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<p>It is curious that the vexing (for me) silence concerning the nLab on the nCafe has been broken on the SBS by that discussion triggered by MathOverflow.</p>
<p>Currently my conclusion is this:</p>
<p>Contrary to what i had expected, few people actually do enjoy developing math together on a wiki page.</p>
<p>I see three stages of development here:</p>
<p>1) non-binding exchange of comments or questions/answers</p>
<p>2) a wiki page</p>
<p>3) a finalized exposition</p>
<p>I see that the majority does embrace 1) and 3). The criticism that has been voiced is that the nLab is too little like 1) and too little like 3). The idea that the nLab is a way to go from 1) to 3) in a useful manner is something that is met with great reservation.</p>
<p>First I thought a little be of advertizement and nudging would break a damn, but now it is clear that it won't. There is a vicious circle that won't break:</p>
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People expect a wiki page to be a finalized exposition and at the same time that expectation scares them away from contributing.
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<p>While we were trying to emphasize that it is already useful to add something imperfect to the nLab, other contributors complain, as just happened a minute ago, that nLab pages are imperfect. And such complaints reinforce fear of imperfection and scare more people away.</p>
<p>There is no way persuasion will break that. It seems that all we can do is be content that we are a chosen few who do something significant, and in 5 years when the nLab is a major resource we'll have to shoulder the fame for that alone. -)</p>
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People expect a wiki page to be a finalized exposition and at the same time that expectation scares them away from contributing.
How much of this do you suppose can be blamed on people's primary exposure to wikis being Wikipedia?
I think we can keep trying to correct people misapprehensions. The new front page standout box might help. But maybe it really is some psychological block.
I remember when Wikipedia didn't expect a Wikipedia page to be a finalized exposition. Ah, those were the days!
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<blockquote>It seems that all we can do is be content that we are a chosen few who do something significant, and in 5 years when the nLab is a major resource we'll have to shoulder the fame for that alone.</blockquote>
<p>Amen :) There is absolutely nothing wrong with adopting this philosophy in my opinion. The nLab is already a wonderful resource that exceeds any reasonable expectation.</p>
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There is absolutely nothing wrong with adopting this philosophy in my opinion.
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<p>I suppose you are right. Maybe the only problem I have, if I am being frank, is that I need to get over a certain disappointment. Not sure why this is bugging me so much.</p>
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I agree with Eric that nLab is doing just fine. But as to why more people aren't joining in: maybe your psychological analysis is correct, but I think this explanation is very partial. I rather tend to the belief that some people would do more here if they had more time (e.g., John Baez); others do a kind of cost-benefit analysis and decide that they don't get enough bang for their buck by getting involved. That's the (somewhat unspoken) sentiment I'm actually getting from some very smart people like Ben Webster and Noah Snyder -- either time is short and they feel this isn't the optimal way to spend it ("what can the nLab do for me?"), or writing out definitions or polishing things semi-anonymously might not give them the same bang in terms of strutting their stuff (like answering questions and winning public reputation points). I don't mean this in a demeaning way at all; I completely understand it.
One, I'd give it more time. Two: you do realize you're very, very different from most other mathematicians? :-)
Thanks for the comment Todd.
Concerning the time aspect, I keep thinking that the nLab is actually a means to save time or use time spent online more efficiently.
Of course if somebody just has no time, than that's it. But IF somebody goes through the trouble of writing an expository piece -- a reply, comment -- into a blog or into a forum in the first place, then it seems to me this same time is much better invested in writing this material into the nLab and then pointing to I.
Much of the reason why I like the nLab is that I feel that I wasted so much time with writing blog entries and comments, that are now mainly bound to be lost an forgotten. Even if someone actively searches for them, the insights gained somewhere in some long blog conversation are almost inevitably lost to posteriority for practical reasons.
This is different as soon as the material is on the wiki, where it is eventually nicely cross linked, commented and suitably rearranged.
