Here, the one-dimensional metric geometry once again conforms to the properties of the royal seal, a dynamic wherein the letters are more clearly perceived in three dimensions. As in Parashah Eikev, one simply cannot help but notice the mathematic and geometric nature of: 1) the narrative; 2) the words used to convey the narrative; 3) the sequences of letters (“paired” as 7s) that are specifically found in the words of the narrative; and 4) the number of times certain specific words and phrases are used, or combined, in relation to one another. The allusions to the Explicit Name are again overwhelming in this regard.
We will examine the sevens mentioned above and other aspects of the geometry in the pages ahead. In the meantime, if you are new to this blog, please read each of the essential constructs listed in the column to the right before proceeding. These pages reveal some of the basic mathematic connections between the letters of God's Explicit Name and the multidimensional geometric characteristics of the luchot, both in the divided state and combined cubic form, along with the internal geometry that casts a shadow known as a magen david. There is a special connection between the Name, the luchot and the geometry of the magen, and together they form a unique signature. We refer to this geometry and its mathematic common denominator as the Signature of the Architect. The purpose of this blog is to show how all of these things connect, and to reveal where the signature geometry is hidden, not only in each week’s parashah, but the physics of time and space, quantum mechanics and celestial dynamics to name a few. Once you are familiar with these constructs you can more fully appreciate each post.
In Parashah Re’eh we will start with the numbers that define the combined cubic measurement of the luchot: 6 x 6 x 6 (216 cubic handbreadths) which are in essence the product of three dimensions with measures of six (these measures are self-embedded in the geometry of the foundation stone: 6 faces in the third dimensions / 6 square or linear handbreadths in the first or second dimension etc). The division is not arbitrary, but rather a function of its geometry. In other words, 216 is self embedded. When all three dimensions are so divided, the result is 42 separate and unique sets of 42 linear handbreadths throughout the geometry as described in the post on "the 42 letters in Sapphire."
6 (First Dimension)
6 (Second Dimension)
(Linear and Square Handbreadths)
6 (Third Dimension)
( Faces / Linear and Square Handbreadths)
The number six is mentioned exactly three times in this parashah in a specific place. These references are clustered in close proximity. Under normal circumstances, a mathematician or statistician would not assign any significance to three six's in a body of text. It would be considered a coincidence. However, the combination of three six's is found so often in Torah that it cannot be dismissed as such.
In Torah, each time we see three six's, it alludes to the dimensions of the luchot and the 216 letters of the Name (6 x 6 x 6 = 216). In Parashah VaYera for example, there were three measures of flour that were each six ounces, and in Parashah Mishpatim, Moshe spent six days in the cloud, then went back and forth for six days delivering the letters of Torah to the people, and these events began (or ended) on the sixth of Sivan, depending on the source. In Parashah Tetzaveh, it was three strands of six, woven into the fabric of the priestly garments. These are specific numbers, sets of numbers and ratios that allude to the mathematic and geometric nature of the luchot, which are in turn a reflection of the letters of God’s Name. Please take time to understand the significance.
In Parashah Re’eh we see this very same reflection but in even more precise terms that correspond to the divided form of the luchot:
15:12 “[your Hebrew slave] may serve as much as six years...”
15:18 “...he has done double the work of a hired hand during the six years...”
16:08 “For six [additional] days you shall eat matzah.”
Its not just six years or six days. It's three six's in the body of text that are grouped together, where one is different from the other two (an embodiment of 'set-theory' in linguistic form) where the one divided side is different from the other two dimensions. Once you look past the story, and perceive the larger reality based on the measure of the luchot (geometry of the foundations stone) or the even larger reality based on the letters of the Name, another world emerges. Contemplate this.
One of the above mentioned six's is different from the other two six's because it reflects this larger reality. It is expressed in terms of days rather than years - one (of six days) is decidedly different from the other two (of six years). This is like the measure of the luchot, where one measure (after division) is different from the other two (6 x 6 x 6 becomes 6 x 6 x 3 but as two tablets). Before its division, the three dimensions of the luchot each measured six handbreadths, but one of those dimensions is now (after division) different from the other two. That’s because one of these dimensions was divided in half to create the shnei luchot (two tablets) before they were brought down by Moshe (paralleling the moment of creation when duality was established). The division along one side resulted in a measure of only three handbreadths along each side of the two halves. So each half is 6 x 6 x 3 (108 cubic handbreadths).
The 108 cubic handbreadths of course echo the gematria of the Hebrew word “chatzei” (meaning “half”) which is also 108. However, the combined measurement of both halves along this side is still six handbreadths, hence three mentions of six where one edge or dimension is different from the other two. That’s a convenient comparison, but can we find a second witness that would confirm that the difference on this side (where the separation occurs) actually alludes to the luchot?
