Sunday, December 24, 2017

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 handbreadths. 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 handbreadths). 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 handbreadths). 



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 handbreadths) the volumetric measure of the combined luchot was 216 cubic handbreadths. After division, there were 108 cubic handbreadths (elements) in each half of the matrix, each half being 6 x 6 x 3 handbreadths (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 handbreadths 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 handbreadths 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). 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.

Sunday, December 17, 2017

VaYigash

This week’s parashah has a beautiful geometric reflection of the letters in God’s Explicit Name, hidden in at least three places, beginning with the text that tells us, ‘...these are the sons of Yaacov's wife Rachel."

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.

Regarding the first instance of the three mentioned above, this Name is hidden within the details of the phrase referring to: “the sons of Yaacov’s wife Rachel,” and its counterpart: “all the souls coming to Egypt... not counting the wives of Yaacov's sons.” 

In this segment of the text, Rachel is specifically identified as Yaacov’s wife. In the case of the other three matriarchs, Bilhah, Zilpah and Leah, the Torah merely says “these are the sons of...” without identifying them as Yaacov’s wives. Rashi finds this noteworthy, saying that Rachel is mentioned singularly as the wife because she was mistress of the household. However, there is another explanation. The ratio and the numbers are a faint reflection of the same math and geometry that appeared in last week's parashah. 

Last week, Pharaoh’s dream encompassed a 14 year period, one in which Yoseph was not only a ruler but the most powerful man in the known world. This 14 year period of time was directly mentioned in the text, while the preceding 14 year period (starting when he was sold a slave) was not directly mentioned. The numbers, the ratio and the nature of the elements all correlate with the male-female polarity of the royal seal or magen david (with 14 elements in one half, opposite 14 elements in the other half) and the corresponding male-female letters of the Name (associated with each tetrahedral point) that sustain a physical universe in like form.

The time in which Yoseph was a slave had to be calculated by subtracting the year in which the “years of plenty” started, from the time when Yoseph was sold. These 2 periods of 14 years stood opposite one another, and also in stark contrast to one another, alluding to the Name of the Architect found in the geometry of the royal seal (three-dimensional magen david) as the 14 elements of the male and 14 elements of the female halves of a star tetrahedron. This in turn is a reflection of the mathematic nature of the Triad Name (recalling once again a tradition that the luchot were “tetrahedrons” and knowing that their combination in the form of a star tetrahedron is one of 5 internal mathematic constructs found with the combined cubic form of the luchot). 

The marriage of the abbreviated forms of this Name can also be seen in the narrative where 1 wife (Rachel) was mentioned by name in the text. She was "different" from the other 3 (Bilhah, Zilpah and Leah) who were not mentioned. This is a reflection of the ratio between the letters of the 4 "couples" that are married together (in unification) or more specifically the Tetragrammaton and those in the Havaya of Adnoot, as explained in the post on Parashah Ki Thetze and also the Marriage of the Letters. It is also a characteristic in a primary geometric component of the royal seal, specifically the tetrahedron, which has 3 points in one (lower) dimension (corresponding to Leah, Bilhah and Zilpah) and 1 point in the dimension above (Rachel) specifically identified as Yaacov's "wife" in the text. This same geometry is observed throughout the Torah, one example being the 4 strands of tzitzith that are doubled over: 3 white and 1 techelet. Each is a facet that is a characteristic of the blueprint (luchot) which is in turn a facet of the Name and its abbreviations.

In this week's parashah we see the same tetrahedral geometry and the same reflection of the male and female halves, where Rachel was the matriarch with 14 male descendants, hence the specific reference to her as Yaacov's wife. As with the previous reflection, these 14 souls are also mentioned directly in the text “...these are the sons of Rachel... in all 14 souls.” The 14 daughters of Yaacov however, are not mentioned directly, but alluded to where it refers to the wives who were not counted (each son by tradition having a twin sister at birth). The combination of male-female “elements” (in the 14 sons mentioned, and the 14 daughters not mentioned) is a very bright reflection of the tetrahedral geometry in the royal seal. These were the daughters of Yaacov, 14 in all (the female) counting Dinah and the triplets of Rachel (2 of which were daughters). In other words 14 male opposite 14 female. So once again we have an allusion to the internal geometry of the luchot (tetrahedrons) in this particular form. For more information on this one-dimensional mathematic expression and its three-dimensional counterpart (which are both reflections of the royal seal and the letters in the Name) see last week's post on Miketz 
and also the post on Emor.

In the second instance, the Triad Name is seen as a mathematic reflection of the words Israel (Yaacov) spoke to Yoseph “Now I can die, I have already seen your face, for you are still alive.” An explanation of this reference will have to wait until next week’s parashah, when this particular geometric reflection culminates in the events and the correlation is complete (in VaYechi). 


