Below are links to web pages concerned with the so-called Bible codes. They are sparked by the article “Equidistant Letter Sequences in the Book of Genesis”, by D. Witztum, E. Rips and Y. Rosenberg, Statistical Science v. 9 no. 3 (1994), 429-438. Many of these sources refer to each other.
A final answer to the above article has been published in the May 1999 Statistical Science. The refutation is, for the most part, readable without technical background. One is struck by the degree to which the authors bend over backwards to avoid making argumentative claims or judgments, and the effort they expended before declaring that the codes have no support.
There are two issues addressed by the review article. One is simply the ability of computers to go fishing for apparent codes. The article illustrates this with an amusing hidden “code” in part of the Unabomber manifesto! The deeper issue is the experiment performed by Witztum et al. which apparently gave their results some statistical (and scientific) significance. It is primarily this issue which the review article takes great pains to analyze.
The issue containing this article was delayed several months, for remarkable reasons described by Executive Editor Leon Gleser (Institute of Mathematical Statistics Bulletin 28(5), Sept/Oct 1999, p.312):
The May issue has been a particular headache, as it contains a review of research done to refute a 1994 paper by Witztum, Rips and Rosenberg …. The impending publication of the review by McKay, Bar Hillel, Bar Natan and Kalai has produced a small avalanche of inquiries, letters of complaint and legal threats that has taken time away from editorial matters ….
A related point: In the review article the authors acknowledge “a considerable debt to several people who donated large amounts of time and expertise but do not wish to be named” (p.172), and two of the references are anonymous (one is given by a pseudonym). There is normally no need for anonymity in science, and in fact scientists typically prefer to get credit for their contributions. This and the “legal threats” mentioned by Gleser indicate to me some very serious non-scientific (and coercive) behavior by the Torah codes community.
The review article eliminates any hope of mathematical or scientific support for the existence of Torah codes. I should add finally that I don’t believe it is supported by the Rabbinic literature either. See, e.g., Kiddushin 30a; Tractate Soferim 6:4; Rema on theShulchan Aruch Orach Chaim 143:4; Ibn Ezra on Exodus 25:30 (te’aseh). Better yet, go to the Tigay webpage (see the link below).
(Technically, the review article only deals with the Torah codes experiments of Witztum et al. However, as their experiments and statistical analysis are the only scientific attempt to prove the reality of any Bible codes, this refutation leaves nothing scientific on the table, and probably has killed the issue. Moreover, the arguments are so overwhelming that I doubt any scientist or mathematician is going to waste his or her time on this issue any more.)
Prof. Barry Simon, IBM Professor of Mathematics and Theoretical Physics, California Institute of Technology, has created a special web page dealing with Torah codes, including his article in the March 1998 issue of Jewish Action as well as a more recent article. At the same location you may link to “On the refereeing in Statistical Science”. (This gives the inside story on how the original article was refereed. See also the link to Kass, below.) Also of interest on his home page is the link to the “Mathematicians’ Statement on the Bible Codes”.
Prof. Brendan McKay, Dept. of Computer Science, Australian National University, is the lead author of the review article. He (together with others) has done a tremendous amount of experimentation to refute not only the Torah codes hypothesis but other quasi-scientific claims as well. His web page contains a great deal of information, as well as a link to the joint Statistical Science article .
Prof. Dror Bar-Natan, Dept. of Mathematics, Hebrew University of Jerusalem, is a co-author of the review article. Follow the link on his web page labeled “Click for a list of my publications” and scroll down to articles 20 and 22. Two rather poignant personal statements about the issue are worth reading. (Scroll down to Bible Codes and click on footnotes 1 and 2.)
Prof. Jeffrey H. Tigay, A.M. Ellis Professor of Hebrew and Semitic Languages and Literatures in the Department of Asian and Middle Eastern Studies at the University of Pennsylvania, gives an extensive and very interesting textual discussion.
Prof. Robert E. Kass was the editor of Statistical Science at the time the article by Witztum, Rips and Rosenberg was published. This statement makes it clear that the journal did not endorse the findings of the article.
Aish HaTorah is an Orthodox Jewish outreach group which has made the Torah codes something of a cause celebre. Follow their Discovery link to find it. This is not meant as a general criticism of Aish, which has a very interesting web site and does a lot of good stuff.