Human consciousness is not ordinarily wired to perceive complex three-dimensional geometry. Were this possible, man could likely see the Hand of God and the concept of faith would cease to exist. That is why these facets of the primordial torah remain hidden from the casual observer and can only be envisioned as a reflection of its geometric properties. If one mistakenly thinks of the geometry as a physical reality, they've missed the point, as the geometry merely 'reflects' the nature of a much larger reality that would otherwise be impossible for man to perceive. It is that reality, originating with the letters of God's Name, that gives rise to the cosmic blueprint/luchot; the physical universe; and the history of mankind as it progresses toward its inevitable conclusion. The purpose of this post is merely to show how the letters correlate with the geometry of the blueprint (their one-to-one correspondence with its various properties) that in turn defines what we perceive as the world around us.
If you've read the post on the Primordial Torah, then you've already seen examples of how everything in the physical universe is literally a manifestation of the specifications in that blueprint. What we've not yet presented in this blog are some of the more deeply hidden aspects of the foundation stone or the secrets of the magen david hidden within, or how these particular internal aspects (the hidden) are attached to the external aspects that are revealed, as demonstrated in that post on the primordial torah. To accomplish this, we'll provide a glimpse (a very small glimpse) of how the tetrahedral geometry of the luchot 'attaches' to specific letters of the Name, by demonstrating the one-to-one correspondence between the letters and elements of the geometry. At the same time, we'll show how these letters establish not only the duality of the universe as described in physics, but also the four forces of quantum mechanics.
The essential constructs listed to the right are of course a prerequisite to understanding this post. If you've not yet read them, please start with the introduction and work forward until you've read the post on the Primordial Torah previously mentioned. Those who have already read the basics, should nevertheless understand how important it is to read what is written here very carefully.
If you are a regular reader of this blog, then you are by now aware that the Primary Letters of this One Unique Explicit Name (that gives rise to the abbreviations known as the Tetragrammaton: yud-key-vav-key, and Adnoot: aleph-dalet-nun and yud) are quite literally the 4 forces in quantum mechanics, as well as their 4 counterparts. The 4 letters of the Tetragrammaton are separated from (and stand opposite) the 4 letters of Adnoot (4 opposite 4) in order to maintain the duality mentioned above. The 'separation' of these letters is depicted on the shviti in most synagogues. Without this division (where the letters are seen in their respective male~female state) the 4-letters and their opposites that define and sustain the polarity of the 4 forces of quantum mechanics would return to a unified state (the Havaya of Ehyeh). Were this to happen, the forces would contract, duality would collapse, and the universe would shrink into a quantum singularity and effectively cease to exist.
To demonstrate how the letters of the Name prevent this from happening, we first need to show how they define the blueprint (luchot) which then defines the universe and everything in it, including its duality. This premise can be visualized by looking at the blueprint's primary internal mathematic construct, which essentially defines the geometry of a tetrahedron, or more specifically, a tetrahedron together with its opposing counterpart, that create the geometry of a star tetrahedron (three-dimensional magen david). It should be noted that tetrahedral geometry is the most basic element of the amplituhedron, or "jewel" at the heart of quantum field theory (a recent discovery now acknowledged in physics).
The first letter of the Tetragrammaton (the yud: י) is shown below in the place and position that best demonstrates its connection to a specific point within the construct that it defines. This of course transcends geometry (the physical) however it is best understood within the context of geometry. Similarly, the first letter of its opposite, which is the first letter of Adnoot (an Aleph: א) is shown below in the place and position that best demonstrates its connection to a specific point within the opposing construct that it defines (seen within the geometry of the luchot as the opposing tetrahedron). Keep in mind as you contemplate the connection between the letters and the geomertry, that the tetrahedrons merge with one another in opposing directions, to create the star tetrahedron within the combined cubic form of the luchot. Notice the opposing points of each tetrahedron have been numbered/labeled accordingly, with the male points in blue and the female points in red for the sake of distinguishing the duality.
The Geometry as it Pertains to the Four Letter Name(s)
click to enlarge
4 Opposite 4
(yud-key-vav-key opposite aleph-dalet-nun-yud)
(only one letter of each 4 is shown)
There are of course 4 points on a tetrahedron, as there are 4 letters in each of these abbreviations, but as stated above, only one of the 4 letters of the Tetragrammaton is shown above (the yud) and even then, only on one face, related to one point, on one tetrahedron (the one on the left). The three remaining letters (two hehs' and one vav) that define their respective portion of the construct (that ultimately give rise to another three 'points of light' within the blueprint) are not shown in the above diagram.
