Math and the Synoptic Problem

A few years ago I set out to write a blog on applying statistical methods to NT scholarship. It was something I was experimenting with. One of the previous diagrams that I have linked to on this blog came from that effort.

The great quarry for this was a statistical analysis of the synoptic problem.

The synoptic problem comes from the observation that the gospels of Matthew, Mark and Luke are very similar, even down to using identical wording in many places. It is the similarity of exact phrases that means that they can’t be just connected by events: they aren’t similar because they are all describing the same story. They are more than that. They must have a literary dependency. There must be copying going on.

So the question scholars want to answer is: what order were they written, and who was copying from what?

Grizel linked me to some work online that applies simple statistical tests to this question. There was some similar work done on the authorship of Isaiah, out of BYU. That study wasn’t controlled at all well, statistically. The study in the link above is a little better designed. As part of my NT Math project, I also ran a statistical analysis of the synoptic problem, using a slightly different method that looked at larger phrases (a wider n-gram), but was basically the same. My results were very much the same as Dave Gentile’s.

The results show that, statistically, there’s almost nothing one can say about the synoptic problem beyond some minimal statistical evidence for Markan priority: i.e. it confirms that Mark came first and was used by Luke and Matthew.

His study shows that the bits that are shared between Mark and the others are a fraction more similar, linguistically, to the bits that are unique to Mark, than to the bits unique to either of the others. So the bits that Mark shares with the others are much more likely to have been written by Mark. Good result.

But Markan priority has long-since been settled in the academy anyway, so the rather weak statistical result is unlikely to set the world on fire.

The interesting question is whether Luke used Matthew, or whether both used a lost source. (The ‘Farrer’ hypothesis says the former, the ‘Q’ hypothesis the latter). And Dave Gentile, and I, both found that the error in our statistical analysis was far too great to make any conclusion on that. The experiment neither confirmed or denied either hypotheses. And, as Dave points out in his analysis, there are many many other possible situations with intermediate forms of the gospels which the statistics are also consistent with.

So one of those (very common) statistical experiments where the results tell you nothing of interest. Which is a shame.

I came to the conclusion that the decisive arguments were likely to arise out of close analysis of textual patterns, like Mark Goodacre’s beautiful fatigue argument for Markan priority, rather than from coarse aggregate statistics.



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11 responses to “Math and the Synoptic Problem

  1. Your question is an interesting one but makes me wonder why one would be an almost plagiarism of the other(s). Today, that might happen from laziness, a desire to achieve something difficult (a degree or respect), or myriads of related reasons. What would motivate writers back then? As a statistician, though, I should be more interested in the numbers …

  2. Erp

    Actually Luke’s author flat out says why; he was combining and improving on previous accounts.

    “Many have undertaken to draw up an account of the things that have been fulfilled among us, just as they were handed down to us by those who from the first were eyewitnesses and servants of the word. With this in mind, since I myself have carefully investigated everything from the beginning, I too decided to write an orderly account for you, most excellent Theophilus, so that you may know the certainty of the things you have been taught.”

    All the gospels were probably meant to be read aloud (most early Christians like most people in the Roman Empire were illiterate) possibly as part of the liturgy (as they still are today in most churches) (Theophilus might be an actual person or could mean any Christian since the name means close friend of God). References would be disruptive digressions in the reading and the gospels were not meant as scholarly texts (think explaining history to elementary school children, teachers rarely give the references [they rarely give them even in High School]).

  3. Grizel

    Thanks for taking a look at this Ian.

    Someone else had mentioned Dave G’s page over at (There has been an on-going thread in the Religion section titled “What counts as a historical Jesus”). I mentioned your blog but the person had heard too many horror stories regarding WordPress and personal PC security (?) so I posted the link for them. I also posted a link there so everyone could view your answer. Hope you don’t mind.

  4. Ian

    @Orange, I think the most likely reason is that the gospels are written later: the start of a literary tradition growing from an oral foundation. The authors are reliant on the stories they have received, and in the case of the synoptics, there may not have been more than one or two decent source texts to start from, so they rewrite them. Erp is right that there is no sense of plagiarism or copying as dishonest at this point. You have to copy by hand any text, so taking something and weaving new information into it isn’t surprising.

    @Grizel, no problem at all. Thanks. I wonder about people who won’t visit certain websites, for fear of security issues. It may be time to figure out how to secure their computer, rather than hiding in the shadows!

  5. TWF

    Well, it may not be a particularly satisfying result, but it is a good one in my book. Not that it’s “easy” or fast, but I would think that course aggregate statistics are the most accessible and least biased analysis that can be done on the Synoptic Problem; the “low hanging fruit”, so to speak. It is certainly worth the exploration, and I applaud your efforts! 🙂 It is important that this work be done, and it is satisfying that you and Dave Gentile achieved similar results independently.

    In my less-scientific study, I’ve personally gotten the impression that Matthew was more of a copier and aggregator (like the weaving copyist you described above), while Luke was more of an editor (more willing to redact parts or alter the story to make it “better”). But that’s not exactly as strong a theory as Mark Goodacre’s fatigue argument. I’m still working on putting it together into a cohesive argument.

    I have noticed that the version of Mark used by Matthew and Luke may not be the version that is included in the Bible. A tiny peek at this is seen in Matthew 17:17, Mark 9:19, and Luke 9:41 where “and perverse generation” is included only in Matthew and Luke. To me, that, at least, opens the door to a Mark serving as part of the mysterious third source.

  6. If I’m reading that statistical work correctly, it means that if one accepts Farrer as a sane starting-point, it looks highly probable that M is a real document, which would be an interesting conclusion. If Luke saw that document (which might just account for the 11.41 Aramaic alms/cleanse issue), then that’s the 3SH.

  7. Ian

    James, by ‘M’ here do you mean the source for Matt Only and Double Tradition, or just Matt Only. If the later, then I’m not understanding your comment (sorry – this is only a hobby, so forgive me if I’m not really on the ball with the terms).

    If the former then I’m not sure the numbers do show that, but I haven’t looked directly. The problem is Matt Only is neither significantly similar to Double Tradition, nor significantly divergent from it (Compared to Luke Only). In my numbers only here, Dave’s results may differ, so I’ll have another look. I assume you are talking about his results, since his are published on his site. But I’m happy to look harder if you can clear up my confusion!

  8. I was using it loosely as meaning Matthew’s special source, which would cover both Matt only and Double Tradition, if one presumes that Luke got the Double Tradition material directly from Matthew. The way this group — Sayings Group 1 in Dave’s results — doesn’t fall into the Matthew group could be used as an argument that there was indeed a second major source in addition to Mark that Matthew used (rather than just being autonomous collation of and expansion upon oral tradition).

    On the other hand, it could just be a matter of genre. It’s good that the stats have shown up such clear groups, but the interpretation of what the groups mean is probably going to go off into other methods.

  9. Ian

    Ah, gotya, thanks James.

  10. Pingback: Statistics and the Synoptic Problem

  11. Pingback: The Synoptic Problem around the Blogosphere | Euangelion Kata Markon

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