Suppose you have an infinite number of point masses, a_n (for all n in Z), positioned at regular intervals (1 unit) in a straight line, extending infinitely in both directions. Additionally, suppose that (instead of a gravity force), there is an 'antigravity' force (inverse square repulsion force) between any two point masses. Now, the masses will stay at rest, as there is a force of pi²/6 on each side. However, consider what happens when we remove mass a_0. If we consider a_1, for example, there is a force of pi²/6 pushing in one direction, and pi²/6 - 1 pushing in the other direction. Obviously, two masses cannot cross each other (as doing so would require overcoming an infinite repulsive force), so the situation can be modelled by [an infinite number of] second-order ordinary differential equations. Is there an analytic solution to this physical problem, i.e. can you determine the position of a_1 at time t=1, for example? Sincerely, Adam P. Goucher