#23 Rhombic representations of the superstring structural parameters 2016, 1680, 3360 and 168

The sum of the numbers of turns in a whorl of the UPA and in a whorl of Cowen's particle = 1680 + 2016 = 3696 = 2×1848, where 1848 is the number of turns in half a revolution of both types of whorl. As 1848 = 43² − 1, two 43×43 regular rhombic arrays of dots sharing one of their corners have 3696 dots surrounding the latter. Each rhombus represents either the outer or the inner halves of the two types of whorls. The number 43 is the 21st odd integer after 1, showing how EHYEH, the Godname of Kether with number value 21, precribes this number. Lining the four sides of each rhombus are 168 dots, where 168 is the number value of Cholem Yesodoth, the Mundane Chakra of Malkuth. This means that the two separate rhombi have eight sides lined by 336 dots (42 per side, where 42 is the 21st even integer). As 3696 dots surround the centres of the two separate rhombi and, as 3696 = 11×336, there are (3696−336=3360) internal dots surrounding their centres (1680 in each rhombus). As 3360 = 15³ − 15, this is the number of dots that surround the diagonal of a 15×15×15 cubic array of dots. This shows how the Godname YAH with number value 15 prescribes the number of dots that are inside both separate rhombi and surround their centres. They embody the superstring structural parameter 3360, namely, the number of turns in each revolution of the ten whorls of the UPA. Including the dot at its centre, each separate rhombus has 1681 dots inside it, where 1681 = 41² and 41 is the 21st odd integer.

As 29² − 1 = 840, the 29×29 array of red dots in each joined rhombus contains 840 red dots other than the shared corner. They symbolise the 840 turns in an outer or inner half of each whorl of the UPA. The number of green dots in the 41×41 rhombus that are outside the 29×29 rhombus = 41² − 1 − (29²−1) = 41² − 29² = (41+29)(41−29) = 70×12 = 840. The number of green and blue dots in each 43×43 rhombus outside the 29×29 rhombus = 1848 − 840 = 1008 dots. They symbolise the 1008 turns in an outer or inner half of each whorl in Cowen's particle. The number of blue dots in each 43×43 rhombus that are outside the 41×41 rhombus = 43² − 1 − (41² − 1) = 43² − 41² = (43−41)(43+41) = 2×84 = 168. The pattern of numbers of dots in the two 43×43 rhombi is:

(168+840) + 840 + 1 + 840 + (840+168) = 1008 + 840 + 1 + 840 + 1008 = 2016 + 1680 + 1.

The two 41×41 rhombic arrays, each with 840 red dots, represent the two halves of each whorl in the UPA, each with 840 turns, and the remainder of each 43×43 array made up of 1008 green and blue dots represents the 1008 turns in the inner or outer halves of each whorl in Cowen's particle.

As pointed out on page 22, isomorphism exists between stright line and circular sacred geometry provided that the smallest circles in the latter have a diameter of 168 units. The Seed of Life is a basic variety of this type of sacred geometry. Its seven circles have a total length of 7×528 = 3696 units. Remarkably, this is the total number of turns in one whorl of the UPA and in one whorl of Cowen's particle. If we reject the possibility of coincidence as highly improbable, there is no more plausible explanation of this than that the Seed of Life encodes the number of circularly polarised oscillations in a whorl of each E₈×E₈' heterotic superstring.

The Kabbalistic meaning of the number 43

The n-tree is the n lowest Trees of Life of the 91 Trees of Life in CTOL. It has (12n+7) triangles with (6n+5) corners and (16n+9) sides. The 7-tree maps the seven subplanes of the physical plane (what physicists call "space-time*). Its 91 triangles have 47 corners and 121 sides, i.e., 168 corners & sides. True to its meaning as corresponding to Malkuth, the 7-tree embodies the number value 168 of the Mundane Chakra of this Sephirah. The number of SLs up to Chesed of the nth Tree = 6n +1. There are 43 SLs up to Chesed of the 7th Tree and 29 SLs up to Kether of the 4th Tree. The number 43 measures the number of SLs up to the first Sephirah of Construction of the Tree that represents this Sephirah.

There are 41 SLs up to the top of the 6th Tree. The 41×41 rhombic array contains (41²−1=1680) dots other the corner shared with the other array. The number of other dots in each 43×43 array = 43² − 1 − (41²−1) = 43² − 41² = (43+41)(43−41) = 84×2 = 168. This is the number of dots that line each separate 43×43 array. The number value of the Mundane Chakra of Malkuth shapes each rhombus embodying the numbers that quantify the oscillatory structure of the whorls of the superstrings of ordinary matter and dark matter.

The 22 Hebrew letters

The 22 letters of the Hebrew alphabet represent the 22 paths connecting the ten Sephiroth (divine attributes) on the Kabbalistic Tree of Life. There are three categories of letters:

Three Mothers (Aleph, Mem, Shin), representing primal forces like spirit, water, and fire;

Seven Doubles (Bet, Gimel, Dalet, Nun, Pei, Resh, Tav), correlating to planets, senses, and physical attributes, with double pronunciations;

Twelve Simples (He, Vav, Zayin, Chet, Tet, Yud, Chaf, Lamed, Samekh, Ayin, Tzadi, Kof), linking to the zodiac, the twelve months, and the body's functions (sight, hearing, etc.).

