Signals of ELS's Codes Systems: Decrement versus Increment

D. Witztum (2020)

BDD, Journal of Torah and Scholarship, Bar-Ilan University Press, No. 35

Abstract

The paper "Equidistant Letter Sequences in the Book of Genesis" by Witztum, Rips and Rosenberg (WRR) was published in Statistical Science Vol. 9, No. 3 in 1994. This paper describes a scientific analysis of selected word pairs which appear as equidistant letters sequences (ELS's) in the Book of Genesis. This analysis focused on ELS's which are minimal in length in large portions of the text studied. We refer to such ELS's as "ELS codes".

An experiment was performed which studied a geometric relationship between names and appellations of famous rabbis, and their dates of birth and death appearing as ELS codes in the text. A clear "signal" indicating a nonrandom relationship was detected. The statistical significance of this signal, measured by randomization of the data, was highly significant, at the level of 0.000016.

In a critical paper by Mckay, Bar-Hillel, Bar-Natan and Kalai (MBBK), published in Statistical Science five years later, WRR's success was attributed to deceit. MBBK assert that they exploited the flexibility available in the selection of appellations to selectively bias the data and produce an artificially "significant" result in Tolstoy's War and Peace. This purportedly demonstrated that the flexibility in the selection of appellations was "more than enough" to produce an artificially significant result in WRR's experiment as well.

In this article, we use mathematical and statistical tools to differentiate between a real signal of ELS codes and a signal created artificially by selectively biasing the data. Artificially created signals of ELS codes in a given portion of text are expected to decrease when we try to detect them in an extended portion of that text (containing the original portion). On the other hand, a real signal of ELS codes may increase significantly in an extended text if the ELS codes are not restricted to the original text selection.

This was examined for the signal created artificially by MBBK. The original portion of the text consists of the first 78,064 letters of War and Peace, this being the length of the Book of Genesis. The new portion is twice this length, also starting with the first letter of the book. A considerable decrement of the signal was observed.

In contrast, a similar examination of the signal detected by WRR for their data list and the Book of Genesis shows an opposite result. The original portion of text contains the first 78,064 letters of the Torah (i.e., Genesis). The new portion is twice this length, starting at the same letter as before. Instead of a decrement, a considerable increment of the signal was observed. The statistical significance of this result is less than 0.001.