Date: Jan 23, 2013 9:49 PM
Author: ross.finlayson@gmail.com
Subject: Re: Non-physicist's curiosity on geometry
On Jan 23, 5:59 pm, 1treePetrifiedForestLane <Space...@hotmail.com>

wrote:

> nnettttikketttt-mania;

> it is not clear, to what you are erferring;

> spherical, cartesian, hyperbolic?

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> > I call them macro-, micro-, and "meso-" scale.

I refer to a spiral space-filling 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. Space-time 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, space-time is flat.

Of course extreme physics is full of infinities: and continuum

analysis basically smooths most of them out, but: normalization, or

re-normalization, is: de-re-normalization.

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