Modeling inherited physiological structures based on hyperbolic numbers

Abstract

The article is devoted to using the mathematics of multi-dimensional hyperbolic numbers and their matrix representations for modeling of different inherited biosystems, which are parts of the holistic body. The list of considered models includes phyllotaxis sequences; Punnet squares of the Mendelian genetics; the main psychophysical Weber-Fechner law, and some others. This modeling approach reveals hidden structural interconnections among different biosystems and leads a deeper understanding of their commonality related to the commonality of their genetic basis. At the same time, it shows the structural connection of inherited biosystems with formalisms of the theory of resonances of oscillatory systems with many degrees of freedom. This complements works of many authors - from antiquity to the present day - on the importance of coordinated oscillations and resonances in the life of living organisms. The modeling approach based on hyperbolic numbers and their bisymmetric matrices reveals that the structural commonality of different inherited biosystems is related to the harmonic progression 1/n and the harmonic mean, which are long known in arts and culture. They are used in the Pythagorean teaching on the musical harmony and the aesthetics of proportions. Besides, the using - for biosystems modeling - of multi-dimensional hypercomplex numbers, which are one of the main tools in modern mathematical natural sciences, opens a bridge between these sciences and biology for their mutual enrichment.