A Modern Alchemical View of the Philosopher's Stone

by Richard and Iona Miller (aka Philo Stone), ©1981

animated buckyball



It is now evident that every stimulus form corresponds to a particular space-time shape in the brain, in terms of electrical activity.  A computer can even now identify these shapes.  These space-time shapes are evidence of relationships between the external world and its representation in the brain.

We have chosen to call these spatio-temporal representations "keys."  These keys seem to operate on "locks" in our brain in a manner similar to "minting" of DNA production and replications.

Magick is practiced fundamentally for the creation of the mystical or immortal body.  This subtle body is also known as the Diamond Body or Philosopher's Stone.  It is independent of time and space and can be seen as a magickal mode of transportation for consciousness.  By tuning in on specific keys, access to specific brain-chemical relationships are available.  Archetypes may be seen as these specific geometrical systems of standing waves, occurring in the brain as space-time shapes or keys.

Resonance effects aid and amplify these standing waves, with specific results.  One may speculate on minimizing the size of one's mystical body, moving consciousness into another dimension, via the energy flows of singularities.

Conceptually, it is a useful model to picture the vehicles of consciousness becoming smaller as we rise on the Planes.  If you picture your carrier of consciousness as synonymous with the smallest available models--massless particles--you are no longer limited by the mechanistic laws of the universe.  You enter the possibilities of the quantum field.  Further, these models also provide resonance with other parts of the body.

Information is embodied in a field, rather than just being a field.  The geometrical images are basically an abstract quantity of information; a field relationship between one point and another in the universe.  Unlike most engineering channels of communication, biological channels are dynamically asymmetric.  Information on change is transmitted across space asymmetrically with respect to the direction of the change of the variable.

This means that if a biological system is to be informed symmetrically about dynamic changes, it requires two channels.  The basic reason for this dynamic asymmetry is that biological channels for control use the concentration of molecules to transmit information at some point along the channel (for example, neurotransmitter release).  This must involve asymmetry since the creation and transportation of molecules is generally accomplished by different means from their breakdown and removal.

Concentration can be made a function of information as long as the change requires an increase in concentration.  Decreasing concentration generally cannot be accomplished as fast through the same channel.  The level of hormones which have issued into the bloodstream cannot be decreased through the action of the same gland.  A decrease in concentration is produced by metabolic processes or through the increase in level of counteracting hormone or chemical.  In either case, the decrease in concentration is produced through quite different channels from the one producing an increase in concentration.

The significance of this asymmetry of unidirectional rate sensitivity in the space-time patterns in the brain is that if it were not for this principle, interaction and cancellation of opposites would prevent the formation of unique space-time patterns for each perception.

An event is registered as a pattern in space as well as a pattern in time.  With the sense of touch, for example, removal does not cancel the sensation, even when the touch was short and momentary.  A distinction can be thus made between quality and quantity.  Quality is given by the channel location, quantity by the firing pattern in the channel.

In living organisms opposites receive their structure of symmetry from a particular combination of spatial and temporal aspects.  It is the geometric properties which makes them capable of being opposites.  This "rein control" implies distinction between quality and quantity.  With each rein, messages are similar and not opposite in character.  The activity of each "rein" determines the quantity, the special identity of the "rein" determines the quality.

Archetypes influence our human lives in this way also.  They intrude upon the patterns of one another, and help balance out our one-sided attitudes.  Sometimes this happens through the shadow, sometimes it is an inspiration of the Self.  In this way archetypes transform from simple information, into image, into energy, into natural consequences in the real world.

Any view of the universe is an interplay between information and energy.  By information we mean those processes which provide recognition and identification of separate existences, and by energy the transformation and displacement of the contents of space.  This interplay between information and energy involves identity, quality and recognition.

One point of entry into manifestation for archetypes is through our thoughts and intentionality.  Whichever comes first, the archetype or the neurotransmitter, thoughts become things.  The neurotransmitter is the chemical link between apparent nothing and something in the human domain.  Even more fundamental is the sub-atomic process of probability underlying and conditioning the process.  This probability itself is archetypal--probably Hermetic.

