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ARTICLE 47 (Part 1)

 

 

by

Stephen M. Phillips

Flat 3, 32 Surrey Road South. Bournemouth. Dorset BH4 9BP. England.

Website: http://smphillips.8m.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 . . . . . . . . . . . . . . . . . .1
The inner Tree of Life embodies the superstring structural
parameter 3360 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
Equivalence of the inner Tree of Life & the I Ching table of 64
hexagrams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5
Equivalence of the I Ching table of 64 hexagrams & the Sri Yantra . . . . . . . . . . . . . .  7
Embodiment of the superstring structural parameter 1680 in the
outer & inner forms of ten Overlapping Trees of Life. . . . . . . . . . . . . . . . . . . . . . . .9
Embodiment of 1680 in the first six polygons enfolded in ten
overlapping Trees of Life . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
Table of codons, anticodons & the amino acids for which they code . . . . . . . . . . . 13
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 . . . . . . . . . . . . . . . . . . .15
How some sacred geometries embody the 60 non-stop/start codons
& their anticodons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .17
Equivalence of the lowest seven Trees of Life & the Sri Yantra . . . . . . . . . . . . . . . . . .19
The Sri Yantra & the lowest seven Trees of Life encode the mRNA
codons & the tRNA anticodons. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .21
Correspondence between the inner Tree of Life, the I Ching table
& the Sri Yantra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
The sum of the 10 Godname numbers is the number of hexagonal yods
in the 2-d Sri Yantra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .25
The Sri Yantra embodies the superstring structural parameter 3360 . . . . . . . . . . . . . . 27
The Platonic solids embody the fine-structure number 137 & the
superstring parameters 248 & 168 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  29

 

 


 

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

 

 

As well as the Tree of Life known to Kabbalists for hundreds of years, which may be called the ‘outer form’ of this blueprint for holistic systems embodying the divine paradigm, there is an ‘inner form’ of this geometrical object. It consists of two sets of seven regular polygons:

triangle, square, pentagon, hexagon, octagon, decagon & dodecagon.

One set is the mirror image of the other. They are joined at the ‘root edge.’ The plane in which they lie passes through the vertical Pillars of Mercy and Severity but not through the central Pillar of Equilibrium, because the outer form of the Tree of Life is really three-dimensional, not two-dimensional, as usually depicted in books on Kabbalah. This means that the Sephiroth Chokmah, Chesed, Netzach, Binah, Geburah & Hod are located at corners of the triangles and hexagons but that Tiphareth and Daath do not coincide with the endpoints of the root edge —only their projections onto the plane of the polygons do.

 

 

 

 

 

 


fig1

 


 

 

 

Figure 2

 

 

The number 137 is embodied in the blueprint of the inner Tree of Life. Its (7+7) enfolded polygons have 94 sectors. When each sector is divided into three tetractyses, 1370 yods are generated, i.e., the number of yods in 137 tetractyses. This proves beyond reasonable doubt that the number 137 is a basic structural parameter of the Tree of Life, in keeping with its central status in physics as a number which determines one of the fundamental constants of nature — the fine-structure constant, whose magnitude sets the scale of the energies of electrons in atoms.

 

 

 

 

 

 

 

 

 


 

 

 


 

 

Figure 3

 

 

 

 

Ten overlapping Trees of Life map the 10-dimensional space-time of superstrings. With their triangles turned into tetractyses, there are 248 (red & violet) yods up to Chesed of the fifth tree — its first Sephirah of Construction. There are a further 248 (blue) yods up to, but not including, Chesed of the tenth tree. Each yod denotes a particle, a gauge field of E8 or E8'. The Godname EL of Chesed with number value 31 prescribes the dimension 248 of E8 because there are 31 emanations up to Chesed of the fifth tree.

