A peculiar (and mathematical) argument for Lucan priority and Matthean posteriority.

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Paul the Uncertain
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Re: A peculiar (and mathematical) argument for Lucan priority and Matthean posteriority.

Post by Paul the Uncertain »

Because in Matthew the sayings are all contiguous, all in chapter 10. In Luke they are spread out across most of the gospel.
Is your argument, then, that this "kills (or at least injures) two birds with one stone," both Q >>> Luke and Matthew >>> Luke ?

Assuming so, then
There is no reason why Luke should have kept them in the Matthean order, since they all wind up in completely different contexts, ...
Is there a reason why Luke ought to have changed the order he found in Q or Matthew? That's when his behavior would be most unlikely. It would also help if there were nothing appealing about the order ... that is, your assumption "There is no reason why Luke should have kept them in order ..." is really true: no reason.

[One possible test: would Matthew work just as well in any different order? If not, is the "fitness" of Matthew's order completely peculiar to his context?]

I don't see this as a computational problem (although qualitative probability counts as mathematics). The chief difficulty for comparing the outcome with chance (e.g. of 5! = 120 possible orderings, if each is equally likely to be chosen, then that this one would be chosen is 1:120, or as Peter said .83%) is that you know for a fact that Luke did deliberately choose the order, just as he deliberately chose every other observable feature of his composition. Whatever the reason the orders agree, it isn't by chance.

What you need is something like a likelihood ratio:

P( order agrees | Luke first ) / P( order agrees | Luke later )

but without numbers - "the numerator is bigger than the denomiantor by a lot" as a justified assertion will do. Chance really doesn't enter into it, now that you've checked that it isn't a plausible explanation.

Your remarks about a past simulation are interesting, though - was that a model of Luke's compsitional decision making? Or was it some version of a "chance" model?
Last edited by Paul the Uncertain on Wed Apr 14, 2021 5:38 pm, edited 1 time in total.
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Ben C. Smith
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Re: A peculiar (and mathematical) argument for Lucan priority and Matthean posteriority.

Post by Ben C. Smith »

Peter Kirby wrote: Wed Apr 14, 2021 4:33 pmFor the purpose of finding the odds, it is simpler for the program to imagine Luke's procedure in reverse: instead of taking all the Matthean blocks, scattering them, and finding a sequence of 5 disconnected blocks in order that correspond to a contiguous series in Matthew... we can rely on the symmetry of the problem, start with the Lukan order of blocks, scatter his sources as representing where they were found in Matthew, and look for a sequence of five contiguous blocks in the Matthean block sources.
I am not sure I realized that the problem was symmetrical in this way. Interesting. That does simplify matters.
Peter Kirby wrote: Wed Apr 14, 2021 5:06 pmBy exact methods, looking at every permutation, I get these results (here "N" is the number of blocks, the sequence length is 5):

('N: ', 5, ', coincidence: ', 0.008333333333333333)
('N: ', 6, ', coincidence: ', 0.015277777777777777)
('N: ', 7, ', coincidence: ', 0.022222222222222223)
('N: ', 8, ', coincidence: ', 0.029166666666666667)
('N: ', 9, ', coincidence: ', 0.03611111111111111)
('N: ', 10, ', coincidence: ', 0.04298638668430335)
('N: ', 11, ', coincidence: ', 0.049815340909090906)
('N: ', 12, ', coincidence: ', 0.05659606982523649)
I recognize 0.008333 as 1 ÷ 120, or the odds of any 5 blocks winding up in the same nonrepeating permutation randomly, so that is a good start! (At least for someone like me: not extremely or naturally statistically inclined.)
By approximate methods, using 1,000,000 randomly selected shuffles for each number of blocks, I get these results:

('N: ', 5, ', coincidence: ', 0.008192)
....
('N: ', 10, ', coincidence: ', 0.043135)
....
('N: ', 20, ', coincidence: ', 0.109337)
....
('N: ', 30, ', coincidence: ', 0.170844)
....
('N: ', 40, ', coincidence: ', 0.228052)
....
('N: ', 50, ', coincidence: ', 0.281696)
....
('N: ', 60, ', coincidence: ', 0.33111)
....
('N: ', 70, ', coincidence: ', 0.376792)
....
('N: ', 80, ', coincidence: ', 0.420394)
....
('N: ', 90, ', coincidence: ', 0.459967)
....
('N: ', 100, ', coincidence: ', 0.497745)

Does this answer the question?
I think it helps tremendously. If I understand correctly, we are down to deciding how many blocks of material are shared between Matthew and Luke, with 10 blocks giving us a 4% chance of Luke having come up with his arrangement at random and 20 blocks already giving us a 10% chance, and so on up to nearly 50% for 100 blocks. So it seems, on Lucan posteriority, that something of a coincidence would be involved, but probably not a huge, gamechanging one. I will have to give some thought to how many blocks there are in all.

