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