The n-Category Café

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.