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Subject: Re: The Universe Is Not A Sphere (doubling spaces, pi ratio spaces)
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From: Ross Finlayson <ross.a.finlayson@gmail.com>
Date: Fri, 29 Nov 2024 10:48:46 -0800
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On 11/29/2024 09:41 AM, J. J. Lodder wrote:
> LaurenceClarkCrossen <clzb93ynxj@att.net> wrote:
>
>> Riemann was a brilliant geometer who made the elementary error of
>> reifying space by claiming parallel lines could meet. Schwarzschild and
>> Einstein carried through with that mistake, making people believe it was
>> intelligent.
>
> Dear Genius,
> Could you please prove his hypothesis for us,
> when you are finished putting him down?
>
> Jan
>
>
>
>

You mean torsion and vortices in free rotation the
un-linear, making for space contraction?


If you take a look at a circle, and a diameter,
then draw inner circles, their diameters the
two radii that is the outer diameter, so that
the sum of the diameters is the same, and then,
the sum of perimeters is the same, because circles
make that for diameter d is perimeter pi d.

So, repeating this ad infinitum, makes smaller
and smaller circles bisecting each diameter,
whose sum diameter is a constant and sum perimeter
is a constant.

Then, all the down, a flat line, the, "perimeter",
or length, is not the same, it's d/2, say.

So, it's like a "pi ratio space", or, say,
"2pi ratio space", that in the infinite limit,
is different what it is according to induction.
In this way it's like Vitali's doubling measure
and Vitali and Hausdorff's equi-decomposability
of a ball to two equal balls, "doubling space",
about "doubling measure", this "pi ratio space",
"pi ratio measures". I think that's cooler than
Banach-Tarski as it's geometrical, about geometry,
that Vitali and Hausdorff were pretty great geometers.


So, now when you look at the gravitational field equations,
and Riemann's Riemann metric contribution, you'll notice
that it's sort of about a linear metric, that though
over and over again and all the down is sub-divided,
to what's a metric in the "merely linear", this,
"un-linear".


Anyways though the usual "Riemannian geometry" is
matters of perspective and projection is all.

I.e. it's Euclidean, the conformal mapping.

One can readily see it's a mathematical device
a conceit, a concession, "Riemannian geometry",
about conformal mapping with free rotation.


So, what Einstein arrived at, is mass-energy equivalency
the kinetic, that's only ever kinematic and rotational,
that it's always, "un-linear", that these days is
often called, "non-linear".

Or, that was the last derivation Einstein authored
into "Out of My Later Years", a culmination of
his thinking.

In my podcasts today is a "Logos 2000: geometry logically",
helping arrive at axiomless natural geometry.

https://www.youtube.com/@rossfinlayson

The usual Newtonian laws of mechanics are a bit
under-defined, so there's room under them to
add definition to mechanics, the kinetic/kinematic.