Friday, October 20, 2017

Richard Fellows’s measurements of the Vaticanus paragraphoi

Over on his blog, Richard Fellows has written up the results of his measurements of the paragraphoi in Vaticanus and plotted them against the measurements of Philip Payne from his recent NTS article. Fellows has linked to his blog in the comments of my last post about it but I thought they were worth highlighting here. In short, he has found that Payne’s “characteristic bars” are not actually characteristic.

This can be seen, for example, in the graph below which plots the the length and marginal extension of paragraphoi at the 28 places where Payne finds them next to digstimai. There is no clear correlation here. (It would be useful to see this same graph using Payne’s own measurements.)

Fellows’s measurements against Payne’s

Here is the end of Fellows’s post:
What we can conclude is that the peer review process has failed us yet again. The measurement errors and questionable statistical method should have been spotted by reviewers.

We can also conclude that online discussion can make much faster progress then peer reviewed journals. The blog posts and comments on the ETC blog have advanced the debate, in large part because Philip Payne and others have been so willing to share their ideas and data. He has also exchanged multiple emails with me. If only all scholars were as willing to engage in online and offline discussion!
Payne has suggested that the discrepancy may be because Fellows is using the online images whereas Payne has access to the excellent facsimile. Certainly, that could be a factor. But I do not think that is the main issue here.

The problem is that we are measuring in millimeters in the first place. What we have is a case of what Charles Seife calls “proofiness,” an improper use of measurements in statistics. The question is not whether we can measure these paragraphoi in millimeters and attach meaning to the differences we find, it’s whether we should in the first place. To my mind, it’s a bit like saying that eating Whataburger will make you 50% happier. It might be true, but measuring happiness in percentages is the wrong way to prove the point.

As Pete Head says, “I don’t think the length of the bars or their distance from anything is of any significance whatsoever. These are written by hand!” Are we to imagine the scribe of 03 using a ruler to make them? Of course not. So a ruler is probably not the right tool for the job.


  1. The right too for the job is common sense. Go figure.

    1. Common sense: a good tool both for manuscript and evaluating Whataburger.

    2. Exactly. Unfortunately, some people can't tell the difference between 'well done' and 'grossly overcooked'.

  2. Payne response to Gurry, part 1:

    Peter Gurry writes, “In short, he [Richard Fellows] has found that Payne’s “characteristic bars” are not actually characteristic.”

    In fact, the very chart you reproduce, confirms that the “characteristic bars” are indeed characteristic. There are three reasons that this is not clearly evident in the chart as you reproduced it.

    First, if you are claiming that a graph shows that “characteristic bars” are not actually characteristic, the graph should make it clear which entries on the chart are “characteristic bars” and which are not. The chart does not do that. In fact, it is misleading in this regard since it clearly distinguishes two groups of bars, one with red x’s and one with diamonds. It labels the red x’s as “Payne’s multi-word variants.”

    This gives the impression that the red x’s mark Payne’s “characteristic bars” at the locations of multi-word blocks of textual variants, particularly since you introduce the chart, “Payne’s “characteristic bars” are not actually characteristic.... There is no clear correlation here.” In fact, however, the two red x’s that are lowest and farthest left are not among the nine “characteristic bars” (including the one Richard Fellows correctly identified at Mark 6:11, 1285B). In order to show the contrast between “characteristic bars” and undisputed paragraphoi, those two should be black, not red.

    Since distigmai mark the location of textual variants, it is simply to be expected that out of twenty, one or more would be multi-word additions. Therefore, that by itself could not make them characteristic bars. Neither of these two undisputed paragraphoi are anywhere close to sharing either of the two physical characteristics of greater extension into the margin or greater total length.

