Hyperbolic Numbers in Modeling Genetic Phenomena

The article is devoted to applications of 2-dimensional hyperbolic numbers and their algebraic 2ⁿ-dimensional extensions in modeling some genetic phenomena. Mathematical properties of hyperbolic numbers and their matrix representations are described in a connection with alphabets of DNA nucleobases, with inherited phyllotaxis phenomena and with the Weber-Fechner law. New methods of algebraic analysis of the harmony of musical works are proposed, taking into account the innate predisposition of people to music. Known data on using hyperbolic rotations, which are particular cases of hyperbolic numbers, in physics and in some biological phenomena, including phyllotaxis laws and structural features of locomotions, are discussed. The hypothesis is put forward that alphabets of eigenvectors of matrix representations of basis units of 2ⁿ-dimensional hyperbolic numbers play a key role in transmitting biological information and that they can be considered as a foundation of coding information at different levels of biological organization. The proposed algebraic approach is connected with the theme of a grammar of biology. Applications of hyperbolic numbers reveal hidden interrelations between structures of different biological and physical phenomena. They lead to new approaches in mathematical modeling genetic phenomena and innate biological structures.