Empires rise and fall, populations and economies boom and bust, world religions spread or wither... What are the mechanisms underlying such dynamical processes in history? Are there 'laws of history'? We do not lack hypotheses to investigate - to take just one instance, more than two hundred explanations have been proposed for why the Roman Empire fell. But we still don't know which of these hypotheses are plausible, and which should be rejected. More importantly, there is no consensus on what general mechanisms explain the collapse of historical empires. What is needed is a systematic application of the scientific method to history: verbal theories should be translated into mathematical models, precise predictions derived, and then rigorously tested on empirical material. In short, history needs to become an analytical, predictive science (see Arise cliodynamics).

Cliodynamics (from Clio, the muse of history, and dynamics, the study of temporally varying processes) is the new transdisciplinary area of research at the intersection of historical macrosociology, economic history/cliometrics, mathematical modeling of long-term social processes, and the construction and analysis of historical databases. Mathematical approaches – modeling historical processes with differential equations or agent-based simulations; sophisticated statistical approaches to data analysis – are a key ingredient in the cliodynamic research program (Why do we need mathematical history?). But ultimately the aim is to discover general principles that explain the functioning and dynamics of actual historical societies. 

The community of researchers working on mathematical history and cliodynamics has been rapidly growing in recent years. We now have our own journal, Cliodynamics: the Journal of Theoretical and Mathematical History. Although this web page is primarily devoted to my personal research, I also try, as much as possible, to reflect the most significant developments in the field as a whole.

Currently my research focuses on two broad questions. The first issue is the one introduced above: what general mechanisms explain the collapse of historical empires. It turns out that such imperial (and, sometimes, civilizational) collapses generally occured during the waves of political instability that periodically affected agrarian societies. A theory explaining these waves, or cycles, is presented and empirically tested in Secular Cycles, coauthored with Sergey Nefedov. The empirical part surveys long-term oscillations in demographic, economic, social, and political structures in England, France, and Russia from medieval to early modern periods, and in the Roman Republic and Empire. While the theory does very well for past agrarian societies, the inevitable question arises, what about our times? Are we about to experience another age of political instability and social disintegration? To answer this question, I am working on a project examining the historical dynamics of the American Republic, from its inception (c.1780) to the present. First draft has been posted in August 2013 (see below). 

The second research direction starts with the observation that large-scale states and empires are a relative rarity in the historical record. The most difficult question, really, is not why they collapse, but how they were possible in the first place. What were the social forces that held together huge empires, encompassing tens of millions of people spread over millions of squared kilometers of territory? I bring a variety of approaches to bear on this question: insights from the multilevel selection theory, agent-based models (in collaboration with Sergey Gavrilets), and systematic empirical surveys of global patterns of "imperiogenesis". Understanding the nature and evolution of large-scale cooperation has also practical implications for such issues as failed states and nation building (see War, Peace, and the Evolution of Social Complexity).