Sunday, March 11, 2018

VaYikra and Tzav

This week’s Parashah VaYikra and also Tzav are on the subject of korbanot (sacrifices and offerings) including those of bulls and goats, peace offerings, meal offerings, wine libations and so forth. Certain offerings required additional constituents measured in precise amounts, and so it might be appropriate to begin a discussion on several different systems of measurement. Each originates with the physical properties of the combined cubic form of the luchot. Since these properties are invariably a function of the 216 letters of God’s Explicit Name, the ratio between one measure and another reflects the number and the nature of the letters in this Name.

The examination will include specific measurements such as: the “hin;” the "log" or “lugim”; the "minim" or "drop;" the bath; the kav; the se'ah; hours; and "parts of hours (halaquim); and the great year. The term minim is a relatively modern term (essentially referring to an accurately measured drop) but the concept and its exact fractional proportion date back to antiquity. Since both VaYikra and Tzav deal with offerings they will be combined for purpose of this post.
 

Before proceeding, we need to mention that some of the information you are about to read requires a broader understanding of certain concepts. The reader is therefore strongly advised to read each of the essential constructs listed in the column to the right before proceeding. These constructs reveal the correlation between the letters of the Name and the multidimensional mathematic and geometric characteristics of the luchot, both in their divided state and combined cubic form, along with an explanation of its internal geometry that casts a shadow known as a magen david. There is a special connection between the Name, the luchot and the geometry of the magen. The purpose of this blog is to show how they connect with one another and to reveal where the signature geometry is hidden in each week’s parashah. Once you are familiar with these constructs you can more fully appreciate each post.

Insofar as VaYikra and Tzav are concerned, the Signature of the Architect  is (once again) hidden within the conversion of measurements. Liquid and dry measures are closely related. Consider for example, that in terms of dry measure, a log is 1/72nd of an ephah, and in liquid measure the log is 1/72 of a bath. An egg is also 1/72 of a hin. The relationship between one measure and another results in three specific ratio's that have a measure of 72 to one. Moreover, two of those ratios pertain to a single type of unit (the log) and one to a different unit (the egg). This is like the ratio for the permutation of letters where the triplets are formed (two letters are from the first position~one from the last position~as is known). The correlation with God's Explicit Name should not go unnoticed

The same ratio is found in the measure of the luchot in side-by-side form: 6 x 12 (72) x 3 = 216 cubic handbreadths. Were these relationships a coincidence, we would not expect other measurements to reflect the same ratio, but they do!  For example, a hin is 1/6th of a bath, an egg is 1/6th of a log and a cab or kav is 1/6th of a se'ah. The 6 hin per bath, the 6 eggs per log and the 6 kav in a se'ah are also significant and correlate with the "three measures of 6" in the dimensions of the foundations stone, or the ratio of the handbreadth to the cubit in those same dimensions (1/6th along each of its three dimensions). Those three "measures" determine the volumetric measure of the stone which of course equates to the number of letters in God's Explicit Name (216). 

The measure of time is no less connected. Consider that a day is divided into 24 hours and that in ancient times, each hour was divided into 1,080 "parts" or halaquim per hour, or what amounts to 108 times 10 "specific units of measure" (108 being the volumetric measure for each of the luchot). The number of parts in a day was thus the 12 hours of the day plus the 12 hours of the night 12 (24 hours) x 1,080 or 25,920 "parts/halaquim." These numbers as they relate to one another are highly significant. The number 25,920 for example, happens to be the number of years in the precession of the equinoxes, or what is sometimes called a great year. So ultimately, the dynamic that defines celestial time, not only originates with the two halves of the cube [of creation] divided into its respective male and female halves (the two tablets or shnei luchot) but each half is a function of the 108 that in turn defines the male and female halves of a complete rotation of the earth on its axis, resulting in 12 hours of day (the male half) and 12 hours of night respectively (the female half). 

The precise periods have varied slightly since the time of the flood for reasons explained in the post on BeHa'alothekha. Insofar as the great year is concerned, there are twelve constellations that rise and fall, through their respective segment of the 25,920 years in the precession of the equinoxes, during which 2,160 years elapse (for each of the twelve). So once again we see how time and space; and the movement of the stars are dictated by the number (and nature) of letters in the Explicit Name (216) which happens to be abbreviated by 12-letters, with a 12-letter counterpart. Contemplate this carefully. Our reality is literally a reflection of the letters in God's Name. See also the post on Ki Thetze for a more detailed explanation of the 4-letter primal forms of the Name and the post on Ki Thavo for a closer look at the 12-letter triad form.  

