#53 How the inner Tree
of Life embodies the superstring structural parameter 176
a) The 47 sectors of the 7 enfolded Type A
polygons making up each half of the inner Tree of Life have 88 sides. When each sector is a
tetractys, two hexagonal yods lie on each side. (88×2=176)
hexagonal yods line the sides of the 47 tetractyses. The root edge shared by the set of 7 enfolded
polygons and its mirror image set has two hexagonal yods. One of them is associated with one set of
polygons and the other is associated with its mirror image. Therefore, 175 hexagonal yods are
associated with each set.
b) The 7 enfolded polygons comprise 41 corners and 88
sides of their 47 triangular sectors. 176 corners, sides & triangles make up the inner form of
an isolated Tree of Life. In the case of overlapping Trees, the topmost corner of the hexagon
coincides with the lowest corner of the hexagon enfolded in the next higher Tree of Life. This
means that 175 geometrical elements are intrinsic to the inner form of each overlapping
Tree of Life, with one other geometrical element being shared.
c) The Type B dodecagon has 181 yods. 176 yods outside
its root edge surround its centre.
d) The first 6 enfolded polygons of the inner Tree
have26 corners and31 sides. The number of yods
lining their sides =26 +
2×31 = 88 (87 are intrinsic to them). The two
separate sets of the first 6 enfolded polygons have (2×88=176) yods lining their sides.
168 of these yods are outside the root edges. 87 is the
number of Levanah, the Mundane Chakra of Yesod, and 168 is the
number of CholemYesodoth, the Mundane Chakra of Malkuth.
e) The number of corners of the first 6 polygons
enfolded in the n-tree = 25n + 1. The 42 polygons of the first 6 types enfolded in the 7-tree have
176 corners. The topmost corner of the hexagon in the inner form of the 7th Tree coincides with the
lowest corner of the hexagon in the inner form of the next higher Tree. Hence, 175 corners are
intrinsic to these 42 polygons. This number parameterises the 7-tree, whilst the number 176
parameterises 7 overlapping Trees of Life.
UPA
The positive/negative UPA consists of 10 separate,
non-touching, closed curves ("whorls"), each of
which spirals five times around its axis of spin
(2½ times in its outer half and 2½ times in its inner half).
The uppermost three whorls ("major") appear thicker than the remaining seven "minor"
whorls.
Each whorl is a helix with 1680 circular turns, called
"1st-order spirillae."
Each 1st-order spirilla in a minor whorl winds 7
times around the surface of a 2-torus. In a major whorl, it winds 7.04 times. The smaller,
circular turns are 2nd-order spirillae. For major whorls, an extra 2nd-order spirilla is added
in every 25 1st-order spirillae, making 176 2nd-order spirillae instead of 175. This is repeated
for all 7 orders of spirillae. The 6 progressively smaller turns represent the winding of a
"string" around the 6 circular dimensions of a 6-torus. This is just one of the many types of the
6-dimensional compactified space predicted by superstring theory that physicists have
considered.
The helical winding of the 5th-, 6th- and 7th-order
spirillae (diagram taken from Occult Chemistry, 3rd ed., 1952). This picture conforms to
the current scientific concept of strings winding around 6 curled-up dimensions of space. It is
confirmed by sacred geometries, suchlike the inner form of the Tree of Life, in which the numbers
175 and 176, recorded by Besant & Leadbeater when they magnified superstrings with micro-psi,
appear naturally as parameters of its geometry and yod composition.
