Reading Flatterland by Ian Stewart (2000) I encountered a chapter about dimensions-a topic I am interested in. That led to information about what dimensions are described as (in physics it has traditionally been 3 directions plus maybe time). With non-Euclidean math and algebra it was possible for mathematicians to evolve the notion of extra dimensions. If one has a 2-dimensional quad/grid one can use that square or power of 2 notation. Eventually one finds cube roots or 3rd power and I guess extra, higher powers although I seem to recall something about Abelian algebra issues with some higher powers.
Regular shapes from geometry can thus be described with natural and real numbers algebraically, although the product of such constructions can be fiction or consistent just in mathematics. Some physicists created the idea of dimensions as being a kind of set theory criteria apparently redefining what a dimension is. So any number of dimensions with what are in effect defined as a given set might coexist with Hilbert Space.
Hilbert Space is a given area with four dimensions inclusive of time wherein any number of dimensions defined as behaviors of motions could exist. Nevertheless the dimensions tend to all exist within the boundaries of Hilbert Space rather than is alternate Universes made of different dimensions of the other kind of definition.
Maybe multiverse theory does not extend dimensions beyond real (Hilbert) space of necessarily within the implicit construction of its math. Obviously I am not a mathematician,
What description encompasses the entire Universe of economic action? Multi-dimensional economic models would provide no finite and simultaneous infinite, accurate set descriptions of actual states of affairs. Economics is a purpose, an antinomy to art yet the flip side of it simultaneously. Economics is a clump of precision engineering of wishes to bring in a harvest of potatoes before the season’s shadows grow long and frosts descend upon the fields. It is a complete world of opportunities and ideas interacting with material, finite material, of which planets are made of.
Garrison Gibson: books and blog 