Question:
I am at an international conference (ICIAM2019) about numerical methods and am surprised by the prevalence of applications directly relatable to arms research.
examples:

One award winner holds his talk about the mathematical problem of radar reconstruction/detection of moving objects, within his talk he describes the situation of a radar "platform" in 8km height using active radar detecting "moving subjects" at ground level, and he goes on about how magnificently tricky this problem is.
people are presenting methods to accurately resolve and simulate shockwaves, and a quick google search reveals that they are working on "inertial confinement fusion".
at after-conference dinner I sat next to people doing numerics in Los Alamos.

I am doing my phd in applied math and numerical methods, and to be honest, I did not anticipate that the people receiving awards and are put on the large stages are doing arms research. I also noticed that the audience, which is presumably smarter than me, is applauding this work.
I am wondering whether or not I would want to be part of this community, and if it is possible to build a career in applied math without directly or indirectly contributing to arms research. Is this something that is shrugged of? I am at a very early stage and would be very grateful for advice from the more experienced folks.

TL;DR:

It is certainly possible to build a career in applied math and computational sciences without directly contributing to arms research.
It is hardly possible to build a career in any research without indirectly contributing to arms research.

One can easily avoid direct contributions to military topics by choosing more abstract mathematical topics, carefully selecting numerical/measurement experiments, applying (actually, not applying) for the particular grants, etc. In this way, a researcher can build a very successful career without direct arms contributions.
Now, due to the nature of computational sciences, this research can be of extreme interest for advancing military technology. Developing an abstract applied mathematical method might contribute (without you realizing it) to a certain military application.
It is certainly true that the research from STEM fields is especially prone to potential military usage. However, that is not limited to STEM. Arts, humanities, and all other research can (and did!) potentially contribute to the advances of arms, directly or indirectly.
The simplest example of indirect contibution that is totally outside of your control:

As a professor, you developed an extremely popular course in numerical methods/philosophy of science/history of art. One of your students successfully finished it and decided to apply to arms research. Now you indirectly contributed to this research by providing your passion, materials, and time.

It is easy and possible to find examples of more "direct" indirect contributions. Say, the study of the art of Kukryniksy can lead to more efficient propaganda methodologies.
I, personally, very appreciate the ethical concerns. And the question of research ethics has become quite a hot topic in recent years. I would not discuss if it is ethical to do research that directly contributes to and targets military applications. It is a choice of the particular researcher that we should, at least, respect. But I will point out that potential indirect contributions to military applications are inevitable for any research field. Moreover, the safest way to not contribute to arms is to do nothing, which is obviously a bad solution altogether.


Question:
I have trouble distinguishing between these two concepts. This is my understanding so far.
A stationary process is a stochastic process whose statistical properties do not change with time. For a strict-sense stationary process, this means that its joint probability distribution is constant; for a wide-sense stationary process, this means that its 1st and 2nd moments are constant.
An ergodic process is one where its statistical properties, like variance, can be deduced from a sufficiently long sample. E.g., the sample mean converges to the true mean of the signal, if you average long enough.
Now, it seems to me that a signal would have to be stationary, in order to be ergodic.

And what kinds of signals could be stationary, but not ergodic?
If a signal has the same variance for all time, for example, how could the time-averaged variance not converge to the true value?
So, what is the real distinction between these two concepts?
Can you give me an example of a process that is stationary without being ergodic, or ergodic without being stationary?

A random process is a collection of random variables, one for each time instant under consideration.  Typically this may be continuous time ($-\infty < t < \infty$) or discrete time (all integers $n$, or all time instants $nT$ where $T$ is the sample interval).

Stationarity refers to the distributions of the random variables. Specifically, in a stationary process, all the random variables have the same distribution function, and more generally, for every positive integer $n$ and $n$ time instants $t_1, t_2, \ldots, t_n$, the joint distribution of the $n$ random variables $X(t_1), X(t_2), \cdots, X(t_n)$ is the same as the joint distribution of $X(t_1+\tau), X(t_2+\tau), \cdots, X(t_n+\tau)$.  That is, if we shift all time instants by $\tau$, the statistical description of the process does not change at all: the process is stationary.
Ergodicity, on the other hand, doesn't look at statistical properties of the random variables but at the sample paths, i.e. what you observe physically. Referring back to the random variables, recall that random variables are mappings from a sample space to the real numbers; each outcome is mapped onto a real number, and different random variables will typically map any given outcome to different numbers.  So, imagine that some higher being as performed the experiment which has resulted in an outcome $\omega$ in the sample space, and this outcome has been mapped onto (typically different) real numbers by all the random variables in the process: specifically, the random variable $X(t)$ has mapped $\omega$ to a real number we shall denote as $x(t)$. The numbers $x(t)$, regarded as a waveform, are the sample path corresponding to $\omega$, and different outcomes will give us different sample paths. Ergodicity then deals with properties of the sample paths and how these properties relate to the properties of the random variables comprising the random process.

Now, for a sample path $x(t)$ from a stationary process, we can compute the time average
$$\bar{x} = \frac{1}{2T} \int_{-T}^T x(t) \,\mathrm dt$$  but, what does $\bar{x}$ have to do with $\mu = E[X(t)]$, the mean of the random process? (Note that it doesn't matter which value of $t$ we use; all the random variables have the same distribution and so have the same mean (if the mean exists)).  As the OP says, the average value  or DC component of a sample path converges to the mean value of the process if the sample path is observed long enough, provided the process is ergodic and stationary, etc.  That is, ergodicity is what enables us to connect the results of the two calculations and to assert that
$$\lim_{T\to \infty}\bar{x} = \lim_{T\to \infty}\frac{1}{2T} \int_{-T}^T x(t) \,\mathrm dt ~~~
\textbf{equals}  ~~~\mu = E[X(t)] = \int_{-\infty}^\infty uf_X(u) \,\mathrm du.$$  A process for which such equality holds is said to be mean-ergodic, and a process is mean-ergodic if its autocovariance function $C_X(\tau)$ has the property:
$$\lim_{T\to\infty}\frac{1}{2T}\int_{-T}^T C_X(\tau) \mathrm d\tau = 0.$$
Thus, not all stationary processes need be mean-ergodic. But there are other forms of ergodicity too. For example, for an autocovariance-ergodic process, the autocovariance function of a finite segment (say for $t\in (-T, T)$ of the sample path $x(t)$ converges to the autocovariance function $C_X(\tau)$ of the process as $T\to \infty$. A blanket statement that a process is ergodic might mean any of the various forms or it might mean a specific form; one just can't tell,
As an example of the difference between the two concepts, suppose that $X(t) = Y$ for all $t$ under consideration.  Here $Y$ is a random variable. This is a stationary process: each $X(t)$ has the same distribution (namely, the distribution of $Y$), same mean
$E[X(t)] = E[Y]$, same variance etc.;
each $X(t_1)$ and $X(t_2)$ have the same
joint distribution (though it is degenerate) and so on.  But the process is not
ergodic because each sample path is a constant.  Specifically, if a trial
of the experiment
(as performed by you, or by a superior being) results in $Y$ having
value $\alpha$, then the sample path of the random process that corresponds
to this experimental outcome has value $\alpha$ for all $t$, and the DC
value of the sample path is $\alpha$, not $E[X(t)] = E[Y]$, no matter how
long you observe the (rather boring) sample path.  In a parallel universe,
the trial would result in $Y = \beta$ and the sample path in that
universe would have value $\beta$ for all $t$.
It is not easy to write mathematical specifications to
exclude such trivialities from the class of stationary processes, and so this is a very minimal example of a stationary random process that is not ergodic.
Can there be a random process that is not stationary but is ergodic? Well, NO, not if by ergodic we mean ergodic in every possible way one can think of: for example, if we measure the fraction of time during which a long segment of the sample path $x(t)$ has value at most $\alpha$, this is a good estimate of $P(X(t) \leq \alpha) = F_X(\alpha)$, the value of the (common) CDF $F_X$ of the $X(t)$'s at $\alpha$ if the process is assumed to be ergodic with respect to the distribution  functions.  But, we can have random processes that are not stationary but are nonetheless mean-ergodic and autocovariance-ergodic.  For example, consider the process
$\{X(t)\colon X(t)= \cos (t + \Theta), -\infty < t < \infty\}$
where $\Theta$ takes on four equally likely values $0, \pi/2, \pi$ and $3\pi/2$.
Note that each $X(t)$ is a discrete random variable that, in general, takes on four equally likely values $\cos(t), \cos(t+\pi/2)=-\sin(t), \cos(t+\pi) = -\cos(t)$ and $\cos(t+3\pi/2)=\sin(t)$,  It is easy to see that in general $X(t)$ and $X(s)$ have different distributions, and so the process is not even first-order stationary. On the other hand,
$$E[X(t)] = \frac 14\cos(t)+
\frac 14(-\sin(t)) + \frac 14(-\cos(t))+\frac 14 \sin(t)  = 0$$ for every $t$ while
\begin{align}
E[X(t)X(s)]&= \left.\left.\frac 14\right[\cos(t)\cos(s) +  (-\cos(t))(-\cos(s)) + \sin(t)\sin(s) + (-\sin(t))(-\sin(s))\right]\\
&= \left.\left.\frac 12\right[\cos(t)\cos(s) + \sin(t)\sin(s)\right]\\
&= \frac 12 \cos(t-s).
\end{align}
In short, the process has zero mean and its autocorrelation (and autocovariance) function depends only on the time difference $t-s$, and so the process is wide sense stationary. But it is not first-order stationary and so cannot be
stationary to higher orders either. Now, when the experiment is performed and the value of $\Theta$ is known, we get the sample function which clearly must be one of $\pm \cos(t)$ and $\pm \sin(t)$ which have DC value $0$ which equals $0$, and whose autocorrelation function is $\frac 12 \cos(\tau)$, same as $R_X(\tau)$, and so this process is mean-ergodic and autocorrelation-ergodic even though it is not stationary at all. In closing, I remark that the process is  not ergodic with respect to the distribution function, that is, it cannot be said to be ergodic in all respects.


