I was talking to Allison about the origin of the solar system, which involved a cloud of matter, and things sortof condensated and drained toward the center, and planets are little eddies and swirls around the main whirlpool which is the sun.
And I asked why everything should all be rotating in the same direction in a plane, which seems sensible for water draining since it's flat to begin with.. but if you start with a bunch of particles flying around in 3D, why gravitate toward a plane, and why all in the same direction?
The main insight is that, if you create a little universe, and put a bunch of particles in it, and each one has a random direction and speed, then naturally they'll all start orbiting each other in some crazy chaotic pattern.. BUT, the system has a center of mass, which seems natural maybe, and that center of mass is moving at some constant speed in some direction, which is a little weirder, but I still buy it.. AND, the entire system has an angular momentum. There is some 3d line passing through the center of mass of the system that everything more-or-less spins around, and a particular direction (clockwise or counter-clockwise) and a particular speed of rotation, on the whole.
That is to say, my insight for today [edit: this was originally written a few months back], is that any random configuration of particles moving around in space defines a 3d vector through space. Even before anything happens with some nebula that's thinking about forming a solar system, you can say "well, the sun will be here, and the planets will be rotating on this plane, in this direction."
There's also the issue of why do things actually form a plane, since they could rotate at odd angles and still keep the same angular momentum.. my current thought is this, if everything glommed together into exactly 2 equally sized balls, then they would necessarily be rotating in a plane, in a certain direction.. and everything else is a gradient towards that, as things glom together, they become more and more in a plane, and more and more in a given direction.
Update: I guess another way of looking at it is that if you manage to spin a basketball very very quickly, it will sortof flatten into a pancake.. and so since random collections of particles are typically spinning, on the whole, around some axis, it makes sense that they would flatten into a pancake.
Of course, the thing bringing the top and bottom of the basketball toward the center is that they are physically attached to the sides of the ball that are moving away from the center, pulling them in. In the case of our particle cloud, that job is done by gravity.