So Seed magazine has endorsed Obama. *Quelle surprise*! I suppose I shouldn’t bite the hand that feeds me, but of course I’m on record as supporting the “anyone else” ticket. I am under no illusion that it will be anything but a lost cause.

One of the things that leads me to believe this is poll data. Poll data is sort of the sociological version of many-body theory.

In physics, “many” often has a particular meaning. According to a guest lecturer we had today who works with semiconductor lasers, “many” means “more than two”. He’s working with the difficult problem of theoretically describing how the interactions between the particles in the laser diode affect the lasing process. One isolated atom undergoing stimulated emission isn’t usually too hard to describe, but once they start bumping into each other and filling bandgaps and undergoing exchange forces and doing all kinds of other horribly promiscuous things with each other… well, you try computing a Hamiltonian for that. You have to be clever and start to take into account the statistical behavior of the system as a whole and not try to keep track of each individual atom. As you might expect, this leads to its own difficulties.

In more basic physics, such as the gravitational interaction between planets, we have the same problem. Treating the motion of just one object in a gravitation field is easy. Take the space shuttle and the earth for example. Assume the earth is so big the shuttle’s gravity doesn’t affect it (a good assumption!) and one equation does the job for you. That’s a single body problem. Now if you have two bodies of comparable size like the earth and the moon, the problem is a little harder but still exactly solvable. You use a trick called the reduced mass and the problem reduces to the one-body problem just like for the shuttle.

Go to three bodies interacting gravitationally and suddenly you find yourself completely and comprehensively hosed. The problem isn’t merely more difficult, it’s absolutely impossible to do exactly. There’s no single equation where you can just plug in some time t and find out where all the planets are. Now there is a very slowly converging series solution, and of course numeric methods are capable of high precision for fairly small numbers of interacting bodies over reasonable time scales (such as the solar system over a few thousand years). But generally speaking there’s no closed form equation which solves the problem. Worse still, many interesting problems like galactic dynamics and the universe as a whole can contain billions of interacting objects. So you have to be clever with your statistics.

For example, in a gas containing trillions of trillions of molecules, PV = nRT can model the aggregate behavior of the system quite well. Some thermodynamics is all you need to derive the equation. Galaxy dynamics are harder, but they can be done on a good computer using some approximations and a few hours (well, lots of hours) of CPU time. Still, it’s easier than manually simulating every single one of the billions of stars.

It’s why polls sample a few hundred or a few thousand people, when millions are voting. It’s not perfect, but the many-body problem is too hard to do more than once, on election day.