The measure of the Mishkan (Tabernacle) is, among other things, a model of particle interaction in quantum field theory (that will be demonstrated in an upcoming special post to be listed among the advanced constructs to the right). It is also a very precise model of space-time. Both models reveal the correlation between our physical reality and its origin in the signature geometry of the letters in the Name. As an example, each of the eight-beam segments containing the kodesh kodeshim (holy of holies) is 60 handbreadths high, by 72 handbreadths long, by 6 handbreadths thick. Do the math (60 x 72 x 6 = 25,920) and you'll find that each of the three walls have a volumetric measure 25,920 cubic handbreadths, which is the same number of years in the precession of the equinoxes that we mentioned above, and this is just one of many examples. These measures are not a coincidence. They are a function of a reality based on the letters of God's Name, which rules the universe. For more on the measure of the Mishkan, see the post on Parashah VaYakhel.

We'll now shift our attention to the hin and one of its fractional proportions sometimes referred to as a dram which is a static measure that is exactly 1/6th of an egg again conforming to the fractional proportions that began with the measure of the luchot (a handbreadth being 1/6th of any three of its dimensions). Thus, as mentioned previously, a hin is a reflection of the letters that define the luchot, as seen in the hin which is 1/6th of a bath; an egg which is 1/6th of a log; and a cab or kav which is 1/6th of a se'ah. These specific units of measure are a reflection of their source in the combined cubic form of the luchot, which is in turn a reflection of the letters in the Creator's Name.

Halachic requirements for various offerings are multiples of these proportions and invariably equate to the number and nature of the letters. For example, the first offering of the day was the morning tamid which required a small amount of oil. How much oil? A "quarter of a hin" to be exact. If you try to find a measuring cup graduated in hin at your local supermarket or even one of the better culinary boutiques, good luck. It is unlikely you’ll find one. What exactly is a hin?

 As it turns out, a hin is 432 drams (R. Culi Me’am Loez) or 72 of the 1/6th units of measure within an egg. What this means is that the quarter hin for the morning tamid consisted of 108 'drams,' and this 'measure' was then juxtaposed against the 108 drams of the afternoon tamid. Sound familiar? It is the volumetric measure for each half of the cube (shnei luchot) which can be mathematically expressed as 108 cubic handbreadths opposite 108 cubic handbreadths, that in turn (and once again) reflect the number and nature of the letters in the Name.

As a sidenote: Throughout history there have been several varieties of drams. However, here it is used to describe one sixth of an egg, which is a continuation of the fractional proportions established by the measure of the cubic form of the luchot discussed above (1/6th; 1/6th; and 1/6th). The fractional proportions that are directly 'defined' by the luchot are one half (1/2); one third (1/3); and one sixth (1/6). Each originates in the combined cubic form of the luchot, its division, and the 216 letters by which it is measured. How? Why? 

In its primal, undivided state, each of its dimensions was measured in terms of 6 handbreadths, and each handbreadth was one sixth (1/6) the measure of any given dimension. When it was divided, it was divided in half (1/2). This resulted in a measure of three handbreadths along one side, where each handbreadth was one third (1/3) the measurement of that side. These proportions became the “three primary” fractional proportions in various systems of measurement, with 1/6th or 1/60th being the dominant ratio(s). A system of measurement based on these proportions is referred to as a sexigesimal system of measurement. So it is that we find 1/6th and 1/60th 'proportions' used as a basis of both ancient and modern systems of measurements. It's just that knowledge of how these proportions originated (from the properties of the luchot) has been lost in antiquity. For halachic purposes, if something is less than 1/60th (smaller than a 'barley corn') it is said not to exist. Chametz is an exception.

At any rate, the Sages of Israel asserted that the morning and afternoon tamid were associated with the male and female halves of creation. These halves originate with the luchot that were each 108 cubic handbreadths. Here we see them in the offerings, just as we saw them above in the measurement of time where they appeared as 1080 "parts" for each hour of the day opposite 1080 "parts" for each hour of the night. We would be remiss if we did not mention that the "measure" for the radius of the moon in miles is 1080 and together with its opposing radius, results in a diameter of 2160 miles (see the post on the Primordial Torah for related details). The two halves that are a function of 108, be they associated with lunar dynamics; or time, as parts/halaquim of an hour; or the measure of the luchot, are all a reflection of a larger reality defined by the cosmic blueprint.

