tea.mathoverflow.net - Discussion Feed (Reopen: Aut(G) = C_3)

Gerry Myerson comments on "Reopen: Aut(G) = C_3" (10389)

Gerry Myerson — Mon, 08 Nov 2010 12:48:38 -0800

Mariano, not very many. In fact, counting the next one, and the one after that, two. I take "too localized" to be very meaningful to the people for whom the software was originally designed, close to meaningless to MO, and I simply don't use it.

HJRW comments on "Reopen: Aut(G) = C_3" (10333)

HJRW — Mon, 08 Nov 2010 07:18:46 -0800

+1 Cam.

Regarding 'Too localized', for what it's worth I'm with Gerry: if it's homework then it's 'Off topic'. I think Scott's comment in the thread that Ryan linked to is a decent characterisation of 'Too localized'.

Cam McLeman comments on "Reopen: Aut(G) = C_3" (10331)

Cam McLeman — Mon, 08 Nov 2010 05:41:40 -0800

To me, this was never a direct matter of homework vs. not homework (though this certainly seemed to be the crux to some of the question's other objectors) -- it's that as a question approaches the "could easily be a homework problem" boundary that we have such a problem identifying, I tend to want to require more from the asker. Even given that the asker was a Ph.D., there is, to me, a big difference between "I was doing some research on automorphisms of Riemannian manifolds, and stumbled upon this lemma I need but which is outside my area" and "A student dropped by my office and wanted to know the answer to this question." Asking and answering the former I have no problem with (especially in the form of Todd's re-write, which as has been pointed out, would be sufficient for a professional mathematician working outside their comfort zone, but not enough for an undergraduate trying to skate by).

Mariano comments on "Reopen: Aut(G) = C_3" (10330)

Mariano — Mon, 08 Nov 2010 05:36:30 -0800

How many examples of questions to which the geographical interpretation applies as a reason to close?

I usually use "too localized" to mean "this is a math problem but it does not belong here".

Gerry Myerson comments on "Reopen: Aut(G) = C_3" (10328)

Gerry Myerson — Mon, 08 Nov 2010 03:22:42 -0800

Ryan, thanks. That thread doesn't seem to have terminated with any kind of consensus. My experience has been that when people vote "too localized" it is seldom for either of the two reasons Scott gave in that thread. It is more often because of the level of the question, and I prefer to vote those "off-topic". High school algebra is off-topic, no? The interpretation Francois gives in this thread does not align with Scott's reasons in that other thread, so I'd say the matter is unresolved. I will stick to my geographical interpretation (unless that makes many unhappy).

Ryan Budney comments on "Reopen: Aut(G) = C_3" (10327)

Ryan Budney — Sun, 07 Nov 2010 22:29:25 -0800

Gerry, we have a thread on the interpretation of "too localized": http://tea.mathoverflow.net/discussion/274/what-does-too-localized-mean-exactly/

Gerry Myerson comments on "Reopen: Aut(G) = C_3" (10326)

Gerry Myerson — Sun, 07 Nov 2010 21:38:24 -0800

I thought "too localized" was for questions like "What's the best math library in West Bicycle, Nebraska?"

Todd Trimble comments on "Reopen: Aut(G) = C_3" (10323)

Todd Trimble — Sun, 07 Nov 2010 17:05:29 -0800

I appreciate the feedback, Tom.

Tom Church comments on "Reopen: Aut(G) = C_3" (10322)

Tom Church — Sun, 07 Nov 2010 17:00:04 -0800

Dear Todd,

For the record, I found the current version of your answer much easier to follow than the original version (I went back and looked at it). So it seems you've found the best of both worlds -- a student who wanted to copy it would have to think to expand it into a proof, and mathematicians can get the idea without the haze of details.

Best,
-Tom

Todd Trimble comments on "Reopen: Aut(G) = C_3" (10321)

Todd Trimble — Sun, 07 Nov 2010 16:31:29 -0800

Francois, that's a very useful formulation of "too localized". Something like this should be in the FAQ (I can't recall whether all these reasons for closing are explained there or somewhere else on this site).

[Was the present question too localized then? Based on just my own answer, I tend to believe "not quite", but it could be a close call.]

In fact, should some sort of consensus emerge from this discussion, then it might be good to put down somewhere more visible.

Anton and Andrew, thank you for your remarks. People here seem pretty vigilant about policing questions that look like homework requests, as is only right, so I can't imagine that MO has acquired anything like a reputation of go-to place to get your HW done. But in this case and others I've seen, people have seemed a little too vigilant and too quick to judge intent from the bare question. Perhaps a warning shot along the lines of, "I'm voting to close unless OP explains better where this is coming from; it looks like a homework request to me" should be employed more often (I think I've seen this used). If the OP responds with something reasonable, keep it open. The random undergraduate passing by will probably be unable to say anything reasonable.

