Diagram of Tree of Life nested within a
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The Diamond Body:
Buckminster Fuller and The Qabala
by Iona Miller, c1992
The Diamond Body
IO [I/O] is the cry of the lower as OI [O/I] of the higher. In figures they are 1001, in Joy. For when all is equilibrated, when all is beheld without all, there is joy, joy, joy that is but one facet of a diamond, every other facet whereof is more joyful than joy itself.
Aleister Crowley, The Dragon-Flies
According to most creation stories, out of primal Nothingness, the All or Everything emerges or emanates. Paradoxically, everything seems to come from nothing. How does nothing become something? Energy "crystallizes" into matter in the womb of empty space, a dynamic Void. Mass is simply a form of energy. This process is structured by an underlying, invisible, geometrical lattice. Actually, it is pre-geometric. Because it has no true physical existence, it is metaphysical (beyond physics). This threshold of matter, where nothing becomes something, is of great philosophical interest.
Actually, materialism (a natural philosophy) is a theory of metaphysics. It is metaphysical thinking to consider static matter as a primary reality. In fact, any attempt to describe reality is metaphysical speculation. In its dynamic form matter cannot be separated from energy. Energy is a property of matter, which can be considered potential energy. The mystic believes in matter, but believes it is more than science has yet discovered. Even before Western science began, mystics believed that mind, consciousness, or spirit is a property of matter. It hardly matters, philosophically, if you consider it as manifesting force or manifesting spirit.
The nature of reality is that matter-energy must be taken together .The theory of relativity conceives of this single substance as a distortion of the structure of space. Physicist Ian Barbour writes that, "...in quantum theory, separate particles seem to be temporary and partial manifestations of a shifting pattern of waves that combine at one point, dissolve again, and recombine elsewhere; a particle begins to look like a local outcropping of a continuous substratum of vibrational energy." That vibrational energy is governed by the laws of probability.
But what subtle forces underlie matter-energy and space-time? All form and power are latent within the void. The Heart Sutra tells us that, "Form is not other than Void, Void is not other than Form." This implies that our human form is not other than void, and biophysics shows this to be true. Our physical makeup is largely emptiness. If we conceive of humans as being most fundamentally electromagnetic entities, instead of chemical beings, we can imagine our finer existence as wave-fronts in space. Our personal "space" is not utterly empty, but cannot be conceived apart from our matter exhibiting itself in particular ways, i.e. as "waves."
Yet, the void state, or primal matrix, is "cosmic zero," and proportionately our most fundamental reality. It is part of the surrealistic quantum realm. It lies within us all, for the relative space between our atoms is astronomical. This is the ground state of existence which mystics seek in their meditation, moving beyond mind and maya. It is that state of consciousness where outer perceptions cease, and consciousness is free to simply be.
Throughout the centuries, various geometrical forms have been revered as expressions or metaphors of higher spiritual truths. These sacred forms and symbols are a natural part of the collective consciousness which emerges in every generation. We project them outwardly from within our psyche because they are so fundamental to our existence. That apprehension is intuitive. Certain typical forms recur in meditation and ceremonial practice, worldwide.
When something emerges from nothing, it does so via non-Euclidean geometry, coming to occupy space/time. Einstein used non-Euclidean geometry to explain the relativity of time and space as the geometry that is produced by matter or matter by geometry. The perception of the transcendental or metaphysical aspects of geometry is intuitive. There are examples of philosophical geometry or geometrical philosophy from around the world. These traditions are found in India, China, Egypt, and Great Britain, to name a few.
Plato, Archimedes, and the Pythagoreans based much of their philosophical speculation around the nature of geometrical form, suggesting that mathematics and structural forms had ultimate status. Our modern science has never forsaken the tradition of seeking the understanding of forms that provide shape and meaning to physical reality. Euclidean geometry describes the nature of the human scale, but non-Euclidean models the cosmos and microcosm. More and more intricate forms of measurement became the basis of the scientific method. Eventually, this led to modern topology -- the study of those properties of geometric figures or solid bodies that remain invariant under certain transformations.
