Etymology of phrase "Let's Go !"

Question: Here in Pittsburgh, we have lots of "Let's go Steelers!" (and some diehards who also say "Let's go Bucs!", but they're dying out). What does that phrase even imply? I assume it's similar to "Go Steelers", which I'm also not sure of the implications. "Go Steelers... to victory!" is a very strange way to phrase the sentence. Does anyone know where this phrase comes from?
Comment: George Bush at college formed a team called the Nads, specifically for this reason.
Answer: Usually, "Let's go [team name]!" is used for teams with two syllables in their names and "Go [team name]!" for teams with just the one. They are used to encourage the team to move and go for it, I suppose.
The source of the cheer + clap is usually attributed to a song by The Routers named "Let's go (Pony)" (YouTube) from 1962:

The Routers first release in September 1962 was the guitar-driven instrumental "Let's Go (Pony)",[6] which reached #19 on the Billboard chart. Its infectious "clap clap clap-clap-clap clap-clap-clap-clap Let's Go!" chant became a favorite of cheerleaders and crowds worldwide.

That said, the Chicago White Sox used a song by Captain Stubby and the Buccaneers named "Let's Go, Go-Go White Sox" (YouTube) as far back as 1959:

The song first appeared in 1959 during the White Sox' run for the AL pennant--the team's first league championship since the infamous Black Sox Scandal of 1919. It was written by former White Sox minor leaguer Al Trace and his friend Walter "Li'l Wally" Jagiello.

However, the song did not become famous until 2005.
I expect that the "Let's go [team name]" cheer and other variants came about after the cheer-and-clap from the song by The Routers became popular.
Answer: Formulas of the type "Let us do something" are as old as the world.

Let us pray/ Let us begin/ Let's go

are standard formulas, a kind of imperative where the speaker includes himself, which in Latin grammar already had the special name hortative.
In the Bible, Genesis 1:26 God says: Let us make mankind in our image ...
And in the King James Bibel, in the story about the Tower of Babel, the people immigrated from the east said one to another:

Go to, let us build a city and a tower, whose top may reach unto heaven ...
Genesis 11

As to "Let's go", this formula can be used in its literal sense at the beginning of a walk, but also metaphorically in all senses a special context may offer.

Etymology of phrase "Let's Go !"


Is french /s/ apico-dental-alveolar or lamino-dental-alveolar?

Question: In french phonology sources, one may find disagreement over how the french /s/ sound is produced:
Some go for resting tip tongue behind lower teeth and the blade touches behind upper teeth, others say the tip tongue touches behind upper teeth.
Can anyone describe the reason?
Comment: Americans make /r/s in two completely different ways (and some Americans use both of them). There's no reason that the French shouldn't make /s/s in two somewhat different ways. Neither sound is going to get mistaken for another consonant.
Comment: You may think they sound different (and I'm sure you can tell them apart). The question is what native French speakers think. Many English speakers brought up in  California cannot tell *cot* from *caught*, whereas to me the difference is perfectly clear. (And even if the French can tell them apart, which /s/ they use may simply give away what part of France they're from.)
Comment: Thank you for your comment. The issue is not about should or shouldn't. These two /s/s are different  with regard to sibilancy and lisp.
Answer: According to a review of the literature (see table 1.1) dating from 1991, the /s/ and /z/ phonemes are realised with:

a tip-down laminal tongue position.

The reports are evenly split between dental and alveolar for the place of articulation of /s/ and /z/, whereas /l/ is very much apical, and /t/, /d/, /n/ are reported as apical [and dental] by the majority of sources.
The study also reported that for laminal /s/ and /z/

tend to be articulated farther back in English than in French
Comment: In table 2.1 of your reference, it says that the /s/ and /z/ phonemes were apical in 32% of the French speakers tested, and laminal in 68% of the French speakers tested. I think table 2.1 answers the OP's question: both pronunciations are used in France.
Comment: Thanks. A very useful working paper and comment advocate for being laminal.


How To Make Custom Welcome Messages In Vanilla Minecraft?

Question: I was wondering how to make your own custom welcome messages in Minecraft using command blocks. I want it to replace the regular welcome message to make it look more professional. I am really looking forward to releasing my server in a couple of days so I want to make a good first impression. Thank you!
Comment: I have tried different websites and videos but they don't seem to work.
Comment: What version of server you have? I thought that vanilla MC has no welcome message? (X joined game is NOT welcome message) What is your welcome message now?
Answer: There is no way to alter the default welcome messages afaik. But you can add your own custom messages after that, using the title command or a custom tellraw message.
Returning player
To set this up, you'll first need a objective to detect when a player has left the game (run once):
# 1.12 and below
/scoreboard objectives add hasLeft stat.leaveGame

# 1.13 and above
/scoreboard objectives add hasLeft minecraft.custom:minecraft.leave_game

This will be on 1 as soon as they log back in. you can then use @a[score_hasLeft_min=1] (1.12 and below) / @a[scores={hasLeft=1..}] (1.13 and above) to target those players.
e.g.
# 1.12 and below
/title @a[score_hasLeft_min=1] title ["",{"text":"Welcome back!"}]
/execute @a[score_hasLeft_min=1] ~ ~ ~ /tellraw @a ["",{"text":"Welcome back "},{"selector":"@a[score_hasLeft_min=1]"},{"text":" to the server!"}]

# 1.13 and above
/title @a[scores={hasLeft=1..}] title ["",{"text":"Welcome back!"}]
/execute as @a[scores={hasLeft=1..}] run tellraw @a ["",{"text":"Welcome back "},{"selector":"@s"},{"text":" to the server!"}]

these commands will

display "Welcome back!" as a title to the player that just logged in and
display "Welcome back [player] to the server!" in chat, visible for everyone.

make sure to set the score to 0 after you displayed your messages to prevent the chat from being spammed:
# 1.12 and below
/scoreboard players set @a[score_hasLeft_min=1] hasLeft 0

# 1.13 and above
/scoreboard players set @a[scores={hasLeft=1..}] hasLeft 0

First time joining player
The Commands above will only provide a "welcome back" to players that came back for the second time. To target players that log in for the first time the easiest way would be something like this:
# 1.12 and below
/execute @a[tag=!firstJoin] ~ ~ ~ /tellraw @a ["",{"text":"A warm welcome to "},{"selector":"@a[tag=!firstJoin]"},{"text":" who joined for the first time!"}]
/scoreboard players tag @a[tag=!firstJoin] add firstJoin

# 1.13 and above
/execute as @a[tag=!firstJoin] run tellraw @a ["",{"text":"A warm welcome to "},{"selector":"@s"},{"text":" who joined for the first time!"}]
/tag @a[tag=!firstJoin] add firstJoin

Since players join for the first time, they won't have the firstJoin tag. you can execute the tellraw (or whatever) off of that, then add the tag to display the message only the very first time they join the server.
Comment: For 1.13 and later: the command to create the objective is `scoreboard objectives add hasLeft minecraft.custom:minecraft.leave_game` and you'll need to replace `@a[score_hasLeft_min=1]` with `@a[scores={hasLeft=1..}]`. You also have to change the `/execute` command to `execute as @a[scores={hasLeft=1..}] run `. Also note that you can use `@s` to refer to what entity you're `/execute`ing a command as.
Answer: If I was you, then I would use a plugin. For example:
https://www.spigotmc.org/resources/welcomemessage.75514/
This plugin lets you customize the welcome message and you can even add colors!
Answer: If you are not opposed to using server- side resource packs, I believe you can replace the "joined game" with a custom message with a language pack.


Installing GRUB from scratch

Question: I am trying to make a scratch linux installation on a PC board that has an x86 processor running on it. It also has a compact flash drive on it to which I have copied my compiled kernel image. The problem I am having is with the bootloader aspect. I want to use GRUB, but I do not really know how to go about getting it onto the compact flash drive. Most documentation I have found is concerned with installing GRUB after you have a working installation of linux up and running. I had thought about using a USB floppy drive and using that with GRUB on a disc to boot the kernel image and from there try the grub-install approach mentioned in the GRUB documentation pages. Any advice on how to (or how not to) proceed will be gratefully received.
Comment: It would seem to me that you must have "running system" in which you compiled your kernel on, true? Where have you compiled your kernel on and how did the kernel end up on the CF-Card from there? These infos could clarify what can be the best way to get GRUB on the CF-Card also.
Comment: @humanityANDpeace Yes I have a desktop linux where I built the kernel and a usb flash writer device where I have copied the kernel to. I will try pointing the grub install at the flash drive and see what happens.
Answer: Well, it's true, that you need a working installation of linux (well I guess more like *nix and probably not even that). I assume you are following some kind of lfs or similar procedure. In this case you already should be in some kind of unix, to be able to build all the packages and then you can run grub-install from there.
So either grub-install --no-floppy /dev/sd<whatever> or for the minimal approach
grub --no-floppy
grub> root (hd1,0)
grub> setup (hd1)
grub> quit

Both will work from within your old system. I assume your old system to have gotten number 0 and your new one no 1 in grub's scheme. Please make very sure that this is correct, for example to find out what numbers grub gave your devices
grub-mkdevicemap --device-map=device.map
cat device.map

Installing GRUB from scratch


Is regression discontinuity a form of instrumental variable regression?

Question: I understand that regression discontinuity determines changes in the fitted line (or coefficient) at the point in a variable which defines whether the person received the treatment/intervention.
It has been said that, as such, RD is a form of instrumental variable regression? Does this mean it is a special case of regression of which heckman (or models which predict treatment) are examples?
Is regression discontinuity a form of instrumental variable regression? If yes, how so?
Comment: Possible duplicate of [Fuzzy RDD issue](https://stats.stackexchange.com/questions/121750/fuzzy-rdd-issue)
Answer: Yes and no. Regression discontinuity comes in two forms: sharp and fuzzy.
Sharp RD is not a form of instrumental variables regression. Rather, it is a very special case of matching. Please see page 289 of Lee and Lemieux (2010) for an explanation:
https://www.aeaweb.org/articles?id=10.1257/jel.48.2.281
The gist is that sharp RD trivially satisfies ignorability (or unconfoundedness) assumption but violates the overlap assumption, which necessitates local continuity as a replacement assumption for overlap. Less technically, if you look at page 318 of Lee and Lemieux, you can see that in the sharp RD case, you only need one equation estimated with OLS.
The other case, fuzzy RD, is a form of instrumental variables regression. See pages 299 and 300 of Lee and Lemieux for the technical explanation, and pages 327 and 328 for the two equations to be estimated with 2SLS. The gist is that the ignorability assumption is no longer satisfied, but we can use the expected discontinuity at the cutoff as an instrumental variable for the actual discontinuity at the cutoff.


