Carrying bricks and bundling reed in theory and practice (Q6619809)

This chapter of a book [\textit{K. Chemla} (ed.) et al., Cultures of computation and quantification in the ancient world. Numbers, measurements, and operations in documents from Mesopotamia, China and South Asia. Cham: Springer (2022; Zbl 1515.01004)] discusses two facets of the administration of labor from the time period of ca. 2100 BC to 1600 BC. Sources are on the one hand administrative records from the kingdom of Ur in the 21st century BC, on the other hand, mathematical texts written between ca. 1800 to 1600 BC. The two corpora concern the production and transport of bricks, and the harvesting, bundeling and carrying of reeds, branches of trees, grasses etc. Both activities were an important part of economic management. Labor performed in brick transport was managed by means of norms how much a worker can carry, and over what distances. In addition, different sizes (and weights) of bricks were in use. Knowing all these parameters enabled administrators to calculate the size of a work force needed for a specific task. Similarly, reed and other plant parts were transported and stored. These could not so easily be measured. Therefore, different kinds of ``bundles'' were applied in their measurement; not all are completely understood. The author edits various tablets as examples of the calculations, mostly from administrative contexts but also excerpts from mathematical texts which concern the economic activities just described. The mathematical texts simplify the tasks to be performed on reed bundles by using round numbers. They calculate the volume of a truncated cone (by a false formula) which is called a reed bundle. In an administrative text, a median diameter and the height of a reed bundle is mentioned; the author assumes that the volume was found by converting the truncated cone into a cylinder. To translate these texts the author recalculates the procedures with smaller measures so as to be able to avoid too many fractions. For brick management, mathematical texts agree with administrative texts on the norms for work. The administrative texts deal with actual situations: a certain number of bricks have to be brought to a construction site, and this implies to calculate the number of workers who are required to complete a task, and to provide these workers. There also had to be records of work that was actually done. In the mathematical texts concerning bricks, additional computations are done which are not required to reach results but may be considered of purely theoretical interest in numerical relations.\N\NFor the entire collection see [Zbl 1515.01004].