August 2012 - Hashem clusters:

Again, here is the very first find, from 2008, involving G-d's Names:

Figure 1

The original search that produced the above result was simply to find the most compact and parallel arrangement for the three key words in red (these are His Names which appear in the plain text of Exodus 6:2-6:3 - which is Hashem's own "commentary" about His Names).

Now, four years later, we take a deeper look at the clustering of the Tetragrammaton (in blue). There are six occurrences of the Tetragrammaton in the cluster (2 overlapping vertically and 4 horizontal). Five of these six occur in a "maximally compact" configuration (the blue occurrences in Figure 2). Maximally compact displays like this have a certain symmetry:

Figure 2

The existence of such a cluster is not necessarily significant, because after all, it is formed in simple situations such as when 3 or 4 occurrences of the Tetragrammaton appear with equal distances between them. However, the combination of the cluster with other elements is signifcant.

Let us see how many other Tetragrammaton clusters are in the Torah, and whether they contain interesting and repeating patterns. We first define precisely the clusters of interest. Using Figure 2 as our guide, we have three criteria:

1) At least three Tetragrammaton occurrences in adjacent rows. Each one is offset horizontally from the one above it by one column in either direction.

2) At least one vertical and overlapping occurrence of the Tetragrammaton, which protrudes no more than one row above or below the horizontal occurrences.

3) At least five total occurrences of the Tetragrammaton.

A systematic search for all such clusters in the Torah found 13 of them, 5 of which we have seen before. What is remarkable about them is that at least 3 themes repeat among them much more than could be expected by chance. The most obvious themes are represented by Figures 1, 3 and 4 (more figures and measurements hopefully to follow in coming months). The three themes are:

(1) Theme 1: Figures 3 and 4 reinforce the phrase "Hashem your G-d" introduced in Figure 1. A first glance might conclude that this is not significant because "Hashem your G-d" appears 325 times in the plain text. However, Hashem (the Tetragrammaton) appears 1820 times in total (including the 325). Why should the 325 occurrences be so heavily "favored" by the clustered Tetragrammatons? Initial measurements indicate that this favored status has only 1 chance in over 2,500 of being coincidental.

Figure 3

2) Theme 2: The cluster in Figure 3 is crossed by the phrase "In the place where Hashem will choose to rest His Name". Either this phrase or a partial version of it ("in the place where Hashem will choose") appears in 4 of the 13 clusters.


Figure 4

3) Theme 3: The cluster in Figure 4 is crossed by the best 1D meeting in the Torah between "I shall be" / "your [singular] G-d". The same 1D pattern appears in 2 places in Torah. Two other clusters among the 13 are crossed or appear within 2 rows of one or the other of these 1D codes. [The single word for "I shall be" is itself another Name for Hashem, which was the other primary search term used from the very start of our searches in 2008.]

The significances of each of these themes 2 and 3 appear to be at least as high as that of theme 1, but further measurements need to be made.

Summary question/thought:

How can the simple geometric clustering pattern that we started with give rise to so many simple, direct and repeating results?