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ARTICLE 47 (Part 2)

 

 

by

Stephen M. Phillips

Flat 4, Oakwood House, 117-119 West Hill Road. Bournemouth. Dorset BH2 5PH. England.

Website: http://smphillips.mysite.com

 


Page Index

Part 1

                                                                                                                                            Page

Table of number values of the Sephiroth in the four Worlds . . . . . . . . . . . . . . . . . . . . . . 3
The outer & inner forms of the Tree of Life . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
Embodiment of the fine-structure number 137 in the inner Tree of Life . . . . . . . . . . . . .7
Tree of Life basis of the E8×E8' heterotic superstring . . . . . . . . . . . . . . . . . . . . . . . . . . .9
Embodiment of the dimension 248 of E8 in the square . . . . . . . . . . . . . . . . . . . . . . . . .11
The Gosset Polytope 421 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
Embodiment of the dimension 496 of E8×E8' in the octagon . . . . . . . . . . . . . . . . . . . .15
Embodiment of the dimension 496 of E8×E8' in the inner Tree of Life . . . . . . . . . . . . 17
Embodiment of the dimension 496 of E8×E8' in the last four polygons
of the inner Tree of Life . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .19
The ‘ultimate physical atom’ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .21
The 1680 yods in a 10-pointed star . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
1680 yods surround the centres of the 2nd-order tetractys sectors of
two joined dodecagons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
1680 vertices, edges & triangles surround the axis of the disdyakis
triacontahedron . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .27
The dodecagon embodies the structural parameter 168 of the E8×E8'
heterotic superstring . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .29
Two joined dodecagons embody the E8×E8' superstring structural
parameter 336 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
The square embodies the superstring structural parameter 168 . . . . . . . . . . . . . . . . 33
The Tetrad Principle determines the superstring structural parameter
168 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  35

   

Part 2

                                                                                                                                   Page

Table of number values of the Sephiroth in the four Worlds . . . . . . . . . . ... . . . . . 3
The inner Tree of Life embodies the superstring structural
parameter 3360 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5
Equivalence of the inner Tree of Life & the I Ching table of 64
hexagrams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
Equivalence of the I Ching table of 64 hexagrams & the Sri Yantra . . . . ... . . . . .9
Embodiment of the superstring structural parameter 1680 in the
outer & inner forms of ten Overlapping Trees of Life. . . . . . . . . . . . . . . .. . . . . . . 11
Embodiment of 1680 in the first six polygons enfolded in ten
overlapping Trees of Life . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . 13
Table of codons, anticodons & the amino acids for which they code . . . . . . . . .15
The (192+192) yods in the first (6+6) polygons symbolize the (192+192)
instances of the bases of the 64 codons & the 64 anticodons . . . . . . .. . . . . . . .17
How some sacred geometries embody the 60 non-stop/start codons
& their anticodons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
Equivalence of the lowest seven Trees of Life & the Sri Yantra . . . . . . . . . . .. .  21
The Sri Yantra & the lowest seven Trees of Life encode the mRNA
codons & the tRNA anticodons. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . .23
Correspondence between the inner Tree of Life, the I Ching table
& the Sri Yantra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .25
The sum of the 10 Godname numbers is the number of hexagonal yods
in the 2-d Sri Yantra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
The Sri Yantra embodies the superstring structural parameter 3360 . . .. . . . . . 29
The Platonic solids embody the fine-structure number 137 & the
superstring parameters 248 & 168 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

 

 


 

SEPHIRAH
GODNAME
ARCHANGEL
ORDER OF
ANGELS
MUNDANE
CHAKRA
1 Kether
(Crown)
                 620
EHYEH
(I am)
                 21
Metatron
(Angel of the
Presence)
                 314
Chaioth ha Qadesh
(Holy Living
Creatures)
                 833

Rashith ha Gilgalim
First Swirlings.
(Primum Mobile)
                 636
2 Chokmah
(Wisdom)
                 73
YAHWEH, YAH
(The Lord)
                 26, 15
Raziel
(Herald of the
Deity)
                 248
Auphanim
(Wheels)
                 187
Masloth
(The Sphere of
the Zodiac)
                 140
3 Binah
(Understanding)
                 67
ELOHIM
(God in multiplicity)
                 50
Tzaphkiel
(Contemplation
of God)
                 311
Aralim
(Thrones)
                 282
Shabathai
Rest.
(Saturn)
                 317
  Daath
(Knowledge)
                 474
       
