"

17 CBS 11319+: Conclusion

In 2300 BC, much of southern Mesopotamia was united for the first time under Sargon of Akkad. Along with his successors, initiated a set of reforms, which included enforcing the use of the Akkadian language over Sumerian. These reforms touched all aspects of the management of empire, including mathematics:

“Metrologies were unified to become increasingly interdependent, while numerals were frequently written with incised cuneiform instead of impressed signs.”[1]

The curviform symbols for System S, introduced in  Table 2, were first used in the proto-Elamite period (c. 3100BC).[2] They continued to be used for nearly a millennium before being replaced by the cuneiform symbols pictured in Table 11.

Table 11. System S updated to include cuneiform symbols. 
Cuneiform Curviform Sumerian Relative Value
The cuneiform for 1 The symbol for an iku or 1. It looks like a small bullet. diš 1 diš
The cuneiform for 10 The symbol for a bur or for an éš. It is a black dot. u 10 diš
The cuneiform for 1 The symbol for an uš. It looks like a large bullet. géš 6 u
The cuneiform for 600 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 cuneiform for 3600 The symbol for a šár. It is a large black dot. šár 6 géš’u
The cuneiform for 36000 The symbol for šár'u. It looks like a large dot with a ring around it. šár’u 10 šár

In order to see the new System S in action, we turn to AO 5676, pictured in Figure 19. AO 5676 was produced in the city of Umma during the Neo-Sumerian period (c. 2036 BC). It is an accounting of a labor contract between the city and a named manager.[3]

 

A color photograph of the front and back of the tablet AO 05676. The tablet is square and covered all over in small cuneiform writing organized into columns.
Figure 19. A photo of the front and back of AO 5676, courtesy of the Louvre Museum.

If you look at the first row in the second column, directly underneath the museum reference number has been written, you can see a long string of system S numerals written in cuneiform. This row has been rendered below in Figure 20.[4]

A rendering of the first line of the second column of AO 05676. It contains a string of cuneiform System S numerals.
Figure 20. A rendering of the first line of the second column on the front of AO 5676.

Activity 19. Refer to Table 11, Figure 20, and Figure 14 to answer the following questions.

  1. Translate the number of men listed on TSŠ 50 in Figure 14 from curviform System S numerals into cuneiform System S numerals.
  2. Translate the number listed on AO 5676 in Figure 20 from cuneiform System S numerals into curviform System S numerals.

 

Media Attributions

  1. Eleanor Robson, Mathematics in Ancient Iraq: a Social History, (2008), 55. ↵
  2. Although initially System S stopped at géš'u and the orientation of script was rotated 90 degrees. Jören Friber, "Three thousand years of sexagesimal numbers in Mesopotamian mathematical texts." Arch. Hist. Exact Sci. 73,  (2019), https://doi.org/10.1007/s00407-019-00221-3, 191. ↵
  3. Robson, (2008), 55. ↵
  4. Rendering based on the transliteration and high resolution image available at “TCL 05, 5676 Artifact Entry.” (2001). Cuneiform Digital Library Initiative (CDLI).  https://cdli.earth/P131747. ↵

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Math History Copyright © by Bradley Burdick. All Rights Reserved.

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