VaYechi

Once upon a time there was a diamond cutter who was an expert in the cutting of various gemstones. He was asked to cut a certain unique stone that was made of sapphire, into two halves. It happened that this particular stone was a cube and the measure of each side was 6 hand-breadths. Before cutting the stone, he studied it to ensure that the division was made according to his employer’s request. The cutter made a mental note of the cube’s 6 faces, its 12 edges and 8 corners, and realized that its geometry was defined by these 26 elements, a number that just happened to be the gematria of his employer’s name.



The cutter was told that when the division was made, each half of this stone should be identical in size and shape (6 x 6 x 3 hand-breadths). The time had not yet come to make the division, but still, he contemplated how to make the cut by envisioning a dotted line down the middle. The cutter noticed that there were 5 faces on each half of what he would cut1. He then counted the edges and noticed that there were 8 on each half, of what he would be dividing. And finally, he noted the 4 corners on each half (before division). When he added them together together, there were 17 elements defining the characteristics of each half.



This particular stone was like no other the cutter had ever seen and so he was very careful in dividing it, so as to ensure the proper result. The twin stones were to be given to the employer’s family. 

An explanation of the story will continue in a moment. In the meantime, if you are new to this blog then you should read each of the essential constructs listed in the column to the right before proceeding. These pages explain some of the basic connections between the letters of God's Explicit Name and the multidimensional mathematic and geometric characteristics of the luchot (tablets of the covenant) 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 that creates a unique signature. The purpose of this blog is to show how they connect with one another and to reveal where this Signature of the Architect 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. Without the background provided by these essential constructs, the posts will make little sense.

Combined Cubic Form of the Luchot
(its geometry before division)

Click to Enlarge

17 Elements                 -               17 Elements
(5 Faces, 8 Lines, 4 corners)         -       (5 Faces, 8 Lines, 4 corners)

The actual story is of course well known. The sapphire block (in Mishpatim) was divided and brought down by Moshe as the luchot. Moshe spent 6 days in the cloud, and for 6 days he brought [the letters of] Torah to the people. It was the 6th of Sivan. The description of the event alludes to the measure of each side and the ratio of the stone that was to be divided (6 x 6 x 6 hand-breadths). 


The measurements of a cube are all equal. Its edges, points and faces are defined by the characteristics of it 26 elements. However, after you divide a cube in half, each half still has 26 elements (although not all of the edges or faces remain equal). 

The 26 elements of a cube (as in the combined cubic form of the luchot) are like the gematria of the Tetragrammaton which is 26. The Tetragrammaton is the root of the Triad Havayah of 72. God is One and Indivisible, and so the division of a cube, and the combined cubic form of the luchot, specifically, into two halves, does not in any way effect the number of elements (the essence) that defines it. It merely establishes "duality," as in the dual (male ~ female) nature of reality, that is well known in physics.



From this 'blueprint' came forth 10 sephirot and 22 Hebrew letters, which were combined and permuted until all 304,805 letters [of the written Torah] had been received. 


In addition to the 26 basic geometric elements that define the outer measure of the luchot (6 x 6 x 6 hand-breadths) the volumetric measure of the combined luchot was 216 cubic hand-breadths. After division, there were 108 cubic hand-breadths (elements) in each half of the matrix, each half being 6 x 6 x 3 hand-breadths (6 x 6 x 3 times 2 = 216).

 Keep in mind that the gematria for the word "half" in Hebrew is 108.

These sapphire twins were given to Israel, but hidden within their mathematic and geometric characteristics, is the Signature of the Architect (the "employer" who ordered the cutting of the stone). The combined cubic form of the sapphire block was/is the cosmic blueprint for the created universe. It should be noted that at this moment in time (as the historical account in VaYechi takes place) the luchot had not yet been divided but were “soon” to be given (along with many secrets) and entrusted to Israel who would be charged with the duty of preserving its specifications (fulfillment of halacha).

Thus...

“When it came time to give birth...”

“...there were twins in her womb.”