Question:
I was reading this article on researching bacteria resistance to silver by removing some of their genes.

Researchers then used "colony-scoring" software to measure the differences in growth and size of each plate's bacterial colony. E. coli strains with genes deleted involved in producing sensitivity, or toxicity, to silver grew larger colonies. Strains with genes deleted involved with resistance grew smaller colonies.

Once you end up with some resistant bacteria and you're done researching it, you can't just flush it down the toilet. How do you safely dispose those colony plates in a way that ensures those bacteria don't get out into the wild and reproduce?

You are absolutely right, flushing down the toilet (or the sink) or simply throwing them into the normal waste doesn't work for biosafety reasons. And it is also not allowed, depending on the country you would do this in, this can lead to hefty fines.
Biologically contaminated lab waste can be inactivated (=all potential dangerous organisms are destroyed) by two ways: Either by heat or chemically. Which ways is used, depends on the kind of waste.
The most commonly used way is autoclaving, meaning treating the waste with steam at high temperatures at higher pressure. The temperature used here is usually 121°C, the exposure time depends on the volume of the waste, since the temperature needs to be reached and kept for at least 20 minutes. See the references for more details.
Liquid wastes (like culture media) can also be inactivated chemically by adding chlorine bleach to decompose the cells. Bleach can also be used to decontaminate surfaces, although here more often alcoholic solutions (70% Ethanol or Isopropanol) are used. After chemical inactivation, the remaining solutions should not be autoclaved as the emerging fumes are either unhealthy (bleach) or explosive (alcoholic solutions) and this is unnecessary, too.
Liquid wastes can also be autoclaved to inactivate them.
Autoclaving has the main advantage that it is rather simple (put the waste into the autoclave, close it and run a appropriate program), the waste can afterwards simply be discarded as normal waste, which may not be the case for chemically inactivated waste, which may need special precaution for disposal.
References:

Decontamination and Sterilization
Decontamination of laboratory microbiological waste by steam
sterilization.
TECHNIQUES FOR STEAM STERILIZING LABORATORY WASTE
Decontamination of Laboratory Microbiological Wasteby Steam Sterilization


Question:
Many of us have experienced the failure of nitrile gloves when exposed to chloroform. What's going on at a mechanistic level when this occurs?
I would guess that the chloroform dissolves some of the polymer into its constituent monomers, but I've never heard anything more definite than that. Is it a similar mechanism to what happens when chloroform is left too long in a plastic bottle?

Nitrile gloves are made of nitrile rubber, or poly(butadiene/acrylonitrile). This polymer is highly soluble in chloroform, with some papers I found indicating that one can dissolve up to 18% in mass of nitrile butadiene rubber in chloroform. Moreover, it permeates easily through NBR, meaning we can expect the dissolution to be fast in addition to thermodynamically
favourable.
Finally, I would not expect the mechanism here to be any different from that of any polymer dissolution by a good solvent. The solvent will permeate through the polymer, intercalate between polymer chains, and solvate them (inducing swelling). Once solvated, the network of polymer chains looses its mechanical properties and they can fully separate. (I wish I could find a good existing illustration for that part, but I can't right now… If anyone can, feel free to edit!)


Question:
It is well known (the simplest textbook example) that a diamond has a well-defined arrangement of sp3 carbon atoms, as each atom is connected to four others in a tetrahedral structure.
But what about the last carbon atoms at the edge? For each of these, three bonds are missing; it has a single bond with one carbon atom inside the structure. What is the hybrid and atomic (electron) structure of the carbon atoms at the edge?
I would appreciate some references explaining this in detail (books or research articles).

Atoms at the edge of a crystal that have an unsatisfied valence are said to have "dangling bonds."  Many elements, in addition to carbon, can have dangling bonds.  Dangling bonds is a subject of current interest because of the impact these structures can have on semiconductor properties.
These dangling bonds are very similar to free radicals, except since they are immobilized in a solid, they are somewhat less reactive than free radicals in solution. Nonetheless, they can react with whatever materials they are exposed to, such as hydrogen, water vapor, oxygen, etc. In addition, if there is a neighboring dangling bond then they can both react with one another to form a bond and satisfy there valence.
When carbon or silicon surfaces are prepared under clean room conditions, the dangling bonds can persist.  In the semiconductor industry this clean room preparation technique is followed by bringing in a doping gas in order to purposefully alter the electronic band structure of the substrate material.
Since unpaired electrons have magnetic properties, in carbon (or any other element) nanostructures where there is a lot more surface area to volume, the concentration of dangling bonds is much higher.  Consequently, the unpaired electrons in the dangling bonds confer magnetic properties on these materials that are large enough to be easily  detectable and to manipulate.
Finally, since dangling bonds represent a non-equilibrium situation, surfaces containing dangling bonds undergo a relaxation or reshaping that is referred to as "surface reconstruction."
Here is a full-text article that should help you get started:
1) Structure of the diamond 111 surface: Single-dangling-bond versus triple-dangling-bond face


Question:
I awoke with the following puzzle that I would like to investigate, but the answer may require some programming (it may not either).  I have asked on the meta site and believe the question to be suitable and hopefully interesting for the community.
I will try to explain the puzzle as best I can then detail the questions I am interested in after.
Imagine squared paper.  In one square write the number $1.$  Continue to write numbers from left to right (as normal) until you reach a prime.  The next number after a prime should be written in the square located $90$ degrees clockwise to the last.  You then continue writing numbers in that direction. This procedure should be continued indefinitely.
Here is a sample  of the grid:
$$\begin{array}{} 7&8&9&10&11&40&41 \\6&1&2&&12&&42\\5&4&3&14&13&44&43\\&&34&&26\\&&33&&27\\&&32&&28\\&&31&30&29\end{array}$$
Note that the square containing 3 also contains 15 (I couldn't put it in without confusing the diagram.  In fact some squares contain multiple entries.
I would have liked to see an expanded version of the diagram.  I originally thought of shading squares that contain at least one number.
Questions
Does the square surrounded by $2,3,9,10,11,12,13,14$ ever get shaded?
If so, will the whole grid ever be shaded?
Is there a maximum number of times a square can be visited?  I have got to 4 times but it is easy to make mistakes by hand.
Are there any repeated patterns in the gaps?
I have other ideas but this is enough for now as I have genuinely no idea how easy or difficult this problem is.
Please forgive me for not taking it any further as it is so easy to make mistakes.
I hope this is interesting for the community and look forwards to any results.
Thanks.
Any questions I'll do my best to clarify.
Side note: I observed that initially at least the pattern likes to cling to itself but I suspect it doesn't later on.

Just for visual amusement, here are more pictures. In all cases, initial point is a large red dot.
Primes up to $10^5$:

Primes up to $10^6$:

Primes up to $10^6$ starting gaps of length $>6$:

Primes up to $10^7$ starting gaps of length $>10$:

Primes up to $10^8$ starting gaps of length $>60$:

For anyone interested, all the images were generated using Sage and variations of the following code:
d = 1
p = 0
M = []
prim = prime_range(10^8)
diff = []
for i in range(len(prim)-1):
    diff.append(prim[i+1]-prim[i])
for k in diff:
    if k>60:
        M.append(p)
    d = -d*I
    p = p+k*d
save(list_plot(M,aspect_ratio = 1,axes = false,pointsize = 1,figsize = 20)+point((0,0),color = 'red'),'8s.png')


Question:
Developers of software have the choice to choose an appropriate license in accordance with the goal(s) of the work.
Can anyone give some recommendations/experiences on which license to pick for software?
What are the pros/cons of "giving away" all the coded work as open source codes?
How to deal with industrial players which would like to benefit from the research code?

Can anyone give some recommendations/experiences on which license to pick for software?

Which license you chose will depend on how free you want your code to be, but free means different things to different people.

For proponents of permissive licenses, free means allowing people now to use the software however they want to right now, not worrying about how free  future derivation are.
For proponents of copyleft licenses, free means ensuring that the software and any derivation of it stays free, being prepared to sacrifice some immediate freedoms to ensure that.

The more permissive a license is, the more people will be able to use it, but the less control you have over it. The more restrictive it is though, the more likely you are to put people off using your software in the first place.
There are a number of free and open source licenses out there, including GPL <=2, GPL 3, LGPL, BSD, Eclipse and so on. There are pro's and cons to each, so read up on what restrictions they place on the code and decide who you want to be able to use it. Warning, whichever you choose someone will complain - this is holy war territory.
Overall it is a subtle balancing act, and it depends very much on the target audience for your software.

A great resource for determining which license is the right license for you is the very comprehensive, interactive license differentiator, from Oxford Universities OSS Watch.

In my opinion, both permissive and copyleft licenses are appropriate for scientific code - the important thing is that the code is open source in the first place. I believe that Science should be Open, and so should the code used to support that science.

What are the pros/cons of "giving away" all the coded work as open source codes?

The idea of giving away your software is that if others find it useful then they will use it.
If they use it they will find, report and often fix bugs, saving your effort of doing the same.
If they like it and your software does almost what they want, they might enhance your software and contribute those enhancements back.
That's a lot of ifs though.

How to deal with industrial players which would like to benefit from the research code?

