Volume 30 Number 92
                 Produced: Sat Jan 15 18:49:06 US/Eastern 2000

Subjects Discussed In This Issue: 

Administrivia - Torah Codes
         [Avi Feldblum]
Torah Codes (4)
         [Yosef Gilboa, Shlomo Godick, Shlomo Godick, Mike Gerver]


From: Avi Feldblum <mljewish@...>
Date: Sat, 15 Jan 2000 18:41:47 -0500 (EST)
Subject: Administrivia - Torah Codes

Just a quick note concerning my stance on the Torah Codes Issue. As far as
I can tell, I see no particular reason to exclude discussion of Torah
Codes on the list. As long as the volume of discussion is held to a
reasonable level, I am willing to have it as one of our many discussion
topics. I personally think that some of the spin-off topics are more
interesting to me than the discussion of the Codes themselves (the
theological implacations or lack thereof for people who fully accept the
the Torah is from HaShem before the code discussions, the use of them on
Jews who do not start with an acceptance of the validity of Torah and
halacha, the implications (or lack thereof) on the textual integrity at
the individual letter level of our current text), but I think that there
is an audience for these topics within the range of the membership
(otherwise no-one would reply to these topics).

Avi Feldblum
mail-jewish Moderator


From: Yosef Gilboa <bfgilboa@...>
Date: Wed, 12 Jan 2000 13:19:20 -0800
Subject: Re: Torah Codes

I would like to ask publicly, to leave the "Tora codes" discussion out
of mail-jewish. Even if the subject is interesting to some of the
participants, it is clearly way out of the scope of a bulletin devoted
to discussion of halachic issues. Perhaps there should be a separate
bulletin devoted to Tora codes or perhaps these postings should be
diverted to one of the existing bulletins devoted to qabbala, where
gimatria is indeed a subject of importance.

Perhaps you should query the "membership" about their opinions.


Yosef Gilboa

From: Shlomo Godick <shlomog@...>
Date: Wed, 12 Jan 2000 19:41:19 +0200
Subject: re: Torah Codes

Stan Tenen wrote: <<
As others have posted, there is a solid refutation of the
"prophetic meaning" of the codes published by Brendan McKay, Dror
Bar-Natan, et al., in Statistical Science, May 1999.  Here is a summary
of their findings that I wrote in email last year:  >>

Solid refutation? I just finished reading Witztum's refutation of the
refutation (see http://www.torahcodes.co.il/persi2.htm and
http://www.torahcodes.co.il/persi4e.html) which seems very convincing.
He recites the history of the testing and counter-testing of the
hypothesis, shows how McKay et al's claims contradict claims made in
their previous papers, and concludes that McKay et al are engaging in
deliberate deception and concealment of data.  The articles are worth

I think that at this point it is a bit premature to eulogize the Torah
Codes theory.  Rips and the four mathematicians that wrote him a letter
of support are considered world-class mathematicians.  I think that
McKay et al's accusations of Rips' "pre-tuning the data", "rewriting"
the rules of the experiment, etc.  (which are alternative ways of
calling Rips a liar) are totally at odds with Rips' known professional
and personal integrity.

I for one am awaiting further developments.

Kol tuv,
Shlomo Godick

From: Shlomo Godick <shlomog@...>
Date: Wed, 12 Jan 2000 21:57:06 +0200
Subject: re: Torah Codes

R. Chaim Mateh wrote: <<
I have heard of the "good" that the Torah Codes have done, i.e.,
convince nonreligious Jews to investigate Judaism further.  I haven't
heard any "harm" stories.  Does anyone know of such harmful effects the
Torah Codes have had.  Not theoretical potential harm, but real-life
harm.  For example, has anyone ever heard of a Baal Tshuva who became
religious only because he believed the Torah Codes to be 100%
scientifically accurate, and then upon finding out that they aren't,
left Judaism and reverted back to nonreligious?  >>

But that still evades the basic question of whether the ends justify the
means.  The Torah Codes hypothesis IMHO should not be presented in
Discovery and Arachim seminars as 100% true (and, by the way, I am not
so sure that it is) so long as the the jury is still out, so to speak.
The academic world still has not had its last say on this still very
controversial topic (and, until Mashiach comes, it may never will).  If
the theory is presented without at least acknowledging the opposition of
some in the academic community, and then later its validity really is
called into question scientifically, this could create a big chillul
HaShem.  On the other hand, showing dedication to emes [truth] by
adopting a tentative stance creates a kiddush HaShem.

