Math Forum / Mathematics / Mathematical Logic / November 2008

Alright, I am going to stop with the preliminaries of this preface and
dive into the book itself.
I could probably spend the next months on the preliminaries and to fix
and consolidate
details such as the Hyperbolic Geometry, especially, "what are lines
in Hyperbolic Geometry"
but I believe in diving into the book is a better option. And as the
time goes by, some of those
details will be clarified.

I feel confident in addition, multiplication, division, subtraction.
About the only thing vexing
me on those is what to make of the "apppended two imaginaries" of the
poles in Elliptic.
What to make of the hyperbolic-equator and the hyperbolic-lines in the
pseudosphere.
The details of the axes in both Elliptic and Hyperbolic are not fully
ironed-out.

The many details of inverses between Elliptic and Hyperbolic, I have
to work out. Some
examples are that lines in Elliptic are longitudes whereas it is
inverted to be latitudes
in Hyperbolic. The question over the Equator in Elliptic versus
Hyperbolic and why is
it so special?

There is the problem of what I am going to call Betweeness of
Integers. This problem is
especially important between 1 and North Pole or between 999....9999
and South Pole.
We have the radix of a finite portion rightwards which we can think of
as "fractions".
This portion is finite but it approaches the North Pole. The problem
with it is that I want
to set up the arc of 000...00001 as a "secondary projected y-axis".

Most of the problems of details lie with the Hyperbolic Geometry and
that is easy to
understand in that our minds are wired to handle Euclid Geometry and
even Elliptic
Geometry with some ease, some fluidity. Most of us who become
mathematicians
could almost take Euclidean Geometry without ever knowing what the
axioms were,
like instructions to some building project where we never bother to
read the instructions
and can assemble the entire kit. When I took Euclidean Geometry in
High School, I
would assemble the theorem as a picture in my mind and only later
apply any axioms.

But in this book where I take Negative AP-adics and from them show
that they are
the intrinsic numbers of Hyperbolic Geometry, I am going to have more
trouble with
them than with Positive AP-adics as the basis of Elliptic Geometry and
AP-Reals
as the basis of Euclidean Geometry.

Also, this book will show that the Old Reals are deficient, and that
they are self-contradictory
and full of phony numbers-- transcendental numbers. The Old-Reals
never even bothered
to distinguish numbers from fractions. It is assumed by
mathematicians, even today, that
the Old Real of 0.3333...... is the same thing as 1/3. Fractions,
according to this book are
not numbers. Fractions are merely a shorthand for dividing. Do I say
that 1 divided by 3 is a
number itself? Well, not really. The process of dividing is not a
number. So this is another
area of the old math that the old mathematicians never cleaned up but
left dirty.

And as for Algebra of Galois theory such as Group, Ring, Field and its
many intricacies. This
book will talk about Algebra but this book puts algebra into its
proper place in the house of
mathematics. The problem with the old mathematicians is that they
loved algebra so much
that they forgot about geometry which is far larger in importance than
algebra. So this book
places Geometry as king over algebra, where algebra is only a subset
of Geometry.

Mathematics has two large compartments. One is Numbers and the other
is Geometry. It is
a duality for mathematics and follows from Physics that physics is
particle wave duality.
So where does algebra stand as far as Numbers and Geometry? Well,
algebra is a part of
Numbers, but algebra is not as big as Numbers. Here I can think of an
analogy. Physics is
particle and wave duality which would comprise numbers and geometry
for mathematics.
But in physics we also have electricity to magnetism duality.
Electricity-magnetism duality
is part of the Particle theory, and here is the analogy-- Galois
theory is to magnetism what
Coordinate system is to electricity.

I could write a whole entire other book pointing out the flaws and
errors of the axioms of the
Old Math and how the Old Reals are phony. That would take alot of
time, not well spent.
So I will mention briefly in this book where the Old Reals and their
axioms erred.

Finally I would like to mention the history of all sciences for which
mathematics is included.
The major science, the king of sciences is physics, and up until the
Atom Totality appeared,
there were many in science who had the awfully warped belief that
mathematics was above
physics. That somehow knowledge would end up with some sort of
mathematical equation.
This book puts math into its proper place as a tiny subset of Physics.
And that Physics
had a revolutionary period in the 20th century with the final
acceptance of the Atomic Theory
started back in Greek times and where the 20th century then
revolutionized Newtonian
Mechanics with Quantum Mechanics. What is so important about that
Quantum revolution
is that mathematics has never had such a overwhelming revolution in
its entire history. Why?
Is it because mathematicians are so conservative that they are
rumdummy obtuse? Is it
because they are so ivorytowered that they would not recognize the
flaws and blemishes
of their science? I think the major answer is because mathematics is
the only science that
does not have "Experimentation" as its final judge. The final judge in
mathematics as we
can see from history is a group of old men with their opinion. Whereas
in physics or chemistry
or biology or anthropology, if a group of old men have an opinion, and
the experiment turns
up that it swerves from the opinion, well, the experiment is believed
in, not the group of old
men. A Cantor who comes along in the late 1800s and espouses fake
ideas about infinity,
is something that a group of old men would easily glum onto and accept
as true, whereas
in the late 1980s when Pons and Fleishmann propose fusion engineering
in test tubes of water
then the Physics community with its experiments easily refute the
claims in a space of 2 to
4 years. Whereas Cantor fakery of the 1880s becomes part of the
accepted math.

So mathematics is like a person whose is blind in one eye, whereas the
experimental sciences
have that extra eye of experimentation that makes their science on far
better foundation.

Enough of the preface, and let me dive into the Introduction.

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