Essays by Stan Tenen

Equal Interval Letter Skip Patterns: Specific Solutions
©1996 Stan Tenen

The following letter was written in response to an article appearing in the October, 1995 issue of Bible Review magazine, by Dr. Jeffrey Satinover, introducing the statistically significant letter distribution patterns found in the Torah to the BR audience. It also responds to letters BR published about Dr. Satinover’s article. (Please note that Bible Review did not publish the following letter by Mr. Tenen.)

In 1999, Mr. Tenen added the following comments:
Additional findings have been published since this letter was written, so some of the proposed explanations in my letter may no longer be plausible.  What's important here is not the particular explanation proposed, but rather the need for a careful exploration of similar possibilities.  It's important to remember that "lack of evidence (based on current knowledge) should not be taken as evidence of lack" – of a simple, non-miraculous explanation for what some have maintained can only be possible by means of miracle or prophecy.  —Stan Tenen, November 1999

28 February 1996

Bible Review Magazine
4710 41st Street, NW
Washington, DC 20016

Dear Letters Editor:

There are several categories or classes of Equal interval Letter Skip (ELS) patterns in B’Reshit. This letter concerns only two. There are other categories and issues that also need consideration that I will not discuss. I believe that these highly speculative ideas, and other non-standard perspectives, are needed if we are going to understand the significance of the ELS patterns.

Often a previous example can help to resolve a current problem. Until fairly recently there was a paradox in the sciences somewhat analogous to that posed by the Equal interval Letter Skip patterns in Torah. When Penrose Tilings (named after physicist Roger Penrose) where first discovered as mathematical objects, they were thought to not exist in nature. This was because it had been rigorously proven that these patterns could not, by themselves, organize themselves to produce both a rule-following and a complete design.

It was thought that except by the wildest of chance, natural Penrose-type patterns would all have defects or incomplete sections – or that the rules describing the pattern would have to be broken. Then, much to everyone’s surprise, (the equivalent of) Penrose Tilings were discovered in nature. How could the paradox be resolved? Professional scientists cannot say that a miracle occurred – and as it turned out, no miracle was required. Penrose Tilings which appear impossible to explain in a world of only 2- or 3-dimensions, are relatively easy to explain from a higher dimensional perspective. They are now understood as slices of a much simpler pattern that can organize itself without inconsistencies.

I am not, of course, suggesting that we must look to some other dimension to explain the presence and meaning of the Equal interval Letter skip patterns. I am suggesting that there may be an unexpected point of view from which the ELS patterns can be understood without confounding either our reason or our faith.

The first class I will discuss consists of the shorter letter skip patterns (mostly less than about 20-letters long) that correlate rabbi’s names with their birth or death dates. The statistical significance of these mostly shorter skip patterns is not as great as with the class(es) of longer letter skip patterns and, because the situation is more complex, the applicability, and thus the credibility, of particular statistical tests is more easily questioned. I would like to propose a possible non-predictive explanation for the shorter, rabbi-name/date, class of patterns. This is based on a different point of view and not on new evidence. Specialists will have to decide if this solution could be correct.

We presume that the rabbi-name/date patterns are predictive because the ELS patterns in Torah are new to us and we believe, therefore, that they were not known to our predecessors. But, if the letter level structure of Torah were known about and understood in generations previous to our own, then a simple solution explaining the presence of rabbi-name/date patterns is available. This is true regardless of how the letter level structure of the Torah came about. Whether it was revealed to Moses or “encoded” by compilers, whether during or near the time of the Babylonian exile (circa 500 BCE) or during the Mishnaic period (circa 200 BCE - 300 CE), does not affect this proposal. All that is required is that the rabbis were aware of the patterns.

If this were the case, then the ELS patterns that correlate rabbis’ names and important dates could have been, what in their day would have been retro-active and not predictive, honorifics. When a particular sage specialized in a particular part of Torah, or had personal qualities or life conditions that paralleled certain sections of Torah, he was identified with that section of Torah, and later he was honored by being given a name consistent with patterns already known to be in that section. Likewise, if necessary, even his putative birth or death date could have been slightly adjusted to conform to the pre-existing Equal interval Letter Skip pattern also previously known to be in the same section of Torah.

I am suggesting that given that these patterns were already known, there is no inconsistency and no miracle if rabbis were then honored by identification with them. Persons mentioned in the Torah and Tanach sometimes have names whose meanings correspond to their nature, function, or position. How better to honor and remember a sage than to emulate the Torah’s example with deserving persons in the Talmudic community? This speculation could be researched and verified or refuted by historians and other specialists.

