Sunday, March 24, 2019

Shemeni and Tazria

Parashah Shemeni will be combined with Tazria because the subject matter of the second is a continuation of the first and the two have a unique connection that reveals a parallel between the Explicit Name and the physics of string theory and what is called the E8 lattice.

In previous posts we have seen that the numbers, sets of numbers and corresponding ratios associated with this Name can be found in such things as: 

  • The geometry of the shnei luchot or tablets of the covenant;
  • The geometry of the magen david or star tetrahedron;
  • Various events that have occurred throughout biblical history;
  • The construction of the tabernacle and its furnishings;
  • The clothing of the priests or cohenim;
  • The movement of the stars;
  • Characteristics of relevant metals on the periodic table;
  • The latticework of certain relevant crystals; and 
  • Biblical and modern systems of measurement.

With respect to the systems of measurement, we noted in last week's post how the mathematic characteristics of the letters in God’s Name were the common denominator between these systems, and how more modern variants are still in use today among the nations. In some cases these measures were further refined for purpose of accuracy, like the minim which is a "measured drop" equivalent to 1/60th of a dram that is in turn 1/6th of an egg. In the vast majority of circumstances however, the mathematic Signature pertaining to the Name is essentially invisible. The origin of the systems and their significance has been lost to antiquity (assuming it was ever known at all). In each case, the Signature, or one of its many reflections, is hidden in numbers, sets of numbers and ratios between sets.

If what you have read above is new to you and this is your first visit to this blog, then 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 basic connection between the letters of the Name and the multidimensional mathematic and geometric characteristics of the luchot (tablets of the covenant) 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 signature geometry is hidden in each week’s parashah. Once you are familiar with these constructs you can more fully appreciate each post.



In this post we will introduce some additional units of measure to further demonstrate that the early systems all revolved around the letters of God’s Name, and in the case of the mikva and its measure, it is attached to numbers and sets of numbers that we see in theoretical physics. Before we get into the details, it is worth mentioning that the first parashah we will discuss is named Shemeni, which refers to the eighth day and the sacrifices that would precede the moment in time when God would reveal Himself to the people.

While this 'revelation' may have started, or at least began to accelerate in this parashah, it is really an ongoing process that will not culminate until the entire world knows God's Name. How is that even possible? Our understanding of science is becoming more advanced everyday, and through these advances we continue to see how intricately connected the letters of this Name are to our reality in the physical universe. Just as He revealed Himself back then, to the people living at the time described in this parashah, He continues to reveal Himself to people today. Where or how does Shemeni enter this equation?

It happens that eight days have a connection to the two primary abbreviations of the Explicit Name, that have a total of 8 letters. These abbreviations can be seen (juxtaposed against one another) in the shiviti of most shules (synagogues) and they are referred to as the Tetragrammaton (yud-key-vav-key) and the Havayah of Adnoot (aleph-dalet-nun-yud). Each abbreviation has four letters. The two 'Names' together, have 8 letters that can be perceived in male~female form as 4 opposite 4. They combine to form the Havayah of Ehyeh (aleph-heh-yud-heh). See the post on "The Marriage of the Letters" for details.

These letters have a geometric connection to the combined cubic form of the luchot which has 4 corners opposite 4 corners (a total of 8 corners) and also the star tetrahedron or “royal seal” of the King, which has 4 points opposite 4 points (a total of 8 points). The star tetrahedron, or what we call the 'royal seal,' is an internal mathematic construct of the cube, or more specifically the combined cubic form of the luchot. This internal construct is three-dimensional but it casts a two-dimensional shadow known as a magen david. The relationship between these abbreviations, the luchot and the geometry of the royal seal is explained more fully in other posts such as Emor and Ki Thetze. Insofar as this post is concerned it is sufficient to know that there are 8 letters involved in the “marriage” of these 2 Names of 4 letters and this is why the eighth day has a unique place in the passage of time.

