tea.mathoverflow.net - Discussion Feed (Is "What is your favourite isomorphism?" appropriate?)

gilkalai comments on "Is "What is your favourite isomorphism?" appropriate?" (8833)

2010-09-04T22:47:14-07:00

Of course, questions about mathoverflow are better be asked in meta.

Mathoverflow is meant for good questions (in term of their academic quality) about mathematics. I do not see a mission drift. From the beginning there were about 5%-10% of the questions which had the nature of not having a single answer. These questions were often quite valuable and they are ranked very highly. Most heavy participants asked such question and people do get a lot from them. In fact, at the early days it was easier for a big list problem to stay open even if its academic content was questionable. So to the extent that there was a drift (at least in the meta discussions)it was towards less tollerance to such questions.

Overall, because of various reasons that I mentioned in some earlier discussions, MO is a better place for big list problems than blogs. (This applies to even extremely successful blogs like Gowers's, and to Tim most recent question http://mathoverflow.net/questions/37610/demonstrating-that-rigour-is-important ) Very shortly, MO is a much better place to get answers. (I do not see how my blog that Scott mentioned has anything to do with anything.)

MO is an academic indeavor and it is important that the way it runs reflects appropriate academic values.

Scott Carnahan comments on "Is "What is your favourite isomorphism?" appropriate?" (8832)

2010-09-04T22:14:18-07:00

I do not think the mission of the site needs to change, and I would prefer if such open-ended questions were not asked on mathoverflow.net. I agree with Harry Gindi that a blog is fine place for open-ended questions for the readers, and I think JSE has had a reasonable amount of success with that on quomodocumque.wordpress.com.

If Gil Kalai is worried about not getting enough readers answering questions on his blog, then it might be a good idea to post material on his blog that attracts more readers that are inclined to answer his questions. Mathoverflow.net has a large readership, but I do not think most of them are here for navel-gazing, since we put some effort into making sure that such introspective questions are rare. It is not in good faith to change the scope of the site simply to take advantage of the fact that there are a large number of readers who might have answers to a particular question. As Ryan Budney said, we run the risk of alienating mathematicians who can contribute on a concrete mathematical level.

grp comments on "Is "What is your favourite isomorphism?" appropriate?" (8831)

2010-09-04T13:52:54-07:00

Ryan makes a good point on mission drift, which is why I think such a question is important. I would be happy to confine the discussion to meta.

Oh wait, most of the community is not registered on meta.mathoverflow.net. How to solve this?

Do we need to change the mission, perhaps? Or what is said about it? Or should we as a community decide that certain exceptions be allowed for the benefit of the community?

If there is support for the questions of such nature to be asked on MathOverflow, in a limited fashion (similar to the moderator election), I encourage such support to start a new thread on meta. Once started, I will contribute more to the discussion in that thread.

Gerhard "Ask Me About System Design" Paseman, 2010.09.04

Ryan Budney comments on "Is "What is your favourite isomorphism?" appropriate?" (8830)

2010-09-04T13:33:55-07:00

It seems like MO is entering a phase of mission-drift, where there is an increasing disparity between what we explicitly say the website is about, and how we behave. Gerhard's suggestion would push this even further. The FAQ says explicitly MO is not a forum for talking about MO, that's what meta is for.

IMO we should strive for more consistency or we will alienate an ever-larger community. I'm sure I'm not the only one getting this kind of feedback from people who have looked at MO but choose not to participate for precisely these reasons.

grp comments on "Is "What is your favourite isomorphism?" appropriate?" (8828)

2010-09-04T12:54:46-07:00

I think Gil has hit on a potentially useful idea. I suggest three changes.

a) Set the date for the one year anniversary.

b) Set the duration for one week, or even 72 hours.

c) Make the question into two :"What is one thing you like about MathOverflow?" and "What is one thing about MathOverflow you want changed?"

There might be a suitable alternative that would serve as a form of time capsule/historical interview/sampling of community feeling that I think would be appropriate for a one year check on this collaborative effort.

I am willing to write up and cast the question(s) if there is moderator and community support for it.

Gerhard "I Want Another Badge, Please" Paseman, 2010.09.04

Cam McLeman comments on "Is "What is your favourite isomorphism?" appropriate?" (8824)

2010-09-04T08:46:37-07:00

I'm intrigued by Gil's idea of fixed duration open-ended questions.

