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    • CommentRowNumber1.
    • CommentAuthorTobyBartels
    • CommentTimeSep 2nd 2009

    This continues where I left off on the Café here.

    One possibility is to allow everything, as long as it doesn't interfere with the good parts of the Lab. If the cranks write articles only on their own topics, don't take up good article names, and don't paste inappropriate links all over the regular articles, then they're mostly harmless. In the short run, I think that this is feasible (I may be alone in that), but in the long run, it means that we're free hosting for alternative theories, which is probably not tenable.

    At the opposite end, we could require that everything (not the words, but the ideas) be published first in a peer-reviewed journal. This is essentially Wikipedia's solution. But of course it rules out many of the contributions that we have so far, particularly many of those by Urs (who has written more than anybody else, of course), but also those by others (including me). Surely we don't want this!

    So we need something in between. For example, we could allow articles on established topics by anybody, thereby encouraging other academics to write about what they know, but allow original research only by a group of official ‘lab technicians’ approved by … some process. Or we could preapprove anybody with a PhD in one of the three relevant fields, although this still includes plenty of cranks, or anybody with tenure at an accredited university (probably still a few cranks), with others required to apply for invitation (or possibly approved by their advisors if graduate students). Keep in mind that the latter would mean that Eric Forgy and I (and perhaps some other original regulars) would have had to apply for invitation! We could also use a sponsorship system like the arXiv, although then we'd still have to decide on guidelines for sponsors to use.

    Keep in mind that much of what we write on the Lab would be considered at least mildly crankish by many others. On the categories mailing list, there are those who find higher category theory a bit silly. On the fom (foundations of mathematics) list, where some of the top researchers in that field hang out, categorial foundations are regarded as silly or worse. I think that there are even a few regular contributors to the Lab that disagree with the emphasis on weak n-categoires or don't like to see discussion of what happens if you don't use the axiom of choice (or worse, excluded middle). It's easy to distinguish ourselves from AP, harder to distinguish ourselves from FS, and perhaps impossible to distinguish ourselves from JA.

    Since comparison with Wikipedia is inevitable, I also want to stress this: Much of what is on the Lab, even in articles on established topics, would be unacceptable at Wikipedia because it would violate the neutrality rule; we give undue emphasis to minority viewpoints. This shows up particularly with foundational questions, with our preference for structuralism and tolerance for constructivism, but it even shows up in core articles on n-categories, with our preference for weak structures and for (\infty,\infty) rather than (\infty,1). (There are also articles where we express outright opinions, although in principle these could be made NPOV.) Some day we may also have to decide what our opinions are, although so far it's really only a matter of deciding on conventions.

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeSep 2nd 2009

    Thanks, Toby. It is good and useful to have this discussion. Thanks for your thoughtful remarks.

    (I feel starting to get a bit overwhelmed time-wise with administrative tasks on the nLab such as thinking and discussing this important topic here, but it is clearly necessary.)

    But here is a quick comment (which may or may not turn out to be of any value):

    as long as the group of contributors is not too disconnected, each cooperative undertaking lives from some intrinsic spirit or culture that invisibly sits above everything and gives people an impression for what the context is and what it is not.

    In this respect, i am thinking of the nLab not as any random wiki, but as the wiki governed by that culture, in as far as this makes sense, that has been established over the years at the n-category Cafe.

    Clearly, the original idea was, and still is as far as I am concerned, that the nLab is a place where especially those people who contribute and interact at the nCafe anyway, in some way or other, find the room to develop material in a more stable, more comprehensive and more useful form than is possible in blog discussion scattered over various entries and comments.

    In that sense, those who consider category theory and higher category as not just abstract general but as entire nonsense are not a reference point for the nLab from the outset, to my mind. Much as a wiki on racing cars wouldn't generally be the place for, say, environmentally concerned people to hang around at and have a strong voice in.

    So that's how, to my mind, the nLab strongly differs from for instance Wikipedia. This just to amplify a point you already made.

    Concerning original research:

    as you also mentioned, the nLab was originally outright intended to be a place where we can develop ideas in a way that is not so easy on the blog. To some extent I think the very fact that there is so much more encyclopedic and Wikipedia-style material on the Lab at the moment is something that probably nobody did foresee in this way before we started with the project. I think it turned out that before engaging in research, a certain need for laying out groundwork and basis was felt and satisfied to some extent: every statement of a new thought requires laying out the context in which this is formulated, and this naturaly leads to lots of standard material being exposed.

    That said, it does of course remain true that we can have no interest in loosing ourselves in a forest of unreliable material whose status may be clear to those who work or worked on it, but opaque to others.

    This means first and foremost to me that in each single entry we want to be sure to leave sufficient indication about which bits of it are of which status. This here is standard, this here is our revisionist reformulation of something standard, this here is something I haven't seen before but consider this proof here or else see my notes/preprint there, while this here is something I haven't checked but which sounds plausible and of of which it would be great if some reader could check it.

    I am thinking -- but maybe I have a wrong perception here, let me know if so -- that we did this reasonably well so far.

    Which doesn't mean that we should not seriously think, as we already did in some forum discussion, about formalizing this status indication procedure more.

    If I recall correctly especially Andrew Stacey had made serveral times suggestions for how one might go about indicating status of material and about implementing a certain system of page-wise or even paragraph-wise peer review, in which contributors could leave comments about to which extent they have checked and can support certain statements made by others.

    I think this is a generally good idea, but requires some serious thoughts concerning its detailed implementation. This, I would think, would be a particularly worthwhile discussion in the context of the general discussion which you start here.

    • CommentRowNumber3.
    • CommentAuthorTobyBartels
    • CommentTimeSep 2nd 2009

    Clearly, the original idea was, and still is as far as I am concerned, that the nLab is a place where especially those people who contribute and interact at the nCafe anyway, in some way or other, find the room to develop material in a more stable, more comprehensive and more useful form than is possible in blog discussion scattered over various entries and comments.

    This suggests another possibility: Original research is welcome from (and only from) those who have already been participating constructively in comments on the Café.

    So instead of (or in addition to) asking Café regulars to come and join the Lab, we'd also have to ask (even insist) that potential Lab regulars come and join the Café.

    • CommentRowNumber4.
    • CommentAuthorDavid_Corfield
    • CommentTimeSep 2nd 2009
    This comment is invalid XHTML+MathML+SVG; displaying source. <div> <blockquote><br/><br/>as long as the group of contributors is not too disconnected, each cooperative undertaking lives from some intrinsic spirit or culture that invisibly sits above everything and gives people an impression for what the context is and what it is not.<br/><br/>In this respect, i am thinking of the nLab not as any random wiki, but as the wiki governed by that culture, in as far as this makes sense, that has been established over the years at the n-category Cafe.<br/><br/></blockquote><br/><br/>I'm certainly in agreement with the idea of a governing 'intrinsic spirit'. But therein lies a difficulty. Part of the enjoyment I have had from Cafe and nLab activity is learning to recognise the individual intrinsic spirits of the contributors. After many years I have a good sense of what this is in John Baez's case, some but a lesser sense for others - Urs, Toby, Todd, etc. Others I have next to no sense at all, e.g., Zoran. <br/><br/>I can't imagine how one could give an explicit account of the kind of spirit welcome here that would carve things optimally. But without some restriction there is a danger of nLab becoming just a collection of disparate material. I have no concern about trusted people being as speculative as they see fit, but somehow they have to earn trust beforehand. </div>
    • CommentRowNumber5.
    • CommentAuthorDavid_Corfield
    • CommentTimeSep 3rd 2009
    Rather than discuss in the abstract, why not consider a case at hand. Is the triadic relation concept sufficiently nSpirited for its inclusion in nLab?

