There’s been a very interesting dicussion in comments on Scott and Anton’s post about the strengths and weaknesses of MathOverflow and nLab, and I thought it might be good to divert to a new post (and use my position as blogger to top-post my thoughts). (edited since the original post. Look below for more)
Now just a moment ago, I followed a link, and started reading the n-Forum, and as a result, discovered that nLab has no page on knot invariants. And I thought, “hmmm, someone should fix that, and I guess that someone should be me.” So, I clicked a link, ended up with a blank page on knot invariants, and immediately realized that that person shouldn’t have been me at all.
What it comes down to for me, is that when I try to edit nLab, I always end up with a blank page, and no idea what I want to say. Andrew’s right that one should keep in mind that one is not writing Wikipedia (I think in my previous nLab forays, I lapsed into Wikipedian without even thinking about it). But still on some fundamental level, I had no idea what I wanted to tell people about knot invariants, or what they wanted to know. And “What knot invariants are.” is my standard explaining my research to a non-mathematician spiel; if there’s one thing I should be able to effortlessly write an nLab page for, that was it. And yet, it felt forced, and it was definitely not fun.
Whereas in my experience, MathOverflow is instantly absorbing and fun. Several other regular users have already told me they’ve found it an addictive time sink. I think the important difference is the level of feedback and interaction. On MO, one really feels as though other users are engaged with your questions and answers, whereas in nLab, I feel like I am talking into empty space. I think the other point is that the hardest part of mathematics is knowing which mathematics to do, so having a lot of concrete suggestions, not just for topics to write on, but questions to answer overcomes a real psychological barrier.
EDIT: Now that I think about it, there may be a good answer to this question. The sense I get from Andrew and Urs is that I haven’t been using nLab selfishly enough. I’ve been thinking about writing things that will be useful for other people, when perhaps I should be writing things that are useful for me to write, with some vague hope that other people will also find them useful and have input. Perhaps I will even try this at some point when I finish up a couple of current project and am in more of a reorganizing stage.
I think another point is that it would never occur to me to have an online lab book, because I don’t have a physical one. Some people (Scott M. and Aaron Lauda are examples that spring to mind) have physical lab books that they write lots of notes and calculations in. I don’t; I never take notes when reading papers, I write all calculations on random papers which I immediately proceed to lose (I’ve been using extra copies of a Number Theory exam recently), I never write anything down in any kind of structured form before I start drafting the paper. I’m not sure I know how to use a lab book, which is why I am probably not yet ready to use nLab.
Secret Blogging Seminar 
The comparison to, for example, the Tricki might be even more appropriate. As excited as I was about the Tricki before its launch, I have yet to use it. But I’ve been using MO constantly.
Ben, I thought what you wrote at [[knot invariant]] was a perfect start, just a quick idea of it followed by breaking it down into more manageable subtopics, to get the ball rolling. I feel sure someone will pop by to write up something on say [[Jones polynomial]], and someone else will add to that, and so on.
Attempting to write something on some sprawling amorphous topic like “knot invariants” is not where I feel most comfortable in the nLab; I find it much easier just to click some well-defined notion (uniform space, distribution) which doesn’t have a page yet and write _something_; there it doesn’t feel like I’m talking into empty space but simply addressing a perceived need. It’s easier sometimes if I’m not particularly expert on the topic but at least know the definition and some illustrative examples and can throw in a helpful point of view or two; there’s none of the problem of embarrassment of riches if I’m not a great expert. I think this is probably how a lot of pages get written up; for example, Urs writes a ton of stubs on the fly about things as he is learning them, and other people add in bits of their own knowledge as the spirit moves them.
Speaking to your last sentence: I don’t know where you would place yourself on the theory builder-problem solver continuum, but it seems to me that MO would be much stronger draw for the problem-solver, with so much to sink one’s teeth into, and nLab would be more attractive for theory builders. People like Urs and Toby and Mike — these are some big-time theory builders by nature; they just _like_ building up stuff like SEAR from scratch; it’s fun for them.
When I look at MathOverflow, everybody’s always answered the questions that I know the answers to. So I expect to try it out the next time that I have a question of my own, but I doubt that I’ll ever be a regular answerer there.
On the other hand, at the Lab, there are lots of blank links that I have some idea how to fill, and (even more so) there are articles begun that I can add to and correct. Then when I’m learning about something new, maybe I can write it up there also.
I don’t see much point in trying to convince you to contribute to the Lab instead of to MathOverflow, and I don’t think that you’re trying to convince me and other nLabbers to do the reverse. We have different styles, and that’s OK.
