In this post on Miketz, we will examine the events of the parashah in terms of the mathematic and geometric patterns that correlate with God's Explicit Name. This Name has 216 letters. A mathematic reflection of these letters is seen in the geometry of a star tetrahedron or three-dimensional magen david, with 72 triangular corners, and it is one of the 5 internal mathematic constructs found within the combined cubic form of the luchot. The luchot themselves have a volumetric measure of 216, but in this post we will focus on the triad nature of the 72 triplets in the Explicit Name.
The first thing we will look at are the 7s in this week’s Parashah.
(There are five star tetrahedrons and one 2D
shadow created in this week’s Parashah. The paragraphs that talk about them are
numbered accordingly so that the reader can easily navigate the text.)
1a) At the beginning of the parashah, Pharaoh has 2 dreams portending the food situation in Egypt and other lands for the upcoming years. He repeats his 2 dreams to Yoseph who then interprets them, so in each case the dream is explained and then repeated. The Torah mentions the number 7 three times and then the same pattern is repeated (we'll get more specific in a moment). This is like the pattern of numbers in Parashah Balak (for those who haven’t read that post yet, a knowledge of it will be needed to more fully appreciate the balance of this post). As in Balak, three 7s can be used to mathematically define a triangular matrix of 7, or one face of a tetrahedron. When each side of this matrix is measured in terms of 7 (7 by 7 by 7) it has 28 elements. In Parashah Balak, Bilaam therefore called for 7 altars, 7 bulls, and 7 rams and he performed the sacrifices three times (one face was left undefined).
How 28 Elements are Used to Populate
Each Side of a Tetrahedron
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In this week’s parashah however, we have the matrix of 7 (7 x 7 x 7) in Pharaoh’s dreams repeated 4 times, so it actually defines all 4 faces of a tetrahedron. In the dream of the cows (41:2-4 and repeated to Yoseph in 41:18-21) they were all beside 1 (Nile) River, and in the dream of the ears of grain (41:5-7 and repeated to Yoseph in 41:22-24), all ears of grain (both healthy and withered) were on 1 stalk. This hints to the fact that we are really dealing with 1 construct, i.e. a tetrahedron.
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Yoseph interprets the dreams in 41:25 saying, “it is all one dream.” This means that it all fits one construct, specifically and in this case, a star tetrahedron, one of the 5 internal mathematic constructs found within the combined cubic form of the luchot. A star tetrahedron is made up of 2 opposing tetrahedrons merged together. Above, we have found the first. But where is its polar opposite to make up the star magen? The answer is in the next verses. Yoseph now interprets the dreams. Just as a tetrahedron was “created” by populating all 4 sides from Pharaoh’s dreams, we will see its polar opposite in the interpretation that Yoseph gives. In order to understand the significance, we first need to look at Yoseph’s interpretation on its own. Once we understand the meaning behind the interpretation, then we can come back and populate the polar opposite of “Pharaoh’s” tetrahedron, in like manner.
2) Yoseph starts his interpretation, and in 41:26 seven is mentioned 4 times, this time as pairs: The 7 fat cows mean 7 years of plenty and the 7 healthy ears of grain mean 7 years of plenty. This is actually a pair of 7s (14) opposite another pair of 7s (another 14). There are 14 elements in a tetrahedron, thus the 14 opposite 14 mathematically allude to a tetrahedron and its polar opposite, that merge together to form a star tetrahedron or three-dimensional form of the magen david.
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This is suggested in 41:26 after Yoseph mentions these 14 opposite 14 when he says, “it is a single dream.” The language infers that the mathematic characteristics allude to a single construct expressed as 14 opposite 14, i.e. a star tetrahedron.
3) Yoseph continues the interpretation in 41:27, and we again find seven mentioned 4 times as pairs: the 7 skinny cows mean 7 hunger years and the 7 withered ears of grain mean 7 hunger years. These are again pairs of 7 and together they equate to 14 opposite 14, which is again a mathematic expression for two tetrahedrons, or star tetrahedron in unified form. Thus we have a tetrahedron in the years of plenty opposite a tetrahedron for the hunger years. This was to show that even the 7 years of famine were a function of the cosmic blueprint, and from God. As Yoseph says in 41:28, “what God is about to do He has shown to Pharaoh1.” Even the hunger years functioned according to the cosmic blueprint. Both good and “bad” are from God and brought into our universe through the cosmic blueprint, and thus must function accordingly.
Now that we see how Yoseph’s interpretation created 2 star tetrahedrons, one for each set of years, we can now examine his interpretation in a different light to find our missing polar opposite of “Pharaoh’s” dream tetrahedron.