    Second, the next lowest and farthest left red x, which represents the characteristic bar at Matt 18:10, 12, should actually be near the top right of the chart. Richard Fellows has acknowledged that his not including the initial dot as part of the bar at Matt 18:10, 12 is a questionable decision. I checked the color of the ink of both the dot and the bar that appears to be an extension of it at Matt 18:10, 12 in the most faithful reproduction of the actual ink colors of Vaticanus, the 1999 Codex Vaticanus B facsimile. In that facsimile, both the dot and the bar extending to its right have the same color. Since it is common for there to be gaps without visible ink immediately to the right of the beginning of bars and since this dot is aligned properly to be an extension of this bar, it probably should be regarded as part of this bar, as can be judged from the first photograph on p. 613 in my NTS article. Compare the three similarly interrupted bars at 1505B lines 26, 29, and 36. When a dot makes sense as part of the bar, but makes no sense interpreted as unrelated to the bar, as this one does, this favors the judgment that it is part of the bar.

    Since Richard Fellows left it open that the dot may be part of the bar, he should not have assigned it a position in the chart without any indication that this excludes the left dot from this bar. Instead of the extension into the margin of 2.24 mm, it probably should be listed at approximately 3.5 mm, namely at the very top of the chart, and its total length probably should be listed at approximately 5 mm, placing it far to the right of the chart. If this chart had highlighted in red only the characteristic bars, it would have illustrated their sharp contrast with the undisputed paragraphoi, especially if it had included the dot with the bar at Matt 18:10, 12.

    to be continued

  3. Payne response to Gurry, part 2:

    Note that by Richard Fellows’ own measurements, the bar (here at Matt 18:10, 12 excluding the left dot), which therefore has by far the least extension into the margin of any of the characteristic bars, is still 2.24 mm. Even with this reduction in length, this lowest extension into the margin of all eight characteristic bars is noticeably longer than the average extension into the margin of the twenty undisputed paragraphoi by the average of his measurements, 1.802 mm.

    Third, this chart omits the characteristic bar at Mark 6:11 that Richard Fellows correctly identified as meeting the all five characteristics of “characteristic bars.” It is approximately 4.9 mm long and extends into the margin approximately 3.7 mm. On the chart it would be the second farthest to the right and higher than all the others. It is followed by a gap in the midst of the following line of text at the exact point where NA28 lists a fifteen word addition to the text apparently derived from the parallel passage, Matt 10:15. This, by the way, confirms that the text of the Gospels in Vaticanus is so old that it is unaffected by any of these 6 blocks of added text marked by scribe B.

    If you look again at Richard Fellow’s chart, remembering that the two lower left red x’s are undisputed paragraphoi, not characteristic bars, and that the third lowest red x should probably be located in the upper right portion of the chart along with the ninth characteristic bar at Mark 6:11, you will see a dramatic contrast between the nine characteristic bars and the undisputed paragraphoi according to Richard Fellow’s own measurements.

    Using Richard Fellows’ own measurements, the 8 characteristic bars adjacent to a distigme extend into the margin on average 2.68875 mm. In contrast, the 20 undisputed paragraphoi adjacent to a distigme extend into the margin on average 1.802 mm. Thus, the characteristic bars extend into the margin approximately 50% farther than the undisputed paragraphoi do. It would be more than 50% if the 9th characteristic bar were included, as it should be, because this bar extends farther into the margin than any of the other 28 bars adjacent to distigmai.

    Similarly, on Richard Fellow’s measurements (even excluding the dot from the bar at Matt 18:10, 12 and not including the characteristic bar at Mark 6:11, which would have increased the average) the average total length of the characteristic bars (4.4175 mm) is significantly longer than the average total length of undisputed paragraphoi (3.762 mm).

    Remember that my NTS article repeatedly refers to five characteristics of the “characteristic bars” and identifies the following characteristics of “characteristic bars” on pp. 620–621:
    1. Each occurs immediately after a distigme.
    2. Each extends noticeably further into the margin than most bars adjacent to distigmai.
    3. Each is noticeably longer than most bars adjacent to distigmai.
    4. Each occurs at the location of a widely recognised, multi-word addition.
    5. A gap at the precise location of this addition follows all seven apparently original characteristic bars.

    By Richard Fellows’ own measurements, none of the other twenty bars adjacent to a distigme, which fulfills the first characteristic, shares more than two of the remaining four characteristics. Since my statistical probability analysis was based on comparing “characteristic bars” according to this definition, Richard Fellows’ measurements have no effect on my statistical probability analysis.

