tea.mathoverflow.net - Discussion Feed (Why is this definition the way it is?)

Andrew Stacey comments on "Why is this definition the way it is?" (15881)

2011-08-30T08:21:32-07:00

Yes, that comment did reveal considerable confusion on behalf of the questioner. Given that the questioner was confused about that, I'm surprised that the apparently satisfactory answers were satisfactory. But I may be being uncharitable, this might have just been one of those "hadn't thought it through" incidents.

quid comments on "Why is this definition the way it is?" (15879)

2011-08-30T06:50:12-07:00

Andrew, since I also mentioned 'level'. The question is not the problem, but what about this comment:

"[...] It seems to me that the right hand side of the equality is (possibly) "bigger" than the left hand side. Let $1^k \in \mathbb{R}^k$ denote the finite, constant sequence, $(1,\ldots,1)$. The limit of $1^k$ as $k$ tends towards infinity does not lie in $\mathbb{R}^{\infty}$, even though we can identify $1^k$ with $(1,\ldots,1,0,0,\ldots) \in \mathbb{R}^{\infty}$ for all $k < \infty.$ I can see that all of the elements of $\mathbb{R}^{\infty}$ can be constructed by the union, but we seem to be able to construct other elements too."

In my opinion, this confusion is the root of the question.

ADDED: I should say 'was' instead of 'is' as it got resolved. But, in my opinion, this 'answered' the original question.

Andrew Stacey comments on "Why is this definition the way it is?" (15878)

2011-08-30T02:56:43-07:00

Quid gave five distinct interpretations of the question. From the question itself I cannot tell which the OP is asking and each, in my mind, requires a different answer. That is why I do not like this question. I think that the level is absolutely fine for MO and that any of those five questions would be perfectly acceptable here. But unless or until the OP clarifies which question they mean, then I cannot see how it is answerable.

My best guess is that the first is the right answer, and then Ryan's answer comes the closest to answering it; though I still think that he isn't clear enough. The key to answering the first version would be to explain exactly why this particular model is a good one to use. Allen says "Because then it is a CW-complex", but so what? Why is actually being a CW-complex better than having the homotopy type of a CW-complex (this would be a very good question, I think)? (Then he goes off with some irrelevance about U(∞) versus U(ℋ)). Ryan at least says:

A key nice result about the weak topology on ℝ^∞ is that any continuous function from a compact space to ℝ^∞ has an image in ℝ^k for some k.

which to me, at least, is the heart of the matter. It says that when dealing with ℝ^∞ then you are effectively dealing with "very big (but finite) ℝ^k", at least if your source space is compact (say, a closed manifold or finite CW-complex). So although we want to deal with the classifying space BU(n), we can pretend in any given circumstance that it is a finite dimensional manifold/CW-complex.

But the rest of Ryan's answer, and of what just about everyone else says, is pretty much model independent and so talks about properties of BU(n) without saying why one particular model is preferable to any other. If the OP is truly asking "why this model and not another" then the answer has to address some property of this model that is not held by another, and explain why that property is important.

In response to other remarks, no matter how often I read the question I do not see any mention of the direct product. There are a heck of a lot of spaces between the direct sum and the direct product which I would expect Jo Mathematician to be vaguely familiar with, far more familiar with than the direct product. With no information as to the field of the OP, I don't see how we can assume that he or she means to compare the direct sum with the direct product. (For what it's worth, the direct product is countable infinite dimensional: the direct sum is dense in it.)

This is the sort of question where even if I don't answer it myself, I feel I am competent enough to judge what is a good answer to it. There is not enough information in the question for me to be able to do that! Allen's answer I just do not like, Ryan's is okay, SPG's doesn't address the issue of different models, Paul Garrett's could be taken in one of two ways: either it is about the homotopy type (in which case it doesn't address the issue of different models) or it is about the specific model (in which case it doesn't address what is special about this particular model), Yemon's is - sadly - also missing the point: most of the time we only care about the homotopy type of BU(k) so the particular model doesn't matter, it would surprise me if M&S's book couldn't work with a different model.

To summarise: there is nothing in this question to indicate that it is of a level below that of MO. That part of the debate I find quite bizarre. However, there is also nothing in this question to indicate exactly what sort of answer would satisfy the OP. I was commenting on it because this is the sort of question where I might have been able to contribute, but without knowing more then I wouldn't know exactly what to contribute. That the OP was satisfied with Allen's and Donu's answers (though exactly how, I have no idea) means that the OP needn't bother responding to my comments. But I still maintain that it is not a good question, and we have not have any good answers yet (though I applaud those who tried for doing so).

quid comments on "Why is this definition the way it is?" (15874)

2011-08-29T20:22:48-07:00

Dear Emerton,

it seems 'evil' has a stronger meaning than I thought. I retract it and appologize. Thank you for confirming the time-line.

Regarding the general question whether typical graduate-level material should be on-topic on MO or not, I agree that a clarification and/or discussion could be useful; indeed, I made a somewhat similar observation a week ago in this thread. Personally, I would not have anything against MO being (or perhaps again being) more open towards this. However, it seems to me this particular question is not the best example for making a case for it.

Thanks again and best wishes!

François G. Dorais comments on "Why is this definition the way it is?" (15872)

2011-08-29T20:01:44-07:00

I'm sorry to interrupt this interesting discussion, but let me throw in a somewhat related "MO rule of thumb":

MO is a good place for mathematicians to ask basic questions in a field outside of their area of expertise.

The reason for this rule is mainly sociological, but it is nevertheless a viable rule. Many professional mathematicians would feel uncomfortable asking questions on MSE or similar sites since those sites are primarily intended for less a experienced audience. Indeed, the most suitable responses to such questions is most likely above the usual standards of these alternate sites. (Note that MSE often has very excellent answers to questions, so don't take this last sentence to mean that MSE is not a good place to ask such questions!)

I don't like throwing big names around just for show, but let me give this example. Last year, Terry Tao asked some relatively basic questions on ultrafilters. Granted that ultrafilters aren't a standard part of the graduate curriculum, but any expert on the topic will concur that these questions are basic knowledge for the area. Terry asked because these questions were relevant to his current work but outside his current knowledge base. Would anyone refer Terry to MSE or elsewhere in such circumstances? Of course not! Is Terry the only mathematician worthy of this exception? Of course not!!!

Emerton comments on "Why is this definition the way it is?" (15871)

2011-08-29T19:41:53-07:00

Dear Quid,

I think "evil" may be a bit of an extreme adjective to introduce into the discussion; I haven't seen it used, or intimated, before now (unless I missed something).

I looked through the question again at the various timestamps, and saw that you are right and I was wrong vis a vis the non-expert/Milnor and Stasheff material. Nevertheless, the question of direct sum vs. direct product is expressed from the very beginning, and the additional material providing context was posted in under 24 hours. And although it wasn't originally made explicit, the fact remains that this question did arise in a legitimate way from reading graduate level texts. (And I find it hard to think that anyone would regard this question as dealing with undergraduate level material.)

In any event, it may be that such questions, asking for very basic clarifications of graduate-level subjects, no longer belong on MO, but then, as SGP suggested, perhaps the FAQ should be updated to reflect this.