@Harry: I'd argue that web logs are better for positing one's own opinions, not for soliciting them from others.

Harry Gindi comments on "Is "What is your favourite isomorphism?" appropriate?" (8816)

2010-09-04T01:11:36-07:00

@Gil: Isn't that what web logs are for...?

gilkalai comments on "Is "What is your favourite isomorphism?" appropriate?" (8815)

2010-09-04T00:41:15-07:00

The isomorphism question looks like a reasonable "big list" question. (I am mainly interested to learn about surprising/important isomorphisms myself and only in second place about things that I can teach at class). I will be very interested to learn what Qiaocho's answer is (either as an answer if the question gets reopen or as a post in Qiaochu's blog).

Pushing things to their logical extreme is not always useful for policy decisions. (Do we mathematicians tend to do it more than others?) On the other hand, Qiaochu's suggestion, pushed even further, can be fruitful.

Let's consider the question "Tell me something interesting about mathematics" (This can be a statement a theorem a proof an example a new area, a connection, an idea, an application... .) Where the only rule is that there can be at most one answer per participant. Of course, we cannot have such a question every week and even I agree that it is much too general. But we can have this question once. So here is a suggestion: As a one-time event, to celebrate the second year universary of MO (in about 13 months or so) let's allow the question "Tell me something interesting about mathematics." Lets agree in advance that the question will be open for 2 months.

Qiaochu Yuan comments on "Is "What is your favourite isomorphism?" appropriate?" (8813)

2010-09-03T18:51:26-07:00

@alex_o: fair enough. I should've said instead that it is very hard to ask a good "fishing expedition" question, and the quality of the answers to such a question does not necessarily correlate with the quality of the question itself. I agree that some questions which might fall under this category can be quite interesting, but it's important to keep in mind that many of these questions were asked when the standards of the site were more lax, and some of them have recently been closed because they are attracting bad or repetitive answers.

Let me suggest taking the concept of fishing expedition to its logical extreme: "what is your favorite mathematical statement?" I am sure you will agree that this is too general to be a sensible MO question (although possibly I am wrong), even though it might generate a wealth of interesting answers. If we can agree on this, then we can agree that some level of specificity is necessary for such a question. I currently believe that this question is not sufficiently specific. If you can convince me that this is not true, I will vote to reopen.

I also do not understand your last comment. The questions may seem similar to you, but the question I suggested is geared towards a specific purpose: pedagogy. That gives a basis for voting on answers: vote up answers that would be good to present to students, and vote down answers that would not be good to present to students. (For example, I personally have an answer I'm dying to add to the question (except that I am not convinced that the question is worth reopening); it is my "favorite," but it is in no way a suitable example for beginning students.)

alex_o comments on "Is "What is your favourite isomorphism?" appropriate?" (8810)

2010-09-03T12:42:06-07:00

@Qiaochu - you seem to have a mental category of "fishing expedition" which you appear to consider to be disjoint with the category of good questions. I tried to unpack the logic behind your comment, and the nearest I can come up with is that you seem to think evidence which is consistent with the category of "good fishing expedition" cannot, by definition, by evidence for anything else.

Since you offer no reasons for why this sort of mental classification makes basic sense, I won't bother to offer any actual arguments either. I will say that many of my favorite mathoverflow questions could plausibly be characterized by someone as "fishing expeditions," i.e. "Quick proofs of hard theorems," "Theorems with unexpected conclusions," etc.

I also find it weird that the question you would have been perfectly happy with is nearly identical to the one that was asked. As near as I can tell, you (and others) had an allergic reaction to the word "favorite."

Pete L. Clark comments on "Is "What is your favourite isomorphism?" appropriate?" (8797)

2010-09-02T23:41:59-07:00

@VP: I don't find your argument against voting to close on the two sites all that compelling. I certainly don't use the same standards to vote to close an MO question as a math.SE question. (For example, there was a question about adding fractions on math.SE that was closed as "off-topic". I left a comment questioning that: surely this is part of "math at all levels", which is the stated purpose of math.SE. Moreover, befitting the much wider scope of math.SE, I vote to close much more rarely on that site.)

One reason to vote to close a question on both sites -- which you need not agree with, but I think is certainly ethically defensible -- is that it is simply too broad to be appropriate for any SE-engine driven Q&A site. These sites are designed to answer specific, focused questions. (Some people want to also ask broader questions under the "community-wiki" label, and that's a defensible position too. It seems that the reaction to this should be to be doing exactly what we are doing: to (i) vote our preferences on the matter, (ii) discuss why we feel a certain way, and (iii) try to keep an open mind.)

