The n-Category Café

I think that you should repost all of the above comments, with their proper threading and attribution, as comments here. Then people will have places to reply to things. Otherwise, this is all far too general for me to think of anything to say!

(Not that I'll have anything to say if you do repost all of the comments, since I already made my comment. But perhaps others will.)

The main problem of the n-lab seems to be the lack of motivating force except altruism. No fun or fame that one can get in the n-café, no academic recognition that one can get while writing papers. This is why I think the main question is to find a process by which selfish mathematicians can “get something” from the n-lab, while at the same time giving some contribution to the community…

There have always been many kinds of mathematical publication: text book, handbook, lecture notes, popular expose, personal letters, …. . Often the best way to learn some mathematics was to get hold of some lecture notes written for physicists! My own preference is for lecture notes that are relatively spontaneous and unpolished. That is the virtue of the this forum. As for personal advantage, please ask my attendant to give that man an obol. No offence intended.

I am sorrily tempted to edit, for instance, the symplectic pages of nLab, but I don’t know how to find time for that.

Toby’s request makes sense to me too.

Tim wrote:

From my point of view, there is another, stronger problem. Whatever I look at on the n-Lab, it’s never of any use to me. What is worse, I cannot conceive of any circumstances in which it would be of use to me. Since, ultimately, the only criterion I can fall back on for whether something that I write will be useful to others is whether it is useful to me, I feel no desire to write anything for the n-Lab—it’s difficult to get up any enthusiasm for writing something that I can’t imagine being useful. In fact, I find it actively unpleasant to go there.

Them’s fightin’ words! :-)

Seriously, those are some awfully strong words, but it might help to follow up on some of them.

I guess, for the sake of making the nLab more inviting, it might help to hear why some people find it “actively unpleasant to go there”. (A Lab enthusiast might react by saying, “well, don’t then” – but it would be better to make this more specific and constructive.) The only specific criticisms I’ve heard are that

1. (At least some of) the articles are half-baked. That is undoubtedly the case, but then it would help to know which ones people think need more time in the oven.
2. The output is visually uninviting (the way the text “splurges across the page” in the words of one critic).

Anything else the matter?

But far more disturbing is

“I cannot conceive of any circumstances in which it would be of use to me.”

Wow!

I have no idea what to make of that. The fact is, there is a lot of insight being packed into some of those pages; maybe you haven’t seen them.

I shouldn’t compare the nLab with Wikipedia directly – we’ve talked about that too – but surely there are many circumstances in which Wikipedia is of use to you? What would prevent someone putting some of the nLab pages to similar use: as a repository of information, in many cases written up by highly informed people who know the relevant literature?

I know for a fact that in some of my comments here, I’ve tried to convey some bits of categorical wisdom, but they get lost under a pile of comments or forgotten and then the same thing will come up again, and I’ll say it again, maybe in slightly different words to see if they’ll stick. I think this is the type of thing that Urs is talking about. While the nLab is imperfect (and still very new and small-scale), I think in time it could be much easier, for some purposes, to find what one is looking for there than here in the Cafe.

Let me give an example. Suppose I google something and the Cafe comes up as a first hit (with a juicy quote from a comment in the thread). Great! But google is unable to direct me to the specific comment with the juice – it only gives me the blog entry, and then I may have to sift through literally hundreds of comments to find the bit I was looking for. The nLab by contrast is much more easily navigable for this sort of thing.

Anyway, as long as people are writing such strong criticisms, they might as well make them constructive. I’m sorry, Tim, but I don’t know to what use I can put your comment, unless you elaborate.

My suggestion to improve nLab: promote people using personal webs. I didn’t even realize that personal webs in nLab existed until the MO/nLab discussion on SBS, but I now have one myself, and am finding it quite useful. At the moment, I’m selfishly keeping it private, but I certainly will start integrating things into nLab eventually.

I think a lot of people are more comfortable with using nLab like a lab notebook if they can do it privately, at least at first. So I say: get people hooked using personal webs, and eventually they’ll move into nLab proper.

Here is an example of how I use the n-Lab.

