Lecture at the IVth Conference on Clifford Algebras and their Applications in Mathematical Physics, Aachen, Germany, May 28-31, 1996. Our conjecture is that there is a broader principle at work which applies even to classical physics. To complete the symmetry, it follows that the laws of physics must be themselves polydimensional, having scalar, vector, bivector etc. In curved space the rank of the geometry will change under parallel transport, yielding a new basis for Weyl's connection and a natural coupling between linear and spinning motion. The text may well serve as a pedagogical tool for either self study or in courses at both the undergraduate and graduate level.
Bibliographies complete many chapters and an index covers the entire book.
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