The second class of ELS patterns I would like to discuss are those that are longer, non-predictive, and extremely statistically robust. These require a somewhat more extraordinary explanation. They appear to be intrinsic to the text and to permeate the text. Although there are skip intervals of 26-letters, 31-letters and a few others, the majority (28 out of 51, in one compilation, see note 1) of the longer skip intervals are either 49 or 50-letters. As it turns out, these are very significant numbers, they are referred to in traditional sources, and they offer a possible explanation.

These ELS patterns are usually displayed on a lattice of letters with so many letters per line by so many lines. It is intended that they be understood to represent the wrapping of the text onto a cylinder in the form of a helix. – Could this be mirrored by or alluded to in the scroll form of the Torah itself?

If the cylinder were 49 (or 50) letters around, the 49-letter interval skip pattern letters would line up in a series of vertical lines (see note 2). One could read them “across the windings,” just like “coded” messages written on a ribbon wrapped on a pole of a particular diameter can be read by rewinding the ribbon onto another cylinder of the same diameter. This coding system was known and used for diplomatic and military purposes in the ancient world. Would it not be natural to use this same system to preserve sacred secrets as well? – Could a Tefillin strap wound on the arm (a cylinder) during prayer be a vestige of this?

How and why was this used in Torah? There are several possible explanations:

  1. The Torah was revealed this way. The use of this system in the ancient world was learned from Torah, or it was given in Torah because it was a form of record already appreciated by the recipients.
  2. The patterns were included at the time of the Torah’s original composition from non-miraculous sources.
  3. The Torah was redacted to include these patterns as a kind of “check sum” as a verification of identity and a test of authenticity so that separate communities could be assured that their Torah was written by acceptable co-religionists and not outsiders, like the Samaritans, for example, who may have copied the sacred text in an unacceptable manner. This could have occurred at or after the Babylonian exile and/or during the time of the composition of the Mishneh and the setting of the Masoretic text.
There are references to the 49 (or 50) letter ELS patterns in traditional sources that can help us decide among these (and other) possibilities. The primeval Torah is said to have been given with the letters written out on the hairs of the beard of Zer Anpin and Zer Anpin comes in 49-levels. Zer Anpin, meaning, perhaps, “lesser face” refers to a kabbalistic image related to the lower 6-sepherot of the sepherotic tree. (see note 3.)

The word B’Reshit, “In the beginning” can be understood to derive from the root ReSheT, which refers to a woven net or network. This is what I believe is at work here. I am suggesting that the text of B’Reshit was, in some meaningful sense, woven (or knotted or braided) and that the letters are therefore intended to be interleaved in some fashion. I am further suggesting that this weave was intrinsic to the text and that it included a cylindrical quality that enabled the 49 (or 50) letter (and the other longer) skip patterns to be immediately seen and read when the text was rolled up in a particular way.

But, why 49 or 50-letters? Could this allude to the Jubilee cycle? Could it be reflective (or determinative) of something in nature? What if the patterns served a specific purpose intrinsic to the Torah text? Beyond assuring the integrity and authenticity of the text, could we be looking at a musical structure with the patterns providing the rhythm, or could they have been intended to enable a person to meditate on the text or on the letter string the text was composed of?

Any or all of these speculations imply that there was patterning in the sequence of the letters of the text that the Author (or authors) wanted preserved. What sort of pattern could this be? This is difficult to speculate on without considerable additional background materials. Discussion of possibilities involving the visual aspects of these patterns is doubly difficult without pictures, but I will try.

We know that the peoples of the high cultures of the ancient middle east had certain technical skills. They were excellent weavers of yarn and cloth. They also produced calendars. Modern inhabitants of Micronesia continue to navigate by the means that their ancestors used to reach Polynesia. They weave sky and tide maps in the form of shallow baskets. These woven maps guide them. Weaving is a traditional way to preserve sacred and scientific information. We could seek clues to the ELS patterns by re-examining the various teachings, anecdotes and legends in the Abrahamic faiths regarding magic carpets, baskets, the Temple and Tabernacle tapestries, Joseph’s dreamcoat, ceremonial or priestly turbans, and even the woven patterns used in mummification. For example, the (questionable) Letter of Aristeas describes extensive wave-work decorating the Temple gifts supposedly proffered by Ptolemy Philadelphus to encourage the Septuagint translation. And, of course, we are told in the discussion of the skills required to build the Tabernacle in Exodus 35:35:

“He has granted them a natural talent for all craftsmanship, to form materials, to brocade or embroider patterns with sky-blue, dark red and crimson wool and fine linen, and to weave.” (Aryeh Kaplan translation, emphasis added)


In modern Judaism, we could re-examine traditions regarding both Tefillin (phylactery boxes bound on the arm, hand and forehead with leather ribbons or straps) and Talitim (fringed prayer shawls) that have braided or knotted features.

