IV.  CONTEMPORARY APPLICATIONS

A.  ARCHETYPAL TOPOLOGIES:

Active participation in the realm of the imagination is central to psychology, alchemy, magick, and physics.  Many, but not all of the imaginal modes involve the concept of topology or topography.  Within the context of the topological fantasy, the various forms of ordering (Tree of Life, the Diamond Body, the V.E.M., etc.) provide a comprehensive means of ascertaining the values of any system of experiences.

Topology is the science of fundamental pattern and structural relationships of event constellations.  It was discovered and developed by the mathematician Euler.  He discovered that all patterns can be reduced to three prime conceptual characteristics: to lines; points where two lines cross or the same line crosses itself; and areas, bounded by lines.(1)

While active invoking of images is essential to the practice of QBL, it is best to balance this through a detached observation/participation in the rising and passing away of phenomena.  Topographical models are paradigms, but they should not be considered ultimate truths, but as allowing access to imaginal realms. While topography is a useful tool, it is also an archetypal perspective.

For example, I suggest that a perspective which sees the necessity for 'archetypal topographies' is just one among many.  We must not be drawn into literalism at such a profound level.  As I mention above, Casey seems to imply a single natural ordering for a particular purpose, within a specific archetypal influence.  Examination of the variety of such attempts to pattern and group archetypes is itself a valuable exercise in exploring archetypal imagination.  What kind of consciousness is it that perceives in terms of organization, integration and preferred positioning of Gods?  Generally, the attempt to discover a unifying wholeness or impose a distinct pattern onto archetypal groupings is a procedure dominated by the archetype of the Self.(2)
 

QBL is a single philosophical system which accommodates both monotheism and polytheism.  These topologies may be used in conjunction with a polytheistic orientation in which consciousness circulates among a field of powers.  Each god, or complex is sovereign in its domain.  There is a circulation in which there are no preferred positions.

The danger in identification with the archetype of the Self is persistent belief in it as the "only" reality.  Archetypal images of order (mandalas) counter disintegration.  However, there is sometimes a psychic value in disintegration.  It brings immediate awareness of distinct separateness among the pantheon of archetypal forces.  Both attitudes, monotheism and polytheism, represent forms of living reality in the phenomenal world.

Topology offers a descriptive basis for both meditation and exploration of the imaginal realm.  The importance of the act of decision for behavior or transformation lies mainly in the fact that by it the individual changes his position.  A "path" is a change of position within a field which otherwise remains sufficiently constant.  It is an abbreviated representation of a sequence of situations.

A path permits changes between regions.  This is both conceptual and physical change.  The actions which are represented in the life-space as regions are coexisting manifolds which possess a certain degree of differentiation.  These "regions" are the spheres of the Tree of Life.

The imaginal paths of the Tree of Life are linked to the concept of locomotion.  They require "working" by the aspirant in a process in time.  The psychological region in which these processes occur determines the dynamic condition of the individual.

Pathworking is a form of "loco-motion," akin to the "illumined lunacy" Hillman describes as the royal marriage, the pre-requisite for the Stone.  It is 0, THE FOOL who makes the journey through the winding paths of the Tree of Life via Tarot imagery.  He is nowhere (now-here) because of his ability to makes quantum leaps.  He is everywhere at once, until we make an observation by using the cards.  He is thus gripped by only one story at a time, which contains many images and its own inherent rhythm.

When one changes position, different loco-motions are now possible and impossible.  Even when a region is still attainable, the course of the path followed has changed fundamentally because of the new point of departure.  This part that you are now is "where you are at."

THE FOOL is a breath-spirit, and Anima is a breath-soul.  This relates them intimately to the airy realm of imagination.  Just as the Fool circulates around the paths of the Tree, anima circulates throughout every cell of the body.

The attributions of these entities leads us in a definite direction: they both focus attention on the breath.

The importance of breath in human life and mystical meditation is not to be underestimated.  The use of breath control has a long-standing tradition in magical and yogic practice.  There is a relationship between meditation states and rhythmic breathing.  If we look further into our Qabalistic modeling, we should find the heart playing a prominent role in this process.  This is, in fact, the case.
 
 

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(1) R. Buckminster Fuller, OPERATING MANUAL FOR SPACESHIP EARTH,
(2) Peter Bishop, "Archetypal Topography,"  SPRING 1981, Dallas, Spring Publications, 1981.
 B.  MEDIATION AND RESONANCE EFFECTS

(This paper is from THE HOLISTIC QABALA, a series of 11 books, written by Richard and Iona Miller.  It has also appeared in print in "Psychedelic Monographs and Essays," Volume Four, Summer 1989)

The use of psychedelics or empathogens traditionally involves effectual  traits or nuances which can parallel endogenous mystical or cybernetic landscapes.  This piece presents an introduction to current descriptions common throughout all three fields.  A promise of increased comprehension so far as metaphor, symbol and effect surrounding these and other cross-correlative fields is reviewed and annotated.

...If the manas is to preform its proper task of controlling senses, it must reflect the ideal pattern that is laid up in the heavens of Buddhi.  Only when that pattern is reflected in its mirror has it the standard of reference by which to judge...nor should we think that the possession of such a divine standard by which to judge attainment is far above us; one to which we may aspire in some dim future.  Here and now the Pattern is within us.
Sri Krishna Prem
 

Theoretically, the practice of meditation is intended to withdraw the personal mind from its persistent preoccupation with external affairs.  It can be seen as a form of training for the mind in switching from matter to psyche.  There is a purpose.  It is to prepare the personal nature so that it is able to reflect and express its relationship with the Universal Self.

Throughout history there have been a number of techniques used to achieve a meditative state.  The most often used first step is a form of rhythmic breathing.  If done correctly, a sequence of strong and unusual body reactions occur.  These also will eventually trigger unusual psychological states via a type of resonance effect.  A closer examination of these resonance-relationships yields information useful in improving the meditation.

Perhaps an example clarifies this:  When a subject is totally relaxed and has achieved a deep meditative state, a slow, rhythmic sine wave pattern can be registered by a cardiograph-type sensing device.  What is being measured is a standing wave in the aorta.  There is a heart-aorta resonating oscillator which affects other parts of the body, including the brain.

Resonance occurs when the natural vibration frequency of a body is greatly amplified by vibrations at the same frequency from another body.  Oscillators alter the environment in a periodic manner.  When in a deep meditative state the regular movement of the body indicates that a standing wave is set up in the vascular system, specifically in the aorta.  This standing wave affects several other resonate systems in the body, all of which are driven by this large signal.

A paper by Paul F.J. New, and several current papers, indicate the presence of a major resonate cavity oscillator located between  the heart and the bifurcation, where the aorta divides itself.  When the timing of the pressure pulses traveling down the aorta  coincide (in phase) with the reflected pressure pulse, a standing wave is achieved.  When this frequency approaches 7Hz., a progressively amplified wave form is created by resonance, resulting in a large oscillation affecting every other circuit in the body tuned to this frequency.

There is a resonance relationship to this frequency  with standing waves on the Earth's crust.  If we assume that the spherical crust of the Earth represents a condenser, then the frequency of resonance can be calculated on the basis of the equation:

  Resonance frequency = C/7.3R2

Where C is the velocity of propagation of electromagnetic waves and R = radius of the Earth.  This frequency has been shown to be 6.4Hz.

Thus, a harmonic frequency corresponding to the pulsation of the electrical charge of the Earth is present in heart/aorta.

The brain may be considered as a piezoelectric gel3, one converting physical vibrations into electrical ones.  Although the body movement from this heart/aorta resonance is relatively small, 0.003-0.009 mm., the head is a dense and tight structure.  By moving up and down, the skull accelerates the brain with mild impacts.  These acoustical plane waves are reflected from the cranial vault and are focused upon the third and lateral ventricles.  A hierarchy of frequencies couple this 7Hz. body movement to the higher frequencies in the ventricles.

That which is that bright within the heart; in that this man resides, innate with mind transcending death, with brilliance innate.
Taittiriya Upanishad

In the book Biomedical Engineering Systems4, Chapter 7 is a major work entitled "Toward A View of Man", by Manfred Clynes.  Clynes is a medical doctor working at the Research Center in Rockman State Hospital, Orangeburg, New York.  This work is considered a breakthrough in the fields of psychology and medicine, known today as the field of psychobiology (biocybernetics).

Clynes took a number of volunteers and shaved their heads, placing a series of electrodes in rosette patterns or various regions of the brain.  These included the temporal, frontal lobe section and occipital region.  In this way, not only were the brain frequencies monitored, but directional shifts in these frequencies could also be determined by the geometry of the electrodes on the scull.

The original purpose of Clynes' work was to find out how precision and order exist in brain processes; to discover what is inherently programmed in man and how he might make use of the inherent programs.

These individuals were given a number of images (form) and colors to concentrate on while their brain was monitored by computers.  Recording from opposite pairs of electrodes simultaneously, he obtained views of the electrical activity from different angles:  mathematically, a spatial differentiation of the electric vector.  What was happening literally was a mapping of consciousness.  A number of very important observations were made:

 1. Certain qualities and relationships were of greater importance to the computer than such quantitative factors such as intensity.  This meant that the brain's systems of identification  are based on differences, rather than intensity of the signal.

 2. Thin lines were found to produce characteristic evoked potentials, irrespective of size.  The form itself is transduced into another form in the brain space time which can be measured.  There is a one-to-one correspondence between the visual form of the stimulus, the response form in the brain, and the perception.

This is, perhaps, the first physical description of the field of an archetype.  It is a geometrical, structuring and has uniqueness.

 3. The process of inhibition is as important for transducing the external world as is excitation.  Concentrating on specific lines of geometry does not constitute the changing stimulus, but their steady presence systematically and radically alters the response to another changing stimulus.

 4. Changes in intensity of a single color produce very simple response shape. Light and darkness (as opposites) show no evidence of being different values of the same variable.  Rather, they seem to be the result of stimulating and also of inhibiting different receptors.  Thus, the evoked potentials to light and darkness in no way may be said to be positive and negative, respectively.  White, for example, appears in this view as the result of mutual inhibition of color.

 5. These experiments clearly imply an inherent form of organization and not a random learning of nerve nets.  It is possible to mentally recognize and perceive the stimulus within the first portion of the invoked potential.  Portions responding (in the brain) which occur later than 0.3 sec. are seen as systematic processes, or tuned circuits to those responses to specific in-coming stimulus.  This is a form of resonance in the brain to specific geometry.  This could also lead to the formation of memory.

 6. Every perception has a unique counterpart as a space-time code form in the brain.  These space-time shapes are evidence of relationships between the external world and its representation in the brain.  They act like keys to "unlock" specific parts of our brain, often being observed below psychological threshold levels (subliminal).

Clynes literally mapped fields in the human brain.  A computer was able to identify and reproduce those geometrical figures from what that human was concentrating on, either as a geometric form or color.  The individual did not even have to look at the pattern but simply concentrate "in his mind's eye."  A standing wave means that the wave is not changed, but is holding itself steady in one certain geometrical thought.

If quantum mechanical properties of matter are actually the conscious property of matter, then one would predict that all phenomena where quantum wave explanations are important, the phenomena could be interpreted better in terms of consciousness.5

Our planet is surrounded by a layer of electrically charged particles called the ionosphere.  The lower layer of the ionosphere starts about 80km. from the Earth.  This charges layer is known to reflect radio waves.

Since this is a highly charges layer, the ionosphere forms a so-called capacitor with the Earth.  This means that there is a difference in electrical potential between the two, the Earth being negatively charged and the ionosphere being positively charged.  This potential varies somewhat but is around 200 volts/m.

This is a fundamental type of electrical generator.  The solar winds, interacting with the upper atmosphere rotation, act as a collector and brushes of a generator.  The lower atmosphere can be seen as a storage battery for this gradient potential.

This electromagnetic field around the Earth can be viewed as a stiff jelly.  When our bodies move and vibrate, these movements are transmitted to the environment.  These fields not only impinge on our body but they also affect the charges inside our body.  When we are standing on the ground, under normal conditions, we are grounded.  Our body then acts as a sink for the electrostatic field and we actually distort the force lines somewhat.

Our body also has its own electrostatic field about itself.  These field-lines are the result of the various biochemical reactions in the body.  This resultant bio-field couples us to the isoelectric field of the planet.

A "tuned system" consists of at least two oscillators of identical resonance frequencies.  If one of the oscillators starts emitting, the other will be activated by the signal very shortly.  Because the coupling is ideal, they will respond to the tiniest signals and begin to resonate.

In 1957, W.O. Schumann6 calculated the Earth-ionosphere cavity resonance frequencies.  His works were updated over the years and the figure now used is at 7.5Hz.  As indicated previously, the micromotion of the body is about 6.8 to 7.5Hz.

It is obvious that when one is in deep meditation, it is possible for the human being and the planet system to start resonating.  There is a transfer of energy.  It is no coincidence that this frequency is in the theta region of brainwaves, the state of maximum regeneration.

Information is embedded in a field, rather than just being a field.  A field is thus an abstract quantity of information; relationships between this point and that point in the universe.

Astral temples are set up to evoke a certain correspondence effect, like a resonance.  These temples are like a physical matrix, one with specific geometrical form and color.

The visualization, in turn sets up a particular EM resonance in the brain.  The reverberation pattern is most explicit.  Clarity is all important.  Distortion minimizes the resonance effect and reduces any amplification to connecting other "tuned" oscillators in the body.

Techniques of extending this harmonious resonance have been known for thousands of years.  These are the different meditative techniques.  Most slow down the metabolic rate of the body so that much less oxygen is required to keep the body going.

As one becomes proficient in meditation, the breathing becomes so gentle as not to disturb the resonate state of the aorta.  An automatic process develops in which the lungs and the diaphragm regulates the heart-aorta system so as to keep them well-tuned.  This helps extend the resonant behavior even with shallow breathing.

In conclusion, the following points should be made regarding the resonant effects available through meditation:

 1. There is a heart/aorta resonance which links up with a number of other critical oscillators, including several in the brain.  It starts at the heart.

 2. Specific geometries or geometrical mandalas (form and color) create resonance effects in the brain.  The pattern is repeated in the brain.

 3. Specific geometrical systems can be used as "keys" to access those specific archetypes.  Access occurs to the psyche.

 4. This linking of resonant cavity oscillators can be seen to form a common thread, going from Hadit (DNA-RNA helix) to Nuit (galactic hydrogen-helium field).

 5. By "tuning" one's meditation, it is possible to amplify and have access to the other resonant systems, in and out of the body.

The Human organism has usually been regarded as a complex arrangement of chemical elements and compounds.  The quantity and structure of these variables are our reference points for states of health.  This is the area of biochemistry and biochemical analysis.

An equally valid approach is to regard the human organism as an aggregation of electromagnetic fields which are constantly interacting and changing as are their biological equivalents.  It has been shown that the human system is an emitter of electromagnetic radiations.7

All biological processes are a function of electromagnetic field interactions.  EM fields are the connecting link between the world of form and resonant patterns.

The patterns are arbitrary forms which are non-physical.  Archetypal forms are based on inherent characteristics and correspondences.  This provides a basis for what we would call resonant phenomena in archetypal systems.  EM fields embody or store gestalts, patterns of information.

An archetype may then be seen as a specific geometrical system of standing waves occurring in the brain as a space-time shape ("key").

In living organisms, opposites receive their structure of symmetry from particular combinations of spatial and temporal aspects.  Like reins on a horse, each of the opposites of the psychological pair has its own place.  This geometric property makes them capable of being opposites.  The activity of each arm determines the quantity; the spatial identity of the rein determines the quality.  There is no monotonic (or linear)  transition from one to the other passing through zero.

A human being, immersed in the galactic hydrogen-helium field, may also utilize the pulsing feedback between man and the galaxy to build up the resonance effects, much like we would tune a radio.  These primary frequencies are multiples of the base frequency 7 Hz.

These four nucleotides provide resonant frequencies for alpha, theta, and delta (the characteristic brain states going from consciousness to deep sleep: 14-2 Hz.).  This resonance relationship can be seen to link with helium inside the body at various chemical sites.

The bridge connecting the solar system resonances and the brain frequencies seem to reside in the DNA-RNA helix.

In a paper by Oliver Reiser8 from the University of Pittsburgh, a relationship is developed between the four helium cores in an atomic nucleus and the matrix forms on the DNA and RNA. Reiser describes them as "radiation belts of thought,"  the four "nucleotides" enter into the dynamics of these nuclear properties. A spheron is a nuclear constituent roughly spherical in shape and spaced in concentric layers.

The platonic solids are the five regular solids described by Pythagoras, now seen to form all crystal formations.  These forms later became the basis of the mathematics known as group theory.  The so-called "resonances" were specific combinations of five regular solids geometry.

"Helions" is Pauling's term for spherons when he modeled the helium in the sun, the heliosphere around the Earth, and the hydrogen-helium plasma of the galactic disc.  An optically activated molecule, such as helium, contains an electron which is coerced into a helical path by electric field.  This one-sided spiral is maintained in the intermolecular transport through protein molecules.  Note that the protein units of "spherical viruses" are packed symmetrically, in accordance with the pattern of cubic symmetry.  Once more we find our way back to Pythagoras and the Platonic solids.
 

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1.  Paul F.J. New, "Arterial Stationary Waves," American Journal of Roentgenology,Vol. 97, no. 2, pp 488-499.
2.  Symposium of Psychotronics, Prague, Czechoslovakia, Sept. 25, 1970. Paraphysical Laboratory Publication, Downton, Wiltshire, England.
3.   When certain crystals are stressed, they produce an electrical current.  This phenomena is known as the piezoelectric effect.  The physical body can be seen to be composed of liquid crystals and amorphous semiconductors (the gel).  When the body is stressed by a force such as heartbeat, it presses the brain on the skull and current is produced.
4.  Biomedical Engineering Systems, McGraw-Hill Books, N.Y., 1970.
5.  Cochran, Andrew A., "Relationships Between Quantum Physics and Biology," Foundations of Physics, Vol. 1, pp 235-250, 1971.
6.  Schumann, W., "Electrische Eigenshwingungen des Hohlraumes Erde-Luft-Ionosphere," Zeitschrift fur Angewandte Physik, Vol. 9, 373-378, 1957.
7.  Presman, A., Electromagnetic Fields and Life, Plenum Press, 1970.
8.  Reiser, Oliver L., Cosmic Humanism and World Unity, Diagram LII, p 463, and Diagram LIV, p 465.
9.  Pauling, Linus, "The Close-Packed-Spheron Theory of Nuclear Fission," Science, Vol. 150, pp 297-305, 1965.
 

REFERENCES

Ambrose, E.J.. Osborne, J.S., and Stuart, P.R. Structure and properties of the cell surface complex. In Liquid Crystals and Ordered Fluids (Johnson, J.F. and Porter, R., eds.). New York: Plenum, 1970.

Becker, R.O.. The effect of magnetic fields upon the central nervous system.  Medical Electronics and Biological Engineering, 1963, 1, 293-303.

Becker, R.O.. Electromagnetic forces and life process.  Technology Review, December, 1972.

