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Brooks, D (2002)

Naked-Eye Quantum Mechanics: Practical Applications of Benford's Law for Integer Quantities

Frequencies - The Journal of Size Law Applications, Special Paper #1, pp. 1-8.

ISSN/ISBN: Not available at this time. DOI: Not available at this time.

Abstract: Benford's Law (1938) predicts that digit frequencies for many scientific, engineering, and business data sets will follow P(dd)=log(1+1/ dd) for digits dd. This law has been used by auditors since 1989 to detect errors and fraud in data sets. Benford also postulated a separate law for integer quantities. This little-known variant of the law is shown to be substantially correct, despite an error by Benford in its derivation. The integer variant is then shown to be extraordinarily common in everyday life, correctly predicting the distribution of footnotes per page in textbooks, sizes of groups walking in public parks and visiting restaurants, fatality counts in air crashes, repeat visits to service businesses, and purchase quantities for goods. The practical value of the integer variant of Benford's Law is illustrated using cases from the author's consulting experience, as a limit toward which a distribution will tend. A potential proof for a universal distribution law for integer quantities (an 'ontic' distribution) combining Benford's Law, Zipf's Law, and Pareto's Law is outlined. The philosophical implications of ‘naked-eye quantum mechanics’ are briefly considered.

@article {, AUTHOR = {Dean Brooks}, TITLE = {Naked-Eye Quantum Mechanics: Practical Applications of Benford's Law for Integer Quantities}, JOURNAL = {Frequencies - The Journal of Size Law Applications}, YEAR = {2002}, NUMBER = {Special Paper # 1}, PAGES = {1--8}, URL = {}, }

Reference Type: E-Print

Subject Area(s): General Interest