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    Yesterday this questions was asked:
    Asking if L^p is isomorphic to L^q. It was quickly closed-- I was one who voted to close, I guess because it seemed like a question whose answer was well-known-- it took me 30 seconds to find the answer in a book on my shelf, and it took Mark Sapir about the same time to do a Google Search. I do sort of think that you shouldn't ask a question of MO whose answer you can find from Google...

    On the other hand, as argued well by Bill Johnson, this is not an _easy_ result-- I couldn't have written down a proper proof without looking in a book. You couldn't set this as homework in a course, unless you'd done some serious background preparation.

    In the end the question was re-opened, and Bill has given a nice (and interesting) answer. I have some sympathy with Bill's perspective here.

    So I wondered if it might be worthwhile to have a meta discussion-- is a question whose answer is quite hard, involved, but ultimately "standard" suitable for MO? My personal take is actually given by the original questioner in a comment: "Perhaps I might rephrase the question to make it less localized. Given two Banach spaces, what methods can one use to prove they are not isomorphic?" I think that very much would have improved the question...

    My personal take is actually given by the original questioner in a comment: "Perhaps I might rephrase the question to make it less localized. Given two Banach spaces, what methods can one use to prove they are not isomorphic?" I think that very much would have improved the question...

    I agree with this. The problem with the situation where the answer is more technical than might be expected from the question is that the questioner might not have known that in the first place and so not be able to understand the full answer. So I would want to see evidence in the question that the questioner was ready for such an involved answer before the answer was given or the question reopened.

    • CommentAuthorgrp
    • CommentTimeNov 3rd 2011 edited

    To echo MatthewDaws, is a question whose answer is quite hard, involved, but ultimately "standard" suitable for MO?

    I would say that questions on Fermat's Last Theorem and some variants fit into this category. How many more of those do you want to see?

    For the present, the community ideal is to ask questions that "don't waste my time". Currently there is no consensus on what that means. Also, writing something which looks like a Wikipedia article was initially discouraged; as time moves on and the community investigates its sense of self, this restriction is relaxed. If you can find a nice characterization of what is a good subclass for this kind of question, I'd like to hear it. I think the one suggested by the echo above is too broad.

    Gerhard "Ask Me About System Design" Paseman, 2011.11.03

    • CommentAuthorquid
    • CommentTimeNov 3rd 2011 edited

    In my opinion the question in question definitely deserved to be closed. This is independent of the dificulty of the result or the fact whether I, or what fractions of mathematicians, know a proof of the result. As documented the question as stated is easily answered by a quick search. Of course, what one then would answer would not be a good answer, but 'no, they are not isomorphic' simply answers the question as asked. If the questioner actually wants something in addition this should be stated, and I think it is important to insist on this.

    Added: rereading the first post of the thread I focused perhaps to much on the specific question. Yet, my general opinion is merely a direct extrapolation of it: any question that asks something that is easily answerable with a quick search should be closed, except if the OP documents/mentions that a search failed (sometimes one searches the wrong way). Even more so if the question contains no motivation or context. In my opinion most of the problematic situations on MO related to mathematical questions arise mainly due to lack of motivation and context in a question. After context and motivation are added or the situation clarfied one can still reopen the question. To me to insist on this type of standard for questions (motivation/context) is not less important than to insist on the mathematical level of the question. (Unfortunately, the highest-voted mathematical question, excluding big-list, on the site is not at all a good example, and the second one only slightly better.)


    Re: the specific question, if you Google

    Lp not isomorphic to Lq

    you don't get an answer from the first two pages of what comes up (I did not check further).

    As I said on the thread, I have been asked this exact question by experts in other areas of functional analysis.

    If someone poses a non elementary question, the answer to which can be found in a book or with the right Google search, why not just give a one line answer? I am sure that if e.g. Tim Gowers asked the question, this is what would have been done (and, no, probably Tim could not prove the theorem off the top of his head; and, yes, Tim would not ask since he would know where to find the answer or would prove it himself).

    • CommentAuthorquid
    • CommentTimeNov 3rd 2011

    @Bill Johnson: For me the google-search is completely different (but this is of course location dependend); fourth result is Carothers's 'A short course on Banach space theory' on google books, direct link to Cor 9.13 asserting exactly this.

    You ask:

    If someone poses a non elementary question, the answer to which can be found in a book or with the right Google search, why not just give a one line answer?

    For the same reason you are, if I rememeber well, massively against answering too simple questions: It encourages this type of questions! And, this encouraging effect or non-learning effect here seems even more relevant to me.

