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Re: Nonphysicist's curiosity on geometry
Posted:
Jan 23, 2013 9:49 PM


On Jan 23, 5:59 pm, 1treePetrifiedForestLane <Space...@hotmail.com> wrote: > nnettttikkettttmania; > it is not clear, to what you are erferring; > spherical, cartesian, hyperbolic? > > > > > > > > > I call them macro, micro, and "meso" scale.
I refer to a spiral spacefilling curve as a natural continuum that founds a geometry in points and space in lieu of points and lines.
Then, for "geometric mutations" in the macro and micro, it is observed that the more we look to the Universe the larger it appears to be, the more closely we look to atomic particles the smaller they appear to be, the only measurement is of change and measurement has effect.
Of course in the general sense of etiquette I'll allude to a variety of rather controversial opinions on the infinite. For example where the universe is infinite or unbounded, mathematically it would be its own powerset (Universe contains itself). There's no smallest length or there are no right angles as the distance between two lengths joined at right angles wouldn't be an integer multiple of the smallest length. Strings of as many orders of magnitude smaller than atoms as they are to us are a simple aversion to the real mathematical infinitesimals of those point particles, and an allusion to the space they are in.
The cosmological constant is an infinitesimal. Spacetime is, in a sense, flat: for gravity and its well or shadow. Simple transformation of coordinates to account for the continuous force of gravity is a notational convenience, spacetime is flat.
Of course extreme physics is full of infinities: and continuum analysis basically smooths most of them out, but: normalization, or renormalization, is: derenormalization.
So, in the macro and micro there are natural geometrical effects of being small and large, mutations or simply sweeping or point, or point or sweeping effects, there are "real" mathematics of the infinite yet to be discovered with concrete application for continuum mechanics.
Find novel mathematical applications of the infinite with use in physics. Today's integral calculus for continuum analysis is quite standard.
Regards,
Ross Finlayson



