Article 58

ARTICLE 58

by

Stephen M. Phillips

Flat 4, Oakwood House, 117-119 West Hill Road. Bournemouth. Dorset BH2 5PH. England.

Website: http://smphillips.mysite.com

Abstract

The inner form of the Tree of Life consists of two sets of seven regular polygons, one set being the mirror image of the other. The polygon in either set that has the most corners is the dodecagon. As it is the tenth type of polygon, three types of polygons are absent from the inner Tree of Life. Previous articles have shown that its seven types of polygons encode information about how this blueprint manifests in holistic systems. If they formally correspond to the seven Sephiroth of Construction, this suggests that the three absent polygons may correspond to the three members of the Supernal Triad, so that the first 10 regular polygons correspond to the 10 Sephiroth. This article uncovers amazing evidence of design, i.e., conceptual coherence, rather than unconnected disorder, that supports this conjecture. Data is provided in the form of the geometrical and yod compositions of the first ten regular polygons. They are found to embody the fine-structure number 137, the superstring structural parameters 168 & 840 and the dimension 496 of the two superstring gauge symmetry groups SO(32) & E₈×E₈.

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Table 1. Gematria number values of the ten Sephiroth in the four Worlds.

SEPHIRAH

GODNAME

ARCHANGEL

ORDER OF
ANGELS

MUNDANE
CHAKRA

1
Kether
(Crown)
620 EHYEH
(I am)
21 Metatron
(Angel of the
Presence)
314 Chaioth ha Qadesh
(Holy Living
Creatures)
833
Rashith ha Gilgalim
First Swirlings.
(Primum Mobile)
636

2
Chokmah
(Wisdom)
73 YAHWEH, YAH
(The Lord)
26, 15
Raziel
(Herald of the
Deity)
248 Auphanim
(Wheels)
187 Masloth
(The Sphere of
the Zodiac)
140

3
Binah
(Understanding)
67 ELOHIM
(God in multiplicity)
50
Tzaphkiel
(Contemplation
of God)
311
Aralim
(Thrones)
282
Shabathai
Rest.
(Saturn)
317

Daath
(Knowledge)
474

4
Chesed
(Mercy)
72 EL
(God)
31 Tzadkiel
(Benevolence
of God)
62 Chasmalim
(Shining Ones)
428
Tzadekh
Righteousness.
(Jupiter)
194

5
Geburah
(Severity)
216
ELOHA
(The Almighty)
36
Samael
(Severity of God)
131
Seraphim
(Fiery Serpents)
630
Madim
Vehement Strength.
(Mars)
95

6
Tiphareth
(Beauty)
1081
YAHWEH ELOHIM
(God the Creator)
76 Michael
(Like unto God)
101
Malachim
(Kings)
140
Shemesh
The Solar Light.
(Sun)
640

7
Netzach
(Victory)
148
YAHWEH SABAOTH
(Lord of Hosts)
129
Haniel
(Grace of God)
97 Tarshishim or
Elohim
1260
Nogah
Glittering Splendour.
(Venus)
64

8
Hod
(Glory)
15
ELOHIM SABAOTH
(God of Hosts)
153
Raphael
(Divine Physician)
311
Beni Elohim
(Sons of God)
112
Kokab
The Stellar Light.
(Mercury)
48

9
Yesod
(Foundation)
80
SHADDAI EL CHAI
(Almighty Living
God)
49, 363
Gabriel
(Strong Man of
God)
246
Cherubim
(The Strong)
272
Levanah
The Lunar Flame.
(Moon)
87

10
Malkuth
(Kingdom)
496
ADONAI MELEKH
(The Lord and King)
65, 155
Sandalphon
(Manifest Messiah)
280 Ashim
(Souls of Fire)
351
Cholem Yesodoth
The Breaker of the
Foundations.
The Elements.
(Earth)
168

The Sephiroth exist in the four Worlds of Atziluth, Beriah, Yetzirah and Assiyah. Corresponding to them are the Godnames, Archangels, Order of Angels and Mundane Chakras (their physical manifestation). This table gives their number values obtained by the ancient practice of gematria, wherein a number is assigned to each letter of the alphabet, thereby giving a number value to a word that is the sum of the numbers of its letters.

(Numbers in this table referred to in the article will be written in boldface).

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1. The 2nd-order Tetractys Pattern in the First 10 Polygons

The inner form of the Tree of Life comprises two similar sets of seven enfolded, regular polygons, one the mirror image of the other:

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

The dodecagon is the tenth regular polygon, so that three polygons are absent from the inner Tree of Life: the 7-sided heptagon, the 9-sided nonagon & the 11-sided undecagon. They are shown coloured white in Figure 1, the seven other types of polygons belonging to the inner Tree of Life being coloured the seven colours of the rainbow. This absence suggests the following analogy between the first 10 regular polygons and the 10 Sephiroth of the Tree of Life:

the three types of "absent polygons" → three Sephiroth belonging to the Supernal Triad, which express the subjective, 3-fold aspect of God (the triple Godhead) and which stand outside all levels of reality;

the seven types of polygons making up the inner Tree of Life → seven Sephiroth of Construction, which express the objective, 7-fold aspect of God and which manifest in His Creation.

Figure 1. The first (10+10) enfolded polygons.

Despite the fact that the geometry of overlapping circles that generates the inner Tree of Life (see here) does not create three of the first 10 regular polygons, these absent polygons, being analogous to the archetypal Supernal Triad as the source of all levels of existence, might be expected to have properties that are analogous to those found in the seven types of polygons, if this analogy between Sephiroth and polygons really holds. Let us now investigate whether this is true.