    Finally, in some sense the question (without the comment) is simply unclear. What does the OP actually want: Really only the mere information (yes/no)? Perhaps, but then unlikely. So what else? A quotable reference? The historically correct refrence? A formal proof? Some intuition why this is so? ...

    Why can't people simply write what they actually want, and why or whatfor they want it. Life on MO would be so much simpler.

    • CommentAuthormarkvs
    • CommentTimeNov 3rd 2011
    @Bill: As I said, googling "Lp and Lq are not isomorphic" (with quotation marks of course) gives the book I mentioned in my comment as the first link. That comment, by the way, was the one line answer to the original question. Your answer is better, of course, but the question does not deserve it. By answering such questions you encourage people to ask questions without doing any homework (which contradicts FAQ).

    But Mark, your reference was in response to my comment. Had it been there when I first looked at the thread I would not have made any comment. Once I did comment, I was more or less obliged to answer the question once it was reopened.

    @quid: I don't consider asking a reasonable advanced question the answer to which can be found in books analogous to asking an elementary question that might even be a homework problem. And thanks for the tip about Carother's book--I had forgotten that the result is in there. The proof he gives likely is from a course he took from me (he was my PhD student). This proof is purely infinite dimensional.


    This is a forum for research questions, so I think we should expect the kind of due-diligence anyone might expect out of a researcher. If you can readily find the answer via a Google search yet you post the question, you're not displaying basic due diligence. Certainly there are things in textbooks where a Google search won't easily find it -- when it's more about internalizing a technique rather than a result with an easy label. We get lots of those types of questions and IMO that's fine.


    OK, will one of you who is so hot on closing reasonable questions please vote to close

    this idiocy,

    which has been open for two days?



    General comment, has anyone else here noticed they sometimes bump-up against the daily vote-to-close limit? It appears to be around 10 or 12 votes. I don't hit the limit often -- maybe just 3 or 4 times.

    So some days I ration my votes towards the threads that deserve it more than others.


    Thanks, Ryan.

    I thought I was pretty quick to vote to close, but I have never hit the daily limit (and in fact did not know that one exists).


    Nothing to see here.

    • CommentAuthorKaveh
    • CommentTimeNov 4th 2011 edited

    grp wrote:

    For the present, the community ideal is to ask questions that "don't waste my time".

    I think the main point is "don't expect others to do what you could easily do by yourself, don't ask others to do your job", so something like the following might be better:

    Users are expected to do their part and try to answer their question by themselves before posting them here and asking for help from others. Search to see if your question is already answered somewhere else (e.g. Wikipedia) before asking a question.

    • CommentAuthorJDH
    • CommentTimeNov 5th 2011 edited
    I object to the rude comments above that refer to a question of a new MO user as an "idiocy". The question in question was evidently asked in good faith by a young mathematician seeking mathematical enlightenment. There seems to be no call here for a public humiliation or the application of that moniker. I think such language has no place in a math seminar or on MO or on meta.MO. Since it is harmful to the MO brand to allow such comments to remain on this site, I request that the posters here or a moderator of this forum edit or delete the comments, at which time I will remove this comment.

    IMO the question was idiotic. I did not call the OP, who as far as know could be a 40+ year old logician, anything. My name is attached to my post and my opinion does not necessarily reflect the opinion of any moderator or other participant on MO.


    Dear JDH and Bill Johnson,

    I'd prefer not to censor this thread, especially as Bill has since made clear that he stands by the comment. At the same time, I'm also uncomfortable with the use of such disparaging language. It's of course fine to say that questions don't make sense, that they are inappropriate, and even that they're boring. But calling people idiots (even indirectly, referring to their questions as 'idiocy') is simply counterproductive. The "idiot" is less likely to accept or understand the point being made, it contributes to the deterioration of civility, and it's discouraging to observers and quiet participants who may already be timid of speaking.

    best, Scott

    I'm still with Bill on this. I don't see why just because an answer can be found by google means it is not worthy of MO. If the answer in the book uses only elementary material that graduate student should either know already or learn easily, then I agree that it is worth considering closing the question. I did not have that reaction to this question or its answer at all. Maybe for some of you the words "cotype" and "type" are no big deal, but I think they are not in a standard graduate curriculum. Moreover, I think an answer by someone like Bill Johnson can be a lot quite enlightening and useful, even if there is an answer published in a book.

    @Scott: I did NOT call the OP or anyone else an idiot. I ask idiotic questions myself from time to time, although I think not (yet) on MO (I did ask one on meta, though).

    @Deane: The votes on the Lp thread suggests that a reasonable number of people agree with you and me.