The third and final instance that we will mention, is one of the more significant in the entire Torah where: “all the souls coming to Egypt with Yaacov... were 66,” together with “all the souls of Yaacov’s house coming to Egypt were 70.” This would seem to be a contradiction, except for the fact that 4 souls were already in Egypt (Yoseph, Aseneth, and their two sons  Ephraim and Menashe). The ratio of 4 to 70 is found numerous times in the Torah. It is found twice in this parashah alone. The first example is mentioned (directly) above. The second example is alluded too indirectly, where “Yoseph gathered up all the money [and] ...brought the money to Pharoah’s treasury.” It is well known that there were 4 treasuries of gold. What is not so well known is that each contained “70 quintles of the precious metal.” The ratio of 4 to 70 is also found in Mishpatim where, Moshe, Aaron, Nadav and Avihu (4) along with the 70 elders ascend before the throne (of God) and it is found in “11 kinds of spices were in it, as follows: stacte, onycha, galbanum, frankincense (4 spices) each weighing 70 maneh,” to provide the obvious examples.



These numbers or sets of numbers, and this ratio in particular (whether the 4 are included or excluded from the 70) holds a very deep secret that is examined at length in the post on "the Incense and the 216 Letters."

In-so-far as this post is concerned, it is sufficient to point out that when a tetrahedron (with its 14 elements) is subdivided by an opposing tetrahedron, the result is not only a magen david (in the geometric form of a star tetrahedron) but the number of elements in each (subdivided) tetrahedron increases (from the 14 mentioned above that were described in the post on Miketz) to 70 elements. There are 4 stellations (or points) on each of the tetrahedrons of the star after the subdivision (see the pictures below).

View of a Star Tetrahedron from the Top
Click to Enlarge


In the meantime, the number of elements resulting from the division is calculated as follows. The subdivision results in 4 tetrahedrons that are half the size of the original, and 1 octahedron in the middle. A single tetrahedron is made up of 4 faces, 4 points (8 elements). The 4 tetrahedrons together thus have 16 faces and 16 points (32 elements). The octahedron in the center has 8 faces and 6 points (14 elements). The lines that cause the division (from the intersection) are one-dimensional and should not be counted twice (as separate elements on each of the resulting geometrics). Therefore the number of lines equals 4 x 6 or 24. The 24 lines together with the 22 points and 24 faces equals 70 elements. The stellations, or points on the star (4 on each) can be further subdivided in like manner, the result being a star tetrahedron with 2 tetrahedrons, each with 4 stellations having 70 elements, with a total of 72 triangular corners that geometrically reflect the 216 letters of God's Explicit Name in their triad form. Note also (below) that a two-dimensional magen david can be seen in the orthographic projection of just one tetrahedron so divided.   

The 70 Elements of a Tetrahedron
(after being subdivided by its polar opposite)


The Orthographic Projection in the Three-Dimensional Magen David Above
(seen as a “shadow” in each 'half' below)


The important thing to remember is that God’s Name is imprinted (mathematically and geometrically) on every aspect of time and within every dimension of physical space in His creation, as well as the intrinsic characteristics of things Jewish.


Monday, December 11, 2017

Miketz

In Miketz, we find mathematic allusions to the letters of the Triad Name hidden in so many forms and so many places that we cannot mention them all in a single post. Some are found in the volumetric measure for the combined cubic form of the luchot. Others emerge from its internal geometry in the form of the royal seal or magen david. 

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.

For those already familiar with the basic concepts, we’ll start our examination of this parashah with the statement that: “...two years passed to the day [and] Pharaoh had a dream.”



Why was it important for this event to occur at this precise moment in time, as it says "two years passed to the day." What happened exactly two years earlier? Pharaoh’s two courtiers, his wine steward and his baker, each had a dream (the year was 2228). We’ll come back to the year in a moment. In the meantime, Yoseph interpreted their dreams and then 3 days later these dreams came true. The baker was executed and the wine steward released as Yoseph had said. Yoseph of course, was relying on the wine steward to tell Pharaoh of his innocence and he failed to do so, thus “two years passed to the day [before] Pharaoh had a dream."

Mathematic and/or geometric shadows of the Triad Name are often embedded in events like this. Some play themselves out over periods of time. Others occur at specific moments in time. Still others are found in a combination of both. In this case it requires this precise "moment in time" for God’s Signature to be revealed. The timing is a function of the mathematic center point between two opposing tetrahedrons (the explanation will be diagrammed in subsequent paragraphs). It was at this moment that Yoseph transitioned from being an imprisoned slave (the lowest state) to being the most powerful man in the known world (the highest state). This can only happen in a cosmic plan of unprecedented proportion. When it does, we can expect to see the Signature of the Architect somewhere mathematically hidden beneath the surface, and indeed we do. How does this reference correspond to the Name of the Architect?



