We will examine all of this in the paragraphs ahead. However, if you are new to this blog, please read each of the essential constructs listed in the column to the right before proceeding. These pages reveal some of the basic mathematic connections between the letters of God's Explicit Name and the multidimensional geometric characteristics of the luchot, both in the divided state and combined cubic form, along with the internal geometry that casts a shadow known as a magen david. There is a special connection between the Name, the luchot and the geometry of the magen, and together they form a unique signature. We refer to this geometry and its mathematic common denominator as the Signature of the Architect. The purpose of this blog is to show how all of these things connect, and to reveal where the signature geometry is hidden, not only in each week’s parashah, but the physics of time and space, quantum mechanics and celestial dynamics to name a few. Once you are familiar with these constructs you can more fully appreciate each post. For more specific information on the 'royal seal' (magen david) see the post on Emor.
In Parashah Eikev, Moshe begins to summarize all that has happened to Israel, and to clarify everything that God requires of His people. Moshe reiterates how he received the luchot (tablets) and the circumstances involving the shattering of the first set (with 'ten' alluding to the shattering of the vessels). He then proceeds to describe the second set. They are referenced so many times and in so many ways, that one cannot help but notice the mathematic and geometric nature of: 1) the narrative itself; 2) the words used to convey the narrative; 3) the letters used (or not used) to form the words; and 4) the number of times certain specific words and phrases relate to one another. The number of allusions to God’s Explicit Name as a geometric function of the royal seal, is overwhelming.
We’ll start by describing the linguistic structure embedded in Moshe’s account of the first set of tablets (note the redundancy).
- 9:09 - “I had climbed the mountain to get the stone tablets...”
- 9:09 - “...tablets of the covenant that God had made...”
- 9:10 - “God gave me the two stone tablets written with God’s Finger.”
- 9:11 - “God gave me the two stone tablets...
- 9:11 - “...as tablets of the covenant...
- 9:11 - "but God then said to me “hurry down... the nation... has become corrupt.”
- 9:15 - “[I] went down... the two tablets of the covenant were in my two hands”
- 9:17 - “I grasped the two tablets and threw them down with my two hands..."
- 9:17 - "breaking them before [their] eyes.”
Notice first of all, the beautiful symmetry of the narrative. Count the number of times the word “tablets” is mentioned (seven times). Then count the number of times the phrase “the two stone (tablets)” is mentioned (twice). Note that this phrase is in the form of a "pair," using the same sequence of letters. Also count the number of times the phrase "two tablets" is mentioned (twice). Note they too form a "pair" using the same sequence of letters. And finally notice how many times the phrase “two hands” is mentioned” (twice) again as a "pair." We’ll explain the significance of the phrases in a moment, but first we’ll examine the account of the second set of tablets.
Moshe then proceeds to describe the second set of tablets like this (again note the redundancy).
- 10:1 - “God [then] said to me, “Carve out two stone tablets like the first ones...”
- 10:2 - “I will write on the tablets the words....”
- 10:2 - “...which were on the first tablets.”
- 10:3 - “I... carved out two tablets like the first...”
- 10:3 - “[I] then climbed the mountain with the two tablets in my hand.”
- 10:4 - “[God] wrote on the tablets the original... ten.”
- 10:5 - “I placed the tablets in the ark and remained there as God commanded”
Count the number of times the word for “tablets” is mentioned in reference to the second set (again there are seven). Then count the number of times the phrase “two tablets” is mentioned (again twice). Notice that this phrase is the only "pair" in the account of the second set. And since the second set was not thrown down, there is no mention of a "pair of hands" (two hands) either. Instead, when Moshe returns, the tablets are now in his “hand” (singular).
Keep in mind that a pair of anything, generally denotes the marriage of opposing halves like male and female. We’ll start with the number of times the word “tablets” is mentioned. With reference to the first set, the word is used seven times. With reference to the second set, the word is again used seven times. In other words, we have a pair of seven's that are distinctly seven opposite seven2, which is the specific 'set' of numbers that constitute a one-dimensional mathematic shadow of a two-dimensional magen david, a pattern that is seen over and over again throughout Torah. We explained the significance of this in great detail, in the post on Emor.
