  The automorphism invariant theory of Crawford[J. Math. Phys. 35, 2701 (1994)]
has show great promise, however its application is limited by the paradigm to
the domain of spin space. Our conjecture is that there is a broader principle
at work which applies even to classical physics. Specifically, the laws of
physics should be invariant under polydimensional transformations which
reshuffle the geometry (e.g. exchanges vectors for trivectors) but preserves
the algebra. To complete the symmetry, it follows that the laws of physics must
be themselves polydimensional, having scalar, vector, bivector etc. parts in
one multivector equation. Clifford algebra is the natural language in which to
formulate this principle, as vectors/tensors were for relativity. This allows
for a new treatment of the relativistic spinning particle (the Papapetrou
equations) which is problematic in standard theory. 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.
