The dual resonance model has been 'enhanced' and updated since it was first posited, and the more complex mathematic equations are the basis of what is now called quantum chromodynamics. So in addition to its duality (dual resonance) we have a more complete picture that oddly enough, conforms even more precisely to the tetrahedral nature of the foundation stone. Connect the dots yourself (the black dots shown below) and you will see the two-dimensional shadow of a star tetrahedron (a magen david). The additional dots (in red, green and blue) are merely facets of its three-dimensional counterpart compressed into two dimensions. The star tetrahedron (what we call the royal seal) is the singularly unique construct in the combined cubic form of the luchot having 72 triangular corners (216). It seems the deeper one delves into the physics of creation (like string theory) the more its geometry conforms to the intrinsic properties of a cube that is specifically measured in terms of 216 elements (essentially geometric reflections of the 216 letters of God's Name).
The mathematic nature of these 5 constructs can be difficult for most people to understand, but it helps to know that they define the properties (the edges, points and faces) of 5 well known geometrics known as platonic solids. Each has a polar opposite shown in the models below. However, one of these constructs is unique and different from the rest, in that it is its own polar opposite. All of them are three-dimensional, but the unique geometry of this one construct casts the familiar two-dimensional shadow known as a magen david that we mentioned above.
This one construct, unique among the five, is known as a tetrahedron. It is pictured on the left, along with its polar opposite (below). All the other constructs (pictured to the right) have different polar opposites (paired with one another by the arrows). Take a moment to understand that they are integral mathematic components of the combined cubic form of the luchot.
Tetrahedron Cube Octahedron Dodecahedron Icosahedron
Tetrahedron Octahedron Cube Icosahedron Dodecahedron
The one unique construct (the tetrahedron and its opposite) are decidedly different from the other four, for several reasons, much like the one thumb is different from the other four digits of the hand, which are fingers. In fact, this is the template within the luchot for the human hand. You might think this is a coincidence but it is not (we will provide additional details in a moment).
We also see this 'specification' in the two tetrahedrons. When their geometry is juxtaposed, the internal subdivision results in one octahedron and four tetrahedrons. Human physiology merely adheres to the design specifications that are seen in various areas of the blueprint. This particular specification is a reflection of the Hand of God (as it pertains to that which was created) through the two hands of man (who is a co-creator). These are the ultimate instruments that propel the ongoing act of creation toward its ultimate conclusion.
Man's hands were not present in the beginning, and so God 'created' with 10 'sayings' (the primal equivalent of vibrating strings). Just as the hands are 5 opposite 5, and where one digit is different from the other four, so too were the sayings which adhered to the specification in the blueprint requiring this underlying pattern. The Maharal talks about the 5 'upper' and 5 'lower' plagues at the time of the exodus (5 opposite 5). The death of the first born was unique, and so one pair of plagues was different from the other four pairs of plagues, in what amounted to a negation of the 10 utterances1 that God used to 'create'. That's why there are 10 sephirot that were 5 opposite 5 (sefer yetzirah). That's why there are 5 special letters in the Holy Tongue that have a dual form, and more specifically, that's why there are 5 string theories reconciled by dual resonance that dictate our existence in the physical universe. Moreover, one theory is different from the other four theories as you will see in a moment.
If you think the Sages of Israel did not understand 'creation,' then consider the blessing (birchat hakohanim) and the shape made by the fingers and arms of the one giving the blessing, covered as it were by the tallit over the head. The tradition originates with an understanding of creation and certain lofty concepts which have long since been forgotten. The tetrahedral geometry within the luchot consists of 5 components in one half, opposite 5 components in the other half, where one (the octahedral core) is different from the other four (which are smaller tetrahedrons) just like the five constructs themselves. Likewise, as mentioned above, there are 5 digits on one hand and 5 on the other, where one (the thumb) is different from the other four (which are fingers). A tetrahedron consists of 14 elements. The hand has 14 visible joints. The gematria of hand (yad in Hebrew) is 14. There are 28 bones in the hand (2 x 14) and 28 elements in 2 tetrahedrons. Everything is connected, and originates in the cosmic blueprint. Two tetrahedrons have 14 elements opposite 14 elements, two hands have 14 visible joints opposite 14 visible joints, 28 in all, and so on.
Just how far does this connection go? As we stated, the models of the 5 constructs and their duals are merely representations of 5 complex mathematic constructs within the luchot, and their duals, which are essentially the geometric DNA of creation, also revealed externally in the two 'halves' of an external, as yet undivided three-dimensional cube, which when divided (and brought down by Moshe) end up with 5 commandments on one and 5 on the other.
This original cube [of creation] (prior to division) is sometimes depicted two-dimensionally and referred to as the cube of metatron (a concept that dates from antiquity) in which we see these 5 three-dimensional mathematic constructs 'flattened' into a two-dimensional reference frame. Certain facets disappear because of the inherent limitation of two-dimensional space, but are nevertheless part of the combination they represent (the combined cubic form of the shnei luchot).
