BeShalach

In Parashah BeShalach, God’s Explicit Name is hidden (literally letter for letter) in the text explaining how: “God’s Angel that was in front... now moved and went behind... 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.” 

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

This mathematic imperative is a function of the cosmic blueprint. Pharaoh wanted to ensure victory so he sent 9 million soldiers to defeat what he thought would be those 3 million men of Israel (instead of 600,000).

 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)

 

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 the same. 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.

 

Vaera and Bo

Vaera and Bo will be combined because they both deal with the plagues in Egypt. Within the sequence of these plagues, as well as their character and the specific language used to describe them, we find numbers and groups of numbers, or ratios, that have a direct correlation with the mathematics and geometry of the star tetrahedron, which of course casts a shadow known as a magen david. In this portion of the Torah we see Moshe use the staff that he pulled from the stone behind Yitro’s house to perform all kinds of wonders. But before we get into that, we should review some of the background information.

If you are new to this blog and have not yet read the essential constructs listed in the column to the right, please do so before proceeding. They explain some of the basic connections between the letters of God's Explicit Name and the multidimensional mathematic and 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. The purpose of this blog is to show how they connect and to reveal where the Signature of the Architect is hidden in each week’s parashah. Once you are familiar with these constructs you can more fully appreciate each post.



In the meantime, for those already familiar with the constructs mentioned above, we'll continue with a small dissertation on Pharaoh, a man who could be easily described as "the great pretender." People thought he was “a god” and he did nothing to dispel that belief. In fact he exacerbated it. The problem (for Pharaoh) was that "a real god" would have no need of a bathroom. Only humans need such things! And so to perpetuate the illusion that he was a god, Pharaoh had a secret toilet installed in the palace. That way he could relieve himself without anyone being the wiser. The problem with Pharaoh's ingenious solution, was that a rather nasty odor would drift through the palace from time-to-time. To make matters even worse, a rat managed to make its way through the pipes one day and bit him on the lower posterior.  All facts considered, Pharaoh decided to have the toilet removed. However, this created an even bigger problem, because now he would have to take morning walks along the Nile in order to relieve himself. There among the reeds he could do his business in private, without anyone noticing. Or so he thought! What he didn’t count on was Moshe interrupting this morning routine. God said to Moshe, “Go to Pharaoh in the morning. He goes out to the water. Stand where you will encounter him on the bank of the Nile.” How embarrassing! You can imagine Pharaoh’s surprise when Moshe interrupted his morning routine, caught him with his proverbial pants down, and exposed him as a mere man. Oh the shame!

The important thing to note, is that the warning for the first plague (where the water was turned to blood) was given outside Pharaoh's palace near the river.



The second plague was somewhat different. Moses went straight to Pharaoh's house in order to deliver the warning. In the case of the frogs, God said to Moshe “Come to Pharaoh [in his house]."



The third plague was also different. There was no warning given at all. In the case of this plague, God  said to Moshe “Say to Aaron, ‘stretch forth your staff and strike the dust of the earth.’ It will turn to lice in all the land of Egypt,” so Pharaoh had no warning that this plague was coming!

The circumstances for each plague create a pattern. In the case of the first plague, the warning was given outside the palace; for the second plague the warning was given inside the palace; and for the third plague there was no warning given at all.



The fourth, fifth and sixth plagues repeat this pattern. For the fourth plague (which consisted of wild beasts) God said to Moshe “Get up early in the morning and place yourself before Pharaoh. He will go out to the water.” So Moshe met him outside the palace. In the case of the fifth plague (the death of domestic animals which provided the food supply for the Egyptians) God said to Moshe “Come to Pharaoh [in his house]” and in the case of the sixth plague (boils) God instructed Moshe to “Take a handful of ashes from the furnace and throw it up into the air... it will settle like dust on... Egypt... when it falls on man or beast... it will cause... boils.” As in the case of the lice, Pharaoh had no warning that this plague was coming. In other words, these three plagues follow the same pattern as the first three plagues where the first warning was given outside the palace; the second warning was given inside the palace; and for the third plague there was no warning given at all. 