Just as only one letter of the Tetragrammaton is shown in the diagram above, so too, only one letter of Adnoot is shown (the aleph: א) and again, only on one face, related to one point, on one tetrahedron (the one on the right). Its three remaining letters (the dalet, nun and yud that define their respective portion of the construct) ultimately give rise to yet another three 'points of light' within the blueprint (but are also not shown). You can contemplate their place and position in the cosmic scheme of things, and the part their corresponding letters play in defining the nature of the Primordial Torah (luchot) on your own.
In the meantime, to see how and where this geometry gives rise, for example, to halachic requirements and actual events throughout history, see the post on Ki Thetze. The connection that these things have to the 4 primordial forces in quantum mechanics (the strong nuclear force, the weak nuclear force, electro-magnetism and gravity) together with their 4 polar opposites (like the plus and minus of electricity) that literally "rule" the universe, should be rather obvious at this point. Although it would be more accurate to say that it is the letters that define (or quite literally are) the 4 forces.
The only other thing to add at this point is that the Name is not limited to the 8 letters of these abbreviations, and all 216 letters have their own unique place, position and orientation within the construct that may be perceived in tetrahedral context as its 72 triangular corner points.
The same 4-letters also exist in triad form as is known (reflecting the triad nature of the One Unique Explicit Name or Triad Havaya of 72). When tripled, these 4-letters become 12 (3 x 4 = 12) and define their respective 'surface' within their respective portion of the 'construct,' and ultimately reveal (within the geometry of the luchot) what is called the 12-letter Explicit Name. Although again, its important to understand that these letters, associated with this 'portion' of the Name, are what 'define' this 'portion' of the blueprint/luchot, which in turn ultimately defines its respective 'portion' of reality. We would only emphasize that these letters are actually a 12-letter subset (abbreviation) of the 216 letters (3 x 72) of the One Explicit Name, just as the 4-letter 'Names" are a subset of the 12. Both subsets are clearly seen in the nature of the geometry that gives rise to the three-dimensional tetrahedral components of the luchot (shown in the diagram below).
In that same picture, one letter of the Tetragrammaton (of the four) is shown in its triad form, in a place and position associated with its portion of the construct. Each letter thus continues to 'define' its respective place in the cosmic blueprint. Note that in the previous subset (of only 4 letters) the definition was limited to two dimensions (one 'surface' of the tetrahedron, which in two dimensions is a simple equilateral triangle). The 12-letter 'definition' of the blueprint however, encompasses three dimensions (all three 'surfaces' at any given point) and really more than that, in that the letters ultimately encompass each of the dimensions within the magen. A more detailed explanation is beyond the scope of this post.
We here provide the connection between the letters of the Name(s) and the geometry, so as to show the geometric basis for meditating on the Name and performing the unifications (yichudim) of its letters as explained by Chaim Vital on behalf of the ARI.
Note also that the letter that is married to the yud (which is the aleph of Adnoot) is also shown here in its triad form, along with the place and position that it defines within the primordial Torah. Again, this abbreviation is derived from (a subset of) the Triad Havaya of 72 (72 triplets) with a total of 216 letters. The 4-letter subset (seen throughout the Torah) is in turn a reflection (or subset) of the 12-letter 'Name'. The 12-letter 'Name' is in turn a reflection of the 216 letters and so on. The 4 letters and/or the 12 letters (as opposed to the 216) are best described as a reflection of a higher dimension, a state that would be (or is) far more difficult for mankind to see or understand. The 4-letter abbreviation is thus written throughout the Torah, the 12 letters are hinted (some examples are listed in the post on Ki Thavo) whereas the 216 specific letters are not only hidden, but hidden in only one place, and perceived (as the Name) only after being properly permuted (into triplets) as is known.
The Geometry as it Pertains to the 12 Letter Name(s)
click to enlarge
12 Opposite 12
(the 12-letter abbreviation opposite its 12 letter counterpart)Again, not all the letters in the triad form of 12 letters are shown above, and the above letters are not "triplets" among the 72. Rather, each of the letters above is from a different triplet. Although, they do form a triplet (3 letters come together) at any given point, and these letters ultimately coincide with the 12-letter (triad abbreviations) of the Explicit Name (12 among 216) on any given point. So a total six different triplets are represented above, but just one letter from each of the six triplets. The remaining points on each tetrahedron correlate with the remaining letters of the remaining triplets. The letters shown should be sufficient for one with understanding, but either way, it's important to understand that it is the letters of the Name that define the nature of the blueprint (luchot) and that the luchot in turn define everything else in the universe. This is why "string theory" and especially type II strings, along with the E8 lattice conform to certain aspects of this geometry, although it would be more correct to say that they "reflect" the nature of the letters in God's Name.
(within its triad or tetrahedral context)
(within its triad or tetrahedral context)
Also keep in mind that a star tetrahedron is the geometric result of the marriage between two separate tetrahedrons (like those pictured above) and that one is female with respect to the other (pointing or facing in the opposing direction). Although again, the geometry is merely a reflection of the marriage between the letters of the Name and its abbreviations that sustain the duality of the universe, and not the other way around.
