Sunday, January 7, 2018

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.   

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