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Numbers and Rules: Excerpts from The Universal History of Numbers and Number: From Ahmes to Cantor

The almost universal preference for the base 10 comes from nothing more than the fact that we learn to count on our fingers, and that we happen to have 10 of them. We would use base 10 even if we had no language, or were bound to a vow of total silence . . . . The obvious practicality of such a non-linguistic counting system using only our own bodies shows that the idea of grouping numbers into packets of 10 and powers of 10 is based on the "accident of nature" that is the physiology of the human hand. Since that physiology is universal, base 10 necessarily occupies a dominant, not to say inexpugnable position in counting systems. If nature had given us six fingers, then the majority of counting systems would have used base 12.

The Universal History of Numbers: From Prehistory to the Invention of the Computer
Georges Ifrah
John Wiley & Sons, $39.95

The first book of arithmetic ever to be printed was the Treviso, a list of rules for performing common calculations, published in 1472. The first book of immense mathematical significance was printed by Johannes Campanus in 1482. It was the Latin translation of Euclid's Elements from its earlier Arabic translation.

Number: From Ahmes to Cantor
Midhat Gazalé
Princeton University Press, $29.95


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