What happens if someone else uses my disqus shortname?

Question: What happens if someone else uses my disqus_shortname?
Answer: If someone else uses your registered shortname on their site, all their comments will appear in your moderation panel.
To avoid this, we suggest adding your domain name to the Trusted Domains section of your Disqus admin panel. This can be found under Settings > General > Trusted Domains. This will prevent other users from loading your shortname on their site.
Comment: This has moved it's now under ```Settings > Advanced > Trusted Domains```


If it is so difficult to see god through mantra japa, why should we do it

Question: What is the use of mantra japa if it's really difficult to attain siddhi of any mantra for physical interaction or getting any wish fulfilled by god. If materialism doesn't matter in our lives, what is the meaning of the present materialistic existence of humanity.
Comment: Which spiritual practice is easy by any means? Going by your logic we should not indulge into any of those? When the goal is highly rewarding the effort that we must put in should be equally great. This is true for all aspects of life not just about spiritual practices.
Comment: There several factors in mantra Siddi foremost is brahmacharya that is why all baba  who attained mantra Siddhartha lived alone in cave
Answer: Firstly, it is as difficult to attain parmatma (God) as much difficult it is to realise the true self. As the true self is God from the very beginning. Realising this is attainment of moksh. Choosing how to realise it is a path of your deciding. One may realise it by chanting mantras, other might realise it by studying hard sciences. Someone else might do the same doing mundane chores throughout the day. As to which path to achieve realisation, is right or wrong, is totally a silly question to ask.
Coming to the meaning of life. I assume you are asking meaning of this current life. Technically, its meaningless, as, if not in this one, you may attain realisation in the next one. Then if there is no meaning, that means life is purposeless? No... Not at all.
Purpose of life are 4 fold. Follow dharm, attain arthic stability. Follow Kam to enjoy pleasures. And lastly moksh.
Comment: Your answer could be improved with additional supporting information. Please [edit] to add further details, such as citations or documentation, so that others can confirm that your answer is correct. You can find more information on how to write good answers [in the help center](/help/how-to-answer).


Dual-Boot OS X Snow Leopard on MacBook Pro

Question: Is it possible to dual-boot Snow Leopard on a Mid-2012 MacBook Pro running Sierra? I have the DMG file so maybe I can make a bootable flashdrive?
Comment: You should be able to, yes. Just create the bootable drive (look at Ubuntu's guide for creating bootable USBs from DMGs). Then partition your internal drive using disk utility (original partition for MacOS, second partition for OS X). Then boot from the bootable USB drive and install onto he new partition. Let me know if you have any questions!
Answer: Unless I'm totally missing something from your question, no mid-2012 MacBook Pro can run a version of OS X earlier than Mac OS X Lion 10.7.4.
More specifically, each of the three mid-2012 MacBook Pros initially shipped with Mac OS X Lion 10.7.4 and the firmware does not support any prior version of macOS. On the positive side they do all support macOS Sierra.
If you have need to dual boot into an older OS, then it will have to be any version from Mac OS X Lion 10.7.4 and above.


An algorithm for Automatic Tag Clustering

Question: Out website dinf is somewhat like StackExchange: people are submitting small definitions of concepts.
We would like to automatically assign those concepts into 'Topics'.
The problem is that dinf by default limits any definition to max of 500 characters.
Which algorithm / module we can use to assign those concepts assuming that all topics are known in advanced?
Answer: The limited size is not especially an issue. However the normal way to do that is to use a supervised classification method (for instance decision trees, but there are many options), and this means training a model from a large enough set of annotated instances.
If obtaining a training set is not possible, you could try some kind of similarity-based approach by comparing every instance against a set of words representing the topic. This is unlikely to work as well as a supervised method trained specifically with this kind of data. Also you would have to evaluate the validity of the predicted topics on an annotated test set anyway.


Does it matter which way you plug stuff into the wall socket

Question: I have a european socket and if you saw one you will know that you can plug stuff either way. But american sockets can only be plugged in only one way. So does it matter which way its plugged it because it works no matter what. I heard somewhere they use more power that way but i don't know if that's true
Comment: If it mattered, I'd expect the plug to be designed so you couldn't plug it in the wrong way.
Comment: possible duplicate of [Why are some AC outlets and plugs polarized?](http://electronics.stackexchange.com/questions/15228/why-are-some-ac-outlets-and-plugs-polarized)
Answer: There are two ways to answer this.
No. Voltage is a relative measurement, and in any AC power system (American or European), one voltage oscillates above and then below the voltage of the other. Thus, from the perspective of the appliance, which has connections only to the two prongs of the outlet, it's impossible to tell one from the other, because the system is symmetrical.

simulate this circuit – Schematic created using CircuitLab
However, yes. There are things in the world besides those two prongs. For example, the Earth. In the US, an electrical outlet really looks something like this:

simulate this circuit
The connection between one half of the outlet and Earth is made near the electrical distribution panel:

Now consider, if someone should touch the half of the outlet connected to Earth, probably nothing bad will happen. However, if he should touch the other half of the outlet, he's likely to get shocked by completing the circuit through some accidental 2nd connection with Earth, or something else touching it (which is about everything).
So although flipping the plug around and inserting it backwards will probably be no problem with regard to the electrical operation of the appliance, it may create a safety hazard by exposing the "hot" half of the outlet, the half not connected to Earth, such that someone might touch it and be shocked.
National regulatory and licensing bodies have different requirements for an appliance to be certified as safe. In particular, the home's wiring can be backwards, or users can force plugs in backwards. Thus, things like double insulation have been developed to render appliances safe even in the presence of a fault like backwards home wiring.
Comment: @PhilFrost You in the US may have devices, which rely on proper orientation of live and neutral wires to be safe. However, european devices (which are usually connected to european wall outlets) do not. They have to work and be safe either way plugged in, even if they aren't doubly insulated.
Comment: @theraginggamer: Yes you should be afraid to touch live wires, no matter what load is connected to them actually. And yes you should refrain from touching the apparent neutral wire, too. This is because your test pen may have fooled you. Those devices are rather error prone, because they rely on capacitive coupling to your surrounding, which may vary.
Comment: in that case i have to ask a question. When i push a test pen in one of the holes it light's up on the left side but doesn't on the right. Even if i plug in something and turn it on it still stays the same way (i torn down a wall socket to test this out). So basicly one is always powered and one isn't. I am afraid to touch them by hand tho
Comment: @theraginggamer, see http://electronics.stackexchange.com/a/73137/17608 for some insight into how those devices work. They detect a changing voltage relative to their surroundings (Earth). They don't detect current. So, if you put it near the "neutral" half, there is no changing voltage relative to Earth, so it does not light up.
Answer: There is a pretty good answer here:
Why are some AC outlets and plugs polarized?
Quoting the accepted answer:

Some systems will employ switches and fuses and such in the input power, and this is best handled by the live connection, not the neutral, so a polarized plug helps ensure this. There are also grounding and 'commoning' issues to be taken into consideration.
  -Majenko

There is also a good discussion about grounding vs. neutral in the comments. Essentially, the neutral is for returning current to the supply while ground is more for safety at the location. I'm paraphrasing here.
Answer: Your question was about the European socket, not about other and polarised sockets.
No, the equivalence of both ways to plug a device to a socket of this type is mandatory by law. CE regulations state the same creeping distances and other means of safety for both pins and all connected circuitry in your home appliances. This is pretty obvious, because you have to rely on the behaviour stated on the boiler plate and/or in the manual of your device regardless of the orientation of the plug.
As the electronics in your device will see only the AC voltage between N and L, and they cannot discriminate between both, as there is no way to do so, also power consumption will exactly be the same.
There's only a minor difference when it comes to failures inside your appliances. And only in Class I devices. Suppose you have a washing machine, which has a housing connected to PE (which can't be interchanged when you turn the plug, because it's connected to both prongs protruding from the outlet) and a defect causing one wire of the two potential live/neutral wires to short to the housing.
If the now grounded wire was by accident the live one, your fuse or circuit breaker will blow. If it was the neutral on, it won't and your device will seemingly operate rather normal.
A RCD will probably fall within both possible orientations.


Armature Missing

Question: Was rigging my model and suddenly the armature disappeared.
Don't remember using weird shortcuts apart from Ctrl+Tab to enter/exit pose mode.
In the outliner it actually shows up as 'active' and 'visible' but cannot see it.
I'm using blender 2.82 The project does not come from older versions, it was created in this one. Already tried Alt+H
Found this: Armature Disappeared
but it doesn't work for me.
Answer: Turns out I was in isolate mode all the time.

Armature Missing


Are there any geometric interpretations to uniform continuity?

