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Copyright 1996-2013by Andrew Catero and Darcy Kntz

The Tree of Life Projectedin the Third Dimension

by Andrew Catero and Darcy Kntz

The Tree of Life is a religious and geometrical glyph of the Universe. The

Tree is described in several texts such as the Sepher Yetzirah 1and Sepher Bahir.2

The Tree is propertied to be the result of the thirty-two Paths of Wisdom

which relate to the number of times that Gods name iyhla (Elohim) is

mentioned in the first chapter of Genesis. The Kabbalists formed this Tree

concept about God and the creation of the Universe from their research.

They did not state the Tree concept of God as fact, but rather they

understood that one cannot truly prove the mysteries of life. Through

combining elements of religion and mathematics, they formulated and

developed this patha path which uses meditation and magic to apply

Kabbalistic concepts and techniques as an aid to knowing oneself andunderstanding the laws and forces of the Universe.

The Tree of Life is formed from ten Sephiroth or spheres and twenty-two

Paths or Foundation Letters. The twenty-two Paths are the letters of the

Hebrew alphabet and the ten Sephiroth are the points which connect the Paths.

The twenty-two Hebrew letters are divided into the three Mother letters, the

seven Double letters and the twelve Elemental or Single letters. The letter

arrangements express several concepts of equilibrium. Each Sephiroth and Pathexpresses a religious principle and a number.

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The traditional glyph of the Tree of Life, in esoteric Kabbalah, is usually drawn as

follows:3

The Traditional Golden Dawn Tree of Life

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The twenty-two Hebrew letters are usually placed on the Tree of Life as shown

above, but Rabbi Aryeh Kaplan suggests, If we draw ten points in three columns in the

simplest manner, we see that they are automatically linked by 22lines. Of these, three are

horizontal, seven are vertical, and twelve are diagonal.5

In other words, the threeMother letters form the three horizontal paths in the Tree of Life. The seven Double

letters form the seven vertical paths and the twelve Elemental letters form the twelve

diagonal paths. This idea is not developed further in this paper, but it may provide

profitable study for the student.

The Hebrew Alphabet (Mother, Double, and Single letters)4

The three Mother letters conceptualize the triune nature of God and form an

equilibrium triangle. The Mother letters also symbolize the three Pillars of the Tree.

The Middle Pillar represents the Pillar of Mildness (or the personal self) with the two

outer Pillars being the Pillar of Mercy (right) and the Pillar of Severity (left). These two

outer Pillars are also seen as positive (active) and negative (passive) forces of nature.

Three Closet-Packed Spheres6

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The seven Double letters have two possible sounds creating opposition. The Double

letters model equilibrium with six spheres forming a circle around one sphere. The

outer six spheres central points are equidistant from the one spheres centre point.

Six Closet-Packed Spheres around One7

The twelve Elemental letters have only one sound with no opposites. The last

principle of equilibrium is to enclose a sphere three-dimensionally using other equally

sized spheres. It takes twelve spheres to enclose one.

Twelve Closet-Packed Spheres8

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In order to express these principles, the Kabbalists have built several different Trees

of Life. The diagram below, from Robert Wangs The Qabalistic Tarot, shows the

development of the Tree of Life. He writes, A) Form of the Tree in Kirchers Oedipus

Aegypticus, 1652. B) Adapted from Robert Fludds, Complete Works, 1617. C) Illustrationfrom Porta Lucis, Ausburg, 1516. D) Illustration from Paamon ve Rimmon, 1708.9

The Development of the Tree of Life

Aryeh Kaplan also illustrated the development of the Tree of Life in his Sefer

Yetzirah. (pp. 22-32). Diagram A) he termed According to the older Kabbalists.

Diagram C) According to the Safed School, based on the Zohar (1:59b). Cf. Pardes

Rimonim7:3. and The 32paths as defined by the Ari. Below is a diagram of a Tree

which Kaplan termed the Natural Array of the Tree of Life and The 32paths as

defined by the Gra.10

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The Natural Array of the Tree of Life

In the Golden Dawn paper called The Microcosm-Man it begins, Thou shalt

know that the whole Sphere of Sensation [or Aura] which surroundeth the wholephysical body of a man is called The Magical Mirror of the Universe. For therein are

represented all the occult forces of the Universe projected as on a sphere, convex to the

outer, but concave to man. This sphere surroundeth the physical body of a man as the

Celestial Heavens do the body of a Star or a Planet, having there forces mirrored in its

atmosphere. Therefore its allotment or organization is the copy of that Greater World

or Macrocosm. In this Magical Mirror of the Universe, therefore, are Ten Sephiroth

projected in the form of the Tree of Life as in a solid Sphere. ... In the Magical Mirrorof the Universe, or the Sphere of Sensation, Man is placed between four pillars of the

Tree of Life as projected in a sphere.11(p. 100.)

