Lambda as a Measure of the Rate of Recursion of Geometric Algebras

Geometric algebras over the real numbers are isomorphic to certain matrices–dyreal, real, complex, quaternionic, or dyquaternionic–depending only on the metric signature s, the number of spatial dimensions minus the number of temporal dimensions. The rank of each kind of matrix depends only on the total number n of dimensions, spatial plus temporal. Geometric algebras over the reals are periodic in s, but recursive in n. The recursion is generated from the anticommuting basis vectors of either the Euclidean plane or the Minkowskian plane. Certain direct products of the geometric elements of these two planes form the basis vectors of 4-dimensional Minkowskian space-time if the resulting basis vectors do not curl up on themselves. If they do, the resulting geometric algebra generates the Standard Model of physics, with 4 real dimensions of space-time and 12 real curled-up dimensions (rather than the 6 complex curled-up dimensions of M-Theory). After eight dimensions, the pattern of geometric algebras repeats itself, resulting in a recursively generated, exponentially expanding space-time lattice with the Standard Model at each node of the lattice. The cosmological constant is set by the rate of recursion, a different process from the curling-up process that sets the Planck scale.