The examination will include specific measurements such as: the “hin;” the "log" (singular) or “lugim” (plural); 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)
(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.