    +1 to Bill Johnson. The level of lots of the questions lately has been rather low. I have no idea why people are so hostile to a precise advanced graduate level question like this.
    • CommentAuthorgrp
    • CommentTimeNov 5th 2011

    I used to read and occasionally post to sci.math. I don't any more partly because of what I consider the dross present, and partly because of the heat of some of the discussions.

    By initially requesting that "behaviour suitable for a seminar" be acheived, as well as focussing on a specific task and a core group of people working to maintain that task, the moderators have nurtured the MathOverflow forum until a large but still unruled community has developed to support some of its activities. While there has been quite a bit of disagreement and heat, there has also been some discussion and perhaps even light and understanding occurring.

    Although I don't agree with Bill Johnson's dsecription of this question, I can understand that he might not think much of it and want to say so. As with Scott, I am loath to censor his opinion, and in fact if he has a weblog or some other platform besides MathOverflow or meta.mathoverflow on which he can let loose, I encourage him to go for it.

    I side with JDH (Joel Hamkins) in asking Bill Johnson to be more moderate in description on both MathOverflow and meta, primarily because it is too easy to start a flamewar and too difficult to repair the damage that occurs from it. If the MathOverflow community were a robust, self-healing entity that could manage itself, I would be less concerned; we are not there yet. In return for such moderating behaviour from Bill Johnson, I welcome requests from him to me to moderate my behaviour for the good of the forum.

    Gerhard "Not Ready To Play Firefighter" Paseman, 2011.11.05

    • CommentAuthorquid
    • CommentTimeNov 6th 2011

    @Andy Putman, but also more generally: for me the problem is precisely that from the question it is not at all clear whether the question is an advanced graduate level question (the answer has to be); it could also be a naive question. In some curricula the definition of Lp is first year undergraduate material; so why not ask whether they are isomorphic. Only, if there is somewhat more information than this terse yes/no question one can judge what is actually asked for.

    Personally, I am quite sensitive to this aspect, possibly due to the fact that I deal a lot with (elementary) number theory question on MO. There you have all kinds of people asking all kinds of things. Just that the question is precise and to answer it is/would be difficult, really does not always make it a reasonable question; you need somewhat more information to decide (in a meaningful way) what to do. Very free after Hardy (but in view of some of the comments above I do not dare to give the precise quote) it is really not difficult to ask really hard questions about the prime numbers.

    Therefore I really think 'MO' should insist that the 'How to ask'-guidelines are somewhat followed. The question under discussion violalates several.

    In particular, this description starts with:

    Ask a focused question that has a specific goal It should be absolutely clear what constitutes an answer to your question.

    Now the current question is certainly focused. But what is the goal and what would constiute and answer; would a simple 'no' have been appreciated as an answer? If not, what else? This ought to be explicitly in the question.

    • CommentAuthorgilkalai
    • CommentTimeNov 6th 2011
    Maybe we should make it a convention that, from now on, whenever somebody asks: "Is it true that X" we understand it not just as a yes/no question but also assume that the OP wants to know why. Of course, not every such question is reasonable but as we have a large number of experts in various fields maybe it is best to leave the call to experts in the specific field.

    After the fact, I think everybody agrees that the question: "Are L_p and L_q isomorphic for some p,q such that p is not equal q" and the answer given to it are very useful and nice contribution to MO.
    quid, I think it is perfectly reasonable for a graduate student to ask a question like "I just learned about ...., and I was wondering if ..... might be true", even if that person does not know whether the answer is easy or difficult, boring or interesting. In fact, I think it is sometimes unreasonable to expect anyone, especially a non-expert, to know this in advance.

    If it turns out that the answer is readily available elsewhere and is not particularly interesting, it is easy enough for someone to post this as a comment and vote to close the question. But if it turns out that the question provokes some interesting and thoughtful responses, then I believe it would be, as Gil says, a useful and nice contribution to MO. I believe in judging the worthiness of a question after the fact and not before.
    • CommentAuthorquid
    • CommentTimeNov 6th 2011

    Alternative suggestion for a convention (indeed this is the one I assume to be in place):

    A question in extreme violation of the 'How to ask' guidelines is closed. As soon as the question is fixed, it gets reopened.

    To some extent this is what happened in this case. After the question got closed, there came two clarifying comments by the OP. And, it got reopened. (After some such experiences questioners might then ask their question in compliance with the guidelines right away. And, questioners unable to fulfil the requirements of the guidelines in all likelihood should not ask on MO anyway; in the present case it seems the OP indeed would have been able to fulfil them.) And, yes, the answer was interesting to me.

    Added in view of Deane Yang's comment.