Question: There are specifically the two forms, continuity and uniform continuity, I'm referring to. So a function is continuous if the graph "doesn't break," but this also applies to a uniform continuous function. What else is required for it to be uniformly continuous? I know the technical definitions (continuity: $\forall \varepsilon \, \forall x \, \exists \delta \, \forall y \, ( \, |y-x|<\delta \, \Rightarrow \, |f(y)-f(x)|<\varepsilon \, )$, uniform continuity: $\forall \varepsilon \, \exists \delta \, \forall x \, \forall y \, ( \, |y-x|<\delta \, \Rightarrow \, |f(y)-f(x)|<\varepsilon \,)$) but in geometric terms, what does it mean?
Comment: Be careful with your geometric interpretation of continuity; while it's good for a globally continuous function, the Thomae function is continuous at almost all points.
http://en.wikipedia.org/wiki/Thomae's_function
Comment: @JulienClancy Although we always have this pathologic (very interesting) cases, I think that intuitive interpretations for this things are important too.
Comment: @JulienClancy Yes, I actually think that is the best thing of mathematics (when outcomes of formality that looked like the intuitive thing at first, are so weird)
Comment: @AndreasHagen Thomae's function is discontinuous at all rational values. It is because of the density of the irrationals over the rationals that there is continuity at each irrational point. Basically, irrational numbers are always "closer together" than rationals.
Comment: There's a good definition of it in nonstandard analysis (i.e. infinitesimals but rigorously). A function is uniformly continuous if, for every (possibly infinite/infinitesimal) $x$ and $y$, if $x-y$ is infinitesimal, then $f(x)-f(y)$ is infinitesimal. For example, $f(x)=\frac1x$ isn't uniformly continuous, since, for infinitely large $N$, $\frac1N$ and $\frac1{N+1}$ are infinitely close but $f(\frac1N)$ and $f(\frac1{N+1})$ aren't. Similarly, $f(x)=x^2$ isn't uniformly continuous since $N$ and $N+\frac1N$ are infinitely close but $f(N)$ and $f(N+\frac1N)$ aren't.
Comment: Of course. But speaking personally, it helps me a lot intuitively to see when and how intuitive behavior breaks down while staying within the technical definition, and to what extent this can occur.  I think Thomae's function illustrates this well.
Comment: I'm curious, is Thomae's function only continous in sequences where $f(x) = 0$ because of sequential irrational numbers or are there continuity in the places where rational numbers are in play as well?
Answer: There's a great theorem about uniform continuity that helped me understand it quite a bit.
If $f \colon \mathbb{R} \to \mathbb{R}$ is a function and if $\lim_{x \to \infty} f(x)/x = \pm\infty$, then $f$ is not uniformly continuous.
Basically, what this means is that the "last" uniformly continuous functions are linear. If your function grows faster than every linear function, it cannot be uniformly continuous. You can apply this intuition to similar functions as well - $f(x) = \sin(x^2)$ is not uniformly continuous because eventually its local growth outpaces an arbitrary linear function.
Edit: Here's the proof. Assume that $f$ is uniformly continuous. Then there is $\delta > 0$ such that $|x - y| < \delta \Rightarrow |f(x) - f(y)| < 1$. If $f(x)/x$ has some limit as $x \to \infty$ then $(f(x) - f(0))/x$ should have the same limit, because $f(0)/x \to 0$. Now,
$\left|\frac{f(x) - f(0)}{x}\right| = \left|\frac{f(x) - f(x - \delta) + f(x - \delta) - ... + f(\delta_0) - f(0)}{x}\right| \leq \left|\frac{f(x) - f(x - \delta)}{x} \right| + \left| \frac{f(x - \delta) - f(x - 2\delta)}{x} \right| + ... + \left| \frac{f(\delta_0) - f(0)}{x}\right| < \frac{x}{\delta}\cdot\frac{1}{x} = \frac{1}{\delta}$
so the limit cannot be infinite. I used $\delta_0$ to be some positive number less than $\delta$; it could be that $x$ is not an exact multiple of $\delta$ and this takes the remainder. In the first equality I used a telescoping sum; in the second I used the triangle inequality; in the third I just counted the number of terms.
Comment: What is the name of this theorem? I would like to refer this in my homework.
Comment: I'm not sure of the name but I'll try to recall the proof and post it.
Comment: However, if we bound a nonlinear function to some closed interval, it may still turn out uniformly continuous. For example $f(x)=x^2$.
Comment: Yes, that point is crucial. We're looking at asymptotic behavior (and in a sense my $\sin(x^2)$ example is asymptotic). It happens that every continuous function confined to a closed interval is uniformly continuous.
Comment: Would you say then that a full characterization of uniform continuity would be given by the theorem stated in your answer (asymptotic condition), and bounding continuous functions to closed intervals (local condition)?
Comment: That last remark about every function that is continuous and bounded to an interval is also uniformly continuous finally solved my homework. Thanks to you both =)
Comment: I think so, yeah.
Comment: No problem @AndreasHagen, happy to be of service :)
Answer: Continuity of $f$ at $a$ means that I can make $f(x)$ as close as I want to $f(a)$ by making $x$ close to $a$. Let us formalize: No matter how small an error tolerance (for all $\epsilon  > 0$), one can make $f(x)$ close to $f(a)$ within this error tolerance ($|f(x)-f(a)|< \epsilon$) by finding a number $\delta$ such that if $x$ is less than $\delta$ off from $a$ then $f(x)$ is less than $\epsilon$ off from $f(a)$.
For uniform continuity, first take an example. Let our error tolerance ($\epsilon$) be $1/2$. If $f(x)$ = x, then if I want to make $f(x)$ at most $1/2$ off from $f(a)$, all I need to do is make $x$ $1/2$ off from $a$ (let $\delta = \epsilon = 1/2$). Usually, however, $\delta$ depends on $x$: if $f(x) = x^2$, then near zero all of the $f(x)$'s are fairly close to each other ($f(x)$ isn't changing very fast), so $\delta$ can be pretty big - if x is kinda close to zero, then $f(x)$ within 1/2 of zero. However, if x is near 100, $f(x)$ is changing very quickly, and thus for $f(x)$ to be close to $f(100) = 10000$, $x$ has to be really close to 100 for $f(x)$ to at most 1/2 off from $f(100)$, or $\delta$ must be teeny. Uniform continuity just says that a minimum $\delta$ works: if $x, y$ are in your interval, no matter how fast $f$ is changing, you are guaranteed that if $x$ and $y$ are within $\delta$ of each other, $f(x)$ and $f(y)$ are within $\epsilon$ of each other.
Answer: I hope that this helps:
by an inscribed triangle I mean a right triangle s.t. the vertices of its longest side are on the graph of function $f$ and the adjacent sides to the right angle (legs) are parallel to $x$-axis and $y$-axis(unfortunately I don't know how to draw a picture here), we call the side parallel to $x$-axis its base and ,the side parallel to $y$-axis its altitude (just here not generally!)
$f$ is uniformly continuous if when we look at the set of all inscribed triangles, the altitude becomes small enough provided that the base becomes small enough.
for example $f(x)=\sin{1/x}$ is not uniformly continuous because near $0$ you can find inscribed triangles with arbitrary small base s.t. their altitude is not small enough.
similarly, $f(x)=x^2$ is not uniformly continuous (I assume the domain is the whole real line) because you can find inscribed triangles with similar property, however, in this case the triangles go far away from $0$.
One can find a similar interpretation for continuity in terms of inscribed triangles which have one of their vertices (other than the vertex with the right angle) at point $(x,f(x))$.
Answer: Suppose $\forall x,y\in E, \frac{|f(x)-f(y)|}{|x-y|}<M$. In other words, the slopes of the secant lines between any two points on the curve are bounded. It also follows that the derivative is bounded if the function is differentiable. If we select $\delta=\epsilon/M$, and $|x-y|<\delta $ then $|f(x)-f(y)|<M|x-y|<\epsilon$ and so $f(x)$ is uniformly continuous. So bounded slopes of secant lines imply uniform continuity.
Suppose the $|f'(x)|<M$ on $[a,b]$.Then $|f(b)-f(a)|<M(b-a)$. Then by the above the function is uniformly continuous.
This is very useful for sines and cosines. Up to a sign, they are each others' derivatives. The maximum absolute value is $1$, so no line with a slope greater than $1$ is ever parallel to a tangent line of sine or cosine, their powers, or their products of powers.
So some geometric properties imply uniform continuity.


Is an interest in the Philosophy of Biology a good reason to pursue grad studies in Evolutionary Biology?

Question: I have always leaned more towards questions surrounding psychology, sociology, and philosophy but fate has me graduating with a BSc in Biology this year. Would it be smart to pursue it further more for the aesthetic beauty I find in its ability to shed light on questions beyond itself than for the science purely in itself?
Comment: I think someone planning to do "philosophy of biology" would be greatly helped by graduate work in biology.  In some fields (other than biology) there are "philosophers" writing about it who have only a weak or warped idea of the field as it is actually practiced.
Answer: My understanding is that taught MSc in evolutionary biology will likely differ in course content from university to university. So whether its a good idea / is going to interest you is hard to predict.
Secondly, what would be looking to do after the masters? That's another way to frame whether masters study is a good choice.
Comment: I agree (very much) with the second point. The first point seems largely irrelevant to me -- of course some programs would be a better fit than others, but the question is really whether OP should seek this degree...if the answer is yes, then OP can carefully choose with program is best.


Front-End Form Submission in Shortcode

Question: The plugin I am working on contains shortcodes with forms on them.  Upon form submission (POST), I do some database work, and then planned on redirecting to another page after the db work is complete.  When I attempt this, I get the "Headers Already Sent" warning.  Within the shortcode function, how do I call my redirect sooner than get_headers?  Do I need to use some separate callback function?
Answer: You have to hook an earlier action to check if the form was submitted. Something like:
<code>function wpa_process_form(){
  if( isset( $_POST['my_form_data'] ) ){
      // process form and redirect
  }
}
add_action( 'init', 'wpa_process_form' );
</code>
Comment: And this is another function that is tied to init, correct?  Not my same shortcode function?
Comment: correct, separate from your shortcode function.

