"

15 TSŠ 671: Introduction, Analysis, and Conclusion

While Activity Activity 16 showed that it is possible to utilize the Eblaite method of division outlined in Chapter 12 to derive the number found on TSŠ 50, there is no direct evidence of this found on the tablet itself. Miraculously a second tablet was found to contain the same exact question as TSŠ 50. A rendering of TSŠ 671 is given below in Figure 16.[1]

A simplified rendering of the front and back of the table TSŠ 671. Each side is represented by a rounded square. Each side is divided into rows: the front in two and the back in 4. The tablet contains cuneiform and System S numerals.
Figure 16.. A simplified rendering of the front and back of the table TSŠ 671.

When read from front to back, the tablet can be transliterated as follows.[2]

Table 10. The transliteration of TSŠ 671.
Row Sumerian English
1 še gur sìla 7 barley silo 7 sìla
2 1 lú šu-ba-ti 1 man receives
3 guruš the workers
4 4 šár’u
5 5 šar
6 3 géš’u 6 géš
From Table 10 we can see that, although it is worded slightly differently, that TSŠ 671 is still concerned with dividing barley of 1 silo amongst men, specifically workers, who are to be paid 7 sìla of barley apiece. Notice however the answer given on TSŠ 671 is wrong!
While a wrong answer may seem uninteresting, it is these types of mistakes that allow Assyriologists to confirm hypotheses. In our case, we are interested in verifying that the Eblaite method of division was also in use in Sumeria. With no direct evidence, one potential way we could demonstrate this theory is plausible would be to identify how a simple error made in the process of applying this method results in the answer given by TSŠ 671.[3]

Activity 17. Refer to Activity 16 to answer the following question.

Below we have the first three rows of the table in Activity 16 filled out correctly. It is your goal to find one reasonable error in filling out the third line that when the table is completed using the Eblaite method of division outlined in Chapter 12 correctly  we get the answer listed on TSŠ 671.

Amount of Barley Number of Men sìla remaining
bàn

 

 The symbol for an iku or 1. It looks like a small bullet. The symbol for an iku or 1. It looks like a small bullet.The symbol for an iku or 1. It looks like a small bullet.The symbol for an iku or 1. It looks like a small bullet.
barig

 

 The symbol for an iku or 1. It looks like a small bullet.The symbol for an iku or 1. It looks like a small bullet.The symbol for an iku or 1. It looks like a small bullet.The symbol for an iku or 1. It looks like a small bullet.

The symbol for an iku or 1. It looks like a small bullet.The symbol for an iku or 1. It looks like a small bullet.The symbol for an iku or 1. It looks like a small bullet.The symbol for an iku or 1. It looks like a small bullet.

 The symbol for an iku or 1. It looks like a small bullet.The symbol for an iku or 1. It looks like a small bullet.The symbol for an iku or 1. It looks like a small bullet.The symbol for an iku or 1. It looks like a small bullet.
gur

 

 The symbol for an uš. It looks like a large bullet.

The symbol for an iku or 1. It looks like a small bullet.The symbol for an iku or 1. It looks like a small bullet.The symbol for an iku or 1. It looks like a small bullet.The symbol for an iku or 1. It looks like a small bullet.

The symbol for an iku or 1. It looks like a small bullet.The symbol for an iku or 1. It looks like a small bullet.The symbol for an iku or 1. It looks like a small bullet.The symbol for an iku or 1. It looks like a small bullet.

 The symbol for an iku or 1. It looks like a small bullet.The symbol for an iku or 1. It looks like a small bullet.The symbol for an iku or 1. It looks like a small bullet.The symbol for an iku or 1. It looks like a small bullet.
1 u gur

 

 
1 géš gur

 

 
1 géš’u gur

 

 
4 géš’u gur

 

 

We conclude that the method of division outlined in Chapter 12 was used widely in ancient Mesopotamia. This method would later be supplanted by an very sophisticated technique that made special use of the sexagesimal place value system.

 

Media Attributions

  1. This rendering is based on the illustration done by Jöran Friberg, A Remarkable Collection of Babylonian Mathematical Texts Manuscripts in the Schøyen Collection: Cuneiform Texts 1 (2007, Springer), 414. ↵
  2. This transliteration is taken from Friberg (2007) 415. ↵
  3. This observation was first made by Duncan Melville "Ration computations at Fara: Multiplication or repeated addition?" Under One Sky. Astronomy and Math- ematics in the Ancient Near East, eds. John M. Steele and Annette Imhausen, (Münster, 2002), 237-252. ↵

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

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