Nested Numeric/Geometric/Arithmetic Properties of shCherbak's Prime Quantum 037 as a Base of (Biological) Coding/Computing

Abstract and figures

Numerous arithmetical regularities of nucleon numbers of canonical amino acids for quite different systematizations of the genetic code, which are dominantly based on decimal number 037, indicate the hidden existence of a more universal ordering principle. Mathematical analysis of number 037 reveals that it is a unique decimal number from which an infinite set of self-similar numbers can be derived with the nested numerical, geometrical, and arithmetical properties, thus enabling the nested coding and computing in the (bio)systems by geometry and resonance. The omnipresent fractal structural and dynamical organization, as well as the intertwining of quantum and classical realm in the physical and biological systems could be just the consequence of such coding and computing. Introduction 1 All living organisms are fundamentally based on information, which holds a central role in their communication and control, and therefore in their structural and dynamical organization. Such contemporary comprehension of living organisms as information systems is the result of a long-lasting history during which the biological field theory has been developed (Gurwitsch, 1912, 1923; Glauber, 1963; Waddington, 1966; Fröhlich, 1968; Presman, 1970; Popp, 1989, 1992). This approach places the biological coding/computing at the very heart of the biological organization, as well as its origin and evolution, since the organic codes (biological codes, biocodes) can be considered as the basic mechanism of macroevolution (Barbieri, 1998; 2008).