As you might suspect, this pattern continues through the next set of three plagues. The seventh plague was hail. God said to Moshe, “Get up early in the morning and stand before Pharaoh.” By this time Pharaoh was starting to see a pattern too, and so he had no intention of going to his regular place along the river. Instead he chose a new place. It was a secret place. He told no one of its location. Still, Moshe was there waiting for him. You can imagine Pharaoh’s surprise. The point of all this is to show that the pattern continues to repeat itself. The eighth plague was locusts. God said to Moshe “Come to Pharaoh [in his house].” The ninth plague was the same as the third in the previous two sets, in that no warning was given at all. God said to Moshe “Stretch out your hand on the sky and there was total darkness.” In this third set of three plagues, we see the same as in the previous two sets. First, Pharaoh is approached outside the palace. Second, he is confronted inside the palace, and then finally, for the third plague in the set, no warning is given.



We have 3 sets of 3 plagues that follow a pattern:

1. a warning outside the palace;
2. a warning inside the palace; and 
3. no warning at all. 



                                    The Triangular Matrix of the First 9 Plagues


                               1st Plague              2nd plague            3rd plague

                                   Blood                       Frogs                     Lice

                          Warning Outside      Warning Inside         No warning


                               4th Plague              5th Plague             6th Plague

                              Wild Beasts       Domestic Animals            Boils

                         Warning Outside        Warning Inside         No warning



                               7th Plague              8th Plague             9th Plague

                                    Hail                       Locusts                Darkness

                        Warning Outside         Warning Inside        No warning


 

Interesting pattern! It was interesting enough for Rabbi Yehuda Lowe of Prague (the Maharal) to make note. The Maharal was one of the most mathematically inclined rabbis in history (although we won’t go into specifics).


You might think this pattern would end after the ninth plague, but in fact it continues. We read in the text pertaining to this plague (which is at the end of these 3 sets of 3 plagues) that it would “last for 3 days,” and that “no one left his place for 3 days” (notice these references are specific references to "time and space" (3 are related to time and 3 are related to space). The mention of the number 3 twice in succession is like the geometry of a two-dimensional magen david, however the 3 sets of 3 plagues expand this similarity. There are a total of four 3s found in these particular events, which are characteristic of a star tetrahedron (which has four pairs of opposing faces with 3 corners). The geometry is ultimately characterized by 72 triangular corners that correspond to the ratio of the triplets, as they relate to the 216 letters in the Explicit Name (explained in posts like: Ki Thetze, and Mattoth). However, the plagues did not end with the ninth, and the worst was yet to come. Interestingly enough, the tenth plague had 3 components involving the death of the first born. This plague was completely unique. Not only was it the most severe (because it resulted in the death of all the first born in Egypt) but it was also the straw that broke the camel’s back. It was this tenth plague that  caused Pharaoh to let Israel go! It was by this plague that: "Every first-born in Egypt [would] die..."



It is worth emphasizing at this point, that the purpose of this blog is not to extol the aesthetic virtue of geometry, or polyhedrons, or any other geometric object including the star tetrahedron. Its purpose is to allow the individual to peer ever so slightly past the superficial  curtain that masks reality, to see the inner workings of the Architect. It is His Name, behind the scenes, that is the focus of this blog. This Name has a unique Signature that is easy to see in the mathematic properties of each set of plagues, and those properties reflect the geometry of the royal seal (star tetrahedron) where the numbers and sets of numbers conform to the nature of the letters in God’s Explicit Name. The magen david or shield of David, was not some image that looks like a six pointed star. David's shield was God, and God has a Name. The image of the six pointed star is merely a mathematic representation of this Name. We find the Signature, not only throughout Torah, but all of creation as well, including such things as physics; celestial dynamics; biology; quantum mechanics; and the history of man, both secular and biblical, to name a few.

Fractal geometry is now being used by scientists to define nature (as mentioned in the last post) and that geometry finds a natural partner in triad structures like 'the monsters,' or the Koch curve for those familiar with such things. In the last post we talked about one face of the star tetrahedron and how, when it was paired with its opposite, it created a two-dimensional magen david, that could be seen as an orthographic projection of its geometry. We also pointed out, that one of the iterations in a fractal transform was 2.16 (1/100 of the number of letters in the Triad Name). Now, in this parashah, we see this same pattern appearing in the characteristics of the plagues.
 

