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    OK, my title is a bit hyperbolic. But it seems to me that, whenever someone asks a question related to mathematical modelling, or with a real world application, it gets voted down. Here are some examples which I think would involve nontrivial math:

    I say "I think" because I'm a very pure person myself, and none of these are near my expertise. But all of them make me think of mathematical questions which I don't immediately see how to answer.

    Maybe the answer is that the asker needs to take responsibility for transforming his or her question into the language of mathematics. But, really, I don't see why. Everyone is perfectly happy if I ask a question like "How should I think about phantom homology in terms of category theory?" Why isn't it valid to ask "How should I think about running in terms of ODE's?"
    • CommentAuthorHarry Gindi
    • CommentTimeDec 8th 2009 edited
    Well, the first one was tagged "algebraic geometry", so I was obliged to make the comment, "I find it hilarious when people tag things like this "algebraic geometry". "Hey! It's got some algebra and some geometry, we're in business!"", which I've deleted since it is no longer relevant. Also, having only downvoted the first question (that I remember), I feel like it's inappropriate since it's not stated in mathematical terms. With a math question, one should expect a certain amount of clarity, and that question surely lacked it.

    Having now seen your edit, I will explain my objection to "How to think of running in terms of ODEs". First of all, simulating running would require a somewhat sophisticated mathematical model of the human body. If the person had come here with a model already partially developed, then that would be another thing entirely. Second of all, it's asking us to translate an imprecise physical concept into something precise. Walking and running are different, but there is no clear line where one becomes the other. I'm sure you know what I mean.

    Now, with phantom homology, this is a purely mathematical subject that I know nothing about, but we've got homology, which is intimately related to category theory, and a good deal of literature including Hochster and Huenke's entire book on the subject. So it's natural to believe that there is a useful interpetation of phantom homology in terms of category theory, which is (at least for now) the best set of foundations for modern mathematics. The distinction is clear.

    Also, I'm going to admit that I hate applied math. I'll let this quote explain for me: "'Imaginary' universes are so much more beautiful than this stupidly constructed 'real' one; and most of the finest products of an applied mathematician's fancy must be rejected, as soon as they have been created, for the brutal but sufficient reason that they do not fit the facts."
    But there are plenty of mathematical papers written on how to take a real world concept and bring it into the language of mathematics. Brownian motion, the heat kernel, markov models, phylogenetic algorithms, the Black-Scholes equation, QFT, Arrow's paradox ... There's always a question as to whether such a paper belongs in a physics/biology/economics journal or a math journal, but it is a question and sometimes the answer is on the math side. Why is it inappropriate to ask questions like this here?

    I also don't think that the "What is the categorical way to do X?" type questions are all that unambiguous. Sure, the definitions of phantom homology and of an abelian category are clear, but fitting them together requires an understanding of aesthetics and intended application which feels to me very similar to trying to build a mathematical model for a real world phenomenon.
    I feel lke the difference is that there is a developed formalism for the second question, while the first question only has a vague feeling of physical intuition.

    Sorry to take your conversion a bit off-topic, but what do you guys think about reopening Is it best to run or walk in the rain? It there any dispute that there is plenty of hard math in certain optimization questions related to moving 3D shapes?

    I think that we shouldn't let the standards here get that blurred, but if the community is absolutely for it, then I'll just have to accept it.

    I feel like quoting Peter Lax, in his acceptance speech for the Abel prize:

    Traditionally mathematics is divided into two kinds: pure and applied. The relation of the two is delicate. The great applied mathematician Joe Keller's definition is: pure mathematics is a branch of applied mathematics. He meant that mathematics, beginning with Newton, was originally concerned with answering question in physics, it is only later that the tools and concepts used were elaborated into theories that took on lives of their own.

    If we take that point of view seriously, if we disallow applied mathematics then pure mathematics goes too. But I am all for applying strict standards; either the question or any likely answers should contain real mathematics, and merely asking us to turn a vague non-mathematical question into a mathematical one is unacceptable. The questioner should be expected to do his own hard work. But I think it should be okay to ask, say, what models of granular flow generate interesting mathematics. Given the crowd that usually hangs out at MO, there may not be many useful answers, but that might change, and I don't think it's right to scare away the people who want to discuss such issues.

    I agree that there is a place for applied mathematics here, but that question (first one in David's list) is awful. Modeling something like that is a nontrivial task that would require a nontrivial amount of time. For a question like that, the person asking should have some sort of plan of attack, if not a partially working model. If you're asking a question like that, you should be very familiar with the material, the clearly stated goals, etc. I can't think of an example offhand of something similar in pure math, but these standards should apply to pure math questions of similar complexity.
    I also have to disagree with the "pure" people. I am by most accounts a pure mathematician myself, and the applied problems are far from easy for me, but are still quite interesting. I personally find the (to me unmotivated and excessively abstract) pure problems posted on this site not to my taste; however I realize that many mathematicians enjoy those questions--I've actually been using this site to try and figure out "why are these subjects considered interesting".