Torah requirements conform to the nature of that blueprint (the shnei luchot or 'tablets') and so we see halacha require a quarter hin or 108 drams of oil in the morning and 108 in the afternoon. The measure of each “half” (and keep in mind that the gematria of the Hebrew word for “half” is 108) was the same as the volumetric measure for each half of the “cube of creation,” where each tablet was “half” of the original cubic form. Take a moment to contemplate the implications.

The total measure of oil, just as the total measure of time, and the total volumetric measure of the luchot, are all numerically identical, and all are equal to (and a reflection of) the letters in God’s Explicit Name (216) divided equally into their male and female equivalents for purpose of creating a universe in like form (the duality seen in physics). Mathematically and/or geometrically, we might describe this as simply 108 elements opposite 108 elements, but it is a pattern that we see consistently, not only in Torah, but virtually every aspect of the physical universe.

The amount of wine for a wine libation, was also given in terms of hin, but the end result was usually a quarter hin (
108) twice, or a half hin (216) and so the connection to both the volumetric measure of the luchot and to God’s Name is consistent. 

There was also a requirement for a third of a hin which would equate to 144 drams that will be explained more fully below. This is very interesting in light of the measurement of the north and south walls of the mishkan, which were in the same proportion as the two walls of the golden section (kodesh kodeshim / holy of holies) in the tabernacle. The external dimensions of these walls were 72 opposite 72, or 144 handbreadths. 

These numbers seemed to fall short of the mark (216) until the third wall came to reconcile the difference (the remaining 72 handbreadths). See the post on VaYakhel for details. The same is true with the measurements in VaYikra and Tzav, where the third (missing) vector is reconciled by additional offerings that result in a continual series of 72s. 

The point is that what we see in the requirements for these offerings is once again a reflection of both the number of letters in the Name and its triad nature that is so rarely discussed anywhere, especially their mathematic or geometric connection to one another in the form of the luchot; cube; and star magen within.



The anointing oil and the amount that Moshe created is also a reflection of these letters. In the portion of Tzav it says: “Moshe took some of the anointing oil... and sprinkled it on Aaron.” This anointing oil was known as the shemen afarsimon (holy anointing oil) and only one batch of it was ever made. It was made by Moshe who fully understood with proper kavanah (direction of the heart) what was required to make the oil.

 Rabbi Yehuda said: “12 lugim were made... and 12 lugim always remained” because even after a portion was used, a miracle occurred and the amount never diminished. Why did he specifically mention the number 12 twice?

The relationship between the 12 at the start and the 12 at the end (like the words used by Rabbi Yehuda to describe it) is like the 12-letter Explicit Name and it's 12-letter counterpart explained in the post on Ki Thavo, and part of the same dynamic seen in the measure of time, with 12 hours of day opposite 12 hours of night (each half being a function of the 108 defined by the cube and ultimately the letters) or the 12 small faces on one half of a star tetrahedron (three-dimensional magen david) opposite the 12 small faces on the other half (also a function of the 108). Each is indicative of a larger reality based on the Creator's Name.

At any rate, returning to the subject of the anointing oil, how does a hin relate to a log? The answer should come as no surprise: 6 lugim are a half hin, or 216 drams. There were 12 lugim of oil (like two halves) and the luchot were brought down twice (2 x 216). Take time to understand the significance of these amounts. Each is invariably a static measure found in one or more combinations of the Eight Dimensions of the luchot that correlate with the letters of the Name.

When adding together various sacrifices and their associated requirements in the form of liquid measures, not only do we see a connection in terms of the number of drams (1 times 216 or 2 times 108) but the various amounts required by halacha are in essence two or three-dimensional reflections of the luchot as seen in the form of two 6s, or three 6s: 6 lugim, 6 lugim and 6 lugim which mirror the three dimensions of the combined cubic form of the luchot that were 6 handbreadths by 6 handbreadths by 6 handbreadths. All reflect the nature and number of letters in the Name.

In the case of the tamid, the progression would continue daily into infinity much like the reflection between two mirrors. The repetition is reminiscent of the three measures of flour (each being 6 ounces) in Avraham’s tent for the Divine Presence and the 6 days in the cloud, the 6 days going back and forth and the start of the event
(or end) on the 6th of Sivan. Each in its own way is a further reflection of the Signature of the Architect that defines the measure of the blueprint for creation. 

Why did Moshe make (only) 12 lugim? It is important to remember: 1) what actually happened; 2) who brought down the luchot; and 3) how many “sets” of “twins” were actually brought down. You may recall that because of the sin of the golden calf, the first twins (2 x 108 = 216) were shattered and a second set brought down (2 x 216 = 432 cubic handbreadths). There happen to be 432 drams (2 x 216 = 432) in 12 lugim.