For purpose of review, there are seven elements in each half of the magen david: three lines, three points and one face (seven elements). When the two-dimensional geometry of the pair (or two halves) are married together, they create the royal seal that is in essence a mathematic or geometric shadow of the Explicit Name, a Name that is more clearly revealed in the three-dimensional form known as a star tetrahedron, which has 72 triangular corners (216) reflecting both the number and (triad) nature of the Havayah (Explicit Name) of 72.
The pair of sevens is a one-dimensional metric expression for the geometry of a two-dimensional magen david. However, the linguistic structure of the text also contains allusions to the three-dimensional magen as well. We see this in the “two hands” mentioned twice in the first account. The gematria or sum of the mathematic value of the letters in the word “hand” is 14. Not only is this the gematria of the word hand, but there are 14 visible joints in the actual hand of a human being. Two hands are thus 14 opposite 14, both in physical and numeric form. These 14 elements parallel the 14 elements in each half of the three-dimensional version of the royal seal or tetrahedron: six lines, four faces and four points (14 elements). That is, they are a one-dimensional metric expression for a three-dimensional reality. A pair of hands (two hands) are 2 x 14, corresponding to the 2 tetrahedrons that are 2 x 14 and “marry” together to form the star tetrahedron, that in turn casts the two-dimensional shadow or magen that we know so well.
There were two sets of luchot that would ultimately be brought down, so we see the two hands (2 x 14) corresponding to the three-dimensional geometry of two tetrahedrons “twice” (2 x 14 and 2 x 14). Each set of luchot, in their combined cubic form, both mathematically and geometrically contain one complete star tetrahedron (2 x 14 and 2 x 14). There are two sets and so we have two star tetrahedrons, and thus two references to two hands (14 opposite 14 and then another 14 opposite 14).
2 x 7 2 x 14
7 Opposite 7 14 opposite 14
Click to Enlarge
There are so many reflections at this point, that they are hard to count. The phrase “the two stone (tablets)” for example, is mentioned twice with reference to the first set of tablets, but this exact terminology is missing from the second set. The gematria or mathematic sum of the letters in “the evanim” (heh-aleph-bet-nun-yud-mem) which is the Hebrew phrase for “the stones,” is 108, so two of the stone(s) is 2 x 108 or 216. This is, once again, not only the volumetric measure of the luchot in terms of cubic handbreadths, but also the number of letters in the Explicit Name. The phrase is mentioned twice, alluding again to the two sets of tablets having been brought down twice. However, as mentioned above, this phrase (where the number of letters in the Name are in the gematria) is missing from the second set.
In the second set, the phrase "the two stone tablets" is not mentioned. Instead we see that they have become simply "two tablets" and so we no longer have a gematria of 108, or a bright mathematic reflection of the letters in the Explicit Name. Without this, the 2 x 108 is missing and the connection to the 216 letters of God's Name is gone (its light being hidden because of the sin). This would suggest that the original internal geometry of the luchot is also somehow slightly different, and that the national destiny will be fulfilled differently. Since the direct connection to the 216 letters is missing from the gematria of the words describing the second set, God's Name is now hidden. This no doubt contributes to the delay and so the redemption must wait for a time when the people are more inclined to draw closer to God (to fully know and embrace His Name).
The phrase “two tablets” is mentioned twice with reference to the first set of tablets, and twice with reference to the second set of tablets. Both are mentioned twice, similarly alluding to the two sets of luchot that were brought down twice.
