December 31, 2008

Organizing the Pages at nLab

Posted by David Corfield

An e-mail discussion migrated to the General Discussion page at nLab , where Urs sensibly suggested it should migrate further here.

John says: In email, David Corfield asked: “I wonder how we can encourage different levels of explanation. A few slick comments gets a concept across to an expert, while more is needed for the non-expert. Might there be parallel pages for the same entry?”

Urs replied: “At least on some entries we already tried to offer different level of explanations. A couple of entries start with a section ‘Idea’ that offers some heuristic ways to tink about the concept. Then comes the formal ‘Definition’ and then after that some helpful ‘Remarks’ etc. I’d think this kind of approach can be used to provide information of use for a wide range of readers.”

John replied: “Multiple pages are a bit awkward… Wikipedia does fairly well at this with just one page, and we can do even better, just by starting with easy stuff and working our way up to harder stuff.

Urs has described how some pages, and eventually all, will have several sections. However, Urs seems to like focusing on high-level folks, while I focus on low-level folks. So, ultimately, it won’t be enough to have just one section called “The Idea”. What “the idea” is depends on how much you know. So, ultimately, the page should start with a very low-level description of the idea, and later move on to more and more sophisticated versions.

This will take a while to develop. I haven’t really begun to invest any serious energy in the nLab, since I’ve been busy finishing papers.

So, for example, my entry on rings beginning with “a ring is a monoid in Ab” was just a cold splash of water meant to wake up people who aren’t used to category theory. A more sane entry would remind people of the usual definition and then explain how it can be compressed this way. But this would take longer to write.

I’m even imagining a fiendish plan where I force my grad students to write nLab articles on topics they’re learning about. Not sure that’s a good idea.

I’m gonna post this on the nLab general discussion page - that’s where this conversation should really be occuring.”

By the way, this General Discussion page needs a table of contents, with links, for people to find information on different topics. It’s sprawling out of control. It’s also possible we should use other pages for talking about specific math topics like Algebroids or Globular Identities. Maybe we need a Math Discussion page and a Physics Discussion page?

Urs says: I was going to address this, too: this discussion page here does not work well. It is hard to see where the last contribution is.

But there is an obvious answer: we want discussion on the blog, don’t we? The blog is designed to allow discussion, the wiki to allow incremental collaborative work. We should have our “general discussion” on the nLab over at the nCafe. The additional advantage would be that everybody reading the blog will always be alerted of the discussion which we are having here.

Eric says: Oh oh! I like the idea of moving the “General Discussion” to the nCafe. That makes a lot of sense. “There to chat, here to work.” If something in the General Discussion becomes elevated to actual content, we can always add that content to the nLab, where it will be indexed, etc.

As far as the level of discussion, my opinion is that we should avoid duplicating “standard” definitions as much as possible (especially material that is already on wikipedia) and take this opportunity to present everything arrow theoretically. I almost think of it as a challenge to define every item via diagrams with as few words as possible.

Now that I think of it, there already is an nLab article on the nCafe which is suitable as a General Discussion and some questions I asked here should have probably been asked there. Sorry about that. This page could serve as a summary of anything there worth keeping.

Now I say: When John says “the page should start with a very low-level description of the idea, and later move on to more and more sophisticated versions”, it’s worth observing that in his exposition he often starts with a condensed sentence or slogan, then utters an archaic oath, and then unpacks it for us. The condensed sentence first might be best for nLab, so that those in the know don’t have to wade through the whole article.

Posted at December 31, 2008 8:42 AM UTC

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Re: Organizing the Pages at nLab

A general comment, before I reply to some details:

It is good to see this discussion about how to proceed with the $n$Lab.

To be frank, it would be even better to just proceed!

One alternative to pondering whether or not some entry should start with a catchy slogan is: just add the slogan if you think it is useful.

Everything on the $n$Lab currently, the total structure as well as every existing entry, is suboptimal. Some more, some less. The task is to improve – incrementally. Add something here, somethimg there. If you are annoyed by how somebody explained something, add your own explanation. This can be done without disrupting what is already there: add a new headline: “Alternative Explanation”, “Easy Explanation”, “Rough Idea”. Conversely, if you are annoyed by how imprecise a given entry is, add a section “Now the true story” and fill in all the details that are missing.

