the polyhex key to the tree of life

FORMATION OF THE TREE OF LIFE June 21, 2010

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The Polyhex Key to the Pathways

he validity of the Tree of Life pathway formula (as expounded in this book) is also supported by my recent (circa 2010) research into sacred polyhex geometry. My new findings in the field of polyhex geometry demonstrate that the hierarchical 3:7:12 division of the pathways is a

natural result of the polyhex geometric model of Creation.

The Geometric Model

The manifestation of the kabbalistic Tree of Life involves the coming together of two primary principles called Spirit and Matter (or Form). The merging of these two principles produces a third middle principle called Consciousness (or more accurately, Soul). The merging process can be illustrated very simply using two overlapping circles. (See the figure below.)

Before the beginning of Time and Space the two circles are separated, but eventually they approach each other, intersect, and partly merge together. The area of their overlap forms the Soul/Consciousness principle.

T

Author

Note

Patrick Mulcahy.

Patrick

Arrow

http://members.dodo.com.au/~astroqab/

June 21, 2010 FORMATION OF THE TREE OF LIFE

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To build the complex form that is the Tree of Life diagram we must replace the Spirit and Form circles with polyhexagons.

The special polyhexagonal form upon which the Tree of Life is based is a structure that consists of nineteen individual hexagons arranged in a composite hexagonal shape. This special polyhexagon is characterized by two sub-groups of component hexagons. Firstly, a group of seven hexagons, six of which are located around the perimeter of the polyhex, and a seventh located precisely at its centre. The second sub-group consists of twelve individual hexagons that fill the main body of the polyhex construct.

Figure 38 : The Merging of Spirit & Form


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You may recognize the significance of the figures seven and twelve as coinciding with the number of Hebrew Double and Simple letters respectively. This is a very important correspondence that we will examine more closely below.

The merging of the two polyhexagons produces interesting results. The Tree of Life diagram is now clearly revealed in the composite hexagonal design (below right). The three white hexagons at the top of the yellow polyhexagon represent the three highest sefirot of the Tree of Life—Keter, Hockmah, and Binah. They remain wholly detached from the Form principle polyhexagon (shaded blue).

Only seven yellow hexagons remain visible in the main body of the Spirit polyhexagon. These represent the seven Hebrew Double letter pathways of the Tree (i.e. as I have delineated them in this book). The correspondence to my original pathway findings is precise as I will demonstrate shortly.

Figure 39 : Tree of Life Polyhexagon


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In numbering the component hexagons (below) I have placed all of the even numbers on the right side of the polyhexagon and the odd numbers on the left. I have chosen to use this convention merely to identify the right side as ‘male’ (even) and the left side as ‘female’ (odd). But it is also interesting to note that this convention shows the natural sequence of the lower sefirotic hexagons (shaded grey) progressing from Tifaret (4) to Hod (5) which is contrary to the traditional numbering system which has Netzah (6) following numerically after Tifaret (4). Thus, this odd/even rule results in a more accurate presentation of the ‘hierarchy of the planes’121 because Hod (as Mercury) represents the lower

121 That is, as described in the teachings of Theosophy.

Figure 40 : The Merging of the Spirit & Form Polyhexes


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mental plane and therefore it should come before Netzah who as Venus symbolizes the astral plane.

The three highest sefirot represent the sacred trinity of divine Powers. The seven Double letter pathways symbolize the seven Heavens/Palaces122, the seven planetary Spirits (or Logoi), the seven angels who attend the Throne of God, etc. They represent supernal powers guiding and administrating the lower worlds. Each of these seven Double letter pathways is the ensouling spiritual source of one of the seven lower sefirot (or ‘planetary spheres’).

122 Hebrew: Shamayim (שמים), and Hekhalot (היכלות).

Figure 41 : The Tree of Life Polyhexagon


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The Form principle polyhexagon includes the seven lower sefirot (i.e. corresponding to the seven grey shaded hexagons) and the twelve Simple letter pathways (corresponding to the twelve blue shaded hexagons above).

An important consequence of the polyhexagon merging and overlapping process is that five of the Spirit principle pathways become concealed beneath the upper portion of the Form principle polyhexagon—that is, they become hidden below the surface of the newly formed Soul principle. My thinking is that these five concealed pathways correspond to the five Final Hebrew

letters—Kaf final (ך), Maym final (ם), Nun final (ן), Peh final (ף), and Tzaddie

final (ץ). The implication of this geometric symbolism is fascinating.