In particular, I have come to regard use of the word "favorite" as a sign that the question is too broad to be useful. It basically just invites any and all answers and allows no real justification for the voting up and down of answers. Why are we ranking people's favorite isomorphisms?

As Qiaochu remarks, there is a kernel of a good question in here. Namely, the OP seems to be interested in teaching the concept of isomorphism and is looking for examples of successful pedagogy in this area. Again, the word "favorite" works against this, because it doesn't make sense to justify your favorite things ("And why exactly do you like raindrops on roses?"), and indeed a lot of people are answering with things like "I don't know whether this would be a good example for students, but I have always liked..." I think the question would be worthy of reopening after being edited to emphasize the pedagogical aspect and enjoining responders to explain why their answer would be helpful for students.

Qiaochu Yuan comments on "Is "What is your favourite isomorphism?" appropriate?" (8793)

2010-09-02T21:38:48-07:00

No, it's not. The reason fishing expeditions are so hard to close is precisely because they're so easy to answer and because everyone wants to contribute. The fact that many of those answers are interesting is, if anything, evidence that the fishing expedition is fishing successfully.

On the other hand I would've been perfectly happy with a question of the form "what are concrete, striking examples of isomorphisms to describe to students," which is the question that some people ended up answering anyway.

alex_o comments on "Is "What is your favourite isomorphism?" appropriate?" (8789)

2010-09-02T20:17:22-07:00

I thought that this question generated a number of excellent responses. While the existence of _some_ interesting answers is not evidence that a question is good, the existence of _many_ interesting answers is.

VP comments on "Is "What is your favourite isomorphism?" appropriate?" (8788)

2010-09-02T20:06:37-07:00

I was a bit surprised to see some familiar names among those who closed the MU question. That brings forth a delicate ethical issue: since there is apparently a substantial overlap between people with voting privileges on both sites and it only takes a few such users to close a question, ought they not to refrain from duplicating their votes? For otherwise, they would be imposing their will at both MO and MU, which can result in mathematical questions disliked by a few powerful users with strong opinions having literally nowhere else to go and lead to very bad feelings on the substantial part of the community that is unable to affect the process.

On the closing itself: the MU closing message states that

It's impossible to objectively answer this question; questions of this type are too open ended and usually lead to confrontation and argument.

I don't see any evidence of this happening at either MO or MU. It is true that the question gathered only 1 up signed vote at MO as of this writing, but it seems disingenuous to close a question not even 6 hours old that has already attracted 17 reasonable, and even insightful, answers. In fact, it looks remarkably like another attempt by the OBN to make everyone else to toe the line. (The MO stated reason for closing is "off topic").

Pete L. Clark comments on "Is "What is your favourite isomorphism?" appropriate?" (8785)

2010-09-02T17:32:39-07:00

Update: once I realized that I had voted to close essentially the same question on math.SE, I found my resolve and voted to close this question.

Pete L. Clark comments on "Is "What is your favourite isomorphism?" appropriate?" (8783)

2010-09-02T16:28:26-07:00

I think it is a bad sign that the most popular answer is a joke (admittedly a good one).

Sadly for me, I think I would like to see the question closed, and I would like for the last close vote to be cast by someone other than me. I don't know quite what to make of this...

Isn't this a good candidate for mathoverflow.tea, or whatever the sister site is that was being discussed? Did anything happen with that?

Tony Huynh comments on "Is "What is your favourite isomorphism?" appropriate?" (8782)

2010-09-02T16:28:00-07:00

I wouldn't mind seeing the question remain open (at least for a little while longer). It has met the criteria of attracting interesting answers (not mine, but some of the others were insightful). Also, given that the question is community wiki, I feel that the OP should be given a little bit of leeway with regards to imprecision.

Yemon Choi comments on "Is "What is your favourite isomorphism?" appropriate?" (8781)

2010-09-02T15:50:26-07:00

As I write this comment, the question has attracted 4 votes to close - I personally don't have an active wish to see it stay open, but perhaps it could benefit from some discussion here. It is not clear to me that what the questioner intends by "isomorphism" is the same as the technical category-theoretic notion, but perhaps I have misread or misunderstood.