Matrix genetics, part 4: cyclic changes of the genetic 8-dimensional Yin-Yang-algebras and the algebraic models of physiological cycles

TL;DR

This paper explores the cyclic permutations of a genetic 8-dimensional Yin-Yang-algebra within a genetic matrix, revealing hierarchical algebraic changes that model biological cycles and potentially explain phenomena in physiology and evolution.

Contribution

It introduces new algebraic models of cyclic genetic processes based on permutations of the Yin-Yang-algebra and connects these models to biological and historical concepts of cyclicity.

Findings

Cyclic permutations lead to new Yin-Yang-algebras from the genetic matrix.

Hierarchical cyclic changes in these algebras model biological and evolutionary cycles.

Connections are made between algebraic cycles and ancient/modern physiological doctrines.

Abstract

The article continues an analysis of the genetic 8-dimensional Yin-Yang-algebra. This algebra was revealed in a course of matrix researches of structures of the genetic code and it was described in the author's articles arXiv:0803.3330 and arXiv:0805.4692. The article presents data about many kinds of cyclic permutations of elements of the genetic code in the genetic (8x8)-matrix [C A; U G](3) of 64 triplets, where C, A, U, G are letters of the genetic alphabet. These cyclic permutations lead to such reorganizations of the matrix form of presentation of the initial genetic Yin-Yang-algebra that arisen matrices serve as matrix forms of presentations of new Yin-Yang-algebras as well. They are connected algorithmically with Hadamard matrices. The discovered existence of a hierarchy of the cyclic changes of types of genetic Yin-Yang-algebras allows thinking about new algebraic-genetic models of cyclic processes in inherited biological systems including models of cyclic metamorphoses of animals. These cycles of changes of the genetic 8-dimensional algebras and of their 8-dimensional numeric systems have many analogies with famous facts and doctrines of modern and ancient physiology, medicine, etc. This viewpoint proposes that the famous idea by Pythagoras (about organization of natural systems in accordance with harmony of numerical systems) should be combined with the idea of cyclic changes of Yin-Yang-numeric systems in considered cases. This second idea reminds of the ancient idea of cyclic changes in nature. From such algebraic-genetic viewpoint, the notion of biological time can be considered as a factor of coordinating these hierarchical ensembles of cyclic changes of types of the genetic multi-dimensional algebras.