measuring grain in the third millennium was by the gur system, that is, using a unit
known as the gur. The gurwas a large unit, divisible into a handful of smaller
constituents: the PIor bariga, the ban 2 and the sila 3. We know that the sila 3 was about
the same size as a liter today. In different places and locations, these subunits were
organized a little differently. In Early Dynastic Lagash, the gurwas made up of 240 sila 3.
Sargonic reforms altered the gurto 300 sila 3 (Powell 1976 : 42 ).^5 When writing a tablet
about grain measurement, Sumerian scribes generally would note at the end of the line
that they were in the gursystem (Figure 15. 4 ). They would not write out x gur, x PI
and so on: they would simply arrange the numbers in the proper orientation so that
context would guide the reader. Sila 3 however were written out.
Note that there are fairly major differences in the numbers in the gursystem. The
cardinal one in Sumerian is always a vertical wedge, whereas one guris a horizontal
wedge. The cardinal two in Sumerian is always two side-by-side vertical strokes; the
way of writing 2 PIis two wedges stuck on top of each other (Figure 15. 5 ).
Thus, in order to read or write an administrative tablet, one had to have a firm grasp
of metrology and how to count in the various systems to grain measurement, land
mensuration, weight, volume, and so on.
BABYLONIAN MATHEMATICS
In comparison with other Near Eastern cultures, Babylonian tablets evince a far
greater degree of mathematical understanding. Egyptian sources show that Egyptians
could find the area of a circle and work well in applied arithmetic (Boyer 1991 : 17 ,
21 ). At its most advanced, Babylonian mathematics far surpassed Egyptian
achievements in this field. A full-scale description of Babylonian mathematics is far
beyond the scope of the present work. Certainly by the Old Babylonian period, the
extant texts record a sophisticated body of mathematical knowledge. They had
algebra: “Many problem texts from the Old Babylonian period show that the solution
of the complete three-term quadratic equations afforded the Babylonians no serious
difficulty, for flexible algebraic operations had been developed.”^6 Babylonians could
solve cubic equations, had algorithmic procedures and understood square roots
(Boyer 1991 : 33 , 28 ).
Such accomplishments are well attested for the second and then late in the first
millennium, that is, in the Old Babylonian and Seleucid periods, from which the vast
majority of our mathematical sources derive (Neugebauer 1969 : 29 ; Boyer 1991 : 26 ).
Robson calculated that the known mathematical corpus as of 2008 was approximately
950 tablets (Robson 2008 : 8 ). Eighty percent of these (that is, 780 tablets) date from
the Old Babylonian period, that is, the early second millennium. Only about 6 percent
date to the third millennium (Robson 2008 : 8 ).
–– Tonia Sharlach ––Figure 15.4
$e gur. ITT 3. 4811. 3 ( 60 ) + 20 + 9 (gur)Figure 15.5 ITT 3. 4850. 2 (gur) 2 (PI)
$e gur, units of barley in the gursystem