Sets of Numbers that Define Plague “Geometry”
Matching the Two-Dimensional Face of a Star Tetrahedron and the
Three-Dimensional Opposing Stellation (in the Middle)
 

Click to Enlarge

The sets of numbers corresponding to the plague are a clear reflection of a two-dimensional face (shown above) and its 3-dimensional counterpart (shown below) on a tetrahedron that has been merged with an opposing tetrahedron (and again this is one of 5 constructs having dual form found within the combined cubic form of the luchot). 

Notice that each face is divided into thirds, leaving a center portion. The center is actually the stellation of the opposing tetrahedron. The picture above is a two-dimensional representation of one face on one tetrahedron. When two tetrahedrons merge together in opposing directions, each triangular face ends up with 3 quadrants having 3 corners (small faces) that are themselves triangles. The sides are each half the length of the original and the triangle in the middle is pointed in the opposing direction. This upside-down triangle is not a face. It is the stellation (or point) on the opposing tetrahedron, that also happens to have 3 faces. However, these 3 faces are in the third dimension. The 3 triangular faces each have 3 corners and the direction of any given corner on any given faces corresponds to its counterpart on the other faces. In other words we see a distinct pattern, one that is identical to the pattern of numbers and sets of numbers describing the plagues. The ratio and geometry of each face corresponds to the 3 sets of 3 plagues with 3 types of warnings. The magen david (in three dimensions) is like a mathematic map of the events that were destined to occur at a specific moment in time. But surely all of this must be a coincidence, and what about the point/stellation in the middle, the center triangle?

We've already mentioned the tenth plague. It was unique, more severe than all the others. The Torah says of this plague, that it effected every firstborn in Egypt, but then specifies who the word “every” pertains to: 1) “the first born of Pharaoh;” 2) "the first born of the slave-girl;" and 3) “the first born of the animals.” There are 3 specific references as to which of the firstborn were affected, just as there are 3 corners to the center triangle (which define the 3 faces on the stellation of the opposing tetrahedron in the 3rd dimension). As the tenth plague was unique, so too is the center “triangle” or stellation. Not only is it in the center of the other three, and not only does it point in the opposite direction, but its 3 faces are in the third dimension.
 

Three-Dimensional Projection of Plague Geometry
Conforming to the Geometry of a Star Tetrahedron
(Demonstrating the Connection to the Signature of the Architect)

Click to Enlarge


The parallel between the numbers, or really groups of numbers and their ratio, one to another, on the face of the star tetrahedron as it relates to the characteristics of the events in Egypt is remarkable. The odds of this being a coincidence is beyond calculation. We say that since all things come from God, there is no such thing as a coincidence. Even the word for coincidence in Hebrew means essentially that it was written from the beginning.



This is just one example. When we peer through the prism of the magen david (looking at these events in terms of the mathematics of the star tetrahedron, or reflection of the 216 letters of the Triad Name) we can see, that much more clearly, the Signature of the Architect who planned it all from the very beginning. All of this is found in the internal geometry of the combined cubic form of the luchot, the “cosmic blueprint” from which the 304,805 letters (of Torah) emerge.

If the nations learn anything from these events concerning the plagues, it should be that it is impossible to thwart God’s plan. Any attempt to do so will only exacerbate the pre-existing problems facing any given nation. The perfect example is found in Pharaoh’s attempt to kill the first born, by which he ended up raising Moshe (his nemesis) in his own household.

Another prime example (that has yet to occur) is that God has already defined the future borders of Israel. They are specified in great detail. These borders are an inheritance. Any nation or group of nations that tries to deny Israel this inheritance should be as concerned for their well being as Pharaoh should have been for his own, and perhaps more so, since the track record of those who oppose God's plan is so clearly fraught with destruction.

There is another interesting connection to the luchot (and thus to God’s Name in their volumetric measure) in this portion of the Torah. The measure of the luchot was 6 x 6 x 6. This measure is also found in the description of Egypt’s borders, where the plagues actually had an ancillary benefit. For many years prior to the plagues, there were border skirmishes between Egypt and its neighbors. That is, there were arguments as to the exact location of the borders. The plagues settled the issue once and for all. Whenever there was a plague, like the blood in the rivers, lice in the ground, or hail from the sky, that plague would end abruptly at the border. The border therefore became officially defined in the minds of everyone concerned, and arguments as to its location were settled once and for all. 

