A response to the review by Joseph A. Tainter of Historical Dynamics

A response to the review by Joseph A. Tainter of Historical Dynamics

("Plotting the downfall of society," Nature 427:488"489)

by Peter Turchin, February 2004

I would like to begin by thanking Joseph Tainter for writing the review of my book (even if I wish it would be a different review), and I hope that he will take my criticisms below as not an ad hominem attack, but as an honest effort to advance our understanding of historical dynamics. This response has two parts: first, I address several specific points made by Tainter, and second, I challenge Tainter to a test comparing the ability of our theories to make scientific predictions.

Specific points

1. Tainter writes: "Turchin attempts in this book to develop quantitative cyclical theory"

"Cyclical" is not correct, because my goal is to develop dynamical theory. Cycles is just one of many possible kinds of dynamics; I did not focus on cycles to the exclusion of everything else. In fact, as a dynamicist I abhor the usual run of the mill of cyclical theories in history, from astrological and numerological to "physiological" (where societies "senesce"). All such theories impose cycles on history by fiat , whereas in nonlinear dynamics we begin by making assumptions about how different variables interact with each other, and then investigate how the resulting dynamics arise as a macro-consequence of micro-mechanisms.

2. Tainter: "Turchin bases his 'mature' approach on the work of the fourteenth-century Arab historian Ibn Khaldun, who sought to explain why desert nomads topple North African dynasties. Ibn Khaldun argued that the founders of dynasties rule well and tax lightly. Succeeding generations, though, develop a taste for luxury, resulting in higher taxation and declining welfare. Late-phase dynasties are challenged by desert nomads who have high degrees of asabiya, defined as collective solidarity or a capacity for collective action. Nomads with asabiya topple dynasties that lack it, starting the cycle anew. Ibn Khaldun perhaps meant his theory as a critique, but Turchin takes it literally."

Au contraire! First, read my assessment of Ibn Khaldun's theory on p. 40 of Historical Dynamics . I believe the text there makes it very clear that I do not take Ibn Khaldun's theory literally. Second, when I get to the nuts and bolts of my theory of asabiya (yes, I do like Ibn Khaldun's term and I adopt it, but I redefine it to suit my purposes, see the terminological note on p. 45) I develop it from the basis of the theory of multilevel selection in social evolution (see Chapter 4).

3. Tainter: "In his 'metaethnic frontier theory,' Turchin proposes that areas where imperial frontiers coincide with major ethnic boundaries function as 'asabiya incubators'. High asabiya allows a peripheral people to expand as an old empire contracts. Turchin builds this idea into quantitative simulations of expansion and contraction in European territorial history from AD 500 to 1900."

There is some mix-up here. I do show simulation results in Chapter 4 to illustrate the dynamical theory I develop there. But in Chapter 5 devoted to territorial dynamics of Europe , 500"1900, my goal is completeley different " I construct an empirical test of the metaethnic frontier theory. In other words, in Chapters 4"5 I attempt to travel all the way from micro-level assumptions to macro-level implications of the theory to an empirical test of the theoretical implications (including an explicit theoretical alternative).

4. Tainter: "one wonders about the ethnic solidarity of Renaissance armies that were filled with mercenaries, a matter that Turchin ignores when he simulates European territorial changes."

This observation proves precisely my point. So what happened to all those Renaissance states, like Milan and Florence , with their enitrely mercenary armies? Right, they were conquered by those states who relied mainly on national soldiers, like Castile with its magnificent tercios . Of course, Spain also employed mercenaries, including the Italians, but the sixteenth century's military professionals knew very well the worth of such troops (with the exception of the Swiss, and they had their own problems). The core of the Spanish army were Castillians; as long as the Habsburgs had enough of them they were unrivaled in Europe .

5. Tainter: "'Demographic-structural theory' builds on Jack Goldstone's excellent work on population growth and state breakdown, and on Turchin's own experience in population biology. This exercise quantifies how political instability and population interact. Unsurprisingly, Turchin's models show that interaction between population dynamics and a state's fiscal health produces cycles of expansion and breakdown."

Naked human minds are simply not equipped to model nonlinear dynamical processes rigorously. This is why we need mathematical models and computers. Furthermore, nonlinear feedbacks, even in simple models, can surprise us by producing completely unexpected dynamics; anybody who has extensive modeling experience has encountered this phenomenon repeatedly. Thus, there is no way to know ahead of time whether any specific model will produce cycles, contrary to what Tainter says. We can only find out by doing it the hard way " developing models from first principles and then numerically solving the resulting differential equations on the computer, in order to ascertain that the assumptions about the interactions between various variables actually would result in oscillations, and what would be the quantitative features of these oscillations (average period and amplitude, etc).

6. Tainter: "Turchin cites archaeological settlement data from Roman Gaul that display two peaks and troughs."

These are actually the least convincing data of the many data sets that I discuss. What about the English and the Chinese data? In particular, what about my time-series analysis of population dynamics and sociopolitical instability in the Chinese data, showing clear evidence of reciprocal feedbacks?

7. Tainter: "The quantification is built on ordinal scaling, judgemental assignment of values, and arbitrary cut-offs."

Any initial attempt to operationalize a theory for empirical testing is bound to be crude, and I acknowledged it when discussing the set-up of the test. I would argue, however, that it is a better research strategy to attempt an empirical test of theory, even if the procedure is imperfect, rather than wait until a perfect approach is developed. Testing procedures usually improve incrementally as a science progresses, but if we do not empirically test theories, science cannot progress.
Can we test Tainter's theory against mine with data?

