We should now proceed to find a neutral, or unitarian, language in which
every concept we use is applicable as well to the unconscious as to matter, in order to
overcome this wrong view that the unconscious psyche and matter are two things.
--Professor Wolfgang Pauli
I. PHILOSOPHY: ROMANCING THE STONE
A. THE PRACTICE OF ALCHEMY
In the alchemical search for the God-head in matter, Paracelsus contended that matter was a living counterpart of the creating deity. A system of correspondences is the foundation of alchemy. The conception of a primal event manifested in different fields is fundamental to alchemy. The process in the retort vessel is analogous to the process of transformation of the psyche. Through alchemy, we can perceive the parallels between macrocosm and microcosm, universe and man.
The metaphorical perception of alchemy grew in the Jungian school of psychology. It emphasizes the process of psychological transformation, or individuation. The model of the vector equilibrium matrix restores a physical basis to the concept of the Philosopher's Stone. This renews the alchemical philosophy which is, like Jungian psychology, concerned with the union of psyche and matter.
There are three primary aspects of alchemy:
1. Alchemy as theory, is a comprehensive philosophical vision of the cosmos, built on the universal correspondence system.
2. Alchemy as practice may be viewed as a creative discipline, an art-form, involving one in the imaginal realm of soul-making.
3. Alchemy, as a transcendental search or quest, has the primary goal of liberation from the world. This is the knowledge of immortality, through the union of opposites.
Paracelsus described alchemy as the voluntary action of man in harmony with the involuntary action of nature. If the center of the creative process takes place in the "heart of man", his intentions take on profound significance. They can now affect, or influence, the destinies of the cosmos. Attainment of this state is known as the production of the Philosopher's Stone or Diamond Body.
B. THE PHILOSOPHICAL CONCEPT OF THE IMMORTAL BODY
The Philosopher's Stone may be equated with the Causal Body, the Resurrection Body, or the Immortal Body. It is a vehicle for consciousness to inhabit, which is qualitatively different than the Astral Body, a double of the physical body.
Alchemy strives for the experience of spiritual rebirth through the union of opposites, or the sacred marriage. The Philosopher's Stone is also a symbol of the embryonic Self. It is the product of the sacred marriage, which has been characterized in alchemy as the union of the Sun (+) and the Moon (-).
Polarized positions, or extremes, may be symbolized variously as positive-negative, male-female, god-devil, spirit-matter, mother-father, etc. This marriage creates a bond by which opposites are united in an image which transcends both original potentials. The whole art of alchemy is contained within the image of a magical or divine child.
One of the alchemical goals is to create an eternal body for post-mortal continuation of the spirit and the soul. Both the western and Chinese alchemists felt this could be accomplished in a lifetime, with the help of God, or the Self. This vessel for immortality is the Diamond Body.
Alchemy, like Jungian psychology, is a creative discipline which embraces all things from the standpoint of soul.
C. THE PSYCHOLOGICAL MEANING OF THE PHILOSOPHER'S STONE
There is an inherent paradox in alchemy: all the while stressing redemption of the physical body, or matter, alchemy is actively striving toward creation of a subtle, immortal body, which has no apparent physical basis.
This central problem in alchemy is the spiritual redemption of the physical body. Alchemy requires resurrection of the soul of body. The challenge one encounters is to "see through" to a unified vision of mundane physical processes with spiritual values. This develops an awareness of the ordering processes inherent in matter. The solution is to visualize the physical as a metaphor for psychic transformation.
Close scrutiny of the foundations of matter ought to reveal some physical analogies to this 'archetype of the spiritual essence inherent in matter.' In alchemy, matter is perceived as a living feminine counterpart of the spiritual father or creator-god. It is an equivalent, not subordinate, principle.
In THE COMMENTARIES OF AL, Aleister Crowley corresponded matter with the goddess Nuit. In other disciplines, Nuit is known as Sapientia Dei, Sophia, Shakti, Isis, Shekinah, etc. In alchemy, she is represented by the Anima Mundi, or World Soul. Nuit, as matter, is the feminine form of Godhead. Inherent in this word 'matter' are the concepts of matrix or lattice; and mater, the mothering womb. This implies a possible dovetailing of traditional attributes of Nuit with specific geometrical systems which operate at the atomic level.
