Luis:
1. three compensating accelerations cancel to give an apparant 'zero'. Look at it closely in fine enough detail and you see fluctuations; hence the 'zero' is a combination of compensating somethings.
Example:
2. Suppose you are looking at the Earth from space. You see a weather system. It is a depression and it is moving east at an accelerating rate. Thus, a rate of change (acceleration) of a rate of change (distance per time). (Noticing the acceleration means differentiating that there are two rates of change; noticing how far the depression has gone means integrating them.)
3. Now; disregarding this big picture: within the air on one side of the system you are aware of a broad river of air; actually part of the rotation of the system but feels just like an airstream going straight ahead when you're in it. (you don't notice the spaceview of the whole system moving sideways.). Suppose this airstream is accelerating. So we have a rate of change of a rate of change; superposed on the whole depression's rate of change of a rate of change.
4. Now; suppose you disregard the airstream movement. You are in an aircraft, a lowspeed gyrocopter, and although the forward propellers are increasing in activity and your craft is accelerating (thus a rate of change of a rate of change); someone on the ground notices that relative to them, your craft is stationary!
5. So we have a rate of change of a rate of change (the accelerating gyrocopter); superposed on a rate of change of a rate of change (the accelerating airstream); superposed on a rate of change of a rate of change (the accelerating depression weather system).
6. Since I supposed that the gyrocopter is stationary relative to the ground; the acceleration and direction of the aircraft is just right to cancel out the acceleration and direction of the airstream plus the acceleration and direction of the whole weather system (or the sideways movement of the airriver, so to speak.)
7. Note the aircraft's movement relative to the ground is zero in the scenario I've chosen. Each of Dick's physics definitions in his website paper amount to stating an initial pattern conservation thus giving a fixed reference point hence a symmetry around zero.
