top of page

Tree of life superstring theory part 113

Updated: Nov 28, 2020


It consists of 16 triangles with 10 corners and 22 sides. Their conversion to Type A triangles (triangles divided into their three sectors) adds 16 corners and (3×16=48) sides, so that there are, upon this conversion, 48 triangles with (10+16=26) corners and (22+48=70) sides, i.e., 144 geometrical elements. Conversion of the original triangles into Type B triangles, i.e., changing the 48 new triangles into Type A triangles, adds 48 corners and (3×48=144) sides, so that there are now 144 triangles with (26+48=74) corners and (70+144=214) sides, i.e., 432 geometrical elements. They include (74+214=288) corners & sides, where 288 = 11 + 22 + 33 + 44. Notice that the construction of the outer Tree of Life from Type B triangles generates (74−10=64=43) corners and (214−22=192) sides, i.e, (64+192=256=44) new corners & sides. Here we see in a simple but remarkable way how the Pythagorean Tetrad expresses the new properties of the sacred geometry of the Tree of Life when it undergoes higher-order transformations.


Separately, the outer & inner Trees of Life have (74+174=248) corners, (214+457=671) sides & (144+282=426) triangles, where 248 is the number value of Raziel, the Archangel of Binah, and the dimension of the superstring gauge symmetry group E8. Each corner corresponds to a root of E8. Its eight simple roots correspond to the six corners coinciding with the locations of Sephiroth on the two side pillars and to the two corners that coincide with Tiphareth and Daath. Its 240 roots correspond to the 240 remaining corners. The six corners are shared with the inner Tree of Life, leaving (174−6=168) corners of the 282 triangles in the inner Tree that are unshared with the outer Tree. The two corners are intrinsic to the outer Tree but project onto the positions of the two endpoints of the root edge. Apart from the six corners, they are the only corners of triangles in the outer Tree that project onto corners of polygons making up the inner Tree. They leave (74−2=72) corners of the 144 triangles making up the outer Tree that are intrinsic to it. The72:168 division of the 240 corners is characteristic of this holistic parameter (see The holistic pattern). Its counterpart in the root composition of E8 is the 72 roots of E6, the rank-6, exceptional group of the symmetry group E8, and the remaining 168 roots of the latter (see here). In other words, the distinction between the outer and inner Trees of Life manifests in the subgroups of E8 as the difference between the symmetries of E6 and the remaining symmetries of E8.


When they are superimposed, the six Sephiroth on the side pillars coincide with the top and bottom corners of the two hexagons and their centres, whilst the two Paths on each side pillar coincide with internal sides of their sectors. No triangles are shared between the outer and inner Trees. To avoid double counting, these 10 shared geometrical elements must be subtracted when ascertaining the geometrical composition of the combined Trees of Life. In this case, they have 426 triangles with (248−6=242) corners and (671−2−2=667) sides, i.e., 1335 geometrical elements. There are 240 corners other than the endpoints of the root edge. The combined Trees have (242+426=668) corners & triangles (666 outside the root edge) and 667 sides (666 outside the root edge). There are (668−2−6=660) corners & triangles other than the two endpoints of the root edge and the six corners that are shared between the outer & inner Trees. 660 = 66×10, where 66 is the 65th integer after 1. This shows how ADONAI, the Godname of Malkuth with number value 65, prescribes the outer and inner forms of the Tree of Life. The number of corners, sides & triangles in the combined Trees = 242 + 667 + 426 = 1335. The number of corners & sides = 242 + 667 = 909. The number of corners & sides outside the root edge that do not include shared, Sephirothic points = 909 − 3 − 6 = 900 = 90×10. The number 90 is a holistic parameter, being the sum of the 10 integers making up the Lambda Tetractys (see here and here). As the table indicates that the (7+7) enfolded polygons have 913 corners, sides & triangles, of which three corners and sides make up the root edge and 10 corners & sides are shared with the outer Tree, the inner Tree of Life has 900 intrinsic corners, sides & triangles outside the root edge. This is discussed in detail here. The number of sides & triangles in the (7+7) enfolded polygons = 457 + 282 = 739. There are 369 sides & triangles on either side of the root edge. This is the sum of the number values of the Godnames of the first seven Sephiroth:

21 + 26 + 50 + 31 + 36 + 76 + 129 = 369 When the 282 triangles of the inner Tree of Life with Type B polygons are tetractyses, they contain 1370 yods (see #3). Each of the 16 primary triangles in the outer Tree of Life has 37 yods inside it when it is a Type B triangle. Each of their 22 sides has two hexagonal yods. The number of yods in the outer Tree of Life when its 16 triangles are Type B = 10 + 22×2 + 16×37 = 646. Starting with the 10 corners of these triangles, its conversion into Type B triangles generates (646−10=636) yods, where 636 is the number value of Rashith ha Gilgalim, the Mundane Chakra of Kether. Separately, the outer & inner Trees of Life have (646+1370=2016) yods. Seven yods are on each side pillar and are shared with the inner Tree of Life because they lie on sides of tetractyses in each hexagon. So are the two hexagonal yods on the Chesed-Geburah Path, which are the centres of the two enfolded triangles. Hence, these have to be subtracted when the Trees are combined in order to avoid double-counting. The number of yods in the pair of superimposed Trees = 2016 − 7 − 7 − 2 = 2000. 630 yods belong to the outer Tree and 1370 yods belong to its inner form, where 630 is the number value of Seraphim, the Order of Angels assigned to Geburah. The 14 polygons of the inner Tree has 68 corners outside its root edge, six of which are shared with its outer form. Hence, (68−6=62) corners outside the root edge are intrinsic to the inner Tree (31 for each set of seven polygons), where 31 is the number value of EL, the Godname of Chesed and 62 is the number value of Tzadkiel, the Archangel of Chesed. Of these, the outermost corners of the two pentagons coincide with the centres of the decagons. Hence, 60 intrinsic corners outside the root edge are pure corners. The number of yods in the combined outer & inner Trees of Life other than such corners = 2000 − 60 = 1940 =194×10, where 194 is the number value of Tzadekh, the Mundane Chakra of Chesed. Here is a remarkable instance of three numbers appearing naturally in the same context that refer to the same Sephirah!

The number of yods lining the 282 tetractyses of the inner Tree of Life = 1370 − 282 = 1088. (502+1088=1590) yods line tetractyses in the separate outer and inner Trees of Life. The number of yods on sides of the (144+282=426) tetractyses in the combined pair of Trees = 1590 − 7 − 7 − 2 = 1574. The number of such yods that are not shared = 1574 − 16 = 1558. They comprise the centres of the two sets of four polygons in the inner Tree if Life that do not coincide with corners (remember that the outermost corner of the pentagon is the centre of the decagon) and 1550 (=155×10) other yods surrounding them. This shows how ADONAI MELEKH, the Godname of Malkuth with number value 155, prescribes how many yods are needed to shape all the sectors of triangles making up the outer and inner forms of the Tree of Life (see also #21).

Firstly, consider the simplest case where the triangles of the outer Tree of Life are tetractyses and the polygons in its inner form are Type A. The former has 70 yods, of which 60 are hexagonal (see here). The latter has 524 yods (see here), of which 80 are corners of sectors (see here) and 444 are hexagonal (see here). There are eight hexagonal yods on the four sides of the sectors of the two hexagons that are shared with the outer Tree of Life because they lie on its side pillars. Although the two hexagonal yods on the Chesed-Geburah Path are also the centres of the two enfolded triangles, they still count as hexagonal yods in determining the hexagonal yod population of the combined Trees of Life. The number of hexagonal yods in the combined Trees = 60 + 444 − 8 = 496. This is both the number value of Malkuth and the dimension of E8×E8 & SO(32) — the two symmetry groups that allow interactions between superstrings that are free of quantum anomalies (see discussion here under the heading "Superstring gauge symmetry group"). What more explicit proof could there be that the Tree of Life encodes superstring theory — or, rather, M-theory, the 'theory of everything' that contains the five versions of superstrings as approximations?