Thanks, Peter. Much appreciated, and please let me know if I have misconstrued the results.
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Re: A peculiar (and mathematical) argument for Lucan priority and Matthean posteriority.

Post by Peter Kirby »

Ben C. Smith wrote: Wed Apr 14, 2021 5:36 pm
Peter Kirby wrote: Wed Apr 14, 2021 4:33 pmFor the purpose of finding the odds, it is simpler for the program to imagine Luke's procedure in reverse: instead of taking all the Matthean blocks, scattering them, and finding a sequence of 5 disconnected blocks in order that correspond to a contiguous series in Matthew... we can rely on the symmetry of the problem, start with the Lukan order of blocks, scatter his sources as representing where they were found in Matthew, and look for a sequence of five contiguous blocks in the Matthean block sources.
I am not sure I realized that the problem was symmetrical in this way. Interesting. That does simplify matters.
Alternatively and, also, equivalently:

If you imagine that you have the original Matthean sources numbered correctly, with the Matthean positions of each block:
0, 1, 2, 3, 4, 5, 6

Then you shuffle to get where Luke positioned, in his order, the respective Matthean blocks:
4, 0, 2, 5, 6, 1, 3

You can go through these Lucan positions of the Matthean blocks and look for a contiguous sequence of increasing positions (here 0, 2, 5, 6 is the longest).
Ben C. Smith wrote: Wed Apr 14, 2021 5:36 pm
Peter Kirby wrote: Wed Apr 14, 2021 5:06 pmBy exact methods, looking at every permutation, I get these results (here "N" is the number of blocks, the sequence length is 5):

('N: ', 5, ', coincidence: ', 0.008333333333333333)
('N: ', 6, ', coincidence: ', 0.015277777777777777)
('N: ', 7, ', coincidence: ', 0.022222222222222223)
('N: ', 8, ', coincidence: ', 0.029166666666666667)
('N: ', 9, ', coincidence: ', 0.03611111111111111)
('N: ', 10, ', coincidence: ', 0.04298638668430335)
('N: ', 11, ', coincidence: ', 0.049815340909090906)
('N: ', 12, ', coincidence: ', 0.05659606982523649)
I recognize 0.008333 as 1 ÷ 120, or the odds of any 5 blocks winding up in the same nonrepeating permutation randomly, so that is a good start! (At least for someone like me: not extremely or naturally statistically inclined.)
By approximate methods, using 1,000,000 randomly selected shuffles for each number of blocks, I get these results:

('N: ', 5, ', coincidence: ', 0.008192)
....
('N: ', 10, ', coincidence: ', 0.043135)
....
('N: ', 20, ', coincidence: ', 0.109337)
....
('N: ', 30, ', coincidence: ', 0.170844)
....
('N: ', 40, ', coincidence: ', 0.228052)
....
('N: ', 50, ', coincidence: ', 0.281696)
....
('N: ', 60, ', coincidence: ', 0.33111)
....
('N: ', 70, ', coincidence: ', 0.376792)
....
('N: ', 80, ', coincidence: ', 0.420394)
....
('N: ', 90, ', coincidence: ', 0.459967)
....
('N: ', 100, ', coincidence: ', 0.497745)

Does this answer the question?
I think it helps tremendously. If I understand correctly, we are down to deciding how many blocks of material are shared between Matthew and Luke, with 10 blocks giving us a 4% chance of Luke having come up with his arrangement at random and 20 blocks already giving us a 10% chance, and so on up to nearly 50% for 100 blocks. So it seems, on Lucan posteriority, that something of a coincidence would be involved, but probably not a huge, gamechanging one. I will have to give some thought to how many blocks there are in all.

Thanks, Peter. Much appreciated, and please let me know if I have misconstrued the results.
Sounds about right.

I would imagine that there is a wide variety of explanations that don't involve Luke taking the Matthean material and arranging it randomly, but I agree that this is a good minimum standard for significance. If the phenomenon is just as likely to be found in a hypothetical exercise where the blocks are randomly rearranged, then we don't have to reach for any kind of special explanation.

You could raise the stakes if you could find an additional similar sequence, as the odds of getting two sequences at random are lower than the odds of getting just at least one.

Tests of statistical significance generally don't go much above p < 0.05 or maybe p < 0.1, as an upper limit to what is usually considered a significant result, so even at just 20 blocks, we don't have that much significance, for finding a single sequence of length 5.
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Re: A peculiar (and mathematical) argument for Lucan priority and Matthean posteriority.

