It is no coincidence, for example, that 26 is the gematria of the Tetragrammaton (which is the 'Name' consisting of four primary letters that are integral aspects of all 216 in the full Explicit Name) and that these letters in turn define 'the measure' of the cosmic blueprint (the geometry of the luchot). It is also no coincidence that 10 is the defining number of its physical geometry by virtue of its 5 internal constructs and their 5 opposing counterparts (5 opposite 5). This part of our reality can be perceived in the 10 sephirot that were said to be 5 opposite 5 (sefer yetzirah); or the 10 forms of the 5 dual letters that are integral components of lashon hakodesh. This "geometry" is also the source for many of the patterns found in both the linguistic structure of the Torah and the character of key events experienced by Israel throughout its history, all of which (being to numerous to mention) are discussed elsewhere throughout this blog.
At any rate, this cosmic blueprint of which we speak, is the complex measured geometry of the foundation stone (evan shetiyah) which is the primordial form of the luchot before division. When it was divided and brought down by Moshe, it was divided in half, effectively resulting in 2 "tablets" (the shnei luchot as we know them) and the template for the male/female nature of the universe. Geometrically, each half of 'the cube' [of creation] had 4 corners that stood opposite their counterparts (the other half) giving rise to a total of 8 corners. This aspect of the geometry 'defines' the three dimensions of physical space (and the forces of quantum mechanics) but it is important to remember that this aspect of the geometry of the luchot is itself 'defined' by the letters of God's Name, and more specifically the letters of its 2 primary abbreviations which are the 4 letters of the Tetragrammaton (yud-key-vav-key) opposite their counterparts in the letters of Adnoot (aleph-dalet-nun-yud). The 'division' of the larger reality (in the letters of God's Name) that resulted in these 8 specific letters, was the catalyst for the division of the luchot. The division of these primal components (letters) into their respective male and female halves, is what allows us to perceive three-dimensional space (in essence our existence in the physical universe).
If we could squash this 'space' back into 2 dimensions, you would have only the (original) 4 letters of the unified version of these Names, which is the 4 letters of Ehyeh (aleph-hey-yud-hey) as explained in the post on The Marriage of the Letters. Similarly, squash the 8 corners of a three-dimensional cube back down into 2 dimensions and you have the 4 corners of a square.
The 4 letters are a self-dual (to borrow a term used in mathematics and/or physics) in that the 8 are the male and female 'halves' of the 4. The 4 corners are likewise a self-dual, in that they are the 8 three-dimensional corners of the cube that compress into the 4 two-dimensional corners of a square, where those male and female halves disappear.
In other words, the letters define the cube [of creation] that we perceive in the physical universe as "something" (which is the actual word used to describe it in Parashah Mishpatim) having a "measure" of 216 (as in its volumetric measure, or the measure of its surface in square handbreadths, also 216); and its measure in terms of degrees (like the 2,160 degrees in its 24 angles of 90 degrees). All of these geometric characteristics (and especially those pertaining to its division) play a direct role in creating our physical reality. Please take time to understand this.
With the above in mind, we can now examine a lie algebra group known as “E8” that is thought to model the relationship between the mathematic aspects of the universe mentioned in the first few paragraphs. The mathematics of the E8 lattice conforms to the pattern established by the cube [of creation](luchot) that of course conforms to the pattern that started the creation-process, established by the 8 letters (of the two Names) that ultimately reduce to the 4 letters of the one Name. The lattice of E8 can be constructed, for example, from binary code1 (a binary system has 2 elements) in this case with rank 4 and a length of 8. Remember those 2 Names of 4 letters that have a total of 8 letters? The binary code is generally represented by H(8,4) signifying the fact that it is a self-dual (currently accepted and well known in certain circles1). The application results in the E8 lattice, but let's assume for the moment that this is just a coincidence.
