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From: Archimedes Plutonium on 1 Jul 2010 03:06


Archimedes Plutonium wrote:
(snipped)
>
> Theorem: in geometry there never can be constructed a infinite-line
> from any number
> of finite line segments.

Let me add to the above "in old math"

> Proof: Since old math does not recognize infinite-numbers, that no
> matter how many
> finite number of line segments we put together, they still will never
> summon into an
> infinite-line-ray. However, if a precision definition is given in
> geometry or algebra saying
> that finite-number means all numbers less than 10^500 and over that is
> infinite-numbers.
> Well, with that definition we can say that an infinite number of
> finite line segments builds
> a infinite-line-ray.

Let me summarize so far. Old Math never well defined what it means to
be a finite-number
versus an infinite-number. Due to this lack of precision, we get a
whole slew of unsolved and
unsolvable problems such as Twin Primes, Goldbach, FLT, Riemann
Hypothesis and thousands of number theory problems. The question then
arises, why can we still prove Infinitude of Primes with such a system
that lacks precision definitions, yet unable to prove
more complicated statements such as Twin Primes? And the answer seems
to be that at a
raw primitive level of complexity such as Infinitude of Regular Primes
is do-able with no precision on infinite-numbers, but with a tiny bit
more complexity such as Twin Primes conjecture or Perfect Numbers or
Goldbach, that the lack of precision of what is a finite-number versus
an infinite number, the lack of precision catches up and prevents
there to
ever be a proof.

So what is the added complexity thrown into the Twin Primes that just
prevents there ever
being a proof? With regular primes we have a contruction mechanism of
"multiply the lot and
add 1". Now with Twin Primes we can have that mechanism by saying
multiply the lot and
consecutively add 1 and subtract 1 giving two numbers separated by an
interval of 2 units.

So now, why does that not work? It does not work because we can never
separate out the
twin primes from the regular primes. And because, well, the Twin
Primes conjecture maybe
false in that as the twin primes runs out, the quad primes the six-
primes, the 8 primes still keep going and a new category of 2N primes
arises to take the place of the vanished twin
primes. So in turn, as the twin primes then the quad primes then the
six primes vanish, a new
category of 2N primes emerges then the 2N+2 primes then the 2N+4
primes and etc etc.

Now if the Twin Primes is that much more complex of a conjecture, just
imagine for a moment
how much more exceedingly complex is the Riemann Hypothesis versus the
tiny bit more complexity of the Twin Primes over the Euclid Infinitude
of Primes.

However, with this disparity in complexity there is a simple solution
that makes all these unsolved problems disappear. It is to well-define
Finite Number versus Infinite Number
and the only way that can be achieved is to pick a boundary line.
There is no better boundary than to use the largest number in Physics
which is 10^500 as the Coulomb Interactions in an
atom of element 109. That number is so huge that there are no more
physical measurement
at that number, nor its inverse 10^-500.

So now, how does that well-defined precision definition of Finite
Number as less than
10^500 and any number over is infinite, how does that render these
unsolved problems
solveable? Easy, for we have a mechanical proof means of unsolvable
problems. If we can
start tabulating twin-primes and can begin to list a set with
cardinality approaching 10^500
of twin-primes then we conclude twin-primes are infinite. For Goldbach
the same story
of showing that the first 10^500 even numbers are the sums of two
primes. For FLT,
to show that there are no pythagorean triples in the first 10^500
numbers. For Riemann
H. to show that all the first 10^500 primes lie in the 1/2 Real strip.

Now some of those tasks or chores are going to take longer than any
computer could
reach. Because 10^500 is so huge that we need shortcut algorithms to
help us. But as the
computers crunch through say 10^20 of these numbers we get the feeling
that there really
is no stopping the verification up to 10^500.

The trouble with the old math is that it viewed the Universe as some
idealistic Newtonian
absolutist Universe, a sort of Platonic ideals running about. Whereas
the Universe is more of a finite arena of measurement and ability to
count and measure and where Physics is
in control over math and where logic is not Aristotelian straight line
logic but rather dualistic
circular logic.

Archimedes Plutonium
http://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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