The Soul principle is formed as a result of the intersection, overlapping, and interaction of the Spirit and Form principles. This area of overlap is indicated in the diagram above by the five green hexagons and their four bounding grey

Figure 42 : The Soul Principle (Green)


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hexagons (i.e. numbered with white numerals). The soul is thus seen to be an admixture of Spirit and Form.

The Soul principle is also seen to be a relatively impermanent principle (or state of being). It manifests only when the Spirit principle merges with the Form principle. The significant implication of this is that when it comes time for the Spirit and Form principles to once again separate themselves the Soul principle dissolves (or disassembles). In terms of our geometric symbolism, the area of intersection between the Spirit and Form polyhexagons disappears. This process of separation occurs during what Theosophists call a period of ‘pralaya’123.

Your first feelings on hearing this proposition may include some disappointment. You may feel that the dissolution of your soul will lead to the loss of your identity (or your existence as an individual). This is not truly the case however. The soul is merely a temporary vehicle that allows the Spirit to involve itself in the substance of matter.124 Your spirit (i.e. monad) remains in existence during the period of Pralaya.

Before the soul’s dissolution during Pralaya, its essence is absorbed into and stored in the monad. I believe this process is made possible by the existence of an occult mechanism involving the five Hebrew Final letter pathways.

123 Pralaya (Sanskrit) [from pra away + the verbal root li to dissolve] Dissolving away, death, dissolution, as when one pours water upon a cube of salt or sugar: the cube of salt or sugar vanishes in the water, dissolves, and changes its form. So during a pralaya, matter crumbles or vanishes away into something else which is yet in it, surrounds it, and interpenetrates it. Pralaya is often defined as the state of latency or rest between two manvantaras or great life cycles. [From: The Rakefet Theosophical Dictionary.]

124 In fact, human-beings are destined to evolve beyond soul-based consciousness. The soul becomes obsolete as a vehicle of consciousness at the 4th Initiation (called the Great Renunciation). It is then transcended and replaced with ‘monadic’ consciousness.


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The five Final letter pathways are concealed beneath the five visible Simple letter pathways of the Soul principle. The five Finals belong to the Spirit principle polyhexagon, but they are covered and concealed by the Simple letter ‘soul pathways’ of the overlapping Form principle. My theory is that the esoteric function of the five Final letter pathways is to gather in and absorb the Knowledge that has been gained during the term of the soul’s existence. By ‘Knowledge’ is meant the combined Wisdom and Understanding (or ‘love-wisdom’) that the soul has acquired during its term of existence. These qualities are collected and stored within the monad during each period of Pralaya.

Figure 43 : Polyhexagon Tree of Life — Hebrew


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Thus, when the Spirit polyhexagon detaches itself from the Form polyhexagon it carries with it the five concealed Final letter pathways because they are part of its fundamental structure. So, nothing of value is lost during a Pralaya.

The Hebrew letters are arranged on the Spirit and Form polyhexagons as per the diagram above.125

The seven Double letter pathways are shaded yellow. The twelve Simple letter pathways are shaded blue. The five Final letters (coloured blue) are positioned on five yellow hexagons near the base of the Spirit polyhexagon (above left). They are bounded by four hexagons containing the letters of the Tetragrammaton—YHVH (orange lettering). This small subset of hexagons

bounded by YHVH (יהוה) basically represents the monad (i.e. the monadic triad). The overlapping hexagons of the soul are merely a garment the monad wears when it descends into the realm of ‘physical existence’.

The twelve Simple letters are expressions of the Form principle, or Great Mother ‘Shekinah’ principle.

The seven Double letters have two variant forms—a ‘soft’ pathway form representing supernal spiritual forces, and a ‘hard’ sefirotic form (i.e. identified by a dagesh, or dot) representing lower, more material projections of the supernal pathways.

The five Finals are differentiated as follows:

Maym Final (ם) = Mother letter

Kaf Final (ך) and Peh Final (ף) = Double letters

Nun Final (ן) and Tzaddie Final (ץ) = Simple letters

125 But note that the arrangement of the twelve Simple letters is somewhat flexible.


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Thus, all the three major Hebrew letter groups—Mothers, Doubles, and Simples, are represented in the five Finals.

