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Let me hypothesize a "broken windows" theory of bad questions. If we don't close questions that are somewhat bad, it makes it more acceptable to ask more questions that are worse. At the very least, it may be perceived by valuable MO users that this is occurring, and they may leave as a result. This is very bad. Our most valuable users are extremely valuable relative to the rest of the users and losing even one of them, in my opinion, greatly outweighs possibly offending the typical user who asks a question that gets closed.
If you disagree with this philosophy, which I think is more or less the philosophy of the moderators etc. (although please correct me if I'm mistaken), then as Gerhard says, you are free to set up your own system somewhere else.
Since I happen to be around here on meta these days and before I leave again:
My opinion is this:
MathOverflow is a resource that is (necessarily) shared by a quite large community with various different interest and ideas.
If in a large math department or just whatever large building there is a common room to be shared by everybody then the more viable strategy to avoid problems and conflicts is that those activities are allowed that do not disturb or alienate too many people. As opposed to a strategy, the analog of which OP suggests as far as I understand, where everything that some people find a cool idea is allowed and then needs to be tolerated by the rest (and this remains true if 'some' is a considerable number). Even more so if the intended activity of these some is outside the purpose for which the room exists in the first place. (This 'outside' does not apply to the recent example, which is ABC I guess, for this there were other reasons, which I won't reexplain here since I did so at (un)reasonable length already. But it does apply to a whole lot of question I think OP has in mind.)
To formulate it slightly more strongly than I mean it and considerably more strongly than I vote:
A question that is not a focused research level mathmatical question is theoretically off-topic on MO; however, it can happen, as any exception to the general rule, that such a question is still tolerate despite it being theoretically off-topic. But, as soon as somebody complains about it, it should be closed.
To get the idea better across why leaving everything open that some might like could be a problem, let me recall from memory, it is meanwhile deleted in case doubts arise to the veracity of my claim please some 10k+ person help me although I cannot be sure the comments to which I refer are still there, that we recently had a question on "Mathematics and marijuana" which was closed quickly (by some including me), which resulted in somebody belitteling or insulting me (depending on how one takes this, and not me personally but those that closed) by saying something to the extent that either we smoke a lot and do not want to get this to be known or are conservative small-minded people (this is not the exact formulation but the meaning was this and the choice of words was at least not friendlier). This comment came though not from a very frequent user of MO still from an occassional one that would be in the standard audience of MO (by academic background), as opposed to some random troll. And then some high rep MO user joined in saying that all this closing is really a big problem.
So, we ought to allow "Mathematics and marijuana" so that some are not unhappy.
Now, in the very end I would have less problem with this question, then with some others we actually have. But, still, if the criterion would be 'some find it interesting' a lot of things would happen, and I have no reason to assume that things like "Mathematics and marijuana" would be the strangest we would see.
I was considering typing
^tl; dr
but the actual post itself caught my eye, so I'll change my response from a simple tl;dr to a much more appropriate
^tl;rd
(really disagree?)
@Alexander Chervov: Well, in theory, I might be strict. But, in practise, I am quite willing to agree to exceptions or at least to a compromise solution; you could see I even participated in various questions that I consider off-topic in theory. In general, I think Gerry Myerson's advice is good. If you really want a certain question reopened, create a meta-thread and present an argument why you think it is a good idea. To continue a bit with my analogy (and use party in a different way). I think it can be a good idea to use a seminar room on occassion for a birthday party, sometimes. But, it should be clear to everybody that this is not the actual purpose of the room. And, as a consequence if on some other occassion somebody objects to the room being used for a party, then those that would like to organize it, should not be overly up-set and insistant, and invoke earlier cases as an argument. Because the effect of this could be just that those sceptical towards too much parties will be more and more hesitant to sometimes agree to them
@Alexander Chervov: it is difficult to discuss this in abstract as "bad question" means different things to different people.
Just briefly, anything that I perceive as an honest mathemcatical question of an at least somewhat advanced nature ('graduate level') is fine with me.
Whether a certain type of question attracts similar ones. Yes, certainly. Based on observation and common sense. One can observe this on small time scales even.
Somebody asks on marijuana, and hours later, somebody else asks referencing this question on some less (potentially) controversial aspect of math and psycholgy.
Some said here they do not ask certain questions as they know they will be closed, so if they'd observe some similar ones that would not be closed, I assume they would then ask them.
Some people arrive here searching on the internet. We had some time ago a (controversial) question on name changes; it turned out OP found the site via searching, due to a somewhat similar question, so thought this was certainly on-topic here.
Somebody else explained here on meta that the first impression of MO was that it was mainly for soft-questions; this was the time of 'department closure', which by the way created in an immediate way a follow-up question ("laid off faculty" or soemthing like this).
Just a small selection.
.
@Alexander Chervov: I think each individual question will not have a dramatic effect; and individually most likely one heated discussion is considerably more likely to make somebody leave than one 'bad' question. But, the worry is that things start going in the wrong direction and then become 'unstoppable'. Perhaps some (possibly including me) are too worried regarding some questions, but then some others in my opinion exagerate greatly the value of a certain type of question. For example, I liked the 'urban legends' questions since I like such stories, but if it never existed would it have changed much anything for anybody?
However, what I think is really the wrong place to worry is mathematical questions that are just a bit too simple, as I can see little harm coming from them; but I can see why others see this differently and also for me this was a bit of a learning process/developpment.
For math.SE I do not know much. But different people have different motivations. I think you give one reason that likely applies to some, but I am quite sute this not all; I think some people just really enjoy this kind of teaching happening there and not here, or just learned about it first and see no reason to particpate in two sites. In any case, conversely, I for example do not forsee participating in a site like math.SE except on rare occassion. (This is not meant against the site; but I know my limitations.)
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