Much of the reason why I like the nLab is that I feel that I wasted so much time with writing blog entries and comments, that are now mainly bound to be lost an forgotten. Even if someone actively searches for them, the insights gained somewhere in some long blog conversation are almost inevitably lost to posteriority for practical reasons.
I think that that's the point I would highlight too. Mathoverflow has a certain fun aspect to it, but I just spent a bit of time answering a question on cohomology theories and thinking "What's the point of putting this in here?".
It's not a question of persuading those that don't put stuff online to start (though that's a worthy goal) but persuading those that already put stuff online that there are different ways to do it and they should think carefully about how they go about it. That means thinking carefully about why people put stuff online. I have a suspicion that this isn't really thought about much: blogs are the "in thing" so everyone has a blog. But blogs are very much one-way things and while there are some people that I am happy to sit at the feet of and learn from, there aren't many.
I think that some good for the n-lab has come out of the MO vs n-lab discussions. It's enabled us to see what other people think of the n-lab and realise how that does or doesn't square with what we think. How much we do about that is up to us.
Comparing the n-lab with other things (blogs, MO, etc), I think that it's strengths are:
I think it would be useful to think about the disadvantages, or at least the perceived disadvantages, to see whether we can do something to mitigate them. For example, we could make the homepage a lot more welcoming and a lot clearer. Of course, these things take time but perhaps it's worth the time to draw new people in.
Another thing I was thinking of: maybe it would help (somebody) if the moment a new edit window opens for a new entry, one already finds some template source code there.
Maybe just a headline "Idea" and below that a query box saying "Does anyone have an idea about this?" Then the headline "Definition" and a query box saying "Does anyone know a nice way to state the definition". Then a headline "References" and a query box "What are good references on this topic"?
That might serve several purposes at once:
it might reduce the inhibition to start a new page by providing some structure,
it might provide the right psychological thing that has been requested. Some people effective said: I don't contribute to the nLab because there are no questions asked there. So we could have all questions automatically asked here :-)
it might make people think of what might go in such an entry and realize that they do have something to say about it
it might increase the readability of the resulting entry by imposing some structure right from the start.
Would something like that be hard to implement, Andrew?
(And we aren't even talking of collaborative research yet, in all of this...)
Is it perhaps that you, Urs, overestimate the frequency of possession of 'mathematical vision'? What's attracted me to look at the topics I do have been glimpses of enormous visions in Mac Lane, Lawvere, then John & Jim, and other category theorists. If your research aims, instead of being the complete transformation of mathematical physics by higher category theory, were much more restricted, e.g., sorting out some specific knot invariant, perhaps the nLab project wouldn't seem so appealing. <br /><br />There lies a tension in nLab as a cross between lab book and reference document. A lab book makes sense as the record of thoughts which belong together as parts of a largely unified project. Think of those of the great physicists of the nineteenth century. Reference documents record stable findings that can be used in a vision-independent way. The more interesting nLab pages reflect a grand project. People may be able to provide exposition of topics that would be useful for someone who works on that grand project, but if they don't feel nLab is a vehicle in which to unfold their own projects, will not feel the inclination to write.<br /><br />Moving from personal lab book to a universal lab book seems to me problematic in the loss of unity of vision. As a first step in this direction nLab is working as a group lab book contributed to by people who share sufficiently much of an outlook. Perhaps what disappoints you is that there ought to be more whose outlook should allow them to participate.
The "vision thing" is something I was going to point out as well, and spent a while thinking about how to say before summarizing lamely that you (Urs) are different from most others. It was also what was behind my suggestion that maybe nLab may be generally more attractive to theory-builders, of which you are an outstanding example.
Andrew makes a good argument about time management; what I meant by "time is short" is that people like Ben and Noah would rather document their stuff by writing them up in papers and moving on to the next challenge. I think he's also right that most people haven't thought deeply about time efficiency of blogging, but here I come back to the idea that a primary purpose of blogging is as egoistic outlet, and that the semi-anonymous nature of nLab building doesn't satisfy the same demands and cravings.
