Physical Sciences and Mathematics Commons^™

Hubble's Law Implies Benford's Law For Distances To Galaxies, Theodore P. Hill, Ronald F. Fox

Research Scholars in Residence

A recent article by Alexopoulos and Leontsinis presented empirical evidence that the first digits of the distances from the Earth to galaxies are a reasonably good fit to the probabilities predicted by Benford’s law, the well known logarithmic statistical distribution of significant digits. The purpose of the present article is to give a theoretical explanation, based on Hubble’s law and mathematical properties of Benford’s law, why galaxy distances might be expected to follow Benford’s law. The new galaxy-distance law derived here, which is robust with respect to change of scale and base, to additive and multiplicative computational or observational errors, …