tea.mathoverflow.net - Discussion Feed (applications of the sphere theorem)

Ryan Budney comments on "applications of the sphere theorem" (14033)

Ryan Budney — Mon, 04 Apr 2011 16:27:39 -0700

@alex_o: this is an issue of promotion of "good culture" i.e. we want people to put energy into writing good questions because we want this to be a place where the expectation (on everyone) is that they take the questions and the answers seriously. The landscape of questions-and-answers is something of a public commons, and putting pressure on people to ask good questions amounts to a desire maintain some common standards.

alex_o comments on "applications of the sphere theorem" (13998)

alex_o — Sun, 03 Apr 2011 15:18:58 -0700

@Anton: Good answers attract upvotes and comments, so I doubt anyone would be disappointed __with MO__ as a result of writing a good answer to a lazy question.

alex_o comments on "applications of the sphere theorem" (13997)

alex_o — Sun, 03 Apr 2011 15:16:27 -0700

@Andrew:

"Writing a great answer to a poor question is a waste of energy."

Don't you think this should be up to each person to decide? To put it bluntly: what gives you the right to tell me what is a waste of my energy?
I may be the type of person who derives great enjoyment from unconfusing people.

"But if the question is poor, who is ever going to read the answer? "

Lots of people, in fact. I, for example have greatly benefited several times from seeing clear explanations to confused and vague questions.

"Why not put that great answer somewhere more visible...."

MO is quite visible.

"MO...needs that initial exchange otherwise it is unfocussed and there is no easy way for the others to know that there is something worth learning from."

On the contrary, it is quite easy to discern that. When I see an expert in a field I am unfamiliar with write a long, detailed response with many upvotes to a rambling and confused question, its a pretty safe bet that I'm going to learn a lot from reading this response.

Shevek comments on "applications of the sphere theorem" (13995)

Shevek — Sun, 03 Apr 2011 12:43:44 -0700

I agree with everything that alex_o has said.

Andrew Stacey comments on "applications of the sphere theorem" (13994)

Andrew Stacey — Sun, 03 Apr 2011 11:24:41 -0700

alex_o: Writing a great answer to a poor question is a waste of energy. Mathematicians are, generally, quite helpful and seem to like explaining stuff. But if the question is poor, who is ever going to read the answer? Why not put that great answer somewhere more visible, say on a wiki? MO is designed for getting answers to questions, and by doing so in public then others can look on and learn as well, but it needs that initial exchange otherwise it is unfocussed and there is no easy way for the others to know that there is something worth learning from.

What you are calling a great answer is not a great answer. It's a great explanation, but to be a great answer it needs to answer an actual question. If it's not possible to discern the question, then it's not possible for it to be answered, and so anything written as an answer is not actually an answer.

markvs comments on "applications of the sphere theorem" (13955)

markvs — Sat, 02 Apr 2011 20:05:20 -0700

PS I also voted to reopen the question.

markvs comments on "applications of the sphere theorem" (13953)

markvs — Sat, 02 Apr 2011 19:58:14 -0700

@Emerton: I know one application of the sphere theorem, the asphericity of knot complements. But the statement was re-proved later , in 1981, by Chiswell, Collins, and Huebschmann avoiding the sphere theorem. So that application was not really essential.

Emerton comments on "applications of the sphere theorem" (13952)

Emerton — Sat, 02 Apr 2011 19:43:43 -0700

I've voted to reopen this question. I don't think it was unreasonable when it was asked, and it has been improved since then. My own impressions (certainly non-expert) were that the sphere theorem is one part of a general theme in the study of positive curvature, the object of which is primarily to demonstrate the limitations on the topology entailed by positive curvature. In short, I always viewed the sphere theorem as an end in itself rather than something to be applied elsewhere, and I am curious to hear from experts as to whether this is truly the case.