Before delving into these numbers we need to backtrack to Toldot when Yaacov and Esav (the twins) are born. It was the 108th year of the millennium. The twins, or 2 being "born" in the 108th year, is a reflection of a larger reality originating with the 'letters' of the Name and the luchot that these 'letters' define, where 2 x 108216. Coincidence? Time moves forward and then "coincidentally," another 108 years pass, at which time (again "coincidentally") Yaacov  reaches the age of 108. He then assigns the royal garment to Yoseph and it just happens (again "coincidentally") to be the 216th year of the millennium. All the numbers are clear reflections of the mathematic template for creation (the luchot) and its division when it was brought down (108 cubic handbreadths + 108 cubic handbreadths = 216 cubic handbreadths).

In the case of this parashah, this same allusion is seen as a reflection of the complex geometry within the luchot, or more specifically the three-dimensional magen david (star tetrahedron) within its combined cubic form, which has 36 triangular corners (3 x 36 = 108) on one tetrahedron opposite 36 triangular corners (3 x 36 = 108) on the other tetrahedron (as explained in the page on 'the sapphire magen david' to the right). The allusion (in this parashah) merely emerges from a different "set" of numbers, pertaining to the exact same geometry. Where is this unique set of numbers found? 

After the events and their respective dates mentioned above transpire, time again moves forward and Yoseph is sold that very year (2216). He works as a slave until his release from prison in the year 2230. Thus, 14 years pass (exactly 14 years) during which Yoseph is a slave. The "moment in time" arrives (in this parashah) for "Pharaoh [to have] a dream" that will result in a complete reversal. What period of time does Pharaoh’s dream encompass? It’s about the next 14 year period of time. The “fulcrum” (or moment in time) between the two "halves," or two 14 year periods, is when Pharaoh has a dream and Yoseph transitions from being a slave, to being the viceroy of Egypt, where he would effectively become the most powerful man in the known world. In other words, the mathematic center point (the dream mentioned above) is at the exact moment in time separating these two 14 year periods. These two periods stand in stark opposition to one another (14 opposite 14) not only in terms of time, but in terms of stature and any number of other polar opposites like feast and famine. Mathematically, this week's parashah brings us to a moment in time (a mo'ed) that separates the two halves of reality that are seen above as 108 opposite 108. How do these two opposing 14 year periods of time equate to 108 opposite 108? What does it mean, and why is it significant? Both sets of numbers originate in the metrics of the luchot and its internal tetrahedral geometry. 

In Parashah Emor we showed how this geometry took the form of pairs, and specifically pairs of opposing 7s and/or pairs of opposing 14s. These pairs are one-dimensional expressions that 'describe' the tetrahedral geometry of the “royal seal” (
7s in two dimensions, 14s in three dimensions). More specifically, the pairing correlates with the metrics for each opposing half. In two dimensions each half consists of 7 basic elements. In three-dimensions, each half consists of 14 basic elements. If you’ve not yet read the post on Parashah Emor, now would be a good time to do so. If you are new to this blog, again, you should read the essential constructs listed in the column to the right before proceeding, as they explain the basic mathematic and geometric characteristics of God’s Explicit Name. 


The Elements of a Two Dimensional Magen David
(as 7 Opposite 7)



An ordinary magen david is essentially a two-dimensional shadow of a three-dimensional star tetrahedron which is characterized by 72 triangular corners. These corners have a direct one-to-one mathematic correspondence to the number of letters in the Triad Name (3 x 72 = 216). The star consists of two tetrahedrons that have been merged or married together in opposing directions. Each tetrahedron consists of 14 elements (4 faces, 4 points and 6 edges = 14 elements) and so two tetrahedrons can be described in terms of the 14 elements on one, opposite the 14 elements on the other (just like Yoseph's 14 years as a slave opposite his 14 years as a ruler in Pharaoh’s dream). The number of triangular corners is ultimately 108 opposite 108, and so these two sets of numbers converge in the geometry of the royal seal. One set represents the number of basic elements in each half. The other set represents the number of corners on each of it triangular faces. It would be one thing if this phenomena was limited to just the narrative of the Torah. It's another to find the same phenomena in the physics of the universe. Contemplate the significance of this before proceeding. If you've read the post on the Primordial Torah, then you've seen how the mathematic characteristics of the cosmic blueprint give rise to the nature of the physical universe, as well as the history of mankind, and there is no doubt as to its statistical significance or the odds that its various measurements (in terms of cause and effect) are far more than mere coincidence (using even the most stringent of statistical analysis).

