The mathematical 'laws' used to predict how cities grow and change over time are often statistical illusions that don't apply to any actual city.
April 1, 2026
Original Paper
On the Meaning of Urban Scaling
arXiv · 2603.30021
The Takeaway
Scientists have long believed that as cities get bigger, they follow predictable scaling rules for things like crime or wealth. This paper proves that these rules are just group snapshots; individual cities follow their own unique trajectories that almost never match the 'law,' meaning our standard models for urban growth are fundamentally flawed.
From the abstract
Urban scaling laws describe how an urban quantity $Y$ varies with city population $P$, typically as $Y \sim P^{\beta}$. These relations are usually obtained from cross-sectional comparisons across cities at a given time (transversal scaling), but their link to the temporal evolution of individual cities (longitudinal scaling) remains unclear. Here we derive explicit expressions for the transversal exponent from the longitudinal dynamics of cities. We show that the measured exponent does not dire