Historical Dynamics: Why States Rise and Fall

Historical Dynamics: Why States Rise and Fall

by Peter Turchin


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ISBN-13: 9780691180779
Publisher: Princeton University Press
Publication date: 05/22/2018
Series: Princeton Studies in Complexity , #26
Edition description: Reprint
Pages: 264
Product dimensions: 6.10(w) x 9.10(h) x 0.80(d)

About the Author

Peter Turchin is Professor of Ecology and Evolutionary Biology at the University of Connecticut. He is the author of Quantitative Analysis of Movement and Complex Population Dynamics (Princeton).

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Historical Dynamics

Why States Rise and Fall
By Peter Turchin

Princeton University Press

Peter Turchin
All right reserved.

ISBN: 0691116695

Chapter One



Why do some polities-chiefdoms and states of various kinds-embark on a successful program of territorial expansion and become empires? Why do empires sooner or later collapse? Historians and sociologists offer a great variety of answers to these and related questions. These answers range from very specific explanations focusing on unique characteristics of one particular polity to quite general theories of social dynamics. There has always been much interest in understanding history, but recently the theoretical activity in this area has intensified (Rozov 1997). Historical sociology is attempting to become a theoretical, mature science.

But why do historical sociologists use such a limited set of theoretical tools? Theory in social sciences usually means careful thinking about concepts and definitions. It is verbal, conceptual, and discursive. The theoretical propositions that are derived are qualitative in nature. Nobody denies the immense value of such theoretical activity, but it is not enough. There are also formal, mathematical approaches to building theory that have been applied with such spectacular success in physics and biology. Yet formalized theory employing mathematical models is rarely encountered in historical sociology (we will be reviewing some of the exceptions in later chapters).

The history of science is emphatic: a discipline usually matures only after it has developed mathematical theory. The requirement for mathematical theory is particularly important if the discipline deals with dynamic quantities (see the next section). Everybody is familiar with the paradigmatic example of classical mechanics. But two more recent examples from biology are the synthetic theory of evolution that emerged during the second quarter of the twentieth century (Ruse 1999), and the ongoing synthesis in population ecology (for example, Turchin 2003). In all these cases, the impetus for synthesis was provided by the development of mathematical theory.

Can something similar be done in historical sociology? Several attempts have been made in the past (e.g., Bagehot 1895; Rashevsky 1968), but they clearly failed to make an impact on how history is studied today. I think there are two major reasons explaining this failure. First, these attempts were inspired directly by successes in physical sciences. Yet physicists traditionally choose to deal with systems and phenomena that are very different from those in history. Physicists tend to choose very simple systems with few interacting components (such as the solar system, the hydrogen atom, etc.) or systems consisting of a huge number of identical components (as in thermodynamics). As a result, very precise quantitative predictions can be made and empirically tested. But even in physical applications such systems are rare, and in social sciences only very trivial questions can be reduced to such simplicity. Real societies always consist of many qualitatively and quantitatively different agents interacting in very complex ways. Furthermore, societies are not closed systems: they are strongly affected by exogenous forces, such as other human societies, and by the physical world. Thus, it is not surprising that traditional physical approaches honed on simple systems should fail in historical applications.

The second reason is that the quantitative approaches typically employed by physicists require huge amounts of precisely measured data. For example, a physicist studying nonlinear laser dynamics would without further ado construct a highly controlled lab apparatus and proceed to collect hundreds of thousands of extremely accurate measurements. These data would then be analyzed using sophisticated methods on a high-powered computer. Nothing could be further from the reality encountered by a historical sociologist, who typically lacks data about many aspects of the historical system under study, while possessing fragmentary and approximate information about others. For example, one of the most important aspects of any society is just how many members it has. But even this kind of information usually must be reconstructed by historians on the basis of much guesswork.

If these two problems are the real reason why previous attempts failed, then some recent developments in natural sciences provide a basis for hope. First, during the last 20-30 years, physicists and biologists have mounted a concerted attack on complex systems. A number of approaches can be cited here: nonlinear dynamics, synergetics, complexity, and so on. The use of powerful computers has been a key element in making these approaches work. Second, biologists, and ecologists in particular, have learned how to deal with short and noisy data sets. Again, plentiful computing power was a key enabler, allowing such computer-intensive approaches as nonlinear model fitting, bootstrapping, and cross-validation.