François G. Dorais comments on "Reopen: Aut(G) = C_3" (10313)

François G. Dorais — Sun, 07 Nov 2010 12:30:09 -0800

I'm with Anton. I think that, for most users, a good litmus test for "too localized" is whether the question can be completely answered by the user in a short comment. Whether or not to leave such a comment is optional, but the mental exercise should allow the user to see if there is some subtlety that needs to be addressed in a full answer.

Andrew Stacey comments on "Reopen: Aut(G) = C_3" (10312)

Andrew Stacey — Sun, 07 Nov 2010 11:09:35 -0800

The objection that a question is a homework problem seems about as relevant as objecting that something would make a nice homework problem.

Agreed. That a question is the same as a homework problem is not in itself sufficient to vote to close, though it is evidence that the level might be too low. However, that someone is asking a problem that they were set as a homework is sufficient. A question is not just a question, it's about the questioner as well. So I would consider who was asking the question when deciding whether or not to vote to close a seeming homework problem.

Harry Gindi comments on "Reopen: Aut(G) = C_3" (10305)

Harry Gindi — Sun, 07 Nov 2010 09:47:04 -0800

Nobody is making the argument that Dummit and Foote should be removed from the mathematics library.

Anton, you have spoken too soon!

Anton Geraschenko comments on "Reopen: Aut(G) = C_3" (10300)

Anton Geraschenko — Sun, 07 Nov 2010 07:20:58 -0800

I mostly agree with Todd. The objection that a question is a homework problem seems about as relevant as objecting that something would make a nice homework problem. There are plenty of interesting results that make good homework questions once they are proven. The possibility that an undergraduate could solve a problem, or even the fact that undergraduates often solve a problem given context, doesn't feel like sufficient grounds for closing a question. I also don't think that an answer being easy to understand is sufficient grounds for closing a question. After all, when you post a question to MO, you're hoping that it's easy for somebody.

While I agree that we wouldn't want MO to have the reputation of being a repository of solutions to homework problems, it is supposed to be a repository of problems and solutions, so some friction is unavoidable. If something makes a good homework problem in a graduate course (or even an upper division undergrad course), it's probably because is made what would've been a good MO question at some point in the past.

I suppose it's largely a question of what reputation MO has, but I really don't get the feeling that we're currently in danger of acquiring the reputation of a great place to go to get your homework done. So long as that isn't an issue, I don't see what's wrong with people being able to find solutions to (these kinds of) homework problems on MO. After all, they can and do already search Dummit and Foote for solutions to exercises in Lang, and nobody is making the argument that Dummit and Foote should be removed from the mathematics library. Even with very high-tech math you can argue that it would be much better for everybody to work it out for themselves, but it's often the case that these things are incredibly confusing even if somebody is carefully holding your hand the whole way (as in a textbook).

It's certainly true that there's value to solving a problem on your own and that we should discourage people from simply avoiding that. But we have no reason to be so insecure about mathematics that we make it artificially more difficult. If somebody just tells you the answer to a question you have or shows you some piece of machinery that swiftly solves your problem, you'll have no trouble finding other problems to build your character. If you digest the answer, I can't imagine what argument anybody could give that you are worse off.

Todd Trimble comments on "Reopen: Aut(G) = C_3" (10280)

Todd Trimble — Sat, 06 Nov 2010 16:25:09 -0700

> so I very much hope that you don't take anything said above personally.

Nope! Not a bit. Even better, I've benefitted quite a lot from this discussion.

HJRW comments on "Reopen: Aut(G) = C_3" (10279)

HJRW — Sat, 06 Nov 2010 16:20:11 -0700

Todd, I personally have no problem with your answer itself. There will always be grey areas to any policy, and obviousness is in the eye of the beholder. I'm glad these issues have been raised, and I think it's been good to have a discussion about them: it's certainly helped me clarify my thinking. As far as I'm concerned, your answer was nothing more than a useful example in that discussion, so I very much hope that you don't take anything said above personally.

Todd Trimble comments on "Reopen: Aut(G) = C_3" (10278)

Todd Trimble — Sat, 06 Nov 2010 16:00:13 -0700

Hi, Cam. Thanks very much for your honesty. I fully understand what you did and why. I think that's very respectable.

It was Martin who seemed ticked off, almost as if to say, "Nice going, Trimble -- you're ruining *everything*!" (I'm exaggerating for humorous effect.) Probably he also downvoted my answer. (But, in the words of Linda Richman, "No big whoop.")

