## March 24, 2007

### Philosophising in Brussels

#### Posted by David Corfield

I’m off to Brussels tomorrow. Fortunately someone pointed out to me that the clocks go forward tonight or I might have missed my train. I’m speaking at a conference called Perspectives on Mathematical Practices 2007. Here are some notes for my talk. Posted at March 24, 2007 9:52 PM UTC

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### Re: Philosophising in Brussels

Wow. Big thanks for clock info!!! :-) I could miss my plane as well (accidentally I also go to Belgium, but to Louvain-la-Neuve, for Ulrike Tillmann lectures).

Thanks once more and have a good philosophising :-).

Posted by: sirix on March 25, 2007 1:55 AM | Permalink | Reply to this

### Re: Philosophising in Brussels

These notes are very interesting.

Posted by: bhb on March 25, 2007 12:43 PM | Permalink | Reply to this

### Re: Philosophising in Brussels

I enjoyed seeing that part of the discussion of two things and 2-things has made it into your talk (slide 6).

Another good class of examples for complicated-looking conglomerates of data that can be realized as mere components of a single $n$-categorical gadget are a plethora of various “cocycle relations” that people usually write out as long lists of symbols with, usually, confusingly many signs scattered all over the place.

Often these can be seen to be nothing but coherence conditions for structure morphisms in higher categories.

Well, I guess the encapsulation of structure is actually a recursive phenomenon:

highly complicated-looking structures may be realized as algebras for operads.

Defining an operad itself in the standard way also takes a couple of lines.

But then we follow Tom Leinster and realize that all this data going into the definition of an operad in turn may be re-assembled into the mere statement of a monad in generalized spans.

And a monad, in turn, is just a component way of saying “lax functor on the trivial 2-category”.

:-)

Posted by: urs on March 26, 2007 7:53 PM | Permalink | Reply to this

### Re: Philosophising in Brussels

As the laws of physics only ever get modified so as to speed up time when one is giving a talk, that material on 2-class functions, inserted in case of an impossible, yet ever hoped for, slowing of time, had to be ignored.

But it would be good to collect some prize examples of this phenomenon.

Posted by: David Corfield on March 29, 2007 10:16 AM | Permalink | Reply to this
Read the post Perspectives on Mathematical Practices 2007
Weblog: Filosofie voor elke dag
Excerpt: Binnenkort komt mijn verslag van de Perspectives on Mathematical Practices 2007-conferentie online. Mijn presentatie ging goed en ik had hierover achteraf met verschillende deelnemers van de conferentie interessante gesprekken. Blogcollega's David Corfiel
Tracked: March 27, 2007 9:58 PM

### Re: Philosophising in Brussels

Mathematics organised by stories or dramatic narratives

By the way, probably you have mentioned this elsewhere, but I’d think that one reason why physics, and in particular what might be called “modern formal high energy physics” has been such a rich source of mathematical insight, at least at the level of conjectures (Witten, Kontsevich,…) is that whatever its relation to the physical world really is (which is an issue of heated – and overheated – debate, as we know #) it does a great job of identifying lots of mathematical entities as secretly being actors in one grand story: it allows to “visualize” all kinds of sophisticated math in terms of something like physical processes.

Posted by: urs on March 28, 2007 11:37 AM | Permalink | Reply to this

### Re: Philosophising in Brussels

Yes, I’d thoroughly agree with that.

It’s interesting, however, how easy it is to slip from there to the position that ‘purely’ mathematical intuition is quite weak so physical intuition is doing a huge amount of the work. Philosophers of physics often fail to observe that mathematics can pay back to physics by lending its intuitive stories. I was discussing this with Jacques Distler once at his blog.

Of course, we take for granted this intuitive story-like aspect of mathematics, due in large part to the expository efforts of a certain person from Riverside.

Posted by: David Corfield on March 29, 2007 9:29 AM | Permalink | Reply to this
Read the post Automated Theorem Proving
Weblog: The n-Category Café
Excerpt: In Brussels, we heard from Koen Vervloesem about attempts towards better automated theorem provers. Readers of my book will know that I devoted its second chapter to automated theorem provers, to provide a relief against which to consider 'real...
Tracked: April 5, 2007 12:40 PM

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