4 Chesed
(Mercy)
                 72
EL
(God)
                 31
Tzadkiel
(Benevolence
of God)
                 62
Chasmalim
(Shining Ones)
                 428
Tzadekh
Righteousness.
(Jupiter)
                 194
5 Geburah
(Severity)
                 216
ELOHA
(The Almighty)
                 36
Samael
(Severity of God)
                 131
Seraphim
(Fiery Serpents)
                 630
Madim
Vehement
Strength.
(Mars)
                 95
6 Tiphareth
(Beauty)
                 1081
YAHWEH ELOHIM
(God the Creator)
                 76
Michael
(Like unto God)
                 101
Malachim
(Kings)
                 140
Shemesh
The Solar Light.
(Sun)
                 640
7 Netzach
(Victory)
                 148
YAHWEH
SABAOTH
(Lord of Hosts)
                 129
Haniel
(Grace of God)
                 97
Tarshishim or
Elohim
                 1260
Nogah
Glittering
Splendour.
(Venus)
                 64
8 Hod
(Glory)
                 15
ELOHIM
SABAOTH
(God of Hosts)
                 153
Raphael
(Divine
Physician)
                 311
Beni Elohim
(Sons of God)
                 112
Kokab
The Stellar Light.
(Mercury)
                 48
9 Yesod
(Foundation)
                 80
SHADDAI EL CHAI
(Almighty Living
God)
                 49, 363
Gabriel
(Strong Man of
God)
                 246
Cherubim
(The Strong)
                 272
Levanah
The Lunar Flame.
(Moon)
                 87
10 Malkuth
(Kingdom)
                 496
ADONAI MELEKH
(The Lord and
King)
                 65, 155
Sandalphon
(Manifest
Messiah)
                 280
Ashim
(Souls of Fire)
                 351
Cholem Yesodeth
The Breaker of the
Foundations.
The Elements.
(Earth)
                 168
 
The Sephiroth exist in the four Worlds of Atziluth, Beriah Yetzirah and Assiyah. Corresponding to them are the Godnames, Archangels, Order of Angels and Mundane Chakras (their physical manifestation). This table gives their number values obtained by the ancient practice of gematria, wherein a number is assigned to each letter of the alphabet, thereby giving a number value to a word that is the sum of the numbers associated with its letters Some of these numbers will be referred to in the article.

 


 

Figure 1

 

 

When the 47 sectors of the seven enfolded polygons are transformed into 2nd-order tetractyses (the next order above the tetractys in which yods are replaced by tetractyses), they contain 3360 yods. This is the number of helical turns in all ten closed curves of the E8×E8' heterotic superstring when they revolve once around the spin axis of the spin-½ particle. Each yod denotes a turn. Physically, it is an oscillation of the circularly polarized standing wave running around the curve. The Godname ELOHIM with number value 50 prescribes the fundamental constituent of quarks because its ten whorls make 50 revolutions, each of 336 turns, about its spin axis. Assigning this number to each of the 336 yods in the first (6+6) enfolded of the inner Tree of Life generates the number 16800 as the number of circularly polarized oscillations in all ten closed curves of the heterotic superstring.

 


fig1

 


 

 

 

Figure 2

 

 

The seven separate regular polygons of the inner Tree of Life have 192 vertices, edges & triangles. They correspond to the 192 lines & broken lines of the 64 trigrams in one half of the I Ching table. The 192 geometrical elements in the second, identical set of seven polygons correspond to the 192 lines & broken lines in the other half of the table. The 24 lines & broken lines in the upper trigrams of the eight diagonal hexagrams correspond to the 24 vertices, edges & triangles in the hexagon, which is the halfway stage in the sequence of seven polygons. The 24 lines & broken lines in the lower trigrams of the eight diagonal hexagrams correspond to the 24 vertices, edges & triangles in the hexagon in the second set of polygons. Each of the 384 lines & broken lines of the I Ching table therefore symbolises a geometrical element composing the two sets of polygons of the inner Tree of Life. This is compelling evidence that the I Ching table is — like the inner Tree of Life — a representation of the same universal blueprint. The counterpart of the yin/yang polarities of lines and broken lines is the distinction between geometrical elements defining the boundaries of polygons and their internal elements, in each case there being 192 in each class.