O Nuit, continuous one of Heaven, let it be ever thus;
that men speak not of Thee as One but as None; and let
them speak not of thee at all, since thou art continuous!(1)
Nuit, as 'zero' or 'naught' represents the field of potentiality.(2) By definition, She may not be represented concretely, or be observed directly and finally. Her presence, however, may be inferred.
Microphysics, by feeling its way into the "unknown" side of matter, parallels the quest of the alchemist. The goal is toward a unified field theory, an all-encompassing model between subatomic and cosmological states of matter.
An analysis of crystals in microphysics (solid state physics) might provide a basis for unifying the philosophical and physical concepts regarding matter. This geometry can describe a system or matrix of unfoldment, bridging the microverse to the cosmos.
The geometry or matrix description of a crystal can act as a "lens." This "lens" enables one to "see" or focus a projection of the physical state of matter into its spiritual counterpart.
Alchemy is the means of "seeing the Philosopher's Stone", itself; it is also a means of "seeing through" the Stone. As such, it is a form of metaphorical perception. The Stone is produced by the transformation in one's own psyche.
The Philosopher's Stone, seen as a magic crystal, is not a spiritual or psychological state, but more a magickal tool or universally applicable instrument of magic. One can attain the ultimate mystical experience through proper application of the Stone. The Stone possesses the "virtue" or healing power to influence or transform things.
The process of making the Philosopher's Stone is a repitition of the creation myth via imagery. The imagery reverses the evolutional direction. It begins with animal images, then proceeds through images of plant life to more fundamental forms. The final goal is symbolized by metal, stone, or crystal.
This language usually presents the ego in a direct line of confrontation and covenant with a single self, represented by images of unity (mandalas, crystals, balls, wise men, and other patterns of order). But according to Jung the self has many archetypal instances. The puzzling relation between self and the archetypes reproduces the ancient enigma of the many-in-the-one and the one-in-the-many.(3)
The alchemical concept of the Stone accomodates either/both a monotheistic attitude (where God is One), or a polytheistic viewpoint (which recognizes the value of the differentiation among archetypal figures). When we can distinguish among divine figures, mythic creatures, and the phenomenal world, we may orient ourselves in the imaginal realm.
The process of alchemy takes place within cetain boundary conditions. It is visualized as occuring within a vessel (i.e. a containing form or matrix). Consciousness and life must be intensified or contained by focusing one's attention. The process of reversal signifies reunion with the unconscious laws of our being. These laws also affect the formation of matter on quantum levels (in the subatomic world of protons, neutrons, electrons, etc.).
The purpose of alchemy is real-I-zation of the many aspects of the Universe. The vessel contains and co-ordinates the manifold of psychic contents.
The vessel is the "lens" or geometrical relationship between these archetypes. It is possible to restore and renew the alchemical philosophy by reuniting psyche and matter through contemporary imagery. One way of pursuing this analogy of the Stone is by examining current concepts in solid state physics.
The mathematical descriptors relevant to the concept of the Stone are already developed. Archetypal ordering processes at the atomic level form a basis for a relationship between life and its crystal counterpart. This unification of vision may be found in the diamond crystal structure.
(1) Aleister Crowley, THE BOOK OF THE LAW, I:27.
(2) Philo Stone, N=50, V=6: ON NUMBER AS FIELD, Carlton, 1981.
(3) James Hillman, THE MYTH OF ANALYSIS, N.Y., Harper and Row, 1972, p. 265.
A. SOLID STATE PHYSICS:
A study of the physical properties of the solid state, viewed as a branch of atomic physics, began in the early years of this century. Solid state physics has come to mean the study of crystals and of electrons in crystal structures. A century ago the study of crystals was concerned only with the external form of the crystal and geometrical symmetry relationships, which described the physical properties.
Many crystalline minerals and gems, particularly quartz have been known and described for several thousand years. One of the earliest drawings of a crystal appears in a Chinese pharmacopeia of the eleventh century A.D. The word crystal itself referred only to quartz until the late middle ages when the word acquired a more general meaning.
A.L. Seeber(1) of Freiburg suggested in 1824 that the elementary building blocks of crystals were small spheres. He proposed an empirical law of interatomic force with both attractive and repulsive regions. This model mathematically caused a lattice array to be the stable equilibrium state of a system of identical atoms.