Next, let us consider the case where both the triangles of the outer Tree of Life and the polygons of the inner Tree of Life are Type A. Inside each of the 16 triangles of the former are nine hexagonal yods. The number of hexagonal yods in the outer Tree = 22×2 + 16×9 = 44 + 144 = 188. The inner Tree of Life has 444 hexagonal yods, of which eight are shared with its outer form. The number of hexagonal yods in the combined Trees of Life = 188 + 444 − 8 = 624. As found in #1, this is the number of hexagonal yods in the seven separate Type B polygons. The 16 triangles in the outer Tree have (10+16=26) corners of 48 tetractyses and the 94 tetractyses in its inner form have 80 corners, of which six are shared as such and two (centres of the two triangles) coincide with hexagonal yods on the Chesed-Geburah Path. Combined, the two Trees of Life have (26+80−6−2=98) corners. Therefore, they have (624+98=722) yods, i.e., 718 yods other than the four yods in the root edge. Of these, 68 are corners of the (7+7) enfolded polygons. This leaves (718−68=650=65×10) yods outside the root edge that are not corners of polygons. This shows how ADONAI, the Godname of Malkuth with number value 65, prescribes the form of the combined Trees of Life. We saw in #17 that ADONAI also prescribes the 650 yods associated with each set of seven enfolded Type B polygons that are not their corners. In each case, this number is the extra number of yods needed to construct the Trees, given their Sephirothic points and/or polygonal corners.

Finally, let us consider the case where the triangles in the outer Tree of Life and the polygons of the inner Tree of Life are Type B (the case that was considered initially in the context of their geometrical compositions). Inside each Type B triangle are 33 hexagonal yods. The number of hexagonal yods in the outer Tree of Life = 22×2 + 16×33 = 572. The 282 tetractyses in the (7+7) enfolded polygons have 174 corners and 1370 yods. Therefore, they have (1370−174=1196) hexagonal yods. Eight of these are shared with the outer Tree of Life. The number of hexagonal yods in the combined Trees of Life = 572 + 1196 − 8 = 1760. We found in #26 at Superstrings as sacred geometry/Tree of Life that the seven enfolded Type A polygons have 176 hexagonal yods. This means that the 70 Type A polygons enfolded in 10 overlapping Trees of Life on each side of the central Pillar of Equilibrium have 1760 hexagonal yods. Embodied in the unified geometry of its outer and inner forms, the Tree of Life has as many hexagonal yods as its inner form has in 10 Trees of Life! This is remarkable, for its demonstrates how a single Tree of Life encodes its potential 10-fold development through a different order of transformation of its geometry. There are eight hexagonal yods shared by the two Trees of Life and two hexagonal yods in the root edge. Hence, (1760−8−2=1750=175×10) hexagonal yods are outside the root edge that are unshared. What emerges here is a division that is analogous to the 175/176 distinction in the augmentation of major and minor whorls of the UPA (see here). The number 175 determines unshared yods and the difference 1 between 175 and 176 determines either shared hexagonal yods or hexagonal yods in the root edge. This quality of being shared by both the outer & inner forms of the Tree of Life is characteristic of this difference when it manifests in other contexts, e.g., the first (6+6) enfolded polygons constitute a holistic subset of the (7+7) polygons and the first six polygons enfolded in seven overlapping Trees have 176 corners, of which 175 are intrinsic to the 42 polygons and one (the topmost corner of the hexagon enfolded in the seventh Tree) is shared with the hexagon enfolded in the eighth Tree because it coincides with its lowest corner. The fact that the seven Trees bear a formal correspondence to the seven Sephiroth of Construction when the ten Sephiroth of the Tree of Life are each replaced by Trees is further indication that the number 176 is a parameter of holistic systems.

25 views0 comments
bottom of page