Cliodynamics vs. the Mayan Calendar: Who Wins?



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The publication of the Feature Article in Nature about my research on American political violence elicited a wave of comments on the Web. The expression ‘feeding frenzy’ comes to mind. I’ve had a lot of fun reading those comments that I came across (and thanks to various people who sent me links). Partly its sheer vanity (hey, I am as human as the next guy), but it is also interesting in other, less trivial ways.

Because 99.9 percent of those who comment on cliodynamics didn’t bother to consult any of my academic articles (no surprise there) or even popular writings, one can trace readily how the ‘signal’ gets degraded in the transmission chain (an interesting study of cultural evolution here). So Laura Spinney’s article in Nature is pretty good because she extensively interviewed me in Frankfurt (but I did not see her text before the publication, I don’t agree with all of her emphases and interpretations). The articles based on her Nature piece are substantially worse, as their authors misunderstand more points and fill in the  gaps with their own musings. And so on. After a few more steps the information content degrades to the level of white noise (or, to put it bluntly, garbage).

But it doesn’t prevent the commenters from passing their judgment on cliodynamics. As far as I can see, most judgments fall into two broad (and mutually contradictory) categories. One is that cliodynamics is crap because it is obviously wrong. The other one is that cliodynamics is crap because what it says is obvious without a need for any sophisticated analytical techniques.

No news here, we all know that the blogosphere is mostly – what would be a polite way of saying it, a garbage heap? Although I must admit, it could be worse. In the Russian blogosphere I would be immediately accused of being a paid agent of – the Liberals, or the Conservatives, or the KGB and personally Putin, or the CIA, or the oil interests, you name it. The closest I came of being accused of pushing the political agenda is by Maria Konnikova of Scientific American, who wrote that “in history … quantification and precise explanation is … so politically useful.” I wonder, to whom? The truth is, some results of my analysis will be unpalatable to the Republicans, others to the Democrats,  and certain ones to me personally, but that’s a separate story.

While we certainly don’t expect the typical denizens of the blogosphere to bother with consulting the sources, might we expect better of the scientists? Apparently not. I am sorry to single out Massimo Pigliucci, who is a dear colleague, but here’s what he said, according to the Yahoo News piece by Natalie Wolchover:

Pigliucci isn’t convinced that the 50-year cycle of violence Turchin has identified in U.S. history reflects more than just a random fluctuation. “The database is too short: the entire study covers the period 1780-2010, a mere 230 years,” Pigliucci wrote in an email. “You can fit at most four 50-year peaks and two secular ones. I just don’t see how one could reasonably exclude that the observed pattern is random. But of course we would have to wait a lot longer to collect new data and find out.”

This sounds like I used data-mining techniques on the 230-year time series to extract cyclical patterns from it. If that was what I did, Massimo would be completely right. But please, I’ve cut my teeth on the analysis of time-series data (just see my CV if you don’t want to take my word for it).

Had Massimo read my paper in JPR, he would have seen that I use the US political violence database as an ‘out-of-sample dataset.’ Stripping it of technical jargon, this means that I developed the hypothesis about what we should observe on one set of data, and then I used a completely different data set to test the hypothesis. This approach allows us to avoid circularity. The well known problem in statistical inference is that if you fit a complex enough model to data, you can ‘explain’ it perfectly without any error. For this reason, when we really want to find out how good our model is, we use it to predict data that was not used in developing the model. And that is what I did.

In the beginning of the paper I describe the predicted pattern (the long secular wave with 50-year cycles superimposed on it). I illustrate this pattern with data from the Roman and French history. Then I test the predictions with a novel dataset on American history.

This is a true scientific prediction, even though it is not about the future – it’s about the pattern for 1780–2010. When I developed the hypothesis (it was published in my 2003 book Historical Dynamics) I had no knowledge of what the US pattern would be, because there was not a database that could tell me this. Later, in 2008 I started compiling the sources for the study that would eventually result in the database. When I analyzed the resulting database I was actually surprised by how ‘neat’ the pattern was (in previous analyses the 50-year cycle was messier, with its period ranging between 40 and 60 years).