Posted by: Urs Schreiber on December 31, 2008 11:39 AM | Permalink | Reply to this

Re: Organizing the Pages at nLab

I like the idea of *adding* new headlines:Alternative Explanation, “Easy Explanation, “Rough Idea
but please then have a toc

as to

As far as the level of discussion, my opinion is that we should avoid duplicating “standard” definitions as much as possible (especially material that is already on wikipedia)

ONLY with a link to the relevant wiki or other source

and take this opportunity to present everything arrow theoretically.

for some of us, that’s a bridge to far
unless you mean in addtion to verbal alternatives

Posted by: jim stasheff on December 31, 2008 1:06 PM | Permalink | Reply to this

Re: Organizing the Pages at nLab

I’d like to second the idea of at least providing a link for terms deemed to be more or less standard. There are a number of spots – I think the entry on enriched categories may be one – where in effect the reader is told “you figure it out!”, which I strongly disfavor if left merely at that. The answer should at least be in the back of the book, as it were.

For really standard terms, like “vector space”, I see no harm in taking opportunities to redefine them arrow-theoretically, with no need to link to the supposedly more standard definition. Speaking as a hardcore category theorist, I think this would be good for its own sake, but minimally it would help make some discussions at the Café a whole lot less baffling, if done thoughtfully.

Posted by: Todd Trimble on December 31, 2008 2:40 PM | Permalink | Reply to this

Re: Organizing the Pages at nLab

in effect the reader is told “you figure it out!”, which I strongly disfavor if left merely at that.

It’s certainly not supposed to be left at that. If the day had 240 hours I would already have tried to fill in many more places where we have loose ends. I am sure the same is true for John and David.

I am hoping that readers who strongly disfavor the state that certain entries are in will feel motivated to improve on the situation! :-)

Posted by: Urs Schreiber on December 31, 2008 3:01 PM | Permalink | Reply to this

Re: Organizing the Pages at nLab

I second the motion to just improve something if you don’t like what you see. I also don’t think that worrying about format should slow down the production of content. Like suggestions above, you can always add “What it Really Means” headings with alternative explanations. The more people that contribute content, the better it will become. People like me who are very interested, but not able to contribute much in terms of content, should be more than happy to contribute by tidying things up. I’m happy to go through pages and make cosmetic changes to free the experts up to just increase the intellectual content.

Posted by: Eric on December 31, 2008 5:08 PM | Permalink | Reply to this

Re: Organizing the Pages at nLab

Todd writes:

There are a number of spots – I think the entry on enriched categories may be one – where in effect the reader is told “you figure it out!”, which I strongly disfavor if left merely at that.

Of course. I write this sort of thing when I want the reader who knows what’s going on — like you, Todd! — to get annoyed and improve the article. If not, I’ll have to fix the darned thing myself someday.

We want a gleaming city full of skyscrapers; right now we have a bunch of mud huts. But you’ll see: someday we’ll have that city. The yearning for perfection should not slow the march to betterment.

The key is to keep typing. Sometimes people ask me “How do you write so much?” And I answer by holding out my hands, palms down, and wiggling my fingers.

But: we need more people to help! Anyone who knows something about categories, $n$-categories, homotopy theory, operads, or anything like that — spend 5 minutes at the nLab today! Start or improve an article! Please!

Posted by: John Baez on December 31, 2008 6:10 PM | Permalink | Reply to this

Re: Organizing the Pages at nLab

Thanks for clarifying! My complaint was written before I saw how that particular entry had been updated, but I thought I had seen a number of entries like that and I mistakenly interpreted the “left to the reader” as “exercise for the reader”. Since I knew how to do that exercise, and you knew I knew, I didn’t realize I was “it”! Just me being dumb. :-)

The message I keep getting [addressed to me personally] is to get off my butt and start typing! (Well, normally I type while seated, but you know what I mean.) Which I’m starting to do, you know. More will come.

Posted by: Todd Trimble on December 31, 2008 7:09 PM | Permalink | Reply to this

Re: Organizing the Pages at nLab

Yes, it would be good if the wiki software could automatically create a table of contents from the headlines given, as happens on Wikipedia. I don’t know how hard it would be to get that. Jacques will certainly know more.

Posted by: Urs Schreiber on December 31, 2008 2:57 PM | Permalink | Reply to this

Re: Organizing the Pages at nLab

“take this opportunity to present everything arrow theoretically.”

why not clicable diagrams, with the translation “in words” appearing after a click?

