Subject: Re: Statistical patterns

From: Timothy John Finney <[email-masked]>
Date: Mon, 1 Sep 1997 17:49:19 +0800 (WST)

Here are the figures which I alluded to before:

NOS = number of states = number of readings in a variation unit.
FRQ = frequency = how often a given number of states occurs in the sampled 
variation units.
FIT = fitted value using the equation F(n) = C x exp[-(a + bn)^2/2], C = 
399, a = 1.50, b = 0.23.

Hebrews + Romans (for variation units listed in the UBS 4th edn apparatus)

NOS	1	2	3	4	5	6	7+

FRQ	?	58	36	21	11	5	3
FIT	89	58	36	21	12	6	6

As you can see, the fit is quite good for 2 to 6 states.

Jimmy Adair is right to point out that the curves that are generated will
depend to a very large extent on the sampling technique. If there is an
underlying law which obeys this equation, then using a different edition,
or simply widening the scope from Hebrews and Romans to the whole Pauline
corpus in the UBS edition, will change the constants of the equation but
not its shape. In other words, changing the sample size or sampling 
technique will generate new members of one family of equations.

Bob Waltz is right to say that the definition of a variation unit will
also affect the results. This is a sticky problem. (Perhaps someone will
one day come up with an indisputable way of defining the density of
variation at consecutive places in the text). Nevertheless, no matter how
the UBS Committee arrived at the given arrangements of variation units and
their readings, it still seems strange to me that they should appear to
fit such an equation. Hence my request for a statistician to enlighten us
concerning possible causes. 

On the significance of the predicted 89 units with 1 state, I take this to
mean that if 228 sections of the UBS text (89 + 58 + 36 + 21 + 12 + 6 + 6)
with a certain standard size were examined, on average 89 (39%) would
display no variation, 58 (25%) would have two possible readings, 36 (16%)
would have three, and so on. Romans and Hebrews together have about 12,036
words, resulting in this standard size being about 53 words. 

One last note. The figure of 6 I inserted for 7 or more states is the sum 
to infinity of a geometric progression which starts with half the 
preceding value of 6 and halves at every step (3 + 1.5 + .75 + ... = 6).

Best regards,

Tim Finney

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

---

From: "Robert B. Waltz" <[email-masked]>
Date: Mon, 1 Sep 1997 14:03:14 -0500 (CDT)

On Mon, 1 Sep 1997, Timothy John Finney <[email-masked]>

>As you can see, the fit is quite good for 2 to 6 states.

Almost too good to be true. :-) But I'll return to this point below.

>concerning possible causes. 

As an experiment, I took a bunch of data which I had on hand --
the readings of all uncials and papyri, plus the minuscules 330 1739,
in Colossians 1. This proved to be a bit more complicated than
it sounds, because of nonsense readings and scribal errors. I did
my best to treat these realistically, and came up with the following
numbers (out of 71 variants):

NOS	1	2	3	4	5	6	7+
FRQ	-	49      17      3       2       0       0

Let's rewrite the above formula as my calculator understands it:

                       2
          -(.23n + 1.5)
          --------------
                2
FIT = 399 e

This gives a total of 58+36+21+12+6+6 = 139 readings.

Normalizing to percents gives us

NOS	1	2	3	4	5	6	7+
FIT	-	42	26	15	9	4	4

Over 71 readings, this gives us
NOS             2       3       4       5+
Expected        30      18      11      12
Actual          49      17      3       2

So the fit doesn't work -- although I agree that the data does look
exponential. (I'm too lazy to fit my own data. :-)

The problem is, we are dealing with *three* variables:

1. The definition of a variant
2. The method of selecting variants
3. The number and nature of the manuscripts in the sample set.

Given that (1) had a vague definition, (2) has as yet no definition
at all, and (3) is something that needs to be explored, perhaps we
shouldn't expect much at this point.

Also keep in mind that we are dealing with very few data points here --
in Tim's set, only six (data for 2, 3, 4, 5, 6, and 7+-order variants);
in mine, an even smaller 4-point data set (or, arguably, 5; we could
throw in the results for 6+).

I suspect Tim is right, and there is an exponential fall-off. But
with only six data points, and a monotonically decreasing function,
we could get a good fit for an exponential even if the actual function
were of some other form.

Now note: I think this is a very important subject to pursue. The
mean number of significant variant readings at each point of
variation has an immense impact on the statistics we can use to
compare manuscripts. I just think we need a greater degree of
rigour here (sorry, Tim. :-)

>words, resulting in this standard size being about 53 words. 

I think this last is a statement that needs to be clarified. Your
actual claim is that 39% of your 53 word samples would show *no variant
of interest to the UBS committee*. (The fact is, of course, that there
are variants in just about every word of the NT). But this, in turn,
gives us some problems. There are instances in the UBS text of as
many as 3 variants in a single verse. (UBS3 had four variants in
Hebrews 13:21; one of them was dropped in UBS4). Taking Hebrews 13:21
as an example, the verse is 30 words long. The variants show
3, 2, and 2 readings. Would this be considered a single point
of variation with 12 readings (3x2x2) or something else?

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

                        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: "Dale M. Wheeler" <[email-masked]>
Date: Mon, 01 Sep 1997 12:18:54 -0700

David Washburn wrote:

>Isaiah 53:8 has LFMOW in the last clause, in parallel with a bunch of 
>singular verbs and pronouns in the rest of the verse.  Some 
>investigation revealed several places, such as Gen 9:25 and 26, where 
>this word can appear to have a singular meaning even though 
>"standard" grammars such as GKC list it as a plural.  