In addition, the Egyptians were consummate mathematicians and surveyors as evidenced by the amazing math and geometry built into the pyramids. In their construction we see the measure of a Royal (or Antediluvian) Cubit; the Meter; Pi; Phi; and any number of other standards. Interestingly enough, even the speed of light is found in the measurements of one of these monoliths (an explanation is beyond the scope of this post). The word for Egypt in Hebrew is Mitzrayim. The root letters of the first two syllables are the Hebrew letters “Mem" and “Resh" (M and R). The Egyptians used a triangle known as MR in their measurements and this is why they were so accurate in their surveys of the land. The name for Egypt (MitzRayim) is not only the name of a specific individual who gave rise to the kingdom, but this individual's knowledge of mathematics and geometry and the triangle MR was derived from his name.



The point of all this is to say that when the Egyptians surveyed the borders after the plagues, and the land of Egypt was said to be 600 miles square (6 hundred x 6 hundred)1. We cannot be absolutely sure what this means, but even on modern maps it is roughly square. The southern and western borders are almost perfectly straight and the corner between the two is essentially a perfect 90 degree angle.

In ancient times, the northern and Eastern Borders were apparently much the same. The description is interesting, both in terms of the numbers and the shape. In Isaiah 19:19 reference is made to a monument that is “on the border of Egypt” but also “in the midst thereof.” How can something be on the border and yet in the middle at the same time? Ancient Egypt was actually split into two kingdoms. There was a northern kingdom and there was a southern kingdom. The monument lay in the middle between the two, thus it was both on the border (of Egypt) “and in the midst thereof” at the same time. When you divide a square in half, like a square of 6 hundred miles, you get two rectangular polygons that are each 6 hundred by 3 hundred (the flattened two-dimensional ratio for each of the two luchot). The 6 x 6 (hundred) “measure” for Egypt (with a border in the middle) dividing between the two kingdoms (halves) is like the first two dimensions of the luchot (6 x 6 handbreadths) where the measure of each half in the third dimension is 3 handbreadths. It’s as if the numbers and sets of numbers are alluding to the fact that Israel would need to leave Egypt before they could receive the luchot and return to the Land of Israel where their knowledge of God, and their connection to God could rise to the next level (a higher dimension).


The ratio of 6 hundred x 3 hundred times 2 kingdoms, is two-dimensionally identical to the ratio of the shnei luchot (2 tablets) that Israel would shortly be receiving at Sinai. Whether there is a connection, or not, it is difficult to say. We only note the similarity because when the ratio of the two-dimensional version is extruded into the third dimension, it has the same ratio as the luchot that were 6 handbreadths x 6 handbreadths x 3 handbreadths, times 2, and where the total volumetric measure corresponds to the number of letters in God’s Explicit Name.
  

Mathematic Relationship Between the
Land of Egypt and the Shnei Luchot
(Two (Twin) Tablets)

Click to Enlarge

The Signature of the Architect is indeed everywhere. Inside of Israel it is much easier to see, just as something that is three-dimensional has more facets than its two-dimensional counterpart, a mere shadow of the original.

The names of the 3 portions of Torah leading up to the point in time when Moshe and company see the undivided form of the luchot (in Mishpatim) and its subsequent division when Moshe brings the two tablets down, suggest that the luchot are about to be given, as well as an understanding (revealing) of God’s Name. Last week's parashah Shemoth (Exodus in English) means “Names” in Hebrew. VaEra means “I revealed myself” and “Bo” means “come,” as if to say “when you leave Egypt and come to Mt. Sinai I [will] reveal my Name to you.” In fact, that's exactly what happens in the next post on Parashah BeShalach. It is in that parashah that we find the 216 letters of His Name as a contiguous stream of letters in the text (not permuted into triplets) but one-dimensionally separated into 3 segments of 72 letters, corresponding to the side-by-side form of the luchot, that is 6 in the first dimension, 12 in the second and 3 in the third (6 x 12 = 72 times 3 = 216). In other words, even though it is not (yet) permuted as is known (still one-dimensional in form) its numbers or sets of numbers, and the ratio between sets, preserves the triad structure in the 3 segments (the triad nature is more accurately perceived in two or three dimensions) as a function of the luchot's three dimensions.

