ARTICLE 6

by

Stephen M. Phillips

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

Website: http://smphillips.mysite.com      

ABSTRACT

Introduction
Previous articles discussed how all levels of reality are mapped by the Cosmic Tree of Life (CTOL). It consists of 91 overlapping Trees of Life with 550 ‘Sephirothic levels’ (SLs). This geometrical representation was shown to confirm the Theosophical teaching about the seven planes of consciousness and their seven-fold division. The lowest 49 trees map the 49 subplanes of the cosmic physical plane and the remaining 42 trees map the 42 subplanes of the six cosmic superphysical planes. Article 5 revealed the remarkable analogy between the E₈×E₈ heterotic superstring constituent of up and down quarks described by the Theosophists Annie Besant & C.W. Leadbeater and the geometrical structure of CTOL — in particular, its embodiment of the structural parameter 251 and the way in which this number defines the cosmic physical plane, of which the superstring is the most physical basic unit. In this article, a certain section of CTOL, namely, the 41-tree, will be shown to incorporate this number as well as other information about the structure and dynamics of the superstring. The analysis will demonstrate that the gematria number values of the Hebrew names of the Sephiroth, their Godnames, Archangels, Orders of Angels and Mundane Chakras characterise the mathematical description of the 41-tree too often to be plausible attributed to chance. This means that, as with any mathematical object possessing true sacred geometry, the presence of these numbers as descriptors of its properties elevates the status of the 41-tree to that of a holistic structure, that is, one that embodies the divine archetypes. For reference, the table below lists these numbers. They are written throughout the text in boldface type.

NUMBER VALUES OF THE SEPHIROTH IN THE FOUR WORLDS
(Cited numbers are in coloured boxes)

1. The ten-fold superstring
Analysis (1) of the clairvoyant observations (2) by the Theosophists Annie Besant (1847-1933) and C.W. Leadbeater (1854-1934) (Fig. 1) of the basic units of matter they called ‘ultimate physical atoms’ (UPAs) proved that these particles are the superstring constituents of the up and down quarks making up atomic nuclei. They noticed two varieties of these spinning particles — so-called 'positive' and ‘negative’ UPAs (Fig. 2), one the mirror image of the other. Both consist of ten closed

curves, or ‘whorls,’ each of which spirals five times around the axis of spin, making 2½ revolutions as it spirals down from the broad

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top of the particle to its pointed end and then 2½ revolutions in a narrower helix as it returns to its top. According to Leadbeater, a whorl is a helical coil with 1680 turns. It was interpreted in Reference 1 as a closed, string-like curve embedded in 26-dimensional space-time. It was proposed (3) in Articles 2 & 5 that the superstring is formed by the wrapping of an 11-brane around ten compactified dimensions of this space-time beyond the ten-dimensional space-time required by superstring theory. This creates ten closed curves, each characterised by 25 spatial co-ordinate variables, so that the total number of space-time coordinate variables for the ten whorls making up a superstring is 10×25 + 1 = 251.

The top of the 41-tree in CTOL is the 251st SL. The top of the 49-tree is the 299th SL. The 251st SL is therefore the 49th from the top of the 49th tree. Since the 49th tree from the top of CTOL is the 43rd from its bottom, the bottom of the 49th tree from the top of CTOL is also the bottom of the 43rd from the nadir of CTOL, i.e., the top of the 41st tree. The 251st SL is therefore both the 49th from the top of the 49th tree and the bottom of the 49th tree from the top of CTOL. This shows how the Godname EL ChAI of Yesod with number value 49 prescribes the 41-tree. There are 251 SLs beyond the 7-tree in 49 overlapping trees, just as there are 251 SLs in CTOL beyond the 49-tree. The section of the 49-tree above the 7-tree is to the latter what the section of CTOL representing cosmic superphysical planes is to the cosmic physical plane. Just as the number 251 is the number of emanations of the six Sephiroth of Construction above Malkuth before the cosmic physical plane is reached, as well as the number of their emanations above the physical plane, so, too, this number is the number of degrees of freedom expressing the geometry of the subquark state of the superstring. Section 2 will discuss its encoding in the inner form of the Tree of Life. Its remarkable encoding in the lowest tree of CTOL representing Malkuth will be discussed in Section 3.

With all its triangles turned into tetractyses, the number of yods in the n-tree is given by Y(n) = 50n + 30.