    As a necessary but not sufficient condition there should be a (reasonably short) chain of connections to core nLab entries. There is an implicit Peircian ring to the article, which suggests that connections might be made to some of the categorical underpinnings of Peirce's logic which Todd revealed. If this later material were included in nLab and it mentioned triadic relation there would be an excellent case for inclusion.

    I'm also worried about the drift of this article into a theory of semiotics. This is hardly a field with an establish orthodox view that would allow depiction of results as facts as done here. The Wikipedia article on semiotics has "Semiotics is only slowly establishing itself as a discipline to be respected." The topic needs to be treated tentatively, by referring to a range of semiotic theories.
    • CommentRowNumber6.
    • CommentAuthorUrs
    • CommentTimeSep 3rd 2009

    One thing we can do immediately to address concerns of this kind at least in part, and which should be done in any case, is to interact. Besides from raising the matter here, which may of course be reasonable, there is always the default option: if you have concerns about any entry of any sorts, you should put a query box into that entry and voice the concern.

    Generally, the more the established nCafe regulars show their presence on the lab through contributions and comments, the more they will establish a recognizable context.

    Buildng the nLab is a bit like building a public library. If there are lots of serious people sitting inside working in a very calm and concentrated atmopshere, everybody entering the building will inevitably be drawn into that atmosphere, lower his voice and start to behave accordingly.

    If however the newcomer finds a deserted building, he or she will establissh himself or herself without feeling any need to constrain.

    • CommentRowNumber7.
    • CommentAuthorUrs
    • CommentTimeSep 3rd 2009

    I should also menton the other important aspect of dropping a quesry box on an entry whenever sombody feels any concern about anything:

    the presence of the query box clearly marks that entry to all outside readers as being potentially controversial.

    This serves much the same purpose as the boxes they have on Wikipedia saying things lilke "This entry is in need of attention of an expert". Or "This entry needs cleaning up".

    So I would say: everybody who feels any concern about anything should, even if he o she doesn't have the time to look into it properly, at least spend half a minute to drop a query box indicating briefly the concern.

    That's what collaborativ interaction is all about, after all.

    • CommentRowNumber8.
    • CommentAuthorAndrew Stacey
    • CommentTimeSep 3rd 2009

    Not pertaining to anything, but I like the idea of a 'quesry box'! I know that it was a typo, but the combination of 'query' and 'queasy' seems to capture the issue perfectly. Rather than just "Here's a question" a 'quesry box' would say "Something here feels wrong, but I can't quite put my finger on it."

    • CommentRowNumber9.
    • CommentAuthorJonAwbrey
    • CommentTimeSep 3rd 2009
    Ah, the Quesrying Beast, with the sound of thirty baying hounds &hellip;
    • CommentRowNumber10.
    • CommentAuthorAndrew Stacey
    • CommentTimeSep 3rd 2009

    If I remember right, he never did catch it, did he?

    (I guess this is off-topic, though)

    • CommentRowNumber11.
    • CommentAuthorEric
    • CommentTimeSep 3rd 2009

    I haven't been paying attention and this has likely been discussed, but if the nLab ever reaches a point where malicious or dubious articles begin to be a problem (which is likely still some time away), I think the community will have grown to the point that requiring a login to modify content becomes reasonable.

    • CommentRowNumber12.
    • CommentAuthorTobyBartels
    • CommentTimeSep 3rd 2009

    I would say that ternary (triadic) relations are as relevant as some of the analysis stuff that Todd, Zoran, and I have been adding. The semiotic example seems out of place: a reasonable enough example on Wikipedia (which had it for a while) but out of place here. On the other hand, if it's connected with Peirce's work, then that could make a difference.

    • CommentRowNumber13.
    • CommentAuthorMike Shulman
    • CommentTimeSep 4th 2009

    I think that the mathematical notion of a ternary relation is certainly quite acceptable for the nlab.

    My immediate reaction to the sign relations at triadic relation (and sign relation) was that they don't belong because they're from a totally different field. But after a second look, I guess that maybe they are coming in under the "philosophy" heading?

    • CommentRowNumber14.
    • CommentAuthorMike Shulman
    • CommentTimeSep 4th 2009

    I spent quite a while trying to compose some sort of coherent thoughts about the general question, but I found myself going in circles. This is a really difficult topic.

    I would prefer it if we could continue allowing anyone to contribute by default. It's already hard enough for a lot of people to begin contributing to a wiki, that I'd rather not put an extra barrier of "approval" in their way. Imagine a graduate student at a university somewhere out of the way, who is excited about higher category theory but all of whose professors are suspicious of abstract nonsense. I'd rather not require such a person to seek approval from their advisor, or by personally asking us (whom they've never met).

    Of course, that does put the onus on us to proactively remove inappropriate content promptly, and even more importantly to come to some sort of agreement on the meaning of "inappropriate." I don't know if I have any thoughts on that yet.

    • CommentRowNumber15.
    • CommentAuthorUrs
    • CommentTimeSep 5th 2009

    I have received some related discussion by email. Must say that I am quickly getting to the point where I am running out of time resources to deal with all this in a fully appropriate way.

    But I want to re-emphasize again the following point:

    whenever anyone runs into anything on the Lab that looks problematic to him or her, for whatever reason, but where just a quick edit won't be a solution, add a query box in which the concern is voiced.

    That may not immediately lead to the most well-formatted results, but it will immediately convey all the important information, namely that there are at least two different maybe conflicting points of view on some topic or some entry.

    Then with time and work and effort, eventually all such places where controversy arises may hopefully be resolved some way or other.

    • CommentRowNumber16.
    • CommentAuthorAndrew Stacey
    • CommentTimeSep 7th 2009

    *Brief silence while I refrain from saying "I told you so"*

    Seriously, though. There are several issues:

    1. Where is the boundary at which you start deleting material? Even our hard-line libertarian agrees that there is a boundary (see our wonderful spam page for proof). However the boundary is defined, it is going to be difficult to deal with cases close to it, so some sort of editorial board will be needed to defer to in those cases. As I said over here, it is much, much better to have these in place before they are actually needed so that they are clearly understood by all contributors. Changing the rules mid-game is generally considered Bad Form.

    2. Who owns a page in the public area? The debate about the timeline has raised this issue. I tried to raise this here. If the nLab is to include original research, then this becomes important. Not just to do with publication and the like, but also in what should and should not be on a given page.

    In short: what are the Aims and Objectives of the n-Lab? How are these to be implemented? What methods will be used to ensure that these aims are adhered to and that you don't get "mission creep"? The 'about' page on the nLab is a start, but is a little vague and open to considerable interpretation.