Best wishes,

Matthew

quid comments on "Why is this definition the way it is?" (15869)

2011-08-29T19:09:14-07:00

SPG, thank you for the response.

spg comments on "Why is this definition the way it is?" (15867)

2011-08-29T18:23:42-07:00

quid,

My apologies. I read your list too quickly. I suppose neither a) nor b), but rather exactly what I quoted the OP asking above (just to avoid confusion, I'd prefer not to endorse any paraphrasings of the OP's question). This was the original question and has not been edited: so I believe the OP's question was there, clearly stated, for all to see who read carefully. I cannot speak for Emerton, but I do not wish to tell the closers how wrong and evil they were, but merely that they erred if their reason for closing was that the question was ambiguous.

spg

quid comments on "Why is this definition the way it is?" (15866)

2011-08-29T17:54:34-07:00

Emerton, this relevant context was provided after the closure, in fact I guess as a consequence of it; and it wasn't a quick closure, and the OP commented before it. Might I ask that Gil, you, and whoever else in addition wishes to tell the closers how wrong they were to at least acknowledge this fact.

SPG, a. or b. or is this the same?

Tom Leinster comments on "Why is this definition the way it is?" (15865)

2011-08-29T17:34:54-07:00

I think I can see both sides.

On the one hand, when you're having trouble understanding a new piece of mathematics, it can be hard to formulate a really focused question. You're fumbling around in the dark, and probably you don't know exactly what it is that's blocking your understanding. So the best you can do is "why is this defined the way it is?", and you hope that someone knows what you mean well enough that they can tap into the source of your confusion and enlighten you. I'm sure there have been questions like this on MO before, and everything's gone just fine.

On the other hand, there were some particularly unfortunate circumstances in this case. Several people genuinely found it hard to know what kind of answer the OP wanted. (The first person to say so on this thread was Qiaochu, who I have never seen being petty or anything other than level-headed.) Ordinarily that would be OK: if commenters request clarification, the OP generally clarifies. That's all part of the process. But in this case the OP didn't, and in fact reacted in a quite emotional way. If he/she had promptly edited the question, or even just written "sorry, I'm a beginner at this stuff and don't know how to make my question any more precise", that would probably have defused things.

I haven't communicated with Andrew about this, so the following is pure guesswork, but I wonder whether for him it was uncomfortably close to a question of the type "write me an expository article about such-and-such". Evidently he could think of lots of things to say on this topic, but he didn't know which ones would be useful to the OP. And when he asked, he didn't get a reply that helped him to narrow it down. So I think I can understand his frustration.

Later on, unpleasant things were written by two other anonymous users, on this forum and in a swiftly-deleted answer on the main site. Even if you think that some people were simply pretending not to understand the OP, there's no one to blame for those pieces of nastiness other than those who wrote them.

spg comments on "Why is this definition the way it is?" (15864)

2011-08-29T17:17:42-07:00

Emerton,

I also find myself wondering what the actual purpose of MO is. This question seems an interesting test case.

On the one hand, I am somewhat sympathetic to those who believe that the question is ill-suited to MO. It has the "feel" of a MathSE question to me, in that it's not a question that would interest an expert in geometry very much---it's the sort of thing one might wonder about out of idle curiosity, or, as happened in this case, because one is exploring an alien land and hasn't figured out the customs yet.

On the other hand, the fact is that it was asked in good faith by a young professional mathematician trying to understand an area far from her or his own. In such situations, it should be easy for professionals in that area to clear up the confusion quickly, or else to reassure that it is something the experts don't know. Is this not what MO is for?

I am a professional mathematician who often wonders about such questions outside my own area of expertise. When I can't ask a local expert to help with a question I suspect should be routine, does this mean that I should turn to MathSE for help?

spg

Yemon Choi comments on "Why is this definition the way it is?" (15863)

2011-08-29T16:57:41-07:00

Put another way: I am sure there are theorems about the Grassman-ish object defined as the set of n-dimensional subspaces of $\prod_{n=1}^\infty {\mathbb R}$, equipped with suitable structure. I suspect they are not the same theorems as the ones about the Grassmanian of n-dimensional subspaces of ${\mathbb R}^\infty$. Without having a copy of Milnor-Stasheff to hand, and not being familiar with the book, it is not clear to me which of these theorems would be the ones of interest.

Yemon Choi comments on "Why is this definition the way it is?" (15862)

2011-08-29T16:55:09-07:00

Why not consider the direct sum?

Ill-fitting parable: when thinking about C*-algebras, you can consider the c_0-sum of a (countable) family of C*-algebras. Why is this defined the way it is?

Emerton comments on "Why is this definition the way it is?" (15861)

2011-08-29T16:34:55-07:00

I agree with Gil and SPG's comments above, to the effect that the question was pretty unambiguous (why consider the direct sum rather than direct product of counably many copies of R), and that a context was provided (a non-expert reading Milnor and Stasheff), and that furthermore this context placed the question squarely in the (stated) purview of MO, namely a question come across while reading a graduate-level book.

I don't see why this question generated so much fuss.

I also wonder what the (actual, rather than stated) point of MO is at this stage: if someone can't come and ask a (possibly confused, but still essentially unambiguous) question about Milnor and Stasheff, what is the minimum technical level of question that people (say those participating in this thread) regard as appropriate?

Ryan Budney comments on "Why is this definition the way it is?" (15860)

2011-08-29T15:34:26-07:00

I still believe the question is a bit too vague. But I decided to answer what I assume is the OP's main concerns, given that they're reading Milnor and Stasheff.

quid comments on "Why is this definition the way it is?" (15859)

2011-08-29T14:19:27-07:00

Gil, yes this comment seemed clear to me (and further clarified an initially vague or if you prefer fairly clear question). As such it might have been useful to edit this information into the question rather than to only have it as a comment in a fairly long comment thread. Perhaps there was some need for editing after all. Yet, in my opinion this question got already answered within the first three comments, before that comment was even made. So, I did not understand the continuing discussion. Except if some people still read it differently than I read it, which in turn would imply the situation is still not clear. Or, the request is for elaboration on the comments, but I honestly never understood the discussion to be mainly about elaboration on these comments, except until your last comment. [Added: where by 'the discussion' I mean your comments and the ones by Andrew you refer to as well as my contribtions; of course earlier parts where in some sense about elaboration or 'level'.]

SPG, thank you for the information. But this starts to be a bit confusing for me. The following questions seem quite different to me:

a. What is the/a motivation of M&S to use the definition they use [direct sum]?

b. Could one use this specific alternative definition [direct product] instead and still do what M&S do?

c. Could one use some other alternative definition to do what M&S do, or does one have to use the one they use?

d. Is the specific alternative definition used/usefull anywhere else in this context?

e. Are other alternative definition used/usefull anywhere else in this context?

