THE UNIFICATION OF

MIND AND MATTER

----------

A PROPOSED SCIENTIFIC MODEL

ROBERT L. SHACKLETT, Ph.D.

WILLIAM C. GOUGH, M.S.

Submitted to the Journal

Subtle Energies

Copyright 1991 by W.C. Gough & R. L. Shacklett

TABLE OF CONTENTS

PAGE NUMBER


ABSTRACT 1




SECTION I: BASIC ISSUES


INTRODUCTION 2


PICTURES OF REALITY 2


THE SCIENTIFIC APPROACH -- A PUZZLE 3


THE PROPOSED MODEL -- THE BASICS 4


BASIC ASSUMPTIONS 6




SECTION II: THE FOUNDATIONS IN PHYSICS FOR THE MODEL


THE ROOTS OF MATTER 7


THE WORLD ACCORDING TO QUANTUM MECHANICS 8


THE BOTTOM OF SPACE-TIME 10


THE QUANTUM VACUUM 12


THE UNIFICATION PROGRAM 14


PATTERNS IN THE PHYSICAL WORLD 15




SECTION III: THE REALITY BEYOND SPACE-TIME


JUNG, PAULI, AND ARCHETYPES 18


MATHEMATICS AND THE MENTAL REALM 24


LANGUAGE AND THE MENTAL REALM 25


EXAMPLE 1: READWARE 26


EXAMPLE 2: MERU 27




SECTION IV: THE MECHANISM FOR LINKING MIND AND MATTER


THE PROPOSED MODEL -- THE DETAILS 29


FIBER BUNDLES 30


NON-LOCALITY 32


TWISTORS AND NON-LOCALITY 34




SECTION V: DYNAMICS OF THE MODEL


THE ISSUE OF DYNAMICS 37


SELF-REFERENCE AND FEEDBACK 37


FRACTALS AND SCALING 38


COMPLEX NUMBERS 39

MATRICES 40


MEMORY 41


INTERPRETATION 41




SECTION VI: EVIDENCE IN THE PHYSICAL WORLD TO SUPPORT THE MODEL


SIMPLE SYSTEMS AND MORPHIC RESONANCE 42


IDENTICAL TWINS 43


THE BRAIN 45


LEAST ACTION AND CONSTRAINTS 49


CONSTRAINTS AND THE BRAIN 52




SECTION VII: PERSONAL APPLICATIONS AND SUMMARY


HUMAN PERCEPTION 53


CONSCIOUS AWARENESS 57


OUR THINKING BODIES 59


EXPERIENCING THE SPACELESS-TIMELESS REALM 60


SUMMARY AND IMPLICATIONS 60


REFERENCES 62

FIGURES

Cover: DNA Molecule (Sec. II)


1. Schematic Representation of the Model (Sec. I)


2. Relation of Levels to Each Other (Sec. I)


3. The Scale of Small Things (Sec. II)


4. Flatlander Observing Effects of a Falling 3D Man (Sec. II)


5. LBL Picture of the Atoms in Mullite (Sec. II)


6. Light Interference Patterns - Mandalas (Sec. II)


7. Experimental Arrangement for Generation of Hebrew and Arabic
Letter Forms (Sec. III)


8. Twistor - From Cover of Twistor Newsletter (Sec. IV)


9. Detailed Description of the Model - Causal Linkages of Model
(Sec. IV)


10. Fractal Fern (Sec. V)


11. Compass Termite Mounds (Sec. VI)


12. Neurons Firing in a Monkey's Brain (Sec. VI)


13. Perception of Invisible Triangle (Sec. VII)


14. Perception of Two Table Tops (Sec. VII)

Robert L. Shacklett, Ph.D.
William C. Gough, M.S.



ABSTRACT

This paper outlines a proposed scientific model with the goal of stimulating a new vision towards resolving the Mind-matter question. Scientific is defined to mean that the "parts" or links already exist as useful concepts in the scientific community. The model with supporting evidence will propose that a connection exists between the realms of Mind and matter and that this connection can be understood in terms of existing scientific concepts without invoking any new interactions or "particles." To consider the proposed unification of Mind and matter, it will be necessary to highlight potential underlying belief systems and the assumptions they entail.