I think also the level of knowledge you need is much less for MO than for nLab- a newbie like me wouldn’t try to write an entry about
-categories without actually knowing something about them, whereas a beginner also has (by definition) questions to ask.
But then again, perhaps you were comparing *answering* questions on MO with writing nLab entries, not with asking questions. All the same, there is no shortage of fellow newbies out there, which could explain MO’s current popularity (which seems to have been much more than the Tricki even at its beginning).
Todd-
I think there may be an oversupply of answers to questions. Of course, the way to correct that is to ask questions.
Akhil, judging by the blog you co-write, you’d be a great addition to the nLab. No one would expect you to write about higher categories — it’s a huge sprawling topic anyway. Just find something well-defined that hasn’t been defined yet, and go! The level of expertise of contributors to many topics on the nLab varies widely, believe it or not.
That’s another good point in the edit. I hope Urs doesn’t mind my saying that he is probably the most selfish nLab contributor, in the best sense of the word. That probably explains why is the most prolific. :-)
I should also just point out that there is some commonality in this question asking feature between the sites. If you have a question about a topic and there is already a page on the nLab, just throw in a query box where you would like more information. Someone is bound to give more details. If you have a question about something that doesn’t exist on the nLab, create the page, say what you know about it and then leave a query box asking for someone to come along and fill in some particular details that you are concerned with. Having said that, you may get an answer sooner at MO. I am not sure.
I think the important point to take from this discussion is that although the fun of the contributors isn’t the only important consideration, it is an important consideration. Yes the product is important, but it’s also worth thinking about whether there are ways make things easier to get involved in and more fun. People can be motivated by fun or by profit, but unless you have one or the other it doesn’t matter how good the output is it’s going to be harder to recruit people.
The real question is how on earth you guys have time for all these nLab, MathOverload, etc. I barely have time to write a blog post every month or two!
@Todd: Thanks for the advice, I’ll take a look!
@Joel
I think many of the people doing these things do not have graduate students or are graduate students. That may help with the time issue. Maybe I am wrong.
@Joel-
I think most of us are not teaching (Noah, Chris, Scott M., David, A.J.) or have relatively light loads (me, Scott C.). So I think that makes a difference. Well, and except for Scott M., the rest of us don’t have kids; I suspect that may be the kicker.
@Joel
I think many of the people doing these things do not have graduate students
^graduate students^small children
Allen-
I’m not sure I know how to interpret that, but I think it means you agree with me.
I should point out that one of the things about a site like MathOverflow is that it replicates something completely different than the nLab – namely, it’s something closer to the face-to-face casual mathematics that you’d discuss with somebody three doors down in your department, rather than trying to build a reference book. Occasionally a few words can clarify a whole ream of the literature for you, or point out what the key points are that you may have been missing, without necessarily being pure or rigorous mathematics.
Tyler, your comment shows that you haven’t understood the aims of the n-lab. Again, this isn’t your fault – it’s ours for not making them clear. The n-lab is not a reference book. It’s a lab book.
Ben’s right. The n-lab is fundamentally a selfish place to be. When I haven’t been dealing with the infrastructure of it, I’ve been working on a page on Frolicher spaces. I use these in my work, and have lots of little bits and pieces that I’ve worked out while I’ve been using them. The n-lab lets me keep all those in one coherent place, instead of in a pile of paper on my desk. That’s the first use. Then, it turns out that other people are interested in Frolicher spaces so they come along and read what I’ve written and comment, question, and add to it. For example, not being an expert in category theory I wasn’t sure of what exactly I needed to prove to show that the subcategory of Hausdorff Frolicher spaces was cartesian closed. So I put a question, which someone answered (Mike Shulman, I think) and sometime I’ll write that in to a proof. Or maybe someone will do it for me.
For me, the biggest difference between the n-lab and all the other realms for online interaction: blogs, forums, mailing lists, and now MO, is the pace. In the n-lab I can work at my own pace, I can read other people’s articles and comment on them in my own time, and I don’t feel rushed.
Over on MO, and in blog comments, I always feel rushed. I feel that if I don’t get an answer in quickly, what was the point? Take the coalgebra structure in cohomology as an example. I was busy crafting a fairly long answer when I got notified that Ben had posted one. I decided that mine was still worth posting (more so when I’d seen Ben’s – sorry, Ben). A day or two later, something else has occurred to me about coalgebra structures which I think might be useful to anyone thinking about that so I’m going to add to my answer. But who’s going to read that addition?
The analogy of a lab book is correct for the n-lab. Lab books contain potentially everything: details of experiments (including, and especially, why they went wrong), notes from seminars, notes from literature, and just doodles from when you were bored. Also, things that are wrong! My wife trained as a chemist and she can’t understand how I’ve managed to get along so far without a lab book.
