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I think that we should have discussed here the question "Integral Representation of Infinite series" before it was closed. Students often have questions about such topics so the replies could have been very useful. Moreover, some of these topics deserve to be better known since they are quite powerful and have widespread application. Finally, I believe that it would have been very easy to reformulate the question to satisfy most of those who voted to close it. That said, why didn't you do the constructive thing and help reformulate the question rather than perform the destructive task of closing it?

I will volunteer to help reformulate it. Could some like-minded folks please add a few votes to reopen it.

EDIT I have added part of my extended answer to the question. Please read it here and hopefully you will be convinced to reopen. Thanks.

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    $\begingroup$ I know we are supposed to judge the question and not the question asker (who has admittedly been doing much better lately), but I suspect the asker's identity contributed to the haste. One could easily say it looked like "just another" of his hasitly asked questions, with minimal evidence that he'd seriously thought about the problem. $\endgroup$ – Jason DeVito Aug 31 '10 at 17:47
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    $\begingroup$ Yes, I am aware of the OP's history. But he appears to be making sincere efforts to improve - which provides even more motivation for helping him by showing him how to better pose his questions. Sledgehammer closing is certainly not the best course of action. $\endgroup$ – Bill Dubuque Aug 31 '10 at 17:52
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    $\begingroup$ @Bill. I completely agree with everything you said (in your post, and in your comment). I was just offering a potential reason for the behavior. $\endgroup$ – Jason DeVito Aug 31 '10 at 18:38
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    $\begingroup$ @Bill: Even though the question is closed, it will still accept comments. If you have some ideas on how to improve the question, perhaps you can post them as comments and Chandru1 can incorporate your suggestions? Getting people to reopen a question that has been edited is easier than getting them to agree to "please reopen the question, and then let's edit it." $\endgroup$ – Larry Wang Aug 31 '10 at 20:38
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    $\begingroup$ @Kaestur: The post should never have been closed in the first place. The moderators should rectify this injustice. IMHO that was an abuse of closing privileges. $\endgroup$ – Bill Dubuque Aug 31 '10 at 21:28
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    $\begingroup$ @Bill: That might be true - I'm not convinced yet - but since you seem to agree that the question could do with some improvement, why not also follow my suggestion? The question closed -> comments with suggestions -> asker edits -> question reopened process is quite common, and helps people learn to ask better questions. $\endgroup$ – Larry Wang Sep 1 '10 at 2:40
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    $\begingroup$ With all due consideration and respect to those who voted to close, with whose arguments I am sympathetic, I have added a vote to reopen. The quality and interest of the one answer already provided is sufficient demonstration of the value of permitting additional answers. Yes, the question as it stands could be improved, but the creative scope afforded by such a general formulation can be stimulating. $\endgroup$ – whuber Sep 16 '10 at 4:00
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I do not see a way to repair the question without altering its intent. It would be fine for me if the question was something like "what are other nice applications of this technique," but the operative word in the question is whether the technique is always applicable, and this question is at the wrong level of generality. I think you are giving the OP too much credit for the question you wanted him to ask rather than the question he actually asked.

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    $\begingroup$ But perhaps I am interpreting the question the way he desired - or very close to it. Much of mathematical writing assumes that the reader will make intelligent choices when there are ambiguities - as there always will be in informal writing. I'm a bit disappointed that the question was so quickly closed because I think many readers could have learned much from the replies - not just the long reply I was in the middle of composing while it was quickly and abruptly closed. E.g. did you know about all the pretty combinatorial applications of the work of Aizenberg, Egorychev, et al.? $\endgroup$ – Bill Dubuque Aug 31 '10 at 18:57
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The FAQ says that "...this is a place for questions that can be answered!" But questions are by their very nature often unclear. It is answers that should be precise. Mathematics is in large part the art of making rigorous good sense out of vague questions. If you don't know how to do that for someone's question, you should step aside for someone like Bill Dubuque who can. To close a question right away is to slam the door in the face of those who may have something constructive to offer, even if you don't. Closing amounts to censorship of those who may be able to help. Couldn't you just request clarification from the questioner and move on? Or couldn't you at least wait for a decent period before closing? So what if a poorly posed question just sits there for awhile with no answers forthcoming?

I had hopes for this site as a friendlier, more accommodating alternative to MathOverflow. I suspect that this is partly what was intended. It's no secret that MathOverflow has a reputation for elitism, but now it seems that the very same mindset (same people, I guess) is taking root here too.

