On revolutions

Sometimes the normal course of events is disrupted by a particularly swift and profound change. Historians have often referred to such changes as "revolutions" and, though they have identified many of them, they have rarely supported their claims with statistical evidence. Here we present a method to identify revolutions based on a measure of the multivariate rate of change called Foote Novelty. We define revolutions as those periods of time when the value of this measure, F, can, by a non-parametric test, be shown to be significantly greater than the background rate. Our method also identifies conservative periods when the rate of change is unusually low. Importantly, our method permits searching for revolutions over any time scale that the data permit. We apply it to several quantitative data sets that capture long-term political, social and cultural changes and, in some of them, identify revolutions, both well known and not. Our method is a general one that can be applied to any phenomenon captured by multivariate time series data of sufficient quality.