One cannot understand arithmetic,
he has to believe in it.

Maria Kuntsevich (1897-1989)

Arithmetic – The Key to The Understanding Nature

Sorry for the digression, but I have to start with the counting rules. In the case of bitwise addition of two non-negative integer numbers, as we move from digit to digit, there arise the signs of transfer to a high-order digit. Please note that no matter if we do it manually or by means of adders, one way or another, in both cases we have a consistent, time-developed dynamic process. In other words, in contrast to the way we usually write, without thinking about the consequences, in formulas, the simplest arithmetic operations (addition) and its inverse operation (subtraction) are not elementary!
Reasonable questions arise. What is the nature of such a trivial operation and how is it constructed?
Proceeding from the fundamental system principles, preference cannot be given to any digits, i.e., all digits must be equivalent. And from this naturally follows a transition to the addition (subtraction) not in one, as we were taught, but in all the digits at the same time, before all signs of the transfer disappear.

If you are ready to overcome the barriers erected since childhood, then everything that follows is quite simple. By limiting the depth of the transfer, we will obtain Incomplete Arithmetic confirmed by irrefutable facts and easily reproducible in tests. Incomplete Arithmetic with the transfer depth equal to 1 is trivial and was called Pre-Arithmetic (September 2006).

Pre-Arithmetic (Prearithmetic) is characterized by extremely small time and full parallelism of execution of operations for each of the digit and, besides, is accompanied by an unavoidable additional component that is called nduction in dynamic systems. Note that this component vanishes and is not observed in arithmetic!
Pre-Arithmetic has its other varieties, including those that complement each other – multidimensional, in particular, similar to mechanical vibrations and electromagnetic fields. Pre-Arithmetics naturally cover all the knowledge known to date, and with it, if you want, generate new Arithmetics, and then new physics and mathematics, Nonlinear Dynamics (Non-Linear Dynamics) and Cryptography.

Pre-Arithmetic and induction components are associated with dichotomic (Dichotomic Sequence) and other unique properties inherent in nature that we do not notice, ignore or ascribe to ph phenomena.

Following the remarkable mutual equivalence of nature and mathematics, it actually comes out that we know only little about Nature. Reality, and (as follows) physics and mathematics are more complex and subtly constructed, i.e., in a manner other than that we previously thought.


It seems that with the understanding that Arithmetic is not trivial and with the introduction of Pre-Arithmetics following from Arithmetic, there is much to rethink and much to consider in a different manner.

Igor Kulakov, Игорь Кулаков