All of which I could imagine, in principle and abstractly [I do not have the expertise to truly judge this], to be things on could answer 'around' this question. I believe that the main intent was to ask a., in particular based on the comment of the OP quoted by Gil Kalai, I repeat the keypart "[...]I would like to understand why (for the purposes of the theory developed in the book) we define infinite dimensional R(inf) the way it is defined in the book[...]"; and before that suspected something like this based on the first reaction to comments. However, it seems to me you think b. is asked. While some of Andrew's comments perhaps suggest that also an answer to c. would be interesting. So, I am confused.

spg comments on "Why is this definition the way it is?" (15858)

2011-08-29T11:57:27-07:00

Gil,

I agree with you that my answer is not entirely satisfying. As I commented in reply to Andrew, the OP asks:

"My question is why do we insist that only finitely many of the xi are non-zero for each (x1,x2,x3,…)∈R∞? "

This is the only sentence in the OP's post ending in a question mark. I think that this is unambiguous without any need for further clarification or interpretation. As for whether the question is suitable for MO, from the FAQ

"MathOverflow's primary goal is for users to ask and answer research level math questions, the sorts of questions you come across when you're writing or reading articles or graduate level books."

Again, it is not really debatable: one comes across this question when reading Milnor+Stasheff, a graduate level book. It's an obvious question, and given current practices maybe better suited for MathSE than MO. Perhaps the problem is that the FAQ needs to be changed to better reflect current practices of 3000+ point users?

Quid, my comment was meant as rhetorical, I do not really believe there are 2 interpretations of the question.

gilkalai comments on "Why is this definition the way it is?" (15857)

2011-08-29T11:47:28-07:00

(Based on the question and his comment) the OP asked the following " I work as a postdoc at the moment, but vector bundles and topology aren't my area. I've realised that they might be very useful for something I'm doing at the moment. So I've got Milnor and Stasheff's book and I'm missing some motivation. I would like to understand why (for the purposes of the theory developed in the book) we define infinite dimensional R(inf) the way it is defined in the book, and especially why we consider sequences with only finitely many non zero entries.

This question is very clear. It may or may not be more suitable to the sister site but there is no more information or clarifications the OP can give us, or any editing which will make the situation clearer.

SPG's answer in the comment "because its technically convenient" is not entirely satisfying (as the answer "since the authors are famous mathematicians we can trust their definitions") The answer "It's the appropriate limiting object, and that's the role it's meant to play -- to be something that contains all the finite-dimensional Euclidean spaces, but 'no more' " gives a clear impression that Ryan is, as usual, on top of things but that he does not really make the effort to explain matters to the OP(which is fine). SPG's answer is not that different than the comment: the definition is technically convenient and if you replace direct sum with direct product, God knows what happend. Allen's answer point out that this definition ensures that the Grasmanian with this definition is a CW complex which allows to use tools from algebraic topology and Allen also points out that in some cases when you consider "too large" objects things may unexpectingly become homotopically trivial.

Andrew, in a series of comments criticizes the current answers and hints that there are several models to be chosen, all homotopically equivalent, each has its advantages and disadvantages; that the situation is actually mathematically quite interesting and he can tell us much more about it except he won't, at least not before knowing what is the OP's shoe size and how tall he is (or something like that). Only then, we will be able to know if the question deserves the good answer Andrew can give (and I am sure he can), or perhaps the answer is more suitable to a wiki that will never be written and that we will never see even if it will be written. As I said, I dont understand this approach.

quid comments on "Why is this definition the way it is?" (15854)

2011-08-29T08:51:01-07:00

Gil, let us simplify this discussion: In the second comment of SPG to SPG's answer two different interpretations are given. Which one is the one that was (originally) intended by the questioner?

Ryan Budney comments on "Why is this definition the way it is?" (15853)

2011-08-29T08:34:21-07:00

@Gil: The question wasn't clear enough for many people. I think when you get questions that are sufficiently outside the scope of MO's mandate you invariably get confusion. The question has several flaws that have been pointed out already, and the OP appears to have abandoned it so it's not clear to me why the question was re-opened, especially without editing.

gilkalai comments on "Why is this definition the way it is?" (15852)

2011-08-29T06:16:23-07:00

Quid, the original question was fairly clear and the motivation and background of the OP also became clear rather quickly. There was no need to further edit the question. There were two satisfying answers and then Andrew cryptically expressed, over several comments, his mathematical concerns with the answers and his ideas about what a good answer should be. Some elaboration on this mathematical issues in an answer could have been much more fruitful than repeatedly nagging the OP. If there are some subtle issues that the OP and rest of us are not aware of then it can be very good to say what they are. (This is quite common for various MO questions.) This could be beneficial to the OP and also (which is not less important) to other mathematicians (including those who offered earlier answers) who found the mathematical issue interesting.

quid comments on "Why is this definition the way it is?" (15851)

2011-08-29T05:19:51-07:00

Gil, it seems to me he [Andrew] explained in quite some detail why he does not/cannot answer the question [73246], for example he says "it is possible to read it in too many different ways and each has a subtly different answer." Do you want him to write an answer for each interpretation? (Leaving aside the fact that he, in this discussion and frequently before, expressed his believe that MO is not the place for lengthy and general expositions.)

What I do not understand is why the questioner or those who think the question is 'good' do not edit the question (or ask another question); as several people suggested quite some time ago. Or, at least explain in detail what they mean, or where they disagree with the reasoning of those who think otherwise.

To repeat and rephrase what I said in an earlier comment, my personal opinion is: The original question (as written) was unclear/vague. Ryan and Donu correctly guessed the intent (as confirmed by latter comments of the questioner). So, the original question (in its spirit) was answered in the comments (the first ones!).

Those interested in answers to follow-up question could simply ask them.

gilkalai comments on "Why is this definition the way it is?" (15850)

2011-08-28T23:40:26-07:00

Regarding the original question: It looks that Andrew Stacy had a lot more to say about the mathematics and could have proivided a great MO answer that would have enlightend the rest of us. But instead Andrew (along with others) wanted to discover very fine details on the background of the person who asked the question and spent a lot of time and energy writing comments about this issue instead. I must say I don't understand it at all.

quid comments on "Why is this definition the way it is?" (15804)

2011-08-26T06:07:28-07:00

It seems to me that the general subject of communication on MO, in particular regarding those involving new users, can be an important discussion. However, discussing it along the lines of one particular incident (in particular this one) seems, for various reasons unfortunate to me (including, but not limited to, the fact that this thread is the meta thread of a particular question yet not the one discussed now; the actual incident is not known and is not knowable anymore to everybody, and what is still visible is so incomplete that it is misleading and, in a negative way, misrepresents Will Jagy's contribution).

I thus created a thread

http://tea.mathoverflow.net/discussion/1124/communication-on-mo-in-particular-with-new-users/ for those wishing

for those wishing to continue the general discussion, independent of the specific incident.

gilkalai comments on "Why is this definition the way it is?" (15798)

2011-08-26T02:07:28-07:00

I also like Will's style and contributions overall. But, in my opinion, Will's first comment above regarding Madalina's question was insulting. (beside being irrelevant to this discussion, and incorrect.) If a mathematician is driven away from MO by insulting/patronizing/hostile reactions to a question he or she poses, we cannot merely regard it as a "misunderstanding". Perhaps we have to doublecheck ourselves.