Heisenberg explained that, "The elementary particles of modern physics can be transformed into each other exactly as in the philosophy of Plato." In "sacred topology", the relationships are more than metaphorical. Metaphysical and physical reality coincide. This is abundantly illustrated in R. Buckminster Fuller's geometrical tour de force, SYNERGETICS I & II. Fuller demonstrates, via synergetics, that the whole is greater than the sum of its parts, because of the relativity of forces. In our universe, as more complex systems are built up, new properties appear that were not foreshadowed by the parts alone. These emergent properties include life, conscious awareness, and beauty.
Plato's Academy in Athens had a policy: "You are not allowed to enter here, unless you know geometry." In the dialogue, Meno, Plato describes Socrates teaching geometry to a slave. In true Socratic form, he does not instruct him directly. Rather, he elicits knowledge from the slave which he did not know he possessed. The diagrams themselves elicit the buried intuitive knowledge of a world inhabited by the gods and by the divine "Forms."
In Plato's view, before birth we were familiar with purely mathematical "objects" and relations, as well as moral ideals or values. He alleged that we lost this knowledge at birth, but can recover it through revelation. For Plato, the virtues paled in comparison with the highest capacity of the soul, which is the mystical beholding of the eternal. Mystics tell us the divine is formless.
Actual space is not empty, but the possibility has always been a controversial problem in philosophy. Aristotle found the concept of a total void unacceptable. Scientists still cannot make a perfect experimental vacuum. Astronomy shows us that matter is averagely distributed, with roughly as much matter between the stars as there is within them. Yet, there are large voids in space, with stars clustered on the outer edges of these bubbles of void. The preponderance is of volumes of empty space over volumes of matter. So, the characteristic feature of the universe is not matter, but empty space.
Again, most of the interior of the atom is empty, as is the space occupied by the galaxies, and the vast regions which separate them. Stars, atoms, and the vacuum are a seamless whole.
The notion of the eternal nature of sacred emptiness is echoed in modern quantum theory. This is not ordinary, but dynamic and receptive emptiness. The central concept in Quantum Field Theory is that of the field, which exists everywhere and everywhen. It is a field of curved space/time. Matter is not separate from its surrounding space. The field can take the form of quanta or particles. It is the fundamental physical entity, the only physical reality.
The field contains the potentiality of all possible states or conditions in the universe. Of these states, the most fundamental is the Ground State, (or "vacuum state"). Matter is rare in the universe. Most of it consists of a very volatile, excited, ionic plasma. Only 5% of matter is neither too hot, nor too dilute, to congeal as a solid, liquid, or gas. This form of matter is so rare it has been described as 'trace contaminants.'
Yet, some form of matter is essential to all activity. All matter is in motion. Activity is the essence of being. From the "cosmic zero", everything -- the totality of "excited states" -- arises by creative processes. It is also the state into which everything subsides by absorption processes. The ground state is characterized by the fact that it stretches to infinity, uniform and changeless. It is the same everywhere and everywhen because of the identity of space/time. Within the universal field the values of the ground state and excited states are all one. An unlimited amount of particles come into being and vanish endlessly. Matter is thus a temporary manifestation of the Void.
The so-called "cosmic zero" was modeled by geometer/philosopher Fuller in the figure he called Vector Equilibrium, (V.E.). It might actually claim to be the first "Buckyball," the one Fuller himself described. This geometry is the precursor of the new elemental' Fullerenes.' The V.E. geometry has been recognized for a long time. It was one of the thirteen Archimedian solids, the cuboctahedron.
But the Greeks were fascinated with regular forms whose faces were all the same, such as the cube. They failed to understand the delicate balancing act the cuboctahedron symbolizes. They simply did not notice that Vector Equilibrium is pristine equanimity because they were looking elsewhere. The Greeks never really comprehended the energic or energetic properties of Vector Equilibrium, i.e. dynamic stability. They had a static, non-relativistic view of natural philosophy.
It remained for Fuller to assert that, "zero pulsation in the Vector Equilibrium is the nearest approach we will ever know to eternity and god." The conceptual model is the closest our minds and senses can come to that cosmic realization, short of mystical revelation. Mind alone cannot fathom the depth of this Void. Geometry is a construct of the intellect.