My current hypothesis is that Maym Final collects the essence of the two Mother letter pathways (i.e. the vertical pathways of Maym and Shin) that infuse the Form principle polyhexagon. Similarly, Kaf Final and Peh Final gather the essence of the seven Double letter sefirot of the Form principle polyhexagon. Lastly, Nun Final and Tzaddie Final collect the essence of the twelve Simple letter pathways of the Form principle polyhexagon. So when the Spirit principle polyhexagon detaches and separates from the Form principle the threefold essence of its experience within the substance of matter (i.e. as recorded by the soul) is taken with it via the five Hebrew Final letter pathways.

You may notice that there are only nineteen pathway hexagons included in the natural structure of the polyhex Tree of Life design. (See the diagram above.) Three of the twenty-two pathways of the Tree of Life appear to be missing. I have also omitted them from the traditional drawing of the Tree of Life (above

Figure 44 : Tree of Life — Traditional & Polyhex Designs


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left). The missing three are the three Mother letter pathways—Alef, Maym, and Shin.

Most kabbalistic commentators assign the three Mother letters to the three horizontal pathways of the Tree diagram126, but my findings indicate that their more metaphysically meaningful placements are with the three vertical pathways of the Middle Pillar of the Tree of Life.

In my view the Double letter Bayt (ב) is assigned to the highest horizontal pathway (i.e. joining Hockmah with Binah) because it is responsible for formulating the first of the seven lower sefirot—Da’at. The sefirah Da’at arises as a result of the interaction between Hockmah and Binah—an interaction facilitated by the horizontal Bayt pathway. The hard form of the letter Bayt consequently emerges as the distinguishing archetype of the sefirah Da’at.

The Tree of Life formation formula (as described in this book) posits the location of the Hebrew letters on the sefirot and pathways of the Tree diagram in a descending hierarchy that follows the sequence 3:7:12—that is, Mothers-Doubles-Simples. For this reason, the formula cannot be reconciled with the traditional numeric method of assigning the letters to the horizontal, vertical, and diagonal pathways. The old method places the three Mother letters on the three horizontal pathways, the seven Double letters on the seven vertical pathways, and the twelve Simple letters on the twelve diagonal pathways of the Tree diagram.

The traditional methodology appears, at first glance, to be most agreeable, but I believe it is an erroneous correspondence. The geometric framework of the Tree diagram is built according to the fundamental esoteric ratio 3:7:12 because it represents a blueprint of the divine Creation. The Hebrew alphabet is also constructed according to the 3:7:12 ratio because it represents the twenty-two divine archetypes. It does not necessarily follow however, that the two are meant to be combined together purely on the numerical basis of this 3:7:12 ratio. In fact, the Sefer Yetzirah states:

126 Without much explanation besides the obvious numerically based correspondence.


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One on three, three on seven, seven on twelve, And all are bound, one to another. These are the twenty-two letters…127

Obviously, a 3:7:12 hierarchical arrangement of the Hebrew letters is indicated by this statement. Clearly, it is a contradiction of the principles of the Sefer Yetzirah to widely intermingle the three classes of Hebrew letters on the Tree diagram (i.e. as does the orthodox numerical letter-pathway arrangement).

To put it simply, the Sefer Yetzirah is saying...

o One (All-encompassing Ain Sof) on three (supernal sefirot) o Three (supernal sefirot) on seven (supernal pathways) o Seven (lower sefirot) on twelve (lower pathways) o And they are all interconnected

(See the figure below.)

127 Sefer Yetzirah, 6:5-6.


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The Zohar is similarly supportive of the hierarchical approach. In its anthropomorphosis of the Tree of Life the Zohar associates the three highest sefirot with the head of Adam, and the lower sefirot with his body. These correspondences combine well with the Sefer Yetzirah’s assignment of the seven Double letters to the eyes, ears, nostrils, and mouth.

Logically, the seven Double letter pathways (symbolizing seven physical attributes of the human head) need to be arranged upon the head of Adam at the top of the Tree of Life diagram.

The Sefer Yetzirah assigns the twelve Simple letter pathways to the torso, limbs, and internal organs of the human body, and therefore logically these should be located within the lower portion of the anthropomorphic Tree diagram—that is, below the head.

Figure 45 : The Hierarchical Arrangement of the Hebrew Letters


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One of the key arguments for the old numerically-based arrangement is that the Sefer Yetzirah describes the twelve Simple letter pathways as ‘diagonal

boundaries’ (גבולי אלכסון).128 It is true that twelve of the Tree of Life pathways are diagonal (or sloping), but the diagonal pathways do not resemble ‘boundaries’ on the Tree diagram. In the hierarchical pathway arrangement however, the twelve Simple letter pathways do resemble diagonal boundaries (or ‘sloping sides’) because they form the twelve bounding sides of six adjacent triangles that surround Tifaret in the lower portion of the Tree diagram. (See the diagram above left. The twelve Simple letter pathways are coloured blue.)