Some reflections are of course brighter than others. There are those that are buried so deeply, that they could easily be considered coincidences were it not for their place and position within the scheme of things. The date of an event, is a good example. Sometimes they are very bright and the significance is rather obvious. At other times they are not.

The blueprint does cast its shadow into the physical universe below, that is undergoing the process of creation. One of these shadows appears in the year 2199, when “Rachel [gave] birth to Yoseph” (VaYetze). The number 21, for example, has special significance throughout the Torah. It is factored by three 7s. The number 99 is also significant and can be factored as three 33s. Ordinarily, something like this would just be a coincidence. However, we've seen these same numbers many times whenever key events are concerned (the three 7s for example were a prominent mathematic feature in Parashah Miketz where three 7s were repeated four times, and the number 7 itself, a total of 28 times). These three 7s are a function of the 7 points of intersection in each of three dimensions, that are hidden between each measured hand-breadths of the evan shetiyah (foundation stone). However, it is also found in its internal tetrahedral geometry, or what we call "the royal seal," (the star tetrahedron (three-dimensional magen david) that is mathematically at the heart of the foundation stone. This tetrahedral geometry has three small faces on any given side, with 3 triangular (3-cornered) facets. The three 7s (associated with the 28 elements in the tetrahedral geometry of the luchot) define each edge of a triangular matrix of 7 and 'create' the face of a tetrahedron defined by 72 three-cornered elements (as shown in the post on Miketz) all alluding to the signature geometry of the Architect (with 3 x 72 or 216 letters). The three 7s also allude to the movement of time (measured in cycles of 7) as it relates to the three dimensions of space. This can be seen in the cubic matrix of 7 that is defined by our calendar related halachic observance (7 days, 7 x 7 days, 7 weeks, 7 years, 7 x 7 years etc). The points of intersection between the measured handbreaths (7 x 7 x 7) are a function of the 42 letter Name, and each measured hand-breadths is a function of the 216 letter Name. For more on this geometry and these unusual sets of numbers see the post on BeHar and Bechuko-thai).

The diagram below shows any one of the two-dimensional surfaces on a star tetrahedron. The grey triangle in the middle is the stellation of the opposing tetrahedron which is "three-dimensional" with respect to the smaller, two-dimensional faces surrounding it. Each of those small faces in turn has 3 triangular corners, so the end result is 3 within 3, within 3 or three 3s (3,3,3). The final 3 is inevitably hidden within the fourth dimension and can only be perceived over time (the three white triangles in the middle are a fractal representation of the fourth dimension with respect to its two and three-dimensional counterparts1. 

This pattern of 3 things within 3 things with 3 more things is prevalent throughout Torah and in many mitzvoth.  On a practical level, the current model of string theory posits a hologram with nine dimensions of space and one dimension of time (three specific 3s plus one) although sefer yetzirah would describe these as 10 vectors in five dimensional space. In the Torah, we see this aspect of the blueprint or combined cubic form of the luchot (three specific 3s) in such things as the plagues of Egypt, where there were 3 types of warnings in 3 places (nine plagues) along with 1 additional plague, corresponding to the 10th plague that was totally unique (as is known). Each is a reflection of the geometry in the blueprint, which is in turn a reflection of the letters of the Triad Name of 72, which has a total of 72 (nine x 8) 3s.

Three (Corners) within Three (Triangles) within Three (More Triangles)
Plus One Different from the Others

The Geometry of any Two-Dimensional Face on the Royal Seal2
(...is One "Face" of a Three-Dimensional Magen David)
(The Grey Triangle is the Stellation of the Opposing Tetrahedron in the 3rd Dimension)
(The 'Blueprint' or Luchot Defines 'the 5' Reconciled by 'Dual Resonance' and the 9 Plus 1 of String Theory)

 
In addition to what is mentioned above, the number of polygonal elements in the first 6 layers of a tetrahedral matrix of 7 is 91 (shown/diagrammed in the post on Miketz). Yaacov just happened to be 91 years old when “Rachel [gave] birth to Yoseph” (one of 'two children' and a geometric reflection of the original moment of creation). It also happens to be the sum of the gematria of the two primary abbreviated forms of the Explicit Name: the Tetragrammaton (Yud-Key-Vav-Key 26) and the Havaya of Adnoot (Aleph-Dalet-Nun-Yud 65) where 26 + 65 = 91. Are these numbers and patterns a coincidence? Or, are they evidence of a sophisticated design (seen here in the historical narrative) that conforms to the internal geometry of a cosmic blueprint of divine origin (the shnei luchot)? We should look for additional witnesses.

