In my last post, I showed,

1. There are three types of numbers (odd, even and irrational).

2. One type of number is reachable by another type or types. Thus,

a. every number is a fruit of (or hanging on) other types of numbers,

b. every number is known (or conscious of) by many other numbers, in addition to its self-awareness.

Thus, however chaotic the number set (especially for the irrational numbers) looks like, every number is reachable via the information of other numbers. In a sense, the number set contains infinite amount of information. Thus, in this new number theory, I will see the “number” itself as an information “agent”.

In the current Math, a number is a point on the number line which is a geometric line. In this new number theory, the “point” of a number is a “knowledge” point, in addition to be a geometric point. By knowing the “point” of number “3”, the number “1/3” is known. That is, the “point” of number “3” actually houses two numbers “3” and “1/3”. The number “3” is reached with an operation on “1/3”, and the vice-verse. In fact, this two way operation forms a loop. Loop (1/3) = 3, and loop (3) = 1/3. Thus, every number “point” actually houses three entities (x, loop, 1/x). That is, every number “point” carries, at least, three distinguishable information, and these information are vitally important for locating other numbers.

Thus, the “Point” of “3” and the “point” of “1/3” is, in fact, the same “point” (a pinched point of 3 and 1/3 via an operation [loop]). This pinched point has the “self-awareness”. By knowing “3”, the “1/3” is also known. Of course, the “1/3” can also be reached via other points,

1/3 = 1/2 - 1/4 + 1/8 - 1/16 + 1/32 - 1/64 + 1/128 - 1/256 + 1/512 - 1/1024 + 1/2048 -... +...

= .33349 - ... + ... = .3333333333333.....

= .33349 - ... + ... = .3333333333333.....

For number x, it is always reachable via its pinched point. For example, x = square root of y, then the pinched point (as an information agent) of x has the information of (x, y, and a loop [square root operation]).

So, every number “point” has self-awareness via a loop (operation) and another number, and it is conscious of by other points. Without this kind of self-awareness and consciousness as a part of the intrinsic nature for numbers, we (as an intelligent being) have no chance to reach any of those numbers. Thus, the terms of “self-awareness” and of “consciousness” are not a figures of speech. Thus, however chaotic the number set (especially for the irrational numbers) looks like, it is highly organized by its consciousness, and every number is reachable via that consciousness of other numbers.

With this new number “point” for numbers, the GD symmetry breaking (giving rise to a loop from a singular point) becomes an innate and spontaneous process, as every number point (geometry point on the number line) has an internal structure. Of course, this is just the beginning. A detailed analysis will be discussed later.

Tienzen (Jeh-Tween) Gong

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