Yeah, there's a big range in Hartshorne exercises all right, and I agree with you totally about having to make distinctions. And I kind of see Mark's point about HW problems here in general, but only up to a point.

And now: can I be brutally honest? I had some trouble at first with the question we're discussing. (I didn't know the Inn lemma or how easy it is.) I'm sure everyone realizes how frustrating it can be when people airily discuss how trivial something is, almost with contempt, when one is not seeing it oneself. So my heart went out a little to the OP, who received his degree the same year I did, and I thought the question deserved a considerate answer. OP might have put more into his question... but we've already discussed this.

Cam McLeman comments on "Reopen: Aut(G) = C_3" (10275)

Cam McLeman — Sat, 06 Nov 2010 15:06:22 -0700

@Todd: I don't think you've upset anyone at all. As you can see, acceptability of questions and answers is by no means a clear-cut issue, and something struggled with on meta on a near-daily basis. It's an unfortunate by-product that the askers and answerers of such borderline questions are by necessity put in the uncomfortable position of watching others debate the significance of the effort they just put forth.

(In case this is what you're referring to, I did downvote your answer, but immediately went and upvoted a different response of yours that I hadn't yet upvoted -- the intent of this being that the downvote was to discourage answering questions like this to the community at large, not to punish you in particular for writing a very clean write-up to a question I think is inappropriate for the site.)

To your other point, there's a big range even among Hartshorne exercises -- there are certainly Hartshorne exercises I would downvote for being inappropriately low-level for the site, and agree that more difficult Hartshorne exercises make for perfectly appropriate questions (assuming they pass all of the other metrics of a good question -- motivation, evidence of effort put forth, etc.)

markvs comments on "Reopen: Aut(G) = C_3" (10274)

markvs — Sat, 06 Nov 2010 14:58:09 -0700

@Ryan: Our graduate course is probably similar to your 3-d year undergraduate course. I just spice it from time to time with some advance topics like Banach-Tarski paradox. I am not against reopening that question and keeping it open since Todd likes it. But I do not agree with his assessment that the answer requires anything "beyond the definitions of Aut and Inn". Still he is right: there were similarly or even more trivial questions on MO and I even answered one of two of them.

Todd Trimble comments on "Reopen: Aut(G) = C_3" (10270)

Todd Trimble — Sat, 06 Nov 2010 14:05:53 -0700

Yeah, I think Mark said in his graduate algebra courses. The general question of what types of "homework" are "fair game" for this site is probably an interesting one which deserves some careful thought. I'm not saying this particular question is a great test case or anything, but I can think of problems from say Hartshorne that I found very difficult when I was a graduate student and probably would still find difficult, and the idea of being able to consult MO on such old unresolved questions is very attractive to me, as though I can at last die peacefully. Perhaps we could discuss this sometime. Or has it already come up here?

Ryan Budney comments on "Reopen: Aut(G) = C_3" (10267)

Ryan Budney — Sat, 06 Nov 2010 13:42:10 -0700

Mark Sapir mentions he gives this as a homework problem in his group-theory courses. I'm pretty sure this was a homework problem in my 3rd year undergraduate algebra class -- this was a class that built up Sylow theorems and Galois theory, modules over PIDs, etc. It was a full-year course. I don't have copies of those assignments anymore, though. If I was in my office I'd check Dummit and Foote "Abstract Algebra" as this is a very standard large source of undergraduate algebra problems.

Todd Trimble comments on "Reopen: Aut(G) = C_3" (10266)

Todd Trimble — Sat, 06 Nov 2010 13:32:30 -0700

I do understand. I did want to bring this up on meta first, but had some trouble signing in. I then wrote Qiaochu (whom I know a little from private emails and other fora), and before I knew it the question was re-opened. And so, having thought about the question a bit, I jumped right in, which I thought was okay. I am a little dismayed that I seem to have upset some people.

Ryan, as long as we're talking: do you have a reference for the assertion that this question (as stated) is a well-known homework exercise?

Ryan Budney comments on "Reopen: Aut(G) = C_3" (10264)

Ryan Budney — Sat, 06 Nov 2010 13:13:06 -0700

Todd, to step back a bit for some perspective, I think there's something of a systematic governance problem going on here. People in general want to spend their time contributing: reading and responding to interesting questions, rather than nit-picking what is appropriate and what isn't. So the natural tendency is to just let everything slide as that reduces friction for all involved.

