Computing abilities in antiquity: The royal judahite storage jars as a case-study

Studying the volume of ancient pottery vessels can shed light on the development of complex societies and state apparatus by revealing the means taken to standardize trade and taxation. It can also shed light on the cognitive abilities of ancient people by investigating their knowledge of computing. This paper explores, as a case study, the volume and shape of the lmlk ("belonging to the king") royal storage jars, which probably represent the highest level of standardization in eighth century BCE Judah. To estimate the volume of these vessels we constructed a computer 3D model for each jar. The variation in the jars' linear dimensions is about 2-3%, a number that is characteristic of human-made objects produced by professionals without employing measurement tools. Had the potters produced jars of the same height, they could have easily reached 3-4% accuracy in the volume. Surprisingly, the variation in the jars' volume is 7-10%. We hypothesize that rather than height the potters focused on the jars' shape and wall width, estimating the volume according to the jars' outer measurements. We propose a simple way that these measurements could have been taken and suggest a formula that could have been employed by the potters and customers for quickly calculating a jar's volume.