It is a privilege to read this article by Høyrup, no doubt based on insights gained through decades of studies. If you want a very short introduction to Mesopotamian mathematics, this is a good place to start.
He tells of how tokens were placed in clay containers for accounting purposes, that later impressions were made on the surface to make it possible to "read" the information without breaking the containers, and how even later, the tokens themselves were dropped, no longer being of any significance. He describes the notation developed.
Later, mathematics developed as a means of ensuring "just measure" (and the author is quick to point out that mathematical justice can also be cruel).
From Shuruppak (-2600), examples of school texts have been found. An example of an "exercise": "A silo containing 40x60 gur ('tuns') of grain, each of 8x60 sila ('litres') is distributed in portions of 7 sila per worker." The answer is 164,571 workers, with a remainder of 3 sila, but the numbers included are surely not from a practical situation. (Already at that time, unrealistic numbers were used in mathematics exercises...)
In 2074, an administrative reform were carried out bringing my thoughts to harsh central planning regimes such as Mao's China or North Korea. Workers were organized in troups, and the overseers were responsible for their unit's performance, with preset goals (read the details in the article). Mathematics was necessary to keep the system running.
The author spends some time on the text "BM 13901". The translation goes as the following:
I have heaped the surface and my confrontation: it is 3/4. 1 the projection you posit, half-part of 1 you break, make 1/2 and 1/2 hold, 1/4 and 3/4 you join: alongside 1, 1 is equilateral. 1/2 which you have made hold from the body of 1 you tear out: 1/2 is the confrontation.
The explanation (in geometrical terms) is fascinating.
It is a remarkable article with insights I will make sure to bring to my classrooms.
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