There are for most practical purposes only three space dimensions, but three more velocity dimensions are required to fully specify a system of particles. This set of 6 specifications (or really 6n coordinates, 6 for each of the n particles) is usually called "phase space." Some important theorems are stated for phase space. For example one can define a constant energy surfaces in phase space (more that just Vx^2 + Vy^2 + Vz^2 sum for all particles, if some particles are charged and there are electric fields) The ergotic theorem states that if you wait long enough, then the system will pass as close as you like to any given point in phase space. This then allows one to makes certain probability calculations more easily, allows gas laws to be derived from first principles, etc.