The Patriarchs Experiment
and Its Extensions
In my view, the Patriarchs experiment presents a new opening in Torah Codes research. The goal of this note is to provide a description and analysis of it using some simple checks.
The starting point, contributed by Art Levitt, was to find a common meeting for the key words אברהם (Abraham), יצחק (Isaac) and יעקב (Jacob) encoded as ELSs. In the class of parallel encodings, the best meeting is the following one:
More precisely, the rectangular window of size 2×27 enclosing the three key words has the smallest possible area for all ELSs of the three key words without any restriction on the skips. (Naturally, this does not include the appearances in the plain text.) This meeting is a pointer in the sense of Dr. Alex Rotenberg. The concept of a pointer suggests that the location of the meeting in the text and/or the 2D tableau defined by the meeting contain additional related information (ELSs for related words).
We see in the plain text the expression מערת
We see in Fig.2 that אדם (Adam) and חוה (Eve) indeed appear in a close proximity to this meeting with the same skip 1272 as Abraham. Adam appears twice: first, sharing a common letter with Abraham, and the second time in the adjacent column. Eve appears in the same column as Adam. Jacob with skip 2544 also appears in the same column.
On the tableau in Fig. 3 we see the parallel meeting of the same ELS for Abraham with the double appearance of Sarah with skip 1272 sharing a common 'ש'.
We did not find a parallel meeting with רבקה (Rebecca). In Fig. 4, a meeting of יעקב (Jacob) with לאה (Leah) is shown. Leah appears with skip 636 in the same column as Jacob (this column also contains Adam and Eve).
The tableau above (Fig. 5) also shows the minimal skip 2 for אבות (Patriarchs) and אמהות (Matriarchs) appearing with skip 1908 in the same column as Abraham, Adam and Isaac.
On the next tableau (Fig. 6) we see the parallel meeting of the same ELS for Jacob with both Rachel and Leah appearing in the same column with the same skip 2544.
As we mentioned earlier, we did not find a close parallel meeting of יצחק (Isaac) and רבקה (Rebecca). However, it turned out that the same ELS for Isaac with skip 1908 has a close meeting with Rebecca with skip 1913, as show in Fig. 7.
The overall picture is shown in the Torah Code tableau below (Fig. 8) on which all the details are put together.
[It is interesting to notice that we discover בלהה (Bilhah) with skip 636 in the same column as Rachel and sharing with her a common letter 'ל'. Nearby we see שפחת (servant) with skip 1 and אחתך (your sister) as an extension of Bilhah. As Chazal tell us, Bilhah was servant and sister of Rachel (Pirkei Rabbi Eliezer, Ch.28).]
Notice also a close meeting of חוה (Eve) and אמהות (Matriarchs). It turns out that very close to Eve there are three parallel appearances of אמא (mother) with skips 636, 1272 and 1908 correspondingly. We see the extensions אם חוה (mother Eve) [in Genesis Eve is called "mother of all living"] and אם אמהות (mother of Matriarchs):
Now we will try to evaluate some of the effects we have seen in the above tableaux. The most appropriate technique of evaluation is to use the proximity measure based on counting the "more favorable placements" of the ELSs. However, so far, this measure has not been implemented. Therefore, other methods, available by existing tools, are used.
There are 48,921 ELSs for Abraham with skips > 1. How many of them are accompanied by a similar or better pair of parallel appearances of Sarah?
It turns out that "our" Abraham with skip 1272 is the second best (out of 48,921).
Similarly, "our" Jacob with skip 2544 is the third best (out of 103,588) among those having a close parallel meeting with the "aggregate" encoding consisting of Rachel and Leah appearing in the same column and having at most one separating letter (see Fig. 11).
The double parallel meeting of Abraham with Adam shown in Fig.2 is the best one out of all 48,921 ELSs for Abraham.
Let us now return to the meeting of Abraham and Sarah. There is a cluster of seven parallel appearances of Sarah near the same ELS for Abraham with skip 1272 (see Fig. 12).
In Fig. 12, the white area is of size 21×21, the center being the middle letter of Abraham, that is 10 in each direction starting with the middle 'ר' of Abraham. It contains one ELS for Sarah with skip 636, three ELSs with skip 1272, two ELSs with skip 1908 and one ELS with skip 2544. This area contains 17 letters 'ש', 34 letters 'ר' and 41 letters 'ה' out of the total 441, so that the product of the frequencies is 2.76e-4. Multiplying by the number of possible placements for Sarah inside the white area with skips 636, 1272, 1908 and 2544, we obtain the mathematical expectation 0.7427.
By Poisson distribution, the odds for having seven or more occurrences are 2.781e-5.