The diagram below shows some of the different systems of measurement, sets of measurements and ratios between sets and how they correlate with one another, using the geometric properties of the luchot as the common denominator. The measurements themselves may be an expression of entirely different systems, measuring entirely different things, but the ratios between one thing and another are always the same and they always match the ratio between the luchot; it's combined cubic form; or its divided form; and that of the Triad Name. It doesn't matter if the measurements are in terms of 108 cubic handbreadths or
108 drams, 108 (tens of) parts (of an hour), or 6 handbreadths, 6 lugim, 6 eggs,  or 2 times 108 drams or 216 drams. Not only are they related to one another in terms of their respective ratio's but those ratios in turn match the characteristics of the cosmic blueprint and the Signature of the Architect who established them in the first place.

Units of Measure
(as they relate to the volumetric measure of the luchot)
 

Click  to Enlarge

1/4 hin   =   108 drams   =   3 lugim
1/2 hin   =   216 drams   =   6 lugim
1    hin   =   432 drams   = 12 lugim


All of the requirements, all of the measurements and all of the events are a reflection of God’s Name. If the event occurs twice then we see a double reflection. Enter the requirement for a third hin of oil or wine. The product of 3 times 144 (a third of a hin) equals 432, which is the same as 2 x 216, or the total amount of anointing oil (in drams) that Moshe made, and the same number of elements in the two sets of sapphire “twins” that Moshe brought down (the first having been shattered).

All of this requires a certain amount of contemplation. However the conclusion is inescapable. The luchot are indeed the “cosmic blueprint” for creation. They provide the specifications for everything that follows. Its characteristics are not only a reflection of the letters of the Name, but the pattern for everything else that follows. We should therefore not be surprised when we see these patterns repeated in the linguistic structure of the text or elsewhere in the physics of the universe. How do we know these requirements (and patterns) are not the invention of men? These requirements and patterns are embedded in both the subatomic and stellar nature of the entire universe. We find them in the physics of time and space, quantum mechanics, biology and celestial dynamics, and though we will not delve into them in this post, it is only because we have done so elsewhere, many times, throughout this blog. 

We mentioned earlier that a hin was 432 drams. Interestingly, the term "dram" is also considered to be 1 teaspoon, not a teaspoon by today’s measure but by its original measure which was 60 minims (a minim being a drop of fixed measure)1. If a dram is 60 minims (60 drops) and a hin is 432 drams, then how many minims are in a hin? The answer is exactly 25,920 minims. That number should also sound  familiar as it was just mentioned above, as the number of years that it takes for the stars in the heavens to make one full circuit in the precession of the equinoxes known as a great year or platonic year. When it was mentioned above, we were talking about the measure of time. Here, we are talking about a liquid measure that occupies space and has volume, but both are identical and both have their origin in the characteristics of the combined cubic form of the luchot. That’s why we say that everything is interconnected and if you trace the connections back to their point of origin, it is always the cube of creation (defined by 216 'measures' that equate to the letters of the Explicit Name). 


Insofar as this post is concerned, the important thing to remember is that the measurement of the luchot, the oil, the wine, the movement of the stars through the heavens, as well as the relationship between actual systems of measurements like the hin, the dram and the minim (or drop) have their equivalency in some fractional proportion of the 216 letters which defines them all (which by the way have been used in one form or another by every nation from time immemorial). Each system of measurement is directly or indirectly connected to the letters of God's One Explicit Name, the knowledge of which was preserved by the Sages of Israel.

In the next post on Shemeni, we will see how these same systems of measurement and other halachic requirements (that mathematically and/or geometrically correlate with the Name) have a connection in physics to the E8 lattice.





________

Footnote 1 - The minim is actually a "drop" (60 drops in a teaspoon or fluid dram). Its a modern term that comes from an ancient concept. The term minim was established because the problem with a drop, was that in practice it would vary, depending for example, on viscosity and temperature. The minim is simply a more modern variant that took this into account to provide for a static measurement. The ratio between one measurement and another is the same i.e. 1/60th. It goes back to the roman concept of a drop (minim) being 1/60th of a fl. drachma or a grana (grain) being 1/60th of a drachma, but this in turn goes back to even more ancient concepts as in the case of the Torah concept of 1/60th, which as explained throughout this post originates in the geometry of the luchot. For the purpose of this post the term minim is used, even though it is more modern, because it is a static amount. 

Thursday, March 8, 2018

Pekudey

In this parashah “[Betzalel] made the robe [for the Cohen HaGadol]” and they “made pomegranates [and] ...pure gold bells, and placed the bells in the pomegranates.” It then says “there was a bell and a pomegranate, a bell and a pomegranate all around the bottom of the robe.” 

