The greatest diffusion story ever told

April 12, 2009 at 6:22 am 5 comments

| Gabriel |

While I do most of my serious work on trivial pop culture things like pop songs, I’m always interested in the big questions of western civ. As such, I figured I’d post something topical for Easter that I’d been playing around with. According to Mark and Matthew,* Jesus returned from the dead and told the eleven remaining apostles to convert the nations. In Acts each of these eleven (along with a twelfth appointed to replace Judas) basically strikes out in a different direction to try to achieve that goal. Whatever else it may be, this is the beginning of a very interesting diffusion story.

Most of the apostles managed to establish local churches and became the first bishops. Although all twelve of the apostles were martyred, their churches survived and new bishops followed them. For instance, the Apostle Peter was executed in 68 and succeeded  by Linus as bishop of Rome. These churches ordained new clergy who in turn established churches in other territories. In the Catholic and Orthodox churches (and I believe the Anglican Communion as well) the concept of “apostolic succession” is a key aspect of legitimacy and so churches have maintained lists of bishops and you can use this to date the point at which Christianity became somewhat institutionalized in a city. (Yes, a city, the Christians converted the urban population much earlier than the rural population. The word “pagan” is actually Latin for “hick”.) Although these Christian sources are partial we have some independent confirmation for the early spread of Christianity, most notably an early 2nd century letter from Pliny to Trajan. In this letter Pliny described his efforts to suppress Christianity in Northern Turkey and even relates how he tortured two Christian women so they would tell him about a mass. Likewise several Roman historians from the early empire mention rumors that various nobles had taken up “Jewish superstitions” and there is even a famous second century piece of Roman graffiti mocking Christians.

In any case, the Christian doctrine of apostolic succession can be understood as diffusion data. Diffusion is just prevalence over time and so if you count the number of cities with a bishop that’s what you get. Unfortunately the data isn’t as fine-grained as we might like and so for most cities I could only find the establishment date to the nearest century. Nonetheless this gives us a crude idea of how Christianity spread. In this graph I show how many cities had bishops by century.


The first thing to note is that this graph is basically an s-curve. By the end of the first century there were only 33 bishops, about triple the number of the original apostles. By the fall of the Roman empire in the West there were hundreds of bishops but Europe didn’t become fully Christianized until the 11th century when the Swedes finally gave up on Odin and Thor. (Of course by this time almost all of the old Eastern empire was now Islamic; you win some, you lose some). Note though that interpreting this as an s-curve is a bit tricky because one of the assumptions of an s-curve is a constant population (in this case a population of cities). In fact it’s not clear what geographic boundaries we’d expect for the population or how many cities big enough to deserve a bishop there were within these boundaries. For instance, there seems to have been a severe population decline in the third century and again during late antiquity (all those Germans were partly filling a demographic vacuum in the Mediterranean). We might thus expect that the number of decent sized cities would shrink during these periods as some cities shrank to the level of small towns or were abandoned altogether.

The second thing to note in looking at the curve is the dog that didn’t bark. Christianity was officially (but very haphazardly) persecuted until the edict of Milan in 313, briefly subjected to (rather mild) persecution again under Julian the Apostate, and then finally given a state monopoly under Theodosius in 391. Thus Christianity experienced a very different policy regime between the 3rd century (when it was most intensely persecuted) and the 4th century (when we see the beginnings of caesaropapism) and you might expect this to affect the diffusion. However the hazard doesn’t change. There’s a very smooth s-curve both before and after Constantine. I think the implication is that the emperors of the dominate did not so much drive Christianity as respond to it.

This seems to be a special case of what Lieberson calls “riding the wave,” which is when prominent people adopt a trend shortly before it peaks. Lieberson provides numerous examples of movie stars who were either born with a name or adopted a stage name shortly before that name peaked in popularity.  If you look only at a small time range it’s easy to misunderstand the prominent people as driving the trend when in fact they are often just responding to it like everybody else. Likewise it seems more appropriate to say that the church caused the Edict of Milan than vice versa.

*Update: I checked and it turns out this part of Mark (the earliest Gospel) probably wasn’t part of the original but was added a generation or two later. The undisputed part of Mark ends with the empty tomb. This is noteworthy because the disputed passage in Mark includes the phrase “go and make disciples of the nations.” Jews used “the nations” to mean non-Jews and this passage may have been added to bolster support for the relatively late decision advocated by Paul to evangelize the gentiles.

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If subroutines Choosing a (Mac) text editor with Stata


  • 1. brayden  |  April 12, 2009 at 4:54 pm

    Why does Amazon refer to him as “Mr. Stanley Lieberson”? I’ve never seen that before.

    • 2. gabrielrossman  |  April 12, 2009 at 5:08 pm

      yeah, that’s weird, in part because if anything it’s “Dr. Stanley Lieberson.” it kind of reminds me of a spam message.
      Dear sir, I am writing to you from Cambridge Massachusetts …

  • 3. perchesk  |  April 12, 2009 at 11:05 pm

    Nice post! I love the original data analysis.

  • 4. Cheryl Toliver  |  April 19, 2009 at 6:17 pm

    Very interesting post. This is definitely a different way to analyze Christianity’s development, at least differnt for me! Thank you!

  • 5. Weekly links – February 12 « God plays dice  |  February 12, 2012 at 5:59 pm

    […] Arbesman, The diffusion of monasteries; also applies to Christianity as a whole (from Code and […]

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