In 1994 Doron Witztum, Eliyahu Rips, and Yoav Rosenberg published an article in the journal Statistical Science. It was entitled Equidistant Letter Sequences in the Book of Genesis. This article describes an experiment which seems to show a remarkable proximity between names of rabbis and their dates of birth or death in the Book of Genesis. These names and dates occur as sequences of letters in the text which are the same distance apart. As an example of an Equidistant Letter Sequence (or, more briefly, an ELS) , it was noticed several decades ago by Rabbi Weissmandel that the word Torah occurs spelled out as T, O, R, H (in their Hebrew equivalents) in the Book of Genesis by starting from the first T. The 50th letter after that T is an O. The 50th letter after the O is an R. And the 50th letter after the R is H. In this example, the "skip length" is 50 letters. It turns out that TORH is spelled out more than 56,000 times in the Book of Genesis (with various skip lengths). Genesis itself is slightly more than 78,000 letters long.THE BIBLE CODE
The editor of Statistical Science, Professor Robert Kass, made the following remark about the article by Witztum, Rips, Rosenberg in his preface to that issue of the journal:
". . . When the authors used a randomization
test to see how rarely the pattern they found might arise by chance alone
they obtained a very highly significant result, with p=0.000016.
Our referees were baffled: their prior beliefs made them think the Book
of Genesis could not possibly contain meaningful references to modern-day
individuals, yet when the authors carried out additional analyses and checks
the effect persisted. The paper is thus offered to Statistical
Science readers as a challenging puzzle."
Several individuals took up the challenge. Below are various links which will give you an idea of the nature of the ongoing debate. The first two are detailed discussions by two prominent critics - Brendan McKay and Barry Simon. The next link is an article by Harold Gans with an introduction by Robert Haralick, much more supportive of the idea that codes do exist in the Bible, and the fourth webpage was put together by R. Haralick himself. The fifth link presents Doron Witztum's point of view. The sixth is a useful website presenting the articles by Randy Ingermanson. The above webpages contain many addition links. A serious rebuttal to the Witztum-Rips-Rosenberg article has been published in Statistical Science (the May, 1999 issue). This 45 page article entitled Solving the Bible Code Puzzle by Brendan McKay, Dror Bar-Natan, Maya Bar-Hillel, and Gil Kalai is available on the web and is the seventh link. The eighth link contains the comments written by Robert Kass for that issue of the journal. Here is the abstract of the article:
"A paper of Witztum, Rips and Rosenberg
in this journal in 1994 made the extraordinary claim that the Hebrew text
of the Book of Genesis encodes events which did not occur until millennia
after the text was written. In reply, we argue that Witztum,
Rips and Rosenberg's case is fatally defective, indeed that their result
merely reflects on the choices made in designing their experiment and collecting
the data for it. We present extensive evidence in support of that conclusion.
We also report on many new experiments of our own, all of which failed
to detect the alleged phenomenon."
1. Scientific Refutation of the Bible Codes
3. A Primer on the Torah Codes Controversy for Laymen
4. Torah Codes: Scientific Statistical Discussion
5. Torah Codes: Doron Witztum speaks out...
7. Solving
the Bible Code Puzzle
Michael Drosnin has written
a book entitled The Bible Code. For most of the
book, Drosnin gives various examples of ELS's in Genesis and in other Books
of the Bible and gives interpretations of what he finds. These usually
take the form of a prediction of some events that have already taken place
or that might possibly take place in the future. Almost immediately
after the publication of this book, various individuals did "Control
Experiments." Imitating Drosnin, they also found many
"predictions" or "messages" in War and Peace , in Moby
Dick, and even in Drosnin's book itself. The conclusion
that one might draw from such control experiments is simply that what Drosnin
does has no validity. Even the proponents of the Witztum-Rips-Rosenberg
experiment have dismissed and strongly criticized Drosnin's claims.
One can find some of their statements at the following website.
To see the results of various control experiments,
see Brendan McKay's website. If you scroll to the section called "Michael
Drosnin's book," you will find numerous links.
A reader of Michael Drosnin's book would get a rather misleading impression
concerning the significance of the publication of the Witztum-Rips-Rosenberg
paper in a peer-reviewed journal and the opinions of the mathematical community
about their work. In response to this, the following public statements
were issued: Public
Statement by Robert Kass, Statement
by 55 Mathematicians.
COMMENTARY: The paper of Witztum, Rips,
and Rosenberg which appeared in Statistical Science in 1994
is a description of an experiment. This experiment involved
many choices: a choice of a list of 34 rabbis, a choice of
certain names and appellations for these rabbis, a choice of how
to designate their dates of birth or death, a choice of which
appearances of these names or dates as ELS's in the Book of Genesis
would be allowed, and a choice of how to measure the closeness in
the text of these appearances of the rabbi's names and dates.
In order for their experiment to have any validity, it is crucial
that all of these choices were made without any prior knowledge of the
outcome of their experiment. That is, all the details of their experiment
had to be chosen in a completely "a priori" way.
Otherwise, the statistical significance of their result would be extremely
questionable. Their paper explains these choices and is fairly readable
for the most part. (It is reprinted in Drosnin's book.)
As we mentioned above, a rebuttal has been published in the May, 1999 issue
of Statistical Science. There is also an earlier article by
Maya Bar-Hillel, Dror Bar-Natan, and Brendan McKay in the May, 1998 issue
of Chance, a publication of the American Statistical Society.
This article, entitled The Torah Codes: Puzzle and Solution, is
written for the general reader and explains the whole issue and
the nature of the authors' objections. It casts serious doubt on whether
the Witztum-Rips-Rosenberg experiment was truly conducted in an a priori
way - an absolutely crucial issue. One can find it on Brendan McKay's
website. Just scroll to "Article in Chance Magazine." Several
other links that one can reach from McKay's website discuss this issue
In
contrast, Drosnin 's approach is not in any way a priori. Although
he often makes assertions about the probability of what he finds,
such probabilities are meaningless since he never states in advance a precise
criterion for what he is looking for. The control experiments
which several people performed show rather clearly the silliness of Drosnin's
approach. In Drosnin's book itself, Dave Thomas found the following
message encoded as ELS's: "The code is a silly snake-oil hoax."