14 Years as a Slave Opposite 14 Years as Ruler



When the 14 elements of the one tetrahedron are merged together with the 14 elements of the other tetrahedron, they subdivide one another and become the stella-octangula, or star tetrahedron (three-dimensional magen david) with 72 triangular corners mentioned above. 

The numbers reflect the geometry of the letters in the Explicit Name with 72 triplets, and the male-female pairing alludes to the division of the letters in male~female form, that was necessary to create a universe in like form. However, at the same time, it alludes to the  (re)unification of the (letters in the) Name: “For the sake of the unification of the Holy One blessed be He...” where the letters associated with the opposing halves will be unified/sanctified in the minds of those who would witness the events soon to transpire in Egypt.



The Merging of Two Tetrahedrons
(Star Tetrahedron)







The Magen David
A Shadow of the Star Tetrahedron
A Three-Dimensional Geometric Construct within 'the' Cube of Sapphire


In last week's parashah, you will remember that the “stars” in Yoseph’s dream had a similar mathematic relationship to the number of letters in the Triad Name, although in that case, the correlation was at the two-dimensional level. Specifically, there were 12 (two-dimensional) stars with 6 points having 3 corners, for a total of 216 points. The numbers, or sets of numbers, and the ratio here, are slightly different, but the resulting mathematic reflection is the same. The 14 opposite 14 (or 2 tetrahedrons in the three-dimensional star) when merged together, again have 72 triangular corners (3 x 72 = 216) and so both, in their own way, reflect the Signature of the Architect in the associated events. The unification of the 11 stars (with the 1 already in Egypt) alludes to how Yoseph’s descent into Egypt would bring about a unification that would sanctify God's Name. Now, in Miketz, we have the 2 opposing 14 year periods of time alluding to the same thing. These mathematic and/or geometric reflections are everywhere, like ripples in a pond, and there are more of these same allusions to the royal seal or magen david (really the geometry of the Name) in this parashah.

In Pharaoh’s dream, for example, there are 14 cows and 14 ears in two dreams (again 14 opposite 14). Remember the luchot were brought down twice and so internally, this would geometrically 'create' two stars. So in the narrative we see two opposing 14s in two dreams. As if to emphasize the underlying significance of the number 14 in the parashah, as it would relate to the Name, the small gematria of Miketz is also 14.



In the cosmic scheme of things, our existence may be little more than a metaphor for God's Name! Even the motion of the stars and planets conform to the geometry of its letters. As the stars move through the heavens, their circular journey takes roughly 26,000 years to complete, alluding to the gematria of the Tetragrammaton (yud-key-vav-key) which is 26. The time period for each constellation in the precession is 2,160 years, a multiple of the number of letters in the Name. Moreover, the axis of the earth moves 1 degree every 72 years in relation to the stars under the rolling vault of heaven, all of which allude to the Triad Havaya of 72 and the mathematic nature of His Signature within the luchot. In this parashah, a reflection of the royal seal and its 72 triplets is hidden in so many places beneath the surface of the text, that it is difficult to ignore.

In addition to the pairs of 14s mentioned above (associated with the three-dimensional form of a tetrahedron) there are also patterns of 7s that correspond to the same geometry in two dimensions (the magen david being a two-dimensional shadow of the star tetrahedron). In fact, the number seven is mentioned a total 28 times in this portion of the Torah, the number being the sum of opposing 14s. Keep in mind that the process started with the dreams of the baker and the steward in the year 2228; that exactly 28 years elapsed between the sale of Yoseph, until the end of the period of time in Pharaoh’s dream (14 + 14 = 28) as well as the two opposing periods of time in which Yoseph's status would be either slave or viceroy (14 + 14 = 28). So the number of times that the number 28 is found in the text as a function of 7s and 14s, characterizing various events, is a further reflection of the geometry in the royal seal and the letters of the Name, but in this case as they apply to the events involving Yoseph.

The breakdown of these twenty eight 7s is quite revealing in and of itself, since they form their own unique pattern over and above what has already been discussed. However, before we explain how and why the breakdown of these 7s is so significant, it is worthwhile reviewing the geometry of the royal seal, and how it correlates with the 216 letters, so that we don’t lose sight of the larger reality (which is how God's Name 'rules' time and space).

