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From: Archimedes Plutonium on 26 Jul 2010 01:19
Alright, I have not really done much to further the science of
probability theory. It really has not moved or budged much from French
probability advances. We have the Fundamental Counting
Principle as a exponental. A test with two choices (true false test)
that has 3 questions would
have 2x2x2 outcomes. With 4 questions would have 2x2x2x2.
So the exponent in probability theory means "total possible outcomes."

And we have the equation of 268! = 10^536
Is like saying that "all possible sequental arrangements" = "total
possible outcomes"

So tonight, let me try to see if I can expand Probability theory into
a whole new ballgame,
or should I say cardgame or dice game. Instead of combinations and
permutations, let me try
to get Probability theory into a geometrical foundation.

Let us start with 268! = 10^536 and view that as "all possible
sequental arrangements of 268
digit numbers" all containing digits from 0 to 9 inclusive (from the
10 in 10^536). And the number 10^536 now becomes the total number of
these all possible sequental arrangements
of 268 digit numbers. Let me give some examples to clear the mind.

0000..001 where there are exactly 268 digits in this number and we
recognize it as 1
Then there is the number 1000..000 and the number 9999..999 and all of
these numbers
has exactly 268 digits. Now, how many numbers in total are there of
these? Well if I am
doing probability theory correctly, no guarantee, then there are
exactly 10^536 of these sequences.

Now this reminds me an awful lot about All Possible Digit Arrangements
to build the AP-adics
but I will not digress there, just point it out.

Now, recently I derived the speed of light out of pure mathematics by
noting strip geometry where we consider meridians as strips and how
many of these strips depends on the width of the strip and that
depends on the units you want to deal with. So if you want speed of
light
in kilometers than the width is 1 kilometer wide. And so we add up all
the meridian strips and we divide by a time factor, begot from
pseudosphere nested inside the sphere. So the speed of light is begot
from geometry and is intrinsic to every sphere. What it means is the
time a light wave travels the distance of the sphere of the up and
down strips, travels the entire distance of all those strips in the
amount of time determined by a pseudosphere inside that sphere.

I bring up the speed of light because I suspect that probability
theory can be turned into
a geometry theory by akin pattern as the speed of light. Only instead
of just the surface of the sphere and pseudosphere involved, we also
have the volume of the sphere involved.

So let us look at this equation of 268! = 10^536 and let us imagine
that every point of a sphere
of its volume is one of the points of

0000..000
0000..001
..
..
..
9999..998
9999..999

where there are 10^536 such numbers all having exactly 268 digits, and
only digits from 0 to 9 inclusive.

Now those are a huge number of "sequental numbers" so huge that we can
safely say that the volume of a sphere is 10^536 such points packed
into the sphere. If we were inside the cosmos as a huge sphere, then
the point at which we were in the Cosmos, corresponds to one of these
numbers of this matrix:


0000..000
0000..001
..
..
..
9999..998
9999..999

The number 10^536 would be the number if you were to compute the
distance from one
point to another and sum all these distances up, your distance would
be 10^536, a unitless distance.

So what have I got so far? I have that the number 268! are all the
points inside a sphere that
creates that sphere. Next, I have that the number 10^536 would be the
summation of all the distances inside the sphere, if they were lined
up, would create a line of 10^536 units long.

So I have factorial creating a sphere with its interior and the
exponent creating a distance if the
line segments inside the sphere were summed.

Let me give example of one such line segment from the two points of
000..001 and 000..008
would be a line whose length is 7.

Now the point 0000..000 would be the center of the sphere and the
point 0000..005 would be
5 units from the center.

Now for small numbers the factorial is less than the exponential, and
only after about 20! does the factorial exceed the exponental. This
may limit where this geometrical probability theory
takes affect.

And a new theory is only as good as what practical use it provides.
The practical use the above provides at the moment is that it tells us
where multiplication is no longer needed or useful because we have a
Space in which only numbers of 268 digits are of any sense. So that if
one multiplies which gives an answer of greater than a number with 268
digits is going
outside the fence of mathematics.

I shall think some more about the above. We need to get away from
probability theory as a number theory and need to inject geometry into
Probability theory and that is what I have started this program, to
make probability a geometry.

Now I maybe able to turn the one number of 268! as all the points that
compose a sphere and turn the number 10^536 as all the points that
build a pseudosphere, whichever nests inside the other.

Geometrical-Probability theory would be a whole new area of
mathematics, and sort of mindboggling to say the least.

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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