 

 

 

 

 

 

 

 


 

fig3

 

 


 

 

Figure 4

 

 

According to E8×E8' superstring theory (one of the five types of superstrings), the unified force between such superstrings is mediated by virtual exchange of the 248 gauge bosons of E8 (ordinary matter) and the 248 gauge bosons of E8' (shadow matter). An ancient symbol of the four elements of Earth, Air, Fire & Water, the square encodes this information. When its sectors are turned into 2nd-order tetractyses, the next higher differentiation of the Pythagorean tetractys:

they contain 248 hexagonal yods (the yods at the corners are omitted so as make clear which yods are being counted). Each one symbolises a Sephirah of Construction as well as a possible quantum state of the spin-1 particle that transmits the force between this type of superstring.

 

 

 

 

 

 


 

fig4


The 248 hexagonal yods in the square denote the 248 gauge bosons of the superstring gauge symmetry group E8.

 

 

 

 

 


 

 

Figure 5

 

 

 

 

 

The E8 root system consists of 240 vectors in an eight- dimensional space. Those vectors are the vertices (corners) of an eight-dimensional object called the Gosset polytope 421. In the 1960s, Peter McMullen drew (by hand) a 2-dimensional representation of 421. In 2007, a four-year collaboration between mathematicians from Europe and the USA announced the results of their calculations of the mathematical structure of E8, using a supercomputer. The image shown here was computer-generated by John Stembridge, based on McMullen's drawing. (Credit: Image courtesy of American Institute of Mathematics)

 

 

 

 

 

 

 

 

 


 

fig5

 

 

The Gosset polytope 421

 

 


 

 

Figure 6

 

 

An octagon whose sectors are transformed into 2nd-order tetractyses has 496 hexagonal yods. Each yod symbolizes a particle involved in the transmission of the superstring force. The number of tetractyses is 80. This is the number value of Yesod, the Sephirah immediately above Malkuth in the Tree of Life. This archetypal pattern is prescribed by the Godnames. For example, it is prescribed by the Godname YAH with number value 15 because each sector of the octagon has 10 tetractyses with 15 corners. There are 576 yods surrounding the centre of the octagon, where 576 = 242 = 12×22×32×42. 33 yods are corners of 1st-order tetractyses, where 33 = 1! + 2! + 3! + 4!. These are examples of how the integers 1, 2, 3 & 4 symbolized by the four rows of the Pythagorean tetractys express the properties of archetypal patterns and holistic systems possessing sacred geometry.

 

 

 

 

 

 

 

 

 

 

 


 


The 496 hexagonal yods in the octagon denote the 496 spin-1 particles that transmit the unified force between superstrings

 

 

 


 

Figure 7

 

 

The number value 428 of Chasmalim, the Order of Angels assigned to Chesed, is the number of yods lying on edges of the 94 tetractyses in the (7+7) enfolded polygons that are intrinsic to it, i.e., not shared with the polygons enfolded in the next higher tree. Separately, these polygons have (248+248) intrinsic yods lying on edges of tetractyses that symbolise the (248+248) roots/gauge bosons of E8×E8'. This is a striking example of how the Godnames, Archangels, Angelic Orders & Mundane Chakras of the Sephiroth mathematically define sacred geometrical structures that embody parameters of scientific significance, in this case the 496 gauge bosons of E8×E8' that mediate the unified interactions between E8×E8' heterotic superstrings. That this particular conjunction of the numbers 496 & 428 is highly unlikely to be a coincidence is indicated by the fact that there are 194 hexagonal yods either in the root edge or on the edges of the 48 tetractyses in the seven separate polygons, where 194 is the number value of Tzadekh, the Mundane Chakra of Chesed — the Sephirah to which the Chasmalim are assigned.

 

 

 

 

 

 

 

 


fig7

 

 


Figure 8

 

 

Outside the root edge of the last four polygons of the inner Tree of Life whose sectors are divided into three tetractyses are 496 yods other than their corners and centres:

This property might be dismissed as a coincidence were it not for the fact that the hexagon & dodecagon have 248 yods and the octagon & decagon have 248 yods. In other words, the yod population 496 splits into two identical numbers (248), in conformity with the prediction by E8×E8' heterotic superstring theory. Even supposing that it were mere coincidence that the last four polygons have 496 such yods, it is highly improbable that subsets of them also by chance have yod populations that add up to 248. It is therefore reasonable to discount chance. This property demonstrates how the universal blueprint of the inner Tree of Life embodies the dynamics of the E8×E8' heterotic superstring.