Andrew Stacey comments on "Why is this definition the way it is?" (15794)

2011-08-25T13:51:56-07:00

Alex, I concur- in whatever I've seen, Will has always been both gracious and professional.

I agree with this statement.

I know that when one says something that inadvertently upsets someone else, then if one is denied the opportunity to set the record straight it can leave a bad taste. Those of us (perhaps myself, I'm not sure) who tend to leave curt comments can learn from this that if someone can take even one of Will's courteous remarks the wrong way, ours are probably more susceptible to misunderstanding.

Over on TeX-SX we have a list of "templates" for likely messages for new users. The point of these isn't that they be prescriptive ("you must choose one of these") but that they lay down a minimum level of politeness. Even if one doesn't use one of these messages, the fact that they are there makes one think a little about the message one is about to leave. Thinking about it, I probably am more polite on TeX-SX than here. That's something I should probably fix.

Nilima comments on "Why is this definition the way it is?" (15793)

2011-08-25T11:50:13-07:00

Alex, I concur- in whatever I've seen, Will has always been both gracious and professional.

Thanks also for clarifying what you meant. Your comment was meant in a narrower sense than I realized.

In general, 'faint-hearted' has pejorative connotations, so perhaps we can collegially agree to an adjective less charged. How about 'daunted', or 'uncomfortable'?

Will Jagy comments on "Why is this definition the way it is?" (15792)

2011-08-25T11:39:31-07:00

Thank you, Alex. I do try, and this episode was upsetting to me as well.

Alex Bartel comments on "Why is this definition the way it is?" (15789)

2011-08-25T11:30:44-07:00

@Nilima Of course, faint-heartedness is honest. Madelina perceived the environment as unfriendly and walked out, and that seems to be largely due to Will's comments. As I said, I haven't actually seen the comments in the thread that Will mentioned. But I have never seen Will attack anyone personally on this site, nor have I ever seen him say anything that would have made me leave the site forever, even if he had said that to me when I was a newcomer. Moreover, it seems clear that Will had the best intentions. That's why I used the word faint-hearted. This is of course a subjective term and is meant to implicitly contain a comparison with how I would have reacted. I simply haven't seen a comment of Will's that would have justified walking out (in my personal view), and I doubt that the ones under discussion were a big exception from the rule.

Now, if I were to leave a comment to the effect of "don't be fooled by the superficial appearance of the question, note that the OP has a good mathematical background, here are some quotes from her home page" and that would prompt the person to walk out, the incident would leave me puzzled as to what I was supposed to do differently. That's the point I was trying to get across.

Nilima comments on "Why is this definition the way it is?" (15788)

2011-08-25T09:03:40-07:00

@Alex, I cannot speak for anyone else.

However: I perceive a difference between an atmosphere of professional questioning/confrontation and a personal one. Admittedly, sometimes this is subtle. For instance:

'This approach you suggest is completely wrong' is qualitatively different from 'You don't know anything about this'. Or:

'You have provided insufficient motivation and background for this problem, and we don't know at what level you seek the answer'
is different from
'I don't know who you are or why you are asking this' or 'I know you have expressed weird ideas elsewhere so why should I take you seriously now?'

The point is: at work, I try to err on the side of questioning, critiquing and attacking the message, and not the messenger. Sometimes I lapse. I will never be accused of being soft mathematically, but I try to be kind in person.

Of course one should seek clarification about a question if it is unclear. I think this can be done politely, professionally, and carefully, and many users already do this. Asking for clarification carefully doesn't mean everything is allowed. Walking out because one perceives an environment as unfriendly isn't faint-heartedness, it's honest.

Alex Bartel comments on "Why is this definition the way it is?" (15785)

2011-08-25T07:11:40-07:00

quid, I agree with your assessment that the motivation is often crucial for making a question suitable for MO or interesting for others. On the other hand, you explicitly suggest that one reason for a new user for being anonymous would be the possibility to just start over again unscathed if the first contributions go wrong. In my experience, this kind of thinking does not tend to improve the quality of the contributions.

@Thierry Actually, you made that point perfectly clear, and I found it very interesting, I probably just failed to address it properly.

Clearly, some people left who should have stayed, but in some (although not all) cases it seems an overreaction to me, and I don't see anything specific in the MO culture that would have to change for particularly faint-hearted people not to leave (except to allow everything and to never question the poster's background or motivation, which would of course mean the doom of MO).

quid comments on "Why is this definition the way it is?" (15782)

2011-08-25T05:31:44-07:00

Alex, I do not think that one can infer from the, also IMO true observation, that among the new users one observes on the site anonymous ones have a much higher risk for a bad start that for one specific individual anon or not makes a large difference. In particular, if the new user pays some attention to the fact of being anon and therefore is moreorless forced to write some motivation (cf. my response to Tom Leinster above). In my opnion, but I have no data, a key point for a good first question is that the motivation is clear, and not in the mathematical sense, but really in the sense why did this user ask the question.

thierryzell comments on "Why is this definition the way it is?" (15781)

2011-08-25T04:28:40-07:00

I think I tried to make too many points in my previous answer. One of the points that Alex and Will appear to be overlooking, and a point that I thought was important, is that **even** for someone who does their homework and waits a while to get a feel for the site before posting (and, of course, starts by posting answers before questions), the first few days of activities can be a bit nerve-wracking. And no amount of anecdotal evidence ("I played by the rules and I had a good experience") can change the fact that some people that should have stayed have left after a single bad experience early on.

MO does a good job of saying upfront that questions are taken very seriously and that people should think before asking. When you're a regular it goes without saying, it's no big deal, and we wouldn't want it any other way; but it puts a lot of pressure on the newbies. Again, I find the MO culture perfectly fine, I just think that we (including myself, btw) could do with a little bit more mindfulness when new users are involved.

grp comments on "Why is this definition the way it is?" (15777)

2011-08-24T21:38:40-07:00

We can't please or appeal to everyone. The situation Will mentioned was quite unfortunate, and should probably forgotten and put behind one. I will take away from it that there is great potential for misunderstanding, and that with new users who may bring benefits to the site, I should appear as much like a helpful and unassuming assistant as possible. I would attempt the care and consideration that Will showed, but I would also act in a way to allow the user to provide additional information at their desire.

This is with the intent of handling new questions that suggest mathematical maturity. Of course, if all new users read the FAQ and other helpful documents before acting, we would not have the number of discussions on meta that we have had.

Gerhard "Ask Me About System Design" Paseman, 2011.08.24

Alex Bartel comments on "Why is this definition the way it is?" (15775)

2011-08-24T21:16:36-07:00

I hadn't seen the question that Will mentioned or the comments, but it seems rather extreme to "never use MO again" because of some sceptical comments on the first question and of a quote from her website, a link to which she provided herself. If, as others have said, this person had observed MO for a few days, she would have seen that the long time users do an important and thorough job, keeping the site useful for mathematicians by closing off-topic questions. To expect that at the same time, one's own questions will never come under any scrutiny is like saying I will never fly again, because the first time I flew, they checked me and my hand luggage, as though they assumed I was a terrorist. One doesn't have to think too many steps ahead to realise that this is done for one's own good (provided one really is a legitimate user).