Preceding the text wherein the above numbers appear, there is a verse that describes what is done with the portion that was ‘separated’ for tithes. In other words, the context of the narrative is that of a separation or division:
14:08 “At the end of each three year period you must bring... tithes”
Three? The words, “at the end of each three" year period" are like the words you would use to describe the division of the luchot, that happens to be “at the end of each three handbreadths," which is exactly where the separation occurs. The parallel between the two forms of separation and the measure of three is hard to ignore. Insofar as the luchot are concerned, the two measurements in combination with one another are still six handbreadths, but the side in question is nevertheless divided and each portion "ends" after three handbreadths. So within the text of Parashah Re'eh, we find the same numbers, sets of numbers and ratios, in perfect context, twice, that just happen to correspond to the measurements of the combined cubic form of the luchot, then its division, as well as the measurement and nature of the division, an event that also, remarkably enough, occurred twice. One thing is a mirror image of the other! Each number in combination with one another, together with the words used to describe them, not only reflect the geometric characteristics of the luchot, but the Signature of the Architect hidden within.
As the text of this parashah continues, we also see the royal seal defined by the same numbers and pairs of numbers, specifically pairs of sevens, that correspond to the one-dimensional metrics of the Name, that correspond to the three-dimensional metrics of the star tetrahedron with its 72 triangular corners (this was explained in detail in Parashah Emor and also the essential construct on the sapphire magen david). However, the same unique pattern appears in this parashah:
15:1 “At the end of every seven years, you shall celebrate the remission year”
This is the first and only singular mention of “seven” in the text. A group is then clustered together in close proximity as four pairs of sevens, where one pair is different in that the word pair is in the form of “sevenths.” In other words, this one pair of 'sevenths' is different from the other three pairs of 'sevens,' but we'll get to that in a moment:
15:09 “The seventh year is approaching and it will be the remission year”
15:12 “...in the seventh year you must [free your Hebrew slave]”
16:03 “As part of [the celebration] you shall eat matzah (no leaven) for seven days”
16:04 “No leaven shall be seen with you... for seven days”
16:09 “Then count seven weeks for yourself....”
16:09 “...you must count seven weeks”
16:13 “You shall celebrate the festival of sukkoth for seven days”
16:15 “Celebrate to God your Lord for seven days...”
Note the beautiful symmetry of the text and the nature of the symmetry in dual form. There are specifically four pairs of sevens in the linguistic structure of the above text. That should sound familiar! The faces of a star tetrahedron (three-dimensional magen david) consist of four pairs of two-dimensional triangles (each with seven elements). Notice however, that one “pair” is different from the other three “pairs” (one pair uses the word “seventh” while the other three pairs use the word “seven”). That should also sound familiar!
It is just like the marriage of the letters in the Tetragrammaton with those in the Havaya of Adnoot, where one pair, is decidedly different from the other three pairs of letters, as described and explained in the post on Massey and Devarim and the advanced construct listed to the right, on the "Marriage of the Letters." Moreover, it is also a reflection of the 3D geometry of a star tetrahedron, where one pair of points is different from the 2D plane of the other three pairs of points. Whenever you see an event or a narrative where there are four 'pairs,' where one is different from the other three, it is a reflection of a larger reality that conforms to the nature of the foundation stone's geometry that in turn reflects an even larger reality that parallels the abbreviated forms of God's Name. If you’ve not yet read either of those posts, we would advise you to study them carefully to more fully appreciate the significance of this pattern that repeats itself throughout Torah. In this case, the letters of these Name(s) form the template for the halacha.
In the post on Massey and Devarim mentioned above, we also showed how a pair of sevens are the elements that create the two halves of the royal seal (a two-dimensional magen david) and how four pairs of sevens accomplish the same thing in three-dimensions (the faces of a star tetrahedron). These four pairs of sevens are in essence four two-dimensional magen davids, which in turn define the faces of a three-dimensional star tetrahedron (shown below) all of which reflect the signature geometry associated with the 216 letters of God’s Explicit Name hidden within the royal seal. In the meantime, you may remember the picture below (from Massey and Devarim) that shows how two opposing pairs of sevens, or two halves of a magen, ultimately form two faces of the star tetrahedron. The picture below is skewed so that you can see the three-dimensional relationship within the two-dimensional components of the star tetrahedron. The small triangles in the middle of each large triangle are where the stellation of the opposing tetrahedron passes through the face of its polar opposite. It has been left in the model below to demonstrate the hidden aspect of the corresponding halacha, where the underlying basis is the marriage of the letters (hidden beneath the surface of the corresponding geometry). The nature of the geometry (of the three-dimensional magen david) is a ten-dimensional mathematic reflection of the 72 x 3 = 216 letters of the Explicit Name, and an identical match for the reality imposed by the halacha.
