Before offering a more detailed explanation, those who are new to this blog should read each of the essential constructs 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 also such things as quantum mechanics, the physics of time and space, celestial dynamics, biology, chemistry (etc). Once you are familiar with these constructs you can more fully appreciate each post.
Here in BeShalach, we find the letters of God's Name, specifically in the lines of text above and more specifically in three consecutive verses that have exactly 72 letters (3 x 72 = 216). Not only do the numbers and sets of numbers allude to God’s Explicit Name, but the actual letters themselves are those of the Triad Havaya of 72. They are sequenced as a one-dimensional string within the narrative, but permuted according to the proper method, as is known. The three verses (in terms of both its numbers and letters) are a ‘witness’ attesting to the Divine Presence at the sea. However, they also provide us with a witness to much more, including how these 216 letters create and define space-time, and 'rule' over that which they create.
These lines of text describe three dimensions with six vectors. You may recall from the post on the mitzvah of the Four Species and the Explicit Name (listed among the essential constructs in the column to the right) that we wave the four species in six directions, essentially inscribing (and thus acknowledging) a unique 'space' with three dimensions and six directions. This continuum is modeled below in terms of its specific North/South, East/West and Up/Down coordinates (the observance of waving the species in these six directions is described in most siddurim).
This "model" can be found in the writings of our Sages without much explanation (we elaborate on its significance more fully in the post entitled The Eight Dimensions). In mathematics these vectors would simply be referred to as the x, y, and z axis for the eight dimensions of euclidean space, although in this case, the space is specifically 'limited' by a value of ±3 (three waves in six directions). So, in the case of this particular mitzvah, the end result is to inscribe a three-dimensional space, measured by 216 of these x, y, and z coordinates, from our place and position within space-time, which is the 0, 0, 0, coordinate within the system.
This places the one observing the mitzvah in the center of what is being inscribed, which is a 'virtual geometric model' for the cube [of creation] (more commonly known as the tablets of the covenant or shnei luchot) which is a model of the mathematic system underlying space-time, defined in terms of the 216 letters in the Name (216 cubic handbreadths / 216~0 degrees in varying multiples etc) and here specifically, in its combined cubic form, prior to its division when brought down by Moshe (the nature of this mathematic system is discussed more fully in the post on String Theory and the Luchot, and also the E8 Lattice).
The 216 letters and their connection to the measure of the luchot are a nice allusion, you might think, but where exactly is this geometry specified in the written Torah? That 'question' brings us to Parashah BeShalach where we now turn our attention back to the passage mentioned in the first paragraph and the actual 216 letters of the Name that are hidden in the sequence. What does it say again?
God’s Angel that was in front...
now moved and went in back of them...
It came between the Egyptian...
and the Israelite...
Moshe extended His Hand [with the sceptre and]
the water [then parted so that it] was on their right...
and left... like [two] walls.”
The narrative describes three very specific dimensions with six very specific vectors: Front/Back (like North/South); Right/Left (like East/West) and Toward God or Away from God which aptly describes the difference between the Egyptians and the Israelites (like Up/Down). The events mirror the very nature of reality. How many letters are there in the sentences above, that 'define' three dimensions? This is where we find the 3 verses with 72 letters each, that also just happen to be 'the' letters of God's Explicit Name. What is 'between' the Egyptians and the Israelites? It is the center point, or the 0, 0, 0, 'coordinate' of the geometry seen in the model below. Permute them once as is known, and the one-dimensional string becomes two-dimensional (in the form of triplets). Permute them twice and they become three-dimensional as in the 3 x 72 cubic handbreadths of the (three-dimensional) luchot.
In each case, be it the mitzva of the four species, or the events transpiring at the sea of reeds, the quantum reality is a specifically defined 'space' with three dimensions and their six "directions" that in turn consists of, but is carefully limited by the 216 'elements' of the matrix, be they 216 x, y, z coordinates, or 216 letters, and in the case of Parsahah BeShalach, the actual 216 letters of the Name. Take time to contemplate this very carefully.
The mathematic and geometric dynamics1 of the combined cubic form of the luchot (defined by the letters of the Name) give rise to every detail of the physical universe and every detail of its various dimensions. For the purpose of this post, we'll stick with the history described by the biblical narrative where we learn, for example, that “[Pharaoh] took 600 chariots... with him” to defeat what he believed would be 3 million people ready to cross the sea. The additional numbers that are related to this event are found in other Jewish sources, however the numbers, sets of numbers and the ratio between sets, always conforms to the internal geometry of the luchot, defined by the letters, and more often than not, the geometry of the royal seal or magen david hidden within (its significance having been explained in the post on Parashah Emor). In this case, we will look first at these 3 million through the mathematic prism of the magen david, and then the ratio of the other numbers as it pertains to 3 million.
3 Million Israelites in Egypt
Egypt's 9 Million Opposite Israel's 3 Million (Above)
This mathematic imperative is also a function of the cosmic blueprint. However, Pharaoh erred in the count not realizing that only 6 hundred thousand men of Israel survived the plague of darkness. The ratio of one to the other is a static measure in the geometry associated with the 216 letters of God's Name (in the star tetrahedron) and so we see this in the associated geometry below.