Before getting into specifics, we need to mention that some of the information you are about to read requires a broader understanding of certain concepts. The reader is therefore strongly advised to read each of the essential constructs listed in the column to the right before proceeding. These constructs reveal the basic connection between the letters of the Name and the multidimensional mathematic and geometric characteristics of the luchot, both in their divided state and combined cubic form, along with an explanation of its internal geometry that casts a shadow known as a magen david. There is a special connection between the Name, the luchot and the geometry of the magen. The purpose of this blog is to show how they connect with one another, and to reveal where this unique Signature of the Architect is hidden in each week’s parashah. Once you are familiar with these constructs you can more fully appreciate each post.



With respect Parashah Pekudey, there is considerable debate in the Talmud and other sources as to specifics regarding the robe, the bells and the pomegranates. Was there a bell next to each pomegranate, or was there a bell inside each pomegranate? Some say there were 36, some say 70 and some say there were 72 pomegranates (and an equal number of bells).




Given the numbers, sets of numbers and ratios between the sets found in the last parashah, relative to the ratio of phi; relative to the measurements of the tabernacle; and their connection to God’s Name, the description of the robe with its components might be altogether different, and so I offer the following for consideration:



The number 70 has an indirect relation to God’s Name through a segment of the geometry in the royal seal (three-dimensional magen david). The number 36 is a facet of the Name as well, in that it is half of 72, but half of 72 is just that (only half) and so its connection is also somewhat indirect. The number 72 has a direct connection to God’s Name, in that it is the number of triplets, but still just one third the number of letters. We pointed out in (last week's) post on Parashah VaYakhel, that without the third wall of the Mishkan, there were only 2 x 72 (handbreadths) or 144 elements, and so the reflection fell 72 short of the mark. However, when we added the third wall, which was 72 handbreadths, the total measurement became 3 x 72 or 216 handbreadths, which properly reflected not only the number of letters in the Explicit Name, but also the triad nature of that Name.

In the case of the robe, if there were 72 pomegranates then there would be 72 bells and we would have the same problem we had in the last parashah concerning the walls (2 x 72 = 144). Each opinion thus far offered, is inadequate to reflect both the number and nature of the letters in His Name. In the case of 72, the total number is missing a vector or component of the triad form (see the post on VaYakhel for a more complete explanation). Briefly, in the case of the walls of the mishkan, there was a third wall (a third set of 72 handbreadths) that came along to reconcile the discrepancy. Is it possible there is yet another number to consider in describing the bells and pomegranates? 


The Torah describes the hem of the robe as having a “bell and pomegranate,” as though they were married together in pairs at the bottom of the robe. In other words, they could have been side-by-side; or maybe one inside the other (as suggested in some sources) but whatever their position, they were somehow juxtaposed one against the other like twins. Notice also that the phrase "bells and pomegranates," is repeated twice! Two sets of twins should sound familiar.

Since there were two items, bells and pomegranates (and the phrase is repeated twice) then by logical inference the form would seem to mirror that of the luchot, which were two mathematic and geometric twins brought down twice in the form of 108 opposite
108 (cubic handbreadths). Might there have been 108 pomegranates opposite 108 bells? 

If this were the case, from a purely hypothetically standpoint of course, how might they be distributed around the bottom of the robe. Consider what happens, for example, if they were not merely adjacent to one another, but also over top of one another, and staggered triangularly as pictured below.

This would mean first, that the 108 bells opposite 108 pomegranates, were like the 108 handbreadths opposite 108 handbreadths in the measure of the north and south walls of the tabernacle when portioned according to the ratio of phi. It would also mean they were like the 108 cubic handbreadths of the luchot, opposite its remaining 108 cubic handbreadths, all of which reflect the number of letters in the Explicit Name. It would however, mean something else. 

If the bells and pomegranates were juxtaposed as a series of triangles they would still be a string of alternating bells and pomegranates, but the staggered juxtaposition would form a series of triangles. 

Question: If there were 108 of each, then how many triangles would there be?
Answer: There would be exactly 72 triangles (72 x 3 = 216) as shown in the model below.

In this configuration, the hem of the robe with its bells and pomegranates would be a mathematic and geometric mirror image, not only of the walls of the mishkan that were both 3 x 72 and 2 x 108 at the same time, as shown in the picture posted last week in VaYakhel, but it would also reflect the mathematic and geometric characteristics of the luchot. The requirement in the written Torah would be met, as there would be "a bell and a pomegranate, a bell and a pomegranate all around the bottom" as specified. More importantly, the characteristics of the bells and pomegranates would mirror the number and the triad nature of the letters in the Explicit Name.
 