    Yes, of course, this is reasonable. All I ask for is that the OP writes something along the lines you just sketched. As documented by the first part of this comment, already if the content of the later two comments of the OP was part of the original question, I would find it considerably better. And, I believe this is also what Andrew meant above. In my observation almost all discussions on mathematical questions arise from the fact that the motivation and background of the OP are unclear, and then some guess-work and discussion starts. I do not want to link to all of them, but just days ago we had one (minor) discussion related to a Galois Theory question, there was a rather heated discussion on meta regarding the why R^infty is defined in the way it is question including another unrelated problem with some algorithmic question, and so on. In my opinion all this mainly because the respective OPs did not provide some personal motivation for asking the question. I mean there has to be some motivation for somebody typing in a question; I just want to know it (roughly and abstractly) and, except for very few exceptions, I accept almost anything as legitimate motivation, yet what seems an appropriate answer depends on which one of the many legitimate motivations was the actual one in the case at hand. In many real-life situations this is not necessary as one can infer this from context; yet on MO there is no a priori context (this is not really true in all cases, but in the present case it is true; how should I know something on motivation and background of 'Lost'?)

    Now, one could also consider it as the reason for the discussion that some people (including me) want/insist that the actual question is answered. But after all MO is a Q&A site, and not a site to write short-essays inspired by some keywords. I think the present question is not an example of this; but there are so many case where people interpreted things into questions, which I am convinced, had very little to do with what the OP actually wanted to know and/or could understand. One could say there is not much problem with this, because somebody else will appreciate the answer. Except that a user asking these questions can get encouraged to ask more and more, and then eventually people get annoyed, yet then it is particullarly unclear why 'suddenly' there is a problem with the questions that were 'good' all the time.

    • CommentAuthorquid
    • CommentTimeNov 6th 2011

    Sorry for posting so much, but I think I should also add some cautionary remark in another direction. Above I discussed problems when questions are over-interpreted. Yet, it also happens on MO that questions are under-interepreted (not sure this is a word). This is much rarer but rather even more problematic.

    I know of some instances where working academic mathematicians (under real indentity) got (in my opinion almost insultingly) superficial answers to their questions in their field. The questions were clear, but there was no context or motivation spelled out, and answerers likely did not recognize the name or did not check the userpage, so assumed a naive context and answered in that spirit, which in these situations was in my opinion rather inappropriate. I do not know whether much harm was done by this (depends on the personality of the questioner), but still I think it is a bit unfortunate.

    So, I consider it as important that there is a general culture of providing background and motivation in questions, to avoid guess-work that both happening explicitly or implictly if one guesses wrongly can be problematic.


    I've kept quiet so far - apart from my initial post - simply because quid's been doing such a great job of saying what I would have said.

    I'll add one thing in support of quid's position. An answer without a suitable question does not, in my opinion, belong on MO because it is sold short there. An answer without a question makes a great wiki article somewhere. Anyone who would like to write one for the nLab (which contains maths of all levels, not just "n") should feel welcome to contribute. There, an article can be properly linked and indexed, it can grow and be developed, and find a much better home than on MO.

    • CommentAuthorAndy Putman
    • CommentTimeNov 6th 2011 edited
    I disagree that this is a bad question. It is clear, it is precise, and it concerns mainstream graduate level mathematics. Moreover, I'm not an expert in analysis, but even to me the question is natural enough that it doesn't really need additional motivation.

    I agree that there are questions which seem weird enough that it is helpful to know why the OP cares, but this is not one of them.

    Finally, I don't see why we are forcing people to describe their background. I post under my own name, but if I posted under a pseudonym it would feel very odd and unnatural to say "For background, I'm an assistant professor at a research university who specializes in geometry and topology". My feeling is that we should assume that someone who posts precise questions about mainstream graduate level mathematics has the background of "generic professional mathematician with a PhD" unless they tell us otherwise. Certainly I would feel insulted if someone questioned my credentials absent some good reason to do so.
    • CommentAuthorgilkalai
    • CommentTimeNov 6th 2011
    Here is an example: Suppose something ask the question: "Is there a finitely presented infinite simple group?"

