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Historical Dynamics: Why States Rise and Fall (Princeton Studies in Complexity)

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I remember that some years ago when I discovered
"Looking at History through Mathematics" by Nicolas Rashevsky
(published in 1968 by the MIT Press)
I was at first enthralled by the title but then fairly
disappointed by the book itself for in fact it contains very
little history: no solid statistical data, not even
qualitative historical trends that would illustrate some
of the theoretical curves. Instead of focusing on sharply
defined questions, Rashevsky raises broad issues such as for
instance (on p. 9 and 117)
why it took 10,000 years rather than a few hundred
for humanity to develop from its cultural state at the
beginning of early urban civilization to its present state.

This former experience explains why I read Peter Turchin's book
with so much pleasure. What a contrast indeed! In
every section stimulating models are blended with quantitative
historical data drawn from the best sources. From the rise of
Islam to the growth of the Mormon Church to Chinese dynastic
cycles "Historical Dynamics" offers a fascinating sample
of sharply defined problems for which models are able to provide
unified understanding.

Finally, I would like to express a wish or a hope.
It would be really great
if this book would attract the attention of a sample
of historians willing to collect additional field data on
the issues that are raised in the book. For instance,
regarding the growth of religious communities, there are
literally hundreds of cases which could be considered, from the
spread of Lutheranism or Calvinism to the growth of the
Amish, Mennonites, Jehovah's Witnesses and many other
religious movements. Needless to say, to be useful such a work
has do be carried out in a uniform and systematic way,
by which I mean
that the SAME data must be collected in each case-study.
This would be an ideal task for a team
of historians from different countries, much in the same way
as observational research in physics or astronomy
is carried out by international teams of researchers.

Table of Contents

List of Figures

List of Tables

Preface

Ch. 1 Statement of the Problem 1

Ch. 2 Geopolitics 9

Ch. 3 Collective Solidarity 29

Ch. 4 The Metaethnic Frontier Theory 50

Ch. 5 An Empirical Test of the Metaethnic Frontier Theory 78

Ch. 6 Ethnokinetics 94

Ch. 7 The Demographic-Structural Theory 118

Ch. 8 Secular Cycles in Population Numbers 150

Ch. 9 Case Studies 170

Ch. 10 Conclusion 197

App. A: Mathematical Appendix 205

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

Bibliography 226

Index 243

There are already several fine reviews, so I will only suggest reading the following works (all of them interesting books dealing somehow with the STATE) in addition to this book: 1) "War in Human Civilization" by Azar Gat (war explained, not just narrated); 2) "War and Peace and War: The Rise and Fall of Empires" by the same author but far easier to read; 3) "Understanding Early Civilizations" by Bruce Trigger (a great comparative review of early civilizations); 4) "History of Government" by S.E. Finer; and 5) Political Thought: 5.1. and 5.2: "The West and Islam. Religion and Political Thought in World History" plus "A World History of Ancient Political Thought" by Antony Black.

Peter Turchin is a highly respected evolutionary biologist who has specialized in the synthesis of theory and empirical data (see his book Complex Population Dynamics for his work in that area). He has now turned the skills he honed explaining animal societies to human societies, and particularly to explaining the rise and fall of empires. In broad terms I would describe his approach as Malthus meets Marx meets social constructionism meets evolutionary game theory. While his model is strictly applicable only to agrarian empires, his explanations of phenomena such rising income equality, intra-elite conflict, and even increased demand for university admissions, resonate so strongly with modern society that it is clear that a modified version of his model will go a long way towards explaining our current political and economic circumstances. There are few aspects of his work that are individually wholly new; Turchin's contribution is a rigorous synthesis of historical case-studies with evolutionary theory and quantitative empirical evidence. His work has the potential to transform our understanding of "macro" social issues in the same way that behavioral economics has transformed our understanding of decision making at the "micro" level. I'll go out on a limb and predict that Turchin will eventually win a Nobel prize in economics.

I'll provide a quick overview of Turchin's work, but this synopsis doesn't do it justice; if you find my overview implausible, please read his books for yourself.

