The Synoptic Problem and its Solution

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1. Hidden Patterns in the Synoptic Gospels
2. Matthew, the Revisionist
3. The Man who Buried Jesus
4. Matthew's Knowledge of Luke
5. Luke, the Eccentric Evangelist
6. The Weak Case for the Existence of Q
7. Further Statistical Analysis
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~ Appendix ~

Statistical Analysis of Verbal Variations

 

In addition to the arguments on behalf of Q reviewed in Chapter 6, there have been attempts to strengthen the case for Q’s existence through the use of statistical analyses. Consider first John Kloppenborg’s presentation of Morgenthaler’s statistical analysis of the variations in agreement in the double tradition material:

A.1 Variations in Agreement in the Double Tradition

Range

No. of

Pericopae

% of total

words

Average

Agreement

Luke

Average

Agreement

Matthew

80-98%

11

13.2%

86.7%

82.8%

60-79%

15

27.8%

68.9%

66.3%

40-59%

15

24.8%

46.4%

44.4%

20-39%

14

25.9%

28.5%

26.9%

0-19%

8

8.2%

12.4%

10.9%

 

63

100.0%

50.6%

47.9%

 

At the opening of his discussion on statistical variations, Kloppenborg makes this statement:

Assuming that Matthew and Luke were independent in their use of a common source, random probability would predict that the two evangelists would agree on only 25% of the words in Q, since either Matthew or Luke could choose to retain the wording of the source or to vary it. Alteration by either Matthew or Luke (or both) would create a disagreement. Only when both chose to retain Q’s wording would there be an agreement.

Kloppenborg’s observation is true as far as it goes. The problem is (and Kloppenborg agrees) that one cannot use random probability to predict the behavior of two authors’ use of the same theoretical text, for the keywords in each pericope would have a higher probability of being reproduced by both authors than would non-keyword text. It is difficult to paraphrase the saying about a camel passing through the eye of a needle without using the words camel and needle. Thus we would realistically anticipate that two authors independently using the same sources would agree on more than 25% of the wording.

However, we now have a problem. The observed data as tabulated by Morgenthaler do not square with Kloppenborg’s predicted expectation of 25% verbal agreement, or with a reasonable accommodation for keyword intersection. The statistical analysis of the texts shows average verbatim agreement to be close to 50%, or double the predicted results.

An observer who is not preconditioned to look for evidence of Q in these data would allow the possibility that they might suggest direct dependence of one author upon the other. For using Kloppenborg’s logic, if one evangelist were dependent upon the other, random probability would predict that the two would agree on 50% of the words in the double tradition, since the later author could choose either to retain the wording of his source or to vary it. The data are thus not incompatible with the possibility that one author was dependent upon the other.

Within the world of Q scholarship however, this is not considered. Q’s existence is assumed as a given on other grounds, so the data must be resolvable within the context of the 2DH. How then does Kloppenborg reconcile the gap between predicted and actual data? His answer: “this is presumably a function of the fact that the double tradition is largely sayings of Jesus and John.”

Is this assumption valid? Clearly there is a tendency for Matthew and Luke in their use of Mark to reproduce sayings of Jesus with closer verbal agreement than they do the non-sayings material. Therefore, Kloppenborg’s rationalization is not without foundation. However, once we examine the data more closely, it becomes apparent that his inference is unsound. The problem becomes visible in a second set of data presented by Kloppenborg, and developed by C.E. Carlston and D. Norlin.[1] This chart appears in both The Formation of Q[2] and Excavating Q[3], and is a critical set of data bearing upon the Synoptic Problem:

A.2:  Carlston & Norlin’s Comparative Data

                               Triple Tradition                            Double Tradition

Content type

 Matt

 Luke

 Avg.

 

 Matt

 Luke

 Avg.

Narrative

50.2

46.9

48.5

 

55.7

51.8

53.7

Words of Jesus       

63.5

68.3

65.9

 

69.5

73.6

71.5

Misc. words

56.7

60.6

58.5

 

87.5

80.9

84.1

Average

56.0

56.0

56.0

 

69.8

72.2

71.0

 

Figure A.2 indicates the percentage of agreement between Matthew and Luke relative to their two apparent sources by selected types of material. Kloppenborg notes that the definition of “agreement” used was “the use of approximately the same word in both Matthew and Luke…expressed...as a percentage of the total words used by either author.”

Carlston and Norlin draw the following conclusion from their data:

[Our samplings] are surely large enough to establish beyond reasonable doubt that Matthew and Luke used Q, as far as the wording of their material is concerned, at least as conservatively as they used Mark. There seems to us to be no reasonable explanation for this phenomenon except a second written source for Matthew and Luke.”

This constitutes a misinterpretation of the data. It is indeed clear that both Matthew and Luke record the words of Jesus in Mark with higher fidelity than they do the narrative text in Mark. It is also clear that Matthew and Luke show higher agreement in all types of content in the double tradition than they do in the triple tradition. However Q theorists err in their inference that these data indicate the use of a common written Q source by Matthew and Luke. In point of fact, they indicate the opposite: these data point decidedly toward direct literary dependency between Matthew and Luke.

To illustrate, consider first that the data do not conform to the predictions we would normally make assuming Matthew and Luke’s common use of both Mark and Q. It is understandable that the authors would both record the words of Jesus with higher fidelity than narrative text as we see that they have done. However, we would not anticipate that either author would record the words of Jesus in Q with higher fidelity than he would the words of Jesus in Mark. Furthermore, since they both selected Mark to provide the fundamental narrative structure for their own Gospels, it is counterintuitive to imagine that either one would reproduce Q’s narrative text with greater fidelity than Mark’s narrative text. To the contrary, if Matthew and Luke had each independently used Mark and Q as primary sources, we would expect the data in the double tradition to look similar to the data in the triple tradition, with the sayings of Jesus and the narrative material respectively being recorded with relatively equal fidelity from both sources. The fact that both authors independently chose to reproduce sayings material and narrative material with greater fidelity from Q constitutes an unexpected result.