1b) If we examine Yoseph’s interpretation, the numbers can be expressed a bit differently. The 2 pairs of 7s in 41:26 and 41:27 are actually 28 (14 + 14), and thus we again have the matrix of 7 with 28 elements that define one side of a tetrahedron. We have one side in the 28 (4 x 7 of 41:26) in the years of plenty and a second side in the 28 (4 x 7 of 41:27) for the hunger years.
The tetrahedron of Yoseph’s interpretation is thus populated as follows: 4 explicit mentions of 7 good things (cows/ears of grain/years) in 41:26 are the first (4 x 7 =) 28 elements to populate the first face of the tetrahedron. With the 4 explicit mentions of 7 bad things (cows/ears of grain/years) in 41:27 we have the second (4 x 7 =) 28 elements to populate the second face of the tetrahedron. With the actual number of good things (cows/ears of grain/years (years only being counted once because there was only one set of 7 years of plenty)) we have 7 by 7 by 7 or 28 elements to populate the third side of the tetrahedron. And with the actual number of bad things (cows/ears of grain/years (years only being counted once because there was only one set of 7 years of famine)) we have 7 by 7 by 7 or 28 elements to populate the fourth side of the tetrahedron. Thus this new tetrahedron is fully populated and the numbers again serve to create a "virtual" tetrahedron using the patterns of numbers in the sequence of events.
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This can now be merged with the first tetrahedron above (“Pharaoh’s dream tetrahedron”) to combine and create the star tetrahedron with its 72 triangular corners that correspond to the 216 letters of God’s Explicit Name. (Notice the numbers we are using: Three 7s; 2 dreams (define a matrix of 7 or face on a magen david) where the numbers all correlate with the Triad Havaya of 72).
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4) Another way to look at these dreams is by focusing only on the different elements in the dreams and their meaning. The 7 cows and 7 ears of grain combine to be 14. The 7 years of plenty and the 7 years of famine are also 14. Thus we once again have 14 opposite 14 or another (complete) merged star tetrahedron.
5) We will point out here, that as we saw last year, there is yet another star tetrahedron created by the 14 years that Yoseph was a slave opposite the 14 years that he was a ruler (see the post on Miketz at the "Sapphire Magen David" site for details).
6) In 41:29-30, we have the 7 years of plenty opposite the 7 years of hunger or the 2D shadow of a star tetrahedron. There are 7 elements in each of the polar opposites that make up the 2D magen david, and so this 7 opposite 7 is by itself the 2D shadow of the star tetrahedron.
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The end result of all of the above patterns (in the mathematic form of magen davids) are as follows:
1) Pharaoh’s dreams and Yoseph’s interpretation merged;
2) Yoseph’s interpretation: 7 years of plenty, and
3) 7 years of famine;
4) Using only the different elements;
5) Yoseph as a slave and as a ruler;
6) The 2D shadow
The following is a little insight into the interconnectedness of the cosmic blueprint based on this week’s parashah.
The number of times it mentions 7 in this week’s parashah is hardly a coincidence. The number 7 is mentioned 28 times! This has several implications: the number 28 is the number of elements in a matrix of 7 that populates a face of a tetrahedron; the number 28 divided by 7 equals 4, or the number of faces on a tetrahedron; the number 28 is also the combined number of elements in the two tetrahedrons that make a star tetrahedron (14 opposite 14). The number 7 taken to the 28th power is a number that has 24 places: 459986536544739960976801. If you take the number of star tetrahedrons and their 2D shadows (created in this week’s Parashah: 6) and split them into their polar opposites, you get 12, or half of 24. This is like the luchot which were each 2 halves of a whole magen david (each being a reflection of the letters in God's Name).
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If we divide 24 by 6 we get 4, or all 4 halves of the luchot, in both the first and second sets; and 4 is also the number of faces on a tetrahedron. It is also the number of letters of 3 of God’s Explicit Names that when added together make the 12 letter Explicit Name (Tri-Tetra-Grammaton) which is once again half of 24, the amount of number-places that 7 to the 28th power creates. When 2 opposing tetrahedrons are merged, they subdivide one another and each of the 8 faces is divided into 3, resulting in 24 small faces (again in the form of equilateral triangles) that are 12 opposite 12 like the 12 letter Name and its opposite (see the posts on VaYishlach and VaYeshev).