In Shemeni we are told “the waters of the mikva [always] remain clean,” and the subject of the parashah deals with purity and the mikva’s role in making clean what is unclean (in that sense). The Signature of the Architect is surely hidden somewhere within the measurements of the mikva, so let’s take a closer look at those measurements. In order to do so, we need to focus on several units of measure in particular. The first is the se’ah and the second is the egg. The volume of a mikva is 40 se’ah. How much is a se’ah

A se’ah is equal to 144 eggs (in Hebrew the word for egg is beytza). Since there are 40 se’ah in a mikva, the total volume of a mikva is 40 (se’ah) x 144 (eggs) or 5760 eggs. There are of course fractional proportions within an egg as well, like a half an egg, a third of an egg, or a sixth of an egg, which happen to be the same fractional proportions that are defined when a cube that is measured in terms of 6 handbreadths (6 x 6 x 6 ) is divided in half. The sapphire block under the throne (seen in Parashah Mishpatim) was divided in half and became the two tablets of the covenant, that were each 6 x 6 x 3 handbreadths. Each handbreadth is either a third or a sixth of any given side.

There are specific “terms” used by the Sages of Israel to describe these fractional proportions, and specifically as they apply to a beytza/egg. For example, Rabbeinu Yitzchak defines a “ke’zayit” (olive) as one half of an egg, and the RamBam defines a “grogeret” (dried fig) as one third of an egg. Rabbi Culi (Me'am Loez) describes a sixth of an egg as a dram. The actual volume or measure of these items, whether it is an olive, grogeret or a dram, does not necessarily have anything to do with the fractional proportion, although there is an approximate equivalency. Rather, the name of the item is assigned to the fractional proportion for practical purposes, like the application of halachic requirements.

Regardless of terminology, 5760 eggs is equivalent to 17,280 grogerets or third-of-an-egg units in the measure of a mikva. Having said that, and as interesting as the above numbers may be, we still have not ascertained whether God’s Name is hidden in the measure of the mikva. In order to test the theory that there is a connection, we would (as an example) need to determine whether the measure of the mikva in one or more units of measure (like the 17,280 grogerets mentioned above) had a relevant connection to the halachic requirements for its use (this would be one method). If the result in anyway corresponds with the nature of, or number of letters in the Name, or the geometry of the luchot or magen david, within the same context as a mikva, then we can safely say that the Signature of the Architect is the underlying basis of the measurement and its requirement. 

The most relevant numbers having to do with the context of purity (which is the subject of the text) happen to be those that immediately follow the mention of the mikva in Shemeni. Those requirements appear in Tazria, where the waiting period for a woman, who has just given birth, is specified. For a girl, the full waiting period is 80 days, and for a boy it is 40 days. If you divide the 17,280 grogerets in a mikva by 80, you get 216, which just happens to be the number of letters in God's Explicit Name. If you divide it by 40, you simply get twice that, or 2 times 216, which is 432 and the combined volumetric measure of both sets of luchot that were ultimately brought down by Moshe (the first set having been shattered). 

In addition to the above, the octaherdal core of the star tetrahedron (which is mathematically defined by the faces of the [foundation] stone or combined cubic form of the luchot) has 3 equal triangular corners and 1 triangular center (4 triangles) on each of its 8 faces, for a total of 5760 degrees in each of its angles (4 x 8 x 180 = 5760) degrees. Each face alone (4 triangles x 180 degrees) consists of 720 degrees, reflecting the signature geometry of the Explicit Name (the Triad Havayah of 72). The multiple of 10 (72 x 10 = 720) finds its origin in the 10 vectors of 5 dimensional space mentioned in sefer yetzirah 1:5. The 8 faces which geometrically correspond to the 8 letters of the two Names (the four letters of the Tetragrammaton and the 4 letters of Adnoot) have a total of 72 x 80 degrees (5760) but 40 of these come from the male half of the octahedron's surfaces. One can easily see the mathematic connection between the halacha for the waiting period mentioned above; the measure of the mikva involved in that halacha; the geometry of the octahedral core of the star tetrahedron at the heart of the foundation stone; and the nature of the E8 lattice (that we will examine in the paragraphs ahead) which is itself a more complete model of the physics behind the entire universe. Its a rather odd coincidence isn't it? Or maybe, just maybe, it's not a coincidence at all, but a reflection of a much larger reality that is dependent on the letters of God's Name.