    In my opinion this is an excellent MO question and it requires no specific background or motivation. It is true that when you type this question in google you get in the second outcome "There exist finitely-generated, and even finitely-presented, infinite simple groups"
    but clicking on the link is not very enlightening. I think we should assume, as a convenient convention, from now on that when somebody ask a yes/no question he really wants to understand why the answer is what it is, get some good references etc.
    Of course, not every question that looks simple or standard is not simple and standard.
    I disagree: I think "Is there a finitely presented infinite simple group?" is a bad MO question. If you do a web search for "finitely presented infinite simple group", you find tons of web pages that discuss exactly this issue, many of which seem much better than the specific link Gil mentioned above. If someone looks over these web pages and needs further information, then they should indicate what they are looking for beyond what is easily available. I'm sure there are people on MO who could write very nice answers to this question, maybe even nicer ones than anything easily found on the web, but the purpose of MO shouldn't be to provoke people into writing mini-essays, especially on topics for which it's easy to find information and references.
    • CommentAuthorquid
    • CommentTimeNov 6th 2011

    @Andy Putman: I did not mean 'background' so much in the sense you suggest. What I think is often useful to know is: a. What lead the questioner to ask the question. and b. To what end will the answer be used/useful.

    I don't know how others communicate, but most of the time even if people I know well ask me something or I ask them something (by email or in person) we will somehow indicate in which context (before which background) the question arose and why now an answer would be useful. To me it simply makes a difference, say, for the level of detail or precision in the answer, to know whether the person .) just wants a rough idea as the question arose somehow in passing and there is now just a general curiosity, .) is preparing a talk and wants to make some side-remarks on the subject, .) is writing a survey article including a chapter on this subject, .) needs the information to decide whether to investigate a subject, .) needs this as part of an ongoing research activity ... So depending on the precise situation I will answer the same question (if stripped from context) asked by the same person, in quite different ways and with quite different time commitments.

    And, to some extent the same is true for MO. If I get the impression that a questioner has a real interest in getting an answer, I will be much more likely to invest some time to give an answer [even if it is a somewhat exotic request, like checking a proof of Goldbach's conjecture, in case you remember]. If, however, as per Gil Kalai's convention, it is already too inconvenient to spell out what type of information is desired, then chances are I will find it too inconvenient to answer.

    @quid : You're under no obligation to answer any question! I'm just arguing that a question like this (precise and at a high level) should not be closed.
    • CommentAuthorquid
    • CommentTimeNov 6th 2011

    @Andy Putman: Yes, of course, I am under no obligation, and I also do (or at least try to) not make my personal preferences the criterion of my voting to close/open. In some sense the question whether this question (in its original form) and question of the general type discussed here 'easily answered by a search' are admissible, boils down to the question to what extent the 'how to ask' guidelines should be binding.

    If they are, I think it is simple: they are not. To quote a part:

    Do your homework Before asking your question, try to solve it. Search Google, Wikipedia, and nLab, check any references you can think of, and try to figure the problem out yourself (maybe even sleep on it).

    And for the current question there is also the 'goal' issue quoted above as well as an entire point entitled 'Background and Motivation' that is not addressed; and for parts of this discussion the last paragraph of 'be precise' seems somewhat relevant, because if now 'is there X?' questions should be considered by convention as 'tell me any/everything about X!' then this starts to fall in the 'unfocused' category.

    So, to sum it up, if I had voted to close this question then as 'not a real [MO] question' for what I consider as strong violation of the 'how to ask'-guidelines. The question is whether this is a legitimate reason to close a question (temporarily).

    • CommentAuthormarkvs
    • CommentTimeNov 6th 2011
    I agree with quid. The OP did not do any work before asking the question, which is a violation of the rules (see FAQ). If he wanted to know general facts about isomorphism of Banach spaces, he should have said so. Anyway, I will vote to close any question where a simple Google search gives a precise answer. I think there is no shortage of questions on MO, and it is important to keep the standards high.

    @Andy: Note that I do not want to impose my opinion on others. I just state what I think, I only hope that there will be enough people with enough reps who share my opinion on that matter.

    Note that I do not want to impose my opinion on others.

    This is an important point that shouldn't get lost in this discussion. The point of having these arguments/debates (as I see it) is not to hammer down hard rules (though sometimes it can become apparent that some major change needs making), but to test ones opinions, to try to persuade others, and to explain oneself.

    Often I think I know what I think, but actually haven't really thought it through. It's only when I come to explain myself, particularly to people who disagree with me, that I find out what I really do think. Sometimes I even change my mind.

    Once I do know what I think, then of course I think that others should think it too. So I'll do my best to persuade them. Then if more people think the way I do, things might shift slightly on the main site towards what I consider to be the right direction. If I can't persuade anyone, then that's a good indication that my thinking wasn't right.

    Even when I know what I think and am unlikely to change my mind, knowing that others think otherwise can still change how I behave and how I express those opinions.

    Having said that, I'll go back into "passive reader" mode now. Quid, and now markvs, are doing very well as far as I can see.