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    $\begingroup$ Alas, I had hoped the same too. The SO model is fatally flawed. Successful moderation requires knowledgeable and experienced moderators - which are very few and far between. It's difficult enough to select them manually - let alone automatically based upon some one-dimensional numerical value (rep) - which has little if any correlation with qualities desired in a moderator. Forums live or die by the quality of their moderation. It will be interesting to see the outcome of this experiment. $\endgroup$ – Bill Dubuque Sep 1 '10 at 18:32
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    $\begingroup$ Now I am confused! «Moderators means real moderators - not high rep users with pseudo-mod powers.» :) $\endgroup$ – Mariano Suárez-Álvarez Sep 1 '10 at 20:55
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    $\begingroup$ Why are you surprised that such denotations are context dependent? I'm happy to see that in this case you inferred the correct denotation. Since you don't have real moderator powers my earlier remarks most definitely did not apply to you - as I've stressed before. $\endgroup$ – Bill Dubuque Sep 1 '10 at 21:27
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    $\begingroup$ @Bill: I beg to differ (but only slightly). The functionality of the site could be tuned to avoid these problems. Maybe the threshold for closure could be raised a bit. At the very least, allow a short grace period to give people like you a chance to respond positively. It takes quite a bit longer to come up with a helpful response than a vote to close. $\endgroup$ – castal Sep 2 '10 at 14:54
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    $\begingroup$ @castal: a closed question can be edited in order to resolve any problems, both by the original poster and by others with sufficient reputation; ideally, people voting to close will leave an explanation of what they object to and this should serve as a guide. In particular, that a question be closed does not mean that it is beyond hope! $\endgroup$ – Mariano Suárez-Álvarez Sep 2 '10 at 15:46
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    $\begingroup$ @Mariano: But rarely are closed questions reopened since the software doesn't have any good way to re-expose the question to help it reach critical mass for reopening. It's far too easy to close and far too difficult to re-open. That's a basic flaw in the software. So closure should not be something done without discussion - except for extreme cases such as spam. If there is any doubt whatsoever it should be discussed here. At the very least that provides notice to be wary to those in the process of composing long thoughtful replies. $\endgroup$ – Bill Dubuque Sep 3 '10 at 5:19
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    $\begingroup$ @Mariano: So how about following your own advice and finally revealing why you voted to close. Everyone else has except for you. $\endgroup$ – Bill Dubuque Sep 3 '10 at 5:20
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The question as asked had a very valid reason to close. It was a vague and ambiguous question.

It does not matter if many students ask this question. It remains vague and ambiguous.

This is not a teaching site. StackExchange sites are meant for specific answers to specific questions.

Also, second guessing what the OP wants and 'constructively' editing the question to what you think they might be asking is just rude, IMO.

If you think there is a specific question hidden in there, feel free to open a new question.

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    $\begingroup$ The question was neither vague nor ambiguous. Namely it read "There are many infinite series which can be represented by integrals. I would like to know whether such type of representation is always possible for an infinite series?" That certainly is a precise question and, moreover, a very natural question. I plan to repost his question if the closed-minded closers do not do the right thing an reopen it. $\endgroup$ – Bill Dubuque Aug 31 '10 at 16:30
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    $\begingroup$ I recall that in fact you recently employed [1] an integral representation to compute a sum, so why not constructively elaborate upon that rather than destructively vote to close? [1] math.stackexchange.com/questions/3503 $\endgroup$ – Bill Dubuque Aug 31 '10 at 16:51
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    $\begingroup$ Re: "Any number can be represented by an integral" Why choose to interpret the question so trivially when there are obviously much less trivial and more interesting interpretations? $\endgroup$ – Bill Dubuque Aug 31 '10 at 17:19
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One compromise (which Harry has suggested on a recent meta.MO thread) would be for the answerer to ask another (more specific) version of the original question, and answer it there. I would be happy to upvote such an effort. As it is, I found the original question to have been vague; I have explained why I voted to close in the comments there. Math.SE (like other SE sites) is intended for specific questions with definite answers. The question asked was too much of a fishing expedition.

