Sunday, September 1, 2019


In Parashah Shoftim there is a shift away from the numbers, sets of numbers and ratios that were prevalent in Parashah Re’eh and Eikev (specifically the numbers six and seven).

You may remember that in those portions, the predominate sets of numbers were three sixes; three sevenths;’ and seven sevens'. These one-dimensional metric expressions are descriptive of three-dimensional cubic ratios like 6 x 6 x 6 and 7 x 7 x 7
as explained in various posts and the advanced construct on the eight dimensions. The letters of God’s Explicit Name are hidden in the geometry of these sets of numbers, and they have a direct connection to the combined cubic form of the luchot with its 216 cubic handbreadths (six-cubed) corresponding to the 216 letters; and also its edges/borders that define a slightly larger matrix (seven-cubed) that in turn define the cycles of time involved in calendar-related halachic observance. 

In the paragraphs ahead we will examine the mathematic differences between Re'eh and Shoftim as they pertain to the differences between the external cubic and internal tetrahedral geometry of the luchot. In the meantime, if you are new to this blog, please read each of the essential constructs (starting with the "Introduction") listed in the column to the right before proceeding. These pages reveal some of the basic mathematic connections between the letters of God's Explicit Name and the multidimensional geometric characteristics of the luchot, both in the divided state and combined cubic form, along with the internal geometry that casts a shadow known as a magen david. There is a special connection between the Name, the luchot and the geometry of the magen, and together they form a unique signature. We refer to this geometry and its mathematic common denominator as the Signature of the Architect. The purpose of this blog is to show how all of these things connect, and to reveal where the signature geometry is hidden, not only in each week’s parashah, but the physics of time and space, quantum mechanics and celestial dynamics to name a few. Once you are familiar with these constructs you can more fully appreciate each post.

In Parashah Shoftim the sixes and sevens and their related constructs give way to an overwhelming preponderance of threes' and fours'. Sets of threes' and fours' in a specific ratio, characterize the elements of a tetrahedron, as found for example in the three edges and three points on each of its four faces. These are the primary attributes of the tetrahedral geometry associated with the royal seal (three-dimensional star magen david) which is one of the five mathematic constructs found within the combined cubic form of the luchot. In this case we would assert that it is embedded here in the linguistic structure of the text, because the text is a letter-form extension of the mathematic characteristics in the luchot (the 'brick' under the throne mentioned in Parashah Mishpatim). These particular numeric clusters begin to appear in Shoftim in the text related to the cities of refuge:

19:02 “You shall set aside three cities in the Land... that God is giving you...
19:03 “You shall measure the distances, and divide [this] into three parts...


19:07 “It is for this reason I am commanding you to separate three cities.”

Notice first, that there are three instances of three and that three things (areas) are to be surveyed, measured, and divided. The above references are revealed to us in the written Torah and on the pshat, or simple level, they deal with the cities. However, the set of three things and the emphasis on measurement and division alludes to the letters of the Explicit Name that are hidden in the geometry of the royal seal. When we examine these sets of numbers through the prism of the magen david, we can more easily see that the 'division' of the geometry is 'measured' by a series of 72 triplets (72 triangular corners).

The three instances of “three” mentioned in the text above, stand in stark contrast to yet another “three" mentioned in the oral portion. The word 'three' that is “hidden” (not mentioned directly in the text) is that pertaining to the categories of unintentional death for which the cities are needed. So ultimately there are four instances of three, where one instance (from the oral portion) is characteristically different from the other three instances (from the written portion). This pattern is consistent with the marriage of the letters (as described in the post by that name) where one couple is decidedly different from the other three couples. It is also consistent with the nature of tetrahedral geometry as you will see in a moment.

In the meantime, it is important to understand that this pattern is established by the letters of the Name, or in this case the primary abbreviations of the Name. The narrative of the text describing the halacha for these cities reflects that same pattern. 

At any rate, there are four instances of three in the halacha pertaining to the cities, where one is different from the other three. These are the one-dimensional metrics (describing the the number of elements) in the geometry of a tetrahedron, which is 'half' of the royal seal. A tetrahedron happens to have four faces, each with three points, where one point is different the other three (because one of those points exists in the next higher dimension ~ the third dimension) whereas the others are found in a lower two-dimensional plane. The bottom line is that this signature geometry is hidden in the tetrahedral construct within the combined cubic form of the luchot, that defines the reality which follows, and so we see these numbers, sets of numbers, and ratios in the narrative.