 


 

 

 


 

 

 

Figure 3

 

 

 

The 384 yin/yang lines of the 64 hexagrams of the I Ching table correspond to the 384 yods in the 42 triangles of the 3-dimensional Sri Yantra. The (24+24) yin/yang lines in the eight diagonal hexagrams correspond to the (24+24) yods that are either hexagonal yods in the central tetractys or centres of the 42 tetractyses surrounding it. The six hexagonal yods in the former are the counterpart of the six lines in the pair of heaven trigrams in the upper left-hand corner of the table. The 168 yods on the 63 edges of the 21 tetractyses in each half of the Sri Yantra are the counterpart of the 168 yin/yang lines in the 28 hexagrams on each side of the diagonal. Their physical manifestation are the 168 circularly polarised oscillations in half a revolution of each whorl of the E8×E8' heterotic superstring.



 

 

 


 

fig3

 

The correspondence between the I Ching table and the Sri Yantra.

 

 

 


 

 

Figure 4

 

 

ADONAI, the Godname of Malkuth with number value 65, defines the lowest ten Trees of Life because they have 65 Sephirothic emanations. EL, Godname of Chesed with number value 31, prescribes them because they have 127 triangles, where 127 is the 31st prime number. When their sectors are turned into tetractyses, there are 1680 yods below the top of the tenth tree (the 65th emanation). This is how ADONAI determines the superstring structural parameter 1680. They belong to 131 tetractyses, where 131 is the number value of Samael, the Archangel of Geburah.

The first (6+6) polygons enfolded in each tree constitute a holistic system because their properties are prescribed by the Godnames of the ten Sephiroth, e.g., ELOHIM, the Godname of Binah, prescribes them because they have 50 corners. When each of their 70 sectors is turned into a tetractys, there are 1680 yods lining the 600 edges of the (60+60) polygons enfolded in the 10 trees that are intrinsic to them in the sense that none of them belong to polygons enfolded in the next higher tree.

Just as the 1680 helical turns of each whorl in the heterotic superstring define its form, so the 1680 yods on edges of the polygons determine their shape. A whorl is a Tree of Life in itself, being the microscopic manifestation of a Sephirah, and therefore can be represented by ten Trees of Life.

 

 


 

fig4

 

 

 

 


 

 

Figure 5

 

 

With their (35+35) sectors constructed from tetractyses, there are (192+192) yods in the first (6+6) enfolded polygons that are intrinsic to them, i.e., unshared with polygons enfolded in adjacent trees. Of, these, (24+24) are intrinsic corners (white circles) of polygons, leaving (168+168) red and blue yods other than corners. The (60+60) polygons of the first six types enfolded in 10 overlapping Trees of Life have (240+240) corners and (1680+1680) yods other than corners. The superstring structural parameter 1680 is embodied not only by the boundaries of the polygons but also by their yod populations. The 3360 yods other than corners symbolise the 3360 turns in one revolution of the ten helical whorls of the E8×E8' heterotic superstring.

A circularly polarised wave comprises two plane waves oscillating 90° out of phase with each other. The (240+240) corners denote the (240+240) plane waves associated with the 240 gauge charges of E8, which are spread over the 10 whorls of the E8×E8' heterotic superstring, 24 to a whorl.

 


 

fig5

 

 

 


 

 

Figure 6

 

 

DNA is made of chemical building blocks called nucleotides. These building blocks are made of three parts: a phosphate group, a sugar group (2-deoxyribose, which is a pentose (five carbon) sugar) and one of four types of nitrogen bases. To form a strand of DNA, nucleotides are linked into chains, with the phosphate and sugar groups alternating along the sides of the ‘ladder’ of DNA’s double helix. The four types of nitrogen bases found in nucleotides are: adenine (A), thymine (T), guanine (G) and cytosine (C). The two strands of the molecule are held together by hydrogen bonding between pairs of complementary nitrogen bases, base A always with base T and base C always with base G.

RNA is a single strand molecule with a much shorter chain of nucleotides than DNA. Whereas DNA contains deoxyribose, RNA contains ribose, whose OH group makes it less stable than DNA. The complementary base to adenine is not thymine but uracil (U). Messenger RNA carries information about a protein sequence to the ribosomes, which synthesize protein in the cell. Transfer RNA is a small RNA chain of about 80 nucleotides that transfer a specific amino acid to a growing polypeptide chain at the ribosomal site of protein synthesis. Groups of three bases (codons) in mRNA hydrogen bond to their complementary anticodons in tRNA. This reads the sequence of the messenger RNA and is attached to the amino acids. Each type of tRNA can be attached to only one type of amino acid. Each codon encodes for a specific amino acid, although a given amino acid may be encoded by several codons. The table lists the 64 base triplets in DNA, the 64 mRNA codons and their complementary tRNA anticodons, together with the amino acid for which they code.