I am fascinating by Tom and Simon’s work on cardinality of categories and magnitudes of metric spaces. I feel there is something deep there and wish I understood it better. I’ve asked a bunch of questions on the n-Cafe and got lots of answers (here for example). At some point, I begin to feel like I’m dominating the comments (maybe like here! :)) with my questions so I start trying to work things out on my own personal corner of the n-Lab. So I created a page for some notes:

cardinality

That page is a mess. Read it with caution! But it is literally my own open “note book”. I hope someone comes along, reads it, and leaves a comment (Thanks Toby!).

After flailing around for a while on my own personal note book, I came up with something that I thought was suitable for the main n-Lab grid. Hence,

Inner Product of Multisets

When the multisets are just sets, we get an “angle between sets” given by

$$\cos\theta_{X,Y} = \frac{|X\cap Y|}{\sqrt{|X||Y|}}.$$

I may be completely chasing my own tail, but I hope this turns out to be relevant for weighted colimits of Set-valued functors (where the weights are rational).

Now, I am trying to understand how to generate a finite category from a directed graph. This has spawned a long discussion on the nLab at finite category. That discussion spawned several additional discussions on the n-Forum:

• finite category
• computad
• Hasse diagram
• covering relation

Then to round things out, to answer some of Mike’s questions (trying to get me to coherently explain somethings I’m not communicating very clearly yet), I started a new page on my own personal wiki web.

Generating Finite Categories

Once (if ever) something develops there that is suitable for the main n-Lab grid, I will transport it there.

That is a sample of how I use the n-Cafe, n-Lab, and n-Forum together in a totally selfish pursuit of trying to understand something. Once I think I understand something sufficiently enough to share my knowledge, I’ll try to contribute something to the n-Lab.

Is there any way to search for a list of open questions on nlab?

You didn’t copy in the sequence leading to this comment, and it isn’t specifically about “folk wisdom” but rather about doing new research (specifically, who are the authors of work done on the $n$Lab). But it fits better in this thread than in the Schur functors thread.

Authorship is definitely something important to think about. I don’t have nearly as much experience as you do in writing papers, and (so far) none at all with coauthorship disputes, but I can definitely imagine problems arising from $n$Lab collaborations if not approached carefully.

The first possibility that comes to mind is to extend the general principle of “decide early on who is a coauthor and stick to it.” Even though we’re working in a different medium, and more publically, it seems that the same principle could apply. That is, at the beginning of a project, the group of people who are setting out to work on that project “lay claim” to it, saying in effect “We are the coauthors of this project and we are planning to do most of the work on it. Other people are allowed and encouraged to watch and chime in, but such participation conveys no expectation of coauthor credit, only at most a mention in the acknowledgements.” In exceptional circumstances, the authors might decide to offer coauthor credit to someone else who has ended up contributing essential aspects, but no one ever has any right to expect this.

I expect there are other possibilities. The Polymath project is using one pseudonym for the entire collaborative group, but this probably isn’t is the right thing for $n$Lab projects. Other thoughts?

From a personal perspective, when Urs was initially talking about the idea of the nLab, I saw it as a place where I could do “tutorial-style” calculations trying to teach myself about “quasi-free differential graded commutative algebras”. Urs has some tutorial-style notes in a pdf document lying somewhere around on the internet (sadly I can’t find it now), he emailed it to me originally. I was thinking that I would use the nLab as a tutorial, Urs would set some questions like:

“Prove the triple-gismo-Chern-transgression Bianchi identity $dC^i_{jk} \wedge \tau(a_{pq}) = b^r_{st}$”

or

“Calculate the space of maps from the Chevally-Eilenberg-Weil-Cartan-something $L_\infty$ algebra to an arbitrary Lie algebra”.

And then I would try to perform the calculation on the nLab. And then Urs would put in some comment boxes with model solutions, showing me tips and tricks for calculating, avoiding the long-winded methods I used. And maybe others would weigh in with other insights.

