Pi
A film by Darren Aronofsky, starring Sean Gullette.
Winner, Directing Award, Sundance Film Festival.
http://www.pithemovie.com/
Reviewed by Robert McLachlan
Maximillian Cohen is riding hunched up on the New York subway, cradling a black go stone in his hand. It's a circle. Pi r^2. The empty go board, its rules unseen, represents the blank universe; a played game, its state. The empty board becomes strangely appealing: clean and symmetric, large enough to suggest an infinite lattice, yet finite, truncating its symmetry to a groupoid. Its cells are not quite square, the game tree is complete. Why break that symmetry? A go master once spent five of his ten hours contemplating the empty board.
Once in play, the rules don't determine the structure. But like the islands of order in our sea of increasing entropy, there are patterns. Maximilian is looking for that emergent structure. He's a mathematician.
In the small field of films featuring mathematicians -- only Hollywood's _Good Will Hunting_ and _Jurassic Park_ and the touching Italian _Death of a Neapolitan Mathematician_ come to mind -- Pi is a winner. It's a movie of ideas, with intersecting streams from Rudy Rucker on cyberpunk, Jorge Luis Borges and Umberto Eco on conspiracies and hidden meaning, George Steiner on prodigies and obsession (maths, music, and chess) and Nabokov on chess and madness, all up there in high-contrast grainy black and white with a cool electronic soundtrack. Hey, _I_ spent three years obsessed with go, _I'm_ a mathematician, _my_ teacher had a stroke just like Max's. This is my movie! Plus, I'm seeing it in Berkeley, where the streets are filled with real crazy people, partly crazy people who've read too many popular science books, and Fields medallists, in equal proportions. That fat guy next to me with sweaty feet is probably Ted Kaczynski's brother.
That stroke -- there's a suggestion that Max's teacher stumbled on something hidden in mathematics that humans just weren't meant to know. Some kind of Godel sentence that fused his mind. Now Max, who wants to model the stock market on a home-built supercomputer that fills his apartment (shades of the Chudnovsky brothers), is getting close also. His full-complex migraines and extensive self-medication don't help much either, although perhaps the pre-fit euphorias spark creativity. He's getting close, and Wall Street devils and Hasidic angels want a piece. The Hasids bail him out, but they want the number in his head -- the Name of God. Max realizes that it's not the number itself that's important, it's its meaning, and the number was given to _him_.
This Name-of-God stuff could be seen as traditional science fiction, or one can read the whole Kaballah sequence as a figment of Max's imagination: religious and persecution mania triggered by overwork. These things happen. This is a film about doing science, meaning, and mania. After all, where does meaning reside? It's partly intrinsic, and partly (lest mathematics degenerate to a list of consequences of axioms) imposed by us. To do science, you have to believe in it and give it meaning; worse, it's usually difficult and likely to fail. Occasionally you have to suspend your critical faculties and just push ahead with some weird idea. You have to hang on to it and not let go. The Pythagoreans believed all was number, and lo, all _was_ number. The potential rewards are great, but there's a risk of becoming a crackpot, or of starting to see too much meaning and too many connections -- mania.
The maths in this film is pretty simple: the stock market time series, the digits of Pi, Archimedes' spiral and the golden ratio. I think that's much better than hiring experts to fill blackboards with the latest jargon. Coincidences and connections and hidden patterns _are_ the stuff of mathematics. And, although it may give the field a bad name, some mathematicians really do study the digits of Pi. The Name of God lends a suggestion of weird science. But think of Godel undecideability, nonstandard real numbers, even standard reals supporting things like the Mandelbrot set, multidimensional string theory, infinite state quantum computing,... A suggestion of weird science is allowed.
Pi is Aronovsky's first film, the traditional low-budget debut. I hope he hasn't used up all his ideas. I can't wait for his next one.
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