Volume, brickage and capacity in Old Babylonian mathematical texts from southern Mesopotamia (Q6619812)

Scribes in Old Babylonian Mesopotamia used different metrological systems depending on the context of what was being weighed or measured. For three-dimensional entities, there was a distinction between capacity (for example filling up baskets) and volume (measured as area times height or depth). An interesting case concerns the measurement of bricks, which were treated differently in administrative and scribal mathematical contexts. Mud bricks, whether sun-dried or baked, were the staple building blocks of Mesopotamian architecture. As such, they came in a range of standardized sizes. Different sizes of bricks meant that different numbers of them went into a standard load, a number known as brickage. Thus, bricks could be measured and quantified in three different ways.\N\NIn this paper, the author considers a collection of Old Babylonian tablets containing academic problems on quantities of bricks, showing how the problems were designed to make students convert between capacity, measuring the content of bricks, volume, considering them as three-dimensional volumes of space, and brickage, the numbers of bricks involved. Not only were different units involved in the different metrological systems, the computations required the students to transfer information from the metrological systems into the abstract sexagesimal place-value system used for multiplication, and back into the metrological systems for the final answer, illustrating the central role in the process of computation of the metrological conversion tables every student had to learn. The author includes transliterations and translations of the subject texts, as well as collations where her reading differs from previously published editions, and a set of composite metrological tables.\N\NFor the entire collection see [Zbl 1515.01004].