The paper will first examine the Mind-matter boundary of space-time from the side that physics is concerned about, being careful to point out that we are using a tool of the mind -- mathematics -- in the process. The paper will illustrate that the boundary is permeable, more like a sponge than the solid wall that conventional science has believed in for so long. Next the paper will take a look at what lies beyond space-time, realizing that this time there is little scientific tradition on which to base the argument that Mind has any connection to physical world of space-time. However, the individual strands of evidence will be woven together until they hopefully become persuasive. This will include the work of Carl Jung and Wolfgang Pauli on archetypes, the relation of the archetypal hypothesis to "number," and modern research on the "hidden" meaning of the ancient sacred alphabets and sacred texts.

Once the realms of matter and Mind have been covered and the linkage established, the dynamics across the linkage will be discussed assuming a self-referencing cosmos in which feedback processes abound. Evidence will be provided from the familiar physical world to support this assumption. To appreciate how the model helps us better understand our individual reality, the nature of human perception will be examined. The concepts of the model will then be extended, and its implications to our world of everyday life will be explored with emphasis upon the connection between the mind and the brain/body complex in health and illness. The model will be used to illustrate the underlying basis for some of the ancient and modern body and mind healing techniques.


SECTION I: BASIC ISSUES


INTRODUCTION

The Mind-matter question is of fundamental significance in philosophy and science. The nature of the connection has been a subject of speculation and dispute ever since Descartes enunciated his famous "Cogito ergo sum" over three centuries ago. This paper presents a proposed scientific model with the goal of stimulating a new vision towards resolving the Mind-matter question. (The use of the capital M in "Mind" will be discussed below.) Both authors have worked jointly to create this new vision. One author (RLS) has focused upon the necessity for a mathematical realm of patterns beyond the physical space-time universe capable of "embodying" Mind, and establishing a credible linkage to that realm based upon accepted scientific principles. The other author (WCG) has focused upon the nature of this realm of patterns beyond space-time and the dynamics of how it manifests into our everyday reality, and establishes meaning through an inner world that includes emotions and feelings.

To consider our proposed unification of Mind and matter, one must be aware of his or her underlying belief systems and the implicit assumptions they entail. Most persons in the Western world hold one or more of the following three assumptions:

1) Space-time is the "container" for all of reality.

2) The meaning of the principal abstract symbols used in
human thought is that numbers only stand for quantities
and that letters only represent the building blocks of
words.

3) The world we perceive is identical to the world "out
there."

If the reader holds any of these assumptions, we request that they be placed in abeyance until completion of this paper.


PICTURES OF REALITY

Any serious probe into philosophical questions requires some degree of consideration be given to the relevant epistomological issues. How do we know what we know (or believe) about "X"? For this paper X is the relationship between Mind and matter. A first approximation might suggest that the question should divide easily between inner knowledge about mental states and outer knowledge arrived at by scientific means.

However, what science has told us may come as a surprise, as the following quote by the mathematician Morris Kline illustrates.

We have therefore come to accept that the real world is not what our unchallenged senses tell us or what our limited perceptions enable us to say but rather what man's major mathematical theories tell us. In the case of Euclidian geometry, although the concepts of point, line, plane, and the like are idealizations, they are idealizations of real objects and one can point to real points, lines, and planes as the reality. What should we point to in the cases of gravitational force and electromagnetic waves? We observe their effects. But what is physically real beyond the mathematics? Not even physical pictures, admittedly imaginative, suffice to explain the nature of these forces and fields. It seems impossible to escape the conclusion that mathematical knowledge is our only grasp of some parts of reality. (Kline, 1985, p. 200)

Hence, this paper will focus attention on understanding mathematical tools as well as how they are used in the quest to comprehend the nature of reality.


THE SCIENTIFIC APPROACH -- A PUZZLE

The perspective of Cartesian dualism, i.e., the separation of Mind and matter, has usually worked to the advantage of science, especially physics, because it made possible vastly simpler models which can adequately be described by (mostly) linear mathematics. Ever since Galileo began using mathematical expressions to summarize the behavior of objects moving under the pull of gravity, physicists have felt no obligation to worry about what effect their thoughts might have on some experiment they might be engaged in. After all, (so the reasoning goes) the thinking process takes place inside one's cranium (or one's "mind"), and brain waves are much too weak to have any measurable effect on a robust physical apparatus. Thus, classical physics and, to a large degree, modern physics has ignored the complexities and non-linearities that would be introduced when the observer is made part of the experimental situation.

