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This chapter provides an introduction to the use of quantitative theories in historical sociology. It first explains why we need a mathematical theory in history before making a case for historical dynamics as a research program, with emphasis on the important role of mathematical models. Using the case of the territorial dynamics of agrarian polities, it proposes a research program for theory building in historical dynamics that involves selecting which of the questions need to be addressed as well as the hierarchical modeling approach and the mathematical framework to be employed. In addition to defining the problem to be addressed, other steps include identifying the primary data set, identifying a set of hypotheses, translating all hypotheses in the list into mathematical models, identifying secondary data, and solving the models using appropriate technology.

This concluding chapter summarizes the main developments discussed in the book, beginning with the proposed research program for investigating historical dynamics and how the approach can be used to study the territorial dynamics of agrarian polities. It then considers asabiya and its impact on metaethnic frontiers; the results of empirical tests on ethnic assimilation; the prediction of demographic-structural theory that population dynamics causes state breakdown; and the theory of geopolitics, applied to test of the effect of a region's positional advantage on the maximum polity size originating from it. The chapter also proposes a combined modeling/empirical approach to investigating history and how the focus of the research program may be expanded beyond the dynamics of agrarian polities (for example, to cases involving nomadic pastoralists, thalassocratic polities such as classical Athens, or hegemonic cycles). Finally, it suggests the term “cliodynamics” (by analogy with cliometrics) as an alternative to “historical dynamics”.

This chapter discusses the dynamics underlying collective solidarity, building the theory by inferring group dynamics from interactions between individuals and polity dynamics from interactions between groups. Groups vary in their capacity for collective action as a result of a complex mix of individual behaviors, such as the ability to detect and punish free-riders. The capacity for collective solidarity, or asabiya, refers to the group capacity for concerted collective action. The chapter first provides an overview of groups in sociology and how human behavior and sociality promote the evolution of solidaristic behaviors before exploring the importance of ethnic groups and ethnicity in collective solidarity. It then considers the link between collective solidarity and historical dynamics, Ibn Khaldun's theory of political cycles, and Lev Gumilev's theory of ethnogenesis. Finally, it examines how collective solidarity relates to modern concepts such as social capital, Emile Durkheim's mechanical and organic solidarity, and individualism and collectivism.

This chapter describes dynamic models of ethnosocial change, referred to as ethnokinetic models, with particular emphasis on ethnic assimilation. It first explains the simplest possible formulation of the process of ethnokinetics before discussing three basic sets of assumptions about how people switch their ethnic identity (a process that may involve linguistic assimilation, religious conversion, etc.). Three models corresponding to these assumptions are presented: the noninteractive model, the autocatalytic model, and the threshold model. The chapter then considers spatial extensions of all three models and examines which model accounts for the historical dynamics of identity switching. It also analyzes several data sets on religious conversion: conversion to Islam in Iran and Spain, the rise of Christianity in the Roman Empire, and the growth of Mormonism. The results provide the greatest degree of empirical support to the autocatalytic model.

This chapter presents case studies of historical dynamics in two polities: France and Russia in the longue durée (from the origins to 1900 C.E.). It first considers the dynamics of asabiya and the associated issues of frontiers and ethnogenesis in France and Russia before discussing the secular cycles involving linked demographic, social, and political processes. Both France and Russia experienced two ethnogenetic events: the Franks and the French, the Rus and the Russians. All four ethnies arose on metaethnic frontiers, and all states went through secular cycles. In the case of Gaul-France, the observed oscillations during the 2000-year period are in agreement with those predicted by the demographic-structural theory. The results also show that the decentralization phases of secular cycles are almost invariably characterized by the “fathers-and-sons” pattern, in which instability occurs in waves about two generations apart.