Thales and Friends

Some of the papers from the 'Mathematics and Narrative' meeting held in Mykonos this July are now available at the Thales and Friends website. I have tweaked mine a little since I submitted it, and this November 21 version should appear there soon, otherwise find it here. I won't adjust it for a while now.

If you have reading access to Nature on-line, you can find a 2 page report (August 4) on the meeting by Sarah Tomlin.

John Baez has agreed to join the advisory board of Thales and Friends. His latest edition - week 223 - of This Week's Finds in Mathematical Physics deals with the idea of entities fibred over other entities:

And here, as usual, the n-category theorists meet up with the topologists - and find that the topologists have already done everything there is to do with ω-groupoids ... but usually by thinking of them of them as spaces, rather than ω-groupoids!

It's sort of like climbing a mountain, surmounting steep cliffs with the help of ropes and other equipment, and then finding a Holiday Inn on top and realizing there was a 4-lane highway going up the other side.

The extra difficulties the n-category theorists have to deal with arise from the lack of 'reversibility' in their more general context. In spaces, if there is a path from A to B, there will be one that runs in the opposite direction. If a path can be deformed onto another path, the deformation can take place in reverse, and so on. Computer scientists studying the computation paths of parallel computers care about this lack of reversibility. Two processors can find themselves following a path to a dead-end, along which they cannot backtrack. See the talks by Philippe Gaucher, Lisbeth Fajstrup and Eric Goubault at the IMA n-categories workshop.