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@Douglas: I downvoted the 2nd one also. I too think that it's a question of timing; I'm pretty sure that question didn't get jumped on as quickly, just because fewer people with the power to do so were reading. Your broader point might still stand, but I really don't think this is a useful example.
I agree with what Pete's just said.
Moreover, I would add that leaving questions open just because someday someone might come along and answer them is just plain wrong. One of MOs strengths is its speed: it's for finding quick answers to quick questions. Even more for mathematicians than for programmers, it's a "save me a little time here" site. I could trawl through oddles of literature looking for information on whether or not a particular LCTVS is paracompact or not, or I could try to get a head start and ask here first. If I don't get an answer but was truly interested in the question then I'd go off and do the hard slog. Or at least, I could do so. So if I scan back through the unanswered questions, how do I know that the questioner is still interested in the question?
I would love to see lots of applied mathematicians on MO. I'd love to see more algebraic and differential topologists as well. Not to mention functional analysts. But the MO community is not going to grow by forcing it, but by being convincing. And part of that is making sure that it doesn't look like a "Grill a Mathematician" site.
It'd be great if Persi joined MO. I'd love to fire more questions at him and I'm sure he'd love to ask questions of the rest of us. I have a vague memory that he's not all that bothered about computers, though, so that might be a pipe dream.
The basic problem with MO is that it is, at heart, based on a precarious balance. There are "questioners" and "answerers". Left at that, the incentives are all wrong and, what with everything else everyone has to do, the system doesn't work too well. The genius of SO is to realise that this can work if the two groups are the same. With software, there's a large enough community that this is a stable solution. I'm not convinced that we can have the same stability in mathematics so we need to impose it artificially.
(PS My example above is a bad one since I'm very interested in paracompactness of LCTVS but haven't gotten round to doing the hard slog yet; however, if I hadn't said it here no-one else would know that.)
And further, addressing @Pete above.
Personally, I think it's (always been) fine to downvote without commenting, and similarly I think it's fine to vote to close without commenting. On the other hand, if you can leave a helpful comment about why you're voting to close, that's better than saying nothing, and at least one of the votes to close should come with an explanation -- which is why I emphasised the role of the final voter.
I just want to make a couple comments which more or less amplify points from Andrew's last post.
First of all, Pete, I can almost guarantee we won't see Persi on MO - he doesn't even use email. (I'll spare everyone a little rant here about the implication that probability is applied math.) But I think parts (not all!) of this discussion are making too much of the pure/applied distinction. I've seen a number of excellent questions in fields that aren't well represented on MO disappear quickly because no one answers or even comments on them. Like this one, for example:
http://mathoverflow.net/questions/12420/asymptotic-non-distortion-of-the-separable-hilbert-space
I don't mean to criticize anyone for not trying to answer this question, but I don't think anyone would say it's not up to MO's standards. This just reflects the fact that many areas of mathematics are not well represented here. The fact that there are few applied mathematicians doesn't necessarily have any deeper significance than the fact that there are few functional analysts.
Persi used to have something on his web page which said that he didn't use e-mail. It doesn't seem to be there any more, though.
Another person that it would be interesting to see here, but who we'll never see, is Don Knuth, who says he stopped using e-mail in 1990.
Knuth also reads (some of?) email sent to him, at least on specific subjects. His answer to me was hand-written and sent through the snail mail, though.
Another well-known older mathematician who posts here is Richard Stanley, who is 65.
To answer Harry's implicit question, Allen Hatcher got his PhD 39 years ago, and James S. Milne is 67.
@fedja, I'd appreciate if you could clarify your earlier comment. I'm not sure what being an algebraist vs. an analyst has to do with MO policy nor what you find disagreeable about it and I'd like to know if it's something the community can address.
I'm once again late to the party, but I would like to say that I agree with most of what Tom LaGatta said earlier, and I agree with what Douglas Zare said regarding applied math questions being held to a higher standard than "pure math" questions.
A few of own "pure math" questions have been asked with only a very vague (or half-baked, or only partially coherent) idea in mind. I post such questions in the hope that the vague idea has some sense (or if it's nonsensical, that someone can tell me why it's nonsensical), and that someone can point me to a reference (if one exists) where the vague idea is made more concrete.
Examples:
http://mathoverflow.net/questions/652/homological-algebra-and-calculus-as-in-newton
http://mathoverflow.net/questions/9945/analysis-analogue-of-orlovs-theorem
http://mathoverflow.net/questions/11716/mirror-symmetry-mod-p-physics-mod-p
http://mathoverflow.net/questions/8772/cohomology-rings-and-2d-tqfts
I would say that all of these questions are vaguer than or as vague as, for instance, the question we had a while back about walking vs. running in the rain. Douglas is right: while vague "pure math" questions seem to be relatively well-received, the applied math questions are often very quickly shut down.
I have assured the OP of that question via a comment that FFT itself can be implemented and that the existing DSP processors are powerful enough. I was an electrical engineer, but stayed silent to stay anonymous. However this discussion is going on and on ..
No, just an electrical engineer who felt that he should do math instead. I still feel I need my anonymity. I would rather not use MO than not have it..
@Pete. Engineering mathematics is very boring. Please have a look at the voluminous book of Erwin Kreyszig and you will surely agree with me. For what it is worth, I found the math which I learned in signal processing courses much more interesting than what I had to learn in the compulsory engineering math courses, and I found the latter extremely depressing. My view is that applied math is more interesting when looked at from the perspective of applications.
