This paper contains some findings concerning the work [2] of Doron Witztum, Ilya Rips and Yoav Rosenberg (briefly WRR) in which they claimed to have statistically proven the existence of a hidden code in the Book of Genesis giving information about personalities living many centuries after the Book of Genesis was written. They claim to have shown significant proximity of Equidistant Letter Sequences (briefly ELS) of names and appellations of certain Rabbis w.r.t their (known) dates of death and birth. Their first test was conducted on a list of 34 most prominent Jewish figures and another test was made on a second list of 32. The first list of 34 Rabbis consists of all Rabbis whose entries in the Encyclopedia of Great Men in Israel by M. Margalioth is at least 3 columns long (such that either their date of birth or date of death is mentioned there). The second list consists of Rabbis having 1.5-3 columns in that encyclopedia.
WRR developed a statistical way to associate to a pair of terms a and b a certain ``distance'' c(a,b) which is a rational number between 0 and 1 representing the quality of the most proximal ELS appearance of a and b. c(a,b) can be regarded as a probability describing how lucky we are that a and b are found so close together in the Book of Genesis (see [2,3]).
WRR considered various appellations for each Rabbi and various standard forms for writing his known dates of birth and/or death. Then they computed all the distances between all pairs of terms consisting of one appellation and one date for the same Rabbi and considered the significance of the combined list of numbers they got for all the Rabbis. (For more details, see [2], [3].) They found an extremely high significance level.
In their experiments WRR had to make a large number of choices. Some of these choices where fixed for the second experiment after being made in the first. Maya Bar Hillel discovered a large number of ``degrees of freedom'' concerning mainly the dates and various cases where the choices made by WRR were wrong according to their own criteria. Brendan McKay found that WRR did not implement the statistical test agreed upon with Diaconis but another one which inflated the significance level by a factor of 100. Dror Bar-Natan discovered vast degrees of freedom concerning the choice of the appellations. All these findings are described in a forthcoming paper by Bar Hillel, Bar-Natan and McKay [1]. Moreover, Bar Hillel, Bar-Natan and McKay showed that by choosing appellations for the 32 Rabbis of the second list in a certain way one can reach the same level of significance reported by WRR in the Hebrew translation of War and Peace. However, Witztum, Rips and Rosenberg claim that all their mistakes were innocent and have little effect on the final outcome, and that the choices they made were correct. They further claim their list of appellations was provided by an independent expert.
We give statistical evidence for the hypothesis that the significance in the second test of Witztum, Rips and Rosenberg is the result of an optimization process in choosing the data, which was stopped when the significance level of the first test was reached. Moreover, our results further suggest that the optimization process was carried out (at least in its final stages) by adding favorable appellations for the Rabbis until the addition of a single appellation moved the significance level beyond that of the first test. It goes without saying that such a procedure, which consists of manipulating the data to reach the desired goal, is completely illegitimate.
We will describe further facts about the WRR paper which are disturbing to its integrity and some directions for further research. In particular, the distributions of pair-distances (in both experiments) are friendly to the statistical tools used by WRR but do not support any reasonable interpretation of the original research hypothesis of a hidden text.