The more that happens, IMO the less relevant a forum MO becomes. math.stackexchange is far more clear about what is appropriate and what is not, so there's less friction. The more interactions like this that I have, the less inclined I am to bother voting to close, as it seems if a thread is closed it will be re-opened without discussion, and answered completely before people pay attention to the concerns of the "closers". If people had created a meta thread before the thread was closed (or had even commented raising objections to closing), of course we should have had discussion at that point but as far as I am aware, that did not happen in this case.

Anyhow, I hope you understand.

Todd Trimble comments on "Reopen: Aut(G) = C_3" (10263)

Todd Trimble — Sat, 06 Nov 2010 12:51:10 -0700

Ryan, that's not really what I meant. The question is why is this such a bad question for MO; I'm just not convinced it's that bad. Okay, so put "easy-ness" aside: IMO there are far worse questions appearing on this site than the one we're discussing, where it looks like the questioner didn't think *at all*. I do agree that Henry's comments are reasonable, and in comments I *did* offer to edit some more so that it looks less like a class handout of a solution. Maybe I'll go back and do just that. Generally I try to write mathematics as clearly as I can; the suggestion is that I went too far this time? (Thanks for the feedback Henry -- I learn from such well-expressed advice.) Added in edit: you make a good point, Ryan, that OP could have designed his question more thoughtfully, but obviously he was new to the site and I think something like Andrew Stacey's comment should have been tendered first, before shutting his question down entirely. Oh well, hindsight is 20/20.

Mariano comments on "Reopen: Aut(G) = C_3" (10257)

Mariano — Sat, 06 Nov 2010 11:44:56 -0700

M.SE is on the way to becoming, in part, a repository of solved homework problems, sadly.

Ryan Budney comments on "Reopen: Aut(G) = C_3" (10256)

Ryan Budney — Sat, 06 Nov 2010 10:52:32 -0700

@Todd, regarding your quote: "Far easier questions have been posed in MO and not closed as `too localized'", if we're to go by the mandate that any question is okay if and only if there is an easier question present on MO, this would be not be productive, long term, for the webpage. We have a very different sensibility than the easy-ness of a problem for acceptability at MO, I hope. I think Henry Wilton's comments above are quite reasonable.

HJRW comments on "Reopen: Aut(G) = C_3" (10253)

HJRW — Sat, 06 Nov 2010 10:24:06 -0700

The OP's doctorate is beside the point. Undergraduates can ask research-level questions, and professional mathematicians can ask homework-level questions, particularly outside their area. Surely the difference between MathUnderflow and MathOverflow in the latter case should lie in the form of the answer? A 'research-level' answer to the question under discussion would probably have been an indication of how to go about the problem (eg 'It's easy to check that a cyclic group of inner automorphisms implies that the base group is abelian, and now the result is straightforward'), or better still, a reference. I think Todd's answer would be great on MU.

Ryan Budney comments on "Reopen: Aut(G) = C_3" (10252)

Ryan Budney — Sat, 06 Nov 2010 09:15:59 -0700

The thing I don't like about this is we're cementing MO's reputation as a website to go to for solutions to homework problems.

I can understand when undergraduates and non-experts have weak write-ups of their questions but for a research mathematician I tend to expect at least a motivational write-up to a problem. In contrast, I'm less concerned about math.stackexchange developing a reputation as a homework solution webpage, as they do not have anything in their mandate specifically against that.

The structure of MO is to have community norms enforced by the community but it appears the community is pulling the website where it will be indistinguishable from math.stackexchange. I don't think this is a good idea. If the websites aren't any different, what's the point?

Todd Trimble comments on "Reopen: Aut(G) = C_3" (10251)

Todd Trimble — Sat, 06 Nov 2010 07:28:54 -0700

Cam: yes, but what passes for a good question is pretty subjective. I am not yet persuaded that this is a "well-known exercise" because AFAICT it's not a one-line proof (as in showing that Inn(G) cyclic => G abelian); there are several parts to the argument that have to be assembled. (If you think it's even easier than in my solution, please enlighten me.) Far easier questions have been posed in MO and not closed as "too localized", and OP is a mathematician who was probably honestly stuck.

Cam McLeman comments on "Reopen: Aut(G) = C_3" (10250)

Cam McLeman — Sat, 06 Nov 2010 06:35:49 -0700

But not homework does not imply good question (for MO, of course)...

Qiaochu Yuan comments on "Reopen: Aut(G) = C_3" (10247)

Qiaochu Yuan — Sat, 06 Nov 2010 03:39:04 -0700

This question was closed pretty quickly, but Todd Trimble disagrees and has voted to reopen. The OP has a doctorate, so the question was less likely to have been homework than I previously thought.