Todd Trimble comments on "applications of the sphere theorem" (13945)

Todd Trimble — Sat, 02 Apr 2011 16:37:37 -0700

I don't find the current version of the question at all offensive; the OP is pretty up-front that his question is one of idle curiosity (as are so many questions on MO!), so responders can take that into account. In any event, I would leave the ethics of cookie-cutter or apparently lazy questions out of consideration; the debate should be about whether this is a 'real' question. To me the question looks like it's fishing around; it's hardly a precise mathematical question.

Anton Geraschenko comments on "applications of the sphere theorem" (13944)

Anton Geraschenko — Sat, 02 Apr 2011 15:43:44 -0700

@alex_o: In addition to Qiaochu's point, I think there are lots of people who have not developed the immunity you describe. Even if good answers to poor questions did not encourage poor questions, I would still rather chase away a dozen poor questions than waste the time of one awesome mathematician and leave her disappointed with MO.

I love analogies, so here's one for the occasion. I know that there are people who follow the links in spam emails, and even people who end up buying stuff (or providing information, or whatever the spammer is after). Otherwise spamming would not be lucrative. Even if those people are satisfied with their purchases, I want to discourage spamming. It pollutes inboxes, wastes (a bit of) the time of people who delete it, and wastes (a lot of) the time of people who don't know better.

Qiaochu Yuan comments on "applications of the sphere theorem" (13943)

Qiaochu Yuan — Sat, 02 Apr 2011 15:15:49 -0700

@alex_o: the problem I have with writing great answers to poor questions is that it encourages poor questions. Poor questions should not be encouraged, as this pollutes the environment at MO for everybody.

alex_o comments on "applications of the sphere theorem" (13941)

alex_o — Sat, 02 Apr 2011 14:55:53 -0700

Anton, you can't deny that there are a number of MO users who repeatedly write many great answers to poor questions. Surely they know what they are getting into by this point?

Generally speaking, yes, some may end up being disappointed. Others, on the other hand, may enjoy writing about the things they love regardless of the behavior of the OP. Moreover, I think those that are disappointed quickly figure out to stop responding to poor questions.

Anton Geraschenko comments on "applications of the sphere theorem" (13939)

Anton Geraschenko — Sat, 02 Apr 2011 14:11:42 -0700

@François: :-). It's a super-duper-power. I did a little shuffle where I revoked my own moderator powers, voted to close, and then reinstated the ♦s. I was mostly just curious if it would work (on faketestsite, I don't have enough rep to vote to close as a non-mod).

François G. Dorais comments on "applications of the sphere theorem" (13937)

François G. Dorais — Sat, 02 Apr 2011 13:53:10 -0700

Anton, how did you manage to get your vote count as a normal user? Is that one of your super-super-powers that I wasn't aware of? Or maybe there is another reason why your name is second on the closer list.

Anton Geraschenko comments on "applications of the sphere theorem" (13936)

Anton Geraschenko — Sat, 02 Apr 2011 12:29:26 -0700

@Pete: I think the question is much better now.

whatever has added the motivation, "I'm just curious", which is okay, but I would really like a bit more about why the OP cares about this particular theorem or how s/he started thinking about it.

@whatever: I realize it's not fun to have people criticize your post. Thank you for not taking it personally, and thank you for editing the question.

Anton Geraschenko comments on "applications of the sphere theorem" (13935)

Anton Geraschenko — Sat, 02 Apr 2011 12:22:39 -0700

@alex_o: I figured somebody take your position, but I didn't want to address it until it came up. Basically, I disagree with your belief that it is a mutually beneficial activity. See the Be Precise section of the How To Ask page for my general thoughts on what is wrong with imprecise questions.

I think lots of mathematicians try to be very helpful in general. This is why MO works in the first place. But when somebody (for whatever reason) asks a question without actually being interested in the answer or without bothering to ask a clear question, it often happens that some helpful person will try hard to answer the question, only to meet disappointment. As an analogy, imagine that somebody comes up to you at tea and asks you to tell them about your field of research. They don't (or won't) tell you about their background, so you think very carefully about how to present your research to somebody with no background. Then, as you are explaining, this person walks away. I hope you see what is outrageous and saddening about this situation. The objection "you wouldn't have started answering the question if you didn't want to" just doesn't hold water.

