When this question: Olympiad problem generalization was first posted, it was immediately met with a number of close vote (or at least that's what I heard). Then a heated discussion ensue about whether it's a correct thing to close the question. Especially when the asker is a newcomer who sounds enthusiastic, have the will to go beyond what was strictly asked for, and state a reasonable nontrivial question (in fact, I am still stuck on certain part); yet within minute the asker was splashed with cold water. A few days ago the question has been closed for good.

I do not understand this. The reason given was that the question is unclear. I find the question very clear. Sure, the asker did not phrase it in precise technical language. But to phrase this question in such language, you would need metric space topology, finite additive content over Euclidean plane, isometry group, and so on. That's not something we would expect from a person who presumably is not an advanced mathematician; and perhaps not even from a mathematician either considering that is quite likely would obscure the question's nature while adding little and is also much longer. Beside, people were able to produce rigorous maths about geometry long before such notion are available. Think about it this way: when you ask a problem (such as how many colours are needed to colour region on a plane), you describe it in easy to understood term (graph colouring), rather than get bogged down with technical details that is ultimately irrelevant (such as whether the boundary of a region is a rectifiable curve or not.

Yes, certain details are also left unspecified (such as what exactly is a "cut"). However, it's just par the course when a problem is being generalized: certain details are bested fill in later, perhaps a formulation that is weaker would be solvable while a slightly stronger version remained intractable for a long time. When Hilbert make his problem list, a lot of question are very unclear, but that does not stop people from working on it. I formulated the cut as a rectifiable curve that is either closed or end on the boundary, while someone else might have formulated it as a piecewise linear curve parallel to axes. Each would be a reasonable answer to the question.

I think closing down the question with the "unclear" reason will send an unmistakenably clear message to anyone who stumble upon the question in the future: mathematics is all about wantonly encoding easily understandable concepts in complicated technical terms until it's completely incomprehensible, and all attempt to generalize a problem would be treated with disdain. That's contrary to the spirit of mathematics.

So please, what do you think about this issue? Why was the question closed? Do you think the standard for "clear" question is unreasonably hidebound?

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    $\begingroup$ One shouldn't always take official closure reasons too seriously. Two people of those who voted to close (possibly for a different reason, only the majority closure reason is shown) have stated clearly in the comments why their roblem with the question was and it has nothing to do with formalism. $\endgroup$ – Michael Greinecker Jan 8 '14 at 5:20
  • $\begingroup$ @MichaelGreinecker: I already address these reasons in the 2nd part of the post. "This is not a forum" is not even a real reason which I cannot address. However, the other 2 reasons are essentially about leaving things unspecified (solution not always exist? well then check for such case; "teaser question"? no this is clearly a generalization so that's all the asker know: the original problem is so trivial that it take less than a few seconds to figure out). However, considering all 5 people choose the "unclear" reason, I think it's the main reason for closing. $\endgroup$ – Gina Jan 8 '14 at 5:28
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    $\begingroup$ Okay, three people stated reasons. And, no you don't have sufficient information to see what everyone voted. $\endgroup$ – Michael Greinecker Jan 8 '14 at 5:55
  • $\begingroup$ @MichaelGreinecker: hm...that was a 3 years old thread, and I remember seeing question with multiple close reasons before. However, I cannot find it now, so perhaps if someone can shed a light on whether it is really the case. In any case, presumably the close reason is still democratic (it have to be chosen by 3 people) so that is something to be addressed. Whether "unclear" is because of leaving details unspecified, or failure to formalize, I think I covered all the base by addressing both. $\endgroup$ – Gina Jan 8 '14 at 6:06
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    $\begingroup$ As Shog9 commented there, off-topic cosure reasons are broken down but this question was not closed as off-topic. And as I wrote before, it is quite usual that a closing reason does not quite fit. There are lots of questions about this here on meta. $\endgroup$ – Michael Greinecker Jan 8 '14 at 6:17
  • $\begingroup$ @MichaelGreinecker:oh I see, thanks for telling me that details; did not know that. Anyway, that's part of this question that I asked for the reason to be stated more openly. $\endgroup$ – Gina Jan 8 '14 at 9:31

This is what the OP replied to the issue that the method for the original case does not always work:

For those of you who believe it doesn't generalize, it is trivial to show that it will always generalize by the same cut that works for the special case. If you took the time to solve the original problem you'd see it works for all rectangles. It's just a question of cut length.

This is what I gave as a close reason in response to that:

Note that I originally did not intend to close-vote your question, but your decision to tell us that we have been spending too little time on your question to see how trivial it is instead of responding to questions for clarifications calls for giving you a better incentive to respond.

The asker declines to put in the answer to the "teaser problem" after people ask for it, the asker does not take the time to check that the people asking for clarification are right and compounds this by accusing them of not seeing the trivial solutions because of not taking enough time.