If you look closely at the three-dimensional tetrahedron below (again half of the royal seal) you will see the four threes'” that characterize its geometry (four two-dimensional faces with three points).

Of course, most mathematicians/statisticians would see this as a coincidence. There is no way to prove that it is anything more. Or is there? The sets of numbers thus far found, represent only half of the royal seal. If subsequent text contains the metrics for the other half, where the context is the inverse of the first half, and where one is again different from the other three, then the odds of it being a coincidence fall to near zero (we would say effectively zero). Indeed, that's exactly what happens in subsequent text.

The same pattern is in fact reiterated a second time in succeeding verses. This second iteration is once again a one-dimensional metric expression for, in this case, the other half of the magen david; it is in fact the contextual inverse of the first instance; and one is decidedly different from the other three. The second iteration takes this form:

19:01 “When the Lord your God has cut down the nations...”
           “whose land the Lord your God is giving you...”

            (At that time there were seven nations "cut down")

19:08 “And when the Lord your God enlarges your territory...”
          “the territory of the Kenites, Kenizites, and Kadmonites...’
           (three more nations)

           [and] “If you faithfully observe all this instruction...”
19:10  “then you shall add three more cities to those [first] three [cities]”

Note the text provides three new instances of three. This second iteration also has a hidden aspect just like the first iteration. These are the verses of Edim Zomemim (plotting witnesses) where we find the three verses that constitute the laws regarding false witnesses for which the cities should not be needed (the inverse of the first three).

The hidden aspect of the second iteration is thus the contextual opposite of the hidden aspect of the first. In addition, the first set of “three” pertain to why the cities are needed (unintentional death). The second set of “three” pertain to when the cities are not (or should not be) needed (since there were false witnesses involved) and again the inverse. The laws are derived from a reading of the text that is ultimately separated into three verses where each is an aspect of the legal process. The division is hidden within the context of the verses, but nevertheless an integral part of the text and the halacha.

If you look closely at the tetrahedron below, which is the inverse of the first half of the royal seal, you will again see that four threes'” characterize its three-dimensional tetrahedral geometry (four two-dimensional faces, each with three points).

These four instances of three,” where one is the inverse, and one is different from the other three, constitute the metrics for the other half of the royal seal.
Whenever patterns of four times three (or
three x four) are seen as part of the narrative; or halachic requirements; or events that occur over time (essentially the history of Israel) and especially where one is different from the other three (like the hidden aspects in the account just described) these patterns invariably reflect the one dimensional metric geometry associated with the three-dimensional tetrahedral geometry (magen david) within the combined cubic form of the luchot, and the abbreviated forms of the Name. The 12 letters Explicit Name, for example, is literally three times the four-letter Tetragrammaton. There are also three primary four-letters Names (YHWH / ADNY / AHYH). Each 'define' this internal aspect of the luchot (the tetrahedral or signature geometry within the foundation stone).

We see this in both two dimensions and three dimensions, but more so in the added detail of the higher dimensions. The two halves appear below:


When these halves are married together, their geometry reflects the marriage of the letters (the three primary four-letter Names where one pair of letters is different from the other three). Each face is now divided into four quadrants where the one in the middle (which is the stellation of the opposing tetrahedron) is different from the other three (see example face below). Or, to put it another way, the three small faces are visible, but another one face is hidden beneath the stellation of the opposing tetrahedron. Ultimately, the geometry is found to contain 72 triangular points (72 x 3) corresponding to the number of letters (and even the nature of those letters) in the Triad Havaya of 72 (216 letters total).

The total number of degrees in the cube that surrounds the (above) star tetrahedron (or the mathematic construct that defines it) is 216 (tens) of degrees, and so the static aspects of the geometry once again hide the Signature of the Architect that is just beneath the surface. There are 24 angles of 90 degrees in a cube (24 x 90 = 2,160 or 216 "tens" of degrees). This is also the time allotted to each of the twelve constellations in the Precession of the Equinoxes (2,160 years) as discussed in the post on the primordial torah.

In summary, for each of the two opposing halves of the above verses, the number three occurs four times. These numbers and specifically this set of numbers (four sets of three times two) define the eight two-dimensional surfaces of a three-dimensional star tetrahedron. Each surface and its polar opposite are themselves defined by the letters of the Name, or more specifically its abbreviations: four quadrants opposite four quadrants where one is different from the other three for each set (as mentioned before, the middle “triangle” on any given face is hidden in the center of the other three, beneath the base of the stellation, like the hidden one of three mentioned above, but it is nevertheless a part of any particular face or two-dimensional surface). The three-dimensional stellation protruding from the face is (again) the stellation of the opposing tetrahedron. It is “hidden” with respect to that face, by virtue of its presence beneath the stellation in the third dimension (with respect to the two-dimensional face from which it protrudes) and so the inherent limitation of two-dimensional space (of which it is not a part) hides the one that corresponds to the base of the next dimension. 