You get a certain intuition in Fourier transforms when you use it for electrical or communications systems. Even now I don't know distributions very well, but I can do some Fourier transform calculations in the non-rigorous, but perfectly natural way.. And I find that trying to bring in the theory of distributions destroy all intuition and messes it up.
It is like, it is much easier to decide whether a "usual" function of a real variable is continuous or not by looking at its graph, rather than trying to check with all epsilons and deltas. You do not mention them at the start of your calculus class, do you?
@Pete. For what it is worth, I myself feel that the question in MO which started this discussion was off-topic.
Anyway, I saw your complaints about understanding Fourier transforms, and so I mentioned all that. Here's some 5 cents more:
For example, the Dirac Delta function approximately occurs when you have a sudden high and brief surge of current in your electrical system. Like what happens when you have a lightning. To get the ideal delta function, you start with a smooth function supported on [-a.-a] which when integrated gives 1. And you let 'a' go to 0, and correspondingly scale the value of the function so that the integral is the same. The Fourier transform of a signal is its "frequency spectrum". You watch in that "frequency domain" what is happening, when you do the above approximation process in the "time domain". This is actually something you can do with constructing some circuit and observing on the "CRO" -- the Cathode Ray Oscilloscope, which is indispensable in every electronics lab, however small. However one does not actually need to set it up so and see it; with some experience one knows what will turn up without actually doing it. For example, when a spark or lightning happens, there is a disruption of noise in your radio or tv. . And it happens no matter the frequency you have tuned it to. This is because the delta function has Fourier transform 1, ie it is a constant in the frequency domain, and therefore the noise created by a signal which looks roughly like it will appear uniformly in every frequency.
Similarly, note that the sudden switching on/off of current is like the step function. That also has a very wide Fourier transform, ie, frequency spectrum, and your radio/television experiences a brief noise when this happens. Same is the case with loose contacts touching and going off. When the contact breaks or makes, there is noise even at high frequencies.
Also note how easy it is to prove the Parseval: The energy(rather, power) is the same, whether you look at the time domain or the frequency domain. It's just a different way of computing energy, which is the same wherever you look from, as per a physical law. How very natural!
The Fourier theory is very nice to study from an electrical or communications perspective. I still like it even after seeing the theory of distributions, which is the one making it all rigorous.
@Ryan. I only said that engineering math is boring when it is seen as a bunch of tools, such as what is given in the book of Kreyszig I mentioned. However it is very interesting when you see it in an applied situation, such as I saw in signal analysis. I am sure the application you mention is also interesting.
It seems it is difficult to convey the problem without actually having taken a course in it. Here's the fundamental dictum of engineering mathematics: "Every function is just its Taylor series around the point you like, and in this Taylor series everything starting from the x^2 term should be ignored".
It is very hard to learn things when presented without any clue of what the hell is going on.
@Ryan. Yes, it is true, it is much better when a mathematician teaches engineering math. But when the syllabus and the book are in a sense fixed, there is not much that can be done. I do not wish to get into all that again and rake up old memories, but one of my engineer friends who also entered math is very interested in properly teaching engineers. He wants to revamp the way the whole stuff is taught, and is an advocate of the idea that only people who have seen rigor are up to the task of engineering math, though the subject itself is not supposed to be rigorous.
@Ryan. My friend is as of now just a postdoc. However I will pass on the information to him and he will be greatly interested, I am sure. Thanks for pointing out.
@Scott Morrison.
You once urged me not to bother replying to calculus questions, etc.. Your point was valid. However, I was once an electrical engineer, and I had a desire to do math, and in the days when I explored the idea or just started making the shift, I must have appeared as a complete dumbass to the professional math students, or profs for that matter. I remember those days, and that was why I was feeling kinder to those amateur chaps.
However in this thread the question had nothing much to gain from MO, as FFT algorithms exist already, and are very effective too on the DSP processors of these days. My feeling was that there was nothing inappropriate in closing the question.
By the way, the question is reopened.
There seems to be a basic philosophical disagreement here regarding what our responsibility is, as a community, to reach out to the wider world. I would like to make two arguments in favor of outreach:
1) Mathematicians have a bad enough perception in the public mind as it is. Anything we can do to convince them that mathematicians are interesting people whose skills have relevance to the real world can only help us out. (We are interesting people whose skills have relevance to the real world, right?)
2) MO is somewhat high up on the public lists of StackExchange sites, so we are going to get a lot of non-mathematician traffic whether we want to or not. The question is whether to view it as a burden or an opportunity.
@Qiaochu: I agree with 1) in principle, but I really don't think MO is a good way to do it because of the signal-noise ratio.
As has been said before by various people several times, there is an argument for having a fairly focused site doing a few things well. Outreach also involves either diagnosis or tailoring to the audience (IMHO). My personal preference is to err on the side of being Stuffy and Uncool and Like Not Chilled Out (but courteous and receptive when the question has been posed helpfully, regardless of its topic).
2) I find this less than convincing. We can make this decision for individual questions, but I am not keen for the site to be swamped with people wondering if we can help get their cat down from the tree, although I don't mind so much being called if there's something strange in the neighbo(u)rhood... Lots of things are popular without being good; lots of things are desired without being healthy.
To recapitulate: your first sentence seems to conflate our responsibility as an academic community with our (purported) responsibility as this online community. I think it's consistent for me to think that in the former role we could and should do more, without thinking MO is the place to do it. Still, I admit that maybe it comes down to my Eeyorish/Benjaminesque turn of personality: this youtube clip (language perhaps NSFW) may perhaps convey something of my underlying prejudices http://www.youtube.com/watch?v=nLb7tOl-pHc