Y(n+5) – Y(n) = 5×50 = 250,

i.e., five successive trees contain 250 yods. As the number of SLs in the n-tree is

S(n) = 6n + 5,

there are S(n+5) – S(n) = 6×5 = 30 SLs in every five trees, i.e., counting from the top of the (n+5)th tree to the top of the nth tree, there are 31 SLs and 251 yods in every five trees (Fig. 3). This shows how the Godname EL of Chesed with number value 31 prescribes the number 251.

The Godname EHYEH of Kether prescribes the numbers 41 and 251 because 41 is the 21st odd integer and 251 is the 126th odd integer, where 126 is the sum of the number values of all different combinations of the letters of EHYEH:

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The 251st SL is the 127th tree level (4), where 127 is the 31st prime number. This shows how EL prescribes the 41-tree. As CTOL has 276 tree levels (5), the 251st SL is the 150th tree level from the top of CTOL, where 150 = 15×10. This shows how the number value 15 of YAH determines the 41-tree. Also, 41 = 26 + 15, where 26 is the number of YAHWEH, the full Godname of Chokmah. There are 167 stages of vertical descent of the Lightning Flash from Kether of the 41st tree (6), that is, 168 stages of descent of the Lightning Flash from Geburah of the 42nd tree generate the 251 SLs in the 41-tree. As shown in Article 5, this is an example of the close association between the number 251 and the number 168 of the Mundane Chakra of Malkuth — a structural parameter of the superstring (see previous articles).

The 41st tree in CTOL is the 51st from its top. 51 is the 26th odd integer, showing how YAHWEH prescribes the 41-tree. 50 trees extend above it, indicating how ELOHIM, the Godname of Binah with number value 50, prescribes this section of CTOL. ELOHIM prescribes the number 251 because below the highest Binah of 50 overlapping trees are 2510 (=251×10) yods (7).

The 251 SLs of the 41-tree comprise the 11 SLs of the 1-tree and 240 SLs in the 40 trees above the latter. As Kether of the 41st tree is the 85th SL on the Pillar of Equilibrium and as Kether of the first tree is the fifth SL on this pillar, the 240 SLs comprise 80 SLs on the central pillar and 160 SLs on the two side pillars, where 80 is the number value of Yesod (“Foundation”). This 160:80 differentiation of the number 240 has its analogy in the UPA/superstring. There are 160 (10×16) co-ordinate variables of the ten whorls of the superstring in the 16-dimensional space beyond superstring space-time and 80 (10×8) transverse co-ordinate variables in relation to the latter, each whorl having eight transverse dimensions in the ten-dimensional space-time in which they exist as such. The 11 SLs belonging to the 1-tree correspond to the ten longitudinal co-ordinate variables of the ten whorls (their extension in ordinary space), whilst the 240 SLs in the 41-tree above the 1-tree correspond to the 240 transverse co-ordinate variables of the ten whorls, each one having 24 transverse co-ordinate variables. This means that the three thicker, so-called ‘major’ whorls in the particle described by Besant and Leadbeater are curves with 72 such variables and that the remaining seven, so-called ‘minor’ whorls (see Fig. 2) are strings with 168 co-ordinate variables.

The 29-tree has S(29) = 179 SLs. The top of the 29th tree is the 91st tree level (8), i.e, the 84th above the 1-tree, which has seven tree levels. According to Article 2 (9), the 26th tree level (50th SL) is the dimension of time. The 179th SL is both the 129th SL and the 65th tree level above the 50th SL. It is also the 168th SL above the 1-tree. There are 72 SLs in the 41-tree above the 29-tree: 251 – 179 = 72. The division:

240 = 72 + 168

is therefore prescribed by ELOHIM and ADONAI, Godname of Malkuth. The division:

127 = 26 + 101

between the 26 tree levels defining 26-dimensional space-time and the 101 higher tree levels up to the top of the 41st tree is defined by YAHWEH because 101 is the 26th prime number.