I found the perspective of a new user as sketched by Thierry very valuable and interesting. But I agree with Will that for a mathematician it is not all that difficult to lurk for a few days or weeks and to do one's homework before participating, and to get a very warm welcome and to enjoy a smooth arrival.

@quid: Experience suggests that starting anonymously, one runs a much much higher risk of a bad start than by investing one's identity into the contributions.

Will Jagy comments on "Why is this definition the way it is?" (15770)

2011-08-24T19:16:20-07:00

Other aspects: I did not post my first question until I had answered several, and had a very good idea what I thought made an acceptable question. I don't know how many anymore, at some point I got disgusted and deleted all with negative or zero score. Then my question, representing years of my work, was complete and had additional material on my website. All that could also be done anonymously, including supplementary materials somewhere, so it is not really tied to my willingness to use my real name. And I had already proved my main conjecture for the first four numbers. It did not read in any way as possibly that of a college sophomore. Eventually it got an answer from Kevin Buzzard, who is a smart man.

http://mathoverflow.net/questions/12486/integers-not-represented-by-2-x2-x-y-3-y2-z3-z

I am capable of finding some way to be nicer to newcomers, or at least to incorporate suggestions from Gerhard or Therry. But I claim that I started on this site the right way.

quid comments on "Why is this definition the way it is?" (15769)

2011-08-24T18:58:42-07:00

A bit unrelated regarding the 'send someone packing' of Thierry: one half-way solution to the risk of a 'bad start', is to start anon/pseudonymous. This way, if something goes wrong early on, one has the option to simply restart. [This is no attempt to justify why I am personally pseudonymous; as I am beyond the starting stage, it can't be anyway.]

thierryzell comments on "Why is this definition the way it is?" (15767)

2011-08-24T17:44:58-07:00

Will: I was not targeting you in particular, and I never doubted your good intentions. But reading this thread, I just had the sudden realization that long-time users enjoy a feeling of legitimacy that allows them to freely criticize (since they've been criticized in turn). But it takes a while for a new user to feel accepted, and a single bad or simply misinterpreted experience can be enough to send someone packing.

I don't want to give up on constructive criticism, but I'll try to be extra-careful, when dealing with newer users, to keep my comments free of conversational landmines. It's the internet after all, and anything written here can easily be misconstrued.

Will Jagy comments on "Why is this definition the way it is?" (15765)

2011-08-24T17:32:57-07:00

Thierry, if this was somewhat for my eyes, I was trying to help. Then it all went to hell.

thierryzell comments on "Why is this definition the way it is?" (15761)

2011-08-24T17:16:31-07:00

Veteran users should not under-estimate how nerve-wracking posting one's first question on MO can be. Things might have been different when MO was a brave new site, but I know that when I joined about a year ago, I took days of observing before asking my first question, and even then I was mortified when my question was unceremoniously edited within the hour (to change the capitalization in my title, no less).

If my question had been the least bit controversial (rather than simply ignored), I would have probably walked away without ever looking back. Comment storms can be especially a turn-off for brand new (and slightly used) users. I think there is room for improvement with the treatment of legitimate newbies on MO right now.

As for questions which are simply wrong for the site, I find too often that they meet rather terse comments ("ask on stackexchange") that do not even bother to explain *why* the question would be better over there. (And by the way, the term "math research" is not ideal to use with people who have no idea there is such a thing as a professional mathematicians; these people are "researching" the answer to their question after all, it must be confusing.)

That being said, the R infinity question irritated me a bit, as it did some of the commenters. Or rather, I should be clearer, I'm not irritated by the question itself, but by posters who leave their questions unattended and ignore comments for clarification. I wish regular users would not even attempt to answer such neglected questions until the *original poster* fixes them. No point in guessing, but this can easily be done while remaining civil about it.

Will Jagy comments on "Why is this definition the way it is?" (15745)

2011-08-23T20:08:27-07:00

understood. nothing worth saying in public.

Ryan Budney comments on "Why is this definition the way it is?" (15744)

2011-08-23T19:50:47-07:00

I've been in e-mail correspondence with Madalina and can confirm Will's comments have not gone down well at all. She's also asked that her original question be deleted and states she never wants to use MO again. I've tried to explain that it was a misunderstanding, that her language made her question look strangely like a calculus homework problem and people were confused. Anyhow, I'd say this is unfortunate.

grp comments on "Why is this definition the way it is?" (15738)

2011-08-23T18:51:01-07:00

Not to cramp your style Will, but if quid can humbly suggest deleting a comment of yours, I think I can meekly suggest editing your (at this writing) 6 word post above. Whether you replace and what with is up to you, but I suggest something like " I'm so sad. I was just trying to be helpful."

Gerhard "Just Trying To Be Helpful" Paseman, 2011.08.23

Will Jagy comments on "Why is this definition the way it is?" (15732)

2011-08-23T17:06:20-07:00

I just noticed this, sure...

5:08 Pacific time, that seems to have worked, I see four comments by Ryan and one in the middle by madalina remaining

Ryan Budney comments on "Why is this definition the way it is?" (15731)

2011-08-23T17:05:11-07:00

If the user wants to wipe her record off MO, deleting that comment would be the best way to go. IMO that would be a nice gesture to start with -- if she wants to resurrect the question the relevant context can be added then.

quid comments on "Why is this definition the way it is?" (15730)

2011-08-23T17:02:26-07:00

Will, if you do not mind, perhaps you could delete your comment with the content of the webpage. I know it was posted with best intentions, and I believe it actually helped the question. But since it served its purpose while the affected user might (we do not know) not have liked it, perhaps it is good to remove it.

Ryan Budney comments on "Why is this definition the way it is?" (15729)

2011-08-23T16:59:26-07:00

I sent Madalina an e-mail, seeing if we can't rescue the question and clarify these misunderstandings.

Will Jagy comments on "Why is this definition the way it is?" (15725)

2011-08-23T16:11:40-07:00

How strange. I never saw any comment about undergraduate homework. However, after reading her web page, it was only then that I realized it was *not* an undergraduate. I thought others would get the same impression I had, so I preemptively put an excerpt from her site that gave a quick idea of her field. The second comment was also mine, and again my own idea.

You are correct, Darij. She has taken off her web link. Wow.

grp comments on "Why is this definition the way it is?" (15723)

2011-08-23T15:32:12-07:00

I don't know if you have it right, but I can't find fault with your interpretation, darijgrinberg. Also, if the discussion on this meta thread is being followed, I can point to some remarks which could be very badly interpreted. Not that we should aim to please everyone, but I can see where a slight misunderstanding could turn a potential user away from the site.

If madalina is reading this, I invite that user to comment on how things look from their point of view, so that at least I can modify my behaviour in some regard.

Gerhard "Intends To Behave More Welcomingly" Paseman, 2011.08.23

darijgrinberg comments on "Why is this definition the way it is?" (15722)

2011-08-23T15:07:46-07:00

Am I getting it right? Somebody commented that the question sounded like undergrad homework; Will then posted his comment about Madalina's website; the former "somebody" subsequently deleted his comment, and now Will looks like a stalker, making Madalina remove the homepage link from her profile and delete the post?