Stay tuned for the next post which will be on BeShalach, where we will examine the implications in more detail.


________
Footnote 1 - It is interesting to note that the area of a 6 hundred mile square (360,000 square miles) is a multiple of 72 and in square feet, it is a multiple of 216 which would suggest this measurement has a connection not only to the Triad Havaya of 72 with 216 letters, but also to the imperial system of measurement. When you divide the 360,000 square miles by 72, the result is 5 hundred, which reflects a primary characteristic (in fact the primary characteristic) for the geometry in the combined cubic form of the luchot with its 5 internal mathematic constructs, one of which is the tetrahedron.   

Shemot

In Parashah Shemot, the mathematic characteristics of the letters in the Explicit Name are concealed in the marriage, when Yitro: “...gave his daughter Tzipporah to Moshe." The circumstances surrounding this particular marriage are among the most fascinating, however the details are not found in the written Torah. We find mention of them in other sources, some of which are cited below. As you might suspect, the connection with God’s Name is in the details, so with that in mind we will reconstruct some of these details in their historical context, starting with Yitro, Moshe and Pharaoh.

Yitro and Moshe had much in common. Just as Moshe was close to Pharaoh, so too was Yitro. Yitro was one of Pharaoh’s closest advisors. Moshe was an advisor in that he was a member of the family. Just as Moshe was eventually forced to flee Pharaoh’s wrath to avoid retribution, so too was Yitro. But we’re getting ahead of the story!



Before Yitro fled from Egypt, he was actually a friend of Pharaoh (or at least as much of a friend as anyone could be, to the ruler of Egypt). Pharaoh would often walk with Yitro and they would discuss things of importance. One day they were walking through the marketplace, and Yitro saw two young girls who were for sale. The girls were twin sisters and remarkably beautiful, so beautiful in fact that Yitro suggested they purchase them. Pharaoh would take one of the girls, and Yitro the other (Midrash Talpios, Bithia / Zohar). The girls however, were not purchased as slaves. Rather, they were adopted and made daughters.

One of these girls was named Batya (Bithia) and she became the “daughter” of Pharaoh. The other girl was Tzipporah who became the "daughter” of Yitro. You may remember that it was Batya who would latter retrieve the reed boat from the river (with Moshe) after it was set adrift to save him from Pharaoh’s decree concerning the death of the first-born males. Batya would later marry Calev, and Tzipporah would later marry Moshe. Keep in mind that Moshe was with Batya in Pharaoh’s house. Since Batya and Tzipporah were twins they looked  alike. So naturally, when Moshe was forced to flee from Egypt and gets to Midian, he is surprised when he stumbles upon Yitro’s “daughter,” the young woman who is the twin sister of the “mother” who raised him. This is why the Midrash says that “Moshe married his mother.” It is not referring to Yocheved (his biological mother) or even Batya (his foster mother) but to Tzipporah who was Batya’s twin sister. But again we’re getting ahead of the story!



Since Tzipporah was not Yitro’s biological daughter, and because of her beauty, Yitro was evidently not anxious to see her given away in marriage. He therefore placed a condition upon anyone wishing to marry her. That condition is a story in-and-of itself, and it is here that we find a connection to God’s Name. You see, when Yitro fled the wrath of Pharaoh, Tzipporah was not the only thing that he took. Pharaoh had an amazing staff (sceptre) that he “inherited” after the death of Yoseph (a sceptre being one of the symbols of kingship). As the story goes, this ScePteR (of SaPhiRe) was the very same one that God had given to Adam. This scepter and a certain mantle were given to Adam in the 216th year of the first millennium as explained in the post on Bereishit and Noach, and so we see our first connection to the 216 letters of the Explicit Name. These items were the symbols of kingship (of the shepherding kind) that would be passed down to certain descendants (a facet of the birthright) until it finally reached Avraham, Yitzhak, Yaacov and eventually Yoseph. The status of royalty (and scepter) went to Yehuda. The sceptre is mentioned in Genesis 49:10, which says that “the sceptre shall not depart from Yehuda, nor the ruler’s staff from between his legs.” The birthright however went to Yoseph (I Chronicles 5:1) and "the garments of Adam were [also] given to Yoseph" i.e. the mantle (coat) given to him by his father Yaacov (Bereishit Rabbah, Targum Yerushalami).   