Kol tuv,
Shlomo Godick

From: Mike Gerver <MJGerver@...>
Date: Wed, 12 Jan 2000 22:44:07 EST
Subject: Torah Codes

I'm glad that the "Torah Codes" have come up again, since I have done
more research on them since my last posting on this topic (in v19n17,
back in 1995), and have changed my opinion from what I thought
then. What I am going to say is not simply a report of work done by
others, who may or may not have expert credentials in statistics, etc.,
but describes my own independent investigation of the claims made by
Witztum, Rips and Rosenberg, and by McKay et al, in the two papers
published in Statistical Science (in the August 1994 and September 1999

Actually my investigation was not completely independent.  I did not
write my own software from scratch, but relied on the els1 program that
I received from Rips.  But since my conclusions are rather unfavorable
to Witztum et al, my use of their software should not make my
conclusions less credible, and I did do some independent checks of
els1. Besides, no one, including McKay et al, has claimed that els1 does
not do what it is supposed to do.

As I noted in my posting in v19n17, there are actually two different
surprising claims made in Witztum et al's paper.  But to explain what
these two claims are, I will have to briefly give some background.  The
authors define a complicated function c(w,w'), where w and w' are two
Hebrew words, typically the name of a famous rabbi and his yahrzeit
date. The definition of c(w,w') also involves a Hebrew text, such as
Breishit. The function c(w,w') is supposed to be a measure of the
closeness in the text of certain equidistant letter sequences (ELS's)
for w and w'. For randomly chosen words w and w', and a text without
special properties, one would expect that c(w,w') is equally likely to
have any value between 0 and 1.  The definition of c(w,w') sounds
reasonable, but has some subtle properties which are not at all apparent
at first, which can mislead your intuition about how it should behave,
as I will explain later. I have no doubt that Witztum et al defined
c(w,w') as they did in good faith, and were not aware of these
subtleties at the time.

Now for the two surprising claims.  First of all, they say that, when
you take an objectively chosen list of famous rabbis' names w, and their
yahrzeit dates w' (or in a few cases their birthdays), and use the text
of Breishit, then the distribution of c(w,w') is far from being a flat
distribution between 0 and 1, but is strongly skewed toward 0.  The
equidistant letter sequences for w and w' are in some sense closer
together in the text, on average, than you would expect by chance.  The
mean value of c(w,w') is something like 1/3, rather than 1/2 as you
would expect.  The second claim they make is that, if you randomly
shuffle the names and yahrzeit dates, so that a given rabbi's name w is
associated with the yahrzeit date w' of another rabbi randomly chosen
from the list, then the distribution of c(w,w') is much less skewed
toward 0, it is much closer to a flat distribution between 0 and 1.  The
text of Breishit seems to "know," better than chance, which rabbi's name
goes with which yahrzeit date.

In early versions of the manuscript, Witztum et al only discussed the
first claim, and estimated that the probability of c(w,w') being as
skewed as it was, just by chance, was something like one part in 1.e+18
(ten to the 18th power).  This estimate assumed that the c(w,w') values
for the different word pairs were statistically independent of each
other.  When the referee pointed out that the c(w,w') values were not
statistically independent, the authors switched to the second claim, as
suggested by the referee. But in their paper, they still mention the
first claim as something surprising. Most readers, and probably the
authors and referee as well, would intuitively assume that, even if the
probability of c(w,w') being so skewed is not as small as one part in
1.e+18, it is still extremely small, and it is very surprising that such
a skewed c(w,w') would occur.

When I first read Witztum et al's paper, I figured one of three things
had to be true. Either 1) the results, and their procedure, were as they
claimed, and no non-supernatural explanation could account for it. Or 2)
the results and procedure were as they claimed, but it was possible to
explain it in a non-supernatural way.  Or 3) the results or procedure
were not as they claimed.

I strongly doubted that (1) was true, but I was hoping that (2) was
true.  I even thought of a non-supernatural explanation that might work,
which is described briefly in my posting in v19n17.  That explanation
involved the existence of long range order (over distances of thousands
of letters) in the text of Breishit, which could have been put there as
a way for scribes to check that they had not left any letters out, but
which was forgotten a long time ago.  It would have been cool to
rediscover something like that about the text of Breishit, although it
would not have proven that Breishit was written by G-d, since a human
writer could have incorporated such long range order in the text.  Also,
if (2) were true, then the authors would be proven innocent of
intentionally deceiving people.