(In my own mind I sometimes liken the building of the nLab to the building of the great cathedrals of Europe. Whoever those genius architects and artisans were has been lost in the mists of time, but then again they probably didn't run around thinking what geniuses they were; they were in the service of God and His vision. So it may be to some extent here -- I think Urs you are to a fair degree able to subordinate your ego-cravings to the pursuit of a big vision.)
Thanks for the feedback. This is good to know. There are several things i feel like saying in reply, but -- we mentioned it -- time is short! :-)
So here just one quick aspect:
it seems to me that when handled the right way, the nLab also saves paper writing time. I am right in the middle of the process of extracting the first to-be-published papers from nLab material and I find the nLab here, too, a great gain and useful tool: instead of fiddling in a big LateX file, i develop all the bits and pieces in nLab entries where they ripen in their own right. Then when it comes to creating a paper I essentially copy-and-paste the relevant nab material togetehr, write some suitable text all around it and there we go.
It's just another aspect of the general slogan: don't work on the nLab instead of doing research. Use the nLab as the central tool for doing your research.
More later, have to get back to my research... Which you'll see in a moment under LatestChanges...
I can agree with this, but most people have not learned to work this way yet. Think of how you organized your work and research before the nLab: typing up lots and lots of notes and apercu in LaTeX. Among your many strengths, you are unusually organized and disciplined, and the nLab style you've developed is an extension and elaboration of that particular research style (which in part may have been a reaction to the fact that you at one point might not have had many people near you to talk with at tea at the high level your research demands -- people like Ben and Noah [to use them again] at Stanford and MIT and Princeton have it easier (-: ).
Perhaps Andrew is similarly organized and disciplined -- he seems that way to me.
I'm the exact opposite of organized and disciplined, but I also don't have a career and am completely isolated except for the internet, so you know why I'm here. :-)
I'll try to find an article I once read about the typical social/evolutional aspect of the development of a wiki. The basic lesson was that generally there is always a small core group of intense contributors (as we've seen), followed by a larger group of intense readers and minor contributors (as we've seen), followed by an even larger group of intense readers (who knows?), followed by an even larger group of casual readers. The size of each group grows exponentially. The core group of contributors is generally less than 2% of the total. That is perfectly normal.
As long as the core group of contributors enjoy contributing and feel they get something out of contributions, e.g. saved time, etc, then just keep on contributing. I'm fairly sure there is a large group of people who read and enjoy both the nCafe and nLab without ever contributing.
Edit: By the way, I've done some research on this topic as I've introduced internal Wikis at the last three corporations I've worked.
By the way, how difficult would it be to add some minor interactive features, e.g. ratings, polls, list of most active contributors, etc. Something to maybe make it more "fun". I like he idea of being able to rate each revision to give feedback to the author. Maybe a simple poll or something, "Did you find this page helpful?" "Did you find this revision helpful?"
I may be in the minority, but I actually don't like the idea of polls and ratings or anything that makes me feel like I'm being "graded" on my work. I would rather have people that I know and respect give me comments directly, rather than regard the (perhaps ill-thought-out) opinions of anonymous button-pushers. In fact, such things would tend to turn me away.
Yes, I'm also against polls and ratings. The reputation system is one of the more uncomfortable things to me about mathoverflow.
I'm also against ratings per se. Although I can see it's value on mathoverflow, there's aspects that I don't like (and I can say that as someone with a fairly high "reputation" over there, higher than one or two of the moderators!) and I wouldn't want that imported over here. On the other hand, I'm all for making it "more fun" so long as it doesn't detract from the rest of it.
One thing I thought of was some sort of relational graph of pages on the n-lab. It shouldn't be hard to whip up a graphviz plot of the pages with links weighted by some sort of internal page rank algorithm (removing the meta pages first, of course). This might even be a more "fun" thing to have on the homepage than the current contents.
