From Genetic Code toward Spacetime Geometry. Proceedings of the 2nd International Conference on Theoretical Approaches to BioInformation Systems

Abstract:

Numerous arithmetical regularities for the nucleon numbers of the canonical amino acids for quite different systematizations of the genetic code, dominantly based on the decimal number 037, indicate the hidden existence of a more universal background regulating system. Generalization of the number 037 reveals the infinite number set whose elements are characterized by self-similarity. Here we show that these numbers are uniquely linked to the numeration process, what for the number 037 reveals its unique relation with the golden means, Φ and ϕ. Modification of Φ, ϕ-polynomials gives the irrationals, Ψ and ψ, which integrate the self-similarity properties and the scaling by powers of 10. Moreover, we show that 037 is the simplest case of integer approximation of Ψ, as well as that they enable a simple and an accurate enough derivation of the fine structure constant. These results are consistent with the Dirac-Eddington large-number coincidence and a quantum gravity theory of the causal dynamical triangulations. Information processing in Nature realized on such principles would lead to the nested codes and the geometrically based “computation” with a further consequence of fractal structural and dynamical organization, which omnipresence is recognized both in physical and biological realm.