It is the contention of this book that the most fundamental geometric form is the Vector Equilibrium Matrix (VEM).  This geometrical form leads directly to the Diamond Body or Cube of Space.  To place oneself inside this structure, or to project this matrix form outward as a visualization, or to climb into a virtual reality depiction of the VEM, creates and generates a resonance within the space-time shapes of the brain.  The Vector Equilibrium Matrix is a geometrical mandala--a solid state mandala--resonating with the psychological analog for the Philosopher's Stone.  A state of grace can be achieved where the key word is Access.


The psychological response from the resonance created from visualizing oneself inside the Vector Equilibrium Matrix is Daath.

Daath: The Vector Equilibrium Matrix

The Astral Temple of Daath is evoked by the following visualization sequence:

 1. A banishing ritual is critical, including a visualization of the containing circle.

 2. A Middle Pillar Exercise.  This sets up the centers for resonance and the foundation points for the Vector Equilibrium Matrix, connecting each center.  Chakra colors are important at this point.

 3. A vertical line should now be envisioned, acting as an axis or Middle Pillar line through each of the chakra points.

 4. Now, focus on the two chakra points corresponding to the heart (Tiphareth) and the center of the forehead (Daath).  These two points become centers for two intersecting circles, (see Figure 1).

 5. Connect overlapping points (from the circumferences of the circles) with vertical lines.  These are the side Pillars.  Now begin to visualize a Tree of Life, (see Figure 2).

 6. Visualize the inter-connectivity of the two geometric figures known as the Vector Equilibrium Matrix.  (See Figure 3 for specific model format).

The superimposition of this matrix over the human figure is reminiscent of the description of Ezekiel's vision in THE BIBLE.  It has been interpreted as the Mystical Body of Christ.

And above the firmament that was over their heads was the likeness of a throne, as the appearance of a sapphire stone: and upon the likeness of the throne was the appearance of a man above upon it.

                                                                          Ezekiel 1:16

Atomic VEM

The mathematical zone of neutral resonance occurs at the centers of each cube, visualized as Tiphareth and Daath.  This allows Nuit into the visualization as the heart of the Diamond Body, that which is naught.  The heart-aorta resonating oscillator link with the brain can be activated by tuning both brain-waves and heart rate to meditational mode.  As this system becomes "tuned," an ideal coupling occurs and a link with the earth-ionosphere is achieved.

It is at this point that specific geometrical manipulations create a series of "gates" or "keys," and access then occurs to specific archetypes.  Direct access to psyche is available and Daath is experienced on the psychological level as gnosis.  A geometric set of building blocks can be stacked to produce the space-time shapes of the brain,  going from Hadit (microcosmic) to Nuit (macrocosmic).

The Vector Equilibrium can be formed into the Diamond Body by the addition of eight tetrahedrons to the truncated corners.  (See Figure 8).  The field formed by these tetrahedrons is known as the Isotropic Vector Matrix.(1)

This I.V.M. is an omnitriagulated web extending throughout all-space.  It is the geometric form within which the primitive Vector Equilibrium forms.  The Vector Equilibrium centers on a nexus point within the subtle net known as the I.V.M.  The Cube of Space can be later enlarged into another V.E.M. by incorporating a larger area of the I.V.M.

These vectors are the most economical lines of energy transference.  They are the path of least resistance which is always favored in natural processes.  They are not only the way energies are likely to move, but the way they "like" to do it.  The conceptual aspect of the geometry is simply a way for our minds to grasp the process.  Fuller contends that even our thoughts are tetrahedronally conveyed in our gray matter.  So, as we are conceiving it, it is manifesting in our very thought process.

This "laddering" geometry, which is found in the Tree of Life, is the foundation of all Magick.  There have been depictions of 3-dimensional Trees of Life, amalgamated such that they build into a solid and fill all-space.(2)

This mathematical, speculative work  was the qabalistic project of Aleister Crowley's star pupil, Frater Achad (Charles Stansfield Jones).  It is very useful to connect current scientific concepts with the topological system furnished by QBL.  This keeps our practice of Qabala contemporary, and offers a spiritual touchstone for our scientific fantasies.  Our geometrical description of the ground state allows the brain to visualize, conceptualize, and experience the effects of the Philosopher's Stone.
(1) R. Buckminster Fuller, SYNERGETICS 2, paragraph 986.142.
(2) Frater Achad, THE ANATOMY OF THE BODY OF GOD, New York, Samuel Weiser, 1926/76.

