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Equidistant Letter Sequences in the Book of Genesis

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Abstract

It has been noted that when the Book of Genesis is written as two-dimensional arrays, equidistant letter sequences spelling words with related meanings often appear in close proximity. Quantitative tools for measuring this phenomenon are developed. Randomization analysis shows that the effect is significant at the level of 0.00002.
... The 99,999 different random permutations of 8 and 64 groups of nucleotide triplets (codons) were chosen in accordance with the Algorithm P of Knuth [35][36][37]. The pseudorandom generator required as input to the algorithm was that provided by Delphi 5 of Borland Inter Inc [36][37][38]. ...
... The 99,999 different random permutations of 8 and 64 groups of nucleotide triplets (codons) were chosen in accordance with the Algorithm P of Knuth [35][36][37]. The pseudorandom generator required as input to the algorithm was that provided by Delphi 5 of Borland Inter Inc [36][37][38]. The result of the models based on the binary patterns of nucleotide and amino acid coding of physicochemical properties (Fig. 1, Table 1) was added to the results of 99,999 randomly produced codes to obtain a total of 100,000 codes of both groups. ...
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... A curious controversy within the discipline of quantitative biblical studies provides an idea for watermarking LLM outputs. Some researchers believed to have detected a code in the book of Genesis in the form of an equidistant letter sequence (ELS) hidden among the 78604 letters of the canonical Hebrew text of this book (Witztum et al. 1994). This so-called Masoretic text, established by the end of the first millennium, was argued to contain coded information concerning famous rabbis of the following centuries, particularly the dates of their birth and death. ...
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Watermarks should be introduced in the natural language outputs of AI systems in order to maintain the distinction between human and machine-generated text. The ethical imperative to not blur this distinction arises from the asemantic nature of large language models and from human projections of emotional and cognitive states on machines, possibly leading to manipulation, spreading falsehoods or emotional distress. Enforcing this distinction requires unintrusive, yet easily accessible marks of the machine origin. We propose to implement a code based on equidistant letter sequences. While no such code exists in human-written texts, its appearance in machine-generated ones would prove helpful for ethical reasons.
... For example, there was a (rather controversial) paper [12] on the so called Bible Code, claiming that the Bible contains statistically significant occurrences of various related words, occurring vertically and/or diagonally, in close proximity. Furthermore, there was an incident with a veto letter by the California State Governor [11]; Although it was considered a "weird coincidence", the first character on each line of the letter could be connected and interpreted as a very provocative message. ...
Preprint
The equidistant subsequence pattern matching problem is considered. Given a pattern string $P$ and a text string $T$, we say that $P$ is an \emph{equidistant subsequence} of $T$ if $P$ is a subsequence of the text such that consecutive symbols of $P$ in the occurrence are equally spaced. We can consider the problem of equidistant subsequences as generalizations of (sub-)cadences. We give bit-parallel algorithms that yield $o(n^2)$ time algorithms for finding $k$-(sub-)cadences and equidistant subsequences. Furthermore, $O(n\log^2 n)$ and $O(n\log n)$ time algorithms, respectively for equidistant and Abelian equidistant matching for the case $|P| = 3$, are shown. The algorithms make use of a technique that was recently introduced which can efficiently compute convolutions with linear constraints.
... Other regularly appearing words have also been found later. This mathematically accurate systemic called Equidistant Letter Sequences (ELS) attracted scientific attention in the 1990´s when Witztum, Rips, and Rosenberg (1994) showed, based on statistics, that in the other religious writings containing the same kind of text (e.g. prayer books) these sequences just do not appear. ...
Preprint
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