This is all clearly laid out in my JPR article. And it has more – it’s not just the pattern in the political violence data; a multitude of other ‘structural-demographic’ variables changed systematically in a way that supports the predictions of the theory.

I know, I know – I am backlsiding into the ‘scientist mode’ again. So to end on a lighter note, here is the best indictment of my work that I have seen so far (it is one of the comments on the Nature piece; I quote it in full):

I think this whole article is filled with useless information, and not even a few good guesses. However, the subject is facinating. For a more scholarly approach to the same issue, try analysis of the Mayan calendar. I am aware that the Mayans were able to work out mathematical predictions for periods of upheaval ;and when I have seen how closely the Mayan predictions correlate to what we know, it is downright eerie. I am not an expert but I know two people who have studied the Mayan calendar intensely. We (all) do not hold superstitious beliefs but it is apparent the Mayan elite were able to obtain some insights that we are clearly missing.

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If you had only cited Nostradamus and mentioned the role of alien astronauts in human evolution and technological development you would have had dozens of positive responses.
Joking aside, a thinkable thought from this episode is that our species is below a level of sufficient multiple intelligences to make it past +– thirty millennia (counting an Early Pleistocene start date for H.sapiens sapiens).

Peter Turchin

As I seem to remember, Nostradamus did get an honorable mention somewhere in the comments. However, the most frequent literary allusion was to Asimov’s Foundation (of course). Sometimes to Michael Flynn, who wrote a science fiction book about something he called ‘cliology.’


It’s become a norm that people comment without bothering to read anything besides a headline. It’s rare when they give anything even a cursory reading.

It’s sad when scientists like Massimo Pegliucci you cited do the same.

‘try analysis of the Mayan calendar…’ – hilarious!

Gene Anderson

Good old Nostradamus…. I think the 50-year cycle looks good and this is a superb piece of work. It doesn’t check very well with China, but is not too far off: major troubles (as opposed to the annual bandit outbreaks) there came every 75-100 years through the dynastic periods. But they varied wildly, from a very few decades to one or two quite long runs of relative peace.
I can well relate to being attacked on the basis of misquotations or misunderstandings–happened to me often enough.

Peter Turchin

Gene, while secular cycles appear to be a universal feature of complex societies, 50-year cycles are more variable. They usually appear during disintegrative phases, when these phases are long enough. In Chinese data 50-y cycles are not present – probably because disintegrative phases there are very short. It has to do with the degree of militarization of the elites. The Chinese elites were literati, so when the state collapse came, they were physically destroyed, or forced into the commoner class en masse. In Europe, the elites were militarized, so it took a long time for them to self annihilate. In Islamic societies with polygamous elites we get fairly short – Ibn Khaldun – cycles. We have worked out details on how cultural characteristics affect secular cycles pretty well.

To tell the truth, to me the 50-year cycles are a ‘nuisance’ dynamics – they are not what I am primarily interested in, but it is a real feature of the data and cannot be ignored. The Nature article focused on them because they are such an obvious part of the US data, but they are not as fundamental as structural-demographic dynamics.

Alan M

“I can well relate to being attacked on the basis of misquotations or misunderstandings–happened to me often enough.” — this happens to all of us who are married . . .



Peter Turchin

I just saw this lament by Sam Harris (via

Unlike him, I am not at all upset at the blogosphere. When I read a ridiculous statement, which has nothing to do with what I said, it just doesn’t connect. The blogosphereans are a lot like my students, and after teaching for 20 years, and reading their evaluations of you, you either get inured, or insane. I focus on the fraction that are interested to learn new things, rather than simply to get passing grades and then a degree. Same with comments in blogs.

