Note: The data used in the analysis below can be found in this Excel spreadsheet, also linked at the bottom of this page. In particular, the correlations are located between rows 37 and 150, and columns HI to LR.
One of the basic assumptions underlying this method of analysis is that different authors (aA, aB, and aC) have natural frequency profiles pA, pB, and pC that are sufficiently different that one can be distinguished from the other. Therefore, it is reasonable to test this assumption before continuing with the rest of the analysis. Because we are testing what copying took place from one synoptic gospel to another, we cannot compare the profiles of the whole of each gospel against each other. Instead, we need to isolate the text unique to each author and compare the profiles of each.
One way of doing this is to compare each author’s sondergut material (HHBC categories 200, 020, and 002 respectively). Alternatively, we can combine all the categories containing words written by just one of the three authors, e.g. c200 + c210 + c211 + c201 (=c2AA), and compare them:
However, the values
do suggest that the differences between the profiles of Mk and Lk are somehow
of a different character than between those of the other pair of synoptics.
This suggests that the Greek used in Mk is different to that used in Lk, in a
way that does not apply to the other synoptic pairings. It may be that, as has
been suggested, that this is due to aMk not having Greek as his first language,
but whatever the reason, it is the case that Lk contains many systematic
language differences from Mk, for example there are around 150 places where Mk has
the narrative present while Lk has the past tense. Systematic differences such
as this would tend to create a negative correlation between Mk and Lk, such as
we see here.
Then, if aMt copied or edited some text from Mk, Mt would contain text from two different authors, and would therefore be likely to be less homogenous than Mk. Finally, if aLk copied or edited text from both Mk and Mt, then Lk would be likely to be less homogenous still. Therefore, by comparing the homogeneity of Mt, Mk, and Lk in turn we may be able to determine which of the authors copied or edited from which others.The HHBC data representing each of Mt, Mk, and Lk is spread across 9 categories, depending on the interaction with the other two synoptics. For example, we can compare those parts of Mt that have no parallels in Mk (c 200 + c201 + c202 = c20X) with those parts that do (c210 + c211 + c212 + c220 + c221 + c222 = c2NX), but also we can compare those parts of Mt that have no parallels in Lk (c2X0) with those that do (c2XN). As a result, we can compare the categories grouped in various different ways to determine how the relationships between the synoptics affect which parts of any one synoptic, which show signs of homogeneity, and which do not. The tests in the group below all compare the profiles of categories representing passages in Mt that do not have parallels in Mk (c20X, with ‘sub-divisions’ c20N, etc.) with those that do have parallels in Mk (c2NX, c2NN, etc.). We can perform comparisons using six different combinations of categories in Mt, depending on the existence and content of parallel passages in Lk.
A similar group of tests can then be used to compare the profiles of the same categories representing passages in Mt that do not have parallels in Mk, with those representing just those words in Mt not used in the parallels in Mk (c21X, c21N, etc.).
We can also compare the profiles of those categories that denote passages in Mt that either have no parallels in Mk, or where the parallels have different words (c2AX, c2AN, etc.), with those where the parallels contain the same words (c22X, c22N, etc.)
The above results show that there is no strong correlation in any of these three groups of tests. However, p201 and p211 (respectively, the profiles of the double and triple tradition words only in Mt) do appear to be sufficiently similar (0.46) to be worth investigating further. An examination of a scatter plot of the two profiles shows that several words in these categories have similar below average frequencies in each. As both categories contain words only in Mt, in passages shared with Lk, this suggests that the frequency with which these words appear in both categories has been affected by copying/editing between Mt and Lk.
Overall, there is no evidence here of homogeneity between those passages in Mt with parallels in Mk and those without, i.e. there is no evidence that the passages in Mt that have parallels in Mk came from the same source as the passages in Mt that have no parallels in Mk. More specifically, where Mt and Mk have identical words in parallel passages, there is no evidence that the words originated in Mt.
The following groups of tests can be considered to be the ‘reverse’ of the previous groups, this time testing for homogeneity in Mk instead of in Mt. The tests in the first two groups below compare the profiles of categories representing passages in Mk that do not have parallels in Mt (c02X, c02N, etc.) with those representing:
These results show that the passages in Mk that have no parallels in Mt have very similar profiles to those passages in Mk that do.
These results are very similar to those in the previous group, showing that the passages in Mk that have no parallels in Mt have very similar profiles to just those words in the Mt-Mk parallels that are in Mk but not Mt. These two groups of results are a strong indication that the words common to Mt and Mk originated in Mk.
The only area where categories in Mk show little signs of similarity are where Mk and Lk share identical words (c022 + c122 + c222 = cX22). Further investigation shows that this is primarily because the profile of the Mk-Lk agreements against Mt (p122) is not similar to any other profile, while p022 and p222 are both similar to p220. This could indicate that the words in c122 came from a source outside the synoptics. However, p122 does have negative correlations with a number of other categories, the most significant being with p2AX (All of Mt except for words shared with Mk). This is due in no small measure to AUTON appearing more frequently in c122 than in any other category, while Mt uses AUTON much less.We can also compare the profiles of categories that denote passages in Mk with either no parallels in Mt, or where the parallels have different words (cA2X, cA2N, etc.), with those that contain the same words (c22X, c22N, etc.)
