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.
Highlights
Amongst the enormous scientific literature that is being published annually, the reaction of the research community to the quality of a particular article, measured by the number of times it is being referred to by others, i.e. is cited, varies dramatically
We show that the waking prince (Hill, 1995a) is more often quoted than the Sleeping Beauties (SBs) whom he kissed, - in this Benford’s law case, wondering whether this is a general effect, - to be usefully studied
Some articles may become instant hits, receive a large number of citations within the first few years of their publication, whereas most of the scientific articles are never cited at all (Seglen 1992), though the proportion of these has been decreasing over time (Lariviere et al, 2008)
Summary
Amongst the enormous scientific literature that is being published annually, the reaction of the research community to the quality of a particular article, measured by the number of times it is being referred to by others, i.e. is cited, varies dramatically. Articles that attract none or only few citations for a long time (sleep) since their publication and suddenly their citation numbers burst (are awakened) are called Sleeping Beauties (SBs) (van Raan, 2004). Such articles achieve prominence following them being cited by some another article (the ”prince”). When unearthed SBs turn out to be application-oriented publications (van Raan, 2015) or having presented fundamental results (Glanzel et al, 2003), often ahead of their time, or are related to important discoveries, many later on winning Nobel Prize for the authors (Li and Shi, 2015). We introduce “Benford’s law (BL)”, an empirical observation that certainly was ahead of its time despite neither being any fundamental result nor being related to any prize winning discovery
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