108 Bells and Pomegranates Triangularly Arranged (Total: 216)
w/ 72
(Virtual) Triangular Forms



(There are 72 Triangular Corners in a Three-Dimensional Magen David)
3 of the 72 'Virtual' Triangles are Depicted Above
(the blue lines are used merely to show the triangular pattern)
(click on the diagram to enlarge it)

Contemplate this for a moment and remember also that when the top angle of an equilateral triangle equals 108 degrees, the sum of the 2 bottom angles equals 72 degrees, and when the top angle equals 72 degrees, the sum of the 2 bottom angles equals 108 degrees. If you wanted the robe to reflect the number and nature of the letters in God's Name, how many bells and pomegranates would you include, and where, and how, would you place them?

Sunday, March 4, 2018

VaYakhel

Throughout this blog it has been asserted and repeatedly demonstrated that the mathematic Signature of the Architect is deeply embedded throughout the entire Torah in a variety of ways, and that it is hidden from the casual observer. In this week's parashah we see once again how this unique signature in the form of certain mathematic and geometric characteristics, is hidden just beneath the surface.

Before we get into the specifics of this parashah, we should mention that some of the information presented in this post requires a broader understanding of certain concepts. The reader is therefore strongly advised to read each of the essential constructs listed in the column to the right before proceeding. These constructs reveal the correlation between the letters of the Name and the multidimensional mathematic and geometric characteristics of the luchot, both in their divided state and combined cubic form, along with an explanation of its internal geometry that casts a shadow known as a magen david. There is a special connection between the Name, the luchot and the geometry of the magen. The purpose of this blog is to show how they all connect and to reveal where the signature geometry is hidden in each week’s parashah. Once you are familiar with these constructs you can more fully appreciate each post. 



In VaYakhel, Betzalel and his assistant carry out the instructions that God gave to Moshe in Terumah. We are told that these men were gifted with the ability to know and understand how to build what God had directed. So with that in mind let's look at what they built and how it correlates with God’s Name.



The Torah says: “...they made 20 [golden] beams for the southern wall [and for] the north[ern wall] they made 20 [golden] beams.” At first glance this appears to be a simple, straight forward description. However, it also contains a great deal more. Embedded within these measurements is an accurate reflection of God’s Explicit Name. How on earth could the signature geometry be hidden within these simple measurements? 


We have shown on numerous occasions that the luchot were each 6 x 6 x 3 handbreadths and that a matrix with this ratio consists of 108 'elements' (cubic handbreadths). There were two luchot, so the measure of the combined form was 6 x 6 x 6, and the total number of elements in the twin matrix was 2 x 108 or 216. The number of cubic handbreadths in the luchot is of course equal to the number of letters in God's Explicit Name. In fact, when the tablets are placed side-by-side, the ratio becomes 6 x 12 (72) x 3 which reflects the number and nature of the 72 "triplets" (72 x 3 or 216 letters). This should be carefully contemplated.

As we proceed through this post you will see how these numbers, sets of numbers, and the ratio between the sets define the architecture of the mishkan (tabernacle).  First, consider the ratio known as 'phi' represented by the symbol φ, also called the golden ratio. Why is it called a "golden" ratio? What's so "golden" about it? You'll see why in a moment. The ratio is well known and can be found throughout the entire universe. Phi is essentially 'nature in action.' The curvature of a seashell is in this proportion. The number of male bees in a hive, to the number of female bees is in this proportion. The growth of leaves and stems in most plants conforms to this proportion, as does the shape of pine cones and sunflowers to name just a few. The hull of a modern ship when shaped to this proportion has the most efficient hydrodynamic advantage. The human body has many examples of this proportion as represented by Da Vinci's Vitruvian Man. The ratio of phi is the "logic of nature," juxtaposed against the chaos that opposes it. In many ancient cultures, it was proof of intelligent design so it should come as no surprise that this ratio is found within a certain mathematic relationship between the walls of the Mishkan and two specific aspects of God's Explicit Name! We see this quite clearly in the specifications of the tabernacle.