Will Jagy comments on "Why is this definition the way it is?" (15721)

2011-08-23T13:58:25-07:00

Never Mind.

Ryan Budney comments on "Why is this definition the way it is?" (15720)

2011-08-23T13:53:29-07:00

That sounds good. Perhaps we should also explain that if her question was answered in the comments she could answer her own question with that comment, and accept that formally as the answer, perhaps with some additional explanation.

quid comments on "Why is this definition the way it is?" (15719)

2011-08-23T13:36:20-07:00

I saw this too, and asked myself the same question. Perhaps rollback, comment explaining why this was done, close as no longer relevant?

Ryan Budney comments on "Why is this definition the way it is?" (15718)

2011-08-23T13:32:38-07:00

madelina just erased the content of her question but did not delete the question. It's not clear to me if she's invested enough in the process to make it worthwhile to unerase the contents, or perhaps we should simply close the question?

Will Jagy comments on "Why is this definition the way it is?" (15717)

2011-08-23T12:46:17-07:00

You are all correct. I regard Madalina as *not* anonymous. Without the website, I would have voted to close, and probably edited her tags as inappropriate.

Not coincidentally, I hope there are some nice answers. I wound up corresponding with Nilima Nigma, and it is clear (this is on a parallel thread) that there is a cycle with under-represented topics (especially somewhat applied topics with unfamiliar jargon), few knowledgeable users means questions may be viewed as off-topic, few quality answers anyway, which tends to drive away qualified people, etc.

EDIT: compare http://mathoverflow.net/questions/73516/research-on-relations-a-b-such-that-points-on-a-are-directly-or-indirectly-influe
where we do not know the background of the OP.

quid comments on "Why is this definition the way it is?" (15716)

2011-08-23T12:37:53-07:00

Will, I think by common standards this user is a real-name user (cf. Angelo, Dmitri, JSE,...). Thanks for your efforts on the question. And, sorry, for the hairsplitting.

grp comments on "Why is this definition the way it is?" (15715)

2011-08-23T12:35:05-07:00

Your example strikes me more as speaking on the perils of presumption than on the afflictions of anonymity.

It is also an example of how adding a little research effort can vastly improve the quality of a post, and reminds me that I should make more efforts in that direction.

It may be time for a "War stories from the battlefront in MathOverflow Quality Posts" thread.

Gerhard "Scholars, Take Up Your Notes!" Paseman, 2011.08.23

Will Jagy comments on "Why is this definition the way it is?" (15714)

2011-08-23T12:23:20-07:00

Ryan, yes, I check for that. And you left the substantive comments there.

Ryan Budney comments on "Why is this definition the way it is?" (15713)

2011-08-23T12:13:01-07:00

@Will: It's helpful that she gave a link to her homepage.

Will Jagy comments on "Why is this definition the way it is?" (15712)

2011-08-23T12:11:10-07:00

Just as one more forlorn comment on how anonymity is, well, bad, I was about to vote to close the very recent question of madalina http://mathoverflow.net/questions/73519/approximate-point-on-implicit-space-algebraic-curve which seemed an obvious college sophomore beginning vector calculus and being unable to find a parametrization for the intersection of two surfaces, also posting three clearly wrong tags.

But then I found she did have a web page or two...

Scott Morrison comments on "Why is this definition the way it is?" (15711)

2011-08-23T11:43:29-07:00

@Tom, a cursory inspection of the logs suggests the three users you mentioned are independent (or at very least making \epsilon effort to look independent).

Tom Leinster comments on "Why is this definition the way it is?" (15708)

2011-08-23T06:39:05-07:00

@quid, no problem at all - I didn't take what you wrote as confrontational. I just wanted to clarify what I wrote previously.

I agree that allowing anonymous users is a net good. I'm in favour of it; but I think this is one of its minor disadvantages.

quid comments on "Why is this definition the way it is?" (15707)

2011-08-23T06:30:01-07:00

Tom Leinster, sorry in case it appeared otherwise, I did not want to be confrontational. Mainly, I wanted to say something somehow in defense of anonymousgradstudent. Regarding the question of anonymity: abstractly, what you say seems certainly true to me; however, in practise, it seems to me that to avoid the type of anonymous contribution we are discussing at the moment would requier a major change of the sign-up procedure, and depending on how it is implemented would exclude all spontaneous contribution or at least restrict it to those possessing, say, (certain) academic email-addresses. Now, perhaps, Fly by Night was actually negatively affected by the self-chosen pseudonymity, but also here the more effective solution in my opinion is something else (cf. below).

Yemon Choi, there are two things. First, it believe that anonymousgradstudent was not only or even mainly motivated by this specific question. It also seems to me that over time the level of MO increased, and whether or not this is good, bad, or neutral, is something one might want to debate (but perhaps also not, and personally I see this rather neutral, so personally I have no strong need to discuss this).

Second, and perhaps of general interested as detailed justification of my voting, which, as I said above, was motivate by 'level', and I still think it was justified in view of what are (or to be precise, what I believe to be) the current standards of MO [but, I would have no problem if the standards were a bit different, and then would adapt to them]: my 'problem' with the question, at the time I vote, that is definitely after the first comment of the questioner (but rather not too much afterwards, though I cannot remember precisely), was that there visibly was some confusion about quite basic things. Considerably later, this also got acknowledged by the questioner, and to me is not at all problematic, except for the fact that it seems to me some do not take into account this developpment when (negatively) judging the voting.

In particular, I do not think it is an accurate description of the situation that (at that time) the true problem/question was really 'what goes wrong with the other definition' (paraphrasing Kevin Walker's reading); in my opinion this question arose only indirectly. As I see it, the original problem was (only) that the definition in the question somehow felt very unnatural to the questioner. (And because this definition felt unnantural while another one felt much more natural, did the idea arise that there must be some immediate or clear problem with the other definition. This is a situation quite different form one where somebody understands one definition as natural and still wonders what would happen with an alternative definition.) Now, Ryan Budney's and Donu Arapura's early comments address precisely this 'unnatural' concern, by giving reasons why the original definition is in fact not an unnatural one in the first place (in particular if one starts from the finite case, as done in the question) and so the question itself should disappear, except in case they should have misunderstood the question (and I together with them). And, then Fly by Night answered not by, say, 'yes, I knew that, but I am still interested what would happen in the other case' or also by 'ah, of course, I missed that, but since I already asked perhaps somebody has some additional insight' but by expressing doubt regarding Donu Arapura's assertion, based on what is really a basic misunderstanding (more or less the same as being confused about the relation between polynomials and formal powerseries). So, that at that point I think one really had good reasons to believe that MO is not a good place to sort out these confusions, which was when I (thus) voted to close. Now, meanwhile, the questioner overcame this confusion and the question was (in my opinion) somehow redefined on the fly, which is fine, and whether or not this redfined question is a good one or not is actually outside my expertise.

