## October 26, 2009

### Math: Folk Wisdom in an Electronic Age

#### Posted by John Baez

With the continued development of the nLab and the Polymath Projects, and the rise of Math Overflow as a competitor to sci.math.research, mathematicians are busy talking about new ways to take advantage of technology. The arXiv is great for papers. Blogs are great for conversations. But how to more effectively gather, store, and make accessible the folk wisdom that traditionally spread through informal person-to-person conversations?

There surely won’t be just one answer to this question. And surely the answers won’t be found just by discussion. We’ll need to grope our way there by trying many different things and seeing what works.

But humans being human, it’s irresistible and probably necessary to talk about this question. Other disciplines must be having similar discussions — does anyone know where? It would be good to see them.

Here on the $n$-Café, conversations keep drifting towards this subject…

… so I’ve taken the liberty of moving some discussion from the Schur Functors thread, where it was a bit of a distraction, to here, where it’s right on topic.

This particular discussion started when Jamie Vicary wrote:

I haven’t really hung around here for a while, I know. I think that’s probably because the kind of posts I really enjoy — the ones which take some pretty fundamental bit of category theory–related mathematics and turn it inside out, until it’s burned into your brain — have become less frequent as the cafe has got older. Maybe this is just because all the possible topics have been covered already! In fact, I sort of got the impression that this change coincided with the instigation of the $n$Lab, which I don’t have the same affection for as I do for this place … but that could all just be in my head. It would be sad if these sorts of fun technical discussion are happening hidden away in $n$Lab comment boxes instead of being chatted about out here in the open.

John Baez replied:

I know it’s not that, because I know dozens more topics that would be great fun to talk about.

One problem is that I’ve spent the last year busily writing papers that were way overdue. Between December 2008 and September 2009 I finished up 475 pages of stuff. This used up all my appetite for writing about math. Luckily that phase of my life over now… but I’m still just gradually recovering. I still feel a kind of pain at the thought of writing about mathematics. And I still have 5 grad students to work with. The situation will probably calm down when I go to Singapore and stop teaching for a year. And I hope it stays calmer.

I also think you’re right that part of the energy has moved over to the $n$Lab. In particular, Urs has almost entirely moved over there. He seems to feel that information here gets ‘buried’ under new layers of blogging, while information there is easier to find. That’s probably true. But I think I prefer talking here. What I like most is to get people excited about things! For this I need a public platform where I can stand in front of a crowd, bellow, and clown around. The $n$Lab is not that.

It sounds like Urs has also been very busy finishing a paper.

I agree, it’s really fun when we take a concept and examine it from various points of view until it’s burned into all our brains. Luckily we have a new team of bloggers at the $n$-Café who are infusing the place with new life.

Todd Trimble also replied to Jamie:

Jamie wrote:

In fact, I sort of got the impression that this change coincided with the instigation of the nLab, which I don’t have the same affection for as I do for this place … but that could all just be in my head. It would be sad if these sorts of fun technical discussion are happening hidden away in nLab comment boxes instead of being chatted about out here in the open.

Aw, but the nLab is open to anyone who wants to come in! We indeed carry on lots of fun technical discussions there.

And, there’s plenty of scope for expanding nLab entries to incorporate all those juicy bits of categorical wisdom.

(The feel is a bit different though. The Cafe is a kind of brightly lit and noisy place, whereas the Lab feels to me a little cooler and not as well lit, as if underground somewhere. Sometimes I like that.)

Urs Schreiber replied to John:

John wrote:

In particular, Urs has almost entirely moved over there. He seems to feel that information here gets ‘buried’ under new layers of blogging, while information there is easier to find. That’s probably true. But I think I prefer talking here.

I also prefer talking here.

Remember the whole idea:

- here on the $n$Café we talk

- whenever we reach some stable insight we archive that on the $n$Lab, so that it doesn’t get lost.

I would like to understand why this simple idea doesn’t resonate with so many regulars here. It seems to me that secretly this is precisely what you all (I really mean you all :-) want but for some reason you don’t see that this is what you want. It’s strange.

Another thing is that I would like to discuss more things here in the Café than I do. But for that I also need reactions. One-way discussions are no fun. Lately I feel that I don’t get any replies here anymore. For whatever reason.

John Baez replied to Urs:

Urs wrote:

I would like to understand why this simple idea doesn’t resonate with so many regulars here.

I can only speak for myself. I think it’s a great idea! However, right now I prefer to spend my limited $n$Café/$n$Lab time talking on the $n$Café rather than writing on the $n$Lab. I’m glad that there are some other regulars, like Todd, who enjoy spending time in the ‘cooler, less brightly lit’ environment of the $n$Lab. But that’s not my thing — at least, not now. Right now, for me, when I want to write, I either want to write This Week’s Finds, or papers that I can publish.

For instance this very entry here. Why do none of you think of it highly enough to produce a coherent version of the information scattered here on the $n$Lab?

I think of it highly enough that I hope to prove my conjecture someday and publish the proof — or get a grad student to do it. I don’t see much personal benefit from putting it on the $n$Lab. But if someone wants to put it on the $n$Lab, that’s fine with me.

I’m mentioning my opinion here not because I’m trying to convince anyone that they’re ‘right’, but merely to get the conversation going. How do other people feel about this stuff?

Todd Trimble replied to John:

But if someone wants to put it on the nLab, that’s fine with me.

That’s a relief, because I just did. :-)

I think Urs makes a good point: there’s a benefit to having some sort of summary of blog discussions, which tend to ramble all over the place, in a place where the essential points can be easily accessed.

On a personal level, I can say that this activity of extracting and condensing and summarizing really forces me to come to grips with what went on in the Cafe, so for me it’s very meaningful activity.

As far as “talking” versus writing goes: I find there’s a fair amount of talk going on in the Lab. The nature of the talk tends to be different: much less discursive or less didactic than in the Cafe, perhaps, but I get a lot out of it. One very interesting thing to me is to observe people like Toby in action down there. He makes a lot of incisive observations here in the Cafe, but somehow the Lab is more his milieu and I’m learning a lot reading things from his POV, which is much more visible in the Lab than here, I find.

I guess you were following the discussions over at Secret Blogging Seminar about Math Overflow and nLab. Ben Webster says he just finds MO a lot more fun, and I guess you’d say the Cafe is a lot more fun. I think too the feeling is that time spent “writing” (as opposed to “talking”) is better spent writing papers, time being so short and all, even though I’m sure Urs would view that as a false dichotomy.

Nevertheless, I hope you in particular will show yourself in the Lab more often and at least make comments there if not writing entries. Are you following what’s going on these days?

Tim Silverman wrote:

(I’ve started the following comment several times over the last few months, and always gave up on it because it seemed negative and kind of whiny, and not at all constructive. But I feel I ought to say something about this. A lot of the comments from n-Lab enthusiasts express a sort of surprise that the whole world isn’t queuing up at their door to buy their better mousetrap, and I feel the need to explain that not everyone is so bothered by mice.)

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.

The fact that other people here do find it useful and are very enthusiastic about it just confirms to me that it is not a case of it doing badly at something I want, but instead is doing well at some purpose quite alien and incomprehensible to me, so that any attempt I might make to contribute would probably only screw things up. When, on a few occasions in the past, I’ve considered contributing to an n-Lab article, I’ve always started by wondering, “So what is the common purpose I’m supposed to be contributing to?” And I find I haven’t the faintest idea. Which makes it difficult to contribute.

Of course, my contributions to the Café are already fairly nugatory, so you may say this is no loss, but I do wonder if some others might feel something similar.

I hope n-Lab enthusiasts won’t feel too offended by these comments. Of course I accept that different people have very different needs and I certainly don’t expect everybody to think the way I do. But conversely, I can’t contribute to everybody else’s project, no matter how much they themselves value it. I can only contribute what makes sense to me.

Urs Schreiber replied to Tim:

Tim wrote:

And I find I haven’t the faintest idea.