There is no question that the science that has evolved out of this simplifying assumption has been enormously fruitful. The physical world does indeed conform, to a very good approximation, to a relatively small set of "laws" capable of being expressed by surprisingly simple mathematical statements. But the technologies that have been spun off from this scientific core carry a subliminal message to the cultures they serve. The message is that the world that science deals with is completely objective; the tacit simplifying assumption about no observer complications has all but been forgotten. The message has certainly been effective. Separation between Mind and matter, according to the Western worldview, is complete.

However, if we look carefully at what goes on when physicists make models of fundamental processes of nature we will see something strange that suggests the separation may be an illusion. Scientists have known for decades that there is a curious sort of correlation between mathematics, an activity of the mind, and the world of matter. Albert Einstein made this comment: "Here arises a puzzle that has disturbed scientists of all periods. How is it possible that mathematics, a product of human thought that is independent of experience, fits so excellently the objects of physical reality? Can human reason without experience discover by pure thinking properties of real things?" (As quoted in Kline, 1985) Nobel Laureate Eugene Wigner was also impressed by this correlation. He described it in terms of the "unreasonable effectiveness of mathematics" and stated that "the enormous usefulness of mathematics in the natural sciences is something bordering on the mysterious and there is no rational explanation for it." (Wigner, 1960, p. 223).

Puzzles with such far-reaching implications would normally attract physicists like ants to a picnic. The fact that this one has been around for so many years without any serious effort on the part of the mainstream physics community to solve it only demonstrates how strong and pervasive is the belief in complete and total separation between mental activity and the physical world.

Nevertheless, mathematics is the tool of choice when it comes to seeking order in a complex universe. Sir James Jeans put it rather bluntly. "The essential fact is simply that all the pictures which science now draws of nature, and which alone seem capable of according with observational fact, are mathematical pictures." (Jeans, 1932)

Thus, we can only conclude that physics conducts its affairs in a rather odd way: The mental realm is used to create marvelously accurate pictures of the matter realm, yet no connection is believed to exist between the two!


THE PROPOSED MODEL -- THE BASICS

In this section we provide an introduction to the model without the supporting arguments or evidence so that the reader will be equipped with a rough map of the territory explored in the rest of the paper.

First, a concise statement to prepare the way:
We propose that a connection exists between the realms of Mind and matter and that this connection can be understood in terms of existing scientific concepts without invoking any new interactions or "particles."

Next, we need to explain just how we are using the term "model." A model is a suggestion or proposal on how to think about some complicated relationship, process, or mechanism ("system" for short). It shows how the system can be broken down into "parts," each of which can be understood in conventional and less complicated ways. When thinking about the original, complex system, one mentally replaces it with the model, i.e., the parts and the relationships between the parts, thereby eliminating or reducing the complexity and permitting some degree of "understanding." The adequacy of the model is measured in terms of how well it helps explain the various phenomena that are related to the system. This process of determining adequacy is often aided by the formulation of hypotheses that subject certain aspects of the model to experimental tests. In this way model building plays an essential role in scientific methodology.

A simple analogy may further clarify what we are doing. Consider the problem of explaining to a naive individual how one's kitchen faucet is "connected" to the ocean. There is a series of parts or linkages that are involved in the system, some of which are visible and readily understandable, such as underground pipes, treatment plants, reservoirs, and even rainfall. But one important link is invisible and lies in the realm of ideas and concepts -- the evaporation process or phase change in water. This would have to be accounted for in more visible or mechanical terms before the model of the system becomes useful as an explanation of the connection.

It should be obvious that there are different models possible for any given system depending on the kinds of explanatory devices that are considered "conventional" by a group or society. A scientific model, for example, would be of little interest to a group accustomed to explaining natural phenomena in terms of the actions of one or more deities. It follows that as a model becomes more widely accepted and utilized by a group (having been properly "tested"), the "parts" of the model go beyond being merely a guide to thinking and begin to take on a "reality" of their own.

Gary Zukav (Zukav, 1980, p. 313) has a rather pithy description of this process: "'Reality' is what we take to be true. What we take to be true is what we believe. What we believe is based upon our perceptions. What we perceive depends upon what we look for. What we look for depends upon what we think. What we think depends upon what we perceive. What we perceive determines what we believe. What we believe determines what we take to be true. What we take to be true is our reality."

