Quantification and computation in the mathematical texts of old Babylonian Diyala
The author studies metrological and computational practices in Old Babylonian mathematical tablets from the Diyala region of Mesopotamia. The region takes its (modern) name from the Diyala river which flows from the Zagros mountains to merge with the Tigris a little below Baghdad. In the Old Babylonian period, the Diyala was home to the kingdom of Ešnunna, and thus occupied a central location between the cities of southern Mesopotamia such as Ur and Nippur, and Assyria in the north. Ešnunna was conquered by Hammurabi in 1762 and tablet production largely ceased.\N\NLittle of the region has been systematically excavated, and the results have been poorly-published. Much that we have comes from emergency excavation before the flooding of the Hamrin valley as a result of construction of the Hamrin dam. The mathematical tablets, in particular, have appeared scattered in technical publications, and the author does a service by compiling an up-to-date catalog of the corpus of 64 mathematical tablets, 34 of which are from Šaduppûm (Tell Harmal) and a further 17 from Me-Turān (Tell Haddad and Tell es-Seeb).\N\NQuantities were recorded in metrological units and notation, then converted into abstract sexagesimal place value numbers for computation (principally multiplication) before the numerical results were converted back into physical units for recording the final answers. The author offers a fine-grained typology classifying the associations between metrological units and abstract numbers in the texts, showing, in the main, that Diyala scribes used much the same techniques and tables as those in southern Mesopotamia, but there were some regional differences in terminology and units, and the occasional use of metrological units directly in computation without visible conversions.\N\NFor the entire collection see [Zbl 1515.01004].
scientific article; zbMATH DE number 7927225