Recent cross-disciplinary work on quantifying historical dynamics has made major contributions to scholarship. However, efforts to specify relationships between scale and information-processing always run a risk of shoehorning messy realities into overly rigid categories. In the case of the first-millennium BCE “Axial Age” in the Old World, networks of collective computing were structured more by cultural systems than by polities, and to understand the relationships between political scale and collective computational abilities, scholars need categories flexible enough to clarify the complementarities between political and cultural systems.