As stated previously, each construct in the luchot has a polar opposite. Specifically, the tetrahedron is its own polar opposite. The polar opposite of the cube however, is the octahedron, and the polar opposite of the octahedron is the cube. The polar opposite of the dodecahedron is the icosahedron, and the polar opposite of the icosahedron is the dodecahedron (and so each has a different polar opposite). String theory conforms to this pattern established in the cosmic blueprint. Each type of string has a one-to-one relationship with each construct in the blueprint (the shnei luchot define this requirement in terms of their geometry).
Specifically, the counterpart of the tetrahedron is found in a "type one," string which is its own opposite. A type one string consists of both 'open' and 'closed' strings (the polar opposites are within the same 'type' of string).
Moreover, the remaining 'types' of strings are all closed. Thus we find that one type (a 'type one' string) is different from the other four types, again just like the constructs in the combined cubic form of the luchot, where one (the tetrahedron) is different from the other four.
The next two types of strings are referred to as 'type two' (A) and 'type two' (B). They too are 'opposites' of one another. One is chiral and the other is non-chiral (again polar opposites but here they are not of the same type). These originate in the combined cubic form of the luchot as the constructs that define the cube and the octahedron (where each is the polar opposite of the other).
The remaining strings are known as HO and HE. The group symmetry of these two are opposites. They originate from the mathematic constructs within the luchot that define the dodecahedron and the icosahedron, which are of course polar opposites of one another. The HO and HE types of strings also have a special connection to the symmetry in what is known as (the physics of) E8, a lie algebra group of 248 dimensions, and where, interestingly enough, all of the numbers and their geometry reflect the nature and even the number of letters in the Triad Name with 72 triplets as explained in the next essential construct on the E8 Lattice and the Explicit Name (link below) and also the post on Shemeni and Tazria as it would pertain to the measure of the mikva. The HO is SO32, and the HE is E8xE8 (with its many significant multiples of 216 as seen in the post just mentioned). The 216 are a mathematic reflection of the 216 letters in the Name. The 32 are a reflection of the 32 'paths' (known in kaballah) which are the sum of the 22 letters of creation plus the 10 sephirot (22 + 10 = 32). The 32 and the 216 give rise to the elements of creation that are 'modeled' in the physics of E8 (although few realize that the significance in the 'creative chain' of events that flow from the 216 and the 32, that ultimately define the dimensions of E8). There is a very precise one-to-one correlation between the internal dynamics in the cube of creation (combined cubic form of the luchot) along with the letters that define it, and, each string theory along with its opposing aspects, down to the smallest detail. I see said the blind man!
The 'symmetry' of the last two, by the way (found in E8) is a function of, or can be expressed in terms of euclidean space defined by 216 specific x, y, and z coordinates, all of which correlate with the 216 letters of the Name (as explained in the post on "The 4 Species and the Explicit Name"). These "coordinates' expand exponentially into the various components or elements of the E8 model that is ultimately a function of the triad nature of the 72 triplets.
What about bosonic string theory2? This is the original version of the theory (somewhat less detailed with inconsistencies that are not reconciled) but which reflect to a certain extent the polar opposite characteristics of the luchot and its most dominant construct, without regard to the remaining constructs.
We've already discussed the correlation between the 4 letters in the abbreviation of God's Name known as the Tetragrammaton and the 4 letters of its opposite in the abbreviation known as the Havaya of Adnoot, as they pertain to the 4 forces in quantum mechanics, and their opposites like the plus~minus of electricity (in the post on "The Eight Dimensions") and so it will not be repeated in this post.
To read the next advanced construct click here: The E8 Lattice and the Explicit Name
Footnote 1 - A further explanation is beyond the scope of this post and requires a reading of the Maharal's teachings on time and space.
Footnote 2 - The bosonic string theory (which lacks the details that would be necessary to complete the model) is a composite of the type one which is its own polar opposite (consisting of both 'open' and 'closed' strings) but it also combines elements of the other 4 types as well (which are all closed). The bosonic theory therefore has a connection to the combined cubic form of the luchot which contains all 5 of the constructs but does not differentiate between them. The unique construct within the luchot, or the most mathematically 'dominant' construct, is the tetrahedron. Just as the tetrahedron has 4 points (tetra meaning 4) and correlates with the 4 letters with a gematria of 26, so too does the 4 variants of the bosonic (theory) which posits 26 dimensions of space-time. One is merely a reflection of the other. The 'heart' of the tetrahedron, by the way, is its octahedral core which consists of 4 pairs of opposing faces and a total of 26 elements (12 lines, 8 faces and 6 points). The bosonic theory posits 26 dimensions where 22 are excess dimensions (in addition to the 4 observable dimensions of space-time, where each of these is a 'pair' of continuums). Again, one thing is a reflection of the other. For example, there are of course 22 letters in the Hebrew Aleph-Bet, that our Sages of old, described millennia ago, as the 22 primordial elements of creation. They knew that 4 of these letters spelled the abbreviated Name Ekeyeh (which was the sum of its two halves: the Tetragrammaton and Adnoot) and that these letters sustained the universe (like the 4 forces of quantum mechanics that 'rule' over its physical existence). How on earth did they know these things? Each element, be it a letter; a geometric facet of the luchot; or an aspect of string theory, is a reflection of a larger reality, which is, in fact, one or more letters of the Name, that define one or more parts of the blueprint, that in turn define one or more facets of the universe.