Posted by: yael on January 2, 2009 9:30 PM | Permalink | Reply to this

Re: Organizing the Pages at nLab

By the way, this General Discussion page needs a table of contents, with links, for people to find information on different topics. It’s sprawling out of control.

Much of the discussion there is no longer active; it could be moved to an archive page, or even removed altogether. (It's always in the history if anybody really needs it, but archives are better if you want it accessible.)

It is hard to see where the last contribution is.

Hit ‘See changes’ at the bottom.

Posted by: Toby Bartels on December 31, 2008 5:38 PM | Permalink | Reply to this

Re: Organizing the Pages at nLab

It is hard to see where the last contribution is.

Hit ‘See changes’ at the bottom.

Yes, but that’s still inconvenient. For instance, this will alert me only of the last change made, not any changes in between that I might have missed.

I think: a Wiki is not a discussion forum. If possible, we should have “GeneralDiscussion” about the $n$Lab here on the blog.

We should maybe create a general-purpose blog entry “General $n$Lab-Discussion” here on the blog, similar in purpose to the entry “TeXnical issues”, and link to that from the $n$Lab, instead of the the current “GeneralDiscussion” page.

Posted by: Urs Schreiber on January 2, 2009 1:59 PM | Permalink | Reply to this

Re: Organizing the Pages at nLab

It is hard to see where the last contribution is.

Hit ‘See changes’ at the bottom.

Yes, but that’s still inconvenient. For instance, this will alert me only of the last change made, not any changes in between that I might have missed.

Hit ‘Back in time’ next (repeatedly, until you've gone back far enough —the time stamps can help here— or it disappears).

I agree that it's inconvenient, and that discussion works better here. But I want people to know that it is possible, especially as some discussion continues to happen there.

Posted by: Toby Bartels on January 3, 2009 5:07 AM | Permalink | Reply to this

Re: Organizing the Pages at nLab

I have now written a bit in the entry

$n$Lab:About

on “What the $n$Lab is and what it is not.” Trying to provide helpful hints on some of the issues which we discussed above.

Posted by: Urs Schreiber on January 2, 2009 1:55 PM | Permalink | Reply to this
Read the post nLab -- General Discussion
Weblog: The n-Category Café
Excerpt: A place for general discussion concerning the nLab.
Tracked: January 4, 2009 1:10 PM

contributing to the nLab

John wrote (by email, as quoted by David in the above entry):

I’m even imagining a fiendish plan where I force my grad students to write nLab articles on topics they’re learning about. Not sure that’s a good idea.

I find it a very good idea. (Maybe with force replaced by encourage).

Myself, I am using the $n$Lab as a notebook for things that I am learning/thinking about, too. If all of us make a note in the $n$Lab on whatever material we come across in our daily work, we’ll have a remarkable win-win situation.

Posted by: Urs Schreiber on January 4, 2009 1:32 PM | Permalink | Reply to this

Re: contributing to the nLab

Such nlab entries by grad students (wish I had some) would be excellent training before writing their thesis. Some bench scientists require students write a grant proposal - again good practice. And who knows the fall out as happens e.g. writing up notes from the master’s lectures - you know who I mean.

Posted by: jim stasheff on January 4, 2009 2:45 PM | Permalink | Reply to this

Re: Organizing the Pages at nLab

John wrote (by email, as quoted by David in the above entry):

However, Urs seems to like focusing on high-level folks, while I focus on low-level folks.

I have two remarks on this:

1st, I’d think it is a good thing if the contributors to the $n$Lab have complementary material to offer. This is one advantage of a collaborative wiki over a private one, the differing points of view that it can offer.

2nd, for the record I should maybe admit that I am using the blog and the wiki mainly because and to the extent that I feel that I personally benefit from it in my research. I am not in a position to spend large chunks of time besides my research with expositional writing, even if I wanted to. What I write are notes that help me as notes for my own research, but written in the conviction and with the evidence that sharing ideas and discussing them is profitable for all parties involved.

I would therefore want to encourage everybody who feels like adding to the $n$Lab at whatever level of sophistication he or she feels would be worthwhile. The wider the range of levels of expertise which is covered at the $n$Lab, the better. I think.

Posted by: Urs Schreiber on January 4, 2009 1:50 PM | Permalink | Reply to this

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