    I agree with Bill Johnson and others that this question should not have been closed. I'll try to paraphrase some of the reasons given for closing and give my responses.

    The question should have been closed because it was not possible to determine what sort of answer the questioner was looking for or what level of detail the questioner would understand.

    This sort of objection is made frequently on meta.MO, and I always find it unconvincing. A typical MO question and answer(s) will eventually be read by many hundreds of people, resulting in some amount of harm or good to the world. The original question asker constitutes a tiny fraction of these hundreds of readers, and for that reason the specific needs and desires of the questioner play a minor role in determining what makes for a good answer (or good question). Of course, if someone, as a matter of personal preference, chooses to only give answers when it is possible to very precisely determine what sort of answer the questioner is looking for, then that's their prerogative. But I don't think lack of knowledge of questioner's motivation and background is a reason to close the question and prevent others from giving useful answers.

    Even if we grant, for the sake of argument, that meeting the specific needs of the questioner trumps all other considerations, I don't think that making a big fuss about ambiguities is usually helpful. If someone asks an ambiguous question Q, which could reasonably be interpreted as Q1 or Q2 or Q3, then one can simply answer "If you mean Q2, then the answer is blah blah...". Or one could ask for clarification in the comments (without voting to close and preventing others from giving useful answers).

    (What I am suggesting is that if someone asks "What is the air speed velocity of an unladen swallow?", it is usually more helpful and efficient to say something like "If you mean European swallow, it's 55 km/h" rather than "What do you mean? African swallow or European swallow?". One might object that my example proves the opposite, since the less helpful second answer turned out to be crucially important in the film I'm quoting from. But I would argue that the specific circumstances in the film are rare in general rarer still in the context of MO questions and answers.)

    The question should have been closed because it is easy to find the answer with a web search.

    I agree that this can sometimes be a reason to close a question. But it's not always easy to determine how easy it is for someone without the right background to find the answer to a mathematical question via googling (see disagreement between Bill Johnson and markvs above), and for this reason I think we should set the bar relatively high for applying this rule. If the question is otherwise unobjectionable (i.e. it's not too elementary), then rather than vote to close, why not simply leave a short comment or answer saying "Here's a link to a paper which proves this standard but difficult result" ?

    • CommentAuthorquid
    • CommentTimeNov 7th 2011

    @Kevin Walker: If the question and the questioner is so irrelevant I wonder why we wait for somebody to ask a question at all.

    • CommentAuthorgilkalai
    • CommentTimeNov 7th 2011 edited
    Consider the following:

    Question A version 1: Is it true that L_p is not isomprphic to L_q when p is not equal to q

    Question A version 2: I am a postdoctorate researcher working in continuous groups. I learned by google search that L_p is not isomorphic to L_q when p is not equal q this look very basic to me but I dont see how to prove it and how basic is it. I will be happy to learn why it is so.

    Question B version 1: Are there finitely presented infinite simple group

    Question B version 2: I am a graduate students interested in fuzzy logic. I learned by google search that there are infinite simple finitely generated and even finitely presented group. I am very intruiged by it but the links I found are not so enlightening. Can somebody explain to me how an infinite simple finitely presented group is constructed.

    I think that the academic content of versions 1 and 2 in both cases are essentially the same. I think also that in terms of the academic content both these questions are good for MO. (In view of Henry objection I demote the finitely presented question from great to good. But it is really for group theorist to call.)

    It seems that some peope in the discussion prefer Versions A2 and B2 to versions A1 and B1. Because they would like to be convinced that the OP did his homeworks and to know something about him, and his motivation and his background. Maybe this is supported by the FAQ part about doing homework.

    On the other hand, once the academic content is good I personally prefer versions 1; they are focused and the background/motivation/google-searches of the OP dont look so relevant to me and, in my opinion, to add them lower the quality of the site as a whole.
    • CommentAuthorgilkalai
    • CommentTimeNov 7th 2011
    By the way, about YES/NO questions. I know a daughter of a well-known mathematician that was very (positively) surprised when she was hosted at dinner with friends and when she asked the host "Can you please pass me the bread?" the response was to pass her the bread and not just the answer "YES" as her father used to react.

    I agree with your previous comment, quid (and with much else you've said here). If the question and questioner were irrelevant, then 'nice and useful' contributions can be obtained very easily by someone posing a question that he already knows the answer to, and then immediately posting his own beautiful solution or insightful comments. That could be an interesting idea for a website, but I don't think that's what MO is for.

    I think MO is for professionals to answer questions of professional interest in ways likely to be useful to the questioner who is honestly in need. It is hard to do that without making the question precise, and also in cases where an answer is easy to find via google, without explaining why the results of a google search are not enough to satisfy the questioner.

