From: Will Wagers 
Date: Tue, 14 Nov 1995 16:14:58 -0600
Subject: Codes in the Pentateuch

Last month on this list, as well as others (May 92 AIBI-L, Oct 95 B-Greek,
Nov 95 Classics), there was a small controversy entitled "Author of Genesis
unveiled". If you hated it, read no further.

I sought out the paper in question - Doron Witztum, Eliyahu Rips, Yoav
Rosenberg, "Equidistant Letter Sequences in the Book of Genesis",
_Statistical Science_ (1994) Vol. 9, No. 3, 429-38 - and was able to
confirm, once again, that I am not a mathematician. The bottom line, as
laymen like to say, is: The authors of the statistical paper conclude: "the
proximity of ELS's [Equidistant Letter Sequences] with related meanings in
the Book of Genesis is not due to chance." They ascribe no cause, and
certainly no higher cause, to the phenomenon. This is exactly what one
accustomed to reading scientific papers would expect in the way of a
conclusion to a controlled experiment. While the authors may someday
embarass themselves or us with their personal feelings, they have certainly
stayed well within the bounds of science here.

Everything I read bore out the explanation given of the paper by Alfred M.
Kriman on Thu, 9 Nov 1995. However, if one does not understand the
scientific meanings of terms like "probability" and "significance" or if
one cannot separate the newspaper article from the paper in one's mind, it
may be worth reading the original paper.

With knowledge of the paper, I will try to respond briefly to some of the
comments made last week on Classics, although by reading Kriman's posting
without memory of last week - all should become clear.

List-member comments:

Michael Hendry:

(1) > No word yet on whether any New Testament names were found in the Old
Testament, or vice versa, which strikes me as a rather obvious question ...

For this experiment, the question is quite irrelevant; because, it would
involve two (or more) different languages and violate both their
statistical premise and their methods.

(2) > ... -- *if* the method is valid, of course, which I seriously doubt.

The statistical method is perfectly valid, although who is to say it could
not be improved. Aware of the volatility of the subject matter, the authors
took great care to involve other statisticians in designing the controls
for the experiment. The results appear in the international, peer-refereed
journal, _Statistical Science_.

(3) > Finally, I hope the journal articles specified whether only con-
sonants were counted:  I will be much more impressed if they found
the Hebrew equivalent of ZE-DE-KI-AH in coded form than if they
just found Z-D-K-whatever.

The word Zedekia found was WHYQDC (I hope I transliterated it correctly).

Mark Williams:

(4) > I wonder whether those researching this gemmatria (for that's what it is,
isn't it?) included _matres lectionis_ in their computations?

Yes, they did include matres lectionis. No, it isn't gemmatria, although
doubtlessly gemmatrians are computing away as we speak.

Jim O'Hara quoting Starobinski 123:

(5) > "The error of Ferdinand de Saussure (if it be an error) will also provide
an exemplary lesson.... One can produce any hypothesis about him: he neither
accepts nor rejects it."

Well, not in this case. The value of a scientific experiment is that one
has a systematic and reproducible means of justifying a hypothesis. (The
hypothesis, I remind, has nothing to do with divine authorship.)

Alfred M. Kriman:

(6) > I didn't find the reported J. Roy. Stat. Soc. article that
was supposed to have preceded this, and no earlier work by the authors
was cited in the Stat. Sci. article.

Quite right, the other citation seems to have been an error.

(7) >  The present study has a component that
might be regarded as gematria in reverse ...

While I take the point, I think this is a bit misleading for most of us who
associate gemmatria with mysticism and charlatanism. Certainly, one should
study the article, as has Mr. Kriman, before making or responding to such a

[To which, David M. Schaps adds:

> I have seen claims for numeralogical patterns in the new
testament, in a book called _Theomatics_. These, however, are
simply what would be called gematrias, summing the numerical
value of the letters and finding significance in the numbers
obtained. As far as I could tell, this book would indeed have
been susceptible to the sort of criticism that David Meadows

(8) > ... the result is surprising.

Indeed, it is.



(I am re-posting the following with the permission of Dr, Kriman, a
physicist who also read the article in question.)
- -----------------------------

I just subscribed [to Classics], so I may have missed a proper citation if
one was
given earlier on Wednesday; in the following comments I refer to

        ``Equidistant Letter Sequences in the Book of Genesis,''
        Doron Witztum, Eliyahu Rips and Yoav Rosenberg,
appearing in
        _Statistical Science_, vol. 9, no. 3, pp. 429-438 (1994).

The introductory section of this article does not require specialist
knowledge to be understood.  FWIW, I recommend it.  The article gives
the impression of having been put through a responsible review process.
I saw no obvious blunders.  The article is nowhere near funny enough
to have possibly been intended as a joke.  Rips is author of some
other, fairly conventional articles in the field of Statistics.

No headline-grabbing ``odds'' are cited in this article, just measures
of significance.  However, from the data given I would estimate odds of
about 400 million to one against the observed results occurring ``by
chance.'' (There is not necessarily any inconsistency if another,
different study comes up with different, more impressive odds.)  This
assumes, of course, no systematic errors in the analysis.

