  We discuss the relation between the q-number approach to quantum mechanics
suggested by Dirac and the notion of "pregeometry" introduced by Wheeler. By
associating the q-numbers with the elements of an algebra and regarding the
primitive idempotents as "generalized points" we suggest an approach that may
make it possible to dispense with an a priori given space manifold. In this
approach the algebra itself would carry the symmetries of translation,
rotation, etc. Our suggestion is illustrated in a preliminary way by using a
particular generalized Clifford Algebra proposed originally by Weyl, which
approaches the ordinary Heisenberg algebra in a suitable limit. We thus obtain
a certain insight into how quantum mechanics may be regarded as a purely
algebraic theory, provided that we further introduce a new set of
"neighbourhood operators", which remove an important kind of arbitrariness that
has thus far been present in the attempt to treat quantum mechanics solely in
terms of a Heisenberg algebra.
