  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.