Front-End Form Submission in Shortcode


webalizer installation

Question: How can I manually install webalizer ? If there is any link providing the details to deploy it to multiple domains. Any help will be highly appreciated.
Answer: What is Webalizer:  (for those wondering)
Webalizer is a fast, free web server log file analysis program, written in C, which produces highly detailed, easily configurable usage reports in HTML format.  It was written to solve several problems with currently available analysis packages.
Webalizer Features:

It is written in C to be extremely
fast and highly portable. On a 200
MHz Pentium machine, over 10,000
records can be processed in one
second, with a 40 Megabyte file
taking roughly 15 seconds (over
150,000 records).
Supports standard Common log file
Format server logs. In addition,
several variations of the combined
log file Format are supported,
allowing statistics to be generated
for referring sites and browser types
as well. Now also has native support
for wu-ftpd xferlog FTP and squid log
formats as well.
Generated reports can be configured
from the command line, or by use of
one or more configuration files.
Detailed information on configuration
options can be found in the README
file, supplied with all
distributions.
Supports multiple languages.
Currently, Catalan, Chinese
(traditional and simplified),
Croatian, Czech, Danish, Dutch,
English, Estonian, Finnish, French,
Galician, German, Greek, Hungarian,
Icelandic, Indonesian, Italian,
Japanese, Korean, Latvian, Malay,
Norwegian, Polish, Portuguese
(Portugal and Brazil), Romanian,
Russian, Serbian, Slovak, Slovene,
Spanish, Swedish, Turkish and
Ukrainian are available.
Unlimited log file sizes and partial
logs are supported, allowing logs to
be rotated as often as needed, and
eliminating the need to keep huge
monthly files on the system.
Distributed under the GNU General
Public License, complete source code
is available as well as binary
distributions for some of the more
popular platforms

Webalizer Installation:
There are a few ways to install Webalizer - such as apt-get, yum, and of course from source.
installing via apt-get or yum is as simple as just running the command
yum -y install webalizer  or apt-get install webalizer -y
Installing through sourcecode

First we need to download the webalizer sourcode first:
wget ftp://ftp.mrunix.net/pub/webalizer/webalizer-2.23-03-src.tgz
Now lets uncompress it
tar zxvf webalizer*
Makesure you have gcc compiler and Gd library installed, you can installed it using yum
yum install gcc gcc-c++ gd-devel
Now go into the webalizer* directory , compile and install it
cd webalizer*
 ./configure
 make
 make install

It is installed and you can checked the version now
webalizer --version
Webalizer V2.23-03 ********other stuff shows here*****

WEBALIZER CONFIGURATION (single domain)

Create a central directory for the webalizer configuration files
mkdir /etc/webalizer
Create two webalizer configuration files, a.example.conf from the
sample file and put it into /etc/webalizer directory. You need to locate the webalizer.conf.sample files and copy it to /etc/webalizer directory
cp /usr/local/etc/webalizer.conf.sample  /etc/webalizer/a.example.com.conf
Modify LogFile, OutputDir and HostName of the  webalizer config files. For example, fora.example.com.conf
vi /etc/webalizer/a.example.com.conf

and changes the content
LogFile /var/log/httpd/access_log
into
LogFile /var/log/httpd/access_log_1  # it depend on your httpd access_log you can search it on /var/log/httpd/ directory
OutputDir /var/www/usage/a
into
OutputDir  /home/praetorian-id.org/public_html/webalizer  # it depend on your apache virtual directory that you set on httpd.conf (/etc/httpd/conf/httpd.conf)
HostName       localhost
into
HostName       yourhostname.org  # it depend on your web hostname

Note:You may want to specify other settings specific to the domain, such as HideReferrer,HideSite, etc.

To process all the virtual sites, run the following command:
for i in /etc/webalizer/*.conf; do webalizer -c $i; done

Now you can see the webalizer files on your site, example :
http://domainname.org/webalizer/usage_20100811.html
How to set Webalizer on multiple virtual domain :
Tha above tutorial are to set the webalizer for singel domain, how about if  you needed to create webalizer for multiple domain ? , you need to makesure that you have create custom log on your every virtual domain setting on httpd.conf it is usually on /usr/local/apache/conf/httpd.conf , here is the eample :
<VirtualHost 18.104.22.168>
    ServerName test.com
    ServerAlias www.test.com
    DocumentRoot "/home/domains/test.com/htdocs"
    CustomLog "/home/domains/test.com/logs/access_log" common
</VirtualHost>

as you can see above, we have set the custom log on /home/domains/test.com/logs/access_log , please also make sure you have create the  /home/domains/test.com/logs directory and set  the permission was set for  domains users
-rw-r--r-- 1 domains users 677485 Dec  1 14:45 access_log
then set the log path on your webalizer conf on /etc/webalizer/
# vi /etc/webalizer/test.conf

LogFile         /home/domains/test.com/logs/access_log
then set it per virtual domain that you have :)
and last thing ,  restart the httpd , if you are using rpm
# service httpd restart

You should see the size of the access_logs on /home/domains/test.com/logs/access_log increase , if not checked the permission and webalizer config on /etc/webalizer/test.com.conf
Do not forget to add cron so the webalizer can be udpated automaticly
crontab -e

add
1 * * * * /root/dowebalizer >>/dev/null 2>&1

i will set the crontab every 1 hour to execute the shell script on /root/dowebalizer
Now create the shell script on /root/dowebalizer
vi /root/dowebalizer

enter the following:
#!/usr/bin/perl
use strict;

my @files = </etc/webalizer/*.conf>;

foreach my $file (@files) {
        chomp($file);
        system("/usr/local/bin/webalizer -c $file");
}

hit escape and save with w!
did this help you?   if so - leave a comment, grade it - and tag it :-)
Comment: How can I install it in a windows servers?

webalizer installation


What are Unity3D Substances?

Question: I recently was a tutorial use substances in Unity3D. I understood that a Substance is a material we can dynamically manipulate at run time, but I am still unclear about it. Could someone shed some light on this?
Answer: Substances are basically dynamically generated materials.
There main purpose is to take the grunt work out of generating tileable materials like bricks and stone roads and the like.  Basically artist wont have to spend time dealing with things like aligning seams and what not.
They also have the advantage of drastically reducing the amount of textures stored on the disk.
They also are resolution independent meaning that you can create the texture at runtime to be as detailed as you need depending on resolution.
This does not however come for free the texture will still have to be store in memory and will cost you as far as RAM consumption.
So you will have some input textures that will be used to dynamically generate your substance.
Wether you should use them or not depends on totally what your trying to achieve.  They are particularly useful if you want to say have multiple looks applied to the same object at different times in your game.
The tech that unity uses is from this company http://www.allegorithmic.com/ and if you want to truly take advantage of this you will probably need to buy a substance editor from them as they make it pretty easy to build different materials.
They have some cool tools just be aware of the performance implications.
So a practical example of use would be:
Say I wanted to make a game where the same environment would look aged when the character came back to it years later.
You would build your substance so that the sliders will expose some cracks on the table and perhaps even some peeling of the finish. All changeable during runtime.  With some exposed parameters also changeable in the editor.
Example of that is here ---> https://www.youtube.com/watch?v=AxAw7LIqIKM
Comment: You got it again. :P . Bdw, could you please share a simplistic practical use of it?
Comment: updated with possible use case and video showing it in action.
Comment: Video is not available anymore.
Answer: They are dynamically generated textures.  http://www.allegorithmic.com
Substances are created with substance designer using stock images, vector graphics, code functions, or other substances to generate a new texture. Substances are VERY convenient and and nice. They really shine when you want to add variety to textures while keeping disk size low (as long as the substance is built correctly).
You can also have unity generate a new substance variant at runtime for individual game objects. Although, the you would need to check if the substance is finished generating the texture as each substance has a runtime as well before applying it, otherwise the object will appear solid blue until it is finished.

What are Unity3D Substances?


Meaning of wolves crossing city street in Collateral

Question: While Max is driving his cab with Vincent in the back seat, they encounter I believe, two wolves crossing the street. I felt like there was some special emphasis put on that scene: Max has slowed down, the music played louder and it felt like some sort of revelation was made in that scene. I was thinking about it, trying to make some connections but simply couldn't tell for sure. The grey wolf fur yet somehow stroke an association with Vince's greyish hair, yet may still being completely irrelevant. What was the true meaning/association in that scene?
Comment: That was the intermission
Answer: It's not a wolf or a fox, it's a coyote.
There is none, it was a happy accident (as mentioned on the movie's wiki page):

One event of note was the filming of the coyotes running across the road; the low-light capability allowed Mann to spontaneously film the animals that just happened to pass, without having to set up lighting for the shot.

Entertainment Weekly theorizes:

There is a metaphorical animal, a coyote crossing the road. This is all in the lead-up to the Korean Nightclub scene, a sequence that is by far the best-known scene in Collateral. It's a bad omen, but it's also bizarrely optimistic: a reminder that none of this really matters, that Los Angeles is still a desert underneath all the palm trees lit up black by the High-Def video. On the soundtrack, Cornell sings, "I can tell you why people die alone." In the hospital Max visits every day in Los Angeles, his mother appears to be in the process of eternally dying. Vincent kills people and feels nothing; ultimately, Vincent winds up dead. The Symbolic Coyote is probably the least troubled character in the film.
Answer: I think it was a little bit of a revelation to both of them.
As the wolf/coyote walked by they both looked at each other, Max looking at Vincent as the lone wolf out there at night and sort of looking at him in awe wishing to be somewhat like him in a way.
Also Vincent looking at the wolf realizing for the first time that he is alone and not reaching the place he wants to be in life and looking at Max and maybe being jealous or in awe of Max.
Either way I love that Mann put that in the movie because you can come to whatever realization you want with it and its still a great movie!!
Answer: The EW theory is dead wrong. First of all, it's a wolf stalking a coyote; not two coyotes. Secondly, the coyote is in no way "the least troubled character in the film." It's running for its life.
The wolf represents Vincent and the coyote represents Max. Max is starting to put together the fact that Vincent is setting him up, as es evidenced by his repeatedly asking, "Why didn't you kill me and find another cab driver?" Vincent sees himself in the wolf, too -- a lone predator stalking it's prey in the darkness. His dialogue with Max, advising him to follow up on his date if he survives the night, is a sign that he has felt the loneliness of his "lone wolf" lifestyle. Both men and both animals are out of their natural element and the two men are starting to realize that they need a change in their lives.
Answer: To be honest there's some truth in all of these answers although the entertainment weekly one is obviously wrong. it did point out an important part that plays with the wolf and coyote scene. Which is the Korean night club scene. During which, Vincent saves Max's life and then stares at him intently as if to tell him "we're in this together". Right before this, he told his mom he was thinking of him as a friend. What came after, was Max showing how angry he was by tossing the briefcase, and Vincent putting Max to a test in which he passed. The symbolism with the wolf and coyote is Max seeing that he is basically being stalked. Vincent seeing what his whole life has been about.
Vincent is ex military and an assassin. His life had been about death. Surely any "friends" he had made has died. Or he killed them. Meeting Max he slowly softens and sees his life has no end. He tells Max about his dad, he jokes with Max, he offers advice. Vincent I believe is having issues with his own demons and it shows when he saves Max's life. Vincent saw the police and knew that they were both screwed at that point. It would have been best for him, to let Max die and carry on by himself. He didn't want to do that anymore I guess.
It's a great tie-in scene. To have that wolf chasing the coyote through the night. Also, later when Max tells him how he really feels by putting that question to him "tell me what's going on in your head" etc. You can see that Vincent is hurt by what Max is saying. Would a lifelong murderous cold deadly assassin ever have his feelings hurt? I think he was changing and knew it by the end that Max had changed him. He welcomed death
Answer: The most interesting thing about this scene I think is not the wolf crossing the road but the the cut scene to the advertisement on the roof of the cab as the cab drives off. Check it out! It says "Silver". Seriously check it out.
Is the symbolism here that wolf is chasing the coyote.  And then Max is the Coyote and Vincent is the wolf but Max has the "Silver" Bullet or the Cab, to kill the wolf.. A little foreshadowing maybe...
I know I know its a long shot but this scene I believe is one of the greatest scenes in a movie. The music, the atmosphere, the use of nature..  The way it slows the movie down for the audience to catch a breathe and see the real world through both Vincent and Max's eyes.. I love it.
Answer: Vincent killed people for a living. He exterminated life. He was a very damaged character, he didn't really care if he lived or died. He had to be like that. He knew any day could be his last, that was his reality. Overthinking was his defense mechanism (from being human). He thought about oblivion, and he ran there anytime he might have struggled with his lifestyle. I believe Max's talk about escaping to his happy place earlier in the movie has something to do with it. The most obvious being- In oblivion, nothing matters. That was Vincent's escape.
Understanding that is important because that was his conflict. We can speculate on his past, but what we do know is he did not seem to mind killing people. In order to be like that, you would have to view people as you would bugs. Inferior and meaningless (for most people). But that would also mean you look at yourself as a bug, in a sense. Also, the only people Vincent interacted with were probably crime lords and killers, therefore reaffirming his stance on people being bugs and solidified his disposition. A place like LA pretty much represented the epitome of that mindset, in a bad way, as he referenced the people being disconnected from each other. That would mean that there was still a piece of him that did not like his "happy place".
But then, here comes Max.
Vincent had this idea that people didn't care about each other, and in his world that was probably true. But Max was a people person. He wanted to cater to people. He wanted to make people feel good. His idea for his company reflected that, a experience so good that you wouldn't want it to end (the limo ride). He visited his dying mother everyday. He had a conscious. Vincent, being the intelligent man he was, could recognize those traits in him. He started to see Max as human, not a bug.
The coyotes represented a few things. First, survival and adaptability. In the middle of this huge concrete jungle full of people, two "wild" animals you wouldn't really expect to see, predators, are defying the odds. They are surrounded by bigger threats than what they pose- and yet they are adapting and surviving, independent from domestication. Also, coyotes are sneaky. They can stay hidden pretty well when they want to. Their intuition is strong, and they usually avoid people. But, in the middle of driving, Max spotted them. Perhaps they showed themselves, as they say animals can sense things about people. Another important note is that Max actually stopped for them. How many people would have? Whether it was to insure their safety crossing the street, or to just watch them- Max made a point to do it. Even in the middle of all the chaos he was in middle of. That was his nature. Vincent recognized that. I think that's when Vincent had it in his mind that Max was probably the one guy in this world that he did not want to kill. I think even at the end, when he was dying and he asked Max if anybody would notice a man dying- what he was really asking was for Max to remember him...to notice him, that he actually existed as he spent much time "not existing". Hiding in the dark, like those coyotes. Just as Max shined some light on them, exposing them, he would do the same for Vincent. He would see him for who he really was, even if it was just him that ever would.  And knowing that, in his final moment of life, was Vincent's ultimate "happy place".


What is Data Lake?

Question: I am familiar with the concept of "Big Data" but how does "Data Lake" differ from Big Data?  Is it derived from Big Data? Please explain.
Answer: Big Data is a term related to extraction of information from big datasets. It is also sometimes used in context of predictions from large datasets. Big Data points to the 'big' aspect of data.
Data lake is a concept of storing and providing data in data system, no matters what size of data it is. Data lake aims to be a single repository of data in a company for better management and access to the data.
Answer: What is a data lake?
A data lake is a centralized repository that allows you to store all your structured and unstructured data at any scale. You can store your data as-is, without having to first structure the data, and run different types of analytics—from dashboards and visualizations to big data processing, real-time analytics, and machine learning to guide better decisions.
Why do you need a data lake?
Organizations that successfully generate business value from their data, will outperform their peers. An Aberdeen survey saw organizations who implemented a Data Lake outperforming similar companies by 9% in organic revenue growth. These leaders were able to do new types of analytics like machine learning over new sources like log files, data from click-streams, social media, and internet connected devices stored in the data lake. This helped them to identify, and act upon opportunities for business growth faster by attracting and retaining customers, boosting productivity, proactively maintaining devices, and making informed decisions.
Data Lakes compared to Data Warehouses – two different approaches
Depending on the requirements, a typical organization will require both a data warehouse and a data lake as they serve different needs, and use cases.
A data warehouse is a database optimized to analyze relational data coming from transactional systems and line of business applications. The data structure, and schema are defined in advance to optimize for fast SQL queries, where the results are typically used for operational reporting and analysis. Data is cleaned, enriched, and transformed so it can act as the "single source of truth" that users can trust.
A data lake is different, because it stores relational data from line of business applications, and non-relational data from mobile apps, IoT devices, and social media. The structure of the data or schema is not defined when data is captured. This means you can store all of your data without careful design or the need to know what questions you might need answers for in the future. Different types of analytics on your data like SQL queries, big data analytics, full text search, real-time analytics, and machine learning can be used to uncover insights.
As organizations with data warehouses see the benefits of data lakes, they are evolving their warehouse to include data lakes, and enable diverse query capabilities, data science use-cases, and advanced capabilities for discovering new information models. Gartner names this evolution the "Data Management Solution for Analytics" or "DMSA."
What is a data lake? | aws
Answer: Data Lakes:
What:
The data lake is a general purpose, highly scalable, low-cost storage tier for raw data. If the data warehouse is a source of purposeful structured data that has been preprocessed and loaded to answer specific business-centric questions, the data lake is the staging area for data that might have importance in the future.
Why?
Given that businesses are moving to a "store everything" mentality across most of the data they produce, it is essential to have a storage tier that can scale to meet the storage needs of tomorrow while also providing benefits today.
Challenges:
The challenges of storing raw data, however, can manifest when the time comes to make use of and provide purpose to these deep pools of raw potential. The challenge is that over the months and years that data is sitting and waiting, changes to the data being produced and a lack of records as to what exactly was being recorded at various points can make older data unusable. This can dramatically increase the lead time to make use of the data or cause years of data to be thrown away due to corruption of data over time.
Technical tip:
So even though the data lake is conceptually a storage area for raw, under-purposed data, there is still a need to provide a moderate level of effort in order to ensure that data corruption doesn't occur along the way, and that the business can make practical use of the data when the time comes to put it into action.
Answer: Big Data is high-volume, high-speed, and/or high-variant information assets that require cost-effective, innovative forms of information processing that enable improved insights, decision-making, and process automation.
The data lake stores a large number of data in their raw format, i.e. unprocessed, from different sources in order to make them usable for Big Data analyses. This data can be structured, semi-structured, or unstructured. The information is stored there until it is needed for an analytical evaluation. Data Lake Definition

What is Data Lake?


Do companies destroy value when they borrow money to pay dividends?

Question: When public companies pay dividends, their stock price will be reduced by the amount of the dividend. This makes sense to me, but I'm wondering if this applies when companies borrow to pay dividends (e.g. for maintaining a dividend payout during a bad year). Debt has interest costs, which the company could have avoided by not paying out the dividends it could not afford to pay. These interest costs look like avoidable value-destroying expenses. Does borrowing to pay dividends destroy value for shareholders? Does this lead to a decline in stock price that is greater than the amount of the dividend when the dividend is paid?
Comment: In some jurisdictions companies are only allowed to pay dividends if they post profits... So `borrow money to pay dividends` is a bit strange of a concept.
Answer: Borrowing money and paying out dividends are separate events. Paying out dividends decreases stock price. Whether the dividends "came from" borrowing is somewhat incoherent; money is fungible. So the only question is whether borrowing destroys value, not whether borrowing money when preceding a dividend destroys value.
In an efficient market, When a company borrows money, that does not affect stock price. Total value is increased, but liabilities are increased equally, so equity value remains constant. Responding to a question in the comments: if a company borrows $100m and now owes $110m in principal+interest, isn't their increase in liabilities ($110m) greater than their increase in total assets ($100m)? No, because their increase in total value is 100m of today dollars, and their increase in liabilities is 110m in tomorrow dollars. If the going interest rate is such that they have to pay $10m in interest, that means that the market has said that 110m tomorrow dollars have the same value as 100m today dollars, so their net book value is unchanged (again, this is assuming efficient markets). Interest is compensation for the risk level of the debt. The company loses money in the sense of paying interest, but it does so by offloading some of its risk onto lenders, and this lower risk level increases its value equal to the interest paid. Looked at another way, the company has money now, which it can apply to some current expenditure, and that expenditure will presumably give a return whose expected value is equal to the interest.
Comment: Wouldn't the debt come with an interest rate making the total amount borrowed different than the total amount to be repaid?  I'd say $100 cash and $0 debt is different from a valuation standpoint than $150 cash and $50 debt is... The difference may not be much but to say there's no difference is a bit of a leap.
Comment: @quid "... that expenditure will presumably give a return whose expected value is equal to the interest." Your question has already been answered.
Comment: @MikeScott Your 'presumably' assumes that no company has borrowed themselves into insolvency. Whether a new piece of debt decreases value for the company depends ultimately on whether it is financially healthy enough to pay the interest as charged.
Comment: @Grade'Eh'Bacon It's not my "presumably"; I was simply quoting the part of the answer where the question is addressed.
Answer: Money is fungible. That means that once my paycheck goes into my pocket, it becomes indistinguishable from the money I picked up off the ground. Often people will treat personal 'windfall' money (especially 'my tax refund', which is just the government paying you back money they over-withheld from you during the year) as money above-and-beyond their regular budget, but once the money has been earned, it is just money - and being responsible with a $500 paycheque and being irresponsible with a $500 tax rebate in the same month just means you were 50% responsible that month.
For a corporation, this remains true with a small caveat - was money borrowed with the express intent to pay the dividend? And why was that decided that way? Assume two cases:

Assume a company has multiple sources of financing, $10B of assets, and pays $100M of dividends per year. Some years, debt will overall go down, based on repayment structures, and various cash intakes through the years. Some years, debt will go up, based on new cash needs like capital investment, etc.. In a year where debt happened to go up by $1B, if that $100M of dividends remained constant, you could argue that the dividend was 'financed by debt', because with no dividend, the company maybe could have just borrowed $900M instead. But a financially healthy company will have its debt levels fluctuate, and it is largely pointless to tie 'this' financing to 'that' project.