    In such cases, I do believe in giving a questioner an opportunity to sharpen the question (via judicious use of comments), rather than summarily closing the question.

    • CommentAuthorquid
    • CommentTimeNov 7th 2011

    @Gil Kalai: Yes, I prefer this. And, well, of course you can construct some context that does not tell that much. Momentarily I am very short on time yet I will give some other variants later. For now would this recent question have worked well on MO without the background? Was it useful to give it?

    Regarding your second comment: you see, the mathematician has diffculty to deal with such yes/no things. Best to avoid them on a site for mathematicians :D


    I'll point to a couple of questions as bad examples. The first one,

    Product algebras

    got 1K looks. Two parts are answered in a standard Real Analysis book and the third part is answered through the right Google search. I don't regard the questions as being idiotic, but the OP is clearly an idiot since he has taught from the mentioned RA book several times.

    This question

    got 2K looks and 44 up votes. Both parts are answered with Google searches. Nevertheless, Will Jagy commented, "This is the best question I have ever seen".


    I should add that the two questions I just mentioned were not asked because of any research need, but just from idle curiosity.

    • CommentAuthorWill Jagy
    • CommentTimeNov 7th 2011
    Bill, looking at my three comments there, it would appear that I was screwing around, and that probably had to do with overblown comments on other questions in the previous few days, by other people. One thing is certain even now, the subject matter of your question is not that intimately known by me. So I think I was quoting someone. I dimly recall the comment about a Jonas Meyer answer making my day. Various kinds of feedback have led me, slowly, to realize that MO is less of a conversation than I had probably wanted, and less of a place for quips as well.

    I'm sorry.

    Will, no need to apologize to me. I like to see people displaying a sense of humor on MO.

    • CommentAuthorWill Jagy
    • CommentTimeNov 7th 2011
    Thank you, Bill.
    • CommentAuthorquid
    • CommentTimeNov 7th 2011

    @Todd Trimble: Regarding

    In such cases, I do believe in giving a questioner an opportunity to sharpen the question (via judicious use of comments), rather than summarily closing the question.

    I believe we are not really, or at least not by much, in disagreement here. In reply to Andy Putman I said (with added emphasize):

    The question is whether this is a legitimate reason to close a question (temporarily).

    To me closing is not at all always permanent, or so negatively connotated as it seems to be for some. The procedure to me is: unclear/somewhat problematic question indentified - comments pointing this out - close - edits to clarify - reopen - answers; where the close (and thus reopen) can be omitted if the questioner is quick to react, or the process stops at close if no edits are forthcoming (or the question is not salvageable). To some extent this is what happened in the present case. Perhaps my stern 'definitely deserved' at the start send the wrong message, what I wanted to say is that in my interpretation of the FAQs and so on one can find several reasons for voting to close this; not that the question is particularly far away from a good question. As said, with some of the comment information included right away it could be already above my vote-to-close threshold.

    A problem when only operating with comments is that some occassional users can take a long time to return and power-users do all kinds of things in between to the question (complain, discuss, answer,...). In some sense it seems to me it should be a more negative experience to return to ones question find some answer(s), with some comments criticising the person answering, and a huge number of comments half of them saying the question is 'bad', half of them that it is not so bad after all, and all this in increasing intensity; than to find ones question closed, with one/two comments pointing out what should be done to get it reopened. And, I would even go so far as to say that I think I would prefer to find my question closed with some polite or neutral comment telling me why this question is a non-MO question and will permanently be closed, than read some almost flame-war circulating around my question that then eventually stayed open or got reopened.

    @Bill Johnson: In my opinion the second question is really an exceptionally well-written MO question. This is precisely the type of information I am interested in for Background and Motivation.

    • CommentAuthorquid
    • CommentTimeNov 7th 2011

    @Gil Kalai: As briefly said it is true that sometimes there is not too much context but even the little information you made up gives some hint. But for example what Bill Johnson wrote in his second questions really creates a context for me that makes the question much clearer; and this adds something even in this case where I know something about the real-world context of the questioner.

    And in the questions you discuss there could also be other scenarios that boil down to the same question: I only give the details for A, I also do not vouch that everything makes perfect sense as I make it up but just to get the idea across:

    The Curious Undergraduate: Last week in the Analysis course the instructor defined the Lp spaces and said they are Banach spaces, so some special form of vecor space. We saw examples showing that these spaces are not equal for different p. However, in Linear Algebra we often saw quite different vector spaces that turned out to be isomorphic. Are some or all of these Lp spaces isomorphic?

