Relativity, dimensionality and manifolds

The whole line of thought that originated with Einstein was about when a surface integral and a volume integral are equivalent, as the integration was performed from an arbitrary point.  Manifold theory was about when these integrals are equivalent.  They were all mathematical proofs of an  integral theory.

I could write the theory of relativity about my kitchen sink, under what conditions could I write the equations of water going down the drain from the point of view of water volume or from the point of view of the surface of the water level. The conditions under which they are equivalent has to do with the conditions under which a smooth, arbitrary volume can uniformly shrink around a water molecule, or, when does a water molecule cease to be a compressible fluid.

Group theory tackles the similar problem.  When will a group of things added up in N dimensions be equivalently multiplied in N-1 dimensions.

Einstein was simply assuming that G, the force of gravity, was universally elastic. It is not, off course, it is finite dx,dy, below which the integral theory is no longer elastic. Unfortunately, the vacuum makes these equivalent integrals invalid, it cannot perform volume integrals. It has a dx,dy,dz,dt that is everywhere limited to three different, finite point types; two of which are slightly different than the third. The vacuum only works because the manifold cannot be separated along any smooth dimension, connectivity is maintained.

How many dimensions can we recurse?

Clearly we have the bitstream version and three recursions over which the vacuum find a multiply.  When I have the theory of counting in my R Code, I will plug in 5/3 instead of 3/2 and see if we get a bitstream plus five dimensions. It sounds like we are honing in on a theory that goes somethng like this:

1) The starting ratio defines the add. 2) The Fibonacci ratio defines the multiply. 3) The starting bitstream defines the fundamental sequence over which Shannon separation is valid.  4) Then the Shannon separation drops by the add ratio for each recursion over the next dimension.