Then there is the letter vav in the word luchot for “tablets.” We mentioned this vav last week in the post on VaEthChanan and explained the significance of the subtraction so we will not repeat the explanation here. However, we have the same unusual change in spelling in this parashah. With reference to the first set of tablets the word luchot is spelled with a vav, except for when Moshe is told to hurry down, where we find half of the references with the vav (one reference) and half without (one reference). In other words, in the symbolic language of letters and their equivalent numbers, as Moshe hurries down, the vav 'begins' to disappear in reference to the luchot in Moshe’s two hands. The light is flickering out, and so the final reference to the luchot of the first set is without a vav when the tablets are cast down and shattered. Had the vav not been “removed,” it would have been impossible for them to fall/shatter (that vav being a letter of God's Name).
Notice also that in Moshe’s narrative pertaining to the second set of luchot, the tablets are diminished by the near-complete absence of the vav, which appears only once in the very first verse, when God Himself refers to the first set: “carve out two stone tablets like the first,” alluding to the intrinsic difference between the first and second sets.
As if the above reflections are not enough, there is one more that is very faint (so faint as to be virtually invisible) but significant. In the post on Behar and BeChuko-thai we talked about the matrix of 7, or the “flow of time” as defined by recurring patterns of 7s and 8s and 49s and 50s. This was made evident over and over again in the nature of the calendar and the halacha as it relates to certain required observances as well as various events. The numbers, sets of numbers and ratios between sets, ultimately defined a cubic matrix of 7 x 7 x 7 elements, which is in reality the outer garments of a cubic matrix that is 6 x 6 x 6 (explained and modeled in man posts like the one on the eight dimensions). The outer garments effectively hide the inner essence of all that happens (the 216 letters of the Explicit Name). The events described, or rather the numbers corresponding to these events, form or create, for lack of better terminology, the physical world that is revealed to us, including but not limited to the history of mankind (7 x 7 x 7: 7 days; 7 x 7 days; 7 weeks; 7 x 7 weeks; 7 years; 7 x 7 years). However, embedded within that matrix, as demonstrated specifically by the intersections or spaces between the elements of this “revealed matrix,” was another internal (hidden) mathematic matrix consisting of 216 elements (a model is pictured below). The elements of the outer matrix (or revealed world) in this model consists of 343 elements, like the gematria of “and God said,” when He spoke the world into existence. These outer elements are the garments (letters) of the written Torah describing so many historical events. The elements of the inner matrix are the spaces between the outer elements, and they number 216 which corresponds to the number of letters in God’s Explicit Name. One matrix (the written Torah) is revealed (nigleh). The other matrix, God's Explicit Name, is mathematically hidden beneath the surface.
You may remember from the post on Behar and BeChuko-thai, that the number of letters in the Torah corresponding to the universe in its present male-female form (after God separated the female from the male) was 304,800 letters, and this was enough letters to populate a cubic matrix of 7 exactly 888 times. In the written Torah, the 216 letters of God’s Explicit Name appear contiguously in the midst of those letters (as three verses having 72 letters). The remaining letters of Torah are “divided,” much the same as the letters of God’s Name are divided in the geometry of the luchot (108 opposite 108) or the 4 letters of the Tetrahedron that are "divided" and stand opposite the 4 letters of the Havaya of Adnoot. If we divide the 888 cubic matrices in like fashion, we get 444 matrices (times 2). It happens that the gematria of the word tablets, meaning luchot (with the vav) is 444. The 2 (tablets) x 444 (the gematria of luchot) = 888, which is the number of cubic matrices of 7 x 7 x 7 (outer garments) that can be formed by the letters in the portion of the Torah cited above.
