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#21 ADONAI MELEKH prescribes the combined outer & inner Trees of Life
We saw in #19 that ADONAI MELEKH with number value 155 prescribes the superimposed outer and inner Trees of Life when their triangles and polygons are both Type B because 1550 (=155×10) yods line their tetractyses. It will now be shown that this complete Godname of Malkuth with the pentagramic representation shown in #11 also prescribes them when the outer Tree consists of Type A triangles and the polygons of the inner Tree are Type B.
There are 10 yods inside each of the 16 Type A triangles of the outer Tree of Life, which have 10 corners and 22 sides, with two hexagonal yods on each one. Number of yods in outer Tree of Life = 16×10 + 22×2 + 10 = 214. Of these, 10 turquoice yods are Sephiroth and 10 other yods (four hexagonal yods on each side pillar and the two hexagonal yods on the Chesed-Geburah Path) are shared with the hexagons and triangles of the inner Tree of Life, leaving 194 black yods, where 194 is the number value of Tzadekh, the Mundane Chakra of Chesed. The inner Tree of Life has 1370 yods when its (7+7) enfolded polygons are Type B (see here). Of these, four yods line the root edge and five turquoice yods in each set of seven polygons are centres of the triangle, square, pentagon, octagon & dodecagon that do not also coincide with corners of polygons. The number of yods in the (7+7) enfolded polygons outside their root edge that surround the centres of these 10 polygons = 1370 − 4 − 5 − 5 = 1356. The total number of yods other than Sephiroth in the outer & inner Trees of Life that are outside the root edge and which surround these centres = 194 + 1356 = 1550 = 155×10. It is amazing that the same number appears in two different contexts. It does so because, as the number value of the complete Godname of Malkuth, the number 155 quantifies in each case the form, or Malkuth aspect, of the combined outer & inner Trees of Life when constructed from tetractyses. As 155 is the sum of the first 10 integers after 10:
1550 is 10 times the sum of the first 10 integers after 10, demonstrating how the Decad arithmetically determines this yod population of the combined Trees of Life. See #11 for how the 10-sided decagon represents the number 155.
48 of the 214 yods in the outer Tree of Life are centres of tetractyses. Therefore, (214−48=166) yods line the (22+48=70) sides of its 48 tetractyses. 26 of these are corners, leaving 140 hexagonal yods, where 26 is the number value of YAHWEH, the Godname of Chokmah, and 140 is the number value of Masloth, the Mundane Chakra of this Sephirah. The seven yods lining each side pillar of the Tree of Life and the two hexagonal yods in the path connecting Chesed and Geburah are shared with the polygons of the inner Tree of Life, so that (166−16=150=15×10) yods lining sides of tetractyses in the outer Tree are intrinsic to it, where 15 is the number of YAH, the older version of the Godname assigned to Chokmah. Ten of the 166 yods lining the 70 sides of the 48 tetractyses are Sephiroth, leaving 156 yods, where 156 is the 155th integer after 1. This shows how ADONAI MELEKH prescribes the shape of the outer Tree of Life with Type A triangles. Starting with the 10 Sephiroth at the corners of the 16 triangles of the Tree of Life and with Daath at the centre of the triangle with Chokmah, Binah & Tiphareth at its corners, (166−10−1=155) yods are needed to line the 70 sides of the 48 tetractyses (see diagram opposite). Starting with a single point (Kether), 165 yods are needed to delineate these tetractyses in the outer Tree of Life, where
165 = 12 + 32 + 52 + 72 + 92.
The 16 Type A triangles in the outer Tree of Life have 48 sectors; the (7+7) Type B enfolded polygons consist of 282 triangles. Combined, they comprise 330 triangles, where
and 33 = 1! + 2! + 3! + 4!. This number with well-known Masonic significance is, therefore, a measure of the geometry of the combined outer & inner Trees of Life. Amazingly, the number 33 also determines the yod population of the inner Tree of Life with Type A polygons, for this is 1370 (see here), which is the number of yods in 137 tetractyses, where 137 (the mysterious, dimensionless number in atomic physics whose reciprocal is the approximate value of the fine-structure constant) is the 33rd prime number!
55 = 12 + 22 + 32 + 42 + 52
385 = 7×55 = 12 + 22 + 32 + 42 + 52 + 62 + 72 + 82 + 92 + 102,
330 = 385 − 55 = 62 + 72 + 82 + 92 + 102.
The number of yods in n overlapping Trees of Life is given by
Y(n) = 50 + 20.*
Therefore, the number of yods in every 31 Trees = Y(n+31) − Y(n) = 31×50 = 1550. As we found above, this is the number of yods other than Sephiroth in the outer & inner Trees of Life that are outside the root edge and surround the (5+5) independent centres of polygons. We conclude that EL, the Godname of Chesed with number value 31, prescribes the yod population of the combined Trees.
* Proof: when they are turned into tetractyses, the (12n+4) triangles of n overlapping Trees of Life have (6n+4) corners and (16n+6) sides, two hexagonal yods lying on each side. The number of yods in n overlapping Trees = 6n + 4 + 2(16n+6) + 12n + 4 = 50n + 20.
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