Lastly, regarding how much time it takes. Time spent on the n-lab isn’t wasted because it’s research. That’s excepting time spent maintaining it, of course, but I suspect that issues like that aren’t the majority concern (but I don’t regard this as wasted time since I think it’s important to give these projects every opportunity to succeed). Time spent on MO does feel a little more frivolously spent. It does feel like the sort of thing that was fun to begin with, but that I’ll find myself spending less and less time on as other things crowd in. Not that I’ll stop, just that I’ll be much more discerning in what questions I even look at (which, actually, is pretty much how it should work).
Also, regarding time, I don’t have graduate students but I am teaching this semester and have three kids. Not sure why that should be relevant, though.
(Gosh this comment is getting long) and to put myself on the spectrum Todd talks about: I am definitely a problem solver.
It sounds like the reason I don’t have time to put much on the nLab, and nothing on MathOverflow, is that I have grad students. But how come they have time for it? It’s no fair.
to Akhil Mathew:
I see form recently revised that you have started working on a bunch of nLab entries.
That’s great!
Maybe you would enjoy logging what you did to the nForum, which is designed to be precisely what so many here request: place for face-to-face discussion that complements the nLab.
The idea is that everyone who make a non-trivial addition to the nLab drops a quick note on the nForum in the category “latest changes”. This helps to interact.
re Todd’s remark:
yes, entirely correct: my use of the nLab is entirely selfish. I use it as a tool that supports my research and scientific activity.
And the only reason why I try to get more of you into this boat is entirely selfish, too: I think that it would serve my personal research and development even more to get more input/comments from others. That’s the onyl reason why I blog, too. It’s all selfish. Seriously.
I am already benefitting a lot from the activity of the nLab regulars. I am not so much benefitting lately from the nCafe, as I don’t get any feedback there anymore. So I am always looking for more resoruces of cool people to interact with.
concerning teaching:
I had to teach last semester. That was one of my most active periods on the nLab: i used the Lab as my teaching tool. wiki-fied everything. The course notes I typed into my personal area, all keywords appearing there I created nLab entries for.
I bet most of you do write up lots of stuff into a private file when teaching, too. Putting the material of such a file on the nLab makes it come alive.
it’s a great experience to have written an entry on something, reflecting the best understanding one has of a certain point, and then a week later to come back to that entry and see how others have imporved it, have added new aspects and pointed out mistakes. It’s that feeling of sustainable progress.
@Urs, #19: Sure I’ll do this.
I’m not sure that this is as true as you think. I prepare my lectures on pads of paper which I can never find again. When I’m teaching a more advanced class some time, maybe then I’ll give nLab a shot.
Working on the nlab is not *completely* selfish for me, in the sense of directly furthering my own research. I confess to an occasional Bourbaki-like encyclopedic urge to write about mathematics and try to reshape it a bit as I go. (-:
I’m still getting into the idea of using the nlab as a lab book. My natural inclination is to be kind of secretive about my new ideas until I’m more sure they’re not cockeyed and I’ve written them up carefully. But to the extent that I’ve gotten myself to use it as a lab book, it’s proving its worth. (And yes, I am definitely a theory builder. (-: ) I have tended to use a personal lab “book” in the past, though, so I already have an inclination in that direction.
I definitely agree with Andrew’s #17 about feeling rushed on MO. It’s about all I can do to keep up with comments on the n-category cafe. To speak to the original point of “talking into empty space” at the nlab, I wonder if following the [latest changes](http://www.math.ntnu.no/~stacey/Vanilla/nForum/?CategoryID=5) threads would make you feel more a part of a community? It certainly does that for me.
Ben @23:
I would definitely be up the proverbial creek without a paddle this semester if I didn’t have old teaching notes to at least as a start to new teaching notes.
I hope it became clear, but maybe explicit emphasis is indicated:
that bit about the selfishness was intentionally a bit over-amplified in order to counteract the apparantly wide-spread perception that working on online resources is time _lost_ for the personal research. It should not be and need not be.
I gather all contributors here are well-familiar with the basic premise of how capitalism works: with everyone being selfish, the _interaction_ of these selfish beings still leads to something beneficial for all.
In the same way, with everyone just very selfishly adding to a joint online notepad, the joint result will still more beneficial to each and every one than each isolated action is.
Mike mentions an encyclopedic urge. Sure: one feels knowledge accumulating inside onself and wants to somehow emanate it once in a while. But instead of replying to various incarnations of one and the same questions on a bunch of blogs and forums, I am being selfish with my time resources and just write one single explanatory entry on the nLab. Then when the question comes up, I’ll just point to that entry. First of all I profit from that, since it saves me time. But the thing is that everyone else then does, too. And in the end my own gain is also much more than just the original time safed.