One of the criticisms in the review is that "Turchin ignores problems of complexity in large societies." Of course, Tainter has published a book in 1988 titled "The collapse of complex societies" (CCS). I read the book and found it very useful and thought-provoking. In the book Tainter outlines a theory of state collapse, which provides an alternative to theories that I discuss in my book. Now, as I discussed in my book, I believe that the best way to achieve progress in science is by explicitly contrasting rival theories. Thus, I propose that we do just that for Tainter's theory and mine. Although I discuss several theories in my book, the most relevant comparison is to the demographic-structural theory, which also addresses the causes of state collapse. Below I sketch the outlines that this exercise might take. My account, naturally, is somewhat one-sided since I am one of the interested parties, and therefore I invite a response by Joseph Tainter (which I will post here if/when I get it).

The first criterion of good theory is that it should operate with clearly defined and potentially measurable quantities. In the demographic-structural theory the main dynamic variables are population numbers (in relation to the carrying capacity of the environment), the numbers of elites, and the fiscal strength of the state. In Historical Dynamics (HD) I discuss several variants of the demographic-structural theory, leading to somewhat different models (depending on the social and other characteristics of the studied states), but here I will focus for simplicity on the core model (see Section 7.2.2 of HD). The variables of the model have been operationalized to the point where they can be estimated, given the right kinds of data.

Contrast this situation with the main variable on which Tainter's theory is based, the complexity. On p. 23 of CCS he defines it as follows: "Complexity is generally understood to refer to such things as the size of a society, the number and distinctiveness of its parts, the variety of specialized social roles that it incorporates, the number of distinct social personalities present, and the variety of mechanisms for organizing these into a coherent, functioning whole. Augmenting any of these dimensions increases the complexity of a society." This definition is endorsed (actually, repeated verbatim) in a 1996 publication ("Getting down to Earth" Island Press). I would argue that this definition does not tell us how to measure complexity of any particular society.

As noted above (in point 7), Tainter criticized imperfections in the procedures I developed for testing various theories in HD. In another place, he criticizes me for using archaeological settlement data for testing the demographic-structural theory. All these criticisms are valid, but let us step back and look at the larger picture. Surely the research program in which we argue about the fine points of empirically testing theories is farther advanced than a program in which we have no idea how to test theories at all!

Second, a good theory should be coherent; that is, its predictions should follow necessarily from its premises (in other words, it should avoid logical and mathematical mistakes). Unfortunately, Tainter does not formalize his theory as a set of mathematical statements. This is actually another strike against it, because any vaguely stated theory is much harder to test (falsify in Popperian terms), and in science we generally value the falsifiability potential. In any case, we can use the verbal description of Tainter's theory (p. 118"123 of CCS). Without going into the details, I will simply state here that the verbal theory, as described, will translate into what is known as the first-order model. This means that the model based on Tainter's assumptions will not predict collapse (increase followed by sustained decline), but only equilibration at a steady point. For details, see Chapter 2 of HD (the first part explains the order thing, the second illustrates the ideas with an application to the geopolitical theory of Randal Collins; what I am essentially saying is that Tainter's theory is just like Collins').

Third, a good theory should successfully pass tough empirical tests. Tainter uses three case studies (Chapter 5 of CCS). I will discuss the case of the Roman collapse since I am more familiar with its history. In fact, when we read pp. 128"152 of CCS we hardly ever see the word "complexity". It reads as a fairly standard compilation of ideas about the Roman collapse put out by Gibbon, Hammond , Jones, Rostovzeff, Frank, etc. The peak was achieved with the establishment of the Principate by Augustus in 27 BCE. After that it was all downhill: revenues were insufficient, population declined, military costs increased, taxation became more and more crushing, the military revolts multiplied, and so on. Fine, but this "decline" went for five hundred years ! (The western Roman Empire collapsed, according to how historians recon it, in 476). And what does have complexity to do with it?

According to the demographic-structural theory, Rome experienced at least three collapses: the first century BCE transition between Republic and Principate, the third century civil wars between the Principate and Dominate, and the collapse of the Dominate in the sixth century. Each of these "secular cycles" was accompanied by population inrease then decline, elite overproduction then "thinning out", and state fiscal health then crisis. The details will be forthcoming as part of the book I am writing together with Sergey Nefedov, tentatively titled "Secular Cycles".

I realize that it may seem weak to cite work in progress, so I will point out that the demographic-structural theory has been rigorously tested with empirical data (but not with Roman). I refer to the time-series analysis of the Chinese population and instability data in Section 8.4 of HD. Of course, that is just one case study, but it shows that it is possible to test sociological theories of state collapse exactly in the same way that natural scientists test their dynamical theories about physical and biological phenomena. And other case studies are forthcoming (as part of the joint project with Nefedov).

If we seriously think about the potential of "complexity" in explaining state collapse, then it seems clear to me that the theory has no chance. Tainter himself cites such disparate examples of collapse as Hopewell , Cahokia, and Rome . The complexity (whichever way we define it) of Cahokia exceeded by far the levels of Hopewell (as is acknowledged by Tainter). Similarly, the complexity of the Roman Empire (with perhaps 60 million inhabitants) by far exceeded Cahokia (with 40,000 inhabitants). How could all of these three societies possibly collapse because they got too complex? Rome was three orders of magnitude more "complex" than Cahokia " clearly some other factor must be involved.

In summary, we can compare the two theories with the following handy table:

Criterion	Complexity theory	Demographic-structural
Operationability	absent	present
Coherence	absent	present
Empirical tests	absent	present
Successfully passing an empirical test	" (proper tests not performed)	yes

I repeat that the discussion above is just a sketch of how we might contrast the complexity and demographic-structural theories using the data. And I am hardly the disinterested party. Therefore I would welcome any comments/rebuttals.