Dear Tim :
Your essay is very interesting,
In my opinion, mathematics that reflects reality, remains a priority for the current science.The Bi-iterative calculation could be the right one, because it has all the characteristics of a pure mathematics.
"NUMBERS"
first are integers
second are geometric shapes
third are physical entities, with infinite degrees of freedom
fourth maintain always the aspect ratio
fifth are elastic ... ..
Sixth are compact, and unseverable by two egual part.
We take an example:
1 + 5 + 7 + 12 =
= 1 + 5 + 7 + (6 + 8 + 10)
= 1 + 5 + 7 + (3 + 4 + 5) + 8 +10)
= 1 + 5 + 7 + (3 +4 +5) + (1 + 6 - 9) + 10
= 1 + 5 + 7 + (3 +4 +5) + (1 + 6 - 9) + 10
= 1 + 5 + 7 + (3 +4 +5) + (1 + (3 + 4 + 5) - 9) + 10
= 13
=2197
Of course, we speek about a cubic equazion.
Recursive calculation, the Fibonacci series and Fractal are wrongly linear, because they consider the space as a bi-dimensional sheet.
The system's Bi-iterative calculation is different, it consider the space, multi-directional and multi-dimensional. In fact, exist only set and sub-set. with (1) we mean (1 * 1 * 1).
Because we live in a complex and varied reality, only a struture able to transform can describe it.
The human brain is divided into two halves, the left hemisphere is masculine, active, called "rational". The right hemisphere is feminine, passive called "irrational".
The most important thing is that these two opposing positions should coexist. (x + 1) and (x - 1) are two limits , i meam the linear structure and the non-linear structure are inseparable.
A system that can not stop,follow the arrow of time. Or rather, it coping itself, reflecting itself. So, we have (x + 1), + 1, + 1, + 1 ....
"The universe was born like that, one bit after another, and continues to do so even now".
(See ANNEX)"The teorem"
sincerly yours
BannouriAttachment #1: 1_1_Theorem_1.jpgAttachment #2: 1_1_Theorem_345.jpg