Reals form a saddle shape? Re: Adics are Riemannian Geometry and Reals are Lobachevsky and Doubly-Infinites are Euclidean

From: Archimedes Plutonium (a_plutonium_at_iw.net)
Date: 09/15/04 

Date: Wed, 15 Sep 2004 02:50:48 -0500

Tue, 14 Sep 2004 10:10:30 -0500 Archimedes Plutonium wrote:
(snipped)

> Sun, 12 Sep 2004 13:53:27 -0500 Archimedes Plutonium wrote:

(snipped)

>
>
> So if we look and examine and research into REals, just the positive
> Reals because
> negative REals are artificial. CAn those REals be seen as forming the
> shape of say a
> trumpet or saddle? Do the Reals have a built-in curvature that the
> Adics have?
> Because the Adics start at a point such as 0 then go to 1 and finally
> go all the way
> around to ....9999 and come back to 0 and 1 again. So do the REals
> have a built in
> curvature? I beleive they do once we examine the messiness of Calculus
> in that we
> need dozens of different definitions of integrals and derivatives and
> we have
> several bizarre theorems in calculus about differentiation and
> integration. I
> suspect this messiness is because the REals were never intrinsic
> points of Euclidean
> geometry and that Calculus before I entered the picture assumed that
> the REals could
> represent a Euclidean Plane.
>
> And that leaves the question of Doubly Infinites. My best guess is
> that the Doubly
> Infinites are the poinst of Euclidean Geometry. Notice how difficult
> it is to reckon
> with pi and e as Adic numbers. But pi and e exist in REals and exist
> in Doubly
> Infinites

You see the way mathematics was discovered and created for the past 5
thousand years was as a tool of practical use to people in their lives.
Not until about the time of Maxwell and then Quantum theory did we begin
to sense a relationship of mathematics to physics which was more than
that of a "tool".

But it was a practical tool that we created the negative sign and the
notion of negative Reals so that the plane is a plane of Real points.

Not until the 1990s when I began to discuss the AtomTotality theory do
we get a different sense of the relationship between mathematics and
physics. In that the AtomTotality theory tells us that mathematics is a
subset of physics. And that all mathematics is begot from how many atoms
exist and the geometry of atoms. So the quantity of atoms creates
numbers and the shape of atoms creates geometry.

Never before in the history of mathematics has anyone asked the most
important questions of number theory. The question of what are the
intrinsic coordinate points of Riemannian and Lobachevskian and
Euclidean Geometry? Numbers that truly exist are coordinate points of
one of these 3 geometries.

Until 1990s, mathematicians have assumed or presumed that the Reals
represent a Euclidean plane with the negative Reals taking up several
quadrants and the positive Reals the other quadrants.

Number theory was about NaturalNumbers and Number theory had a huge
backlog of unsolved problems such as FLT, Riemann Hypothesis, etc etc.
The reason there was a backlog was because finite-integers were not the
NaturalNumbers at all but a fake-plastic set. The Adics were really the
NaturalNumbers. And the Adics form a geometry which is that of nested
spheres where the 2-adics is one sphere and the 3-adics another sphere
that collectively produce Riemannian Geometry.

Now if we examine the Reals closely as we examined NaturalNumbers to see
if there is any flaws leaking out of mathematics by using the REals. And
there truly is gaping flaws. We see it in Calculus in that we have a
blizzard of different types of integrals such as Lebesgue etc etc. We
see thorny differentiation theorems talking about discontinuity. So the
question quickly arises because of the messy definitions of Calculus
when using Reals as to whether the REals were ever meant to be the
numbers of Calculus.

And like my calling to attention that FLT and all the Number theory
problems are easily solved when NaturalNumbers are taken to be the
Adics. So, again, can I straighten out this blizzard of mess of
integration and differentiation involving Reals?

I think the root problem is that the REals are not numbers that form a
Euclidean Plane. That the invention of the negative Real concept may
have been a helpful tool but is not what REals are.

I speculate that there is no negative REals. And that the REals can not
be used in a Euclidean Plane. I speculate that the Reals, like the Adics
have only one sign and the sign for Adics is positive because the Adics
have a built-in negative where ...99999 is -1. So to say that a Adic
exists that is say -.....9999 is ridiculous. I speculate that the REals
are all negative signed already and innately and intrinsically. I
speculate that the Reals form a saddle shaped geometry. I speculate that
REals are the intrinsic coordinate points of Lobachevsky Geometry or
hyperbolic geometry just as the Adics form Riemannian geometry.

I speculate that if you created a Calculus on hyperbolic geometry that
the REals you use will eliminate the mess of integration and
differentiation that now exists in REal Analysis.

So that leaves Doubly Infinites.

Karl Heuer circa 1993 said that I could not have this equation:

     Euclidean Geom. equal to Riem G. plus Loba G.

But I disagreed with Karl then and to this date.
I think I can get that equation from

    Doubly Infinites equals the Adics combined with Reals

Because Adics are infinite strings leftward and finite rightward and
Reals the reverse but when both are combined make for Doubly Infinite.

I know the Adics have a sphere shape to them because they curve back
around starting at 0 going to 1 then 2 and finally up to ....9999 which
is -1.

But can I give an argument of the shape of Reals as to being a saddle
type shape? That is difficult at this moment. It involves only positive
REals for the negative Reals were a plastic add-on. So the only argument
I can offer at this moment in time is to be able to pick through all the
various forms of integration and differentiation definitions, to sort
through that blizzard mess and to find a spot in which those definitions
make sense if they were on the surface of a saddle shape or trumpet
shape which is hyperbolic geometry. If I can do that then I am closer to
the understanding that the REals are the intrinsic coordinate points of
Lobachevsky GEometry and that their past history use as a Euclidean
Plane was a misappropriated use and a fakery.

Archimedes Plutonium
www.archimedesplutonium.com
www.iw.net/~a_plutonium
whole entire Universe is just one big atom where dots
of the electron-dot-cloud are galaxies

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