It should also be emphasized that one point of any given tetrahedron is always different from its other three points because any three points are always found within one two-dimensional plane, whereas the remaining point stands above in the third dimension. This is because, when the letters of the Tetragrammaton and those of Adnoot are married together, one couple (the vav and the nun) are combined differently as is known, so one couple is different from the other three. The luchot are defined by the letters, and thus its geometry conforms to the characteristics of those letters. The physics of time and space and quantum mechanics merely adhere to this 'signature' geometry (of the Name). Consider this carefully.
We can easily demonstrate this relationship in both the internal and external geometry of the luchot, where each letter of the Name "defines" its respective place and position within the cosmic scheme of things. The geometry of the blueprint, that in turns defines various aspects of the universe, can be found in specific aspects of physics (like the quantum mechanics mentioned above) and also the physics of time and space which has 4 observable dimensions, each with two continuums/directions etc. (again 4 opposite 4 because it too, is a reflection of the Name). Moreover, it can be found in biology (a link to an explanation of where it is found in Human DNA will be provided at the bottom of this page) and also chemistry, and even celestial dynamics, just to name a few. Examples of both the 4-letter and the 12-letter (abbreviation of the) Name, and what these letters actually 'define' in the physical universe are provided throughout the blog. This specific abbreviation (of 12 letters) is elaborated upon more fully in posts like Ki Thavo.
It is sufficient at this point to understand that the marriage of the opposing letters, be they 4 opposite 4, 12 opposite 12, or 108 opposite 108 (explained in posts like the Primordial Torah and the marriage of the letters) is mirrored in the geometry defined by those letters, or more specifically, the two tetrahedrons which have 4 points opposite 4 points; 12 small faces opposite 12 small faces; 36 triangular corners (108) opposite 36 triangular corners (108); etc.; and that these components/elements 'merge' (marry/unify) to create a star tetrahedron with 72 triangular corners, reflecting the more complete geometry associated with the connection between all 216 letters of the One Unique Explicit Name and the blueprint/luchot that it defines.
The same geometry can be found in the external cubic geometry as well (the cubic form is revealed externally while the tetrahedral form is hidden internally) much like the Hand of God is often hidden behind the scenes or beneath the surface of events that are characterized by the letters hidden within the corresponding geometry. The Hand (gematria 14) has 14 visible joints and 28 bones (which 2 x 14). The 'hidden' Hand of God (which is geometrically hidden within the blueprint as a mathematic construct) has 14 elements (a tetrahedron consists of 6 lines, 4 faces and 4 points = 14 elements). Two opposing tetrahedrons have 14 elements opposite 14 elements (28 elements) like two opposing hands that have 14 visible joints opposite 14 visible joints (28 visible joints) etc. Although once again, it should be emphasized that the mathematic and/or geometric attributes of human physiology are a reflection of the specifications in the blueprint/luchot which are in turn a reflection of an even higher reality in the letters of the Name (that may be perceived as a function of its geometry).
The Combined Cubic Form of the Luchot
(216 Cubic Handbreadths)
The Tetrahedral Geometry Hidden Within the Luchot
(2 Tetrahedrons: 14 elements opposite 14 elements)
(2 Tetrahedrons: 14 elements opposite 14 elements)
(72 Triangular Corners = 216)
Note that each 'point,' of each tetrahedron hidden within the cube (internally) corresponds with each 'point' that is revealed externally on the surface of the cube. Just as there are 8 points that are 4 opposite 4 revealed three-dimensionally on the outside (3 different spacial orientations) there are 8 points that are 4 opposite 4 hidden three-dimensionally on the inside (times the 8 different spacial orientations corresponding to the 8 different two-dimensional surfaces of the star tetrahedron) resulting in a representation of ten-dimensional space (or 11 depending on the observer's descriptive preference). These are just a few of the many striking examples of the connection between the blueprint/luchot that God "looked into" to create the universe, the letters of the Name that define that blueprint, and the physics describing the current model of the universe in such things as String Theory which posits 10 dimensions; M-Theory which posits 11; the 4 forces (and their opposing polarity) of quantum mechanics; and the 4 observable dimensions of space-time (also with opposing polarity in the two directions or continuum's of each dimension).
The Two Dimensional Shadow
This post is actually a prelude to an explanation of the connection between the letters of the Name and the secret/measure of the incense (that was taught to Moshe by the angel of death). In the meantime, we would remind the reader that God's Name and the specific letters of this Name that are found in the Torah, were given to the Jewish people and only the Jewish people. Pity the nations who utter the names of false gods and false religions arising from incorrect assumptions that originated after the flood (as explained in the post on Bereishit and Noach).
You can read another of the advanced constructs here: Eggs and Olives (Systems of Measurement)