A Geometric Representation or Model of a Cubic Matrix of 7 (the measured lines)
containing an Internal Matrix of 6 (the measured spaces with 216 Elements)
containing an Internal Matrix of 6 (the measured spaces with 216 Elements)
Click to Enlarge
Once again, we see with amazing clarity, the interconnectedness between the luchot; God’s Name; the events that are described in the Torah; the word level of the text in the Torah; even the letter level of the text in the Torah, as well as everything else in the physical and nonphysical universe. All have this unique inexplicable mathematic and geometric connectedness that defies logic. The absolute precision of the various combinations, the number of repetitions of these combinations, together with what they represent in terms of, for example, complex three-dimensional geometry, two-dimensional geometry (etc.) would simply have been beyond the ability of any man or group of men to compose. It is as if the numbers, and sets of numbers, and ratios between sets, pre-existed the text itself, and the text were an extension of those numbers. This accounts for why we find the mathematic value of the letters so perfectly reflecting the same combinations. They are all an integral part of the royal seal and the letters of God’s Name that are so well hidden beneath the surface. Who could write a meaningful narrative that was so mathematically and geometrically perfect? Only the Architect Himself. As it says... “written with God’s Finger.”
As an addendum to this week's parashah, several universities have demonstrated a new technology for storing data. These scientists have successfully used femtosecond lasers, to write this data in five-dimensions within the crystalline structure of quartz. Unlike conventional hard drives, the data, once it is written to the crystalline structure, is stable for millions of years, if not eternity. It can even withstand temperatures over 1000 degrees Fahrenheit. Moreover, crystal plates (like those in a single hard drive) could hold as much as 360 terabytes.
There are several interesting parallels that come to mind. Our Sages said that, contained within the Torah (or really the tablets of sapphire-like crystal) was a record of everything that had ever happened and everything that would ever happen in the future, along with the names of every individual and everything they had ever done. In other words, it would contain a record of everything, down to the last detail. The combined cubic form of the luchot contains 5 intrinsic mathematic constructs (one of which is the tetrahedron that we discussed in this post). The luchot were “carved” from a crystal-like sapphire. The scientists in comparison, use a laser to "carve" their data into quartz crystal within the three-dimensions of its substance, and encoded additional information in terms of polarity (male-female) and the intensity of the beam (brightness of the light) using a total of five-dimensions. A half-wave plate matrix controlled the polarization of light and there was no need for moving parts. The laser imprinted dots arranged in 3 planes, separated by a distance of 5 microns.
Inspired by their knowledge of this cosmic blueprint and its intrinsic nature (as it relates to God's Name) there are those who seek to revolutionize the way we store data. At this very moment, development is underway for a similar mass data storage drive using Sapphire (the closest medium to the luchot) instead of quartz, to capitalize on its numerous advantages, all of which correlate with the nature of the cosmic blueprint where the Signature of the Architect is hidden. God willing, within the near future, this new technology will not only be available to the public, but recognition of this unique signature and the Name it represents, will become more commonplace and ever-present in our daily lives.
Either way, all would appear to be on the “write” track (and yes that was a pun ~ sorry). The scientists by the way, dubbed the crystals “superman memory crystals” after the technology featured in the now famous superman films, where superman’s father recorded all knowledge in the crystals that were given to superman. Superman’s name was “Kal-El” (Voice of God). With the help of his father Jor-El, he escapes a dying world in a one-of-a-kind vessel (like Noach). He is given up by his real parents to adoptive parents (like Moshe) with all of the parallels being somewhat obvious. The fact that science seems to be catching up to what may well be the Torah equivalent is interesting to say the least.
Footnote 1 - One-dimensional metric geometry is a term that equates mathematic formulae with higher dimensionality. In this case, the two-dimensional geometry of a magen david (which is the marriage of two triangles in opposing directions) is expressed in terms of one dimension as a set of numbers that equate to the number of elements (7) in each half, that correspond to it's expanded geometry in a higher dimension (7 opposite 7).
Footnote 2 - Seven opposite seven is a repetaing pattern in the written Torah, because it is a mathematic aspect of the Primordial Torah, or combined cubic form of the luchot. This is why events echo these characteristics. The Shekhina, for example, is said to have gradually departed, and that this progression went from the first firmament, to the seventh firmament. The Shekhina then returned (came back progressively) as it moved from the seventh firmament back to the first firmament (as is known) the 'events' once again reflecting the two-dimensional metric geometry of the royal seal (seven opposite seven) which is a complex mathematic construct hidden within the combined cubic form of the luchot.