Easter, Early Christians, and Cliodynamics

It's Easter, and instead of continuing with my series on the New Caliphate, which is quite gloomy, I thought I would take a break from it and write something more appropriate for the holiday. I'll post the next installment in the series after the holidays.

Corpus Christi procession. Oil on canvas by Carl Emil Doepler

But I also want to do something "cliodynamicky," because that's what this blog is about. Fortunately, I have just the thing, resulting from my early analyses of the dynamics of religious conversion, which was included in Chapter 6 in my 2003 book Historical Dynamics.

One of the cases I looked into in that chapter was conversion to Christianity. My interest was motivated by Rodney Stark's delightful book, The Rise of Christianity: How the Obscure, Marginal Jesus Movement Became the Dominant Religious Force in the Western World in a Few Centuries. Stark developed a quantitative model for the growth of the numbers of early Christians. The model is based on the idea that it is people who convert people. This simple idea (which is supported by sociological studies of religious conversion) is similar to the "autocatalytic" model in chemical kinetics. Basically, the more converts there are the more likely an unconverted unbeliever to encounter them and become converted. So the predicted dynamics is initially exponential -- an accelerating curve.

To get at the shape of the curve, Stark made a guess that there could be around a thousand converts in the Roman Empire in 40 CE, shortly after the crucifixion of Jesus. He then proposed that their numbers grew at the rate of 40% per decade. Several years after he made these estimates, a colleague attracted his attention to the reconstruction by the American Classicist Roger Bagnall of the growth of Christianity in Egypt. Bagnall came up with an estimate of how many Christians there were in Egypt based on the number of people with identifiable Christian names mentioned in Egyptian papyri.

Since Stark was unaware of Bagnall’s data at the time when he constructed his prediction, we have here a true prediction here (in technical terms, test of theory with out-of-sample data).

When I wrote my 2003 book, I fitted the autocatalytic model to Bagnall's data and found that it was very close to the curve guesstimated by Stark. Here's what it looks like:

Source: Peter Turchin

As you can see, the proportion of Christians grows very slowly for the first 200 years following the Easter of 30 AD (the most probable year of the Crucifixion). Then, it suddenly explodes during the fourth century. Actually, nothing changes in the generating mechanism -- slow initial growth followed by blow-up is what exponential models do. Eventually, the curve bends down and approaches 1, because the proportion of converted cannot exceed that upper limit.

So what we see here is an interesting example of how predictions in Cliodynamics can be tested with data. But the story gets better.

Two years after I wrote the chapter on conversion in Historical Dynamics, I happened on a reference to a German dissertation that gave a list of Pagan and Christian office-holders between 324 and 455. The dissertation was by R. von Haehling, entitled "Die Religionszugehörigkeit der hohen Amtsträger des Römischen Reiches seit Constantins I. Alleinherrschaft bis zum Ende der Theodosianischen Dynastie," published in Bonn in 1978.

I immediately realized that von Haehling's data enable us to make another test of the autocatalytic model.What I then did was to plot von Haehling's numbers on top of the previously published curve:

Source: Peter Turchin

The results are quite amazing. We see that the curve fitted to the Bagnall data (showing the proportions converted before 300 CE, filled circles) does a very good job predicting the course of Christianization in the von Haehling data (after 330 CE, hollow circles). The two data sets, each collected using different methods and from different parts of the Roman Empire, merge seamlessly -- and line up very closely to the theoretical curve.

It's possible to do history as an analytical, predictive science!

Happy Easter!