It’s so very simple:

From time to time you (especially you) write long and detailed technical comments into this blog here. Apparently with a faint idea of this being useful to somebody, be it yourself.

The very simple idea of the $n$Lab is: whenever you do that, copy some of that to the Lab under a recognizable entry title. This way it will be preserved in a more useful form so that the effort you invested anyway will have been more worthwhile spent

We all wasted so much time and energy in blog discussions here whose good insights are effectively lost and gone and will never be resurrected without going through all the same effort once again. I don’t have the time to do that anymore. That’s why I write stuff into the Lab and keep just the pointers to it here.

Jamie Vicary replied to Urs:

Urs said

We all wasted so much time and energy in blog discussions here whose good insights are effectively lost

I don’t understand that! Type “Schur functor” into Google — this discussion is the top hit! Reading through this discussion as it stands gives a great introduction to the subject.

Of course, if the material were tidied up and presented nicely, it would obviously be easier for people to learn from it. That’s a great use for the $n$Lab, and it’s developing into a fantastic resource. But then what happens is that somebody has a question about the material they read on the $n$Lab, and asks it by putting up one of those comment boxes in the $n$Lab instead of appending to this discussion. Disaster! There are hundreds of people who frequent this blog, half a dozen of whom would probably love to get into a discussion about some aspect of Schur functors, and I would bet you that they’re not monitoring the $n$Lab’s “recent changes” page as closely as they’re monitoring the Cafe’s “recent comments” list.

If you banned the use of the question mark on the $n$Lab, that would make me happy :). People can write things there, but if there’s something they’re not sure about, they should have to write it here!

Toby Bartels also replied to Tim:

Tim wrote:

I’ve always started by wondering, “So what is the common purpose I’m supposed to be contributing to?” And I find I haven’t the faintest idea.

That's OK; neither have we.

So… what do you think, dear reader?

Posted at October 26, 2009 5:48 PM UTC

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### Re: Math: Folk Wisdom in an Electronic Age

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.)

Posted by: Toby Bartels on October 26, 2009 8:18 PM | Permalink | Reply to this

### Re: Math: Folk Wisdom in an Electronic Age

I wrote:

Otherwise, this is all far too general for me to think of anything to say!

But it doesn't seem to have been a problem for others, so never mind!

Posted by: Toby Bartels on October 26, 2009 11:52 PM | Permalink | Reply to this

### Re: Math: Folk Wisdom in an Electronic Age

Toby wrote:

I think that you should repost all of the above comments, with their proper threading and attribution…

I should. Alas, it’s more work than I want to do.

Posted by: John Baez on October 26, 2009 11:52 PM | Permalink | Reply to this

### Re: Math: Folk Wisdom in an Electronic Age

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…

Posted by: yael fregier on October 26, 2009 8:25 PM | Permalink | Reply to this

### Re: Math: Folk Wisdom in an Electronic Age

I think you may have a wrong diagnosis. I would say the problem is that people think that they should do altruistic writing in the nLab, rather than selfish writing.

Posted by: Ben Webster on October 26, 2009 10:09 PM | Permalink | Reply to this

### Re: Math: Folk Wisdom in an Electronic Age

I think this is quite understandable, and we need to keep discussing it here (it’s an active topic at the Lab too).

Altruism is part of it, but for me and I guess some other regular contributors who comment on each other’s work, we also want to be seen as taking care with our work and doing a good job and earning each other’s respect. We know who we are, and many of us work hard at it.

Perhaps the activity of writing in the nLab is attractive only for certain personality types. I’m okay with that. Far more worrisome to me is the fact that some people say not only do they find it unpleasant to look at, they can’t imagine any possible use for it.

Posted by: Todd Trimble on October 26, 2009 10:15 PM | Permalink | Reply to this

### Re: Math: Folk Wisdom in an Electronic Age

You can always create your own personal wiki web and make it read only. That way we can easily reference your material and it is still part of the nLab.

Posted by: Eric Forgy on October 26, 2009 10:58 PM | Permalink | Reply to this

### Re: Math: Folk Wisdom in an Electronic Age

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.

Posted by: Gavin Wraith on October 26, 2009 9:43 PM | Permalink | Reply to this

### Re: Math: Folk Wisdom in an Electronic Age

I’m an occasional observer here, trying to learn your language of maths. I’ve tried to do this by immersion; drop into a foreign language, get seriously confused, pick out the bits you understand from the pattern of conversation, and then check your understanding to other applications. I could not do this without the casualness and elicit conversations and personal relationships of this group, which forms a way in for me.

Posted by: Josh W on October 28, 2009 6:48 PM | Permalink | Reply to this

### Re: Math: Folk Wisdom in an Electronic Age

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

Posted by: Eugene Lerman on October 26, 2009 9:58 PM | Permalink | Reply to this

### Re: Math: Folk Wisdom in an Electronic Age

The same way you find the time to write a technical comment here?

One way of going about it is write your criticism(s) as a comment posted to the nForum. We also have lots of discussions right in the nLab, either in query boxes or directly on the pages. It works pretty much the same way it does here, I find.

We’d like to hear from you!

Posted by: Todd Trimble on October 26, 2009 10:26 PM | Permalink | Reply to this

### Re: Math: Folk Wisdom in an Electronic Age

By the way, “tex” on the nLab is pretty much (if not entirely) identical to the “tex” on the nCafe, but on the nForum, you need double dollar signs.

Posted by: Eric Forgy on October 26, 2009 10:39 PM | Permalink | Reply to this

### Re: Math: Folk Wisdom in an Electronic Age

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.

Posted by: Todd Trimble on October 26, 2009 10:04 PM | Permalink | Reply to this

### Re: Math: Folk Wisdom in an Electronic Age

Todd exclaimed

Them’s fightin’ words! :-)

Yes, and since I don’t want a fight, I didn’t say them for a long time. I don’t want to spoil something that clearly works for a lot of people. At the same time, I feel bad to have people constantly urging me to do something that I’ve tried to do and couldn’t. Also, some others possibly seem to feel the same way as me.

surely there are many circumstances in which Wikipedia is of use to you?

Yes, there are. But people keep saying that the n-Lab shouldn’t be like Wikipedia—which it isn’t! But I’m finding it hard to work out what it should be like.

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 believe you. Since I haven’t been able to extract it, I’m inclined to believe I’m just not the right audience for the n-Lab.

I should unpack the “no conceivable circumstances” remark a bit, though. Some places, I look at some maths (or other information) and think, “Well, I’m not ready to understand that yet/am not really interested in that area at the moment—but I could imagine coming back and benefitting one day.” I don’t get that with the n-Lab. But I don’t exclude the possibility that the n-Lab could mature into something very different, which I found more useful. But I do get the impression that a lot of things would have to change. But I don’t want to positively recommend those changes (even if I can work out what they are) in case that screws things up for other people who are already benefitting, e.g. you.

I’m trying to put together a more constructive and detailed comment at the moment, though I don’t know if I’ll succeed. It’s really got to be a “Why I’m not working on n-Lab” post. I’m not interested in writing “criticism” as such, and particularly not if it comes across to n-Lab enthusiasts as though I’m criticising their beautiful baby. That’s not what this is about. There are all sorts of worthwhile things in the world that are no use to me personally, and quite likely this is one of them.

Posted by: Tim Silverman on October 26, 2009 11:40 PM | Permalink | Reply to this

### Re: Math: Folk Wisdom in an Electronic Age

Okay Todd, as the unnamed critic in your post, I should make some comments. The first thing that I should say is that your metric space nLab entry looks good, it reads good and when I tap it underneath it almost sounds hollow (*).

This should be contrasted with the entry for elliptic cohomology, which I think would count as half-baked. The contents of this page seem to go for ever.

I want to make various comments about the nLab page style, but am too tired to do that in detail, so let me just mention two things. Firstly, I find lots of underlined, green inline hyperlinks to be very distracting: do they need to be green and underlined? (And does a pluralising “s” have to be in a different colour?) Secondly, looking at the Schur functors page, the title of the page does not jump out to me, “Contents” and “Ideas and definition” are far more prominent; all three of these headers are set in via <h1> tags, with the actual title being slightly camouflaged in green.