    What model do you want to use for the nLab? Here are two extremes:

    1. The "University model": Everyone has an office and there's a public library and a common room where you can get a cup of tea. In this model, everyone gets their own private web and can do what they like, but the public area is for expository and uncontroversial stuff only.

    2. The "Hot desking model": Leave your desk for two minutes and someone else will have come and swiped it.

    It would be nice to have something within the two extremes.

    But you need to start with the central aims and objectives and make them precise. Only then will you see how they should be implemented. Even Toby's suggestion of "formal consensus" is a definite system. At the moment, there are emails, discussions, nlab pages, cafe pages, all sorts of stuff.

    You may notice that I've tried to be careful with my choice of pronouns. There are a few characterisations of what the n-lab should involve above that would exclude me. And although I'm sure that it's not what was intended, there are a few comments on this issue that make me think of the word "clique". I would rather something that was as open as it could be as regards contributions, but that had a system of authentication built in. Then I could sign a page (revision) and say "This looks good/okay/bad to me". Then when I read a page on stuff that I don't know much about, I'll look at who's signed it to see at what level I should accept the material.

    Sort of like peer review, only a system that might actually work.

    But really, these are add-ons. Firstly, what and who is the nlab for? Those who were in from the start should answer that. Then you can work out the rest.

    • CommentRowNumber17.
    • CommentAuthorUrs
    • CommentTimeSep 7th 2009
    This comment is invalid XHTML+MathML+SVG; displaying source. <div> <blockquote> I told you so </blockquote> <p>Yup. And I did agree.</p> <p>What is missing or failed so far are attempts to seriously implement anything. Doing that will need first of all someone with sufficient time resources.</p> <p>I am still hoping though, as indicated above, that as long as there is a minimum number of active regulars, that their active presence will catalyze a reasonable self-organization. That would at least be the ideal. At least as of the time being I see energy invested into the Lab itself be of more direct use than energy invested into thinking about formal administration.</p> <p>But as a first step, maybe we should start implementing the following:</p> <p>via CSS or the like (you know this better than me) let us create more types of highlighted boxes. We want a choice of boxes for indicating various things: that a certain paragraph is a personal research idea of some, that a certain idea has been approved by somebody, that it is not being approved by somebody, such things. Ideally these boxes would come with little graphic icons that try to indicate their main point, much like they have on Wikipedia for some purposes.</p> </div>
    • CommentRowNumber18.
    • CommentAuthorTobyBartels
    • CommentTimeSep 7th 2009

    Even our hard-line libertarian agrees that there is a boundary (see our wonderful spam page for proof).

    Ah, but I didn't actually delete anything; it's all there in the history. I would like to stick to that model, unless we reach the point that we would otherwise be overwhelmed with the stuff.

    But you need to start with the central aims and objectives and make them precise. Only then will you see how they should be implemented.

    These were left vague at the beginning, I think deliberately. It may be hard to make these precise without test cases to drive the decisions. Now that we have some people complaining that some entries are not within the scope, we can ask them to delineate the scope; I created this thread to invite them to do so. I honestly think that, in the absence of test cases, it would be better to first decide on a decision-making procedure. In that vein, I reoffer my suggestion (and also my desiderata).

    I would rather something that was as open as it could be as regards contributions, but that had a system of authentication built in.

    I like this idea, but I don't really know how to design it. The simplest would be to allow each user to rate each entry (with two variables, a revision number and a rating, the latter being at least ‘good’, ‘bad’, ‘mixed’, or the default ‘unknown’). More complicated systems, involving rating parts of an entry (and possibly obviating ‘mixed’), would also be useful but (of course) more complicated. Aside from having to program that, we might have to also program a log-in system, certainly if any unscupulous crackpots come along. (I assume that everything signed by Urs was written by Urs, but I have no way to know this!)

    Firstly, what and who is the nlab for? Those who were in from the start should answer that.

    As for ‘who’, it's for me. Of course, it's for other people too, but I know me best, so I'll answer ‘what’ with just myself in mind, and let other people answer ‘what’ with themselves in mind.

    And as for ‘what’, it's for writing and reading about mathematics (and related things) that I'm interested in, with an emphasis on higher category theory. (You can see what I'm interested in on my Lab page.) So far, I'm having more fun writing than reading, although there is certainly a lot of neat stuff to read too.

    • CommentRowNumber19.
    • CommentAuthorTobyBartels
    • CommentTimeSep 7th 2009

    I am still hoping though that as long as there is a minimum number of active regulars, that their active presence will catalyze a reasonable self-organization.

    Well, that is what is happening now. But since there are disputes as to what should be on the Lab, we need to talk about it. And if we're ever going to tell contributors that something should not be on the Lab, then we need a basis for saying so.

    • CommentRowNumber20.
    • CommentAuthorAndrew Stacey
    • CommentTimeSep 7th 2009

    I guess a couple of technical points are in order. Firstly, space is cheap. Our main limitation on the lab turned out to be memory. Increasing our memory also increased our storage space vastly beyond what we need. The only place where we would actually notice junk would be if it slows down the database queries to such an extent that they become noticeable. Hopefully we'll reach that point anyway with decent material, in which case we'll have to solve the problem anyway so solving it a little early because we carry a little junk is relatively harmless. I guess that the other place where it could slow us down is if these junk posts create junk traffic. If they are true spam, then we blank the page and the 'robots.txt' keeps the search engines out of the history so the links don't get noticed. If they are merely mathematical junk, then who's going to follow the links to these parts of the lab? I doubt that too many links would be generated.

    I'd rather the lab be inclusive and accept even such daft ideas as, who knows?, ways of constructing elliptic operators on infinite dimensional manifolds - something that, on the face of it, has absolutely no categorical implication or inference at all.

    Because what I think the nlab is (okay, I couldn't wait for everyone else's answer) is a meeting place. It's the blackboards at the conference where people congregate to talk. Some people talk loudly, others hang around at the edges listening in. That's what I want it to be. So I don't want people scurrying off to their own private labs to do their work in semi-secret.

    On the other hand, I do want to know who I'm talking to. Of course, when I get to know someone then I can form an informed opinion of the worth of their writings. But in the beginning, I need some guidance. So it'd be nice if the user pages could have a little biographical information - maybe we should have a simple template that each user page has at the start. If we can implement a way to sign stuff on the nLab (similar to how Jacques signs his posts at the cafe), then this would open up the possibilities of being sure who posted something, and signing revisions of pages to say "I agree" or otherwise.

    But I also want to be able to say: this is my blackboard at the moment; anyone's welcome to join in, but the key is "join in" not "take over". Clearly, that can't be allowed on every page and so some topics should have two pages: an expository and a messy page. Or many messy pages. For example, the timeline could branch. Rafael could have a page which is in the public nlab but which is clearly "his" page where he keeps the timeline in sync with the one on Wikipedia. But there's clearly a feeling that the "official" timeline on the nlab should not be "owned" by one person. So the "official" timeline draws information from Rafael's but also takes into account other's opinions. And the "rules" there would be that whilst additions and corrections are welcome, deletions only take place if "enough" (of the "right"?) people agree. Much as the nLab itself.