There are 8 faces on (the) two tetrahedrons that form a three-dimensional magen david (star tetrahedron) as shown in the picture below. Each face is triangular. Each face has a polar opposite, and each face has 7 basic elements (3 lines, 3 points and 1 face) those opposites being 7 opposite 7. When each triangular face is married to its polar opposite, the result is a magen david. There are 8 triangular “halves,” and the 4 faces of one “merge” with the 4 faces of the other (in geometric male-female fashion). The marriage of the 4 with there 4 counterparts, creates 4 two-dimensional magen davids. It's important to remember that these pairs (at the two dimensional level) are actually the 8 faces of the star tetrahedron (at the three-dimensional level). So even though they are "married together," they nevertheless remain separate and apart from their counterparts by virtue of their position in the third dimension. The geometry is identical to the nature of the abbreviations of the Name: the 4 letters of the Tetragrammaton (Yud Key Vav Key) opposite the 4 letters of the Havaya of Adnoot (Aleph Dalet Nun Yud) that are (in unified form) the 4 letters of Ehyeh (Aleph Heh Yud Heh). The letters must remain separate and apart or else the "duality" (in physics and quantum mechanics) would collapse and universe would return to it's original state prior to creation.

The picture below shows two opposing faces (in red and blue) that constitute one magen david (of the 4 that ultimately define the faces of a star tetrahedron). The faces are skewed because of the angle in which they are viewed, so that you can see where they are in relation to one another and to the other three pairs of triangular faces.



2 of the 8 Opposing Faces on a Star Tetrahedron
(Components of a Two-Dimensional Magen David)




We see pairs of 7s (or two halves of a magen david) and always in opposing form, because of their geometric origin in the Primordial Torah. However, we also see them as triplets (three 7s) where the number 7 is mentioned three times in succession like 7, 7, & 7; and/or 7 x 7 x 7).

Three 7s mathematically allude to the 3 dimensions of physical space that move through 1 dimension of time, as seen in the measure of the luchot as 7 x 7 x 7, which is the primordial origin of time, found in cycles of 7, defined for example by calendar related halachic observance (mentioned many times throughout the blog). 


In addition to what has been explained above, three 7s is also a one-dimensional expression for “the measure” of each side; of each face; of each triangular half of a tetrahedron (with 7 elements per face). You can see this in the picture below, where each of the three sides on any given face of this tetrahedron are measured in terms of 7 places or positions, and how this results in a total of 28 places/positions in the triangular matrix. 
  

How Three 7s or 28 Elements Define
the Edges and Points of any Given Face on a Tetrahedral Matrix of 7


What’s interesting is that three 7s with 28 places/position (like the period of time involving Yoseph that we mentioned above) can define any given face, or they can define the entire star tetrahedron when it is expressed in terms of its 14 elements opposite 14 elements (28). One is its two dimensional reflection, the other is its three-dimensional reflection. In this parashah we see the interconnectedness of these numbers, sets of numbers, ratios between the sets, in both two-dimensional and three-dimensional magen davids, as well as the numbers characterizing the events that are unfolding.

Having examined 7s and 14s as they relate to the two-dimensional triangular or three-dimensional tetrahedral geometry, and their relation to the royal seal (which is a reflection of the number and nature of the letters in God’s Name) we will proceed to examine the significance of the breakdown in the 28 times the number 7 is mentioned in the text.

The breakdown (that we will list in a moment) consists of two opposing groups of three 7s, followed by another two opposing groups of three 7s. There is a brief separation in the text and then we see two pairs of 7s followed by another
two pairs of 7s. Finally, these patterns transition to one (single) pair of 7s; followed by a second (single) pair of 7s; followed by a third (single) pair of 7s; followed by a fourth (single) pair of 7s. Notice also that it progresses from groups of threes, to groups of twos, to groups of ones, a progression that nicely correlates with the concept of one, two and three-dimensional space.

The pattern starts with the three's:

41:2,3 & 4: three 7s
41:5,6 & 7:
three 7s
 
(then there is a separation in the content of the text before the next two groups appear)

41:18, 19 & 20:
three 7s
41:22, 23 & 24: three 7s
 
(there is another separation in the text and then mention of 7s appear as two pairs)

41:26:
two pairs of 7s
41:27: two pairs of 7s
 
(then the pattern shifts again to single pairs of 7s)

41:29 & 30: first
pair of 7s
41:34 & 36: second pair of 7s
41:47 & 48: third pair of 7s
41:53 & 54: fourth pair of 7s

In each case, the pairs (insofar as what they are describing) oppose one another, in one form or another, like fat cows versus skinny cows; or healthy ears versus shriveled ears; years of plenty versus years of famine, etc; like the opposing nature of the letters in the geometry of God’s Name and the nature of their reflection in the geometry of the royal seal.

These numbers; opposing sets of numbers; and ratios, are geometrically unmistakable. Three 7s define any given face of a tetrahedron. Four mentions of three 7s define all four triangular faces of a tetrahedron (shown below) where the measure of each face is defined in the text by reference to three times 7 places/positions, or the 28 elements (on each face).