Too tired to say more now.

(*) That’s one way to test if bread has been baked long enough.

Posted by: Simon Willerton on October 27, 2009 1:15 AM | Permalink | Reply to this

### Re: Math: Folk Wisdom in an Electronic Age

We’ve discussed changing the default stylesheets to make the headers smaller, but seemingly no one has done it. If there are really people for whom this is a serious deterrent, then clearly we should do something about it!

I actually prefer links that are both colored and underlined.

Posted by: Mike Shulman on October 27, 2009 1:42 AM | Permalink | PGP Sig | Reply to this

### Re: Math: Folk Wisdom in an Electronic Age

I actually prefer links that are both colored and underlined. That way I can tell where they begin and end (except over line breaks).

I also like underlined links. I wouldn't mind if they weren't coloured, as long as they're underlined.

I'm old-school. I think that web sites shouldn't bother specifying any style information that isn't somehow relevant to the content. Then we readers and users of the web can tell our browsers to use a stylesheet that makes the entire World Wide Web look the way that we like it, without affecting how anybody else sees it. Then we can all be happy!

Unfortunately, with the web as it is today, there is not much point in designing a stylesheet that makes things look the way that you like it, since just about every web site in the world will override everything in it. You can tell your browser not to let that happen, but then you miss the style changes that are relevant to the content.

Posted by: Toby Bartels on October 28, 2009 8:00 AM | Permalink | Reply to this

### Re: Math: Folk Wisdom in an Electronic Age

Thanks, Simon. This is the kind of feedback that could be very useful. (And sorry if I gave offense by the way I quoted your words – I was not feeling unsympathetic towards them when I wrote them, and I imagine others may feel the same way you do.)

I can see what you mean about the particular article you mentioned; it’s not the kind of article I would spend any time looking at myself. If truth be told, there are a lot of items like that lying around the Lab. I’ve written a number myself, which I need to get back to and clean up. The impression it may leave is that there are a lot of buildings (or mud huts, to use a metaphor of John Baez) lying around in a state of half- or quarter- (or $2^{-n}$-)completion, with a lot of mud and lumber strewn about, while the builders have moved on to another lot. And that’s just not very attractive to the reader. I think that’s fair criticism.

As for the aesthetics of the textual layout: again I’m not unsympathetic. The pluralizing “s” you mention is something I myself create a lot of times, mainly out of laziness (I won’t go into the technical reason this sort of thing gets perpetrated, but my fellow Lab technicians will know the cause), but I’ll keep an eye out for it. I’m not sure what to say about both green and underlined; not knowing anything about the design, I would guess that’s something easily fixed if there’s demand for it (the green is replaced by gray if you’ve clicked on the page in your recent history). I guess you’re saying that color ought to be enough.

The tables of contents thing I haven’t done myself; there’s some sort of automatic generation I think that other people use, and I suppose it could be tweaked. Now that we’re discussing formatting details, I suppose one thing I don’t like much is the lower-case convention in titles, but for some reason that is the convention.

Taken separately, these things might seem little, but little annoyances have a way of accumulating to big ones.

Thanks for taking the time to give specific criticisms; they’re helpful to know.

Posted by: Todd Trimble on October 27, 2009 3:30 AM | Permalink | Reply to this

### Re: Math: Folk Wisdom in an Electronic Age

The impression it may leave is that there are a lot of buildings … lying around in a state of half- or quarter- (or $2^{−n}$-)completion, with a lot of mud and lumber strewn about, while the builders have moved on to another lot. And that’s just not very attractive to the reader. I think that’s fair criticism.

Is there anything we can do about this, though? The $n$Lab is definitely a place for working on half-completed things, and I wouldn’t want to banish them all to personal webs. My initial reaction is that it’s the attitude of the reader that needs modification here. I still feel like people are expecting the $n$Lab to look polished like Wikipedia. What can we do to make people not expect that? Put a big flashing banner at the top of every page saying “The $n$Lab is not Wikipedia”?

Is it worse to have a half-baked page than to have no page at all? The only reason I can think of is that it might waste some of your time reading it until you realize how half-baked it is. Maybe we should have a prominent “read at your own risk” label at the top of half-baked pages?

I suppose one thing I don’t like much is the lower-case convention in titles, but for some reason that is the convention.

I think I know the reason, or at least one reason. When creating an en passant link, it’s much easier to type

a group object in some [[category]] is...


than

a group object in some [[Category|category]] is...


Like the lazy pluralization, I think this is a case of the $n$Lab being optimized for the user rather than the reader.

I always tend to focus on content rather than presentation myself; time is scarce enough without worrying about whether the links have a pleasing color or should be underlined or not. But maybe if this sort of thing matters to a lot of people, we ought to put some more work into it.

Posted by: Mike Shulman on October 27, 2009 5:52 AM | Permalink | PGP Sig | Reply to this

### Re: Math: Folk Wisdom in an Electronic Age

The argument about capitalization is an artifact of the time before we had redirects. Now that we have redirects, we could in principle move every page to a capitalized page and use redirects so that the link

[[category]]

redirects to the page

[[Category]].

If there was interest, I could start the process of migrating things. I’m sure some lab elves would also volunteer to help. It is good to establish some standard now that interest seems to be increasing.

One reason not to do a wholesale movement to capitalized pages yet (which I agree looks better) is that the “Linked From” at the bottom of each page does not yet work with redirects, so for example, all the “Linked From” entries at the bottom of [[category]] would be lost if we redirected to [[Category]]. I HOPE this gets fixed one of these days for multiple reasons. This being one of them.

Posted by: Eric Forgy on October 27, 2009 6:47 AM | Permalink | Reply to this

### Re: Math: Folk Wisdom in an Electronic Age

I’m somewhat floored by the proposal to change the names of all pages to be capitalized. I feel like at some point the lab elves are going to be overworked. Moreover, I like not having to add a redirect every time I want to link to a new page. If people (including me, sometimes) are too lazy to add redirects or use pipe-links even for plurals, I’m scared of telling them to do it for capitalizations, which will affect all pages and links.

If this is really a problem, then I think a better way to deal with it would be to patch instiki so that a page can specify a separate “title display” name from its “actual” name. (I also proposed this way back when we were discussing redirects and page-names containing Unicode.)

Posted by: Mike Shulman on October 27, 2009 7:52 AM | Permalink | PGP Sig | Reply to this

### Re: Math: Folk Wisdom in an Electronic Age

Having the ability to name a page something different than the link to that page would be a neat feature to have, but we’d still need to change the name for all pages we wanted to have changed. The manual labor is the same either way.

The whole point of having lab elves is to make the user’s life easy. If you want to create a page with lower case, go ahead and do it. A lab elf will come by later and rename the page to the correct capitalized version. Voila. If you wanted to create a page and be nice to the lab elves, you could do something like

[[Foo|foo]]

when you create the page. But even that is not necessary. There are enough lab elves to do this for you.

The goal of a lab elf (or at least this one) is to make the users life easier. I don’t even want people to use pipe-links. Just put in a link the way you want. If it doesn’t point to the right place due to something silly like capitalization or singular vs plural, then a lab elf will fix it. You might even be surprised to find that a lab elf has already created the appropriate redirect for you and the link works anyway.

The priority is and always has been to get content on the nLab and clean it later. I’d be happy if everyone just stopped using pipe links AND stopped putting s’s outside links AND stopped worrying about capitalization AND not worry about whether their links work or not. SOMEONE will take care of it for you eventually.

You might be surprised to find that the page you want to link to already HAS a redirect, so there really is no reason for ANYONE TO EVER write a pipe-link like

[[category|categories]]

because

[[categories]]

[[category]].

I say, when you are writing an article, just put the link in a sentence and not worry about whether the link is correct. Just make sure the entire word is in the double brackets. There are many eyes watching the nLab who can easily fix these things for you and many things have already been fixed.