Also, I think it would be good to have some sort of certification system whereby people can read a page and then "sign" it according to how much they believe the mathematics. This would not be on relevance, but on accuracy. Those pages where people are developing ideas could benefit from this, I think. For example, it'd be nice to know if someone's read the theorems on Froelicher space and whichever Isbell page it was. I don't want people to put a load of query boxes just saying "Looks alright to me", but if there was some way that people could "sign" the pages then that'd be useful both as an author and a reader. I think we've discussed this a bit elsewhere, though.
I didn't mean to associate a rating or poll with what is going on at MathOverflow, which I agree is off putting. There, you rate the contributor. That is NOT what I had in mind. I had in mind a way to rate (or grade) a page. This would give some useful feedback. For example, if 20 people read a page and bothered to rate it as "This page needs improvement" then seeing that, some contributor might get the hint to go and improve the page. I definitely would not suggest a means to grade contributors, but a graded page is a different thing altogether in my opinion.
No big deal either way. Just throwing ideas out there.
Possible check boxes for a reader survey:
Maybe we could create a pull down menu and submit button. I don't know. Just thinking out loud.
PS: In a perfect world, when a reader sees an imperfect page, they would perfect it, but we do not live in a perfect world.
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<p>Quick comment re David:</p>
<p>I have a hard time believing that it is the type of content I am concerned with that makes me better suited for the nLab than others. Others here have very diferent content and seem to be doing just fine.</p>
<p>Recently, as you know, i was taking nLab notes of various seminars on various subjects. if I had had more time, all of that would have been greatly suited to be further nLab-ified. To some extent some others are further developing that now, but I wuld like to see much more activity in that direction.</p>
<p>Every further set of pdf notes posted to the nCafe makes me sad. How much more worthwhile would all the effort invested into these pdfs be had it been typed directly into the nLab -- with exactly the same typing effort.</p>
<p>I can accept that the nLab apparently requires a certain personality prerequisite . But I don't think that one content is better suited here than other.</p>
<p>And concerning the visionarity: I am not sure what to make of this. I am looking into mathematical physics/theoretical physics, seeing which mathemtical tools apply where, so that it works. It seems more a labor than a vision. And lots of other people are doing it, too. While you call me visionary, I am struggling not to be left in the dust of people like Lurie, Costello, Freed and so on.</p>
<p>To sum up, I have a hard time believing that there are <em>in-principo</em> reasons not to work on the nLab.</p>
<p>And I hope we are not getting to the circulous conclusion at some point of te kind:</p>
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I can't contribute to the nLab because that seems to be the place where only people like Mike, Toby, Todd, Zoran, Urs are contributing. QED.
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How about
I can't contribute the the nLab, because that is based on a structural approach to mathematics related to higher category theory, which I is not the mathematics that I know and work on.
? I never thought that the Lab was supposed to be about mathematics in general, but instead about mathematics/physics/philosophy related to higher category theory, featuring the style of thinking about these things that appears on the Café, or something like that. (Of course, this is the topic of the thread on the scope of the Lab.) But Urs's exhortations seem to imply that it is about all of mathematics. For now, at least, it is clearly not.
For now, the nLab is many things not. But in general, "math related to higher category theory", which I read as "math from the point of view of higher category theory" seems to involve all math.
I think it has become clear that whatever sensible thing people do, there is a good category-theoretic or higher category-theoretic way to look at it.
I mentioned this before, but let me just mention it again: Luries Structured Spaces is a claim that VAST pieces of standard mathematics have their natural home in oo-category theory.
Stuff like that is what the nLab should expose.
I think it has become clear that whatever sensible thing people do, there is a good category-theoretic or higher category-theoretic way to look at it.
Our saying things like this may also turn some people off. Not that I think we shouldn't say them, but there are a lot of people who have yet to be convinced of anything like this, and I can understand their not feeling like contributing to a wiki that's based around a philosophy they don't understand or don't agree with.
Please, please, no reader surveys with check boxes. If there are problems with the page, just please say directly (as Anonymous Coward if need be) what the problems are and not make people guess. I'm sorry, I really hate the very idea (doesn't matter if it's contributors or pages), and I repeat: it would seriously turn me away.