 

 


 

6

Codons and anticodons for the amino acids

Amino Acid
DNA Base Triplets
mRNA Base Codons
tRNA Base Anticodons
alanine
CGA, CGG, CGT, CGC
GCU, GCC, GCA, GCG
CGA, CGG, CGU, CGC
arginine
GCA, GCG, GCT, GCC, TCT, TCC
CGU, CGC, CGA, CGG, AGA, AGG
GCA, GCG, GCU, GCC, UCU, UCC
asparagine
TTA, TTG
AAU, AAC
UUA, UUG
aspartate
CTA, CTG
GAU, GAC
CUA, CUG
cysteine
ACA, ACG
UGA, UGC
ACA, ACG
glutamate
CTT, CTC
GAA, GAG
CUU, CUC
glutamine
GTT, GTC
CAA, CAG
GUU, GUC
glycine
CCA, CCG, CCT, CCC
GGU, GGC, GGA, GGG
CCA, CCG, CCU, CCC
histidine
GTA, GTG
CAU, CAC
GUA, GUG
isoleucine
TAA, TAG, TAT
AUU, AUC, AUA
UAA, UAG, UAU
leucine
GAG, GAT, GAC
UUA, UUG, CUU, CUC, CUA, CUG AAT, AAC, GAA,
AAU, AAC, GAA, GAG, GAU, GAC
lysine
TTT, TTC
AAA, AAG
UUU, UUC
methionine
TAC
AUG
UAC
phenylalanine
AAA, AAG
UUU, UUC
AAA, AAG
proline
GGA, GGG, GGT, GGC
CCU, CCC, CCA, CCG
GGA, GGG, GGU, GGC
serine
AGA, AGG, AGT, AGC, TCA, TCG
UCU, UCC, UCA, UCG, AGU, AGC
AGA, AGG, AGU, AGC, UCA, UCG
stop
ATG, ATT, ACT
UAA, UAG, UGA
AUU, AUC, ACU
threonine
TGA, TGG, TGT, TGC
ACU, ACC, ACA, ACG
UGA, UGG, UGU, UGC
tryptophan
ACC
UGG
ACC
tyrosine
ATA, ATG
UAU, UAC
AUA, AUG
valine
CAA, CAG, CAT, CAC
GUU, GUC, GUA, GUG
CAA, CAG, CAU, CAC

 

 

 

 

 

 


 

Figure 7

 

 

 

The 384 instances of the nitrogen bases in the 64 codons of mRNA and the 64 anticodons of tRNA are symbolised by the 384 yods in the (6+6) enfolded polygons other than the endpoints of their shared root edge. The Godname ELOHIM with number value 50 and the Godname YAHWEH with number value 26 prescribe the 384 instances because the (6+6) enfolded polygons have 50 corners, each set of six polygons having 26 corners.

There are (27×3=81) instances of A, C & G bases in the (33=27) bases that contain only them. There are (37×3=81) instances for the 37 codons that contain at least one U base. These codons include the three stop codons UAA, UAG & UGA. There are (34×3=102) instances of bases in codons that include the U base and which encode solely for amino acids. Hence, the 192 instances of bases consist of 81 instances of A,C & G bases in the 27 codons containing only them, nine instances of bases in the three stop codons and 102 instances of bases in the 34 other codons. This 81:9:102 division compares with the pattern of yods associated with each set of six polygons. The 90 yods associated with the first four polygons symbolise the 90 instances of either A, C & G bases in the 27 codons or the bases in the stop codons. The 102 yods of the octagon and decagon symbolise the 102 instances of bases in the 34 codons containing a U base. Similarly for the anticodons. A yod and its mirror image in the other set of polygons denotes an instance of a base and an instance of its complement. The two sets of polygons are the sacred geometrical basis of human mRNA and tRNA.

 


fig7

 


 

 

 

 

 

Figure 8

 

 

The 60 mRNA codons and their 60 anticodons have their counterparts in:

  1. the inner Tree of Life as the 60 red yods lining the boundaries of the enfolded triangle, square, pentagon & dodecagon and as the 60 blue yods lining the boundaries of the hexagon, octagon & decagon;
  2. the pair of dodecagons as the 60 hexagonal yods in either one;
  3. the disdyakis triacontahedron as the 60 faces in each half of the polyhedron.

