# A Statistical Approach to the Synoptic Problem: Part 1—Triple Tradition

This article aims to contribute to the body of empirical data—particularly in the matter of the thousands of words involved in the “minor agreements” between the Gospels of Matthew and Luke against the Gospel of Mark—which must be accounted for by any viable theory that attempts to describe the interrelationships between the Synoptic Gospels, the so-called Synoptic Problem. It should be clear why the Synoptic Problem has become such a battleground:[1] Whatever solution is adopted will have tremendous influence on Gospel scholarship, all the way from textual criticism to the attempts to summarize the theologies of the respective Gospels.[2] With stakes that are so high, it is important to analyze the available data on an objective empirical basis. To that end, I have developed and adapted several new methods of quantifying and testing synoptic theories. The method I will discuss here is to evaluate all the options of linear dependence between three authors. Only six theoretically possible options exist, and the question to be asked is whether any of the options can stand up to objective empirical analysis or whether they all fail the test.

## Six Theoretical Options of Linear Dependence

Theoretically speaking, it is possible that no literary dependence among the Synoptic Gospels exists at all.[3] On the other hand, all kinds of complicated schemes of interdependence are theoretically possible. Even in the case of linear dependence, the simplest of the hypothetically possible schemes of interdependence, it is theoretically possible that only two of the gospel writers had some literary relationship and the third was completely independent of the other two. The method I will discuss here is intended to test out the viability of the various schemes of linear dependence in which all three authors are involved, of which there are six theoretically possible relationships:

• Matthew→Luke→Mark
• Mark→Luke→Matthew
• Luke→Matthew→Mark
• Mark→Matthew→Luke
• Luke→Mark→Matthew
• Matthew→Mark→Luke