Vladimir Dinets

Believe it or not, pre-contact Mesoamerican calendars actually did predict the times of upheaval. Check out this paper:…85.1263T


oops… the link wasn’t generated properly, so you’ll have to copy-past the whole URL, sorry.

Peter Turchin

The link doesn’t work


It should… strange. Anyway, the paper is available online, just search by its title: Aztec Drought and the “Curse of One Rabbit”. Here’s the summary:

Sixteenth-century Aztec codices preserve a record of at least 13 drought years in central Mexico during the prehispanic and early colonial period. Climate-sensitive tree-ring records recently developed for Mexico confirm 9 of the 13 Aztec drought dates, including the extended drought related to the infamous “famine of One Rabbit” in 1454. One Rabbit is the first year of the 52-yr Aztec calendar cycle, and folklore suggests that famine and catastrophe accompany its return. The Mexican tree-ring data indicate that severe drought occurred immediately before 10 of the 13 One Rabbit years during and before the Aztec era A.D. 882 1558. This relationship between drought and the year preceding One Rabbit is statistically significant and suggests a real climatic origin for the “curse of One Rabbit.”

Peter Turchin

Thanks, Vlad. Found it on the journal site:

Looks interesting – will give it a read and post my reaction.

Peter Turchin

I read the article (Aztec Drought and the “Curse of One Rabbit”). Nice pictures, but:

1. The article is not about periodicity of political violence, but about possibly periodic recurrence of drought; specifically, on the first year of the Aztec Calendar Cycle (One Rabbit).

2. The statistical support for the hypothesis is very weak. The P-value is 0.1, or only one in ten (the usual cut-off P-value is 0.05). Lots of coincidences happen at that rate. Furthermore, the rain deficit actually coincides with the year before One Rabbit. So the actual P-value is even worse than 0.1, if you are allowed to search in the vicinity of One Rabbit for a match.

Conclusion: Cliodynamics 1: Mesoamerican Calendar 0


Come on, don’t take it too seriously. Of course, “calamity” doesn’t mean “violence” in this case, although in the Aztec world drought and violence were often connected. P-value is a bit high, but the authors had to work with a really small sample size. What is really interesting for me in this paper is that the Aztec belief was not yet another superstition – one could call it science-based.

Alexander Sadykov

A black / white reaction to the blogosphere, of course, is not unexpected. However, this reaction provoked a key marketing question – Is there a demand for such things as cliodynamics in modern society? Or more generally – Do we really want to know our future?

Allow a brief historical tour. We are all accustomed to the fact that over the past 200 years, humanity has reached great progress in most science and technology. This is true, however, let’s look at those areas where progress has been very modest (if any at all). Perhaps the first thing that comes to mind is the demography, population dynamics and social dynamics. The works of Malthus, Euler and Condorcet still remain at the forefront of science. It seems that humanity is very concerned about the amenities, but it is not interested in their own destiny. This is hardly an accident; most likely this is the sad result of competition between the so-called “soft” and “hard” sciences.

On the other hand, the Mayan calendar, regardless of its scientific value, plays an important role in maintaining a high level of consumer demand (through the psychological impact on consumer incentives), which is so needed today for the economic recovery.

So, ignorance – is the power!
Cliodynamics 0: M. Calendar 1

Peter Turchin

Судью на мыло!

Категорически согласен!
Нам не дано предугадать,
как смена судей нам зачтется.

Dan Eisenberg

A mesoamerican archaeologist colleague/friend informs me that the picture above is an Aztec sunstone. It appears this is a quite common mistake based on google image search results.

John M

FYI, the image on this page that you labeled the Mayan calendar is nothing of the sort. The image is of the Aztec Sun Stone, which was probably produced around AD 1450/1500 and now resides in the Museum of Anthropology in Mexico City. Any debate about Maya calendrics and doomsaying aside, the image you presented is from a society that had a distinct language, history, and religion from anything Mayan and was separated in time and space from the Maya heartland by at least 1,000 years and 1,000 km. It may seem like an inconsequential difference, but if your work is about the identification of historical trends based on careful and painstaking research, mistakes like this do not inspire confidence.

