The Supremacy of the Number One

Authors

  • Rodrigo González González UNIVERSIDAD DE SONORA https://orcid.org/0000-0002-1178-0562
  • Roberto Núñez González Universidad de Sonora
  • Rodrigo Iván González Valenzuela University of Sonora

DOI:

https://doi.org/10.36790/epistemus.v17i34.275

Keywords:

Benford´s Law, significant digits, information validation, Simon Newcomb

Abstract

In this paper, is presented in a general way a mathematical curiosity that quickly attracts attention per se, which describes a peculiar pattern that the first digits of data obtained from various ordinary situations and many real processes comply, known as Benford’s Law or the Significant-Digit Phenomenon. In addition to analyzing and reproducing the fulfillment of this singular mathematical principle that the significant digits for some typical examples found in the literature follow, the fulfillment of this law in cases of particular interest is also analyzed, and possible potential applications are described.  

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References

S. Newcomb. “Note on the Frequency of Use of the Different Digits in Natural Numbers”, American Journal of Mathematics, Vol.4, No.1/4 (1881), pp.39-40. DOI:10.2307/2369148. DOI: https://doi.org/10.2307/2369148

A. Berger and T.P. Hill. An Introduction to Benford's Law, Princeton University Press. 2015. DOI: 10.1515/9781400866588 DOI: https://doi.org/10.1515/9781400866588

S.J. Miller. Benford's Law. Theory and Applications, Princeton University Press. 2015.

DOI: 10.1515/9781400866595 DOI: https://doi.org/10.1515/9781400866595

M.J. Nigrini. Benford's Law. Applications for Forensic Accounting, Auditing and Fraud Detection, John Wiley & Sons, Inc. 2012. DOI: 10.1002/9781119203094 DOI: https://doi.org/10.1002/9781119203094

F.A. Benford. “The Law of Anomalous Numbers”, Proceedings of the American Philosophical Society, Vol. 78, No.4 (1938), pp.551-572.

C.R. Tolle, J.L. Budzien and R.A. LaViolette. “Do Dynamical Systems follow Benford's Law?”, Physics Today. Chaos, Vol.10, No.2 (2000), pp.331-336. DOI: 10.1063/1.166498 DOI: https://doi.org/10.1063/1.166498

C. Amante and B. W. Eakins. ETOPO1, 1 Arc-Minute Global Relief Model: Procedures, Data Sources and Analysis. NOAA Technical Memorandum NESDIS NGDC-24, 19 pp, March 2009. http://www.ngdc.noaa.gov/mgg/global/relief/ETOPO1/docs/ETOPO1.pdf

T.A. Mir and M. Ausloos. “Benford's law: a 'sleeping beauty' sleeping in the dirty pages

of logarithmic tables”, Journal of the Association for Information Science and Technology 69(3). (2018), pp. 349–358. DOI:10.1002/asi.23845 DOI: https://doi.org/10.1002/asi.23845

P.Y. Leonov, V.P. Suyts, A.N. Norkina, V.M. Sushkov. “Integrated application of Benford's Law tests to detect corporate fraud". Procedia Computer Science, V.213 (2022), pp. 332-337. DOI: 10.1016/j.procs.2022.11.075 DOI: https://doi.org/10.1016/j.procs.2022.11.075

G. Whyman. “Origin, Alternative Expressions of Newcomb-Benford Law and Deviations

of Digit Frequencies”, Applied Mathematics, 12 (2021). pp. 576-586.

DOI: 10.4236/am.2021.127041 DOI: https://doi.org/10.4236/am.2021.127041

D. Crisan, A. Irimia, D. Gota, L. Miclea, A. Puscasiu, O. Stan, H. Valean. “Analyzing

Benford’s Law’s”, Powerful Applications in Image Forensics. Appl. Sci. 11, 11482. (2021).

https://doi.org/10.3390/app112311482 DOI: https://doi.org/10.3390/app112311482

Lorenz

Published

2023-04-24

How to Cite

González González, R., Núñez González, R., & González Valenzuela, R. I. (2023). The Supremacy of the Number One. EPISTEMUS, 17(34), 70–76. https://doi.org/10.36790/epistemus.v17i34.275

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