> But there is a sarcastic answer which seems to be written specifically to embarrass the questioner. >

I assume you mean Mark Sapir's answer, which I did not find at all antagonistic to the OP but rather an attempt to show what is wrong with the question itself.

If you want to attribute bad motives to a user ("which seems to be written specifically to embarrass the questioner") you should have the courage to accuse under your real name.

I think my only guideline, which is not to delete questions with potentially significant answers without permission from the author, is reasonably clear and sound. Moderators do this when deleting stuff, and we also regularly undelete questions deleted by their owners for the same reason (see here).

Please do not delete questions with potentially significant answers without first asking permission from the authors of these answers.

Apparently votes to [un]delete can be repeated (unlike votes to close), so this oscillation between deleted and undeleted could go on indefinitely.

I was completely unaware of this; I thought this was like for open/close. If I had known this my opinion would have been clear from the start (as opposed to undecided). In my opinion this obvioulsy implies that deletion should only happen in very clear cases or after discussion that leads to this conclusion essentially without oposition. If not this ccould lead to complete chaos. [Added: or significant extra work for the moderators]

In answer to Andy Putman's question far above, I would propose limiting deletions to cases where the question, answers (if any) and comments (if any) are all clearly spammy/undergrad-homeworkish/crackpotish. If reasonable people might disagree on whether a question is in this class, then it shouldn't be deleted. I think the site would function just fine if there were no deletions at all.

Imagine a world in which the stackexchange software allowed only moderators to delete. Would MO be a disaster and unusable in this case? Of course not. I think that such a set up would be much preferable to the current situation, where any three easily irritated 10k users can delete a question.

[certain] researchers who choose not to participate because of irrelevancies on the site

where irrelevancies means the occasional silly question, does not seem to me that important. I of course wish as many relevant people participate in the site, but I also expect people to be able to filter out a modicum of things they do not care for—even an Eminently Unimportant Mathematician like me manages to deal with it (I can't remember the last time one of my 'favorite tags' showed up in a question, although I know they do work because a semester ago a question by Kevin Lin appeared in yellow...)

I don't think the aspiration to have everyone on board is reasonable, and if some people are not willing to participate in the site, well, we will read their papers.

In what way will deletions of closed month-old questions or also if it happens more quickly affect whether, to give a current example, user Mike Massa asks questions and they are thus on the front page for a while?

There is, IMO, zero mathematical content in the thread.

[ADDED: Sorry regarding the answers I was apparently completely off.]

I'll say something about why I think this question is interesting (although not phrased particularly well). Mathematics has always been inspired by mathematical phenomena appearing in nature. By "nature" I mean everything in the physical world - physics, chemistry, biology etc., though for the purposes of this discussion I exclude human activity. There are examples of inverse square laws in nature, there are examples of exponential decay, and so on. Maybe there are directly observable examples of modified Bessel functions: who knows. Looking at how mathematics appears in nature often leads to new mathematics: take string theory, for instance, which may or may not be a good physical theory, but has certainly led to advances in mathematics.

So I think questions of the form "does such-and-such a piece of mathematics appear in nature?" are potentially interesting. Of course you could ask an unlimited number of such questions, but what makes this one stand out is that (i) there appears to be at least one example of prime numbers popping up non-coincidentally, and (ii) there don't appear to be so many examples that it's boring.

Out of interest, how would the pro-deletion people react to a question along the following lines? "I've been investigating such-and-such an abstract dynamical system, and when I ran some numerics on it, I discovered to my surprise that the period was always a prime number of units of time. Are there other examples of dynamical systems with unexpected prime number periodicity?" That's not phrased enormously well either, but would you consider a question of this type so beyond the pale that it deserved deletion?

Regarding the off-topic matter, if you have an easy deduction of the result described in that n-Category Café post from the result in your paper with Guba, I'd like to see it. I tried to find one years ago, when Fiore and I first did that work, but with no success: I couldn't see a direct way of deducing either characterization from the other. I also discussed this with Guba when he was visiting Glasgow in about 2005. But let's continue this discussion at the Café.

Mark, Andy, Bill, and others who want to delete this, you may not be able to understand what value others see in this question, but you'll observed that others do see value in it. I think that under those circumstances, it would be respectful not to prevent everyone from reading it.

The fact that there were almost no interesting answers is interesting in itself. Maybe the famous cicadas really are the only known instance of this phenomenon. Judging this question to be a failure for that reason is like judging a scientific experiment to be a failure because it did not produce the result expected.

I wasn't very impressed, either, with the unconstructive tone of some of the answers. Yes, the OP could have been clearer about the term "nature" and the role of coincidence, but I thought it was pretty obvious what was meant. If the question is undeleted I might have a go at improving it.

I think deletion should be kept for obvious homework questions that receive no answer, spam, and the like.

I think the "a real mathematician" argument flawed. In fact, a closed question reflects better on MO since it shows that the community is able to identify poor questions (it also shows how politely (or not) people react to poor questions). An aseptic community is not attractive and might be argued to discourage just as many people.

If at some point the software can be improved again, it might make sense to prevent such questions from appearing on positive lists (such as "most votes"). Although they might serve their purpose in searches since they discourage the repetition of poor questions.

Yet, the gleefullnes and the feeling of superiority some display in doing so is a bit shocking.