As mentioned above, Adam received this mantle and scepter in the 216th year of the first millennium. He passed it to Seth (the gilgul of Hevel) after he had walked the earth as a man for 216 years, as his father before him (again see the post on Bereishit and Noach for details). Its counterpart (the royal mantle) was given to Yoseph in the 216th year of the third millennium). Each event corresponds to the number of letters of the Explicit Name, and both demonstrate the significance of its possession.



It was therefore perfectly natural for Pharaoh to covet this sceptre and the title that it implied (assuming he understood its significance). So too did Yitro, but apparently for different reasons (since it was made of sapphire) which is why he stole it from Pharaoh before fleeing Egypt. 


When Yitro arrives in Midian and settles there, he uses his powers of occult to plunge the staff into the bedrock behind his house. There it would remain until one was found worthy to pull it from the stone, someone who would unite his people and lead them to freedom; and someone worthy of marrying his daughter Tzipporah. If that sounds familiar, it should. It is the premise of the Arthurian legend (King Arthur of mythic renown). Indeed the story of Moshe was taken into the diaspora by Jews who were fleeing roman persecution. Many of these people ended up in the British Isles (the origin of the term brit-ish, is itself found in the Hebrew words for covenant (brit) and man (ish). The story of how Moshe came to remove the real “sword in the stone” is rather interesting. There were many men who desired Tzipporah, but none were able to pull the staff from the ground. One day after Moshe arrived, he was walking through the garden and saw this unusual staff. There were strange marks on it which tradition says were the letters of a mystical Name of God. The Maharal says that it consisted of 10 letters corresponding to the 10 sayings of creation and that the [polar] opposite of each letter was a letter pertaining to one of the 10 plagues that Moshe would see when he returned to Egypt to free the people from bondage. But once again we’re getting ahead of the story!



When Moshe grasped the scepter, the power preventing it from being removed from the ground by anyone but God’s intended, immediately yielded to the one who was destined to possess it. Tzipporah married Moshe and the rest is history (except of course the real identity of the mythical King Arthur in British mythology). The above stories are loaded with allusions that one could contemplate without end. If you remember anything from this post, remember that the scepter—which was the symbol of kingship not only for Israel, but of all mankind—the scepter, with it's inherent connection to the 216 letters (as detailed in the post on Bereishit and Noach) —the scepter, that was passed from king to king before and after the flood—was miraculously pulled from the stone only by Moshe, who was the intended leader of Israel. Also remember that the star tetrahedron is a mathematic or geometric representation of the merging of male and female, which is a form of marriage like the marriage of Tzipporah and Moshe.

Now, about that sceptre....

 It is said that the sceptre (or ruler’s staff) was created on Friday evening (the 6th day) on the twilight of creation, like the measure for any given dimension of the combined cubic form of the luchot (6 handbreadths). Adam received the sceptre while he was in a garden (the Garden of Eden) just as Moshe retrieved it from a garden (at Yitro’s). When Adam died it was given to Enoch and after Enoch, it was given to Noah’s son Shem (who brought it aboard the ark). Shem gave it to Avraham and Avraham to Yitzhak. It was eventually given to Yaacov who brought it to Egypt during the famine (in the Hebrew year 2238). Yaacov bequeathed it to Yoseph but when Yoseph died it became the property of Pharaoh, who acquired all of Yoseph’s belongings (Shemoth 3, 2:21 Me’Am Lo’Ez pg. 67).
 


It is said the Yitro desired it because it was made of sapphire. Sapphire? In Hebrew, the word is “sanphirinon” (Shemoth Rabbah 8:3) spelled סנפירינון (samech-nun-peh-yud-resh-yud-nun-vav-nun sophit) which comes from the greek word σαπφειρινον meaning “sapphire-like.” 


Sound familiar? It should. The substance is the same as that of the block that Moshe saw under the throne of God (in Mishpatim) which was later divided and brought down as the luchot (6 handbreadths x 6 handbreadths x 3 handbreadths times 2 tablets = 216 or the same number of elements in the matrix as there are letters in the Triad Name). It is the substance with a clarity of “72” having a trigonal (three-sided) crystalline structure that alludes to the Signature of the Architect (see the post on the nature of sapphire).