Moral: Do not waste time worrying about getting links to work. Do not use pipe-links and do not put s’s outside of links. Broken links are good. We will fix them with an appropriate redirect. In the end, this will make linking more robust for the entire nLab.

Posted by: Eric Forgy on October 27, 2009 8:19 AM | Permalink | Reply to this

### Re: Math: Folk Wisdom in an Electronic Age

The whole point of having lab elves is to make the user’s life easy. If you want to create a page with lower case, go ahead and do it. A lab elf will come by later and rename the page to the correct capitalized version. Voila.

In my opinion, the reason for having a convention is not to make life easy for the reader, the user, or the elf. The reason is so that one person doesn't link to [[foo]], the next to [[Foo]], and the next to [[foos]], and then later two or three different pages are written. Only then do we make the convention [[foo]] (rather than the others) for the convenience of writers as Mike explained.

Posted by: Toby Bartels on October 28, 2009 7:38 AM | Permalink | Reply to this

### Re: Math: Folk Wisdom in an Electronic Age

I lay the blame for [[]]s squarely on Urs’ shoulders ;) For a while, I was spending a huge amount of time trying to clean up things like spurious [[]]s and [[infinity-something-or-other]]. I even created a page

Note on Formatting

and each time I made such an edit, I would leave a signature at the bottom of the page. However, Urs would leave a trail of formatting fouls faster than I could clean them up, so I eventually gave up :)

I still think a prominent link to something like would be a good idea.

I would highly recommend people to put the “s” inside the square brackets and let the lab elves take care of making sure the correct redirects exist.

Posted by: Eric Forgy on October 27, 2009 5:05 AM | Permalink | Reply to this

### Re: Math: Folk Wisdom in an Electronic Age

I lay the blame for [[]]s squarely on Urs’ shoulders

Actually, I happen to like it better this way.

But if somebody instead puts an “s” inside a link, that won’t me make so upset that I will quit the project.

To me it seems that there are more way more interesting aspects to this than questions of formatting. Makes me sad to see all the formatting discussion here. We should go back to usenet times where everything was ASCII code and people cared about content.

Posted by: Urs Schreiber on October 27, 2009 9:29 AM | Permalink | Reply to this

### Re: Math: Folk Wisdom in an Electronic Age

Urs wrote:

To me it seems that there are more way more interesting aspects to this than questions of formatting. Makes me sad to see all the formatting discussion here.

Me too. There are so many untried things we could do with the internet that it seems a bit unfortunate to focus on whether certain letters in certain websites are green. It’s like Christopher Columbus focusing his attention on which fabric to use on the deck chairs, instead of which direction to sail!

But in reality, Columbus probably did spend hours talking about trivial stuff like this. And if nice fabric on the deck chairs makes people more willing to sail to unknown continents, it’s probably worthwhile.

Later I will try to say more about new things we could try. And Yael Fregier has some interesting things to say, too.

Posted by: John Baez on October 28, 2009 4:15 AM | Permalink | Reply to this

### Re: Math: Folk Wisdom in an Electronic Age

It’s like Christopher Columbus focusing his attention on which fabric to use on the deck chairs, instead of which direction to sail!

But in reality, Columbus probably did spend hours talking about trivial stuff like this. And if nice fabric on the deck chairs makes people more willing to sail to unknown continents, it’s probably worthwhile.

If I were Columbus, I would not take on board anyone who asks about deck chairs. I would take the guy who says: “Your ship has a hole? No prob, we’ll find some fix. I want to see India!”

Luckily the $n$Lab does not quite fit that metaphor.

And indeed, somebody should try to improve the formatting appearance of the $n$Lab. Somebody is a busy guy, though. Somebody should improve a lot of things.

Es gibt nichts Gutes ausser man tut es.

Posted by: Urs Schreiber on October 28, 2009 11:26 AM | Permalink | Reply to this

### Re: Math: Folk Wisdom in an Electronic Age

Although I’m pretty curious what ideas you have in mind, John, I think there are far too many people out there who don’t use ANY of the possibilities of the internet that have already been tried for a couple of years. Any idea why they don’t and how to change that?

Somebody is a busy guy, but that is not the only reason he/she did’nt do the important job:

This is a little story about four people named Everybody, Somebody, Anybody, and Nobody.

There was an important job to be done and Everybody was sure that Somebody would do it.

Anybody could have done it, but Nobody did it.

Somebody got angry about that because it was Everybody’s job.

Everybody thought that Anybody could do it, but Nobody realized that Everybody wouldn’t do it.

It ended up that Everybody blamed Somebody when Nobody did what Anybody could have done.

Posted by: Tim vB on October 28, 2009 12:14 PM | Permalink | Reply to this

### Re: Math: Folk Wisdom in an Electronic Age

Tim vB wrote:

Although I’m pretty curious what ideas you have in mind, John, I think there are far too many people out there who don’t use ANY of the possibilities of the internet that have already been tried for a couple of years. Any idea why they don’t and how to change that?

As they get older, most people become reluctant to spend much time exploring new technologies, especially when they feel quite happy with life as is. This is well-known, and there are lots of plausible reasons for it.

Maybe that’s okay. I don’t really feel a great urge to hasten the widespread use of the new technologies we’re talking about. In fact there can be advantages to letting a smallish number of people try things for a few years and work out the bugs before a large crowd joins in. And I think it’s pretty much inevitable that lots more people will eventually join in. Youngsters seem to do it quite naturally. And as Planck said, “Science progresses funeral by funeral.”

Posted by: John Baez on October 28, 2009 4:35 PM | Permalink | Reply to this

### Re: Math: Folk Wisdom in an Electronic Age

I think I get your point, but “age” was not on my mind at all when I wrote my last post. There are a few reasons that come to my mind why people would not participate in any kind of online activity:
- poverty (cannot afford a computer with internet access),
- education (don’t speak English, not used to read much),
- lack of curiosity,
- unpleasant experiences of any kind with new technologies,
- ugh, age.
None of this applies to the people I had in mind though, except, maybe - sigh - age.
What I had in mind was e.g. experts like to talk to other experts they know and like, maybe they don’t find a place online where they can do that undisturbed? (The conversation could be polished and published later by someone else, like all these books containing letters exchanged by some important historic figures).
Maybe we should think about how to make communication more effective and attractive than thinking about new tools (I get the unpleasant feeling that I just stated the obvious, please feel free to ignore me :-).

Posted by: Tim vB on October 28, 2009 6:36 PM | Permalink | Reply to this

### Re: Math: Folk Wisdom in an Electronic Age

Urs wrote:

If I were Columbus, I would not take on board anyone who asks about deck chairs. I would take the guy who says: “Your ship has a hole? No prob, we’ll find some fix. I want to see India!”

Luckily the nLab does not quite fit that metaphor.

Yes, luckily! If you were Columbus, and this were a ship, you’d make some of us walk the plank!

Here is a quote from Columbus’ diary:

Monday, 6 August. The rudder of the caravel Pinta became loose, being broken or unshipped. It was believed that this happened by the contrivance of Gomez Rascon and Christopher Quintero, who were on board the caravel, because they disliked the voyage. The Admiral says he had found them in an unfavorable disposition before setting out.

So you see, he did have to deal with less than enthusiastic crew members.

Posted by: John Baez on October 28, 2009 4:51 PM | Permalink | Reply to this

### Re: Math: Folk Wisdom in an Electronic Age

I would highly recommend people to put the “s” inside the square brackets and let the lab elves take care of making sure the correct redirects exist.

And I would recommend that people put the s outside the brackets by default. It's better if the lab elves only have to make things pretty than have to make things work in the first place. Of course, if you want to take the trouble to make things pretty yourself, you can; put the s inside the brackets and then make a redirect for it at the target page, or write [[foos|foo]] if the page doesn't exist yet. But if you write [[foos]] when the page doesn't exist yet (or worse, when it does, but has no redirect), then you'll invite people to create the page at the wrong name (or worse, create a duplicate).