Yoseph grows to be a man and in the year 2216 another shadow appears when... Yoseph “reaches the age of 17,” so Yaacov “assigns to Yoseph [the royal] garment” (VaYishlach). Within days, he is “sold” and becomes a slave. The years of happiness in which Yaacov was together with Yoseph (17 years) come to an abrupt end, but another shadow is cast. A period of 22 years begins, years in which they are separated. During this time, Yoseph becomes ruler of Egypt and a famine engulfs the land. Yoseph’s brothers come to Egypt and are eventually reunited with Yoseph. In the year 2238 they bring their father Yaacov to Egypt and at long last, Yaacov and Yoseph are once again together. Yaacov says to Yoseph “I have seen your face and you are still alive,” revealing yet a third shadow, a period of time that will last for another period (an opposing period) of 17 years (years in which they are together again as opposed to being apart from one another). Yaacov says to Pharaoh, “My journey through life has lasted 130 years” (VaYigash) and then later in this weeks parashah Yaacov.... breath[s] his last having lived to be 147 (147 - 130 =  the 17 years they were together again).

With Yaacov’s death, the stage is set for the eventual exodus from Egypt and the events at Mt. Sinai where Moshe goes up, sees the sapphire block, it is divided in 2 and given to Israel as the luchot. These 2 luchot contain the plans and specifications for the events herein described (and quite literally everything else). The 17 elements on the 2 halves of the cube (before division) cast their shadows below in the events that transpire, and so we see the 2 periods of 17 years in which Yaacov and Yoseph are together (as when the luchot were in combined cubic form) separated by 22 years (like the 22 letters that ultimately emerge from the primordial form of the Torah). The 22 years are a reflection of the 22 letters (22 primordial forms of energy) that were combined and permuted to create the universe (a limited subset take form in the 304,805 letters of the written Torah). These geometric aspects of the primordial torah cast their shadows and so we see them manifested as Yaacov and Yoseph separated for 22 years, like the letters that came forth when the two halves of the luchot were separated from one another (divided and brought down). 
The lower 'events' are the mirror image of the upper/higher reality.

Are these numbers, sets of numbers and patterns merely a coincidence? Taken individually there is certainly that possibility, but considering that opposing periods of time (that conform to very specific 'opposing' aspects of the internal or external elements of cubic geometry and the measured geometry of one stone in particular) continue to repeat themselves throughout the Torah, the interconnected nature of the various elements suggest otherwise. The history of mankind reflects the mathematic characteristics of the blueprint either way, and the mathematic and geometric characteristics of the Name hidden beneath the surface, that we see in so many mathematic and geometric forms, that all bear witness to the Signature of the Architect who so carefully designed everything from the beginning. 


There are additional shadows in this parashah that allude to the Triad Name, for example: “Yoseph died at the age of 110” having had 10 years subtracted from his life for the 5 things said against his father Yaacov and translated (5 times) without rebuttal (5 opposite 5). This has already been explained in other posts and will not be repeated here.

_____

Footnote 1 - With 5 faces on each 'half,' there are 10 halves that are '5 opposite 5'. This is an external reflection of the internal geometry within the combined cubic form of the luchot (5 mathematic constructs opposite 5 counterparts, or more specifically the geometry giving rise to the platonic solids, and well known in mathematics).

Footnote 2 - The concept being integral to the third iteration of what is called the Sierpinski Fractal (or Sierpinski Triangle) a two-dimensional representation of higher dimensionality.