Male "Half" of the Magen David



As we said above, the four mentions of three 7s define the four triangular faces of one tetrahedron. One tetrahedron? It takes two tetrahedrons to make a star tetrahedron or magen david (the royal seal) to properly reflect the Signature of the Architect with 216 letters. If we consider the "half" of the star tetrahedron above as the "male" half, then where’s the female half?  You'll find out in a moment.

In the meantime, the next set of numbers consists of two pairs of 7s, which (in terms of basic elements) define four faces on one tetrahedron. This is followed by another two pairs of 7s that define the four faces on the other tetrahedron. The two together, define the 8 faces (4 opposite 4) of the star tetrahedron with its 72 triangular corners (3 x 72 = 216).


Magen David Within
the Combined Cubic Form of the Luchot



With the completion of the above Signature in the three dimensional form of the royal seal, we seem to have a lop-sided equation. The four mentions of three 7s in the first section above (involving 4 references to three 7s) essentially "create" one tetrahedron by themselves. The second section defined two tetrahedrons (a complete star tetrahedron). Where's the other half of the first tetrahedron? We mentioned this missing half several paragraphs above, but we're about to find it in the next set of numbers, where 4 more pairs of 7s are mentioned.

Specifically, there are 4 more (single) “pairs” of 7 mentioned, and these define yet another tetrahedron. So now we have, for lack of any better words to describe the mathematic aspects of the story, a "female" tetrahedron to go with the lonely "male" tetrahedron first mentioned above. The end result is that the sequence starts with the male "half," of a tetrahedron, followed by another male but this time with a female tetrahedron, followed by another tetrahedron or "half" of the first tetrahedron. Altogether, the mathematic components for two complete star tetrahedrons are found in these numbers.


Keep in mind that the geometry of a tetrahedron is hidden internally within a cube, and that the two luchot were divided and brought down twice. The two combined cubic forms would have two star tetrahedrons (consisting of four regular tetrahedrons) mathematically hidden in their internal geometry. The first set was shattered. The second remained intact. The luchot were “divided,” like the male half and the female half above, found in the sequence of numbers mentioned in the text.


Female "Half" of the Magen David



It is worth emphasizing again, that the star tetrahedron (royal seal) is merely a geometric reflection of the nature of the letters in the Explicit Name. In the cosmic scheme of things, God separated the letters of His Name into their respective male-female counterparts in order to create and maintain a universe in like form. The 4 letters of Ekeyeh, were thus divided and became the 4 letters of the Tetragrammaton opposite the 4 letters in the Havaya of Adnoot (Aleph-Dalet-Nun and Yud). We see a reflection of the mechanics of this in the commandment of tzitzith (4 opposite 4 on 4) as explained in the post on Ki Thetze. Just as the 4 letter abbreviation was divided, so too was the 12 letter (abbreviation) of the Explicit Name, as seen in its reflection in the 12 stones on either side (and in the middle) of the Jordan River, as explained in the post on Ki Thavo. Here we see the same thing in the geometry of the royal seal, which casts its shadow below in the form of the events taking place in this week's parashah involving Yoseph and this is worth contemplating.

No matter how we break down the geometry, its source above (in the letters of God's Name) in recombinant form, return to either 4, 12 or 108 (letters) which can be represented by just one tetrahedron (one of the five internal mathematic constructs in the combined cubic form of the luchot). Without its polar opposite (in male-female combination) it exists only as one construct. The physical universe cannot exist in this form. However in the world above, where there is perfect unity, no such division is needed. The reflection of the Name in this parashah is seen both in its unified state (above) and in its divided state (below) where we say“...for the sake of the unification of the Holy One, blessed be He, and His Name... to unify the [letters of the] Name,” lest we mistakenly think He is somehow “divided,” when in fact He is a perfect unity. 

The text itself is a witness to this reality. The 7s found in the dream about cows (41:2-4) that are then repeated to Yoseph (41:18-21) are all beside one river (the Nile). The 7s found in the dream concerning the ears of grain (41:5-7) that are then repeated to Yoseph (41:22-24) are all on one stalk. The language used in the description of the dreams where we find these 7s (where each is associated with one thing: either the river or the stalk) hints to the fact that the numbers are associated with one specific construct, like the numbers that define one tetrahedron. These stand opposite another specific construct, the opposing tetrahedron. The two (opposing tetrahedrons) however are also one unified construct in the form of a star tetrahedron as defined by the numbers corresponding to its various elements. And so when Yoseph interprets the dreams in 41:25 he says, “it is all one dream,” which is tantamount to saying that the previous two are really one, just as the opposing abbreviations of the Name, are really one. The words of the song: "...life is but a dream," comes to mind, and they may be a more accurate description of reality than anyone thinks.