If we examine these sets of numbers in two dimensions (rather than three) you will notice that the outer geometry of the surface consists of three revealed “areas” with three specific points or corners. This is like the three areas with three cities specifically mentioned in the text. However, notice also the hidden area in the middle (beneath the stellation) that has three corners. This is like the hidden aspect involving three categories of unintentional death for which the cities are needed. The text/halacha adheres to the geometry established by the internal (hidden) mathematic aspects of the cosmic blueprint, which in turn adheres to the letter-pattern associated with the signature geometry. 

The division (into four quadrants per face) seen above results from the marriage of the tetrahedrons and does not occur otherwise. Without the marriage of the geometry (or its origin in the marriage of the letters that create the geometry in the first place) the connection to the text remains completely hidden beneath the surface. The geometric parallel between the letters of God’s Name, the text and the star tetrahedron is statistically significant and cannot be attributed to coincidence (the odds would be considered off-the-scale) and it is one more example of how the letters of God’s Name (that define the blueprint or combined cubic form of the luchot) ultimately define our reality. This is true not only in biblical history, but also the the physics of time and space, quantum mechancs, biology, chemistry and celestial dynamics as explained in the post on the primordial torah.

The same mathemetic or geometric characteristics hold true for the second iteration as well. Ultimately, the mathematics of the “cosmic blueprint” characterize the edges, faces or points of the royal seal corresponding to the 216 letters of the Name that in turn defines or requires these laws/events. However, as you may have noticed, the number of threes' as a function of the two-dimensional geometry is, in this case, incomplete. That is, the first iteration corresponds to only one two-dimensional face and the second to its polar opposite. That leaves two remaining faces as yet undefined (including their hidden aspect in each respective dimension). Where, or how do these undefined mathematic aspects of the star within the luchot, fit into the cosmic scheme of things as it would relate to Israel’s future? Do we find these anywhere in the text? The answer is no.  However, these additional, as yet undefined aspects or events, may be found in the opinions of our Sages who say that there will be additional cities of refuge that will be created during the time of Mashiach.

According to them, there will be Jews who unintentionally caused the death of people during for example the diaspora (like the modern case of vehicular manslaughter). Since these people were unable to expiate those acts by exile in a city of refuge, they will want (or need) at some point in the future, to do so. When Mashiach comes, there could be many generations of souls that will seek to do this, and even more cities of refuge will be established for that purpose. Some of our Sages say there will be 9 cities, others 12, and still others 15 cities of refuge (Sifre 185, Tosefta Makkot 3). Given the premise that there is a very real connection between the letters of God’s Name and everything that happens to Israel, contemplate the letters in terms of their geometric characteristics in the faces of the second dimension (i.e. the luchot and/or the magen david within) and see if you can determine which of these opinions is correct, and then see if you can explain why.

In the meantime, despite all of the parallels we see above, some might think that the connection these threes' have to tetrahedral geometry is a coincidence, and so for the benefit of those less familiar with the overwhelming number of similar 'coincidences' seen in previous posts, we will provide several more witnesses to confirm the connection these things have to God’s Name.

Flashback to verse 19:08:  “And when the Lord your God enlarges your territory...”
                                           “the territory of the Kenites, Kenizites, and Kadmonites...’
                                            (three more nations).

These “three more nations” were in addition to the seven nations that had already been defeated when the Land was conquered under the leadership of Joshua (a total of 10 nations). This is like the threesevenths” alluding to three dimensions with a measure of seven, where any given two-dimensional face equates to sevensevens” as in last week’s parashah. That is, three dimensions in a matrix of seven, with 7 x 7 x 7 “elements” defined by our cyclic observance of calendar related halacha, have two-dimensional faces consisting of 7 x 7 elements. The internal spaces of this cubic matrix coincidentally number 216 corresponding once again to the number of letters in God’s Name. There comes a time when you just have to accept the fact that everything is interconnected and that one way or the other, the dots always connect back to the letters of the One Unique Explicit Name or Triad Havaya of 72.

