Subject: Ms half-lives

From: Timothy John Finney <[email-masked]>
Date: Thu, 9 Jan 1997 13:04:07 +0800 (WST)

I sent a message a week ago, but I don't think that it got through to
everyone. D.C. Parker seems to have got it as he says he doesn't believe
that there was a standard life time for a papyrus manuscript. 

Just in case my earlier post didn't get through to everyone, here is a 
summary:

I made a histogram of extant NT papyri and uncials, plotting number vs 
century. (When a ms was dated c. 200 I said it was 2nd C., etc.) Instead 
of seeing a gradual increase in number vs. time, as I was expecting, I 
saw something completely different.

For the papyri, the number increases in what looks like an exponential 
fashion for the 2nd and 3rd centuries, peaks, drops down, peaks again 
around the 6th/7th C. then falls away.

For the uncials, the number peaks around the 4th C. and drops away, but 
flattens out for a couple of later centuries (6th and 7th again?) before 
dropping down to zero.

Upon reflection I interpreted this as follows (thanks to my friend Tim 
Sullivan for suggesting the word saturation):

The papyri picture might be explained in terms of maximum likelihood of 
deposition in the sand, and, consequently, maximum likelihood of digging 
up later, corresponding with a couple of historical events: the 
persecutions of the 3rd C. and the Moslem conquest around 640.

The uncial histogram might be explained as rapid production within an
organisation that has suddenly changed from being illegal and poor (hence
use of papyrus) to being legal and supported. It can be interpreted as
being consistent with large scale parchment scripture production
continuing until saturation was reached in the 5th century i.e. everyone
who had the resources to commission one (probably beyond individuals but
within reach of bishops) had one. After that, production was for new
churches and replacement of worn out mss. 

Now for the contentious point. We have about 18 uncials from the 4th
century. Du Placy estimated 1600 - 2000 mss were produced in the 4th C.
That means a 1% survival rate. At this point my rusty physics suggested
that a situation analogous to radioactive decay was at hand. If 1% of mss
have survived the random destruction process after 1600 years, then
assuming exponential decay (i.e. number lost proportional to number extant
in any given time period) leads to a NT uncial half-life of about 250
years. 

This is an estimate of the average life span. In fact there is an average
life of all NT uncials ever produced. There must be. We don't know it, but
the number I derived is a reasonable estimate provided that the no. of mss
lost in a given time period is proportional to the no. extant in that
period. 

As to how long an individual ms will last, all the wiles that beset mss
will come into play, resulting in some living shorter, some longer than 
this estimate, according to some kind of statistical distribution 
(Gaussian?).

Another point. Looking at the initial rise in numbers, exponential growth
seems to be at play. That is, the rise might be explained as a doubling
every X years. How big is X? Strangely, it is about the same for the
uncials and papyri: just over twenty years. This might be interpreted as
reflecting the doubling time of the Church in Egypt in the 2nd C., but is
probably not much to do with the Church's population in the case of the 
parchments.

And, to the glee of the weary reader, a last point. I did a histogram for
the minuscules given in the UBS4 insert. The same kind of picture emerges
but with a much slower initial growth. The peak is reached at about the
11th C. then drops down again -- perhaps the decline can be interpreted as
due to the contraction of demand for Greek New Testament mss. 

In conclusion, histograms of date vs number for the Greek New Testament mss 
represent samples of the original population. Assuming exponential growth 
and decay of this population allows a doubling time and half-life for the 
class of mss under study to be derived. The half-life estimate depends on 
an estimate of the total population at some point. I used Du Placy's 
estimate of 4 to 5 copies per century for 400 sees in the 4th C. Happily, 
his estimate of 4 - 5 copies per century is consistent with the doubling 
time that can be derived from the initial portion of the uncial 
histogram. All This relies on the mss being correctly dated in general. 
It can be looked on as a confirmation that the datings are sound, 
especially the correspondence of population peaks in the papyri with 
known times when mss would be likely to end up in the sand.

Profuse apologies for this monstrous post.

Tim Finney

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

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From: "James R. Adair" <[email-masked]>
Date: Thu, 9 Jan 1997 10:31:14 -0500 (EST)

Tim's discussion of ms half-lives is interesting and thought-provoking, 
though I think some caveats must be kept in mind.  The radioactive decay 
analogy works only to the extent that conditions of ms destruction remain 
constant over time.  So, for example, rampant destruction of mss during a 
persecution would skew the data, as would changes in technology (shift 
from uncial to minuscule script, introduction of paper, invention of 
printing).  If these factors can be taken into consideration, however, I 
would think that the assumption of a more or less constant rate of ms 
destruction between the fourth and the fifteenth centuries might be 
valid.  What kind of boundaries did you have in mind, Tim?

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: "Professor L.W. Hurtado" <[email-masked]>
Date: Thu, 9 Jan 1997 15:59:40 +000

On how many mss might have been produced, economic factors figure in 
also.  Seems to me vaguely that historians refer to economic 
crunch(es) in the 3rd century Roman empire.  Might this be relevant?

L. W. Hurtado
University of Edinburgh,
New College
Mound Place 
Edinburgh, Scotland EH1 2LX
Phone: 0131-650-8920
Fax: 0131-650-6579
E-mail:  [email-masked]

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From: "Robert B. Waltz" <[email-masked]>
Date: Thu, 9 Jan 1997 10:06:54 -0700

>valid.  What kind of boundaries did you have in mind, Tim?

Since I'm on deadline today, I haven't had time to read and respond
to Tim's remarks in detail. But let me offer a thought.

The objection here boils down to saying, "Sometimes things happen."
Which is precisely true, but not the point.