Weaving, braiding, and knotting were available technologies in preliterate and bardic societies. Their usefulness can be extended to a literate environment by adding narrative writing to the spaces between the meaningful parts of the woven patterns. Both the narrative and the woven network are then preserved together. Public allegiance to the integrity of the narrative would then also automatically preserve the woven network for those in the know.

There are many pressures that could have allowed knowledge of these patterns to fall into disuse and to eventually not be studied. There is also ample reason why kabbalistic descriptions and discussions of these patterns, such as those I am suggesting (below) are related to discussions of Zer Anpin, could become difficult for us to recognize the significance of today.

But whatever the causes may be for the current obsurity of these teachings, I am suggesting that professionals now have in the ELS patterns good reason to reread traditional sources to check for the possibility that the Torah includes a ReSheT (network) of woven patterns. These might represent the paths of the visible planets, stars and constellations, fleshed out with the narrative text that we now translate as the stories of the Bible. (...or something similar to this.) The ReSheT both preserves the vital calendar information and, perhaps as I outline below, it also becomes an aid to meditation.

What sort of patterns are made by the motions of the visible planets, These patterns show what we call epicycles. Visually, they look like the spiraling patterns produced by the popular “Spirograph” toy. They form basket-weaving and wreath-like patterns in the heavens. It is possible to interpret these basket-weaving patterns as what mathematicians now call torus knots (which also look like wreathes with various numbers of braided windings and layers). Without going into details here, I believe it can be shown that the longer ELS patterns, such as the predominant 49 and 50-letter skips, are direct evidence that (what kabbalists call the primeval) Torah was originally composed not on parchment rolled into scrolls as it is now, but that it was actually written on the hairs of the beard of Zer Anpin, that Zer Anpin refers to some aspect of an assembly of these epicyclic wreath or basket-weaving patterns which really has 49 (or 49+1=50) levels or layers, with the hairs in the beard being the actual lines (or threads) of the woven (torus knot) pattern, and with each thread corresponding to the orbital path of a heavenly light visible in the sky.

Perhaps in some sense, real or symbolic, meditation on the patterns of Zer Anpin was intended to enable us to project the patterns of the temple of heaven (the sky) onto the temple of our body (our mind). It might even be possible that a real and repeatable meditative experience might ensue when a person unified his mind with the heavens in this way. Could this be what is alluded to in the Talmudic story of Rabbi Akiva, a master of the alphabet, who visited PaRDeS, paradise, in his meditations? Again, specialists will be needed to tell if this was historically possible and what real or imagined effects such an exercise might have. (Although I cannot include more discussion here for reasons of space, there is additional evidence that something of this sort may have been intended.)

I do not believe that we should default to easy answers. The discussion above may offer an explanation for some of the ELS patterns. Other explanations may be required for the patterns, such as the names of dozens of fruits and trees woven into the Garden of Eden narrative, that are not covered here.

Scholars and scientists have noted that technology that is not recognized can appear to be like magic. There may be something real here for religious believers and skeptical scholars. It may be that there are deeper philosophical explanations than “It is a miracle of God” or “It was redacted by clever compilers”. Intellectually courageous religious and academic scholars have good reason - and an obligation - to break new ground when they are confronted with a serious and well-substantiated paradox in their current understanding. It may be that, just as with Penrose’s Tiles, paradox will lead to new synthesis.

This is surely worth the extra effort. We are, after all, arguably examining a root document of western civilization which millions of persons claim is sacred to them.

Stan Tenen, 6 February 1996


  1. Email correspondance from Ari Schachter, 1987.
  2. If, for example, the cylinder were 49-letters around, the 50-letter patterns would be off-set by one letter each turn and they would form a slightly slanted, but still distinct stripe. The same holds for the 48-letter skip patterns, but they would be slanted in the opposite direction. Even the 26-letter and other skip patterns could be seen on diagonals, but somewhat less distinctly depending on how slanted they appeared.
  3. See, for example, Aryeh Kaplan, Sefer Yetzirah, The Book of Creation, pages 237-9, Samuel Weiser, York Beach, Maine, ©1990


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