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I see two three four votes to re-open the question:

I need mathematical proof that the distance from zero to 1 is the equal to the distance from 1 to 2.

The question was closed as "not a real question" and currently there are two three four votes to re-open it. From the high number of votes and extremely high number of views—momentarily, Zev's answer is at +44 +46 and the number of views approaches 2.5k—I conclude that this question is interesting to a substantial number of users of this site.

Since voting to re-open without notifying anyone is doomed quite likely to fail, I open this thread in order to have a discussion.

I'm not particularly thrilled about this question and I suspect that the main reason for the number of views is its argumentative nature. I have to admit that I only skimmed the question and answers. I have no strong feelings about this question and I'll likely abstain myself from voting. However, I'd be strongly in favor of keeping it protected if it should be re-opened in order to avoid try to minimize advice on saving oxygen or the like.

Added: I would be very interested in reading opinions and reasons of those who voted to re-open or think about doing it.

Edit: Now that all but one of the re-open votes have withered away, I think this case can be considered closed.

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  • $\begingroup$ I don't really want to read the existing discussion, but there is a point worth making here about the way modern mathematicians view the notion of proof and someone might as well make it if it hasn't been made already. $\endgroup$ Commented Jun 28, 2011 at 4:21
  • $\begingroup$ I completely agree on the protected question. $\endgroup$ Commented Jun 28, 2011 at 5:57
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    $\begingroup$ BTW, Am I the only one, who thinks such questions should, at least, be CW?.. $\endgroup$ Commented Jun 28, 2011 at 6:33
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    $\begingroup$ @Grigory: I totally agree with that. $\endgroup$ Commented Jun 28, 2011 at 6:51
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    $\begingroup$ To second Grigory's remark: would whoever casting the final opening vote (if it happens), flag for moderator attention to convert to CW? $\endgroup$ Commented Jun 28, 2011 at 12:31
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    $\begingroup$ @Willie: Can't you just make it CW now (if you want to)? $\endgroup$ Commented Jun 28, 2011 at 13:08
  • $\begingroup$ @Jonas: possibly. But I'm wary of "unintended consequences" in the software. (For example I don't know whether Mod action of CW would affect the protected status, or the closed status.) $\endgroup$ Commented Jun 28, 2011 at 15:13
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    $\begingroup$ ...And one more thing: I don't like too much, how advocates of reopening don't try to convince anybody (or even explain their POV), but just silently vote to reopen... $\endgroup$ Commented Jun 29, 2011 at 6:52
  • $\begingroup$ I liked "doomed" better. It had a nice fatalistic, choiceless ring to it. :-D $\endgroup$ Commented Jun 29, 2011 at 7:49
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    $\begingroup$ @Gri Was that meant as a joke? The problem with silent closing votes is much worse than silent reopening votes. Moreover, it's much easier to close than to reopen - a fundamental asymmetric design flaw in the software platform. $\endgroup$ Commented Jun 29, 2011 at 15:19
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    $\begingroup$ @Bill In general, I agree with you. But in this particular case there is a discussion here, on meta, and everybody here agrees that the question is pure offtopic -- yet there are more and more reopen votes. AFAICS, the only way to avoid "close-reopen war" is to settle it on meta -- and what is your suggestion? $\endgroup$ Commented Jun 29, 2011 at 15:22
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    $\begingroup$ @Gri I don't think there has ever been a close/open war here. In general the asymmetry between closing and reopening is so severe that I don't mind if some questions get reopened that shouldn't because far too many questions have been closed that should not have been. Five very conservative and/or biased folks should not be able to censor the content of a general mathematics site. The software model does not work well for a general site like this. (Note: I did not vote either way on this particular question). $\endgroup$ Commented Jun 29, 2011 at 15:27
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    $\begingroup$ @Bill (I don't think too many questions are closed, and I certainly don't believe in unmoderated sites.) Note only, that I don't suggest that "5 biased folks" should be able to do all they want (e.g. to reopen clearly offtopic question) -- on the contrary, I suggest we should discuss all controversial cases on meta $\endgroup$ Commented Jun 29, 2011 at 15:36
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    $\begingroup$ @Bill: just for my understanding: what's asymmetric about five votes closing a question and five votes reopening a question? $\endgroup$ Commented Jun 29, 2011 at 15:37
  • $\begingroup$ @Gri Being here for 4 months, I don't think you were around in the early months of the site - when it was much worse. There have been many complaints about the asymmetry of the open / close design. Nowadays it's not as bad because a more representative sample of the main site is on meta, so there is more of a chance to open questions that were wrongly closed. I agree that meta discussion is one way to work towards solutions. $\endgroup$ Commented Jun 29, 2011 at 15:39

