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December 15, 2007

A Dialogue on Infinity

Posted by David Corfield

The application Alexandre Borovik and I submitted to the John Templeton Foundation as part of their funding of the core theme of infinity was successful. We intend to discuss and disseminate ideas via a blog – A Dialogue on Infinity. Many aspects of what we will look into are relevant to the Café so there will be cross-posting. Posted at December 15, 2007 5:57 PM UTC

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Re: A Dialogue on Infinity

Over on your new blog “A Dialogue of Infinity”, the signatory of the post “The aims of the project, as seen by a philosopher” is Alexandre Borovik, as is “The aims of the project, as seen by a mathematician”. I figured the first might be a mistake.

This looks like a very promising start! Looking forward to more.

Posted by: Todd Trimble on December 15, 2007 8:13 PM | Permalink | Reply to this

Re: A Dialogue on Infinity

That’s because Alexandre as been posting extracts from our already written joint application.

Posted by: David Corfield on December 16, 2007 12:13 AM | Permalink | Reply to this

Re: A Dialogue on Infinity

Congratulations!

As of April 2007 approximately 1.4 new blogs were being created every second — that’s 120,000 per day. But the blog revolution is just beginning to affect math, science and philosophy. People are just beginning to learn how to use blogs to maximum effect. We’re just sort of blundering around…

I hope you do interesting new things!

Posted by: John Baez on December 16, 2007 12:41 AM | Permalink | Reply to this

asymptotics; Re: A Dialogue on Infinity

The new blog “A Dialogue of Infinity” is wonderful!

It does, however, by the medium interpreted as the message, raise the question of the asymptotics of the ratio of knowledge per blog to the number of blogs, as the number of blogs approaches infinity.

More subtlety emerges if one replaces “knowledge” with “wisdom” in the above sentence.

I’m sure there is a better way to pose this question, n-Categorically.

Posted by: Jonathan Vos Post on December 17, 2007 4:45 PM | Permalink | Reply to this

Re: A Dialogue on Infinity

approximately 1.4 new blogs were being created every second

At some point effort should go in the opposite direction. I already get the kind of headache from trying to follow all blogs I feel I should follow that I used to get from trying to follow all arXiv postings that I felt I should follow.

After a certain point, the reaction is disappointing for both sides: one gives up.

So it would be good to invest some serious thinking into resonable blog mergers.

There are, for instance, one or two blogs in our blog roll here, whose posts would feature rather well right among the posts we have here, as part of the nn-Café.

Posted by: Urs Schreiber on December 17, 2007 7:42 PM | Permalink | Reply to this

Re: A Dialogue on Infinity

Alas, that would just convert the problem into one internal to the Café. It’s sometimes hard to keep up as it is, on busy days.

Posted by: Tim Silverman on December 17, 2007 11:01 PM | Permalink | Reply to this

Re: A Dialogue on Infinity

Yeah, it’s that strange feeling when one can’t even keep up with the discussion on one’s own blog!

Days are too short. And if I were in charge, I’d make christmas be every four years. Like the world cup.

Posted by: Urs Schreiber on December 17, 2007 11:13 PM | Permalink | Reply to this

Re: A Dialogue on Infinity

Scrooge!

Posted by: jim stasheff on December 18, 2007 12:36 AM | Permalink | Reply to this

Re: A Dialogue on Infinity

Seconded!

(And I agree with John Armstrong’s final comment.)

Posted by: Beans on December 20, 2007 5:15 AM | Permalink | Reply to this

Re: A Dialogue on Infinity

Instead of getting everyone to change the rules so Christmas is held only on leap years, it might be easier to convince mathematicians to join us on the nn-Category Café.

But, not much easier.

I’ve invited both John Armstrong and Jeffrey Morton to do so, but they didn’t take me up on it. I’ve had more luck getting Todd Trimble to post here… but then he didn’t have a blog beforehand.

I’m afraid people may want to have their own blogs, even if they like ours, just to assert their own individuality. They may not want to join our collective, even if we kindly invite them, saying “We wish to improve ourselves. We will add your biological and technological distinctiveness to our own.”

Posted by: John Baez on December 18, 2007 6:41 AM | Permalink | Reply to this

Re: A Dialogue on Infinity

Yeah, there is something to having my own place, especially given its rather different mission. However, I’d be glad of a guest post.

Maybe once I polish off the last of this paper about spans I’ll make a cross-post. Other than that, though, the bulk of what I’m doing is far more basic than the usual level here, and it’s mostly on topics other than higher category theory.

Posted by: John Armstrong on December 18, 2007 8:31 AM | Permalink | Reply to this

Re: A Dialogue on Infinity

I’d be glad of a guest post.