There is yet another witness to the significance of these numbers in the sets pertaining to this verse, where the first seven nations that were conquered; were defeated in seven years; that then took another seven years to divide amongst the tribes. Here we have the same set of numbers. The threesevens” alluding again to the three dimensions of seven are discussed in such posts as Re’eh, Eikev, Behar and Bechuko-thai. In Re’eh, for example, we have the “three times” required of every man, for Pesach, Shavuot and Sukkoth (involving “sevens of days”) taking the same form.

Coincidence? Not hardly. One way or the other, the events are all hidden reflections of the 216 letters of God’s Explicit Name that are an intrinsic part of the combined cubic form of the luchot (6 x 6 x 6 handbreadths = 216 cubic handbreadths) where the outer garments (in the letters of Torah) form a matrix of 7 x 7 x 7: seven days; seven times seven days; seven weeks; seven times seven weeks; seven years; and seven times seven years” (wherein the 216 are hidden) and where these letters mathematically define the actual flow (in cycles) of time, that restrict, confine, or otherwise limit “movement” through the physical universe (see "Part I" of the post on "The Eight Dimensions").

You would think that the number of allusions would at some point subside but they are seeming endless. The above reference to threes' in Shoftim, and the patterns they form, for example, now expand into patterns of four and sets of fours, that also happen to be an integral part of combined (male-female) tetrahedral geometry, but more specifically reflecting the exact number and the nature of the marriage between the letters:

20:02 “Before you [go into] battle...
“the priest shall come forward and address the troops...”
20:03 “He shall say to them...”
“Shema Yisrael... you are about to do battle...”

1) “Let not your courage falter...”
2) “Do not be in fear...”
3) “or in panic...”
4) “or in dread of them...”

There are specifically four admonitions made by the priest mentioned directly in the text of the Torah. Our Sages discussed these four admonitions and said they were the counterparts to the four techniques used by the enemy to frighten their opponents:

1) the clashing of shields,
2) the braying of horses,
3) the yelling of the soldiers, and
4) the sound of the enemy’s trumpets
    (Mishnah Sotah 8:1)

In these admonitions we see four things standing opposite four things. This is like the male and female counterparts in the two primary abbreviated forms of God’s Name, the four letters of the Tetragrammaton opposite the four letters of Adnoot, as discussed more thoroughly in the post on Massey and Devarim and "The Marriage of the Letters." These eight letters are a subset of the 216 letters represented geometrically as four points on one tetrahedron opposite four points on the other. One might suspect that this too is a coincidence, after all, don't these letters combine to form the four letters of Ehyeh? If this is more than just a coincidence (and statistically significant) then where is this alluded to in the text? Our Sages provide the answer.

In addition to the text that conforms to the male-female abbreviation and the geometry corresponding to the letters, there were four admonitions that fulfilled four 'purposes' listed by our Sages:

1) the Jewish people suffered from a lack of training
2) small number of soldiers, inferior numbers compared to established nations
3) disparity in the number of chariots
4) lack of physical superiority due to time spent in study and prayer

The fulfillment in these four ('purposes') is a direct reflection of the marriage between the letters, that is fulfilled in (or results in) the four letters of Ehyeh.

In the beginning of this post we saw “four instances of three.” Now we have “three instances of four.” One is the geometry of the royal seal that in turn reflects the number and nature of the letters in the Name. The other is a direct reflection of the number and nature of the marriage between those letters (the two halves of a male~female universe).

This geometry not only represents or reflects the male and the female aspects of the letters in God’s Name, but also characterizes the entire physical and nonphysical universe. Each tetrahedron has four faces and four points. When they are married together, each of the two-dimensional faces is divided into four smaller faces (three fours). These four small faces each have three points (four threes). Moreover, during the process of “unification,” which is the intent of so many mitzvot, the marriage of the two results in another four (the smaller faces on each of the large faces). This is like the four letters of the Tetragrammaton and the four letters of Adnoot whose unification results in the four letters of Ekeyeh. The geometry reflects the characteristics of the letters. These same letters define the four forces of quantum mechanics that “rule” the universe. These four forces and their four polar opposites (like the plus and minus of electricity) are merely extensions of these letters. Without the division of the four letters of Ekeyeh into the their male~female counterparts in the four letters of the Tetragrammaton and the four letters of Adnoot, all matter would collapse, duality would disappear, and the universe would collapse.

But perhaps we can find a second witness to this particular connection as well, and maybe even a third witness, who can testify to all of the above connections. In fact, as if in response to the assertions made above, Parashah Shoftim proceeds to specify the halachic requirement for the minimum number of witnesses:

19:15 “A legal matter can be valid only on the testimony of two witnesses or more.