    If we are a little more careful to differentiate between well-known material and local variations, it'll be easier for newcomers to pick up the local style and write accordingly.

    I know that "terms of service" and "codes of conduct" and "style matters" go a bit against the grain, but they're not to limit behaviour, but rather make the hidden terms, codes, and style (which are there) open and transparent.

    I'd like the nLab to be a small version of what the wider mathematical community should be like.

    • CommentRowNumber21.
    • CommentAuthorJonAwbrey
    • CommentTimeSep 8th 2009
    What he said.
    • CommentRowNumber22.
    • CommentAuthorTobyBartels
    • CommentTimeSep 8th 2009

    Andrew, thank you for the technical information in the first paragraph of your latest post. I'm glad to hear it. And that being so, I'm inclined to agree with the second paragraph.

    On the other hand, I know that there are regulars who don't feel so charitable to ‘daft ideas’, so I'd like to hear from them, and I have mentioned this thread to them in email, so … please speak up, guys! Even if you don't agree with me. (^_^)

    • CommentRowNumber23.
    • CommentAuthorTobyBartels
    • CommentTimeSep 8th 2009

    By the way, another technical improvement that we'd want to go with the whole rating an individual version thing is a diff between arbitrarily numbered versions. (Although given how well the diff works, it might be better to download the source and check for oneself.)

    (Is there a thread already devoted to the rating topic?)

    • CommentRowNumber24.
    • CommentAuthorMike Shulman
    • CommentTimeSep 8th 2009

    I'm not against the idea of the nLab as a meeting place where anyone and everyone can come to work, although I hadn't been thinking of it that way. It's kind of an exciting thought.

    However, I don't want to lose the nLab's current unique perspective on established topics. One of the things I especially enjoy about writing on the nLab is "playing Bourbaki" as a category theorist: writing definitions in the "correct" categorical way, including intuition regarding higher category theory on pages about homotopy theory, and so on. I think that with articles on established topics written this way it actually provides a really valuable resource for young (and old) category theorists -- this sort of outlook on things is often hard to find outside our community. Especially our attitude that embraces such outlooks rather than hold them up arm's length as an object of disgust.

    Now this isn't necessarily specific to category theory; in general I think it is a more open and accepting, or "sneer-free," response to unorthodox ideas. I also enjoy writing things on the nlab in a constructively acceptable way (and debating with Toby about the right way to do that), but that doesn't necessarily have a lot to do with higher category theory.

    If the nLab is a meeting place for all mathematicians (and physicists and philosophers, but as a mathematician I naturally focus on the math), could we still maintain that outlook and attitude, but without being taken over by cranks? I'm interpreting Andrew's technical info as concluding that "if the cranks write only their own pages, then it won't really bother the rest of us" -- but I'm specifically thinking about our idiosyncratic treatment of "mainstream" topics, which we really don't want cranks taking over.

    • CommentRowNumber25.
    • CommentAuthorDavid_Corfield
    • CommentTimeSep 9th 2009
    This comment is invalid XHTML+MathML+SVG; displaying source. <div> <blockquote><br/><br/>I don't want to lose the nLab's current unique perspective on established topics.<br/><br/></blockquote><br/><br/>Exactly. Otherwise the effort in writing nLab may as well be spent improving Wikipedia. A research programme (to use Lakatos's phrase) is being exposed and explored here. Which isn't to say there's complete unanimity about how best to view things n-categorically. But contributions with no connection to the thrust of the programme are simply distracting and make nLab less of a "a really valuable resource for young (and old) category theorists", clouding a (reasonably) coherent vision.<br/><br/><blockquote><br/><br/>I also enjoy writing things on the nlab in a constructively acceptable way (and debating with Toby about the right way to do that), but that doesn't necessarily have a lot to do with higher category theory.<br/><br/></blockquote><br/><br/>But it also possibly may have something to do with higher category theory, and often does. </div>
    • CommentRowNumber26.
    • CommentAuthorMike Shulman
    • CommentTimeSep 9th 2009

    But it also possibly may have something to do with higher category theory, and often does.

    This is true.

    So how can we describe this "research programme" in a way that gives us something to point to when deciding that certain content is or isn't within our mandate?

    • CommentRowNumber27.
    • CommentAuthorJonAwbrey
    • CommentTimeSep 9th 2009
    Reader Advisory ---

    Not for the Lakatos intolerant ...

    Jon
    • CommentRowNumber28.
    • CommentAuthorTobyBartels
    • CommentTimeSep 10th 2009

    The constructive stuff is usually relevant to internalization; that's category theory if not higher category theory. Besides that, I've often been struck how, quite unintentionally, thinking categorially and thinking constructively often seem alike.

    • CommentRowNumber29.
    • CommentAuthorDavid_Corfield
    • CommentTimeSep 10th 2009
    This comment is invalid XHTML+MathML+SVG; displaying source. <div> <blockquote><br/><br/>Not for the Lakatos intolerant ...<br/><br/></blockquote><br/><br/>One reason for such intolerance would be a concern that articulating the notion that research takes place most effectively among organised groups of people who share sufficiently in a common outlook would make plain that jotting down one's own idiosyncratic ideas is unlikely to be of any use.<br/><br/>My colleagues seem to be too nice about this, e.g., suggesting you move your material to a personal web at nLab, but as for me I can say that in no single one of your contributions to nLab have I had the sense that you have any understanding whatever of what the higher category theory project is about.<br/><br/>Explain to us if you would what <a href="http://ncatlab.org/nlab/show/cactus+language">cactus language</a> has to do with anything else in nLab. And what does <a href="http://ncatlab.org/nlab/show/differential+logic">differential logic</a> have to say to the n-category project? <br/><br/>In what way are you doing any other than importing your writings from this <a href="http://mywikibiz.com/Directory:Jon_Awbrey">directory</a> because you imagine that you'll gain an audience for it here? </div>
    • CommentRowNumber30.
    • CommentAuthorDavid_Corfield
    • CommentTimeSep 10th 2009
    This comment is invalid XHTML+MathML+SVG; displaying source. <div> <blockquote><br/><br/>So how can we describe this "research programme" in a way that gives us something to point to when deciding that certain content is or isn't within our mandate?<br/><br/></blockquote><br/><br/>No doubt with difficulty. I would want the content to provide (n-)category theoretic insight into established mathematics or to be suggestive of ways that mathematics (including mathematical physics and logic) might be developed in a (n-)category theoretic way. I would suggest that even well-established maths which doesn't fit the bill be excluded, unless there is some sense that it can be profitably seen (n-)category theoretically. For example, I wouldn't see the point in writing up the <a href="http://en.wikipedia.org/wiki/Green%E2%80%93Tao_theorem">Green-Tao theorem</a>. However, there would be room for filling out terms which were mentioned in existing pages, even if this just relied on standard definitions. </div>
    • CommentRowNumber31.
    • CommentAuthorJonAwbrey
    • CommentTimeSep 10th 2009
    • (edited Sep 17th 2009)

    David,

    There are several different issues here that probably need to disentangled.

    • I naturally appreciate the offer of some extra workspace to develop content — the Sandbox is getting a bit unwieldy even for this old Sand Reckoner — and I would have inquired about that sooner, or more likely later, anyway.