Final remark on pseudonymity of the questioner: I agree, in this case, that no information on the background of the questioner was available contributed to the problem. However, to blame this mainly on the nonusage of the real name is in my opinion a fallacy. IMO, a better solution, real name or not, would have been to start or end the question by a line or two of motivation for the question. like: 'I am a researcher in Genral Field F [and for Rough Reason R] I am reading Book B outside my field.'

Tom Leinster comments on "Why is this definition the way it is?" (15705)

2011-08-22T21:23:32-07:00

@quid: you may very well be right that it's three separate people. For the sake of promoting peaceful conversation, let me emphasize that I said nothing stronger than "I wonder".

The main point I wanted to make was that when many of the participants in a conversation are anonymous, and especially when the discussion gets heated, the suspicion of sock puppetry can arise in a way that would be unlikely if real names were used. (Of course, actual sock puppetry can arise too.) It hadn't occurred to me before that this was a side-effect of allowing anonymous users.

Yemon Choi comments on "Why is this definition the way it is?" (15703)

2011-08-22T18:37:38-07:00

By contrast the contribution of anonymousgradstudent seems very honest to me, perhaps overly so, and it is in some sense valuable.

Agreed.

perhaps, there is some need for (another) general discussion on which mathematical questions are acceptable on MO

I may be misunderstanding your reading of the situation, but let me reiterate: my problem was not with the topic or level of the question, but how it was worded and what it left unsaid, and to some extent with the OP's responses to requests for clarification. This is why I neither downvoted, nor voted to close, nor upvoted, nor voted to reopen.

quid comments on "Why is this definition the way it is?" (15702)

2011-08-22T18:19:57-07:00

Personally I am almost sure the three are different persons. 'stuffin dude' seems like some outsider to the site who tried to be funny (if I remember well, the answer was posted very quickly after the second legitimate answer, so when the question was very visible), or this is pure trolling.

By contrast the contribution of anonymousgradstudent seems very honest to me, perhaps overly so, and it is in some sense valuable. It might not be friendly towards some (at least indirectly, including me), but it raises a legitimate concern, and I think it is better to voice this concern, rather than to leave in silence.

While this has been discussed already several times, perhaps, there is some need for (another) general discussion on which mathematical questions are acceptable on MO; after all several frequent contributors to MO reopened the question. I do not think it would be good to have it in this thread, and somehow I do not want to be the one to start the thread...just a thought that cross my mind when rereading this discussion.

François G. Dorais comments on "Why is this definition the way it is?" (15693)

2011-08-22T14:32:12-07:00

Here is an 'answer' that was recently deleted from this question. I'm copying to meta since this is what the author apparently wanted.

I'd put this on the meta, but it doesn't allow for anonymous comments.

Why don't you math gods quit preaching and just make your decision to close or not? You can't win by acting like you have supreme wisdom. All you do is get people fired up and in the mood to argue.

Whether a question is suitable is very subjective. Just as much as you need a faq on how to ask questions, you need a faq on when the rulers of the house shouldn't preach. I don't want to hear your long winded rants about why some question isn't suitable.

Someone has to act as the dictator here. Just do it and quit using these times as an opportunity to make out like you're some kind of math god.

The author is stuffin dude.

For users with 10K reputation, the original can be seen here.

Tom Leinster comments on "Why is this definition the way it is?" (15692)

2011-08-22T13:18:08-07:00

+1 Mariano.

Something I find particularly unpleasant about this episode is the quantity of comments, some quite rude, from anonymous users. The anonymous OP, "Fly by Night", wasn't exactly rude but was at least unhelpful, I would say, when others suggested that he/she clarify the question. Then "anonymousgradstudent" wrote provocative things here. Then there was an answer to Fly by Night's question by an anonymous user called "stuffin dude" (an account created only today). That answer was simply abusive towards those who thought the original question unsuitable, and was quickly deleted.

So of course, I wonder whether these three anonymous accounts, all on the side of the OP, are really three different people. I'm not making any accusations, and anyway I'm sure the moderators will handle this in their usual capable way. But whether there's sock puppetry going on or not, just the suspicion of it is bad for the atmosphere of the site. Broadly I'm in favour of allowing anonymous accounts, but I think this episode does bring to light one of its hazards.

Mariano comments on "Why is this definition the way it is?" (15691)

2011-08-22T12:10:46-07:00

Dear anonymousgradstudent,

I would appreciate it enormously if you refrained in the future to call jerks —and even involuntary jerks— people who are using their actual names to participate in MO (votes to close, for example, are quite non-anonymous) while remaining anonymous yourself. I don't have any problem with anonymity, and I think people calling people jerks for MO-reasons is slightly silly but manageable (this is the Internet, after all!) but the asymmetry of this particular situation strikes me as very undesirable in a professional site like this.

Andrew Stacey comments on "Why is this definition the way it is?" (15681)

2011-08-22T00:52:36-07:00

I see that it's been reopened, with neither editing nor the reopeners joining this discussion. That's a shame.

I'd like to reiterate the points I was trying to make.

For such a general type of question, the background of the asker is all the more important as it can help answerers figure out what sort of answer would suit. In this case, I had no idea that the asker was a post-doc, and I still have no idea what field they work in. Only in the comments (and that much later on) was it clear where the definition came from (a particular book) - this is important since the tenor of the post is that this is the definition of the Grassmannian, an assertion that is just plain false.

At one point, Fly-by-night says in a comment:

The question was simple: given the application in mind, why do we insist that only finitely many of the xi are non-zero?

The difficulty is that I don't see any application in the question!
Allen's answer is not all that great, unfortunately. It feels like a "Well, this might be the sort of thing you're looking for" kind of answer. The initial statement implies that other models aren't amenable to algebraic-topology tools, which is false, and the "striking example" is extremely misleading as it compares two completely different things that wouldn't normally be compared. Let me make it clear that I don't see this as a particular fault of Allen's, but rather that the question was so vague that this is the best sort of answer that it can get (short of a 5-page detailed exposition of all the different models for BU with their respective advantages and disadvantages).

What I would have liked to have seen in the question was:

The background of the asker: what field are they in (don't know, but not algebraic topology; plus, given the question, an indication of their level of understanding of functional analysis would have helped), what level are they at (post-doc), why (given that alg-top isn't their field) are they interested in an alg-top question, where did they encounter this definition (Milnor and Stasheff's book), which other books have they looked in to find out about this.
Detail on the kind of answer that would satisfy: what techniques are they interested in using from algebraic topology? In particular (in light of the answer(s)), are they really interested in working with actual CW-complexes, or just with things of the homotopy type of CW-complexes?

I saw many comments that were basically trying to draw out this information from the asker, but with no proper responses. That's why I cast the final vote to close.

Gerry Myerson comments on "Why is this definition the way it is?" (15680)

2011-08-22T00:28:10-07:00

I think one of the many differences between MO and math.stackexchange is that over there if someone asks an unclear question most often people will try to guess what the person really wanted to ask, will post answers of the form "if what you mean is ..., then the answer is ...," whereas on MO if someone asks an unclear question most often people will vote to close it (perhaps leaving a comment urging the person to clarify). I think both sites have it just about right. I think we're entitled to have higher standards for question presentation on MO than on m.se, and to enforce these standards by closing questions.