The english is usually translated incorrectly because the Hebrew words really don’t make sense, at least on the simple level. Whenever there is an unusual combination of words in the Torah, it is generally related to lofty matters that relate to certain secrets. This is like the twins in the womb of Rivka and also Tamar that we saw in Toldot and VaYeshev, where the Torah says regarding Rivka: “when it came time to give birth... there were twins in her womb,” and then for Tamar: “when it came time to give birth... there were twins in her womb," in each case as though no twins existed until that time. The description of the events is identical. Both allude to the sapphire twins (luchot) that would be divided into twins when it came time for them to be brought down by Moshe (and specifically brought down twice). The mathematic corollary is a very bright reflection of these events.

Insofar as the text pertaining to the minimum number of witnesses is concerned, what this verse actually says is: “by the mouth of two witnesses or by the mouth of three witnesses” a legal matter may be decided. There is a big difference between two witnesses or three witnesses. The problem is that the language doesn’t make any sense. What is the minimum requirement? It does not say that “two or more” are required, as is often translated (that would actually make sense). Rather, it says the matter is decided “by the mouth of two witnesses” OR “by the mouth of three witnesses.”

The problem is that if a legal matter requires two witnesses, then three are not necessary. Conversely, if it requires three witnesses, then two are not enough. So which is it? It can’t be both unless both are the same thing. But how can “the two” and “the three” be the same thing? The only time that two witnesses are the same as three witnesses, is in the case of the luchot which are mathematic and geometric twins: 2 tablets x 108 (cubic handbreadths) but also exist as a series of cubic triplets corresponding to the letters of God’s Explicit Name: 72 x 3 (cubic handbreadths). Both witnesses (either the two 108s, or three 72s) equate to the ultimate witness (216) Who is God Himself.

The implication is that the real witness is God Himself who sees everything. He is the One who in the end provides testimony that condemns, and because of this, man cannot escape the consequences no matter how hard he tries. This includes cases where an earthly court may have erred. The only way that either two witnesses or three witnesses would suffice, is when it refers to the letters of God’s Name found within the geometry of the two that provide testimony (the "tablets of testimony" as they are sometimes called) that also happen to be three witnesses in the form of the triplets that also correspond to God's Name. Interestingly, this is not unlike the two groups of threes that are mentioned above whose numbers define two faces of a star tetrahedron (the two faces being one 'two-dimensional' magen david) reflecting again the nature of the letters in God’s Explicit Name.

These two witnesses testify to what God requires of man, things for which he is ultimately accountable, but at the same time, these two witnesses are three witnesses (the triplets) relating to the Triad nature of the Explicit Name. Both constructs testify to what was spoken “by the mouth” of God, who gave us these witnesses in the first place. The tablets of “testimony” are geometrically two halves in two dimensions and three cubic triplets in the third dimension at the same time.

There is also another “witness” to this assertion. The “two witnesses or three witnesses” mentioned above are actually mentioned twice in this parashah, like the luchot that were brought down twice. Flashback to verse 17:6 where this minimum requirement is given a second time: “a person shall not be put to death; only by the mouth of two witnesses, or three witnesses [shall he be condemned].” The Torah does not mention anything twice unless it has a very specific purpose. In this case, the tablets of testimony that are mathematic twins and triplets at the same time, are twice mentioned.

In summary, we see in the case of Parashah Shoftim that the sets of four threes and three fours specifically reflect the geometry that corresponds to the number and nature of the letters of God’s Name and these letters are completely and irrevocably attached to Israel’s destiny. Moreover, once again, we see with amazing clarity, the interconnectedness between the luchot; God’s Name; the events that are described in the Torah; the word level of the text in the Torah; even the letter level of the text in the Torah, as well as everything else in the physical and nonphysical universe. All have this unique inexplicable mathematic and geometric connectedness that defies logic. The absolute precision of the various combinations, the number of repetitions of these combinations, together with what they represent in terms of, for example, complex three-dimensional geometry, two-dimensional geometry (etc.) would simply have been beyond the ability of any man or group of men to compose. It is as if the numbers, and sets of numbers, and ratios between sets, pre-existed the text itself, and the text were an extension of those numbers. This accounts for why we find the mathematic value of the letters so perfectly reflecting the same combinations. They are all an integral part of the royal seal and the letters of God’s Name that are so well hidden beneath the surface. Who could write a meaningful narrative that was so mathematically and geometrically perfect? Only the Architect Himself. As it says... “written with God’s Finger.”

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