Linus Pauling updated this idea in an article entitled "The Close-Packed-Spheron Theory of Nuclear Fission" (SCIENCE, Vol. 150, 1965, 297-305). He discovered that the arrangement of spherons (nuclear constituents) are roughly spherical in shape and packed in concentric layers. They have intimate connection with certain Platonic solids (the tetrahedron, the octahedron, and icosahedron). He also found that "resonances" enter into the dynamics of nuclear constituents.
An ideal crystal is constructed by the infinite regular repetition in space of identical structural units in the form of parallelpipeds. In the simplest crystals such as copper, silver, gold and the alkali metals the structural unit contains a single atom. More generally the structural unit contains several atoms or molecules, up to perhaps 100 in an inorganic crystal and 10/5 in protein crystals.
We describe the structure of all crystals in terms of a single periodic lattice. A group of atoms is attached to each lattice point situated in each elementary parallelpiped. This group of atoms is called the basis; the basis is repeated in space to form the crystal. There are fourteen Bravis or space lattices possible. The diamond structure is the densest pack of atoms.
The space lattice of a diamond is a face-centered cubic (f.c.c.). A primitive basis of two identical atoms at 0-0-0;1/4-1/4-1/4 is associated with each lattice point. The tetrahedral bonding of the diamond structure has four nearest neighbors, and twelve nearest neighbors. There are eight atoms in a unit cube.
The Diamond lattice is relatively empty. The maximum proportion of the available volume which may be filled by hard spheres is only 0.34, or about 46 percent of the filling factor for a closest-packed structure. Carbon, silicon, germanium, and grey tin crystallize in the diamond structure. The diamond structure is the result of covalent bonding. In covalence an atom shares electrons with surrounding atoms. Two atoms sharing a pair of electrons makes a bond.
B. THE VECTOR EQUILIBRIUM MATRIX:
The vector equilibrium matrix, as discussed by Buckminster Fuller (2) in SYNERGETICS 1 and 2, describes the most economical lines of movement within the atomic nucleus. These are the preferred pathways for energy exchange, because they are the paths of least resistance. The equilibrium point between + and - is zero. The vector equilibrium is a true zero reference point for energetic mathematics, according to Fuller.
The vector equilibrium modelling is important for conceptualization in philosophy and quantum physics. It is a graphic depiction of the nuclear tendencies to implosion and explosion. These forces are mathematically reversible, and always in exact balance.
This zero point is never directly observed as physical experience. This is reflected, perhaps, in mystical thought by the phrase, "I am Isis; no man hath lifted my veil." We can see no further into nature than fluctuating fields of energy which constitute the constant background motion. All that is, is in motion. But it is sustained by the ground state or "cosmic zero."
The vector equilibrium matrix is a system, not a structure. When the goddess Nuit is corresponded with the vector equilibrium matrix, She may be seen as nuclear nothingness. This Goddess of infinite Space is the zero point, where waves pass through waves without interference lines. She is the womb from which all that is born in materiality emanates forth.
This vectoral phase or mathematical zone of neutral resonance occurs between the outwardly pushing electromagnetic wave propagation and inwardly pulling gravitational coherence. The specific crystal structure represents the state of equilibrium in bonding. The vector equilibrium matrix is the mathematical description of this zone of neutral resonance.
The diamond structure, using Seeber's small sphere model, packs together the most compact spheres of equal radius. This f.c.c. pack produces the densest form of matter, the diamond.
Before examining the philosophical importance of this geometric configuration, it should be firmly fixed in the mind's eye:
[Cubic close-packed crystal structure]
[Model showing the structure of a diamond]
[Expanded model showing the basic pattern]
A visual image of the vector equilibrium matrix (V.E.M.) can be constructed via the following steps:
1. Begin the visualization of the Bravis lattice for a face-centered cubic crystal. See Figure. The center point is the equilibrium point or zone of neutral resonance. There is no atom at this point as this is the zero point of equilibration. Visualize the three tetrad axes of the cube, XYZ coordinates, which join the centers of the six plane faces.
