We review some of the essential novel ideas introduced by Bohm through the implicate order and indicate how they can be given mathematical expression in terms of an algebra. We also show how some of the features that are needed in the implicate order were anticipated in the work of Grassmann, Hamilton, and Clifford. By developing these ideas further we are able to show how the spinor itself, when viewed as a geometric object within a geometric algebra, can be given (...) a meaning which transcends the notion of the usual metric geometry in the sense that it must be regarded as an element of a broader and more general pregeometry. (shrink)

It has been proposed that the implicate order can be given mathematical expression in terms of an algebra and that this algebra is similar to that used in quantum theory. In this paper we bring out in a simple way those aspects of the algebraic formulation of quantum theory that are most relevant to the implicate order. By using the properties of the standard ket introduced by Dirac we describe in detail how the Heisenberg algebra can be generalized to produce (...) an algebraic structure in which it is possible to describe space translations in a way that is analogous to the description of rotations in a Clifford algebra. This approach opens up the possibility of going beyond the limits of the present quantum formalism and we discuss briefly some of the new implications. (shrink)

A method originally conceived by Bohm for abstracting key features of the metric geometry from an underlying spinor ordering is generalized to the projective geometry. This allows the introduction of the spinor into a projective context and the definition of an associated geometric algebra. The projective spinor may then be regarded as defining a pregeometry for the projective space.