It turns out that the geometry of E8 also has 2 primary symmetries that preserve the lattice2 much like the 2 male~female abbreviations of the Name we mentioned earlier. These symmetries just happen to possess additional measurements that are identical to the nature and number of the 216 letters in the Triad Havaya of 72, or the Explicit Name. If you've read the essential constructs to the right, this really should come as no surprise.
It should also be obvious that the 8 correspond to the 8 stellations (tetrahedrons) of the star tetrahedron defined by the geometry of the combined form of the luchot or foundation stone as it is called. Recombine the two tetrahedrons that form the star tetrahedron so that the male/female aspect of the stellated geometry disappears, and we're left with the 4 tetrahedral corners of the original tetrahedron, its primal form. The 8 tetrahedral corners that reduce to 4 tetrahedral corners, in turn defines the geometry of the surrounding 3-dimensional cube. The nature of this geometry is what gives rise to the nature (physics) of the universe.
All of this is pre-determined by the "foundations stone" (evan shetiyah) which was the primal form of the luchot/tablets made of a sapphire-like crystal with tri-gonal or tetrahedral properties.
Before providing details on the lattice described above, pertaining to the letters of God's Name, it might be worth mentioning (just to give you an idea of its complexity) that it took 18 mathematicians and computer scientists 4 years using a computer to crunch the numbers and fully model the group. The geometry is pictured below and you can click on the image to enlarge it.
The E8 Lattice
Where do we see the 'measure ' of the luchot and its connection to the letters of God's Explicit Name in this complex system? If you look through a proverbial magnifying glass, you will find that each point of the E8 lattice is surrounded by 2160 symmetrics (known by physicists and mathematicians as ‘8-orthoplexes’). You will also find that there are 17,280 symmetrics (known as ‘8-simplices’). The first number should sound familiar. There are 216 letters in the Explicit Name, and this is merely a multiple of these letters, like the many multiples and their derivatives that define the passage of time, as seen in such things as the 2,160 years that each constellation takes to pass through the precession of the equinoxes, and the 1,080 halaquim/parts (a unit of measure) for each hour of the day and night. Any one hour of the day (1,080 halaquim) opposite any one hour of the night (another 1,080 halaquim) equals 2,160 halaquim. All of these characteristics originate in the number of degrees in a 3-dimensional cube (2,160 degrees in its twenty-four 90-degree angles). The other numbers mentioned above will be discussed in a moment.
With regard to the 2,160 years, it should be noted that the total period of time in this precession is 25,920 years (12 constellations times 2,160 years = a great year of 25,920 years). With regard to the 2,160 halaquim, it should be noted that the total number of halaquim in a day is also 25,920, in essence a localized reflection of a great (celestial) year. Notice that both are measurements of time.
The number 25,920 is also the number of “drops” in a “hin,” demonstrating how our reality is intricately connected to the letters of the Name. Everything in God's creation is interconnected. Each measure, for each of its most essential aspects, be they 216 of a particular unit, or 10 x 216 such units (2,160) or 10 x 12 x 216 (25,920) are all reflections/multiples that originate with the letters that “define” our physical reality, as seen in the measure of the day, the measure of the great year, or the measure of the hin to name just a few (you will see many other examples throughout this blog). Here we see the 216 letters “define” a fundamental aspect of physics. We even see its corresponding abbreviations: 2 (male/female) Names with 4-letters (4 dimensions) having a total of 8 letters (8 dimensions) further define these aspects of the universe.
Human Consciousness (real consciousness) is dependent on man's ability to "see" God, or more specifically how God's Name rules the universe. That moment in time will arrive when science catches up with kabbalah, which is in essence, the ancient knowledge of God's Name and how that Name "rules" the universe, a knowledge that to a large extent, has long been forgotten.