    Therefore, Gurry is incorrect in stating that Payne’s “characteristic bars” are not actually characteristic and in alleging that “There is no clear correlation [between characteristic bars and undisputed paragraphoi].”

    to be continued

  4. Payne response to Gurry, part 3:

    Gurry asserts that I have made “an improper use of measurements in statistics” and compares it to “saying that eating Whataburger will make you 50% happier. It might be true, but measuring happiness in percentages is the wrong way to prove the point.” But nothing in my argument is about “measuring happiness in percentages.” Gurry appeals to a fear of statistics without identifying how my use of statistics is improper.

    We face a simple fact that begs for an explanation. Why do all nine of the bars that fit the definition I have given for characteristic bars, 100% of them, coincide with a multi-word textual variant in the NA28 apparatus even though on average such multi-word NA28 variants occur on average somewhere on a Vaticanus line only once every 31.8 lines of Vaticanus text? The odds of this happening in a random distribution is less than one in 33 trillion (= 33 billion in the UK). This does not appear to be mere coincidence, especially since all nine of them are a particular kind of multi-word textual variant, namely a multi-word addition to the text, and since all eight by the original scribe B have a gap at the exact point on the line where the widely acknowledged, multi-word block of added text occurs.

    To identify the meaning of text critical marks in manuscripts requires finding a pattern. When I initially identified the pattern of distigmai coinciding with the locations of textual variants and demonstrated with chi-square results that showed that the likelihood of these occurring by coincidence is less than one in 10,000, there was also some initial skepticism on the part of people who did not understand what a chi-square test is. Every subsequent study of distigmai in Vaticanus of which I am aware, however, has concluded that they do in fact mark the location of textual variants. This includes a Ph.D. dissertation on the Vaticanus distigmai and Peter Head’s own study.

    I have identified a similar pattern in the use of distigme-obelos symbols in Vaticanus with comparable chi-square test confirmation. My definition has proved to have predictive value since the additional characteristic bar Richard Fellows correctly identified has all five characteristics of characteristic bars. This raises its chi-square value significantly higher than that which I gave in support of my identification of the meaning of a distigme, namely to mark the location of a textual variant. Like all the other characteristic bars by the original scribe of Vaticanus, this one at Mark 6:11 has a gap in the text at the exact location of a widely acknowledged, multi-word (in this case 15 word) addition to the text. One does not need to use any statistical test to know that this is a remarkable pattern and that my explanation of the symbols fits the data perfectly.

    Gurry writes, “Are we to imagine the scribe of 03 using a ruler to make them? Of course not. So a ruler is probably not the right tool for the job.” I never indicated that scribe B used a ruler to measure bars. When looking for patterns we use the tools we have at hand. Should I not use my eyeglasses to look for patterns because scribe B did not use eyeglasses? Should I not use the NA28 apparatus to identify the locations of multi-word additions to the text since scribe B did not have the NA28 apparatus? Should Paul Canart not have used a high-powered, internally lighted loupe to confirm that fifty-one distigmai match the color of original ink on the same page of Vaticanus because scribe B did not have a high-powered, internally lighted loupe?

    to be continued

  5. Payne response to Gurry, part 4:

    Gurry writes, “As Pete Head says, ‘I don’t think the length of the bars or their distance from anything is of any significance whatsoever. These are written by hand!’” Peter Head can think what he likes. He also still asserts that distigmai are from the sixteenth century even though he has seen the photograph of a distigme at the location of known Greek textual variant in the fourth or fifth century LXX G and even though Paul Canart has identified fifty-one distigmai that match the original ink apricot color of Vaticanus and has identified some distigmai with apricot color-ink protruding from under dark-chocolate brown ink matching the color of the reinking of Vaticanus ca. AD 1000. There is even one distigme with one apricot color dot and one dark-chocolate color dot shown in normal and enlarged photographs in Plate 8 of Le manuscrit B de la Bible. David Parker also rejected a 16th century dating of the distigmai in ‘Through a Screen Darkly: Digital Texts and the New Testament’, JSNT (2003) 395–411 at 408 n. 17.