There were 20 beams on one side of the Mishkan and 20 beams on the other. If the 20 beams of each wall are divided to the nearest beam according to the ratio of phi (1/φ x 20) then the two portions of the wall are 12 beams and 8 beams respectively. Each beam was 1 1/2 cubits in width, which is the same as 9 handbreadths. The portion consisting of 12 beams would thus be 108 handbreadths and the remaining portion (which was the holy of holies) consisted of 8 beams, which would be 72 handbreadths. The sum of the two portions (108 + 72) equaled the length of the wall. The point dividing the two segments was also the point dividing the 'Holy of Holies' from the remaining area. To put it another way, the
20 beams of each wall were 180 handbreadths. The holy of holies, or inner portion, comprised 72 of these handbreadths, and the outer portion comprised the remaining 108 handbreadths.
 
Do those numbers sound familiar?  Of course they do! In terms of these proportions, the 108 handbreadths on the southern wall, opposite the 108 handbreadths on the northern wall were just like the luchot with a volumetric measure of
108 cubic handbreadths opposite 108 cubic handbreadths. These portions and their respective number of elements correspond to the number of letters in God’s Explicit Name. So too does the remaining portion, in that there are 72 handbreadths on the southern wall opposite 72 handbreadths on the northern wall. However, since there are only 2 x 72 (handbreadths) the remaining measurements would seem to be deficient!



The number of letters in God's Explicit Name is a function of 3 times 72 (the Triad Havayah of 72 consisting of triplets). The above model has only 2 'measures' of 72, so it appears to be missing a component or vector of the triad form of God’s Name.


Where is the third "set" of 72? Have we forgotten something? What about the third wall? So far, we’ve only discussed two walls. The tabernacle was closed at the end as pictured below. It also had a western wall in addition to the northern and southern walls. Care to guess what the measurement of the western wall was?



That's right! It turns out that this wall was made of 8 beams as well. These 8 beams were also each 9 handbreadths in width (8 x 9 = 72 handbreadths). There's our missing set! The total measure of the tabernacle where the ("golden" ark was present) was 3 x 72 or 216 handbreadths. The total measurement (of 216 handbreadths) is clearly divided into 3 groups (in the form of 3 walls) precisely conforming to, and mathematically reflecting the triad nature of the Name.



In summary, the walls have multiple characteristics that reflect the characteristics of the Explicit Name and the measure of the luchot, either in terms of the 108 x 2 (216) handbreadths associated with the twin matrix, or in terms of its triad form, 72 x 3 (216) handbreadths. The ratio of one to the other (phi / φ) as it relates to the Name and the measurement of His tabernacle, thus "defines" what He has created in the properties of nature which adheres to this ratio.

(Click to Enlarge)


The Section with the Golden Ark of the Covenant
is a reflection of the letters in God's Explicit Name


Once again we see the secret, subtle, sublime Signature of the Architect, hidden just beneath the surface of what appears to be ordinary circumstances (in this case the measurements of the tabernacle) in order to confound the casual observer. The significance of all this does not end with the examples above, and so, for the beggars among us who are not satisfied with a crust of bread, there is a bit more information to follow.




In addition to what has been mentioned thus far, the sum total of the opposing halves (180 handbreadths opposite 180 handbreadths) is the like the sum total for the two halves of a circle which is 360 degrees (180 + 180 = 360). This is like the two-dimensional shadow of a specific sphere within a specific cube (the combined cubic form of the luchot) with a specific measure, and thus a geometric absolute within the cube of creation defined by its 216 cubic handbreadths. That sphere is .5236 the volume of the cube that surrounds it, which happens to be the ratio between the royal cubit (the King's system of measurement) and the metric system (the royal cubit is .5236 of a meter).   

We have already mentioned that when the 20 beams of the wall are divided to the nearest beam according to the ratio of phi, the two resulting portions consisted of 12 beams and 8 beams respectively. What we have not yet mentioned is that the star tetrahedron with its 72 triangular corners (as a geometric reflection of the Triad Havayah) coincidentally has 12 edges and 8 vertices. The signature numbers of 72, 108 or 216, are repeatedly found as multiples in the total degrees of its various internal and external angular properties (like 2,160 in the 24 x 90 degree angles of the cube). 

We also mentioned that the beams were covered with gold. You may remember in the portion of Tetzaveh, we showed how metallic gold had a crystal lattice that was face-centered cubic, with a measured hardness of 216 MPa; and that the latticework of gold had 24 triangular (or three-sided) facets (for a total of 72 corners).


While the external measure of the Holy of Holies consisted of 3 walls, each 72 handbreadths (mentioned previously) its internal measure (less the thickness of the wall) was 60 handbreadths by 60 handbreadths by 60 handbreadths (6 x 6 x 6 times 10-cubed) or 216,000 (cubic handbreadths). All of these measurements taken together reflect the nature of the cosmic blueprint (cube [of creation] or shnei luchot) that in turn reflect the nature and number of letters in the Explicit Name.