The V.E. center is primal "emptiness." It is a mathematical anomaly where the normal laws of the space/time continuum break down. It is not a symbol of ultimate order. It looks like a very rational, orderly system, but it is ultimately irrational. It defies logic. V.E. is the breeder of wave-particle duality, the uncertainty principle, and non-locality at the quantum level. It is a zone of neutral resonance where waves can pass through waves without interference, according to Fuller. Yet, it never physically exists as a structure, since nature abhors a vacuum.
In quantum mechanics a system can never have an energy of exactly zero. There is no such thing as absolute emptiness. However, the minimal motion of the ground state is called zero point energy, or zero point motion. Cosmic zero exists, paradoxically, in the realm of the psyche (our conceptualization) and in quantum reality in the atomic nucleus expressed as force. It is the form of formlessness, the root metaphor. It also forms the roots of the cosmic Tree of Life, since there is a fine-to-non-existent line between organic and inorganic matter on the quantum scale.
Physics is the patterns of organic energy, all of which are dynamic, alive. Mass is energy, so the subatomic world is always restlessly in motion. Inert matter is full of motion when we look closely at it . The activity of matter is its essence.
Vector Equilibrium emanates/condenses from a center in twelve fundamental directions. This emergent energy moves outward through space/time in the form of a cuboctahedron, alternating with its mathematical reciprocal, an octahedron-within-a-cube. It is a truncated cube with 50 symmetrically positioned topological features. Vector Equilibrium has the same surface area as a sphere, yet contains no volume, i.e. it contains "nothing."
The Vector Equilibrium system has 12 vertices, 8 triangular faces, 24 edges, and 32 planes. It is omnidirectional equilibrium, symbolically and physically speaking. As such, it is a perfect symbol for "holding the tension of the opposites," or "uniting the opposites." Yet, it is more than a metaphor. It is an archetypal image which bridges the macrocosm with the microcosm. It is a living example of the Hermetic Axiom, "As Above, So Below," uniting spiritual and literal reality. V.E. makes it possible to make conceptual models of other dimensions (hyperspace), mathematically and mystically.
In the V.E. figure, equilibrium between positive and negative is zero. It is the equalization of the forces of push/pull, radiation/gravitation, or tension/compression. Fuller alleged it" represents the limits of the mind's ability to conceptualize 'in'." For Fuller, all of space/time is undergird with a pre-geometric matrix, which is an infinite field of vector equilibria. An entire universe can be seeded from one V.E., self-generating to fill all space/time. There may be no ultimate physical building-block of matter, but there is one single entity that undergirds and composes everything in the universe, according to Fuller. The basic element of the universe is dynamic patterns.
This field constitutes a "cosmic blueprint" which Fuller called the Isotropic Vector Matrix (I.V.M.), a living continuum. The allocation of divinity to this "mother of all fields" marks its archetypal character. As a variation on the theme of Celestial Goddess, it symbolizes the embodiment of nature. Like a modern Isis, it iterates the theme of the underlying, inseparable cosmic web or net, connecting all.
The living Void gives birth to all phenomenal forms. It pulsates with the rhythm of creation and destruction of material particles. Another goddess, Nuit, is the essence of Infinite Space. She is infinite energy density pervading the entire cosmos. She is the receptivity of the void to the wavelength of radiation. Adjusting the geometry of the void influences the propagation of radiation. The goddess Ma-at, or Balance, is another expression of the same universal V.E. energy.
The Upanishads identifies Brahman with the void:
Brahman is life. Brahman is joy. Brahman is the Void. Joy, verily, that is the same as the Void. The Void, verily, that is the same as joy.
The geometry of Vector Equilibrium is inferred from that of closest-packed spheres of equal radius. It just happens to be the geometry which underlies all matter since it is found in the nucleus of all atoms as sub-atomic force. Here, in the interior of the atoms, Newtonian physics does not apply. This is a probabilistic, acausal world. Here synchronicity prevails over chronicity.
This uniform geometrical field, with the property of Divine consciousness, is the basis for a geometrical model of reality spanning the abyss between the metaphysical and the physical. It is not the first model in history to attempt to do so. There is an ancient geometrical model which shares a common framework with the Vector Equilibrium.
THE GEOMETRY OF THE QABALA
The ancient mystical system of the Qabala is formulated around the geometrical glyph known as the
Tree of Life. This sacred geometry system came down to us through Judaism and Hermetic Philosophy.
