  Why is space 3-dimensional? The first answer to this question, entirely based
on Physics, was given by Ehrenfest, in 1917, who showed that the stability
requirement for $n$-dimensional two-body planetary system very strongly
constrains space dimensionality, favoring 3-d. This kind of approach will be
generically called "stability postulate" throughout this paper and was shown by
Tangherlini, in 1963, to be still valid in the framework of general relativity
as well as for quantum mechanical hydrogen atom, giving the same constraint for
space-dimensionality. In the present work, before criticizing this methodology,
a brief discussion has been introduced, aimed at stressing and clarifying some
general physical aspects of the problem of how to determine the number of space
dimensions. Then, the epistemological consequences of Ehrenfest's methodology
are critically reviewed. An alternative procedure to get at the proper number
of dimensions, in which the stability postulate (and the implicit singularities
in three-dimensional physics) are not an essential part of the argument, is
proposed. In this way, the main epistemological problems contained in
Ehrenfest's original idea are avoided. The alternative methodology proposed in
this paper is realized by obtaining and discussing the $n$-dimensional quantum
theory as expressed in Planck's law, de Broglie relation and the Heisenberg
uncertainty relation. As a consequence, it is possible to propose an
experiment, based on thermal neutron diffraction by crystals, to directly
measure space dimensionality. Finally the distinguished role of Maxwell's
electromagnetic theory in the determination of space dimensionality is
stressed.