    Conversely, I actually do find most applied math interesting and motivated, but I don't know any techniques or results. I have to disagree with fpqc's last comment in that it would not be clear to me at a first (or even 20th) glance what was "a nontrivial task." Until I tried to do it, I thought inverting matrices was a trivial task--actually doing this with your own code can be quite hard.

    Short story long, I think applied math is if anything under-represented on the site, and I would hope that these questions are given their own time and opportunity to find their own place here.
    • CommentAuthorsigfpe
    • CommentTimeDec 8th 2009

    I doubt they're asking for a model in the sense of an accurate simulation. People who work in animation frequently use ad hoc formulae for this kind of thing. Some sines and cosines to model the circular motion of feet and then some basic geometry to do the "inverse kinematics" to figure out where the knee should be. I modded it down because this is a routine task. There is all kinds of interesting mathematics here if you want to generalise the problem. But that is *not* what the poster was asking for.

    I think questions 2-4 were interesting however.

    I happen to be better qualified to judge "pure" questions than applied questions in most cases, and there are still only a handful of 3000+ reputation users, so if there is a question that doesn't look like a good question to me, but I'm not absolutely sure, I'd rather close it (and reopen it later if it turns out I was wrong) than let it slide, setting the precedent that poor questions are acceptable. I don't have a problem with people saying that the moderators at MO are a bit trigger-happy with closing questions, but that they are fair-minded and will reopen the question if you make a good case. It's more important to me to keep the quality of the material high than to be super welcoming.

    That said, I (almost) always leave a comment (or vote up a comment) explaining why I've downvoted or closed a question. If I can't put into words what's wrong with the question, then there is likely nothing wrong with it. I don't think I'm putting topics outside my areas of interest at very much of a disadvantage with this strategy. I agree that it's a shame that some areas are so poorly represented.

    sigfpe's arguments are convincing me that there may not be anything interesting in the running question. (Or, if there is, that it hasn't been discovered yet.) My approach to that would be to pass the question by or, if I was certain I knew what I was talking about, leave a comment saying "Experts tend to solve this sort of thing by ad hoc formulas; there are no real models." I am not very bothered by closing a question if there is no good answer that could be given; I am more bothered that I think people are assuming any problem is dull if it relates to the real world.

    Anton, I'll try to bear your priorities in mind. I think you've shown very good judgment in what you've closed, and I'll feel less annoyed when I disagree with you now that I know that you expect people to argue back.

    @Ilya: obviously I'm not going to vote to reopen my own question, I think that would be an abuse of privileges. Why don't you vote to reopen and see what happens?

    I notice that Tom Leinster has expanded on his reaction. I have some sympathy for his point of view; I would argue, though, that I think that this particular subject comes up more often than most and that as professional mathematicians we should be aware of ways to sell our subject - but maybe that's an argument for a single meta-question rather than lots of little ones. I also tried quite hard to ensure that the question was focussed and had a possible answer that didn't involve going in to all the details of the mathematics of walking in the rain.

    One slightly bizarre reason for reopening it would be to allow it to sink down in the morass. I think that the fact that it was closed has kept it further up the "active" list than if it had merely been answered and forgotten. If I'm reading the reputation scores correctly, then it is currently 11-4 in favour, with 2 favourites. I suspect that if it hadn't been closed, it wouldn't have gotten half of those votes.

    More generally, I'm not in favour of closing questions that turn out afterwards to not have a good answer. I think that closing a question sends the message that this shouldn't have been asked. Slightly more borderline is the type of question that shouldn't have been asked in that way (the one on Badiou and Mathematics springs to mind); I would still vote to close these but with a "revise and resubmit" comment. But closing a question just because it turns out later to have been a daft question sends the wrong message, I think. I like to keep in mind the following quote about working for Pauli:

    It was absolutely marvellous working for Pauli. You could ask him anything. There was no worry that he would think a particular question was stupid, since he thought all questions were stupid.


    I've woken up and thought more about this. I'll take the liberty of reposting Tom Leinester's comment on the running in the rain post:

    What I disliked about the question was that Andrew didn't present any evidence that there was anything mathematically interesting going on. (Indeed, he used the words "particularly dull".) It's very easy to ask questions of the form "Here's a real-world situation. Is there any interesting math behind it?" You could rattle off dozens of such questions. Whether there turns out to be interesting math behind this question is beside the point. – Tom Leinster

    This poses the central question very well. I am thinking about it, and I think I disagree.

