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Why does this question have three votes to reopen?
+1, Felipe. :)
I'm not sure if I did the right thing: I just cast the second vote to re-close the question. Gil Kalai's edits leave it much improved at the style level. But I'd like more content edits (and if I knew with any definiteness what kind of content edits I'd like, I'd make them myself).
I'm tempted to suggest a moderator take the following action:
Then I think more, and ask myself "Self, why do I want this question to be CW?". The best answer I can get is so that more broadly the community feels comfortable improving the question. But I don't have a lot of data that MOflowers feel comfortable editing each others' questions even when they are CW, so that's not good. And the more I think about it, the more I'm comfortable with the question as is.
So then I'm tempted to recommend the following course of action for a moderator:
I can at least justify suggesting that, because the comments (mine included) are mostly in the flavor of a Meta discussion, with some math that should be in the answers; and because I worry that users will see 28 comments (and counting) and decide not to leave an answer?
I don't know. This is why I hope I'm never a moderator at a site like this.
-Theo
I just wanted to mention (again) that the question has also been posted at math.SE and has received several good answers there. Given that, I am especially confused as to why the question needs to stay open on MO.
@theojf,
wow, I was tempted to follow your suggestion about the comments, but there are just too many of them for me to delete! This in itself is, I think, really bad. People need to get in the habit of bringing long comment threads like this to meta.
@drbobmeister1: I don't really understand why you think having the question open at MO will yield fundamentally better answers than having it open at math.SE. I suppose you are aware that many of the top users on MO also follow math.SE and answer questions there? Now it is a fact that most of the people who have answered this question on math.SE are not MO regulars...but this should not be surprising because no one has answered the question on MO. This seems to be rather strong empirical confirmation of my feeling that this question is on topic for a general interest math site rather than a site devoted to questions and answers by research mathematicians.
The argument "I would like to see what research mathematicians have to say about this" for keeping a question open has been advanced before on the meta site, but it has not been popular overall, and in particular not with the founders of the site. There are any number of sites and opportunities for research mathematicians to do "outreach" and educate others on mathematics (for instance: math.SE!). MO is one of very few sites which is "for us". Perhaps I am simply wrong on this, but I find it hard to believe that "What is the geometrical meaning of the third derivative?" is a question that a research mathematician would encounter in the course of her work. Aside from being elementary, it is also too broad and vague: it doesn't admit a definitive answer.
(As a thought experiment, let me place myself in the hypothetical situation of being asked to referee a paper with the title "The Geometrical Meaning of the Third Derivative" for a research journal. I would find the title very strange: it gives no indication of the specific problem the author is trying to solve. If the abstract did not state some crisp result or add some particular context, I would be well on my way towards recommending that the paper be rejected.)
Finally, I am confused by your characterization of this question as "seemingly elementary". In what way is it only seemingly elementary? This question makes no reference to any concepts beyond first semester calculus: in the realm of research mathematics, that's about as elementary as it gets. One could certainly imagine a research mathematician giving a very sophisticated answer to this question -- see for instance the portion of Bill Thurston's essay "On Proof and Progress in Mathematics" where he enumerates several different ways of thinking about the derivative, finally mentioning "#37" [poetic license: he gives 7 previous descriptions, not 36] which is so sophisticated that I would have to pull a differential geometry text off my shelf to fully parse it. But this does not mean that "What is the derivative of a function?" is not an elementary question or that it is an appropriate MO question. I think most or all of us here enjoy reading top mathematicians (who are also good writers!) like Terry Tao and Tim Gowers give us their take on elementary concepts. But they don't do this on MO: they have blogs, they give lectures, they write beautiful expository articles, and so forth.
P.S.: I find it somewhat distracting to conduct a discussion with someone called "drbobmeister1". May I ask you to consider using your real name, as do I and most of the contributors here?
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