Post by Aleph One »

[Edit: Oops, looks like a had a quite old tab open of this thread when I made my reply and I've seen that Peter has already addressed all this stuff with the variable number of shared blocks and all so my first paragraph is now greatly superseded! :cheeky: ]

So in simple terms, we're asking, "if Luke took these 5 blocks of text from Mathew, threw them in a hat, and pulled them out 1 by 1 (and used them in that order), what are the chances they would end up in the same order as Matt had them originally?" In that case there are !5 ways to order the blocks, which is [5*4*3*2*1=] 120 permutations. Since obviously only 1 of those permutations is the correct order, the likelihood of stumbling upon it by chance is 1/120 or 0.83% (like Peter said). Another thing that Peter said that may be relevant is noting that picking out one specific case where Luke keeps Matt's order may not look so lucky when considering all the other instances where he did not. (If you look at one winning ticket at the race track you say "what are the chances" but if you have a pile of 100 random tickets then finding a winner is mundane). I'm not sure if this applies here though.

So generally the idea is it would be strange for Luke to go through Matt, copy down 5 blocks he likes, then to draw from that list 1-by-1, in order, when he could just as easily use any block at any time (and just cross each off the list as he goes)? I guess it's somewhat stranger than to imagine Matt writing this section of his gospel by scanning through Luke, and each time he finds something he likes he writes it into his text and continues scanning, but by how much? I knows there's scholarship on how ancient authors composed manuscripts using sources that may he helpful but it might be hard to establish an individual author's adherence to standard practices.
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Re: A peculiar (and mathematical) argument for Lucan priority and Matthean posteriority.

Post by Ken Olson »

Ben C. Smith wrote: Wed Apr 14, 2021 4:04 pm
Ken Olson wrote: Wed Apr 14, 2021 3:58 pm Sometimes John Kloppenborg says things that baffle me (other examples available upon request).
I would be interested in such examples.
The other examples I had in mind are less about descriptions of the synoptic data and more about how he represents other (i.e., Farrer, scholarship) and may seem like (or be) pet peeves:

(1) In his review of Mark Goodacre’s The Case Against Q, Kloppenborg takes Goodacre to task for calling Matthew’s Sermon on the Mount “a rag-bag”(New Testament Studies 49 (2003) 210-236; I haven’t checked the reference in Goodacre).
If the other two assumptions could be rendered credible, the MwQH might indeed offer a plausible
accounting for Luke’s arrangement. But there are two problems. First, that Matt 6.19–7.27 is a ‘rag bag’ is repeatedly asserted but not defended beyond citing a comment of Graham Stanton.45 Such is hardly the view of most Matthean commentators: Bornkamm related the structure of Matt 6.19–7.6 to individual petitions of the Lord’s Prayer and in this is followed (with some modifications) by Lambrecht and Guelich.46 Others see the Lord’s Prayer as the centre of an extended chiastic structure (Grundmann; Luz); others still divide Matt 6.19–7.12 into one (Gnilka) or two (Hagner) topically arranged units before the concluding section (Matt 7.13–27). With an even finer analysis, Dale Allison sees Matt 6.19–34 as divided into four ‘paragraphs’ and unified by a common theme, and 7.1–12 as
the ‘structural twin’ of 6.19–34.47 Matt 7.13–27 likewise displays a deliberate structure controlled formally by the contrast of the two ways (7.13–14, 24–7) and thematically by contrast between superficial adherence to Jesus’ teaching and full adherence and the respective consequences.

Of course one might argue that Luke failed to perceive the design of Matthew’s sermon. But once editorial misperception becomes part of a scenario, the explanatory power of such a thesis is diminished.
Which of the five designs of Matthew’s Sermon that Kloppenborg lists (Bornkamm, Grundmann, Gnilka, Hagner, Allison) was the one Luke was supposed to perceive (and presumably value and preserve)? And are the scholars who perceive the other designs guilty of (perhaps non-editorial) misperception for failing to perceive Matthew’s design correctly?

(2) From the same review:
Detractors of the MwQH regularly note that Luke shows no knowledge of Matthew’s additions to Mark in the triple tradition.27 Goodacre is quick to point out that this objection is actually formulated from the perspective of the 2DH, for it ignores the Mark–Q overlaps, ‘Q’ material itself, and the minor agreements, all of which on the MwQH are materials which Matthew added to Mark and which
Luke took from Matthew.

