| List of Figures | p. viii |
| List of Tables | p. x |
| Preface | p. xi |
| Statement of the Problem | p. 1 |
| Why Do We Need a Mathematical Theory in History? | p. 1 |
| Historical Dynamics as a Research Program | p. 3 |
| Delimiting the Set of Questions | p. 4 |
| AFocus on Agrarian Polities | p. 4 |
| The Hierarchical Modeling Approach | p. 5 |
| Mathematical Framework | p. 5 |
| Summary | p. 7 |
| Geopolitics | p. 9 |
| APrimer of Dynamics | p. 9 |
| Boundless Growth | p. 9 |
| Equilibrial Dynamics | p. 11 |
| Boom/Bust Dynamics and Sustained Oscillations | p. 12 |
| Implications for Historical Dynamics | p. 14 |
| The Collins Theory of Geopolitics | p. 16 |
| Modeling Size and Distance Effects | p. 16 |
| Positional Effects | p. 20 |
| Conflict-legitimacy Dynamics | p. 23 |
| Conclusion: Geopolitics as a First-order Process | p. 25 |
| Summary | p. 27 |
| Collective Solidarity | p. 29 |
| Groups in Sociology | p. 29 |
| Groups as Analytical Units | p. 29 |
| Evolution of Solidaristic Behaviors | p. 31 |
| Ethnic Groups and Ethnicity | p. 33 |
| The Social Scale | p. 34 |
| Ethnies | p. 36 |
| Collective Solidarity and Historical Dynamics | p. 36 |
| Ibn Khaldun's Theory | p. 38 |
| Gumilev's Theory | p. 40 |
| The Modern Context | p. 42 |
| Summary | p. 47 |
| The Metaethnic Frontier Theory | p. 50 |
| Frontiers as Incubators of Group Solidarity | p. 50 |
| Factors Causing Solidarity Increase | p. 51 |
| Imperial Boundaries and Metaethnic Fault Lines | p. 53 |
| Scaling-up Structures | p. 57 |
| Placing the Metaethnic Frontier Theory in Context | p. 59 |
| Mathematical Theory | p. 63 |
| A Simple Analytical Model | p. 64 |
| A Spatially Explicit Simulation | p. 68 |
| Summary | p. 75 |
| An Empirical Test of the Metaethnic Frontier Theory | p. 78 |
| Setting Up the Test | p. 78 |
| Quantifying Frontiers | p. 79 |
| Polity Size | p. 81 |
| Results | p. 83 |
| Europe: 0 -1000 c.e.83 | |
| Europe: 1000 -1900 c.e.86 | |
| Positional Advantage? | p. 89 |
| Conclusion: The Making of Europe | p. 91 |
| Summary | p. 92 |
| Ethnokinetics | p. 94 |
| Allegiance Dynamics of Incorporated Populations | p. 94 |
| Theory | p. 95 |
| Nonspatial Models of Assimilation | p. 95 |
| Spatially Explicit Models | p. 99 |
| Empirical Tests | p. 104 |
| Conversion to Islam | p. 105 |
| The Rise of Christianity | p. 111 |
| The Growth of the Mormon Church | p. 112 |
| Conclusion: Data Support the Autocatalytic Model | p. 113 |
| Summary | p. 116 |
| The Demographic-Structural Theory | p. 118 |
| Population Dynamics and State Breakdown | p. 118 |
| Mathematical Theory | p. 121 |
| The Basic Demographic-Fiscal Model | p. 121 |
| Adding Class Structure | p. 127 |
| Models for Elite Cycles | p. 131 |
| Models for the Chinese Dynastic Cycle | p. 137 |
| Summing up Theoretical Insights | p. 138 |
| Empirical Applications | p. 140 |
| Periodic Breakdowns of Early Modern States | p. 140 |
| The Great Wave | p. 143 |
| After the Black Death | p. 145 |
| Summary | p. 148 |
| Secular Cycles in Population Numbers | p. 150 |
| Introduction | p. 150 |
| "Scale" and "Order" in Human Population Dynamics | p. 150 |
| Long-Term Empirical Patterns | p. 155 |
| Reconstructions of Historical Populations | p. 155 |
| Archaeological Data | p. 161 |
| Population Dynamics and Political Instability | p. 164 |
| Summary | p. 167 |
| Case Studies | p. 170 |
| France | p. 170 |
| The Frontier Origins | p. 170 |
| Secular Waves | p. 176 |
| Summary | p. 184 |
| Russia | p. 184 |
| The Frontier Origins | p. 184 |
| Secular Waves | p. 191 |
| Summary | p. 196 |
| Conclusion | p. 197 |
| Overview of Main Developments | p. 197 |
| Asabiya and Metaethnic Frontiers | p. 197 |
| Ethnic Assimilation | p. 198 |
| Demographic-Structural Theory | p. 199 |
| Geopolitics | p. 199 |
| Combining Different Mechanisms into an Integrated Whole | p. 200 |
| Broadening the Focus of Investigation | p. 203 |
| Toward Theoretical Cliodynamics? | p. 204 |
| Mathematical | |
| p. 205 |
| Translating the Hanneman Mod | |
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