Saturday, June 27, 2020

Balak

In Parshah Balak we find a special geometric theme connecting the letters of God’s Explicit Name to the action that Pinchas took to honor that Name. This same theme is found in Parashah Miketz and both are similar to the geometry in Chukath, where various events conform to the nature of tetrahedral geometry. We often refer to this geometry as the 'royal seal' (three-dimensional magen david) because of its multidimensional mathematic connection to the letters of the Name.

We will examine this theme from all angles in the paragraphs ahead. However, if you are new to this blog, please 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 this 'Signature' is hidden, not only in each week’s parashah, but the physics of time and space, quantum mechanics and celestial dynamics to name a few. Once you are familiar with these constructs you can more fully appreciate each post. Those who have already read these essential constructs, will recognize the tetrahedral geometry associated with the letters of God's Name in the narrative of this parashah as well.

You may remember from the last post, that the Hebrew word ‘gematria’ (that essentially translates as ‘geometry’ in English, from the Greek geometria) refers to the measurement of the earth, as mentioned in posts like the one on Parashah BeHa'alothekha. However, it also carries over to the measurement of other things such as the numeric value of various letters. It is therefore important in the study of Torah. To the rest of the world letter-geometry is relatively unknown because in mathematics, geometry generally involves physical or spacial constructs involving two-dimensional or three-dimensional shapes as well as combinations of those shapes. There are still other forms of geometry, like the one-dimensional metrics in the numbers and sets of numbers, and ratios between sets, that give rise to higher dimensionality (and we’ll provide an example in a moment). All of these forms of geometry converge in the letters, words, sentences, and even the characteristics of the events that are seen in the Torah. Parshah Balak provides another example of this convergence, and we see once again how it connects with the tetrahedral geometry within the cube [of creation]/(shnei luchot) and ultimately the letters of God's Name. As in the last post, the sets found here, are in groups of sevens.

The story conveyed in this week's parashah is well known. A hateful king named Balak wanted to curse Israel, so he offered to pay a less than respectable “prophet” named Bilaam to do the dirty work. Bilaam was willing enough, but he wasn’t stupid. He knew that it was impossible to curse Israel, and he told Balak that it would be a waste of time. Undeterred, Balak persisted in his request until Bilaam agreed to try anyway. In order to "construct" the curse, Bilaam directed Balak to build seven altars and prepare seven bulls and seven rams for sacrifice. During the sacrifice, God suddenly spoke to Bilaam who then ended up blessing Israel. Balak was of course perturbed by this turn of events, but insisted Bilaam try again. The whole process was repeated a second time. Another seven altars were built, another seven bulls were sacrificed, and another seven rams. God again spoke to Bilaam, who again ended up blessing Israel. Balak was of course persistent so he asked Bilaam to try again. So the whole thing was repeated a third time. Balak built seven more altars, and another seven bulls and seven rams were sacrificed. Was the outcome any different? No, it was not. To the utter dismay of Balak, Bilaam once again blessed Israel. Balak then declared: “I wanted you to curse Israel, and instead you have blessed them three times!” This is a very special "set" of numbers!

A number of questions  arise regarding the “geometry” of these events: 1) Why did each attempt require seven altars? 2) Why did each sacrifice require seven bulls and seven rams? 3) What exactly was Bilaam “creating”? 4) What effect did the three “blessings” have on Israel?

The first thing you should note is that the geometric character of the sacrifices was three instances of three 7s. These numbers along with the 42 actual korbanot (sacrifices) are a very precise reflection of the geometric measure of the foundation stone (as shown in the post on 42 Letters in Sapphire). However, at the same time, three 7s are also a mathematic function of its internal tetrahedral geometry as seen in posts like the Seven Eyes of God. In our posts on Parashah Emor, BeHar & BeChuko-thai, and also Miketz, we saw this signature geometry manifest itself in such things as repeating pairs of 7s as 14, and pairs of 14s as 28. This same pattern is repeated an inordinate number of times throughout the Torah (we even see it in its linguistic structure). In terms of one-dimensional metric geometry, these numbers reflect the characteristics of not only the foundation stone, but the two opposing tetrahedrons (male~female) that are an aspect of it's internal geometry. The marriage of the one-dimensional geometry can be expressed as either two or three-dimensional magen davids. The characteristics of the magen in turn reflects the geometry and the number of letters in God’s Explicit Name that are mathematically hidden between the lines of these events. 

Normally, we look at these numbers as pairs, but here they appear as triplets. Instead of repeating pairs of 14s (or repeating pairs of 7s) we have repeating sets of 7 things with another 7 things and then 7 more things. The normal pairing becomes a triad. What could this geometry possibly represent? As it turns out, it's the same geometry from a different mathematic angle, and it too alludes to God’s Name in the form of a magen david, as you will see in a moment. It is merely a variation on a geometric theme involving the royal seal, wherein the 216 letters of God’s Explicit Name are hidden from the casual observer. In this case, we have a matrix of elements (7, 7 and 7 times three) that consists of 28 elements.