The Larger Triangles are External
(revealed as part the outer surface)
The Smaller Triangles in the Middle, are Internal
(concealed as part of the inner geometry)
We would only add at this point, that the number seven is mentioned in this parashah a total seven times1 in this one section (excluding the word 'seventh') but that should come as no surprise to the readers of this blog. It is reminiscent of the matrix of seven that was also seen in last week’s post consisting of 7 x 7 (x 7) elements; where any given face in two dimensions is seven times seven; and where the cubic form is the external (revealed) mathematic framework for the internal (hidden) mathematic nature imposed by the larger reality: the 6 x 6 x 6 (216) cubic handbreadths of the luchot; which in turn hide the ultimate reality, which is the 216 letters of the Explicit Name.
In another section of that post, the number seven is (once again) mentioned in reference to three festivals. A cubic matrix having three dimensions measured by seven 'elements' is defined (and limited by) mathematic repetitions of 7s & 8s, and 49s & 50s that just happen to conform to our observance of time-related halachic requirements that “sustain" the physical universe. The matrix of seven with its 343 letters/elements are essentially a mathematic reflection of the sustaining utterance that at any moment in time results in the ongoing process of creation (7 x 7 x 7 = 343 which is the gematria of “and God said”) when he spoke the world into existence. This mathematic/geometric construct is further alluded to, in the text describing the requirements for “three times each year," (a measure of time):
16:16 “three times each year... all your males will be seen in the presence of God...”
16:16 “...on the festival of matzahs” (seven days)
16:16 “...on the festival of shavuot” (after seven x seven days)
16:16 “...on the festival of sukkoth” (seven days)
These three “times” (comprised of sevens) allude to the matrix of seven defined by its three dimensions (the outer framework of reality) where each dimension is limited in scope by the 7s & 8s, and 49s & 50s that are integrated into the cycles of observance related to “things-Jewish,” and where it again constitutes an external (revealed) matrix that hides the Hand (breadths) of the signature geometry behind the scenes, hidden in the internal (hidden) matrix consisting of three sixes (geometric model below).
By now you should be able to see that the linguistic structure is not a coincidence, but a reflection of a larger reality that is entirely dependent on the letters of the Name.
The Measured Geometry of the Luchot Defines Cycles of
(click to enlarge)
(click to enlarge)
Lines/Edges = Outer (Revealed) Matrix of 7 x 7 x 7 (343 'Elements')
(a subset of the letters in Torah at any moment in time)
Spaces = Inner (Hidden) Matrix of 6 x 6 x 6 (216 Elements)
(the cubic handbreadths of the luchot...
...letters of God's Name hidden beneath the surface of our physical state)
...letters of God's Name hidden beneath the surface of our physical state)
The small cubes (the spaces pictured inside the above matrix) in between the 343 "elements" (lines/edges) are the intersections where the elements of the outer matrix connect with those of the inner matrix. There are 216 such spaces hidden beneath the surface of the matrix created by our halachic observance (in cycles of 7) which corresponds to the number of letters in God's Explicit Name. The spaces are a geometric manifestation of the 216 letter Name and the lines are a geometric manifestation of the 42 letter Name as shown in the post on the 42 letters in sapphire. It is, in essence, "the Hand" (of God) in the glove of reality (the created universe). This is why the Sages of Israel said that we are co-creators (with the Holy One Blessed be He) and that without our observance, the universe would cease to exist.
As if to echo this larger reality, the text of Re'eh includes one more reference to “seventh,” for a total of three instances, the third being: “You shall... eat matzah with the seventh day as a retreat.” This “seventh” is the third and final reference to the word “seventh” in the parashah. The total thus comes to seven mention’s of the word seven (7) and three mentions of the word “seventh” (7th) reflecting the three dimensions of seven in the outer matrix that corresponds to the flow of time and this aspect of reality in the physical universe. At the same time, it reflects the nature of the 10 sephirot, divided into the three upper and seven lower “dimensions,” the means by which God interacts with the created world.
For more information on the matrix of seven, and the 343 (7 x 7 x 7) elements that are "defined" by our observance, see last week's post on Parashah Eikev and also the post on Behar and BeChuko-thai where we provide more details and explain additional significance.
In summary, we see once again in this parashah, the interconnectedness between the luchot; God’s Name; the events described in the Torah; the word level of the text; the letter level; even the mathematic spaces in the matrix created by the letters; as well as everything else in the physical and nonphysical universe. Everything, together, displays this wonderful, unique, inexplicable mathematic and geometric connectedness that defies logic. The nature of the various combinations, the number of repetitions of these combinations, together with what they represent in terms of complex three-dimensional geometry or two-dimensional geometry, would simply have been beyond the ability of any man or group of men to compose. The numbers, sets of numbers, and ratios between sets, are the underlying superstructure of the text which is an extension of those numbers. This is why even the mathematic value of the letters reflects the nature of the combinations. They are all a part of the royal seal wherein the Signature of the Architect is hidden. Who could write a meaningful narrative with such mathematic and geometric perfection? Only the Architect Himself. And who would preserve knowledge of His Great and Powerful Name? Only the Jewish people.
Footnote 1 - There are three pairs of "sevens" in the text, and one singular mention of the number seven (that is not paired).