I have a confession: I am terrible at math! I avoided statistics courses and one of the hardests things was trying to recover basic highschool math for the GRE a few years ago So I may not be the best to represent the next two contributions involving calculations of probability. Although written before the Hendrick/Ehrman debate in 2003, it is important to mention the work of Ernest Best, Ch 11 Uncanonical Mark (197-205) in Disciples and Discipleship (Edinburgh: T&T Clark, 1986), from his review of E.J. Pryke’s Redactional Style in the Marcan Gospel, and A. H. Criddle, “On the Mar Saba Letter Attributed to Clement of Alexandria,” Journal of Early Christian Studies 3.2 (1995): 215-20.
Best sets up an experiment, comparing Secret Mark (SM) (or “uncanonical Mark” [199-200]) to other Markan pericopes. Of Mark’s stylistic features listed by Pryke, SM has impersonals (‘they come’) in II.23, redundant participle (‘she coming’; cf. 12:42; 14:40; 7:25) II.24, “and immediately” II.26/III.1, redundant participle (‘Jesus coming’, cf. 1:35; 7:24; 8:13) III.1, “immediately” (cf. 1:28; 3:6; 6:45; but see 6:25; 14:45 where it may not be redactional) III.2, archesthai [begin] + infinitive III.5, gar [for] explanatory (‘for he was rich’) III.6, genitive absolute (‘it being evening’) III.7, parenthetical clause (‘for he taught him the mystery of the kingdom of God; cf. 13:10; 8:15; alternatively clause an example of gar explanatory) III.9-10, ”redundant” participle (‘rising from there’, cf. 7:24; 10:1; such participles usually fall at beginning of incidents unlike III.10 at conclusion) III.10 – the Markan characteristics are spread out through SM whereas in canonical Mark (CM) they tend to cluster in the seams (200) (passages underlined in Greek text on p. 201, for a translated SM text with verses see here). If one assumes the author was Mark, either a) he joined together a number of incidents, or b) there is a reason why he edited the material extensively at some points (e.g., III.5-7 possibly join of two incidents) (201). Building on Smith’s painstaking details of parallels of SM to CM but going in a new direction, Best attempts to isolate phrases rather than individual words (underline relevent phrases, label them by page & line number [i, ii, iii], where a phrase continued from one line to the next it is identified by the earlier line or a long phrase like III.3 broken into sections [ii and iii] to make full value of their similarity apparent). Each phrase is assigned a value = if it contains two significant words unvaried in comparison with some phrase in CM it is valued at 3, if some minor variation (e.g., change of person, number, tense, mood, gender, ‘Jesus’ to ‘he’) valued at 2, if more than one significant change valued at 1, and very common phrases (‘he said to them’) or vague parallels valued at 1 (201-2). Of 157 words in SM, 91 fall into passages with similarity rated 2 or 3; two phrases get a value 1, fifteen a value 2 and ten a value 3 and totalling these obtains a correlation figure of 62 (2 x 1 + 15 x 2 + 10 x 3) (203). He compares this with Mk 10:17-22 and finds that the similar phrases are shorter and contain fewer significant words than those in SM since, of 94 words, 26 have values 2 or 3. Three passages get a value 1, four a value 2, four a value 3 and the weighted correlation figure is 23 (203-4). On Mk 1:40-45, of 97 words 23 get values of 2 or 3; two passages get a value 1, seven a value 2, one a value 3 and the weighted correlation figure is 19 (204). On Mk 7:24-30, of 129 words 17 get values of 2 or 3; eight passages get a value 1, six a value 2 and none a value 3 and the weighted correlation figure is 20 (204). Thus, he concludes SM is too much like Mark so it is the work of an imitator picking up Mark’s phrases (204). SM is a mosaic of Markan phrases and an example of ’overkill’ by an imitator, though we cannot know the date the imitator worked (noting where Smith notes paralells to Matt/Luke he thinks it possible SM postdates all 3 Synoptics) (205). For a summary (204):
SM 157 words, 91 (values 2 and 3), 58.0%, Weighted Correlation Figure 62, Fraction of Total Number of words .395
1:40-45 97 words, 23 (values 2 and 3), 23.7%, Weighted Correlation Figure 19, Fraction of Total Number of words .196
7:24-30 129 words, 17 (values 2 and 3), 13.1%, Weighted Correlation Figure 20, Fraction of Total Number of words .155
10:17-22 94 words, 26 (values 2 and 3), 27.7%, Weighted Correlation Figure 23, Fraction of Total Number of words .245
Criddle notes most critics accept the Letter to Theodore (LT) as genuinely Clement with exceptions like C.E. Murgia, H. Musurillo, Q. Quisnell and E. Osborn (215), the last insisting LT is a pious forgery familiar with post-Eusebius traditions and imitating the style but misunderstanding Clement’s ideas (e.g., took too literally Clement’s image of heretics breaking in the back door to steal the Church’s teaching [Strom. 