An Ancient Relation between Units of Length and Volume Based on a Sphere

The modern metric system defines units of volume based on the cube. We propose that the ancient Egyptian system of measuring capacity employed a similar concept, but used the sphere instead. When considered in ancient Egyptian units, the volume of a sphere, whose circumference is one royal cubit, equals half a hekat. Using the measurements of large sets of ancient containers as a database, the article demonstrates that this formula was characteristic of Egyptian and Egyptian-related pottery vessels but not of the ceramics of Mesopotamia, which had a different system of measuring length and volume units

Scaling the state: Egypt in the third millennium BC

Discussions of the early Egyptian state suffer from a weak consideration of scale. Egyptian archaeologists derive their arguments primarily from evidence of court cemeteries, elite tombs, and monuments of royal display. The material informs the analysis of kingship, early writing, and administration but it remains obscure how the core of the early Pharaonic state was embedded in the territory it claimed to administer. This paper suggests that the relationship between centre and hinterland is key for scaling the Egyptian state of the Old Kingdom (ca. 2,700-2,200 BC). Initially, central administration imagines Egypt using models at variance with provincial practice. The end of the Old Kingdom demarcates not the collapse, but the beginning of a large-scale state characterized by the coalescence of central and local models