The three vertical Mother letter pathways unite the four sefirot of the Middle Pillar of the Tree of Life, but they are not included in the polyhexagonal structure of the Tree. This reflects the mysterious nature of these three pathways. They represent the fluid essence of Being. Their movement, interaction, and intermingling produces the flowing stream of awareness that we call consciousness, and necessarily also the illusion of time and space. Because of this, they move within and beneath the surface of consciousness and are not directly perceived by it. Only their effects are perceptible. What is inferred is that consciousness is not a fixed enduring principle, but rather, is a fluid process.

Interestingly, in the polyhexagon Tree diagram, the Shin (Fire) pathway is invisibly located beneath the Tet (Leo) hexagon. The Fire of Shin is associated with Nachash—the ‘Kundalini Serpent’. Tet also means serpent, and Leo (ruled by the Sun) is a fire sign that epitomizes the fiery principle of consciousness.

The Maym (Water) pathway is invisibly located beneath the Tzaddie (Aquarius) hexagon. Of course, Aquarius is known as the ‘Water Carrier’129, and is also

128 Sefer Yetzirah, 6:1. Note that it does not, however, describe the three Mother letter pathways as ‘horizontal’, or the seven Double letter pathways as ‘vertical’.

129 The Tzaddie pathway carries the Water of Maym from the sefirah Hesed to the sefirah Geburah.


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strongly associated with the consciousness principle. These two signs, Leo and Aquarius, form the vertical axis of the Fixed zodiacal cross.

The Alef (Air) pathway is invisibly located beneath the Bayt (Saturn) pathway hexagon. This is appropriate because Bayt is chief of the seven Double letters, and Alef is chief of the three Mother letters. Also, Alef is thought to stand invisibly behind Bayt during the process of Creation (which is why Berashit130 begins with a Bayt and not an Alef).

You may have noticed in the diagrams that the two Simple letter pathways Qof (Pisces) and Sameck (Sagittarius) are placed differently in this polyhex arrangement—i.e. compared to the arrangement I described in earlier chapters. The reason for this slight deviation is that although normally these two pathways extend from Hesed and Geburah to Yesod, they are also capable of extending to Da’at (i.e. from Hesed and Geburah). This only occurs during the process of ‘divine inspiration’ (i.e. conscious contact with the monad)—an experience that rarely happens in an average person’s lifetime. In the polyhexagon Tree diagram these two pathways are placed in their elevated positions adjacent to Da’at. Thus, this particular pathway configuration reflects the conscious alignment strived for by Disciples (or Tzadikim) on the Path. The state of consciousness that this configuration represents grows stronger and more stable as a disciple continues on his/her path of inner development.

For disciples and initiates, the Fire (Shin, ש) of creative inspiration flows from Da’at to Geburah (i.e. representing the Abstract Mind) along the Sameck

(Sagittarius) pathway. The Water (Maym, מ) of spiritual intuition flows from Da’at to Hesed (i.e. representing the Intuitive Mind) along the Qof (Pisces) pathway.

While the Sameck and Qof pathways remain exclusively attached to the sefirah Yesod they symbolize the presence in a person’s mind of worldly illusions

130 That is, the Book of Genesis.


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(Sagittarius) and glamours (Pisces). These illusions are fostered within, and perpetuated by the collective mindset of mundane human society. They effectively fill the pathways of Sameck and Qof with a darkness that blocks access to the higher sefirot Geburah and Hesed. But as a person frees themselves from the glamours and illusions of society they simultaneously become consciously open to the higher sefirot and thus to divine impressions entering into and through the human soul (i.e. flowing from Da’at to Hesed and Geburah).

The divine inspiration that is received through the pathways of Sameck and Qof is expressed and applied (in the mundane world) via the lower and complementary pathways of Zayn (Gemini) and Yud (Virgo). Together these four pathways constitute the Mutable Cross of the Heavens (i.e. the cross of mutable zodiacal signs). On the Tree of Life, the primary creative-evolutionary purpose of the Mutable Cross is to positively transform the human expression of the psychic influence of the astrological Moon (i.e. as it is felt within the sefirah Yesod).

