Let us look at the question Evaluate $\int_0^{\pi/2}\frac{x^2\log^2{(\sin{x})}}{\sin^2x}dx$

I understand, that the formulation is rather short, but we have at least two precise, large answers. I would never vote for closing this question, but I understand that I may be wrong. Meantime, I have voted for reopening it. Am I right?

Edit: I am not asking for reopening the question about integral. I want to know how should I behave in the future. The suggested link does not answer my question.

  • $\begingroup$ This belongs in this thread. $\endgroup$ – amWhy Aug 26 '18 at 11:54
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    $\begingroup$ Related: (1), (2), (3). These should all now be linked in the sidebar with more descriptive titles. $\endgroup$ – Xander Henderson Aug 26 '18 at 13:40
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    $\begingroup$ The good thing about the Q is that it provides at least a "note" as some context. Other than that this Q&A to me just seems a bit pointless, but maybe I just don't get the point, but then maybe the point of it all should be explained. Okay, there is some integral, then some fumble around with some more or less standard techniques to get it. Sure it "looks cool" in a way and I couldn't do it, but still it seems of no actual value to me. $\endgroup$ – quid Aug 26 '18 at 15:10
  • $\begingroup$ For the asker: Your only question, prior to your edit, which followed others pointing out dupes, previously linked, was: "Am I right?" In the future, when you think a question should be reopened, (1) vote to reopen it (you said you did so); if you still feel strongly about why it should reopened, make your case at the first link above, in the "Request for reopen and undelete votes" thread. So, in fact you had already been told how to behave in a similar situation now, and in the future, even before your "edit". $\endgroup$ – amWhy Aug 26 '18 at 15:35
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    $\begingroup$ I voted to close the question because it presents a problem with no motivation or context. The fact that a similar-looking integral can be evaluated is not very surprising - we all know that randomly changing parts of an integral can make the integral become unsolvable with elementary functions. What is the reason for replacing $\log$ with $\log^2$? Trivially, there is an infinite collection of unmotivated integrals that could be posted in exactly the same way. So I feel we can ask the OP to give us some reason why the integral in the question is worth evaluating. $\endgroup$ – Carl Mummert Aug 26 '18 at 19:27
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    $\begingroup$ The question on main has been reopened. Hooray! $\endgroup$ – Gerry Myerson Aug 26 '18 at 21:36
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    $\begingroup$ There's nothing wrong with closing questions with good answers if the questions are warranted to be closed. If we reverse the case: assuming the question had no answers, would that question be closed too? $\endgroup$ – Andrew T. Aug 27 '18 at 7:04
  • $\begingroup$ The question on main has been put on hold. $\endgroup$ – Joel Reyes Noche Aug 28 '18 at 4:32
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    $\begingroup$ "I may be wrong...Am I right?" These are the wrong questions to ask. You have >10k reputation; at this milestone you are considered responsible and so are given access to the moderator tools. You should use them wisely, but there is no correct way of using them. No matter your opinion, no matter what you do, people will disagree. Don't loose sleep over it :-) $\endgroup$ – user1729 Aug 28 '18 at 8:53
  • $\begingroup$ (But, of course, asking a question such as yours on meta is a good idea. Discussion is a healthy thing.) $\endgroup$ – user1729 Aug 28 '18 at 9:00
  • $\begingroup$ Incidentally, no one has pointed out that this question is 3.5 years old. I believe that this should be a factor when you are considering the fate of a question. $\endgroup$ – user1729 Aug 28 '18 at 9:00
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    $\begingroup$ @CarlMummert Why don't you first calculate the integral (in your style) before posting the whole thing above? Honestly speaking, do you have any idea how to do such an integral? Are you frustrated they are so difficult to you and want them all closed and deleted? Then I might begin to understand you. Can you explain the motivation of the integrals and series in the notebooks of Ramanujan? What if he lived today and posted all his results on a site like this? His questions should have been closed? Have you ever heard of doing mathematics for the sake of the art of mathematics? $\endgroup$ – user 1591719 Sep 2 '18 at 17:29
  • $\begingroup$ @user23571113 "Can you explain the motivation of the integrals and series in the notebooks of Ramanujan?" Well, sometimes at least the motivation was having misunderstood what the point of something existing was, viz. the motivation was ignorance. Who cares about that integral? Maybe some amateurs and maybe some professionals as a hobby. But what's the scientific value of it? Maybe there is some. But then somebody should step forward and explain it. $\endgroup$ – quid Sep 2 '18 at 18:12
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    $\begingroup$ @quid If so, why do you let people invest years of work for this site and not tell them from the very beginning that a clear scientific value of each integral and series should be stated at every single post? You have a lot to close and delete, just don't be friendly more with others! In Inside Interesting Integrals there are pretty many integrals arising from physics problems (just an example), and also this one might be related at some point (although, I never consider doing them because they might have applications in the real work) to some problems of the real world. $\endgroup$ – user 1591719 Sep 2 '18 at 18:52
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    $\begingroup$ @quid Maybe it's time to close/delete all of them, and the users enjoying these questions should pack and leave this place at once. And then it's the tone you present things. This is the last time I'll ever post a question/answer on this site. $\endgroup$ – user 1591719 Sep 2 '18 at 18:54