Bernal, J.O.. General discussion.  Transactions of the Faraday Society, 1933, 29, 1082.

Blair, Lawrence.  Rhythms of Vision, New York, Warner Books, 1975.

Brown, F.A., Jr. Electrical and magnetic sensitivity: Some orientational influences on nonvisual, terrestrial electromagnetic fields.  Annals, New York Academy of Science, 1971, 188, 224-241.

Bulkley, D.H. An Electromagnetic Model for Dynamic Turnover and the Continuous Self-Replication of Biological Macromolecules, Rogue Press, 1973.

Burr, H.S. and Northrup, F.S.C. The electrodynamic theory of life.  Quarterly Review of Biology, 1935, 10, 322-333.

Elliot, H.C. Neural tube and spinal cord in Textbook of Neuroanatomy, Philadelphia, J.B. Lippincott Co., 1963.

Fowler, R.H. and Bernal, J.D. Note on the pseudo-crystalline structure of water.  Transactions of the Faraday Society, 1933, 29, 1049.

Freedericksz, V. and Zolina, V. Forces causing the orientation of an anistropic liquid.  Transactions of the Faraday Society, 1933, 29, 944.

French, Vernon, Bryont, P.J. and Bryont, S.V. Pattern regulation in epimorphic fields, Science, September 10, 1976, 969-981.

Garrison, W. Destiny and geomagnetism.  Popular Electronics, July 1971.

Koestler, A. The Roots of Coincidence.  New York: Random House, 1972.

LeShan, L.A. Toward a general theory of the paranormal.  Parapsychological Monographs, 1969, no. 9.

Lund, E.J. Bioelectric Fields and Growth.  Austin:  University of Texas Press, 1945.

McGinnes, J.E. Mobility gaps: "A Mechanism for Band Gaps in Melanins."  Science, 1972, 177, 896-897.

McKenna, T.J. and McKenna, D.J. "Organismic Thought" in The Invisible Landscape.  New York:  Seabury Press, 1975.

Miller, R.A., Webb, B., Dickson, D. "A Holographic Concept of Reality." Psychoenergetic Systems, 1975, Vol. 1, 55-62.

Muses, C.A. On the modification of random fluctuations by a target- seeking process utilizing random energies.  Bio-Medical Computing, 1970, 1, 75-80.

Needham, J. "The Hierarchial Continuity of Biological Order."  Order and Life, 1936, 1, 109-168.

Presman, A.S. Electromagnetic Fields and Life.  New York:  Plenum.  1970.

Pullman, B. and Pullman, A. Quantum Biochemistry. New York:  Interscience.

Purett, L. Magnetic reversals and biological extinctions.  Science News, 1971, 100, 287-302.

Ravitz, L. Electromagnetic field monitoring of changing state-function, including hypnotic states.  Journal of the American Society of Psychosomatic Dentistry and Medicine, 1970, 17, 199-129.

Szent-Gyorgyi, A..  Bioenergetics.  New York:  Academic Press, 1957.

Szent-Gyorgyi, A..  Introduction to a Submolecular Biology.  New York:  Academic Press, 1960.

Szent-Gyorgyi, A..  Electronic Biology and Cancer, New York, Marcel Dekker inc., 1976.
Thom, R.  Structural Stability and Morphogenesis.  Massachusesetts, W.A. Benjamin Press, 1975.

Tien, H.C..  Pattern recognition and psychosynthesis.  American Journal of Psychotherapy, 1969, 23, 53-66.

Van Iterson, G., Jr..  A simple arrangement to demonstrate liquid crystals.  Transactions of the Faraday Society, 1933, 29, 915-919.

Wheeler, J.A..  Geometrodynamics.  Lectures, Course on Weak Interactions, Enrico Fermi Internal School of Physics.  Varenna, Italy, Summer, 1959.
 

C.  MAGICAL USE OF STANDING WAVES AND
      GEOMETRICAL MATRICES

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.

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
 

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]
 
 
 
 
 

[The Four Worlds]
 

 D.  THE MAGICKAL ALTAR: THE DOUBLE CUBE

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
 

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)
 
 
 

[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  .
 
 
 

[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 mystery of meditation and Vector Equilibrium.
 

______________________________________________________________________________
(1) Aleister Crowley, BOOK 4, Dallas, Sangreal Foundation, Inc., 1972, p61.
 
 
 

[Tiphareth: Diamond Body/Throne-Chariot]
 
 

 D.  DAATH: THE THRESHOLD OF THE WORLD OF FORM

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)

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.
 
 

[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.
 
 
 
 

[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)

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.
(3) Gershom Scholem, MAJOR TRENDS IN JEWISH MYSTICISM,
(4) Gershom Scholem, KABBALAH, N.Y., The New American Library, Inc. 1974, p158.
 
 
 

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



IV.  CONTEMPORARY APPLICATIONS

A.  ARCHETYPAL TOPOLOGIES:

Active participation in the realm of the imagination is central to psychology, alchemy, magick, and physics.  Many, but not all of the imaginal modes involve the concept of topology or topography.  Within the context of the topological fantasy, the various forms of ordering (Tree of Life, the Diamond Body, the V.E.M., etc.) provide a comprehensive means of ascertaining the values of any system of experiences.

Topology is the science of fundamental pattern and structural relationships of event constellations.  It was discovered and developed by the mathematician Euler.  He discovered that all patterns can be reduced to three prime conceptual characteristics: to lines; points where two lines cross or the same line crosses itself; and areas, bounded by lines.(1)

While active invoking of images is essential to the practice of QBL, it is best to balance this through a detached observation/participation in the rising and passing away of phenomena.  Topographical models are paradigms, but they should not be considered ultimate truths, but as allowing access to imaginal realms. While topography is a useful tool, it is also an archetypal perspective.

For example, I suggest that a perspective which sees the necessity for 'archetypal topographies' is just one among many.  We must not be drawn into literalism at such a profound level.  As I mention above, Casey seems to imply a single natural ordering for a particular purpose, within a specific archetypal influence.  Examination of the variety of such attempts to pattern and group archetypes is itself a valuable exercise in exploring archetypal imagination.  What kind of consciousness is it that perceives in terms of organization, integration and preferred positioning of Gods?  Generally, the attempt to discover a unifying wholeness or impose a distinct pattern onto archetypal groupings is a procedure dominated by the archetype of the Self.(2)
 

QBL is a single philosophical system which accommodates both monotheism and polytheism.  These topologies may be used in conjunction with a polytheistic orientation in which consciousness circulates among a field of powers.  Each god, or complex is sovereign in its domain.  There is a circulation in which there are no preferred positions.

The danger in identification with the archetype of the Self is persistent belief in it as the "only" reality.  Archetypal images of order (mandalas) counter disintegration.  However, there is sometimes a psychic value in disintegration.  It brings immediate awareness of distinct separateness among the pantheon of archetypal forces.  Both attitudes, monotheism and polytheism, represent forms of living reality in the phenomenal world.

Topology offers a descriptive basis for both meditation and exploration of the imaginal realm.  The importance of the act of decision for behavior or transformation lies mainly in the fact that by it the individual changes his position.  A "path" is a change of position within a field which otherwise remains sufficiently constant.  It is an abbreviated representation of a sequence of situations.

A path permits changes between regions.  This is both conceptual and physical change.  The actions which are represented in the life-space as regions are coexisting manifolds which possess a certain degree of differentiation.  These "regions" are the spheres of the Tree of Life.

The imaginal paths of the Tree of Life are linked to the concept of locomotion.  They require "working" by the aspirant in a process in time.  The psychological region in which these processes occur determines the dynamic condition of the individual.

Pathworking is a form of "loco-motion," akin to the "illumined lunacy" Hillman describes as the royal marriage, the pre-requisite for the Stone.  It is 0, THE FOOL who makes the journey through the winding paths of the Tree of Life via Tarot imagery.  He is nowhere (now-here) because of his ability to makes quantum leaps.  He is everywhere at once, until we make an observation by using the cards.  He is thus gripped by only one story at a time, which contains many images and its own inherent rhythm.

When one changes position, different loco-motions are now possible and impossible.  Even when a region is still attainable, the course of the path followed has changed fundamentally because of the new point of departure.  This part that you are now is "where you are at."

THE FOOL is a breath-spirit, and Anima is a breath-soul.  This relates them intimately to the airy realm of imagination.  Just as the Fool circulates around the paths of the Tree, anima circulates throughout every cell of the body.

The attributions of these entities leads us in a definite direction: they both focus attention on the breath.

The importance of breath in human life and mystical meditation is not to be underestimated.  The use of breath control has a long-standing tradition in magical and yogic practice.  There is a relationship between meditation states and rhythmic breathing.  If we look further into our Qabalistic modeling, we should find the heart playing a prominent role in this process.  This is, in fact, the case.
 
 

______________________________________________________________________________
(1) R. Buckminster Fuller, OPERATING MANUAL FOR SPACESHIP EARTH,
(2) Peter Bishop, "Archetypal Topography,"  SPRING 1981, Dallas, Spring Publications, 1981.
 B.  MEDIATION AND RESONANCE EFFECTS

(This paper is from THE HOLISTIC QABALA, a series of 11 books, written by Richard and Iona Miller.  It has also appeared in print in "Psychedelic Monographs and Essays," Volume Four, Summer 1989)

The use of psychedelics or empathogens traditionally involves effectual  traits or nuances which can parallel endogenous mystical or cybernetic landscapes.  This piece presents an introduction to current descriptions common throughout all three fields.  A promise of increased comprehension so far as metaphor, symbol and effect surrounding these and other cross-correlative fields is reviewed and annotated.

...If the manas is to preform its proper task of controlling senses, it must reflect the ideal pattern that is laid up in the heavens of Buddhi.  Only when that pattern is reflected in its mirror has it the standard of reference by which to judge...nor should we think that the possession of such a divine standard by which to judge attainment is far above us; one to which we may aspire in some dim future.  Here and now the Pattern is within us.
Sri Krishna Prem
 

Theoretically, the practice of meditation is intended to withdraw the personal mind from its persistent preoccupation with external affairs.  It can be seen as a form of training for the mind in switching from matter to psyche.  There is a purpose.  It is to prepare the personal nature so that it is able to reflect and express its relationship with the Universal Self.

Throughout history there have been a number of techniques used to achieve a meditative state.  The most often used first step is a form of rhythmic breathing.  If done correctly, a sequence of strong and unusual body reactions occur.  These also will eventually trigger unusual psychological states via a type of resonance effect.  A closer examination of these resonance-relationships yields information useful in improving the meditation.

Perhaps an example clarifies this:  When a subject is totally relaxed and has achieved a deep meditative state, a slow, rhythmic sine wave pattern can be registered by a cardiograph-type sensing device.  What is being measured is a standing wave in the aorta.  There is a heart-aorta resonating oscillator which affects other parts of the body, including the brain.

Resonance occurs when the natural vibration frequency of a body is greatly amplified by vibrations at the same frequency from another body.  Oscillators alter the environment in a periodic manner.  When in a deep meditative state the regular movement of the body indicates that a standing wave is set up in the vascular system, specifically in the aorta.  This standing wave affects several other resonate systems in the body, all of which are driven by this large signal.

A paper by Paul F.J. New, and several current papers, indicate the presence of a major resonate cavity oscillator located between  the heart and the bifurcation, where the aorta divides itself.  When the timing of the pressure pulses traveling down the aorta  coincide (in phase) with the reflected pressure pulse, a standing wave is achieved.  When this frequency approaches 7Hz., a progressively amplified wave form is created by resonance, resulting in a large oscillation affecting every other circuit in the body tuned to this frequency.

There is a resonance relationship to this frequency  with standing waves on the Earth's crust.  If we assume that the spherical crust of the Earth represents a condenser, then the frequency of resonance can be calculated on the basis of the equation:

  Resonance frequency = C/7.3R2

Where C is the velocity of propagation of electromagnetic waves and R = radius of the Earth.  This frequency has been shown to be 6.4Hz.

Thus, a harmonic frequency corresponding to the pulsation of the electrical charge of the Earth is present in heart/aorta.

The brain may be considered as a piezoelectric gel3, one converting physical vibrations into electrical ones.  Although the body movement from this heart/aorta resonance is relatively small, 0.003-0.009 mm., the head is a dense and tight structure.  By moving up and down, the skull accelerates the brain with mild impacts.  These acoustical plane waves are reflected from the cranial vault and are focused upon the third and lateral ventricles.  A hierarchy of frequencies couple this 7Hz. body movement to the higher frequencies in the ventricles.

That which is that bright within the heart; in that this man resides, innate with mind transcending death, with brilliance innate.
Taittiriya Upanishad

In the book Biomedical Engineering Systems4, Chapter 7 is a major work entitled "Toward A View of Man", by Manfred Clynes.  Clynes is a medical doctor working at the Research Center in Rockman State Hospital, Orangeburg, New York.  This work is considered a breakthrough in the fields of psychology and medicine, known today as the field of psychobiology (biocybernetics).

Clynes took a number of volunteers and shaved their heads, placing a series of electrodes in rosette patterns or various regions of the brain.  These included the temporal, frontal lobe section and occipital region.  In this way, not only were the brain frequencies monitored, but directional shifts in these frequencies could also be determined by the geometry of the electrodes on the scull.

The original purpose of Clynes' work was to find out how precision and order exist in brain processes; to discover what is inherently programmed in man and how he might make use of the inherent programs.

These individuals were given a number of images (form) and colors to concentrate on while their brain was monitored by computers.  Recording from opposite pairs of electrodes simultaneously, he obtained views of the electrical activity from different angles:  mathematically, a spatial differentiation of the electric vector.  What was happening literally was a mapping of consciousness.  A number of very important observations were made:

 1. Certain qualities and relationships were of greater importance to the computer than such quantitative factors such as intensity.  This meant that the brain's systems of identification  are based on differences, rather than intensity of the signal.

 2. Thin lines were found to produce characteristic evoked potentials, irrespective of size.  The form itself is transduced into another form in the brain space time which can be measured.  There is a one-to-one correspondence between the visual form of the stimulus, the response form in the brain, and the perception.

This is, perhaps, the first physical description of the field of an archetype.  It is a geometrical, structuring and has uniqueness.

 3. The process of inhibition is as important for transducing the external world as is excitation.  Concentrating on specific lines of geometry does not constitute the changing stimulus, but their steady presence systematically and radically alters the response to another changing stimulus.

 4. Changes in intensity of a single color produce very simple response shape. Light and darkness (as opposites) show no evidence of being different values of the same variable.  Rather, they seem to be the result of stimulating and also of inhibiting different receptors.  Thus, the evoked potentials to light and darkness in no way may be said to be positive and negative, respectively.  White, for example, appears in this view as the result of mutual inhibition of color.

 5. These experiments clearly imply an inherent form of organization and not a random learning of nerve nets.  It is possible to mentally recognize and perceive the stimulus within the first portion of the invoked potential.  Portions responding (in the brain) which occur later than 0.3 sec. are seen as systematic processes, or tuned circuits to those responses to specific in-coming stimulus.  This is a form of resonance in the brain to specific geometry.  This could also lead to the formation of memory.

 6. Every perception has a unique counterpart as a space-time code form in the brain.  These space-time shapes are evidence of relationships between the external world and its representation in the brain.  They act like keys to "unlock" specific parts of our brain, often being observed below psychological threshold levels (subliminal).

Clynes literally mapped fields in the human brain.  A computer was able to identify and reproduce those geometrical figures from what that human was concentrating on, either as a geometric form or color.  The individual did not even have to look at the pattern but simply concentrate "in his mind's eye."  A standing wave means that the wave is not changed, but is holding itself steady in one certain geometrical thought.

If quantum mechanical properties of matter are actually the conscious property of matter, then one would predict that all phenomena where quantum wave explanations are important, the phenomena could be interpreted better in terms of consciousness.5

Our planet is surrounded by a layer of electrically charged particles called the ionosphere.  The lower layer of the ionosphere starts about 80km. from the Earth.  This charges layer is known to reflect radio waves.

Since this is a highly charges layer, the ionosphere forms a so-called capacitor with the Earth.  This means that there is a difference in electrical potential between the two, the Earth being negatively charged and the ionosphere being positively charged.  This potential varies somewhat but is around 200 volts/m.

This is a fundamental type of electrical generator.  The solar winds, interacting with the upper atmosphere rotation, act as a collector and brushes of a generator.  The lower atmosphere can be seen as a storage battery for this gradient potential.

This electromagnetic field around the Earth can be viewed as a stiff jelly.  When our bodies move and vibrate, these movements are transmitted to the environment.  These fields not only impinge on our body but they also affect the charges inside our body.  When we are standing on the ground, under normal conditions, we are grounded.  Our body then acts as a sink for the electrostatic field and we actually distort the force lines somewhat.

Our body also has its own electrostatic field about itself.  These field-lines are the result of the various biochemical reactions in the body.  This resultant bio-field couples us to the isoelectric field of the planet.

A "tuned system" consists of at least two oscillators of identical resonance frequencies.  If one of the oscillators starts emitting, the other will be activated by the signal very shortly.  Because the coupling is ideal, they will respond to the tiniest signals and begin to resonate.

In 1957, W.O. Schumann6 calculated the Earth-ionosphere cavity resonance frequencies.  His works were updated over the years and the figure now used is at 7.5Hz.  As indicated previously, the micromotion of the body is about 6.8 to 7.5Hz.

It is obvious that when one is in deep meditation, it is possible for the human being and the planet system to start resonating.  There is a transfer of energy.  It is no coincidence that this frequency is in the theta region of brainwaves, the state of maximum regeneration.

Information is embedded in a field, rather than just being a field.  A field is thus an abstract quantity of information; relationships between this point and that point in the universe.

Astral temples are set up to evoke a certain correspondence effect, like a resonance.  These temples are like a physical matrix, one with specific geometrical form and color.

The visualization, in turn sets up a particular EM resonance in the brain.  The reverberation pattern is most explicit.  Clarity is all important.  Distortion minimizes the resonance effect and reduces any amplification to connecting other "tuned" oscillators in the body.

Techniques of extending this harmonious resonance have been known for thousands of years.  These are the different meditative techniques.  Most slow down the metabolic rate of the body so that much less oxygen is required to keep the body going.

As one becomes proficient in meditation, the breathing becomes so gentle as not to disturb the resonate state of the aorta.  An automatic process develops in which the lungs and the diaphragm regulates the heart-aorta system so as to keep them well-tuned.  This helps extend the resonant behavior even with shallow breathing.

In conclusion, the following points should be made regarding the resonant effects available through meditation:

 1. There is a heart/aorta resonance which links up with a number of other critical oscillators, including several in the brain.  It starts at the heart.

 2. Specific geometries or geometrical mandalas (form and color) create resonance effects in the brain.  The pattern is repeated in the brain.

 3. Specific geometrical systems can be used as "keys" to access those specific archetypes.  Access occurs to the psyche.

 4. This linking of resonant cavity oscillators can be seen to form a common thread, going from Hadit (DNA-RNA helix) to Nuit (galactic hydrogen-helium field).

