Thu Jan 9 17:13:04 1997

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Date: Thu, 9 Jan 1997 16:08:54 -0700
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From: "Robert B. Waltz" 
Subject: Re: Ms half-lives
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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"  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?).

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 
>decay proceeds randomly, unaffected by the outside world (at least 
>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, 
>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.

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 
>like the radioactive decay analogy.  All I'm saying is that I don't think 
>we can push the analogy too far.

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

Bob Waltz
waltzmn@skypoint.com

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