The significance for superstring physics of the number 176 found as a parameter
of the inner Tree of Life and in the 7-tree has been discussedhere for case (a) and here for case (b). The 176 yods outside the root edge that surround the
centre of the Type B dodecagon indicate the shape-forming character of this number. In an
analogous fashion, according to Besant & Leadbeater, every 25 nth-order spirillae in the three major whorls
of the UPA comprise 176 (n+1)th-order spirillae, whereas they comprise 175 (n+1)th-order spirillae in every
minor whorl (n = 1-7).* The winding ratio is (176/25=7.04) for the former and 175/25=7) for the latter. The
three major whorls are the superstring counterpart of the three members of the Supernal Triad, whilst the
seven minor whorls are the counterpart of the seven Sephiroth of Construction. Besant & Leadbeater referred
to them in the Theosophical terminology of the three "solar Logoi" and the seven "Planetary Logoi":
"The Anu is a sun in miniature in its own universe of the
inconceivably minute. Each of the seven whorls is connected with one of the Planetary Logoi, so
that each Planetary Logos has a direct influence playing on the very matter of which all things are
constructed. It may be supposed that the three conveying electricity, a differentiation of Fohat,
are related to the Solar Logos."
Occult
Chemistry,
3rd
ed., p.
14.
The two Theosophists did not,
of course, imply in this statement that the building block of all matter throughout the universe mysteriously
depended for its properties on a humble star in a particular galaxy known as the Milky Way! Their remark needs to
be understood as expressing the Law of Correspondence applied to all
holistic systems, whatever their scale. The 3:7 pattern exist in the Anu/superstring in the distinction between its
major and minor whorls because it is the microscopic manifestation of the universal pattern underlying ten-fold
holistic systems, e.g., the 10 dimensions of superstring space-time (see here) and the 10 superstrings making up the hydrogen atom (see here).
The reason why three of the 10 whorls of the UPA are augmented by
having an extra (n+1)th-order spirilla added to every set of 25 consecutive nth-order spirillae is that major
whorls correspond to the members of the Supernal Triad which, being complete in themselves, must be represented by
single Trees of Life, whilst the seven minor whorls correspond to the
seven Sephiroth of Construction which must be represented by overlapping Trees. The first six enfolded polygons enfolded in the Tree of Life have
26 corners, of which one (corner of hexagon) is shared with the polygons enfolded in the next
higher Tree. The first six polygons enfolded in each Tree have 25 independent corners that are intrinsic to the
inner form of that Tree. As each whorl is 10-fold, it must be represented by 10 overlapping Trees. The six orders
of spirillae above the 1st-order represent the six compactified dimensions of space predicted by superstring
theory. They form a 6-torus, S6, with decreasing radii of
successive circles S. The complete graph K7:
The complete graph
K7.
The 2-torus.
K7 needs 7 colours to be coloured so
that no two adjacent areas have the same colour. This is the number needed to colour any map
onthe 2-torus, which has the same genus as
K7.
can be drawn on a 2-torus because it has genus 1, and can be
coloured with seven colours. They manifest in the toroidal compactification of the subquark state of the
E8×E8 heterotic superstring as the seven (n+1)th-order spirillae winding around a 2-torus
whose axis is a circular nth-order spirilla. A set of 25 1st-order spirillae in a whorl is the manifestation of the
25 corners intrinsic to successive, overlapping Trees. As they are expressing Sephiroth of Construction, such a
Tree-of-Life section of 25 corners/1st-order spirillae is equivalent to:
major whorls 7 overlapping Trees, whose first six types of polygons have 176 intrinsic corners. This
means that 25 1st-order spirillae are compounded from 176 2nd-order spirillae. A similar analysis applies to each
higher order of spirilla;
minor whorls
the 7-tree, whose first six types of polygons have 175 intrinsic corners. This means that 25 1st-order spirillae
are compounded from 175 2nd-order spirillae. Similarly, for each higher order of spirilla.
The paranormally observed augmentation of major whorls and the number 25, 175 & 176 generating it have a
geometrical basis in terms of higher dimensions of space being represented, firstly, by Trees of Life
and then by seven Trees of Life.
