John Conway <conway@math.princeton.edu> wrote:
I didn't read the piece I snipped, but presume that it is supposed to guarantee to find (in particular) a 25-sphere configuration in 4D if one exists. I can't really see how it can do that, while still being approximate. Do you think it can?
No, of course not. Why would you presume I attempt such a guarantee, when it is patently impossible? I claim that if there are no (25,4,1+2epsilon) configurations, the algorithm would say so. This is important, because if there are no (25,4,1) configurations, there must be an epsilon for which there are no (25,4,1+2epsilon) configurations. I also claim that every (25,4,1) configuration is represented in the output by an approximation that describes the coordinates of the centers to within epsilon. Each of these can be converted to a (25,4,1-2epsilon) configuration. Dan