In ancient Kabberlistic text known as the "Sefer Yetzirah" (The Book of Formation), the three "Mother Letters" (Otiyot Immot): Aleph (א), Mem (מ), and Shin (ש) are considered the "mothers" because, according to the Kabbalah, they are the foundation from which all other things in the universe were created. Each corresponds to a primary element, a season, and a part of the human body.

This classification into three sets, one of three letters, one of seven letters and the third of twelve letters, means that the number 22 is the sum:

22 = 3 + 7 + 12 = 10 + 12.

The numbers 10 and 12 manifest in the UPA and Cowen's particle as the ten half-revolutions in each whorl of the former and the twelve half-revolutions in each whorl of the latter. The 10:12 division manifests in the outer Tree of Life as:

1. the 10 Paths making up its "trunk," defined as:
point (Kether)
line (Binah-Chokmah)
triangle (Geburah-Chesed-Tiphareth)
tetrahedron (Hod-Netzach-Yesod-Malkuth).

(this is a set of 10 points, 10 lines, five triangles & one tetrahedron, i.e., 26 geometrical elements, where 26 is the number value of YAHWEH, the Godname of Chokmah), and

2. the 12 Paths that belong to its "branches" (this is the remainder of the outer Tree of Life, consisting of 12 lines and 11 triangles).

Each whorl of the UPA containing (10×168=1680) turns in its 10 half-revolutions constitutes the trunk; each whorl of Cowen's particle containing (12×168=2016) turns in its 12 half-revolutions constitutes the branches of the micro-physical manifestation of the Tree of Life blueprint. However, the two types of whorls do not co-exist in exactly the same universe. This is because the UPA is the E₈'-singlet subquark that exists in one 10-d space-time sheet, whilst Cowen's particle is an E₈-singlet state existing in the second 10-d space-time sheet that is parallel to the first but separated by a narrow gap that extends along the 10th dimension of space required by M-theory. The two types of particle interact only gravitationally, not by any of the forces that operate separately in each universe between pairs of similar types of particles. They do share 21 of the 22 compactified dimensions, i.e., a point on one type of whorl can be occupied by a point on the other type only with respect to these 21 dimensions. One type of whorl cannot cross the gap along the 22nd dimension, otherwise it could exist in exactly the same 10-d space-time as a whorl belonging to the other species of superstring; they do co-exist in the same 9-d space, but they can never truly coincide because they are always separated from each other by a gap that extends along the 10th dimension of 11-d space-time. Matter in one universe would be invisible to matter in the other universe and would just pass through it without being detected by humans or any other form of life that inhabited the other universe — that is, unless they were astronomers who could detect the gravitational influence of that matter on galaxies and stars in their own universe.

The seven enfolded polygons in each half of the inner Tree of Life have 42 sides. Its two separate halves have 84 sides of total length 84² = 7056. This is the same as the length of the 84 sides of the 42 sectors of the seven hexagons circumscribed by seven basic circles of diameter 168, which (as pointed out earlier) is the diameter of a circle needed to establish isomorphism between sacred circular and straight-line geometries. This is an example of such equivalence, the 42 outer sides of the seven hexagons corresponding to one half of the inner Tree of Life with 42 sides and the 42 internal sides of their sectors corresponding to its other half with 42 sides. The hexagon has five sides outside the root edge. The length of the (42−5=37) sides of the six other polygons = 37×84 = 3108 = 1⁴ + 3⁴ + 5⁴ + 7⁴, where each side has the length

84 = 1² + 3² + 5² + 7².

This is also the total length of the sides of the five enfolded polygons other than the triangle and square.

When enfolded, the triangle, square, pentagon & dodecagon have the same number of sides (21) as the enfolded hexagon, octagon & decagon do outside their shared side. Therefore, the seven enfolded polygons consist of the former with 20 sides outside the root edge and the latter with 22 sides. The total length of the former = 20×84 = 1680; the total length of the latter = 22×84 = 1848. The total length of the sides in the two separate sets of seven enfolded polygons = 84² = 2×1680 + 2×1848 = 3360 + 3696 = 7056. It was pointed out earlier that the seven circles of the Seed of Life have a total length of 7×528 = 3696. This is the same as the length of all the sides of the two separate sets of enfolded hexagons, octagons & decagons.

As 1680 + 2016 = 3696 = 22×168, the number of circularly polarised oscillations in both a whorl of the UPA and Cowen's particle is the number generated by assigning the number value of the Mundane Chakra of Malkuth to each of the 22 Paths of the outer Tree of Life. This property could, of course, be merely a coincidence. But the weight of mathematical evidence presented here makes this circumstance highly unlikely, especially given that  the 22 letters of the Hebrew alphabet divide into a subset of 10 and a subset of 12 that not only correspond to the distinction between the trunk and branches of the outer Tree of Life with, respectively, 10 Paths and 12 Paths but also reproduce the numbers 1680 and 2016 themselves — the number of oscillations, respectively, counted and predicted in the two types of whorl — when each letter is weighted with the number 168.

Work in progress.

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