Whenever you have something you want to post the the Café, just send the source code by email to one of us hosts.

If it happens regularly, you can also use our guest account, if you like.

the bulk of what I’m doing is far more basic than the usual level here

That’s an argument in favor of having it here! :-)

Posted by: Urs Schreiber on December 18, 2007 4:36 PM | Permalink | Reply to this

Re: A Dialogue on Infinity

John A. wrote:

…the bulk of what I’m doing is far more basic than the usual level here, and it’s mostly on topics other than higher category theory.

That’s exactly why we need it! Too much of the stuff here is at a very advanced level; we need more posts that explain fundamental concepts from scratch. The lack of these probably keeps some good people from joining in the discussions here. That makes me unhappy.

And, despite the title of this blog, the subject was never meant to be limited to nn-categories… and it’s not. Everything in math, physics and philosophy is fair game. I’ve recently been talking about math videos, math rap songs, a math journal that only accepts rejected papers, the Egg Nebula, the field with one element, and why the integers are 3-dimensional. The nn-category theme is just a sort of glue that holds things together.

So, we’d be very glad to have you join our Café. But, we’d also be happy to get some guest posts!

Posted by: John Baez on December 18, 2007 4:53 PM | Permalink | Reply to this

Re: A Dialogue on Infinity

Well, not to get off onto the hackneyed “what is blogging” discussion, but I have sort of a different take on the whole matter. I think it’s a feature rather than a bug to have a huge number of different weblogs out there, particularly because each one gets to have its own voice.

Air traffic controllers talk about the “big sky” theory of transportation. There’s a lot of planes out there, and there are more and more every day. Why aren’t they bumping into each other? Because you have almost no idea how enormous the sky is. There’s a lot of planes, but there’s so much more sky that collisions in the air (apart from ascent and descent) are almost unheard of.

There’s a lot of internet out there, too. Much more than there is sky, even. I have my space where I like walking through the background of everything I can (up next: calculus!) and you have space to hash out applications of n-categories to mathematical physics (along with whatever else strikes your fancy). David and Alexandre can move over to devote some space to an extended discussion about infinity, while Berkeley and Cornell graduates each band together to advertise what they’re working on. Isabel finds statistics in everyday life, Craig frets about his dissertation, and Zero Divides pushes gamely through advanced calculus for the first time. And there’s still no end in sight to the space we have to work with. There’s a lot of sky out there.

The catch is that without contacts we lose cross-pollinations that could lead to new things. We can’t just be voices crying in the wilderness or we may as well move back to diaries. I think that this is the issue you’re concerned about with the proliferation, along with the signal-to-noise ratio.

But I don’t really think that it’s a problem. You’ve got an active community of regulars here – certainly more comments than I have, and I’ve got around 500 silent lurkers a day coming by my little corner. We all link to each other. When you say something I find particularly interesting, I post a link over here, and (I’d hope) people link to me when I say something worthwhile. Information does get around, even as spread out as we seem.

As for the 120,000 weblogs a day, what that number doesn’t mention is the 50,000 that people bet bored with and walk away from because they don’t have much to say, the 9,000 that have a handful of readers other than the author and function more as newsletters, or the 60,000 that were created by spam-bots and viral marketing agencies. Signal stands out pretty easily, even in a sky this big.

Posted by: John Armstrong on December 18, 2007 6:34 PM | Permalink | Reply to this

Re: A Dialogue on Infinity

I have enough to do keeping up with you guys much less running my own blog!

Posted by: jim stasheff on December 18, 2007 12:50 PM | Permalink | Reply to this

Nonequilibrium blogospherics; Re: A Dialogue on Infinity

This maps to the distinction between “lumpers” and “splitters” in Anthropology; and the merging versus splitting off departments and subdepartments in universities.

In mathematical modeling of the corporate world, there is the folk theorem that in equilibrium macroeconomic conditions, there is an equilibrium between, on the one hand, acquisitions and mergers, and, on the other hand, start-ups and spinoffs of existing corporations.

In that model, changes in environment (i.e. booms, bubbles, depressions), or in law (i.e. the singularity in how corporations were established around 1800 AD in the USA), or in tax structure, or in underlying technology (i.e. industrialization, automation, internet) can make big changes in the distribution of number of firms versus firm size.

Such models come variously in stochastic versions, in continuous differential equation versions, and in agent-based versions.

n-Catgory Theory may explain the underlying structures and transformations of structures and transformations.

Posted by: Jonathan Vos Post on December 18, 2007 8:31 PM | Permalink | Reply to this

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