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).
From this we see that the halachic requirements in combination with the geometry of the luchot and the mathematic characteristics of God’s Name, gives us the measure of the mikva. Moreover, we learn that 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, and 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 measure of the mikva that is a required part of the process.
God is of course "the Master of the Universe," and this is in fact the 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?
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