The only news item I read on this was a copy of an AP item that came via
this group.  I didn't find the reported J. Roy. Stat. Soc. article that
was supposed to have preceded this, and no earlier work by the authors
was cited in the Stat. Sci. article.  I didn't look for the _Biblical
Review_ article.

If they were posted I must have missed it, I apologize then but

        **  Could someone please post proper citations  **
        **          for the other articles?             **

Please excuse the long posting.  Search on ``==>'' to skip to next topic.

I'm not sure this has anything to do with Classics, but that hasn't
seemed to stop anyone else from commenting...
(At least the methodology is relevant, and could easily be adapted for
classical texts.  At least it's not ``Physics.'')

Mark Williams  asks:
>I wonder whether those researching this gemmatria (for that's what it is,
>isn't it?) included _matres lectionis_ in their computations?  If they
>did, wouldn't it throw everything off?

==> Response on gematria:

Will Wagers ( replied:
>No, gemmatria is the (theological) interpretation of a word according to its
>numerical value.

The question turns out to be trickier than one would expect.  The numerical
values of characters are used extensively because half of the ``words''
used in one part of the study are actually dates of birth or death.

Usually, gematria of Hebrew uses the numerical values of proper nouns
and words in the Hebrew lexicon.  The present study has a component that
might be regarded as gematria in reverse: certain systematically chosen
characters are interpreted as dates, so that some characters from various
different words are interpreted according to their numerical values.

Even if one ignores this ``reverse gematria,'' I think some of the
characters in the source texts originally represented numbers, but become
part of words.  (The original texts are a specified version of Genesis,
an equal-length initial segment of a Hebrew translation of Tolstoy's
_War and Peace_ used as a control, and various randomized versions of
these texts used as bases for the statistical analysis.  I don't know
to what extent old Hebrew numbering was used in the Tolstoy translation.)
I don't know what to call this pieces-of-numbers-and-words-into-words
procedure, but by some definitions it might be closer to gematria than
the reverse gematria mentioned above.

Call it Kabbala.

[14 NOV You're right about the gematria question; on rereading, my answer 
seems somewhat disingenuous, and it is.  I was merely looking for a small 
issue by which to approach a discussion that had grown too wide-ranging.  I
made my limited point and presented my reasons, for others to judge on
the merits.  In the abstract, this is essentially what Witztum et al.
have done.]

A bigger problem may arise from different meanings of ``significance''
in statistics and in exegetical work.  Roughly, statistical analysis can
often tell you that an event is meaningful, without telling you what it

==> Response on mater lectionis:

The authors write ``In transliterating foreign names into Hebrew, the
letter [aleph] is often used as a _mater lectionis_; for example,
`Luzzatto' may be written [lamed,vav,sadi,tet,vav] or
[lamed,vav,sadi,aleph,tet,vav].  In such cases we used both forms.''

(It wasn't a major issue because mostly Hebrew and Yiddish names
were used.)

Other natural questions concern whether they ignore vowels, whether they
distinguish word-final character forms, which spellings they use, etc.
These questions are all settled somewhat arbitrarily.  The arbitrariness
arises in part from their concern to be statistically ``fair.''  (That
is, not to overdesign the study in a way that is somehow rigged to produce
the desired result.)  In part also, the choices are somewhat arbitrary
because, if the method and results are robust, then they should work
even if many of the detailed decisions are made in ways that are ``wrong''
for Genesis.

Questions about the _original_ nature of Hebrew writing are not really
relevant to the _validity_ of the work described in this article.  It
may concern the explanation. If you can abide this, then you may be
satisfied with the answer that, of course, they ignored Masoretic marks
altogether.  If this answer does not satisfy, reading the article
probably will not either.

==> Response on whether it matters:

I may try to report in a future post exactly how the scheme works, but
here's a first attempt anyway:

The authors construct a sieve for meaningfully paired names and dates
systematically hidden in a text.  They apply this sieve to Genesis
and get a count (several, actually).  They apply the same sieve to
a control text and to randomized versions of both texts, in order to
get an idea of whether the count for Genesis is high.  It seems to be
improbably high.

The one-paragraph explanation naturally leaves a lot of open questions
(e.g., what is ``meaningfully paired,'' ``systematically hidden''?).
Giving detailed answers amounts to adjusting the holes in the sieve.
If Genesis is special, the sieve should still pick that up, to a greater
or lesser extent.  If errors have crept into some ``truer'' original
text, the sieve should be robust against it.  This impression I have
appears to contradict the report of David M. Schaps (F21004@VM.BIU.AC.IL)
based on a seminar by Rips, but is really a quantitative issue: how
large is the typical separation between related pairs, and what is the
typical ``minimal'' stride needed to find a word, compared to the length
of a ``passage.''

There is no discussion of the relative contribution of J and E text
regions to the improbably high count.  There's really no attempt to do
anything but statistics that are purposely anachronistic and apparently
unlikely to have anything directly to do with the book (at least in the
paper I've seen).

If I understand it correctly, the result is surprising.  The authors
offer their materials at cost so anyone can duplicate their study and
look for possible sources of error.  Thanks anyway.

"Alfred M. Kriman" 

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