From Osher Doctorow
Probable Influence/Causation (PI) is additive/subtractive rather than
multiplicative/divisive, and extra dimensions are fundamentally
additive/subtractive in several deep ways.
(a) Each added dimension introduces one or more (usually more) very
important variables.
(b) Except for fractals, added and total dimensions are positive
integers, and integers are closed (that is to say, produce integers)
under addition and subtraction but not generally division.
M. A. S. Cruz, F. Dahia, and C. Romero, in "Inducing charges and
current from extra dimensions," (they are in U. Federal de Paraiba
except for Dahia who is at U. Federal de Campua, all Brazil), arXiv:
0705.2252 v2 (gr-qc), 15 May 2007, 8 pages, prove more or less that
the mere addition of dimensions over the 4 usual spacetime ones is
decisive in producing arbitrary distributions of electrical charges
and currents, with or without Riemannian geometry (they use in fact
flat Minkowski geometry in 5 dimensions), and something similar was
found by the Wesson school of Canada which they cite in regard to
matter (the induced-matter theory or IMT) using Kaluza-Klein theory
except without the compaction of the 5th dimension - except that IMT
uses Riemannian geometry.
The result is good for Superstring/Brane Theory and bad for Loop
Quantum Gravity (LQG), even though it is only enunciated in 5
dimensions.
It also reminds me of Steven Weinberg's early distrust of geometry in
terms of curvature, although I don't think that topology is the answer
either. Continuity and differentiability in terms of differential
equations and probability of continuous random variables, play very
important roles arguably, as do 0-Lebesgue-measurable objects like
branes (which are continuous).
Osher Doctorow
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