It is one of the main currents of thought in the Western Occult Tradition. A mathematically accurate image of the Tree of Life can be constructed by dividing a vertical line into four equal lengths and filling in four intersecting circles, using a fourth of the line as radius. The nexus points are the positions of the 10 spheres, and connecting paths join the centers of the spheres.
GEOMETRIC CONSTRUCTION OF THE TREE OF LIFE
1. Begin by imagining a vertical line, A-Z
2. Divide the line into four equal segments.
3. Using the segment length for a radius, inscribe four interpenetrating circles whose centers
lie along the vertical line. These represent the Four Worlds, or Planes of existence.
4. The points-of-intersection are related to the numbers of Spheres on the Tree of Life
as diagramed 1 - 10.
5. With vertical lines (Red) join 3-5-8 for Left-Handed Pillar of Severity; join points 2-4-7
for the Pillar of Mercy. Line 1-6-9-10 forms THE MIDDLE PILLAR.
6. The blue lines mark the paths between the Spheres.
The spheres represent states of consciousness or ways of being, while the paths are ways of transition or change. It symbolizes all ways of being and becoming. Like the quantum field, it contains the potentiality of all possible states or conditions in the universe. It is just the ancient way of saying it, and it turns out to be physically provable. The ancient model coincides with state-of-the-art physics. The 10 spheres and 22 paths yield a total of 32 planes of reference, like the Vector Equilibrium.
This "tree" was first described in writing in the Sephir Yetzirah, or The Book of Formation. Legend says the book came to Abraham, from God, through an angel. Today, we might say it was "channeled" from a divine source. Jewish scholar, Gershom Scholem dates the workaround the third to sixth century. However, there is some astronomical evidence that the system does date from the time of Abraham, approximately 4,000 years ago.
Whether the patriarch was the first to receive the revelation, or not, this archetypal consciousness map encodes a system of spiritual wisdom and growth in geometrical form. It describes the nature of the universe, consciousness, and the creation. It seems to have intuitively anticipated the discovery of the physical nature of reality. The glyph itself was used as a meditation devise by students of the Qabala, an oral wisdom tradition. One aim of the qabalists was to see the Tree always, everywhere, in everything. Another essential doctrine of Qabala is that humans possess a "spirit body" that can detach itself from the physical body and ascend to higher planes.
Most modern students of Qabala are familiar with the standard 2-dimensional representation of the Tree, which is drawn "flat," even though the circles are always conceived of as spheres. There is also a long tradition of a so-called 4-dimensional Tree of Life diagram, based on The Book of Formation. This geometrical figure consists of two interfacing pyramids surrounding a central core, within an enclosing cube.
This octahedron-within-a-cube happens to be the crystal structure of diamond, a face-centered-cubic lattice. Recalling that Abraham is also the patriarch of the Moslems, it is interesting to note reference to a spiritual body, a "diamond body", in the writing of Shaikh Amad Ahsa'i from the 13th century. Speaking of a substance akin to that of the medieval Philosopher's Stone, he equated the "diamond body" with the "Resurrection Body" of the faithful believer in the Paradise of the future Aeon.
For the Qabalists, meditation on this figure provided a mystical body as a vehicle for consciousness in imaginal space. This diamond body was used during meditation to enter the inner court of Divinity, symbolized by the center of the figure. Here the Beginning and End of time are co-temporaneous, space ceases to be a hindrance, and the mystic beheld the ecstatic vision of the Lord on His Throne. The geometry was a "gateway" to another dimension of experience.
This Alpha-Omega point has all the physical qualities of VectorEquilibrium. The ancient meditation practice was known as Merkabah mysticism, and those who practiced it called themselves, "Riders in the Chariot." They claimed to see into the future. This insinuates that the figure is a "vehicle" for moving consciousness through imaginal time and space. It seems to be a metaphysical "time machine," or inter-dimensional gateway.
As in most design or mandala meditations, the aspirant pictures him or herself at the center of the figure through visualization, contemplation, and identification. Through this process of centering, these mystics came to know themselves and God. Perhaps they learned, as Fuller later discovered, of the unusual anomalous conditions of perfect equilibrium. This meditation provided a specific technique for escaping from time. Its realization meant instantaneous enlightenment, a paradoxical leap out of Time. It yields transcendence.