The "reason" for closing such questions is that they are poor questions. Questions should be judged on their own merits, and not on the basis of the quality of answers which they may have attracted. That being said, terrible questions (like the one you cite) can sometimes attract high quality, well thought out answers. I concede that such questions should probably be dealt with in a more nuanced manner. However, I do not think that there is a clear consensus on this issue, so let me take a stand (upvote to agree, downvote to disagree):

Low quality questions with higher quality answers should be closed, but should not be deleted.

Simply Beautiful Art made (in my opinion) a very good case for this course of action. There are (essentially) three parties who are potentially affected by the closure of a question:

  1. The original asker, who is not harmed because they have an answer to their question.
  2. The people who have donated their time to provide answers, who are not harmed because their answers are still visible.
  3. The community at large (i.e. other users who might someday look for an answer to the same question), who are not harmed because closed questions are not removed from the site (unless they are highly downvoted and have no answers with positive scores).

Thus no harm is done by closing a low quality question with high quality answers. On the other hand, I do think that harm is prevented by this course of action, as it sends the signal that such questions really shouldn't be asked, and it prevents Johnny-come-latelies from providing further answers.

  • $\begingroup$ I have accepted your answer, although there might be a harm: T\there is no possibility of obtaining even more interesting answers. $\endgroup$ – Przemysław Scherwentke Aug 27 '18 at 15:32
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    $\begingroup$ Again, a question should be judged on the merits of the question, not the potential for great answers. If you really think that a question has the potential for a great answer, it might be better to create new question which gives more context. You can even link back to the original question. If your new question is interesting enough and attracts interesting answers, you could even request that the two questions be merged. $\endgroup$ – Xander Henderson Aug 27 '18 at 18:32
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    $\begingroup$ There is a possibility of improving the Question and reopening it, after which potentially "more interesting answers" could be posted. I'd encourage those with a desire to give better or even alternative solutions to encourage the improvement of the Question. It may be that the OP will learn more from the revision of the Question to site standards than from any of the Answers given, $\endgroup$ – hardmath Aug 31 '18 at 4:33
  • $\begingroup$ @hardmath Indeed, that is always a possibility. However, in the case of the question which started this conversation (and others like it), I don't hold out much hope. The question is a tricky integral. It is unmotivated and devoid of context. Only the original asker can possibly provide that context, and (after all this time---the question is three years old) I don't think that it is likely that they will do the work to improve the question. $\endgroup$ – Xander Henderson Aug 31 '18 at 5:26
  • $\begingroup$ Maybe because I lean more towards the interactive rather than repository aspects of the site, I’m not sure I agree with keeping closed questions around. Although the closing may signal that the question has issues, if the question isn’t deleted we may implicitly convey that we are actually OK with questions with those issues. $\endgroup$ – Carl Mummert Sep 3 '18 at 6:39

I fundamentally agree with reopening the question. Clearly some people feel that the question in, er, question is a poor question. It is not. It is a highly interesting question that produced two highly interesting answers. (Not the most-upvoted answer.)

The only thing left to ponder here is, is it an obvious homework question for which zero effort has been expended? In this case, no. It is a difficult integral that someone wanted to see done, given that a result for a similar, slightly less-complicated integral was known. I do not see how such problems do anything but make the site better.