Peter Turchin

Bah, I threw this in as a neat image. It’s not labeled in any way, so I could hardly mislabel it. And thank you, I am perfectly aware of the difference between the Mayan and Aztec cultures.

Also, this is a blog – if you want to ctiticize my science, address your critique at my scientific articles.

John M

Actually, it is labelled (it has a meta tag that has Mayan calendar, leave your cursor over it for a moment and you’ll see). Do you really want to be so flip about everything you put on a blog? It’s got your name on it, not mine. You titled this page “Cliodynamics vs. the Mayan Calendar,” not me. You put am image up of the Aztec sun stone, not me. You didn’t even check the tag or the source, not me. So, am I really supposed to take from that the idea that you know perfectly well the difference between the two societies without asking? And am I really supposed to take from your response that you are careful in your science? If you complain at the beginning of the page (and in the comment above) that people are not meeting you face to face on the grounds of your original writing, why should I start reading your work now if I can see that you don’t much care to be accurate on your blog?

Images matter. People fight for flags. People fight for religious icons. People fight because of pictures they see — a man standing in front of a tank, a man setting himself on fire. Part of science is how you present your ideas to the public, so in case you missed it, I did criticize your science. Just remember, we don’t get to pick and chose how people read our work or which work they read (even blogs) it all goes into the hopper.

I took a look at your JPR piece. I have all sorts of questions and comments that probably fall into the nit-picky camp — most of them have to do with the creation of artificial boundaries of what does and does not count as political instability events as well as the artificial and permeable boundaries of states as units of study. Many of them could probably be answered if I read further into your longer works, but like most of us, I only have so much time. But just to give you a sense of the flavor of my questions, here are a few — I am sure you have heard them before.

One could make the argument that violent crimes (as legally defined events and therefore political) as well as capital punishment (also a political event) could be correlated with the success of the state in meeting the needs of its constituents, with labor supply, etc… So why not include them as an index of political instability? It seems to me that many of the incidents of instability (lynching, riots, and rampages) are expressions of violence that the state was unable to control — things that got out of hand. But what of violence perpetrated by the state on its constituents (not just civil war) such as police abuse (and there are lethal examples of that). Etc…

One might also ask about your criteria for when you choose to limit your view to a single state (internal political violence) and when you allow that state to be changed by external events (the influx of immigrant labor). For example, in the JPR piece you state that “oscillations of instability should be positively correlated to labor oversupply.” You also note that “The 1940s and 1950s were the second peaceful period in US history.” True — in terms of internal political instability… but if some of that were a result of having enough jobs to meet labor needs (as we might expect from the correlation of labor supply to instability), wouldn’t we have to explain how so many of those jobs were related to a war industry that was directly involved in political instability in Europe and Asia. You can call it peaceful only to the extent that you are willing to ignore WWII.

We could play the “what if” game indefinitely. But I hope that by mentioning just a couple of my questions you can see how your JPR piece might lead a reader to critique your definitions which, as clearly described and explained as they are, are nevertheless artificial and arbitrary. Slight tweaking in one direction or another might change the big picture. I would want to see you try many different combinations to see which creates the most regular cycle before I am anywhere near convinced of its reality. I imagine that you will refer me right back to your response to Massimo — that your predictions and your data collection were independent and therefore your findings are valid. Nonetheless, I would still want to see many iterations, many variations, and especially many failed attempts to be more convinced myself.

I would also want to see counterfactual cases. Nations, for example, that had remarkable stability relative to their population size and world events. Maybe it is my own narrow view, but I wonder where Canada and Scandinavian countries fit in this regard.

