From Prehistory to the Invention of the Computer

By Georges Ifrah
John Wiley & Sons, Inc. NY, 2000
$39.95 US/$59.95 Canada

France’s L’Express has called George Ifrah the "Indiana Jones of arithmetic." His new book, The Universal History of Numbers is certainly an historical tour de force. This 633-page volume traces the history of numbers from prehistory to the invention of the computer. From Sumer to Silicon Valley, it’s all laid out in grand style with myriad illustrations, tables and charts. At first glance, this book appears to be a bean counter’s dream.

Of course it’s not really about bean counting, it’s about numbers themselves and the systems that man has developed for using them to advantage.

For those of us interested in Hebrew studies, the pages focusing on the history of numbers in the ancient Near East will be of special interest. Some 29 pages are devoted to the discussion of Hebrew number systems, and another 5 discuss the Hebrew calendar. The Hebrew mentality about numbers is quite alien from our own more Hellenistic Western mentality. During the Middle Ages for example, both Jewish and Muslim writings abound in what are known as chronograms – a method of writing dates that represent an art form in their own right. A chronogram "consists of grouping, into one meaningful and characteristic word or short phrase, letters whose numerical values, when totaled, give the year of a past or future event" (Ifrah, quoting G.S. Colin, p. 250). For example, the Hebrew phrase "One drop of dew in five thousand" is found on a Jewish tombstone in Toledo. Of and by themselves, the words seem meaningless. But if we add up the numerical value of the letters in "drop of dew" we have the date of the death of the person buried there – "83." The person died in the year "eighty-three [= drop of dew] on five thousand" – that is, the year 5083 of the Hebrew era (corresponding to 1322-1323 C.E.).

In Biblical times, both in Hebrew and Greek, letters were used for numbers. Writes Ifrah, "…it was the sum of the number-values of the letters in a word that mattered." He cites as an example the number 26. "That is why the number 26 is a divine number in Jewish lore, since it is the sum of the number-values of the letters that spell YAHWEH, the name of God" (Ifrah, p. xxi).

Ifrah’s book helps us understand how varied have been the ways in which cultures have developed and used numerical and mathematical systems. The author is a former math teacher and an independent scholar. In researching his book, Ifrah interviewed mathematicians, historians, archaeologists, and philosophers the world over. With those for whom the history and use of numbers in any language or cultural setting is a lifelong fascination, this book would be a worthy addition to one’s personal library.