    Thinking that “the length of the bars or their distance from anything is of any significance whatsoever” does not explain the extraordinary 100% coincidence of the nine characteristic bars adjacent to a distigme with a multi-word textual variant listed in NA28. Remember that by Richard Fellows’ own measurements the nine characteristic bars are on average over 50% longer than the twenty undisputed paragraphoi adjacent to a distigme. Is this all mere coincidence? Anyone who quibbles that one or two undisputed paragraphoi might by a tiny fraction of a mm be slightly longer and have slightly greater extension into the margin that the shortest characteristic bar should take heed to Peter Head’s comment, “These are written by hand!”

  6. Philip, just real quickly on your five characteristics. 1 is coincidence; 2-3 are imagined rather than real and the need to use millimeters just proves the point; 4 is anachronistic since the NA28 apparatus was not widely recognized when 03 was produced; 5 is merely noting what we already knew about 03 in that it has two ways of marking the same thing, namely, a paragraph break. Therefore it is incorrect to say there are five characteristics of your "characteristic bars." There are none.

  7. Payne response to Gurry, part 1:

    I agree that characteristic1 is coincidence only for the undisputed paragraphoi. In contrast, it is statistically implausible that the combination of these five features is mere coincidence for the distigme adjacent to characteristic bars. The standard use of obeloi in Greek literature, including use by scribe B in Vaticanus, namely to mark the location of added text, makes it a natural complement to the distigme. The Vaticanus distigmai mark the location of textual variants of any sort. The addition of the obelos specifies that the variant is a block of added text. This use, then, is not coincidence, but deliberate addition of the obelos to mark the location a of specific kind of textual variant, namely a block of added text. The exact location of that block of added text is identified by the following gap in the text that only the original scribe could leave. It is this combination of characteristics that in 100% of their occurrences identifies the exact location of a widely acknowledged, multi-word block of added text that makes the claim of mere coincidence implausible.

    Richard Fellows’ own measurements confirm that characteristics 2 and 3 are not imagined rather than real. I challenge anyone to identify any other graphic feature in Vaticanus that can be similarly distinguished by a subset containing at least 9 members of a set containing at least 29 members where the subset is on average over 50% greater in some respect (here extension into the margin) than the remaining members of the set and where 100% of the members of the subset share a significant characteristic (here all coinciding with a multi-word NA28 textual variant) that only 10% of the remaining members of the set share and where the graphic distinction of the subset is unrelated to the significant characteristic. This is not an imagined difference. It is an obvious and easily confirmed difference.

    to be continued

  8. Payne response to Gurry, part 2:

    Characteristic 4 is not anachronistic. It is irrelevant that the NA28 apparatus was not widely recognized when 03 was produced, as you should know since I explained this in my NTS article pages 611-612. The NA28 apparatus is an appropriate basis for assessing whether distigme-obelos symbols are text-critical symbols since NA28 identifies ‘variants of text-historical
    relevance’ (NA28, 49*). Multi-word additions have undisputed importance in their text-historical relevance. Scribe B marked added text in the LXX prophets with obeloi and explanations that text was added. This proves he or she regarded blocks of added text as significant. ‘Or she’ reflects Eusebius’ record of the employment o ‘girls skilled in penmanship’ in Origen’s scriptorium at Caesarea, Eusebius, Hist. eccl. 6.32.2 (trans. J. Oulton, LCL, 1959) II.69–69.

