This question here was closed because it's "not a real question".

My understanding of the situation is that actually it is a real question (I'll elaborate on this) but Zeynel doesn't know the jargon (like "piecewise smooth") we get taught in classes. I think it is self destructive to just throw out all these sorts of people (ones without formal training). I would like this site to be a much more open environment.

Now I think that this is actually a real question, and infact it is a mathematically important one. There is a famous paradox about staircases being longer than straight lines even though it looks like they converge to the same curve - this sort of issue is a bit subtle, I would say it lives in analysis.

I would like also to second what whuber said:

Let's be a little generous and perhaps offer assumptions needed for this to have a meaningful interpretation and to be true, recognizing that it comes from a non-mathematician seeking help. E.g., "all piecewise differentiable curves are rectifiable."

and quote what Bill Thurston said on his MO profile:

I enjoy questions that seem honest, even when they admit or reveal confusion, in preference to questions that appear designed to project sophistication

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    $\begingroup$ Yeah, I'm actually not thrilled with my vote to close in retrospect. I think the reason is that the OP was trying to ask a specific question, but may have been unfamiliar with analysis. $\endgroup$ – Akhil Mathew Oct 6 '10 at 2:55
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    $\begingroup$ Although I was too late to get a chance to vote to reopen (since the question in question has already been reopened) I would like to second the sentiment of muad's post here. In general, I hope that people here will be generous in their interpretation of non-experts' questions. $\endgroup$ – Matt E Oct 6 '10 at 3:12

It should not be necessary even to ask for a re-opening. There are at this time 2 votes to open within an hour of closing, and two answers that took the question seriously. The re-open votes, answers and positive comments involve at least five different users, most of whom (I presume) would support an opening.

That this meta thread exists is entirely an artifact of the asymmetrical vote-to-close process. This closure, like many others, would not have occurred under a two sided voting procedure.

Closure wars are caused by asymmetrical close/reopen voting process.

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    $\begingroup$ @T..: I happen to agree with you and I suspect that the majority of voting users on this site do so as well. But be that as it may, no amount of campaigning on this meta site will get this policy changed. It is an issue to be taken up at the meta.SE level. $\endgroup$ – Pete L. Clark Oct 5 '10 at 21:55
  • $\begingroup$ @Pete: (1) documenting a few ridiculous cases won't hurt in getting it changed, and (2) until it is changed, it can also help in preventing the hair-trigger closings. Most of the 5 votes to close came from users who post to the meta. $\endgroup$ – T.. Oct 5 '10 at 21:59
  • $\begingroup$ (Now at 4 votes to reopen within 2 hours of closing.) $\endgroup$ – T.. Oct 5 '10 at 22:03
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    $\begingroup$ The idea of documenting what you see as ridiculous cases is great, but you should document them in some thread on meta.SE, for otherwise someone else will need to document your documenting... $\endgroup$ – Mariano Suárez-Álvarez Oct 6 '10 at 1:51
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    $\begingroup$ @T..: Sure, I agree that your post does no harm. But in the campaign for exhibiting the ridiculousness of the current closing mechanism, you might want to choose examples that are even more ridiculous than this. After all, this question got reopened within a few hours, so, were I a defender of the status quo, I might see this as an example of the system working as it is supposed to work. $\endgroup$ – Pete L. Clark Oct 6 '10 at 2:39
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    $\begingroup$ @Pete: instead of 10 mouse clicks we had a (closure - metathread - reopening - more meta) cycle. You wrote quite a few words yourself, which I assume took considerably longer than clicking on "keep open". I don't see these inefficiencies as examples of how the system is supposed to work. Where Math.SE is structured to promote meta-discussion of math.SE rather than Q & A, it is a system failure. $\endgroup$ – T.. Oct 6 '10 at 10:25
  • $\begingroup$ @Mariano: yes, I am compiling a list for separate posting. $\endgroup$ – T.. Oct 6 '10 at 10:26

I agree that the question should be reopened (and have voted accordingly).

Earlier today this question was asked on MO, and was closed as "not a real question". I think this is the correct response for a research-oriented math website, and I cast one of the closing votes.

Afterwards, I got an email from Zeynel asking about why the question was closed. I replied and invited him/her to post on math.SE. (I noticed that s/he posted here shortly before I sent my email.)

I do think that in a general purpose math site like this it is appropriate to find the real question here and answer it. In this regard, Zeynel included in his/her email to me (but not in either of the question postings) a certain math link. Based on this, I think the question concerns the idea that a differentiable curve becomes more and more like a straight line segment the closer one zooms in on its graph. (And I must say that I regard part of this confusion as an artifact of badly written recent calculus books who describe this phenomenon as "local linearity". Ugh!)

I will now go back to the question and add this link, which I think clarifies the OP's intent.

  • $\begingroup$ What's the best way for me to phrase the question "What's wrong with calling it 'local linearity'?" for posting on the parent site? You've got me intrigued and it feels like a Q&A worth having over there. $\endgroup$ – Isaac Oct 5 '10 at 22:12
  • $\begingroup$ @Isaac: the phrasing you suggest sounds fine to me. To make sure people know what you're talking about, you should either link to or excerpt a passage from a calculus text using this terminology. (Unfortunately, it will be easy to find one!) $\endgroup$ – Pete L. Clark Oct 6 '10 at 2:32

I voted to reopen. The question is now open again.

Mine was one of the answers posted before the question got closed. I think it is a common intuition that a nonlinear curve can be well approximated by line segments provided you make them small enough. I think it is a good question to ask if this intuition is backed by any rigorous results.

I feel the OP was unduly penalized for not being schooled in the usual language of mathematics. Educating him would be more productive.


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