Modeling inherited physiological structures based on hyperbolic numbers
The article is dedicated to utilizing the arithmetic of multi-dimensional hyperbolic numbers and their matrix representations for modeling of various inherited biosystems, that are elements of the holistic physique. The listing of thought of fashions contains phyllotaxis sequences; Punnet squares of the Mendelian genetics; the principle psychophysical Weber-Fechner regulation, and a few others. This modeling method reveals hidden structural interconnections amongst completely different biosystems and leads a deeper understanding of their commonality associated to the commonality of their genetic foundation. On the similar time, it reveals the structural connection of inherited biosystems with formalisms of the idea of resonances of oscillatory programs with many levels of freedom.
This enhances works of many authors – from antiquity to the current day – on the significance of coordinated oscillations and resonances within the lifetime of dwelling organisms. The modeling method based mostly on hyperbolic numbers and their bisymmetric matrices reveals that the structural commonality of various inherited biosystems is said to the harmonic development 1/n and the harmonic imply, that are lengthy identified in arts and tradition. They’re used within the Pythagorean educating on the musical concord and the aesthetics of proportions. In addition to, the utilizing – for biosystems modeling – of multi-dimensional hypercomplex numbers, that are one of many most important instruments in fashionable mathematical pure sciences, opens a bridge between these sciences and biology for his or her mutual enrichment.