Scale: The Universal Laws of Growth, Innovation, Sustainability, and the Pace of Life, in Organisms, Cities, Economies, and Companies

by Geoffrey West

Before addressing some of the consequences of this phenomenon, let me first elaborate on some of its salient features. Simple power laws and exponentials are continuously increasing functions that also eventually become infinitely large, but they take an infinite time to do so. Another way of saying this is that in these cases the “singularity” has been pushed off to an infinite time into the future, thereby rendering it “harmless” relative to the potential impact of a finite time singularity. In the case of growth driven by superlinear scaling, the approach to the finite time singularity, represented by the solid line in Figure 76, is faster than exponential. This is often referred to as superexponential, a term I’ve already used earlier when discussing the growth of cities.