The Accounting Historians Journal
Vol. 13, No. 2
Harry Zvi Davis BARUCH COLLEGE, CUNY
ACCOUNTING MEASUREMENT AND CAPACITY LIMITS OF TECHNOLOGICAL DEVICES*
Abstract: In this paper the capacity limits of technological devices used in ancient Egypt are used to explain the Biblical phrase that in accounting for grain the Egyptians ran out of numbers.
The Bible describes accounting for the quantity of grain that Joseph stockpiled during the seven years of plenty in anticipation of the seven years of hunger. "And Joseph laid up corn as the sand of the sea, very much, until they left off numbering; for it was without number" [Genesis 41:49].
The phrase "without number" is puzzling. How was it possible to run out of numbers? The set of numbers is unbounded. A larger number can always be created by adding one to the previous number.
A study of the ancient Egyptian numbering system [Gardiner, p. 191] confirms the impossibility of running out of numbers. The Egyptians had symbols representing the number one, ten, and all powers of ten up to a million [see Figure 1]. Symbols were repeated to show multiples of numbers. For instance, 152,123 was expressed as: and 966 was expressed as:
Furthermore, multiplication was occasionally employed to ex-press larger numbers. For instance, 10,100,000 was expressed as 100,000 x 101: and 470,000 was expressed as (100,000 X
4) + (10,000 X 7): In such a numbering system one cannot run out of numbers.
We suggest a solution based on the assumption that in Joseph's time the Egyptians used an abacus for numbering. This assumption has not been proven but there is some supporting evidence.
Herodotus [circa 450 B.C.E.] describes his experiences in Egypt and explains that "in the writing of characters and reckoning with pebbles, while the Hellenes carry the hand from the left to the right, the Egyptians do this from the right to the left" [p. 23, emphasis supplied].
*The author is grateful for the help of Y. Elman and D. Carmichael.