We have described our model as being scientific. This means that the "parts" or links already exist as useful concepts in the scientific community. The fact that they happen to be based on physics and mathematics does not imply that skill with these tools is required to appreciate the model. After all, our Western culture has had no problem in accepting the pictures of the invisible world of sub-atomic matter provided by mathematical physics. Even the most bizarre creation of general relativity, the black hole, (which must remain invisible forever) is given substantial credence by a mathematically unsophisticated public.

Figure 1 is a simplified illustration showing the relationship of the basic components of the model.. At the top is the physical world of space, time, and (large-scale) matter. At the bottom is the spaceless, timeless, and non-material world of Mind. In between these two realms are the mathematical connections that provide the "pictures" that we are using to link particles to patterns in this non-material world..

Even with no further elaboration of the model we can point out that Einstein's "puzzle" described in the preceding section has a rather obvious solution. The reason that the physical world conforms so well to the mathematical pictures created in the mind is precisely because there exists a causal linkage between the two realms. The idea of separation, having been dogma for so long, needs to be seen once again as an approximation rather than an absolute.

It should also be pointed out that the proposed linkages "work" in both directions. This is in contrast with the mainstream view that has matter (or brain) as the causative agent and mind (or thought processes) as dependent "epiphenomena." This bi-directional causality is the basis for the continuous feedback and interplay between the two realities.

Finally, we need to emphasize that our model concerns Mind and matter -- a territory that encompasses much more than mind and body (see Assumption 3 below). Therefore, if the model helps understand those aspects of subtle energies and parapsychological phenomena, for example, which occur outside the body, we believe it would be equally useful in clarifying many aspects of the body-mind connection, such as the placebo effect and health/attitude issues.


BASIC ASSUMPTIONS

In every scientific discourse there is an underlying metaphysical context or worldview which remains unspoken but agreed upon, because without this tacit understanding the discourse would be meaningless to the participants.

In the present instance, although we are using conventional scientific terminology, it is the scientific worldview itself that is being challenged. Therefore, to ensure a basis for understanding what we are presenting, it is essential that we describe in the best way we can the worldview or metaphysical context out of which our model arises. We will do this by setting forth several basic assumptions which are necessary (but probably not sufficient) to define the boundaries of the expanded worldview.

1. The 4-dimensional space-time physical world is the "lowest" of a hierarchy of levels. We view them as nested in a "Chinese box" configuration rather than arranged in a tree structure or pyramid. (Such levels are traditional ways of categorizing the range of human experience.) (Wilbur, 1981)

2. Current physics provides an adequate description of the "inanimate" physical world. The four fundamental forces of physics -- gravity, electromagnetism, the strong force, and the weak force -- account for the interactions of matter, with the Principle of Least Action governing the dynamic processes involving these forces. There is no necessity to introduce any new forces or entities into the model.

3. The level adjacent to the physical is the mental realm, designated herein as Mind (with a capital M). Individual minds (with a lower case m) are sub-units of (Universal) Mind. The mental realm is different from the physical world, i.e., of higher dimensionality. It is intrinsically spaceless, timeless, and non-material; its contents are essentially patterns including those that are represented by mathematical symbols. Figure 2 illustrates the way the levels relate to each other.

4. Space-time provides an interface between the physical and mental realms and is the "stage" or foundation upon which physicists build mathematical structures representing matter and its dynamic interactions.

5. Consciousness is common to all levels of the hierarchy. The entity called the "self" or "I" is an individualization of Universal consciousness. Its boundary in the physical appears well defined but becomes more diffuse as the self extends beyond the physical realm.

In connection with this last assumption, "consciousness" probably needs to be defined for the purposes of this paper. We find it necessary to go beyond the dictionary which tends to limit the meaning to a state of awareness. We define consciousness to include an essence that is behind awareness -- that which energizes or vitalizes an entity and provides its sense of being. Consciousness at its core is ineffable to us because we are part of it.

It needs to be emphasized that, although the worldview described above is open-ended with the number and extent of levels unspecified, our model is confined to the connection between only the lower two -- the physical and the mental.





SECTION II: THE FOUNDATIONS IN PHYSICS FOR THE MODEL


THE ROOTS OF MATTER

In Assumption 4 we state that space-time is the interface between the physical and mental reals. In effect, this means that we believe the search for the locus of the Mind-matter connection should begin within the realm of space-time but below the level of the particles of physics. The main reason we are focussing on this area is that science has already looked everywhere else in the world of matter and found no trace of a force or process that satisfactorily accounts for the breadth of phenomena with which we are dealing. It is not the lack of good data that has led science to this negative conclusion. Rather, it is the restrictive worldview that assumes that space-time is an absolute boundary.

