#70 The inner form of seven overlapping Trees of Life encodes the geometrical composition of CTOL

The 91 overlapping Trees of Life in CTOL comprise 3108 corners, sides & triangles.	The (49+49) polygons of the inner form of 7 Trees of Life contain 3108 hexagonal yods.

n overlapping Trees of Life have:

(6n+4) corners of triangles;
(16n+6) sides of triangles;
(12n+4) triangles.

Total number of geometrical elements ≡ N(n) = 34n + 14.

49 overlapping Trees of Life constitute a representation of the 49 subplanes of the cosmic physical plane — the lowest of the seven cosmic planes of consciousness. This is the cosmic counterpart of the physical plane mapped by seven overlapping Trees of Life. The number of geometrical elements making up 49 overlapping Trees = N(49) = 1680 = 168×10, i.e., the number of yods in 168 tetractyses. This is the number of circular turns in each helical whorl of the UPA/subquark superstring (see here). To every circularly polarised oscillation in this standing wave there corresponds a geometrical element that is a structural component of 49 Trees of Life. The cosmic physical plane is the cosmic manifestation of Malkuth and this is why its Tree of Life representation embodies the gematria number value 168 of Cholem Yesodoth, the Mundane Chakra of this Sephirah. See also here. This amounts to a spectacular connection between a purported, paranormal observation published over a century ago, the Theosophical doctrine of the seven planes of consciousness and mathematical properties of their representation by Trees of Life. The logical consistency between its features renders highly improbable the sceptic's suggestion that coincidence could be at work here.

The Cosmic Tree of Life (CTOL) maps the seven cosmic planes. The number of geometrical elements in its 91 overlapping Trees of Life = N(91) = 3108. This is the sum of the fourth powers of the first four odd integers:

3108 = 1⁴ + 3⁴ + 5⁴ + 7⁴.

It is a striking example of the Tetrad Principle (formulated here) at work in describing global properties of holistic systems. This number can also be expressed as a square array of the cubes of these four odd integers:

When their (47+47) sectors are tetractyses, the (7+7) enfolded polygons of the inner Tree of Life contain 444 hexagonal yods (see here). The (49+49) polygons enfolded in seven overlapping Trees of Life contain (7×444=3108) hexagonal yods. This is the number of corners, sides & triangles in CTOL. It is, of course, not a miraculous coincidence. Instead, it is one of many striking examples discussed in this section of how sacred geometries embody properties of holistic systems quantified by the same parameters.

A set of seven overlapping Trees is analogous to the complete set of 91 Trees because both sets are representations of the seven Sephiroth of Construction. The lowest seven overlapping Trees of Life map the seven subplanes of the physical plane (the space-time continuum) discussed by Theosophical writers. They bear a one-to-one correspondence with the seven Sephiroth of Construction, just as the seven planes and the seven cosmic planes do. The inner form of seven overlapping Trees of Life embodies the same number quantifying hexagonal yods that symbolize the seven Sephiroth of Construction as that quantifying the geometrical composition of the outer form of 91 Trees of Life. This fact is powerful evidence of the truth of the hermetic axiom "As above, so below" (see also here), for it illustrates how analogous sections of CTOL embody the same parameters (in this case, the number 3108).

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