A History of Mathematics From Mesopotamia to Modernity

28 A History ofMathematics

admired for solving quadratic equations, can we extend a similar recognition to the scribes of Fara

for doing rather long divisions? There has indeed been quite a controversy about what the Fara

scribes were supposed to do in answering the question; see Powell in Fauvel and Gray 1.E.5, or for

a more recent view, Melville, ‘Ration Computations at Fara: Multiplication or Repeated Addition’

in Steele and Imhausen (2002). Again, this question is perhaps best left unanswered, or as a point

for discussion. Friberg would probably justify calling the scribes ‘mathematicians’ not in terms

of their use of unrealistic examples, but in the formation of a community—again that Kuhnian

word—with a common project, whose language was a language of numbers. Training for practical

purposes seems, here too, to have generated a class of impractical exercises, if entirely different

from those which followed 500 years later.

However, this impracticality, characteristic of the school-texts which have survived, disappears

when we look at a different family of texts, the accounts from the harsh period known as

Ur III, which were the work of practisingscribes and administrators. (What kind of texts survive

from which period is at least partly chance, depending on the kind of site excavated.) Dating from

the twenty-first centurybce, these are in time between the Fara texts and the OB ones, and they are

both utilitarian and highly ‘mathematized’. The period, under King Šulgi, was one of increasingly

rigid centralized control of production; the aim, for a variety of industries—seed production, cattle

raising, fishing, milling, and so on—is to calculate the expected yield and the extent to which

the farmers or managers fulfil their targets. Analogies with old Soviet planning or indeed mod-

ern Western management come to mind. Accounts were complicated by the fact that almost any

quantity had a special system of units to measure it. However, the scribe is, on the whole, up to

the calculation; as usual, there are tables of conversion factors to help. Here is an example which,

according to Damerow and Englund (Nissen et al. 1993, pp. 141–2), represents ‘the calculation of

the harvest yield of the province of Lagash for the third year recorded in the text’ (Fig. 7). We begin

Fig. 7The tablet recording harvests from Lagash, AO3448.