This is the first of what I would consider the three founding texts of cliodynamics, at least of Turchin's contributions (along with War and Peace and War in 2006 and Secular Cycles in 2009). The focus of this book - why agrarian polities experience recurring periods of territorial growth and decline - is somewhat more narrow than those addressed in the later of the founding texts; the mathematical theory is also, thankfully, more explicitly addressed and the beginning of the book contains a primer on dynamics which should be useful for the many historians whose mathematical knowledge is, putting it kindly, limited. The concept of order in dynamics recurs throughout the book and is maybe the most important mathematical notion for historians to be introduced to in this text, though I do not claim to be an expert.
Turchin then goes on to apply the scientific method - or something approximating it - to his line of historical enquiry, though this is somewhat complicated by the fact that most historical theories are verbal. Thus, Turchin's general methodology is to translate verbal models into mathematically explicit ones which he then tests against the data to evaluate the theories and see which fits the empirical results the best. In regard to the question of the territorial growth and decline of agrarian polities he addresses mainly the "geopolitical" model of Randall Collins (though Turchin's definition of geopolitics is clumsy), the neglected asabiyyah theory of Ibn Khaldun, the demographic-structural theory developed by Jack Goldstone in the 1990s and a set of theories focusing on ethnic assimilation including the meta-ethnic frontier theory - though it can be argued that such theories must be inherently related to asabiyyah.
The geopolitical models addressed are shown to be inadequate, largely because when translated into equations the Collins model predicts only first-order differential dynamics (feedbacks are immediate except on the increase in R, geopolitical resources, which at most simply delays territorial growth whereas the constriction of logistic loads, L, and marchland advantage, P, operate with immediate feedback). A separate model focusing on marchland advantage is subject to a spatially explicit test which shows it to be inadequate. However, Turchin's analysis of these theories is more a matter of destruction than innovation.
His address of Khaldun's theory is far more insightful, and refreshing given the ostensible neglect of Khaldun's work in the West. Khaldun's notion of "asabiyyah" is redefined by Turchin as, roughly, a society's capacity for collective action. The mathematical formulation of Khaldun's theory was fairly encouraging but, as Turchin stresses, the model is specific to the conditions of the mediaeval Maghreb - where elite polygamy significantly increases the reproduction rate of the elites.
He then moves on to address meta-ethnic frontier theories and tests several theories of "ethnokinetics". He also includes an intriguing and readable discussion of the group selection controversy in evolutionary biology (a field closer to Turchin's original area of study - ecology and zoology). Turchin constructs a 0-9 numerical index of cultural divisions to define meta-ethnic frontier theories based on differences in religion, nomadism vs sedentary living, technology and other factors and also imposes a minimum time for a "high" value of this index to be present before it can be considered a meta-ethnic frontier. The test of the meta-ethnic frontier theory is a bit simplistic, but it comes out well; the theory predicts a large quantity of empires forming on meta-ethnic frontiers, a large quantity of non-empires forming outside meta-ethnic frontier theories, a small quantity of non-empires on a meta-ethnic frontier theory (sometimes a polity will be swallowed by a more aggressive one before it can mature) and no cases of an empire forming outside a meta-ethnic frontier. Turchin's imposition of a territorial minimum to define an "empire" is a little arbitrary but some point must be chosen. The data from Europe - and there is a tendency towards eurocentrism in this book - is resoundingly in favour of the theory, except for the anomaly of the Italian empire (though it could be argued this is due to the cumulative effect of several frontiers of middling intensity and short time period which are not picked up by Turchin's model, but I digress). Turchin also explores several models of assimilation, translating them into mathematical theories, with the autocatalytic model being the clear victor. He does, however, veer dangerously close to accepting multiple esoteric theories of mixed reliability in his quest to co-opt previous ideas into his theories - including Fischer's great wave theory (reasonable, if overly general and too focused on economic variables) and Gumilev's ideas about ethnogenesis (which sound plausible until he starts talking about cosmic rays slamming the Earth and imbuing individuals with the passion and energy).
Finally, Turchin considers the demographic-structural theory but builds upon it by endogenising population (which is treated as an exogenous variable in Goldstone's model). Turchin shows that, unlike the geopolitical model, some forms of demographic-structural theory can predict sustained oscillations in the strength of polities - but here Turchin drifts somewhat from his original research question by modelling the ambiguous variable "state resources" rather than territory. The stress is on *some*, as the models do not exhibit sustained oscillations unless the right parameters are chosen, particularly the elite extinction rate in the stateless period. The theory is then applied fairly successfully to several datasets but with a particular focus on English and Chinese population dynamics. Two more detailed case studies are addressed: France and Russia. Here we begin to see Turchin fusing demographic-structural theories with ideas of ethnogenesis, proposing in each case a two-step formation of ethnies, from Franks to French and Rus to Russian respectively, with a chaotic intercycle in between.
The conclusion provides a convincing synthesis of the theories addressed and an evaluation of the progress he has made on each area, as well as laying out the three main cycles (or "wheels within wheels within wheels") addressed by cliodynamic theory: asabiyyah cycles (time scale usually many centuries), secular cycles (usually 2-3 centuries) and father and sons cycles (usually 40-60 years, or about two generations), though the focus of cliodynamics currently appears to be on secular cycles.
Turchin's work is fairly readable, even if the mathematics is a little opaque at times, and is certainly not long. Sometimes Turchin takes the reader through the maths and sometimes he "banishes" it to the appendix, which can be frustrating but is probably for the benefit of some readers. Either way the book is filled with a series of clear and beautifully drawn graphs, and I can say with some confidence that this text is a hearty push towards history becoming a mature field, a science.