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Pete L. Clark comments on "what’s meaning of geometrical meaning of third derivative of a function at a point?" (12057)

Pete L. Clark — Mon, 20 Dec 2010 03:00:30 -0800

@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?

drbobmeister1 comments on "what’s meaning of geometrical meaning of third derivative of a function at a point?" (12056)

drbobmeister1 — Mon, 20 Dec 2010 02:20:22 -0800

@theojf: I appreciate your "worry that users will see 28 comments (and counting) and decide not to leave an answer"; my impression was that a question, once closed, can't be answered. Am I wrong
in this? More precisely, exactly what restrictions fall upon a closed question? Maybe this information is in the FAQ, and though I find myself studying it more and more, I can't recall this issue being addressed
there. In any event, I suspect folks might be hesitant to answer a closed question, or one that might soon be closed. My own experience is that preparing an answer, especially a mathematical answer,
requires taking the time to do so; people are hesitant to invest the time when a question is "under the onus". Comments, being "lighter" than answers, don't require as much effort.

drbobmeister1 comments on "what’s meaning of geometrical meaning of third derivative of a function at a point?" (12053)

drbobmeister1 — Mon, 20 Dec 2010 02:04:08 -0800

I assume that Pete Clark refers to Gil Kalai's reposting at http://math.stackexchange.com/questions/14841/what-is-the-meaning-of-the-third-derivative-of-a-function-at-a-point.
I just read all the answers, and I agree that there are at least two "good" ones--specifically, those by Alexei Averchenko and Jasper Loy. Not to be overly critical, but I don't consider
answers whose substance is merely terminological--i.e., along the lines of "the third derivative is the jerk", to be particularly good. Now, as good as the "good" answers on the math.stackexchange.com
page are, they are not of the caliber I would hope to see on MO. The answers (at least to this question) on MSE seem to me to be, basically, re-iterative. What I like about MO, what feeds
my mathematical soul about MO, is that answers often have a creative spark--one gets the benefits of witnessing creative mathematical minds in action to a greater degree. I feel I have a much
greater chance of having my personal mathematical worldview enhanced by the discussions in this (the MO) environment. This is the reason I think there is a positive "good" in
allowing even *seemingly* elementary questions to remain open.

drbobmeister1 comments on "what’s meaning of geometrical meaning of third derivative of a function at a point?" (12050)

drbobmeister1 — Mon, 20 Dec 2010 00:49:53 -0800

Addendum to my last comment: I agree that the original question, viz. "what’s [the] meaning of geometrical meaning of third derivative of a function at a point?" (again, the bracketed
words are mine), if taken literally, is clearly a question for meta or philosophy; after all, it asks "what's [the] meaning of geometrical meaning . . . "

gilkalai comments on "what’s meaning of geometrical meaning of third derivative of a function at a point?" (12046)

gilkalai — Sun, 19 Dec 2010 22:36:48 -0800

I did not have a strong feeling about if this question is appropriate for MO to start with (certainly it needed the editing), and I dont know should it be reclosed now that it is open in math.SE. (I offered it in Math. SE when it was closed on MO.) In general, I tend to vote open for borderline questions especially when I see people giving or willing to give good answers. There were only very few cases (many months ago) that questions that I regarded very good were closed and in any case I think our decisions justify strong feelings very rarely.

Scott Morrison comments on "what’s meaning of geometrical meaning of third derivative of a function at a point?" (12041)

Scott Morrison — Sun, 19 Dec 2010 20:50:56 -0800

@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.

Pete L. Clark comments on "what’s meaning of geometrical meaning of third derivative of a function at a point?" (12038)

Pete L. Clark — Sun, 19 Dec 2010 20:07:04 -0800

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 comments on "what’s meaning of geometrical meaning of third derivative of a function at a point?" (12036)

theojf — Sun, 19 Dec 2010 19:40:11 -0800

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:

Wipe all comments (repost them here with a note)
Hit the question with the Wiki Hammer
Encourage users to edit the question

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:

Wipe all comments, and repost the comments here with a note.

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

drbobmeister1 comments on "what’s meaning of geometrical meaning of third derivative of a function at a point?" (12035)

drbobmeister1 — Sun, 19 Dec 2010 19:30:11 -0800

@voloch and all: If you check out the original OP, AJAY, you'll see he lists as his website ominstituteofscience.webs.com.
Visiting that website, you'll see it apparently fronts for a very small school, OM INSTITUTE OF SCIENCE. Given these facts,
my hunch is that the OP is somewhat inexperienced in his use of the English language, indeed, he omits an article in
his first posting: "what’s meaning of [the] geometrical meaning . . . " (bracketed text mine). Based on these observations,
I suspect that AJAY originally meant the state the question as revised by Gil Kalai. As to whether the revised question
is too elementary for MO, I re-iterate my comment on the question, "Like many simple questions in mathematics,
it opens the way to some much deeper ideas." OK, that's all for now.

Pete L. Clark comments on "what’s meaning of geometrical meaning of third derivative of a function at a point?" (12005)

Pete L. Clark — Sat, 18 Dec 2010 20:03:20 -0800

+1, Felipe. :)

voloch comments on "what’s meaning of geometrical meaning of third derivative of a function at a point?" (12004)

voloch — Sat, 18 Dec 2010 19:26:28 -0800

"What’s the geometrical meaning of third derivative of a function at a point?" is too elementary or vague for MO. The question asked, however, was a different one "what’s meaning of geometrical meaning of third derivative of a function at a point?". That's too meta. Maybe it should have been asked here.

grp comments on "what’s meaning of geometrical meaning of third derivative of a function at a point?" (12000)

grp — Sat, 18 Dec 2010 17:45:42 -0800

My take is that there are some MathOverflow answerers looking for "a right question", and that this one is close to a right question. The commentary shows eagerness to contribute, and may stem from a desire to improve on the existing technical writeups on this subject. Such improvement may mean getting someone else to answer the question.

If someone would take the courage to edit the question, the revised question might still be closed, but not before a few good answers were attempted.

Gerhard "Ask Me About System Design" Paseman, 2010.12.18

Anton Geraschenko comments on "what’s meaning of geometrical meaning of third derivative of a function at a point?" (11998)

Anton Geraschenko — Sat, 18 Dec 2010 17:24:39 -0800

http://mathoverflow.net/questions/49820/whats-meaning-of-geometrical-meaning-of-third-derivative-of-a-function-at-a-poin

Why does this question have three votes to reopen?