"

4 VAT 12593: Conclusion

You may be surprised that the basic unit of length discussed in Chapter 3, the rod, was not one of the lengths listed VAT 12593. In fact, the smallest length that appeared on VAT 12593 was 10 rods. During this time period, the Early Dynastic Era, all lengths larger than a rod were referred to in terms of rods using the sexagesimal system, which modern Assyriologists shorten to System S. We say that a number system is sexagesimal if the numerals can be grouped by sixty to form a larger numeral. The system also uses ten as a sub-base, allowing us to introduce a new numeral for groups of ten. While VAT 12593 only has three of the numerals, we have included all of the numerals used during the Old Dynastic Period in Table 2 below.

Table 2. The Sumerian symbols for System S.
Symbol Name Relative Value
The symbol for an iku or 1. It looks like a small bullet. diš 1 diš
The symbol for a bur or for an éš. It is a black dot. u 10 diš
The symbol for an uš. It looks like a large bullet. géš 6 u
The symbol for a third danna. It looks like the symbol of an uš with a dot in the middle of it. géš’u 10 géš
The symbol for a šár. It is a large black dot. šár 6 géš’u
The symbol for šár'u. It looks like a large dot with a ring around it. šár’u 10 šár

System S was used to count distances, but was also used to specify discrete amounts of most objects like humans and animals.[1]

As we can see in Figure 3, numbers in System S were written by simply repeating numerals as needed, but making sure to use the fewest number of numerals necessary. Numerals were also stacked and bunched together in order to conserve space and improve legibility.

The system for area, which modern Assyriologists shorten to System A, was not purely sexagesimal. VAT 12593 contains all but one of the numerals in use during the Early Dynastic Period. We have included this last numeral along with the rest in Table 3 below.

Table 3. The Sumerian symbols for System A.
Symbol Name Relative Value
The symbol for an iku or 1. It looks like a small bullet. iku 1 iku
The symbol for èše. èše 6 iku
The symbol for a bur or for an éš. It is a black dot. bùr 3 èše
The symbol for a bur'u. It looks like the symbol for a bur with hash marks placed over it. bùr’u 10 bùr
The symbol for a šár. It is a large black dot. šár 6 bùr’u
The symbol for šár'u. It looks like a large dot with a ring around it. šár’u 10 šár

Unlike distances that used a sexagesimal number with unit ninda, the numerals for area were used only for area and had a fixed size. The basic unit for area, iku, was 100 square ninda or 3600 square meters. The word ganá  included on VAT 12593 in the column for area was not a unit, but rather a determinative to clue the reader that these numerals refer to System A rather than another system like System S.[2] This is often necessary because these systems share symbols. Thus, much like the Sumerian language, Sumerian numerals were context sensitive.

Activity 3. Recall that a ninda is approximately 6 meters. Use Figure 3 to answer the following questions.

  1. What is the area of the largest field listed on VAT 12593 in square meters?
  2. Modern day Iraq is approximately 440,000 square kilometers. What fraction of modern Iraq would be covered by the largest field listed on VAT 12593.
  3. Based on this, do you think VAT 12593 was purely a practical list of areas of fields?

 

 

  1. There were separate systems for dead animals, jars of liquid, and rations of food. Hans J. Nissen, Peter Damerow, and Robert K. Englund, Archaic Bookkeeping: Writing and Techniques of Economic Administration in the Ancient near East (1993), 28. ↵
  2. Jöran Friberg, A Remarkable Collection of Babylonian Mathematical Texts Manuscripts in the Schøyen Collection: Cuneiform Texts 1 (2007, Springer), 378. ↵

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