There are people who would like to know where this scepter is today. However, I very much suspect that it will not be found at all. Rather, it will seek out the individual to whom it belongs at the proper time, much like the anointing oil that fled from Ishai’s sons, but flowed toward David HaMelech.



In the meantime, since this blog is about the mathematic and geometric Signature of God’s Name, it is at this point worth mentioning something that is referred to as “the emblem of fractal geometry,” which some mathematician’s have referred to as “the Thumbprint of God.” It is the "end result" (assuming it actually ends, which it does not) of an applied formula pertaining to a form of geometry that seems to exist somewhere between dimensions. What is unique about this form of geometry is that its most basic component is a "triplet," best represented by a broken line and fixed by two identical additional lines. However, it is also represented in triangular form, for example, in the Sierpinski fractal mentioned in last week’s post. All of this might sound cryptic, but what it means is that no matter how infinitely large or small (the number of iterations) may be, they can be represented by the same two-dimensional elements. Those elements are the components of a magen david, which is a shadow of the star tetrahedron (the three-dimensional construct to which we’ve referred so many times, because of its connection to the letters of the Triad Name.) One of the best examples of fractal geometry in action is shown below. This one is referred to as the Koch Snowflake and the example is animated to the 7th iteration.

What this amounts to is the fact that mathematicians all over the world have been staring at this concept for many years without ever realizing its underlying significance, or that the geometry has a connection to the letters of God’s Name. Certain curves in fractal geometry are a prime example. The 20 segment curve where DS = 2.160 (to the 2nd decimal place) and the step in the generator is minimal (k = 2) is shown below. This equates to a 2-dimensional orthographic projection of 1 side (of 8 sides) on the star tetrahedron, that subdivides into 72 triangular corners. No one seems to have noticed the connection to the royal seal (magen david) or the 216 letters of God's Explicit Name.

                                                                           k=2

The large upside-down triangle in the middle

is the two-dimensional shadow of

the stellation of the opposing tetrahedron

A mathematician by the name of Benoit Mandelbrot (Yale University) (who revealed the M-set) is really the father of fractal geometry. It was he who coined the term fractal. Mandelbrot was a Jew who grew up in Nazi occupied France. He spent 4 years eluding capture and deportation to the camps. When he was young he was fascinated by visual geometry. It was from this fascination that fractal geometry emerged.

Fractal geometry is actually a whole new kind of mathematics and it makes some traditional mathematicians a bit nervous. Unlike traditional math that defines smooth curves and comfortable shapes, fractal geometry can define everything in the universe from the craggy projections of mountains below to the movement of the clouds above, in fact literally everything. If you think the mathematic or scientific community is unaware of this, think again. It has created a firestorm of controversy! For more information on fractal geometry and its significance, watch Nova Season 36, Episode 4, entitled "Hunting the Hidden Dimension."

Meanwhile, in consideration of all the above (and in the interest of curiosity) let’s advance a hypothetical description of the sapphire sceptre. It is for the most part a story or fable; a parable of sorts (for purpose of instruction) the kind of tale that one might tell to children (and mathematicians) about what the sceptre might look like, and those who were destined to inherit it. 

Like all stories, this one starts at the beginning and so we’ll start with the usual: “Once upon a time,” and add that there was a king who wished to give his son the keys to the kingdom. Along with that birthright, he would provide his son (and his son’s descendants) with the symbols of kingship which included a sceptre and a royal mantle. The king wished to hide his signature within these things so that if the identity of the rightful heir was ever challenged, the signature could be revealed and remove all doubt. And so he created a scepter, a staff by which his descendants would be known, a staff that a shepherd might use to protect his flock. 

The king in this fairytale was much more than just a king. He was also the mathematician of mathematicians, and so he decided to place his signature upon the staff in these terms, so they would match the numbers that not only reflect  the letters of his name, but the geometry of the royal seal and the official documents and records of the kingdom.

To that end, he made a staff with 3 sides, like a triangle (a 2-dimensional shadow of a tetrahedron) where the length of each side was 3 “fingers” (3/5th’s of a hand of 5, and fractionally the same as 6/10ths, or ‘.6’ of one hand, which happens to also be a static measurement of 5.236 centimeters, if one bothers to put his fingers to a calculator).

