March 19, 2016

How typical is our evolving 3-manifold?

Filed under: Letters from Ionia — Tags: , , , — zankaon @ 6:49 pm

If functions (defining continuity of manifolds?) don’t behave well, such as continuous but non-typical, and hence not smooth, and likewise for our overall Regional volume V_R  3-manifold, which is mainly characterized (hence mathematically more typical) by non-differentiated finer than Planck scale; then is not just our coarser than Planck scale, a very atypical perspective, mathematically speaking?

Might the nature of time , in regards to our evolving 3-manifold and alleged divergent set, System S≡{U_T’, …} of total universes, wherein U_T≡{{V^3_R}_p}, be considered as both always exponentially changing, and thus analytical; likewise for mapping to integers in such  model ?

Thus would the ‘flow of time‘  seem to be  smooth and analytical? In contrast, our finite appearing (coarser than Planck scale) 3-manifold high perch has just finite order differentiation; whereas the overall coarser to finer 3-manifold is not smooth. So our mixture of 2 manifolds would seem to differ in smoothness attribute, as well as continuity, but not in cardinality.

So we would seem to reside in a mixture of 2 topologically inequivalent manifolds, an exponentially changing 1-manifold being well behaved (smooth, and analytical?), but not typical for most manifolds. Whereas the overall coarser to finer 3-manifold is not well behaved (non-smooth), but typical for manifolds; such as 3-manifold version of Weirstrauss function?

That is, what we perceive as a whole, is actually a composite of 2 topologcally inequivalent manifolds, described both as well behaved but not typical for temporal change; while the coarser to finer scale is not well behaved yet typical, in comparison to most other manifolds.

also  zankaon website, SRM page.


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