You're probably thinking that 3 times 7 equals 21, not 28; or that 7 + 7 + 7 times three equals 63, and; even if you multiply them together, you wouldn't get 28 because 7 x 7 x 7 = 343. That’s true if you are looking for the number of elements in a two-dimensional array, or three-dimensional cubic matrix. However, please remember, we are looking at these numbers through the lens of set theory, and "the set" is not consistent with cubic geometry, nor does it correspond to the number of elements of its one-dimensional metric equivalent. Rather, the set corresponds to the nature of a tetrahedral matrix that is expressed in terms of two-dimensional space (triangular geometry). In BeHar & BeChuko-thai the cubic matrix was identified by (or confined within) a "measure" of 7 & 8, and further defined (confined) in the third dimension by 49 and 50, which are the borders of a cubic matrix consisting of 6 x 6 x 6 (216) elements. The numbers here in Parashah Balak essentially define the "limits" or outer edges of a triangular array (in two dimensions) or tetrahedral matrix in three dimensions. 

Each triangle is measured by three edges, that are in turn "measured" by the number of elements along those three edges, so multiplying them together will not give you the number of elements in the triangular array. When you populate a triangular array with 7 elements along each of its three edges, the total number of elements that populate the array is 28 (you will see this graphically in a moment so you'll be able to 'measure' the array with your own eyes)

You already know that there are 28 elements in two tetrahedrons (14 opposite 14). A single tetrahedron consists of 6 edges, 4 faces and 4 points (14 elements) and so two tetrahedrons obviously have twice that many. The star tetrahedron or 'magen' resulting from the marriage of two tetrahedrons is again, like a 'royal seal' with its 72 triangular corners, wherein the 216 elements of the mathematic signature are hidden in the geometry. This is an example of a static 'measurement' that does not vary with size (72 triangular corners).

We can describe an array or matrix in many ways. A cube or square is one thing. A triangle or tetrahedron is another. You might use one-dimensional metric expressions like 3 times 72 to describe two dimensions. Or, you could say it was 6 x 6 x 6, or simply 216 in referring to its three-dimensional space. It's just a way to mathematically express a higher dimension (like that of the combined cubic form of the luchot) in terms of its measurement in a lower dimension. Geometry can be expressed in a multitude of ways. For example, tetrahedral geometry can be described in terms of its structural elements, like the number of faces, points, and edges (14 on one or 28 on two) or it can be described in terms of its size 'measured' by 7 x 7 x 7 elements along its three edges (which would also "coincidentally" require 28 elements). Perhaps now, the significance of the numbers chosen by Bilaam for his sacrifices will make more sense. Just keep in mind that the outcome was a blessing to Israel regardless of Bilaam or Balak's intent, because the actions that were emblematic of the royal seal, pertained to the King of Israel (HaShem).

Now listen very carefully. The number 28 is where the static aspects of tetrahedral geometry (like the number of faces, lines and points of any two tetrahedrons) converge with the (static) measure of a specific tetrahedron that is 7 by 7 by 7 and 'populated' by 28 elements (again, this will be graphically represented in a moment).

To understand the importance of this point of convergence, consider the luchot. The combined cubic form of the shnei luchot also has a point of convergence. It happens to be the number 216. The cube is 'measured' in terms of 216 elements. When a cube is 6 x 6 x 6, it has a volumetric measure of 216 cubic handbreadths (the size being potentially variable) but it converges with the static aspects of cubic geometry, such as the total number of degrees in all of its twenty-four angles. All cubes consists of 6 faces that each have 4 angles (a total of 24 angles) and each angle is 90 degrees. So the total number of degrees equals 2,160 (216 "tens") of degrees. This is just one small window that allows us to perceive (mathematically) where a cube's geometry converges with a specific measure of a specific cube, and in this case it happens to be the luchot with a volumetric measure equivalent to the number of letters in the Explicit Name. Please contemplate this carefully. 

Keep in mind that you can measure a cube anyway you want, using any unit of measure (feet, inches, yards, centimeters, whatever) but this point of convergence between the static aspects of a cube's geometry and its potentially variable measures occurs only when the cube is defined by 216 cubic handbreadths (6 x 6 x 6) which just happens to be the measure of the luchot. There are of course additional points of convergence.

Those 216 elements are also a static aspect of the tetrahedral geometry within the cube (a tetrahedron being one of the five internal mathematic constructs in a cube). The star tetrahedron has 72 triangular corners (216) and so again we see the point of convergence. However, this point of geometric convergence occurs again, only when the measure of the external cube is 6 x 6 x 6 like the combined measure of the luchot. This is the Signature of the Architect that is the subject of this blog, and it is found in the measure of just about everything in the universe, from the physics of time and space, to string theory, quantum mechanics and celestial movements. The connection is absolutely undeniable as demonstrated in the post on the primordial torah.

Another point of convergence can be seen in the ratio between the volume of a sphere inside a cube (defined by the surfaces of a cube) and the volume of the cube that surrounds it. That ratio is .5236 regardless of the size of the cube. That is, the volume of the sphere is .5236 the volume of the cube around it. However, in the case of the cubit-cubed (six handbreadths cubed) it's measurement also happens to be .5236 of a meter-cubed. That is "convergence," and it only occurs when the cube is the cubit-cubed (6 x 6 x 6 handbreadths) with a volumetric measure of 216 cubic handbreadths.