He would make the length of each side equal to 24 handbreadths. That way, the combined length of the 3 sides would be 72 handbreadths (alluding to his name). However, 72 handbreadths also just happens to be 2 x π (Pi) in meters which is one of the fundamental aspects of mathematics.

The 24 handbreadths of each side (that are each 3 fingers in length) therefore end up being .666 x π (Pi) in meters (a little more than the height of a man). The 3 fingers and the .666, together would also bring to mind the 3 “sixes” describing the measure and the ratio of the king's blueprint (6 x 6 x 6) that would be used to define the kingdom. 

6 x 6 x 6 Handbreadths

A handbreadth is 1/6 of a royal or sacred cubit. It is 1/6th of 1/6th of π (Pi) meters. That's 8.72666 centimeters (there are 6 of these handbreadths in a cubit). Please note the sequence of integers in the fractional portion: 8.72666. Thus, the length of 3 “fingers,” would be 5.236 centimeters which coincidentally happens to be 10 times the ratio of a cubit to a meter (which is .5236) as defined within the primordial torah (luchot) as the ratio between the volume of the sphere within, and the cube without (that ratio being well known in mathematics). Seriously? Must be a coincidence!

You may already understand the meaning of this fairytale. The king is God and the kingdom is the physical universe (creation). The blueprint for the kingdom is the combined cubic form of the luchot (the principle having been adequately demonstrated in the post on the primordial torah).
 
The combined cubic form of the luchot was coincidentally .5236 meters per side (6 handbreadths = .5326 meters). When it was divided and given to Israel it would have 10 commandments (just as the measurement of any given side of the sceptre would be a factor of 10 in relation to the aforementioned ratio). All of the numbers for our hypothetical sceptre allude to the King’s system of measurement, by which all things are calculated and compared, both physical and non-physical.

The 3 original or primary sides that are each 3 fingers in length (and 24 handbreadths in length) further allude to the King’s Signature (in the geometry of the star tetrahedron) since it has 24 small triangular faces that ultimately define (3 x 24 or) 72 triangular corners (72 x 3 = 216) as depicted in one of the figures above dealing with fractal geometry. The Signature would thus be hidden from the casual observer.

Click to Enlarge

 

 
You may  remember that in the narrative of our story above, we said that when “the king” designed the scepter, he started with a triangle of 3 sides. In the picture above, you can see what happens when the fractal set previously mentioned is applied to just the third iteration. There are many possibilities. I like this one because it so eloquently reveals the mathematic and geometric connection between the Name, the royal seal (magen david) and the luchot.

Needless to say, the above story is just a story, except for the mathematic and geometric correlations that do in fact connect to God’s Name; and the substance of the sceptre actually being like-sapphire, which it is; and the fact that the length of 3 “fingers” is exactly 10 x .5236 centimeters; or that the ratio of those 3 fingers to a hand (with its 10 fingers) is 6/10ths (.6) and also 1/6th of the ratio of a cubit to a meter (.5236); and that the sapphire cube that is 6 x 6 x 6 handbreadths really is a cube of 1 cubit, or .5236 meters; or that the 10 commandments that were part of the divided cube (luchot) were “a measure” by which man is judged; all of which is factual. 

Nevertheless, the description in our story is just hypothetical. It is full of coincidences pertaining to actual facts and thus hypothetical. Whether it is in anyway true, is anyone’s guess. It is posited here, because it is perfectly acceptable to draw logical inferences from known facts. And besides, it made for a good story and served as the vehicle for revealing how certain fundamental numbers and ratios really do correspond to God’s Name and the many things mentioned in the Torah!

_______

Author's Note: The scepter that is modeled above (shown without the head so that the facets of the staff can be examined) is 6 handbreadths in length (like each dimension of the evan shetiyah). It has 48 external facets with a total length to the 288 handbreadths, like the "288 sparks" (explained by the ARI) that equate to the shattering of the vessels. The total length of these facets is equal to the number of square handbreadths on the surface of the luchot (288 square handbreadths). The number 288 is the sum of 216 (the number of letters in God's Name) and 72 (which is the number of triplets pertaining to this Triad Name). The head of the scepter (not shown) is a sapphire star tetrahedron.