 5. By "tuning" one's meditation, it is possible to amplify and have access to the other resonant systems, in and out of the body.

The Human organism has usually been regarded as a complex arrangement of chemical elements and compounds.  The quantity and structure of these variables are our reference points for states of health.  This is the area of biochemistry and biochemical analysis.

An equally valid approach is to regard the human organism as an aggregation of electromagnetic fields which are constantly interacting and changing as are their biological equivalents.  It has been shown that the human system is an emitter of electromagnetic radiations.7

All biological processes are a function of electromagnetic field interactions.  EM fields are the connecting link between the world of form and resonant patterns.

The patterns are arbitrary forms which are non-physical.  Archetypal forms are based on inherent characteristics and correspondences.  This provides a basis for what we would call resonant phenomena in archetypal systems.  EM fields embody or store gestalts, patterns of information.

An archetype may then be seen as a specific geometrical system of standing waves occurring in the brain as a space-time shape ("key").

In living organisms, opposites receive their structure of symmetry from particular combinations of spatial and temporal aspects.  Like reins on a horse, each of the opposites of the psychological pair has its own place.  This geometric property makes them capable of being opposites.  The activity of each arm determines the quantity; the spatial identity of the rein determines the quality.  There is no monotonic (or linear)  transition from one to the other passing through zero.

A human being, immersed in the galactic hydrogen-helium field, may also utilize the pulsing feedback between man and the galaxy to build up the resonance effects, much like we would tune a radio.  These primary frequencies are multiples of the base frequency 7 Hz.

These four nucleotides provide resonant frequencies for alpha, theta, and delta (the characteristic brain states going from consciousness to deep sleep: 14-2 Hz.).  This resonance relationship can be seen to link with helium inside the body at various chemical sites.

The bridge connecting the solar system resonances and the brain frequencies seem to reside in the DNA-RNA helix.

In a paper by Oliver Reiser8 from the University of Pittsburgh, a relationship is developed between the four helium cores in an atomic nucleus and the matrix forms on the DNA and RNA. Reiser describes them as "radiation belts of thought,"  the four "nucleotides" enter into the dynamics of these nuclear properties. A spheron is a nuclear constituent roughly spherical in shape and spaced in concentric layers.

The platonic solids are the five regular solids described by Pythagoras, now seen to form all crystal formations.  These forms later became the basis of the mathematics known as group theory.  The so-called "resonances" were specific combinations of five regular solids geometry.

"Helions" is Pauling's term for spherons when he modeled the helium in the sun, the heliosphere around the Earth, and the hydrogen-helium plasma of the galactic disc.  An optically activated molecule, such as helium, contains an electron which is coerced into a helical path by electric field.  This one-sided spiral is maintained in the intermolecular transport through protein molecules.  Note that the protein units of "spherical viruses" are packed symmetrically, in accordance with the pattern of cubic symmetry.  Once more we find our way back to Pythagoras and the Platonic solids.
 

______________________________________________________________________________
1.  Paul F.J. New, "Arterial Stationary Waves," American Journal of Roentgenology,Vol. 97, no. 2, pp 488-499.
2.  Symposium of Psychotronics, Prague, Czechoslovakia, Sept. 25, 1970. Paraphysical Laboratory Publication, Downton, Wiltshire, England.
3.   When certain crystals are stressed, they produce an electrical current.  This phenomena is known as the piezoelectric effect.  The physical body can be seen to be composed of liquid crystals and amorphous semiconductors (the gel).  When the body is stressed by a force such as heartbeat, it presses the brain on the skull and current is produced.
4.  Biomedical Engineering Systems, McGraw-Hill Books, N.Y., 1970.
5.  Cochran, Andrew A., "Relationships Between Quantum Physics and Biology," Foundations of Physics, Vol. 1, pp 235-250, 1971.
6.  Schumann, W., "Electrische Eigenshwingungen des Hohlraumes Erde-Luft-Ionosphere," Zeitschrift fur Angewandte Physik, Vol. 9, 373-378, 1957.
7.  Presman, A., Electromagnetic Fields and Life, Plenum Press, 1970.
8.  Reiser, Oliver L., Cosmic Humanism and World Unity, Diagram LII, p 463, and Diagram LIV, p 465.
9.  Pauling, Linus, "The Close-Packed-Spheron Theory of Nuclear Fission," Science, Vol. 150, pp 297-305, 1965.
 

REFERENCES

Ambrose, E.J.. Osborne, J.S., and Stuart, P.R. Structure and properties of the cell surface complex. In Liquid Crystals and Ordered Fluids (Johnson, J.F. and Porter, R., eds.). New York: Plenum, 1970.

Becker, R.O.. The effect of magnetic fields upon the central nervous system.  Medical Electronics and Biological Engineering, 1963, 1, 293-303.

Becker, R.O.. Electromagnetic forces and life process.  Technology Review, December, 1972.

Bernal, J.O.. General discussion.  Transactions of the Faraday Society, 1933, 29, 1082.

Blair, Lawrence.  Rhythms of Vision, New York, Warner Books, 1975.

Brown, F.A., Jr. Electrical and magnetic sensitivity: Some orientational influences on nonvisual, terrestrial electromagnetic fields.  Annals, New York Academy of Science, 1971, 188, 224-241.

Bulkley, D.H. An Electromagnetic Model for Dynamic Turnover and the Continuous Self-Replication of Biological Macromolecules, Rogue Press, 1973.

Burr, H.S. and Northrup, F.S.C. The electrodynamic theory of life.  Quarterly Review of Biology, 1935, 10, 322-333.

Elliot, H.C. Neural tube and spinal cord in Textbook of Neuroanatomy, Philadelphia, J.B. Lippincott Co., 1963.

Fowler, R.H. and Bernal, J.D. Note on the pseudo-crystalline structure of water.  Transactions of the Faraday Society, 1933, 29, 1049.

Freedericksz, V. and Zolina, V. Forces causing the orientation of an anistropic liquid.  Transactions of the Faraday Society, 1933, 29, 944.

French, Vernon, Bryont, P.J. and Bryont, S.V. Pattern regulation in epimorphic fields, Science, September 10, 1976, 969-981.

Garrison, W. Destiny and geomagnetism.  Popular Electronics, July 1971.

Koestler, A. The Roots of Coincidence.  New York: Random House, 1972.

LeShan, L.A. Toward a general theory of the paranormal.  Parapsychological Monographs, 1969, no. 9.

Lund, E.J. Bioelectric Fields and Growth.  Austin:  University of Texas Press, 1945.

McGinnes, J.E. Mobility gaps: "A Mechanism for Band Gaps in Melanins."  Science, 1972, 177, 896-897.

McKenna, T.J. and McKenna, D.J. "Organismic Thought" in The Invisible Landscape.  New York:  Seabury Press, 1975.

Miller, R.A., Webb, B., Dickson, D. "A Holographic Concept of Reality." Psychoenergetic Systems, 1975, Vol. 1, 55-62.

Muses, C.A. On the modification of random fluctuations by a target- seeking process utilizing random energies.  Bio-Medical Computing, 1970, 1, 75-80.

Needham, J. "The Hierarchial Continuity of Biological Order."  Order and Life, 1936, 1, 109-168.

Presman, A.S. Electromagnetic Fields and Life.  New York:  Plenum.  1970.

Pullman, B. and Pullman, A. Quantum Biochemistry. New York:  Interscience.

Purett, L. Magnetic reversals and biological extinctions.  Science News, 1971, 100, 287-302.

Ravitz, L. Electromagnetic field monitoring of changing state-function, including hypnotic states.  Journal of the American Society of Psychosomatic Dentistry and Medicine, 1970, 17, 199-129.

Szent-Gyorgyi, A..  Bioenergetics.  New York:  Academic Press, 1957.

Szent-Gyorgyi, A..  Introduction to a Submolecular Biology.  New York:  Academic Press, 1960.

Szent-Gyorgyi, A..  Electronic Biology and Cancer, New York, Marcel Dekker inc., 1976.
Thom, R.  Structural Stability and Morphogenesis.  Massachusesetts, W.A. Benjamin Press, 1975.

Tien, H.C..  Pattern recognition and psychosynthesis.  American Journal of Psychotherapy, 1969, 23, 53-66.

Van Iterson, G., Jr..  A simple arrangement to demonstrate liquid crystals.  Transactions of the Faraday Society, 1933, 29, 915-919.

Wheeler, J.A..  Geometrodynamics.  Lectures, Course on Weak Interactions, Enrico Fermi Internal School of Physics.  Varenna, Italy, Summer, 1959.
 

C.  MAGICAL USE OF STANDING WAVES AND
      GEOMETRICAL MATRICES

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.

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
 

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]
 
 

 
 

[The Four Worlds]
 

 D.  THE MAGICKAL ALTAR: THE DOUBLE CUBE

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
 

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)

 
 

[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  .

 
 

[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 mystery of meditation and Vector Equilibrium.
 

______________________________________________________________________________
(1) Aleister Crowley, BOOK 4, Dallas, Sangreal Foundation, Inc., 1972, p61.

 
 

[Tiphareth: Diamond Body/Throne-Chariot]
 
 

 D.  DAATH: THE THRESHOLD OF THE WORLD OF FORM

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)

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.
 
 

[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.
 

 
 

[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)

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.
(3) Gershom Scholem, MAJOR TRENDS IN JEWISH MYSTICISM,
(4) Gershom Scholem, KABBALAH, N.Y., The New American Library, Inc. 1974, p158.
 
 
 

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

IV.  CONTEMPORARY APPLICATIONS

A.  ARCHETYPAL TOPOLOGIES:

Active participation in the realm of the imagination is central to psychology, alchemy, magick, and physics.  Many, but not all of the imaginal modes involve the concept of topology or topography.  Within the context of the topological fantasy, the various forms of ordering (Tree of Life, the Diamond Body, the V.E.M., etc.) provide a comprehensive means of ascertaining the values of any system of experiences.

Topology is the science of fundamental pattern and structural relationships of event constellations.  It was discovered and developed by the mathematician Euler.  He discovered that all patterns can be reduced to three prime conceptual characteristics: to lines; points where two lines cross or the same line crosses itself; and areas, bounded by lines.(1)

While active invoking of images is essential to the practice of QBL, it is best to balance this through a detached observation/participation in the rising and passing away of phenomena.  Topographical models are paradigms, but they should not be considered ultimate truths, but as allowing access to imaginal realms. While topography is a useful tool, it is also an archetypal perspective.

For example, I suggest that a perspective which sees the necessity for 'archetypal topographies' is just one among many.  We must not be drawn into literalism at such a profound level.  As I mention above, Casey seems to imply a single natural ordering for a particular purpose, within a specific archetypal influence.  Examination of the variety of such attempts to pattern and group archetypes is itself a valuable exercise in exploring archetypal imagination.  What kind of consciousness is it that perceives in terms of organization, integration and preferred positioning of Gods?  Generally, the attempt to discover a unifying wholeness or impose a distinct pattern onto archetypal groupings is a procedure dominated by the archetype of the Self.(2)
 

QBL is a single philosophical system which accommodates both monotheism and polytheism.  These topologies may be used in conjunction with a polytheistic orientation in which consciousness circulates among a field of powers.  Each god, or complex is sovereign in its domain.  There is a circulation in which there are no preferred positions.

The danger in identification with the archetype of the Self is persistent belief in it as the "only" reality.  Archetypal images of order (mandalas) counter disintegration.  However, there is sometimes a psychic value in disintegration.  It brings immediate awareness of distinct separateness among the pantheon of archetypal forces.  Both attitudes, monotheism and polytheism, represent forms of living reality in the phenomenal world.

Topology offers a descriptive basis for both meditation and exploration of the imaginal realm.  The importance of the act of decision for behavior or transformation lies mainly in the fact that by it the individual changes his position.  A "path" is a change of position within a field which otherwise remains sufficiently constant.  It is an abbreviated representation of a sequence of situations.

A path permits changes between regions.  This is both conceptual and physical change.  The actions which are represented in the life-space as regions are coexisting manifolds which possess a certain degree of differentiation.  These "regions" are the spheres of the Tree of Life.

The imaginal paths of the Tree of Life are linked to the concept of locomotion.  They require "working" by the aspirant in a process in time.  The psychological region in which these processes occur determines the dynamic condition of the individual.

Pathworking is a form of "loco-motion," akin to the "illumined lunacy" Hillman describes as the royal marriage, the pre-requisite for the Stone.  It is 0, THE FOOL who makes the journey through the winding paths of the Tree of Life via Tarot imagery.  He is nowhere (now-here) because of his ability to makes quantum leaps.  He is everywhere at once, until we make an observation by using the cards.  He is thus gripped by only one story at a time, which contains many images and its own inherent rhythm.

When one changes position, different loco-motions are now possible and impossible.  Even when a region is still attainable, the course of the path followed has changed fundamentally because of the new point of departure.  This part that you are now is "where you are at."

THE FOOL is a breath-spirit, and Anima is a breath-soul.  This relates them intimately to the airy realm of imagination.  Just as the Fool circulates around the paths of the Tree, anima circulates throughout every cell of the body.

The attributions of these entities leads us in a definite direction: they both focus attention on the breath.

The importance of breath in human life and mystical meditation is not to be underestimated.  The use of breath control has a long-standing tradition in magical and yogic practice.  There is a relationship between meditation states and rhythmic breathing.  If we look further into our Qabalistic modeling, we should find the heart playing a prominent role in this process.  This is, in fact, the case.
 
 

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(1) R. Buckminster Fuller, OPERATING MANUAL FOR SPACESHIP EARTH,
(2) Peter Bishop, "Archetypal Topography,"  SPRING 1981, Dallas, Spring Publications, 1981.
 B.  MEDIATION AND RESONANCE EFFECTS

(This paper is from THE HOLISTIC QABALA, a series of 11 books, written by Richard and Iona Miller.  It has also appeared in print in "Psychedelic Monographs and Essays," Volume Four, Summer 1989)

The use of psychedelics or empathogens traditionally involves effectual  traits or nuances which can parallel endogenous mystical or cybernetic landscapes.  This piece presents an introduction to current descriptions common throughout all three fields.  A promise of increased comprehension so far as metaphor, symbol and effect surrounding these and other cross-correlative fields is reviewed and annotated.

...If the manas is to preform its proper task of controlling senses, it must reflect the ideal pattern that is laid up in the heavens of Buddhi.  Only when that pattern is reflected in its mirror has it the standard of reference by which to judge...nor should we think that the possession of such a divine standard by which to judge attainment is far above us; one to which we may aspire in some dim future.  Here and now the Pattern is within us.
Sri Krishna Prem
 

Theoretically, the practice of meditation is intended to withdraw the personal mind from its persistent preoccupation with external affairs.  It can be seen as a form of training for the mind in switching from matter to psyche.  There is a purpose.  It is to prepare the personal nature so that it is able to reflect and express its relationship with the Universal Self.

Throughout history there have been a number of techniques used to achieve a meditative state.  The most often used first step is a form of rhythmic breathing.  If done correctly, a sequence of strong and unusual body reactions occur.  These also will eventually trigger unusual psychological states via a type of resonance effect.  A closer examination of these resonance-relationships yields information useful in improving the meditation.

Perhaps an example clarifies this:  When a subject is totally relaxed and has achieved a deep meditative state, a slow, rhythmic sine wave pattern can be registered by a cardiograph-type sensing device.  What is being measured is a standing wave in the aorta.  There is a heart-aorta resonating oscillator which affects other parts of the body, including the brain.

Resonance occurs when the natural vibration frequency of a body is greatly amplified by vibrations at the same frequency from another body.  Oscillators alter the environment in a periodic manner.  When in a deep meditative state the regular movement of the body indicates that a standing wave is set up in the vascular system, specifically in the aorta.  This standing wave affects several other resonate systems in the body, all of which are driven by this large signal.

A paper by Paul F.J. New, and several current papers, indicate the presence of a major resonate cavity oscillator located between  the heart and the bifurcation, where the aorta divides itself.  When the timing of the pressure pulses traveling down the aorta  coincide (in phase) with the reflected pressure pulse, a standing wave is achieved.  When this frequency approaches 7Hz., a progressively amplified wave form is created by resonance, resulting in a large oscillation affecting every other circuit in the body tuned to this frequency.

There is a resonance relationship to this frequency  with standing waves on the Earth's crust.  If we assume that the spherical crust of the Earth represents a condenser, then the frequency of resonance can be calculated on the basis of the equation:

  Resonance frequency = C/7.3R2

Where C is the velocity of propagation of electromagnetic waves and R = radius of the Earth.  This frequency has been shown to be 6.4Hz.

Thus, a harmonic frequency corresponding to the pulsation of the electrical charge of the Earth is present in heart/aorta.

The brain may be considered as a piezoelectric gel3, one converting physical vibrations into electrical ones.  Although the body movement from this heart/aorta resonance is relatively small, 0.003-0.009 mm., the head is a dense and tight structure.  By moving up and down, the skull accelerates the brain with mild impacts.  These acoustical plane waves are reflected from the cranial vault and are focused upon the third and lateral ventricles.  A hierarchy of frequencies couple this 7Hz. body movement to the higher frequencies in the ventricles.

That which is that bright within the heart; in that this man resides, innate with mind transcending death, with brilliance innate.
Taittiriya Upanishad

In the book Biomedical Engineering Systems4, Chapter 7 is a major work entitled "Toward A View of Man", by Manfred Clynes.  Clynes is a medical doctor working at the Research Center in Rockman State Hospital, Orangeburg, New York.  This work is considered a breakthrough in the fields of psychology and medicine, known today as the field of psychobiology (biocybernetics).

Clynes took a number of volunteers and shaved their heads, placing a series of electrodes in rosette patterns or various regions of the brain.  These included the temporal, frontal lobe section and occipital region.  In this way, not only were the brain frequencies monitored, but directional shifts in these frequencies could also be determined by the geometry of the electrodes on the scull.

The original purpose of Clynes' work was to find out how precision and order exist in brain processes; to discover what is inherently programmed in man and how he might make use of the inherent programs.

These individuals were given a number of images (form) and colors to concentrate on while their brain was monitored by computers.  Recording from opposite pairs of electrodes simultaneously, he obtained views of the electrical activity from different angles:  mathematically, a spatial differentiation of the electric vector.  What was happening literally was a mapping of consciousness.  A number of very important observations were made:

 1. Certain qualities and relationships were of greater importance to the computer than such quantitative factors such as intensity.  This meant that the brain's systems of identification  are based on differences, rather than intensity of the signal.

 2. Thin lines were found to produce characteristic evoked potentials, irrespective of size.  The form itself is transduced into another form in the brain space time which can be measured.  There is a one-to-one correspondence between the visual form of the stimulus, the response form in the brain, and the perception.

This is, perhaps, the first physical description of the field of an archetype.  It is a geometrical, structuring and has uniqueness.

 3. The process of inhibition is as important for transducing the external world as is excitation.  Concentrating on specific lines of geometry does not constitute the changing stimulus, but their steady presence systematically and radically alters the response to another changing stimulus.