2. The diamond crystal has atoms at each point, as shown in Figure 2. Note that the primitive cell is a rhombohedral cube inside the cubic lattice, with a 60 degree phase shift between planes. Characteristics of this f.c.c. lattice are give as the following:
Volume, conventional unit cell a3
Lattice points per cell 4
Volume, primitive cell 1/4(a3)
Lattice points per unit volume 4/a3
Number of nearest neighbors 12
Nearest-neighbor distance a/21/2
Number of second neighbors 6
Second neighbor distance a
Visualize the rhombohedral primitive cell and its relationship to the diamond crystal lattice.
3. The next step is to visualize the close-packed crystal structure. This shows the relationship of the 12 nearest neighbors. See Figure 3. The changes in planes visualization (Figure 2 to Figure 3b) begins to form the matrix relationship between planes. Visualize a "change of rotation" in the primitive cell.
4. This stage, arrived at via a visualized rotation of planes, produces what is known as the Diamond Body. See Figure 4. This physical structure has a history of traditional use in Jewish mysticism where it is known as the Merkabah, or Throne-Chariot of God. This figure is described in detail in the SEPHIR YETZIRAH, or BOOK OF FORMATION. Visualize two pyramids, base-to-base, within a cube (octahedron within a cube).
The Vector Equilibrium Matrix is the reciprocal view of this figure. It is the hidden, occult, or implicate aspect of the Diamond Body. It expresses the energetic quantum aspects of the Diamond Body. They are two sides of the same coin. The Diamond Body connects the centers of the plane faces of the cube with one another. The V.E.M. connects the centers of each line, leaving a truncated cube.
[covalent bonding diagram]
[rhombohedral primitive cell]
5. The final stage of visualization yields the geometric figure known as the Vector Equilibrium Matrix. This system results from forming plane surfaces between the centers of each atom. It represents the most economical lines of movement between closest packing of spheres. It is a matrix in that it sets up an archetypal ordering process. Visualize the twelve nearest neighbors connecting to each other with 6 square faces and 8 equilateral triangular faces, along 24 edges.
This yields a figure with the following properties:
8 triangular faces
6 square faces
24 edges = 50 symmetrically positioned topological features
The synthesis of psychological opposites contained in the figure of the V.E.M. is quite interesting. It is composed of the minimal number of graphic elements required to depict the relationship of '3' and '4'.
The figure shows the relationship between a threefold process and a fourfold goal. Deity, or godhead, is expressed in symbolism by triangles. The soul is depicted in its static quaternity form by the squares.
Three symbolizes an essentially monotheistic process, the total cycle of growth and dynamic change. While four is structural wholeness in its eternal aspect. Four shows the static, stabilizing influence of the polytheistic psyche.
Neither 3 nor 4 alone are an adequate symbol of wholeness. The quaternity alone is not an adequate symbol for totality as the dynamic, developmental, and temporal aspect is lacking. In other words, fourness may not be actualized without submitting to the threefold process of realization in time.
Psychologist Edward Edinger comments on Jung's view:
Jung does not consider the quaternity a completely adequate symbol for totality. Rather a union of quaternity with trinity in a more complete synthesis is required...The theme of twelve, for instance, includes both three and four in its factors.
The trinity archetype seems to symbolize individuation as a process, while the quaternity symbolizes its goal or completed state. Three is the number of egohood; four is the number of wholeness, the Self. But since individuation is never truly complete, each temporary state of completion or wholeness must be submitted once again to the dialectic of the trinity in order for life to go on.(3)
The Vector Equilibrium Matrix encompasses the union of the masculine trinity with the feminine quaternity. It depicts the union of soul and spirit, of the soul with the divine. As a synthesizing symbol, it is an embodiment of spirit and soul, distinct but attached. They are united through the twelve vertices.
(l) A.L. Seeber, "Versuch einer Erklarung des inneren Baues der festen Korper," ANNALEN DER PHYSIK (Gilbert) 76,
29-248, 349-372 (1824).
(2) R. Buckminster Fuller, SYNERGETICS, SYNERGETICS 2, N.Y., Macmillan Publishing Co.
(3) Edward F. Edinger, EGO AND ARCHETYPE, Baltimore, Penguin Books Inc., 1973.
[Vector Equilibrium Matrix diagrams 1-5 Regenerative Patternings]
C. THE COMMON GROUND BETWEEN PSYCHE AND MATTER:
Within the current laws of physics, there is always an overview law or paradigm. More often than not, this structuring is not immediately evident within the specific law. This overview is implicate to the specific, still enfolded within it, yet a priori to it. The limited, objective viewpoint is defined as explicate.