The point of convergence goes even further when the cubit-cubed is divided, as when the luchot were brought down by Moshe. There are 108 corner-points associated with one tetrahedron and 108 corner-points associated with its opposite (in its static geometry) just as there are 108 cubic handbreadths in each of the luchot (each half the cube) and 108 with its opposite (in the other half of the cube) in its metric equivalent. That is convergence! If you consider the measurements in the celestial dynamics of the sun, the earth and the moon that correlate with this ratio of 108 opposite 108 (that we explained in great detail in the posts on BeHa'alothekha and the primordial torah) then you'll understand why this set-point (where convergence occurs) is so important. It just happens to be the number of letters in the Explicit Name, but it also accurately defines the measurement of the very universe in which we live. This paragraph should be read, and then re-read, until you understand its significance, along with the posts just mentioned, where certain aspects are explained in even greater detail.

The significance of the point of convergence in tetrahedral geometry, between the static parameters and the measured parameters should now be more apparent as it is the point where the 28 static 'elements' of two tetrahedrons and the 28 metric elements of each face (when measured in terms of 7 x 7 x 7 elements) connect with the internal geometry in the combined cubic form of the luchot, where both the 216 static aspects (like the total number of degrees in the angles or the total number of angles in the tetrahedrons) and the 216 metric aspects (its volumetric measure in handbreadths) reflect so clearly the letters of God's Name. If you would like more information on this particular geometric theme in the Torah, be sure to read the last part of the post on Miketz.

When an author writes a book, his name generally appears at the beginning of the book, and usually on the cover. In this case, the author we're talking about is the 'Author' of the Universe, God Himself. So we might expect to get a glimpse of this same Signature in this same form, at the very beginning of His blueprint (Torah) and indeed we do! It's just hidden from the casual observer. Our Sages tell us that God hides the fact, that He hides Himself from mankind1.

Since “a picture is worth a thousand words,” consider the very first verse of the Torah which says: “In the beginning God created the heavens and the earth.” That’s how it is in English, but in Hebrew the sentence consists of 28 letters. Why 28 letters? That’s the number of elements hidden in the one-dimensional metrics of the royal seal, or magen, but where all 216 letters of the King’s Name appear in the three-dimensional metric equivalent. It is the point of convergence between the letters of the Name and the measure of the tetrahedrons within the luchot insofar as their static and metric attributes are concerned. Since there are 28 letters in this verse, we have the exact number of letters required to populate a triangular matrix whose three edges are limited to 7 elements. If we load the triangular matrix (one surface of a tetrahedron) with 28 elements (in this case letters) so that each edge is 7 by 7 by 7, we can visualize the geometry more clearly.



In the diagram above, the right face of the tetrahedron shows the 28 letters of the first verse with 7 letters along each of the three edges (7 x 7 x 7). On the left face, the letters are simply replaced by numbers so that you can see the mathematic corollary. The array is not square, nor is the matrix in the form of a cube (as in the case of the luchot). Rather, it is a triangular matrix, as in the case of one face on a tetrahedron (a 'dual' mathematic construct within a cube).

When the same geometry is multiplied three times, as in the case of Balak's sacrifices, it is tantamount to geometrically "constructing" three faces of a tetrahedron. The three faces however actually 'create' a fourth face (ex nihilo ~ out of nothing). The bottom 'face' of the tetrahedron is 'created' by default, from the edges of the other three faces. Just keep in mind that the fourth face 'created' by Bilaam's three 'blessings,' is as yet undefined. This one 'face' is therefore distinctly different from the other three faces, as we've explained many times. Any one face is found within a single two-dimensional plane, whereas the other three faces rise above into the third dimension. This is true of it's points as well, except that the relationship is reversed. There are three points in any given two-dimensional plane whereas the one remaining point rises above the rest into the third dimension. These characteristics are a reflection of the abbreviated letters of the Explicit Name (the Tetragrammaton and Adnoot) where one couple (the Vav and the Nun) are "married" differently than the other three couples (as explained in our post on Ki Thetze and related constructs like the marriage of the letters). This is why one of the bows is different from the other three in Shemonei Esrei. It's also why one of the strands of tzitzith (half tekhelet) is different from the other three. Each of these mitzvoth is a 'reflection' of the King's Name, in the marriage between the letters that result in Ehyeh.

God is known as Elohim and this often confuses people among the nations who see the "plurality," of "the Name" and incorrectly assume there are either several 'gods' or that God somehow has a split personality, when in fact this is not the case. The letters and even the gematria of Elohim are best translated as: "the God [singular] of natural forces [plural]" but it alludes to the four forces (four letters) of the Tetragrammaton and its counterpart Adnoot. What are the "forces" of "nature"? The four forces of quantum mechanics are little more than a virtual metaphor for these letters that constitute a larger reality, where one couple is different from the other three. That is why gravity is the one natural force that is different from the other three natural forces (the small and the weak nuclear force and electro-magnetism). The one pertains to the large celestial objects in the universe, while the other three pertain to the small atomic structure of the universe, and there are other distinct differences as well. The four natural forces are merely a reflection of the four letters of Ekehyeh (which is the marriage of the male~female letters from the Tetragrammaton and those of Adnoot) that rule over God's creation. You can see this marriage relationship on the shviti in most shules or synagogues.

