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Is there any documented study of geometry in contemporary primates?
While I think the question is interesting, I think it's interesting to me because I'm interested in evolutionary biology and neuroscience. In particular, the question doesn't have any mathematical content, it doesn't really have anything to do with being a mathematician, and mathematicians aren't likely to know anything about the subject. So I voted to close as off topic. But now I see the question has two votes to reopen (neither of which is the OP), so clearly not everyone agrees with me. Thoughts?
I agree with your initial assessment; this is not a question the average mathematician would be any more qualified to answer than the average non-mathematician.
I voted to reopen this question, since I would be interested to see a knowledgeable answer. The fact that the "average" MO user (as mentioned in the meta-discussion) or that "most MO users" are not likely to be knowledgeable about it does not seem relevant---such an objection after all would apply to most all of our questions---the right question, instead, is whether any MO user knows biology, and I would rather wait and see. The situation is similar to the more philosophical questions that are often closed here, even when there are MO users who can answer knowledgeably and mathematically. – Joel David Hamkins 30 mins ago
I can see where you're coming from, but I don't agree. If somebody were to ask a question like "how should I learn to fly a kite?", I know for a fact that there are active MO users who can answer knowledgeably (and perhaps even mathematically) and that there are MO users who would be interested in seeing such an answer, but I would not hesitate in closing such a question as off topic. I don't see how the question we're discussing is fundamentally different.
@Anton: I agree with you, but perhaps you should also have copied this comment from the OP, which seems to argue that this question is indeed different:
I contend that it is important for mathematics to know why and how we can do or practice mathematics. For instance to isolate mathematical results and presentation from specific biological aspects of our cognition, which can be subtle... One way of studying this is to compare with other living species.
This might be relevant to understanding how very young children learn abstract concepts, but I have some serious doubts about the relevance to research level mathematics, which happens at an entirely different level of abstraction (as far as we know, anyway).
I can rephrase the question in a way that has nothing at all to do with mathematics:
Is there experimental evidence that contemporary (non-human) primates display any significant capacity for higher abstract thinking?
As far as I know, this much weaker question does not have any affirmative answers that aren't heavily disputed within the scientific community.
@Harald: yes, I should have pasted that comment next to my example, but I didn't realize it applied directly to it. I should probably modify my example now that you've pointed out that it doesn't quite do the job I want. Consider the question, "How can I get a good night's sleep?" Surely there are MO users who have something to say on this topic and MO users who'd like to see answers to it, and getting enough rest is even important for being able to function as a mathematician, but I think this question is clearly off topic.
The sleep question is still quite different from the abstraction among primates question, but I'd like to hear exactly what reasoning would bin the primates question as MO-suitable and the sleep question as MO-unsuitable. (I guess it's also possible that somebody would argue that the sleep question is MO-suitable)
I would vote to close this question, and would vote to reclose if it becomes opened. I completely agree with Anton's reasoning.
But here's more: I happen to have a friend from grad school who I think is eminently qualified to answer this question. She is a researcher in primate cognition, and had (when last I checked) personal and professional ties to another mutual friend, who is currently a graduate student of philosophy and has previously studied mathematics and physics.
If the question gets reopened, I will ask her about it!
Certainly you could still ask her without the question being reopened. The fact that you found the question interesting and relevant has nothing to do with whether or not other people agree (and this is precisely what the question being reopened is contingent upon!). I feel like carrying out the entire question/answer on meta at this point would be a good compromise. It seems to me like the recent problems with VA, etc have made it so people are afraid to vote to close anything but homework questions.
The sleep question is still quite different from the abstraction among primates question, but I'd like to hear exactly what reasoning would bin the primates question as MO-suitable and the sleep question as MO-unsuitable. – Anton
It seems to me that the following attempts to answer that question, even if it wasn't stated as a response to it:
The fact that users of MathOverflow may be slightly more interested on the average about the answers to this question than the rest of the internet population seemed to me to justify to ask it there. – ogerard
It seems to me a rather weak response, but it is a response none the less. (Assuming mathematicians aren't more interested than the general population in how to get a good night's sleep.) Still not sure I buy it, though.
I would bet that Gromov has something to say about this topic (warning: 8.5MB file) ...
Someone should suggest to Gromov to come over to MathOverflow! :-)
@Kevin: neat! Thanks for posting that.
@ogerard: Thanks for joining the discussion here! It sounds like the basic argument for posting on MO is that there isn't a better place to do it, but that hasn't ever been a sufficient argument by itself, even in cases where the question was likely of more interest to research mathematician. For example, there are a whole bunch of threads about "discussion-y" questions on MO. See all these threads for more on this. It sounds like everybody understands my reasons for voting to close about as well as they're ever going to, so I won't bother trying to clarify them unless somebody asks me to. I still don't understand people's reasons for voting to reopen, so I invite them to clarify if possible.
A possible better place for this question: the Wikipedia Science reference desk.
I would also look at the Wikipedia article on animal cognition, particularly the section on mathematics, which is packed tightly with citations.
The question What is the most compelling reason to believe Church’s thesis? seems indeed suitable to me. Ihas been discussed already, but it doesn't seem that a strong agreement was found (see critch's comment).
I'd flag it to reopen, but maybe people who closed it will persuade me I should not. In any case it seems a much better question than anything about primates.
At the moment, the question has been reopened, but there are currently four votes to close. Anton and Scott are presumably both in favor of closure, and since there are four votes to close already, I feel that one of them voting to close cannot be considered overruling the voting system, since either one of them will be a fifth vote.
