence "moving" the start of that linux partition, could cause some headaches. Not unfixable headaches, but headaches nonetheless.
Comment: No I want to use the unallocated space (19.53 gigabytes) and increase the linux partition.
Comment: Nonetheless, you need to resize that partition from a live session, with that partition not mounted via fstab , etc. A mounted system can't be resized.
Comment: I'm running an Ubuntu 16.04 LTS live session and have /dev/sda3 unmounted [link](https://imgur.com/a/vIrM4), but I still can't resize it.
Comment: This sounds like what you are wanting to do:
Answer: Following is a quote from the GParted Manual that explains why partition sda3 cannot be increased in size:

To grow or move a partition, unallocated space must be available adjacent to the partition.
If you are growing a logical partition, then the unallocated space must be within the extended partition.
If you are growing a primary partition, then the unallocated space must not be within the extended partition.
You can move unallocated space to be inside or outside of the extended partition by resizing the extended partition boundaries.

For more details see GParted Manual - Resizing a Partition.
Note that if you move the start of a partition then as mentioned in the other answer you may need to restore the ability to boot.  This is also described in the GParted Manual - Moving a Partition.


How are Japanese company division, section or department names translated?

Question: How are Japanese company division, section or  department names usually translated to English e.g. 「システム開発1部ソリューション1課」? Does it translate it to System Development Department 1 Solution Section 1?
Comment: Correct in my experience
Answer: Division, Department and Section are usually translated as 事業本部 / 事業部、部 and 課 respectively. But the names of organizational units differ from company to company. For example, in mass-media (TV and press) and advertising agencies where I had worked, Division, Department and Section were respectly called 局、部、課.
Goverment organizations also use 局、部、課.
金融部 will be Finance Department, but I don't think the use of the word, 'team' as a nomencrature of the organizational unit is so popular. You have a taskforce team, or new business / product / design development team as a sub- unit in a department or section, but we don't see the title of the manager / chief of XX Team of its own instead of 部 and 課 so often.
Comment: I'm a bit confused to find the significant change in the editing of the OP's  text, where the OP asked about the indication of Team i.e. Finance Team in an organizational chart. Please note that my answer corresponds to OP's original form of the question.
Answer: It really depends on the company but I work for a department similar to one you described (minus the numbers) and it is translated quite similarly to what you have said.
Some discrepancies would be things like whether the department is written as a Kanji-base or a Katakana-base.

金融部 > Finance Department
ファイナンス部 > Finance Department

Also note that some companies do not use 課 but instead implement team names or project names / acronyms instead.

金融部 MZHチーム > Finance Department MZH Team
サービスソリューション部、 システム開発「さくら」 Service Solutions Department, System Development Team - Sakura


Will capital gains affect my tax bracket?

Question: I am marginally in a lower tax bracket based on W2 income. If I add capital gains from stock sales, then this tax bracket would go higher. Does capital gains actually affect your tax bracket or are they just taxed separately (based on long-term vs short-term gains/losses) ?
Answer: I think you're misunderstanding how tax brackets work. If you make $1 more and that bumps you into a higher bracket, only THAT particular dollar will be taxed at the higher tax bracket rate... Not your entire income.
Short term capital gains are treated as income.  Long term capital gains have a special tax rate currently.
Comment: That's an important distinction regarding how tax brackets work. I was not fully aware of that. [How tax brackets work](http://fairmark.com/begin/bracket.htm)
Answer: I'm not sure where you are, but in the United States capital gains are taxed at a lower rate than other types of income.
On the 1040, captial gains income is separated from earned income, and income tax is calculated just on earned income. Then capital gains tax is calculated on capital gains income, and then added to income tax afterward.


Do drupal themes require CSS3?

