All is number

Abstract

Rational numbers, which correctly describe many recognizable patterns in the physical world, are often seen to converge in the process to irrational limits or even singularities. As a common example, atomic numbers are well known as fundamental parameters in chemistry, but by demonstrating that the periodicity of atomic matter is simulated by the convergence of rational fractions, from unity to the golden ratio, the importance of limiting processes and irrational limits in the modeling of chemical systems and of phenomena such as superconduction is emphasized. Other limiting formulae feature in atomic spectral series, radioactive decay, circular measure, absolute temperature, the speed of light, structure of the solar system and gravitational collapse. In virtually all cases, the convergence involves the irrational golden ratio and the golden spiral, the essential properties of which are briefly reviewed in summary of the arguments developed in this volume. The suspicion that molecular shape should have a related number basis could not be substantiated. Only in the double-helical base pairing of DNA could any correlation between molecular structure and number theory be demonstrated. It is tempting to conjecture that the ubiquitous appearance of irrational limits signals the inadequacy of the R3 number system to provide a detailed account of the four-dimensional world. © Springer-Verlag Berlin Heidelberg 2013.