There is another hopeful development, this time in social sciences. I am referring to the rise of quantitative approaches in history, or cliometrics (Williamson 1991). Currently, there are many investigators who collect quantitative data on various aspects of historical processes, and large amounts of data are already available in electronic form.

These observations suggest that another attempt at building and testing quantitative theories in historical sociology may be timely. If we achieve even partial success, the potential payoff is so high that it warrants making the attempt. And there are several recent developments in which application of modeling and quantitative approaches to history have already yielded interesting insights.


Many historical processes are dynamic. Generally speaking, dynamics is the scientific study of any entities that change with time. One aspect of dynamics deals with a phenomenological description of temporal behaviors-trajectories (this is sometimes known as kinematics). But the heart of dynamics is the study of mechanisms that bring about temporal change and explain the observed trajectories. A very common approach, which has proved its worth in innumerable applications, consists of taking a holistic phenomenon and mentally splitting it up into separate parts that are assumed to interact with each other. This is the dynamical systems approach, because the whole phenomenon is represented as a system consisting of several interacting elements (or subsystems, since each element can also be represented as a lower-level system).

As an example, consider the issue raised at the very beginning of the book. An empire is a dynamic entity because various aspects of it (the most obvious ones being the extent of the controlled territory and the number of subjects) change with time: empires grow and decline. Various explanations for imperial dynamics address different aspects of empires. For example, we may be concerned with the interacting processes of surplus product extraction and warfare (e.g., Tilly 1990). Then we might represent an empire as a system consisting of such subsystems as the peasants, the ruling elite, the army, and perhaps the merchants. Additionally, the empire controls a certain territory and has certain neighboring polities (that is, there is a higher-level system-or metasystem-that includes the empire we study as a subsystem). In the dynamical system's approach, we must describe mathematically how different subsystems interact with each other (and, perhaps, how other systems in the metasystem affect our system). This mathematical description is the model of the system, and we can use a variety of methods to study the dynamics predicted by the model, as well as attempt to test the model by comparing its predictions with the observed dynamics.

The conceptual representation of any holistic phenomenon as interacting subsystems is always to some degree artifical. This artificiality, by itself, cannot be an argument against any particular model of the system. All models simplify the reality. The value of any model should be judged only against alternatives, taking into account how well each model predicts data, how parsimonious the model is, and how much violence its assumptions do to reality. It is important to remember that there are many examples of very useful models in natural sciences whose assumptions are known to be wrong. In fact, all models are by definition wrong, and this should not be held against them.

Mathematical models are particularly important in the study of dynamics, because dynamic phenomena are typically characterized by nonlinear feedbacks, often acting with various time lags. Informal verbal models are adequate for generating predictions in cases where assumed mechanisms act in a linear and additive fashion (as in trend extrapolation), but they can be very misleading when we deal with a system characterized by nonlinearities and lags. In general, nonlinear dynamical systems have a much wider spectrum of behaviors than could be imagined by informal reasoning (for example, see Hanneman et al. 1995). Thus, a formal mathematical apparatus is indispensable when we wish to rigorously connect the set of assumptions about the system to predictions about its dynamic behavior.

1.2.1 Delimiting the Set of Questions

History offers many puzzles and somehow we must select which of the questions we are going to address in this research program. I chose to focus on territorial dynamics of polities, for the following reasons. Much of recorded history is concerned with territorial expansion of one polity at the expense of others, typically accomplished by war. Why some polities expand and others fail to do so is a big, important question in history, judging, for example, by the number of books written about the rise and fall of empires. Furthermore, the spatiotemporal record of territorial state dynamics is perhaps one of the best quantitative data sets available to the researcher. For example, the computer-based atlas centennia (Reed 1996) provides a continuous record of territorial changes during 1000-2000 c.e. in Europe, Middle East, and Northern Africa. Having such data is invaluable to the research program described in this book, because it can provide a primary data set with which predictions of various models can be compared.

The dynamic aspect of state territories is also an important factor. As I argued in the previous section, dynamic phenomena are particularly difficult to study without a formal mathematical apparatus. Thus, if we wish to develop a mathematical theory for history, we should choose those phenomena where mathematical models have the greatest potential for nontrivial insights.