Occultist, Paul Foster Case published an array of this type in his book, The Tarot (1947). Aware of the ancient mystic practice, he included the figure in his study of Qabala, calling it alternately the Key of the Cosmos and Numbers, or the Cube of Space. Again, we have the form of the octahedron-within- a-cube. Vector Equilibrium and the Cube of Space are mathematical duals, or reciprocals of one another. They "jitterbug" back and forth as the figure grows outward to fill all space. They are two ways of looking at the same geometrical phenomena.
Case pointed out that its construction was based on the six-pointed Star of David, (or Shield of David), also known as "The Star of the Macrocosm." His descriptors of zero as a sacred, empty, consciousness field reiterate the qualities of Vector Equilibrium.
Zero is a symbol of the absence of quality, quantity, or mass. Thus it denotes absolute freedom from every limitation whatever. It is a sign of the infinite and eternal Conscious Energy, itself No-Thing, though manifest in everything. It is That which was, is, and shall be forever; but it is nothing we can name. Boundless infinitely potential, living light, it is the rootless root of all things, of all activities, of all modes of consciousness. In it are included all imaginable and unimaginable possibilities, but it transcends them all. The Qabalists call it: (a) No-Thing; (b) The Boundless; (c) Limitless Light. Pure Conscious Energy, above and beyond thought, to us it is Superconsciousness.
With their fascination for completely regular figures, the Greeks devised a way of establishing XYZ coordinates within a cube. Our science and method of orientation has been stuck with that model ever since. However, nature's own most economical coordination is in triangles and tetrahedra, rather than squares or cubes. VectorEquilibrium is more in line with modern Quantum Mechanical models than the Newtonian XYZ. It expresses more degrees of freedom.
So, close examination of the underlying geometry of the Tree of Life reveals that the ancients were not lacking a very deep intuitive awareness of the true structure of matter and the universe. The underlying geometrical matrix of the multi-dimensional Tree is, in fact, Vector Equilibrium. To find the commonality -- the harmony --the figure of the V.E. must be subjected to a transformation process, i.e. rotation.
To bring the two figures into synch, simply rotate the V.E. to any edge of its containing cube. If the 3-dimensional V.E. is drawn flat, the inherent geometry of the Tree of Life is immediately revealed, including some of the so-called "hidden" paths.
A symbolic representation of the optimal union of opposites, it means in psychological terms, "holding the tension of the opposites." This is the essence of the Tree of Life. The theme of union of opposites has reverberated down through the ages. It was the process/goal of alchemy, creation of the Philosopher's Stone.
Now, Jungian psychology carries the torch of this philosophical pursuit. Both Vector Equilibrium and the Tree of Life express this most elegantly and economically in terms of minimal graphic elements.
Diagram of Tree of Life nested within a Vector Equilibrium
By combining the vectors of a V.E. nested within a cube, it is possible to derive the nexus points on which
to construct the entire Tree of Life. In The Anatomy of the Body of God, (1925), Frater Achad, (magickal name of Charles Stansfield Jones), revealed an amplified Tree of Life projecting from a center in six directions.
Rather than a flat depiction, his revelation showed Trees radiating in the four cardinal directions, plus up
and down. This is another variation on the theme of XYZ coordinates. Yet, V.E. can be shown, once again,
to be the skeletal matrix on which the figure congeals. The geometrical duals yield all the necessary nexus points to form the entire Tree of Life, including the 11th mystery sphere, Daath. Achad's advice for modern Qabalists says,
...since the "Tree" is everywhere the same in every part of space, once its general attributions are fixed in the mind, it is not well to confuse ourselves by too much attempt at progressed expansion of the idea. Rather we would return and contemplate the Centre from which All proceeds, thus obtaining the Pure Essence Here and Now.
This concept of a self-generating, self-iterating, all-space filling, crystalline system seems to herald the modern discovery of the fractal nature of the universe. Whether we look at the macrocosmic, mesocosmic,
or microcosmic level, we find the same principle operating. By following any portion of the consciousness
map "backwards" and "downwards" to the center, we have a conceptual means of entering that most
pristine state of consciousness where All becomes No-Thing.
These systems are virtually pre-geometrical. They don't really exist in nature, per se. Yet they are the invisible lattice, or bare bones, of our physical and spiritual life, of all life and manifestations. In this pre-geometry we have a blueprint for the formation of all matter, all form. This is the geometry of closest-packed spheres in the nucleus of the atom.