Firstly, if you want to prohibit commercial use of your code, you can select a license with a no commercial re-use clause.
Secondly, if you think someone might use your software to power a service, without ever actually distributing the code to anyone else, then you could consider the Affero GPL which plugs that particular copyleft loophole.
Thirdly, you can do the above and offer a dual license option. Offering GPL or AGPL licenses for public download, and commercial licenses for a fee gives you the best of both worlds, and means that you might even be able to generate some revenue from commercial sales of your software which can help support your scientific activities.
Note, if you are going to do this, offer it from the outset - that is likely to cause less friction from your open source contributors than starting to offer commercial licenses later on. If your community becomes popular, you don't want people accusing you of selling out if you weren't straight about the possibility of commercial exploitation later. Ideally you should set up a suitable Contributor License Agreement (CLA) before you start accepting third party contributions into your codebase.
This answer to this question provides some good information on this option too.


Question: As the title says. It is common sense that sharp things cut, but how do they work at the atomical level?

For organic matter, such as bread and human skin, cutting is a straightforward process because cells/tissues/proteins/etc can be broken apart with relatively little energy. This is because organic matter is much more flexible and the molecules  bind through weak intermolecular interactions such as hydrogen bonding and van der Waals forces.
For inorganic matter, however, it's much more complicated. It can be studied experimentally, e.g. via nanoindentation+AFM experiments, but much of the insight we have actually comes from computer simulations.
For instance, here is an image taken from a molecular dynamics study where they cut copper (blue) with different shaped blades (red):

In each case the blade penetrates the right side of the block and is dragged to the left. You can see the atoms amorphise in the immediate vicinity due to the high pressure and then deform around the blade. This is a basic answer to your question.
But there are some more complicated mechanisms at play. For a material to deform it must be able to generate dislocations that can then propagate through the material. Here is a much larger-scale ($10^7$ atoms) molecular dynamics simulation of a blade being dragged (to the left) along the surface of copper. The blue regions show the dislocations:

That blue ring that travels through the bulk along [10-1] is a dislocation loop.
If these dislocations encounter a grain boundary then it takes more energy to move them which makes the material harder. For this reason, many materials (such as metals, which are soft) are intentionally manufactured to be grainy.
There can also be some rather exotic mechanisms involved. Here is an image from a recent Nature paper in which a nano-tip is forced into calcite (a very hard but brittle material):

What's really interesting about it is that, initially, crystal twins form (visible in Stage 1) in order to dissipate the energy - this involves layers of the crystal changing their orientation to accommodate the strain - before cracking and ultimately amorphising.
In short: it's complicated but very interesting!


Question:
I've been looking into the math behind converting from any base to any base. This is more about confirming my results than anything. I found what seems to be my answer on mathforum.org  but I'm still not sure if I have it right. I have the converting from a larger base to a smaller base down okay because it is simply take first digit multiply by base you want add next digit repeat. My problem comes when converting from a smaller base to a larger base. When doing this they talk about how you need to convert the larger base you want into the smaller base you have. An example would be going from base 4 to base 6 you need to convert the number 6 into base 4 getting 12. You then just do the same thing as you did when you were converting from large to small. The difficulty I have with this is it seems you need to know what one number is in the other base. So I would of needed to know what 6 is in base 4. This creates a big problem in my mind because then I would need a table. Does anyone know a way of doing this in a better fashion.
I thought a base conversion would help but I can't find any that work. And from the site I found it seems to allow you to convert from base to base without going through base 10 but you first need to know how to convert the first number from base to base. That makes it kinda pointless.
Commenters are saying I need to be able to convert a letter into a number. If so I already know that. That isn't my problem however.
My problem is in order to convert a big base to a small base I need to first convert the base number I have into the base number I want. In doing this I defeat the purpose because if I have the ability to convert these bases to other bases I've already solved my problem.
Edit: I have figured out how to convert from bases less than or equal to 10 into other bases less than or equal to 10. I can also go from a base greater than 10 to any base that is 10 or less. The problem starts when converting from a base greater than 10 to another base greater than 10. Or going from a base smaller than 10 to a base greater than 10. I don't need code I just need the basic math behind it that can be applied to code.

This seems a very basic question to me, so excuse me if I lecture you a bit. The most important point for you to learn here is that a number is not its digit representation. A number is an abstract mathematical object, whereas its digit representation is a concrete thing, namely a sequence of symbols on a paper (or a sequence of bits in compute memory, or a sequence of sounds which you make when you communicate a number). What is confusing you is the fact that you never see a number but always its digit representation. So you end up thinking that the number is the representation.
Therefore, the question to ask is not "how do I convert from one base to another" but rather "how do I find out which number is represented by a given string of digits" and "how do I find the digit representation of a given number". Once we have the answers, it will be easy to answer the original question, too.
So let us produce two functions in Python, one for converting a digit representation to a number, and another for doing the opposite. Note: when we run the function Python will of course print on the screen the number it got in base 10. But this does not mean that the computer is keeping numbers in base 10 (it isn't). It is irrelevant how the computer represents the numbers.
def toDigits(n, b):
    """Convert a positive number n to its digit representation in base b."""
    digits = []
    while n > 0:
        digits.insert(0, n % b)
        n  = n // b
    return digits

def fromDigits(digits, b):
    """Compute the number given by digits in base b."""
    n = 0
    for d in digits:
        n = b * n + d
    return n

Let us test these:
>>> toDigits(42, 2)
[1, 0, 1, 0, 1, 0]
>>> toDigits(42, 3)
[1, 1, 2, 0]
>>> fromDigits([1,1,2,0],3)
42

Armed with conversion functions, your problem is solved easily:
def convertBase(digits, b, c):
    """Convert the digits representation of a number from base b to base c."""
    return toDigits(fromDigits(digits, b), c)

A test:
>>> convertBase([1,1,2,0], 3, 2)
[1, 0, 1, 0, 1, 0]

Note: we did not pass through base 10 representation! We converted the base $b$ representation to the number, and then the number to base $c$. The number was not in any representation. (Actually it was, the computer had to represent it somehow, and it did represent it using electrical signals and funky stuff that happens in chips, but certainly those were not 0's and 1's.)


Question:
When searching graphs, there are two easy algorithms: breadth-first and depth-first (Usually done by adding all adjactent graph nodes to a queue (breadth-first) or stack (depth-first)).
Now, are there any advantages of one over another?
The ones I could think of:

If you expect your data to be pretty far down inside the graph, depth-first might find it earlier, as you are going down into the deeper parts of the graph very fast.
Conversely, if you expect your data to be pretty far up in the graph, breadth-first might give the result earlier.

Is there anything I have missed or does it mostly come down to personal preference?

I'd like to quote an answer from Stack Overflow by hstoerr which covers the problem nicely:

That heavily depends on the structure of the search tree and the number and location of solutions.
   If you know a solution is not far from the root of the tree, a breadth first search (BFS) might be better. If the tree is very deep and solutions are rare, depth first search (DFS) might rootle around forever, but BFS could be faster. If the tree is very wide, a BFS might need too much more memory, so it might be completely impractical. If solutions are frequent but located deep in the tree, BFS could be impractical. If the search tree is very deep you will need to restrict the search depth for depth first search (DFS), anyway (for example with iterative deepening).
But these are just rules of thumb; you'll probably need to experiment.

Rafał Dowgird also remarks:

Some algorithms depend on particular properties of DFS (or BFS) to work. For example the Hopcroft and Tarjan algorithm for finding 2-connected components takes advantage of the fact that each already visited node encountered by DFS is on the path from root to the currently explored node.


Question:
The Feynman lectures are universally admired, it seems, but also a half-century old.
Taking them as a source for self-study, what compensation for their age, if any, should today's reader undertake?  I'm interested both in pointers to particular topics where the physics itself is out-of-date, or topics where the pedagogical approach now admits attestable improvements.

The Feynman Lectures need only a little amending, but it's a relatively small amount compared to any other textbook. The great advantage of the Feynman Lectures is that everything is worked out from scratch Feynman's way, so that it is taught with the maximum insight, something that you can only do after you sit down and redo the old calculations from scratch. This makes them very interesting, because you learn from Feynman how the discovering gets done, the type of reasoning, the physical intuition, and so on.
The original presentation also makes it that Feynman says all sorts of things in a slightly different way than other books. This is good to test your understanding, because if you only know something in a half-assed way, Feynman sounds wrong. I remember that when I first read it a million years ago, a large fraction of the things he said sounded completely wrong. This original presentation is a very important component: it teaches you what originality sounds like, and knowing how to be original is the most important thing.
I think Vol. I is pretty much OK as an intro, although it should be supplemented at least with this stuff:

Computational integration: Feynman does something marvellous at the start of Volume I (something unheard of in 1964), he describes how to Euler time-step a differential equation forward in time. Nowadays, it is a simple thing to numerically integrate any mechanical problem, and experience with numerical integration is essential for students. The integration removes the student's paralysis: when you are staring at an equation and don't know what to do. If you have a computer, you know exactly what to do! Integrating reveals many interesting qualitative things, and shows you just how soon the analytical knowledge painstakingly acquired over 4 centuries craps out. For example, even if you didn't know it, you can see the KAM stability appears spontaneously in self-gravitating clusters at a surprisingly large number of particles. You might expect chaotic motion until you reach 2 particles, which then orbit in an ellipse. But clusters with random masses and velocities of some hundreds of particles eject out particles like crazy, until they get to one or two dozen particles, and then they settle down into a mess of orbits, but this mess must be integrable, because nothing else is ejected out anymore! You discover many things like this from piddling around with particle simulations, and this is something which is missing from Volume I, since computers were not available at the time it was written. It's not completely missing, however, and it's much worse elsewhere.
The Kepler problem: Feynman has an interesting point of view regarding this which is published in the "Lost Lecture" book and audio-book. But I think the standard methods are better here, because the 17th century things Feynman redoes are too specific to this one problem. This can be supplemented in any book on analytical mechanics.
Thermodynamics: The section on thermodynamics does everything through statistical mechanics and intuition. This begins with the density of the atmosphere, which motivates the Boltzmann distribution, which is then used to derive all sorts of things, culminating in the Clausius-Clayperon equation. This is a great boon when thinking about atoms, but it doesn't teach you the classical thermodynamics, which is really simple starting from modern stat-mech. The position is that the Boltzmann distribution is all you need to know, and that's a little backwards from my perspective. The maximum entropy arguments are better--- they motivate the Boltzmann distribution. The heat-engine he uses is based on rubber-bands too, and yet there is no discussion of why rubber bands are entropic, or of free-energies in the rubber band, or the dependence of stiffness on temperature.
Monte-Carlo simulation: This is essential, but it obviously requires computers. With Monte-Carlo you can make snapshots of classical statistical systems quickly on a computer and build up intuition. You can make simulations of liquids, and see how the atoms knock around classically. You can simulate rubber-band polymers, and see the stiffness dependence on temperature. All these things are clearly there in Feynman's head, but without a computer, it's hard to transmit it into any of the students' heads.

