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The Great Adventure That is Counting

Geetha Venkataraman

By Georges Irfah Volume I: The World’s First Number Systems. Translated from the French by David Bellos and  E. F. Harding; Volume II: The Modern Number System. Translated from the French by David Bellos, E. F. Harding, Sophie Wood and Ian Monk; Volume III: The Computer and the Information Revolution. Translated from the French by E. F. Harding with assistance from Sophie Wood, Ian Monk, Elizabeth Clegg and Guido Waldman
Penguin Books, Delhi, 2005, pp. 715, pp. 544 & pp. 409, Rs. 595.00, 595.00 & 425.00

VOLUME XXIX NUMBER 10 October 2005

Imagine a world where you ask your schoolteacher questions like ‘Where do numbers come from? Who invented zero? How did the Romans do their sums using Roman numerals’ and you set your teacher off on a research quest, which traverses continents and produces as a by-product a three-volume book on the history of numbers. Georges Irfah was one such school teacher in France. This three volume series is an attempt primarily to answer the question as to where, when and why did the ‘great adventure that is ‘counting’ begin? What is its current state? Can we trace the present information and computer age to a time in prehistory when the human mind took the great leap forward and invented numbers?   Many books have attempted to introduce the informed layperson to the beauty that is mathematics by exploring the wondrous results, applications and ideas that are ubiquitous in the subject by tracing these historically and culturally. Irfah tries to do the same but with a single focus on ‘numbers and number systems’. In this sense, the three-volume set is specialist in nature. The first two volumes, which should be treated as a unit, explore the origins of numbers, number systems, the advent of place value for numerals and also the historic origins of the modern number system. The third volume traces briefly the sequential development of arithmetic, algebra and calculus and reaches its main focus: the history of automatic calculation from its humble beginnings in clockwork to present day computers.   What methods did human societies use before numbers were invented? They still had to keep track of livestock, make sure that every member of their hunting party had returned. It seems that many societies in pre-history had evolved a system of keeping a tally without any knowledge of numbers. So while they did not have counting numbers, a mark on a stick or a notch on a bone or a knot on a rope, kept track of the outgoing livestock and a crossing of the marks when the livestock returned allowed them to find out whether any of the livestock were missing. This notion of keeping track of a quantity (without actually defining it, for example, the total livestock) by comparing it with another quantity that is known to be equal (for example, the marks on the stick) is a very basic idea in modern set theory, that of cardinality. Different ...

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