**by
Steve Stephenson**

Revised April 24, 2008 (copyright)

Jens Høyrup wrote,

Analysis of the errors in two Old Babylonian “algebraic” problems shows

(1) that the computations were performed on a device where additive contributions were no longer

identifiable once they had entered the computation;

(2) that this device must have been some kind of counting board or abacus where numbers were

represented as collections of calculi;

(3) that units and tens were represented in distinct ways, perhaps by means of different calculi.

It has been known for more than a century that Babylonian calculators made use of

tables of multiplication, reciprocals, squares, and cubes. It is also an old insight that such

tables alone could not do the job—for instance, a multiplication like that of 2 24 and 2 36

(performed in the textVAT 7532, obv. 15, ed. [Neugebauer 1935, I, 294]) would by necessity

require the addition of more partial products than could be kept track of mentally, even if

simplified by means of clever factorizations. It has therefore been a recurrent guess that the

Babylonians might have used for this purpose some kind of abacus—Kurt Vogel [1959, 24]

also pointed to the possibility that the creation of the sexagesimal place value system might

have been inspired by the use of a counting board.

Below are snapshots of performing the multiplication of 2 24 and 2 36 on The Stephenson Abacus™. It's such a straightforward process that the question arises: Could it be that the Old Babylonians used a counting board very similar to The Stephenson Abacus™?

Note that the multiplication makes no use of any memorized or written multiplication tables; relying instead only on addition of partial products that are produced by duplicating tokens, and by doubling and halving tokens.

©
2006-2008 Stephen Kent Stephenson. Some
Rights
Reserved.

This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 United States License.

sks23cu AT gmail

This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 United States License.

sks23cu AT gmail