I applaud the goal you advance at the end of the JPR piece: “Understanding what causes outbreaks of political violence is a necessary basis for learning how to eventually eliminate them.” But seeing a temporal pattern is not the same as explaining it. For me, you have not crossed the boundary between correlation and causation. Now, the challenge for me (not for you) is to decide for myself what evidence would convince me that you had crossed that boundary and I will be up front in saying that, right now, I could not tell you where that line lies. So, perhaps the most valuable result for me of reading your piece is that it leaves me with the challenge of better defining my own criteria for judging an argument. I honestly don’t know that you could convince me because I probably fall more into the camp of “patterns this big explain very little” because I tend to be more interested in local variations rather than broad patterns — but we work under a big tent, there is room for us all.

Peter Turchin

John M,

My blog is very distinct from my science articles. The blog allows me to run ideas and comments in the informal mode. And I can do fun things that do not belong in an article. It’s my blog, and I choose the way I run it. It would help to have a sense of humor when reading my blog.

Thanks for your comments about my JPR paper. I actually agree that crime is an important variable to look at. I did not do so in my JPR article for two reasons. First, time-series on crime already exist. I am using those data in the book that I am currently writing on structural-demographic analysis of American history. But there was no comparably good data on political violence, so my main goal in the JPR paper was to develop such data. Second, previous analyses with other historical societies (in Secular Cycles) suggest that while crime, like political violence, responds to structural-demographic pressures, the relationship is more complex. To give an example, a large factor (but not the only one) responsible for the recent decline of homicide rate in the USA is simply due the US incarcerating the largest proportion of population compared to any other country. So the dynamics of crime incidence are affected by a more complex set of factors, and it is not a good idea to lump crime and political violence together. However, now that I have developed the political violence database, you or anybody else can do so (lump them together), and are welcome to it.

You and others my take issue with some of the categories I used in analysing data. To address these questions I made the whole database publically available. You and others are welcome to impose different categories and analyse it in different ways. That’s how science proceeds – in an incremental manner and by others checking the published results.

Finally, the issue of interstate warfare. This category should be definitely analyzed separately from internal warfare, because in many ways these processes are antagonistic. External attack tends to unify the country and suppress internal wars, while a country in the middle of an internal war is not particularly well equipped to attack others. The relationship between internal and external warfare is more complex than this, but the main point is that by lumping the two together you lose a very important signal.

John M

I get your point about having a sense of humor — but what is funny to one person is not funny to all. Furthermore, you complain that your message has degraded as it has passed through many different hands. By putting an image of the Aztec sun stone in a blog with a Maya title, you are doing exactly the same thing and there are people who feel very strongly about their national and cultural symbols being accurately and respectfully represented. Blogs may be places to be creative and have fun, but they also stand as a public record of one aspect of your research. Of course you can do whatever you want on them, but you cannot control how people read it — all you can do is do your best to be respectful and precise. Of course, it’s up to you.

As to keeping interstate warfare separate, I don’t think you can — and the reasons why are in your article. Internal factions ally themselves with outside factions. It is not as simple as external and internal attacks. Libya would have gone differently without outside influence. The American Revolutionary and Civil Wars may have ended differently without extra-national influence (like Union access to British saltpeter to make gunpowder). Maybe WWII wasn’t the best example — but even within the US there were factions that were for and against involvement.

Peter Turchin

Thanks to Dan Eisenberg and John M for pointing out that the image in this post was mislabeled as the ‘Mayan Calendar.’ It turns out that I can actually edit the label (well, I am new at this game of blogging), and I changed it to the ‘Aztec Sunstone.’ This change does not affect anything that I wrote in the blog.


Superb, what a website it is! This webpage gives useful facts to us, keep it up.

I do not write many comments, but i did some searching and wound up here Cliodynamics vs.
the Mayan Calendar: Who Wins? | Social Evolution Forum.
And I do have a couple of questions for you if it’s allright.
Is it just me or does it give the impression like some of the
comments appear as if they are left by brain dead individuals?
😛 And, if you are writing on other places, I’d like to keep up with anything
fresh you have to post. Could you list of all of all your social pages like your twitter feed, Facebook page or linkedin profile?

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