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20 MS 2735: Introduction and Analysis

We saw in Part V  how the proto-cuneiform number systems of Mesopotamia gave way to cuneiform around the time of the Akkadian Empire (c. 2300 BC). Over time the developments of new, smaller units and fractions of units slowly worked towards the development of the sexagesimal place value system, or SPVS for short.[1]

To illustrate this transition we will look at the tablet MS 2735, pictured in Figure 22.[2] MS 2735 is a tablet of unknown origin that has been dated from its content to the Old Babylonian period (c. 1900BC-1600BC), and it is now kept in the Schøyen Collection, Oslo, Norway. MS 2735  contains a portion of the cuneiform metrology table for System A discussed in Chapter 18.

A rendering of the tablet 2735. It is a small rectangular tablet made up of 12 lines containing cuneiform numerals from System A and System S.
Figure 22. A simplified rendering of MS 2735.

The signs for System A are all listed on the left side of the tablet from 1 ubu ganá to 1 èše ganá. On the right side of the table is a column of System S numbers. These numbers are stated without any units. Nonetheless they are intended to represent the System A numerals, which represent area of a field, as an abstract number. To achieve this, each metrology had a specified base unit. All other amounts would be converted to System S as a number of those units.

Activity 22. Refer to Figure 22, Table 11, and Table 13 to answer the following questions.

  1. Looking at 6 rows of MS 2735, what is the base unit used to convert System A into System S. Keep in mind that géš and diš had the same sign in System S.
  2. Verify that rows 1 through 11 all conform to the base unit you identified in part 1.
  3. Based on your answers to part 1 and 2, how would expect to convert 1 èše to System S using this base unit?

 

Media Attributions

  1. For a wonderful discussion of this development, read Eleanor Robson, Mathematics in Ancient Iraq: a Social History, (2008), 75-83. ↵
  2. Rendering based on the drawing by Jöran Friberg, A Remarkable Collection of Babylonian Mathematical Texts Manuscripts in the Schøyen Collection: Cuneiform Texts 1 (2007, Springer), 117. ↵

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

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