The main evolutionary function of the four signs (and pathways) of the Cardinal Cross is to stabilize the expression of the astrological Sun upon the Path of Righteousness. Thus, on the Tree of Life diagram we see the four cardinal sign pathways anchoring and holding the sefirah Tifaret (i.e. the Sun) upon the Middle Pillar of the Tree. Their role is to hold Tifaret steady so that it doesn’t drift too far towards the left-hand Pillar of Severity, or conversely, too far towards the right-hand Pillar of Mercy. As long as Tifaret’s central position upon the Middle Pillar is maintained then it retains direct access to

‘HaShem’131—that is, to the forces of Shin (ש) and Maym (מ) flowing through the ‘invisible’ Middle Pillar pathways. When this condition is fulfilled, a human-being becomes a Tzadik—i.e. one who is faithfully aligned upon his/her ‘path of righteousness’.

131 Hebrew – The ‘Name’, spelled Shin-Maym, referring to the divine Name of God.


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The four signs (and pathways) of the Fixed, or Cherubic Cross are responsible for refining the four main faculties132 of human consciousness as represented by the four ‘directional’ sefirot—Hesed, Geburah, Hod, and Netzah. These faculties are associated with the four elements and the four magical implements—the Cup, the Wand, the Sword, and the Disk (or Pentacle). The four cherubic ‘animals’ represent active intelligent expressions of the four esoteric elements. They signify powerful forces that are responsible for the diversity of life and life experience on our planet. On the Tree diagram their four pathways form a square enclosure whose four walls intersect at the four ‘corner’ sefirot—Hesed, Geburah, Netzah, and Hod.

132 That is, the intuitive mind, the abstract mind, the rational mind, and the astral body (or desire mind).

Figure 46: Tree of Life : 3+7+12 Pathways


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The 3-7-12 hierarchical structure of the Tree of Life diagram inclines me to think that an update is needed to the original polyhex Tree model that I described in my book The Hexagonal Geometry of the Tree of Life. The model I depicted in that book was constructed as follows…

3-Hex (x3) = 3 supernal sefirot

4-Hex (x7) = 7 lower sefirot

5-Hex (x22) = 22 pathways

The above arrangement is useful as a basic model of the Tree of Life, but if a more metaphysically accurate presentation is desired then a change is needed because (as has been demonstrated) the seven supernal Double letter pathways (i.e. located in the upper part of the Tree diagram) manifest before the seven lower sefirot and the twelve Simple letter pathways. The seven Double letter pathways should therefore be associated with the seven tetrahexes (i.e. 4-hexes).

The revised model looks like this…

3-Hex (x3) = 3 supernal sefirot

4-Hex (x7) = 7 supernal pathways (Doubles)

5-Hex (x22) = 7 lower sefirot (Doubles) + 12 lower pathways (Simples) + 3 Mother letter pathways

Although the original model appears simpler, the revised model represents a more accurate depiction of the Tree of Life manifestation process. The formation of the Tree of Life begins with the appearance of the three supernal sefirot. Then the seven supernal pathways emerge between them. And then finally the seven lower sefirot and twelve lower pathways manifest.


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Thus, it is more logical to have the simpler polyhexes (i.e. those with fewer component hexagons) arranged upon the upper portion of the Tree, and the more complex polyhexes (i.e. the 5-Hexes) assigned to the lower section (coloured red in the diagram).

In the diagram133 the three trihexes are coloured yellow, the seven tetrahexes are coloured blue, and the twenty-two pentahexes are coloured red. The twelve pentahexes that I have ascribed to the twelve Simple letters are (as explained in my book134) geometrically different from the other ten pentahexes in the 5-hex group because they are able to ‘tile the plane’ in the most simple manner

133 This arrangement of the polyhexes is only one of many possible variations.

134 See: The Hexagonal Geometry of the Tree of Life.

Figure 47: The Polyhex Tree of Life (Revised)


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possible. As shown in the diagram above, the remaining ten pentahexes (of the group) are assigned to the seven Double letters and the three Mother letters.

The three Mother letter pathways are displayed on the right-hand side of the diagram. They are concealed beneath the other pathways of the Tree. They flow into the Tree of Life in a manner similar to the entry of the soul into the confines of its prepared physical vehicle. The three Mother letter pathways galvanize and energize the sefirot of the Middle Pillar, and they trigger the commencement of the creative-evolutionary process that occurs within the branches of the Tree.

the polyhex key to the tree of life

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