 4. Changes in intensity of a single color produce very simple response shape. Light and darkness (as opposites) show no evidence of being different values of the same variable.  Rather, they seem to be the result of stimulating and also of inhibiting different receptors.  Thus, the evoked potentials to light and darkness in no way may be said to be positive and negative, respectively.  White, for example, appears in this view as the result of mutual inhibition of color.

 5. These experiments clearly imply an inherent form of organization and not a random learning of nerve nets.  It is possible to mentally recognize and perceive the stimulus within the first portion of the invoked potential.  Portions responding (in the brain) which occur later than 0.3 sec. are seen as systematic processes, or tuned circuits to those responses to specific in-coming stimulus.  This is a form of resonance in the brain to specific geometry.  This could also lead to the formation of memory.

 6. Every perception has a unique counterpart as a space-time code form in the brain.  These space-time shapes are evidence of relationships between the external world and its representation in the brain.  They act like keys to "unlock" specific parts of our brain, often being observed below psychological threshold levels (subliminal).

Clynes literally mapped fields in the human brain.  A computer was able to identify and reproduce those geometrical figures from what that human was concentrating on, either as a geometric form or color.  The individual did not even have to look at the pattern but simply concentrate "in his mind's eye."  A standing wave means that the wave is not changed, but is holding itself steady in one certain geometrical thought.

If quantum mechanical properties of matter are actually the conscious property of matter, then one would predict that all phenomena where quantum wave explanations are important, the phenomena could be interpreted better in terms of consciousness.5

Our planet is surrounded by a layer of electrically charged particles called the ionosphere.  The lower layer of the ionosphere starts about 80km. from the Earth.  This charges layer is known to reflect radio waves.

Since this is a highly charges layer, the ionosphere forms a so-called capacitor with the Earth.  This means that there is a difference in electrical potential between the two, the Earth being negatively charged and the ionosphere being positively charged.  This potential varies somewhat but is around 200 volts/m.

This is a fundamental type of electrical generator.  The solar winds, interacting with the upper atmosphere rotation, act as a collector and brushes of a generator.  The lower atmosphere can be seen as a storage battery for this gradient potential.

This electromagnetic field around the Earth can be viewed as a stiff jelly.  When our bodies move and vibrate, these movements are transmitted to the environment.  These fields not only impinge on our body but they also affect the charges inside our body.  When we are standing on the ground, under normal conditions, we are grounded.  Our body then acts as a sink for the electrostatic field and we actually distort the force lines somewhat.

Our body also has its own electrostatic field about itself.  These field-lines are the result of the various biochemical reactions in the body.  This resultant bio-field couples us to the isoelectric field of the planet.

A "tuned system" consists of at least two oscillators of identical resonance frequencies.  If one of the oscillators starts emitting, the other will be activated by the signal very shortly.  Because the coupling is ideal, they will respond to the tiniest signals and begin to resonate.

In 1957, W.O. Schumann6 calculated the Earth-ionosphere cavity resonance frequencies.  His works were updated over the years and the figure now used is at 7.5Hz.  As indicated previously, the micromotion of the body is about 6.8 to 7.5Hz.

It is obvious that when one is in deep meditation, it is possible for the human being and the planet system to start resonating.  There is a transfer of energy.  It is no coincidence that this frequency is in the theta region of brainwaves, the state of maximum regeneration.

Information is embedded in a field, rather than just being a field.  A field is thus an abstract quantity of information; relationships between this point and that point in the universe.

Astral temples are set up to evoke a certain correspondence effect, like a resonance.  These temples are like a physical matrix, one with specific geometrical form and color.

The visualization, in turn sets up a particular EM resonance in the brain.  The reverberation pattern is most explicit.  Clarity is all important.  Distortion minimizes the resonance effect and reduces any amplification to connecting other "tuned" oscillators in the body.

Techniques of extending this harmonious resonance have been known for thousands of years.  These are the different meditative techniques.  Most slow down the metabolic rate of the body so that much less oxygen is required to keep the body going.

As one becomes proficient in meditation, the breathing becomes so gentle as not to disturb the resonate state of the aorta.  An automatic process develops in which the lungs and the diaphragm regulates the heart-aorta system so as to keep them well-tuned.  This helps extend the resonant behavior even with shallow breathing.

In conclusion, the following points should be made regarding the resonant effects available through meditation:

 1. There is a heart/aorta resonance which links up with a number of other critical oscillators, including several in the brain.  It starts at the heart.

 2. Specific geometries or geometrical mandalas (form and color) create resonance effects in the brain.  The pattern is repeated in the brain.

 3. Specific geometrical systems can be used as "keys" to access those specific archetypes.  Access occurs to the psyche.

 4. This linking of resonant cavity oscillators can be seen to form a common thread, going from Hadit (DNA-RNA helix) to Nuit (galactic hydrogen-helium field).

 5. By "tuning" one's meditation, it is possible to amplify and have access to the other resonant systems, in and out of the body.

The Human organism has usually been regarded as a complex arrangement of chemical elements and compounds.  The quantity and structure of these variables are our reference points for states of health.  This is the area of biochemistry and biochemical analysis.

An equally valid approach is to regard the human organism as an aggregation of electromagnetic fields which are constantly interacting and changing as are their biological equivalents.  It has been shown that the human system is an emitter of electromagnetic radiations.7

All biological processes are a function of electromagnetic field interactions.  EM fields are the connecting link between the world of form and resonant patterns.

The patterns are arbitrary forms which are non-physical.  Archetypal forms are based on inherent characteristics and correspondences.  This provides a basis for what we would call resonant phenomena in archetypal systems.  EM fields embody or store gestalts, patterns of information.

An archetype may then be seen as a specific geometrical system of standing waves occurring in the brain as a space-time shape ("key").

In living organisms, opposites receive their structure of symmetry from particular combinations of spatial and temporal aspects.  Like reins on a horse, each of the opposites of the psychological pair has its own place.  This geometric property makes them capable of being opposites.  The activity of each arm determines the quantity; the spatial identity of the rein determines the quality.  There is no monotonic (or linear)  transition from one to the other passing through zero.

A human being, immersed in the galactic hydrogen-helium field, may also utilize the pulsing feedback between man and the galaxy to build up the resonance effects, much like we would tune a radio.  These primary frequencies are multiples of the base frequency 7 Hz.

These four nucleotides provide resonant frequencies for alpha, theta, and delta (the characteristic brain states going from consciousness to deep sleep: 14-2 Hz.).  This resonance relationship can be seen to link with helium inside the body at various chemical sites.

The bridge connecting the solar system resonances and the brain frequencies seem to reside in the DNA-RNA helix.

In a paper by Oliver Reiser8 from the University of Pittsburgh, a relationship is developed between the four helium cores in an atomic nucleus and the matrix forms on the DNA and RNA. Reiser describes them as "radiation belts of thought,"  the four "nucleotides" enter into the dynamics of these nuclear properties. A spheron is a nuclear constituent roughly spherical in shape and spaced in concentric layers.

The platonic solids are the five regular solids described by Pythagoras, now seen to form all crystal formations.  These forms later became the basis of the mathematics known as group theory.  The so-called "resonances" were specific combinations of five regular solids geometry.

"Helions" is Pauling's term for spherons when he modeled the helium in the sun, the heliosphere around the Earth, and the hydrogen-helium plasma of the galactic disc.  An optically activated molecule, such as helium, contains an electron which is coerced into a helical path by electric field.  This one-sided spiral is maintained in the intermolecular transport through protein molecules.  Note that the protein units of "spherical viruses" are packed symmetrically, in accordance with the pattern of cubic symmetry.  Once more we find our way back to Pythagoras and the Platonic solids.
 

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1.  Paul F.J. New, "Arterial Stationary Waves," American Journal of Roentgenology,Vol. 97, no. 2, pp 488-499.
2.  Symposium of Psychotronics, Prague, Czechoslovakia, Sept. 25, 1970. Paraphysical Laboratory Publication, Downton, Wiltshire, England.
3.   When certain crystals are stressed, they produce an electrical current.  This phenomena is known as the piezoelectric effect.  The physical body can be seen to be composed of liquid crystals and amorphous semiconductors (the gel).  When the body is stressed by a force such as heartbeat, it presses the brain on the skull and current is produced.
4.  Biomedical Engineering Systems, McGraw-Hill Books, N.Y., 1970.
5.  Cochran, Andrew A., "Relationships Between Quantum Physics and Biology," Foundations of Physics, Vol. 1, pp 235-250, 1971.
6.  Schumann, W., "Electrische Eigenshwingungen des Hohlraumes Erde-Luft-Ionosphere," Zeitschrift fur Angewandte Physik, Vol. 9, 373-378, 1957.
7.  Presman, A., Electromagnetic Fields and Life, Plenum Press, 1970.
8.  Reiser, Oliver L., Cosmic Humanism and World Unity, Diagram LII, p 463, and Diagram LIV, p 465.
9.  Pauling, Linus, "The Close-Packed-Spheron Theory of Nuclear Fission," Science, Vol. 150, pp 297-305, 1965.
 

REFERENCES

Ambrose, E.J.. Osborne, J.S., and Stuart, P.R. Structure and properties of the cell surface complex. In Liquid Crystals and Ordered Fluids (Johnson, J.F. and Porter, R., eds.). New York: Plenum, 1970.

Becker, R.O.. The effect of magnetic fields upon the central nervous system.  Medical Electronics and Biological Engineering, 1963, 1, 293-303.

Becker, R.O.. Electromagnetic forces and life process.  Technology Review, December, 1972.

Bernal, J.O.. General discussion.  Transactions of the Faraday Society, 1933, 29, 1082.

Blair, Lawrence.  Rhythms of Vision, New York, Warner Books, 1975.

Brown, F.A., Jr. Electrical and magnetic sensitivity: Some orientational influences on nonvisual, terrestrial electromagnetic fields.  Annals, New York Academy of Science, 1971, 188, 224-241.

Bulkley, D.H. An Electromagnetic Model for Dynamic Turnover and the Continuous Self-Replication of Biological Macromolecules, Rogue Press, 1973.

Burr, H.S. and Northrup, F.S.C. The electrodynamic theory of life.  Quarterly Review of Biology, 1935, 10, 322-333.

Elliot, H.C. Neural tube and spinal cord in Textbook of Neuroanatomy, Philadelphia, J.B. Lippincott Co., 1963.

Fowler, R.H. and Bernal, J.D. Note on the pseudo-crystalline structure of water.  Transactions of the Faraday Society, 1933, 29, 1049.

Freedericksz, V. and Zolina, V. Forces causing the orientation of an anistropic liquid.  Transactions of the Faraday Society, 1933, 29, 944.

French, Vernon, Bryont, P.J. and Bryont, S.V. Pattern regulation in epimorphic fields, Science, September 10, 1976, 969-981.

Garrison, W. Destiny and geomagnetism.  Popular Electronics, July 1971.

Koestler, A. The Roots of Coincidence.  New York: Random House, 1972.

LeShan, L.A. Toward a general theory of the paranormal.  Parapsychological Monographs, 1969, no. 9.

Lund, E.J. Bioelectric Fields and Growth.  Austin:  University of Texas Press, 1945.

McGinnes, J.E. Mobility gaps: "A Mechanism for Band Gaps in Melanins."  Science, 1972, 177, 896-897.

McKenna, T.J. and McKenna, D.J. "Organismic Thought" in The Invisible Landscape.  New York:  Seabury Press, 1975.

Miller, R.A., Webb, B., Dickson, D. "A Holographic Concept of Reality." Psychoenergetic Systems, 1975, Vol. 1, 55-62.

Muses, C.A. On the modification of random fluctuations by a target- seeking process utilizing random energies.  Bio-Medical Computing, 1970, 1, 75-80.

Needham, J. "The Hierarchial Continuity of Biological Order."  Order and Life, 1936, 1, 109-168.

Presman, A.S. Electromagnetic Fields and Life.  New York:  Plenum.  1970.

Pullman, B. and Pullman, A. Quantum Biochemistry. New York:  Interscience.

Purett, L. Magnetic reversals and biological extinctions.  Science News, 1971, 100, 287-302.

Ravitz, L. Electromagnetic field monitoring of changing state-function, including hypnotic states.  Journal of the American Society of Psychosomatic Dentistry and Medicine, 1970, 17, 199-129.

Szent-Gyorgyi, A..  Bioenergetics.  New York:  Academic Press, 1957.

Szent-Gyorgyi, A..  Introduction to a Submolecular Biology.  New York:  Academic Press, 1960.

Szent-Gyorgyi, A..  Electronic Biology and Cancer, New York, Marcel Dekker inc., 1976.
Thom, R.  Structural Stability and Morphogenesis.  Massachusesetts, W.A. Benjamin Press, 1975.

Tien, H.C..  Pattern recognition and psychosynthesis.  American Journal of Psychotherapy, 1969, 23, 53-66.

Van Iterson, G., Jr..  A simple arrangement to demonstrate liquid crystals.  Transactions of the Faraday Society, 1933, 29, 915-919.

Wheeler, J.A..  Geometrodynamics.  Lectures, Course on Weak Interactions, Enrico Fermi Internal School of Physics.  Varenna, Italy, Summer, 1959.
 

C.  MAGICAL USE OF STANDING WAVES AND
      GEOMETRICAL MATRICES

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.

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
 

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]
 
 

 
 

[The Four Worlds]
 

 D.  THE MAGICKAL ALTAR: THE DOUBLE CUBE

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
 

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)

 
 

[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  .

 
 

[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 mystery of meditation and Vector Equilibrium.
 

______________________________________________________________________________
(1) Aleister Crowley, BOOK 4, Dallas, Sangreal Foundation, Inc., 1972, p61.

 
 

[Tiphareth: Diamond Body/Throne-Chariot]
 
 

 D.  DAATH: THE THRESHOLD OF THE WORLD OF FORM

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)

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.
 
 

[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.
 

 
 

[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)

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.
(3) Gershom Scholem, MAJOR TRENDS IN JEWISH MYSTICISM,
(4) Gershom Scholem, KABBALAH, N.Y., The New American Library, Inc. 1974, p158.
 
 
 

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




 

V.  CONCLUSIONS: THE QUINTESSENCE

A.  NEURAL FEEDBACK AND BRAINWAVE TRAINING

"Gentlemen, I have a confession to make - half of what we have taught you is in error; and furthermore we cannot tell you which half it is."
--Sir William Osler
(to a graduating medical class)
 

A man named Caton first discovered electrical rhythms within the brains of animals in 1875.  It was over 50 years later when Hans Berger showed that man also had these rhythms.  His original search was in the hopes of finding the physical link between man's mind and his body.

It was this mind/body question which led him to dedicate his life to finding this link.  He became interested in the work of Caton and others and set up his own laboratory to further investigate the electrical activity of the brain.

After 20 years of research, he was first able to record the brain rhythms of a human.  He spent another 10 years convincing his colleagues that this rhythm came from the neurons of the brain, not from blood flow or connective tissue.  His original studies also showed that this rhythm changed with age, was vulnerable to sensory stimulation, and was affected by body chemistry.

World War II broke out and Hans Berger never finished his original work: crack the code of brain rhythms and their link to "psychic functions."  Since that time, no one else has either.  Later research centered around the more practical applications of the EEG to epilepsy, brain metabolism, brain functions and the levels of consciousness.
 

 1.  BASIC METABOLIC RATE (BMR):
Brain metabolism is directly related to body metabolism.  One facet of the human body that the EEG will monitor is that of brain metabolism.  Such gross metabolic dysfunction as liver and kidney failure are easily seen with the EEG.  Epilepsy is also seen as resulting in a metabolic dysfunction within the brain.  Because of these and other important factors, the EEG was incorporated into the medical systems of Western society.

The EEG is also a good reflection of how well oxygen is metabolized in the blood.  Your body needs oxygen in order to convert food resources into energy.  Any deviation in oxygen intake and carbon dioxide output changes the EEG reading.  Both hyperventilation and hypoventilation cause the EEG pattern to slow down.  The amount of sugar, as a food resource, also affects the EEG.
 

 2.  BRAIN ACTIVITY AND THE SOURCE OF ALPHA WAVES

The EEG is considered to monitor "gross" neuronal activity.  It does not monitor individual neurons per se, but large groupings.  Whenever rhythms are seen in the EEG, it is the net result of many thousands of neurons "in unison."

Because alpha is seen so easily in the EEG, it was originally thought that there must be some kind of intracranial control mechanism (pacemaker) that caused all of those neurons to fire in unison.

Recently two Dutch scientists claimed to have proven the existence of such an alpha-pacemaker.  It supposedly was located in the thalamus, located in the brain stem.  It was thought to gate impulses from the body (spinal cord) into appropriate locations in the brain.  Hand impulses are thus gated into that part of the brain designated as hand.  Alpha, then was thought to be a very rhythmic gating of the information from the body to the brain.

This rhythmic gating results in alpha.  It is thought to be the result of a very relaxed state.  Non-rhythmic gating, resulting in dyssynchronous brain wave activity, was considered a type of coping response to impinging stimuli.  Since the pacemaker theory of alpha is still tentative, it has not yet received wide recognition within the scientific community.  This is a result of a very complex relationship between autonomic nervous system activity, brain metabolism, age, and a host of other pertinent factors.
 

 3.  LEVELS OF CONSCIOUSNESS

One of the most important facets of the EEG is that it is an excellent indicator of levels and states of consciousness.  Audio or visual inspection can determine whether a person is alert, relaxed, drowsy, asleep or even dreaming.  Specific detail and arbitrary limit-points for various levels of consciousness are now defined by EEG parameters.  The field of altered states of consciousness (ASC) and exploration and control of consciousness are all a direct result of this very important tool.

It is often through the introduction of these new tools that new techniques and discoveries are made.  The tremendous advances in electronics made in the past decade have advanced sophisticated equipment that stimulated psycho-physics and research in new ideas in science.  This is especially true in the area of biofeedback and self-control technology.
 

 4.  BIOFEEDBACK TRAINING

The technique of biofeedback is based on the fundamental process of instrument learning.  A situation gives rise to several variable behaviors.  One response is in some way rewarded or reinforced.  Learning occurs as this response occurs successively more and more quickly and reliably.

Essential to this learning process is the receiving of information in a feedback loop, similarly to servo systems.  This can be done via visual or auditory stimuli, which tell us when we have made the correct response or moved closer to our goal.

This is made possible by using electronic feedback loops (such as those provided by an Electroencephalophone or EEP) and a psychological technique called operant conditioning.  The first successful attempts were attributed to Joe Kamiya in the late 1950's.  Essentially, his technique gave a signal when he achieved specific levels of consciousness.  Its full potential has yet to be realized.

Behavior has traditionally been divided into two categories:

 1. Voluntary control, such as walking, writing, muscular activities; and,

 2. Autonomic control, such as heartbeat, blood pressure, brain-wave production, visceral body processes.

We learn to guide our behavior by receiving feedback on the results and then making appropriate adjustments.  This is the place where the voluntary and involuntary behavior differ.  While we can receive feedback in our writing, we do not have such access to those from the visceral activities.
If provided with this absent (bio)feedback via electronic means, it has been shown conclusively that we can learn to exert a "voluntary" control of\over inner bodily functions.  Yogis have done it for centuries, taking years to learn the disciplines of mind control, self-hypnosis, and autonomic regulation.