    So thanks to all for that.

    • To keep from burdening this thread with tangential matters, the discussion of the evident stub-links at cactus languange and differential logic probably ought to be split off to separate topics. Maybe we could use them to experiment with the idea of using the nforum as a discursive extension of the nlab base space.

    • With regard to the following desideratum:

    One reason for such intolerance would be a concern that articulating the notion that research takes place most effectively among organised groups of people who share sufficiently in a common outlook would make plain that jotting down one's own idiosyncratic ideas is unlikely to be of any use.

    Putting aside the oldie but baddie pun on "lactose intolerant", I heartily endorse that sentiment, but when it comes to graph theory, which was the context of the contention in progress, it is you, you, my friends who are the idiosyncrats.

    That's okay, it really is, there is no sin in wiping the slate clean and starting all over again from scratch — wiki-style — I simply felt it my duty to remind you that you can't really expect the rest of an established field to join you in that.

    Okay, I need to take a break and pick up the rest of the issues later …

    Jon

    • CommentRowNumber32.
    • CommentAuthorUrs
    • CommentTimeSep 10th 2009

    Concerning the issue at graph: I haven't really been following this discussion, but quite generalIy think we can, did and should stick to the maxime that where an entry introduces its own ideosyncratic language in an established field for a good reason it is free and encouraged to do so but should alert the reader of it and will be all the better the more details on the standard point of view it provides alongside in a subsection dedicated to that.

    • CommentRowNumber33.
    • CommentAuthorJonAwbrey
    • CommentTimeSep 10th 2009

    Urs,

    Re: "all the better the more details on the standard point of view it provides alongside in a subsection dedicated to that"

    That is precisely why I opened a new page at graph theory, to record the definitions that I actually use on a recurring basis --- things like graph, digraph, tree, rooted tree, cactus, along with their labeled and colored versions. I observed at the outset that there are many dialects of graph theory, but in my experience with the subject ( ≥ 30 years), most of the terminological and territorial disputes achieved a modus vivendi a long time ago. Again, there is no reason for any of that to obstruct genuine innovation --- which is happening all the time --- it is simply information about the lay of the land outside this e-clave.

    • CommentRowNumber34.
    • CommentAuthorTobyBartels
    • CommentTimeSep 10th 2009

    Jon, what indiosyncracy are you talking about ???

    Even Urs seems to have (being ignorant himself) swallowed your line that the page graph introduces idiosyncratic terms, when it DOES NOT! (If you want idiosyncratic terminology, then look at digraph.)

    What graph does introduce, which might be confusing you, is an idisoyncratic way of phrasing definitions, but I've decided that this was a bad idea and will be changing shortly.

    • CommentRowNumber35.
    • CommentAuthorTobyBartels
    • CommentTimeSep 10th 2009

    Also, Jon, despite our bickering at graph, I am really in favour of your participation at the nLab. So I would like to reask David's question

    Explain to us if you would what cactus language has to do with anything else in nLab. And what does differential logic have to say to the n-category project?

    but this time from the perspective of friendly curiosity, rather than hostile rejection. Actually, since those entries are really undeveloped now, I would be just as happy if you did this for your other material, such as Peirce's logic of information, or whatever you think would give the best answer.

    And I also ask this in a way meant to be relevant to this thread: What should the scope of the Lab be, and how does this fit in? I'm happy to have it, but I'd also like to hear how it fits in with this larger project that has attracted you.

    • CommentRowNumber36.
    • CommentAuthorJonAwbrey
    • CommentTimeSep 10th 2009

    Toby,

    I think this thread is worth keeping on topic --- at any rate, on the topic that I see in the background. There are many questions of group dynamics, communities of inquiry, sociology of knowledge, social-technical architecture --- and what many of my own cohorts cudgeled our collective wits about a decade ago under a host of headings like the "scholarship of integration" and "transdisciplinarity" --- that are compelling in their way but not always easy to get a handle on in our workaday busy-ness.

    So I'll break out separate topics for those subject matter issues when I get around to discussing them.

    Speaking of workaday busy-ness, read my …

    • CommentRowNumber37.
    • CommentAuthorTobyBartels
    • CommentTimeSep 10th 2009

    I created this thread, and the topic of this thread is how to decide what material the Lab should cover.

    In fact, I created this thread because David Corfield thought that your articles did not belong on the Lab.

    So what I am asking you here is very much on topic !!!

    Start a new thread if you prefer. There should be a ‘Start a New Discussion’ link near the top.

    • CommentRowNumber38.
    • CommentAuthorTobyBartels
    • CommentTimeSep 10th 2009

    I should also add: One reason that it's hard to get a handle on quesions like communities of inquiry is that the discussions can get very abstract and theoretical. Sometimes it helps to bring them down to earth, asking: How does this topic fit in with this community of inquiry?

    • CommentRowNumber39.
    • CommentAuthorMike Shulman
    • CommentTimeSep 10th 2009

    I have to say that it is also not clear to me how your contributions fit into the nLab, Jon. Perhaps I fall somewhere in between Toby and David. I would like to be accepting, but I don't yet see how what you've been writing about integrates with the "aims and ideals" of the rest of the project, and what purpose is served by having it on the nlab instead of somewhere else. I say this especially because it seems to me that your outlook on mathematics is very different from the one that the rest of us share, and you also seem to take offense when we try to modify anything you've written.

    • CommentRowNumber40.
    • CommentAuthorTobyBartels
    • CommentTimeSep 10th 2009

    Here is Jon's new thread, for those following along: http://www.math.ntnu.no/~stacey/Vanilla/nForum/comments.php?DiscussionID=69

    (Not much there yet.)

    • CommentRowNumber41.
    • CommentAuthorDavid_Corfield
    • CommentTimeSep 11th 2009
    This comment is invalid XML; displaying source. Well we wouldn't want to miss the next 'Die Lineare Ausdehnungslehre, ein neuer Zweig der Mathematik', would we? But you guys ought to visit philosophy talks some more and witness their endless stream of formal systems that never lead anywhere. <br /><br />As a pointer to Jon for some material on Peirce which certainly does belong on nLab, go to Geraldine Brady's <a href="http://people.cs.uchicago.edu/~brady/" >page</a>:<br /><br />Brady, G. & Todd H. Trimble. A Categorical Interpretation of C. S. Peirce’s System Alpha. Journal of Pure and Applied Algebra 149, 2000, pp.213-39.<br /><br />Geraldine Brady and Todd H. Trimble. A string diagram calculus for predicate logic. Preprint, November 1998.
    • CommentRowNumber42.
    • CommentAuthorJonAwbrey
    • CommentTimeSep 11th 2009
    • (edited Sep 16th 2009)

    DC: "As a pointer to Jon for some material on Peirce which certainly does belong on nLab, go to Geraldine Brady's page"

    Already bookmarked. I corresponded with Gerry a few months ago about her Peirce 2 Skolem, which is partially online but seems to be out of print. Most of the links on that page are broken, so I couldn't find several of the papers listed — I also wrote Todd about a reprint, but the address given on the journal page is apparently out of date. My own notes on Peirce's 1870 "Logic Of Relatives" are here.