    I downvote questions all the time because I know that the answer is elementary (example). On the same grounds, I downvote applied questions where I can see a solution using undergraduate math that I think should be obvious to a professional mathematician. (Not finding an example right now.) But, if I think about the question a little and don't get anywhere, I ignore it and wait to see what other people post. Running in the rain seems borderline to me.

    I think that the right standard here is the same as for pure math: show that you have put some thought into the problem, usually by mentioning what you've already tried. In particular, it would be good to indicate you have some understanding of what a mathematical model looks like. I tried to do this when I asked my physics question.

    I still think, though, that people are holding applied questions to a higher standard, and one that seems unreasonable to me. I'll see if I can give some examples in a bit.

    That running question still didn't meet the standard that you just stated. I'm completely for holding everyone to high standards.

    @David, when you say

    This poses the central question very well. I am thinking about it, and I think I disagree.

    Which bit are you referring to?

    As mathoverflow's answer to Jon Skeet, I think that your opinions are very important, and explaining what you do is useful to the rest of us so thanks for doing so. Please carry on.

    I should say, in case it's not obvious, that the "walking in the rain" question was partially an attempt to figure out what is a good question for MO. I've said this elsewhere but I think it worth repeating here to be sure everyone understands. That's one reason why I think that closing it was unfortunate - it means that it can't be used as a test case for the community. I also want to say that I have absolutely no issues with that question being voted down nor with anyone expressing (politely, as Tom has done) their opinions on it.

    Ultimately, I'm still trying to figure out where MO fits in in my arsenal of mathematical resources. Not being an algebraic geometer, it's not proving a good fit in my research so my questions have more pedagogical or just plain "that's interesting, or is it?" motivation. This naturally puts them nearer the borderline but if it helps clarify said borderline then that's still a useful endeavour.

    • CommentAuthorHarry Gindi
    • CommentTimeDec 9th 2009 edited
    I find your questions interesting, for what it's worth. Also, if you don't post questions related to your research, how do you think we'll ever take MO back from the algebraic geometers?!

    Oh, and for a moment there, I thought you were saying that I was MO's answer to Jon Skeet. That would have been funny, since he's helpful and knowledgeable, and I've got a thread full of people jumping down my throat because I'm "too mean" (see running question). That would be like an anti-Jon-Skeet.

    @fpqc: I already have posted questions relevant to my research. They are languishing down in the depths at the moment because no-one around here has anything useful to say. I'm not sure what a good strategy would be for increasing the number of, say, functional analysts around here. Any suggestions?

    Ask a bunch of questions, then tell all of the functional analysts you know to come check out the site while they're stil near the top. They'll see the illusory thriving community of functional analysts here and decide to register.

    I'm not exactly sure that will work, but I always love elaborate plans that resort to trickery.
    This thread just drew the running question to my attention. There is certainly an enormous amount of effort put into modelling running, but just because we don't have any experts in the mathematics of biomechanics around Math Overflow doesn't mean it's an uninteresting question!

    (re sigfpe's comment, in numerous fields -- notably medicine and anthropology -- the study of motion is *not* done ad hoc.)
    • CommentAuthorKevin Lin
    • CommentTimeDec 9th 2009 edited

    @fpqc, are you also for holding everybody to high standards for politeness and tolerance? ... ;-)

    I'm for high standards of politeness, but low levels of tolerance for bad questions. I mean, I'm polite to every member who has asked or answered any question that displays some amount of premeditation and thoughtfulness.
    • CommentAuthorKevin Lin
    • CommentTimeDec 9th 2009

    Sure, but there's no reason to be impolite to people who you perceive to not have displayed enough premeditation and thoughtfulness.

    Does humor count as a reason?

    Being impolite is essentially never humorous, at least where I come from. That said, in non-academic social circles I often feel left out by my inability to "put someone down" in a "funny" way...


    I posted some thoughts on downvoting and commenting on another thread, but they apply pretty well here as well.

    @Andrew: One strategy I used early on to get people to start using MO is to find (or ask) a question that I think somebody knows the answer to and email them a link. Something like

    Hi X,
    Here's a question that I'd like to know the answer to for which you probably have an answer:


    @Anton: my main problem with that is that I don't know who are the right people to email. If I did, I'd just send them the question directly.

    Meanwhile, one of your topics on functional analysis already has 8 votes (at 10:21 AM EST), so there must be some people who are interested.
    I'm coming a little bit late to this discussion, but just received some very nice emails from Anton about my difficulties with the question:

    Which I think are quite related.