Question: Do drupal themes require CSS3 or can they just be HTML5?
Comment: it's very inconvinient to theme stuff without css
Answer: Theoretically, they can "require" neither.
CSS3 is a version of CSS, and while it can incorporate CSS3 in a theme, CSS2 or CSS1 elements (except those deprecated) would still function in a Drupal site and theme. Be aware however, that without CSS of any type, you will not have colour, size, position, fonts
or other similar customization of layout outside the browsers default, which will differ from user to user. Take note that most modules and themes will use CSS3 elements.
HTML5 likewise, is a version of the HTML "standard", which really isn't a standard. HTML5 in particular is still under construction by the industry and subject to change at any time, for any reason. Drupal 8 core while technically sets its document type as HTML5, it uses more HTML 4.xx, xhtml than HTML5. Drupal 7 core primarily uses xhtml, yet another variant on the standard. Therefore, you can use 4.xx, xhtml or earlier elements, without using any HTML5 (especially for browser specific elements) to maximize compatibility. Take note however, that most modules and themes now heavily use the new options provided by HTML5 in Drupal 7 or 8, even back ports of Drupal 6.
Comment: Actually, Drupal 7 uses XHTML+RDFa; it's Drupal 8 that sets the doctype to HTML5. Out of the box, Drupal 7 doesn't use any HTML5 tag.
Comment: that's what happens when you are thinking about one thing but looking at and referencing code that represents something completely different :)
Answer: I do not think you quite grasp the meaning of what those are.   A Drupal them doesn't technically require ANY CSS, and really only the simplest of HTML.
Answer: Neither CSS3 or HTML5* are necessarily required.
*Drupal incorporates HTML5, but you would be perfectly fine creating a majority if your
In fact most websites are still built using normal'ol CSS and HTML
When you hear people talking about CSS3 and HTML5 (if they are talking about it correctly) they're really referring to all the amazing stuff like transitions, animations,  tags and data="" attributes.
A modern website doesn't necessarily require all of those features provided by CSS3. I develop themes using the Omega4 framework and I rarely use even 5%-10% of the power provided by those languages and I consider my themes relatively modern.
Answer:
CSS3 and HTML5 is basically dependent on browser not on Drupal. You
  can use any CSS3 or HTML5 code considering browser support it.

https://www.drupal.org/node/1516366#comment-5832208
To Answer your question NO does not need CSS3 and it can only be run by using a HTML5.

Do drupal themes require CSS3?


Do the laws of physics work everywhere in the universe?

Question: Do the laws of physics change anywhere in the universe? Or will they change from place to place in the universe?
Answer: There's another question on this site about whether the laws of physics change over time. I think that the answers to that one (including mine) apply pretty much perfectly to this question about whether the laws change in space.
We expect the fundamental laws of physics to be the same throughout space. In fact, if we found that they were not, we would strongly expect that that meant that the laws we had discovered were not the fundamental ones.
It's very sensible to ask whether the laws as we currently understand them vary with respect to position. People do try to test these things experimentally from time to time. For instance, some experiments to test whether fundamental constants change with time are also sensitive variations in the fundamental constants with position.
Some cosmological theories, especially some of those that come under the heading of "multiverse" theories do allow for the possibility that the laws are different in different regions of space, although generally only on scales much larger than what we can observe. In general, in such theories, the truly fundamental laws are the same everywhere, but the way the evolution of the Universe played out in different regions is so different that the laws appear quite different.
One way this can happen is by the mechanism of spontaneous symmetry breaking. When the Universe cooled down from very high temperatures, it probably underwent various transitions, more or less like phase transitions, in which an initially symmetric state turns into a less-symmetric state. In those transitions, there may be different ways that the final state can come out, and they may be quite dramatically different -- completely different sorts of particles may exist, for instance. There could be different regions of the Universe in which the symmetry breaking went different ways, in which case the "apparent" laws would be utterly different in different regions, but probably only on scales many orders of magnitude larger than what we can see.
Answer: One thing not mentioned is Noether's theorem. This theorem states that if there is a symmetry in the system, there is also a conserved quantity, and vice versa.
Some examples of the theorem in action:

Rotational symmetry $\leftrightarrow$ angular momentum. If you set up an experiment, its behavior doesn't change depending on the direction you observe the experiment from. This symmetry is rotational symmetry, and its existence implies angular momentum is conserved.
Time symmetry $\leftrightarrow$ energy. The results of experiments don't depend on when it is performed. This is time symmetry, and implies energy is conserved.
Translational symmetry $\leftrightarrow$ linear momentum. If the laws of physics don't depend on where the experiment is performed, then linear momentum is conserved.

All these things can be tested. If we measure conservation of angular momentum, then we know that rotational symmetry exists. Similarly, if we measure conservation of linear momentum - and we do - then the laws of physics do not depend on position. In other words, they do work everywhere in the universe.
Comment: Certainly, and Noether's theorem is a mathematical theorem, not a physical theory, so it can be proved. However, measurements pertaining to the kinds of experiments you mention are only local, so the conservation may only be local. OTOH, I think it's very reasonable to believe that those symmetries and conservation laws *are* global, I'm just playing devil's advocate.
Answer: The aim of physics theoretical research  is to formulate mathematically the "laws of physics" in such a form that the formulae will work anywhere in the observed/known  universe. We can test well our immediate neighbourhood, analyse signals coming from the beginning of the Big Bang and expect that the final Theory Of Everything (TOE) will be consistent through the whole. Physics is not there yet.