For Volume II, the most serious problem is that the foundations are off. Feynman said he wanted to redo the classical textbook point of view on E&M, but he wasn't sure how to do it. The Feynman Lectures were written at a time just before modern gauge theory took off, and while they emphasize the vector potential a lot compared to other treatments of the time, they don't make the vector potential the main object. Feynman wanted to redo Volume II to make it completely vector-potential-centered, but he didn't get to do it. Somebody else did a vector-potential based discussion of E&M based on this recommendation, but the results were not so great.
The major things I don't like in Vol. II:

The derivation of the index of refraction is done by a complicated rescattering calculation which is based on plum-pudding-style electron oscillators. This is essentially just the forward-phase index-of-refraction argument Feynman gives to motivate unitarity in the 1963 ghost paper in Acta Physica Polonika. It is not so interesting or useful in my opinion in Vol. II, but it is the most involved calculation in the series.
No special functionology: While the subject is covered with a layer of 19th-century mildew, it is useful to know some special functions, especially Bessel functions and spherical harmonics. Feynman always chooses ultra special forms which give elementary functions, and he knows all the cases which are elementary, so he gets a lot of mileage out of this, but it's not general enough.
The fluid section is a little thin--- you will learn how the basic equations work, but no major results. The treatment of fluid flow could have been supplemented with He4 flows, where the potential flow description is correct (it is clear that this is Feynman's motivation for the strange treatment of the subject, but this isn't explicit).
Numerical methods in field simulation: Here if one wants to write an introductory textbook, one needs to be completely original, because the numerical methods people use today are not so good for field equations of any sort.

Vol. III is extremely good because it is so brief. The introduction to quantum mechanics there gets you to a good intuitive understanding quickly, and this is the goal. It probably could use the following:

A discussion of diffusion, and the relation between Schrödinger operators and diffusion operators: This is obvious from the path integral, but it was also clear to Schrödinger. It also allows you to quickly motivate the exact solutions to Schrodinger's equation, like the $1/r$ potential, something which Feynman just gives you without motivation. A proper motivation can be given by using SUSY QM (without calling it that, just a continued stochastic equation) and trying out different ground state ansatzes.
Galilean invariance of the Schrödinger equation: This part is not done in any book, I think only because Dirac omitted it from his. It is essential to know how to boost wavefunctions. Since Feynman derives the Schrödinger equation from a tight-binding model (a lattice approximation), the galilean invariance is not obvious at all.

Since the lectures are introductory, everything in there just becomes second nature, so it doesn't matter that they are old. The old books should just be easier, because the old stuff is already floating in the air. If you find something in the Feynman Lectures which isn't completely obvious, you should study it until it is obvious--- there's no barrier, the things are self-contained.


Question: As of 2024, according to  , Voyager 1 is around one light·day away from Earth and still in radio contact. When Voyager 1 sends messages to Earth, roughly how many photons are (1) transmitted and (2) received per bit?

For an exact calculation we need to address a few choices: (you can change them, the answer will not be tremendously affected)

What is the receiver? Let's assume a 70 m dish, like this one [CDSCC] in the Deep Space Network.
[Voyager 1] can transmit at $2.3 {\rm GHz}$ or $8.4 {\rm GHz}$. Let's assume $8.4 {\rm GHz}$, for better beam forming (but probably it can only use the lowest frequency at the highest power, so this could be too optimistic).
Does "received" mean all photons hitting the antenna dish, or only those entering the electronic circuit of the first LNA? A similar question can be asked for the transmitter in the space craft. We'll ignore this here since losses related to illuminators or Cassegrain construction will not even be one order of magnitude, insignificant compared with the rest.

Answers:
A) Voyager sends $160$ bits/second with $23{\rm W}$. Using $8.3 {\rm GHz}$ this is $4 \cdot 10^{24}$ photons per second, or $2.6 \cdot 10^{22}$ per bit, because for frequency $f$ the energy per photon is only
$$E_\phi=\hbar\, \omega=2\pi\hbar f=5.5\cdot10^{-24}{\rm J} \ \
\text{or} \ \ 5.5 \ \text{yJ (yoctojoule)}.$$
B) The beam forming by Voyager's $d=3.7{\rm m}$  dish will direct them predominantly to Earth, with $(\pi d/\lambda)^2$ antenna gain, but still, at the current  distance of $R=23.5$ billion kilometers, this only results in $3.4\cdot10^{-22}$  Watt per square meter reaching Earth, so a receiver with a $D=70{\rm m}$ dish will collect only $1.3$ attowatt ($1.3\cdot 10^{-18}{\rm W}$), summarized by:
$$
  P_{\rm received} = P_{\rm transmit}\ \Big(\frac{\pi d}{\lambda}\Big)^2 \ \frac1{4\pi R^2}\ \frac{\pi D^2}4
$$
Dividing by $E_\phi$ we see that this power then still corresponds to c. $240000$ photons per second, or $1500$ photons per bit. If we assume $f=2.3{\rm GHz}$ this becomes $415$ photons per bit. And if we introduce some realistic losses here and there perhaps only half of that.
C) (Although not asked in the question) how many photons per bit are needed? The [Shannon limit] $ C=B \, \log_2(1+{\large\frac{S}{N}})$, relates bandwidth $B$, and $S/N$ ratio to maximum channel capacity. It follows that with only thermal noise $N=k\, T_{\rm noise}\,B$, the required energy per bit is:
$$ E_{\rm bit} = \frac S C = k\, T_{\rm noise} \ \frac{2^{\,C/B}-1}{C/B}
\ \Rightarrow \  \lim_{C\ll B}\ E_{\rm bit} = k\, T_{\rm noise} \log 2,
$$
where $C\ll B$ is the so-called "ultimate" Shannon limit. With only the CMB $(T_{\rm noise}\!=\!3{\rm K})$ we would then need $41 {\rm yJ}$, or $41 \cdot 10^{-24}\,{\rm J}$, per bit.
That's only $7.5$ photons at $8.3 {\rm GHz}$. But additional atmospheric noise and circuit noise, even with a good cryogenic receiver, could easily raise $T_{\rm noise}$ to about $10{\rm K}$ and then we need $25$ photons per bit at $8.3 {\rm GHz}$, and even $91$ at $2.3 {\rm GHz}$. So clearly there is not much margin.


Question:
This is a question from /u/apivan19 on reddit. The original post can be found here.
I have some proteomics data that was given to me with the UniProt gene identifiers in column 1. I've been trying to convert these to normal gene symbols using various programs, but it is proving to be difficult.
The Uniprot website does it fairly decently, but it is not able to convert all of them and then adds some unknown genes into my list.
For example, I will give it 5439 genes in UniProt notation, and will say "5420 of 5439 UniProt identifiers have been converted to 5450 gene symbols"... which is ridiculous.
I tried using David to change the symbols, but it returns them to me in some ridiculous, random order and there's no way I can sort... actually there might be but it'll take a second.
What are some of the easiest ways to do this? It's already very time consuming and am looking for simpler solutions

I tend to use Ensembl Biomart for such queries since there are APIs for various programming languages, e.g. biomaRt, and, maybe more interestingly, via a REST API (although it’s a pretty terrible one).
To translate identifiers from different databases, proceed as follows:

Choose database “Ensembl genes”
Choose dataset your desired oganism
Go on “Filters” › “Gene:” › “Input external reference ID list”

Select the chosen source database
Provide a list of IDs, delimited by newline

Go to “Attributes” › “Gene:” › untick “Transcript stable ID”

If Ensembl IDs are desired, leave “Gene stable ID” ticked …
Otherwise untick it; go to “External:”, tick your desired identifier format

Click “Results” at the top left. This gives a preview that can be exported into various formats; alternatively the top centre buttons “XML” and “Perl” provide the query in XML (for SOAP/REST requests) and as a (horrendously formatted) executable Perl script.


Question:
My father explained to me how rockets work and he told me that Newton's Third Law of motion worked here. I asked him why it works and he didn't answer. I have wasted over a week thinking about this problem and now I am giving up.
Can anyone explain why Newton's Third Law works?
For reference, Newton's third law:

To every action there is always opposed an equal reaction: or the
mutual actions of two bodies upon each other are always equal, and
directed to contrary parts.