The key here is that some level of debt is actually healthy in most industries. This is because debt is cheaper than equity, in the sense that debtholders might only want a 4% interest payment, but shareholders might expect a total return of 10%, between dividends and value growth of their shares. This remains true until so much debt is taken on that the company actually has insolvency risk, where it might possibly default on debt and have to declare bankruptcy.

Alternatively, assume a company is similarly positioned, has $10B of assets, and regularly pays $100M of dividends. Assume profit is down one year, cash reserves dry up, and it looks like paying the dividends won't be possible. Management has 2 options to try and keep the dividends constant - sell assets or take on debt. They take on $100M of debt. Now the same thing happens 2 years in a row. Suddenly 5 years later the company has an extra $1B in debt as a cash crunch starts to snowball, and interest rates they are getting become less favourable, and the risk of insolvency rises. In this case, every time they take on debt, their debt to equity ratio continues to rise, and they are ultimately becoming more and more risky from a potential bankruptcy perspective.

So, in cases where the company is not financially healthy to take on more debt, taking on debt to pay dividends, rather than responsibly deferring dividends for that year, could be a sign that management is unable to 'correct the ship' and bring the company back to profitibility.
It is not whether debt 'was used for' dividends [because fungible money means that is not truly a relevant concept], the key question is - can the company afford more debt at all, and is this dividend coming at the cost of insolvency risk? This comes back to your theory that taking debt increases interest costs and therefore might itself destroy value - that is only true if the debt is unaffordable, and otherwise could form part of a healthy mix of debt and equity financing. No single line item on the financial statements tells you whether something is good or bad, the context is relevant to understanding the impact of a particular item.
Comment: Very high level, I think this is philosophically right. The devil is in the details about running a company, however, and specifically the way different expenses are categorized -- i.e. a dollar spent on paying interest on a loan is not the same as a dollar spent on payroll is not the same as a dollar spent on purchasing land. Each of those will have different taxes levied on them, and depending on the locale of the business, spending them can be widely differently incentivized. To OP's query, it is very possible to imagine a scenario where borrowing to pay dividends may be very net positive.
Comment: Maybe not indistinguishable, if you cash your paycheck for Anthony dollar _coins_, which are used by essentially nobody except Federally-subsidized entities like transit systems and USPS. It is very unlikely money you found on the ground will be in this unpopular but still absolutely legal form :-}
Answer: Not inherently. If the company growth rate is greater than the interest rate there is no negative consequence. All good debt is good debt because you earn more from your investments than the cost servicing the debt. Bad debt is the opposite.
Interest rates have been very low for publicly traded companies, historical lows.
If a company's revenue stream is disrupted, and other capital sources are disrupted, then the debt will compound the issue. Dividends would likely have been cut long before then.
Answer: Companies borrow money all the time. It is a much easier source of cash, than having it floating around the company all the time. You should in general try to limit capital not in use, which then as a matter of fact also applies to cash. As long as the cash flow is positive, and the yearly result is positive, borrowing to pay dividend shouldn't be an issue at all. Cash - liabilities - obligations - assets - equity - it is all just capital you either have or owe in different grades of liquidity.
In a well balanced system there really is only a miniscule difference between the opportunity cost of having cash around, and the interest cost of borrowing it.


how to check database table permissions in java? (DataBase independently)

Question: Does anyone know a way (in java) to check permissions to a specific table for a user? It has to work on the most Databases. SELECT right is simple to check (just trying to execute a simple SELECT statement), but how to check INSERT permission?
Answer: You can use the DatabaseMetaData to get this information. It should work in most cases. However, it might be inaccurate in special cases, if the privileges can not be represented in this abstract way:
DatabaseMetaData metaData connection.getMetaData();
metaData.getTablePrivileges();
metaData.getColumnPrivileges();

Answer: though not a direct solution but the only option that comes to my mind is to use TRY CATCH blocks, issue an INSERT statement and then checking the error message in java.sql.SQLException  object returned in case of exception.
Comment: it is not a good idea for many reasons. For example, because there can be some triggers in database.


What is the difference between path and directory?

Question: I don't understand the difference between path and directory. Could someone explain to me with examples?
Comment: see this page: http://tldp.org/LDP/intro-linux/html/sect_03_01.html
Answer: A directory is a "folder", a place where you can put files or other directories (and special files, devices, symlinks...). It is a container for filesystem objects.
A path is a string that specify how to reach a filesystem object (and this object can be a file, a directory, a special file, ...).
Example: you have (probably, depending on your system) a file where system messages are logged, called syslog.
It normally sits in a directory named log which is contained in a directory named var which is in the root directory of your filesystem.
Now, /var/log/syslog is a path to that file (an absolute path in that case), as /var/log is a path to the directory that contains the file. /var/spool/../log/syslog is also a path to the syslog file too (if /var/spool exists).
Paths can be relative, too. So if your current directory is /home/user, the path ../../var/log/syslog is a relative path to the same file, too (you know it's relative because it doesn't start with /).
And in your home directory, if you create a symlink to /var/log like this:
ln -s /var/log myvarlog

then myvarlog/syslog is another path to our file.
Comment: Unfortunately, there is no way to know downvoters motivations. In any case, your answer is absolutely correct.
Comment: I'd like to know the reason for the downvotes. Is there something incorrect in the answer?
Answer: Directory is where you are.
Path is how to get there.
/var/www/public/site/pages/

pages is a directory
/var/www/public/site/pages/ is the path to files in that directory.  This is an absolute path.
/var/www/public/site/ is the path to that directory.
./pages/ may be a path to files in that directory, if you are currently working in /var/www/public/site/.  This is a relative path.
Comment: sorry but no. cwd is current working directory which means where you are.
Answer: On Linux, The terminology "directory" usually have two different meanings:
A. Unopened directory. Part of a "normal"(can be used to store data freely, like tmpfs or ext4, not used to expose kernel functionality, like procfs or sysfs) filesystem, usually consist of uniquely named pointers to other parts of the filesystem(other files or directories).
B. Open file description of a directory. A kernel object, which is a handler to A or some sort of interface to a kernel functionality.
The terminology "Path" is just a string which let you refer to one instance of A when constructing an instance of B.


How to Classify Documents whether they are similar to previous documents or not?

Question: I am a newbie in machine learning.I have 100 text documents.I need to build a model on those 100 text documents and if i give new documents it has to give whether this new document is similar to those 100 documents or not.Which is the best model for this problem?
Comment: If you want a binary response you need training data for a classifier, otherwise you can return the similarity according to some embedding. Even then training data helps because similarity is subjective.
Answer: Only way to check which is best model is to try different in practise and compare. Do you have any documents to train with that are not similar? Do you have labels or topics assigned to these 100 ?
Assuming you have some irrelevant documents you can use a "spam" approach to this type of problem.
I would begin with Bag of Words representing of your documents for a Naive Bayes model generation (common, good performing, baseline here) - this link http://sebastianraschka.com/Articles/2014_naive_bayes_1.html#naive-bayes-and-text-classification is a good explanation of this for documents .
I would also try using a library like Python gensim that will allow you to try its various methods, and you could try that library's Doc2Vec method. Then train a linear discriminant classifier like Log. Regression with the document vectors it gives you, and try see if its resulting accuracy is better than the Naive Bayes method.
Answer: The simplest method to test if a new document is like previous documents is to hash them and look for collisions. Hashing items put them into "buckets". If two items are in the same "bucket" (aka, collide), they are similar.
Generally, people use locality-sensitive hashing (LSH) for document similarity.
The process is:

Shingling - Pick a window size and slide the window over a document
MinHash - Compute the hashes of the text shingles a number of times and pick the minimum to reduce data size
LSH - Bucket items with the same MinHash values

Alternatively, you can compute the Jaccard Similarity between hashed documents and choose a similarity threshold.
The algorithm is covered in detail in Chapter 3/"Finding Similar Items" of Mining of Massive Datasets book.