The matrix pictured below is just another way of demonstrating the geometry of the 28 in the form of 7 x 7 x 7. Again, please do not confuse the 28 (structural) elements in two tetrahedrons (in terms of the number of edges, points and faces) with the number elements required to 'measure' any given face, like 7 x 7 x 7 (on three edges). They are different ways of expressing/describing the same thing. However, in this case, they also happen to be the "point of convergence" mentioned in the preceding paragraphs, like the 216 that define the luchot. In fact, 216 is not only the point of convergence in the cubic geometry of the luchot, it is also the one-dimensional metric point of convergence between the combined cubic form of the luchot, and the one-dimensional metrics of tetrahedral geometry (28) within the luchot that in three dimensions have 3 x 72 or 216 corner-points. Consider all of this carefully.



There are several questions that come to mind. Why does the first verse of the Torah have these geometric characteristics? And what possible motive did Bilaam have for appealing to God by building seven altars, performing seven sacrifices followed by another seven sacrifices, and repeating the exercise three times?


In answer to the first question, we already mentioned that an author usually signs his work, and so it is natural that we find an allusion to this Signature in the very beginning of the Torah. In the beginning, before God created the universe, he looked into the Torah (luchot) and so the universe that eventually came forth adhered to the 'specifications' found in those luchot. Since one of those specifications is a geometric aspect of a tetrahedron, which is one of the five mathematic constructs found in a cube/luchot, we find that same geometry attached to the first verse.

That "signature" defines the edges, borders and faces for the geometry of not just one tetrahedron, but also its polar opposite that faces the opposite direction. Together they form a star tetrahedron, and the shadow cast by this geometric is of course the magen david that we see on the flag of Israel. The letters of the first verse (in Torah) would therefore seem to be one of the brighter reflections of this geometry and the Signature of the Architect that it represents. In addition, the numbers and the sets of numbers related to this geometry establish a pattern that is then repeated throughout the Torah (as we demonstrated for example in the post on Emor). We've referred to this pattern many times in the past as the royal seal, but it is really much more than that, since it contains some of the more complex specifications (in the Primordial Torah) that result in actual historical events, like those we see here in Balak that will actually continue to unfold in Parashah Pinchas and Mattot).

Back to Bilaam’s motives ~ since each surface of a tetrahedron can be described as a matrix of 7 by 7 by 7 elements (like the letters of the first verse in Torah) the sacrifices of Bilaam on seven altars, with seven bulls and seven rams, on three occasions, have great significance! They correlate with the royal seal and the mathematic characteristics that reflect the geometry God's Name. So it would appear that Bilaam was literally "calling upon God's Name" to accomplish his goal. We saw the same thing in the geometry (and the reality it created) in the post on Parshah Chukath, where the letters of God’s Explicit Name were mathematically or geometrically hidden in the halacha of the red heifer and then manifested in actual events over a period of time, specifically the nine sacrifices with provisions for a tenth by Mashiach. The motives in Chukath were pure. The motives of Balak and Bilaam were not.

We previously mentioned that in both cases (here in Balak, and also in Chukath) one face of the tetrahedron was 'created' by default, but initially left undefined (as explained above). In the case of the red heifer in Chukath, Israel ‘filled in the blanks’ (over time) by performing nine sacrifices, which defined the remaining geometry. Bilaam, on the other hand, used the “blessings” to create an impure vessel and Israel filled in the blanks (of the remaining geometry) quite differently.

Let's look at this “vessel” more closely, and specifically how Israel filled in the blanks. As we previously mentioned, when you combine three triangles and bind them together in the third dimension (along their edges) the first three triangles actually create a fourth triangle 'ex nihilo' (out of nothing). That’s because the bottom edge of each triangle becomes the edges of a fourth triangle or 'bottom' of a tetrahedron. When Bilaam acted those three times (7 x 7 x 7) his actions mathematically created three faces of a tetrahedron (characteristic of the letters of God's Name). Those three faces resulted in the creation of one last face (or vessel) and all that remained was for Israel to ‘fill in the blanks,’ of that as yet undefined face. The same thing occurred in last week's parashah, where Moshe's calling out ceremony defined the geometry of three faces. The one remaining face created by default, was "filled in" by Israel over time, during the course of 9 subsequent sacrifices of the red heifer. In both of these cases, the people of Israel filled in the blanks by what they did. In the case of Bilaam's vessel, the one last face remained undefined (by him) and dependent entirely upon the future actions of Israel. We'll see how the events corresponding to this undefined "face" play themselves out in a moment when the idolatry resulting from the trap set by the Midianites and Moabites, ends up in a plague.

It is important at this point to remind readers that the geometry we see here is not in anyway Bilaam's. It was/is a function of the mathematic properties of the luchot, and simply part of God's plan, an aspect of the cosmic blueprint (combined cubic form of the luchot) that is, more specifically, and in fact, a reflection of the letters in His Name. That's why we see the mathematic aspects of the royal seal stamped on so many events. All of the events (while they may be conveyed in Torah) come from God's Name. It's just that man is given free will, and sometimes we fill in the blanks in a way that adversely affects our well being. The problem with a blessing is that it can lead to a curse. That’s exactly what happened in this case. When Bilaam blessed Israel those three times and peace prevailed instead of war, it led to idolatry with the Moabites which was chilul HaShem (a desecration of God’s Name). So what happened?

