Abstract

In my first paper, I attempted to show that the octave of music is a projection of the Double Ratio of Projective Geometry and that the octave structure of the piano is reflected in the geometrical structure of the complete quadrilateral. This led to the very fruitful conjecture that the dynamic processes of geometrical thought are intimately involutionary and generates real and imaginary groups of Growth Measures! Thus, I began to envision the wonderful concept that it is possible to model geometrical thought! This prompted the realization that in order to continue my development of a Universal Cosmic Language that unifies physical and spiritual science, I required a 4 Abstracts Submitted for Storrs 2009 Geometrical Calculus that unified Projective Geometry, Euclidean Geometry, and Non-Euclidean Geometry. Fortunately, the innovative mathematician W. K. Clifford (1845-1879), while analyzing the papers of Hermann Grassmann (1809-1877), expanded his concept of Geometric Algebra into Clifford Algebra. Building upon Clifford Algebra, David Hestenes, Garret Sobczyk and their disciples have developed an extremely powerful Unified Language for Mathematics and Physics which I am now further evolving to include Mathematical Spiritual Science. This wonderful language expresses a completely coordinate-free differential calculus in which invariance is implicit; consequently, there is no longer any need to resort to coordinates or matrices; for example, its advantages far exceed those of Holors which are only sub-spaces of universal multivectors! In this paper I will attempt to show that the structure of the four fundamental action forces of nature are all geometrically implied by this wonderful Unified Language and that it inspires me to believe that the structure of the Quark, as envisioned by Spiritual Science, may soon be decoded.