Subject: Mathematical Error

From: [email-masked] (Robert B. Waltz)
Date: Fri, 7 Jun 96 16:01 CDT

TCers --

Once again, I pay the price for trying to think too quickly. In this
case, the price was a mathematical error concerning the rate at
which manuscripts would have to be destroyed.

This time I'll give you the correct figure, *and* the reasoning, so you
can perhaps apply it to other samples.

Let r be the probability that anu random manuscript will be destroyed.
(Thus 1-r is the probability of its survival to the present day.)
This is, of course, a simplistic assumption; older manuscripts are
more likely to be destroyed. But this doesn't affect the argument
much.

The odds of *both of two* manuscripts being destroyed is thus r
squared, for all of three mansuscripts is r cubed, and so forth. In
general, for any n, the odds of all three being destroyed is r to
the nth power.

So for any set of n manuscripts, the odds of at least one surviving
is one minus r to the nth power.

If we choose n=100 and want at least a 5% chance of all manuscripts
being destroyed (the usual cutoff used by statisticians), we must solve
the equation

     100
1 - r    = .95

This gives us a "destruction rate" of 97% -- that is, at least 97%
of the manuscripts must be destroyed to have a 5% chance of all
100 being destroyed.

If we want a 50% chance of all 100 being destroyed, we find r
to be 99.3%.

So the destruction rate needed to observe the behavior found by
Lake, Blake, and New, while high, is not impossible.

***

Now let's see how many other comments I can respond to before I have
to get back to work....

Holmes:

>2) Virtually all of us, I would argue, are "reasoned eclectics" with regard
>to method (for definitions, see pp. 336-338)--i.e., we utilize some
>combination of internal and external considerations in reaching decisions
>about textual variants.  In contrast to a "rigorous eclecticism" which
>essentially eschews external evidence (e.g., Keith Elliott) or a "historical
>documentary" approach which attempts to avoid internal considerations (e.g.,
>Dearing), the rest of us appear to utilize a combination of both kinds of
>evidence--e.g., Robinson again (4:57 p.m., 6/4/96): "in light of both
>internal and external evidence."  In terms of method, we are all
>"eclectics," and for some to position themselves over against "the eclectic
>school" (or some such term)--as if they were not part of it--creates
>confusion.  The central locus of our differences is not with regard to
>method, but with regard to the history of transmission.  The *method*
>outlined by, e.g., the Alands, Metzger, Colwell, Amphoux, Fee, Holmes, etc.
>(see p. 344)--and, I would suggest, Robinson and Waltz--is very, very
>similar.  The differences in the view of the history of the text among this
>same group, however, are tremendous; a comparison of Kurt Aland and Amphoux
>is esp. instructive in this regard (cf. p. 350).  There is no such thing as
>"*the* eclectic hypothesis" (M. Robinson, 9:47 p.m., 6/6/96; emphasis
>added)--i.e., a single view of transmission history held by all those who
>utilize a "reasoned eclectic" methodology.

Nice to see somebody *finally* quoting a book that's actually in my
own personal library. :-)

For the most part I would agree with this comment. But -- technically
speaking -- it is not true of my method (nor, as Robinson's rejoinder
shows, of his). *Most* of the time I apply both internal and external
criteria (with a bias toward the latter). However, there are instances
in which I do not apply internal criteria at all: the cases where all
pre-Byzantine text-types agree. Similarly Robinson: If the Byzantine
text is united, he does not apply internal criteria.

Still, I will not really argue with the label. I at least agree with
Holmes (against Robinson) that variations are to be dealt with on a
case-by-case basis. I just have unusually strict criteria for where
I apply internal evidence.

>4) The critical question for textual criticism today--and here the
>discussion started by Robinson and Waltz is right on target--is precisely
>the history of the text.

