Archimedes Plutonium wrote:
> Archimedes Plutonium wrote:
> (snipped)
> > When I wrote the AP-adics book, I was attacking two
> > math ideas. One was a better formulation of P-adics from Hensel's p-
> > adics and so I came up with the AP-adics. But a second attack was to
> > further the idea that
> > Geometry was this:
> > Euclidean Geometry = Elliptic unioned to Hyperbolic Geometries
> > Written in short: Eucl = Elliptic + Hyperbolic
> Having all the numbers finite is neat because I can rewrite that
> equation in
> symbol form as this:
> | = ) + (
(1) Euclidean geometry is the Elliptic geometry unioned with
Hyperbolic geometry
(2) | = )(
In (2) we see how the union occurs in that we simply reverse a
triangle's
sides of concavity into a reverse concavity yielding a straight line.
And I should mention a third equation in this process of connecting
geometry
to algebra:
(3) Given a Doubly Finite Number which is native to Euclidean Geometry
such as
1000..00d3333..33 where the symbol ".." indicates these are restricted
by a boundary
of finite as 10^500 decimal place value. We have:
1000..00d333..33 = 1000..00r + r333..333
So we have numbers in Elliptic geometry that are the integers and
numbers in
Hyperbolic geometry which we considered to be the decimal fractions.
> The idea is that the Elliptic geometry is the inverse of Hyperbolic
> geometry
> and where the application of a curve ) on another curve ( ends up with
> a
> straight line segment.
> Now to translate that into number algebra we simply go to inverses
> where +2 is the inverse of -2. So if we have a curve ) that is all
> positive
> finite numbers applied to a curve ( of all negative finite numbers,
> they
> cancel leaving behind a straight line segment.
> Or, we can do the transform via multiplication inverse where curve )
> is positive integers and curve ( is multiplicative inverses cancelling
> to form a straight line segment.
> > And where I use the three and only three number-systems as native to
> > one of those geometries such as this:
> > Doubly Infinites = +AP-adics unioned -AP-adics
> > But with this book of Correcting Math, I have run into
> > a serious problem. In the AP-adics book, those numbers are defined as
> > having a infinite-component
> > and in Doubly Infinites there is no finite-component.
> > In this book, I define Finite as 10^500 or less (inverse
> > included). And I throw out as meaningless the infinity
> > or infinite-numbers.
> > So this book of Correcting Math ruins my previous book of AP-adics.
> > But I can salvage the AP-adics book.
> > I simply retitle it as Eucl Geom. = Ellipt unioned Hyperbolic. So I
> > switch the emphasis to the geometry
> > aspect of that previous book.
> Actually it appears that all finite numbers makes my other book
> easier. I now
> can see that the finite numbers from 0 to 10^500 cover a hemisphere
> and where
> the South Pole becomes the number 10^500 and then returning to the
> North Pole
> of 0, we have negative numbers in the return and where we consider the
> point one
> unit shy of the North Pole as (-)999..99 where that is one less than
> (-)10^500
> And I set up Euclidean geometry as a finite geometry going from one
> extreme end of
> (-)10^500 to the other extreme end of 10^500
> Both the Elliptic and Hyperbolic geometry can be represented by a
> sphere and where
> one is concave outwards, the other is concave inwards and putting the
> two together
> they cancel one another yielding a Euclidean straight line segment.
> So rather than harming my previous work of Eucl = Ellipt + Hyperb,
> it appears that as I make all the numbers Finite, that it helps the
> program and it gives more clarity.
thereof,
is I want to jog my memory by reading the last pages of this book to
recollect where I departed.
In the 3rd edition I should detail how the Calculus is rendered more
clear
and easier with the definition of Finite as the boundary at 10^500
(with its
inverse).
Now there is one last item I want to convey before leaving. It is an
item I
brought up in the AP-adics book of considering these three different
Infinite-Integers.
(a) 1000....0000 = South Pole and 100% of the distance from North Pole
to South Pole
in Elliptic geometry.
(b) 1000....0000 = 10% of the distance from North Pole to South Pole
and is one decimal
place missing of (a) since it is 10%
(c) 0000....00100...0000 that number which is peculiar or strange. It
definitely exists
if you demand that Infinite Numbers exist. (Although I no longer
demand any infinity
concept and that Physics is all finitary.)
I bring this topic up, here at the end, because I suspect this
peculiar number offers a proof
that the definition of Finite versus Infinite requires one to pick out
a "known finite number"
such as 10^500 and declare all other numbers beyond as the realms of
incognitum or
infinite.
I believe this strange number 0000....00100....00000 is what Old Math
believed as Finite
in the best definition of Old Math had for "finite." If the reader
recalls, the best that the
Old Math ever did for finite definition was to say that a number is
finite if its string of digits
leftward ends in zeroes. For example: 747 was finite in Old Math
because it was
0000....0000747. Noone ever bothered the old-timers of math because
the discover that
a number has a FrontView with BackView blinded them of ever asking
whether
07777.....77777 would be a finite-number according to the best
definition of finite by the
old math and its old timers.
So a number like 0000....00100....00000 seemed to fit the bill for the
Old Math,
old timers definition of finite as ending in zeroes leftwards. And
noone can say
exactly where that "1" digit was. It was far smaller than 10% of the
distance
to the South Pole from North Pole. In fact, one could say that the
distance
was an infinitesimal distance from the North Pole in the direction
heading for
the South Pole.
So I leave this book with this strange number, and I suspect this
number can
prove that the only way of defining Finite versus Infinite is to
actually pick out
a large finite number such as any of the Planck Units in physics and
to say--
that is the end of Finite and that all numbers beyond are either
meaningless
since there is no more physics going on, or that all numbers beyond
are in
the realms of incognitum to infinite.
So this special number is a tool to use in a proof that to define
Finite in mathematics
requires one to select a large finite number and call it the boundary
between
finite and infinite, or finite and meaningless. And since Physics has
no
infinities, well, it means that infinity is meaningless.
Bon voyage.
I need to wrap my head around Plutonium day which is rapidly coming
up-- Nov 7,
auf wedersehn
Archimedes Plutonium
www.iw.net/~a_plutonium
whole entire Universe is just one big atom
where dots of the electron-dot-cloud are galaxies
|