The top of the 16-tree is the 101st SL and the 52nd tree level (10), where 52 is the 26th even integer. This is the 76th tree level from the top of the 41-tree and the 90th SL from the top of the 1-tree. This shows how YAHWEH ELOHIM with number value 76 defines the division:

168 = 78 + 90

that mirrors how the number value 168 of Cholem Yesodoth, the Mundane Chakra of Malkuth, divides into

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78 and 90, the component number values of, respectively, the two words Cholem and Yesodoth:

Forty-one overlapping trees have 496 triangles (11). Remarkably, the number of Malkuth and the dimension of the superstring symmetry groups is embodied in 41 trees as the number of simplest shapes creating their 3-dimensional structure, these shapes being marked out by the 250 corners of their triangles. This should be compared with the fact that an heterotic superstring with 250 spatial co-ordinate variables possessed by its ten whorls is the source of 496 gauge bosons transmitting the unified, E₈×E₈- or SO(32)-symmetric, superstring force. That such a number central to superstring physics should occur in a section of CTOL whose structure has already been shown to be analogous to the ten-fold superstring is no accident. Instead, it is an example of the way in which ‘analogous sections of CTOL encode the same parameters characterising holistic systems, such as 251 and 496 (see Article 5 for more examples).

The 12 trees extending beyond the 29-tree to the 41st tree have 72 SLs and the 28 trees extending beyond the 1-tree to the 29th tree have 168 SLs. This 72:168 differentiation corresponds in the superstring described by Besant and Leadbeater to the 72 E₈ gauge charges carried by the superstring in its three major whorls, 24 spread out over each whorl, and to the 168 gauge charges similarly carried by the superstring in its seven minor whorls. E₈ has the exceptional subgroup E₆, studied as physicists as a possible symmetry group that accommodates the Standard Model of particle physics. It has 72 roots and six simple roots, whilst E₈ has 240 roots and eight simple roots, that is, 168 more roots than E₆. Symmetry breaking of E₈ into E₆ may account for the difference between the major and minor whorls if each whorl does, indeed, carry 24 of the 240 E₈ gauge charges, 72 of which are gauge charges of E₆.

The 22-tree has 137 SLs, of which 126 are above the 1-tree. They include the 72 SLs of the 13-tree above the 1-tree. 72 is the number of roots of E₆, which is a subgroup of E₇, an exceptional subgroup of E₈ with 126 roots. The top of the 22-tree is the 70th tree level and the 91st stage of descent of the Lightning Flash. The differentiation:

240:126:72

between the roots of E₈, E₇ and E₆ corresponds to the number of SLs in, respectively, the 41-tree, the 22-tree and the 13-tree that are above the 1-tree.

Chesed of the 23rd tree is the 139th SL and the 128th SL above the 1-tree, above which are 112 SLs to the top of the 41-tree. The next higher SL (Daath of the 23rd tree) is the 140th SL and the 48th SL on the central pillar. The 112th SL from the top of the 41-tree is therefore both the 140th SL and the 48th SL on the central pillar. This 128:112 division of SLs corresponds to the 128:112 differentiation of the 240 roots of E₈ that is known to mathematicians. It is therefore prescribed by the number value 140 of Malachim, the Angelic Order assigned to Tiphareth, the number value 48 of Kokab, the Mundane Chakra of Hod and the number value 112 of Beni Elohim, the Order of Angels assigned to Hod. In fact, this differentiation is found to be defined by the number values of all the Godnames, Archangelic Names, Angelic Names and Mundane Chakras because it is a property of any Tree of Life pattern. Indeed, the sum of the first four Godnames EHYEH, YAHWEH, ELOHIM & EL is 128 and the sum of the next two Godnames ELOHA and YAHWEH ELOHIM is 112.

The 251 SLs of the 41-tree comprise 91 SLs up to Chesed of the 15th tree and 160 SLs beyond it. The former consists of 60 SLs on the side pillars and 31 SLs on the central pillar. The divisions:

251 = 91 + 160

and

91 = 31 + 60

correspond in the superstring to the 31 space-time co-ordinate variables of its ten whorls in 4-dimensional space-time, to their 60 co-ordinate variables defined in the 6-dimensional compactified space of superstring space-time and to their 160 co-ordinate variables defined in the higher, 16-dimensional space outside superstring space-time. This is how the Godname YAH with number value 15 and the Godname EL with number value 31 prescribe vis-à-vis, respectively, 10- and 4-dimensional space-time the number of spacetime co-ordinates of its ten whorls.

YAH and YAHWEH prescribe the division of the 251 co-ordinate variables into (10×10 + 1 = 101) spacetime co-ordinate variables defined vis-à-vis 11-dimensional, supergravity space-time and 150 (=15×10) variables defined in the higher, 15-dimensional space because 15 is the number value of YAH and 101 is the 26th prime number, where 26 is the number value of YAHWEH. The division is prescribed also by ELOHIM because there are 50 SLs on the central pillar in the 41-tree above the 101st SL, whilst 101 is the 50th odd integer after 1. YAHWEH ELOHIM with number value 76 prescribes this division because the 101st SL is the 151st SL from the top of the 41-tree, where 151 is the 76th odd integer. The 101st SL is also the 76th tree level from the top of the 41-tree.