Yet, Vector Equilibrium is more than an expression of nuclear forces. It is "an endlessly interlinked chain
of atomically self-renewing links of omni-equal strength or of an omni-directionally interlinked chain matrix
of ever renewed atomic links, "according to Fuller. No single configuration of matter persists indefinitely.
All is change and recombination. V.E. describes the most economical lines of movement within the atomic nucleus. And, it also is the structural matrix of a very ancient and sophisticated consciousness-changing technology. Through it we remember deep knowledge of our true nature.
Noting the metaphysical aspect of physics, physicist Wolfgang Pauli said, "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. "
We have, in the V.E. model, a language or information transfer system that bridges both the physical and the spiritual, Fuller says, "In this model the physical and metaphysical share the same design." The mundane and supernatural share the same design: "As Above, So Below." It creates a mystical revelation described as ecstatic, blissful, joyful, transcendental.
Goethe's Faust opens with the mage contemplating the qabalistic, geometric design of the Macrocosm:
What jubilation bursts out of this sight
Into my senses--now I feel it flowing,
Youthful, a sacred fountain of delight,
Through every nerve, my veins are glowing.
Was it a god that made these symbols be
That sooth my feverish unrest,
Filling with joy my anxious breast,
And with mysterious potency
Make nature's hidden powers around me, manifest?
Am I a god? Light grows this page--
In these pure lines my eye can see
Creative nature spread in front of me.
But now I grasp the meaning of the sage:
"The realm of spirits is not far away;
Your mind is closed, your heart is dead.
Rise student, bathe without dismay
In heaven's dawn your mortal head."
(He contemplates the symbol.)
All weaves itself into the whole,
Each living in the other's soul.
How heaven's powers climb up and descend.
Passing the golden pails from hand to hand!
Bliss-scented, they are winging
Through sky and earth--their singing
Is ringing through the world.
In Aion, psychologist Carl Jung reiterates the identity of psyche and matter: Psyche cannot be totally different from matter, for how otherwise could it move matter? And matter cannot be alien to psyche, for how else could matter produce psyche? Psyche and matter exist in the same world, and each partakes of the other, otherwise any reciprocal action would be impossible.
To know ourselves is to know the nature of cosmos. The yogis and masters tell us that matter is mind or consciousness at its most fundamental or gross level. From the dawn of history mankind has employed sacred geometries for metaphysical orientation and creating consciousness maps. Most maps of the psyche imply a "journey" either to the heights or depths of experience. Long ago Heraclitus alleged, and mystic artist William Blake agreed, that the way up and the way down are one and the same. Riders in the Chariot rose to a plane above the Throne to gaze down on its resplendent beauty.
Metaphysical models usually speak of an ascent to utopian heights or "inner planes." Psychological models are usually concerned with descents into the subconscious depths and use subterranean imagery. These depths were the familiar territory of shamans for millennia. Both the occult and transpersonal psychology models include heights and depths of human experience. Maslow introduced the concept of "peak experiences" to psychology.
We may have the erroneous idea that peaks, or heights, or "highs" are "good." This is mainly because we are enculturated to strive upward. This is only one of a myriad of states of consciousness, and it belongs to manically over-achieving heroic ego. Negatively directed, this same energy can produce an all-time high in a sociopath or criminally insane personality, during a heinous act. All that is "up" is not "good"; and, all that is "down" is not "evil." This misapprehension is the root of the notion of a spirit/matter duality, where all matter is inherently "evil". In this belief system, "we exist: therefore we are sinful." Yet, our heights and depths contain the first-hand experiential knowledge that 'we are one.'
This old system of orientation and modeling the universe, with its ascents and descents of the soul, was adequate for many years. However, for the modern individual, with a consciousness that is not earth-bound, the old hierarchical model is no longer the best metaphor. Today we are not confined to the spectrum of reality dictated solely by our finite senses.
We are directly aware of physical realities ranging from the sub-atomic to the cosmic. Our perceptions are amplified with technology. New ways of seeing lead to new philosophical perspectives. We can align our mystical worldview with physical reality. The true nature of physical reality remains a mystery. Even for physicists, it has an elusive quality. No one really knows just what a quantum, a photon, or an atom "really is" or what it is doing when we're not looking at it.