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I voted to close the question for a few reasons. One is in line with Pete Clark's comment - the question had attracted a huge amount of answers. I think there were nearly 20, but I have a hard time remembering because most of them were not actual answers, but instead caustic replies. Another is because I do not believe that this question borders on the philosophical: if one goes to standard definitions for distance, than "proving" that the distances are equal is no more than a one line proof. But this question removes all such common definitions despite its low-key presentation (at least, it appears so to me).

It also seems to me that this question requires the answer to define what the numbers 0, 1, and 2 are and to define distance. There are many ways to do this. Which one is appropriate? Further, what answer would satisfy the OP? Suppose someone were to approach it with a formal system, and through logic and set theory arrive at an answer? Even mentioning such things scares me - although I am studying math, I stay as far away from this sort of thing as possible. Ultimately, it's paradoxically inaccessible and widely recognized.

So then one would fall back on an answer like Zev's, which although excellent in that sardonic sort of way, admittedly doesn't answer the question.

The question and answers seem absurd (again alluding to Zev's answer).

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    $\begingroup$ Thank you very much for this assessment. $\endgroup$ Commented Jun 28, 2011 at 6:53
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    $\begingroup$ I count 14 answers in total. There are only two deleted ones. One is the oxygen thing and the other one tries to make a point with "invent your own maths. its just in your head." and culminates in the brilliant punchline "you can ask him to change number system to use rubic cube colors instead of number. then, monalisa will become theory of relativity." $\endgroup$ Commented Jun 28, 2011 at 6:57
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    $\begingroup$ I strongly agree with this opinion. $\endgroup$ Commented Jun 28, 2011 at 10:38
  • $\begingroup$ Well, I think there certainly are times when a valid answer to a question is "That's not the question you really want to ask." I think my answer probably serves the OP's purpose of getting ammunition for his next encounter better than one that actually does explain one or more of the methods for rigorizing notions of 0, 1, 2, and "distance", despite the fact that the question as asked technically required those things. But I agree that the question was attracting too many answers, and that "protected" status doesn't look like it'd be sufficient; so closing seems like the right thing to do. $\endgroup$ Commented Jun 28, 2011 at 18:30
  • $\begingroup$ @Grigory: That would be the OP's purpose in asking the question, regardless of whether he said so or not - but as usual, an explanation of where one's question arose is useful in informing potential answerers. As to my answer, it's on-topic because it's presenting a position about the philosophy of mathematics that's relevant to the OP's question, albeit with extraneous material about how to effectively use it in the situation the OP described. If you think it's really necessary, I could make the advice about how to effectively use it into a comment, or send it to the OP privately. $\endgroup$ Commented Jun 29, 2011 at 16:21
  • $\begingroup$ @Zev I'm not really sure anymore, what I want to say, sorry. $\endgroup$ Commented Jun 29, 2011 at 16:24
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If you are attempting to monitor close (and reopen) votes and have 10k rep -- as you do -- you can do so through

https://math.stackexchange.com/tools?tab=close&daterange=last7days

e.g. the "tools" menu available to 10k users, and the "close" tab within them.