[Geometrical Construction of Tree]

Geometrical Construction of the Tree of Life.


Tree of Life
Spheres 1-2-3=Archetypal; 4-5-6-=Causal; 7-8-9=Astral; 10=Physical



And the likeness of the firmament upon the heads of the living creatures was as the color of the terrible crystal stretched forth over their heads above.

                                                                                                 Ezekiel 1:22

Tetracyts Tree

Magick and yoga are the two major divisions of Mysticism.  One is exaltive, the other reflective.  Through the correspondence system, Magick seeks to exalt the imagination and the soul.  Yoga provides a discipline through which the mind may be emptied of its contents at will.

The aspirant becomes a mystic when he is favored with an immediate experience of the divine.

This experience of ultimate reality is so awesome that he strives to attain further heights of ecstasy and holy rapture.  The True Will of a mystic is to merge into Godhead at Kether.  The vision of the Diamond Body, or Throne Chariot, is a mystical experience possible on this path.

In magickal practice, the Altar is placed in the very center of the magickal circle.  This makes the Altar the pivot-point of all operations.  The Altar represents the True Will of the magician.  It is the physical representation of his intent.

All the other magical weapons are arrayed on the altar.  The Wand represents the Will of the creative self; the Cup is intuition, the Sword indicates the qualities of the mind, and the Pentacle represents the physical body.  The proper use and direction of these weapons depends upon the Altar.  The intent of the celebrant is critical to the proper use of his faculties.  This is a law under which he works.

Only the Lamp, hanging overhead, is exempt from this prescription.  This is because it represents the inextinguishable light from above, that of the Higher Self, and is not subject to the desires of the magician, except his desire for self-transformation.

The Altar is a geometrical construction in the form of a vertically-positioned Double Cube.  It embodies the magician's knowledge of the laws of Nature.

The Altar is a double cube, which is a rough way of symbolizing the Great Work; for the doubling of the cube, like the squaring of the circle, was one of the great problems in antiquity.  The surface of this Altar is composed of ten squares.  The top is Kether, and the bottom Malkuth.  The height of the Altar is equal to the height above the ground of the navel of the Magician.  The Altar is connected with the Ark of the Covenant, Noah's Ark, the nave (navis, a ship) of the Church, and many other symbols of antiquity...(1)

[insert The Double Cube: Magickal Altar]

 The Altar, the central shrine of the temple, in the form of the double cube, is derived from the geometry of the Tree of Life, itself.  When the double cube Altar is superimposed over the geometry of the Tree of LIfe, it coordinates Spheres 1-9, Kether through Yesod.  There are centralized nexus points at Sphere 6, Tiphareth (the Heart) and Daath.

The true Temple consists of the body/soul (Sphere 10, Malkuth) of the magician in coordination with the transformative matrix provided by the Tree.  Magicians and yogis have always considered the body to be their Temple.  Note also the connection between the resonant cavities in the brain and the name given the gates to this area--the temples.

The double cube pervades and penetrates the physical body during meditation.  Spheres 1-9 (the Altar) are conjoined with Sphere 10 (the body of the mystic).  Sphere 10 might also be representing the earth, itself.  Meditation produces linking with electrostatic fields in the ionospheric cavity of the earth.  Thus, the meditation process is "grounded," literally and figuratively.

The resonance effect produced by this means is described by the Qabalistic axiom: Kether is in Malkuth; and Malkuth is in Kether.

We can examine each section of the double cube separately.  When the geometry of the Tree is superimposed over the human form, the bottom cube centers in the region of the heart.  The top cube centers in the middle of the brain, in that region known as the 3rd Eye.  See Figure  .

[insert Tree of Life Interpenetrating the Human Form]

This figure is related to biological processes through the endocrine system.  Daath would be linked with the pituitary and pineal glands, Tiphareth with the heart and lungs, Yesod with the gonads, etc.  The two cubes interface at the throat (thyroid gland).  This reflects the associations of chakras and glands in yoga.

The bottom cube centers in Tiphareth, Beauty.  It contains the geometry of the Diamond Body.  It is formed by joining the centers of the six plane-faces of the cube.  Connect the vertices to form an octahedron.  Fill in the Bravis lattice.  It may help to make several xerox copies, and color the forms in different colors, until you can internalize them and rotate them in your mind.