Territorial dynamics is not the whole of history, but it is one of the central aspects of it, in two senses. First, we need to invoke a variety of social mechanisms to explain territorial dynamics, including military, political, economic, and ideological processes. Thus, by focusing on territorial change we are by no means going to be exclusively concerned with military and political history. Second, characteristics of the state, such as its internal stability and wealth of ruling elites, are themselves important variables explaining many other aspects of history, for example, the development of arts, philosophy, and science.

1.2.2 A Focus on Agrarian Polities

There are many kinds of polities, ranging from bands of hunter-gatherers to the modern postindustrial states. A focus on particular socioeconomic formation is necessary if we are to make progress. The disadvantages of industrial and postindustrial polities are that the pace of change has become quite rapid and the societies have become very complex (measured, for example, by the number of different professions). Additionally, we are too close to these societies, making it harder for us to study them objectively. The main disadvantage of studying hunter-gatherer societies, on the other hand, is that we have to rely primarily on archaeological data. Agrarian societies appear to suffer the least from these two disadvantages: throughout most of their history they changed at a reasonably slow pace, and we have good historical records for many of them. In fact, more than 95% of recorded history is the history of agrarian societies. As an additional narrowing of the focus for this book, I will say little about nomadic pastoralist societies and leave out of consideration thalassocratic city-states (however, both kinds of polities are very important, and will be dealt with elsewhere).

This leaves us still with a huge portion of human history, roughly extending from -4000 to 1800 or 1900 c.e.,1 depending on the region. One region to which I will pay much attention is Europe during the period 500-1900 c.e., with occasional excursions to China. But the theory is meant to apply to all agrarian polities, and the aim is to test it eventually in other regions of the world.

1.2.3 The Hierarchical Modeling Approach

There is a heuristic "rule of thumb" in modeling dynamical systems: do not attempt to encompass in your model more than two hierarchical levels. A model that violates this rule is the one that attempts to model the dynamics of both interacting subsystems within the system and interactions of subsubsystems within each subsystem. Using an individual-based simulation to model interstate dynamics also violates this rule (unless, perhaps, we model simple chiefdoms). From the practical point of view, even powerful computers take a long time to simulate systems with millions of agents. More importantly, from the conceptual point of view it is very difficult to interpret the results of such a multilevel simulation. Practice shows that questions involving multilevel systems should be approached by separating the issues relevant to each level, or rather pair of levels (the lower level provides mechanisms, one level up is where we observe patterns).

Accordingly, in the research program described in this book I consider three classes of models. In the first class, individuals (or, perhaps, individual households) interact together to determine group dynamics. The goal of these models is to understand how patterns at the group level arise from individual based mechanisms. In the second class, we build on group-level mechanisms to understand the patterns arising at the polity level. Finally, the third class of models addresses how polities interact at the interstate level. The greatest emphasis will be on the second class of models (groups-polity). I realize that this sounds rather abstract at this point; in particular, what do I mean by "groups"? The discussion of this important issue is deferred until chapter 3. Also, I do not wish to be too dogmatic about following the rule of two levels. When we find it too restrictive, we should break it; the main point is not to do it unless really necessary.


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Table of Contents

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 Model into Differential Equations 205

A.2 The Spatial Simulation of the Frontier Hypothesis 206

A.3 Demographic-Structural Models with Class Structure 208

A.4 Models for Elite Cycles 212

Appendix B. Data Summaries for the Test of the Metaethnic Frontier Theory 214

B.1 Brief Descriptions of "Cultural Regions" 214

B.2 Quantification of Frontiers 215

B.3 Quantification of Polity Sizes: The First Millennium c.e. 224

B.4 Quantification of Polity Sizes: The Second Millennium c.e. 225

Bibliography 226

Index 243

What People are Saying About This

Randall Collins

This book is clearly the state of the art in formal modeling and computer simulation of long-term historical changes in territorial states. Elegantly formulated and clearly written, it takes an important topic to a new level of formal sophistication.
Randall Collins, University of Pennsylvania


An important, original, and timely book—richly detailed and beautifully thought out.
Jack A. Goldstone, University of California, Davis


"An important, original, and timely book—richly detailed and beautifully thought out."—Jack A. Goldstone, University of California, Davis

"This book is clearly the state of the art in formal modeling and computer simulation of long-term historical changes in territorial states. Elegantly formulated and clearly written, it takes an important topic to a new level of formal sophistication."—Randall Collins, University of Pennsylvania

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