    Jon

    • CommentRowNumber43.
    • CommentAuthorMike Shulman
    • CommentTimeSep 11th 2009

    But you guys ought to visit philosophy talks some more and witness their endless stream of formal systems that never lead anywhere.

    I think I've been to quite enough philosophy talks in my lifetime (although that wasn't very many). I only have so much time to spend listening to things that never lead anywhere. (-:

    • CommentRowNumber44.
    • CommentAuthorGuest
    • CommentTimeSep 17th 2009
    &gt;you can't really expect the rest of an established field to join you in that.

    But somehow I don't think we are looking for graph-theorists (in concrete terms - colourings, Hamiltonian cycles and whatnot) to join a group project on developing higher category theory. With this argument, one might as well say that if we wanted to include material on path-integral formalism (not an unreasonable idea, given the Kantization project), we should include the perspective of every field that uses that mathematical formalism - such as people who work on stochastic calculus. I don't think there was every any claim made that we are free from bias here. That being said, it is always exciting to see new ways in which existing mathematics can be reinterpreted or rediscovered from the POV of higher categories.
    • CommentRowNumber45.
    • CommentAuthorTobyBartels
    • CommentTimeSep 17th 2009

    I didn't think that the Guest could comment on this thread? (Not that I mind the comment, but it would be nice to know who's saying it, even if you only sign with your name in the comment text.)

    • CommentRowNumber46.
    • CommentAuthorUrs
    • CommentTimeSep 17th 2009
    This comment is invalid XHTML+MathML+SVG; displaying source. <div> <p>Just for emphasis, some contributors here might want to remember what it says on thee <a href="http://ncatlab.org/nlab/show/About">About</a> page:</p> <blockquote> on the nLab we do not hesitate to provide non-traditional perspectives, definitions and explanations of terms and phenomena if we feel that these are the right perspectives, definitions and explanations from a modern unified higher categorical perspective; </blockquote> <p>and then</p> <blockquote> at the same time we want to indicate clearly which part of an entry is traditional common material, which is a modern but widely-accepted reformulation and which is genuinely the result of original research by a contributor or by several contributors; </blockquote> </div>
    • CommentRowNumber47.
    • CommentAuthorUrs
    • CommentTimeSep 17th 2009

    This reminds me: Andrew, you might want to update the "History" and the "Technology"-section at the About page.

    • CommentRowNumber48.
    • CommentAuthorzskoda
    • CommentTimeSep 17th 2009
    Everybody can include whatever he likes as a scope. No democratic pressure of others.
    • CommentRowNumber49.
    • CommentAuthorAndrew Stacey
    • CommentTimeSep 28th 2009

    I've been pondering this a little this week. Here's some thoughts.

    First, a declaration of interest. I'm keen for the n-lab project to succeed because I see it as a great example of using technology to make it easier to do mathematical research. I'm not particularly bothered about higher category stuff, being still at the stage of trying to figure out all the ordinary category theory that I've scrupulously avoided for many years. I'm not adverse to higher stuff, just not there yet myself. But I do think that mathematics is missing out on modern technology and I'd like to see it put to better use. A while ago I tried starting a blog (and other stuff) to think about this, but all that that taught me was that I'm a much better doer than thinker so I joined in here and help out as I can.

    What I think that the n-lab is developing into is a lab book. For a lab scientist, the lab book is everything. In it you record details of your experiments, you take it with you to the library to note down interesting facts, you take it to seminars to take notes. That seems to me to cover everything in the n-lab: we have original research, we have expository stuff, we have seminar notes. The big thing about the n-lab is that it is a communal lab book. Basically, you've left your lab book open on your desk and one of the other inhabitants of the laboratory has come along and added, corrected, or just looked at what you've written.

    This view makes it clear that it's not just an n-wikipedia. Lab books are personal, even group ones. You do copy stuff out of books in the library, but you tend just to copy the bits that are relevant and as you do so, you probably rephrase them into your own language.

    On that basis, almost anything goes as far as content (within fairly broad terms), but it does need good systems of navigation and of marking what type of content is what. Exactly how that is done is actually a different question: that's a question of implementation, this is a question of deciding what to implement.

    But a lab book, even a fairly open and public one, still has a definite sense of ownership. And that's also something that I don't think should be lost here. This project was set up by a group of people (I'm not too clear just who was in the original group) with, at the very least, the intention that it be useful to them. If it stops being so, they will leave and with them will go a lot of the driving force behind it. I can only guess at their motivations, of course, but I would suspect that they would hope that it be useful to others as well, first to those who "think like them" (note the commas), second to those who don't think like them but would like to know how they think, and third just to anyone who wants to learn.

    So what I would propose is a "statement of (mathematical) purpose" by the original group (of course, that (c|sh|w)ould include phyiscal and philosophical) for the n-lab. That then defines the laboratory. Anyone can join the laboratory, and thus anyone can add or modify content on the n-lab, but the lab book (i.e. n-lab) is definitely to serve that purpose. The hope is that this would mean we could retain the sense of ownership of the n-lab without sacrificing the openness to new contributors or to ideas from seemingly unconnected areas.

    To sum up. The basic idea is that of Urs' above, it's a place for discussing racing cars, not hydroelectric power. That's made clear on a sign on the front door. Anyone coming in through the door understands that. Within the lab, people can discuss hydroelectric power if they want to, but they understand that someone may come along and alter their discussion to one about running racing cars on water power, because that's the common purpose of the laboratory. If there is a very loud group of people all discussing hydroelectric power and it gets to the point that the rest of us can't hear ourselves think about the racket, then we point very pointedly to the notice on the front door. If that doesn't work, then we think again. But even if we have to ask someone to leave (which I truly hope never happens in the real situation), they can't complain because the notice was clear on the door: "The Racing n-Car Rally Group".

    Of course, there is much to sort out on implementation, but that's secondary to this and cannot realistically take place until the main aim and objective of the n-lab has been clarified.

    • CommentRowNumber50.
    • CommentAuthorAndrew Stacey
    • CommentTimeSep 28th 2009

    Two asides (originally in the above but it was too long):

    1. I would say that this should cover the private webs as well. There's space in the model for people to have private lab books but they should still be members of the laboratory. (When I say "members", I mean in the loose sense above: they've walked in through the door, gotten a spare lab coat off the peg, and set up a retort stand.)

    2. We shouldn't try to be all-encompassing. Mathematics benefits from lots of different viewpoints. Once something's been done once, it's easy to do again - it would be easy for someone to set up their own lab elsewhere.

    • CommentRowNumber51.
    • CommentAuthorUrs
    • CommentTimeSep 28th 2009

    I agree, Andrew. And it seems we agreed about this before. I did once write something along the lines you are asking for at HowTo. I am not sure that I can provide what you seem to be askig for beyond that.

    I keep getting away with the feeling that you have a very particular idea about what a text on aim and objectives of the nLab should be, but are waiting for somebody (me?, Toby?) to write it so that you can compare if it matches your view.

    Maybe it would be better if you simply write up what you think needs to be written up. Then we can discuss it here and likely produce a widely accepted quasi-official statement after a bit of discussion.