Recent research into control of heartbeat, blood pressure, body temperature, brainwave production, and pain control indicates that conscious control is possible.   Research into control of brainwaves through the use of biofeedback techniques has centered around alpha waves, and more recently, theta.  Some of the more well-known researchers are Kamiya, Kasamatsu, Brown, Hart, Peper, Mulholland, Stoyva, Green, Walters and Green.

In discussing biofeedback research and results, one runs into a problem of semantics.  It is the idea of learning to "control" one's brainwaves.  It must be emphasized that in using these techniques, a person is not learning to directly control the neuronal electrical activity of action potentials and synaptic events in the cerbral cortex.  One learns to control the subjective or mental event associated with the presence of alpha or theta.

Like self-hypnosis it requires not-doing or letting it happen.  Very typically people "try" to enter alpha; then they "try not to try"; finally, they simply learn how to let go into the state.  The experience may be different for each person each time depending on their frame of reference.

Changes in brainwave patterns, or blood pressure, body temperature and deep muscle tension are "physiological correlates of psychological processes that the subject learns to control."
 

 5.  BRAIN WAVE PATTERNS

The pattern of neuronal activity in the cerebral cortical section of the brain can be recorded electrically.  This is done by measuring the electrical potential difference between two points on the scalp.  The record is known as the electroencephalogram (EEG).  Brain waves manifest themselves as oscillating voltage.  They have two main dimensions: the frequency of oscillation and the amplitude.

The frequency predominantly determines the amplitude of the brain wave, but there can be fluctuations of amplitude at a given frequency.  Brain waves are broken up into four main categories, determined by the frequency of the wave.  The borders of these categories are more or less arbitrary.  The following table is therefore only approximately correct:
 
 

[Brainwave Table]
 
 
 
 
 
 
 
 

 Beta:  This is the brainwave of normal waking consciousness.  It is characterized as the state of being awake, alert, and concentrating.  If this state is maintained for a prolonged period, it becomes associated with feelings of tension, worry, fear, or anxiety.  Lower brain states are necessary on an occasional basis to maintain the alert aspect of this state.  A visual-identification in the mind's eye occurs, a state where image are identified with form and specific objects.

 Alpha: This is also a conscious state, but identified with the mental experience where images are not identified.  It has come to be associated with feelings of pleasure, pleasantness, tranquility, serenity and relaxation.  It can also imply a relaxed concentration.  It is also a place of light sleep and dream states.

 Theta:  This state is traditionally labeled unconscious by western medicine.  In recent years, however, people trained with autogenics can achieve this state and retain consciousness, similar to meditators.  Theta has come to be associated with such things as hypnogogic imagery, day dreaming, sleep, and creativity.  It has also been shown as the state where healing and regenerating of tissue occurs.

 Delta: This state is predominantly associated with non-dreaming sleep or deep sleep.  There are some reports of individuals achieving this set of brainwave patterns and still retaining consciousness.  If it is achieved while maintaining a conscious state, "out-of-body" experiences (OOBE) are subjectively experienced and reported.
 

 6.  SLEEP CYCLE

The EEG pattern changes throughout the night.  These changes can determine when dreaming occurs.  The chart below is an average sleep cycle during those eight hours.
 
 

[sleep cycle diagram]
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

Stage 1 is the drowsy period of sleep, characterized by what is known as sleep spindles (spindle-alpha).  Stage 2 is a sleep state where response to external and/or internal stimulation can occur.  This stage is characterized by what is known as K-complex waves.  Stage 3 means you are on your way to Stage 4.  Stage 4 is deep sleep.  It is also delta state and is not associated with dreaming.  REM state (Rapid Eye Movement) is where most dreams occur.

Notice how an individual spends most of the first part of the night in State 4 sleep.  The later part of the night is spent mostly in REM sleep.  Therefore, most dreams occur toward the end of the night's sleep.  When deprived of REM sleep, temporarily personality changes occur with other psychological changes.  When lost sleep is made up, the person spends more the sleep cycle in lighter REM stages.  In a sense, this makes up for that lost dream time.

Although there is a lot of variable data on EEG changes with age, there is a basic curve that shows the usual rate of development and change with time.  Primarily the EEG frequency of a person starts very low, about 1-2 cps in a newborn infant, gradually increasing in frequency until the age of 19, where the normal adult rhythm, while awake, is about 20 cps.
 
 

[frequency chart]
 
 
 
 
 
 
 
 
 
 

Things which lower the EEG frequency are:

  sedative drugs, LSD,
  large doses of alcohol,
  very low blood sugar,
  lack of oxygen

Things which raise the EEG frequency are:

  caffeine,
  small doses of alcohol, barbiturates,
  low blood sugar,
  excess of carbon dioxide

Hypnosis, per se, has little effect on the EEG, unlike meditation which influences it directly.  What is contained in the hypnotic suggestion will change frequencies and make the difference, for example, suggestions for relaxation, increased warmth, and blood flow.
 

 7.  HOW THE EEP WORKS

The EEP generates a feedback signal by picking up the very low voltage brain-wave signals with two or more electrodes.  A high-gain circuit amplifies the signal and drives a wide band filter.  This filter passes signals in the alpha through delta range and attenuates signals of higher and lower frequencies.

The feedback is usually in the form of a modulated white-noise with modulation at the brain wave frequency.  There usually two controls, one for amplitude variation and the other to discriminate frequency bands for tighter control.

The cerebral cortex is the outermost part of the brain.  It is this convoluting mass of tissue that gives man superior intelligence.  The cortex of each hemisphere is divided into four main areas, called lobes.  Alpha is found predominantly on the occipital lobe or back-part of the brain.  This is the section which deals with visual systems.  Alpha is also found in the frontal lobe, but not as easily.  Theta is found more commonly on the temporal lobe, while the speech, sensory, and motor areas tend to show primarily beta activity.

Electrode placement usually uses a ground or reference point under one ear.  The potential generated between the two electrodes is very important.  Therefore, the second electrode is usually placed in the occipital region, just under the inion ("bump" on the back of the head) and to one side about 1 inch.  The side chosen is the same side that the "ear" electrode is on.  This gives the optimal gradient for easily monitoring brain signals.
 

 8.  POTENTIAL APPLICATIONS

Pleasure, relaxation, and sleep are associated with alpha-theta output.  The combination of relaxing, clearing the mind and turning inward can be a very pleasant and rewarding experience.  Learning to relax and to go from alpha to theta has proved to be beneficial to the insomniac.  In some cases, it can also be a sleep-substitute.

Hypnosis subjects are much more susceptible to suggestion when in lower alpha states.  It is now possible to achieve states of consciousness within several weeks of training equivalent to those of Zen masters with 20 years meditation effort.  The main drawback is that when one learns these states, continual reinforcement is necessary for similar continued ability, day-by-day.  It is a use-it-or-lose-it situation.

One of the main purposes for sleep is to transfer information and experiences from short to long-term memory.  Concentration, learning and recall ability can and is greatly enhanced with alpha-theta control exercises.  Recall capability is greatest in alpha state.  Also, by learning to exclude all external stimuli when trying to achieve the alpha-theta control, increases one's ability to concentrate.

The reverie state which is indicated by theta and low-frequency alpha seems to increase hypnagogic and dream-like images.  There is also a link between reverie and hypnagogic imagery and creativity.  These images are critical for the creative process.

Other biofeedback directions include:

 1.  EMG (Electromyograph) for hypertension, deep muscle contol, and reading improvement by eliminating "subvocalization."

 2.  THERMAL FEEDBACK for controlling body temperature at various points on the body.  Current research shows that most individuals can raise or lower finger temperatures about 8 F.; useful in the control of migraine and tension headaches.

 3.  GSR (Galvanic Skin Response) is used as a lie detector and supposedly is a way of communicating with certain plants.  although the latter is highly questionable, there is a statistical significance in the change of skin resistance in certain fish 8 hours before major earthquakes, offering a possible early-warning system for high-risk areas.

These are just a few of many suggested possible applications.  Biofeedback research should provide more new discoveries and ideas for years to come.  The latest possibility is its incorporation with Virtual Reality to heighten the experience even more.

V.  CONCLUSIONS: THE QUINTESSENCE

A.  NEURAL FEEDBACK AND BRAINWAVE TRAINING

"Gentlemen, I have a confession to make - half of what we have taught you is in error; and furthermore we cannot tell you which half it is."
--Sir William Osler
(to a graduating medical class)
 

A man named Caton first discovered electrical rhythms within the brains of animals in 1875.  It was over 50 years later when Hans Berger showed that man also had these rhythms.  His original search was in the hopes of finding the physical link between man's mind and his body.

It was this mind/body question which led him to dedicate his life to finding this link.  He became interested in the work of Caton and others and set up his own laboratory to further investigate the electrical activity of the brain.

After 20 years of research, he was first able to record the brain rhythms of a human.  He spent another 10 years convincing his colleagues that this rhythm came from the neurons of the brain, not from blood flow or connective tissue.  His original studies also showed that this rhythm changed with age, was vulnerable to sensory stimulation, and was affected by body chemistry.

World War II broke out and Hans Berger never finished his original work: crack the code of brain rhythms and their link to "psychic functions."  Since that time, no one else has either.  Later research centered around the more practical applications of the EEG to epilepsy, brain metabolism, brain functions and the levels of consciousness.
 

 1.  BASIC METABOLIC RATE (BMR):
Brain metabolism is directly related to body metabolism.  One facet of the human body that the EEG will monitor is that of brain metabolism.  Such gross metabolic dysfunction as liver and kidney failure are easily seen with the EEG.  Epilepsy is also seen as resulting in a metabolic dysfunction within the brain.  Because of these and other important factors, the EEG was incorporated into the medical systems of Western society.

The EEG is also a good reflection of how well oxygen is metabolized in the blood.  Your body needs oxygen in order to convert food resources into energy.  Any deviation in oxygen intake and carbon dioxide output changes the EEG reading.  Both hyperventilation and hypoventilation cause the EEG pattern to slow down.  The amount of sugar, as a food resource, also affects the EEG.
 

 2.  BRAIN ACTIVITY AND THE SOURCE OF ALPHA WAVES

The EEG is considered to monitor "gross" neuronal activity.  It does not monitor individual neurons per se, but large groupings.  Whenever rhythms are seen in the EEG, it is the net result of many thousands of neurons "in unison."

Because alpha is seen so easily in the EEG, it was originally thought that there must be some kind of intracranial control mechanism (pacemaker) that caused all of those neurons to fire in unison.

Recently two Dutch scientists claimed to have proven the existence of such an alpha-pacemaker.  It supposedly was located in the thalamus, located in the brain stem.  It was thought to gate impulses from the body (spinal cord) into appropriate locations in the brain.  Hand impulses are thus gated into that part of the brain designated as hand.  Alpha, then was thought to be a very rhythmic gating of the information from the body to the brain.

This rhythmic gating results in alpha.  It is thought to be the result of a very relaxed state.  Non-rhythmic gating, resulting in dyssynchronous brain wave activity, was considered a type of coping response to impinging stimuli.  Since the pacemaker theory of alpha is still tentative, it has not yet received wide recognition within the scientific community.  This is a result of a very complex relationship between autonomic nervous system activity, brain metabolism, age, and a host of other pertinent factors.
 

 3.  LEVELS OF CONSCIOUSNESS

One of the most important facets of the EEG is that it is an excellent indicator of levels and states of consciousness.  Audio or visual inspection can determine whether a person is alert, relaxed, drowsy, asleep or even dreaming.  Specific detail and arbitrary limit-points for various levels of consciousness are now defined by EEG parameters.  The field of altered states of consciousness (ASC) and exploration and control of consciousness are all a direct result of this very important tool.

It is often through the introduction of these new tools that new techniques and discoveries are made.  The tremendous advances in electronics made in the past decade have advanced sophisticated equipment that stimulated psycho-physics and research in new ideas in science.  This is especially true in the area of biofeedback and self-control technology.
 

 4.  BIOFEEDBACK TRAINING

The technique of biofeedback is based on the fundamental process of instrument learning.  A situation gives rise to several variable behaviors.  One response is in some way rewarded or reinforced.  Learning occurs as this response occurs successively more and more quickly and reliably.

Essential to this learning process is the receiving of information in a feedback loop, similarly to servo systems.  This can be done via visual or auditory stimuli, which tell us when we have made the correct response or moved closer to our goal.

This is made possible by using electronic feedback loops (such as those provided by an Electroencephalophone or EEP) and a psychological technique called operant conditioning.  The first successful attempts were attributed to Joe Kamiya in the late 1950's.  Essentially, his technique gave a signal when he achieved specific levels of consciousness.  Its full potential has yet to be realized.

Behavior has traditionally been divided into two categories:

 1. Voluntary control, such as walking, writing, muscular activities; and,

 2. Autonomic control, such as heartbeat, blood pressure, brain-wave production, visceral body processes.

We learn to guide our behavior by receiving feedback on the results and then making appropriate adjustments.  This is the place where the voluntary and involuntary behavior differ.  While we can receive feedback in our writing, we do not have such access to those from the visceral activities.
If provided with this absent (bio)feedback via electronic means, it has been shown conclusively that we can learn to exert a "voluntary" control of\over inner bodily functions.  Yogis have done it for centuries, taking years to learn the disciplines of mind control, self-hypnosis, and autonomic regulation.

Recent research into control of heartbeat, blood pressure, body temperature, brainwave production, and pain control indicates that conscious control is possible.   Research into control of brainwaves through the use of biofeedback techniques has centered around alpha waves, and more recently, theta.  Some of the more well-known researchers are Kamiya, Kasamatsu, Brown, Hart, Peper, Mulholland, Stoyva, Green, Walters and Green.

In discussing biofeedback research and results, one runs into a problem of semantics.  It is the idea of learning to "control" one's brainwaves.  It must be emphasized that in using these techniques, a person is not learning to directly control the neuronal electrical activity of action potentials and synaptic events in the cerbral cortex.  One learns to control the subjective or mental event associated with the presence of alpha or theta.

Like self-hypnosis it requires not-doing or letting it happen.  Very typically people "try" to enter alpha; then they "try not to try"; finally, they simply learn how to let go into the state.  The experience may be different for each person each time depending on their frame of reference.

Changes in brainwave patterns, or blood pressure, body temperature and deep muscle tension are "physiological correlates of psychological processes that the subject learns to control."
 

 5.  BRAIN WAVE PATTERNS

The pattern of neuronal activity in the cerebral cortical section of the brain can be recorded electrically.  This is done by measuring the electrical potential difference between two points on the scalp.  The record is known as the electroencephalogram (EEG).  Brain waves manifest themselves as oscillating voltage.  They have two main dimensions: the frequency of oscillation and the amplitude.

The frequency predominantly determines the amplitude of the brain wave, but there can be fluctuations of amplitude at a given frequency.  Brain waves are broken up into four main categories, determined by the frequency of the wave.  The borders of these categories are more or less arbitrary.  The following table is therefore only approximately correct:
 
 

[Brainwave Table]
 
 
 
 
 
 
 
 

 Beta:  This is the brainwave of normal waking consciousness.  It is characterized as the state of being awake, alert, and concentrating.  If this state is maintained for a prolonged period, it becomes associated with feelings of tension, worry, fear, or anxiety.  Lower brain states are necessary on an occasional basis to maintain the alert aspect of this state.  A visual-identification in the mind's eye occurs, a state where image are identified with form and specific objects.

 Alpha: This is also a conscious state, but identified with the mental experience where images are not identified.  It has come to be associated with feelings of pleasure, pleasantness, tranquility, serenity and relaxation.  It can also imply a relaxed concentration.  It is also a place of light sleep and dream states.

 Theta:  This state is traditionally labeled unconscious by western medicine.  In recent years, however, people trained with autogenics can achieve this state and retain consciousness, similar to meditators.  Theta has come to be associated with such things as hypnogogic imagery, day dreaming, sleep, and creativity.  It has also been shown as the state where healing and regenerating of tissue occurs.

 Delta: This state is predominantly associated with non-dreaming sleep or deep sleep.  There are some reports of individuals achieving this set of brainwave patterns and still retaining consciousness.  If it is achieved while maintaining a conscious state, "out-of-body" experiences (OOBE) are subjectively experienced and reported.
 

 6.  SLEEP CYCLE

The EEG pattern changes throughout the night.  These changes can determine when dreaming occurs.  The chart below is an average sleep cycle during those eight hours.
 
 

[sleep cycle diagram]
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

Stage 1 is the drowsy period of sleep, characterized by what is known as sleep spindles (spindle-alpha).  Stage 2 is a sleep state where response to external and/or internal stimulation can occur.  This stage is characterized by what is known as K-complex waves.  Stage 3 means you are on your way to Stage 4.  Stage 4 is deep sleep.  It is also delta state and is not associated with dreaming.  REM state (Rapid Eye Movement) is where most dreams occur.

Notice how an individual spends most of the first part of the night in State 4 sleep.  The later part of the night is spent mostly in REM sleep.  Therefore, most dreams occur toward the end of the night's sleep.  When deprived of REM sleep, temporarily personality changes occur with other psychological changes.  When lost sleep is made up, the person spends more the sleep cycle in lighter REM stages.  In a sense, this makes up for that lost dream time.

Although there is a lot of variable data on EEG changes with age, there is a basic curve that shows the usual rate of development and change with time.  Primarily the EEG frequency of a person starts very low, about 1-2 cps in a newborn infant, gradually increasing in frequency until the age of 19, where the normal adult rhythm, while awake, is about 20 cps.
 
 

[frequency chart]
 
 
 
 
 
 
 
 
 
 

Things which lower the EEG frequency are:

  sedative drugs, LSD,
  large doses of alcohol,
  very low blood sugar,
  lack of oxygen

Things which raise the EEG frequency are:

  caffeine,
  small doses of alcohol, barbiturates,
  low blood sugar,
  excess of carbon dioxide

Hypnosis, per se, has little effect on the EEG, unlike meditation which influences it directly.  What is contained in the hypnotic suggestion will change frequencies and make the difference, for example, suggestions for relaxation, increased warmth, and blood flow.
 

 7.  HOW THE EEP WORKS

The EEP generates a feedback signal by picking up the very low voltage brain-wave signals with two or more electrodes.  A high-gain circuit amplifies the signal and drives a wide band filter.  This filter passes signals in the alpha through delta range and attenuates signals of higher and lower frequencies.

The feedback is usually in the form of a modulated white-noise with modulation at the brain wave frequency.  There usually two controls, one for amplitude variation and the other to discriminate frequency bands for tighter control.

The cerebral cortex is the outermost part of the brain.  It is this convoluting mass of tissue that gives man superior intelligence.  The cortex of each hemisphere is divided into four main areas, called lobes.  Alpha is found predominantly on the occipital lobe or back-part of the brain.  This is the section which deals with visual systems.  Alpha is also found in the frontal lobe, but not as easily.  Theta is found more commonly on the temporal lobe, while the speech, sensory, and motor areas tend to show primarily beta activity.