As it happened, however, (3) seems to be true. Here is what I found.

First of all, the highly skewed distribution of c(w,w') is real.  But
the different values of c(w,w') are so highly correlated with each other
that the probability of this happening by chance is something like 1
part in 10, rather than one part in 1.e+18.  There is no reason to think
that it did not just happen by chance in the case of Breishit, with the
list of rabbis used by Witztum et al. I have no doubt that Witztum et al
did not realize this when they started their research, and were
genuinely surprised by the highly skewed c(w,w'), and convinced they had
made a significant discovery.  Even after the referee pointed out that
the c(w,w') values are not independent, I doubt whether they, or even
the referee, realized how strongly correlated they are.  The authors
still felt they had discovered something important, and just needed to
make some adjustment in the way they presented it, in order to
rigorously prove that it was unlikely to occur by chance.

But the second claim made by Witztum et al does not seem to be true.
The problem is that their list of names includes not only names of the
form "Rabbi so-and-so" but also nicknames like "Vilna Gaon", "Maharal,"
etc.  Their paper gives no objective criterion for choosing which of
these nicknames to use.  As pointed out by McKay et al, the positive
result that Witztum et al obtain, regarding the second claim, depends
entirely on these nicknames.  McKay et al include a lot of other,
irrelevant criticisms in their paper, but this point, the central point
of their paper, appears to be true.  I have verified that when you
eliminate the nicknames, and only use names of the form "Rabbi
so-and-so," then the skewedness of c(w,w') does not change significantly
when you randomly shuffle the names and yahrzeit dates.  The mean value
of c(w,w') is still about 1/3.

McKay et al insinuated that Witztum et al had purposely chosen their
list of nicknames in order to get a positive result.  Witztum et al
denied this.  But this argument is besides the point.  Unless Witztum et
al can demonstrate that their list of nicknames was chosen objectively,
then their result doesn't prove anything about G-d being the author of
Breishit. And it seems hopeless for them to demonstrate that the list of
nicknames was chosen objectively.

As a reply to McKay et al, Witztum reported another test he did, which
is posted at http://www.torahcodes.co.il/ben/ben_hb.htm, using "Ben
so-and-so" with the rabbis' father's names, instead of the rabbi's own
names.  This test, Witztum pointed out, did not have any arbitrariness
in the names, since there was no use of nicknames.  He got a significant
positive result, comparing the skewedness of c(w,w') when each rabbi was
assigned to his own yahrzeit date, to the skewedness of c(w,w') when the
names and dates were randomly shuffled.  The probability of this result
occurring by chance, Witztum calculated, was about 4.e-5.

I did my own analysis of the "Ben ..." test, and I found serious
problems with it. The names and yahrzeit dates of the rabbis were
obtained from the 1961edition of the "Encyclopedia of Great Men of
Israel," including only those rabbis whose entries in the encyclopedia
took up between 1.5 and 3 columns.  I did not have access to the
1961edition of the encyclopedia, but I found the 1956 edition in the
library.  There were about a dozen minor discrepancies between the data
given in the 1956 edition of the encyclopedia, and the data used by
Witztum (which were identical to the data in the published version of
Witztum et al).  When I used the data exactly as it was given in the
1956 edition of the encyclopedia, then the result for the "Ben..." test
became much less significant.  Instead of a 4.e-5 probability of it
occurring by chance, the probability of it occurring by chance was a few
percent.  In other words, it was quite likely to occur by chance.

It's possible, of course, that the data in the 1961 edition of the
encyclopedia agrees entirely with the data used by Witztum et al.  More
likely, they will have sources which give different yahrzeit dates,
which they claim are more accurate.  But it is very unlikely that a few
random errors would have made such a huge difference in the statistical
significance. And who knows how many other sources they found, which
they did not use, which give still other yahrzeit dates?

The fact remains that Witztum and the other "codes" advocates have still
not produced a convincing demonstration of a statistically significant
positive result, at least not one that I am aware of.  And the more
times I check these claims and find them not to be valid, the less
inclined I am to spend the time (a few days) to check an additional
claim.  Maybe I am being unfair to them, but there are other things that
I must devote time to, like my job, my family, learning, and

Mike Gerver, <mjgerver@...>


End of Volume 30 Issue 92