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ELOHA prescribes the division of the 240 SLs in the 41-tree above the 1-tree into the 168 SLs of the 29-tree above the 1-tree and the 72 SLs above the 29-tree because its number value 36 is the number of tree levels in the 41-tree above the 29-tree: 127 – 91 = 36.

Counting from the highest (adi) plane, the 41st tree represents the second subplane of the second plane—the Theosophists’ anupadaka plane. Its Kether — the 251st SL — is the Malkuth of the 43rd tree representing the lowest subplane of the adi plane. The 251st SL therefore denotes the lowest (Malkuth) level of the lowest subplane of this plane. As the lowest point of the highest 49 trees in CTOL, this SL represents the completion of a cycle of 7-fold differentiation in the emanation of each of the seven Sephiroth of Construction. Although the 49-tree is itself such a cycle, only trees 43–49 belong to both cycles, whilst the 251st SL is the last SL of the uppermost 49 trees to be part of the emanation of both cycles. It is this property that makes the 41-tree and its highest point unique.

2. The inner form of the Tree of Life
The Tree of Life has an inner as well as an outer form (Fig. 4). The former consists of two identical sets of seven regular polygons that enfold in one another and share their root edge (Fig. 5). As was pointed out in previous articles, the seven polygons encode the 49-tree representing the cosmic physical plane and the five polygons in the other set with most corners encode the 42 trees of CTOL representing the six superphysical planes. It is remarkable that their composition is such that the five polygons with the least number of corners (the first five separate polygons containing 26 corners) encode the lowest 26 trees of CTOL that bear a formal correspondence to the lowest 26 tree levels denoting the 26 dimensions of spacetime, whilst the five separate polygons in the set of seven with the largest number of corners (the last five) have 41 corners and 251 yods (Fig. 6), that is, they encode the 41-tree with 251 SLs — the very number of space-time co-ordinates of ten whorls in

26-dimensional space-time! The reason why the five largest polygons encode this structural parameter of strings is that they constitute a new Tree of Life pattern prescribed by the ten Godnames, as now shown. Their properties are set out below: 

	pentagon	hexagon	octagon	decagon	dodecagon
Number of corners =	5	6	8	10	12
Number of yods =	31	37	49	61	73

5 separate polygons
1. Number of corners of 5 polygons = 41 = 21st odd integer.

 

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2. Number of corners of 41 tetractyses in 5 polygons = 41 + 5 = 46 (= 48, including the separate root edge);

3. Number of sides of 5 polygon = 41;

4. Number of edges of 41 tetractyses = 2×41 = 82;

5. Number of corners + edges of tetractyses = 46 + 82 = 128 (= 131, including the separate root edge);

6. Number of corners + edges + triangles = 128 + 41 = 169;

7. Number of yods = 251;

8. Number of yods other than corners = 251 – 41 = 210 = 21×10;

9. Number of yods along boundaries of polygons = 3×41 = 123 (127, including the separate root edge; 127 = 31st prime number). Number of boundary yods in (5+5) polygons = 2×123 = 246;

10. Number of yods along edges of tetractyses = 5×41 + 5 = 210 = 21×10;

11. When the five separate polygons become enfolded, four of their edges coincide with the fifth, so that (4×2=8) corners, four edges and (4×4=16) yods (including (4×2=8) hexagonal yods) disappear, whilst a corner of the pentagon coincides with the centre of the decagon.

5 enfolded polygons
1. Number of corners = 41 – 8 = 33 (31 outside root edge);

2. Number of corners of 41 tetractyses = 33 + 4 = 37 (35 outside root edge);

3. Number of sides of 5 polygons = 41 – 4 = 37 (36 outside root edge);

4. Number of corners + sides of polygons = 33 + 37 = 70 (67 outside root edge);

5. Number of edges of tetractyses = 82 – 4 = 78 (77 outside root edge);

6. Number of corners + edges of tetractyses = 37 + 78 = 115 (112 outside root edge);

7. Number of corners, edges + triangles = 115 + 41 = 156 (153 outside root edge, where 153 = 76th odd integer after 1);

8. Number of yods = 251 – 16 – 1 = 234 (230 outside root edge);

9. Number of yods other than corners = 234 – 33 = 201 (199 outside root edge). 201 = 101st odd integer, where 101 = 26th prime number;

10. Number of yods along boundaries of 5 polygons = 37×2 + 33 = 107 (103 outside root edge, of which (103 – 31 = 72) are not corners);

11. Number of yods along boundaries of tetractyses = 3×33 + 2×37 + 4 = 177 (173 outside root edge; 173 = 87th odd integer). 

