Cliodynamics

We provide empirical evidence that the distribution of empires' lifetime is exponential with a typical time-scale of 300 years. After introducing and computing a proxy measure for the dimension of a large polity we interpret the data by means of a simple dynamical model for the empires' evolution. The resulting theory suggests that the behavior of a long-lived empire is qualitatively different from a short-lived one. They all experience an initial expansion phase but while the former goes through a contraction period over the last $20\%$ of its life, the latter stays essentially unchanged after reaching its maximum size. In both cases, a sudden collapse occurs when the empire's size is still close to its own historical average.