A recent post asked "why does physical space need to be 3-dimensional?" However, the thread became infected with personal insults and was (properly) closed. I felt sorry that PeterDonis, whose posts I respect, was subjected to this abuse ! I have read several posts which start by assuming that our universe has a certain topology, such as a shell universe. Could anyone refer me to paper(s) that postulate a universe which starts with particles thinly spread out in multiple spatial dimensions, 10, 11, or perhaps even Hilbert space, none of the dimensions being degenerate. Then, taking advantage of the instability of orbits for spatial dimensions greater than 3, describes the collapse of matter within this hyper-space into either singularities, or into 3-D sub-manifolds with perhaps varying topologies, for each of which orbits become stable. Note that such a paper need not assume that our universe actually started this way, but would be entirely a mathematical exercise.