(there are 6 lines of the middle triangle that are the 6 edges of the
three-dimensional stellation from the opposing tetrahedron)
three-dimensional stellation from the opposing tetrahedron)
The 6 hundred thousand (men) who made their way to the sea were 1/5th of the original number of men (3 million ) before the plague, and so we see this ratio in the geometry as well. In this case, it is found in the number of polyhedrons created by the marriage between the two tetrahedrons (1 being different from among the 5).
Click to Enlarge
In each case, we see the specific numbers and sets of numbers and the ratio between sets (corresponding to the events) in the geometric properties of the star tetrahedron (which is 1 of the 5 mathematic constructs within the blueprint for creation). The ratio is identical. What is important to understand is that the events are a geometric reflection of the letters in God's Explicit Name (as found in the royal seal or magen david). Most notably, "the plan" actually called for 3 million people to cross the sea. The number is a function of one particular aspect of the blueprint (see 1st figure above as it relates to the other numbers seen in the other figures). So 3 million it was! There is another opinion that is based on different numbers but the ratio is always the same as the geometric parameters. The point is, there is a very real connection between the letters of the Name, their corresponding geometry in "the cosmic blueprint," and specifically one of its internal constructs (the star tetrahedron) and the events that actually happened.
Interestingly enough, the plan did not end with the above reflections! There were additional specifications and those also appear in the mathematic dynamics of the blueprint. Pharaoh wanted to reach the escaping Israelites and destroy them as quickly as possible, so he had 3 horses attached to each of the 6 hundred chariots (normally there would only be 2 attached). He also had his soldiers armed with 3 different kinds of weapons. The soldiers in turn, each had 3 opinions as to what they should do with the Israelites' when they caught them.
3 Horses HaShem (216 Letters)
3 Weapons < against > (72 Letters found in the 3 verses)
3 Opinions (at the crossing of the Red Sea)
It was God versus the Egyptians, and there was simply no contest. The graphic illustration (above) is presented without further explanation because in each case the connection between the events and the geometry of the royal seal (magen david) is rather obvious and needs no further elaboration. The connection between the numbers and the ratio between the numbers of these events and the geometry for the various elements of the magen david in both two dimensions and three dimensions, is crystal clear.
The only thing we might add is that the three-dimensional geometry associated with the letters of God's Name (shown above) towers over the two-dimensional geometry associated with that of "the Egyptians," who were mired below in the more-limited "lower dimension," the implication being obvious. It is worth emphasizing once again, that in a star tetrahedron, there are 72 triangular corners or 216 points altogether. See the post on Miketz for a diagram of this mathematic phenomena).
Remember those 6 hundred thousand Israelites represented by the 6 lines on the stellation in the 3rd figure above? Its mirror opposite (the stellation on the opposing tetrahedron) also had 6 lines. Why? Pharaoh sent 6 hundred chariots to oppose those 6 hundred thousand people who were waiting to cross the sea. The characteristics of these events were specified in the plan (a mathematic aspect of the luchot) from the very beginning. It was literally "fixed in stone."
If any of the numbers cited in our sources were different, the ratios and the geometry would break down completely, the symmetry pictured above would evaporate and these connections would cease to exist.
Once again, our purpose here is not to extol the virtues of geometry, star tetrahedrons or magen davids. The point of all this, is to show that the events below are a reflection of a larger reality found in the cosmic blueprint (Primordial Torah) in the form of the twins (luchot) and one of its internal constructs (the star tetrahedron) and specifically its intrinsic mathematic and geometric properties, all of which are mere shadows of the 216 letters in God’s Explicit Name.
Footnote 1 - A close examination of the 216 letters in these sentences shows that the dimension dealing with front to back (north/south) is actually repeated twice along with the one dimension pertaining to the Israelites and the Egyptians (which is mentioned only once). The text pertaining to the dimension dealing with right to left (east/west) is technically just outside of the sequence containing the 216 letters. However, since the front/back (north/south) dimension is mentioned twice, the sequence of 216 letters still references three dimensions and six directions. It's just that two of those 'dimensions' are compressed into one. The total number of dimensions mentioned, therefore consists of the three inside the sequence and the one outside the sequence (the one being decidedly different from the other three). This is like the three dimensions of space, in which we move freely, and the one dimension of time, in which our movement is limited (one is different from the other three). The same is true in quantum mechanics where one force is different from the other three. All of these characteristics mirror the characteristics of the letters in the Name, or marriage of the Tetragrammaton and Adnoot, where one pair is subtracted and the other three pairs are added (one pair is different from the other three pairs). The letters are the template for reality. That's why the luchot have a volumetric measure of 216 cubic handbreadths. They are the mirror image of their Creator's Name that consists of 216 letters. When the events in BeShalach occurred (where the 216 letters appear in the text along with reference to three dimensions and six directions) the luchot (with 216 cubic handbreadths in three dimensions with six directions) had not yet been brought down. In time (50 days to be exact) they would be brought down, and in fact , they would be brought down twice, over 'time,' like the first dimension in the sequence of 216 that was mentioned twice. The first 'set' was shattered and never received, and so a second set (a duplicate of the first set) is brought down. The set that was received of course consisted of two identical tablets, just like the sequence of 216 letters with essentially two identical references to the same dimension. The events mirror a much larger reality that is dictated by the nature of the Primordial Torah with its various dimensions and internal geometry.