in our Paper in Statistical Science

by Doron Witztum

1. The Accusations of McKay et al:

In their article, "Solving the Bible Code Puzzle" which is scheduled to appear in the May 99 issue of Statistical Science, McKay, Bar-Natan, Bar-Hillel, and Kalai (MBBK) write the following about the statistical test that Witztum, Rips and Rosenberg (WRR) utilized:

"To correct the error in treating P

Further on (Section 10), they name the test that was published in our article "the test

Even before this, Dr. McKay had written the following letter, which was published in "Galileo" (issue #27, March-April 98):

Dr. McKay's letter (which, by the way, is typical of his style) should surprise us for its impudence. Dr. McKay can assume that the readers of

"After a great success in measurement for the second list as well, Prof. Diaconis suggested that we use a new method of measurement, and try it out on the second list. This is what we did, and the surprising results of the experiment...." (translated from the

Now let us compare my statement to what Dr. McKay

"Prof. Persi Diaconis, world renowned mathematician and statistician...

Amazing? - But this isn't all. We will now unfold before the reader with entire course of events, and clarify what

Our paper, "Equidistant Letter Sequences in the Book of Genesis," was submitted for publication to

Prof. Persi Diaconis sent the following letter to Prof. Aumann on September 5, 90:

Professor Robert Aumann

Department of Economics

Mail Code 6072

Stanford University

Stanford, CA 94305

Dear Bob:

I am glad to report we are in agreement about the appropriate testing procedure for the paper by Rips et al. A permutation test is to be performed. There are four basic sets of data/test statistics, I will call them additive, multiplicative, with and without Rabbi. For each there is a 32X32 table of distances. It is my understanding that for each such table, one million permutations will be performed. For each permutation SIGMA

In case of ties, the interval of ties will be broken at random. If half the proportion of such breaks amount to better than 1/4000, that table is successful. Otherwise not.

I hope that the authors agree to make their findings public no matter what the outcomes. Please let me know when you need from input from me.

Persi Diaconis

A number of things are not clear in this letter. For example: 1) It isn't clear what the intention is in the adjective "additive," vis a vis one of the statistics. 2) It isn't clear what the "distances" are that make up each table. 3) It seems that he is referring to

In order to clarify all of these, Prof. Aumann wrote the following letter to Prof. Diaconis on September 7, 90:

Professor Persi Diaconis

Department of Statistics

Stanford University

Stanford, CA 94305

Dear Persi,

Thanks for your good letter of September 5, about the paper submitted by Rips et al. to the PNAS.

Since it's important to clarify the precise rules of a statistical test before performing it, allow me to set down here a few points of clarification.

The same 1,000,000 permutations may be used for each of the four basic tests. The million will consist of the identity permutation plus 999,999 others. All million will be different from each other.

The sample to be examined is that of their "second experiment" (Table 3 of their submission). For each of the four basic tests, the exact same procedures as reported on in their paper (Tables 5 and 7) will be done for each of the 1,000,000 permutations. (Incidentally, "bunching" or "twenty percent" might be a more suggestive name for the test you call "additive").

The precise tie-breaking rule (agreed on by phone today) is this: Out of the million permutations, let there be s that are ranked smaller than the identity, and t with which it is tied (excluding itself). Then the test is successful if and only if s+(t/2) < 250.

Again, with many many thanks for all your help on this,

Bob Aumann

Bellow his name, Prof. Aumann added in handwriting:

"given to Persi by hand in Sequoia hall, September 9, 1990, 2:50 PM. He looked it over and approved."

That is, the details in Prof. Aumann's letter were approved by Prof. Diaconis.

When Prof. Aumann came to Jerusalem

It is thus clear that the exact description of the experiment, as detailed in the Statistical Science paper, was inspected by Prof. Diaconis and the other referees before the experiment was performed.

To conclude this chapter, I will quote from a letter that Prof. Aumann later wrote to Prof. Bar Hillel on January 17, 97, in which he describes the chronology of our research in its various stages. At what he calls Stages J and K, he writes:

"J. The details of a formal test are agreed between Diaconis and Aumann (I'm trying to avoid pronouns, because they often lead to confusion).

K. The formal test turns out significant at a level of 16 out of a million. (That is, the best result of the four statistics is 4 out of a million, and then Bonferoni.)"

Yes! On September 9, 93, Prof. Bar-Hillel received from Prof. Aumann "all of my correspondences with Prof. Persi Diaconis concerning the work of Rips et al" (Prof. Aumann's words on the accompanying letter).

If so, why are MBBK hiding the relevant information, and in its stead, raising accusations that have no basis? It seems that they have no trust whatsoever in their other claims. At any rate, if we might use Dr. McKay's own words quoted above from his letter to