The evolution of binary system from predynastic Egypt to Leibniz era

Document Type : Special Issue Dedicated to Prof. Esfandiar Eslami

Authors

1 Department of Mathematics, Islamic Azad University, Kerman Branch, Kerman, Iran

2 Department of Mathematics, Shahid Bahonar University of Kerman, Kerman, Iran

Abstract

Egyptians of the predynastic era had a good decimal number system for counting and addition. Although, up to some times, they had problem in counting beyond a million, by the dawn of their history, Narmer, the founder of the first Egyptian dynasty had accountants that could record 400,000 cows and 1,422,000 goats of a war booty. Except for some ambiguities in the case of Mayan number system, specialists in the history of mathematics can guess that  how the counting system of the various civilizations evolved into one of the number systems in base 10, 20, 60, etc. There is a puzzle in the mixture of the  Egyptian decimal and binary number systems which we are going to discuss and present a justification for it. The novelty of the present paper is the study of the evolution of the binary number system from the predynastic Egypt down to the Leibniz era who, by the benefit of  Khwarazmi's  "Indian Arithmetics,"  completed this evolution by representing integers in $0-1$ forms and performing the hybrid decimal/binary Egyptian arithmetic operations purely inside the $0-1$ system. The second author is pleased to dedicate his share of this paper to  Esfandiar Eslami  showing  his love and appreciation for decades of his friendship and collaboration (since 1967) and, of course, the young coauthor joins the joy of this dedication to her former professor.

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References

[1] Ares, J., Lara, J., Lizcano, D., and Martnez, M. A. (2018), Who Discovered the Binary System and Arithmetic? Did Leibniz Plagiarize Caramuel? Sci. Eng. Ethics. 1,173-188. doi: 10.1007/ISBN 11948-017-9890-6.
[2] Egypt Today sta . (2021), Bread: types of Egyptians' indispensable food. Egypt Today. CAIRO { 11 November 2021.
https://www.egypttoday.com/Article/1/109827/Bread-types-of-Egyptians-indispensable-food
[3] Gamow, G. (1988) One, Two, Three,... In nity; Facts and Speculations of Science. Dover Publications INC., New York. ISBN: 0486256642; ISBN13: 9780486256641
[4] Ghorbani. A. (1996), Biography of Mathematicians of Islamic Era. The University Publishing Center, Tehran, Iran. ISBN: 964-01-0265-2 (In Persian)
[5] Guicciardini,N. (2003) Reading the Principia: The Debate on Newton's Mathematical Methods for Natural Philosophy from 1687 to 1736. Cambridge University Press.
[6] Haddon, A.C. (1890), The ethnography of the western tribes of Torres Straits. Journal of the Anthropological institute of Great Britain and Ireland 19, 297-437.
[7] Hall, A. R. (1980). Philosophers at War: The Quarrel between Newton and Leibniz. Cambridge University Press. p. 356. ISBN 0-521-22732-1.
[8] Harris, J. (1987) Australian Aboriginal and Islander mathematics. Australian Aboriginal Studies 2, 29-37. To cite this  le use: http://www.aiatsis.gov.au/lbry/dig-prgm/e-access/serial/m0005975-a.pdf John Harris
[9] Ifrah, G. (2000). The Universal History of Numbers: From prehistory to the invention of the computer. Translated from the French by David Bellos, E.F. Harding, Sophie Wood and Ian Monk. John Wiley and Sons Inc.
[10] Ineichen, R. (2008). Leibniz, Caramuel, Harriot und das Dualsystem. MDMV 16, 12{15.
[11] Lande, D.R. (2014). Development of the Binary Number System and the Foundations of Computer Science, The Mathematics Enthusiast, 11(3),513-540. DOI: https://doi.org/10.54870/1551-3440.1315 Available at: https://scholarworks.umt.edu/tme/vol11/iss3/6
[12] Mark, J.J. (2017). Jobs in Ancient Egypt. World History Encyclopedia, Retrieved from https://www.worldhistory.org/article/1073/jobs-in-ancient-egypt/
[13] Mungello, D. E. (1971). Leibniz's Interpretation of Neo-Confucianism. Philosophy East and West, 21(1), 3-22.
[14] Perkins, F. (2010). Leibniz: A Guide for the Perplexed. London, GBR: Continuum International Publishing.
[15] Porubsky, S. Binary system. Retrieved 2023/10/19 from Interactive Information Portal for Algorithmic Mathematics, Institute of Computer Science of the Czech Academy of Sciences, Prague, Czech Republic, https://www.cs.cas.cz/portal/AlgoMath/NumberTheory/Arithmetics/NumeralSystems/PositionalNumeralSystems/BinarySystem.htm
[16] Radjabalipour, M. (2009). Egyptian fractions. Mathematical Culture and Thought; Iranian Mathematical Society, 28(1), 1-38. (In Persian)
[17] Radjabalipour, M. (2024). A history of fractions. (In preparation.)
[18] Shirley, J.W. (1951). Binary Numeration before Leibniz. American Journal of Physics, 19, 452{454.
[19] Zacher, H.J.(1973). The Main Writings on Dyadik by G.W. Leibniz { A contribution to history of the binary number system. Frankfurt A.M.: Vittorio Klostermann. ISBN: 978-3-465-00998-6
Journal of Mahani Mathematical Research

Articles in Press, Accepted Manuscript
Available Online from 06 June 2024

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  • Receive Date: 03 April 2024
  • Accept Date: 05 June 2024

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