Why do you want to know?
I'm not kidding.  That's actually an important question.  The answer really depends on what you intend to do with the information you are given.
Newton's laws are an empirical model.  Newton ran a bunch of studies on how things moved, and found a small set of rules which could be used to predict what would happen to, say, a baseball flying through the air.  The laws "work" because they are effective at predicting the universe.
When science justifies a statement such as "the rocket will go up," it does so using things that we assume are true.  Newton's laws have a tremendous track record working for other objects, so it is highly likely they will work for this rocket as well.
As it turns out, Newton's laws aren't actually fundamental laws of the universe.  When you learn about Relativity and Quantum Mechanics (QM), you will find that when you push nature to the extremes, Newton's laws aren't quite right.  However, they are an extraordinarily good approximation of what really happens.  So good that we often don't even take the time to justify using them unless we enter really strange environments (like the sub-atomic world where QM dominates).
Science is always built on top of the assumptions that we make, and it is always busily challenging those assumptions.  If you had the mathematical background, I could demonstrate how Newton's Third Law can be explained as an approximation of QM as the size of the object gets large.  However, in the end, you'd end up with a pile of mathematics and a burning question: "why does QMs work."  All you do there is replace one question with another.
So where does that leave you?  It depends on what you really want to know in the first place.  One approach would simply be to accept that scientists say that Newton's Third Law works, because it's been tested.  Another approach would be to learn a whole lot of extra math to learn why it works from a QM perspective.  That just kicks the can down the road a bit until you can really tackle questions about QM.
The third option would be to go test it yourself.  Science is built on scientists who didn't take the establishment's word at face value, went out, and proved it to themselves, right or wrong.  Design your own experiment which shows Newton's Third Law works.  Then go out there and try to come up with reasons it might not work.  Test them.  Most of the time, you'll find that the law holds up perfectly.  When it doesn't hold up, come back here with your experiment, and we can help you learn how to explain the results you saw.
That's science.  Science isn't about a classroom full of equations and homework assignments.  It's about scientists questioning everything about their world, and then systematically testing it using the scientific method!


Question:
Is the butterfly effect real? It is a well-known statement that a butterfly, by flapping her wings in a slightly different way, can cause a hurricane somewhere else in the world that wouldn't occur if the butterfly had moved her wings in a slightly different way. Now, this can be interpreted as a figure of speech, but I think it's actually meant to be true.
I can't imagine though that this is true. I mean, the difference in energy (between the two slightly different wing flaps), which actually can be zero (the only difference being the motion of the air surrounding the close neighborhood of the two slightly different flapping pairs of wings), is simply too small to cause the hurricane 10 000 miles away.
So how can this in heavens name be true? By asking I'm making the implicit and realistic assumption that in the atmosphere no potential energies can be released when a small difference in the air conditions occurs (like, for example, the release of energy contained in the water of a dam when the water has reached a critical level and a small perturbation can cause the dam to break, with catastrophic consequences).

Does the flap of a butterfly's wing in Brazil set off a tornado in Texas?

This was the whimsical question Edward Lorenz posed in his 1972 address to the 139th meeting of the American Association for the Advancement of Science. Some mistakenly think the answer to that question is "yes." (Otherwise, why would he have posed the question?) In doing so, they miss the point of the talk. The opening sentence of the talk immediately after the title (wherein the question was raised) starts with Lest I appear frivolous in even posing the title question, let alone suggesting it might have an affirmative answer ... Shortly later in the talk, Lorenz asks the question posed in the title in more technical terms:

More generally, I am proposing that over the years minuscule disturbances neither increase nor decrease the frequency of occurrences of various weather events such as tornados; the most they may do is to modify the sequences in which they occur. The question which really interests us is whether they can do even this—whether, for example, two particular weather situations differing by as little as the immediate influence of a single butterfly will generally after sufficient time evolve into two situations differing by as much as the presence of a tornado. In more technical language, is the behavior of the atmosphere unstable with respect to perturbations of small amplitude?

The answer to this question is probably, and in some cases, almost certainly. The atmosphere operates at many different scales, from the very fine (e.g., the flap of a butterfly wing) to the very coarse (e.g., global winds such as the trade winds). Given the right circumstances, the atmosphere can magnify perturbations at some scale level into changes at a larger scale. Feynman described turbulence as the hardest unsolved problem in classical mechanics and it remains unsolved to this day. Even the problem of non-turbulent conditions is an unsolved problem (in three dimensions), and hence the million dollar prize for making some kind of theoretical progress with regard to the Navier-Stokes equation.

Update: So is the butterfly effect real?
The answer is perhaps. But even more importantly, the question in a sense doesn't make sense. Asking this question misses the point of Lorenz's talk. The key point of Lorenz's talk, and of the ten years of work that led up to this talk, is that over a sufficiently long span of time, the weather is essentially a non-deterministic system.
In a sense, asking which tiny little perturbation ultimately caused a tornado in Texas to occur doesn't make sense. If the flap of one butterfly's wing in Brazil could indeed set off a tornado in Texas, this means the flap of the wing of another butterfly in Brazil could prevent that tornado from occurring. (Lorenz himself raised this point in his 1972 talk.) Asking which tiny little perturbation in a system in which any little bit of ambient noise can be magnified by multiple orders of magnitude doesn't quite make sense.
Atmospheric scientists use some variant of the Navier-Stokes equation to model the weather. There's a minor (tongue in cheek) problem with doing that: The Navier-Stokes equation has known non-smooth solutions. Another name for such solutions is "turbulence." Given enough time, a system governed by the Navier-Stokes equation is non-deterministic. This shouldn't be that surprising. There are other non-deterministic systems in Newtonian mechanics such as Norton's dome. Think of the weather as a system chock full of Norton's domes. (Whether smooth solutions exist to the 3D Navier-Stokes under non-turbulent conditions is an open question, worth $1000000.)
Lorenz raised the issue of the non-predictability of the weather in his 1969 paper, "The predictability of a flow which possesses many scales of motion." Even if the Navier-Stokes equations are ultimately wrong and even if the weather truly is a deterministic system, it is non-deterministic for all practical purposes.
In Lorenz's time, weather forecasters didn't have adequate knowledge of mesoscale activities in the atmosphere (activities on the order of a hundred kilometer or so). In our time, we still don't quite have adequate knowledge of microscale activities in the atmosphere (activities on the order of a kilometer or so). The flap of a butterfly's wing: That's multiple orders of magnitude below what meteorologists call "microscale." That represents a big problem with regard to turbulence because the magnification of ambient noise is inversely proportional to scale (raised to some positive power) in turbulent conditions.

Regarding a simulation of $1.57\times10^{24}$ particles
My answer has engendered a chaotically large number of comments. One key comment asked about a simulation of $1.57\times10^{24}$ particles.
First off, good luck making a physically realistic simulation of a system comprising that many particles that can be resolved in a realistic amount of time. Secondly, that value represents a mere 0.06 cubic meters of air at standard temperature and pressure. A system of on the order of 1024 particles cannot represent the complexities that arise in a system that is many, many orders of magnitude larger than that. The Earth's atmosphere comprises on the order of 1044 molecules. A factor of 1020 is beyond "many" orders of magnitude. It truly is many, many orders of magnitude larger than a system of only 1024 particles.


Question:
From what I can tell and what thus far all people with whom I discussed this subject confirmed is that time appears to "accelerate" as we age.
Digging a little, most explanations I found basically reduced this to two reasons:

As we age physically, a time frame of constant length becomes ever smaller in contrast to the time we spent living
As we age socially, we are burdened with an increasing amount of responsibility and thus an increasing influx of information which impairs our perception of the present

To be honest, neither sounds entirely convincing to me because:

In my perception "local time" (short time frames that I don't even bother to measure on the scale of my lifetime) is also accelerating. Just as an example: When I wait for the bus, time goes by reasonably fast as opposed to my childhood tortures of having to wait an eternity for those five minutes to pass.
Even after making a great effort to cut myself off from society and consciously trying to focus on the moment, the perceived speed of time didn't really change. (Although I did have a great time :))

Which leads me to a simple question (and a few corollaries):

Am I just in denial of two perfectly plausible and sufficient explanations, or are there actual biological effects (e.g. changes in brain chemistry) in place, that cause (or at least significantly influence) this?
Is there a mechanism, that "stretches out" time for the young brain so that weight of an immense boredom forces it to benefit from its learning ability, while it "shrinks" time as the brain "matures" and must now act based on what it has learned, which often involves a lot of patience?
If there is such a mechanism, are there any available means to counter it? (not sure I'd really want to, but I'd like to know whether I could)

This is not really a biological answer, but a psychological one:
One important fact to consider is that the perception of time is essentially a recollection of past experience, rather than perception of the present.
Researchers who study autobiographical memory have suggested that part of this effect may be explained by the number of recallable memories during a particular time period. During one's adolescence, one typically has a large number of salient memories, due to the distinctness of events. People often make new friends, move frequently, attend different schools, and have several jobs. As each of these memories is unique, recollection of these (many) memories gives the impression that the time span was large.
In contrast, older adults have fewer unique experiences. They tend to work a single job, and live in a single place, and have set routines which they may follow for years. For this reason, memories are less distinct, and are often blurred together or consolidated. Upon recollection, it seems like time went by quickly because we can't remember what actually happened.
In other words, it can be considered a special case of the availability heuristic: people judge a time span to be longer in which there are more salient/unique events.
Incidentally, (and to at least mention biology), episodic memory has been shown to be neurally distinct from semantic memory in the brain. In particular, a double dissociation has been shown for amnesics who suffer from semantic or episodic memory, but not both.
My apologies for the lack of citations, but a good bit about autobiographical memories can be found in:

Eysenck, M.W., & Keane, M.T. (2010). Cognitive Psychology: A
  Student's Handbook.

You may also be interested in some responses or references to a related question on the Cognitive Science StackExchange:
Perception of time as a function of age


Question:
I discovered this site which claims that "$7$ is the only prime followed by a cube".  I find this statement rather surprising.  Is this true?  Where might I find a proof that shows this?
In my searching, I found this question, which is similar but the answers seem focused on squares next to cubes.
Any ideas?