    • CommentRowNumber52.
    • CommentAuthorUrs
    • CommentTimeSep 28th 2009

    Sorry, I meant I wrote something like this at About.

    • CommentRowNumber53.
    • CommentAuthorAndrew Stacey
    • CommentTimeSep 28th 2009

    I did once write something along the lines you are asking for at HowTo.

    My apologies. I interpreted that as being simply to update the technical info.

    I keep getting away with the feeling that you have a very particular idea about what a text on aim and objectives of the nLab should be

    I have a very particular idea about what "aims and objectives" are in general. What the specific ones should be for the n-lab is not something that I feel too qualified to answer. But aims and objectives should be testable and verifiable. In a little (but not much) more detail:

    Aim: The purpose(s) of the project.

    Objective: A method to achieve that purpose.

    Target: Something that can be objectively tested to see if it has been reached.

    So, we might have:

    Aim: To increase collaboration between mathematicians.

    Objective: Provide a place on the internet where mathematicians can explore and discuss ideas (the n-lab).

    Target: Five peer-reviewed collaborative publications from projects started on the n-lab.

    The problem is that while I could have a stab at writing that for the n-lab, I don't really know enough about the core mathematical aims to do so. What I could try doing is a template setting out the broad aims with a blank (or something daft) where the mathematical content should go.

    To make it a little more concrete for you, as I put in my 'declaration of interest', I'm keen for this to work as an experiment in using technology to make it easier to do mathematics. So on that basis, I have lots of ideas for little tweaks and hacks to make it run more smoothly. However, if I'm continually changing things around then that makes it harder for the users to get to know the system. Also, it's difficult for me to figure out which to concentrate on. That's what was really so annoying about the latest changes debacle: not that I'd spent loads of time on it (I hadn't really), but that I could have been doing so, and so I'd like to know before I begin which ideas are best to work on. (I should point out that I'm not asking for an ideal system, obviously some ideas aren't implementable but that only becomes clear once one has tried.) Knowing what the fundamental aim of the n-lab is would help me to design my own set of objectives and targets as the sysadmin/tech support.

    • CommentRowNumber54.
    • CommentAuthorDavid_Corfield
    • CommentTimeSep 28th 2009
    This comment is invalid XML; displaying source. I wonder whether setting a specific target, i.e., the 5 papers, is advisable. In that the project relies on the intellectual energy of the participants, the target risks nLab being seen as a failure if that energy is not directed towards paper writing. As it is, I've enjoyed hearing more than I would otherwise have done of Todd, Toby and Mike's views. I also enjoy that nLab allows Urs to explain his vision in a more permanent setting. I wish I understood more of Zoran's. Of course it would be wonderful if other higher category theorists showed up. <br /><br />So as an objective, this starts out well:<br /><br /><blockquote ><br /><br />Objective: Provide a place on the internet where mathematicians can explore and discuss ideas (the n-lab).<br /><br /></blockquote><br /><br />I would add the homepage clause "...especially insofar as these subjects touch on higher algebraic structures", and add 'record'. So<br /><br /><blockquote ><br /><br />Objective: Provide a place on the internet where mathematicians can explore, discuss and record ideas, especially insofar as these subjects touch on higher algebraic structures.<br /><br /></blockquote><br /><br />In that the objective is to explore and discuss, I still don't understand the revised phrasing on the home page <br /><br /><blockquote ><br /><br />We think of this place as the library, or alchemist’s laboratory, in the back room of the n-Category Café. You come here to work and go there to chat (where chat is short for work by discussion).<br /><br /></blockquote><br /><br />According to that definition, there's plenty of chat at nLab.<br /><br />Finally, I would tend to be strict as to exclusion. If no case can be made for connections to higher algebra, then I don't see the point of inclusion. This is already reasonably generous as there's much which could be categorified. <br /><br />Talking of being strict, what happened to the case of <a href="http://www.math.ntnu.no/~stacey/Vanilla/nForum/comments.php?DiscussionID=69" >Cactus Language & Differential Logic</a>?
    • CommentRowNumber55.
    • CommentAuthorAndrew Stacey
    • CommentTimeSep 28th 2009

    I wonder whether setting a specific target, i.e., the 5 papers, is advisable.

    One can debate that, and it would be interesting to hear how people would define targets for the n-lab (and for those who don't like targets, these can be purely internal and just as a measure of what it is sensible to spend time on - if something isn't helping us achieve a target then our efforts would be put to better use on a different aspect), but my original list wasn't intended as a template, just as a simple illustration of the difference between 'aim', 'objective', 'target', and 'wishy-washy-mission statement'. It was to make the point that these things are not just buzz-words but do have real meaning and, when used correctly, are extremely useful.

    Finally, I would tend to be strict as to exclusion. If no case can be made for connections to higher algebra, then I don't see the point of inclusion.

    At the risk of being seen as too facetious, or at being taken seriously, my response would be: Okay then, I'll stop adding content!

    To be honest, I don't see any connection between what I do and "higher algebra". A couple of things that I've done have pages at the n-lab: Froelicher space and it's attendant pages, and Tall-Wraith monoid has also recently turned up. Presumably there's some link there, but if there is then I don't see it. Not being steeped in "higher algebra" means that I don't know even know how to figure out what is and what isn't. So if my additions run the risk of being deleted just because they don't link to "higher algebra" then I'd consider not adding them and saving the time and effort.

    To make it more concrete, I mentioned to Urs a little while ago that I'd like to put my notes on "differential topology of loop spaces" on the n-lab. There's a fair amount of content there, but it would take a little time and effort to translate the LaTeX into iTeX. Urs seemed to like the idea, but I have no idea whether or not that's connected to "higher algebra". Seems about as far from it as it can get, certainly there's no algebra involved. So if that's at risk of being deleted, I'll save the effort and get on with other things.

    Don't get me wrong, I do agree with boundaries. But I'd prefer to see the content boundaries as being fairly broad. If you think of the research laboratory model, it's the person and not the specific subject that determines whether they put something in the lab book. So someone coming in through the door accepts that this is a place dedicated to researching "higher algebra" (whatever that is), but then if they decide to make a few notes while they're there on spectral sequences then that's fine: the pay-off is worth it.

    If you think of it from the other side, you'll see why this is better. I don't feel a member of the "core group" in the n-scene. But clearly I have something to contribute to the n-group's work (or at least, Urs and John seem to think so). So how are you going to persuade me to contribute? If I have to be continually deciding "Do I put this at the n-lab? Do I put this at the Top-lab?" then that's highly irritating and I'll just decide to stick with one and forget the other.

    The other reason for being inclusive is that you never know what's going to be useful. Again, taking the lab book model, you browse through a recent journal (does anyone still do that?) and note that, say, the Dirac operator on the loop space can be defined using co-Riemannian structures. Looks intriguing, you say, so you make a brief note of it and then forget it. A year later, you start thinking about Riemannian structures and looking at categorifying them. Then, as categorists tend to do, you wonder what happens if you reverse all the arrows. Then you wonder if someone did that for ordinary Riemannian structures, and lo! and behold! you look up co-Riemannian structure and come across your old notes. Only now, being on the n-lab, someone else has been along and filled in all the details for you.