How groups manage to escape the prisoners' dilemma and cooperate is a central question of evolutionary biology. Turchin argues that the social construction of "other" along meta-ethnic frontiers (which are often defined in terms of factors other than ethnicity, in particular religion), is necessary to enable group cooperation which allows empire building. This is why empires almost invariably arise along frontiers. A ruling class with a high potential for collective action ("asabiya" - a term Turchin borrows from the 14th century political philosopher Ibn Khaldun), will expand while financing its wars by taxing the peasants. In the early days of the empire, the elite are relatively austere warriors, and low population densities allow peasants to produce a significant surplus, so elite requirements do not overburden peasant production. As population densities increase, the surplus produced per peasant decreases because each has less land, but at the same time rents charged by the elites increase as land becomes scare. Peasants become poorer, though the elite continue to do well. Wealth inequality increases, and eventually the peasant base cannot sustain the high expectations of the growing elite population. Consequently, some of the elite class find themselves without land to sustain their lifestyle, while others become extremely wealthy due to control of scarce resources. This gives rise to intra-elite conflict. Social cohesion declines due to increasing inequality, both between elite and peasant classes and within the elite. The result is that peasants who are desperate and weakened by poverty are drawn into elite infighting. A combination of civil war, famine and plague reduces the population of the weakened state. The population decline ultimately leads to lower food prices and increased wages for the poor, but the loss of social cohesion is not so easily reversed. The recovery is thus impeded by continued infighting, and sometimes an outside group with higher asabiya takes over before another expansion phrase is triggered.

Turchin has three books developing his approach. "War and Peace and War: The Life Cycles of Imperial Nations" is the popular introduction. It describes the approach without any math or equations, and applies it to a range of historical empires. This is the place to start for a general introduction, particularly if you are not mathematically inclined. However, it is not formally rigorous and will not convince you if you are sceptical. "Secular Cycles" (with Sergey Nefedov) supports the theory with quantitative empirical data. It applies the model to two cycles in each of England, France, Rome and Russia. This is the book to read if you are comfortable with numbers and need to be convinced by empirical evidence. "Historical Dynamics: Why States Rise and Fall" provides the theoretical framework, discussing, for example, why an explanation of cyclical dynamics requires a feedback loop. It is quite mathematical, and while you don't have to work your way through all the equations, you should be comfortable with mathematical models generally. Turchin's model was inspired by Jack A Goldstone, "Revolution and Rebellion in the Early Modern World." This is also an excellent book. It is written in a more traditional historical style; the model is informal, rather than formal, and the argument is supported by historical analysis of particular revolutions, rather than by quantitative data. In these respects it is similar to "War and Peace and War," though it is substantially longer. If you are looking for an extended analysis in a more traditional style of social history, this a great book.

This review pertains to all three of Turchin's books, and I am posting the same review for all of them.

In mathematics, logic, combinatorics and informatics constitute

its base and dynamics its tip. The two archtypical dynamical theories, mathematical physics

(dynamics of matter) and finance (dynamics of money) leave unaccounted the vast phenomena of biological and social sciences. The latter is the topic of this excellent book, that is

recommended to all dynamicists/mathematicians with interest in social applications of their discipline.

The book treats mostly social dynamics from a historical point of view and it has a solid scientific attitude, i.e., it considers history as an exact science. The level of mathematics is adequate (not very technical) ideal for an introduction to this field.

The author has an excellent grasp of dynamics theory in general and social dynamics in particular.

Some advanced topics are left out like the evolutionary dynamics viewpoint

and game theoretic dynamics viewpoint. These are exciting roads of future research.

Definitely, an excellent contribution to social mathematical dynamics that

I found clearly written and inspiring. Warmly recommended.

Turchin uses the tools and perspective of population biology to model some important aspects of the growth and collapse of empires. The relatively dry and mathematical style of the book makes it slow reading, but it leaves less ambiguity than most books about history. He has no obvious political biases - it often seems that his main bias is a preference for the tools of biologists over the tools of historians.

One important aspect of his approach is that it models the dynamics of a feature that is roughly described by terms such as solidarity, trust, and cooperation. He convinced me that he has described some of the influences that cause that feature to increase and decrease (the section title "Frontiers as incubators of group solidarity" says a good deal about his model).

Some aspects of the book left me wondering whether his eccentric worldview added anything to my understanding of history, but occasionally he comes up with ideas that have implications that are clearly new to me, such as his suggestion that monogamy can help an empire continue it's expansion for a longer time.

