I was finishing up Penrose's The Road to Reality before bed today, thinking to myself how incredibly ropey the last few chapters seemed and gnashing my teeth ever so slightly when Penrose couldn't help but mention his belief in consciousness as a non-computational quantum phenomenon, with which I have previously taken issue--without, perhaps uniquely for this blog, any swearing.
(Fuckarsebitchtits!)
Anyhow, the book was winding down, and I was juuuuuuuuuuust getting ready to put it aside, when I noticed something, on page 1042 of the Knopf hardback edition...
What appears to be true, in essence, is that there is something deep in the idea of a quantum field theory based on the mappings of Riemann spheres into complex manifolds...
...Which just made me sit up and go "Whoa now, Bessie."
Let me explain.
When I started my university years as an undergraduate, I was into physics. As time passed, I got more and more into mathematics and less and less into physics because the mathematics was so much prettier (and it didn't catch fire when I tried to set it up). Nowadays I'm just about as far from physics as you can get in a lot of ways, but I still have, in the back of my head, this daydream of one day dipping my toe back into mathematical physics somehow, maybe looking for loopspacey maths that I can apply to loop quantum gravity or (God help me) string theory or summat. But this was just pipe dreams and whimsy for the most part.
But...
It turns out...
A piece of pretty abstract and very strongly topological maths that I've been writing up to include in my General Exam paper involves Schubert varieties in the Grassmannian model for the loopspace of a compact Lie group. Believe it or not, some of these Schubert varieties are known to have the homotopy type of...the space of holomorphic mappings of the Riemann sphere into certain complex manifolds.
*GASP*
Am I secretly doing quantum field theory? We're through the looking-glass, people.
Posted by aloysius at July 03, 2006 01:34 AM |