How do you make std::shared_ptr not call delete()

Question: I have functions that take in std::shared_ptr as an argument so I am forced to use std::shared_ptr, but the object I am passing to the function is not dynamically allocated. How do I wrap the object in std::shared_ptr and have std::shared_ptr not call delete on it.
Comment: This is a horrible idea. The only reason for a function to accept a `shared_ptr` is if it intends to store a reference to the pointee (i.e., share ownership). Invalidating the object while that reference is stored somewhere will not go well. If the function in question does **not** store a reference, it should not accept an owning pointer type.
Comment: A use case for this is where you have something like `FILE *` where the type can either be managed (e.g. via `fopen`) or not (e.g. `stdin`) and you have a class that uses the object beyond the call that created it (e.g. creating a parser or logger). In that case, you would want to pass a "do nothing" deleter with stdin, but an `fclose` deleter with an `fopen`ed file.
Comment: @Casey A real life application I have come across where this idea makes sense is with a `shared_ptr`.  I may have a function that takes an ostream and stores a reference to it as a shared pointer for later use.  Now let's say I want to output to `std::cout`.  I cannot delete `std::cout`, but I can guarantee that it will exist for at least as long as my function will retain the shared pointer.
Comment: @KenLi Except that `std::shared_ptr` and `boost::shared_ptr` are virtually identical.
Comment: boost::shared_ptr was basically the prototype for what became std::shared_ptr.
Comment: @CortAmmon: Agree.  I came to this question from here: https://stackoverflow.com/questions/2159452/c-assign-cin-to-an-ifstream-variable  ... which is about passing `std:cin` or an opened file (`std::ifstream`).
Comment: possible duplicate of [How to release pointer from boost::shared\_ptr?](http://stackoverflow.com/questions/1525764/how-to-release-pointer-from-boostshared-ptr)
Comment: @WillDean not a duplicate, this question has nothing to do with boost library.
Answer: MyType t;
nasty_function(std::shared_ptr<MyType>(&t, [](MyType*){}));

Comment: Note:  Any function you pass a shared_ptr to might also grab ownership of the object, so the OP needs to make sure that either (a) that is not happening or (b) the lifetime of the object is longer than the lifetime of everything that has shared ownership of it.
Comment: @Angew: No coincidence. Just plain copy and paste. Demonstrates a more C++11ish alternative.
Answer: Specify a no-op deleter when creating the shared pointer. E.g. like this:
void null_deleter(MyType *) {}

int main()
{
  MyType t;
  nasty_function(std::shared_ptr<MyType>(&t, &null_deleter));
}

Answer: The best way to do this is to use the aliasing constructor:
nasty_function(std::shared_ptr<MyType>(std::shared_ptr<MyType>{}, &t));

Compared to the null deleter approach, this doesn't need to allocate a control block, and is noexcept.
As noted by @Casey and @Nevin, this should only be done when you are sure that the function won't attempt to take shared ownership, or if the object would outlive everything that might "own" it.
Comment: I just want to add a note about @T.C's answer using the aliasing constructor. If you use this technique, you will not be able to take a `std::weak_ptr` on the resulting `std::shared_ptr`.
Comment: Great hint.  As a note on versions: this is [a feature of Cx+11](http://www.codesynthesis.com/~boris/blog/2012/04/25/shared-ptr-aliasing-constructor/) but also available from boost 1.35 as `nasty_function(boost::shared_ptr (boost::shared_ptr(), &t));`
Comment: Does it mean that you have a `shared_ptr` without a control block?
Answer: Boost.Core provides a null_deleter function object exactly for this purpose.
Citing the documentation:

The header <boost/core/null_deleter.hpp> defines the boost::null_deleter function object, which can be used as a deleter with smart pointers such as unique_ptr or shared_ptr. The deleter doesn't do anything with the pointer provided upon deallocation, which makes it useful when the pointed object is deallocated elsewhere.

Example from the documentation:
std::shared_ptr< std::ostream > make_stream()
{
    return std::shared_ptr< std::ostream >(&std::cout, boost::null_deleter());
}

Comment: Alas, this still does not have appeared to made it into the std....
Answer: i was just searching for a solution, saw this question. found nothing and made a great one this is my code
class HBitmap : public shared_ptr<HBITMAP__>
{
public:
    HBitmap();
    HBitmap(HBITMAP Handle);
    bool autoDelete = true;
};

Win32::HBitmap::HBitmap(HBITMAP Handle)
: shared_ptr<HBITMAP__>(Handle, [&](HBITMAP hBitmap)  {if(autoDelete)DeleteObject(hBitmap);})
{
}

this solution is a combination of lambda expressions and inheritance.
very well formed. fast. you can't expect anything more. not only you can set the deleter, but if you do some modifications, you can use a std::function<void(pointer)> as a custom deleter. with lambdas you can run free and do what ever you want.
Answer: You can do this trick:
A a;
shared_ptr pa(&a);
foo(pa);
new (&pa) shared_ptr();  // pa "forgets" about a

Comment: Also, ignoring everything else, at a minimum you leak the control block.
Comment: Placement new to overwrite the pointer without calling its destructor. Clever. Purely academically (because the entire question is pretty horrible): any idea whether this has well-defined behaviour?
Comment: @Thomas Of course not. The second line is UB already (for breaking a Requires clause on the constructor); you don't even need the placement new.


Acyclic group and finite CW-complex

Question: Is there a nontrivial example of an acyclic group $G$ such that its corresponding Eilenberg space $K(G,1)$ is homotopy equivalent to a finite CW-complex ?
Comment: It would be helpful to say what you mean by "nontrivial". If it means "nontrivial group" I would move the adjective accordingly.
Answer: I presume by "acyclic" you are referring to homology with $\mathbb{Z}$ coefficients.  There are many such examples.
For instance, you can take two elements $u,v$ in the free group $F_2$ of rank 2 that satisfy the $C'(1/6)$ small-cancellation condition, and also such that $u,v$ together generate the abelianisation $\mathbb{Z}^2$.  Explicit examples are easy to construct.
The small-cancellation condition then implies that the corresponding presentation complex $X$ is aspherical, and the assumption about the abelianisation implies that $X$ has the homology of a point.  But $\pi_1X$ is an infinite hyperbolic group, in particular non-trivial.
Comment: @AndréHenriques Sure, take $F_2 = \langle a,b\rangle$. A suitable pair of elements is $a(aba^{-1}b^{-1})^5$ and $b^6a^2b^3a^{-1}b^{-8}a^{-1}$. I believe the longest common piece is $a^2b$, and $3$ is less than one sixth of the length of each word, which is cyclically reduced. Counting exponent sums, we see that they generate the abelianization.
Comment: If explicit examples are easy to construct, it might be worth constructing some explicit examples for the interested readers.
Comment: @AndréHenriques -- that would be a great thing to do, but unfortunately I don't have time.  If you click through to the wikipedia page, you'll see that small-cancellation conditions are quite explicit, and easy to fulfill, as Rylee's example shows.  Someone who's genuinely interested in answering the question won't have any difficulty building an infinite family of examples of presentations using this recipe (though it is a little trickier to show that you get infinitely many different isomorphism types).
Answer: The Higman group with presentation
$$\langle{a,b,c,d}\mid{aba^{-1}b^{-2}},~bcb^{-1}c^{-2},~cdc^{-1}d^{-2},~
dad^{-1}a^{-2}\rangle$$
is perfect, and the 2-complex associated to this presentation
has Euler characteristic 0. Hence this complex is acyclic.
It is in fact aspherical, but it may be simpler to observe that
Higman's group is also an iterated generalized free product with
amalgamations $(A*_{\langle{b}\rangle}B)*_{F(a,c)}(C*_{\langle{c}\rangle}D)$, where $A,B,C$ and $D$ are copies of the Baumslag-Solitar group $BS(1,2)$, generated by $\{a,b\}$, $\{b,c\}$, $\{c,d\}$ and $\{d,a\}$, respectively. We may assemble a 2-dimensional Eilenberg-Mac Lane complex for the Higman group in a similar way.

Acyclic group and finite CW-complex


Google has no datasheet for ACX502ALM-7 LCD/resistive touchpanel

Question: I have an ACX502ALM-7 series LCD+touchpanel combo. Google cannot find me a datasheet for it. Can any one of you? I'd like to possibly interface it (at least the touch screen part) to an Arduino Uno. Or do you know how to determine the pinout of the touchscreen? It's a 4-wire type.
Comment: Probably a simple resistive touch screen...
Comment: @Passerby, yeah.. but even that has a pinout, which I don't know? can I somehow measure it with a multimeter?
Answer: The four signals of the touch screen are TOP, BOTTOM, LEFT and RIGHT. In the touchscreen there are two resistive films and an insulator gap which is closed by your finger pushing the screen. At each edge there is a conductive stripe. TOP and BOTTOM stripes are connected to the first resistive film. LEFT and RIGHT stripes are connected to the second resistive film.
You can detect the pinout easily with a multimeter by measuring RESISTANCE between each pin pair and finding out the pairs to which the pressing of the finger affects to. When you find a pin pair to which your finger has a definitive effect, slide your finger upwards and then sidewards to find out if that's the vertical or horizontal film pair.
Answer: Majority of touch screens use simple resistive matrices for interfacing. The four wires work like a pair of potentiometers. As the screen is touched, the resistance changes. You measure this with a couple of analog input pins on your Arduino. You can also use a multimeter to test.
See  http://www.practicalarduino.com/projects/touch-control-panel for details.


Is there any work being done to create a C# compiler to produce native exe's?

Question: Is there any work being done to create a C# compiler to produce native exe's? e.g. the output is a native exe and NOT a .NET assembly.
Answer: If you want a standalone deployment (i.e. without needing the framework), there are a few options - see here. However, I'm not aware of anything that will reliably produce purely unmanaged code. What is the use-case you have in mind? For embedded etc there is micro-framework, CF, etc.
Answer: Why don't you try NGen. For exemple Paint.NET use nGen to create native images after installation.
Answer: There is such solution for Mono, this is 'mkbundle' - static linking instead of using JIT/CLR/GAC, I guess
Answer: You'd still have to provide the libraries in some form so either you'd still have to have a runtime installed, or the native exe would have to be huge.
Comment: The compiled exe size can be controlled by using split libs.
Answer: .NET linker
You might find this interesting to read as well: .NET Internals and Native Compiling.
Note that for the reflection to work a lot of information about the code will always have to present.
Answer: There are two active projects. They are geared toward CIL-based operating systems, but the current iteration of MOSA Compiler Framework runs on Windows (unit tests etc.) and has limited boot support. Cosmos used to have a Windows architecture and a few plugs, but they don't do Windows any more - only booting into a CIL environment.
Cosmos is much futher along however, they have pretty much nailed object support. MOSA is only bare-metal (static methods) for now - although it is done the 'proper' way and well unit-tested (and I think making faster progress). Give it a few more months and then go back and have a look.
Niether has a JIT at the moment (which doesn't matter since you don't want one). It is all compiled to machine code ahead of time.