He makes some serious attempts to test his models against the available data. It's hard to tell whether enough data is available to adequately test such ambitious claims.

The biggest limitation of the book is that he assumes Malthusian conditions. While it is likely that some of his analysis applies to the industrial world, he thinks it's premature to ask how much of it applies today. That means it ought to be of interest mainly to historians for now.

This is a very good effort. The author goes through basic knowledge about complex systems and its basic math and then slowly brings historical trends and changes into the picture. This is a very good way to learn about history and a very easy way to remember historical events if the reader follows Turchin's approach.

Again a good read for those who want to learn history using the most natural approach.

First we see that it seems impossible to account for imperial cycles purely in terms of geopolitical factors such as area (A), war success (W), and geopolitical resources (R). A(t) would have to oscillate agree with the observed rise and fall of empires, but the simplest reasonable differential equations A'=cW, R=cA, W=cR-(constant outside pressure), lead to A'=cA-a, which means that A(t) either grows exponentially or dies off to 0. Nor can we obtain oscillatory A(t) by introducing logistic effects. Assuming that the efficiency of R's contribution to W deteriorates as a negative exponential function with distance from the centre, we get A'=ce^{-A/h}A-a (in the one-dimensional case, where distance is proportional to area), and A ends up at a stable equilibrium.

Turchin's first attempt at producing oscillatory A(t) is to introduce "collective solidarity" as a factor, so that A'=cSe^{-A/h}A-a, or, using the first two Taylor terms of the exponential, A'=cS(1-A/h)A-a. Collective solidarity spreads like a disease, so it satisfies a logistic equation S'=rS(1-S). But r is not constant. Collective solidarity is generated at the frontier (where there is a notable common enemy) while deteriorating in the centre (where everyone is living comfortably). Let's say that r is linear with r=R at the border and r=0 at a distance b from the border. Then the average r is R(1-A/2b). Thus we have A'=cS(1-A/h)A-a and S'=R(1-A/2b)S(1-S). This system is capable of producing oscillatory A(t). The behaviour of the system is highly chaotic, however. Periods and sizes of empires are highly irregular. It is possible to find some historical data which exhibits such chaotic behaviour (p. 70), but typically the time-span of an empire's rise and fall is around two to three centuries, which cannot be accounted for by this model.

A second model predicts the period of empires better. The population is assumed to satisfy a logistic model with sustainable population k, N'=rN(1-N/k). Here N(1-N/k) represents 'room to grow' and may thus be taken as a measure of surplus production. Thus tax income will be proportional to this factor, so that state resources are governed by S'=(tax income)-(spending)=N(1-N/k)-bN. Further, N and S are connected by the fact that the sustainable population is a function of S; let's assume k(s)=1+cS/(s+S). Here we have taken N=1 to be the anarchy population (i.e., k=1 when S=0), which is an equilibrium. A small perturbation from the anarchy equilibrium can set off an empire cycle. The periods of such cycles are around two to three centuries and are stable under reasonable changes in the parameters (i.e., halving or doubling taxation and spending, halving or doubling the birth rate factor r, etc.). Even conquering an anarchy land (i.e., adding 1 to N and increasing the sustainable anarchy population to 2) or an equal state (i.e., doubling N, S, and the sustainable anarchy population) does not alter the period much.

I wish to offer a modification to Turchin's latter model. Turchin's model actually does not predict state downfall very well. Empires collapse only because Turchin stipulates that S cannot go negative. The trajectories don't actually crash back to the anarchy equilibrium. Instead they crash to some point S=0, N=big, from where the trajectory will zigzag its way back to anarchy along the N-axis by resetting S to zero at every iteration. If one allows the state to go into modest debt it actually recovers and reaches a population even bigger than before, then crashes into greater debt, recover again to even greater population, and so on. This is because a negative S can give a negative k which means positive N(1-N/k) which means big surplus production, which is absurd. In fact, already k<1 makes no sense, since it makes no sense for a state to go below the anarchy population in order to catch up on debt. Thus I suggest replacing k by max(k,1). We should also replace bN by max(bN,S), so that the state cannot spend money it does not have. With these alterations the trajectories become beautifully smooth and reach the anarchy equilibrium without hidden resets.