(5+5) polygons have (2×31 + 2 = 64) corners (62 outside the root edge), (2×35 + 2 = 72) corners of 82 tetractyses (36 per set of 5 polygons), (2×36 + 1 = 73) sides of polygons (73 = 21st prime number), (2×77 + 1 = 155) edges of tetractyses, (2×112 + 3 = 227) corners + edges (227 = 49th prime number), (2×153 + 3 = 309) corners, edges + triangles (309 = 155th odd integer), (2×230 + 4 = 464) yods and (2×199 + 2 = 400) yods other than corners. They also have (2×103 + 4 = 210 = 21×10) yods along their 73 sides.

Below is shown how the number values of the ten Godnames quantify these properties:

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The last example of Godnames prescribing the properties of this Tree of Life pattern of (5+5) enfolded polygons is particularly remarkable because it convincingly demonstrates how the character of each prescription is consistent with the metaphysical nature of the Sephirah. In this case, the Godname ADONAI MELEKH of Malkuth, signifying the outer form of the Tree of Life, determines the shapes of the two sets of five regular polygons in terms of either their 155 edges or the 155 intrinsic geometrical elements per set.

3. Encoding of the 41-tree in the 1-tree

As the lowest tree in CTOL, the 1-tree has a formal correspondence to the last Sephirah, Malkuth. Figure 7 shows that, when each of its 19 triangles is divided into their three sectors which are then turned into tetractyses, the resulting 57 tetractyses contain 251 yods. They comprise the 11 yods at the corners of the triangles, i.e., SLs, and 240 yods created by the construction of each triangle from three tetractyses. They are the counterpart of the 11 SLs of the 1-tree and the 140 higher SLs in the 41-tree. As shown in Article 4, the Godnames of the ten Sephiroth prescribe not only the seven regular polygons enfolded in the Tree of Life but also a new pattern comprising the first six polygons of this set. Associated with each overlapping

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tree in CTOL are seven enfolded, regular polygons, the first six of which have 26 corners prescribed by YAHWEH (see Article 4 for how all the Godnames prescribe the first six polygons). Of these, the uppermost and lowermost corners of the hexagon are joined to their counterparts in adjacent hexagons, which means that there are 25 independent corners of the first six polygons per set. Enfolded in the lowest ten trees, which are prescribed by ADONAI because its number value 65 is the number of their SLs, are 60 polygons of the first six types with 10×25 + 1 = 251 corners. These corners denote the space-time co-ordinate variables of the ten whorls of the UPA/superstring, there being 25 spatial ones per whorl.

Properties of the 1-tree, 41-tree and the 60 polygons enfolded in the 10-tree are compared below: 

PARALLELS BETWEEN 1-TREE, 41-TREE & 60 POLYGONS ENFOLDED IN 10-TREE

The fact that the 251 corners of the 60 polygons enfolded on one side of the 10-tree comprise the 11 highest and lowest corners of the ten hexagons and 240 other, unshared corners, 24 per set of polygons, suggests that, since the SLs of the 41-tree are analogous to these corners, the 40 trees of the 41-tree above the 1-tree should be regarded as divided into ten groups of four trees, each having 24 SLs because successive trees have six SLs. Figure 8 

shows that the 12 uppermost trees in the 41-tree have 72 SLs corresponding to the 72 transverse co-ordinate variables of the three major whorls of the basic unit of matter described by Besant and Leadbeater and that the lowest 29 trees have 168 SLs corresponding to the 168 transverse co-ordinate variables of the seven strings that are the minor whorls. The latter SLs span 84 tree levels, where

84 = 1² + 3² + 5² + 7².

