The Light of Torah Codes
Professor Rips' survey of codes about light is here.
Below are some highlights from that report, and a few additional points.
The following table from Dr. Rotenberg is a kind of double echo, in code, clustered precisely around G-d's first utterence "Let there be light" in the third verse of the Torah (Genesis 1:3). This utterance forms the axis of the code (the main vertical ELS). Every word from the original verse appears as an ELS, or crossing in the text, not once but twice. Dr. Rotenberg also highlighted the axis extensions "by day" and "for a luminary", in purple and pink (which also repeat). and "in the morning", parallel, in brown.
All of these ELSs (and no others) appear on pages 114 and 115 of Dr. Rotenberg's book, published in 2005.
All but one of the words above is yet again repeated in the extremely compact additional table, below, discovered by Professor Haralick in May 2007. The one exception is that the name "Hashem" appears in the latter table instead of "G-d". The axis ELS in the new table is again a (different) ELS occurrence of "let there be light".
For the first table we calculate a p-level for only the repetitions, of only the original Genesis 1:3 words. It is 1 in at least 1,000. For the second table, the p-level is near 1 in 8,000.
Notice that the exact vocabulary used in our measurements, in both tables, was strictly pre-determined. The original Genesis 1:3 verse defined the exact words measured (as repetitions only) in the first table, and that first table defined the exact words measured in the second table.
Now we will highlight two basic tables of Nachum Bombach from Professor Rips' report, and show how they lead to the series of (now three) other tables.
From these two tables, the basic concepts can be combined into the idea that "G-d formed (created) waves of the light from light". This can be further shortened to "waves of light" and "were formed". For this simple pair of ELSs, גלי אור (waves of light) and נוצרו (were created [formed]), we found a significant 1D formation, with p-level 1:1,100:
This was already a prime example of one set of codes directly leading to another. The situation became doubly interesting upon discovering a few weeks later that the same two key words also form a one-column code, with p-level 1:1,200:
And it became triply interesting later still, upon discovering the same key words in parallel formation. This third result (below) has probability at the 1:100 level.
Finally, it is worth repeating the following table from Nachum Bombach. It illustrates another aspect of unreported successes:
I doubt if there are even a handful of choices that are as fitting as the word Hashem in this table. But since Hashem was not a pre-specified choice (only "light from light" was specified in advance), we do not calculate a p-level. This is one of a great many examples of an ELS which we know is significant but for which we do not give official p-levels.
Such under-reported successes could actually dwarf the more easily calculated results that we favor for publication.