This is certainly true. Suppose $n^3 - 1$ is prime, for some $n$. We get that $n^3-1 = (n-1)(n^2 + n + 1)$ and so we have that $n-1$ divides $n^3 - 1$. If $n-1>1$ then we're done, as we have a contradiction to $n^3 - 1$ being prime.


Question:
A quick google around and all I seem to be able to find are people talking about the physics & the chemistry of the capacitors but not how this affects choosing which to use.
Avoiding talking about the difference in their make-up, and the larger capacities found in electrolytic caps, what are the main thoughts that drive which type of capacitor to use for an application?
For example, why do I see it suggested to use ceramic caps for power decoupling per microprocessor & a larger electrolytic capacitor per board? why not use electrolytic all around?

1. Capacitors
There are a lot of misconceptions about capacitors, so I wanted to briefly clarify what capacitance is and what capacitors do.
Capacitance measures how much energy will be stored in the electric field generated between two different points for a given difference of potential.  This is why capacitance is often called the 'dual' of inductance.  Inductance is how much energy a given current flow will store in a magnetic field, and capacitance is the same, but for the energy stored in an electric field (by a potential difference, rather than current).
Capacitors do not store electric charge, which is the first big misconception. They store energy.  For every charge carrier you force onto one plate, a charge carrier on the opposite plate leaves.  The net charge remains the same (neglecting any possible much smaller unbalanced 'static' charge that might build up on asymetrical exposed outer plates).
Capacitors store energy in the dielectric, NOT in the conductive plates.  Only two things determine a capacitor's effectiveness: its physical dimensions (plate area and distance separating them), and the dielectric constant of the insulating between the plates.  More area means a bigger field, closer plates mean a stronger field (since field strength is measured in Volts per meter, so the same difference of potential across a much smaller distance yields a stronger electric field).
The dielectric constant is how strong a field will be generated in a specific medium.  The 'baseline' dielectric constant is \$\varepsilon\$, with a normalized value of 1. This is the dielectric constant of a perfect vacuum, or the field strength that occurs through spacetime itself. Matter has a very large impact on this, and can support the generation of much stronger fields.  The best materials are materials with lots of electric dipoles that will enhance the strength of a field generated within the material.
Plate area, dielectric, and plate separation.  That's really all there is to capacitors.  So why are they so complicated and varied?
They aren't.  Except the ones with much more than thousands of pF of capacitance.   If you want such ludicrous amounts of capacitance as we mostly take for granted today, such amounts as in millions of picofarads (microfarads), and even order of magnitudes beyond, we are at the mercy of physics.
Like any good engineer, in the face of limits imposed by the laws of nature, we cheat and get around those limits anyway. Electrolytic capacitors and high capacitance (0.1µF to 100µF+) ceramic capacitors are the dirty tricks we used.
2. Electrolytic capacitors
Aluminum
The first and most important distinction (for which they're named for) is that electrolytic capacitors use an electrolyte.  The electrolyte serves as the second plate.  Being a liquid, this means it can be directly up against a dielectric, even one that is unevenly shaped.  In aluminum electrolytic capacitors, this enables us to take advantage of aluminum's surface oxidation (the hard stuff, sometimes deliberately porous and dye impregnated for colours, on anodized aluminum which amounts to an insulating Sapphire coating) for use as the dielectric.  Without an electrolytic 'plate' however, the unevenness of the surface would prevent a rigid metallic plate from getting close enough to gain anything advantage from using aluminum oxide in the first place.
Even better, by using a liquid, the surface of aluminum foil can be roughened, causing a large increase in effective surface area.  Then it is anodized until a sufficiently thick layer of aluminum oxide has formed on its surface.  A rough surface of which all will be directly adjacent to the other 'plate' – our liquid electrolyte.
There are problems, however.  The most familiar one is polarity.  Anodization of aluminum, if you couldn't tell by its similarity to the word anode, is a polarity-dependent process.  The capacitor must always be used in the polarity that anodizes the aluminum.  The opposite polarity will allow the electrolyte to destroy the surface oxide, which leaves you with a shorted capacitor.  Some electrolytes will slowly eat away this layer anyway, so many aluminum electrolytic capacitors have a shelf-life.  They are designed to be used, and that use has the beneficial side effect of maintaining and even restoring the surface oxide.  However, with long enough disuse, the oxide can be completely destroyed.  If you must use an old dusty capacitor of unsure condition, it is best to 'reform' them by applying a very low current (hundreds of µA to mA) from a constant current power supply, and let the voltage rise slowly until it reaches its rated voltage.  This prevents the very high leakage current (initially) from damaging the capacitor, and slowly rebuilds the surface oxides until the leakage is hopefully at acceptable levels.
The other problem is that electrolytes are, due to chemistry, something ionic dissolved in a solvent.  Non-polymer aluminum ones use water (with some other 'secret sauce' ingredients added to it).  What does water do when current flows through it? It electrolyses! Great if you wanted oxygen and hydrogen gas, terrible if you didn't.  In batteries, controlled recharging can reabsorb this gas, but capacitors do not have an electrochemical reaction that is reversed.  They're just using the electrolyte as a thing that is conductive.  So no matter what, they generate minute amounts of hydrogen gas (the oxygen is used to build up the aluminum oxide layer), and while very small, it prevents us from hermetically sealing these capacitors.  So they dry out.
The standard useful life at maximum temperature is 2,000 hours.  That's not very long.  Around 83 days.  This is simply due to higher temperatures causing the water to evaporate more quickly.  If you want something to have any longevity, it is important to keep them as cool as possible, and get the highest endurance models (I've seen ones as high as 15,000 hours).  As the electrolyte dries out, it becomes less conductive, which increases ESR, which in turn increases heat, which compounds the problem.
Tantalum
Tantalum capacitors are the other variety of electrolytic capacitors. These use manganese dioxide as their electrolyte, which is solid in its finished form.  During production, manganese dioxide is dissolved in an acid, then electrochemically deposited (similar to electroplating) onto the surface of tantalum powder which is then sintered.  The exact details of the 'magic' part where they create an electrical connection between all the tiny pieces of tantalum powder and the dielectric is not known to me (edits or comments are appreciated!) but suffice it to say, tantalum capacitors are made from tantalum because of a chemistry that permits us to easily manufacture them from a powder (high surface area).
This gives them terrific volumetric efficiency, but at a cost: the free tantalum and manganese dioxide can undergo a reaction similar to thermite, which is aluminum and iron oxide.  Only, the tantalum reaction has much lower activation temperatures - temperatures that are easily and quickly achieved should opposite polarity or an overvoltage event punch a hole through the dielectric (tantalum pentoxide, much like aluminum oxide) and create a short.  This is why you see tantalum capacitors voltage and current derated by 50% or more.  For those unaware of thermite (which is a lot hotter but still not dissimilar to the tantalum and MnO2 reaction), there is a ton of fire and heat.  It is used to weld railroad rails to each other, and it does this task in seconds.
There are also polymer electrolytic capacitors, which use conductive polymer that, in its monomer form, is a liquid, but when exposed to the right catalyst, will polymerize into a solid material.  This is just like super glue, which is a liquid monomer that polymerizes solid once it is exposed to moisture (either in/on the surfaces it is applied to, or from the air itself). In this way, polymer capacitors can be mostly a solid electrolyte, which results in reduced ESR, greater longevity, and generally better robustness.  They still have some small amount of solvent in the polymer matrix however, and it is needed to be conductive.  So they still dry out.  No free lunch sadly.
Now, what are the actual electrical properties of these types of capacitors? We already mentioned polarity, but the other is their ESR and ESL.  Electrolytic capacitors, due to being constructed as a very long plate wound into a coil, have relatively high ESL (equivalent series inductance).  So high in fact, that they are completely ineffective as capacitors above 100kHz, or 150kHz for polymer types.  Above this frequency, they are basically just resistors that block DC.  They won't do anything to your voltage ripple, and instead will make the ripple be equal to the ripple current multiplied by the capacitor's ESR, which can often make ripple even worse.  Of course, this means any sort of high frequency noise or spike will just shoot right through an aluminum electrolytic capacitor like it wasn't even there.
Tantalums are not quite as bad, but they still lose their effectiveness with medium frequencies (the best and smallest ones can almost hit 1MHz, most lose their capacitive characteristic around 300–600kHz).
All in all, electrolytic capacitors are great for storing a ton of energy in a small space, but are really only useful for dealing with noise or ripple below 100kHz.  If not for that critical weakness, there would be little reason to use anything else.
3. Ceramic Capacitors
Ceramic capacitors use a ceramic as their dielectric, with metallization on either side as the plates.  I will not be going into Class 1 (low capacitance) types, but only class II.
Class II capacitors cheat using the ferroelectric effect.  This is very much akin to ferromagnetism, only with electric fields instead.  A ferroelectric material has a ton of electric dipoles that can, to some degree or another, be oriented in the presence of an external electric field.  So the application of an electric field will pull the dipoles into alignment, which requires energy, and causes a massive amount of energy to ultimately be stored in the electric field.  Remember how a vacuum was the baseline of 1? The ferroelectric ceramics used in modern MLCCs have a dielectric constant on the order of 7,000.
Unfortunately, just like ferromagnetic materials, as a stronger and stronger field magnetizes (or polarizes in our case) a material, it begins running out of more dipoles to polarize.  It saturates.  This ultimately translates into the nasty property of X5R/X7R/etc type ceramic capacitors: their capacitance drops with bias voltage.  The higher the voltage across their terminals, the lower their effective capacitance.  The amount of energy stored is still always increasing with voltage, but it is not nearly so good as you would expect based on its unbiased capacitance.
Voltage rating of a ceramic capacitor has very little effect on this.  In fact, the actual withstanding voltage of most ceramics is much higher, 75 or 100V for the lower voltage ones.  In fact, many ceramic capacitors I suspect are the exact same part but with different part numbers, the same 4.7µF capacitor being sold as both a 35V and 50V capacitor under different labels.  The graph of some MLCCs' capacitance vs. bias voltage is identical, save for the lower voltage one having its graph truncated at its rated voltage.  Suspicious, certainly, but I could be wrong.
Anyway, buying higher rated ceramics will do nothing to combat this voltage related capacitance falloff, the only factor that ultimately plays a role is the physical volume of the dielectric.  More material means more dipoles.  So physically larger capacitors will retain more of their capacitance under voltage.
This is also not a trivial effect.  A 1210 10µF 50V ceramic capacitor, a veritable beast of a capacitor, will lose 80% of its capacitance by 50V.  Some are a little better, some are a little worse, but 80% is a reasonable figure.  The best I have seen was a 1210 (inches) keep about 3µF of capacitance by the time it hit 60V, in a 1210 package anyway.  A 10µF 1206 (inches) sized 50V ceramic will be lucky to have 500nF left by 50V.
Class II ceramics are also piezoelectric and pyroelectric, though this doesn't really impact them electrically.  They have been known to vibrate or sing due to ripple, and can act as microphones.  Probably best to avoid using them as coupling capacitors in audio circuits.
Otherwise, ceramics have the lowest ESL and ESR of any capacitor.  They're the most 'capacitor-like' of the bunch.  Their ESL is so low that the primary source is the height of the end terminations on the package itself  Yes, that height of an 0805 ceramic is the main source of its 3 nH of ESL. They still behave like capacitors into the many MHz, or even higher for specialized RF types.  They also can decouple a lot of noise, and decouple very fast things like digital circuits, things electrolytics are useless for.
In conclusion, electrolytics are:

lots of bulk capacitance in a tiny package
terrible in every other way

They are slow, they wear out, they catch fire, they will turn into a short if you polarize them wrong.  By every criteria capacitors are measured by, save for capacitance itself, electrolytics are absolutely terrible.  You use them because you have to, never because you want to.
Ceramics are:

Unstable and lose a lot of their capacitance under voltage bias
Can vibrate or act as microphones.  Or nanoactuators!
Are otherwise awesome.

Ceramic capacitors are what you want to use, but aren't always able to.  They actually behave like capacitors and even at high frequencies, but can't match the volumetric efficiency of electrolytics, and only Class 1 types (which have very small amounts of capacitance) are going to have a stable capacitance.  They vary quite a bit with temperature and voltage.  Oh, they also can crack and are not as mechanically robust.
Oh, one last note, you can use electrolytics just fine in AC/non-polarized applications, with all their other problems still in play of course.  Just connect a pair of regular polarised electrolytic capacitors, with same polarity terminals terminals together, and now the opposite polarity ends are the terminals of a brand new, non-polar electrolytic.  As long as their capacitance values are fairly well-matched and there is limited amount of steady state DC bias, the capacitors seem to hold out in use.


Question:
Having recently graduated from my PhD program in statistics, I had for the last couple of months began searching for work in the field of statistics. Almost every company I considered had a job posting with a job title of "Data Scientist". In fact, it felt like long gone were the days of seeing job titles of Statistical Scientist or Statistician. Had being a data scientist really replaced what being a statistician was or were the titles synonymous I wondered?
Well, most of the qualifications for the jobs felt like things that would qualify under the title of statistician.  Most jobs wanted a PhD in statistics ($\checkmark$), most required understanding experimental design ($\checkmark$), linear regression and anova ($\checkmark$), generalized linear models ($\checkmark$), and other multivariate methods such as PCA ($\checkmark$), as well as knowledge in a  statistical computing environment such as R or SAS ($\checkmark$). Sounds like a data scientist is really just a code name for statistician.
However, every interview I went to started with the question: "So are you familiar with machine learning algorithms?"  More often than not, I found myself having to try and answer questions about big data, high performance computing, and topics on  neural networks, CART, support vector machines, boosting trees, unsupervised models, etc. Sure I convinced myself that these were all statistical questions at heart, but at the end of every interview I couldn't help but leave feeling like I knew less and less about what a data scientist is.
I am a statistician, but am I a data scientist? I work on scientific problems so I must be a scientist! And also I work with data, so I must be a data scientist! And according to Wikipedia, most academics would agree with me ( etc. )

Although use of the term "data science" has exploded in business
  environments, many academics and journalists see no distinction
  between data science and statistics.

But if I am going on all these job interviews for a data scientist position, why does it feel like they are never asking me statistical questions?
Well after my last interview I did want any good scientist would do and I sought out data to solve this problem (hey, I am a data scientist after all). However, after many countless Google searches later, I ended up right where I started feeling as if I was once again grappling with the definition of what a data scientist was. I didn't know what a data scientist was exactly since there was so many definitions of it, (  but it seemed like everyone was telling me I wanted to be one:

etc....the list goes on.

Well at the end of the day, what I figured out was "what is a data scientist" is a very hard question to answer. Heck, there were two entire months in Amstat where they devoted time to trying to answer this question:

Well for now, I have to be a sexy statistician to be a data scientist but hopefully the cross validated community might be able to shed some light and help me understand what it means to be a data scientist.  Aren't all statisticians data scientists?

(Edit/Update)
I thought this might spice up the conversation. I just received an email from the American Statistical Association about a job positing with Microsoft looking for a Data Scientist. Here is the link: Data Scientist Position. I think this is interesting because the role of the position hits on a lot of specific traits we have been talking about, but I think lots of them require a very rigorous background in statistics, as well as contradicting many of the answers posted below.  In case the link goes dead, here are the qualities Microsoft seeks in a data scientist:

Core Job Requirements and Skills:
Business Domain Experience using Analytics

Must have experience across several relevant business domains in the utilization of critical thinking skills to conceptualize complex business problems and their solutions using advanced analytics in large scale real-world business data sets
The candidate must be able to independently run analytic projects and help our internal clients understand the findings and translate them into action to benefit their business.

Predictive Modeling

Experience across industries in predictive modeling
Business problem definition and conceptual modeling with the client to elicit important relationships and to define the system scope

Statistics/Econometrics

Exploratory data analytics for continuous and categorical data
Specification and estimation of structural model equations for enterprise and consumer behavior, production cost, factor demand, discrete choice, and other technology relationships as needed
Advanced statistical techniques to analyze continuous and categorical data
Time series analysis and implementation of forecasting models
Knowledge and experience in working with multiple variables problems
Ability to assess model correctness and conduct diagnostic tests
Capability to interpret statistics or economic models
Knowledge and experience in building discrete event simulation, and dynamic simulation models

Data Management

Familiarity with use of T-SQL and analytics for data transformation and the application of exploratory data analysis techniques for very large real-world data sets
Attention to data integrity including data redundancy, data accuracy, abnormal or extreme values, data interactions and missing values.

Communication and Collaboration Skills

Work independently and able to work with a virtual project team that will research innovative solutions to challenging business problems
Collaborate with partners, apply critical thinking skills, and drive analytic projects end-to-end
Superior communication skills, both verbal and written
Visualization of analytic results in a form that is consumable by a diverse set of stakeholders

Software Packages

Advanced Statistical/Econometric software packages: Python, R, JMP, SAS, Eviews, SAS Enterprise Miner
Data exploration, visualization, and management: T-SQL, Excel, PowerBI, and equivalent tools

Qualifications:

Minimum 5+   years of related experience required
Post graduate degree in quantitative field is desirable.

People define Data Science differently, but I think that the common part is:

practical knowledge how to deal with data,
practical programming skills.

Contrary to its name, it's rarely "science". That is, in data science the emphasis is on practical results (like in engineering), not proofs, mathematical purity or rigor characteristic to academic science. Things need to work, and there is little difference if it is based on an academic paper, usage of an existing library, your own code or an impromptu hack.
Statistician is not necessary a programmer (may use pen & paper and a dedicated software). Also, some job calls in data science have nothing to do with statistics. E.g. it's data engineering like processing big data, even if the most advanced maths there may be calculating average (personally I wouldn't call this activity "data science", though). Moreover, "data science" is hyped, so tangentially related jobs use this title - to lure the applicants or raise ego of the current workers.
I like the taxonomy from Michael Hochster's answer on Quora:

Type A Data Scientist: The A is for Analysis. This type is primarily concerned with making sense of data or working with it in a fairly static way. The Type A Data Scientist is very similar to a statistician (and may be one) but knows all the practical details of working with data that aren’t taught in the statistics curriculum: data cleaning, methods for dealing with very large data sets, visualization, deep knowledge of a particular domain, writing well about data, and so on.
Type B Data Scientist: The B is for Building. Type B Data Scientists share some statistical background with Type A, but they are also very strong coders and may be trained software engineers. The Type B Data Scientist is mainly interested in using data “in production.” They build models which interact with users, often serving recommendations (products, people you may know, ads, movies, search results).

In that sense, Type A Data Scientist is a statistician who can program. But, even for quantitive part, there may be people with background more in computer science (e.g. machine learning) than regular statistics, or ones focusing e.g. on data visualization.
And The Data Science Venn Diagram (here: hacking ~ programming):

see also alternative Venn diagrams (this and that). Or even a tweet, while humorous, showing a balanced list of typical skills and activities of a data scientist:

See also this post: Data scientist - statistician, programmer, consultant and visualizer?.


Question:
I've heard it suggested that "solid tantalum" capacitors are dangerous and may cause fire, may fail short circuit and are fatally sensitive to even very short over voltage spikes.
Are tantalum capacitors reliable?
Are they safe for use in general circuits and new designs?