Glad somebody remembers where we all started. :-)

>In particular, I would interested to
>hear what some of the discussants have to say about Wachtel's recent and
>wide-ranging treatment of the Byzantine tradition. (Thumbnail sketch of
>Wachtel: the Byz text of the Cath Epistles is the result of a long process
>[traces of which are evident already in the earliest period] of smoothing
>and standardization, and reached its definitive form in the ninth c.  It is
>very unlikely that its origin is the result of a formal recension of the
>fourth century; instead, one must reckon with a series of editorial
>revisions [i.e., _diorthosis_] in every epoch.  His findings substantially
>relativize the idea of "text types," to the extent that they are associated
>with recensional theories, and highlight the importance of the minuscules.)

Unfortunately, I have not seen the article, so I cannot comment directly.
But I will admit to that it surprises me. From what I have seen -- and
I will admit that this is based mostly on manuscripts, with very little
examination of the Church Fathers -- there is almost no hint of the
Byzantine text in the Catholics before the ninth century. Whereas, in
the gospels, a text that is about 80% of the way to a full-blown
Byzantine text appears in the fifth century in A and W, supported
by the purple uncials in the sixth century. Admittedly in the case
of the gospels there was further evolution between the fifth and
ninth centuries (e.g. the insertion of the story of the adulteress),
but most of the action was before that date.

>5) The role of scribes in the transmission of the NT text has come up in the
>last few days.  In light of what can be learned about how books were made
>and read in the ancient world, t may be that the traditional focus in NT
>textual criticism on scribes as "shapers" of the text is misplaced.  In a
>lecture given in 1994 (due out any time now in a volume from Brill edited by
>David Parker and C.-B. Amphoux) it was suggested that active reader/users,
>practicing the customary and expected activity of _diorthosis_, may have
>been responsible for many of the distinctive variant readings associated
>with the "western" textual tradition.  Now Wachtel makes a similar point, as
>has Harry Gamble (_Books and Readers in the Early Church_ [Yale, 1995]).
>This reminds us that not only scribes and the scriptorium but also readers
>and the church were important factors in the tranmission of the NT.  How
>might this consideration reshape how we envision the transmission history of
>the NT?

This strikes me as reasonable. I can think of at least one instance
where (please note: this is a *wild* speculation) it *may* have led
to the dissemination of a whole new text-type. I'm thinking of the
Photian schism, which (if I read my very unclear history books
correctly) had to do in part with the purity of the clergy. This
might possibly revive interest in Origen -- and lo and behold,
shortly after the Photian schism ended, we find a number of manuscripts
with a rather "Origenic" type of text. (Those manuscripts being the
members of family 1739.) I repeat -- wild speculation, but a possible
instance of the above.

Schmid:

>I should point out that I stressed the influence matter to the
>extreme in order to emphasize the problems involved. Assuming
>influence from (other) text-types implies by consequence the
>assumption of existing text-types. But text-types are exactly what
>we are trying to define. It is by no means clear that we all refer
>to the same "thing". May be you can refrain from the logical
>implications (letting the historical problems aside) of
>"influence", I simply cannot. Text-types, the least one can say, refer to a
>certain distinct _pattern_ of readings. Even within the Byzantine "text-type"
>slightly different patterns are detectable. So, to my mind, the question
>is what
>distinct _pattern_ of readings makes for example the Peshitta the "earliest
>substantial witness" for the Byz. text of the Gospels (Bob on Thu, 6 June
>1996)?

This is one of the things I was hinting at in my later discussion on this
subject. It's a difficult matter -- if we take our earliest proto-Byzantine
witnesses (A, N, W, Peshitta), we find that all agree with the later
Byzantine text 80% of the time or more (in my sample, anyway) -- but they
don't agree at the same points. This could indicate that all have been
influenced by the Byzantine text in different places -- but also that they
have been influenced by different forms of that text. I cannot see how
to prove the matter one way or another.

Unless I am to understand from this that Ulrich Schmid does *not* consider
the Peshitta to be primarily Byzantine.