Either way, the halachic requirements in combination with the geometry of the luchot and the mathematic characteristics of God’s Name,is equal to the measure of the mikva. Even its use, as it would pertain to the requirements for a boy or a girl, is dictated by the nature of those letters. The numbers are not arbitrary. There is a specific reason for the numbers involved in the requirements. They are crystal clear reflections of the letters in God's Name and the numbers and sets of numbers that ultimately define the cosmic blueprint or shnei luchot. God makes clean something that is unclean and His Signature is embedded throughout the 'specifications,' as seen in the above measures (in terms of both time and space) that are a required part of the process.

God is of course "the Master of the Universe" (a title given Him by Avraham). From the parashah we learn that when something in His universe is unclean, contact with it makes whatever touches it equally unclean (although again the words pure or impure might be more accurate). Either way, we immerse ourselves and we immerse objects such as when newly acquired utensils must be teveled

The halachic requirement ultimately boils down to a process involving the rectification of the soul, and the ensuing social stability it provides to the people of Israel. When the need for rectification arises, the mikva (immersion in water) provides a solution, but there could be more going on than might first appear. As an example, look at our requirement to rest on the seventh day. The concept has a larger role that we often miss. The land must rest every seventh year (the shmitah) and God Himself rests every seven thousand years. Does the concept of purity extend further as well? Is it possible that other things are 'made clean' in similar fashion? Perhaps a stellar process (involving the underlying physics of the universe) that ensures some sort of cosmic stability, but a process for which man is completely unaware? Is there another aspect to this? If so, what process might be involved, and where might it be found, in what set of numbers? In what context? At this point, we can only hazard a guess as to this aspect of a larger reality, but it could be much the same.

For those of you who took the red pill, the following may be of interest. If you've read the advanced construct's on String Theory and the Luchot, and also the E8 Lattice and the Explicit Name, then you may already know that the measure of the mikva is closely related to the E8 model. More specifically, it appears that certain aspects in the physics of string theory and also that of gravity, in quantum mechanics (which are both related to the stability of the universe) all have a connection to, or rely upon, the same numbers or measurements found in the mikva for their continued existence. In order to get a glimpse of this hidden connection, we need to understand that string theory, and specifically the heterotic string (a hybrid of the 26-dimensional bosonic and 10-dimensional superstrings) are an integral part of the universe that God created. OK. So what does this have to do with His Name and the mikva or the continued existence of the universe? This brings us to the E8 Lattice.

In mathematics, there is a lie algebra group known as “E8” that mathematically models a part of this relationship. As an example, you may remember that we started this post by referencing 2 primary abbreviations of God’s Explicit Name that each have
4 letters. When the 8 letters are married together they create a third (unified) abbreviation. The mathematics of the E8 lattice is an identical match. It can be constructed, for example, from binary code1 (a binary system has 2 elements) in this case with rank 4 and a length of 8. Remember those 2 Names of 4 letters that have a total of 8 letters? The binary code is generally represented by H(8,4) signifying the fact that it is a self-dual. The application results in the E8 lattice, but let's assume for the moment that this is just a coincidence.

The geometry of E8 has 2 primary symmetries that preserve the lattice2 much like the 2 abbreviations of the Name we mentioned earlier. It just happens that these symmetries  possess additional measurements that are identical to those of a mikva and the letters of the Triad Havaya of 72, or the Explicit Name. Before providing details, it might be worth mentioning (just to give you an idea of its complexity) that it took 18 mathematicians and computer scientists 4 years using a computer to crunch the numbers and fully model the group. The geometry is pictured below. 