All that said, if you don't want to decide whether Eric or I am right, then ignore this and do whatever you want. The worst that will happen is that there will be duplicate pages, and maybe I'll grumble that it's Eric's fault for giving advice that I disagree with, but it's happened before and it can be fixed. So if you want to write something, then write it.

Posted by: Toby Bartels on October 28, 2009 8:06 AM | Permalink | Reply to this

### Re: Math: Folk Wisdom in an Electronic Age

I played around with the stylesheets a bit on my personal web; here is a test page. In particular, I made the top-level headers in the main text a bit smaller than the “page name” header at the top of the page. Is this any better? It could be made even smaller, but then the use of size to distinguish between first-, second-, third-, and fourth-level headers inside the page would be difficult.

On the other hand, size is not really a great way to distinguish different levels of headers anyway. I think a better way would be to use a numbering scheme. So I also took advantage of the counter system used for numbering theorems to automatically number headers (1, 2, …) and subheaders (1.1, 1.2, 2.1, 2.2,…) and so on. (At the moment the number of first-level headers starts at “2” because the Page Name header is also an <h1> tag; probably there would be some way around this but I haven’t figured it out yet.) This would be a bigger change to implement on the main lab, but I think it could improve readability. Thoughts?

Posted by: Mike Shulman on October 27, 2009 6:39 AM | Permalink | PGP Sig | Reply to this

### Re: Math: Folk Wisdom in an Electronic Age

Oops. I didn’t actually mean Todd’s Schur functor page above, I actually meant his metric spaces page. That’s much more appropriately baked! As I pointed out, I was in the process of falling asleep. I’ve fixed it.

Posted by: Simon Willerton on October 27, 2009 9:06 AM | Permalink | Reply to this

### Re: Math: Folk Wisdom in an Electronic Age

Small disclaimer: I don’t consider it my page. I think I might have started the entry (I’d have to track back through the history to be sure), but Toby Bartels played a big role in the creation as well, and if you read through the lines and know of Toby’s preoccupations, you will see the very visible imprint of his hand. In particular, he is often at pains to present material in a way that is CC (constructively correct), and that’s one thing that I’ve come to appreciate more and more as I get to know him through his work at the nLab.

Posted by: Todd Trimble on October 27, 2009 1:44 PM | Permalink | Reply to this

### Re: Math: Folk Wisdom in an Electronic Age

This should be contrasted with the entry for elliptic cohomology, which I think would count as half-baked.

The link you provide is not to the entry on elliptic cohomology, but to the entry A Survey of Elliptic Cohomology which collects, well, pointers to survey material. I find that collection very useful, indeed. There is a table of contents and a summary. I can’t yet see what is bugging you about it. Though i wouldn’t mind if you had an idea for how to prettify the content.

The entry on elliptic cohomology is here. At the moment this just contains notes taken in an introductory talk on elliptic cohomology. I am not sure if “half-baked” is the right word for entries like this one, I would call them “stub”s.

Under a “half-baked” entry I would undrestand for instance hyperstructue. That was lots of fun interactig there with Mike Shulman and others.

Posted by: Urs Schreiber on October 27, 2009 9:12 AM | Permalink | Reply to this

### Re: Math: Folk Wisdom in an Electronic Age

A: let’s work on something together

B: hm

A: see, I brought a notebook, let’s write out what we just said

B: hm

A: okay, I’ll give it a start, here is a note on what I said, here a note on what you said

B: …

A: and then, let’s see, we can maybe connect this here and

B: …

A: ah, let me redo this, so we have this and that

B: …

A: let me see, ah, right, now it works, that makes me think of something else, let me start a new page

B: …

A: hm, cool, did you know that, look what I have drawn here now

B: …

A: ah, interesting, I need to start yet another page

B: …

A: er, what about you? Are we still on this together?

B: me? Let me see what you have… Ah, did you use green color there? Bah, how disgusting. And you have an “s” there is that right? Phew.

A: what, which “s”? You mean this here?

B: yeah, and you keep going on and on and it seems you are not even finished yet.

A: ?!?!

Posted by: Urs Schreiber on October 27, 2009 9:39 AM | Permalink | Reply to this

### Re: Math: Folk Wisdom in an Electronic Age

I agree.

I just wish I had the courage to put all my half-baked (or as someone more accurately put it, $2^{-n}$-baked) ideas on the lab just in case there is someone who would either help me or run off and work the stuff out into the wonderful thing I have partially glimpsed.

More often than not I have questions, sometimes silly, sometimes really gnarly, for experts that here in the wrong corner of the antipodes I do not have access to ;_;

The next comment, to save someone the time will be, I’m sure, ‘Use MO’, but the sort of in-depth discussion I’m after is not suited to such a thing. Maybe I haven’t quite grokked (to borrow a word from JB) this place yet.

Just a little whinge… I think I’ll go and start an nLab page.

Whoops, it’s already there. Back to work then.

Posted by: David Roberts on October 28, 2009 12:20 AM | Permalink | Reply to this

### Re: Math: Folk Wisdom in an Electronic Age

I just wish I had the courage to put all my half-baked (or as someone more accurately put it, $2^{-n}$-baked) ideas on the lab just in case there is someone who would either help me or run off and work the stuff out into the wonderful thing I have partially glimpsed.

That’s a great use for the personal web (which I notice you have). It’s slightly more undercover than the nLab itself, I find. (I have some half-baked stuff of my own on my web.) But people do pop by, and maybe something will come of it!

Anyway, give it a shot. MO could work too, depending on how skillfully crafted the question is, but it might feel more comfortable just to put tentative groping stuff on your own web, and see what happens. As it grows and begins to solidify, it could probably be ported in bits and pieces over to the Lab.

I think we’re all on a learning curve here.

Posted by: Todd Trimble on October 28, 2009 1:25 AM | Permalink | Reply to this

### Re: Math: Folk Wisdom in an Electronic Age

I am sorry, but I need to get back to this one here, which keeps bugging me:

This should be contrasted with the entry for elliptic cohomology, which I think would count as half-baked. The contents of this page seem to go for ever.

Maybe it is worthwhile pointing out that this is one of the $n$Lab pages that I am feeling hugely happy about, because I managed to get a bunch of Berkeley grad students involved in adding stuff there.

This is the entry-point page of a seminar they were and still are running at MPI in Bonn. I took notes of the first few sessions, but then I ran out of time.

It’s so cool that they continued posting notes there themselves. (In particular Ryan Grady did.)

Given that Lurie’s notes that the seminar is about are the best source to date on the constructoin of TMF, and given that this is now the only (and I do think the seminar was and is well done) online available introductory seminar on this stuff, this page and the pages it links to is now – by all accounts – one of the best online sources on ellitpic cohomology and TMF for anyone out there who wants to start learning this stuff.

I really think so, and would have hoped that this admirable effort of those students raises some more paternalistic instincts than just a complaint that – it’s too long. It’s not too long. It’s great.

What it currently is: it is unpolished. These are mainly raw notes taken real-time during a talk. If you feel you need to complain about this page, please also take the time to go through it a bit and do polish it a bit. Others spent time and energy to produce this, everbody who cares should be easily able to hugely profit from it, and so give something back and invest five minutes on such a page to improve it a bit more.

Posted by: Urs Schreiber on October 29, 2009 1:39 AM | Permalink | Reply to this

### Re: Math: Folk Wisdom in an Electronic Age

When I had a visiting appointment at Princeton 1968-69 (before some of you were born! well, at least mathematically),
Steenrod ran what he titled: “A small seminar for half-baked topological ideas” - no completed work was to be presented. It was very inspiring.

Posted by: jim stasheff on November 1, 2009 1:19 AM | Permalink | Reply to this

### Re: Math: Folk Wisdom in an Electronic Age

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.

Posted by: Ben Webster on October 26, 2009 10:19 PM | Permalink | Reply to this

### Re: Math: Folk Wisdom in an Electronic Age

Do I remember correctly that there’s a page which lists personal areas? A list of recent changes to pages in personal areas would certainly be handy.

