Positive UPA  Negative UPA 

The tetractys 
The Tree of Life






Whorl
Each whorl is a closed helix with 1680 circular turns, or 1storder spirillae. 
=

The gematria number value of Cholem Yesodeth, the Mundane Chakra of Malkuth, is 168: This is the number of points, lines & triangles below the top of the 1tree constructed from 19 Type A triangles with 25 sides:
Below the apex of the 1tree are:
(10+19=29) corners of triangles; (25+ 3×19 = 82) sides of triangles; (3×19=57) triangles. Total = 168. 

Each 1storder spirilla consists of 7 2ndorder spirilla
spaced evenly around a circle; each 2ndorder spirillae comprises 7 3rdorder spirillae, and so on.
The 7thorder spirilla is 7 "bubbles in koilon" spaced evenly around a circle. The 6 higher orders
of spirillae represent the winding of curves around the 6 compactified dimensions predicted by
superstring theory. 



(Place cursor over image to enlarge)

240 =
The 240 hexagonal yods in the 48 tetractyses of the 7 separate polygons making up half of the inner Tree of Life denote, in context of superstrings, the 240 roots of the exceptional Lie group E_{8} that determines the forces between E_{8}×E_{8} heterotic superstrings. 
The 1tree with 19 Type A triangles contains 240 yods other than Sephirothic corners of these triangles. They denote the 240 roots of the superstring gauge symmetry group E_{8}. 

The three major whorls of the UPA correspond to the Supernal Triad of Kether, Chokmah & Binah (called in Theosophy the 'First, Second & Third Logoi'). 72 gauge charges of E_{8} are spread along the major whorls, 24 per whorl. The seven minor whorls are the manifestation of the seven Sephiroth of Construction (corresponding to what is called in Theosophy the seven 'Planetary Logoi'). They carry the remaining 168 gauge charges of E_{8}. The 240 E_{8} gauge charges are spread along the 10 whorls of the UPA/subquark superstring, 24 per whorl. The difference in thickness between the major whorls and the minor whorls is the result of the breakdown of the symmetry of E_{8} into that of E_{6}, the rank6, exceptional subgroup of E_{8} that has 72 gauge charges. 

Each whorl in the UPA is a helix with 1680 circular turns. It is 10dimensional, the six higher orders of spirillae being closed curves that wind around the six compactified dimensions (actually progressively smaller circles) predicted by superstring theory. A dimension is represented by a Tree of Life, so that a whorl is geometrically represented by 10 overlapping Trees of Life. As the microscopic Tree of Life, the UPA has 10 whorls corresponding to the 10 Sephiroth. Each Sephirah can be represented by a Tree of Life with 10 Sephiroth, each of the latter by a Tree of Life, and so on. 
The Godname of Malkuth — the physical manifestation of the Tree of Life blueprint — is ADONAI. Its number value is 65, which is the number of Sephirothic levels in the 10tree. This is equivalent to a tetractysdivided decagon that is enclosed in a square. ADONAI prescribes the 10 dimensions of spacetime predicted by superstring theory and mapped by 10 Trees of Life. EL ("God"), the Godname of Chesed with number value 31, also prescribes them because the 10tree has 127 triangles, where 127 is the 31st prime number. EHYEH ("I am"), the Godname of Kether wiith number value 21, prescribes the 10tree because 21 Sephirothic levels are on each side pillar of it.



Each of the 10 whorls spirals five times around the axis of the UPA. Each revolution of the 10 whorls comprises 3360 helical turns (1storder spirillae), 336 per whorl. An outer or inner halfrevolution of a whorl comprises 168 turns and a quarterrevolution comprises 84 turns.

84 = 1^{2} + 3^{2} + 5^{2} + 7^{2}. 336 = 4^{2} + 8^{2} + 16^{2} = 2^{2}×84

Divided into their sectors, the (70+70) polygons enfolded
in 10 overlapping Trees of Life are composed of 3360 points, lines & triangles that are
unshared with the outer Trees (shared geometrical elements are coloured green). Each set of (7+7)
enfolded polygons has (168+168=336) geometrical elements that
are unshared with its outer Tree of Life. 