A plague struck Israel. It was bad. It was real bad. In fact, it was so bad that Israel would have been entirely destroyed had it not been for the actions of 1 man ~ or more specifically,  1 very unique man who was willing to risk the wrath of his peers to do the right thing. Because of this 1 man, Israel was spared. Think about that for a moment. It speaks of the power of 1 to change the course of history. Who was this 1 very special man? It was Pinchas of course, and change history he did!

To understand how he changed history, we flashback to the plague. The ‘butterfly effect’ of Bilaam's three "blessings" (each 7 by 7 by 7) resulted in the death of 24,000 people. The number 24,000 is a mathematic iteration of a higher dimension in a mathematic expansion of the blueprint's characteristics as graphically shown below (where 7 becomes 8 in the cubic geometry of the luchot). The same geometry was also graphically demonstrated in the post on BeHar and BeChuko-thai and also on the page entitled "The Eight Dimensions). In this case Bilaam's 7, 7, and 7 became 8 thousand, 8 thousand, and 8 thousand. So his 3 “blessings” led to a plague in which 24,000 people died (3 x 8 thousand = 24 thousand). With the last three words of Parashah Balak (emphasis on 'three' words) the one remaining face (of Bilaam's vessel) was now "defined," and so literally, the last three words in Parshah Balak are the Hebrew words for the number 24,000, which are immediately followed by the first (one) word spoken by God in the next parshah, which happens to be the name of the 1 man (Pinchas) who had the gumption to defend the honor of God’s Name and stop that plague. Contemplate this very carefully.

Again, when you have three things opposite one thing, it is like a tetrahedron where three points exist in one plane (the two-dimensional triangle that is the base of a tetrahedron) while the one remaining point is hidden in the three-dimensional space above. They are geometric variations on a theme, like we find in musical sonata's, but here the variations are merely different reflections of the letters in the Name and/or its primary abbreviated forms. The one act of Pinchas was 'above' the three acts of Bilaam, and the plague wherein 24,000 died was stopped in its tracks.



The bottom "face of the above tetrahedron (which is simply an aspect of the geometry within the luchot) was 'created' ex nihilo by Bilaam's sacrifices, but Israel filled in the blanks. The picture above shows the 'geometry' of Bilaam's "blessings,” opposite the results (plague) that struck Israel. The geometry ultimately defined the 'reality' of these events. Had Israel instead sanctified God's Name, then it would have been 24,000 Midianites/Moabites who would have died. As it was, Pinchas was the 1 man who sanctified God's Name and stopped the plague.

How did God reward Pinchas? Numerous opinions exist to answer that question, one of which is that the parashah (in question) was named after Pinchas. However, I would like to add another opinion to the mix. Since we are talking about kiddush HaShem (the sanctification of God’s Name) you might suspect that the number of people who died in the plague would somehow be a function of the number of letters in God’s Name, and that this would somehow reflect the character of Pinchas, who was the 1 man that did something about it. Let's run the numbers.

If you divide the number of people who died in the plague (24,000) by the number of letters in God’s Name (216) you get a rather unusual fraction. A fraction, as a function of the letters of God’s Name, would normally indicate that something is mathematically irrelevant, or statistically insignificant, because there is really no way to attach any significance to the context of random numbers. However in this case, the fraction is actually quite unusual and has great significance. The odds of dividing a 5 digit number by a 3 digit number, for example, and getting this particular fraction are astronomical.

When 24,000 is divided by 216, the result is 111.111111111 into infinity. Given everything above, I think it safe to assume that the geometry corresponding to the letters in God’s Name (as it pertains to the sanctification of His Name in this parashah) alludes to, attaches to, or otherwise points to this 1 man who had enough respect for God’s Name to do something about its desecration.

You may have noticed that the geometry of this parashah, as it corresponds to the Name, is still incomplete. There is only one tetrahedron expressed in the equation that corresponds to this mix of events. It takes two tetrahedrons to make a star tetrahedron (magen david). In the next two posts on Pinchas and Mattoth, we'll see where the letters of God's Name define the opposing (missing) half of the equation (the missing half of the tetrahedral magen)  complete with the events corresponding to the "opposing" half, when Moshe completely destroys the Midianites for their nefarious involvement.

In the meantime it should be emphasized that the above story is one of many involving the Jewish people as they 'pass through' to become what was destined from the beginning. The nations may bless or they may curse, but the outcome will nevertheless unfold according to God's plan. Those that bless will be blessed and those that curse will be cursed, just as Balak and Bilaam will be, as the story continues to unfold. If you are Jewish then have faith in God. If you are not, then find a way to bless Israel. If you conspire to defeat Israel, it is tantamount to conspiring against God Himself, and the outcome is inevitable. 


______________________

Footnote 1 - Thank you Tsofiya

Saturday, June 20, 2020

Chukath

The procedures for implementing the halachah of the red heifer as well as the history of the nine sacrifices, conform to the nature of tetrahedral geometry in a three-dimensional magen david and a function of the cube [of creation] in the combined cubic form of the shnei luchot (two tablets / 'primordial torah' before division). This geometry, in turn, is a reflection of the number and nature of the letters in God's Explicit Name (HaShem HaMeforash). 