Posted by: David Corfield on October 26, 2009 10:44 PM | Permalink | Reply to this

### Re: Math: Folk Wisdom in an Electronic Age

Posted by: Ben Webster on October 26, 2009 10:46 PM | Permalink | Reply to this

### Re: Math: Folk Wisdom in an Electronic Age

Here is a list all of nLab “webs” (public and private):

Wiki Webs

If you really wanted an nLab page that you owned with your name on it, simply create it on your own wiki web and provide a link on the main nLab grid. It is all part of the n-Community.

I’m pretty sure most objections about the n-Trifecta (n-Cafe, n-Lab, and n-Forum) can be addressed and are likely based on misunderstandings. It is good to air all complaints here to give us a chance to clarify things.

Posted by: Eric Forgy on October 26, 2009 10:52 PM | Permalink | Reply to this

### Re: Math: Folk Wisdom in an Electronic Age

At the moment, I’m selfishly keeping it private, but I certainly will start integrating things into nLab eventually.

When you write pages with titles like travel plans, I wonder if maybe you're keeping it more private than you intend? As it is, you are the only person who can read it; if you want others to read it (while only you can write it), then you need to edit the web and select the option to Publish it.

(Or possibly you know all that, and I'm just misinterpreting the title of a page that, after all, I cannot read!)

Posted by: Toby Bartels on October 27, 2009 12:02 AM | Permalink | Reply to this

### Re: Math: Folk Wisdom in an Electronic Age

While I certainly wouldn’t object to people reading that page, it’s intended as a to-do list for me and not really structured for other people’s convenience (it includes notes like BUY A PLANE TICKET! and Is this actually happening?).

Posted by: Ben Webster on October 27, 2009 4:27 PM | Permalink | Reply to this

### private webs

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.

I’m curious about the relative attractiveness of a personal web on the nlab versus running a copy of Instiki locally (on your laptop, say).

Of course, for sharing with others, whether with the world at large (on a public web) or with a small number of collaborators (on a private, password-protected, web), you need an Instiki installation on a public webserver. In that case, ncatlab.org is your friend.

But, for a ‘personal notebook’ kinda thing, I would have thought people would prefer one running locally (usable offline, etc).

Posted by: Jacques Distler on October 27, 2009 2:11 AM | Permalink | PGP Sig | Reply to this

### Re: private webs

Ssssh!

You’ll ruin the Grand Plan.

Personal webs are just to get people addicted to the lab book concept. Once they’re hooked, they’ll be clamouring for more and then we supply them with pure, unadulterated n-lab.

Posted by: Andrew Stacey on October 27, 2009 9:58 AM | Permalink | Reply to this

### Re: private webs

Andrew wrote:

Personal webs are just to get people addicted to the lab book concept.

Sure.

I was just wondering how the location of the lab book affected its addictive properties.

Ben filled me in:

I use 3 different computers daily and a 4th one with some regularity, so something that’s trapped on a computer is worthless to me.

When I think about it, that rather much mirrors my own usage.

I have two Instiki installations: one on golem, and one on my laptop. The former is what I use for most of my notebooky stuff. The latter is used mostly for slideshows. When I’m giving a talk, I don’t want to rely on having a working internet connection.

(The installation on my laptop is also used for development and testing — probably not something that would affect you. The installation on golem also provides the Instiki website and the Geometry & String Theory seminar page.)

The reason why the notebooky stuff goes on the public webserver, rather than on my laptop is, indeed, all about availability from anywhere.

I guess that answers my question …

Posted by: Jacques Distler on October 27, 2009 6:07 PM | Permalink | PGP Sig | Reply to this

### Re: private webs

The main reason is convenience; things are already set up on nLab, and I use 3 different computers daily and a 4th one with some regularity, so something that’s trapped on a computer is worthless to me. If I start using my web a lot, I may try to figure out how to keep a local copy.

Posted by: Ben Webster on October 27, 2009 4:24 PM | Permalink | Reply to this

### Re: private webs

so something that’s trapped on a computer is worthless to me.

Yup. LaTeX authoring in the Cloud, one of the cool aspects of the $n$Lab.

Posted by: Urs Schreiber on October 27, 2009 4:47 PM | Permalink | Reply to this

### Usage Example: Finite Category

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:

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.

Posted by: Eric Forgy on October 26, 2009 11:45 PM | Permalink | Reply to this

### Re: Usage Example: Finite Category

Sounds like with your inner product of multisets, you’re getting close to the bag of words kernel, we discussed here. But you’ve normalised the kernel, which is what is often done in practice.

People also weight the kernel if there is reason to think some types of element in the multiset are more important than others.

Posted by: David Corfield on October 27, 2009 11:05 AM | Permalink | Reply to this

### Re: Usage Example: Finite Category

Thank you David. I’ll definitely have a look. I’m having fun with multisets by just thinking of them as vectors and interpreting results in set theoretic terms.

You also provide another usage example. By putting stuff out there for many eyes to see, you get valuable feedback on how what you’re doing relates to other things. I’d never get that feedback otherwise. Thanks!

Posted by: Eric Forgy on October 27, 2009 5:45 PM | Permalink | Reply to this

### Re: Math: Folk Wisdom in an Electronic Age

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

Posted by: Mike Stay on October 27, 2009 12:50 AM | Permalink | Reply to this

### Re: Math: Folk Wisdom in an Electronic Age

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

Not directly. We have a page request for help, but that was only ever used by one person, who had his questions answered long ago, so it's been retired. (Although people could start using it again if they wanted to, I supppose.)

Open questions can often be spotted in the distinctive green guise of query boxes, although most of these are not open questions mathematically. You could find these systematically with a grep through a download of the source; I forget the proper way to get that these days.

So basically, no, at least not conveniently.

Posted by: Toby Bartels on October 28, 2009 8:26 AM | Permalink | Reply to this

### coauthorship

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?

Posted by: Mike Shulman on October 27, 2009 12:51 AM | Permalink | PGP Sig | Reply to this

### Re: coauthorship

That sounds like a good idea. I don’t think such a policy should necessarily be enforced on an n-Lab-wide scale, but could be enforced on a case by case basis with a clear notice at the top of any page stating precisely what you said, e.g. stating the coauthors clearly and that any other contributor is welcome but should not expect to be a coauthor, etc.

Posted by: Eric Forgy on October 27, 2009 4:21 AM | Permalink | Reply to this

### Re: coauthorship

One of the earliest discussions on the n-lab was on this topic: authorship

Posted by: Andrew Stacey on October 27, 2009 9:36 AM | Permalink | Reply to this

### Re: Math: Folk Wisdom in an Electronic Age

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.

Posted by: Bruce Bartlett on October 27, 2009 10:04 AM | Permalink | Reply to this

### Re: Math: Folk Wisdom in an Electronic Age

without getting any credit for it.

Bruce, please: put a standout box saying: the following is something that Bruce Bartlett thought up.

If fact, we urge you to do that. Entries are supposed to clearly indicate which bits are standard, which are new.

I have a lot of original research in nLab entries that will eventually go in some publication of mine, which is flagged as being precisely that:

for instance

- here I give my proof that the Moore complex functor from cosimplicial algebras to dg-algebras is lax monoidal

- here I demonstrate that the simplicial deRham complex has a nice simple interpretation using synthetic forms

- here I construct the internal fundamental geometric $\infty$-groupoid induced from an interval object (hm, it seems I forgot to flag that one as being my idea, but I suspect that it is well known to somebody else anyway… )

And so on.

And concerning secret insights: if it’s really secret than don’t put it on the $n$Lab, but put it in your personal read-protected web.

It’s all so very simple, isn’t it?

(I am really wondering: isn’t it?)

Posted by: Urs Schreiber on October 27, 2009 10:46 AM | Permalink | Reply to this

### Re: Math: Folk Wisdom in an Electronic Age

Not to mention that each entry history records all authors and their precise contributions anyway.

So if you are after quickly collecting credits for bits of insight, you are better off putting them into the Lab then hiding them away in your paper notebook.

If you are being scooped, the nLab entry with its specific revision number page is something you can in fact point to. Your private notebook is not.

