Space as a “bucket of dust”

A pregeometry of space is considered, in which the only structure imposed on individual points is a uniform probability of adjacency between any two arbitrarily chosen points. This probability is not specified (but only assumed small) and neither is the total number of points specified (but is assumed large). It is shown that the most likely distribution of points has similarities with a closed three-dimensional space of constant positive curvature, in particular, the number of points at a given distance from an arbitrary origin is proportional to sine-squared of the distance from that origin.