




by
Stephen M. Phillips
Flat 4, Oakwood House, 117119 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 finestructure number 137 in the inner Tree of Life . . . . .
. . . . . . 7
Tree of Life basis of the E_{8}×E_{8}' heterotic superstring .
. . . . . . . . . . . . . . . . . . . . . . . . . . 9
Embodiment of the dimension 248 of E_{8} in the square . . . . . .
. . . . . . . . . . . . . . . . . 11
The Gosset Polytope 4_{21} . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . .13
Embodiment of the dimension 496 of E_{8}×E_{8}' in the octagon
. . . . . . . . . . . . . . . . . . . 15
Embodiment of the dimension 496 of E_{8}×E_{8}' in the inner
Tree of Life . . . . . . . . . . . . . .17
Embodiment of the dimension 496 of E_{8}×E_{8}' in the last
four polygons
of the inner Tree of Life . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . .19
The ‘ultimate physical atom’ . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . 21
The 1680 yods in a 10pointed star . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . 23
1680 yods surround the centres of the 2ndorder 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
E_{8}×E_{8}'
heterotic superstring . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . .29
Two joined dodecagons embody the E_{8}×E_{8}' 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 nonstop/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 2d Sri Yantra . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . .25
The Sri Yantra embodies the superstring structural parameter 3360 . . . . . . .
. . . . . . . 27
The Platonic solids embody the finestructure number 137 & the
superstring parameters 248 & 168 . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . 29



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 threedimensional, not twodimensional, 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.

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 finestructure constant,
whose magnitude sets the scale of the energies of electrons in
atoms.

Figure 3
Ten overlapping Trees of Life map the 10dimensional
spacetime 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 E_{8} or
E_{8}'. The Godname EL of Chesed with number value 31
prescribes the dimension 248 of E_{8} because there are 31
emanations up to Chesed of the fifth tree.

Figure 4
According to E_{8}×E_{8}'
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 E_{8} (ordinary matter) and the 248 gauge
bosons of E_{8}' (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 2ndorder 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 spin1 particle that transmits the force between
this type of superstring.


The 248 hexagonal yods in the square denote the 248
gauge bosons of the superstring gauge symmetry group
E_{8}.


Figure 5
The E_{8} root system consists of 240
vectors in an eight dimensional space. Those vectors are the vertices
(corners) of an eightdimensional object called the Gosset polytope
4_{21}. In the 1960s, Peter McMullen drew (by hand) a
2dimensional representation of 4_{21}. In 2007, a fouryear
collaboration between mathematicians from Europe and the USA announced
the results of their calculations of the mathematical structure of
E_{8}, using a supercomputer. The image shown here was
computergenerated by John Stembridge, based on McMullen's drawing.
(Credit: Image courtesy of American Institute of Mathematics)

The Gosset polytope
4_{21}

Figure 6
An octagon whose sectors are transformed into
2ndorder 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 = 24^{2} =
1^{2}×2^{2}×3^{2}×4^{2}. 33 yods are
corners of 1storder 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 spin1 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
E_{8}×E_{8}'. 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
E_{8}×E_{8}' that mediate the unified interactions between
E_{8}×E_{8}' 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.

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 E_{8}×E_{8}' 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
E_{8}×E_{8}' heterotic superstring.
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).
Figure 10
As
13^{2}
– 1 = 168 and a parallelogram
constructed from two 2ndorder tetractyses has 13 yods along
each side, a 10pointed array of 10 parallelograms has 1680
yods surrounding its centre. They comprise 90 yods in each
inner 2ndorder tetractys and 78 yods in the remainder of a
parallelogram. This reproduces the gematria number values of
the two Hebrew words in Cholem Yesodoth, the Kabbalistic name of the Mundane
Chakra of Malkuth:

Figure 12
The semiregular 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 E_{8}×E_{8}' 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.

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.

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.