Posted by: Urs Schreiber on October 27, 2009 10:56 AM | Permalink | Reply to this

### Re: Math: Folk Wisdom in an Electronic Age

Okay, maybe I’ll start putting some of my ‘secret insights’ on the $n$Lab and flagging them as mine. I hadn’t known that was something you’re already doing.

I agree that it’s good to make such ‘secrets’ public early, instead of stewing around fearing that someone else will guess them. This is one good thing about the arXiv, but the $n$Lab is better when it comes to sketchy initial work.

Maybe I’ll start by working with Todd on that Schur functor conjecture.

Okay, I just did a little bit. Not much, because mainly today I’m trying to write This Week’s Finds!

Posted by: John Baez on October 27, 2009 10:24 PM | Permalink | Reply to this

### Re: Math: Folk Wisdom in an Electronic Age

Okay, maybe I’ll start putting some of my ‘secret insights’ on the $n$Lab and flagging them as mine.

Cool. I am sure as soon as you’ll start doing it people will talk about “Baez’s wiki” just as they talk about “Baez’s blog” here and will embrace it.

(That may sound funny, but I am being serious. That would be a good thing.)

Posted by: Urs Schreiber on October 28, 2009 11:36 AM | Permalink | Reply to this

### Re: Math: Folk Wisdom in an Electronic Age

I was thinking that I would use the nLab as a tutorial, Urs would set some questions […] 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.

It would be neat to see stuff like this on the Lab. I did write an exercise somewhere (near the bottom), since it seemed to fit, although I also wrote the answer. This is more directly interactive, and you really need at least two people (Urs and Bruce, in this case) working together to make it happen. But if two people want to do that on the Lab, why not?

Posted by: Toby Bartels on October 28, 2009 8:14 AM | Permalink | Reply to this

### Re: Math: Folk Wisdom in an Electronic Age

So when Urs spoke about the $n$Lab, 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!).

I am still interested in interacting with you. Am hoping we will collaborate on the $n$Lab on something for about a year now. Just a little bit of exchange would already be welcome.

It would for instance be nice if you replied on the nForum to the long replied I posted in reaction to your nLab entry on Chern-Simons theory. I was so happy when you created that page and a little later Ben Webster started knot invariant, almost as if a reaction to that. But then I never heard anything back from you.

Posted by: Urs Schreiber on October 28, 2009 11:44 AM | Permalink | Reply to this

### Re: Math: Folk Wisdom in an Electronic Age

While I am totally sympathetic to the argument that you have other things to do, I think trying to keep insights about your research secret is a very perverse way of going about things. The hard thing to do in math is not to do things before other people, but rather to get them to pay attention to what you’ve done, and get them to understand why its important, so you want to present things at as high a level of bakedness as possible.

Posted by: Ben Webster on October 28, 2009 4:47 PM | Permalink | Reply to this

### n-Lab Style

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.

Posted by: Andrew Stacey on October 27, 2009 10:30 AM | Permalink | Reply to this

### Re: n-Lab Style

AS: 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.

I think the gang at ProofWiki have done an admirable job of adapting and redecorating the underlying MediaWiki framework.

Posted by: Jon Awbrey on October 27, 2009 11:44 AM | Permalink | Reply to this

### Re: n-Lab Style

Ack! My eyes!

I must disagree with you about the design of ProofWiki. It’s too bright, too busy, and screams “Don’t take us seriously.”

Posted by: Ben Webster on October 27, 2009 4:36 PM | Permalink | Reply to this

### Re: n-Lab Style

$Hm^3$, you would love the color we painted our house…

The only other model that comes to mind right off — but it’s more about function than form — would be Sloanes’s Online Encyclopedia of Integer Sequences (OEIS) with its outrigger SeqFan List. It’s one of the oldest math co-labs I know of, predating the Web by a decade at least, and it does have a lot to do with maintaining a treasure-trove of folklore that you just can’t find in one place anywhere else. Sloane has just this week transferred his OEIS IP to the auspices of an independent foundation, and the whole OEIS-Works is in the process of shifting paradigms to a MediaWiki platform under the name of “OeisWiki”.

Posted by: Jon Awbrey on October 28, 2009 4:36 AM | Permalink | Reply to this

### Re: n-Lab Style

I’m going through the hundreds of RSS feeds this morning and saw JA’s response before your comment and the example I was going to give was YOUR page on Froelicher spaces. :)

I think that is an awesome example of nice mathematics on the web.

Posted by: Eric Forgy on October 27, 2009 5:34 PM | Permalink | Reply to this

### Re: Math: Folk Wisdom in an Electronic Age

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.

Posted by: Tim vB on October 27, 2009 11:01 AM | Permalink | Reply to this

### Re: Math : Folk Wisdom in an Electronic Age

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?

Posted by: Jon Awbrey on October 27, 2009 11:26 AM | Permalink | Reply to this

### Re: Math: Folk Wisdom in an Electronic Age

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.

Posted by: David Corfield on October 27, 2009 11:28 AM | Permalink | Reply to this

### Re: Math Folk Wisdom in an Electronic Age

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.

Posted by: Jon Awbrey on October 27, 2009 1:20 PM | Permalink | Reply to this

### Re: Math: Folk Wisdom in an Electronic Age

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]

Posted by: bob on October 27, 2009 2:32 PM | Permalink | Reply to this

### Re: Math Folk Wisdom in an Electronic Age

If you turn your computer $\uparrow \mathop{side} \downarrow$

Posted by: Jon Awbrey on October 27, 2009 2:40 PM | Permalink | Reply to this

### Re: Math: Folk Wisdom in an Electronic Age

As ‘DC’ points out, we were a bit premature about announcing the 999th post. That’s actually good: it gives us more time to buy champagne and confetti.

Posted by: John Baez on October 27, 2009 8:47 PM | Permalink | Reply to this

### Re: Math: Folk Wisdom in an Electronic Age

Will you post some of the champagne so we can download our share?

Posted by: Tim vB on October 28, 2009 10:05 AM | Permalink | Reply to this

### Re: Math: Folk Wisdom in an Electronic Age

No, you have to come to the actual café.

(Maybe you didn’t know this, but there’s an actual $n$-Category Café where us regular members spend most of our days sipping coffee and working on our laptops. That’s how we post so much!)

Posted by: John Baez on October 28, 2009 5:12 PM | Permalink | Reply to this

### Re: Math: Folk Wisdom in an Electronic Age

Sorry, can’t do that. As you all know there are several metrics on earth compatible with the well known topology, e.g. space, time and money. If I travel the time-geodesic to California I’ll run out of money somwhere above the Atlantic, if I take the money-geodesic the event of the 999th post becomes space-like separated from my current position (meaning I’ll be much much too late), and in order to take the space-geodesic I’d have to fly my own plane, because none of the commercial airlines does that. I could try to apply some arbitrary diffeomorphism, but I gather from your knowledge of GR that you probably built the n-cafe in a covariant way.

Posted by: Tim vB on October 29, 2009 7:29 AM | Permalink | Reply to this

### Re: Math: Folk Wisdom in an Electronic Age

Maybe you didn’t know this, but there’s an actual n-Category Café where us regular members spend most of our days sipping coffee and working on our laptops.

Did I ever tell you about how two years ago or so a package was delivered to the Hamburg math department that said “To the $n$-Category Café” on its address sticker?

I had meant to scan that address sticker in and show you all. But now it seems I lost it…

Posted by: Urs Schreiber on October 28, 2009 6:19 PM | Permalink | Reply to this

### Inklings @ The Eagle and Child; Re: Math: Folk Wisdom in an Electronic Age

This would be the Math/Physics/CS foundational equivalent of The Eagle and Child, familiarly and alliteratively known in the Oxford community as The Bird and Baby, or simply The Bird. Later pub meetings were at The Lamb and Flag across the street, and in earlier years the Inklings (Owen Barfield, C. S. Lewis, J. R. R. Tolkien, and Charles Williams) also met irregularly in yet other pubs, but The Eagle and Child is the best known.

