Benford's law: a 'sleeping beauty' sleeping in the dirty pages of logarithmic tables

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 center of attention (are awakened). Thus, in the present study, we show that Newcomb (1881) and Benford (1938) papers are clearly SBs. The former was in deep sleep for 110 years whereas the latter was in 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 (1995a). In so doing, we show that the waking prince (Hill, 1995a) 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.

18 pages, 4 figures, 3 tables, 79 references, Accepted for publication in Journal of the Association for Information Science and Technology

References in corpus (5)

• Defining and identifying Sleeping Beauties in science
• Attention decay in science
• Breakdown of Benford's Law for Birth Data
• Benford's law predicted digit distribution of aggregated income taxes: the surprising conformity of Italian cities and regions
• The Benford law behavior of the religious activity data

Cited by in corpus (5)

• Benford's law first significant digit and distribution distances for testing the reliability of financial reports in developing countries
• The Newcomb-Benford law: Scale invariance and a simple Markov process based on it
• Benford's laws tests on S&P500 daily closing values and the corresponding daily log-returns both point to huge non-conformity
• Intriguing behavior when testing the impact of quotation marks usage in Google search results
• Note on pre-taxation reported data by UK FTSE-listed companies. A search for Benford's laws compatibility