In the Golden Dawn paper titled On the Work to be Undertaken Between the

Portal and 5=6 it is written in section 5(The Tree of Life in the Aura) that, In the

aura which interpenetrates and surrounds our physical bodies. We are to build up a

replica of the Tree of Life. The Pillar of Severity is on our right side, the Pillar of

Mercy on our left, and the Pillar of Beneficence in our midst. (p. 90). He further adds,

In that case the Pillar arrangement becomes slightly altered or extended so as to

produce 4 Pillars about an invisible axis, the Middle Pillar. 12 (p. 92). The Golden

Dawn has illustrated the three dimensional Tree of Life as follows:13

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The Golden Dawns Three Dimensional Tree of Life

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Pat and Chris Zalewski reprints a Golden Dawn paper which gives an

example of the Orders method of applying the Tree of Life onto the celestial

sphere. (p. 6). The Celestial Sphere can also relate to the Sphere of Sensation

also called the Aura or the Magical Mirror of the Universe. When the Tree ofLife is considered not as a plane but as a solid figure, and when it is projected

in the Sphere, the North Pole of the Sphere will coincide with Kether, and the

South Pole with Malkuth. As we have before sufficiently learned the Ten

Sephiroth are repeated not alone, in each whole figure, but also in the parts

therefore, so that every material thing created will have its own Sephirah and

Paths. Now as the North Pole corresponds with Kether, and the South Pole

corresponds with Malkuth, the central Pillar of the Sephirotic Tree will form

the invisible Axis of the Sphere, the Central point coinciding with Tiphereth.

This latter Sephirah together with that of Yesod will be completely hidden

from view, so that Tiphereth will be the exact centre of the Sphere. Also the

Sephiroth Chokmah, Binah, Chesed, Geburah, Netzach and Hod will be

duplicated. As also the Paths of Aleph, Beth, Gimel, Vau, Cheth, Kaph, Mem,

Qoph and Shin, and so many others will be even quadrupled. But although

Tiphereth and Yesod will be concealed, there will be four special points where

the influence of each will be indicated.14 (pp. 6, 9.)

In the Sepher Yetzirahwe read in Chapter 1, Section 4, Ten is the number of the

ineffable Sephiroth, ten not nine, ten not eleven. Understand this wisdom, and be wise

by the perception. Search out concerning it, restore the Word to its creator, and replace

Him who formed it upon his throne. 17The Golden Dawns three dimensional Tree of

Life contravenes what was taught in the Sepher Yetzirahby having five Pillars instead of

three; sixteen Sephiroth rather than ten and forty-eight Paths instead of the twenty-

two. Fuller also writes, Thus from the Ain Soph Aur flow out the ten Sephiroth orPrinciples; hence the decade is considered the perfect number by the Qabalah, the all-

embracing unit emerging from the No-Thing (0-1), and the unity which ultimately is

to be radiated back into No-Thingness (1-0).18

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The illustration of the Tree of Life as projected on the Northern Sphere:15

The Tree of Life Projected on the Northern Sphere

The illustration of the Tree of Life as projected on the Southern Sphere:16

The Tree of Life Projected on the Southern Sphere

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Frater Achad (Charles Stansfeld Jones) also produced a three dimensional Tree of

Life, but it is slightly different from the Golden Dawns version. Frater Achads three

dimensional Tree of Life was illustrated as follows:19

Frater Achads Three Dimensional Tree of Life

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In the Sepher Yetzirah, the natural array of the Tree of Life is built following the

arrangement of the numbers three, seven and twelve. Triangles are formed by the

connections of the Sephiroth and Paths. The Kabbalists used this Tree as a startingpoint. They changed the arrangement of several Paths to express particular ideas. One

of them is the idea that life is three dimensional if not more dimensional. How is the

Tree of Life formed in three dimensional space? In other words what is the minimum

shape used to separate the inside of itself from the outside. What gives everybody their

uniqueness is that they are physically separate from others yet are still able to relate and

share their experiences with others. The Kabbalists tried to understand these feelings

and express them through the Tree of Life.

To build a three dimensional Tree, what shapes having a total of ten Sephiroth

(vertexes) could be formed. The Tree of Lifes ten Sephiroth become vertexes which are

points at which the lines (paths) of an angle intersect. The six upper Sephiroth form an

Octahedron. The Octahedron consists of six vertexes and twelve paths. The next shape

would have to be four vertexes or less. As Buckminster Fuller has proven, it takes a

minimum of four vertexes to enclose space. The shape formed is the Tetrahedron. The

Tetrahedron contains six paths. These two shapes total eighteen paths. If one places

these two shapes together at a certain angle, they will resemble the Tree of Life. The

four remaining paths are vertical paths. The first two Paths are from Kether to

Tiphereth and Tiphereth to Yesod. These Paths are part of the Middle Pillar. The last

two Paths connect Chesed to Netzach and Geburah to Hod.

In building the three dimensional Tree, one reason for using the Tetrahedron and

Octahedron is contained in The Complete Golden Dawn Cipher Manuscript. We read in

Cipher Folio number 47(4=7 Admission, Part 4), H[e]g[emon] shows tetrad [four]

& hexad [six] of Yetz[iratic] & G(e)omantic Tree of Life. 20 The Octahedron andespecially the Tetrahedron are shapes that appear throughout the Golden Dawns

ceremonies and teachings. The Octahedron compressed from its three dimensional

form into two dimensions looks identical to the Tree of Life from Kether to Tiphereth

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except for the two Paths that go from Chesed to Kether and Geburah to Kether. The

Octahedron now becomes a Hexagram which is the shape of the Banner of the East.