BTW this has been an ongoing issue for as long as I have been on this site - almost 6 years. There are long-standing disagreements as to how questions involving evaluation of difficult integrals, sums, and other computations should be treated on this site. But I have yet to see any demonstration that these questions are anything other than a good thing that has brought some really smart people to contribute lots of great techniques to the site. Maybe I am wrong - but would someone who is convinced I am wrong tell me the downside of these questions?

  • $\begingroup$ Is this a "highly interesting question" because it's on the topic of mathematics? Or is there some feature that makes it more valuable than most questions? You mention "difficult integral". Are you advocating specifically for "difficult integrals" or is a more abstract principle relevant? Are "not so difficult integrals" less valuable as questions? Do you have a proposal for how curators are to quickly discern which questions are the "difficult integrals"? (note that a high-effort method mostly boils down to "treat all integral questions as difficult integrals") $\endgroup$ – user14972 Sep 18 '18 at 22:10
  • $\begingroup$ ... Do you advocate the position that "difficult integrals" are so valuable or so obvious that there should be no burden on the poster (or editors that find the post appealing) to do something that distinguishes their difficult integral post from not so difficult integral posts? $\endgroup$ – user14972 Sep 18 '18 at 22:13
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    $\begingroup$ @Hurkyl: It is highly interesting because I and several other users think it is so. And it is not a homework problem. I am advocating for letting the people who find certain questions interesting answer those questions as they want. How do I know which people find which questions interesting? Easy: they provide excellent answers. I don't know why this has to be so complicated. $\endgroup$ – Ron Gordon Sep 18 '18 at 22:14
  • $\begingroup$ The only way I see to implement the position you advocate is "never close anything". Are you advocating for the implementation "never close anything"? Or... are you specifically addressing the topic of historical questions rather than new questions? My previous comments assume you are saying things relevant to the reception of new posts. $\endgroup$ – user14972 Sep 18 '18 at 22:15
  • $\begingroup$ @Hurkyl: Nope. I am advocating for "close less." There are obvious candidates for closing: obvious homework**, poorly formatted questions, questions containing offensive, demented, or any of like like content, nonsensical questions, questions not about mathematics, and so on. Again, this is not hard. **Anyone who is expert in a certain area can tell what's homework and what's not in a millisecond. $\endgroup$ – Ron Gordon Sep 18 '18 at 22:19
  • $\begingroup$ Fine. You are advocating "never close anything that is a readable, sensical inoffensive question on the topic of mathematics (except obvious homework)". I will continue to abbreviate that as "never close anything (except obvious homework)" unless that genuinely causes confusion. $\endgroup$ – user14972 Sep 18 '18 at 22:23
  • $\begingroup$ Going back to a previous point... in the post you bring up "difficult integral" as if that matters -- as if it is an indicator that one can use in a prior estimate of value. That is something that needs expanded upon. In the comments, you fall back on the posteriori judgment of waiting to see how people respond, but such a method of estimating value is absolutely useless for making judgments on new questions. $\endgroup$ – user14972 Sep 18 '18 at 22:31
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    $\begingroup$ @Hurkyl: Yeah, that is what I am advocating. People (and I am guessing you) do not agree. Fortunately, for integrals and sums, I have a gold badge so I can reopen unilaterally. Doesn’t always work but it should. (I have advocated that position before.) Point is, I believe in letting people enjoy the site and I do not see how questions that produce great answers are a problem. You mock, but you really never addressed my question. $\endgroup$ – Ron Gordon Sep 18 '18 at 22:34
  • $\begingroup$ Right; I believe the distribution of value of questions is such that many are harmful. But I'm not trying to convince you of that -- I'm engaging with you in the hope to get agreement with the premise that there is a distribution of value of questions, and our main disagreement is simply over our threshold of how bad something needs to be to be harmful. And if there is agreement on that premise, to try and spark discussion on how to refine the collective judgment (both prior and posteriori) to better discern which questions are more likely to be of higher value. $\endgroup$ – user14972 Sep 18 '18 at 22:46
  • $\begingroup$ @Hurkyl: OK, I can get on board with this discussion. I agree with what you say in general. To nitpick, I do not think we agree on the distribution - that is, our differences may not be a simple threshold. I think there is real disagreement on what causes harm in the first place, not simply the amount of harm. That said, I think we can agree on mechanisms to identify and take action on questions that some of us think may be harmful but others do not. I for one think that closers should get one bite at the apple, no more. That’s my suggestion. $\endgroup$ – Ron Gordon Sep 18 '18 at 23:13

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