The implicate law can be considered as more encompassing than the explicate since it enfolds the explicate plus something undefinable. A specific example is gravity and its explicate relationship to the force of gravity. The force of gravity is explicate in that it is measurable within a limited context. Gravity is not even understood in physics.
Explicate ordering may be used for practical application in a limited context. This form of ordering does not, however, tell us anything about the Totality. The word "transformation" is thus used to describe a simple geometric change within a given explicate order. What occurs in the broader context of the implicate order appears as a quantized transformation: metamorphosis.
This form of transformation is characteristic of psyche. In Greek, psyche literally means butterfly. The butterfly does not evolve, but rather its quantized change occurs within a vessel of transformation--the cocoon. The new science of chaos theory postulates a so-called "butterfly effect" which contends that a simple movement of the butterfly's wing in Indonesia can create a hurricane thousands of miles away.
Psyche also expresses this chaotic sensitivity to changes in initial conditions. You never know quite where it will go next. Fundamental characteristics of psyche render it undefinable, from the explicate point-of-view. It is ceaselessly becoming, and the mystery of consciousness lies in its hidden (or occulted) implicate nature.
The implicate order may be seen to apply both to matter (organic and inorganic) and consciousness. This is equivalent to the alchemical goal of uniting psyche and matter. It requires, however, redefining our concept of consciousness.
Both parapsychology and analytical psychology have defined consciousness in terms that are most appropriate to "ego-consciousness." It is linear, directed thinking. Ego-consciousness is linear, directed, transcendence-oriented and monotheistic. It is heroic, and as such is goal-oriented and produces the fantasy of moving consciousness through a series of hierarchal stages of development.
There is another way of imagining exitence, where soul rather than spirit is the primary motivation. In fact, there are differing styles of consciousness, depending on our perspective. Styles of consciousness are relative to one another. Within our developing framework, we might consider ego-consciousness as explicate.
However, anima-consciousness mediates implicate order. Anima-consciousness, as conceived by James Hillman's school of imaginal psychology, is a multi-centered polytheistic perspective. Its concerns are being-in-soul, not becoming more, better, best or perfect. It is perceived as a coincidence of processes. All phases are present at once, enfolded in any part. It is experienced as a series of superimposed images. It is reflective and concerned with inter-relationships. It is diffused, not focused awareness. It mediates the unknown, or unconsciousness--that which is yet to unfold and still lies hidden behind the 'veil.'
'Anima' is the Latin form of the Greek word, 'psyche.' They are cognate. James Hillman has called anima the archetype of psyche. As psyche means butterfly, he says it indicates "a consciousness that does not soar but stays attached, that hovers and flutters over the field of natural events."
Anima-consciousness comes through images, multi-sensory images, from the primitive gut reaction to the most exalted vision. It brings awareness that fantasies are everywhere, conditioning our perception of reality and our place in it. Images and fantasies are not separate from our reality, but are fundamental to our notions about reality. Jung says, "image is psyche."
Anima, as the archetype of psychic consciousness, makes us aware of our areas of unconsciousness. Soul, in its relationship with spirit, constantly invades the day-world of consciousness with images, fears, moods and mystery. It is elusive, ambiguous and paradoxical.
The interaction of spirit and soul, discrete yet connected, represents the sacred marriage, or coniunctio. So, one task is to distinguish them, one from the other. They have been confounded in theology, philosophy, psychology, and science. Descarte equated the ego with the soul, a grievous mis-representation. Anima, is a diffuse consciousness that seeks to re-create and unify with spirit in the royal marriage.
This mode of perception is conscious of its unconsciousness and can recognize the potential latent in the unknown aspect (the promise of the divine child). This style of consciousness can be characterized as illumined lunacy, and was a characteristic of many of the saints and sages throughout history.
When we can get outside of our culturally-programmed heroic consciousness and experience the world of imagination, dreams and creativity, the ego realizes that there are possibilities far outside of its sphere of observation.
There is an inevitable uncertainty principle in the realms of both matter and psyche. The autonomy of psyche's stream of consciousness assures we will never know her next move. And in physics an electron's position and momentum cannot be simultaneously measured. When we attempt to grasp one part of nature, we lose consciousness of another--it gets "fuzzy."
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