Electrode placement usually uses a ground or reference point under one ear.  The potential generated between the two electrodes is very important.  Therefore, the second electrode is usually placed in the occipital region, just under the inion ("bump" on the back of the head) and to one side about 1 inch.  The side chosen is the same side that the "ear" electrode is on.  This gives the optimal gradient for easily monitoring brain signals.
 

 8.  POTENTIAL APPLICATIONS

Pleasure, relaxation, and sleep are associated with alpha-theta output.  The combination of relaxing, clearing the mind and turning inward can be a very pleasant and rewarding experience.  Learning to relax and to go from alpha to theta has proved to be beneficial to the insomniac.  In some cases, it can also be a sleep-substitute.

Hypnosis subjects are much more susceptible to suggestion when in lower alpha states.  It is now possible to achieve states of consciousness within several weeks of training equivalent to those of Zen masters with 20 years meditation effort.  The main drawback is that when one learns these states, continual reinforcement is necessary for similar continued ability, day-by-day.  It is a use-it-or-lose-it situation.

One of the main purposes for sleep is to transfer information and experiences from short to long-term memory.  Concentration, learning and recall ability can and is greatly enhanced with alpha-theta control exercises.  Recall capability is greatest in alpha state.  Also, by learning to exclude all external stimuli when trying to achieve the alpha-theta control, increases one's ability to concentrate.

The reverie state which is indicated by theta and low-frequency alpha seems to increase hypnagogic and dream-like images.  There is also a link between reverie and hypnagogic imagery and creativity.  These images are critical for the creative process.

Other biofeedback directions include:

 1.  EMG (Electromyograph) for hypertension, deep muscle contol, and reading improvement by eliminating "subvocalization."

 2.  THERMAL FEEDBACK for controlling body temperature at various points on the body.  Current research shows that most individuals can raise or lower finger temperatures about 8 F.; useful in the control of migraine and tension headaches.

 3.  GSR (Galvanic Skin Response) is used as a lie detector and supposedly is a way of communicating with certain plants.  although the latter is highly questionable, there is a statistical significance in the change of skin resistance in certain fish 8 hours before major earthquakes, offering a possible early-warning system for high-risk areas.

These are just a few of many suggested possible applications.  Biofeedback research should provide more new discoveries and ideas for years to come.  The latest possibility is its incorporation with Virtual Reality to heighten the experience even more.


 B.  VIDEO FEEDBACK: SELF-REALIZATION THROUGH
      YOGATRONICS

Abstract: A video feedback system is proposed, using a standard home computer and other immediately available hardware. Current research in the fields of brain chemistry and the brain's response to color, sound, and geometry is reviewed. A specific geometrical formula is developed, and physical analogs to current Jungian constructs known as archetypes are postulated. A series of electronic meditations are developed to create brain-body loops for interaction and self-realization, similar to those described in eastern Yoga.
 

Introduction:

Biological feedback (bios-life, feedback-return to the source) experimentation has been found to be particularly well-suited to the Western mind. The concept of time is muchmore important, everyone is in a hurry. Consequently, the western mind looks for "short-cuts", using technology. Research and experience has shown it to be a rapid and promising means toward such goals as self-awareness, health, and self-exploration.

Recent technological advances such as biofeedback instruments, have enabled man to realize the potentials of his inner power. These include mental concentration for problem solving, appetite control, preventive medicine, training to control heart-rate, blood pressure, and skin-temperature, anxiety, and others. Every day there are new examples, where this concept of technology enters our life. The state of this art has become very sophisticated.

The purpose of this paper is to show that, with currently existing technologies now standard in most homes, a technological transcendence is available, similar to ancient Eastern experiences of Kundalini. Health and expanded mental capability would be by-products. Using interactive multi-media, the television can now be used to change habits, personality, weight and other characteristics while broadening our self-realization.

The application of biofeedback research to the everyday lives of people has many implications. These can range from mass brain washing to expanded consciousness for all mankind. By integrating several fields of study, advanced technology now provides new tools for achieving altered states of consciousness.

Populations can be re-programed and individuals can become self-enlightened. An electronic meditation, using the most recently available information, is developed to create brain-body loops for interaction and control. The individual learns about the process of his own internal dialogue and can come to both sense, and later manipulate the loop of consciousness. Most of the hardware already exists and resides in most homes..
 

 Biofeedback Research:

The technique of biofeedback is based on the fundamental process of instrument learning. A situation gives rise to several variable behaviors. One response is in some way rewarded or reinforced. Learning occurs as this response occurs successively more and more quickly and reliably. Essential to this learning process is the receiving of information in a feedback loop, similarly to servo systems. This can be done via visual and auditory stimuli, stating when we have made the correct response or moved closer to our goal.

This is made possible by using electronic feedback loops (such as those provided by an Electroencephalophone or EEP) and a psychological technique called operant conditioning. We learn to guide our behavior by receiving feedback on the results and then making appropriate adjustments. This is the place where the voluntary and involuntary behavior differ. While we can receive feedback in our writing (for example), we do not have such access to those from the visceral activities. If provided with this absent (bio) feedback via electronic means, it has been shown conclusively that man can learn to exert a "voluntary" control over inner bodily functions.

Recent research into control of heart beat, blood pressure, body temperature, brainwave production, and pain seems to indicate that a conscious control is possible. In discussing biofeedback research and results, one runs into a problem of semantics. It is the idea of learning to "control" ones brainwaves. It must be emphasized that in using these techniques, a person is not learning to directly control the neuronal electrical activity of action potentials and synaptic events (in the cerebral cortex). One learns to control the subjective or mental event, associated with the presence of alpha or theta waves.

Changes in brainwave patterns, or blood pressure, body temperature and deep muscle tension are physiological correlates of psychological processes that the subject learns to control.  Some of the more outstanding developments in biofeedback research include the following examples:

 1. Relaxation: Any degree of rapid, self-induced relaxation can be obtained by a number of biofeedback techniques. These include using one's muscle activity to operate the signals of an Electromyograph (EMG), even to the point of each individual muscle cell becoming relaxed.

 2. Mental concentration for problem solving: The brain wave patterns which accompany effective and efficient mental activity are well-known. They are now used via Electroencephalograph (EEG).

 3. Appetite control: When the compulsion to eat exists, the psychology and brain waves reflect this "drive state". The individual can train himself to recognize such a state by means of signals of his psychological activity which are displayed to him. He can then train himself to distinguish and continue to reproduce a non-compulsive state.

 4. Preventive medicine: The physiologic activity of each troublesome system can be used to "feedback" information about its own functioning. These include heart rate, blood pressure, respiration, skin temperature, gastric activity, intestinal motility, muscles and so on.

 5. Training to control heart rate: In using feedback techniques there are two major areas; (1) a wide variety of cardiac irregularities, particularly tachycardia, bracycardia, extra systoles and auricular flutter, and (2) psychologic anxiety and fear reactions.

 6. Training to control blood pressure: Can be life-saving when the patient has the ability to maintain his blood pressure low enough to prevent developing both the symptoms of high blood pressure (headaches, dizziness) as well as preventing the more serious results in high blood pressure.

 7. Training to control skin temperature in specific areas: An easy physiologic activity which individuals can learn to bring under control. Many disease processes involve constriction of the blood vessels in the hand (or foot or other areas). With feedback training, this vasoconstriction can be markedly reduced, with the consequence of relief from pain and coldness.

 8. Anxiety: Numerous studies now indicate that a restful, relaxed but interested subjective state is associated with alpha activity. Clinical emphasis is on assisting the subject to produce lower frequencies with higher amplitudes.

 9. Education: Simple feedback systems are now used in conjunction with computer assisted teaching machines. It is well-known that the attention span of children is short. An accurate indicator of the length of each span of attention would be extremely useful in maximizing the use of teaching machines.

 10. Drug use: A patient can increase the effectiveness of his drug treatment. Since feedback techniques are applicable to all body systems, they decrease intestinal contractions, lower blood pressure, change skin temperature, etc.  They also alleviate associated problems (muscle tension, anxiety, irregular heart beats, respiratory distress, etc.). The patient can reduce undesirable side effects of the drugs he needs to take.

 11. Lie Detector: Some newer modifications with Galvanic Skin Response (GSR) have been used to determine stress potentials. The surface of the body does contain information about internal state functions; it is just a question of isolating variables.

Combined with video imagery received from a television screen, feedback becomes a means for human beings to experience a focused centeredness, not unlike trance states produced by Tibetan monks and other adepts.
 

Video Feedback:

Video feedback is a continuously progressing feed-forward loop of light traveling through a video recording and projection system. It usually interfaces a television camera and a television screen or monitor. Through the manipulation of the television camera, it is possible to create, manipulate and define video images.

Biofeedback involves the externalization of internal states and processes. This permits easier manipulation of the process. Video feedback involves the interlocking of internal and external loops. In effect, there are electronic mandalas with great powers for focusing concentration, stimulating artistic appreciation and altering conscious perception.

Electronics creates video mantras through mantratronics, yogatronics and video light loops. Video systems detect patterns of energy at the camera, and then processes these patterns and projects them onto a screen. Video feedback loops the screen back to the camera. Patterns arise which can grow brighter (positive feedback), fainter or remain constant (negative feedback).

The next stage is to add the human brain and other autonomic functions into the light loop. As the brain might act as the "camera," the signal sent to the processor could also be altered, in such a form as to "more efficiently move the brain into a previously determined state of awareness."

Today, video feedback has been only used to permit eye-hand manipulation of the described interlocked loops. This then helps the individual to understand and manipulate his own inner loops (eye-hand) more easily. But what if we were to monitor brain waves? The signal could be "processed" and a computer could then direct an "altered" signal to the screen monitor. This "altered" pattern would be calculated to be "most efficient" feedback in assisting the brain achieve the "desired state".

We are not talking about those auditory and visual cues one uses to single out motor units and control their isolated construction. There are specific patterns, colors and sounds which, in themselves, move the individual toward those pre-determined states. With this in mind, the system for feedback would include:

 a. Brain/body monitors/amplifier system. These signals then "go" to a ...

 b. Gating system, which sets threshold and level sense with timing parameters. The brain/body information is now ready to go to ...

 c. Pattern recognition (associative, memory, array). The signals then go to a ...

 d. Probabilistic synthesis control system. This has the ability to be pre-programed for specific signal forms to the ...

 e. Video/audio feedback devices. These deliver the "altered" stimuli to complete the loop. The new evoked responses are registered, and the process begins anew.

The key is the Probabilistic synthesis control system. It is here that the feedback loop system can be altered for specific goals or direction of meditation. For example, in Florida several grade school systems use a brain-video feedback system. The children watch their lessons on TV. When their attention begins to wander, their individual brain patterns drop in frequency. At a certain (predetermined) frequency, the lesson is stopped (by a computer) and a new stimulus is given to the child (usually an action scene, i.e. Western). This "snaps" the consciousness of the child back to "attentive" and the lesson is resumed.

This simple form of video feedback in Education has improved reading and math skills 40-80% above norms. Imagine what advanced research in computer-graphics might yield.
 

Pattern Recognition:

A primary function of the brain is in the recognition of patterns. This is the ability to perceive general inter-relationships between different parts of an input signal. These signals are usually visual, acoustical or tactile. It can also do this for ideas and concepts.

The perception of such unexpected relationships lies at the very heart of humor and creativity. The difficult part of pattern recognition is to see past the local variations, into the pattern lying beneath. This is not a signal-to-noise ratio problem because the patterns beneath are not necessarily the same.

Recognition does not seem to be simply a matter of recall from a vast memory, because we can distinguish patterns (like speech) without ever having heard them previously. Techniques like filtering, adaption, correlation, recollection, etc. are used today. The understanding of recognition is largely a matter of understanding how to deploy these various activities.

Equally important with pattern recognition is pattern synthesis. These are the techniques of generating the complex electric nerve signals which give rise to speech and coordinated muscle movement. The ability to speak or write reveals a genuine creative ability. In some sense, pattern synthesis is the converse of pattern recognition. The synthesis process must play an important role in the use of context in recognition.

Memory and it's function completes the primary functions of the brain. There are three basic types of memory:

 1. Short-term is responsible for the events of the last few seconds. It is very accurate. It involves the storage of the signal long enough to bring context to bear on the recognition process.

 2. Long-term is used to recall knowledge we have acquired, events experienced and ideas from previous thoughts. It is associative in character and stores can not be addressed except by association. This means that some quality of the signal processing mechanism makes some signals more suitable for memorizing than others.

 3. Similarity function store contains the signal processing algorithms. These are the acquired habits of thought. Once stored, they are very difficult to erase but very easy to ignore.
 
It is in the short-term and long-term memories that we remember "facts" and explicit techniques, while it is in the function-store that we either learn or know how to think. Other functions of the brain would include signal processing, learning and adaption. I will discuss these in a later section.

At the heart of the problem of pattern recognition is the concept of similarity. Since no two patterns are identical, the act of pattern recognition is the act of perceiving a degree of similarity between an observed pattern and that in memory. This enables us to then classify the new one. It is therefore critical to apprehend different kinds of similarity, and a very important part of pattern recognition involves selecting the appropriate similarity function.

Pattern recognition nearly always involves some form of iterative process before a firm decision is made. It is either necessary to solve simultaneous equations, or to form a hypothesis of what the pattern must be (usually with highly inadequate data). If the latter, then it must be tested, until it becomes more or less recognizable.

The importance of context in the process of pattern recognition is clear. The kind of similarity to look for in correlating two signals depends on context. A pattern is really nothing more than a feature in the context of other features. This decoding of signals by the use of contextual information is a vital part of all aspects of pattern recognition.
 

A Model for Pattern Recognition:

The repeated pattern of iterative feedback loops reflects a further repeated pattern and demonstrates how signals are processed by the brain. As modeled, a pattern is nothing more than the inter-relationships of the subpatterns comprising it, and these subpatterns are the inter-relationships of various features. Conversely, features are only recognizable in terms of their contexts (the patterns they comprise), and patterns are only recognizable in terms of their environment.

It is therefore expected that all aspects of pattern recognition are performed in the same system. The model proposed has three main iterative loops of which the signal analyzer, the similarity function and the addressing of the associative stores are optimum. Patterns in general differ not so much by some quantitive measure as by some qualitative dissimilarity, or quality of the pattern.

Figure 1 shows a complete block diagram for pattern recognition with a small home-type computer:
 

 
 

(insert figure)
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

Figure 1: Block diagram for pattern recognition feedback loops.
 
 

This type of system was first proposed by Hill (1) in 1969 for a speech recognition machine:

 1. The analyzer contains transducers and circuits which transform the signal into sequences of features.

 2. The associative store should contain templates of feature sequences as well as templates of deep structure and class. The function is to bring contextual information to bear upon the recognition process. Correlation eliminates or reduces errors, and plays a major role in synthesis.

 3. The comparator is where the input feature sequences are organized into a form in which they can search the associative store for similar storage.

 4. The similarity function store contains the algorithms specifying the various types of similarity and classes of patterns it can handle. If you wish the machine to learn, it is into this store that the new algorithms would be written, representing new points of view.

 5. The generalizer is a higher level pattern recognizer in that it identifies similarities between classes. Via the store selector it directs the search through the associative store to those parts of it which are most likely to contain the patterns sought.
 

Every computer whose operation and structure is completely known will consist of two independent systems, the hardware and the software. The hardware contains the memory, input, and output devices, and perform the actual work. The software provides the instructions for what to compute, which alone determines the meaning of the computation.

For example, one could monitor the state of every computing element at all times and, in the case of a binary language, portray this by a table of zeros and ones as a function of time. However, without the knowledge of the software, such a tabulation provides no clue to the meaning of what is being computed. The software alone determines the intelligence content of the computer output.
 

The Software:

New research has demonstrated the capability of showing clear relationships between specific brain output patterns of a given artist and specific types of expressive, artistic activity. In addition, it has recently become possible to isolate aspects of the brain's evoked response to sensory stimuli, physical and imagined.

Clynes (2), a medical doctor who worked at the Research Center in Rockman State Hospital in Orangeburg, New York,  has shown that characteristic and highly repeatable response shapes or waveforms can be recorded from motor activity during the overt expression of a specific emotion or idea or during physical articulation of rhythmic pulses in music from a particular composer.

Recent and current research is showing that the brain's evoked response to a sensory stimulus can be broken down and analyzed in such a way as to relate specific peaks in the evoked response waveform to specific aspects of either the stimulus itself or the processing behavior of the participant. The evoked response is primarily dependent on two factors:

 1. The physical parameters of the stimulus, or

 2. The significance or meaning of the stimulus that is dependent on subjective experience.

E. Roy John (3), a pioneer in the understanding of the brain states:

"When an experienced organism receives a novel and meaningless stimulus and generalization occurs, this new afferent input in a familiar context activates the representational system in such a way as to cause release of a common mode of activity like that stored during the learning experience."

and

"Analogous data from experiments with human beings indicate that phase-locked potentials are released at the time that absent stimuli are expected to occur. Furthermore, the waveshapes released when particular visual stimuli are imagined resemble the waveshapes of potentials evoked by actual presentation of the imagined stimuli."

Clynes took a number of volunteers and shaved their heads, placing a series of electrodes in rosette patterns on various regions of the head. These included the temporal, frontal lobe section and occipital regions of the brain. In this way, not only were brain frequencies monitored, but directional shifts in these frequencies could also be determined by the geometry of the electrode configuration on the skull.

The original purpose of Clynes' work was to find how precision and order exist in brain processes; to discover what is inherently programmed in man and how he might make use of that inherent program.

These individuals were given a number of images (form) and colors to concentrate on while their brain was monitored by computers. Recording from opposite pairs of electrodes simultaneously, he obtained views of the electrical activity from different angles: mathematically, a spatial differentiation of the electrode vector. What he was mapping was consciousness (literal).

He literally mapped fields in the human brain. A computer was able to identify and reproduce those geometrical figures which that human was concentrating on, either as a geometric form, or color of some object. The individual did not even have to look at the pattern, but simply concentrate "in his mind's eye". A standing wave means that the wave is not changed, but is holding itself steady in one certain geometrical thought.

A number of very important observations were made:

 1. Certain qualities and relationships were of greater importance to the computer than such quantitative factors such as intensity. This meant that the brain's system of identification is based on differences, rather than intensity of the signal.

 2. Thin lines were found to produce characteristic evoked potentials, irrespective of size. The form itself is transduced into another form in the brain "space-time" which can be measured. There is a one-to-one correspondence between visual forms of the stimulus, the response forms in the brain, and the perception.

This is, perhaps, the first physical description of the field of an archetype. It is a geometrical structuring and has uniqueness.

 3. The process of inhibition is as important for transducing the external world as is excitation. Concentration on specific lines of geometry does not constitute the changing stimulus, but their steady presence systematically and radically alters the response to another changing stimulus.