The E8 Lattice


Where do we see the letters of God's Explicit Name and the requirements for the mikva in this complex system? Each point of the E8 lattice is surrounded by 2160 symmetrics known as ‘8-orthoplexes’ and 17,280 known as ‘8-simplices.’ Do those numbers sound familiar? They should. The total number of degrees in the angles of the evan shetiyah (foundation stone ~ original form of the luchot before division) adds to 2160. There are 216 letters in the Explicit Name, which defines the measure of the blueprint/luchot, which in turn defines everything else like the passage of time, as seen in the 2,160 years that it takes each constellation to pass through the procession of the equinoxes. The total period of time is 25,920 years (called a great year) which, as we saw in last week’s post, is equal to the number of “drops” in a “hin” and also the number of “halaqim” (parts) in a 24-hour day. Everything is connected, and when you connect the dots, it invariably boils down to some facet of the Name or the geometry of the luchot (tablets).

In this case, each measure, be it 216 or 10 x 216 (2160) or 10 x 12 x 216 (25,920) are all multiples that originate with the letters of the Name that “defines” the day, the great year, or the measure of the hin. Here we see the 216 letters “define” a fundamental aspect of physics. We even see its corresponding abbreviations (2 Names with 4 letters, having a total of 8 letters) further define these fundamental aspects of the model. Remember the 17,280 symmetrics in the form of the ‘8-simplices’ mentioned above?

The other primary group in E8 involving 8-simplices, consists of 17,280 symmetrics. The number of these symmetrics is 3 times the number of shallow holes surrounding the origin in the lattice. So the number of shallow holes is 5760. Both of those numbers should also sound familiar. Each is a key measurement of the mikva. The number of grogerets in a mikva, for example, is 17,280, and the measure of a mikva in eggs is 5760. That’s a strange coincidence isn’t it? Or maybe, just maybe, it’s not a coincidence. Maybe the physics of the universe really does revolve around the letters of God's Name!

Remember the 8 letters in the two abbreviations? We've been examining the E8 group with reflections in its geometry that result in multiple groups of 8 intersections. The sacrifice for the 8th day in Shemeni is about God's presence descending to the tabernacle (His dwelling place in the physical universe) and subsequently revealing Himself to the people. The specific mathematic and geometric characteristics of the letters in God's Name were hidden in the measurement of the tabernacle (see the post on VaYakhel). Just as the measurements of the tabernacle hide the characteristics of the letters in His Name, so too does the E8 lattice where the letters are also a function of its mathematic and geometric properties. The numbers that correspond to the multiple intersections of this lattice, that model certain aspects of the universe, are either multiples of its 216 letters, or sets of numbers and ratios that correspond to its abbreviations that we see so often throughout the Torah. Or, is this too a coincidence?

We know that the shnei luchot (or two halves of the cosmic blueprint of creation) are a reflection of His Name, as are the systems of measurements in the Torah and the mikva. Is it so hard to believe that the Architect, who created the strings of energy and the gravity that binds us to the surface of the earth, did not specify their measurements in the same terms? The characteristics we find in E8 are just another reflection of the specifications in the  blueprint wherein the measurements for the entire universe are found. At some point it becomes necessary to accept the fact that all of these relationships are a reflection of a larger reality, and that the larger reality really does center around the letters of God’s Name.

These letters and their proper pronunciation along with when, and under what circumstances they are permissible to pronounce, have been preserved by the Sages of Israel so that one day mankind would be able to recognize the work of his Creator, and accept, honor, and bless the One Name that rules the kingdom!

For more information on E8, God's Name and the physics of string theory, see the advanced construct entitled: The E8 Lattice and the Explicit Name

_________________

Footnote 
1 - The Hamming Code
Footnote 2 - The Weyl/Coxeter Group










Saturday, March 9, 2019

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 lower dimensions was measured in terms of 6 handbreadths. This "division is the result of a geometric precedent set by the 6 faces that define the combined cubic form in the higher, or 3rd dimension (each 2D face is 1/6th of the 3D cube) and so each handbreadth in each lower dimension must be one sixth (1/6) the measure of any given dimension. This is (literally) the origin of the sacred (royal) handbreadth.

When the foundation stone (mathematic foundation of the universe)  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 (see also the 'essential construct' on the origin of the 360 "portions" of a circle or sphere listed to the right). 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 being the only (halachic) 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, which is itself a refection of the Creator's Name.

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 measurement and
geometric nature of the luchot is the “cosmic blueprint” for creation. it provides 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.





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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. 

Sunday, March 3, 2019

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?