The top cube is Daath, the Mystical Sephirah, or Upper Room.  The nexus point of this cube is Knowledge or Gnosis, the Cosmic Downloading Channel, uplink to the Archetypal.  The Vector Equilibrium joins the centers of the lines forming each plane face.

The center of the V.E.M. coincides with resonant neural cavities in the center of the brain.  This system is coordinated by the High Priestess (Key II, going from Tiphareth to Kether, intersecting Daath).  This is regulated by the pituitary and pineal glands which lie at the far ends of the cavity.


This matrix depicts the standing wave set up in the aorta and brain.  It illuminates "secret paths" on the Tree of Life.  It might be viewed as a form of the Tree of Knowledge.  The temptation would be to stop at this point (Daath) and not merge back into the soul's proper home.  It is the fate of many souls who remain trapped within Time.  They are enthralled with the phenomenal world, and do not wish to cross the Abyss.

There is a curious phonetic similarity between this word Abyss and the Indian word, abhyas, which means spiritual practice or exercise.  There is indeed an Abyss between intent and practice.  In the middle of being there is non-being.  This is the mystery of meditation and Vector Equilibrium.
(1) Aleister Crowley, BOOK 4, Dallas, Sangreal Foundation, Inc., 1972, p61.
[Tiphareth: Diamond Body/Throne-Chariot]


We are now in a position to examine the correspondences between DAATH and the Vector Equilibrium Matrix.  We might also elaborate on the mystical state produced by use of the figure.

One of the earliest Qabalistic documents, THE BOOK BAHIR, contains an intriguing passage, in this regard:

It is I who have planted this 'tree,' that all the world may delight in it, and with it I have spanned the All and called it 'All'; for on it depends the All, and from it emanates the All, all things need it, and look upon it, and yearn for it, and from it all souls go forth.  I was alone when I made it, and no angel can raise himself over it and say: I was there before thee; for when I spanned my earth, when I planted and rooted this tree and caused them to take delight in each other and (myself) delighted in them--who could have been with me to whom I might have confided this secret?

This tree of God, which is the tree of the world but at the same time the tree of souls, is spoken of in other fragments of the Bahir.  In some passages, however, it is not represented as something planted by God, but as the mythical structure of God's creative powers.(1)

nested star

When we recall the properties of the V.E.M. there is an interesting correspondence with this "mythical structure of God's creative powers."

   12 vertices
     8 triangular faces
= 50 symmetrically positioned topological features
     6 square faces
   24 edges

In this sense, the V.E.M. = 50.  The Hebrew word for 'All', 'every' also = 50.  This word is spelled Kaph-lamed (k-l).  The numeration for V.E.M. itself might be V=6, E=5, M=40  = 51, the number of the Hebrew Jubilee, a very holy number.  One can only speculate on the meaning of "All + 1."

As stated in the beginning of this treatise, Aleister Crowley declared:

The theogeny of our Law is entirely scientific.  Nuit is Matter, Hadit is Motion, in their full physical sense.(2)

It may seem strange that Infinite Space is equated with matter.  But even in the deep vacuum of space, there is still motion, matter and energy.  Empty space is not empty, but suffused with fluctuating fields of energy.  As this energy matters it warps or bends space/time around it.  Matter and its surrounding space are inseparable.

Crowley gave the numerological attribution of Nuit as N=50, V=6 = 56.  Curiously, we also find this number in the Isotropic Vector Matrix, I.V.M. = 56.  In Synergetics, there are 56 axes of cosmic symmetry, (533.22).

[DAATH; Vector Equilibrium Matrix]

[Figure : Isotropic Vector Matrix]

There is further correlation with the Hindi form of Nuit, Shakti:

 Sh=300, A=1, K=20, T=400, I=10 = 731

The meaning may not be readily visible, without further corroborating.  The Qabalists added the digits of numbers together, for example 731 is 7 + 3 + 1 = 11.  This type of reduction gives further information on the implicate meaning in words.

Now, we readily see that NV = 56 = 11; IVM = 56 = 11; Shakti = 731 = 11.