 4. Changes in intensity of a single color produce very simple response shape. Light and darkness (as opposites) show no evidence of being different values of the same variable. Rather, they seem to be the result of stimulating and also of inhibiting different receptors. Thus, the evoked potentials to light and darkness in no way may be said to be positive and negative, respectively. White, for example, appears in this view as the result of mutual inhibition of color.

 5. These experiments clearly imply an inherent form of organization and not a random learning of nerve nets. It is possible to mentally recognize and perceive the stimulus within the first portion of the evoked potential. Responses (in the brain) which occur later than 0.3 seconds are seen as systematic processes, or tuned circuits to those responses to specific in-coming stimuli. This is a form of resonance in the brain. They act like keys to "unlock" specific parts of our brain, often being observed below psychological threshold levels (subliminal).
 

Geometry and Archetypes:

It is now evident that every stimulus for corresponds to a particular space-time" shape in the brain (in terms of electrical activity). A computer can even identify these shapes, much like "looking into someone's mind and seeing their pictures". 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 replication. An archetype may then be seen as a specific geometrical system of standing waves occurring in the brain as a "space-time" shape or "key".

In living organisms, opposites receive their structuring of symmetry from particular combinations of spatial and temporal aspects. Like the reins on a horse, each of the opposites of the physiological pair has its own place. While they do balance motion, in themselves they do not cancel each other. This geometric aspect makes them capable of being opposites. The activity of each arm determines the quantity of the turn; the spatial identity of the rein determines the quality. There is no monotonic (or linear) transition from one to the other, passing through some form of "zero".

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. This must involve an 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 a 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 uni-directional 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. In this case, memory could become impossible (as defined).

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 spacial identity of the "rein" determines the quality.

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

The Vector Equilibrium Matrix:

The use of geometry and geometrical forms as video tools offers intriguing possibilities. They allow experiential interaction with archetypes or god-forms. They also grant access to those specific altered states where one experiences the eternal aspect of sacred time: A consciousness of immortality.

A geometrical image is developed in the book THE DIAMOND BODY: A Modern Alchemical View of the Philosopher's Stone (4).  This image comes from the field of solid state physics, corresponding to both the Jewish mystical traditions and current concepts in imaginal psychology. A mathematical model is generated to assist the development of anima consciousness via a visualization exercise, called The Diamond Body Exercise, (DBE).

A series of biological resonances occur between specific internal-state functions and the "outside". These resonance relationships are discussed and specific models are given to aid visualization and resonance. This practice of meditation develops a common ground, uniting psyche with matter. Through the stabilization and equilibrium fostered in the individual during meditation sessions, the individual is brought into increased harmony with the environment. More important, a "repair function" is now available, one able to reverse those entropic functions related to libido.

The DBE is a breakthrough in meditation techniques. Steeped in mystery, the Merkabah Chariot of Sephir-Yetzirah, Ezekiel's vision and "the Cube of Space" are all the samething. It is a regeneration meditation for immortality. And, it is now available to the common household....

It is the contention of this book that the most fundamental (pre)geometric form is the Vector Equilibrium Matrix (VEM). The vector equilibrium construct, first proposed by Buckminster Fuller (5), describes the most economical lines of movement within the atomic nucleus. This geometry form leads directly to the Diamond Body of Cube of Space.

To place oneself inside this structure, or to project this matrix form outward as a visualization, creates and generates a resonance within the "space-time" shapes of the brain. The Vector Equilibrium Matrix is a geometrical mandala resonating with the psychological analog for the Philosopher's Stone!

The Vector Equilibrium Matrix is a visual tool which connects macroscopic structures to quantum modes. It graphically depicts the sphere, whose center is everywhere and whose circumference is nowhere. It can be used as an access tool for realizing multiple quantum ordering.

To begin to understand this form of order, a new tool for perception is needed. The new concepts of order involve the discrimination of the relative differences in "space-time" (and similarities). Attention should now be given to similar differences and different similarities (6).  Such a format in mathematics is called a ratio, or matrix field. "The universe is a cosmic computer on the pre-geometric level of information in which space and time appear as secondary statistical constructs." (7)

The Vector Equilibrium Matrix is such a matrix field; although seen as a geometry at any stage, it is pre-geometric in that it describes the change from one stage to the next. It is a quantized state of information.

A video projection of this Diamond Body structure is now possible, with rotation of axis and "rising on the planes" (from spherical coordinates). The resulting geometries create specific "space-time" patterns in the brain. The resulting patterns allow "access" to those specific archetypes (associated with specific "space-time" patterns). They are known as "Star Gates" or "planetary gates" in mystical literature.
 

Real-Time Color Graphics:

Most problems in complex structure and function require visualization. And, as the size of the structure increases (like "rising on the planes"), a third dimension is needed to give visualization perspective (context).

Real-time color graphics systems have unique advantages for display of information. Studies of the structures and interactions of large biological molecules require both coordinate data and three-dimensional visualization. Software has been developed that now allows real-time display of color line and surface displays (8).  Now that we have hardware and software for selective display of complex objects in color and stereo with real-time rotation, depth cueing, and interaction, a program is now underway to insert the Vector Equilibrium Matrix into this program for use in a video feedback system.

This real-time color graphics system would respond to logic circuitry in the similarity function store.  The feedback from the video section would get up an iteration loop, going from the "space-time" patterns in the brain to the television. A rotation or depth cueing ("rising on the planes") would create a similar (and very specific) corresponding change in the "space-time" pattern.

Most important, this could be done as a pre-programmed response, directing our brain to specifically desired "experiences" or archetypal encounters.
 

Considerations In Design:

A general purpose bio-medical preamplifier should form the front end of any comprehensive system. Accurate frequency discriminations (2-20 Hz) and the feedback system should be capable of responding to peaks or zero crossing of in-band signal oscillations. It must be able to change in signal amplitude.

This means that a good variable threshold detector and envelope follower should be included in the over-all system. The input section should be capable of either AC or DC coupling, depending on specific applications and providing a choice of fixed gain of about 10(3) or variable gain of about 10(5). Other measures such as time spent producing the desired signal are useful but more expensive. They are also less likely to be needed.

The major sources of error are those due to biological sources, electrodes, amplifier, interaction between the amplifier and sources, filtering techniques, and detection circuitry. For example, as EEG signals are among the smallest recordable through gross methods, they are the most plagued by "leakage" from muscle potentials (EKG signals).

Thus, it is necessary to use differential amplifying techniques in order to obtain accurate results, subtracting background signals, commonly a problem between closely placed electrodes. Other factors presenting problems are the high impedance of biological sources, typical 100K ohms or higher on the skin. The body is also a rather good radio/TV antenna, picking us unpredictable DC noise.

Complete designs for comprehensive biological monitoring/feedback units are described by Rosenboom (9).  He and a number of other artists built these units to drive
electronic synthesizers and color organs in the early 1970's. They were essentially creating "alpha-concerts".  A number of shows were performed and the specific logic and hardware is outlined. There is even a design for an Evoked Response Peak Detector design by R. Koehler in this volume.
 

Summary:

The purpose of this paper is to show that, with existing technologies in hardware/software, it is now possible to use the home computer/television as a very powerful tool, where health and expanded mental capabilities are only by-products.

A new dimension in learning and self-realization is available for the home. Biofeedback research has advanced the fields of medicine and health. It is now possible to control and direct specific autonomic functions previously either not available or semi- control over a ten year yoga program. Video feedback systems are now successfully used in learning/education programs.

New models on pattern recognition and the nature of information nets allow for simple models which could be used with home computers (large memory).

The research of Clynes and Hill shows a clear relationship between specific brain output patterns and specific geometry.  A first state for describing the physical analogs to unique archetypes is developed. Specific geometrical images will invoke specificbrain responses.

A formula emerges. The Vector Equilibrium Matrix is a visual tool which connects (or describes) the change from one state to another. It is the method in which a specific "space-time" pattern changes into another with uniqueness. This matrix has already been set into a grid of values and qualities, based on Jewish mystical traditions and current concepts in imaginal psychology.

A mathematical model is generated to assist the development of anima consciousness via a visualization exercise called The Diamond Body Exercise. A video projection of this Diamond Body structure is now possible, in the home. The resulting effects lead to the possibility of pre-programmed response, directing our brain to specifically desired "experiences" or archetypal encounters.

Previous designs for biofeedback systems using audio and visual are described. The immediate applications of this in the home are staggering. Populations can be re-programed and individuals can become self-enlightened. Electronic meditation creates brain-body loops for interaction and control. This state of control is a form of technological transcendence. On the mundane level, this proposed system could be used to loose weight, stop smoking and change other deep habits.
 

Conclusions:

There is obviously a very immediate need for research. The implications of this range from mass brain washing to expanded consciousness for all of mankind. Approximately 95% of the households in the United States have at least one television set. Home computers will be similar with another ten.

The design problems for this type of system are minimal. Hardware now exists in a variety of markets and is competitive. The installation is also simple, plugging RF inputs to the  antenna leads of any TV system. All bio-monitoring equipment is similarly fashioned to the body, with some form of isolation (optical). They probably will be available within five years through such game systems as Odyssey or Atari.

The next advance will be a brain switch, via neuro-electronic correlates. Already there is known to be another "sensory motor" in-put in the microwave region (0.3-3.0 GHz) (10).  A feature called Contingent Negative Variation (CNC) has been isolated as a facet of the EEG through computer fourier analysis and somehow corresponds to will. The two are related somehow but not known.

CNV relates to the cessation of neutral scanning when an object or event is recognized. An individual could learn to trigger the appearance of the CNV even without the presence of any object. It is conceivable that this "switch" could trigger an implanted brain-terminal to some central computer. Data transmission might be via direct brain communication in this microwave region.

The other side of this technological advance is that unscrupulous advertiser who might attempt to sell his products via sub-liminal geometrical/color patterns in his
advertisements. Since most of us do not have conscious awareness of this new sense, it obviously is submerged into the unconsciousness. If this is true, and it does in fact appear so, then one country could conceivably broadcast specific microwave patterns toward their neighbor to somehow affect the social or group consciousness.

It appears as if, with all other "breakthroughs", it is a double-edged blade. The future could contain such changes with this type of system, that the "school" concept is
changed, and classes are in the home. While only 10% of the cerebral cortex is used now, a major jump in use and access will occur with the advent of this concept in learning.

It is quite conceivable that the future will also allow for new concepts in our relationship to "time" and "space". Uniting psyche with matter has always been
associated with immortality:
 
 

"To practice the ecology of the soul is to recycle ones consciousness"
   Viduru Telemahandi
   The Church of Self Amplification.
 

 FOOTNOTES:
 

(1) Hill, D.R. (1969). An ESOTerIC approach to some problems in automatic speech recognition. Int. J. Man-Machine Studies, 1, 101.

(2) Clynes, M. and Milsum, J. (ed.) Biomedical Engineering Systems, Chapter 7: "Toward A View of Man", McGraw-Hill Books, N.Y., 1970.

(3) John, E.R., "Switchboard Verses Statistical Theories of Learning and Memory", Science, Vol. 177, No. 4052, 1972.

(4) Stone, Philo: THE DIAMOND BODY: A Modern Alchemical View of the Philosopher's Stone, ITI. Ltd., NY (1983).

(5) Fuller, Buckminster: SYNERGETICS 2, Macmillan Pub., NY (1979).

(6) Bohm, David: Wholeness and the Implicate Order, London, Routledge & Kegan Paul, 1980.

(7) Professor David Finkelstein at Yeshiva University in a lecture.

(8) Langridge, R., et al: "Real-Time Color Graphics in Studies of Molecular Interactions", Science, Vol. 211, No. 13, Feb. 1981, pp 661-666.

(9) Rosenboom, David (ed): Biofeedback and the Arts: Results of  Early Experiments, A.R.C. Publications, Vancouver, Canada, 1976.

(10) Frey, Allen N.: "Human Perception of Illumination with Pulsed Ultrahigh Frequency Electromagnetic Energy", Science, Vol.181, July 1973, p556-8.
 
 

 BIBLIOGRAPHY:
 

Bohm, David: Wholeness and the Implicate Order, London, Routledge & Kegan Paul, 1980.

Clynes, M. and Milsum, J. (Ed.): Biomedical Engineering Systems, Chapter 7: "Toward A View of Man", McGraw-Hill Books, NY, 1970.

Frey, Allen H.: "Human Perception of Illumination with Pulsed Ultrahigh-Frequency Electromagnetic Energy", Science, Vol.181, July 1973.

Fuller, Buckminster: Synergetics 2, Macmillan Pub., NY, 1979.

Hill, D.R.: Int. J. Man-Machine Studies, #1, "An ESOTerIC approach to some problems in automatic speech recognition", ;101, 1969.

John, E. Roy: :Switchboard Verses Statistical Theories of Learning and Memory", Science, Vol. 177, #4052, 1972.

Langridge, R. et al: "Real-Time Color Graphics in Studies of Molecular Interactions", Science, Vol. 211, #13, Feb. 1981.

Rosenboom, David (Ed.): Biofeedback and the Arts: Results of Early Experiments, A.R.C. Publications, Vancouver, Canada, 1976.

Stone, Philo: The Diamond Body: A Modern Alchemical View of the Philosopher's Stone, ITI, Ltd, NY (to be published).
 



C.  THE DIAMOND BODY:
      A VIDEO-YANTRA FOR SELF-REALIZATION

There is an inherent relationship between numbers and archetypes. Several cultures have made use of these correspondences. For instance, the letters of the Hebrew, Greek, and Mayan alphabets correspond directly with numbers and the archetypal patterns (or gods) they represent.

Number encodes the behavior of archetypal dynamics. Archetypes are given to manifesting themselves in an "ordered sequence." The number field is a subjective and objective reality. Number can express a qualitative aspect as well as measure quantities.

The element connecting the sequence of archetypal images with the series of natural numbers seems to be the libido, psychic energy (psychological term), or psi energy (parapsychological term). The archetypes constitute eternal timeless forms of order on one hand, which become temporal forms when our consciousness begins to operate with them. Jung has described number as the most accessible primitive manifestation of this transcendental spontaneous principle of movement in the psyche.

The underlying field potential of the natural number sequence (Nuit) provides a common framework for the alchemical marriage of psyche and matter which forms the Philosopher's Stone. It is possible to formulate individual transformative equations in the field of numbers and archetypes. Understanding occurs when the human beingresonates with the pattern of the number field. (Note the derivations of pattern = pater = father; matrix = mater = mother).

This experience of "one world," the unified field of psyche and matter, is part of a magickal process, that of creating the Philosopher's Stone. It involves a conscious pathworking, participating in archetypal patterns through active imagination. Active imagination functions primarily through the process of visualization. This may be aided by electronic means! It is easier to hold a visualization when it is projected onto a video screen.

In magick, one uses the will to pursue a self-motivated course of action, involving ceremonial or ritual. Rituals involve employment of geometrical "keys" to evoke specific archetypal patterns into manifestation on the intellectual, emotional, or physical plane.

Ceremonial elements are coordinated by drawing from the system of correspondences known as QBL, or Qabalah. In QBL, the numbers 1-10 (Spheres) express archetypal modes-of-being, and 0-XXI (Paths) represent the dynamics of their interrelationship as they relate to the transformative process of the human psyche. Thus, the glyph of the Tree of Life represents every possible condition of human existence, both the givens and the potentials. From it, we can determine the motivation-factor at the core of any temporal development which emerges from the latent pattern in the number field.

To sum up: numbers appear to represent both an attribute of matter and the unconscious foundation of our mental processes. For this reason, number forms, according to Jung, that particular element that unites the realms of matter and psyche. It is "real" in a double sense, as an archetypal image and as a qualitative manifestation in the realm of outer-world experience. Number thereby throws a bridge across the gap between the physically knowable and the imaginary. In this manner it operates as a still largely unexplored midpoint between myth (the psychic) and reality (the physical), at the same time both quantitative and qualitative, representational and irrepresentational.(1)

The circuit of the Tree of Life may be projected in six directions: Above, below, E.,W.,N.,S. from directions given in the ancient Hebrew text, Sephir Yetzirah, The Book of Formation.

This projection forms an octahedron within a cube, the crystalline structure of the diamond. These trees have a common center in Malkuth, the physical plane. The points of the octahedron lie in the centers of the plane faces of the enclosing cube. This is the Diamond Body or Philosopher's Stone, a symbol of the Self.

There is a connection between the strict mathematical order of this crystal form and the concept of archetypes. In Number and Time, M.L. Von Franz quotes Werner Nowacki concerning the spiritual aspect of symmetry elements in crystals:

Symmetries are formal factors which regulate material data according to set laws. A symmetry element or a symmetry operation is in itself something irrepresentational. Only when--as in the present case--it has an effect upon something material does it become both representational and comprehensible. As primal images the symmetry groups underlie, as it were, crystalized matter; they are the essential patterns according to which matter is arranged in a crystal.(2)

The geometrical dual of the Diamond Body figure (the Philosopher's Stone was a "double thing") is the Vector Equilibrium Matrix. This geometry coincides with the 6-directional projection of the Tree of Life, discovered by Frater Achad (Charles Stanfield Jones) and described in The Anatomy of the Body of God.

Combining the geometry of the Tree of Life with the V.E.M. is a way of graphically showing equilibration and symmetry amongst the various components of existence, both psychological and physical. This geometrical glyph forms a meditation key useful as a visualization aid to achieve Self-Realization.
 

 
 

(Enclose Picture A)
 
 

 
 

PLATE B
 
 
 
 
 
 
 
 
 
 
 
 
 
 

THE MACROCOSMIC SNOWFLAKE

From Frater Achad; Anatomy of the Body of God, N.Y., Weiser, 1976. pg. 53.
 
 

(Enclose Picture B)
 
 
 
 
 
 
 
 
 
 
 
 
 

HEXAGRAM OF THE HEART CENTER
Figure shows the relationship of the Vector Equilibrium Matrix to the geometrical circuit of the Tree of Life. The geometrical progression centers on Tiphareth, the Heart Center. With infinite expansion, the spherical progression of the center would encompass the entire Cube, as shown.
 Meditation upon a geometrical form, or talisman, is a rudimentary form of feedback. Modern techniques for influencing EM fields include biofeedback. Biofeedback (bio means life; feedback means return to the source) experiments indicate that man can practice control over his inner body functions.
 
 

(Enclose Picture C)
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

Biofeedback experimentation has been found to be extremely well suited to the Western mind. Research and experience has shown it to be a rapid and promising means toward such goals as self-awareness, self-exploration, and self-control. This could mean anything from balancing the personality to breaking unwanted habits.

In Tibetan Buddhism, a YANTRA is an instrument of contemplation or meditation which aids concentration by narrowing down the psychic field of vision and restricting attention to the center. It provides a focus for self-immersion with the purpose of realizing inner experience.

Other types of psycho-physical changes might occur as one contemplates the form of the Philosopher's Stone. As in certain methods of yogic experience of the psychic spectrum becomes progressively subtle as one moves toward the center of the V.E.M.

