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Etiquette: I would like to ask for a reason for which my question was closed

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    • CommentAuthorkakaz
    • CommentTimeMar 13th 2010 edited
     
    Question is here http://mathoverflow.net/questions/17964/is-there-a-known-way-to-formalise-notion-that-certain-theorems-are-essential-on . I follow moderator remarks and change it initial state to more defined one. Should I reopen it, or it is not acceptable? I do not gain badge of "question troll" or "spammer" so I ask here for Your opinion.
    Thanks
    Kazek Kurz ( kakaz)

    PS: thank You for remark, I changed link.
  2.  

    I won't try to answer this question now, but I'll note that the link in the above post doesn't work, as it ate a period at the end of the sentence. This one should work, though.

    • CommentAuthorkakaz
    • CommentTimeMar 13th 2010
     
    I kindly ask for some explanation, because I see that certain people vote for closing it, but there is no note why, beside from Tom Leinster. And I try to follow remark by Tom, which maybe is not enough, but I would like to know.
  4.  

    I think Tom Leinster's comment is a good summary of the reasons people had in mind for closing: "At present I find it very difficult to see what would qualify as a definitive answer." You should have a look at the page http://mathoverflow.net/howtoask, in particular the first two points "Ask a focused question that has a specific goal" and "Be precise".

    That said, personally I think your revised question isn't awful, although I think it still admits the trivial answer that there is no natural decomposition of mathematical truth into "theorem" nuggets, and the granularity of a chosen decomposition is just as much (actually, maybe more so!) a product of the social environment of mathematics we work in as the perceived importance of results. There's no "formal" answer to measuring importance that avoids this problem and uses any of the data (e.g. the Mizar graph) you mention.

    • CommentAuthorkakaz
    • CommentTimeMar 13th 2010 edited
     
    Scot: thank You. Trivial answer is worth as opinion. To give trivial answer it is no fault if there is no better one. But to say that there is only trivial one because we simply do not know, it is probably strange. I do not think that trivial one is the only possibility.

    You say something very interesting: "there is no natural decomposition of mathematical truth into theorems". It is most interesting position, I may call it fascinate hypothesis! It would be fantastic if it would be true! But how we can know?

    We always learn by stating theorems and proofs, it is here mainly fashion, personal opinion of lecturer? Could we live without it? Formalized algebra systems like Mizar shares some kind of uncertainty, or freedom in choice of its foundations. But then I suppose rest is pretty determined up to some level. When You choose Your language and axioms then probably rest of the system is crystallized. Of course every theorem is kind of "association" of formulas, and may be stated in slightly different way.and proved with slightly different way. But maybe there is deeper structure in the level of more elementary sentences? How could we check it? By analyzing real data is probably the most natural way, isn't it?

    Privately I believe that it is worse: mathematic is pure aesthetic and in some meaning random process, so probably we give our attention to theorems which are interesting for us only because of convention:historical (present development), cultural or even based o fashion of a time.I believe that mathematics is in fundamental way nonformalizable in general as human knowledge. But certain areas may be formalized. Importance of mathematical facts is strongly related to someone creativity and knowledge. So it is pretty subjective and vague. But I see many vague sentences here in this position. And question about possibility of such analysis and its properties it is not so vague I presume. Also I think someone may get at least great blog post if he will perform such analysis strictly enough ;-)

    As to meritum: it is obvious that at present there is no such formal answer, as there is nearly no formalized mathematics in suitable way, so no quality data to obtain. Citation or learning practice is fully subjective, historical etc I presume we should here look for more objective and formal data. Mizar is probably the only example ( I am not sure so I ask) of reverse mathematics in such scale and quality. Then many questions arises, like: how much freedom is here, are there different ways for the same results, what is structure of mathematical theories with proofs ( lattice?), could we find algorithm which as important theorems give us in agree with intuition or opinion. As regards to Your opinion: how big changes may be obtained by moving to different decompositions of mathematical knowledge? Could we change importance rank ( suppose we have given algorithm for computations of rank) of any mathematical fact in any way we choose only changing mentioned decomposition? I do not suppose very formal answers, but I do not think it is not interesting, or not useful for someone to think about it.

    I leave my question in a state like it is. In my opinion it is interesting fact that it was closed so fast.
    Best regards
    K.K
    • CommentAuthorKevin Lin
    • CommentTimeMar 13th 2010
     

    I don't think these comments and questions are uninteresting. But it is clear that they will lead to a lot of discussion, which is not a bad thing, but it is not the intention of the site to be a discussion forum. The general community consensus also seems to agree that to allow discussions on the site would be distracting and counterproductive to the primary goals of the site.