Robinson also comments on this general topic:

>But A and W (not the root beer), with their early date and substantially
>Byzantine texts, do imply the existence of earlier complete exemplars (at
>least of the gospels) with a substantially Byzantine text in their
>respective regions of copying (and I see a clear Egyptian hand in A, with
>a more Armenian-style hand in W).

I agree that A has a rather "Egyptian" feel -- indeed, I would speculate
(here I go again....) that A was based on a *more* Byzantine model that
was sporadically corrected toward the Alexandrian text. I say this because
A is disproportionally Alexandrian on big, obvious readings (e.g. Luke
22:43-44) -- the kind of variation that even the most casual scribe could
not overlook. Of course, this could just be block mixture.

But, as noted, I can't see how this affects how we reconstruct the Byzantine
text.

Robinson, on a different subject:

>> It could certainly be argued that this has happened with the NT text
>> as well. The best example is the ending of Mark. Without saying which
>> is original, it is clear that two major forms circulated -- with and
>> without 16:9-20. But the longer form clearly prevailed because it
>> was *superior* -- i.e. it looked complete.
>
>The question of "circulated" is debatable.  With only 3 Greek MSS omitting
>the long ending entirely, one has to wonder as to how extensively this
>form ever did "circulate".  Even the forms with the shorter ending appear
>in only a handful of Greek MSS, and then in conjunction with the long
>ending, so it may be questioned whether even that ending (which would
>also have "looked complete") really had much independent circulation
>beyond it-k or possibly some few Old Latin companion MSS.  My view is
>much simpler: the longer form prevailed because it was in fact part of
>the originally-circulated form of Mark, and later competing readings
>never really gained much popularity, let alone any ascendancy.

This argument isn't based on originality. All I am saying is that the
longer ending will tend to survive by "natural selection."

Carlson:

>I think it is too reductionistic to examine the effects of Diocletian's
>persecution as yet another persecution (albeit a longer and perhaps harsher
>one) and of Constantine's liberalization without regard to the fact that
>they occurred within decades of each other.  We have the collocation of
>one of the longest and harshest persecutions (one that did target the
>Scriptures) and one of the most permissive legal treatments of
>Christianity in centuries.
>
>The two events jointly have a greater impact than what one would
>conclude by examining them separately.  In other words, I understand
>Diocletian's persecution together with the nearly immediate legalization
>of Christianity by Constantine to be part of the same "bottleneck."

I'm willing to accept this view -- but in that case, we need once
again to look at the Decian persecution. The situation was almost
identical: A relatively severe persecution (the worst experienced to
that point), followed *immediately* by Gallienus's edict of toleration,
which provided the Christians with more security than they had ever had
until that time.

Robinson again, on Holmes

>>The *method* outlined by, e.g., the Alands, Metzger, Colwell, Amphoux,
>>Fee, Holmes, etc....-- and, I would suggest, Robinson and Waltz--is
>>very, very similar.
>
>As regards myself, I really think not, in light of what I have stated
>above.  Wallace similarly thinks not, and (I suspect) Ehrman would
>concur with me on this point.  I will cheerfully place all others in
>the same bucket if that is where they want to be *;-)  Waltz of course
>seems to be in neither category.

Gee, thanks. What, then, does that make me (other than obviously insane)?

Sorry, I couldn't pass up making *some* sort of comment on this. :-)

Robinson again:

>I appreciate the comment, but I more than anyone else realize how
>undeveloped and unexplored is the territory within my theory.  Just so
>long as it clearly gets differentiated from the KJV/TR crowd, as well
>as from that of Pickering or Hodges/Farstad, I will be content.

If nothing else, I sympathise with Maurice. The fact that his *result*
looks, to us outsiders, much like Hodges/Farstad does not mean that
his methods are similar. Just as I *do* feel some distance from, say,
Aland and Metzger, even if my text agrees with their fairly frequently.

And with that, I had better get back to the outside world.

Bob Waltz
[email-masked]