    B. Ehrman, as others, argues that ‘even readings that are not attested in the fragmentary remains of the ante-Nicene age ... are by and large best understood as deriving from documents of the first three centuries ... The vast majority of all textual variants originated during … the second and third centuries.’ B. Ehrman, The Orthodox Corruption of Scripture: The Effect of Early Christological Controversies on the Text of the New Testament (2nd. ed.; Oxford: Oxford University Press, 2011) 33. Cf., similarly, E. Colwell, ‘The Origin of Texttypes of New Testament Manuscripts’, Early Christian Origins: Studies in Honor of Harold R. Willoughby (ed. A. Wikgren; Chicago: Quadrangle, 1961) 128–38, at 138 and B. Aland, ‘Die Münsteraner Arbeit am Text des Neuen Testaments und ihr Beitrag für die frühe Überlieferung des 2. Jahrhunderts: Eine methodologische Betrachtung’, Gospel Traditions in the Second Century: Origins, Recensions, Text, and Transmission (ed. W. Petersen; Notre Dame/London: University of Notre Dame, 1989) 55–70, at 65, ‘Fast alle Varianten, die in den Papyri vorkommen, waren vorher schon aus späteren Handschriften bekannt.’ This highlights the value of the NA28 apparatus for identifying early textual variants. Surely, you do not dispute that the NA28 is an excellent source for identifying early multi-word additions to the text or that scribe B was clearly interested in multi-word textual variants, do you? Scribe B proves this interest by using the obelos to mark multi-word additions throughout the prophetic books and even marks the location of five additional places of added text where there is no obelos in the Vaticanus text. My use of NA28 is not anachronistic. It is precisely the kind of use for which NA28 was created.

    Regarding characteristic 5 you write, “5 is merely noting what we already knew about 03 in that it has two ways of marking the same thing, namely, a paragraph break.” You mischaracterize characteristic five, which is: “5. A gap at the precise location of this addition follows all seven [now eight with Mark 6:11, 1285B] apparently original characteristic bars.” You write as though this characteristic were merely “5. a gap.” The point of characteristic 5 is not merely that there is a gap in the line following these eight distigme + characteristic bar combinations, but most importantly that that gap occurs “at the precise location of this addition.” This makes this characteristic a very precise and limiting characteristic.

    Your final assertion is: “Therefore it is incorrect to say there are five characteristics of your "characteristic bars." There are none.” As I have shown above and in detail in my NTS article, each of the characteristics does, indeed, describe the characteristic bars. None of the twenty undisputed paragraphoi, which I acknowledge do fulfill the first characteristic by coincidence, share more than two of the remaining four characteristics. It is precisely the ability of these characteristics to distinguish between these two groups (characteristic bars and undisputed paragraphoi) that demonstrates that they are meaningful and practically useful characteristics.

  9. Thanks, Philip. Your position is quite clear at this point. I will leave it to others now to decide whether they think your "bars" are something other than normal paragraphoi.

  10. In order to better understand Payne's arguments, I took a look at Turner's comments on the use of the paragraphus and spacing in Greek MSS. The following are quotations from Turner and Parson's "Greek Manuscripts of the Ancient World," 2nd edition. I highlighted the relevant comments by enclosing words in double brackets.

    "A space deliberately left blank is also to be considered as a mode of punctuation. Its purpose may be to seperate lemma (a passage quoted in order that it may be explained) from a comment (58), [[ to close a period (54, 60, 69; used in conjunction with a paragraphys, 55, 57) ]] , or to indicate a change of speaker in dramatic texts." (page 10 in the Introduction)

    "The paragraphus takes the form of a simple horizontal stroke placed between the lines of writing. It is usually placed below the line to be marked. In the form 'paragraphe' this term is used by Isocrates. The sign appears in our oldest papyri: in 51, the Thessaloniku papyrus from Derveni (iv liii B.C.), it serves to separate a quoted hexameter verse from the surrounding prose; in 52 (tragedy, early iii B.C.) it marks a change of speakee. In dramatic texts thereafter this is its regular function, whether in tragedy (24, 26-9, 31-4), comedy or Platonic dialogue (19). In hexameter verses it may show the end of a section (11), in lyric verses a division into stanzas or inside the triadic structure (17; 15, 21, 22, 74); [[ in prose, either alone or in conjunction with a space (55, 57) or an oblique dash (66) in the line it marks the end of a section. ]] In documents it may divide sections of an account (88) or a letter (P. Lond VII 2008, 247 B.C.) or a law-code, or separate the subscriptio from the text." (page 10 in the Introduction)