7:17]) (216). Criddle aims to show LT, excluding the SM excerpts, has too high a ratio of Clementine to non-Clementine traits to be authentic (216). Based on Stählin’s index (has an incomplete listing of the occurrence of words in quotations by Clement from texts like the Bible), Smith lists 7 words in LT not in Clement previously and 15 only once before, yet he has indiosyncratic criteria for what counts as a new word vrs a new form of a previously occurring word (e.g., he treats the comparative & superlative of an adjective as new words and the active & middle of a verb as separate words). Correcting this as far as possible, Criddle finds 5 words used only once in LT not elsewhere in Clement (aperatos, apographon, aprophulaktōs, prosporeuomai, phthonerōs) and 10 words used once in LT in Clement only once (andrapodōdēs, asphalōs, ensōmatos, exaggellō, exantleō, Hierichō, hierophantikos, katapseudomai [2 times in LT], mēchanaō [active voice in LT, Clement uses once in the middle], prosepagō). Prosporeuomai (come, approach) and Hierichō (Jericho) are used to show where to put SM passages in CM (III.12, 14) so are discarded, which leaves 4 non-Clementine words and 9 Clementine words used only once in LT, whereas a sampling of Stählin indicates around 3/8 or 37.5% of Clement’s vocabulary consists of words used once and once only (617). Then it gets tricky with mathematical formulas on pp 217-18 (I reproduce it below for a math whiz who reads this) but basically he determines that, by using the above fraction, for every increase in the total vocab of 8 words in a new work/fragment of Clement previously unknown we would estimate 5 words used only once by Clement to occur again in the new work. This ratio of 8 to 5 disagrees with LT’s 4 to 9, showing too many words used previously only once and not enough words previously unknown (discrepancy is significant at the 2.5% level by a χ2 test) (218). Several words in LT used only once by Clement are rare in other patristic texts (andrapodōdēs, exantleō, hierophantikos) and the use of ensōmatos in a phrase (sarkikōn kai ensōmaton) recalls how Clement uses it once elsewhere in another context, while new words like apographon and aprophulaktōs are uncommon in Greek writers and phthonerōs is rare in patristic Greek. Finally, LT is not unusually close to any given work of Clement (e.g., 17 words in LT not found in the Stromateis and only approx 12 words in LT found only once in the Stromateis), so LT brings together words scattered throughout Clement but often with new meanings and non-Clementine ideas (218). LT picked words in Clement but not in other Patristic writers and avoided words not in Clement but found in other Patristic writers, so (s)he brought together more rare words/phrases from Clement than compatible with genuine Clementine authorship (!) (218). Furthermore, the agreement Smith finds between the quantitative rhythms of LT and the 3rd book of the Stromateis appears greater than one would expect in an authentic fragment of Clement as short as LT (218). That all the prepositions common in Clement appear at least once in LT while no other prepositions do is too good to be true (218) and, in one case, of the 12 prepositions in LT the 10th most common apo is used once in a phrase where we would expect the preposition ek but by using apo brings LT closer to the average of prepositions in Clement’s works (219). Looking at quotations/allusions to biblical passages in LT, he finds Jude 13, Prov 26:5; 1 Thess 5:5; Tit 1:15 directly quoted where each used only once in Clement previously and Rev 2:24; Matt 25:29b, Ecc 2:14; 2 Cor 3:17b not previously found in Clement (though Matt 25:29a quoted several times), thus giving 4 new quotations and 4 only once previosly in Clement. From Stahlin’s index we find that most cited passages in Clement are quoted only once, so using similar arguments to the above we would expect the number of quotations previously occuring only once to be less than half of the number of previously unknown quotations which conflicts with the equal numbers of both cases in LT (again an imitator of Clement) (319). He concludes LT does not accurately reflect Clement’s view of gnostic Christians with deeper insights into available texts (not access to forbidden texts) (319-20).
To avoid misrepresenting the math, let me just quote directly from Criddle on pp. 217-18: ”In simple models of vocabulary statistics, such as those of Herdan and Simon, the size of this fraction is independent, for a given writer, of the total size of the vocabulary used by that writer. Thus if a previously unknown work by an author with fraction α of his vocabulary used only once increases his total vocabulary by x, then (x – (y+z))/x = α, where y is the number of words in the new work previously used only once and z is the number of new words used more than once in the new work. (z would be small in the absence of “clumping” together of infrequently used words, in practice enough “clumping” occurs to make z ≈ x/10). In more accurate models α slowly falls as total vocabulary rises so that α > (x – (y+z))/x ≈ 4/5 α; thus α > (x – (y+z))/x < (x-y)/x, with α ≈ ½, we have α ≈ (x – y)/x. ” This leads him to note α is about 3/8 and how we should estimate of 8 new words 5 used previously, while LT has the ratio of 4 to 9.
Let me know what you think about the arguments that SM is too Markan to be Mark or LT to Clementine to be Clement? There is a rebuttal of both positions in Scott Brown’s book which I will get to in the post on Brown and I know Charles Hedrick responded as well to Best’s argument with other Markan pericopes at the forthcoming book on the York conference on Secret Mark (thanks to Tony Burke for the preview of the contents). I have a conference Thursday-Saturday so I will probably get back to posting on Secret Mark (especially the contributions of Scott Brown, Stephen Carlson, Peter Jeffrey, and Francis Watson) next week.