    The Teacher in Preparation: Tomorrow I will introduce Lp spaces in my analysi class. I won't say much beyond the definition. I will give examples that show that for different p the Lp spaces are different. Now, somehow it seems obvious that they are not isomoprhic either. But I fail to see how to prove this. Also I quickly checked some references, yet could not find this. Yet this ought to be known, no? I am not so much after detailed or technical information, it is mainly just that I now this gap in my knowledge became apparent to me I would like to fill it and to know whether this is just me not seeing this at the moment or whether this is really more difficult than it might look (or even different than I suspected). Even if it should be rather simple, I won't have time to cover this in class. However, I might just mention the result. If I do so, I like to give the original reference to give the students some feel for the time-line of mathematical development.

    A Teacher having been asked by a CUG: Yesterday I introduced Lp spaces in an undergraduate class. I gave an example showing that they are differen for different p. Now, a bright student asked whether they are all pairwise non-isomorphic. Somehow I was stumped. I said I think so, but do not know for a fact. Now I searched a little but did not find much. I would be particullarly interested in an accessible exposition or perhaps even only a sketch that I might be able to give/communicate to the student (if it exists).

    A temporarily confused expert without specific motivation: Thinking about some problem in [something not too far away from Banchspaces] I more or less unmotivatedly started to wonder how one shows that the Lp spaces are all non-isomorphic. I thought this can't be that hard, I will just do it as an after-lunch excercise. But, now I spent two hours in vain and searched a bit in the literature, yet nothing. I am almost sure I saw this once somewhere, but now I am at a loss to find it, or might this be wrong or unknown after all?

    In some sense these are all the same question A, or special cases of the general interpretation advocated. Yet for example for the undergraduate it might make sense to somehow make sure that there is no confusion about what isomorphic should mean/tyically means in this context, while in all other cases doing so could seem odd. And, some other minor differences should be apparent anyway from the scenarios.


    From Todd's post:

    If the question and questioner were irrelevant, then 'nice and useful' contributions can be obtained very easily by someone posing a question that he already knows the answer to, and then immediately posting his own beautiful solution or insightful comments. That could be an interesting idea for a website, but I don't think that's what MO is for.

    Sounds like a good use of the nLab to me.


    @quid: thanks for your thoughtful reply. It may be obvious to say, but I think an important consideration for

    To me closing is not at all always permanent, or so negatively connotated as it seems to be for some.

    is how negatively a closing is likely to be received by someone who is new to MO. (The negative connotations it may have for more practiced users such as the ones having this discussion are perhaps secondary.) Lots of questions get closed not quite with a polite and neutral comment, but with a somewhat dismissive or curt comment like "Not research-level; voting to close". That's not to say that that's always an inappropriate response, but --

    Perhaps a good rule of thumb to apply is this: if the question is indeed low-level and easily answerable, then fine. (Here, by easily answerable, I mean, roughly, something just about any professional could answer without resorting to Google.) If on the other hand a yes/no answer can be easily found via Google, although the proof is not so easy, maybe one could say just that -- and still cast a vote to close -- but without giving an impression of smacking down a question. Maybe something like, "The answer is well-known -- see here [link]. Is there something more you wanted/needed to know?": a little invitation, just in case the author is not exactly 'Lost' but there's something more to it.

    A related issue is just how fast closings generally happen. A person posts a question, has to leave the computer for an hour, comes back, and bam! The question is closed. And then, to resurrect it, one has to have the fortitude to appeal the decision before this august group, in public, with perhaps less than assured command of the English language. I'm sure that can be hard for some new users. I don't know what can be done about that, but anyway, in general I would like to see a slightly longer grace period for questions that indicate some potential. Like one day, say?

    A problem when only operating with comments is that some occasional users can take a long time to return and power-users do all kinds of things in between to the question (complain, discuss, answer,...). In some sense it seems to me it should be a more negative experience to return to ones question find some answer(s), with some comments criticising the person answering, and a huge number of comments half of them saying the question is 'bad', half of them that it is not so bad after all, and all this in increasing intensity;

    Yes, and we've certainly seen this type of thing happen! (I am remembering in particular this, although it doesn't quite fit what we're discussing now: -- that and the whole episode over Doron Zeilberger's post.) But I figure a day or -- really pushing the envelope here -- two days, shouldn't in general be too onerous a time to wait for the OP to reply, in cases of potential interest. This may require some collective restraint.

    @Andrew: yes, I was thinking that too. But there are no reputation points, and no badges there. Just the humble satisfaction of knowing that insights have a permanent, publicly available home.