    I understand that GMAW is merely an introductory work on palaeography and does not replace specific detailed study of individual MSS such as Vaticanus. With that said, I want to highlight that in prose texts a paragraphus traditionally marks changes in the story, i.e.a new paragraph, and the paragraphusis sometimes used in conjunction with a space in the text (but not always) to mark these changes in the story, just exactly as we find them being used in Vaticanus. If Payne is correct, then, the use of a paragraphus to mark a textual variation would be outside the traditional use of this scribal device. Its use in the manner Payne suggests would be lost to probably every user of Vaticanus outside of the original scribes. As has already been stated in the ETC blog comments, for such an interpretation to hold true one would expect introductory material on the level of Eusebian Canon Tables in Vaticanus. Obviously no such table is known to have existed in the MS. If one postulates something like an introductory key to these textual markings to have existed in Codex B, it would be unique indeed.

    Another item that has been noted already by others in the comments of the ETC blog are the very small differences in the horizontal line length between each paragraphus. We are talking about a difference of approximately 1 millimeter. Using a calibrated Digital Caliper measuring tool, I measured the ballpoint pen that I currently have in my pocket at exactly 1 millimeter. Thus, the graphic characteristic of the horizontal that is postulated to visually highlight a textual variation is the width of the tip of a modern ballpoint pen. If we take into consideration the width of a 4th century reed used in the production of Vaticanus, the writing point very well may have been greater than 1 millimeter. Therefore, it is very difficult to interpret these differences in length as deliberate scribal attempts at highlighting textual variation and are more likely normal variation that is to be expected in a hand written document.

    1. I appologize for the typos. Hopefully the points being made are understood in spite of my typing mustakes.

    2. To add to my lengthy comments above, I measured a line drawn with this same ball-point pen between 0.85-0.95 millimeters in width.

  11. Peter Head wrote to me that gaps in the text and paragraphoi appear both to have the same purpose of marking a pause in the thought of the text. The gaps are undoubtedly part of the original composition of Vaticanus. Head argues that since the bars are occasionally independent of gaps in the Vaticanus text, they are a later addition to the text, not part of its original production. In going through the Vaticanus New Testsament again, I found many lines where there is a paragraphos but not a gap, many lines where there is a gap but not a paragraphos, and many lines having both a gap and a paragraphos. The problem with regarding the paragraphoi as part of the original composition of Vaticanus is not just that they are redundant with gaps on the same line, but that they convey differing judgments about where to break the text in every instance where only one occurs. Unless patterns can be documented that explain distinct purposes for the paragraphoi from the gaps and that also explain all their differing locations, the gaps and paragraphoi do appear to preserve differing judgments regarding where to break the text. This supports Peter Head’s view that the paragraphoi were not part of the original composition of Vaticanus.

    Only scribe B could put these eleven gaps in the text at the exact location of these eleven multi-word additions, and the original apricot color ink in three of their distigmai and one of their obelos portions supports scribe B as their source. Since the obelos is standard symbol scribe B used to mark blocks of added text and since all eleven of the characteristic bars coincide with block of added text at the exact point scribe B left a gap in these eleven lines, scribe B is the natural source for both these eleven gaps and their associated distigme-obelos symbols that explain what occurs at the gap. If that is the case, there could have been no confusion originally between the obeloi in distigme-obelos symbols and paragraphoi since there were no paragraphoi in Vaticanus then.

    The only case in which it would make sense for both the paragraphoi and obeloi to be present in the original production of Vaticanus is if they were both present in each of the exemplars scribe B was copying. If that were the case, this would be just one more example of scribe B faithfully copying each exemplar, even though it preserved different judgments as to where to break the text. But since that would require each of Vaticanus’s exemplars to have both gaps and paragraphoi entailing both redundancy and differing judgments, it seems more likely that when scribe B penned the distigme-obelos symbols there were no paragraphoi with which the obeloi could be confused.

    Consequently, although the ‘characteristic bars’ are what led me to identify them as part of distigme-obelos symbols, their extra extension into the margin—over 50% greater on average—compared to the undisputed paragraphoi probably had no relationship originally to the paragraphoi. Nevertheless, these characteristic features of the distigme-obelos symbols are of great value to us in confirming that they are not simply paragraphoi that just happened to occur adjacent to a distigme.