When its 12 sectors are each constructed from three tetractyses, the dodecagon has 180 yods surrounding it centre. They represent the 180 instances of the four nitrogen bases C, G, U & A. The three groups of four sectors arranged in a cross each contain 60 yods. A yod from each group denotes an instance of a base in the 60 non-stop/start codons.

 

 

 

 

 


fig8

 

 

 


 

 

 

 

 

Figure 9

 

There are 384 yods up to the top of the seventh, overlapping Tree of Life. The 42 triangles of the Sri Yantra have 378 yods, whilst the central triangle has six hexagonal yods on its edges, a total of 384 yods. Both sacred geometries express the seven-fold nature of holistic systems, the seven trees representing the seven Sephiroth of Construction. Their equivalence is further demonstrated by the fact that there are 259 corners, edges & triangles up to the top of the seventh tree, whilst the 43 triangles in the Sri Yantra are composed of 259 corners, edges & triangles.

 

 




 

 


fig9

 

 


 

Figure 10




When its triangles are turned into tetractyses, there are 384 yods up to the top of the seventh Tree of Life. They correspond to the 384 yods in the 3-dimensional Sri Yantra whose 43 triangles are turned into tetractyses. They also denote the 384 instances of the four nitrogen bases in the 64 codons of messenger RNA and in the 64 anticodons of transfer RNA. This is the Kabbalistic and Sri Yantra basis for the DNA molecule. There are 192 blue yods from the top of the seventh tree down to the Path joining Chesed and Geburah of the fourth tree and 192 red yods below it. They denote the 192 instances of the bases in tRNA and mRNA.

 


 

fig10

 

 


Figure 11



 

Constructed from tetractyses, the first (6+6) enfolded polygons of the inner Tree of Life have 384 yods other than the endpoint of their shared root edge. They are the counterpart of the 384 yin/yang lines in the table of 64 hexagrams used in I Ching, the ancient Chinese system of divination. They are also the counterpart of the 384 yods in the 43 triangles of the 3-dimensional Sri Yantra. The six green yods at the centre, top & lowest corners of the two hexagons that coincide with the positions of Sephiroth correspond to the six yang lines in the two ‘Heaven’ trigrams of the hexagram in the top left-hand corner of the table and to the six hexagonal yods in the central triangle that are arranged at the corners of a hexagon. The two sets of 21 corners of the (6+6) polygons are the counterpart of the two sets of 21 yin/yang lines in the seven other hexagrams forming the diagonal of the table and to the centres of the 21 tetractyses in each half of the Sri Yantra. The (168+168) yods other than corners of polygons are the counterpart of the (168+168) yin/yang lines in the (28+28) off-diagonal hexagrams and to the (168+168) yods on the edges of the (21+21) tetractyses.

 


 

fig11

 


 

 

Figure 12

 

 

When each of the 42 triangles in the Sri Yantra is divided into its three sectors and each sector then turned into a tetractys, 636 hexagonal yods are generated. This is the sum of the number values of the Godnames of the ten Sephiroth.

 

 

 

 

 

 


 

fig12

 


 

 

Figure 13







Assigning the number 10 (the Pythagorean Decad) to the 336 yods on the 126 edges of the 42 triangles of the 3-dimensional Sri Yantra generates the number 3360 — the number of turns in one revolution of the ten whorls of the E8×E8' heterotic superstring. This demonstrates how the Sri Yantra and the inner Tree of Life are equivalent representations of holistic systems like the heterotic superstring. Each half of the Sri Yantra with 168 yods defines the number (1680) of circularly polarized oscillations made by all ten closed curves of the superstring during half of a revolution around its spin axis. The inner and outer halves of the superstring correspond to the two halves of the Sri Yantra. They are prescribed by the Godname EHYEH with number value 21 because 21 triangles in each half surround its central triangle.

 

 

 

 

 


fig13

 


Figure 14




Consider the faces of the Platonic solids divided into their sectors. Each polyhedral edge is the side of an internal triangle with a corner at the centre of the solid. When the sectors in the faces and their internal triangles are turned into tetractyses, the average number of yods in the first four Platonic solids is 168. This is how these regular polyhedra, which the ancient Greeks believed were the shapes of the particles of the elements Earth, Water, Air & Fire, determine the structural parameter 168 of the superstrings making up atoms.

The average number of yods in their faces is 137. This is the integer that approximately determines the magnitude of the fine-structure constant, which in turn determines some of the properties of atoms.

The first four Platonic solids have 38 faces. Their 120 sectors have 248 vertices & edges. They embody the dimension 248 of the superstring gauge symmetry group E8.

 


fig14

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