On the Paper of Witztum, Rips and Rosenberg on Equidistant Letter Sequences in the Book of Genesis

Gil Kalai

Abstract:

In their paper [2] Witztum, Rips and Rosenberg (WRR) claimed to have statistically proved 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. Their test was first conducted on 34 most prominent Jewish figures and another test was made on a second list of 32.

We give statistical evidence to the hypothesis that the significance in the second test of Witztum, Rips and Rosenberg was achieved via an optimization process in choosing the data, which was stopped when the significance level of the first test was met. It goes without saying that such a procedure is completely illegitimate.

Moreover, our results further suggest that the optimization process was done (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. This compliments earlier findings of Bar-Natan, Bar Hillel and McKay which also indicate that optimization by choosing favorable appellations took place.

WRR informed in their 1987 preprint [3] a significance level of $1.29 \cdot 10^{-9}$ for the first experiment and $1.15 \cdot 10^{-9}$ for the second experiment. It turns out that these numbers are unreasonably close together. The gap between them is significantly small with respect to random divisions of the 66 Rabbis into two parts of 34 and 32 Rabbis respectively, with respect to random perturbations of the original lists, and with respect to the list obtained by moving to the second list a certain Rabbi which was on the first list by mistake (according to WRR's criterion). The gap between these significance levels is considerably smaller than the typical affect of an addition of a single appellation to a single Rabbi.

The square of the ratio between the two significance levels reported by WRR is comparable to the typical effect of adding an appellation. This agrees with an optimization process of adding favorable appellations which stops when reaching the significance level of the first test.

Standing alone this finding gives strong statistical evidence that the work of WRR is deceptive and gives interesting insight into the nature of their deception. Our findings do not stand alone but complement the comprehensive study by Bar Hillel, Bar-Natan and McKay who studied various aspects of the two experiments conducted by WRR and reached the same conclusion.