Therefore, we are setting aside this limiting assumption and expanding our purview beneath the "roots" of matter into realms beyond the material. The left-hand side of Figure 3 is a representation of the territory to be explored on a length scale of centimeters in negative powers of ten starting with the human dimension of a finger breadth and proceeding downward to the so-called Planck length 33 orders of magnitude smaller. (The Planck length represents the "bottom" of physical space where the concept of location loses its meaning due to quantum uncertainty and fluctuation.) About half way down this scale is the realm of the elementary particles. These entities lie at the threshold of a region that physics has only recently started to explore theoretically -- the quantum vacuum. While not an integral component of our model, the vacuum is nevertheless a most fascinating region and will receive special attention later.

In order to "see" anything on this scale of smallness high power magnifying instruments are needed. The right-hand side of Figure 3 shows the kind of instrument appropriate for a given size object. A scale of energy in electron volts shows the photon or particle energy needed to resolve detail at various levels of smallness -- the smaller the object, the higher the energy. The highest energy machine shown is the Superconducting Super Collider (SSC) now on the drawing boards. As a multi-billion dollar, multi-national venture, it demonstrates that peering into the vacuum is a very expensive proposition. As accelerator machines go, the SSC may very likely be the "end of the line."

The question naturally arises as to how physics can explore any further without instruments. In the past mathematical theory was used to get us to the particle level. We believe, that for extending beyond the particle level, mathematics will continue to be used as the probe of choice in science. The primary difficulty is that direct experimental testing of a particular theory using physical apparatus will not be possible. However, any theory that deals with the roots of matter is constrained by the requirements of cosmology, the science that is concerned with the origin and structure of the universe. The criterion that ultimately will have to be met is an overall consistency with data generated both by astronomy and particle physics.


THE WORLD ACCORDING TO QUANTUM MECHANICS

Mathematics provides the "pictures" of the invisible realms beyond the reach of optical magnification. The procedure is roughly as follows. The raw measurement data provided by a complex array of apparatus is compared to numbers generated from the mathematical theory of the process or system under study. If suitable agreement is obtained the theory can then be used to predict "visual" aspects of the system. This is the approach used to "see" atoms using the scanning tunneling electron microscope. (Wickramasinghe, 1989) Here the theory not only guided the design of the equipment; it supervises the processing of the tiny electrical signals from the apparatus and turns them into video display pictures.

The theory behind our current conception of matter is called quantum mechanics. It has been combined with Einstein's special theory of relativity and Maxwell's theory of electromagnetism to produce a more refined version called quantum electrodynamics. "QED" is regarded as the most precise tool ever devised for the description of charged particle interaction. Thus, there is good reason for accepting quantum theory's portrayal of the world of the very small in spite of the fact that the pictures it presents are so contrary to common sense. Since our model will build upon this base of quantum mechanics, it is important to understand some of its characteristics. Here is a brief listing of several of the main implications of quantum theory that are relevant to this discussion. For a fuller account, Nick Herbert's book, Quantum Reality is highly recommended. (Herbert, 1985)

1. The physical world operates according to probabilities rather than as clockwork. Once a physical system is specified, the theory produces a "wave function" (expressed in terms of space-time variables) which contains all the information that can be obtained by a "measurement" on the system. But rather than predicting a specific result of a measurement the wave function only yields the probabilities for a whole spectrum of possible results. The process of measurement (or observation) converts this set of potentia into one actuality. This "collapse of the wave function," while still a subject of controversy among quantum physicists, we believe can be attributed to a "choice" made by consciousness (which can lie beyond space-time). (Stapp, 1972; Wigner, 1963)

2. Matter is mostly empty space. For an atom, the size of its nucleus would be like a flea in the center of the vast space of the Astrodome in New Orleans. Yet, there is a "hardness" to solids which are composed of atoms. The reason is a result of the quantum properties of atom's electrons summarized in Pauli's "exclusion principle" which states that no two electrons can occupy the same quantum state. The electron cloud surrounding the atomic nucleus strongly resists compression; thus atoms take up space even though the constituent particles of the atom are no larger than mathematical points. This example of the vast difference between the ordinary experience of perception and the picture provided by mathematics brings into sharper focus the problem of what is meant by the term "real."