MOSA (Compiler Framework)
COSMOS (IL2CPU)


Can the numerical method for a set of ordinary differential equations be non-conservative?

Question: I have a set of highly coupled ODE that I am solving. I'm just not understanding whether the quantities will be inherently conserved because it's an ODE. Everything I'm seeing on Google is for PDE's.
Comment: One such problem is integrating an orbit in a gravitational field.  We know that the energy and angular momentum are conserved in such problems.  If there are errors in the numerical integration, these constants may not be conserved.  I have heard there are integration techniques that deal with this, but am not familiar with them.
Comment: @RossMillikan : For conservative systems you can use symplectic integrators. They preserve the conserved quantities to at least the integration order, i.e., the drift away from a tightly oscillating near constant is slower than the order of the method. -- The most known and abused (in reducing it to symplectic Euler, not computing the force correctly,…) symplectic integrator is the Newton-Cromer-Störmer-Verlet method. See [Hairer et al.](http://www.unige.ch/~hairer/preprints) on [geometric numerical integration](http://www.math.mcgill.ca/~gantumur/docs/down/gniverlet.pdf)
Answer: Numerical methods for ODEs are more often than not found to be non-conservative when solving systems having conserved quantities. How non-conservative they are depends on things like the step-size, the order of the method and how long "time" you integrate over.
A typical example of this is found when numerically solving for plantary orbits (e.g. the Earth around the Sun). Below are some plots showing the numerical solution of such a system for different ODE solvers taken from this paper:

All three methods deviate from the true analytical solution (in blue) after enough orbits. If we look at the total energy, which should be conserved, we see that the last integrator conserves it very well while the first two don't:

Integrators that have this property is often called symplectic integrators. Such integrators can always be constructed for systems that derive from a Hamiltonian (as is often the case for physical systems).
If you are solving a system that have conserved quantities then monitoring the conservation of these is often a good way of checking the "goodness" of the numerical solution.


Downsampling fft results to a graphics display

Question: I'm new to dsp.  I've got a complex signal that was sampled at 192kHz then an fft of 16384 bins created.  This now needs to be plotted on a graph for a real time spectrum display.  The problem is if you want to plot the whole spectrum consisting of a 192kHz span, you will be plotting 16384 points on a display that many times will be 1600 pixels wide for example.  The result is you get an ugly mess on the screen.  So far I have been downsampling the signal by just plotting every 8th point. The problem is though, when I look at other spectrum displays that also perform 16384 fft's, they show much more data.  I have effectively dropped some on the peaks that the other software doesn't.
So the question is, how does one do the downsampling properly?
Thanks
Comment: You can also use what is sometimes called Polyphase FFT or Presum FFT. Here are some links: [link1](http://www.dxatlas.com/rocky/Advanced.asp), [link2](http://www.dsprelated.com/showmessage/45449/1.php), [link3](http://www.dsprelated.com/showmessage/123311/1.php).
Answer: Ok, here is the answer...hopefully this will help someone else.  Read this thesis:
http://skemman.is/stream/get/1946/15343/37285/3/SS_MSthesis.pdf
This gives a very easy and comprehensive overview of how to do just what I needed. I do believe this particular case is different than the usual downsampling. It fits the situation perfectly.
The thesis describes several methods of downsampling for display purposes. For example the practice of just dropping every nth sample, performing an average over the bucket of samples corresponding to the downsample ratio and more advanced methods.  The one I will be looking at is called Largest Triangle Three Bucket.
Basically you divide your original samples into buckets consisting of samples equal to your downsampling factor.  For example if you have a sample set of 10,000 points and you want to only display 2000, you will divide your original samples into 2000 buckets containing 5 sample each.
You then rank every point in the bucket by calculating the area of a triangle it forms
with the selected point in the last bucket and the average point in the next
bucket.
This seems to work really well in preserving the visual representation of data.
Comment: Could you please describe the parts of the thesis that are relevant to your question? The link could become invalid.


Mars be magneticly shielded

Question: Can Mars be magneticly shielded by Phobos placed in L1 point of Mars (between Mars and Sun)? Magnetic shield will aid in Martian atmosphere regrow.
Comment: There is a list of many magnetic shielding of Mars questions [here](https://space.stackexchange.com/a/27539/12102). The time scales are millions or billions of years so the benefit in the short term is minimal. It also requires *a source* for he magnetic field, does Phobos have a strong field? Also an orbit at or near L1 will suffer some instabilities, it may require a propulsion system to stay there long term.
Answer: Moving Phobos around takes an enormous amount of energy and as it does not have a magnetic field moving it to L1 wouldn't help anyway. Also, Phobos appears to be a rubble pile, so moving it is extremely difficult, it barely sticks together as it is and contains a significant amount of empty space. From Wikipedia: "The porosity of Phobos was calculated to be 30% ± 5%, or a quarter to a third being empty." Any force you apply to Phobos is likely to either simply compact it or break it up.
It might be better to invest that energy directly in building a magnetic field. This Japanese plan to build an artificial magnetic field for Earth makes more sense on Mars as it is much smaller, has no large seas and is geologically stable:
http://www.nifs.ac.jp/report/NIFS-886.pdf
Atmospheric erosion is an issue on geological timescales only; as such it is not relevant to terraforming or colonization. So there is no particular need to do any mega-projects to add magnetic shielding. Leave that for the technological capabilities of our descendants 100,000 years in the future.
Answer: Phobos is very small, 27km on its longest axis, so it wouldn't do much of anything to affect Mars no matter where it is.
Comment: you might want to add that a magnetic field is required and address if Phobos has one or not, and if it's strong enough. There is a list of many magnetic shielding of Mars questions [here](https://space.stackexchange.com/a/27539/12102), further information might be available in some of those posts.
Answer: To create a field like Earth's, you need to invest about $10^{20} J$ into creating the field (see this SE  Physics item). You might be able to save a couple factors of two, but that still leaves you needing something comparable to a year's entire energy output of the United States.
Interestingly, The mass of Phobos is about $10^{16} kg$, so the energy to lift it to L1 is somewhat comparable to the magnetic energy needed. So there's a possibility to go the other way around:  If Phobos was already at L1, could we drop it into a low orbit to get the energy needed to create a shielding field?
Comment: I think the idea of going to L1 is that you can shield Mars' atmosphere from much of the solar wind with a much smaller field at that point, than the field would have to be at the planet. I don't know *how much* smaller though.

Mars be magneticly shielded


Is it worth converting a steel frame Trek Roadie to a Cyclocross?

Question: I have a Trek Elance 330 from the 80s and love it!  However, I find myself needing something that can handle fire roads (gravel jeep paths) and am wondering if it is worth the effort.   Also, if it would result in an effective ride.  I am fine with the higher center of gravity, won't be doing any rock hopping, and won't be buying a new bike.  Has anyone converted their steel frame?  What experience can you share?  Thanks!  :)
Answer: I've done a conversion on an old steel Schwinn, and these look similar. I'm not sure how in-depth you want to go, but at the most basic level you only have to worry about two issues:

Tire clearance
Brake clearance

Tire Clearance
The most popular size of cyclocross tire is 700x32. You may find that a knobby cyclocross tire will fit between your fork, but not clear the bottom bracket or chainstays in the rear triangle or vice versa. If you have a tire clearance issue with the rear triangle I would abandon hope right then. If the rear is fine but the front is tight, you can consider a new fork.
Brake clearance
The brakes on that bike may not have arms that are wide enough or long enough to properly place the pads on the rim without touching the tire. IF that's the case you can check a touring source like Rivendell for brakes with longer, curvy arms.
Note: If the bike came with 27 inch rims, you may have a hard time finding tires and your clearance issues may be even tighter. If that's the case you can look at switching to 700 wheels, but you may find on an older bike that it expects a narrower hub. With a steel frame  you can consider carefully bending the forks.
Is it worth it?
Well - to me it's worth it if you will ride it. Start with the tires - that's the cheapest first step. Move on to brakes and fork only if you have to.
Comment: If the frame is structurally sound now, I wouldn't worry about it much. As long as you are sticking to fire roads and good condition single/double track you should be fine. If you find your self bunny-hopping a lot or dropping more than a typical city curb then I would be sure to inspect the frame joints frequently.
Comment: Fantastic!  Thanks for the Rivendell link!  The bike has 700 wheels, as Benzo mentions below.  A new fork is a great idea, I was thinking of one with suspension, but am worried about stress on the frame.  Is that a valid concern in your opinion?
Answer: On first thought, I would say NO due to the lack of cantilever brake mounts. Caliper brakes which come on this bike limit tire choice a lot.  But if you don't plan to do traditional cross racing and are just looking to ride this bike on fire roads and gravel paths, then I think you can make it work fine.  The issues you'd have in a cross race would be dealing with a buildup of mud and leaves between your tire and brake / fork and it may be harder to get traction on loose ground, mud, and sand.
However, this bike originally shipped with 700x28c tires, so you may be able to bump up the tire size a little bit.  You may want to try some 700x30c tires like Michelin Mud Cross tires. Even if you can't get bigger tires squeezed in there, I take my road bike with 700x28 tires on this kind of terrain all the time, so just go with the biggest thing you can fit. You'll enjoy the ride a lot more on fat tires.
You could also consider throwing on some Tektro R539 brakes which should clear 32c tires if your current brakes don't. This is what ships on the All-city Mr. Pink which claims 32c clearance.
Here's a great link to a vintage trek catalog with the orignal specs for the bike:
http://www.vintage-trek.com/TrekBrochure1987.htm
Comment: No racing here, just long distance riding.  Do you have knobbies on your road bike?  Isn't that a great brochure!
Comment: I have some ritchey speedmax cross tires which I sometimes ride on my road bike. Otherwise I try to wing it on my Panaracer t-serv tires which have a less aggressive tread.  That brocure is an awesome retro find.