Math Explains History III. Reactions to our paper



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Although publishing in PNAS is a bit of a pain (there are a lot of pesky formatting and other requirements) and expensive (in particular, we had to pay, so that you all could have free access to our article), the redeeming feature of this journal is that they practically guarantee good press exposure. I am aware of at least twenty articles in newspapers and popular magazines, in half a dozen languages, that discuss the significance of our results.

The quality of coverage is quite variable. If you are interested, take a look at the Cliodynamics in Popular Media page. Articles toward the top are better written ones (for those who read Russian, check the excellent article by Alexander Markov on

At the bottom I put the article in the Daily Mail – if you want to get some laughs, read the comments following the article.

Mainstream historians have also weighed in. Several authors of news articles (those in Nature, the New Scientist, the Conversation, Publico, and de Volskrant) solicited opinions from historians and social scientists, who were not part of our team. Their general verdict is quite positive. The methods and approaches of Cliodynamics are gradually gaining acceptance among the broader community of historical and social scientists.

Naturally enough, there are also critical reactions. One comes from Neville Morley, Professor of Ancient History at the University of Bristol (UK).

I am familiar with Morley’s work on population history of the Roman Republic (in fact, we cite him in our book Secular Cycles). His review post on our article is even-handed and not entirely unsympathetic. Still, there are several misconceptions that I’d like to address.

In particular, he says:

NM: It is undoubtedly symptomatic that the authors think of themselves as engaging with a tradition of social-scientific research, not with historians

In actuality, we are as interested in engaging with historians as with social scientists. In fact, Seshat, the massive database project, which is currently the core of my research program, cannot succeed without active involvement of dozens, if not hundreds, of historians and archaeologists. And, judging from our experience so far, it is going to happen.

Having said this, I fully realize that most historians have no interest in what we are doing, and I am very comfortable with that. I expand on the relationship between Cliodynamics and traditional history in this blog. In any case, I see my responding to Morley’s concerns in this blog as one way of engaging with historians.

NM: each conquered polity had a certain chance of taking over the ‘cultural genome’ of its conqueror – i.e. adopting its traits of military technology.

This is not correct. In the model, military technology diffuses out without respect for any warfare or conquest activities. What happens when one polity is taken over by another is that the defeated society may be assimilated by the conqueror, so that the ultrasocial traits of the winner are copied into the ‘cultural genome’ of the loser.

NM: It is these claims that have led the study to be reported in the non-academic press as ‘explaining’ history and ‘predicting’ the rise and fall of empires.

To clarify, we use ‘prediction’ not in the sense of predicting the future, but as a scientific prediction, in which predictions from two, or more alternative models are compared to data. The logic is explained here.

NM: It’s difficult to escape the sense that the model is based on a very old-fashioned model of societal expansion – from a specialist perspective, the bibliography is equally striking for its omissions…

First, it’s worth pointing out that PNAS imposes a strict limit on the number of citations. Fortunately, T. Greer comes to our defense in the comments, by pointing out that we are perfectly aware of the citations that we would have included, if we could.

Second, our model is far from old-fashioned. It is definitely not in the mold of ‘conquest theories’ (e.g., by Franz Oppenheimer) or even of the more modern theory of Robert Carneiro. The heart of our model is the evolution of ultrasocial norms and institutions by means of cultural multilevel selection. This is a fairly novel idea, which was seriously developed only during the last decade or so. Our PNAS model is only the first step in empirically testing it. A much more comprehensive test will become possible only after we make progress with the historical database of cultural evolution.

NM: the results are liable to seem to most pre-modern historians either rather banal or hopelessly flawed.

Well, being both flawed and banal is a logical impossibility. You’ve got to choose one, or the other. So I will close this blog with two quotes:

“All truth passes through three stages: First, it is ridiculed; Second, it is violently opposed; and Third, it is accepted as self-evident.”

– Arthur Schopenhauer

“Theories have four stages of acceptance: i) this is worthless nonsense;  ii) this is an interesting, but perverse, point of view; iii) this is true, but quite unimportant;   iv) I always said so.

-J.B.S. Haldane


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Many thanks for this – and I’d also like to thank T.Greer for his comment on my post (on the basis of his suggestion, I’ve been planning to visit this blog as soon as I have some time). It’s clear that I’ve underestimated the constraints of publishing in PNAS, never have tried it myself; this would explain, I think, your references to social scientific rather than historical theories of social development, and perhaps also the fact that you cite Toynbee (which I still find a little odd, given his almost negligible reputation in contemporary historical studies, but he seems to be taken more seriously in some areas of US social science).

I’m glad you felt that I was basically sympathetic to the enterprise (if unpersuaded as yet by some aspects of the specific argument). Several of the points you note above are actually more sympathetic in intent than you seem to have gathered; my comment on prediction was aimed at the reception of the paper in the wider media rather than what you actually say (basically, Voeten’s point in his post at The Monkey Cage), and my banal/flawed remark was entirely related to likely reactions from mainstream historians, expressly not my own. Both the approach (statistics, modelling, development of generalised theory) and the rhetoric (social-scientific rather than humanistic) are likely to be deeply unsympathetic to the majority of ancient historians than I know, even those interested in large-scale questions about the development of ancient empires. That’s their problem, you could certainly say, and I do think they would be missing out on an interesting research project.

Peter Turchin

Neville, thanks for this reply. As you say, your blog made it quite clear which opinions were yours and which were likely reactions from mainstream historians. My post was addressing both your comments and those other reactions together, in the spirit of engaging in the debate the historical profession as a whole (if such a thing exists).

Funnily enough, the Toynbee citation was also a result of the PNAS policy. The PNAS editors have a policy against profanity, and insisted that we either remove “One damn thing after another” or make very clear that it is a quote. On the other hand, I personally don’t hold Toynbee in quite as low esteem as most historians. True, his methods and conclusions in A Study of History were flawed, but you have to give him credit for trying to come up with general principles of history. Which is, of course, why he is held in low esteem by mainstream historians. Also, his other writings have merit, in particular, I found Hannibal’s Legacy quite interesting.

By the way, I am currently in Oxford in a workshop on our database project, Seshat (which is why I am responding with a delay). I will be very curious to see what impact it will have when we achieve the critical mass of data and start publishing papers, hopefully in 2-3 years time.


‘The PNAS editors have a policy against profanity, and insisted that we either remove “One damn thing after another” or make very clear that it is a quote.’

You can’t make it up!


I find myself ever more impressed with Toynbee, above all as a by-product of my current research on modern interpretations of Thucydides; Toynbee takes an eminently sensible line on the long-standing question of Thucydides’ speeches (pointing out that the current practice of including indirect rather than direct speech in historical accounts is no less a rhetorical convention), and seems genuinely inspired to seek to uncover the underlying consistences of historical events. As you say, this is precisely why mainstream historians become ever more sceptical, and his influence was greater in the social sciences.

Kirill Pankratov

There is a slight error in the link to the Russian site with a review (it links to discussion thread instead of the article itself). The correct link:

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