3. Exact simultaneous measurement of certain pairs of variables of a physical system is impossible. This is the conclusion represented in Heisenburg's famous "uncertainty principle." Specifically, the principle refers to pairs like position and momentum, or energy and time. The impossibility is not merely a result of an inherent "clumsiness" in the measurement process but is built into the system in such a way that a choice made to determine one quantity with precision automatically smears out the measurement of the other. The principle has a direct bearing on how far into the vacuum our mathematical probes can reasonably be expected to go.

4. A physical system, once separated, retains a "connectedness" through the quantum wave function. This is, perhaps, the most bizarre and controversial of the predictions of quantum mechanics since it implies linkages that transcend space, time, and the conventional interactions of the four basic force fields. But considerable experimental effort has confirmed that "local" connections are inadequate to explain reality; this justifies incorporating "non-locality" into our model. A more comprehensive discussion of non-locality appears below in connection with the detailed description of the model.


THE BOTTOM OF SPACE-TIME

The mathematics of quantum theory rests squarely on the same foundation used by classical physics -- space and time (suitably modified, of course, to accommodate the invariance requirements of special relativity). What happens when the quantum theory is used to examine its own foundation? Even though the attempt to answer this question will seem like opening a can of worms it is important to do so, because it is here, at the underbelly of physics, that we will find the links to the realms beyond space-time.

In the rest of the paper we will occasionally use some technical words in order to convey more precisely certain mathematical ideas. The following definitions are intended to help make our terminology more meaningful:

Dimension: There are many different ways to define the dimension of a space. (Stewart, 1987) Usually it refers to the number of independent coordinates (expressed as a positive integer) needed to locate a point in a "space." A line or curve requires only 1 coordinate to locate a point on it, namely, the distance from some reference point. Hence, a line is said to be 1-dimensional. A plane or surface is 2-dimensional, etc. A space of dimensionality greater than 3 is sometimes called a "hyperspace." Later we will discuss fractal dimensions and their importance to our understanding of the natural world.

Since it is difficult to visualize higher dimensional spaces it is useful to look at a picture of a conventional three dimensional man falling through a two dimensional flatland space. Figure 4 shows a two dimensional flatlander observing the effects on his space. (Rucker, 1984) At one level the parts of the 3D man are all connected, yet the effects appear separate to the 2D flatlander. If there was a flatlander psychic, she might give a warning of where a "future" event would take place. However, it there were a flatlander shaman who could interact with the mind of this higher dimensional being and convince him to put his arm up straight so that it would fall through the existing body hole then the enlargement of the body hole could be avoided and there would be less damage to flatland and its inhabitants. So there are some strange things that can happen in this hierarchical world of "intelligent" dynamic patterns that we are postulating.

Manifold: This refers generally to an abstract spatial construction or geometric form whose points may be defined by n parameters, in which case it is an n-dimensional manifold.

Topology: This is a broad field, but we are using the term to refer to the study of properties of manifolds, particularly those properties that remain the same when a manifold is subjected to operations that deform it, such as twisting or stretching. In this sense, a coffee cup is topologically equivalent to a doughnut.

Space: This term usually refers to the ordinary 3-dimensional space we are used to. But the term is often used in physics and mathematics to refer to purely abstract manifolds, usually of higher dimensionality than 3. Such spaces or manifolds may be curved, as is the 2-dimensional surface of a sphere where the geometrical laws of Euclid no longer hold true.

Space-time: This is the marriage of ordinary space with time, resulting in a 4-dimensional manifold. In this marriage time and space are treated as equal partners as required by the special theory of relativity. A point in space-time represents an "event," while a line (or curve) represents a history. Usually physical laws that are expected to hold universally (i.e., regardless of the state of motion of a hypothetical observer) are expressed in the 4-dimensional setting of space-time.

Realm and Reality: Although not strictly technical terms, it is helpful to clarify the way we use these two words. By "realm" we mean a domain within which something occurs. The physical world plus time is equivalent to the space-time realm. The mental realm is within the spaceless-timeless realm. "Reality" is our perception of a given realm. We can reach consensual agreement on physical reality but have greater difficulty doing so on mental reality.

Now that we have clarified some of our terminology, we can return to the examination of the structure of space-time and see what happens when the "microscope" of quantum theory is used. The story starts with Einstein's theory of general relativity which is a theory of curved space-time where the curvature is directly related to the amount of mass and/or energy present. He took the mystery out of gravity by showing that all gravitational phenomena known at that time (around 1915) could be accurately accounted for on the basis of the curvature of space-time. Later on, others used his equations to predict phenomena which Einstein initially was unaware of, such as an expanding universe and black holes.