That said, I have nothing to say about the particular question that gave rise to this discussion as I have not been involved in it.

Kevin Walker comments on "Why is this definition the way it is?" (15679)

2011-08-21T18:11:43-07:00

Quoth anonymousgradstudent:

I think it was utterly obvious what the question was, and the objections that the question was unclear are utterly pedantic and childish.

I don't think you're helping yourself or your cause by being strident like this. Even though I disagree with the people who wanted to close the question, I think they acted in good faith and weren't being childish, jerky, pedantic or whatever. In all aspects of life, but especially on the internet, it's good to give people the benefit of the doubt and make the most charitable assumptions possible when there is ambiguity about their motives, intentions, etc.

Todd Trimble comments on "Why is this definition the way it is?" (15678)

2011-08-21T15:30:16-07:00

There's also always the downvote button, which may be appropriately used if the question is unclear. I can think of an instance where I applied the downvote button, explained why I did so (the specific needs of the questioner were not at all clear from the very broadly posed question), and the eventual outcome was very satisfactory, as I was able to give an answer tailored to the specific needs of the OP, and was sincerely thanked by him.

quid comments on "Why is this definition the way it is?" (15677)

2011-08-21T12:06:05-07:00

I did not say anything on the question but voted to close (and still think it was correct). So, some justification:

I voted when already some comments were around, in particular the questioner had already commented too, but for some reason not replied to Ryan Budney's first two comments. To me they are/were very much to the point. Indeed, the first comment by the questioner suggested to me some confusion about basic notions, and thus this seems good for math.SE but rather not MO. Thus, close.

Now, not to appear like a total jerk, let me add that being confused about something basic, is nothing bad in in my book. Certainly, happens to me from time to time, and I am (too) well past my PhD. But, I also see nothing wrong with consulting a more basic resource for something basic.

Qiaochu Yuan comments on "Why is this definition the way it is?" (15674)

2011-08-21T11:19:40-07:00

I think it was utterly obvious what the question was, and the objections that the question was unclear are utterly pedantic and childish.

I think I could mount a stronger objection about making comments like this anonymously.

I think the point is that nothing "goes wrong" until you decide to use it for something, and since we don't know what sort of applications the OP has in mind the question is underspecified.

This was my problem with the question as well.

If this discussion isn't getting anywhere, there's a simple solution: anyone who is convinced the question is actually equivalent to Question X, which is obviously what was intended by the OP and perfectly reasonable, should edit the question accordingly, and then we will presumably all vote to reopen.

anonymousgradstudent comments on "Why is this definition the way it is?" (15673)

2011-08-21T10:54:20-07:00

Here is an example of what I am talking about.

In this case the OP does ask, "What are advantages of the Spec approach? Specific theorems?"

But again, one shouldn't need to explicitly state such things to be understood, and questions shouldn't be closed just because the obvious questions that the OP intends to ask are not explicitly spelled out. Plus, if you really think that the question needs to be clarified, then just ask the OP to clarify!!

Granted, this is an old question, and our community has changed since then, but my points still stand.

Donu Arapura comments on "Why is this definition the way it is?" (15672)

2011-08-21T10:53:49-07:00

I'm a bit on the fence with this. Personally, I don't mind the question (most us have asked versions of "why do it like this?" questions to our friends and mentors the past), but I can see why it might be considered too vague here. Perhaps some minor edits, and a little more context, would clear most of the objections.

Also I hope anonymousgrad doesn't get too disillusioned. We're only human as you said.

anonymousgradstudent comments on "Why is this definition the way it is?" (15671)

2011-08-21T10:41:54-07:00

I agree with Kevin Walker.

I think it was utterly obvious what the question was, and the objections that the question was unclear are utterly pedantic and childish. There are many other MO "why?" questions to which you could raise the exact same pedantic objections. We are not robots but human beings. We need not spell everything out in machine-readable form to be understood.

Just because you're not trying to be a mean jerk doesn't mean you don't come off as a mean jerk. (That said, I don't think you were really being a jerk, @Ryan Budney.)

Noah Snyder comments on "Why is this definition the way it is?" (15670)

2011-08-21T10:17:03-07:00

I think the point is that nothing "goes wrong" until you decide to use it for something, and since we don't know what sort of applications the OP has in mind the question is underspecified. That said, presumably people who think about the infinite Grassmanian know what it's useful for, and hence could give a reasonable answer. I wouldn't have voted to close this question.

Kevin Walker comments on "Why is this definition the way it is?" (15667)

2011-08-21T07:03:06-07:00

I'm surprised the question generated so many objections. It was clear to me that the question was, basically, "If we define R^\infty in the more naive way, without the finitely-many-non-zero condition, what goes wrong when constructing the infinite grassmannian?" This certainly won't make it into some future Best MO Questions Ever anthology, but I think it falls well short of being a good candidate for closure. I voted to reopen.

Ryan Budney comments on "Why is this definition the way it is?" (15665)

2011-08-21T00:36:28-07:00

@anon: I think everyone was trying to be pleasant in that thread. It's easy to misinterpret any action as being jerk-ish if you don't understand the motivations of the supposed "jerk". I'm fairly sure I understand the rough idea of the motivation of everyone that voted to close the thread -- and if you read the FAQ maybe you'll come to understand it too, specifically, the types of questions that MO is about and the how-to-ask tips. That, and the OP didn't really respond productively to the comments. It would be nice to move the conversation towards specifics rather than whether or not people are simply jerks.

Yemon Choi comments on "Why is this definition the way it is?" (15664)

2011-08-21T00:19:27-07:00

AGS: sorry to hear that you feel this way, I hope that you reconsider.

For my own part: I wish there were a way to close questions which made it clearer that I feel it is the question which has faults, not the questioner. If I criticize the question, it's because I would like the OP (or someone else, even) to write a better one. And "better" does not mean "more advanced"! As a teacher and former tutor-of-sorts, I feel there is a huge difference between "I don't understand X" and its dreaded cousin "Tell me about X", and "I don't understand how the lecturer/professor/Gromov got from statement A to statement B" or "are there examples of Slithy Toves except for this small list I already know about"?

anonymousgradstudent comments on "Why is this definition the way it is?" (15663)

2011-08-20T23:41:36-07:00

I think that many people are being unnecessarily mean. I am an active MO user and I think that there's been a rise in MO users being jerks lately. It's a shame and it reflects very poorly on our community (both the MO community and the mathematical community at large). If this continues I may stop using this site.

Qiaochu Yuan comments on "Why is this definition the way it is?" (15662)

2011-08-20T22:27:39-07:00

I agree with your objections in the comments. This question was not phrased in a way that made it easy to tell what kind of answer the OP would find satisfying.

Yemon Choi comments on "Why is this definition the way it is?" (15661)

2011-08-20T21:47:24-07:00

A case of shutting the stable door well after the horse has bolted, but I thought given the length and nature of the comment thread to this question that it could do with a meta thread. This would give people who perceive the violence inherent in the system a better place to explain why the "main police" should stop picking on questions like this. Or something.