The number 7 is the primary numeric component in calendar related halachah, something we did not mention at all in this week’s post. If you add the 28 times it mentions 7 in this week's Parashah, you get (2 + 8 =) 10, the number of commandments on the luchot from which halachah (expressed as 7) is based on. There are 7 days in a week, and 8 is the start of the next level (see post on BeHar and BeChuko-thai to see this clearly). The product of 7 x 8 is 56, the number of octahedrons in a tetrahedral matrix (see Miketz post at "Sapphire Magen David"). The number 28 (which is the number of times 7 is mentioned in this week’s Parashah) is half of 56, like the luchot are 2 halves of the combined cubic form. These are but a few of the patterns of numbers in this week's parashah and how they connect with one another in terms of the measure of the luchot and to the number of letters in God's Name. Yet from these patterns, we can get an amazing glimpse of the internal workings of the cosmic blueprint, where every part of the universe is interconnected with a larger reality.
It is worth pointing out that the 28 elements (of the triangular matrix) can also be expressed as 7 x 7 x 7 or 343 elements (in a cubic matrix). See the posts on VaYera and BeHar and BeChuko-thai for an explanation. It is mentioned here solely to point out just how mathematically interconnected the cosmic blueprint is with our reality.
Now we will focus on the number 2 in the 72 triplets of God’s Explicit Name. The 2 luchot, which have a combined cubic volume of 216 handbreadths (the number of letters in God’s Explicit Name) are also seen throughout this week’s parashah. If one studies it carefully, they will see these "twin" aspects subtly assert themselves in the narrative.
The first occurrence in this week’s Parashah begins with (41:1) “And it happened at the end of two years to the day…” This was the 2 years that Yoseph was (still) in prison after he interpreted the dreams of Pharaoh’s chamberlains (as we saw in last week's post on Parashah VaYeshev, these 2 years allude to the second set of 2 luchot).
The second occurrence in this week’s Parashah, is when Pharaoh has 2 dreams. Since there is only one meaning to the dreams, he could have had only one dream. The fact that he had 2 dreams hints to the larger reality, that is the 2 luchot (that were not twins until they were divided and brought down by Moshe). Each dream has 2 parts: the good thing (cows/ears of grain) gets swallowed (replaced) by the bad thing (cows/ears of grain). The same is true of the luchot (not that they were “bad”) but the first set were ultimately replaced by the second set. The sets were nevertheless opposites of one another. The second set was not as ‘lofty’ as the first set (they being created out of heavenly fire) thus the lesser one (carved by Moshe down here on earth) “replaced” the greater one.
Yehudah presses Yaacov that they must go down to Egypt to get more food. In 43:10 he says, “For had we not delayed, by now we could have returned twice.” This is alludes to the luchot that would be brought down twice after the people endured the trials of Egypt and made ready to accept Torah.
The third occurrence is when 2 sets of children are mentioned. Reuven offers his 2 sons (Chanoch and Pallu) in a promise to bring back Binyamin. In 42:37 he says, “You may slay my two sons if I fail to bring him (Binyamin) back to you.” This is conceptually like the first set of 2 luchot that were broken. The same reflection is seen in 41:50 when it says, “Now to Yoseph were born two sons…” The following verses describe the birth of Menashe and Ephraim. They too were twins like the luchot. These 2 correspond to the second set of 2 luchot that survived intact. Menashe and Ephraim were born in the year 2233 (two sets of twin numbers). The date or "moment in time" alludes to the two (halves of the first set) and the two (halves of the second set) of luchot that were brought down. Each had a combined cubic volume of 216, the number of letters of God’s Explicit Name, also known as the Triad Havayah of 72. Thus on each set of luchot there was a triad aspect (the measure of the third dimension in handbreadths after division) and so we see this reflection in the date where there are 3 measures in the first set and 3 in the second set (resulting from the division).
A star tetrahedron with its 72 triangular corners is one of the mathematic constructs in the combined luchot. Thus the double 3s for the double 2s that were brought down.
A star tetrahedron with its 72 triangular corners is one of the mathematic constructs in the combined luchot. Thus the double 3s for the double 2s that were brought down.
This all goes back to the 2 luchot, the 2 aspect of the 72 triplets (108 opposite 108 in the volumetric measure of each tablet) that correspond to the 216 letters of God’s Explicit Name.
The commandments were inscribed on the luchot, and they too are hinted at in this week’s parashah.
In 42:3, the 10 brothers go down to Egypt. They return home, but come back a second time with Binyamin in tow. Both times, there are 10 brothers who go down to Egypt (because Shimon was imprisoned as collateral by Yoseph in Egypt). Their descent is a rather bright reflection of the cosmic blueprint, where the 10 commandments on both the first and second sets of luchot were brought down twice.