Summary:
"When used properly" tantalum capacitors are highly reliable.
They have the advantage of high capacitance per volume and good decoupling characteristics due to relatively low internal resistance and low inductance compared to traditional alternatives such as aluminum wet electrolytic capacitors.
The 'catch' is in the qualifier "when used properly".
Tantalum capacitors have a failure mode which can be triggered by voltage spikes only 'slightly more' than their rated value. When used in circuits that can provide substantial energy to the capacitor failure can lead to thermal run-away with flame and explosion of the capacitor and low resistance short-circuiting of the capacitor terminals.
To be "safe" the circuits they are used in need to be guaranteed to have been rigorously designed and the design assumptions need to be met. This 'does not always happen'.
Tantalum capacitors are 'safe enough' in the hands of genuine experts, or in undemanding circuits, and their advantages make them attractive. Alternatives such as "solid aluminum" capacitors have similar advantages and lack the catastrophic failure mode.
Many modern tantalum capacitors have built in protection mechanisms which implement fusing of various sorts, which is designed to disconnect the capacitor from its terminals when it fails and to limit PCB charring in most cases.
If 'when', 'limit' and 'most' are acceptable design criteria and/or you are a design expert and your factory always gets everything right and your application environment is always well understood, then tantalum capacitors may be a good choice for you.

Longer:
Solid Tantalum capacitors are potentially disasters waiting to happen.
Rigorous design and implementation that guarantees that their requirements are met can produce highly reliable designs.  If your real world situations are always guaranteed to not have out of spec exceptions then tantalum caps may work well for you, too.
Some modern tantalum capacitors have failure mitigation (as opposed to prevention) mechanisms built in. In a comment on another stack exchange question Spehro notes:

The data sheet for Kemet's Polymer-Tantalum caps says (in part) : "The KOCAP also exhibits a benign failure mode which eliminates the ignition failures that can occur in standard MnO2 tantalum types.".

Strangely, I can find nothing about the "ignition failure" feature in their other data sheets.
Solid Tantalum electrolytic capacitors have traditionally had a failure mode which makes their use questionable in high energy circuits that cannot be or have not been rigorously designed to eliminate any prospect of the applied voltage exceeding the rated voltage by more than a small percentage.
Tantalum caps are typically made by sintering tantalum granules together to form a continuous whole with an immense surface area per volume and then forming a thin dielectric layer over the outer surface by a chemical process. Here "thin" takes on a new meaning - the layer is thick enough to avoid breakdown at rated voltage  - and thin enough that it will be punched through by voltages not vastly in excess of rated voltage. For an eg 10 V rated cap, operation with say 15V spikes applied can be right up there with playing Russian Roulette. Unlike Al wet electrolytic caps which tend to self heal when the oxide layer is punctured, tantalum tends not to heal. Small amounts of energy may lead to localised damage and removal of the conduction path. Where the circuit providing energy to the cap is able to provide substantial energy the cap is able to offer a correspondingly low resistance short and a battle begins. This can lead to smell, smoke, flame, noise and explosion. I've seen all these happen sequentially in a single failure. First there was a puzzling bad smell for perhaps 30 seconds. Then a loud shrieking noise, then a jet of flame for perhaps 5 seconds with gratifying wooshing sound and then an impressive explosion. Not all failures are so sensorily satisfying.
Where the complete absence of overvoltage high energy spikes could not be guaranteed, which would be the case in many if not most power supply circuits, use of tantalum solid electrolytic caps would be a good source of service (or fire department) calls. Based on Spehro's reference, Kemet may have removed the more exciting aspects of such failures. They still warn against minimal overvoltages.
Some real world failures:

Wikipedia - tantalum capacitors

Most tantalum capacitors are polarized devices, with distinctly marked positive and negative terminals. When subjected to reversed polarity (even briefly), the capacitor depolarizes and the dielectric oxide layer breaks down, which can cause it to fail even when later operated with correct polarity. If the failure is a short circuit (the most common occurrence), and current is not limited to a safe value, catastrophic thermal runaway may occur (see below).

Kemet - application notes for tantalum capacitors

Read section 15., page 79 and walk away with hands in sight.

AVX - voltage derating rules for solid tantalum and niobium capacitors

For many years, whenever people have asked tantalum capacitor manufacturers for
general recommendations on using their product, the consensus was “a minimum
of 50% voltage derating should be applied”. This rule of thumb has since become
the most prevalent design guideline for tantalum technology. This paper revisits this
statement and explains, given an understanding of the application, why this is not
necessarily the case.

With the recent introduction of niobium and niobium oxide capacitor technologies,
the derating discussion has been extended to these capacitor families also.
Vishay - solid tantalum capacitor FAQ

. WHAT IS THE DIFFERENCE BETWEEN A FUSED (VISHAY SPRAGUE 893D) AND STANDARD,
NON-FUSED (VISHAY SPRAGUE 293D AND 593D) TANTALUM CAPACITOR?

A. The 893D series was designed to operate in high-current applications (> 10 A) and employs an “electronic” fusing mechanism. ... The 893D fuse will not “open” below 2 A because the I2R is below the energy required to activate the fuse. Between 2 and 3 A, the fuse will eventually activate, but some capacitor and circuit board
“charring” may occur. In summary, 893D capacitors are ideal for high-current circuits where capacitor “failure” can cause system failure.
Type 893D capacitors will prevent capacitor or circuit board “charring” and usually prevent any circuit interruption that can be associated with capacitor failure. A “shorted” capacitor across the power source can cause current and/or voltage transients that can trigger system shutdown. The 893D fuse activation time is sufficiently fast in most instances to eliminate excessive current drain or voltage swings.
Capacitor guide - tantalum capacitors

... The downside to using tantalum capacitors is their unfavorable failure mode which may lead to thermal runaway, fires and small explosions, but this can be prevented through the use of external failsafe devices such as current limiters or thermal fuses.

What a cap-astrophe

I was working at a manufacturer that was experiencing unexplained tantalum-capacitor failure. It wasn't that the capacitors were just failing, but the failure was catastrophic and was rendering PCBs (printed-circuit boards) unfixable. There seemed to be no explanation. We found no misapplication issues for this small, dedicated microcomputer PCB. Worse yet, the supplier blamed us.

I did some Internet research on tantalum-capacitor failures and found that the tantalum capacitors' pellets contain minor defects that must be cleared during manufacturing. In this process, the voltage is increased gradually through a resistor to the rated voltage plus a guard-band. The series resistor prevents uncontrolled thermal runaway from destroying the pellet. I also learned that soldering PCBs at high temperatures during manufacturing causes stresses that may cause microfractures inside the pellet. These microfractures may in turn lead to failure in low-impedance applications. The microfractures also reduce the device's voltage rating so that failure analysis will indicate classic overvoltage failure. ...

Related:
AVX - surge in solid tantalum capacitors
Failure modes and mechanisms in solid tantalum capacitors - Sprague / IEEE abstract only.  - OLD 1963.
AVX - FAILURE MODES OF TANTALUM CAPACITORS MADE BY DIFFERENT
TECHNOLOGIES - Age ? - about 2001?
Effect of Moisture on Characteristics of Surface Mount Solid Tantalum
Capacitors - NASA with AVX assistance - about 2002?
Hearst - How to spot counterfeit components
Sometimes it's easy :-) :

Added 1/2016:
Related:
Test for reverse polarity for standard wet-aluminium metal can capacitors.
Brief:
For correct polarity can potential is ~= ground.
For reverse polarity can potential is a significant percentage of applied voltage.
A very reliable test in my experience.
Longer:
For standard wet Al caps I long ago discovered a test for reverse insertion which I've not ever seen mentioned elsewhere but is probably well enough known. This works for caps which have the metal can accessible for testing - most have a convenient clear spot at top center due to the way the sleeve is added.
Power up circuit and measure voltages from ground to can of each cap. This is a very quick test with a volt-meter - -ve lead grounded and zip around cans.

Caps of correct polarity have can almost at ground.

Caps of reverse polarity have cans at some fraction of supply - maybe ~~~= 50%.

Works reliably in my experience.
You can usually check using can markings but this depends on intended orientation being known and clear. While that is usually consistent in a good design this is never certain.


Question:
Today in chemistry class we were discussing Organic Chemistry. We discussed what organic compounds basically are and then I asked the teacher whether $\ce{CO_2}$ is organic or not. She told that it is as it contains carbon and oxygen with a covalent bond. I told her it can't be as it is not found in animals (naturally). I am very confused about it.
I need some good reasons to agree with either explanation. (I have searched the internet already but found no great insights as of now).

It is entirely arbitrary whether you call it an organic compound or not, though most would not.
The distinction you make that organic compounds should be found in living things is not a useful criterion. Moreover you are wrong that carbon dioxide isn't: it is both made and used by living things. Animals make it when they metabolise sugars to release energy; plants consume it when they build more complex organic molecules through photosynthesis. In fact most organic molecules are, ultimately, derived from $\ce{CO2}$.
Even more importantly most molecules considered organic are neither made by nor are found in living things. Chemists make new carbon compounds all the time (tens of millions in the history of chemistry) and most have never been made by animals or plants.
The organic/inorganic terminology is mostly very simple: covalent compounds containing carbon are organic. The only fuzzy area is around very simple molecules like $\ce{CO2}$ where the distinction doesn't matter much. So we would not normally think of diamond or silicon carbide as organic. But we might (though many would not) call calcium carbide organic because it contains a $\ce{C2}$ unit with a carbon-carbon triple bond.
However since the terminology is mostly very obvious and also somewhat arbitrary, it isn't worth much argument to sort out those very simple but awkward edge cases.