Subject: Statistical patterns

From: Timothy John Finney <[email-masked]>
Date: Thu, 28 Aug 1997 10:56:36 +0800 (WST)

Jim Deardorff has noticed a statistical pattern in the frequency of 
long parallel strings. I have noticed a similar pattern in the frequency 
of the number of readings in a variation unit.

Taking the forty four variation units in Hebrews that are given in the 
UBS edition, there are 22 with two possibilities, 11 with three 
possibilities, 6 with four, 3 with 5, and so on.

Noting this apparent geometric progression, I counted the variation units
in Romans and added them to the picture. I can't remember the exact
figures off hand, but they did not form a geometric progression and looked
a bit like a Fibonacci series. After much trying of distributions, I found
that the numbers did not fit the Poisson distribution, as one might expect
for accidental events, but fitted a transformed Gaussian distribution i.e.
N = A exp -(a - bx)^2, where N is the number of variation units with x
readings. I have worked out A, a, and b, but I haven't got those here either.

Strange, isn't it? Any statisticians out there who can explain why the 
number of readings in a variation unit appear to obey such a law?

Best regards,

Tim Finney

[email-masked]
Baptist Theological College
and Murdoch University
Perth, W. Australia

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From: "James R. Adair" <[email-masked]>
Date: Wed, 27 Aug 1997 23:38:35 -0400 (EDT)

> possibilities, 6 with four, 3 with 5, and so on.

My initial impression for why the number of variants in a variation unit
seem to follow Fibonacci or transformed Gaussian patterns (and I'd have to
look up the latter!) is that it is largely accidental.  If instead of
analyzing the variation units in the UBS apparatus you look at those in
the NA-27 apparatus, your numbers will change completely, and I would
guess that the curve would be different as well.  Again, if you look at
the apparatus of a major critical edition, the curve will change once
again, although I think the curve that you would get from examining
Tischendorf or Von Soden or IGNTP would be more meaningful than UBS.
Although it may be that variation units with small numbers of variants are
more common than those with large numbers, the curves that are generated
will depend to a very large extent on the sampling technique: how many mss
do you collate? do you count purely orthographic variants? how do you
group clusters of variants?  Finally, if we do find that plotting the
number of variants in the variation units throughout a NT book produces a
curve that can be approximated by some mathematical formula, what are the
implications of this discovery?

Jimmy Adair
Manager of Information Technology Services, Scholars Press
    and
Managing Editor of TELA, the Scholars Press World Wide Web Site
---------------> http://scholar.cc.emory.edu <-----------------

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From: "Robert B. Waltz" <[email-masked]>
Date: Thu, 28 Aug 1997 07:35:36 -0500 (CDT)

On Thu, 28 Aug 1997, Timothy John Finney <[email-masked]>
wrote:

[ ... ]

>implications of this discovery?

Several comments on this (since it's a subject I've looked at in some
depth). First, Tim's sample is small, so a pattern might not tell us
much. But more important is the question of "What is a variant?"
This has been dealt with elsewhere, but just take the case of
O (DE/GAR) (QEOS/LOGOS). One variant with four readings? Or two with
two readings each? The number of readings in a variant will depend
in large measure on the editors of the edition -- e.g. the users of
Claremont Profile Method type systems seem very much to prefer
binary (two-reading) variants.

Then, too, part of the difference between UBS and NA is that UBS cites
many more manuscripts. This will naturally increase the number of
minor variants in lesser manuscripts.

But let's assume, for the sake of the argument, that we have come up
with an absolutely hard-and-fast system for deciding "what is a variant"
(there are several articles in Epp & Fee on this, though I don't think
they've resolved the matter). Let's say that we have created a fixed
list of manuscripts. Assume whatever we need to to get a set of numbers.
What do they mean?

Now we have to remember that there are two sources of readings. One is
ancient readings, of genetic significance. The other is accident. Based
on my observation, variants where there are two readings (except for
haplographic errors) are usually genetic. Variants where there are
four or more, by contrast, almost never fall along text-type lines.
An analogy I have used is that of a crystal: Tap it lightly and it
will break at a facet (a text-type division). To make it break
into four or more pieces, you have to hit it so hard that the crystal,
rather than breaking along facets, *shatters.*

What this shows is that one needs also to examine the nature of variants.
Is it a reading that invites errors of some sort? Is it a difficult
readings that invites corrections? Such will generally have more readings
(I think).

