Saturday, November 20, 2004
Even spacetime is big in Texas
I'm still at the Philosophy of Science Association meeting in Austin, where I have thus far been foiled in my attempts to buy a PSA T-shirt. The other disappointment was that I arrived too late to hear a plenary talk by Steven Weinberg. But otherwise it's been going well. We had a fun little session yesterday on the dimensionality of space. Craig Callender from UCSD gave an overview of various attempts to "prove" that space must be three-dimensional. Apparently it was Immanuel Kant who first tried to use Gauss's Law to show that space must be three-dimensional. That seems a little backwards to us today, since you have to assume that gravity has a 1/r2 force law to do it; it seems more sensible to derive the force law from the dimensionality rather than the other way around. (I also learned that Newton calculated how elliptical orbits would precess if the force law wasn't precisely 1/r2, a fact that later gained significance as a proof of general relativity.) Then there are crazier proofs based on the anthropic principle. An example (which Craig didn't use) that I originally heard from Mark Wise is the "tying your shoes argument" -- in more than three spatial dimensions, there's no such thing as a knot, so it wouldn't be possible to keep your shoes from falling off, which makes civilization very difficult. I pointed out to Mark that this also ruled out fewer than three dimensions, so it's a pretty powerful argument. Perhaps you could use 2-branes to keep your shoes on, though. I'll have some of my grad students look into it.
Another talk was by Nick Huggett and David Hilbert (no, not that Hilbert) of the University of Illinois at Chicago on perceptions of three dimensions. This talk started with some abstract ideas from Poincare, and slid into an empirical psychological study of how three-dimensionality is ingrained into our brains. Not hard-wired, though; Linda Henderson in the audience mentioned an experiment in which subjects were trained to think in four-dimensional intuition. I personally wouldn't classify these issues as philosophy, but as psychology, since they involve empirical investigations of how the mind actually works. Of course there is a good question about whether philosophy is really a science; to me the answer is clearly "no." Science is about constructing models and trying to fit them to the world, using empirical data to decide which models are better than others. (Glossing over some details here.) Philosophy includes the stuff that is non-empirical, although there is obviously a great deal of connection. Moral philosophy and logic are fine examples of disciplines that are just not science at all. Indeed, philosophy of science is not a science (although sociology of science is). It's okay not to be a science! Some of my best friends are non-scientists.
My own talk was on the good reasons we have for suspecting that there may be more than three dimensions of space. I didn't say anything new; the argument was basically that we need to quantize gravity, string theory is our best current hope for a quantum theory of gravity, and string theory predicts the existence of extra dimensions. Of course, all of these statements are controversial, even if not "new." If Peter were there, I suspect he would have disagreed with the statement that string theory is our best hope for quantizing gravity. To me, it clearly is, and I've been hoping for a while to sit down and type out a clear exposition of why I think so. But I would first want to talk more generally about quantum gravity and stuff, and right now I have to go to Sweden! Happy Thanksgiving; you'll be in Risa's competent hands while I'm gone.