  In this paper we start from a basic notion of process, which we structure
into two groupoids, one orthogonal and one symplectic. By introducing
additional structure, we convert these groupoids into orthogonal and symplectic
Clifford algebras respectively. We show how the orthogonal Clifford algebra,
which include the Schr\"oodinger, Pauli and Dirac formalisms, describe the
classical light-cone structure of space-time, as well as providing a basis for
the description of quantum phenomena. By constructing an orthogonal Clifford
bundle with a Dirac connection, we make contact with quantum mechanics through
the Bohm formalism which emerges quite naturally from the connection, showing
that it is a structural feature of the mathematics. We then generalise the
approach to include the symplectic Clifford algebra, which leads us to a
non-commutative geometry with projections onto shadow manifolds. These shadow
manifolds are none other than examples of the phase space constructed by Bohm.
We also argue that this provides us with a mathematical structure that fits the
implicate-explicate order proposed by Bohm.