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    $\begingroup$ Do you have enough expertise in this area to know that it does not have a specific answer? Did you see the partial answer that I posted? $\endgroup$ – Bill Dubuque Aug 31 '10 at 22:37
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    $\begingroup$ @Bill: I've seen your answer, and while it is interesting, I don't think the existence (or possibility of existence) of a good answer is a sufficient reason for the question to stay open. Asking a vague question (to give a more extreme example, "What's your favorite theorem?") can admit a specific answer without being a specific question. $\endgroup$ – Akhil Mathew Sep 1 '10 at 0:09
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    $\begingroup$ Your comment to the OP said "This question could be interesting if you had a specific example of an infinite series in mind..." But he's clearly asking about general techniques so why would you require him to have a "specific example in mind"? Please exercise extreme care when voting to close questions outside your expertise. $\endgroup$ – Bill Dubuque Sep 1 '10 at 0:42
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Out of respect for the effort and time of the questioner and answerer(s), I think one should not vote to close a question before discussing it on meta, unless the question is extremely hopeless. It gives no harm if questions like this one would stay open, at least until a consensus is achieved.

Closing procedure is very prone to false positives. Only 5 votes is enough for a question to get closed, while the number of users with the right to vote to close is increasing everyday. That's why I completely agree with the title of this thread.

If the goal is to keep the site clean, then I suggest using downvotes rather than close votes. Unless the user is a troll, downvotes are as effective as close votes.

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  • $\begingroup$ The solution to false positives in closing is meant to be reopening. This has the same rep requirement as closing. False positives may still occur, of course, but since we have a way to address them, perhaps you could explain why you think that method is not good enough? $\endgroup$ – Larry Wang Sep 4 '10 at 0:31
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    $\begingroup$ Once it's closed it gets much less exposure, so it will never get enough critical mass to reopen unless someone makes a crusade to do so and, as we see here, even that may not work. The system is fundamentally flawed. $\endgroup$ – Bill Dubuque Sep 4 '10 at 3:17
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    $\begingroup$ @Bill: When the question gets edited, it gets bumped up to the front page. A question that gets closed is likely to need editing (that is, at least 5 high-rep users think that the present form has problems). This is how most closed questions get reopened. Could you expand a little on why you think the system is flawed? If you have some concrete ideas for improvement, it might be worth posting as a separate feature-request. $\endgroup$ – Larry Wang Sep 5 '10 at 18:33
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    $\begingroup$ @Kaestur: I suspect that once a post has the "red scarlet" badge of "[CLOSED]" stamped on its title, it makes it far less likely that people will view it, thus greatly decreasing exposure needed for reopening. Is there any easy way to gather statistics to see if this is so? What percentage of closed questions have been reopened? What percentage were discussed here first before being closed? I think that, at the least, there should be a notice posted to meta before closure so that it gets exposure. One should be able to vote not to close before closure. $\endgroup$ – Bill Dubuque Sep 5 '10 at 19:03
  • $\begingroup$ @Bill: About the statistics - it may be possible with data explorer, I am not familiar enough with the tool to say more. About the "vote against closure" option - that is a very popular feature-request that was declined by Jeff Atwood quite a while back. As you can see, many people share your opinion on the usefulness of this feature. $\endgroup$ – Larry Wang Sep 5 '10 at 20:18
  • $\begingroup$ Users with >2k rep can see a list of recently closed questions and a list of close votes, reopen votes, and closed questions. We may want to add some links to the section of the faq that lists the rep levels to raise awareness of powers like these. $\endgroup$ – Larry Wang Sep 5 '10 at 20:21
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    $\begingroup$ @Kaestur: I'd be very interested to see Jeff's argument against voting for non-closure, but your link above is not to that but to a db dumps question. Do you know the correct link? As for being able to see close votes what good does that do if you cannot do anything to stop it? It seems it is purposely designed to encourage closure, not to prevent it. Such bias is misguided. $\endgroup$ – Bill Dubuque Sep 5 '10 at 20:57
  • $\begingroup$ @Bill: Sorry for the confusion. I have fixed the links in my comment. $\endgroup$ – Larry Wang Sep 5 '10 at 21:42
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    $\begingroup$ @Kaestur. Thanks for the link. I'm happy to see that almost everyone else in that thread also seems to agree that the current closing system is flawed. But I'm sad to see that Jeff Atwood doesn't agree that this is a problem. Hopefully soon there will be a better open source platform that avoids the many SO/SE problems. $\endgroup$ – Bill Dubuque Sep 5 '10 at 23:14

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