6 MS 3047: Introduction and Analysis

Like VAT 12593, MS 3047 is another tablet from the Early Dynastic period. While its provenance is unknown, it most likely also comes form Šurrupag.^[1] 

Figure 5 is a rendering of MS 3047 where all System A numbers have been removed.^[2]  Such numbers appeared in the first 6 cells in the righthand column and the last cell in the middle column. If we ignore the last row, the rest of the tablet should look very similar to the rendering of VAT 12593 in Figure 3. Indeed, MS 3047 is also a multiplication table, where rather than squaring each side length, we are multiplying two different side-lengths.^[3] 

With the contents of VAT 12593 and our knowledge of Systems S and A, it is possible to work out the areas for ourselves. Let us take for example the second row of MS 3047. In order to multiply 1 u ninda by 1 géš’u ninda, we begin by multiplying 1 u ninda by 1 géš ninda. Recall that 1 géš is 6 u (see Table 2). From VAT 12593 the area of a field that is 1 u ninda by 1 u ninda is 1 iku (see Figure 3). Figure 6 shows how to visualize this geometrically. We conclude that the area of a field that is 1 u ninda by 1 géš ninda is 6 iku or 1 èše (see Table 3).

In order to now find the product of 1 u ninda by 1 géš’u ninda, we recall that 1 gés’u is 10 géš. We just figured out that the area of a field that is 1 u ninda by 1 géš ninda is 1 èše. Figure 7 shows how to visualize this geometrically. We conclude that the area of a field that is 1 u ninda by 1 géš’u ninda is 10 èše or 3 bùr 1 èše.

Note that Figure 7 shows the true aspect ratio of a rectangle with the dimensions listed on MS 3047. We can safely conclude that no such fields ever existed, but rather this is again a metrological-mathematical problem meant to serve as a reference or to train scribes.^[4]