Have we got numbers - full history

Cryptologia, Apr 2000 by Kruh, Louis

Ifrah, Georges. The Universal History of Numbers: From Prehistory to the Invention of the Computer. John Wiley & Sons, Inc., 605 Third Ave., New York NY 10158 USA. 2000. 634 pp. $39.95.

This two-inch thick, 9.75" x 9.25" volume contains a fascinating history of the invention of numbers, counting and calculating from the earliest archeological evidence of the methods of prehistoric people to the late 20th century. Ifrah takes readers through the art and science of numeration as it has developed all over the world, which he uncovered during a ten-year odyssey from Europe to China, via the Classical World, Mesopotamia, Latin America, and, importantly, India and the Arab lands. He talked to mathematicians, historians, archaeologists, and philosophers. He deciphered ancient writing on crumbling walls; scrutinized stones, tools, cylinders, carved bones and elaborately knotted counting strings.

Ifrah brings numbers to life, explaining their logic, and the practical situations which made them necessary. He enumerates the words and symbols used for arithmetic and also explains how to use each system, providing illustrations, diagrams, riddles, and puzzles. Nearly every page displays handsome numerals, counting devices, and illustrations of their use. In simple language he: describes what is known the human ability to count, as well as other animals' counting ability; recounts the amazing story of the development of the current Indo-Arabic number system, from the first crude methods, by counting with fingers, toes and other body parts, to the invention of the first numerals; tells the surprising invention of the number zero, up to the story of the metric system and the invention of binary "0"s and "1"s system that lead to the invention of computers.

As expected, codes and ciphers are featured in several areas. In the section, Code and Ciphers in Cuneiform Numerals, Ifrah tells how the scribes of Susa and Babylon spent time playing cryptic games with numerals. Some of these games involved numerical transposition and he provides examples of inscriptions that include numerical transpositions. There is also an illustration of an astrological table with cryptograms still waiting to be deciphered.

In Coded Cryptograms and Mystical Numerology, Ifrah explains how "Coded cryptograms were also used in theological speculation" because Mesopotamian scribes "acccorded great weight to the numerical transpositions of the names of the gods." Actually, the Assyro-Babylonians believed the celestial world was a "numerologically harmonious" one, where the numerical value of a name was a vital trait of the person who owned it. As a result, some of the Babylonian gods were represented by cuneiform numerals from the early part of the second millennium BCE and consistently throughout the first millennium Illustrations of early cuneiform tablets list the names of gods with their corresponding numbers.

Chapter 20, Magic, Mystery, Divination and Other Secrets includes Secret Writing and Secret Numbers in the Ottoman Empire, The Art of Chronograms, and Gnostics, Cabbalists, Magicians, and Soothsayers with many examples and dozens of illustrations of secret notations, chronograms, and secret numeral systems used by Turkey, Egypt, Syria, and Greeks, Muslims and Jews.

Ifrah's amazing undertaking has spawned an equally amazing book that will inform, amuse, and delight readers, especially those with curious minds.