Benford's Law and the Universe

Abstract

Benford's law predicts the occurrence of the $n^{\mathrm{th}}$ digit of numbers in datasets originating from various sources of the world, ranging from financial data to atomic spectra. It is intriguing that although many features of Benford's law have been proven and analysed, it is still not fully mathematically understood. In this paper we investigate the distances of galaxies and stars by comparing the first, second and third significant digit probabilities with Benford's predictions. It is found that the distances of galaxies follow reasonably well the first digit law and the star distances agree very well with the first, second and third significant digit.