In summary, patterns of 7s, in the form of three 7s and/or pairs of 7s are found throughout the entire Torah and in each case, the numbers conform to the geometry of the royal seal and the letters of the Name hidden in its geometry.

Having mentioned all of the above, with a special focus on the twenty eight 7s in the first part of this post; and showing how they divide into, for example, three 7s; followed by two times two pairs of 7s etc., and their connection to God’s Name and the magen david, it is worth examining the mathematic characteristics of the triangular matrix of 7 (half of a magen david) more closely, and also its three-dimensional counterpart, the tetrahedral matrix of 7 (which we’ve not yet done). When we look at the geometry associated with this part of the “blueprint,” an interesting pattern emerges, one that matches the actual words of the Torah describing the nature of the events and considerably more!

The diagram below uses triangular elements to measure and define the edges, points, and ultimately the face of a triangular matrix of 7. Keep in mind that these divisions are the result of the measured geometry of the evan shetiyah discussed at length in the essential constructs to the right. We’ve made the 7 elements themselves triangles (triangles within a triangle) since this is the actual result of the lines of measure that would run through the foundation stone. You can see (as you should have noticed in the previous models) that the edges are defined by three 7s, and the total number of “elements” (triangles) is twenty-eight. Using this method however, which is more consistent with the letters in the Triad Name and the nature of the magen david, you’ll notice that this creates a “counterpart” to each element in the form of another triangle, but the counterpart points down, instead of up, like the two halves of the royal seal.


Click to Enlarge

The points on each of the above triangles represent the 28 elements in the triangular matrix delineated by 7 lines ( the white triangles that are pointed down, are the female counterparts to the blue that are pointed up). It is worth noting that a square array of 7 consists of 7 x 7 (or 49) elements. That’s easy to calculate. The number 49 is the simple product of the two dimensions. The triangular matrix however, is different, and more restricted. It cannot be calculated by the product of its two dimensions, as you can see from the above diagram.

As mentioned many times throughout this blog, there are things hidden beneath the surface of various two-dimensional constructs (underlying the text of the Torah) that are not revealed until they can be observed in three-dimensions. So, in our quest to know and understand the relationship between God’s Explicit Name, the royal seal in the form of the magen david (which is essentially a mathematic construct within the combined cubic form of the luchot) and how these in turn relate to the physical universe and the events that shape the history of Israel, we will now “extrude” our two-dimensional royal seal (as a triangular matrix of 7) into three-dimensions. Keep in mind as we do, that this geometry is a reflection of the characteristics of the 216 letters in the Explicit Name (the 72 triangular corners of a star tetrahedron, in essence being a geometric reflection corresponding to the nature of the letters in the Name). The diagram below shows a three-dimensional tetrahedral matrix of 7 (7 lines of delineation) in the measure of the cube that surrounds it.



Click to Enlarge

Tetrahedral Matrix Delineated by the Seven Lines
of the Cube that Surrounds it


The left side of the model is the two-dimensional face (pictured previously) but here it is shown in three dimensions as it relates to the tetrahedral matrix. The right side (of the model) shows that each of the blue triangles (that are “elements” in the triangular matrix of 7) are small tetrahedrons in the third dimension. However, as it turns out, the white triangles pointing down, are not tetrahedrons at all. Rather, they are the triangular faces of an octahedron. The octahedron is also one of the five mathematic constructs within a cube, but its defining characteristics are its 4 faces on one side, opposite 4 faces on the other. These faces have a direct one-to-one relationship with one another, providing a perfect geometric reflection of the 4 opposite 4, in the nature of the letters for the two primary abbreviations of the Name, the 4 letters of the Tetragrammaton opposite the 4 letters in the Havaya of Adnoot.

Its easy to count these two types of elements at the two-dimensional level. Its not so easy at the three-dimensional level. If you create a computer model in three-dimensions (which is pictured above) and then break it down and count the total number of each type of element, you will get the results shown below. There may be a formula for doing this, but a one-dimensional mathematic expression somehow detracts from the beauty that can be seen in this “aspect” of the cosmic blueprint (luchot) and would lose the very clear connection that God’s “plan” has to the history of Israel (in the mishmash of what would otherwise be meaningless numbers).

As it turns out, the sum total of the numbers, sets of numbers and the ratio between sets, is actually quite astonishing. Each side is defined by “three 7s,” and there are of course 4 sides. This is just like the 4 instances in the story of Yoseph, where three 7s are mentioned. These numbers are external to the matrix and “revealed” (nigleh) in the story. Its internal characteristics however are hidden beneath the surface and that’s where it starts to get interesting.