 

 

 


 

fig8

 

 

 


Figure 9

 

 

The basic unit of matter was depicted in 1878 by an American pioneer of colour therapy, Dr. Edwin D. Babbitt, in his book "The Principles of Light and Color" and in 1952 in the 3rd edition of the book Occult Chemistry written by the Theosophists, Annie Besant and Charles W. Leadbeater, who called it the ‘ultimate physical atom,’ or UPA. They noticed two types of UPA, one the mirror image of the other. The UPA consists of ten closed curves, each of which revolves five times around the axis of spin of the particle. Each curve is a helix with 1680 circular turns. Three curves (‘major whorls’) are thicker and brighter than the other seven (‘minor whorls’). They are the microscopic manifestation of the ten Sephiroth of the Tree of Life. The ten whorls have 16800 helical turns (3360 turns per revolution).

 

 

 

 

 

 

 

 


fig9

 

 


 

Figure 10

As 132   – 1 = 168 and a parallelogram constructed from two 2nd-order tetractyses has 13 yods along each side, a 10-pointed array of 10 parallelograms has 1680 yods surrounding its centre. They comprise 90 yods in each inner 2nd-order tetractys and 78 yods in the remainder of a parallelogram. This reproduces the gematria number values of the two Hebrew words in Cholem Yesodeth, the Kabbalistic name of the Mundane Chakra of Malkuth:

 

 

 

 


 

fig10

 

 



 

fig12

 


 

 

 

Figure 12

 

 

The semi-regular polyhedra are divided into two groups of 13 (15, if enantiomorphs are included). They are called the Archimedean solids and the Catalan solids (their duals, in which vertices & faces are interchanged). The Catalan solid with the most faces is the disdyakis triacontahedron. It has 62 vertices, 180 edges & 120 triangular faces. Each edge can be thought of as the base of an interior triangle with a corner at the centre of the polyhedron. If these triangles are divided into their sectors, it can be calculated that 1680 vertices, edges & triangles surround an axis passing through any two diametrically opposite vertices. This is the number of turns made in each helical whorl of the E8×E8' heterotic superstring as it revolves five time around its axis of spin. It is an indication that the disdyakis triacontahedron is the polyhedral version of the Tree of Life, which encodes the same structural parameter of superstrings.

 

 

 

 

 

 

 

 


 

fig12

 


Figure 13

 

 

 

The Decad specifies the dodecagon as the tenth regular polygon. Construction of each of its sectors from three tetractyses requires 168 more yods. 84 yods lie on edges of tetractyses inside sectors and 84 yods either lie on edges of sectors or are centres of tetractyses. This 84:84 division of the superstring structural parameter 168 is characteristic of holistic systems embodying the universal patterns of sacred geometry. A dodecagon has 156 hexagonal yods. 155 hexagonal yods are associated with each of the two joined dodecagons. 155 is the number value of ADONAI MELEKH, the Godname of Malkuth, and 168 is the number value of its Mundane Chakra. This demonstrates how the Godname of the Sephirah signifying the material universe determines the form of the basic units of matter.

 

 

 

 

 

 

 

 


 

fig13

 


 


fig14

 


 


fig15

 

 


 

Figure 16

 

 

The fact that 168 yods surround the centre of a square whose sectors are each divided into triangles which are then constructed from tetractyses is an illustration of the Tetrad Principle, whereby the fourth member of a class of mathematical objects, or the fourth stage in its construction from tetractyses, always represents a parameter of the Tree of Life. In this case, the square is the fourth stage in the sequence:

point—line—triangle—square—pentagon, etc

and the superstring structural parameter 168 is the number of yods needed for its fourth stage of construction from tetractyses.

 

 


fig16

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