Wednesday, May 16, 2012

Computability and the internal structure of zero

In the article “The unreachable number principle, “, I wrote the following equation,

                                         (A – B = 0, but A and B are different numbers)

With this equation, the entire mathematics will be changed.

Again, in the article “Zero or zeros, “, I wrote, “In general, the validity of mathematics relies not on any correspondence to a reality. ... Yet, this ‘Prequark Chromodynamics’ is the direct consequence of the fact that zero (0) has a very rich internal structure. That is, this new mathematics does have a correspondence on the physical reality.”

Thus, although we can develop a new math by making the above equation as a definition, we can actually prove the above equation as it is a fact of the physical reality. The following is the proof.

Pi, the ratio of a circle's circumference to its diameter.

Pi (N), the calculated Pi value to Nth digits with the Turing computer.

Pi (C), the calculated Pi value after countable infinite steps with the Turing computer. 

D(N) = Pi – Pi(N)

D(C) = Pi – Pi (C) > 0

M1 = D(C)/2

M2 = M1/2
Mn = Mn-1/2

P(M1) = Pi(C) + M1 = Pi – M1

For P(M1)  < Y < Pi, Y is unreachable by all means (theoretically or else), as P(M1) is the last known (reachable) number by a Turing computer.

P(M2) = Pi(C) + M1 + M2 = Pi – M2
For P(M2) < Z < Pi, Z is also unreachable by all means.

In fact, the D(C) is the uncertainty in numbers, similar to the h-bar in physics. Thus, 

                               Z – Y = 0
is the direct consequence of this Mathematics uncertainty principle, while Z and Y are two different numbers. That is, there is very rich internal structure in zero (0). I have introduced the concept of “Colored numbers” to accommodate this Mathematics uncertainty principle, and it is available in the book “Super Unified Theory (ISBN 0-916713-02-4, Copyright # TX 1-323-231, Library of Congress Catalog Card Number 84-90325)”, 

Chapter 7 --- Colored numbers (page 53 – 61).

I will also discuss this in the future posts.

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