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  #53 How the inner Tree of Life embodies the superstring structural parameter 176


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 Yesodoth, 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.


7 orders of spirillae

5th, 6th and 7th-order spirillae

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 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 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:

K7 2-torus

K7 mapped on the 2-torus 

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 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:

  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.

* 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. On average, 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 Occult Chemistry. 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 #9denoting 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.

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