Still, the objection cannot be evaded so easily. What the objection normally has in view are the Matthean additions to Markan pericopae in Matt 3.15; 12.5–7; 13.14–17; 14.28–31; 16.16–19; 19.9, 19b; 27.19, 24, all of which Luke lacks. Two of these offer no difficulty to the MwQH: Matt 14.28–31 (Peter’s maritime outing) and 19.9 (Matthew’s qualification of the divorce prohibition with mh; ejpi; porneiva~) are additions to Markan pericopae that Luke omits entirely. Goodacre does not comment
on the Matthean additions in 12.5–7; 13.14–17; 19.19b; 27.19, 24, and instead focuses his defence on Matthean additions to Mark at Matt 3.15 and 16.16–19.
In this case, my problem was that Kloppenborg had already directed Robert Derrenbacker’s dissertation, later published as Ancient Compositional Practices and the Synoptic problem (2005), arguing that ancient authors followed one source for any particular passage and did not conflate different sources (i.e., one source at a time). Here he’s asking why, on the Farrer theory, Luke did not conflate Mark and Matthew by adding Matthew’s additions to Mark when he’s following his Markan source. (I gave a paper on this in the Q section at the SBL conference).

(3) This one is my personal pet peeve from Kloppenborg’s review of my contribution, “Unpicking on the Farrer Theory,” in Questioning Q, from Biblical Theology Bulletin 36 (2008) 43:
Ken Olson responds to F. Gerald Downing’s claim that Luke’s treatment of Matthew on the
MwQH does not cohere with how ancient editors worked, and claims that “unpicking sources”
—which is what Luke did on the MwQH—is not as uncommon as Downing supposes. Olson’s
treatment of Josephus, however, does not make his point, and although he cites T.J. Luce’s
analysis of Livy (Livy: The Composition of His History [Princeton, NJ: Princeton University
Press, 1977]), it does not appear that he has followed Luce’s argument carefully, which
seems rather to support Downing.
Kloppenborg completely misconstrues what I was arguing in the paper. I agree with Downing that ancient authors follow one source at a time and that “unpicking sources” would be an unusual procedure. I argue, however, that Downing’s claim that ancient authors looked for “common witness” in their sources to reproduce in their own work is mistaken and actually violates the one-source-at-a-time procedure and also that Downing has failed to show that Luke would have to have unpicked the Markan material from his use of Matthew in his four example pericopes. There is a large number of exceptions to his claim that Luke must have unpicked Mark from Matthew. That Luke might sometimes have followed Matthew when Matthew was following Mark and sometimes not is not an unusual procedure.

Kloppenborg’s misunderstanding may be based on one paragraph (or maybe the title?) where I point out that on the pericope level authors could be said to “unpick” when they choose to follow one source instead of another. I posed the rhetorical question of whether Luke on the 2DH had “unpicked” Mark (or Q from Mark?) when he chose to follow the Q version instead of Mark a Mark-Q overlap passage. I was not, however, defending unpicking at the micro-level and never suggested that the Farrer Theory needed to assume it. That should have been clear from the body of the paper and the conclusion.

(4) This one comes from Jeffrey Peterson. Kloppenborg criticized Michael Goulder for referring to Luke’s use of Mark as a fact (“Is there a new paradigm?” 33-34). What Goulder wrote: “Luke’s use of Mark is a fact (or generally accepted as one)” (“Is Q a Juggernaut?” 670). In The Formation of Q Kloppenborg wrote “That Matthew both conflates Mark with Q and displaces Markan stories is a matter of empirical fact,” (Formation (1987) 72; to be fair, that was before Kloppenborg started engaging with other solutions to the synoptic problem and their theoretical underpinnings).

End of rant on Kloppenborg.

Best,

Ken
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Ben C. Smith
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Re: A peculiar (and mathematical) argument for Lucan priority and Matthean posteriority.

Post by Ben C. Smith »

Thanks, Ken. Very enlightening.

It is always fun to find contradictions and misunderstandings in a reputable scholar's body of work, but it also makes me queasy to wonder how often I myself indulge in self contradictions or misunderstandings either without noticing myself or without others calling my attention to it (or, far worse, with others calling my attention to it but me not understanding their point).
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Re: A peculiar (and mathematical) argument for Lucan priority and Matthean posteriority.

Post by Ken Olson »

Ben C. Smith wrote: Wed Apr 14, 2021 6:20 pm It is always fun to find contradictions and misunderstandings in a reputable scholar's body of work, but it also makes me queasy to wonder how often I myself indulge in self contradictions or misunderstandings either without noticing myself or without others calling my attention to it (or, far worse, with others calling my attention to it but me not understanding their point).
I know. Some mean-spirited people might even suggest I do such things myself, at least occasionally.
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Re: A peculiar (and mathematical) argument for Lucan priority and Matthean posteriority.