This illustrates the powerful Tetrad Principle, formulated in Article 1 (12). The 11 SLs of the 1-tree correspond to the 11 uppermost and lowermost corners of the ten hexagons enfolded in the 10-tree. The lowest corner of the one enfolded in the 1-tree is distinct from the rest in that it does not share its position with corners of other hexagons. This corner denotes the time co-ordinate of the superstring, whilst the uppermost corner of each hexagon denotes the longitudinal space co-ordinate of a whorl represented by the corresponding tree. This difference between the ten space co-ordinate variables and the time co-ordinate corresponds in the 1-tree to the ten SLs and Daath, which, being Yesod of the second tree, is

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an SL only of that tree, not the first tree. Such an exact, four-way correspondence:

cannot be reasonably dismissed as due to coincidence. Instead, it reflects the profound connection between the properties of the Tree of Life as the cosmic blueprint and features of the superstring constituents of quarks — the truly elementary particles yet to be discovered by particle physics but described over a century ago with the aid of one of the siddhis, or paranormal mental faculties, known to yogis.

4. Conclusion
The interpretation of the fundamental unit of matter observed clairvoyantly by Annie Besant and C.W. Leadbeater as the superstring constituent of up and down quarks implies that the superstring is a more complicated object than the simple picture of a closed string considered by physicists before so-called ‘d-branes’ and ‘M-theory’ ushered in the second revolution in string theory. Although consistent with the superstring prediction of a compactified, 6-dimensional space because the six higher-order spirillae of each whorl wind around these dimensions, the stringy, ten-fold whorls of the particle require it to be a higher-dimensional membrane as well. If this exists in the 26-dimensional space-time predicted by quantum mechanics for spinless strings, 251 space-time co-ordinate variables are needed to describe the ten closed curves which, as proposed by the author in Article 2 and Article 5, are formed by the curling up of the 11-brane proposed around ten higher, compactified dimensions. Just as Article 5 showed that this number quantifies cycles of emanation of Sephiroth leading to what Theosophists call the cosmic and solar physical planes, so it expresses the geometrical degrees of freedom of the superstring as a higher-dimensional object. Encoded in the Tree of Life is the map of all seven cosmic planes of consciousness (the ‘Cosmic Tree of Life,’ or CTOL). A section of this prescribed by the ten Godnames bears a remarkable analogy to the structure of the superstring predicted by the author and confirmed by century-old, paranormal descriptions of the basic units of matter. That this is no coincidence is further shown by the characterisation of the geometry of this section of CTOL by the number 496, which is both at the heart of superstring theory and the gematria number value of Malkuth, the physical universe, as well as by the encoding of the number 251 in the outer and inner forms of the Tree of Life. The precise parallelism between these encodings reflects the profound design of the Tree of Life as the cosmic blueprint not only for realms of higher consciousness traditionally associated by religions with the after-life but also for the basic units of matter making up the physical universe. Matter as well as man is made in the ‘Image of God.’

References
1. Extra-sensory Perception of Quarks, Stephen M. Phillips (Theosophical Publishing House, Wheaton, U.S.A., 1980); ESP of Quarks and Superstrings, Stephen M. Phillips (New Age International, New Delhi, India, 1999).
2. Occult Chemistry, Annie Besant and C.W. Leadbeater, 3rd ed. (Theosophical Publishing House, Adyar, Chennai, India, 1951).
3. See Articles 2 & 5 at this website.
4.For the definition of tree levels, see p. 15 in Article 5 at the author’s website. The number of tree levels in the n-tree ≡ T(n) = 3n+ 4. The 41-tree has T(41) = 127 tree levels.
5.The number of tree levels in n overlapping Trees of Life ≡ Ť(n) = 3n + 3. Therefore, Ť(91) = 276.
6.For the definition of the Lightning Flash, see p. 15 in Article 5. The number of stages of descent of the Lightning Flash from the top of the n-tree = 4n + 3. For the 41-tree, this is 167.
7.Proof: The number of yods in n overlapping Trees of Life = 50n + 20. 50 overlapping trees have 2520 yods. Of these, ten yods are above Binah of the 50th tree, leaving 2510 yods below this point.
8.Proof: using the formula given in (4), T(29) = 91.
9.Phillips, Stephen M. Article 2: “The physical plane and its relation to the UPA/superstring and spacetime,” (WEB, PDF).
10. Proof: using the formula given in (4), T(16) = 52.
11.Proof: the number of triangles in n overlapping trees ≡ t(n) = 12n + 4. Therefore, t(41) = 496.
12. Phillips, Stephen M. Article 1: “The Pythagorean nature of superstring and bosonic string theories,” (WEB, PDF), p. 4.

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