The Tetrad (the
number 4) expresses the superstring structural parameter 176 through the factorisation 176 = 4×44. Assigning 7 (the
fourth odd integer) to the 25 yods in a Type A square (symbol of the Tetrad) generates the number
175. This is the seventh decagonal number: P107 = 175 (see Table 2 here). Given that the Tree of Life has 10 Sephiroth, seven of which are
Sephiroth of Construction, this polynomial number has a Kabbalistic quality that is confirmed by the following
properties of the inner Tree of Life:
associated with each set of 7 enfolded polygons are 175 hexagonal yods lining the sides of
their sectors;
175
corners, sides & triangles are intrinsic to the 7 polygons enfolded in each overlapping Tree of
Life;
the
first 6 types of polygons enfolded in the 7-tree have 175 corners intrinsic
to them.
* Leadbeater discovered the cause of the thickening of the major
whorls relative to the minor ones by counting the number of spirillae of the next higher order in sample sections
of 100 spirilla of a given order in a major whorl. He noticed that, whatever the order of the spirilla, there were
704 spirillae of the next higher order in such a section, i.e., four extra spirillae were added. Onaverage, therefore, one extra spirilla of the next higher order was added to every 25 spirillae, so that,
instead of comprising (25×7=175) spirillae of the next higher order, the 25 spirillae were, on average, made up of
(175+1=176) such spirillae. Did this actually pertain to every section of 25 spirillae? The four extra spirillae
might, of course, have been added randomly instead of in a uniform fashion. But this is unlikely, as Leadbeater
would have noticed if, say, one or more extra higher-order spirillae had appeared only in some subset of the 100
spirillae other than that of 25 spirillae, causing the spacing between spirillae to vary occasionally during his
counting of specimen sections, so that he would have mentioned this in his book OccultChemistry. Instead, he explicitly referred to the augmentation being due to an addition, on
average, of one spirilla in every 175 spirillae. He did not say whether he checked if 25 consecutive
spirillae in a major whorl did, indeed, comprise 176 spirillae of the next higher order. However, the
assumption that this was, indeed, the case is supported by the sacred geometries discussed above, which not only
embody the number 176 as a parameter but show it divided up into one component that is shared and 175
components that are intrinsic in some sense. In case e, the geometry of the inner form of seven overlapping Trees
of Life show a connection between the 25 corners intrinsic to the first six enfolded polygons and either the
175 corners intrinsic to these polygons in the 7-tree or the 176 corners intrinsic to seven overlapping Trees.
The extra (176th) spirilla is denoted by the apex of the hexagon enfolded in the inner form of the seventh Tree.
This is shared (therefore not counted) for the case of the 7-tree and unshared (therefore counted) for seven
overlapping Trees. Notice that seven points in 26-dimensional space-time that are spaced evenly
along the circumference of a circle are mapped by 175 spatial coordinates, to which the shared time coordinate must
be added, making 176 space-time coordinates. Alternatively, 25 separate points in the 11-d space-time predicted by
M-theory would be determined by (1 + 25×10 = 251) space-time coordinates, of which 175 would be measured relative
to the Cartesian coordinate axes pointing in the direction of the seven compactified dimensions that the
theory predicts (176 coordinates when the time coordinate is included). The appearance of these two numbers in
a paranormal context is natural, given that UPAs are embedded as E8×E8 heterotic
superstrings in 11-dimensional space-time but contain some oscillatory
modes in 26-dimensional space-time. This, together with the fact that the 1-tree has 19
Type A triangles with 25 sides that contain 251 yods (see #9) denoting these space-time coordinates, is
convincing evidence that the UPA is such a superstring. It indicates that sections of 25 spirillae of
a given order are complete Tree of Life patterns in themselves because 25 distinct points in 11-dimensional
space-time have 251 space-time coordinates, of which (25×7=175) refer to the seven compactified dimensions. To
dismiss the appearance of these numbers as the product of chance is unconvincing because it is too implausible.
Quite apart, of course, from ignoring all the evidence accumulated by the author's books that supports as
genuine the micro-psi ability of Besant & Leadbeater — evidence that explains why various numbers
predicted by string and superstring theory turn up in their accounts at least 70 years before physicists began
to consider these theories.
UPA.png "7 orders of spirillae")
