Eliezer, I was going to point out that you never defined "phase space", but Roland beat me to it. It's a small hole in an otherwise excellent post.

Roland,

Eliezer is using the physics jargon meanings of speed and velocity: speed is a magnitude, a raw number; velocity is magnitude and direction together. A car might be travelling at a speed of 65 mph; if you include a direction, e.g., 65 mph east, then you've got its velocity.