The portion of the 3 walls above (wherein each of the 72 handbreadths is found) is comprised of 8 beams on each of the 3 walls (thus a total of 24 beams just like the 24 facets in the latticework of gold). The golden section of the tabernacle (Holy of Holies) with its 3 walls of 8 beams, is a mirror image of the crystalline structure in metallic gold on the periodic table of elements. Although it might be more accurate to say that the gold; the tabernacle; the mathematic and geometric characteristics of the magen david within the sapphire cube, and indeed everything (witness the ratio of phi in nature) all bear witness to the One Who created the universe, and that the Signature of this Architect is hidden within the nature of each component.

(from left to right)
Three-Dimensional Magen David in the Cube of Creation
Face-Centered-Cubic Lattice of Gold
Holy of Holies in the Tabernacle



(Click to Enlarge)

With the above in mind, lets take a look at some of the more advanced geometric parallels between God's Name, the Tabernacle and the magen david in the third dimension. Each of these measures should be contemplated as they apply to the letters of God's Name.

Three-Dimensional Magen David
External Ratio ~ Cubic
Number of Triangular corners = 216
8 Primary (Large) Faces
24 secondary (small) faces (w/ three-corners) = 72 triangular corners

~

Gold
External Ratio of its Crystalline Structure ~ Cubic
Hardness = 216 MPa
Each side/face = 8 lines
24 tri-angular (
three-sided) facets = 72 corners

~

Golden Section (Holy of Holies) of the Tabernacle
Internal Ratio ~ Cubic
Product of Internal Ratio = 216 (ten-cubed handbreadths)
Each side/face = 8 beams
24 beams =
three sides/walls of 72 handbreadths
 
~

  • Every face on a star tetrahedron or triangle of a magen david has 3 angles.
  • Each of the 3 angles is 60 degrees (3 x 60 = 180).
  • The north and south walls of the Mishkan were 180 handbreadths in length.
  • The internal measure of the Holy of Holies was in the form of 3 measures of 60.
  • The angles of the (equilateral) triangular faces on the star tetrahedron (or magen david) are 60 degrees, 60 degrees, and 60 degrees. 
  • The internal measurements of the Holy of Holies is 60 x 60 x 60 (handbreadths)
  • The 3 measures of 6, or 3 measures of 60 mentioned above, reflect the measure and ratio of the combined cubic form of the luchot defined by 3 measures of 6 (6 x 6 x 6)
  • When the face of any triangle (on the magen) is "tilted back" into the third dimension as would be the case on a star tetrahedron (which is three-dimensional) the ratio of the angles of one to another changes in terms of its 2-D orthographic projection.
  • When the top angle is 108 degrees, the sum of the 2 bottom angles is 72 degrees.
  • When the top angle is 72 degrees, the sum of the 2 bottom angles equals 108 degrees (72 + 108 = 180 or the measurement of the walls).
  • When the walls of the Mishkan are proportionally divided according to the golden ratio, there are 8 beams and 12 beams respectively. The 8 beams are 72 handbreadths and the 12 beams are 108 handbreadths (72 + 108 = 180 handbreadths).
  • The magen david (in the third dimension) has 8 vertices and 12 edges and the sum total of its various related angles are multiples of 72 and/or 108 degrees.
  • The star tetrahedron or magen david (in 3 dimensions) has 8 primary (large) faces with 72 corners.
  • The tetrahedrons of the "star" have 12 secondary (small) faces with a total of 108 corners (72 + 108 = 180 corners).

All of the above are mathematic or geometric reflections of characteristics within and without the original sapphire cube that was 6 x 6 x 6 (216 cubic handbreadths): the two luchot that were 2 x 108 cubic handbreadths (216) or in their ratio of a single side-by-side matrix of 72 x 3 cubic handbreadths (216); and the geometric characteristics of the magen david in the third dimension. All have a direct correlation with God's Name. Is this a coincidence or is it the result of careful design, and if it is of design, then who is the designer? The answer should be somewhat obvious!


This week's post will end with one last assertion. As hard as it may be to believe, it can be shown in the geometry of the 3 walls consisting of 8 beams covered in gold (with its 24 facets) together with the resulting internal measurements, that these numbers, sets of numbers and ratios between sets, provide an accurate reflection of the number of letters in the written Torah. However, an in-depth explanation of this particular mathematic relationship is beyond the scope of a weekly post because it involves aspects of the twins that are far more complex. However, a glimpse of this relationship can be seen in the post on  “The Eight Dimensions.”