Many historical processes are dynamic. Populations grow and decline. Empires expand and collapse. Religions spread and wither. Natural scientists have made great strides in understanding dynamical processes in the physical and biological worlds using a synthetic approach that combines mathematical modeling with statistical analyses. Taking up the problem of territorial dynamics--why some polities at certain times expand and at other times contract--this book shows that a similar research program can advance our understanding of dynamical processes in history. Peter Turchin develops hypotheses from a wide range of social, political, economic, and demographic factors: geopolitics, factors affecting collective solidarity, dynamics of ethnic assimilation/religious conversion, and the interaction between population dynamics and sociopolitical stability. He then translates these into a spectrum of mathematical models, investigates the dynamics predicted by the models, and contrasts model predictions with empirical patterns. Turchin's highly instructive empirical tests demonstrate that certain models predict empirical patterns with a very high degree of accuracy. For instance, one model accounts for the recurrent waves of state breakdown in medieval and early modern Europe. And historical data confirm that ethno-nationalist solidarity produces an aggressively expansive state under certain conditions (such as in locations where imperial frontiers coincide with religious divides). The strength of Turchin's results suggests that the synthetic approach he advocates can significantly improve our understanding of historical dynamics.

List of Figures viiiList of Tables xPreface xiChapter 1. Statement of the Problem 11.1 Why Do We Need a Mathematical Theory in History? 11.2 Historical Dynamics as a Research Program 31.2.1 Delimiting the Set of Questions 41.2.2 AFocus on Agrarian Polities 41.2.3 The Hierarchical Modeling Approach 51.2.4 Mathematical Framework 51.3 Summary 7Chapter 2. Geopolitics 92.1 APrimer of Dynamics 92.1.1 Boundless Growth 92.1.2 Equilibrial Dynamics 112.1.3 Boom/Bust Dynamics and Sustained Oscillations 122.1.4 Implications for Historical Dynamics 142.2 The Collins Theory of Geopolitics 162.2.1 Modeling Size and Distance Effects 162.2.2 Positional Effects 202.2.3 Conflict-legitimacy Dynamics 232.3 Conclusion: Geopolitics as a First-order Process 252.4 Summary 27Chapter 3. Collective Solidarity 293.1 Groups in Sociology 293.1.1 Groups as Analytical Units 293.1.2 Evolution of Solidaristic Behaviors 313.1.3 Ethnic Groups and Ethnicity 333.1.4 The Social Scale 343.1.5 Ethnies 363.2 Collective Solidarity and Historical Dynamics 363.2.1 Ibn Khaldun's Theory 383.2.2 Gumilev's Theory 403.2.3 The Modern Context 423.3 Summary 47Chapter 4. The Metaethnic Frontier Theory 504.1 Frontiers as Incubators of Group Solidarity 504.1.1 Factors Causing Solidarity Increase 514.1.2 Imperial Boundaries and Metaethnic Fault Lines 534.1.3 Scaling-up Structures 574.1.4 Placing the Metaethnic Frontier Theory in Context 594.2 Mathematical Theory 634.2.1 A Simple Analytical Model 644.2.2 A Spatially Explicit Simulation 684.3 Summary 75Chapter 5. An Empirical Test of the Metaethnic Frontier Theory 785.1 Setting Up the Test 785.1.1 Quantifying Frontiers 795.1.2 Polity Size 815.2 Results 835.2.1 Europe:0 -1000 c.e.835.2.2 Europe:1000 -1900 c.e.865.3 Positional Advantage? 895.4 Conclusion: The Making of Europe 915.5 Summary 92Chapter 6. Ethnokinetics 946.1 Allegiance Dynamics of Incorporated Populations 946.2 Theory 956.2.1 Nonspatial Models of Assimilation 956.2.2 Spatially Explicit Models 996.3 Empirical Tests 1046.3.1 Conversion to Islam 1056.3.2 The Rise of Christianity 1116.3.3 The Growth of the Mormon Church 1126.4 Conclusion: Data Support the Autocatalytic Model 1136.5 Summary 116Chapter 7. The Demographic-Structural Theory 1187.1 Population Dynamics and State Breakdown 1187.2 Mathematical Theory 1217.2.1 The Basic Demographic-Fiscal Model 1217.2.2 Adding Class Structure 1277.2.3 Models for Elite Cycles 1317.2.4 Models for the Chinese Dynastic Cycle 1377.2.5 Summing up Theoretical Insights 1387.3 Empirical Applications 1407.3.1 Periodic Breakdowns of Early Modern States 1407.3.2 The Great Wave 1437.3.3 After the Black Death 1457.4 Summary 148Chapter 8. Secular Cycles in Population Numbers 1508.1 Introduction 1508.2 "Scale" and "Order" in Human Population Dynamics 1508.3 Long-Term Empirical Patterns 1558.3.1 Reconstructions of Historical Populations 1558.3.2 Archaeological Data 1618.4 Population Dynamics and Political Instability 1648.5 Summary 167Chapter 9. Case Studies 1709.1 France 1709.1.1 The Frontier Origins 1709.1.2 Secular Waves 1769.1.3 Summary 1849.2 Russia 1849.2.1 The Frontier Origins 1849.2.2 Secular Waves 1919.2.3 Summary 196Chapter 10. Conclusion 19710.1 Overview of Main Developments 19710.1.1 Asabiya and Metaethnic Frontiers 19710.1.2 Ethnic Assimilation 19810.1.3 Demographic-Structural Theory 19910.1.4 Geopolitics 19910.2 Combining Different Mechanisms into an Integrated Whole 20010.3 Broadening the Focus of Investigation 20310.4 Toward Theoretical Cliodynamics? 204Appendix A. Mathematical Appendix 205A.1 Translating the Hanneman Model into Differential Equations 205A.2 The Spatial Simulation of the Frontier Hypothesis 206A.3 Demographic-Structural Models with Class Structure 208A.4 Models for Elite Cycles 212Appendix B. Data Summaries for the Test of the Metaethnic Frontier Theory 214B.1 Brief Descriptions of "Cultural Regions" 214B.2 Quantification of Frontiers 215B.3 Quantification of Polity Sizes: The First Millennium c.e. 224B.4 Quantification of Polity Sizes: The Second Millennium c.e. 225Bibliography 226Index 243