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 84 as a parameter of sacred geometries
#30 Examples of the holistic parameter 84

a) The 2nd-order tetractys has 85 yods, where

85 = 40 + 41 + 42 + 43.

Surrounding its central one (white yod) are 84 yods, where

84 = 12 + 32 + 52 + 72.

What this means is that 84 differentiations of Sephiroth higher than Malkuth become expressed in the last one — the 85th — when generating the outer form of a holistic system, symbolised by this yod. The example par excellence of this on the cosmic scale is provided by the Cosmic Tree of Life. Its 91 Trees of Life comprise 84 Trees that extend above the 7-tree mapping the seven subplanes of the physical universe and express the six Sephiroth of Construction above Malkuth.

b) A Type B triangle has 46 yods. Two such joined triangles have 88 yods. 84 red yods are outside the root edge containing four black yods. Alternatively, given the two joined triangles, 84 more yods are needed to transform them into Type B triangles.

c) The Lambra Tetractys (see here) is a tetractys of 10 integers. It is the arithmetic representation of the fundamental structure of holistic systems. The sum of the nine integers surrounding the circled, central integer 6 is 84.

d) The lowest Tree of Life in any set of overlapping Trees is the 1-tree. It is made up of 80 yods, where 80 is the number of Yesod (see table in #1). There are two hexagonal yods on either side of the central Pillar of Equilibrium up to its apex that belong to the second Tree. There are 84 yods up this point. They comprise 48 red yods up Chesed, the first Sephirah of Construction, and 36 black yods above this Sephirah. 48 is the number value of Kokab, the Mundane Chakra of Hod, and 36 is the number value of ELOHA, the Godname of Geburah.

e) Of the 84 yods surrounding the centre of the 2nd-order tetractys, 48 red yods are hexagonal yods of the seven 1st-order tetractyses expressing the seven Sephiroth of Construction and 36 black yods are either corners of 1st-order tetractyses or hexagonal yods of the 1st-order tetractyses at the three corners of the 2nd-order tetractys (in both cases, they symbolize the Supernal Triad of Kether, Chokmah & Binah).

f) Outside the root edge are 84 yods lining the sides of the first six enfolded polygons. They comprise 48 red yods on the sides of the square, hexagon & decagon and 36 black yods on the sides of the triangle, pentagon & octagon. It is readily verified that these are the only possible combinations of polygons with either 36 or 48 yods lining their sides outside the root edge. Associated with each set of the first six enfolded polygons are 168 yods other than their corners, where 168 is the number value of Cholem Yesodeth, the Mundane Chakra of Malkuth. Remarkably, the former combination of polygons has 90 yods and the latter combination has 78 yods, where 90 is the number of Yesodeth and 78 is the number of Cholem:

(78+90) yods other than corners in 1st 6 enfolded polygons

In other words, the region of the 1-tree above Chesed, whose 36 yods correspond to the 36 yods lining the triangle, pentagon & octagon, determines the number of Cholem, whilst the region up to Chesed, whose 48 yods correspond to the 48 yods lining the square, hexagon & decagon, determines the number of Yesodeth! The likelihood that this could be coincidental is implausible in the extreme. Instead, what this remarkable property demonstrates is the way in which the geometrical basis of the ancient Hebrew Godnames, Archangelic Names, Orders of Angels & Mundane Chakras remains mathematically meaningful in sacred geometries other than the one that has been historicallly associated with them, namely, the outer form of the Tree of Life (Otz Chiim). It is because they have a mathematical meaning that they transcend their cultural origin.

As we saw in #7, the 36:48 division appears in the 3-dimensional Sri Yantra as the 36 corners of its first & second layers of triangles and the 48 corners of its third & fourth layers of triangles.

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