So when Urs spoke about the nLab, that’s the way I personally thought I was going to be using it. But then I had to finish my PhD, and then I had to start my new job, and then I got a bit lazy/distracted, and I never got round to that particular thing (I still intend to sometime soon!). Of course, in the meantime the nLab has grown into a big thing, but I haven’t contributed much on the core business of “taking insights from the n-category cafe and putting them onto the nLab” because secretly, I want to keep some of those insights secret, I feel proud of myself for Googling them and sniffing them out of the n-category cafe comment thread, and I feel I’ll be shooting myself in the foot if I deliver them ready-baked as a convenience to the public at large, without getting any credit for it. They represent avenues for further research. One of the troubles for me is that when an insight is in an n-category cafe thread, it is clear to all that this is a personal take on things (not at all established wisdom) by whoever posted that comment. When it is written down in the nLab, it is by definition in a more coherent form, a long way “downstream” from its original appearance as an n-category cafe post, and anyone reading that nLab page is entitled to think that this information is now “well known” and “public knowledge”; ie. he/she feels less of a burden to cite the maker of that nLab page.

I completely agree with Simon’s sentiment that the style of the n-lab is a load of rubbish. My problem is that I have no idea what would make it better because I’m not a graphics designer and have no real feel for what is good design and what is not.

So my first request: could people please tell me of websites that get it right, or at least better than the average. Find me a website that is mathematical (or, at a pinch, scientific) in content where it is actually pleasant to read the mathematical content on the screen.

And as a paranthetical comment, it’s a unknown character wiki! You can muck around with the style without knowing the system password. Just have a look at the page on Frolicher spaces for a simple example.

There are hundreds of brilliant people who would have much to say but don’t, at least not on the internet, I think the most important question is “why is that and how can we change it”?
I have no idea what a good knowledge base should be like, but at least I can tell you where you shouldn’t look:
I earn some extra money as a software developer (currently working for BMW in Munich helping with the software for all these microprocessors that the new model has), you should definitly ignore all big software companies. The knowledge base of IBM is particulary hideous.

I’ve known the $n$-lab since it was just an $(n-1)$-lab … and I’ve watched the $n$-cafe, intermittently, for quite a while longer than that. Both of them are showing all the signs of having reached a critical 2-furcation point in their dynamics, one that I’ve observed many times before in other groups, both large and small.

One path leads toward a self-critical, inquiry-oriented co-lab — the other path leads toward a self-congratulatory country club.

Can you choose wisely, Grace Hopper?

Something like the nLab has to be a good idea for the kind of established material that tended to be repeated over a range of different threads. But even with established material it’s much better to follow the discussions during the construction of a page than come to it when all is done and dusted. It’s like the comparison between attending Bourbaki meetings and reading their works.

The kind of page that has the potential to be very useful is one like completion. There’s much that could still be done there. For example, it’s not clear to me when in the ‘List of completions’ we have examples of enriched category completions: Cauchy completion of a metric space (yes) of a uniform space (no?), Dedekind completion of a linear order (yes for 2-enriched categories?).

So why not head along to the page and add something? If it’s a query, when you’re editing write

+– {: .query}
QUESTION HERE
=–

I’ve just done that now for my query above by adding

+– {: .query}
David: It’s not clear to me when in the ‘List of completions’ we have examples of enriched category completions: Cauchy completion of a metric space (yes) of a uniform space (no?), Dedekind completion of a linear order (yes for 2-enriched categories?).
=–

Simple.

JB: How to more effectively gather, store, and make accessible the folk wisdom that traditionally spread through informal person-to-person conversations?

JB: Other disciplines must be having similar discussions — does anyone know where? It would be good to see them.

The vicissitudes of the phrase transition from dialogical, informal, tacit, $\operatorname{up-close} : \operatorname{person} \to \operatorname{person}$ wisdom to detached, formal, written, abstract information is a subject as old as Socrates. That very problematic was, not too co-incidentally, one of the concerns that Maryanne Wolf addressed in her Proust and the Squid, a book I referred to in an earlier note that somehow got un-written again.