I think we agree on maintaining high quality of questions on MO. This (paired with what I said above) is one reason cookie-cutter questions raise a red flag in my mind. Questions along the lines of "What is the meaning of theorem X?" or "What are applications of Y?" which do not explain why X or Y were chosen are very easy to ask and hard to answer, so they're a hotbed for situations where the asker is not engaged.

Pete L. Clark comments on "applications of the sphere theorem" (13932)

Pete L. Clark — Sat, 02 Apr 2011 12:02:21 -0700

As I wrote in the comments, I am not sure the question is so bad, but there is clear room for improvement. What Anton suggests would make for a much better question.

As an update, so far the first of Anton's three bullet points has been met. (For good measure, I just edited the question to add a link to the relevant wikipedia article). If the OP can address either the second or the third bullet point, I will be satisfied enough to vote to reopen the question.

alex_o comments on "applications of the sphere theorem" (13931)

alex_o — Sat, 02 Apr 2011 12:00:31 -0700

"I would be somewhat outraged and saddened to see people pouring their time into writing long well thought-out answers to the same question about, say, the Riemann-Roch theorem"

Why?? The people who write fantastic answers to poorly thought out questions do so because they want to. No one is being held at gunpoint. They must derive some pleasure and enjoyment from writing their answers - else, they wouldn't do it. The OP obviously benefits as well. So everyone benefits - except you, it seems, who is "outraged and saddened" at seeing two people engage in a mutually beneficial activity.

More generally, I'm extremely sympathetic to the argument that MO must have high standard for questions, else it will be overrun by poor questions. I'm not at all sympathetic to the argument that "Asking others to put in great effort without giving any indication that you even care puts me off" is a good reason to close a question. If others feel the same way, they'll simply forego writing answers. In summary: I agree with the conclusion (close the question) but not the arguments that support it.

Anton Geraschenko comments on "applications of the sphere theorem" (13929)

Anton Geraschenko — Sat, 02 Apr 2011 11:15:41 -0700

applications of the sphere theorem

This question leaves a bad taste in my mouth, not because of the underlying question, but because of the cookie-cutter, no-effort (apparently) way it is asked. The entire body of the question is

I am looking for interesting applications of the 1/4-pinched sphere theorem......[is it just a beautiful theorem or can you use it in concrete situations to derive some conlusions difficult to see otherwise?]

The brackets are mine; that stuff was added after Mariano's comment. Grammar and spelling aside,† this post gives the impression that the asker googled for "list of theorems" and plugged a result into the above sentence. I don't know what the 1/4-pinched sphere theorem says, but I would be somewhat outraged and saddened to see people pouring their time into writing long well thought-out answers to the same question about, say, the Riemann-Roch theorem. Asking others to put in great effort without giving any indication that you even care puts me off. In its current form, this question has my vote to close.

I figured it's worth explicitly listing what this user can do to improve the question:

Explain what the 1/4-pinched sphere theorem says. If you're going to ask a question that's not really looking for an answer, I feel like it is more important to provide background.
Explain why you care about it. Again, if you're not looking for a specific answer, it is very important to specify why you are asking the question. See this section of the How To Ask page: Ask a focused question that has a specific goal. It's not clear what your goal is.
Explain what you know. The other question asked by the same user was also of the form, "what are applications of theorem X?" It got a warmer reception because the user at least explained where she was coming from.

Information about the purpose of the question is ultimately something only the asker can provide, and it is something that should not be very hard for the asker to provide, so there is no excuse for saying, "whoever wants to can reformulate the question to make it better; I just want answers."

† Checking for use of the SuperMegaEllipsis is a proposed heuristic for immediately detecting bad posts. I think it's a pretty good one.