The number for the spiritual form of matter expressed as feminine deity is 56, which reduces to 11.  Crowley calls '11', the "Key to All the Mysteries."

Gareth Knight has linked Daath with the Isis Mysteries.  He says this mythology is the safest way to work the sphere Daath.  It is through this sphere that the Isis force functions.  According to Gareth Knight, in EXPERIENCES OF THE INNER WORLDS:

The various cycles of Isis mythology give contact with archetypes on different levels. ...the path of transmutation and sublimation of the psyche towards the consciousness of Daath can be trodden with a minimum of danger, for this particular line of meditation will build forms into the psyche which will hold the forces contacted whether in the depths of the instincts or the heights of consciousness.  These states have to be worked over and over again on a higher arc.  Isis was able to perform miracles, to heal, to bring the dead to life.  Indicates the ability to impart to others, even through the senses, the wonder and beauty, the glory and the joy and the power of the immortal spirit.

The Isotropic Vector Matrix is an omnitriangulated, omnidirectional grid which is the matrix, or mothering system, which fosters both the V.E.M. and the Diamond Body.  We could use her initials imaginatively.  This subtle representation could be "seen through" as the Isis Veil Mandala.

This symbolism reiterates our topological position on the Tree of Life.  We are traveling up the HIGH PRIESTESS path (which corresponds with the archetypes Isis, Artemis, Diana, Blessed Virgin Mary, etc.)  The path intersects or traverses the region of Daath.

Iona as Artemis
"Artemis," ©1976 photo by Robert Avalon

[Figure : The Veil of Isis]

 The concept of the Veil of Isis of the gnostic sects could be approximately equated with the Hebrew description of the veil before the Throne of God.  The Jews called this veil Pargod.  Gershom Scholem described this veil:

Metatron describes to Rabbi Ismael the cosmic veil or curtain before the throne, which conceals the glory of God from the host of angels.  This cosmic curtain, described in the BOOK OF ENOCH, contains the images of all things which since the day of Creation have their pre-existing reality, as it were, in the heavenly sphere.  All generations and all their lives and actions are woven into this curtain; he who sees it penetrates at the same time into the secret of Messianic redemption, for like the course of history, the final struggle and the deeds of the Messiah are already pre-existently real and visible.(3)

Atomic Vector Equilibrium Matrix

Elsewhere, Scholem goes on to state that the pargod (curtain or veil) separates the One Who sits on the Throne from the other parts of the Chariot.  Upon it are embroidered the archetypes of everything that is created.

...all the souls are initially woven into a curtain (pargod) that hangs before the Throne of Glory, and this symbol of "the curtain of souls" was both adopted and adapted by a number of classic kabbalistic texts.  The entire past history and future destiny of each single soul is recorded in this curtain.  The pargod is not just a mythical fabric composed of spiritual ether which contains or is capable of receiving a record of each man's life and works; it is in addition the abode of all those souls that have returned from below to their native land.(4)

Thus, the pargod is a "consciousness field."  It is interesting to note the semantic similarity to the Eastern form of this topological area.  In India, this spiritual region is known as Parbrahm.  Brahm being the God of physical manifestation, they are essentially the same.

There are a series of mystical experiences at Daath, which in yoga are termed Jhana states, or Knowledge ecstasies.

Those who experience these states are called Gyanis or Gyani Yogis.  Their discipline includes three major divisions describing their intent:

 1. Detachment (Vairag)

 2. Discrimination (Viveh)

 3. The Six Riches (Khat Sampatti) including balance (equanimity), self-restraint, indifference or freedom from ceremonial worship, patience, faith, and deep meditation.

These qualities may be seen as corresponding with the magical Virtues of Daath--Detachment.  Perfection of Justice and the application of the Virtues untainted by personality considerations.  Confidence in the future.


(1) Gershom G. Scholem, ON THE KABBALAH AND ITS SYMBOLISM, Schoken Books, New York, 1965, trans. Ralph Manheim.
(2) Aleister Crowley, THE COMMENTARIES OF AL, Samuel Weiser, Inc. New York, 1975.
(4) Gershom Scholem, KABBALAH, N.Y., The New American Library, Inc. 1974, p158.

[The Double Cube: Geometrical Duals of Tiphareth and Daath]


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