Before we get into specifics, it is worth mentioning that the word "gematria" in Hebrew essentially means geometry. However, the word 'geometry' specifically refers to the measure of the earth, as explained (with sources) in the post on the The Primordial Torah. It is closely related to the word 'geology,' which is the study of earth (the word 'ge[a]' referring to 'earth' and 'gaia' referring to "mother earth'). It is common to consider the gematria of various letters in the study of Torah (gematria here being the numeric 'measure' of the letters). To the rest of the world, this form of geometry is relatively unknown. In mathematics, geometry generally involves physical geometry, or spacial geometry, which is the study of shapes, two-dimensional, three-dimensional or more, as well as combinations of those shapes. However, there are still other forms of geometry that are not generally recognized as such, like the geometry of numbers and sets of numbers. In the case of Torah, we find all of these forms of geometry converging in the letters, words, sentences, and even the characteristics of the events that are part of the narrative.

We will examine the connection to the parah adumah in a moment. In the meantime, if you are new to this blog, please 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 this 'Signature' is hidden, not only in each week’s parashah, but the physics of time and space, quantum mechanics and celestial dynamics to name a few. Once you are familiar with these constructs you can more fully appreciate each post. Those who have already read these essential constructs, will recognize the tetrahedral geometry of the 'royal seal' (magen david) in the procedural implementation of the parah adumah.

When it was sacrificed, the priest would take some of its blood in his left ‘palm’ and then with the finger of his right hand sprinkle it seven times toward the communion tent. A 'palm' is four fingers and so the blood from 'the 4' was sprinkled 7 times with the one finger of the right hand, toward the tent.

Historic events or halachic procedures are often characterized by 4 x 7 (28) instances of 'something' that happens to coincide with the numbers, sets of numbers and the ratios that are characteristic of two tetrahedrons, and where two tetrahedrons are specifically the male~female components of a star tetrahedron or magen david, as detailed and modeled in such posts as Emor and also Massey and Devarim). 



Each Face of a Tetrahedron is a Triangle
A Triangle Consists of 7 Elements
One Tetrahedron has 4 Faces
Total = 28 Elements

You might at first be inclined to think that this is a nice mathematic coincidence. However we've shown in many posts, including those mentioned above, how 4 x 7 (generally as two pairs of 7s) results in 28 elements that are characteristic of events, halacha, and even the linguistic structure of the text throughout the Torah; and how they constitute what amounts to a 'royal seal' embedded on an official document. In each case, the numbers, sets of numbers, and ratios are a mathematic reflection that is equivalent to the Signature of the Architect in the form of a magen david. In some cases the geometry is three-dimensional, like two tetrahedrons as 2 pairs of 7s (with 28 elements). In other cases it is two-dimensional like a triangle as 1 pair of 7s (with 14 elements). One is merely a shadow of the other, and regardless whether the numbers are characteristic of tetrahedrons or triangles, they are invariably 'paired' opposite one another, like the opposing halves of a magen david (example: it took seven years to conquer the land, and then another seven years to divide it).

We previously demonstrated the three-dimensional significance of these numbers in the post on VaEra & Bo where they paralleled the events of the plagues, or more specifically, where the numbers pertaining to the events defined the geometry of the magen david in terms of the edges, points, and faces of a star tetrahedron. It should be emphasized once again that these numbers are merely a geometric reflection of the 216 letters of God’s Name that defines everything (and we'll get more specific in a moment).

At any rate, the above numbers involving the priest, the blood and the sprinkling suggest (and it is only a suggestion at this point) that this may be another example of where we see a reflection of the letters of the Explicit Name in the halacha or the events described in the Torah. Of course it would be nice if we had a second witness whose testimony could be used to determine whether this was just a mathematic coincidence, or whether it really is a reflection of God’s Name in this particular geometric form. Not surprisingly, we do find a second witness. 

As part of the procedure established by Moshe for the sacrifice of the red heifer, the priest engaged in what is called a “triple calling-out ceremony,” where he brings everyone’s attention to “this cedar” and “this hyssop” and “this crimson wool.” There were 4 types of hyssop and 7 types of cedar, in addition to the one type of crimson wool specified in the Torah. Those numbers are the very same numbers as those above, where the blood of the red heifer was taken from 'the 4' of the left hand and sprinkled 7 times with the one finger of the right hand toward the tent. Each time, we have the same numbers, the numbers that correspond to God’s Name in the geometric form of the magen david.

If indeed this represents the geometry of the letters of God’s Name, and if indeed the events are conforming to those letters, then we might also expect a third witness to confirm this, especially since the geometric form of the magen david is all about 3s (and even more especially when it is three-dimensional). Well guess what? There is indeed a third witness, and a very good one at that! We see it in the additional requirements for the sacrifice which are also tantamount to a mathematic reflection of the letters in God’s Name, but this time the procedure provides a more detailed definition of the faces, edges, and points of the magen in the form of a star tetrahedron. Before we begin, let's first look more closely at the geometry.