Unlike the two previous groups of tests, here there is much less indication of homogeneity. However, this is in large part due to the fact that cA2X, cA2N, and cA22 all contain c122, and c122 is not similar to any other category, as reported above:
Overall, the above results show a great deal of homogeneity in Mk, but a lack of it in Mt. This is a strong indicator that the passages shared between Mt and Mk originated in Mk. The lack of similarity between p22X and p12X does not affect this indication, but instead just provides information about the choices made by aMt when copying/editing from aMk. The lack of similarity between p122 and the profiles of any other categories (in any of the synoptics) has a similar cause, but in this case it suggests that the sharing of words between Mk and Mt was later affected by the sharing of words between Mk and Lk.As previously noted, one of the key indicators of directionality is the possible correlation between the profiles of categories containing words common to two of the synoptics and words unique to one or the other. There are four basic tests that can be used to look for ‘authorship’ of words common to any pair of the synoptics (e.g. c2XX in the case of Mt-Mk). However, two of these tests have already been used when testing for homogeneity, leaving just two to test here. Both look for similarity between an author’s sondergut material, and the words he has in common with another author:
There are then six variations on each of the above, depending on the existence and content of any parallels in Lk (X, N, A, 0, 1, 2), giving the following tests:
As previously noted, if whatever copying/editing took place included selectively choosing or replacing many individual words (rather than complete sentences), then the profile of the words common to any two of the synoptics may not have a strong correlation with the profile of the words in passages unique to one or the other, and that may be the case here.
Although the differences between the results of these two groups of tests are not great, what differences there are suggest that it is more likely that Mk was first, i.e. that the words common to both Mt and Mk came from Mk. The differences between these two groups of results are greatest for c221, i.e. triple tradition words common to Mt and Mk but not Lk (difference = 0.37 – 0.06 = 0.31).
The following tests can only provide limited (if any) information on directionality. However, using the directionality information from the previous tests, they may provide additional information on how the source material of the Mt-Mk parallels in copied/edited.
The previous results have indicated that the source material came from Mk, so we can use that as an assumption in the following tests. As with the homogeneity tests, there are six variations on each of the above two tests, as follows:
There are no significant positive correlations here, and thus nothing to refute the assumption that the Mt-Mk parallels originated in Mk.
The results of these groups of tests are not conclusive as to the mix of individual words vs. complete sentences that were copied or replaced. However, such indications as do exist support the conclusions of the tests for homogeneity, which are that the passages shared between Mt and Mk came from Mk, and also that aMt mainly selected or rejected complete sentences from Mk, but did change or add many individual words as well.
The greatest indication of Mt changing individual words comes from the Mt-Mk double tradition (c120 + c220 + c210 = cNN0), where we see:
This material (that is not in Lk) includes what is known as ‘The Great Omission’ from (approximately) Mk 6:47a - 8:27b, as well as the death of John the Baptist and some other items. In this material the relative frequency of use of various words varies greatly between Mk and Mt, in particular the use of IHSOUS:
Here we see that the material that aMt chooses not to use (c120) contains the word IHSOUS a relatively small number of times, whereas in the material he adds (c210) he uses IHSOUS frequently.The following tests compare the profiles of categories representing passages in Mt that do not have parallels in Lk (c2X0, c2N0, etc.) with those representing:
Here we see quite different results from those in the Mt–Mk comparisons, with some significant correlations in Mt between the profiles of passages with parallels in Lk, and those without. The strongest correlation occurs when comparing sondergut Mt (c200) with the double tradition passages in Mt (c20N), i.e. where there are no parallels in Mk. This in itself is a strong indication that the Mt-Lk double tradition did not originate in Lk.
The correlation is nearly as strong when comparing sondergut Mt with just those words from the double tradition that are in Mt but not Lk (c201), suggesting that c201 consists mainly of complete sentences, rather than just a selection of individual words, i.e. that the double tradition was created largely by selecting and copying complete sentences, and changing relatively few individual words.
However, when looking at the categories corresponding to the triple tradition passages in Mt (c211 + c221 + c222 + c212 = c2NN), the correlations indicate that the copying/editing between Mt and Lk involved changing a much greater number of individual words. This is particularly so for the words also shared with Mk (c221 + c222 = c22N):
As with the previous two groups of tests, the strongest correlation again relates to the double tradition. We have:
This evidence supports the view that the double tradition material originated in Mt, and that words common to Mt and Lk were mainly re-used in Lk in the form of complete sentences, with only a small percentages of the words from Mt being removed or replaced by aLk in the process.With regard to passages in Mt that are part of the triple tradition (c211 + c221 + c222 + c212), we have:
Although these two groups of tests appear to indicate that all the passages in Lk that do not have parallels in Mt have similar profiles to all those that do (p0X2 – pNX2 = 0.52), the correlation is actually only significant where Lk does not share words with either Mt or Mk (p0A2 – p1A2 = 0.70). This indicates that the only parts of Lk that are homogenous are those categories containing words unique to Lk, which in turn suggests that the words in Lk common to either Mt or Mk did not come from the same source as the words unique to Lk.