    Anton points out that the question, as stated, is pretty trivial. I can't argue with that, and certainly some sort of 'punishment' is deserved for that. On the other hand (as I mention briefy in a comment there), it is closely related to some 'real' math (my provisional definition for that at the moment is 'papers have been published on the question within the last 10 years in Annals').

    My question for those of you here, then, is what should be done with these questions. My first thought was to try to get the original question edited, but it was suggested that I simply re-ask the question in math-speak. I have no problem doing that in this case, and it is quite closely related to what I do, but it could lead to a fair amount of closing-and-cleaning.

    As a last thought on this subject, part of the reason that I feel a little bad penalizing this question is that I've started (and seen started) a number of questions in this manner, and it is very easy to be blind to reasons that the question doesn't make sense, or has a trivial answer. Maybe one solution is to replace these sorts of questions start with ones like 'there is obviously something going on with the order of dealing; can anyone tell me if this has been turned into math?', or (maybe better) 'can somebody tell me what formalisms have been used to study shuffling, and what can be done with them?'. That last one might be about the same as current questions along the lines with 'what's the deal with K-theory'.
    Don't feel bad about penalizing this question, just be happy that nobody caught your question, I guess. I mean, you can always ask the question again, once the necessary work has been done to fix the problems with it.
    Sorry, I think I was confusing - I could ask the question right now, since I'm very familiar with the mathspeak formulation, as well as the partial answers we have. I was really asking whether that was the appropriate response for vague-but-close-to-real-math questions, before I end up posting and immediately answering a bunch of questions and annoying people.
    I feel like it was an appropriate response. Others may disagree.

    I don't know enough information about your particular questions, but I'd like to say that questions can be closed for many reasons, for example, for being outside the core competency of people on MathOverflow.

    Thus, even a very well-written and interesting question is likely to get closed if its main topic is far enough from pure math to suggest that the experts in this particular question would be concentrated in other places.

    The questions within the core competency of mathematicians, that is, mathematical questions, are sometimes vague, like, indeed, many questions about K-theory. But it's often immediately clear for the person who worked on K-theory what the question is, even if it is sloppily written, poorly thought or contains incorrect statements.

    This is the way community works — and I don't think I have an easier way to formulate what types of questions will be welcomed by voters and moderators than "they should be interesting to mathematicians". Perhaps somebody will be able to explain it better than me.

    "questions can be closed ... for being outside the core competency of people on MathOverflow."

    Ilya, that standard doesn't make since to me, because we don't know who may be lurking. I would agree that closing a question because it is outside the core competencies of mathematicians makes sense*, because this is a place for mathematicians.

    But I don't see why we should close a question because the current main users of MO wouldn't be good at it. For example, I don't think any of us knows much about numerical analysis. But, if a numerical analyst is lurking, see such a question and answers it, then she joins our community and this becomes one of our competencies. I think this is all to the good.

    Apologies; my post must have been unclear, since I intended to include numerical analysts and other people with math competencies which may be currently under-represented into the "community" and "people on Math Overflow".

    Let me give an example of question that I would consider a good candidate for closing as "good, but doesn't belong here": a question asking to write a good code in a specific programming language to solve a specific math program. Those questions will find a rich base of highly competent people to discuss it on Stack Overflow.

    Here's a specific example which in my opinion is very well-suited for StackOverflow (where it was posted).

    I was an active participant of Stack Overflow before I found Math Overflow, and I would really like to answer the above question. But I've come to realize that the best thing to do if such a question is posted on MO is to "transport" it somehow to SO. For example, it doesn't really fit the "arXiv+" classification scheme.

    Again, my post was not intended to convey any more complicated thoughts than the observation above.


    @Ilya: It is interesting that the answer you linked to begins with the words “I think this belongs on MathOverflow, but I'll answer since this is your first post.” I can see now an inverse turf war looming. On MO: “This is programming. Take it to SO.” And on SO: “This is math. Take it to MO.”

    Sometimes questions are "too localized," which I think is probably the only good reason in the topic closure list. For example, posting a question about a technique in data analysis would be fine, while asking a question asking about how to analyze a specific data set is inappropriate. There was a thread like this recently, if anyone remembers what I'm talking about.
    I have seen many answers to "fpqc", here and in mathoverflow, but nobody signs with that acronym . Also, "fpqc" gets no answer if I type it in "Users" .What does this mean?
    • CommentAuthorHarry Gindi
    • CommentTimeDec 11th 2009 edited
    I am a man of many names and many mysteries is what it means. (Anton requested that I use my real name, so I changed it from fpqc to my real name. My irc handle is fpqc.) By the way, I wish everyone still called me fpqc.