Generalized crystallography, the genetic system and biochemical esthetics

Abstract

The article is written for the special journal issue dedicated to Alan L. Mackay on his 90th birthday. The remarkable ideas of Alan L. Mackay about generalized crystallography, its connections with encoding of information, and also the interrelationship between art and science generate many ideas and their consequences. Mackay paid a special attention to the theme of five-fold symmetry, Fibonacci numbers and the golden section, which are essential in the structures of quasicrystals and living bodies. The present article considers a continuation of this theme in relation to the genetic coding system and to ratios of musical harmony. Hidden connections between the matrix representations the genetic code system and the golden section and the Pythagoras’s theory of esthetics of proportions are described. Such connections testify the validity of the molecular-genetic foundation of many known facts about inborn feeling of harmony in our perceptions, which becomes a part of the scientific field of “biochemical esthetics” (the term first introduced by Russian biophysicist S. Shnoll, 7). Data from theory of resonances and mathematics of noise-immunity coding of information are used in the article.