List of Figures viii List of Tables x Preface xi Chapter 1. Statement of the Problem 1 1.1 Why Do We Need a Mathematical Theory in History? 1 1.2 Historical Dynamics as a Research Program 3 1.2.1 Delimiting the Set of Questions 4 1.2.2 AFocus on Agrarian Polities 4 1.

2.3 The Hierarchical Modeling Approach 5 1.2.4 Mathematical Framework 5 1.3 Summary 7 Chapter 2. Geopolitics 9 2.1 APrimer of Dynamics 9 2.1.

1 Boundless Growth 9 2.1.2 Equilibrial Dynamics 11 2.1.3 Boom/Bust Dynamics and Sustained Oscillations 12 2.1.4 Implications for Historical Dynamics 14 2.2 The Collins Theory of Geopolitics 16 2.

2.1 Modeling Size and Distance Effects 16 2.2.2 Positional Effects 20 2.2.3 Conflict-legitimacy Dynamics 23 2.3 Conclusion: Geopolitics as a First-order Process 25 2.4 Summary 27 Chapter 3.

Collective Solidarity 29 3.1 Groups in Sociology 29 3.1.1 Groups as Analytical Units 29 3.1.2 Evolution of Solidaristic Behaviors 31 3.1.3 Ethnic Groups and Ethnicity 33 3.

1.4 The Social Scale 34 3.1.5 Ethnies 36 3.2 Collective Solidarity and Historical Dynamics 36 3.2.1 Ibn Khaldun's Theory 38 3.2.

2 Gumilev's Theory 40 3.2.3 The Modern Context 42 3.3 Summary 47 Chapter 4. The Metaethnic Frontier Theory 50 4.1 Frontiers as Incubators of Group Solidarity 50 4.1.1 Factors Causing Solidarity Increase 51 4.

1.2 Imperial Boundaries and Metaethnic Fault Lines 53 4.1.3 Scaling-up Structures 57 4.1.4 Placing the Metaethnic Frontier Theory in Context 59 4.2 Mathematical Theory 63 4.2.

1 A Simple Analytical Model 64 4.2.2 A Spatially Explicit Simulation 68 4.3 Summary 75 Chapter 5. An Empirical Test of the Metaethnic Frontier Theory 78 5.1 Setting Up the Test 78 5.1.1 Quantifying Frontiers 79 5.

1.2 Polity Size 81 5.2 Results 83 5.2.1 Europe:0 -1000 c.e.83 5.2.

2 Europe:1000 -1900 c.e.86 5.3 Positional Advantage? 89 5.4 Conclusion: The Making of Europe 91 5.5 Summary 92 Chapter 6. Ethnokinetics 94 6.1 Allegiance Dynamics of Incorporated Populations 94 6.

2 Theory 95 6.2.1 Nonspatial Models of Assimilation 95 6.2.2 Spatially Explicit Models 99 6.3 Empirical Tests 104 6.3.1 Conversion to Islam 105 6.

3.2 The Rise of Christianity 111 6.3.3 The Growth of the Mormon Church 112 6.4 Conclusion: Data Support the Autocatalytic Model 113 6.5 Summary 116 Chapter 7. The Demographic-Structural Theory 118 7.1 Population Dynamics and State Breakdown 118 7.

2 Mathematical Theory 121 7.2.1 The Basic Demographic-Fiscal Model 121 7.2.2 Adding Class Structure 127 7.2.3 Models for Elite Cycles 131 7.2.

4 Models for the Chinese Dynastic Cycle 137 7.2.5 Summing up Theoretical Insights 138 7.3 Empirical Applications 140 7.3.1 Periodic Breakdowns of Early Modern States 140 7.3.2 The Great Wave 143 7.

3.3 After the Black Death 145 7.4 Summary 148 Chapter 8. Secular Cycles in Population Numbers 150 8.1 Introduction 150 8.2 "Scale" and "Order" in Human Population Dynamics 150 8.3 Long-Term Empirical Patterns 155 8.3.

1 Reconstructions of Historical Populations 155 8.3.2 Archaeological Data 161 8.4 Population Dynamics and Political Instability 164 8.5 Summary 167 Chapter 9. Case Studies 170 9.1 France 170 9.1.

1 The Frontier Origins 170 9.1.2 Secular Waves 176 9.1.3 Summary 184 9.2 Russia 184 9.2.1 The Frontier Origins 184 9.

2.2 Secular Waves 191 9.2.3 Summary 196 Chapter 10. Conclusion 197 10.1 Overview of Main Developments 197 10.1.1 Asabiya and Metaethnic Frontiers 197 10.

1.2 Ethnic Assimilation 198 10.1.3 Demographic-Structural Theory 199 10.1.4 Geopolitics 199 10.2 Combining Different Mechanisms into an Integrated Whole 200 10.3 Broadening the Focus of Investigation 203 10.

4 Toward Theoretical Cliodynamics? 204 Appendix A. Mathematical Appendix 205 A.1 Translating the Hanneman Mod.