    But I agree that there have to be boundaries. That's what the sign over the door is for. Figuring out what that sign should say is part of the purpose of this discussion.

    I suspect that if we can make navigation a lot easier, and get the design sorted out, then some of your concerns will be met. If all the "junk" is in the corner, and it's clearly marked as "junk" then everyone can happily ignore it until someone suddenly finds a use for those two lumps of "uselessium".

    Above, Urs challenged me to come up with a template for this sign. I'll do that. But as it's a template, it'll need a few blanks filling in. So here's the challenge for you, David. Fill in those blanks. Give me a mathematical (physical, philosophical) aim for the n-lab.

    • CommentRowNumber56.
    • CommentAuthorDavid_Corfield
    • CommentTimeSep 28th 2009
    I certainly wasn't intending to suggest that entries such as Froehlicher spaces or Tall-Wraith monoids be excluded. If you think the wording is likely to deter people from contributing material with that proximity to higher algebra, then it should be changed. I think it would be very difficult to come up with any wording which captures things precisely so that it is at once obvious what falls inside and what outside. Perhaps easier then to adopt case law practice and reason in terms of precedent, hence my interest in the differential logic case. If nobody else is prepared to come out and say they want it excluded, then there's little point in our having this discussion.
    • CommentRowNumber57.
    • CommentAuthorAndrew Stacey
    • CommentTimeSep 28th 2009

    I certainly wasn't intending to suggest that entries such as Froehlicher spaces or Tall-Wraith monoids be excluded.

    I didn't think that you were. My point was that, in the laboratory analogy, I'm a bit like an invited researcher. I'm here to help out with some of your questions on smootheology, and you're prepared to give me a bit of lab space to work on my own stuff while I'm here.

    What I'm trying to get at, but stumbling a bit I'll admit as the ideas are being formed (quantum-like) as they are observed, is that my view of the n-lab is more about people than about subjects. I see this running through a lot of what has been said, including you. But it's not wholly either. Even if it was Urs who started it, a page on the Oxford Comma would be a bit out of place. Essentially, one wants a way of saying that the "closer in" you are, the broader the range of subjects you are allowed to introduce.

    That sounds awfully hierarchical, which is going to raise huge shouts from certain quarters!

    There are, of course, ways of making it less hierarchical which basically go along the lines of: the more you help out with the core purpose of the n-lab, the more tolerant we'll be of your side projects. I recently came across 'stackoverflow' which has an automatic reputation system which works a bit like this (readers of the algtop list may detect a theme here!).

    If you think the wording is likely to deter people from contributing material with that proximity to higher algebra, then it should be changed. I think it would be very difficult to come up with any wording which captures things precisely so that it is at once obvious what falls inside and what outside.

    I want something that is clear. I fully agree with your comment, but I think that there's still room for improvement.

    Perhaps easier then to adopt case law practice and reason in terms of precedent, hence my interest in the differential logic case.

    How British! But, as another Brit, how could I disagree?

    If nobody else is prepared to come out and say they want it excluded, then there's little point in our having this discussion.

    But this specific discussion was about much more than that particular subject. Before one can have cases, one needs some general principles that need to be worked out. Not everything is case law, rather case law is the practical interpretation of the general law as laid down by parliament (gosh, Google's "suggest a term" feature in the firefox search box is fantastic for finding the right spelling).

    So maybe we need to find "twelve good men and true" (though I hope we'd be a little less sexist, and of course there's nothing perfect about 12) and you can prosecute and Jon can defend. Perhaps the defence has started making its case over in the other discussion.

    I don't feel remotely qualified to comment on that particular case, though, so I'm more interested in the generalities. I realise that this is a little frustrating for you, and I apologise for that! Perhaps it should be said that if we can't find "twelve good men and true" for a particular topic then the prosecution case is automatically carried (the implication being that not enough of the group have a clue what it's about so it ought not to be there).

    However, I'm feeling the presence of thin ice here. I'd like to make it abundantly clear that if the choice is "cacti and Toby" or "neither" then I'll join the cactus train. Even if I haven't the foggiest idea where it's headed.

    • CommentRowNumber58.
    • CommentAuthorUrs
    • CommentTimeSep 28th 2009

    I don't know if you (any of you) noticed, but the idea that everything is best seen from the perspective "higher algebra/higher geometry" is more alive than ever. This is exciting times. See things like scheme as locally affine structured (infinity,1)-topos.

    Part of the nLab goal I see more in unravelling the secret higher structure behind apparently "ordinary" concepts.

    But apart from that, it would seem that anything category-theoretic is very at home in the Lab, even if no higher connection is (yet) available.

    So I would think material which is much less evidently of higher nature than what Andrew is working on would already qualify for the nLab. Andrew's work on loop spaces is even manifestly a higher thing. Dirac operators on loop space etc. pp. are supposed to be aspects of "2-Dirac operators". That's what all this geometric model for elliptic cohomology-business is about, anyway.

    Certainly, I would be more than happy to see Andrew's differential topology of loop spaces on the nLab.

    • CommentRowNumber59.
    • CommentAuthorTobyBartels
    • CommentTimeSep 28th 2009

    I'm not sure what to write for the whole Lab, so I'll write a very personal version for myself. (If everybody does this, then we just take a colimit, right?)

    Aim: To amuse myself. (That sounds flippant, but it's why I'm here. Fortunately I'm not the sort of person who's amused by trolling, and you wouldn't be asking my opinion if I were.)

    Objective: To write about mathematical ideas that interest me, which I've already summarised for the Lab (hereby included by reference), to read what the other contibutors write (at least in summary, and closely if it also interests me), and to work out ideas collaboratively through editing and discussion. Secondarily, to work on the organisation of the Lab so that it will be useful for me and others.

    Target: I continue to want to contribute, indefinitely.

    • CommentRowNumber60.
    • CommentAuthorJonAwbrey
    • CommentTimeSep 29th 2009
    • (edited Sep 29th 2009)

    Re: Andrew Stacey

    First, a declaration of interest. I'm keen for the n-lab project to succeed because I see it as a great example of using technology to make it easier to do mathematical research. … But I do think that mathematics is missing out on modern technology and I'd like to see it put to better use.

    This is something that I've been thinking and working on for the last 30 years or so. Getting a handle on the work takes expanding the clearing from mathematical knowledge representation to knowledge representation in general and then looking at the cognitive and cultural activities that provide us with provisional knowledge — processes that fall under the collective heading of inquiry.

    • CommentRowNumber61.
    • CommentAuthorMike Shulman
    • CommentTimeSep 29th 2009

    I haven't really digested all of this yet, but my gut reaction is very much against an output-measure such as 5 papers. I could count the nlab a success even if no traditionally peer-reviewed papers are ever published based on projects worked on there.

    • CommentRowNumber62.
    • CommentAuthorAndrew Stacey
    • CommentTimeSep 29th 2009

    I haven't really digested all of this yet, but my gut reaction is very much against an output-measure such as 5 papers.

    I'm strongly tempted to go back and edit that post (I shan't, of course). I didn't mean these statements to be taken seriously. They were examples of the sort of thing one might come up with. The point, such as it was, was that targets should be measurable: one should be able to say objectively and definitely whether or not a target has been reached.