The Tetrahedron compressed into two dimensional form exactly matches the lower

four Sephiroth and their Paths. The Banner of the West also expresses the concepts offour and six. The Banner is a triangle with a cross in the centre which becomes the

fourth point thus forming a Tetrahedron.21

In conclusion, the ancient Greeks and todays current mathematical system is based

on the square with its ninety degree coordinate system. As previously explained, the

Tree of Life which represents the Universe is structured with triangles and not squares.

The Pillars in the Golden Dawn ceremonies pose an interesting question for aspiring

Kabbalists as well as mathematicians. The tops of the Pillars are red Tetrahedrons

symbolic of the path of light. The bottom of the Pillars are black square cubes

symbolizing the path of darkness. By building the three dimensional Tree, the

Kabbalah offers a way out of the state of darkness.

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The Tree of Life is now built three dimensionally as shown:

The Three Dimensional Tree of Life in Geometric Form

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The Banners of the East (white) and West (black)

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The Two Dimensional Tree of Life

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The Three Dimensional Tree of Life

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Notes:

1. Rabbi Nehunia ben haKana [?]. Aryeh Kaplan. The Bahir: Illumination. Yorke Beach,

ME: Samuel Weiser, 1979.

2. Rabbi Akiba ben Joseph [?]. William Westcott. The Sepher Yetzirah: The Book ofFormation and The Thirty-two Paths of Wisdom. Fourth Revised edition. With Hebrew

text. Notes and bibliography by Darcy Kntz. Edmonds, WA: Holmes Publishing

Group, 1996. Aryeh Kaplan.Sefer Yetzirah, The Book of Creation: In Theory and Practice.

Yorke Beach, ME: Samuel Weiser, 1990.

3. J.F.C. Fuller. The Traditional Golden Dawn Tree of Life in The Secret Wisdom of the

Qabalah: A Study in Jewish Mystical Thought. London: Rider and Co., 1937, based

upon the illustration facing page 60.

4. Chic and Sandra Tabatha Cicero. The Hebrew Alphabet (Mother, Double, and

Single letters) in Self-Initiation into the Golden Dawn: A Complete Curriculum of Study for

Both the Solitary Magician and the Working Magical Group. St. Paul, MN: Llewellyn

Publications, 1995, page 151.

5. Aryeh Kaplan. Sefer Yetzirah. Weiser, 1990, page 32.

6. R. Buckminster Fuller in collaboration with E.J. Applewhite. Synergetics: Explorations

in the Geometry of Thinking. Macmillan Publishing Co., 1979.

7. Fuller in collaboration with Applewhite. Synergetics. Macmillan Publishing Co., 1979.

8. Fuller in collaboration with Applewhite. Synergetics. Macmillan Publishing Co., 1979.

9. Robert Wang. The Qabalistic Tarot: A Textbook of Mystical Philosophy. Yorke Beach,

ME: Samuel Weiser, 1983, page 31.

10. Aryeh Kaplan. Sefer Yetzirah. Weiser, 1990, pages 28-30.

11. Israel Regardie (ed.) with Gerald Yorke. The Microcosm-Man in The Golden Dawn:

An Account of the Teachings, Rites, and Ceremonies of the Order of the Golden Dawn. St. Paul,

MN: Llewellyn Publications, 1989, pages 100-106.12. Israel Regardie (ed.) with Gerald Yorke. On the Work to be Undertaken between the

Portal and 5=6 in The Golden Dawn. Llewellyn Publications, 1989, pages 87-94.

13. Robert Wang. The Qabalistic Tarot. Weiser, 1983, before page 46.

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14. Pat and Chris Zalewski. Astrology and the Golden Dawn in The Equinox and Solstice

Ceremonies of the Golden Dawn. St. Paul, MN: Llewellyn Publications, 1992, pages 6-12.

15. Pat and Chris Zalewski. The Equinox and Solstice Ceremonies of the Golden Dawn.

Llewellyn Publications, 1992, page 7.16. Pat and Chris Zalewski. The Equinox and Solstice Ceremonies of the Golden

Dawn. Llewellyn Publications, 1992, page 8.

17. Westcott. The Sepher Yetzirah. Holmes Publishing Group, 1996, page 17.

18. J.F.C. Fuller. The Secret Wisdom of the Qabalah. Rider and Co., 1937, page 62.

19. Frater Achad. The Anatomy of the Body of God: Being the Supreme Revelation of Cosmic

Consciousness. Illustrations by Will Ransom. New York: Samuel Weiser, 1972, page 64.

20. Darcy Kntz. The Complete Golden Dawn Cipher Manuscript. Edmonds, WA: Holmes

Publishing Group, 1996, page 144: lines 18-19.

21. Pat Zalewski. The Banners of East and West in Golden Dawn Enochian Magic. St.

Paul, MN: Llewellyn Publications, 1990, page 174.

Copyright1996-2013by Andrew Catero and Darcy Kntz

The Authors have asserted their moral rights. All rights reserved.