The total number of small tetrahedrons is 84 (the age of Yaacov when he married 4 young women). When you factor this number by 4, which is the number of letters in the Tetragrammaton, the result is 4 times 21, and 21 is again three 7s. In other words, the total of the external and internal number of “small tetrahedrons” in the matrix is the same as the pattern of numbers that define its edges (4 sets of three 7s) and they in turn are the same as the “numbers” that define the “story” or the events that actually happened. But surely that must be a coincidence? Lets see if we can find a second witness.

The sum total of the octahedrons (the counterpart of the small tetrahedrons) in this tetrahedral matrix, is 56.  When this number is factored by 4, the number of letters in the Havaya of Adnoot (which is the counterpart of the 4 letters of the Tetragrammaton mentioned in the preceding paragraph) the result is 4 x 14. The 14 is of course a pair of 7s, so the 4pair” of 7s that are seen in the number of octahedrons, are just like the numbers that follow the three 7s in the actual story, which are two times two pairs of 7s. In other words, the twenty-eight 7s in the parashah, that amount to a one-dimensional expression for (or define) a tetrahedral matrix of seven, externally (in the 4 instances of three 7s) are also found mathematically hidden, internally, within the same matrix. That “coincidence” should stagger the imagination, and the questions we should be asking ourselves are: what does all of this mean and who could design a blueprint with such detail, and play with the engineering of history, so as to “define” the events in the letters and the words of Torah? There is really only one answer. It took a Master Mathematician and Designer, capable of transcending the normal limitations of time and space, to bring about the events in question, all in accordance with the mathematic specifications of the blueprint (or combined cubic form of the sapphire luchot). Think about this for a moment.

In addition to the above, there are 7 "levels" in
a tetrahedral matrix of 7, that are like 7 thousand years or 7 millennia. The total number of all the elements (tetrahedrons and octahedrons) in the first 6 levels, as in the 6 millennia (before the millennial shabbat) is 91. The number 91 is the sum of the gematria of the 4 letters of the Tetragrammaton (26) and the gematria of the 4 letters of Adnoot (65) alluding to the unification (and sanctification) of God’s Name that will occur at the end of the 6th millennium, by which time everyone will know God’s real Name and understand the significance of its letters (and right now you should be thinking about the 4 male-female forces in quantum mechanics, and the male-female “directions” for the 4 dimensions of space-time which are both very real reflections of the letters of these two abbreviations).

One final aspect of the tetrahedral matrix of 7, is that the total number of intersecting points on the outside of the triangular faces, on each of the small tetrahedrons, that define the 3 edges of each large face, is 18. The 4 faces which have these 18 points, collectively have 4 x 18, or 72 points (pictured on the in dark blue outer triangles below). This is another mathematic reflection of the 216 letters associated with the Signature of the Architect, hidden in the geometry of the royal seal.


Click to Enlarge 

Tetrahedral Matrix of Seven
18 Points of Intersection Define the Edges
on Each of 4 Faces
4 x 18 = 72 



If you sit back and contemplate the implications of everything that has been said so far, even for a moment, you will realize how important the nation of Israel and the Jewish people are to God’s plan. The history of the Jewish people provides the brightest reflection of this process, because it is the most central part. Nothing has changed. As a friend once said, God does not make mistakes and there is no need for "Plan B” in the cosmic scheme of things. The plan is the same as it has always been (past, present and future) and it is still in full force and effect.

The truth is that God has a plan for everyone, not just the Jewish people. It's just that the further you get from the source, the less visible the connection. All the more reason for each and every person to determine what role they play in that plan, and make absolutely sure that they are acting in accordance with God’s will (and not merely doing something absurd because some cleric demands it). Those who seek to delegitimize Israel, for example, or God forbid, wipe it from the face of the earth entirely, as heard in the rhetoric coming from more than one nation at this particular moment in time, simply do not understand the dire consequences they face, for attempting to do so. 


Trying to abrogate God’s promise(s) to Israel is foolhardy. One way or the other, such actions will eventually come back to haunt those would would try, or at the very least embarrass them or destroy them altogether. Whether their life is effected by one calamity or another, depends only on the degree to which an individual or a nation is determined to destroy Israel (measure for measure). The sophisticated nature of the blueprint (that is itself an extension of the letters in God’s Name as demonstrated in this case by the events surrounding Yoseph’s sojourn in Egypt) should serve as a warning to even the most simple-minded person, that such attempts are futile. The end result always boomerangs on those who have the audacity to think they can thwart God's plan. Such “logic” and the inevitable actions that result, are the absolute pinnacle of arrogance and stupidity. 
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