A tetrahedron has 4 faces. Each face is a triangle with 7 elements (3 points, 3 lines and 1 face). The '4' with '7' make 1 (three-dimensional) tetrahedron. Note that it takes two tetrahedrons to create one star tetrahedron and that here are two instances of 4s, 7s and 1s in the text of the parashah alluding to the combined geometry. When a tetrahedron is merged with another tetrahedron to create a star tetrahedron, each face is further subdivided into 3 smaller faces (as you can easily see above) with the stellation of the opposing tetrahedron in the middle of any given large face. The sum total of triangular corners on each small face in the third dimension (after the marriage of the two) is 72, with each mathematically corresponding to the number of triplets in the Explicit Name. That’s why we say that the star tetrahedron (magen david) is a geometric reflection of the letters of the Name. Not only are there 216 ‘positions’ that correspond to each letter, but each is a function of 72 triangles, reflecting the triad nature of the Name, much like the characteristic of sapphire that has a measured clarity of 72 with trigonal crystalline facets. Now let's see how this corresponds to the procedure established by Moshe, and to the events themselves independent of the procedure.

The procedure that Moshe established for the burning of the red heifer required the priest to:
  1. Kindle the fire
  2. Place the cow on the fire
  3. Take some cedar, hyssop and crimson wool 
Thus far, the procedure requires 3 things, and the 3rd thing specifically requires (another) 3 things.

The cow was then burned and the ashes divided into 3 parts. The first part was placed in the chail which was the wall facing the women's gallery. The second part was deposited on the anointment hill (on the Mt. of Olives) and the third part was given to the guards near the Temple for use as necessary.

So now in addition to the 3 things, where the 3rd thing includes another 3 things, we have these 3 things divided into and among another 3 things. This is like a triangle that has 3 more triangles inside, that each in turn have 3 more triangles inside. 

The content of the text and the procedure it describes therefore have something in common with both the triad nature of the letters in the Name (a series of triplets) and the triad nature of the mathematics defining a three-dimensional magen david. But again, it doesn't end with just the above description. To better visualize the relationship between one thing and another, consider the following:

The priest would exclaim:

Behold this cedar wood
       
Behold this cedar wood      Behold this cedar wood

The others would  reply:

Yes

Yes     Yes
In order to show how these procedural requirements mirror the characteristics of a star tetrahedron (reflecting the geometric characteristics of the 216 letters) let's "map" this part of the procedure on the surface of the first face of a tetrahedron and its opposing stellation (and each additional procedural element in turn) to see how the halacha conforms to the characteristics of the magen. Since this part of the procedure pertains to 1 face and its opposing stellation, it accounts for 18 of the 72 triangular faces.

Closeup of the 1st Face and Opposing Stellation
(Click to Enlarge) 


Notice: 1) how the 3 small faces are a geometric match for the 3 times the cedar was called out, and 2) how the 3 sides on the base of the opposing stellation provide a corresponding reflection of the 3 times the others responded "yes," and 3) how the 3 faces of the opposing stellation correspond mathematically to the 3 places where the ashes were placed. The first tetrahedron is a reflection of what the priest did. The opposing tetrahedron is a reflection of the parts that others played in the process, essentially male~female counterparts of one another. The procedure would of course continue. 

This time the priest would exclaim:

Behold this hyssop
       
Behold this hyssop      Behold this hyssop

The others would again reply:

Yes

Yes     Yes

The mapping of this procedure onto the 2nd surface is essentially the same as the previous, again defining the characteristics for this part of the magen. The 2nd face and the 2nd opposing stellation add another 18 of the 72 triangular faces of the star tetrahedron, and so we now have half the number of triplets (36) accounted for in these 2 faces.
Closeup of the 2nd Face and Opposing Stellation
(Click to Enlarge)




Notice again how the 3 small faces are a geometric match for the 3 times the hyssop was called out; and how the 3 sides on the base of the opposing stellation provide a corresponding reflection for the 3 times the others responded "yes"; and how the 3 faces of the opposing stellation correspond mathematically to the 3 places where the ashes were placed. The first tetrahedron is again a reflection of what the priest did and the opposing tetrahedron is again a reflection of the parts that others played (male~female). The procedure would of course continue.

This time the priest would exclaim:

Behold this crimson wool
       
Behold this crimson wool      Behold this crimson wool

The others would again reply:

Yes

Yes     Yes

The pattern continues to repeat itself. The next part of the procedure provides the content for the 3rd face and the 3rd opposing stellation. Again, the geometry of the procedure reflects the letters of God’s Name in the geometric form of a magen david, with yet another 18 of the 72 triangular faces, on the surfaces/faces corresponding to 54 of the triangles/triplets.


Closeup of the 3rd Face and Opposing Stellation
(Click to Enlarge)


Each of the 3 small faces again corresponds to the calling out, but this time for the crimson wool, and each of the 3 small faces on the opposing stellation again corresponds to the 3 responses, and the 3 places the ashes were deposited. 

So far, all of these conform beautifully to the geometry of a star tetrahedron. However, there is yet another face to account for, because a tetrahedron has 4 faces, and thus far we've only mapped 3 because the procedure involved only 3 items (cedar, hyssop and crimson wool). In what possible way could the 4th face correspond to the Parah Adumah? 

