CONCEPT
Superlinear Scaling
The regime unique to cities in West's data — outputs grow faster than inputs, producing increasing returns, open-ended growth, and the same amplification of pathology that accompanies innovation.
Superlinear scaling describes systems whose outputs grow faster than their inputs — where the scaling exponent exceeds 1.0. In West and Bettencourt's data, socioeconomic quantities in cities — patents, wages, GDP, creative output — scale at approximately 1.15 with population. Doubling a city's size produces roughly 115% increase in innovation and economic output. The same exponent governs crime rates, rates of infectious disease transmission, and stress-related illness. Superlinear scaling is the mathematical signature of systems whose terminal units grow rather than remaining invariant — the structural property that, among complex adaptive systems, is unique to cities. It produces open-ended growth rather than the sigmoid mortality of sublinear systems, but it amplifies destructive outputs at exactly the rate it amplifies creative ones. The mathematics offers no mechanism for separating the two.
In The You On AI Field Guide
The discovery that cities scale superlinearly was one of the most unexpected findings of West and Luis Bettencourt's Santa Fe Institute research program. Biological intuition predicted that cities, like organisms,