Post by Ken Olson »

Ben and Peter,

Are your models examining the question of how likely it is that *all* of Luke's five blocks could be in the same order as their counterparts in Matthew by random chance? What if we could show that there was a good reason to put two (or even three) in that order, and only two or three were random (or unexplained)? That would seriously undermine the mathematical argument, wouldn't it? Or have I missed something in the analysis?

Best,

Ken
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Ben C. Smith
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Re: A peculiar (and mathematical) argument for Lucan priority and Matthean posteriority.

Post by Ben C. Smith »

Ken Olson wrote: Wed Apr 14, 2021 7:13 pm Ben and Peter,

Are your models examining the question of how likely it is that *all* of Luke's five blocks could be in the same order as their counterparts in Matthew by random chance?
Yes.
What if we could show that there was a good reason to put two (or even three) in that order, and only two or three were random (or unexplained)? That would seriously undermine the mathematical argument, wouldn't it? Or have I missed something in the analysis?
I can think of some very particular circumstances in which it would make sense both for Matthew and for Luke to put their sayings in the same order. For example, if the sayings formed an acrostic like some of the psalms do, but Matthew wanted an acrostic only about half a chapter in length while Luke used an acrostic to organize the main sections of his entire gospel, then both evangelists would have the same reason for deliberately putting the sayings in that order.

Apart from such a specific rationale in which the best overall order of sayings could be deduced independently, I think that any attempt to explain Luke putting the sayings in that order only manages to push the problem back a level rather than to resolve it. Carlson, for example, initially tried to suggest that each of Luke's new contexts made perfect sense on its own, which I granted (at least for the sake of argument), but then pointed out that the coincidence then becomes that the new contexts should all happen to align with the old order despite there being no inherent reason for that to be the case. (To his credit, he understood this, and that is when the math began.) And that is on the supposition that all five can be explained contextually; if only two or three can, then we certainly fare no better. Without a rationale that actually serves to organize the sayings naturally regardless of context (like the alphabetical order of an acrostic would), it seems to me that we are always just pushing the coincidence back a level like that, and it still remains.

So I guess what I am saying is that, if your good reason is more like the acrostic, then you will probably have a point. If it is more like what scholars are usually looking for in Lucan redaction, though, then it probably does not explain the coincidence; it only postpones its analysis a bit.

Fortunately, I am pretty sure, based on Peter's numbers, that there is not much coincidence to be explained. If the number of blocks shared by Matthew and Luke are even as few as 20 or 30, then the result is not significant enough to have to look beyond simple coincidence, as Peter said.

ETA: A textual commentary would be another great reason to scatter a catena of sayings yet retain the same order. Commentaries on other texts do exactly that. So, if we can look at Luke's treatment of Matthew 10 and discern that he has split those sayings up in order to comment on each one, thus explaining the intervening material, that works. (This appears incredibly unlikely to me in the case at hand, but I am just throwing out different kinds of rationales which would do the trick.) Or I have seen some modern literary works which entitle each chapter or section according to some other work, like a poem, line by line.
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Re: A peculiar (and mathematical) argument for Lucan priority and Matthean posteriority.

Post by Peter Kirby »

Ken Olson wrote: Wed Apr 14, 2021 7:13 pm Are your models examining the question of how likely it is that *all* of Luke's five blocks could be in the same order as their counterparts in Matthew by random chance? What if we could show that there was a good reason to put two (or even three) in that order, and only two or three were random (or unexplained)? That would seriously undermine the mathematical argument, wouldn't it? Or have I missed something in the analysis?
This is part of why I suggest it is basically just an initial filter for significance:

"I would imagine that there is a wide variety of explanations that don't involve Luke taking the Matthean material and arranging it randomly, but I agree that this is a good minimum standard for significance. If the phenomenon is just as likely to be found in a hypothetical exercise where the blocks are randomly rearranged, then we don't have to reach for any kind of special explanation."

If it met this initial test, then we might want to consider various hypotheses, including those that include "a good reason to put two (or even three) in that order," etc.
Ben C. Smith wrote: Wed Apr 14, 2021 7:30 pmFortunately, I am pretty sure, based on Peter's numbers, that there is not much coincidence to be explained. If the number of blocks shared by Matthew and Luke are even as few as 20 or 30, then the result is not significant enough to have to look beyond simple coincidence, as Peter said.
I am somewhat optimistic that there could be an argument developed along these lines if we had more to note besides just this one sequence of 5 blocks. But, yeah, if sticking to the usual limits for tests of significance (in this case, p > 0.1 for total number of blocks >= 20), this could just be a coincidence.
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