As for Jimmy Adair's question about what this tells us, I think the
answer is that we need to know the distribution first. Potentially it
could tell us something about text-types or scribal habits -- but we
can't base any conclusions simply on the readings in the UBS edition.
Nor even, I would argue, on the readings in NA27, unless we can add
many more manuscripts to the collations.

For what it's worth....

-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-

                        Robert B. Waltz
                     [email-masked]

Want more loudmouthed opinions about textual criticism?
Try my web page: http://www.skypoint.com/~waltzmn
(A site inspired by the Encyclopedia of NT Textual Criticism)

---

From: Jim Deardorff <[email-masked]>
Date: Thu, 28 Aug 1997 17:41:48 -0700 (PDT)

I'm still interested in hearing if any members of this list think that tc
can explain the verbal agreements between Mt-Lk's "Q" verses in which
strings of up to 27 consecutive words are duplicated.  If so, what
might be the most likely means?

Those who work on the synoptic problem but don't buy into the two-document
hypothesis (2DH: Mark-Q priority) believe that redaction criticism (RC) is
responsible for it.  Those who favor the 2DH, however, must feel that tc
can explain it, as they assume that Matthew and Luke were written
independently, and that Matthew was (first) written in Greek and so that
no translator was involved either.  But I've never seen any proposed
explanation of how scribal assimilation or "harmonistic corruptions," as
Metzger refers to it, could leave behind a frequency distribution that
follows the exponential or geometric-progression distribution very well
for Q-verse word strings up to 10 words long, and then deviates radically
from it for the longer strings.  For the one test case I could find in
which independence of the translator/editor can probably be assumed, the
distribution followed the geometric progression all the way out to 10 or
so, with none of these very long strings existing.

I've checked out the 9 longest duplicate strings of "Q" using both N-S 26
and N-S 21, and they stay unchanged during that interval of time.  If any
here are interested, you might look into N-S 27 to see if they survive
there also, unchanged. 

They are:
  27 consecutive, perfectly agreeing, words long: 
      in Mt 11:25-27 & Lk 10:21-22
  26, in Mt 24:50-51 & Lk 12:46
  26, in Mt 6:24     & Lk 16:13
  25, in Mt 8:9-10   & Lk 7:8-9
  24, in Mt 7:7-8    & Lk 11:9-10
  24, in Mt 3:8-10   & Lk 3:8-9
  20, in Mt 3:10     & Lk 3:9
  19, in Mt 11:7-8   & Lk 7:24-25
  16, in Mt 12:42    & Lk 11:31

The excessive word-string lengths continue on down to lengths of 10 or 12
words, below which there are so many more shorter strings that the normal
geometric progression prevails.

>From what I read in Metzger (I hope his book doesn't have very many
serious mistakes; I certainly find it fascinating reading as a beginner in
this field), there are a lot of mechanisms that can cause variant
readings: all the errors that come under the "accidental heading" and
most of the "intentional" scribal errors.  Against these you have the
"harmonistic corruptions."  Is it reasonable to explain the nine verbal
agreements listed above, and another 20 or so, as due to the latter?  One
would then need to explain why a whole host of shorter strings also did
not get harmonized; i.e., why would the scribal harmonization be so
selective?  Although a few of the above nine verses are among the more
memorable discourse verses, others are not. 

I do see this as a problem needing consideration, since various scholars
of the synoptic problem in the past, such as William Farmer, view these
verbal agreements as proving beyond doubt that Matthew and Luke were not
written independently.  The assumption is made that the presently accepted
Gospel text, and that as of a century ago also, are pretty close to the
truth of how the Gospels appeared within a few decades after being
written, regarding the presence of these long duplicated strings.  I tend
to go along with this, but perhaps it places too much reliance upon the
work of text critics in deducing the present majority text?

Jim Deardorff