QFT, Homotopy Theory and AI?

post by ThomasR · 2010-10-30T10:48:13.992Z · LW · GW · Legacy · 2 comments

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What do you think about the new, exiting connections between QFT, Homotopy Theory and pattern recognition, proof verification and (maybe) AI systems? In view of the background of this forum's participants (selfreported in the survey mentioned a few days ago), I guess most of you follow those developments with some attention.

Concerning Homotopy Theory, there is a coming [special year](http://www.math.ias.edu/node/2610), you probably know Voevodsky's [recent intro lecture](http://www.channels.com/episodes/show/10793638/Vladimir-Voevodsky-Formal-Languages-partial-algebraic-theories-and-homotopy-category-), and [this](http://video.ias.edu/voevodsky-80th) even more popular one. Somewhat related are Y.I. Manin's remarks on the missing quotient structures (analogue to localized categories) in data structures and some of the ideas in Gromov's [essay](http://www.ihes.fr/~gromov/PDF/ergobrain.pdf).

Concerning ideas from QFT, [here](http://arxiv.org/abs/0904.4921) an example. I wonder what else concepts come from it?

BTW, whereas the public discussion focus on basic qm and on q-gravity questions, the really interesting and open issue is the special relativistic QFT: QM is just a canonical deformation of classical mechanics (and could have been found much earlier, most of the interpretation disputes just come from the confusion of mathematical properties with physics data), but Feynman integrals are despite half a century intense research mathematical unfounded. As Y.I. Manin called it in a recent interview, they are "an Eifel tower floating in the air". Only a strong platonian belief makes people tolerate that. I myself take them only serious because there is a clear platonic idea behind them and because number theoretic analoga work very well.

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