16800 yods surround the centre of the 7pointed star



Superstring theory requires the symmetry group of the unified interaction between heterotic superstrings to be either SO(32) or E_{8}×E_{8}, both with dimension 496. In the latter case, heterotic superstrings of ordinary matter have a unified force that is described by the symmetry group E_{8} with dimension 248. 
There are 248 hexagonal yods in a square with 2ndorder tetractyses as its sectors. Each yod symbolizes a root of E_{8}, the rank8 exceptional group. The square also provides an arithmetic representation of the dimension 496 of the two possible superstring symmetry groups SO(32) & E_{8}×E_{8}: 
There are 248 yods below the top of the 1tree with its triangles turned into Type A triangles. The eight yods outside the 1tree denote the eight simple roots of E_{8} and the 240 yods other than Sephiroth denote its 240 roots.


It is no coincidence that sacred geometries reproduce the 720:240:720 pattern in the vertices & edges in the compound of two 600cells that is the Petrie projection of the 4_{21} polytope. Rather, what is appearing in the polychorons is a universal archetype that is embodied in ancient sacred geometries and which manifests in spacetime as the whorls making up the UPA/subquark superstring.

Correspondence between the geometrical or yod compositions of the first four Platonic solids, the disdyakis triacontahedron, the inner & outer Trees of Life and the inner form of the 10tree 

The sum of the 70 odd integers after 1 assigned to the 70 yods of the Tree of Life = 5040. This is the number of turns in the three helical major whorls of the UPA/subquark superstring. It is the sum of the first 40 odd integers after 1 (blue) assigned to the 40 yods outside the (red) Lower Face and the next 30 odd integers 83141 (green) assigned to the 30 yods in the Lower Face. 
The subquark state of the E_{8}×E_{8} heterotic superstring remoteviewed by the Theosophists Annie Besant & C.W. Leadbeater over a century ago consists of 10 closed curves, or "whorls." They bear a correspondence to the 10 Sephiroth of the Tree of Life. The three major whorls correspond to the Supernal Triad and the seven minor whorls are the counterpart of the seven Sephiroth of Construction. Each whorl is a helix with 1680 circular turns. The three major whorls have (3×1680=5040) turns. Sacredgeometrical embodiment of 504 & 5040 Heptagon Type C dodecagon Disdyakis triacontahedron Each edge and each side of a sector in the green faces of the disdyakis triacontahedron are sides of internal grey triangles with the centre of the polyhedron as their shared corner. The (180+360=540) internal triangles have (540×3=1620) sectors with (60 + 120 + 540×3 = 1800) internal sides & 540 internal corners surrounding the centre, i.e., 3960 geometrical elements. The number of geometrical elements in the faces and interior that surround the axis = 1080 + 3960 = 5040. They include 1680 elements (red cells) either in the faces (1080) or sides (600) of sectors of internal triangles created by the edges of the disdyakis triacontahedron, leaving 3360 elements (1680 elements in each half of the polyhedron).* This is the polyhedral counterpart of the 1680 helical turns in the first major whorl and the 3360 turns in the second & third major whorls. * Alternatively, surrounding the axis are 1680
geometrical elements comprising 180 corners of sectors in the faces, 180 edges & 1320
geometrical elements in the internal triangles created by edges. This totals 1680 elements, leaving
3360 elements. 


3dimensional projection of a rotating 24cell 
3dimensional projection

The 240 vertices of the 4_{21} polytope coincide with the positions of the 240 roots of E_{8}, the rank8, exceptional Lie group. This polytope is a compound of two 600cells. The 120 vertices of a 600cell can be partitioned into those of five disjoint 24cells. As each vertex defines one of the 240 root vectors of E_{8}, there is a geometrical basis for dividing its 240 gauge charges into 10 sets of 24. The outer half of the UPA is the counterpart of one 600cell, the 120 gauge charges denoted by the 120 vertices of the five 24cells being spread out along the five halfrevolutions of the 10 whorls in the outer half. The inner half of the UPA is the counterpart of the other 600cell. The 2½ revolutions (five halfrevolutions) of the whorls that make up each half are the counterpart of the five 24cells in each 600cell. The 840 vertices & edges in each 600cell are the geometrical counterpart of the 840 circular turns in the five halfrevolutions of the outer or inner half of each helical whorl. The 1680 vertices & edges belonging to the compound of two 600cells in the Gosset polytope are the counterpart of the 1680 circular turns in each helical whorl of the UPA. 70 turns "carry" an E_{8} gauge charge: 1680 = 24×70. This correlation is irrefutable evidence that the UPA paranormally described over a century ago is a state of the E_{8}×E_{8} heterotic superstring (see Article 62 for more details). 