Am I alone in just not liking how the n-Lab looks? I really don’t like the way it spreads across the page. I’m finding it hard to put my finger on it but I prefer how the n-Cafe looks, how this Secret Blogging Seminar looks and how wikepedia looks. Somehow the text just splurges at me and isn’t inviting me in to read it.
I also think that many of the pages I’ve looked at on the n-Lab also look half-digested, and I don’t like reading other people’s half-digested ideas, unless of course I am really deep into figuring something out.
I certainly don’t like putting out reams of half-digested thoughts (unless I’m stuck and need some help), possibly because of the adage that people will only read your stuff once, so you’d better make it as good as you can for the first time they read it.
I have started keeping something like a lab book and I wish I had seriously started doing it 15 years ago. I wouldn’t have so many random bits of paper lying around. However, my lab book is a *book*. I can scribble and doodle in it — draw lots of pictures, arrange things however I like on the page — these are things I can’t so easily do on a computer. I always have to figure things out long-hand first — if I compost things on a computer then it feels different. More importantly, if I *edit* things on a computer then it looks editted on a computer.
Somehow I just don’t feel like the n-Lab is the somewhere I want to work *at the moment* (I never say never).
Anyway, I should end on a positive note: a senior colleague came up to me the other day and said “Who’s responsible for putting things on the n-Lab? I just found it *really* useful.”
Maybe that’s why it’s called a laboratory, and not an encyclopedia!
It grew out of the observationn that some of the half-digested discussion at the nCafe would have a better chance of being more fully developed by moving it to a wiki page.
But I’d be interested in examples of more apalling half-digested entries. Maybe we need to mark more of them with “under construction” or the like.
Here’s my conjecture It satisfies the primary need of people to be useful. When you simply write about something you don’t really know how necessary is what you write — perhaps, if you’re smart, you have a good understanding but it’s still not direct.
On the contrary, when you see somebody asking a question, it’s completely obvious that this person needs an answer. It’s like a direct stimulation of the brain, you’re hardwired to like it.
Urs said:
“Maybe that’s why it’s called a laboratory, and not an encyclopedia!”
Sure. My point wasn’t that you should make it different, my point was that it doesn’t seem to suit the way I am comfortable working at this point in time. (I don’t like working at a computer as much as I like working with pen and paper.)
However, I think there’s definitely some confusion out there with people thinking that it *is* supposed to be an encyclopedia. A natural line of thought would be “It’s a wiki so it must be a pedia.” Of course this thread should be changing that…
If you want to see something half-baked on the nLab, all you need to do is go to “Recently Revised” and find something I write.
I represent the low end of the spectrum of sophistication. My goal is mostly to learn because I know that the material on the n-Lab will be helpful for my own selfish pursuits. I am constantly dropping query boxes on n-Lab pages or asking questions on the n-Forum. I am also one of the Lab Elves. I think I’ve probably read (not necessarily understood) every page on the n-Lab and I often make minor editorial/typographical improvements.
When I write something speculative or tentative on the n-Lab, I try to label it as such clearly at the top of the page. When I want to write down some thoughts that are too speculative even by my standards, I take it to my own personal wikiweb page and try to develop things there (also in the open) with feedback from whoever drops by. Once an idea is developed enough, I often move it to the main n-Lab grid.
As an example, I was trying to cook up a concept of an inner product for sets. I have a lot of doodling on a page on my own wikiweb:
http://ncatlab.org/ericforgy/show/cardinality
After a couple failed attempts, I realized that what I was doing was reinventing multisets. After some more trial and error, I came up with (what is obvious in hindsight) a nice definition for the inner product of multisets, which now resides on the main n-Lab grid at
http://ncatlab.org/nlab/show/inner+product+of+multisets
Currently, I’m trying to generalize Hasse diagrams of prosets to Hasse n-diagrams of n-prosets. I’m trying to work that out on the main n-Lab grid, but should probably move it to my own personal wikiweb until it makes sense. I’m probably just reinventing something anyway.
Between, the n-Cafe, the n-Lab, and the n-Forum, I have learned a LOT. The three pieces of the n-Community provide a very nice trifecta.
PS: My involvement is far from altruistic and is mostly selfish as well, but by representing the low end of the sophistication spectrum, I can’t help think that my questions help others who were probably thinking the same thing, but were afraid or not willing to ask.
When I initially left a comment I seem to have clicked the -Notify me
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