However, this is only the beginning of the mystery. Let us examine Matthew’s usage of both sources more closely. In the triple tradition he intersects with Luke on 50.2% of the narrative text and 63.5% of the sayings material. The ratio of 50.2 to 63.5 is .79. Meanwhile, in the double tradition we find that Matthew intersects with Luke on 55.7% of the narrative and 69.5% of the sayings. The ratio of 55.7 to 69.5 is .80. Thus we find that Matthew, writing independently, manages to achieve a statistically identical ratio of intersection (.79 vs. .80) with Luke in narrative and sayings matter. Moreover, this pattern exists in Luke’s data as well. Luke intersects with Matthew on 46.9% of narrative and 68.3% of sayings material in Mark. The ratio of these (46.9/68.3) is .69. Luke’s double tradition statistics are 51.8% narrative and 73.6% sayings. The ratio of the two, 51.8/73.6, is .70.  In summary:

                                                                   Matthew                                Luke

 

Triple

Double

 

Triple

Double

        Narrative

50.2

55.7

 

46.9

51.8

        Words of Jesus

63.5

69.5

 

68.3

73.6

        Ratios

.79

.80

 

.69

.70

 

The statistical equality of these ratios should raise red flags. For within the context of the Q theory, the data indicate that Matthew and Luke both used Q with precisely the same percentage increase in their fidelity of replication of both narrative and sayings material. The odds are slim that two different authors independently using the same two texts would achieve these results by random chance. For it means that both authors chose to increase their accuracy of reproduction of both Q’s narrative and sayings material in identical proportions relative to Mark.

These data do not correspond to results we would anticipate from two independent writers. As noted previously, we would first expect them to treat both sources similarly, in which event Carlston and Norlin’s data under the double tradition would look the same as those under the triple tradition. Barring that, if Matthew and Luke did not regard Mark and Q as equally authoritative sources, we would then expect them to each handle their sources differently according to their respective editorial instincts and biases. This would have produced a lower incidence of intersection between the two. The last thing we would imagine is that they would both increase their fidelity of reproduction of Q over Mark by close to identical percentages. Though this is conceivable, it is an unusual result. Accordingly we must ask whether there is another scenario that could more comfortably resolve the data. In fact there is.

Though Carlston and Norlin’s data are not in harmony with predicted behavior of two independent authors, they are exactly what we would predict from one author’s direct dependence upon the other. To illustrate, let us consider first the triple tradition statistics. Carlston and Norlin indicate a composite average of 56.0% intersection across all content types. If both authors were randomly editing Mark and independently determining whether to retain or alter each word, they would each need to average 75% replication of Mark in order to generate an intersection of 56.0% words in common. (75% x 75% = 56%). Clearly however, due to the presence of keywords that have a higher likelihood of having been recorded by both authors, the two authors must each average somewhat lower than 75% retention of Mark’s wording in order to produce a common agreement of 56% between them.

Now let us assume that Q did not exist, and that Matthew drew the double tradition material directly from Luke. This is the equivalent of saying that the double tradition exists without change in its original wording and sequence within the Gospel of Luke. In other words, this scenario is the mathematical equivalent of Luke hypothetically “reproducing his Q source” with 100% fidelity. If Matthew then relied upon Luke and maintained the same 70% rate of replication than he did Mark, the double tradition data in Carlston and Norlin’s chart would be predicted to show Matthew’s replication of his Q source to be 70%. (100% x 70% = 70%). Such a process would also predict Luke’s intersection with Matthew of about 70% as well, the actual statistics varying only by the total number of words used by both authors. Carlston and Norlin’s actual data are 69.8% for Matthew and 72.2% for Luke—exactly in line with what the data should look like if Matthew used Luke directly in the same manner that he used Mark.

Furthermore, Matthew’s direct use of Luke would necessarily produce data showing increases in fidelity in the double tradition across all content types. And by defining one author’s editorial variances from Q as zero (Luke “reproduces Q” with 100% fidelity) the data would inevitably appear to show equivalent increases in the proportional use of the alleged Q text by both authors. Mathematically, it cannot be otherwise.

Thus, we have two scenarios. Either Matthew and Luke both used Mark and Q, and through unexpected editorial behavior produced statistical results that look quite peculiar. Or one was dependent upon the other, thereby producing statistical results that are entirely within the bounds of normal expectations. The latter of the two scenarios resolves the data efficiently, the former does not. Thus, the latter is the preferred solution absent a demonstration on other grounds that there cannot have been literary dependence between Matthew and Luke.

The remarkable irony is that Carlston and Norlin’s statistical data are alleged to confirm the use of Q by both Matthew and Luke. However, upon closer examination, we find that these same data can be interpreted in an entirely different light. In point of fact, they contain a compelling demonstration that one of the authors, either Matthew or Luke, must have been directly dependent upon the other, and that Q cannot have been a medial factor in the equation.



[1] Carlston and Norlin, Statistics and Q, pp. 59-78

[2] Kloppenborg, Formation, p. 44

[3] Kloppenborg, Excavating Q, p. 58

From The Myth of the Lost Gospel, Evan Powell
Copyright (c) 2006, 2011