If you are familiar with the history of the Parah Adumah, then you know there were 9 sacrifices. The number (9) matches the number of corners on the remaining face of the star tetrahedron. The number of sacrifices would complete the geometry except for the  remaining stellation, but we'll get to that in a moment.





Keep in mind that while the procedure may have been established by Moshe, the historical events were out of his hands, yet they continue to reflect the geometric characteristics of a star tetrahedron (missing only its opposing components that we'll get to in a moment). 

In the meantime, the history of those sacrifices bears closer examination. Mishnah Parah 3:5 provides more detail about the 9 Parah Adumah's made throughout history, and the one that will be made by Mashiach in the future:

(Click to Enlarge)



Moshe was obviously the first. However, the sages compare Ezra to Moshe and say that Ezra could have given the Torah, and in a sense he did, as he revitalized the Torah and taught it to everyone upon their return to the Land. As a leader, he brought his people out of exile and built the Second Temple. The third ‘first’ is Yishmael ben Piavi, who was said to be more righteous than his two counterparts, even though he was the last in time. Each of these three men were different from the other two in their respective triad.




What this means is that the nature of the men who performed the sacrifices also reflects the geometry of the royal seal. Each face of a triangle consist of three points. One of those points is always different from the other two. That's because any two points are in one dimension, while the third point must rise above, into the second dimension. This is simply the geometric nature of a two dimensional triangle. The same is true for its three-dimensional counterpart, the tetrahedron, except that it has three points in any given two-dimensional plane, while the fourth point rises above into the third dimension. The same is true with the men who were involved in the 9 sacrifices. In fact, these same characteristics are found throughout the Torah as a function of the historical narrative (as can be seen in other posts).
In the meantime, we mentioned above that we were still missing a component to complete the geometry, specifically the stellation of the opposing tetrahedron. We find it's counterparts in the future sacrifice that Mashiach will make where the calling out ceremony matches the 3 sides of the 3 faces on the opposing stellation. So the last stellation provides a "place" for one final (or 10th) sacrifice. The 9 sacrifices made by other Sages will stand geometrically opposite the 9 characteristics (3 x 3) of the sacrifice that Mashiach will make, a sacrifice that is a singularly unique, in that it will be the last. The "end will be en-wedged in [the] beginning," as Mashiach will understand the mystery and meaning of the sacrifice as did Moshe.

With the completion of this face and corresponding events, both past and future, ascribed to their respective place in the cosmic scheme of things, we have the final 18 of the 72 triangles accounted for. Thus all of the triplets that would correspond to the 216 letters of God's Explicit Name are now found in the above geometry. The Signature of the Architect (in the form of the royal seal) is the framework of the procedure, also the history of the procedure, and even the future of that procedure. We see this in the actual events that have thus far occurred over time.

If you tried to match these characteristics to any other 'geometry,' (excluding that which corresponds to God's Name) then the entire pattern would fall apart, which again suggests that "the Name" really does 'rule' over everything. The reason for the sacrifice is of course still a secret (known only to Moshe, R. Eleazar and Mashiach).

In closing, we should remind readers that it is the Jewish people (the family of builders mentioned in the parables that are part of the posts on Metzora, Emor and BeHa'alothekha) who have preserved this knowledge for the benefit of mankind; it is the Jewish people who observe it, so that the matrix of time and space remains stable (as demonstrated in BeHar and BeChuko-thai); and it is the Jewish people who fulfill it, so that mankind can recognize the Author of the system, their Creator, and see His Unique Signature throughout every aspect of His creation. It is however, incumbent on the individual to seek out this information from competent Torah sources. Additional information on where the Signature of the Architect appears in quantum mechanics, the physics of time and space, biology, and celestial dynamics to name a few, can be found throughout other posts on this blog. Thanks for reading! 

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Footnote 1  – Was during the time of Shimon ben Shatach and Yehudah ben Tabbai. He performed his Parah Adumah after Choni HaMagel brought the rain. 

Footnote 2 – Was in the days of Hillel and Rabban Yochanan ben Zakkai.


Footnote 3 - The Mishnah in Sotah 9:15 states, “When Rabbi Yishmael ben Piavi died, the splendor of the Priesthood disappeared.” He was wise and rich, and many priests ate at his table. 


Footnote 4 - See Babylonian Talmud Kedushin 31a and Avoda Zara 23b-24a, for the fascinating story about how far one should go in honoring their parents. Some say that God caused Benjamin’s stone on the Breastplate of the High Priest to become lost, hinting to the fact that the Jews were fighting amongst themselves. At the time close to the end of the Second Temple, there were tremendous schisms in Judaism, and Benjamin symbolized unity, as he was not part of the brothers’ plot to sell Joseph. By his stone becoming lost, the Jews were to get a last minute wakeup call that they had lost their unity. They replaced the rare stone from Dama ben Nesina’s coffers. In the merit of his honoring his father, Dama was blessed with a Red Heifer in his flock, which he sold to the Jews for the same price they had offered him for the stone. 


A special thank you to Uri Strauss
for constructing the Table of the 10 Parah Adumahs and mapping them to the face of a magen david.