The most interesting result here is the negative correlation between pAN2 and p2N2 (= -0.48). Examining the scatter plots of these and other categories shows that this is mainly due to there being a number of words with above average frequencies in c1N2 (which is part of cAN2) that have below average frequencies in c2N2:
Unlike the equivalent tests for the ‘ownership’ of the identical parallels in Mt and Mk, there are significant differences between the results of these two groups of tests, indicating that many of the words shared with Lk originated in Mt. The evidence is strongest for the words in the double tradition:
These results show that p220 (words common to Mt and Mk only) and p022 (words common to Mk and Lk only) are similar, indicating that both categories contain words mainly originating in the same source, i.e. Mk. This is the reason that p222 is similar to both p220 and p022, indicating in turn that c222 also contains words mainly originating in Mk.The previous results indicate that the double tradition (c202) words common to both Mt and Lk most likely originated in Mt, while the origin of the words in Mt-Lk agreements against Mk (c212) is uncertain. The following tests may help to clarify this.
There is little evidence of editing choices here, except in the case of the double tradition (c202), where the results support the previous evidence that indicates that the double tradition consists mainly of sentences originating in Mt.
The double tradition result in this group of tests appears to contradict previous results, since p202 is similar to both p201 and p102, suggesting that c202 originated in both Mt and Lk. The key indicators here are:
As p102 is not similar to p002, but is similar to p202, and p202 is similar to p200, it is reasonable to suppose that p102 might also be similar to p200. However, this is not actually the case. Instead:
More specifically, some of the double tradition text may have originated in S (in addition to Mt, as previously suggested). However, because p200 (sondergut Mt) is very similar to both p201 and p202, any text originating in S must have been edited by aMt before any of it was used within Lk. Then, after aMt had made his mark on the text, aLk added his own changes, leaving p102 still similar to p202, but not similar to sondergut Lk.The following tests all compare the profiles of categories representing passages in Mk that do not have parallels in Lk (cX20, cN20, etc.) with those representing passages in Mk that do have parallels in Lk (cX2N, cN2N, etc.).
On the assumption that aLk copied/edited text from Mk (as suggested above), we would expect to see significant correlations in these tests. However, although some do exist, they do not form a clear pattern. In particular, there is some evidence that the ‘Mk-Lk double tradition’ (i.e. c021 and c022, where there is no sharing with Mt), may have originated in Mk, and some evidence that the triple tradition words common to all three synoptics (c222) also originated in Mk, but little else. Overall, there are enough correlations greater than 0.4 to suggest that Mk was the source of the words common to Mk and Lk (with Lk changing many individual words), and nothing to suggest otherwise.The following tests all compare the profiles of categories representing passages in Lk that do not have parallels in Mk (cX02, cN02, etc.) with those representing passages in Lk that do have parallels in Mk (cXN2, cNN2, etc.).
There is little evidence here of any significant degree of correlation between categories in Lk. The exception is cA02 (sondergut Lk + double tradition words only in Lk), where we have:
However, because p012 does not have such a strong correlation with p002, again a little more investigation is needed:
From these results we can see that c012 is most likely to come from the same source as c002 and c112. However, the correlations indicate that p012 contains a higher percentage of individual words, which is consistent with the view that aLk significantly altered the Greek of the passages he took from Mk that are not in Mt.
The lack of correlation between p002 and both p022 and p122 suggests that words shared between Mk and Lk did not come from Lk, but they came from Mk instead.
The following tests check for correlations between the profiles of cX22 (and variations cN22, cA22, etc.) and the equivalent Markan and Lukan categories.
These tests support previous results suggesting that the main source of the words common to all three synoptics was Mk. However, they do not provide any strong indication of the sources of the words common to Mk and Lk but not Mt, i.e. those in c022 and c122.
The lack of any significant correlations in the first group of tests above and the negative correlations in the second group suggest that the words common to both Mk and Lk could have originated in Lk. However, this appears to contradict previous results and others (below), that suggest that the words in Mk that are common to either Mt or Lk originated in Mk:
The key to understanding this problem is knowledge of the differences between the Greek used in Mk and that used in Lk, in particular that Lk ‘corrects’ or ‘improves’ the Greek used in Mk. For example, cX22 contains above average use of EIPON, with below average use in cX12, while the converse is true of EIS. As previously mentioned, this causes a negative correlation between the profiles of many of the categories in Mk when compared with categories in Lk.