“The Inklings was an informal literary discussion group associated with the University of Oxford, England, for nearly two decades between the early 1930s and late 1949.[1] Its more regular members (many of them academics at the University) included J. R. R. “Tollers” Tolkien, C. S. “Jack” Lewis, Owen Barfield, Charles Williams, Christopher Tolkien (J. R. R. Tolkien’s son), Warren “Warnie” Lewis (C. S. Lewis’s elder brother), Roger Lancelyn Green, Adam Fox, Hugo Dyson, R. A. “Humphrey” Havard, J. A. W. Bennett, Lord David Cecil, and Nevill Coghill. Other less frequent attenders at their meetings included Percy Bates, Charles Leslie Wrenn, Colin Hardie, James Dundas-Grant, Jon Fromke, John Wain, R. B. McCallum, Gervase Mathew, and C. E. Stevens. The author E. R. Eddison also met the group at the invitation of C. S. Lewis.”

Posted by: Jonathan Vos Post on October 28, 2009 6:38 PM | Permalink | Reply to this

### Re: Math: Folk Wisdom in an Electronic Age

Urs wrote:

Did I ever tell you about how two years ago or so a package was delivered to the Hamburg math department that said “To the n-Category Café” on its address sticker?

No, you didn’t. That’s cute! And it wasn’t a joke?

Before the $n$-Category Café was built, I spent a lot of time on the newsgroup sci.physics.research, known affectionately as “spr”. So I was very pleased when in Beijing I discovered there was a café called “SPR Coffee”.

Posted by: John Baez on October 28, 2009 9:29 PM | Permalink | Reply to this

### Re: Math: Folk Wisdom in an Electronic Age

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.

Posted by: Roger Witte on October 28, 2009 2:02 PM | Permalink | Reply to this

### Re: Math: Folk Wisdom in an Electronic Age

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

Posted by: Christine Dantas on October 28, 2009 8:03 PM | Permalink | Reply to this

### Re: Math: Folk Wisdom in an Electronic Age

E.g., try WikiMindMap relativity over wikipedia (english) and expand.

Posted by: Christine Dantas on October 28, 2009 8:09 PM | Permalink | Reply to this

### Re: Math: Folk Wisdom in an Electronic Age

That’s hilarious! I just tried it with subject “mathematics” and got back “undefined”.

Seriously, that is something I’d like to do; we mentioned it briefly in this discussion over at the forum.

I have the technology, just haven’t the time right now - ask me again next week when I’ve given this talk.

Posted by: Andrew Stacey on October 29, 2009 9:26 AM | Permalink | Reply to this

### Re: Math: Folk Wisdom in an Electronic Age

I have just sent them an email reporting the bug.

Posted by: Christine Dantas on October 29, 2009 11:50 AM | Permalink | Reply to this

### Re: Math: Folk Wisdom in an Electronic Age

Spoilsport!

Posted by: Andrew Stacey on October 29, 2009 2:15 PM | Permalink | Reply to this

### Re: Math: Folk Wisdom in an Electronic Age

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.

Posted by: Zoran Skoda on October 28, 2009 10:30 PM | Permalink | Reply to this

### Re: Math: Folk Wisdom in an Electronic Age

It probably reflects my age or else my years of editorial servitude but the hyperlinked navigability of the n-lab is for me a _dis_advantage. I never knwo whether I need to follow a link (especially for a term I think I understand but seems to be using in an unfamilair way) or whether follwoing the link is a distraction.

Posted by: jim stasheff on October 29, 2009 2:51 PM | Permalink | Reply to this

### Re: Math: Folk Wisdom in an Electronic Age

It probably reflects my age or else my years of editorial servitude but the hyperlinked navigability of the n-lab is for me a _dis_advantage. I never knwo whether I need to follow a link (especially for a term I think I understand but seems to be using in an unfamilair way) or whether follwoing the link is a distraction.

I’d say the way the hyperlinkage works is very traditional: just as in any printed traditional lexicon every term that has an entry of its own is marked as such.

It is true though that we tend to emphasize some maybe unfamiliar higher categorical aspects. But that’s part of the point of having the $n$Lab.

Posted by: Urs Schreiber on October 29, 2009 4:21 PM | Permalink | Reply to this

### Re: Math: Folk Wisdom in an Electronic Age

I guess my linear thinking is also an obstacle to communication. e.g. I don’t usually read an article with a lexicon handy!

Posted by: jim stasheff on October 29, 2009 8:00 PM | Permalink | Reply to this

### Re: Math: Folk Wisdom in an Electronic Age

How do you like the hyperlinks in the articles of the Online Encyclopedia of Mathematics? Isn’t that similar? Would you want to remove these, too?

Posted by: Urs Schreiber on October 29, 2009 9:56 PM | Permalink | Reply to this

### Re: Math: Folk Wisdom in an Electronic Age

Curious! In the one article HPT which I looked at, I didn’t find them distracting, but i also didn’t see them as necessarily hyperlinks, rather just as emphasized concepts. Something about the layout on the page?

Posted by: jim stasheff on November 1, 2009 1:25 AM | Permalink | Reply to this

### Re: Math: Folk Wisdom in an Electronic Age

The cafe is acting up just now, It won’t let me complete a search for ‘BV theory’ so that I could reply to let y’all know that I’ve messed with the entry over at the lab, a reminder that some stuff there is only slightly more baked than here at the cafe.

It would be good for those of us who spend more time here to let us know when there’s been a significant addition or change over there.

Posted by: jim stasheff on November 1, 2009 1:31 AM | Permalink | Reply to this

### Re: Math: Folk Wisdom in an Electronic Age

Jim wrote in part:

The cafe is acting up just now, It won’t let me complete a search […]

I don't even bother using the Café's search function anymore, I just use Google and add site:golem.ph.utexas.edu to the search terms (although this picks up the String Theory Coffee Table too).

It would be good for those of us who spend more time here to let us know when there’s been a significant addition or change over there [at the Lab].

Significant additions or changes to the Lab should be logged here.

Posted by: Toby Bartels on November 1, 2009 5:42 PM | Permalink | Reply to this

### Re: Math: Folk Wisdom in an Electronic Age

But I’m never there
well, hardly ever
shame on me but life’s too short

Posted by: jim stasheff on November 1, 2009 9:13 PM | Permalink | Reply to this

### Re: Math Folk Wisdom in an Electronic Age

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.

Posted by: Jon Awbrey on October 29, 2009 12:56 PM | Permalink | Reply to this

### Re: Math: Folk Wisdom in an Electronic Age

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.

Posted by: Eugenia Cheng on November 28, 2009 5:23 PM | Permalink | Reply to this

### Re: Math: Folk Wisdom in an Electronic Age

Eugenia wrote:

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.

According to Urs, this is okay, because we should all be using the nLab as our own personal “lab book that we happen to keep lying around openly”.

Ben Webster replied by saying that he’s never used a notebook. I know you do use a notebook… but I can imagine all sorts of reasons why you might not want to use the nLab as your notebook. And a bunch of these reasons apply to me, too.

For one, it’s hard to quickly draw pictures on the nLab. For another, my notebooks are chaotic and disorganized, and utterly incomprehensible to anyone but me.

Jim Dolan has switched from using paper notebooks to using a tablet PC with software that lets you draw, scribble and also type. But nobody could read his notebooks except him — at least, not without special training.

I just realized another reason why I don’t use the nLab as a notebook. I do like to explain things clearly enough that other people can understand them… and I do like to do it in ways that don’t become published papers… but when I do, it’s This Week’s Finds!

I might someday start using the nLab a lot more; I’m not trying to dig in my heels here. I’m just trying to understand why I’m not tempted to yet. I sometimes feel I should, but that’s not the same as wanting to.

On the other hand, I sort of like the idea of using the nLab as a kind of adjunct to This Week’s Finds, to present ideas more formally than I do there. For example, this.

Posted by: John Baez on November 28, 2009 10:53 PM | Permalink | Reply to this

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