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  3108 geometrical elements in CTOL

91 overlapping Tree of Life consist of 3108 points, lines & triangles.* This number is the sum of the fourth powers of the first four odd integers:

3108 = 14 + 34 + 54 + 74.

This beautiful property reveals the unique status of this number of Trees of Life in CTOL as a representation of the 91 subplanes of consciousness. Such mathematical design cannot be, plausibly, dismissed as the product of chance. Instead, it is undeniable evidence of the transcendental origin of CTOL. Other remarkable, geometrical properties of CTOL are discussed in the author's new book. Its embodiment of this number is an illustration of the Tetrad Principle, formulated in Article 1, whereby defining parameters of holistic systems are numbers expressed by either the fourth member of a class of mathematical object or its first four members. Another example of this Pythagorean principle at work can be found here when the cubes of the first four odd integers in the 4×4 array shown opposite are replaced by their squares, generating the holistic parameter 496:

496 = 13 + 33 + 53 + 73.

This is the mysterious number at the heart of superstring theory whose sacred-geometrical basis is demonstrated in Superstrings as sacred geometry.

The inner form of the Tree of Life is the set of (7+7) enfolded regular polygons:

triangle, square, pentagon, hexagon, octagon, decagon, dodecagon.

They have 444 hexagonal yods (see here). As 3108 = 7×444, the (49+49) regular polygons making up the inner form of seven overlapping Trees contain 3108 hexagonal yods:

3108 hexagonal yods in inner form of 7 Trees of Life

In terms of the formal correspondence between the Tree of Life and the tetractys, the seven hexagonal yods in the latter correspond to the seven Sephiroth of Construction. Amazingly, the 3108 such yods in the inner form of seven Trees, each expressing one of these Sephiroth, denote the 3108 points, lines & triangles needed to construct the 91 Trees of Life that map the seven cosmic planes of consciousness, each formally corresponding to a Sephirah of Construction. This is how EL ChAI, the Godname of Yesod with number value 49, prescribes the geometrical composition of CTOL. It is a powerful example of how analogous sections of CTOL are characterised by the same parameters. The physical universe mapped by seven Trees of Life is analogous to CTOL itself mapped by 91 Trees of Life because each plane of consciousness is an expression of one of the seven Sephiroth of Construction, the physical plane being just their material manifestation. In fact, every plane is simply that aspect of their collective reality which is experienced from the perspective of the particular Sephirah of Construction that corresponds to that plane.

Another way in which EL ChAI determines the number 3108 is now explained: The section Polygonal numbers introduces the concept of polygonal numbers. PNn, the nth polygonal number of order N, is the number of dots needed to construct n N-gons nested inside one another with n dots equally spaced along each side of the outermost N-gon:

Polygonal number

PN1 = 1. Writing P3n ≡ Tn, P4n ≡ Sn, P5n ≡ Pn, P6N ≡ Hn, P8n ≡ On, P10n ≡ Dn & P12n ≡ dn, the sum of the first seven non-trivial polygonal numbers (i.e., numbers larger than 1) of orders corresponding to the seven regular polygons of the inner Tree of Life is:



 Σ (Tn + Sn + Pn + Hn + On + Dn + dn) = 3108.

(see the entry for c8 in Table 2 here). Therefore, the 49 polygonal numbers in this 7×7 array add up not only to the number of geometrical elements in CTOL but also to the number of hexagonal yods in the seven sets of seven regular polygons (i.e., 49 polygons) that make up the inner form of seven overlapping Trees of Life. The property demonstrates the remarkable harmony between the arithmetic and geometric aspects of the inner Tree of Life. The cosmic Whole (CTOL), composed of 3108 points, lines & triangles and mapping the seven cosmic planes, and its physical counterpart (the seven subplanes of the physical plane) embody the same number! This is simply because they bear a formal correspondence to each other, being different differentiations of the seven Sephiroth of Construction.

* Proof: n overlapping Trees of Life consist of (12n+4) triangles with (6n+4) corners & (16n+6) sides. Number of points, lines & triangles in n overlapping Trees = 34n + 14. For n = 91, this is 3108.

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