Physics is another interpretation of reality. We have become aware of a vast physical dimension without and an equally vast realm of psyche within. They are available for exploration. And there are ancient and modern technologies which aid us here. In terms of modern orientation and consciousness models, an omnidirectional system allows more degrees of freedom. This freedom is a conceptual, imaginal, and physical reality.
Buckminster Fuller said that in whole systems the directions are always out and in. "In and out are the relevant directions, not up and down." Models or maps based on "in and out", rather than "up and down", allow us to conceive of particular states or conditions. As a metaphor, "in and out" is a typical characteristic of the phase states of matter. It is either in or out of phase or synchronization. During observation, matter is either in solid physical existence (particle) or out of solid physical existence (wave).
This wave-particle duality exists within us all. This uncertainty surrounding substantive existence leads to paradox. We cannot grasp one part of nature without another part slipping through our fingers. Photons, neutrons, and even atoms have no definite form until they are measured. Wave-particle duality is a mystery. However, this primal characteristic of atoms, and the energy exchange in their cores, is the basis of our physical existence. The emergence of stable matter requires the balancing of tendencies toward implosion and explosion. This is the function of Vector Equilibrium.
Physicist David Bohm modeled an "in and out" universe of implicate (in) and explicate (out) order. Yogis focus on the in and out breath during pranayama, and the experience connects them with cosmic time. The psychological tendencies, introversion and extroversion, express the polarity in ways of being. In cybernetics there is input (I) and output (O), the direction of the signal determining if it is I/O or O/I. Vector Equilibrium is the most economical model using geometry to express the ultimate union of the opposites. It creates the paradoxical state that is neither in nor out, up nor down, neither this nor that.
For Fuller, the balancing of the tension of the opposites was achieved in his tensegrity sphere. It is stabilized dynamically to neither explode nor collapse. This original "Buckyball" is a tangible example of Vector Equilibrium. According to Fuller, "matter" itself is a contained explosion, and the Vector Equilibrium is its austere image. It is a system not a structure. It underlies structure or formation of something from apparent "nothingness."
Vector Equilibrium is the lattice or invisible framework, and its blueprint is the cuboctahedron. Its explicit form can enfold on itself until it compacts down into an octahedron, then a tetrahedron, the prime geometrical form. This is accomplished by doubling up on the vectors on the edges. This creates the difference, for example, between carbon, diamond, and silicon atomic structures. They are all face-centered cubic crystals. Coincidentally these elements are symbolic icons in our culture. They are the hallmarks of technology.
A simple way to visualize the Vector Equilibrium is through the closest packing of spheres which underlies the geometry of crystal formation. Imagine a cluster of ping pong balls glued together, 12 around 1, then building out further and further. If you imagine vectors connecting the centers of each ball, IN THE THIRD LAYER you can find the Vector Equilibrium.
The vectors that radiate out from the center are exactly equal to the vectors that bond the faces. No other structure can make this claim. This is the symmetry the Greeks missed, because it is an energetic process, manifesting force, not a thing. Vectors are not points in space traveling through time. Vectors map energy events. Time determines a vector's length -- the time it takes an energy event to happen. There must be time for wave functions to propagate. We know a musical note requires time to exist, because a note is nothing in an instant.
Time is a duration. If we ask ourselves "a duration of what?", we can only answer "...of nothing, or something." All "somethings" are composed of matter, and the nature of matter is consciousness. So time becomes a duration of consciousness. Energy is substance. Substance is energy at the quantum level. Our substance is energy, and consciousness is fully capable of quantum leaps.
Fuller's energy mapping uses energetic triangles, in which three lines are not just lying there but are busy stabilizing the angles opposite them. Fuller describes the dynamic domain of "reality" as a broad spectrum of energy events, across a small portion of which our senses can "tune." Vector Equilibrium allows us to conceptually, metaphorically, and spiritually bridge the abyss between the mystical and scientific perspectives through sacred geometry. It is a key to the implicate and explicate order.
The Macrocosmic Snowflake within a Vector Equilibrium grid.
The Preceding Article is an excerpt from the book, The Diamond Body, by Iona Miller, c1984.