The largest city in a society consistently grows at the two-thirds power of the total population, a rule that has held for 10,000 years.
April 25, 2026
Original Paper
An energetic theory of urbanization in ancient societies
SocArXiv · zbqyx_v1
The Takeaway
Human urban growth follows a strict physical law of energy and networks that transcends culture or politics. Whether in ancient Mesopotamia or the modern United States, the scale of the biggest city is predictable based on the total number of people. This pattern suggests that city growth is a biological and physical process rather than a purely social one. Resources and information flow through human networks in a way that dictates city size with mathematical precision. Planners and historians have long assumed that policy drives urban concentration, but the math tells a different story. The physical constraints of energy consumption limit how large a central hub can become.
From the abstract
Urbanization is one of the most consequential and best-documented processes in the archaeological and historical record, yet we lack a general quantitative theory to explain it in ancient societies. I address this gap by developing a model of urbanization that integrates the comparative insights of archaeology and history with settlement scaling theory and human macroecology. The model proposes that urbanization---measured as the population size of a polity's largest settlement relative to polit