In my own thinking, I have dubbed it the problem of the “formalization arrow”. I can’t recall if I ever wrote that out loud yet, but my co-author and I expressed the basic idea in a paper on “Conceptual Barriers to Integrative Universities”, the initial version of which was presented at a conference on “Re-Organizing Knowledge, Trans-Forming Institutions”. Discussions like that were rampant at the end of the Last Millennium — now that I think back, themes like that have been hot topics of the “contemporary conversation” for as long as I can remember — not quite as far back as Socrates, it just seems that way.

You guys forgot to celebrate the 666th posting, … an occasion lost to address higher kinds of wisdom.

[Note: originally post claimed this was the 999th post at the Café. Then we found 9 of these hadn’t been published, so we’re only on 990. – DC]

I think that there is an issue, which this thread has not previously raised, about different groups of people wanting subtly different things from nLAB

1) Professional Mathematicians
2) Amateurs
3) Students

Thus the publishing/plagiarism issue is very serious for the first group and of least importance for the second.

Similarly the finished/unfinished issue is most serious for the third group and least relevant to the first.

I’m not certain whether this would be of any help. I would very much like to see how n-cat concepts are interconnected at a conceptual level, so I wonder whether it would be possible to run something like this:

http://www.wikimindmap.org/

That is, a “mindmap” over a math wiki like nLab.

I think that would help beginners or those not having time or desire to go into details, but at the same time, since the nLab is a place for notes and ideas, to see the map forming and evolving as you, the experts, are working.

Christine

Telegraphically few comments.

I would not like all pages capitalized. Dictionaries do not do this either.

I see many colleagues saying that it is important to distinguish wikipedia-style from nlab-style. I think it is good and great that we do not have the LIMITATIONS of wikipedia (only conventional, testable, published material etc.), why I still think it is desirable to have also the entries of the wikipedia style within the architecture of nlab; the classical contours are sometimes needed like bones to support the flesh.

I saw from many people that outsiders to the nlab consider it a bit complicated (at first sight who knows what all these beasts are like elves, latest changes, ruby and instiki, and even all that nonstandard math content). So at least it is good to define most ordinary and basic things first in rather conventional way, and than in further paragraphs or in separate entries to do it super-modern style (or in very special circumstances) like via using path integrals and infty-topoi.

I disagree slightly with John that nlab has lack of the noise and social forces which he likes at the cafe. There are querees, latest-changes discussions, corrections by others, and once one is engaged in this the circle of updates, corrections, disagreements and so on, one really feels “to react”. I myself read nlab (even when not writing it) two orders of magnitude more often than cafe, and heard from other people about it more often (and got several letters from unknown people about my edits in nlab, while less for those at cafe).

Finally, I like mathematics and nlab is focused enough on it to fit that liking. Cafe sometimes fits, but sometimes it goes into some lame intellectual exercises of different nature, like entry “Satanist rocketeer puzzle” which I found uninteresting, incomprehensible, off-topic and distracting, I would label it a spam.

The writings of Michael Polanyi — I’m thinking especially of Personal Knowledge, The Tacit Dimension, and the late summation Meaning — have a lot to say about the source and the target of what I’ve dubbed the “formalization arrow”.

Looking around, I see that his ideas have already made an appearance at the Cafe, back at this point.

If I’m not mixing things up too badly in my memory, it was Polanyi who emphasized the concept of overlapping consensus — and the picture he drew of that reminds me so much of the emblematic figure of a manifold that I can’t help thinking he must have been channeling Riemann … or Kant.

I seem to be the opposite of Jamie Vicary. I prefer the posts that do not contain any mathematics, such as this one. I like the ones that discuss issues surrounding mathematics, rather than actual mathematics. I love discussing mathematics in person, which is different.

I have not contributed to the nLab, nor do I wish to write any mathematics on a blog, because I think I should save my writing time for writing papers to publish. Others have said the same in this thread.

In terms of using the nLab, I find it offputting that most of the articles I have read seem to have such a personal bias to their presentation.

In general the online world is a huge time-sink and I have to be careful to limit myself, otherwise I will never get done the twenty thousand milion trillion billion other things I have to do. I quickly become depressed that other people have the time and energy to follow all this online stuff as well as do anything else.