In 43:34 Binyamin gets 5 times as much of a portion as his brothers. In next week’s Parashah VaYigash (45:22) Yoseph gives 5 changes of clothing to Binyamin (again 5 times as much as the brothers) and so the portions are 5 opposite 5, like the 10 commandments that were divided this way on the luchot2. Once again we have two halves that are 5 opposite 5. They are even divided this way in the Torah, as one half (5) are in this week’s Parashah, and the other half (5) are in next week’s Parashah.
And finally, in 43:11 Yaacov tells the brothers what things they should bring from their land as tribute to Egypt. He enumerates:
1) Balsam,
2) Honey,
3) Wax,
4) Lotus,
5) Pistachios, and
6) Almonds.
This is a one-dimensional reflection of the external measure of the luchot: 6 x 6 x 6 = 216, which is ultimately a reflection of the letters in God’s Explicit Name. If we take 6 and divide it by 2 (luchot) we get its measure in the third dimension: 3, which is the next number we will examine, like the 3 in the 72 triplets of God’s Explicit Name (having already examined the 2s and 7s).
1) Balsam,
2) Honey,
3) Wax,
4) Lotus,
5) Pistachios, and
6) Almonds.
This is a one-dimensional reflection of the external measure of the luchot: 6 x 6 x 6 = 216, which is ultimately a reflection of the letters in God’s Explicit Name. If we take 6 and divide it by 2 (luchot) we get its measure in the third dimension: 3, which is the next number we will examine, like the 3 in the 72 triplets of God’s Explicit Name (having already examined the 2s and 7s).
As we saw previously, the 7s all correspond to the 3D magen david (and its 2D shadow) and the 72 triangular corners that correspond to the nature of the letters in God’s Explicit Name (216). The triplets are hinted to in many places in this week’s parashah as well.
In Pharaoh’s dreams (as seen above) when he relates them to Yoseph, it mentions 7 in groups of 3. Yoseph gets 3 names: 1) Yoseph, 2) Avreich, and 3) Zaphenath-paneah. When Yoseph is 30 years old, he gets married and becomes viceroy of Egypt3. The brothers are put in prison for 3 days (42:17) and therefore it is on the 3rd day (42:18) that Yoseph tells them they must leave behind one brother as collateral and go home to get Binyamin. In 43:1 we have a rare 3 word verse. In 43:15, in coming to Egypt a second time, the brothers take 3 things with them: 1) Tribute, 2) Double money, and 3) Binyamin. At Yoseph’s residence, when they all sit down to eat there is a unique seating arrangement (43:32); they served Yoseph separately; they served the brothers separately; and they served the Egyptians separately. Thus there were 3 groups of people being served at 3 separate tables. At the end of the Parashah, Yehudah answers Yoseph and says 3 things: (44:16) “what can we say, how can we speak, and how can we justify ourselves?” In 43:12 Yaacov instructs the brothers to take “double the money” and also “the money that was returned to you,” a 2 + 1 reference (3) that correspond to the corners of a triangle, where 2 are found in one dimension and the other is above, in the third dimension. In 43:21-22 the brothers tell the man in charge of Yoseph’s house that they brought back the money that was returned to them and they also have more money to buy more food. They are told that they can keep the money for “the payment has reached me,” but when they leave, the money (for the new food) is found returned in their sacks. Thus we have the polar opposite of the “double money” and the original money that they (tried to) return (but didn’t). The ratio of the sets of numbers is again 2 + 1 (3) or the corners of another triangle (the other half of the first half) that "merge" to create a magen david (in this case a 2D shadow of the 3D star tetrahedron). And finally, the brothers go down to Egypt 3 times. Twice they come from Canaan to buy food, and the last time they had barely left the city when Yoseph’s men catch up to them and they find Yoseph’s goblet in Binyamin’s sack and, once again return. These numerous mentions of 3 things, are all reflections of the triad nature of God’s Explicit Name which is made up of 72 triplets.
You have now seen just how deeply the Signature of the Architect (sometimes known as the Triad Havayah of 72) is embedded throughout this week’s Parashah.
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Footnote 1 – Notice the chapter and verse: 41:28. This hints to the 4 faces of 1 tetrahedron that are each populated by 28 elements.
Footnote 2 – (This was to rectify the fact that the 10 brothers got the 2 pieces of silver in Parashah VaYeshev. Binyamin here got the 5 portions opposite the 5 changes of clothing to show that he (and his descendants), too, were bound by the 10 commandments on the luchot.)
Footnote 3 – Yoseph, too, was bound by the 10 commandments as here we have 30, or 3 x 10. The 10 is a reference to the 10 commandments.
