suppose the 2 plates have the same dimensions, and you start grinding, by rubbing them over each other with dilute paste, then part of the time the edges are u

suppose the 2 plates have the same dimensions, and you start grinding, by rubbing them over each other with dilute paste, then part of the time the edges are uncovered, while the centers are nearly always covered, so the centers should grind faster. and both try to go concave, this is however self-limiting: if the centers are ground slightly more than the edges, then the edges protrude and would grind faster again to catch up. the used motions translating and rotating in 2 dimensions, result in spherical surfaces being the only solutions, concave and convex, flat and flat, and convex and concave. its just that because of the initial phenomenon (the centers trying to grind faster than the edges, because the edges are unexposed part of the time) that you get spontaneous symmetry breaking and you get a concave and convex surface pair. this unstable equilibrium at flat can be made stable by using 3 surfaces, A,B,C and going through AB, BC, CA, and repeat, so that the only valid solution becomes an optical flat (but this is not how your window panes are made, they simply float liquid glass on a molten lead bath)