In Parashah 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.
Parashah 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 hand-breadths (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 hand-breadths 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 hand-breadths) with a volumetric measure of 216 cubic hand-breadths.
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 hand-breadths 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 hand-breadths) 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 Ehyeh (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 Parashah 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 Parashah 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
