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Is this question acceptable?: How expensive isknowledge: knots, links, 3 and 4-manifold theory algorithms

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    • CommentAuthorRyan Budney
    • CommentTimeAug 18th 2010 edited
     
    [Edit by Anton: link to the question is http://mathoverflow.net/questions/35946/how-expensive-is-knowledge-knots-links-3-and-4-manifold-algorithms]

    There were 4 upvotes on Shor's comment that this thread is more suitable for a wiki.

    I look at MO's list of big-list questions and scratch my head. Many of those threads are long opinion-pieces, while this is a big list of actual research-level mathematics, questions with definite answers. The false beliefs in mathematics thread, colourful language, "first serious schemes course", math puzzles for dinner, fundamental examples, single paper everyone should read, etc.. those threads seem less in line with MO's policies than this thread.

    I could see an argument for closing all big-list threads on MO (one that I have a good amount of sympathy for). But I'm not sure how you keep the above threads and not this one.

    The main problem with this thread from the point of view of MO is it's somewhat encyclopedic, but all big list threads have that issue. FYI, I created this thread because there's getting to be quite a bit of redundancy in other threads, pointing out the basics of what's algorithmically known about 3-manifold theory. It's nice to have something to point to and say: those types of questions are answered here.

    Examples: http://mathoverflow.net/questions/35680/complete-knot-invariant/35682#35682
    http://mathoverflow.net/questions/4798/classification-of-homology-3-spheres
    http://mathoverflow.net/questions/4155/classification-problem-for-non-compact-manifolds
    http://mathoverflow.net/questions/840/the-core-question-of-topology
    http://mathoverflow.net/questions/11540/what-are-the-most-attractive-turing-undecidable-problems-in-mathematics

    Anyhow, I'm curious to hear your opinion.
    • CommentAuthorVP
    • CommentTimeAug 18th 2010
     

    I've upvoted Peter's comment because I completely agree with it. I don't mind seeing that question at MO, since it obviously almost conforms to the rules ("almost" refers to the fact that it includes a large number of highly structured but essentially independent subquestions), but MO provides very inefficient infrastructure for assembling a large body of encyclopaedic knowledge, which you've explicitly stated as your goal. Several examples you've quoted are "soft" questions, but I think that a better model for comparison would be recent questions about P vs NP paper: the P vs NP wiki is an attempt to address the issues systematically.

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    Why not make this a community wiki question in the SO sense? Over there, a community wiki question is meant to have one answer that everyone edits and improves - essentially a wiki page. So post an answer yourself summarising the existing answers and invite everyone to add their answer to that one. Once the necessary time limit has expired (two days?), you can accept your answer thus ensuring that it will always stay at the top.

    Anyone without enough rep to edit a CW answer can leave a new answer with the line "I don't have enough rep to add this to the above answer so would someone please do it for me.".

    • CommentAuthorMariano
    • CommentTimeAug 18th 2010 edited
     

    One can translate Andrew's proposal as follows: use MO as a wiki.

    You could instead use a real wiki, though. Wikipedia could probably make use of such a list, for example.

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    +1, Mariano. Also, the nLab is always looking for people to add this kind of information.

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    Okay, then perhaps I'd delete the thread, and grow this Wikipedia page

    http://en.wikipedia.org/wiki/Computational_topology

    instead, creating associated pages to that, for various groups of algorithms. One of the problems with the Wikipedia solution is not all the algorithms in use have been fully written-up yet (Wikipedia has strong policies on these kinds of issues) but I suppose that's a relatively small problem as far as things go.
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    Ryan, if you're worried about Wikipedia's policies on that, then do try the nLab. We're very happy with original research!

    • CommentAuthorVP
    • CommentTimeAug 18th 2010
     

    Or you can start your own wiki with policies that are more appropriate. Although I am hopelessly behind the times in terms of installing complicated software, I once spent a day and fully installed a complete wiki and a web server on my computer, so it's not impossible.

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    My preference is Wikipedia. The ways in which it's not ideal aren't killer. And by-and-large you get more random contributions there than with another format (barring MO as a wiki). And Wikipedia is a lot like MO, in that it has a high Google profile so these pages get noticed right away.

    A small anecdote to support that -- just a month after I created the Mazur Manifold page on Wikipedia, I was giving a talk at another university and I mentioned Mazur manifolds. Someone in the audience piped up that they just read it on Wikipedia last week. That made me happy.
    • CommentAuthorMariano
    • CommentTimeAug 18th 2010
     

    Installing an instance of the wikimedia wiki software takes about 5 minutes if you know how to do it---sensible linux distros will make installing the software trivial, but each wiki needs a tiny amount of setup. Google will find a few very good guides; the two times I did this, it ended up being a matter of following the steps in one of those.

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    Alright, I've ported this MO thread to Wikipedia, here: http://en.wikipedia.org/wiki/Computational_topology and the more discussiony/directiony parts here: http://en.wikipedia.org/wiki/Talk:Computational_topology

    I'll close the MO thread now.
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    Oh, I apparently can't delete my own question. So if people could help me close it that would be great. Or if an admin would delete it, that'd be good, too. Perhaps it would be better to close it than delete, that way people could find it and chase the links to Wikipedia if they're interested.
    • CommentAuthorpeterwshor
    • CommentTimeAug 18th 2010
     

    Definitely don't delete the question. Put a link to the wikipedia article on it, and it's probably a good idea to close the question to avoid duplication. I think it's a great question, but it's much more suited to a wiki than an MO-style website. And since there's no general math wiki, wikipedia is probably the best place. I've found it pretty good for math questions.

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