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 wake-up 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.