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#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 have 26 corners and 31 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 Cholem Yesodeth, 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 parametrises the 7-tree, whilst the number 176 parametrises 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" aound 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 discussed here 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 minature 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 differentation 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 on the 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 stae 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 spillae 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:

1. associated with each set of 7 enfolded polygons are 175 hexagonal yods lining the sides of their sectors;
2. 175 corners, sides & triangles are intrinsic to the 7 polygons enfolded in each overlapping Tree of Life;
3. the first 6 types of polygons enfolded in the 7-tree have 175 corners intrinsic to them.