Take the decay of radioactive atoms. If you look at one atom
of, say, U-238, you *cannot* predict when it will break down.
But if you observe enough of them, you can say that -- no matter
*what* happens -- after about 5 billion years (the half-life of
U-238), half of them will be gone.

Tim is not stating a thesis ("manuscripts break down after 500
years," or the like). He is stating an observation and making
a hypothesis. In fact, he is almost certainly right, too: In
a large enough universe of manuscripts, they *will* break down
in a pattern approximating radioactive decay.

Radioactive decay is a statistical process. It is absolutely
uniform when you are working with trillions of atoms. When
you are dealing with tens of thousands of manuscripts, you will
see bumps and valleys in the graph. (Just as you would if you
tracked the decay of tens of thousands of radioactive atoms.
There aren't enough of them.) This has no effect on the rule.

Unsolicited testimonial, based on incomplete data -- but at least
it is the comment of someone trained in physics. (For once,
something I'm *supposed* to know something about. :-)

Bob Waltz
[email-masked]

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From: "James R. Adair" <[email-masked]>
Date: Thu, 9 Jan 1997 16:02:47 -0500 (EST)

> There aren't enough of them.) This has no effect on the rule.

I agree that radioactive decay is uniform, since, as Bob mentioned, there 
are huge numbers of atoms (in a mole of U, 6.02 x 10^23, if I remember 
correctly--that's several hundred, what, sextillion?).  But radioactive 
decay proceeds randomly, unaffected by the outside world (at least 
largely so--but compare C-14 dating fluctuations).  On the other hand, 
the "decay" of a group of mss created in a certain century, while 
generally decaying exponentially, may be affected by outside influences, 
such as the ones I mentioned (persecutions, changes in technology, 
etc.).  I suppose over a long enough period of time even ouside 
influences might possibly fit into some sort of pattern of random 
interference, but I don't think 1000 years or so (or 2000) is long 
enough.  So, as a general description of the phenomenon of ms decay, I 
like the radioactive decay analogy.  All I'm saying is that I don't think 
we can push the analogy too far.

Jimmy Adair

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From: "Robert B. Waltz" <[email-masked]>
Date: Thu, 9 Jan 1997 16:08:54 -0700

I don't know if I should go on about this, since no one else seems to
be interested -- but *I'M* interested, so I will keep talking. :-)

On Thu, 9 Jan 1997, "James R. Adair" <[email-masked]> wrote:

>correctly--that's several hundred, what, sextillion?).

Footnotes: the number of atoms in a mole is always the same. The
number looks right, though. (I'm too lazy to go downstairs and dig
up my CRC handbook.)

As for what the number is, it depends on whether we're using
American or British numberation. In America, yes, that's 600
sextillion. In Britain, it's 600 thousand trillion.

>But radioactive 
>largely so--but compare C-14 dating fluctuations).

There is actually some very slight evidence emerging of radioactive
decay being dependent on outside conditions. But the effects are
minimal -- not enough, e.g., to account for C-14 fluctuation. We're
talking about changes in the .01% range, if I recall correctly
(and I may not).

>On the other hand, 
>enough.

The point here is that we are looking at it from *outside*. The
manuscript era is over. There is no new production (a factor
which also figures into the decay rate).

It's true that something like Diocletian's persecution would
have caused an unusually large number of manuscripts to be
lost. But this would be followed, inevitably, by a period of
increased manuscript copying and more careful preservation. So
it would even out.

The problem here is not time but the small number of manuscripts.
Atoms are so numerous that radioactive decay can be modeled as a
continuous process. Manuscripts must be treated as discrete.
(Which, incidentally, brings us from the range of differential
equations to difference equations -- which are much harder to
solve. At my college, They taught us differential equations after
only three semesters of calculus. They never taught us difference
equations at all....)

>So, as a general description of the phenomenon of ms decay, I 

That I actually agree with... at least, it needs to be investigated
before we start placing much faith in it. :-)

Bob Waltz
[email-masked]

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From: "Lewis Reich" <[email-masked]>
Date: Thu, 9 Jan 1997 18:14:56 -500

On  9 Jan 97 at 16:08, Robert B. Waltz wrote:

> >I agree that radioactive decay is uniform, since, as Bob mentioned,
> >there are huge numbers of atoms (in a mole of U, 6.02 x 10^23, if I
> >remember correctly--that's several hundred, what, sextillion?).
> 

Yes, it's Avogadro's number  and yes, it's correct.

Lewis Reich
[email-masked]

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From: "Ronald L. Minton" <[email-masked]>
Date: Thu, 9 Jan 1997 18:53:32 -0600 (CST)

Where can I find a recent descriptive list of Textual Criticism and 
manuscript web sites?  

--
Prof. Ron Minton: [email-masked]   W (417)268-6053  H 833-9581
Baptist Bible Graduate School 628 E. Kearney St. Springfield, MO 65803

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From: Maurice Robinson <[email-masked]>
Date: Fri, 10 Jan 1997 00:02:51 -0500 (EST)

> crunch(es) in the 3rd century Roman empire.  Might this be relevant?

I would think so, to an extent.  However, in the pre-4th century period,
the church was basically a persecuted body, and yet it still managed to
prepare and obtain at least minimal copies of the NT scriptures for its
use, so the possibility of sacrificial giving to support obtaining of
papyrus (which even under an economic crisis would probably still remain
cheap) would probably be quite likely and would not necessarily impede
normal production of NT MSS by local churches or individual Christians to
any great degree.  Of course, economics might preclude the use of
professional scribes for the purpose, but I suspect that such was rare in
any case in the era before the legitimization of Christianity while the
church was under threat of persecution.

_________________________________________________________________________
Maurice A. Robinson, Ph.D.           Professor of Greek and New Testament
Southeastern Baptist Theological Seminary     Wake Forest, North Carolina
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~