Benford's law: A “sleeping beauty†sleeping in the dirty pages of logarithmic tables

Tariq Ahmad Mir and Marcel Ausloos

Journal of the Association for Information Science & Technology, 2018, vol. 69, issue 3, 349-358

Abstract: Benford's law is an empirical observation, first reported by Simon Newcomb in 1881 and then independently by Frank Benford in 1938: the first significant digits of numbers in large data are often distributed according to a logarithmically decreasing function. Being contrary to intuition, the law was forgotten as a mere curious observation. However, in the last two decades relevant literature has grown exponentially—an evolution typical of “Sleeping Beauties†(SBs) publications that go unnoticed (sleep) for a long time and then suddenly become the center of attention (are awakened). Thus, in the present study, we show that the two papers, Newcomb () and Benford (), Newcomb (, American Journal of Mathematics, 4, 39–40) and Benford (1938, Proc. Am. Phil. Soc., 78, 551–572) papers are clearly SBs. The former was in a deep sleep for 110 years, whereas the latter was in a deep sleep for a comparatively lesser period of 31 years up to 1968, and in a state of less deep sleep for another 27 years, up to 1995. Both SBs were awakened in the year 1995 by Hill (, Statistical Science, 10, 354–363). In so doing, we show that the waking prince (Hill, ) is more often quoted than the SB whom he kissed—in this Benford's law case, wondering whether this is a general effect—to be usefully studied.

Date: 2018
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