Submitted by Tommer Wizansky, SLAC graduate student.

This question has become an integral part of any modern, fundamental theory of nature and in fact plays a central role in many of the other great puzzles presented at SSI. Attempts are made to explain the hierarchy problem through gravity "leaking" into other dimensions; supersymmetry suggests spacetime is 11 dimensional; the fermion mass spectrum can possibly be justified through the overlap of wave packets in a fifth dimension; and we have even mentioned string theory. Indeed, the dimensionality of the universe deserves a place among the great puzzles.