21 MS 2735: Conclusion

In Activity 22 we expected 1 èše ganá to equal 600 sar or 1 géš’u sar. However the Akkadian sign for géš’u does not appear on MS 2735. In its place is the same symbol as for u. We are left to conclude that during the Old Babylonian period, System S discarded all but two signs as pictured in Table 15. To avoid confusion, we will refer to the symbol for diš as a vertical wedge and the sybmol for u as a Winkelhaken^[1]

Table 15. System S updated to include SPVS.

SPVS	Cuneiform	Curviform	Sumerian	Relative Value
			diš	1 diš
			u	10 diš
			géš	6 u
			géš’u	10 géš
			šár	6 géš’u
			šár’u	10 šár

In order for this system to work, numbers always had to be written in descending order. So a Winkelhaken written before a vertical wedge is worth 10 times the value of the vertical wedge, and a vertical wedge written before a Winkelhaken is worth 6 times the value of the Winkelhaken. This is why we call this a place value system because the position of a sign determines its value.

While this system provides a benefit of simplicity, with that simplicity comes confusion. Because the Old Babylonian SPVS did not have a the concept of a placeholder, it is impossible to tell the value of a single sign out of context. This is illustrated by the Activity 22. Because the sar value of 1 èše ganá was written as a single Winkelhaken, it could potentially be interpreted as u sar, géš’u sar, šár’u sar, or an even larger number that did not previously have a symbol. The context of MS 2735 in which 1 iku ganá equals 1 géš 4 u sar, we can determine definitely that the Winkelhaken for 1 èše ganá is meant to represent 1 géš’u sar. 

In order to translate the Old Babylonian SPVS without losing its sexagesimal character Otto Neugebauer^[2] introduced modern base sixty notation. We use normal base ten notation for the numbers 1 through 59, but then introduce a comma to separate the sexagesimal place value. For example, 1 géš 4 u would be written in modern base sixty as 1,40.