Hand sums

The ancient art of counting with your fingers



Taken from:

http://bcm.bc.edu/issues/spring_2002/ll_hand.html

We instinctively reach for pencil and paper whenever we are faced with a mathematical problem, yet in antiquity all people did their arithmetic mentally. When the sums became too large or the problems too complex to keep in memory, reckoners could hold intermediary results by various means. They could use counters--notches on a stick or pebbles in a pile--or employ an abacus or dustboard. They could also represent numbers by using their fingers.

Dactylonomy--expressing numbers by the position of the fingers--was known in classical antiquity, although its origins are obscure. The Greco-Roman author Plutarch, in his Lives, mentions the practice as being used in Persia in the first centuries of the Common Era, so the source of the system may lie in Iran. Indeed, Arab and Persian poets of the classical period could allude to someone's lack of generosity by saying that the person's hand made "ninety-three"--a closed fist, the sign of avarice.

The Arabs called dactylonomy the "arithmetic of the knots [finger joints]." Several verses of the Koran seem to refer to it; and early Muslims interpreted certain gestures made by the prophet Muhammad as indicating numbers: Muhammad is said, for example, to have extended his right forefinger while pronouncing his profession of faith--"I bear witness that there is no god but God and that Muhammad is his prophet"--because the extended forefinger means "one," signifying God's unity.

Finger reckoning was widely used in medieval Islamic lands. The polymath al-Jahiz advised schoolmasters to teach the "arithmetic of the knots," which he placed among the five methods of human expression. Similarly, al-Suli, in his Handbook for Secretaries, wrote that scribes preferred dactylonomy to any other system because it required neither materials nor an instrument, apart from a limb. Furthermore, it ensured secrecy and was thus in keeping with the dignity of the scribe's profession. Books dealing with dactylonomy, such as a treatise by the mathematician Abu'l-Wafa al-Buzajani, gave rules for performing complex operations, including the approximate determination of square roots.

Dactylonomy was also used in early medieval Europe. The system described in various Muslim treatises is curiously reminiscent of that expounded in the seventh century by the Venerable Bede, the Anglo-Saxon theologian, in the first chapter of his De temporum ratione, entitled "De computa vel loquela digitorum." Using Bede's technique, a person could express and calculate with numbers between one and 9,999, although it was seldom used for values with more than two digits.

Bede's system seems to have fallen into disuse in the West after the early Middle Ages, but a similar system continued to be used in Islamic lands until modern times.

In Algeria, along the Red Sea coast, and on the island of Bahrain, the system was modified for commercial transactions involving pearls and other rare and costly merchandise. Because buyer and seller did not wish to reveal to bystanders the terms of a transaction, the two negotiators, sitting face-to-face, would hide their right hands under a cloth and touch each other's fingers according to a precise code. The system did not distinguish between ones, tens, hundreds, and thousands, but the parties involved in the transaction knew which sum was meant.

Jonathan M. Bloom

Jonathan M. Bloom is the Norma Jean Calderwood University Professor of Islamic and Asian Art at Boston College, an appointment he shares with his wife, Sheila Blair. He is coauthor, with Blair, of Islam: A Thousand Years of Faith and Power (2000), which was the companion book to the PBS documentary series Islam: Empire of Faith. His essay is drawn from his latest book, Paper before Print: The History and Impact of Paper in the Islamic World (2001), published by Yale University Press. Reproduced by permission. The book is available at a discount from the BC Bookstore via the BCM Web page: www.bc.edu/bcm