Remember the 17,280 symmetrics in the form of the ‘8-simplices’ mentioned above? The number of these symmetrics is three times the number of 'shallow holes' surrounding the origin in the lattice. So the number of shallow holes is 5,760. Both of these numbers are significant. The 17,280 symmetrics equates to the measure of a mikva in terms of 'grogerets,' while 5,760 happens to be the 'measure of a mikva, in terms of 'eggs.' What is not so commonly known is that "the number of days (a measure of time that is) allotted to man is (also) equal to the measure of a mikva." So the limits associated with man's 'dominion' over the earth (5,760 years) are seen here as a function of the physics in the E8 lattice. That’s a strange coincidence isn’t it? Or maybe, just maybe, it’s not a coincidence. Maybe the physics of the universe really does revolve around the letters of God's Name and the two things are connected in ways we can only begin to imagine!
Is there a second witness to that effect? Those 5,760 shallow holes in the lattice are also a third of what amounts to 72 times the 80 years that may be allotted to an individual's life. We are told that a man's years are 70, but 'with strength' they are (lengthened to) 80. Crunch those numbers, and you can see that 72 x 80 = 5,760 x 3 = 17,280) or to express it another way: the 17,280 that are integral aspects of the lattice that defines certain aspects of the universe, divided by the 216 elements of reality (letters of the Name) is equal to (or defines) the 80 years in the lifespan of the average man. Both relate to the length of time that a man (or mankind) has been allotted. So once again we see how the letters of God's Name 'rule' over His creation.
Did you notice that the context of these patterns is remarkably similar? In the previous case, the numbers were a function of the time in which man would have dominion over the earth (5,760 years). In this case, they are a function of the time in which an (average) individual may remain upon the earth (80 years). In each case a measure of time is involved. In each case, the numbers and sets of numbers conform to the underlying 'definitions' imposed upon them by the nature and number of the letters in the Name; their corresponding numbers in the measure of the luchot; the measure of the mikva, where it's observance is invariably a measure of human character and indicative of the stability of society; and finally, the physics associated with string theory, gravity and the E8 lattice which are necessary functions corresponding to the stability of the universe.
The E8 lattice by the way is a lie algebra group of 248 dimensions, which is coincidentally the number of commandments that parallel the number parts of the human body that are the subject of the "second purification" mentioned in the "Eighth Gate" of Shaarey Kedushah.It also happens to be the gematria of Raziel (248) who was the angel that taught "the mysteries" of creation (which happen to involve a lie algebra group of 248 dimensions) to Adam (as is written).
Remember the 8 letters in the two abbreviations? We've been examining the E8 group with reflections in its geometry that result in multiple groups of 8 intersections. The sacrifice for the 8th day in Parashah Shemeni is about God's presence descending to the tabernacle (His dwelling place in the physical universe) and subsequently revealing Himself to the people in that universe (essentially to mankind). If you've read the post on VaYakhel, then you know that the letters are mathematically revealed in the measure of the tabernacle (God's house). Here they are revealed in the E8 lattice that is a mathematic and/or geometric model of an even larger house, which is the physical universe in which mankind resides. Or, is this too a coincidence?
We know that the shnei luchot (or two halves of the cosmic blueprint of creation) are a reflection of His Name, as are the systems of measurements in the Torah and the mikva. Is it so hard to believe that the Architect, who created the strings of energy and the gravity that binds us to the surface of the earth, did not specify their measurements in the same terms? This is the Signature of the Architect behind the scenes. The characteristics we find in E8 are just another reflection of the specifications in the blueprint wherein the measurements for the entire universe are found. At some point it becomes necessary to accept the fact that all of these relationships are a reflection of a larger reality, and that the larger reality really does center around the letters of God’s Name.
These letters and their proper pronunciation (sound being vibrating strings of energy) have been preserved by the Sages of Israel so that one day mankind would be able to recognize the work of his Creator, and acknowledge, accept, honor and bless the One Name that rules the kingdom!
The next advanced construct deals with the story of the cubit-cubed and the imperial (royal) system of measurement: The Story of the Cubit-Cubed