Lawrence,
In those terms, you are closer to my thinking, although I don't understand all the models. To the extent that the sphere scale transmits information on the state of the group, I grok -- I think that in physical terms, this information is the inertial state. To explain:
From basic geometry, let's assign the dimensionless point a value of negative 3. That would impart a value of negative 2 to the 1-dimension line, and to the 2-dimension plane, negative 1. So the three-dimensional domain is zero, and we have the order of zero to 4 dimensions:
-3, -2, -1, 0, +1
Matching sphere kissing numbers to these values, we find 0, 2, 6, 12, 24.
The first non trivial kissing number is in three dimensions: 12. What my model finds, is that this zero-valued 2-sphere (S^2) is a recurring singularity of non-zero dimension in the n-dimensional Euclidean order of kissing spheres. To see why this is not the contradiction that it appears to be, let's go back to the flat 2-dimension plane, with a value of negative 1:
This space has to be complex, because only the field of complex numbers is algebraically complete. So consider for a moment the real Cartesian plane, with 6 spheres kissing an identical sphere. Then consider the negative (hyperbolic) space bounded by the spheres. We find a closed loop, and that is what I mean by a string -- the space of fluctuating energy on the boundaries of moving kissing spheres, whose fundamental dimension is 2. When we use 2 dimension analysis on the complex plane, then, the possibilities for string configuration are no longer confined to a closed loop -- closed and open strings "dance" on the manifolds of the recurring S^2 throughout the n-dimensional Euclidean sphere kissing order. We learn:
1. 3 is the minimum dimension for the origin of inertia;
2. Mass is the product of space and time alone, from zero average vacuum energy density;
3. Negative space ("brane") surfaces promise a non-perturbative path to a unified theory.
I find by straightforward numerical calculation from this mnodel that the 4 dimension horizon is identical to the 10 dimension limit, so supersymmetry is a result, rather than an assumption. A tiny epsilon term added to the zeroth term of the kissing order, calculated from first principles using complex analysis, explains the low baryonic content and locally weak gravity of our universe.
Tom