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  • $\begingroup$ Thank you, I'm aware of that. My rationale is: Given the high number of views and strong feelings that were apparently produced, it would be good to collect some arguments why it should remain closed or why it should be re-opened. $\endgroup$ Commented Jun 28, 2011 at 4:50
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    $\begingroup$ @theo that is fine, I was just addressing "Since voting to re-open without notifying anyone is doomed to fail" by making sure others with 10k rep are aware of this page and can in fact monitor close and open votes to taste, etc. $\endgroup$ Commented Jun 28, 2011 at 4:51
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Regarding your last sentence, protection does very little to avoid such advice. A problem I have with the question is that it invites such advice. I initially found the argumentative way the question is written to be entertaining, but it ultimately was the main reason I voted to close. The question invites social advice as much as mathematics.

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I cast the first reopen vote. Here are some things I was thinking about that led me to do so:

  • I think it's most definitely not "difficult to tell what is being asked here. This question is ambiguous, vague, incomplete, overly broad, or rhetorical and cannot be reasonably answered in its current form." So closing it as "not a real question" is inappropriate. If it were closed as off-topic [edit:] or subjective/argumentative, I might have thought a bit more about it.
  • I think it's absurd to close a question because it hits a certain number of answers. That's not a listed reason to close and I cannot fathom how that makes sense.
  • I think the question was generating some interesting mathematical content, even if there was a good bit of noise.
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    $\begingroup$ Thank you very much for this explanation, much appreciated. $\endgroup$ Commented Jun 29, 2011 at 18:25
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    $\begingroup$ I voted this answer up, even if I'm not sure if I agree or disagree. I understand the reasoning, but I'd like to point out that the closure reasons are only a very rough indicator of what the people actually thought. @all: Before this answer gets downvoted into oblivion, please consider leaving a comment what exactly it is, that you disagree with. Note also that Isaac had the courtesy not to vote the other answers down that expressed a contrary opinion. $\endgroup$ Commented Jun 29, 2011 at 18:33
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    $\begingroup$ @Theo: While it's true that the closure reasons are just rough indications, a plurality of people chose "not a real question" as a better fit than "off-topic" or "subjective/argumentative" and as I'd said, I don't see "not a real question" as a valid choice in this case. $\endgroup$ Commented Jun 29, 2011 at 18:40
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    $\begingroup$ (Re: 1) IMO, OP has a question but it's mathematical part is "overly broad, or rhetorical and cannot be reasonably answered" on mathematical QA site (maybe for (roughly speaking) philosophy.SE or rhetoric.SE it would be a real question; and I don't say that any offtopic can also be considered NARQ -- but sometimes when real OPs question lies somewhere outside the scope of site trying to ask it here produces NARQ). Sorry for not too clear comment, and thanks again for explaining your POV. $\endgroup$ Commented Jun 29, 2011 at 19:16
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    $\begingroup$ (Re: 2) There's nothing bad in question having a lot of good answers; but a question having a lot of non-mathematical answers is certainly a problem. $\endgroup$ Commented Jun 29, 2011 at 19:17
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I answered this question - or at least posted something which was supposed to address some of the issues. I don't think it was caustic. But what I did think about the question was that it was ill defined in that it was unclear what kind of response would be helpful. I am a pure mathematician in a family of engineers and physicists, so I posted the kind of thing which would make it real to them. But there are echoes in the question of Zeno's paradoxes and Euclid - how do you actually pin things down so they make sense. And also of Euclid and the need to put geometry on a sound footing. SO there's genuine mathematical content there.

The main problem, though, was that the issues raised by the supposed interlocutor were insufficiently explicit. It was like being part of a Socratic dialogue without a dialogue partner. It really needed to be more explicit about the argument against, or for the person who posted it to be more active in helping to define the question in response to the wide variety of answers received. Without that it lacked focus, for me.

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