Subject: Re: Thomas/Synoptic Parallels Date: Wed, 21 Oct 1998 14:31:24 -0700 From: Bob Schacht To: miser17@epix.net CC: crosstalk@info.harpercollins.com At 04:00 PM 10/21/98 -0400, Stevan Davies wrote: >... >If we have 90 accepted // sayings in Thomas, the chance of >coincidental similarity in order between TH and MT or MK or Lk for >three of them or, indeed, a few sets of three, is pretty high. >Shuffle two decks of cards, subtracting the K and Q and record the result. >Do it again and record the result. How often will the same three >cards be in sequence for those sets of 88 cards? ... I'm gonna attempt to actually pin numbers to this problem. First of all, this is basically a probability problem of sampling without replacement. Therefore the probability of *any particular* three-saying sequence would be (1/90) times (1/89) times (1/88) = 1.418681193962e-6 = .000001418681193962 if the sayings were drawn at random. Now the trick is, of course, to state the null hypothesis more precisely than you have done. Since the usual impression is that GThomas is the random one, you need to enumerate exactly how many three-saying sequences in Matthew (or Luke, or Q) are there in this list of 90 sayings? Suppose the answer is "88" (Take the 90 sayings; order them as they are in Matthew; how many ADJACENT sequences of 3 sayings in Matthew?) Adjacency makes the math simpler. What I mean by adjacency is that if we sort the 90 sayings in order by their appearance in Matthew and number them consecutively from 1 to 90, then "1,2,3" forms an adjacent sequence, but "1,4,5" does not. In this sense, there would be 88 triplets in Matthew, and the question would then be the probability that they would appear in the same sequence in Thomas should be 88 x 1.418681193962e-6 = 1.248439450687e-4 = .0001248439450687 which is still a pretty small probability. If you wanna count "1,4,5" sequences (i.e., same order in Matthew and Thomas, even if separated by intervening sayings in Thomas), then the number of possible matching sequences multiplies quite a bit, but at the cost of making the matching sequences seem less dependent. So it looks to me that a consecutive matching sequence in Thomas would NOT be very likely on the initial hypothesis that the sayings in Thomas are "randomly drawn" from the same sequence as in the synoptics. OK, I've made a start. Now the other number hawks on CrossTalk can correct my mistakes. BTW, I wanna go back to Renee's interesting comments on her data: no one has yet commented on her identification of 3(?) sequences within Thomas that have a very high correlation with synoptic material. I'd like it if someone were to go back and check those sequences with the following hypothesis in mind: H0 ('aitch-zero' i.e., null hypothesis): Thomas was formed by copying selected sayings from first one synoptic gospel, then another, interspersed with an eclectic assortment of quotes from unknown sources. There's another applicable statistic here: if we consider the synoptic gospels collectively, we could do a Wald-Wolfowitz Runs test. That is, you take all the GThomas sayings in order (all 114 or 156 or whatever of them). For each saying write "A" if it has no synoptic parallel, and "B" if it has any synoptic parallel. You then have a sequence of letters like AABABAABBBABBBBAABAABB... or maybe, as Renee suggested, something more like AAAAAAAAAABBBBBBBBBBAAAAAAAAAAAABBBBBBBABBBB. The idea of Wald-Wolfowitz is that if the order is random, then consecutive runs of the same letter should not be very long (the longer the run, the rarer it should be). This test can be found in standard statistics books such as Blalock. Using this kind of notation with, say, I = no parallel, M = Markan parallel, N = Special Matthew parallel, L = Special Luke parallel, Q = Q parallel, then H0 above could be expressed something like this: GThomas = IIMMMMMMMMMMIIIIQQQQQQQQQQIIIIIINNNNNNNNNNIIIIIIIIIIMMMMMMMMMMIII I assume that special rules will be needed, e.g. triple tradition material will always be recorded as 'M', etc. Bob ******************************* Robert M. Schacht Northern Arizona University Ubi caritas et amor, Deus ibi est. (Where charity and love are [found], God is there) 9th century latin hymn