    • CommentAuthorkakaz
    • CommentTimeMar 14th 2010
     
    @Kevin: it is mainly matter of answers. Now we have very interesting and definite answer from Joel David Hamkins. It is worth of note, that it is very strict and pointing into rich area of mathematics.
    • CommentAuthorMariano
    • CommentTimeMar 14th 2010
     

    I think my vote was the last vote that got the question closed, originally. I see it got reopened now. While Joel's answer is quite interesting---I share Ben's view that it is an answer to a rather different question, though...---the question is very clearly blog-material. One way to check this is to see the long list of comments kakaz has made.

    In principle, I believe that everything can attract an interesting answer from someone---specially from people like Joel! But while witicisms like «there is no stupid questions, only answers» are witty, there are good questions and bad questions.

    I wish someone had asked a question having Joel's answer as an answer...

    • CommentAuthorYemon Choi
    • CommentTimeMar 14th 2010
     

    Although I haven't though about the original question seriously, and have only given JDH's answer a cursory read, I am inclined to agree with Mariano.

    • CommentAuthorkakaz
    • CommentTimeMar 15th 2010
     
    Thank You for Your opinion here. I see that this question is hard to be treated as serious for mathematicians. It is interesting, because many people here are able to say that certain theorems are important. Answer which was given by Joel is of course correct one, and very interesting, although I comment it, because from it follows that probably there is no analyse what importance means. I see here a few important points:
    1. it is not known if such analysis is possible. If Scott Morrison (message above) is right, it do not make sense beside equivalent axiom class identification as in reverse mathematics.
    2. there is no much sources for data. If we would like to base on some certain data about relation between theorems we should have data with formalized models. That is we should have formally constructed theories with axioms, theorems and proofs, as in Mizar. But I do not know any other such complete system.
    3. It may be that results are particularly dependent on formalization model. It is interesting to check how far. It seems obvious that different formalization are possible. But it is not clear how they differ form each other. Maybe not so much? Maybe there are some patterns?
    4. If we measure importance of theorem by its descendants tree deepness probably we should obtain the same resultants as with reverse mathematics, because axioms are roots in such tree and then gives us the deepest tree. But is that the only possible way of measuring: see point 1.

    Thank You for Your time. It was pleasure to discuss such matter here,although for most of You it was not interesting;-)
    Thanks
    Kazek
  11.  

    Kakaz wrote:

    for most of you it was not interesting

    I don't think that's a good conclusion to draw.

    Maybe lots of people found it interesting, and maybe not. But with most of these debates about why a question is closed, the issue is independent of whether a question is interesting. It's about whether a question is appropriate.

    Since MO started six months ago, there's been a constant process of trying to figure out what an "appropriate question" for the site is. I think there's something like a consensus now, though that consensus will probably shift about as time passes. There are lots of questions on this site that are appropriate but don't particularly interest me personally. There are a few questions that are appropriate but hardly seem to interest anyone (judging by the response). Then there are questions that are interesting but inappropriate, perhaps because they don't fit the MO question-and-answer format. Maybe (like your question) they look like they belong in a blog, rather than here.

    So, a question being closed doesn't mean that it's not thought to be interesting.

    • CommentAuthorkakaz
    • CommentTimeMar 16th 2010
     
    @Tom, I say it without wrong thoughts. It just happens. I am amateur in mathematics so it is not very rare that I am wrong. Just this is conclusion because in my opinion it was good question here. As there is many question at least vague in the same level ( for example question about discrete analogy to every (!!) continuous notion, question why 2 is different than other numbers etc) my question has three parts, and was treated as vague mainly because people do not bother with separate two parts beside first one.

    For example third was, if someone knows about big formalized area of mathematics in form like in Mizar has, and was related to coq and Isabele, which probably are the most known such frameworks. And nobody even notice this part of question which in fact was very defined and strict question.

    So as I presume, it was rather some kind of touchiness, or even prejudice from the community here. I understand it. I suppose it was because my question suggests that it is possible to develop some kind of empirical metamatematics. Probably for mathematicians it looks dirty. I do not know if it is possible, or if it have any sense, but in fact here I do not understand why it was called so vague comparing with many other question. And for example "trivial answer" from Scott Morrison above although simple is still very good answer, and is far from triviality! But probably it looks like philosophy for many people here. And mainly because is not yet formalized ( if at all possible).

    Thanks for Your remark.
    • CommentAuthorMariano
    • CommentTimeMar 16th 2010
     

    Mentioning touchiness and/or prejudice is, well, quite prejudicial and a bit condescending...

    I have no problem with metamathematics, philosophy or dirty things in general and, in my experience, most mathematicians have no such problems.

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