Unveiling hidden features of social evolution by inferring Langevin dynamics from data

Abstract

Are there hidden dynamical common patterns in the evolution of social and cultural history? While the growing availability of digitized social data invites us to answer this question, prevailing quantitative methods often rely on deterministic snapshots or average effects. Such approaches overlook the continuous and inherently uncertain nature of historical trajectories. In this paper, we propose a framework for modeling historical dynamics as stochastic processes described by stochastic differential equations (SDEs). By viewing historical change through the lens of continuous-time dynamics, this framework provides a natural language to describe how structural trends and inherent random fluctuations interact to shape societal evolution. This approach allows us to handle the uncertainty in fragmentary historical records, moving beyond the dichotomy of structural determinism versus pure chance. We demonstrate that adopting this stochastic perspective unlocks a rich suite of analytical capabilities unavailable to static models. Specifically, we introduce methods to: (1) quantify the irreversibility; (2) detect exogenous perturbations; (3) perform multiple imputation for missing historical records. This framework offers a unified methodology for dissecting the stability, contingency, and dynamics of historical change.