The top answer does not have anything to do with mathematics (other than the fact that Pete is a well-connected academic in a science-related field). The second answer is an answer by the questioner himself, and it is also barely related to mathematics. I think that the question is rather clearly off topic and will not receive a satisfying answer above and beyond Pete's generous offer to find out from a colleague in another field. The difference between this question and the questions on child-rearing, career advice, LaTeX, etc. is that while those questions weren't great, they are things not only that mathematicians would find interesting, but additionally, they were questions being posed to people who would at least have firsthand experience. I am personally against having such questions, but since many people here disagree with disallowing them altogether, I think we should at least restrict questions to those that are at least in principle answerable by a mathematician.
This fails to weed out the "How does one fly a kite?" question, which means that it is not strong enough, but it seems like it's something that people would agree with in general.
@Harry, actually, I'd just decided I wasn't going to vote to (re)close. I'd be genuinely interested if someone gave an nice answer, although I'm not holding my breath for one.
@Scott: Allowing bad or off-topic questions breeds more bad or off-topic questions. When such questions are allowed to be asked, they are used as a justification for reopening other such questions. The evidence for this is in this meta thread and the comment thread for the post in question. I mean, it's your decision, but I feel like you should at least take this into consideration.
I understand that it's probably best to let borderline questions go when the question is asked by a VIP, but it seems like this has now extended to flat-out off-topic questions as long as the question isn't homework and the person who asked the question objects politely enough.
At the moment, the question has been reopened, but there are currently four votes to close. Anton and Scott are presumably both in favor of closure, and since there are four votes to close already, I feel that one of them voting to close cannot be considered overruling the voting system, since either one of them will be a fifth vote.
I voted to close the first time around and I'm following the sanity-preserving rule (enforced on non-moderators) that you can only vote to close once per question, but I do still think the question is clear-cut off topic, and every intuition pump I have leads to the same conclusion. I'm honestly putting in a good effort to understand the argument for reopening, but it's not getting through ... I'm a bit disappointed about that.
I'm not too worried about this question breeding more off topic questions. In any particular case, I'm more interested in coming to the right conclusion than in being consistent, and I think I can convince enough people to do the same. Though I'm having trouble seeing where people are coming from when they say this question is not off topic, the difference in opinion is not so huge that I want to use moderator super powers.
Anton, my reason was that I would be interested to see a knowledgeable answer (rather than anything about whether the question would find a place elsewhere). I find the question to be at least as mathematical as questions about child-rearing, TeX or tenure. – Joel David Hamkins
Though I agree that those questions are not mathematical, if a question can be construed as something like career advice for mathematicians, I'm much less likely to think it's off topic. All those questions can be, but this one can't.
@Anton: that [my argument "it's like arguing that we shouldn't close homework questions because the existing sites for homework help aren't any good"] doesn't seem like a very good analogy, because there are plenty of perfectly good homework help sites, whereas none of us seem to know of any site where this question would receive the attention of the relevant experts. – Pete L. Clark
If somebody argued that MO draws the largest and most capable audience for helping people with homework, I would probably agree. I stand by my proposal that the Wikipedia science help desk is a better place for this question. (Note: in general, I don't think that a question doesn't belong on MO just because there's a better site for a question, but in this case, I would actually argue that MO is the wrong place for this question. I also don't think that a question belongs on MO just because there isn't a better site for it.)
+1 Noah!
I was on the fence regarding these issues (which is why I've remained silent), but I think your comment is the most sensible and reasonable one so far, and I support your proposal.
(I'm not saying that the other comments have been unreasonable -- to the contrary, this entire discussion has been refreshingly civil and very reasonable as a whole.)
Noah, I think I understand where you're coming from. I feel like I should probably clarify why I care so much about drawing sharp boundaries around MO. If I understand correctly, the basic argument is that a question is either good or it isn't. If it's good, we should take it, and if it's bad, then it'll flop anyway so there's no sense in closing it. I fundamentally disagree with this.
I think the value of a site like MO is in its ability to bring together people interested the same thing at the same time. MO is not supposed to be a fun site for mathematicians; its singular purpose is to be a tool for researchers to push forward their collective understanding of mathematics. It happens that mathematicians think this is really fun (otherwise they'd be doing something else), which is what makes the site work so well. But the site only serves its true purpose as a research tool to the extent that it is clear to everybody that it is a research tool rather than something else. To put it another way, I'm not worried about bad questions that will flop: they're not interfering much. I'm worried about "good" questions which will attract lots of attention, maybe get some really interesting answers, but undermine my goal of getting mathematicians to think of MO as basically a serious tool.
Now I've painted a very stern picture, but only to emphasize the fundamental goal of making better mathematics and better mathematicians. It happens that a certain amount of casual atmosphere and playing around makes for better math. I basically agree with the sentiment in the blog post Stack Overflow: Where We Hate Fun. I'm happy to leave questions open, but if a "good" question is going to encourage people to come to the site for the wrong reasons (or discourage people in the mood to do some real math from coming to the site), then it will make it harder for the right people to connect. In those situations, I will argue that "MO is not the right website for this" and campaign for closing the question.
Of course I realize that mathematicians are interested in other things as well, and I have no objection to those other interests being fulfilled. I hope I've made a convincing (or at least coherent) argument that those other interests should often be fulfilled on other websites, and that even if there is no other website better suited for a given purpose we should sometimes actively discourage people from using MO for that purpose.
Anton, I agree with what you just said completely.
Here's a radical idea/feature request: make it much less obvious that a question has been closed.
Don't modify the title, don't put a big "closed" box at the bottom, just a small line of text saying "You may no longer add answers to this question.", perhaps with a link that shows who "closed" it.
Essentially, I'd just like a way to "sink" questions quickly off the front page, while otherwise treading as softly as possible.
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