GKC #103f, n. 3 and 91,l,3 notes that in some cases this form *must* be
singular (eg., Isa 44:15).

Waltke-O'Connor 11.1.2d just says that it can either be singular or
plural, with the singular "...'to him'(as if lemo + pronoun -o..." and 
the plural "...'to them' (as if le + pronoun -hem/-am..."

The enclitic mem (W-O'C 9.8) is not all that uncommon with prepositions, 
eg., B.:MOW, K.:MOW, MIM.EN.W.

>Recently, I 
>also noticed that the Westminster BHS Morph database consistently 
>lists it as L with a singular pronoun suffix.  

This is one of those things that I'm fixing in the MorphBHS revision
I'm currently doing; namely, I'm changing those which are plural to
plural and leaving the ones that are singular as singular (some are
clearly judgment calls, and you all will be at the mercy of my 
judgment for this next release...in the following release, I'll be 
putting for the first time alternates into the MorphBHS and so those
will have alternates tags).

>Conventional wisdom 
>suggests that it is consistently a plural, and hence translate the 
>last clause of v.8 as "the judgment of my people, to whom [plural] 
>the stroke was due."  I have doubts about the translation, and there 
>is also a significant textual variant there.  But before addressing 
>my thoughts on the variant, I wonder if anybody on the list has more 
>solid info on the singular/plural nature of the word as it stands in 
>MT.

I personally don't have a problem with the translation of the last
clause as "...because of [MIN] the transgression of my people [he 
received the] stroke due [or "for", ie., advantage] them."

Aside from the GKC, etc., info, there is a lot of discussion about 
this in KBS, in which LFMOW is listed as a *separate* word/lemma (??), 
with copious references to several grammars and articles.

>My thought is that it is sort of an elision or phonetic ellipsis, 
>kind of like the English phoneme 'm.  If one says "I'll go get 'm" 
>context is necessary to know whether 'm is standing for "him" or 
>"them."  My initial reaction is that LFMOW is a similar phenomenon, 
>but I have no idea how strongly this idea might be supported by other 
>grammatical-transcriptional features of the actual text.

Such elisions would normally be the result of speakers hurrying the
pronounciation of some word and thus would historically follow the
occurrence of the word being shortened.  GKC seems pretty sure that
the LFMOW form is an ancient form of suffix which has been dropped
in later Classical Hebrew, and only re-appears in the poets because
they are trying to "sound" old or archaic or "high" in their 
language.  W-O'C p. 189, n. 5, point out that Ugaritic also has
the long variant form of bm, km, and lm.

I really don't see much reason to resort to the LXX variant here.

XAIREIN...

***********************************************************************
Dale M. Wheeler, Th.D.
Research Professor in Biblical Languages        Multnomah Bible College
8435 NE Glisan Street                               Portland, OR  97220
Voice: 503-251-6416    FAX:503-254-1268     E-Mail: [email-masked] 
***********************************************************************

---

From: Jim Deardorff <[email-masked]>
Date: Mon, 1 Sep 1997 13:21:32 -0700 (PDT)

> As you can see, the fit is quite good for 2 to 6 states.

Tim,

You do have an excellent fitting equation there.  But with four parameters
at your disposal, (C, a, b, and the ^2 rather than some other power), and
only 5 or 6 data points, it had better fit pretty well! 

The amount of data you have above is around 50% (though still less in one
case) of what the Gospel parallels provide for duplicate word strings.  If
it were of comparable length, it's quite possible that if you were to
require a fit by a two-parameter curve, the simple exponential or
geometric progression would work better than anything else, once you
decided on just what the rules are for counting variants, etc.

But I don't see what gain in knowledge that would produce.  Surely those
verses or sentences that exhibit an unusally large number of variants will
be relatively rare, if for no other reason than from definition of
"unusual."  So you're almost bound to find some monotonically decreasing
curve that will approximate the distribution.  In one case the very few
rare values of FRQ=1 or 2 for large n may occur at n = 8,9, and 11, say,
and in another at n = 8,10 & 13, say -- this I have been referring to as
"sampling error." 

Although a similar statement could be said of the Gospels' duplicate
word-string parallels, there we run into the peculiarity that what occurs
in the region you labelled "7+" exhibits far too many occurrences to be at
all consonant with the monotonic fall-off shown for n=3,4,5,6. 

After finding zero occurrences for n = 8 or 10 or 12, do you then notice
one or two instances of an occurrence for n=13 and another for n=16 and
17? If so, I think you'd be interested in knowing why -- was the sentence
so difficult to understand, relative to almost all other sentences in the
gospel/book, that it caused a huge number of variants?  Or was the grammar
of the sentence so bad in the earliest ms that it caused later dependent
mss to correct it in many various ways?  If so, why were these anomalous
sentences so much more anomalous than others that it caused a disruption
in the monotonic decrease of FRQ with n, with an upturn after many zeroes? 
Or can such anomalies be simply explained as inevitable sampling error? 

With the Gospels' duplicate word-string parallels, one can also examine
the anomalies, with the importance being that one can see if they fit into
any proposed solutions of the Synoptic Problem -- bolster one and rule
others out.  Although this latter problem may not be of particular
interest to TC, I still wonder if TC can hazard any guesses as to whether
or not harmonistic corruption could have caused the anomalies in the
frequency distribution at large values of n or "I," as I called it.

Jim Deardorff