The number of corners of the n sectors of an n-gon = n + 1. The separate heptagon (n=7), nonagon (n=9) & undecagon (n=11) have 27 sectors with 30 corners. Enfolded, they have (30−2−2=26) corners, the two mirror-image sets having 50 corners, where 26 is the number value of YAHWEH, the Godname of Chokmah, and 50 is the number value of ELOHIM, the Godname of Binah. These two Sephiroth head the Pillars, respectively, of Mercy and Judgement in the Tree of Life. As such, their Godnames prescribe the

Figure 2. The 2nd-order tetractys character of the first 10 separate polygons.

geometry of the three absent polygons in the simplest possible way. The seven separate polygons of the inner Tree of Life have 48 sectors with (48+7=55) corners, where 55 is the tenth triangular number:

1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 = 55.

Figure 2 shows the first 10 polygons arranged in a tetractys, the numbers denoting their corners. As they are analogous to the three Sephiroth of the Supernal Triad, the three absent polygons are located at the corners of the tetractys. The dodecagon occupies its centre because, as the last of the polygons making up the inner Tree of Life, it corresponds to Malkuth, the final Sephirah of Construction. The two triplets of polygons: (triangle, square, pentagon) & (hexagon, octagon, decagon) correspond to the two triads of

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Sephiroth of Construction: Chesed-Geburah-Tiphareth & Netzach-Hod-Yesod (Fig. 3). The 10 separate polygons have (27+48=75) sectors with (30+55=85) corners. This is the number of yods making up the 10 tetractyses in a 2nd-order tetractys. Moreover, the tetractyses at its three corners contain 30 yods, the seven other tetractyses containing 55 yods. The former are analogous to the 30 corners of the 27 sectors of the three absent polygons and the latter are analogous to the 55 corners of the 48 sectors of the seven polygons in the inner Tree of Life.

Figure 3. The two triads of Sephiroth of Construction.

The white centres of the three corner tetractyses correspond to the centres of the three absent polygons, their 27 blue yods correspond to the 27 corners of the latter, the seven black centres of the seven coloured tetractyses correspond to the centres of the seven polygons and their 48 red yods correspond to the 48 corners of these polygons (the six red corners of tetractyses correspond to the six corners of the hexagon and the 42 red hexagonal yods correspond to the 42 corners of the six other polygons). We see from these detailed correspondences that the 2nd-order tetractys symbolizes the first 10 polygons, with that part of it corresponding to the Supernal Triad symbolizing the three absent polygons and that part corresponding to the seven Sephiroth of Construction symbolizing the seven types of polygons in the inner Tree of Life. Here is mathematical confirmation that an analogy between the 10 Sephiroth of the Tree of Life and the first 10 types of polygons does, indeed, exist; there are far too many correspondences to be attributable, plausibly, to chance.

Tabulated below are the geometrical compositions of the 10 Type A polygons, the three absent Type A polygons and the seven Type A polygons of the inner Tree of Life (numbers in brackets refer to both sets):

Table 1. Geometrical composition of the 3, 7 & first 10 polygons.

10 polygons

3 absent polygons

7 polygons

separate

enfolded

separate

enfolded

separate

enfolded

Number of corners of sectors (C)

85 (170)

65 (128)

30 (60)

26 (50)

55 (110)

41 (80)

Number of sides of sectors (S)

150 (300)

139 (277)

54 (108)

52 (103)

96 (192)

88 (175)

Number of sectors (T)

75 (150)

74 (148)

27 (54)

27 (54)

48 (96)

47 (94)

Number of geometrical elements

310 (620)

278 (553)

111 (222)

105 (207)

199 (398)

176 (349)

Comments

1. The Godname EL of Chesed with number value 31 prescribes the geometrical composition of the 10 separate polygons because they have 310 (=31×10) corners, sides & triangles. Both sets of 10 separate polygons have 620 geometrical elements. 620 is the number of Kether ("Crown") (Fig. 4).

Figure 4

2. The first (10+10) enfolded polygons have 553 geometrical elements, i.e., 550 elements outside their shared side. This is remarkable for two reasons: 1. 550 = 10(1+2+3+4+5+6+7+8+9+10), i.e., the Decad determines the geometrical composition of the first (10+10) enfolded polygons; 2. the number of SLs in the Cosmic Tree of Life is 550 (see here). Embodied, therefore, in the geometrical composition of the first (10+10) enfolded polygons is CTOL! It is the polygonal counterpart of the 550 geometrical elements in the faces of the five Platonic solids (see here);

3. Figure 5 shows the 74 sectors of the first 10 enfolded polygons (the sectors of the three absent polygons have black sides). They have 65 corners, where 65 is the number value of ADONAI, the

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Figure 5. The 74 sectors of the first 10 enfolded polygons.

Godname of Malkuth, and the sum of the first 10 integers after 1:

2

3

4

65 =
5 6 7

8

9

10
11

ADONAI prescribes the lowest 10 overlapping Trees of Life because they have 65 SLs (see here), so it is highly appropriate that it should determine the geometrical form of the first 10 enfolded polygons. They also have 65 sides outside their shared side. Both sets of 10 enfolded polygons have (65+1+65 =131) sides, where 131 is the number value of Samael, the Archangel of Geburah. The sectors of the 10 enfolded polygons have 139 sides. Remarkably, this is the number of yods in the first five enfolded polygons of the inner Tree of Life (Fig. 6).