As far as scope goes: IMO there is no area of mathematics that doesn't have potential to become registered somehow in the nLab. I am not very comfortable about having the nLab feature a particular style; it would seem a bit self-conscious at any rate to say anything about the nature of the style, and likely to discourage others from contributing. Let these things evolve as they may.
Hm, I'm just now reading over the interesting discussion about scope of the nLab. My previous comment was written in ignorance of that discussion.
After I posted my last comment I realized that Toby might have been expressing a concern that those various lecture notes I had typed into the nLab recently were outside of its scope.
Whether or not Toby meant to express that, I should maybe emphasize why I think these particular lecture notes were about core topics of the nLab:
the one on Stolz-Teichner formalism is really about higher parallel transpoprt and its relation to higher cohomology. It is clear that to me this is, apart from its higher-categroriAL :-) context a core topic.
The other about elliptic cohomology was about the re-interpretation of TMF as the collection of global sextions of an oo-scheme. Clearly nLab stuff.
Finally the gromov-Witten invariants stuff is one of the few concrete realizations of path integral quantizations leading to functorial quantum field theory that are availble. I think everything related to functorial quantum field theory is a core topic.
In fact on the page higher category theory we say (probably I said) that one of the central motivations and results for higher category theory is the cobordism hypothesis and its relation to functorial QFT.
Maybe all this was clear, but last night after thinking about this thread here i thought maybe I should say this explicitly.
re Mike's comment:
if anyone says he or she doesn't like the higher categorical perspective, then I'd be happy not to see him or her contribute here. I am not trying to get those in the boat. And i think we shouldn't, lest the nLab won't be the nLab anymore.
But i think there are many more people embracing the higher category theory perspective on math than we have seen here being active. In any case, as I see it we are at the truning point where higher category theory clearly takes over as the right context (turning point read from a historical perspective: something that may last a decade or two). I would like to see the nLab be part of that momentum.
re Todd's and Eric's exchange:
I am with Todd in that I also feel that I don't want any checkboxes or credit points or the like here. Think about how that would look like on, say, MathSciNet to see the sense in which I wouldn't like it here on the nLab.
But on the other hand I would be interested in hearing feedback. Several times now people have told me of other people they met who said they found the nLab in general or some partuclar entry extremely useful. It would be nice to learn of that positive feedback. Also it would be nice to learn of negative feedback on entries. It would only help us make things better.
But I am not sure about how to get hold of that information systematically. Maybe there is no good way.
I'm not nitpicking -- honest I'm not -- but what sort of data points do we actually have that the vast majority who have useful feedback don't edit? I'm guessing that the assertion may be based on Eric's past experience with other collaborative wikis (and such experience is certainly valuable to have around here), but unless we have data on who exactly is reading nLab articles, it could be hard to say so with much authority.
At any rate, the question of how to elicit more useful feedback is a very good one. I wish I had a good answer.
After I posted my last comment I realized that Toby might have been expressing a concern that those various lecture notes I had typed into the nLab recently were outside of its scope.
For the record: I wasn't.
I can easily do a list of the IPs that look through the n-lab. Now and then I've thought that it might be fun/useful/nice to have some meta-data like this available. Maybe one of those "where do all our readers come from?" maps. The other things I thought of were automated lists of "pages added yesterday" and "pages revised yesterday" (quick versions of "all pages" and "recently revised") and a graph showing how the pages link together.
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a graph showing how the pages link together.
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<p>Is that possible? I was thinking this might be really interesting, to see a graph of the nLab with entries as vertices and links as edges. It might also help us understand better what we are doing.</p>
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Have a look at this page to get a vague idea of what's possible. Obviously, that's a genealogy graph so is somewhat constrained (which is what makes it so wide). Other things are possible. I had a bit of fun with this back in Sheffield and did a department genealogy graph and a department collaboration graph.
That page crashes Firefox. Will try with IE.
Can read the page with IE. Xcept for images.
Can download the graph and scope with Inkscape.
Not too pretty though. Labels overrun their ellipses.
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