It is the asker who treats people with "disdain" and refuses to engage in communication in the "spirit of mathematics".

The post here insists in the title that the question is clear and then insists that being unclear is ok because obviously the question is comparable to Hilberts problems. This is classical manipulative discussion to state two contradictory arguments, so that one can later always refer to the part of the post that is convenient. The post also does not address at all the reason I gave for closing, while a comment insists on having addressed everything in the post. I do not think that this style of discussion should be welcome here.

TL;DR: I closed the post because the question lacked any detail, contained wrong assumptions AND the asker explicitly refused to address questions by insisting on wrong claims and by insisting that others are just too lazy to check that said wrong claims are correct. And I already gave this reason in the comment thread there.

  • $\begingroup$ I think you are attributing too much malice to other people's post. In that case, let's me explain my point of view, as I think there is a perfectly good explanation for things happened, rather than accusing Elliot of being disdainful, or me of being manipulative. First, this question address all your reasons for closing. One of your reasons are "not well-stated and certainly not "perfectly mathematical precise"", which I addressed in the 2nd paragraph: requiring that is unreasonable due to the amount of advanced technical details and will just be unnecessary formalism. The asker might... $\endgroup$ – Gina Jan 8 '14 at 9:40
  • $\begingroup$ ...not have the maths knowledge required to even state that precisely. Another reasons are "there is no reason to assume that a single cut always works or that there is always a unique single cut". I addressed that in the next paragraph. I certainly do not compare the importance of that problem to Hilbert's, but there is one comparable aspect: both are not standard textbook problem with standard solution, and there are no textbooks to guide you. In a textbook problem, you might be guaranteed existence and uniqueness of solution, but here, it's a generalization of a problem into unknown... $\endgroup$ – Gina Jan 8 '14 at 9:43
  • $\begingroup$ ...territory, so we should expect these issue. Even in a standard textbook problem (say, solve a quadratic), certainly you would not consider the lack of clarification on whether the solution exist and unique. In Hilbert's problem, plenty of stuff are undefined: for example, there is no notions of a method back then, so negative solution to #10 need to wait until the concept of algorithm were invented. In that question, same thing: if a piecewise linear curve is too easy, but arbitrary curve is intractable, perhaps try something in between. After all, all of these are generalization to the... $\endgroup$ – Gina Jan 8 '14 at 9:48
  • $\begingroup$ ...original problem. Finally for your last objection, I agree with you that Elliot is wrong on the existence of solution, but I think it's quite a reasonable mistake if the asker were unaware of their own hidden assumption. You did point that out by giving an example, but I think you give too little time for the asker to response. I think it is better to assume that mistake were made and only attribute malice when the asker still refuse to admit wrong after the evidence were pointed out. Now back to me and this question. I did not say that it is fine to be unclear. I said that Hilbert's... $\endgroup$ – Gina Jan 8 '14 at 9:52
  • $\begingroup$ ...problems are very unclear, but that does not means people cannot give it a reasonable interpretation. This question is clear despite the lack of details: the question stated very clear what the original problem is, and that the question is about generalizing it. It's expected that definition are filled in if needed. Hypothetically, if someone ask how to generalize , say Banach-Tarski to other shape, would you close it down? Such a question are clear, even though you would need to fill in the definition of exactly what "shape" means. Of course, your answer would depend on the definition... $\endgroup$ – Gina Jan 8 '14 at 10:03
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    $\begingroup$ @Gina It might be reasonable for the OP to think that something was clear, but that does not make his comment anything but rude and dismissive of those people trying to help. $\endgroup$ – Tobias Kildetoft Jan 8 '14 at 10:07
  • $\begingroup$ ...but any reasonable definition that generalize the problem reasonably all answer the question; after all, they are not standard textbook problem. Now, if you still think that such a question is still unclear, please tell me your reason. Presumably, that would also give your opinion on the 2nd question, that is whether the unclear standard is too hidebound. $\endgroup$ – Gina Jan 8 '14 at 10:08
  • $\begingroup$ @TobiasKildetoft: I would certainly find it unacceptable if the OP is actually rude and dismissive. But I think that is an unreasonable interpretation of the OP's comment, considering that it could be explained that the OP is mistaken (eg. underestimate the difficulty of the problem due to a wrong solution), and nobody pointed out the error until near the end, then the OP never even get the chance to response. I think that it's better if we don't attribute malice right away. $\endgroup$ – Gina Jan 8 '14 at 10:15
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    $\begingroup$ @Gina The OP has a chance to respond, he can still commend on the question, edit the question, and nothing keeps OP from joining this meta discussion. $\endgroup$ – Michael Greinecker Jan 8 '14 at 11:19

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