The will is used to focus the psyche, balancing the continuous flux of mental activity. Once the adept understands the working of the senses in perceptual filtering, (s)he should harness the mind. Mental fluctuations are produced by the psyche's contact with phenomenal existence. Stilling the mind yields access to fundamental patterns underlying manifestation.

Meditation nears the center of the figure, the symbol of final release. It represents the innermost center of consciousness, the abode of the supreme goddess Nuit, whose mysterious presence is experienced in the depths of one's being. The anomaly at the center of the V.E.M represents the threshold of matter.

This center which is nowhere (Now-Here) marks the limit of the spiritual quest where outer life ends and inner life begins. The Qabalists expressed this by the phrase "Kether is in Malkuth." In the nexus of the V.E.M. there is no shape, and no form, for ALL is immersed in the void.

Ideally, this visual yantra is internalized; it becomes a psychic complex constellating the higher Self. This cosmic truth, embodied in the adept, produces illumination.

In another type of meditation, known as RISING ON THE PLANES, the adept can experience both evolution and involution. The ability of the Philosopher's Stone to generate its own geometrical projection toward infinity makes it a "ladder" reaching from microcosmic to macrocosmic proportions.

After using a pre-recorded videocassette program of the Diamond Body geometry to imprint the matrix in the mind, the adept can mentally construct the entire image of the Philosopher's Stone from the center. This is a recreation of the cosmos unfurling itself in the process of evolution.

Once the whole image has been visualized (its shorthand form is the V.E.M.), he begins his meditation from the outermost periphery of the figure. Moving consciousness inwards, plane after plane, he symbolically reproduces the dissolution of all the cosmic principles represented by the Spheres and Paths.

Through such a meditation, the adept experiences the drama of ascent and descent of the soul into the phenomenal world. This "purifies" the adept's consciousness through an initiatory death and rebirth. After attaining the sought-after identification with the Self, the extended consciousness which is symbolized by the V.E.M. contracts on itself and vanishes into the VOID (outside of the geometrical parameters of space and time).
 

______________________________________________________________________________
(1) Von Franz, M.L., Number and Time, Northwestern University Press, Evanston, 1974.
(2) Ibid.
 
 

 D.  SOME FINAL COMMENTS

Our original aim, as stated, was to find a unitarian language or code, with corresponding concepts between the unconscious and matter.

This unitarian language was postulated as alchemy, and developed through recourse to the philosophy of Qabala and the fields of physics, psychology, and magick.

A cross-disciplinary description was developed for the Philosopher's Stone, the goal of alchemy.  The Stone was described as consisting of the geometrical reciprocals, the Vector Equilibrium Matrix and the Diamond Body.  This description is mathematical as well as philosophical.

Cross-references were developed between Western (magick) and Eastern (yoga) forms of mysticism.  In doing so, we created an immortal body, and "made psyche matter."

A model of Nuit as the Isotropic Vector Matrix was developed, ("thou art continuous...").  Also, She was postulated as the "nuclear nothingness" in the center of the V.E.M. and the Ain of the Diamond Body figure.  The ALEPH/TAU of sacred time--the realm of immortality, because it is prior to the world of transient forms.  This spiritual matrix of all matter is indeed eternal. 'Nothing' matters, with or without it!

This model, giving a conceptual description of the spiritual aspect of subatomic processes, is an on-going description of the original creation.  It allows us to conceptualize the spiritual aspect of the subatomic threshold of matter.

We described application of the Stone: the process of applying one's Self produces psychological insight and mystical experience.  We can choose to apply ourselves to the Great Work, and immerse ourselves in the autonomous stream of psychic imagery, becoming a frequent traveler in that realm.

We explored the unity of psyche and matter by describing physical properties of archetypes, but without falling prey to literalism.  While the correspondences are explicit, they remain metaphorical.  We have attempted to unite our spiritual position with the body, through the medium of resonance.

We have, within the modelling, fulfilled or justified the key descriptors used by medieval alchemists to transmit the qualities the Stone must possess to be judged true.

Practical and speculative information was communicated.  But the art of soul-making requires individual work: the Great Work.  Jung described the alchemical task:

The adept produces a system of fantasies that have a special meaning for him.  Although he keeps within the general framework of alchemical ideas, he does not repeat a prescribed pattern, but following his own fancy devises an individual series of ideas and corresponding actions which it is evident have symbolic character.  He starts with production of the medicine that will unite his spiritual position with the body.  The image of the self (golden quaternity) draws a quintessence out of the chthonic spirit.(1)
 
 

[The Diamond Body Meditation Aid]
 
 

 Presentation of concepts is a form of circulatio, tying together the beginning (Aleph) and the end (Tau) of the book.  And like circulatio, this material can be worked again, and again, and again.

We've attempted to sublimate, or ennoble matter.  And attempted to coagulate spirit, or "make it matter," in a physical form (i.e. a book, art-piece, or other creativity).

We have attempted to show that spiritual science is independent of any particular religious bias, either monotheistic or polytheistic.  The V.E.M. figure is a symbolic unification of both modes.

The mystical paths of diverse religions confer the same topological realm, whether experiences are called by Christian, Jewish, Muslim, or Hindi names.  The available experiences have been described by the Saints of all religions.  There was a Way for souls to go home to godhead before Buddha, or Christ, or Confuscious, etc.

There are two routes on the Path of Return: that of exaltation of the imagination, or of the via negativa, or detachment from the inner drama.  Both are ways of ridding the soul of mind and matter.  These are progressively subtle distinctions.

Jung has said, "...Who now has any sympathy with the perplexities of an investigator who busies himself with magical substances."

When the "magical substances" and the concerns of microphysics are congruent, we have "seen through" the Philosopher's Stone.  We have peered into the Stone, itself and seen the marvel of the Creation.  And we have also seen by means of the Stone, into the process of soul-making.

There is no conceptualization past this point, except to empty out the mind of all symbolic contents and merge back into God.  This of course is the Vision Across the Abyss.  It is further working of Path 13, II, THE HIGH PRIESTESS which the aspirant must cross to reach the final goal, Kether.

Perhaps the following correspondences will provoke further intuitions from the reader:

 DIAMOND BODY = 179 + 86 = 265 = 13

 13 = Love, Unity

 490 = 13 = perfect

 463 = 13 = crystal, glass

 571 = 13 = balance

 580 = 13 = rich, ancient

 607 = 13 = Adam Primus

 706 = 13 = lilies or roses

 832 = 13 = Albedo Crystalli

 850 = 13 = blue, my perfect one

 346 = 13 = a spring, spring water, a water pipe or channel, good pleasure, the Will-power

 418 = 13 = The Word of the Aeon, ABRAHADABRA

 bohu = 13 = emptiness, chaos, void

 hegen = 13 = Sound, muttering, thought, musing
 

______________________________________________________________________________
(1) C.G. Jung, ALCHEMICAL STUDIES, Princeton University Press
 
 
 

C.  THE DIAMOND BODY:
      A VIDEO-YANTRA FOR SELF-REALIZATION

There is an inherent relationship between numbers and archetypes. Several cultures have made use of these correspondences. For instance, the letters of the Hebrew, Greek, and Mayan alphabets correspond directly with numbers and the archetypal patterns (or gods) they represent.

Number encodes the behavior of archetypal dynamics. Archetypes are given to manifesting themselves in an "ordered sequence." The number field is a subjective and objective reality. Number can express a qualitative aspect as well as measure quantities.

The element connecting the sequence of archetypal images with the series of natural numbers seems to be the libido, psychic energy (psychological term), or psi energy (parapsychological term). The archetypes constitute eternal timeless forms of order on one hand, which become temporal forms when our consciousness begins to operate with them. Jung has described number as the most accessible primitive manifestation of this transcendental spontaneous principle of movement in the psyche.

The underlying field potential of the natural number sequence (Nuit) provides a common framework for the alchemical marriage of psyche and matter which forms the Philosopher's Stone. It is possible to formulate individual transformative equations in the field of numbers and archetypes. Understanding occurs when the human beingresonates with the pattern of the number field. (Note the derivations of pattern = pater = father; matrix = mater = mother).

This experience of "one world," the unified field of psyche and matter, is part of a magickal process, that of creating the Philosopher's Stone. It involves a conscious pathworking, participating in archetypal patterns through active imagination. Active imagination functions primarily through the process of visualization. This may be aided by electronic means! It is easier to hold a visualization when it is projected onto a video screen.

In magick, one uses the will to pursue a self-motivated course of action, involving ceremonial or ritual. Rituals involve employment of geometrical "keys" to evoke specific archetypal patterns into manifestation on the intellectual, emotional, or physical plane.

Ceremonial elements are coordinated by drawing from the system of correspondences known as QBL, or Qabalah. In QBL, the numbers 1-10 (Spheres) express archetypal modes-of-being, and 0-XXI (Paths) represent the dynamics of their interrelationship as they relate to the transformative process of the human psyche. Thus, the glyph of the Tree of Life represents every possible condition of human existence, both the givens and the potentials. From it, we can determine the motivation-factor at the core of any temporal development which emerges from the latent pattern in the number field.

To sum up: numbers appear to represent both an attribute of matter and the unconscious foundation of our mental processes. For this reason, number forms, according to Jung, that particular element that unites the realms of matter and psyche. It is "real" in a double sense, as an archetypal image and as a qualitative manifestation in the realm of outer-world experience. Number thereby throws a bridge across the gap between the physically knowable and the imaginary. In this manner it operates as a still largely unexplored midpoint between myth (the psychic) and reality (the physical), at the same time both quantitative and qualitative, representational and irrepresentational.(1)

The circuit of the Tree of Life may be projected in six directions: Above, below, E.,W.,N.,S. from directions given in the ancient Hebrew text, Sephir Yetzirah, The Book of Formation.

This projection forms an octahedron within a cube, the crystalline structure of the diamond. These trees have a common center in Malkuth, the physical plane. The points of the octahedron lie in the centers of the plane faces of the enclosing cube. This is the Diamond Body or Philosopher's Stone, a symbol of the Self.

There is a connection between the strict mathematical order of this crystal form and the concept of archetypes. In Number and Time, M.L. Von Franz quotes Werner Nowacki concerning the spiritual aspect of symmetry elements in crystals:
 

Symmetries are formal factors which regulate material data according to set laws. A symmetry element or a symmetry operation is in itself something irrepresentational. Only when--as in the present case--it has an effect upon something material does it become both representational and comprehensible. As primal images the symmetry groups underlie, as it were, crystalized matter; they are the essential patterns according to which matter is arranged in a crystal.(2)


The geometrical dual of the Diamond Body figure (the Philosopher's Stone was a "double thing") is the Vector Equilibrium Matrix. This geometry coincides with the 6-directional projection of the Tree of Life, discovered by Frater Achad (Charles Stanfield Jones) and described in The Anatomy of the Body of God.

Combining the geometry of the Tree of Life with the V.E.M. is a way of graphically showing equilibration and symmetry amongst the various components of existence, both psychological and physical. This geometrical glyph forms a meditation key useful as a visualization aid to promote Self-Realization.
 

(Enclose Picture A)

THE MACROCOSMIC SNOWFLAKE

From Frater Achad; Anatomy of the Body of God, N.Y., Weiser, 1976. pg. 53.
 
 

(Enclose Picture B)
 

HEXAGRAM OF THE HEART CENTER
Figure shows the relationship of the Vector Equilibrium Matrix to the geometrical circuit of the Tree of Life. The geometrical progression centers on Tiphareth, the Heart Center. With infinite expansion, the spherical progression of the center would encompass the entire Cube, as shown.
 Meditation upon a geometrical form, or talisman, is a rudimentary form of feedback. Modern techniques for influencing EM fields include biofeedback. Biofeedback (bio means life; feedback means return to the source) experiments indicate that man can practice control over his inner body functions.
 
 

(Enclose Picture C)
 

Biofeedback experimentation has been found to be extremely well suited to the Western mind. Research and experience has shown it to be a rapid and promising means toward such goals as self-awareness, self-exploration, and self-control. This could mean anything from balancing the personality to breaking unwanted habits.

In Tibetan Buddhism, a YANTRA is an instrument of contemplation or meditation which aids concentration by narrowing down the psychic field of vision and restricting attention to the center. It provides a focus for self-immersion with the purpose of realizing inner experience.

Other types of psycho-physical changes might occur as one contemplates the form of the Philosopher's Stone. As in certain methods of yogic experience of the psychic spectrum becomes progressively subtle as one moves toward the center of the V.E.M.

The will is used to focus the psyche, balancing the continuous flux of mental activity. Once the adept understands the working of the senses in perceptual filtering, (s)he should harness the mind. Mental fluctuations are produced by the psyche's contact with phenomenal existence. Stilling the mind yields access to fundamental patterns underlying manifestation.

Meditation nears the center of the figure, the symbol of final release. It represents the innermost center of consciousness, the abode of the supreme goddess Nuit, whose mysterious presence is experienced in the depths of one's being. The anomaly at the center of the V.E.M represents the threshold of matter.

This center which is nowhere (Now-Here) marks the limit of the spiritual quest where outer life ends and inner life begins. The Qabalists expressed this by the phrase "Kether is in Malkuth." In the nexus of the V.E.M. there is no shape, and no form, for ALL is immersed in the void.

Ideally, this visual yantra is internalized; it becomes a psychic complex constellating the higher Self. This cosmic truth, embodied in the adept, produces illumination.

In another type of meditation, known as RISING ON THE PLANES, the adept can experience both evolution and involution. The ability of the Philosopher's Stone to generate its own geometrical projection toward infinity makes it a "ladder" reaching from microcosmic to macrocosmic proportions.

After using a pre-recorded videocassette program of the Diamond Body geometry to imprint the matrix in the mind, the adept can mentally construct the entire image of the Philosopher's Stone from the center. This is a recreation of the cosmos unfurling itself in the process of evolution.

Once the whole image has been visualized (its shorthand form is the V.E.M.), he begins his meditation from the outermost periphery of the figure. Moving consciousness inwards, plane after plane, he symbolically reproduces the dissolution of all the cosmic principles represented by the Spheres and Paths.

Through such a meditation, the adept experiences the drama of ascent and descent of the soul into the phenomenal world. This "purifies" the adept's consciousness through an initiatory death and rebirth. After attaining the sought-after identification with the Self, the extended consciousness which is symbolized by the V.E.M. contracts on itself and vanishes into the VOID (outside of the geometrical parameters of space and time).
 

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(1) Von Franz, M.L., Number and Time, Northwestern University Press, Evanston, 1974.
(2) Ibid.
 

 D.  SOME FINAL COMMENTS

Our original aim, as stated, was to find a unitarian language or code, with corresponding concepts between the unconscious and matter.

This unitarian language was postulated as alchemy, and developed through recourse to the philosophy of Qabala and the fields of physics, psychology, and magick.

A cross-disciplinary description was developed for the Philosopher's Stone, the goal of alchemy.  The Stone was described as consisting of the geometrical reciprocals, the Vector Equilibrium Matrix and the Diamond Body.  This description is mathematical as well as philosophical.

Cross-references were developed between Western (magick) and Eastern (yoga) forms of mysticism.  In doing so, we created an immortal body, and "made psyche matter."

A model of Nuit as the Isotropic Vector Matrix was developed, ("thou art continuous...").  Also, She was postulated as the "nuclear nothingness" in the center of the V.E.M. and the Ain of the Diamond Body figure.  The ALEPH/TAU of sacred time--the realm of immortality, because it is prior to the world of transient forms.  This spiritual matrix of all matter is indeed eternal. 'Nothing' matters, with or without it!

This model, giving a conceptual description of the spiritual aspect of subatomic processes, is an on-going description of the original creation.  It allows us to conceptualize the spiritual aspect of the subatomic threshold of matter.

We described application of the Stone: the process of applying one's Self produces psychological insight and mystical experience.  We can choose to apply ourselves to the Great Work, and immerse ourselves in the autonomous stream of psychic imagery, becoming a frequent traveler in that realm.

We explored the unity of psyche and matter by describing physical properties of archetypes, but without falling prey to literalism.  While the correspondences are explicit, they remain metaphorical.  We have attempted to unite our spiritual position with the body, through the medium of resonance.

We have, within the modelling, fulfilled or justified the key descriptors used by medieval alchemists to transmit the qualities the Stone must possess to be judged true.

Practical and speculative information was communicated.  But the art of soul-making requires individual work: the Great Work.  Jung described the alchemical task:

The adept produces a system of fantasies that have a special meaning for him.  Although he keeps within the general framework of alchemical ideas, he does not repeat a prescribed pattern, but following his own fancy devises an individual series of ideas and corresponding actions which it is evident have symbolic character.  He starts with production of the medicine that will unite his spiritual position with the body.  The image of the self (golden quaternity) draws a quintessence out of the chthonic spirit.(1)
 
 

[The Diamond Body Meditation Aid]
 
 

 Presentation of concepts is a form of circulatio, tying together the beginning (Aleph) and the end (Tau) of the book.  And like circulatio, this material can be worked again, and again, and again.

We've attempted to sublimate, or ennoble matter.  And attempted to coagulate spirit, or "make it matter," in a physical form (i.e. a book, art-piece, or other creativity).

We have attempted to show that spiritual science is independent of any particular religious bias, either monotheistic or polytheistic.  The V.E.M. figure is a symbolic unification of both modes.

The mystical paths of diverse religions confer the same topological realm, whether experiences are called by Christian, Jewish, Muslim, or Hindi names.  The available experiences have been described by the Saints of all religions.  There was a Way for souls to go home to godhead before Buddha, or Christ, or Confuscious, etc.

There are two routes on the Path of Return: that of exaltation of the imagination, or of the via negativa, or detachment from the inner drama.  Both are ways of ridding the soul of mind and matter.  These are progressively subtle distinctions.

Jung has said, "...Who now has any sympathy with the perplexities of an investigator who busies himself with magical substances."

When the "magical substances" and the concerns of microphysics are congruent, we have "seen through" the Philosopher's Stone.  We have peered into the Stone, itself and seen the marvel of the Creation.  And we have also seen by means of the Stone, into the process of soul-making.

There is no conceptualization past this point, except to empty out the mind of all symbolic contents and merge back into God.  This of course is the Vision Across the Abyss.  It is further working of Path 13, II, THE HIGH PRIESTESS which the aspirant must cross to reach the final goal, Kether.

Perhaps the following correspondences will provoke further intuitions from the reader:

 DIAMOND BODY = 179 + 86 = 265 = 13

 13 = Love, Unity

 490 = 13 = perfect

 463 = 13 = crystal, glass

 571 = 13 = balance

 580 = 13 = rich, ancient

 607 = 13 = Adam Primus

 706 = 13 = lilies or roses

 832 = 13 = Albedo Crystalli

 850 = 13 = blue, my perfect one

 346 = 13 = a spring, spring water, a water pipe or channel, good pleasure, the Will-power

 418 = 13 = The Word of the Aeon, ABRAHADABRA

 bohu = 13 = emptiness, chaos, void

 hegen = 13 = Sound, muttering, thought, musing
 

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(1) C.G. Jung, ALCHEMICAL STUDIES, Princeton University Press