Originally Posted by apostate87

actually, the nature of my reasoning is different. just like you can't tell certain things from say force that you can from momentum, there are certain things you can tell from logic that you can't tell from pure mathematics. if an object, say a ball, has a center of mass C which does not move in any of the three spacial directions AT ALL at all points in time between T1 and T2, then if it did begin to move, it would have to have an acceleration, a jerk, and so forth and so on to infinity.

For the ball, the center mass would only be one small point, not three points. When you mention spatial directions, I think you getting into an atomic view (if that's even a word). it would be impossible; infinity is impossible. arbitrarily large or small, no, but infinite yes. as well as zero. so i agree there are no absolutes, although i disagree that rest exists. if rest existed, the graph of its position would be impossible to construct unless it were done by parts, and since everything continuous moves as a function of time (and i assume you can't define these motions by parts... because that means the velocity is undefined in certain places, which is absurd) rest can only exist at instants on the graph. rest cannot be sustained. motion is absolute. not absolute motion, but motion nonetheless. i believe, at the very least, everything oscillates in a sinusoidal manner. but that's just me.