The inner Tree of Life has (168+168=336) geometrical elements unshared with its outer form

The previous page discussed ways in which the Godname YAHWEH prescribes the geometrical and yod composition of the outer & inner Trees of Life, the Sri Yantra and the seven diatonic scales. In all these analyses, the number 13 played a central role. It also features in how the inner Tree of Life embodies the superstring structural parameter 168. This was discussed in # 36. But the analysis will be repeated here in the context of the number 13 in order to demonstrate further its ubiquitous presence in holistic systems.

The table shows that the 47 triangular sectors of the seven enfolded, Type A polygons have 41 corners & 88 sides. Of their 176 geometrical elements, three green corners (top & bottom of hexagon, outer corner of triangle) coincide with corners of triangles belonging to the outer Tree of Life, whilst the two green, vertical sides of sectors in the hexagon are sides of triangles in the outer Tree; they form either the Pillar of Mercy or the Pillar of Judgement. Therefore, five corners are either shared between the inner & outer forms of the Tree of Life or are endpoints of the root edge, whilst two sides of the 47 sectors in each set of 7 enfolded polygons are shared. The number of unshared corners outside the root edge = 41 − 5 = 36. The number of unshared sides outside the root edge = 88 − 2 − 1 = 85. The number of unshared corners, sides & triangles in the seven enfolded polygons outside their root edge = 36 + 85 + 47 = 168. Both sets of seven enfolded polygons have (168+168=336) geometrical elements outside the root edge that are unshared with the outer Tree of Life. The number of geometrical elements that are either in the root edge or shared between the outer & inner Trees of Life = 5 + 3 + 5 = 13. The seven enfolded polygons have (176−3=173) geometrical elements outside the root edge, so that the number of geometrical elements in the (7+7) enfolded polygons = 3 + 2×173 = 349. Hence, 349 − 13 = 336. This relates the superstring structural parameter 336 (number of circularly polarised waves in one revolution of each whorl of the UPA) to the number (349) of bits of geometrical information needed to construct the inner Tree of Life. The number 13 is the number of bits of information either defining the root edge or shared with the outer Tree of Life. It quantifies those geometrical elements that either do not shape the 14 regular polygons (root edge) or are not intrinsic to them (green corners or sides).

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