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

by Geoffrey West

I want to emphasize that this situation is qualitatively quite different from classic Malthusian dynamics, where this is no such singularity. The existence of a singularity signifies that there has to be a transition from one phase of the system to another having very different characteristics, analogous to the way the condensation of steam to water which subsequently freezes to ice epitomizes transitions between different phases of the same system, each having quite different physical properties. And indeed, underlying such familiar phase transitions are singularities in the thermodynamic variables characterizing the system (water) but in terms of temperature rather than time (0°C for freezing and 100°C for boiling). Unfortunately, for cities and socioeconomic systems the phase transition stimulated by the finite time singularity is from superexponential growth to stagnation and collapse, and this could lead to potentially devastating consequences.