In spite of the elegance and success of Einstein's theory, being strictly a classical theory it is unable to accommodate the requirements of quantum theory. Decades of effort have gone into the attempt to produce a quantum theory of gravity with little success. The central problem can be understood in terms of the uncertainty principle. When there is a high degree of specificity for position, such as points lying within a Planck length of each other, the curvature of the space-time manifold becomes correspondingly uncertain leading to ambiguities in the meanings of position, time, and energy. What is even more troublesome is the non-linear feedback relationship between curvature and energy expressed in Einstein's equations. A tiny fluctuation in either quantity reverberates back and forth resulting in a kind of microscopic chaos in the fabric of space-time. Physicists have resorted to some rather creative terminology to describe this state of affairs: for example, quantum foam, cosmic Swiss cheese, wormholes in space-time. (Tobin, 1975)

This impasse, where two major physical theories, both highly successful in their respective domains, refuse to be compatible at the bottom of space-time, forces theoretical physics to look seriously at a completely different approach to the problem. Rather than working from the large to the small, or from the familiar to the unfamiliar, it might make more sense to try working in the opposite direction, from the very small up to the large. The implication is that space-time is not the nice, smooth, continuous and well-behaved structure it has been assumed to be. It very probably has much richer topological features that are intrinsically quantum-like.

It is not necessary for the purposes of our discussion to have a definitive answer to the question about the nature of space-time. All we need to know is that the manifold is not a continuous mathematical structure with points arbitrarily close together; it has "holes" in it. (Renteln, 1991) If this is indeed the case, the logic of geometrical thinking compels some kind of higher dimensional "medium" for this multiply-connected topology to exist in. The term "sponge-like" seems to be an apt metaphor for this new kind of space-time, since it implies a surrounding medium that permeates it. It is our contention that this medium can be identified with the spaceless and timeless realm of Mind.


THE QUANTUM VACUUM

Before continuing with the arguments supporting the model, it is appropriate to take a more detailed look at the region between manifest matter and the Planck length. This quantum "vacuum" has been explored both theoretically and, near the surface, experimentally. Some of its properties are significant for our discussion:

1. The vacuum is packed with energy of almost infinite density. Estimates vary, but the numbers are all beyond imagination. If the mass of the entire universe were converted into energy it would be less than that in one cubic centimeter of vacuum. For reasons which are still obscure, this enormous store of energy remains invisible and unavailable on the average. Since it does not seem to influence any physical processes, at least to a good approximation, it is convenient to treat it as a large constant, subtract it out of any theory, and measure all energy changes from the so-called "zero point" at the surface of the vacuum. This is comparable to measuring elevations from sea level rather than the deepest part of the ocean.

2. The vacuum is a hotbed of highly energetic "virtual" particles. Quantum fluctuations at the surface of the vacuum are displayed in the form of fleeting particle-antiparticle "pairs," emerging into matter form for brief moments and then being reabsorbed into the vast sea of energy. If sufficient energy is delivered from outside, say from a large particle accelerator, the pairs that are created are permanent, i.e., they do not instantly disappear back into the vacuum again; instead they are available for experimental purposes. The conservation laws of physics (energy, momentum, charge, etc.) appear to hold exactly in all these processes.

3. The vacuum can be polarized by sufficiently strong electric fields. The term "polarization" refers to a process in which positive and negative electric charges, initially close enough together so no long-range effects are apparent, are separated by an external force so that their individual electric influences no longer cancel out. In the case of the vacuum, virtual electron-positron pairs, i.e., particle-antiparticle pairs, which exist for only an instant, can be separated long enough to reveal their presence to experimental probes. (Greiner, et. al., 1985) For example, one of us (RLS), using precision X-ray techniques to measure atomic energy levels, showed that vacuum polarization did, indeed, have measurable consequences at the level of atoms. (In effect, this was a "Lamb shift" measurement confirming the existence of small spectrum changes for heavy elements.) (Shacklett, 1957)

4. The vacuum may be a possible source of energy. Extraction of energy from this seemingly inexhaustible reservoir has been a fond hope ever since its existence has been established through QED. Research proceeds on two fronts. Theoretical articles on possible large scale effects of this vacuum energy have been published in mainstream physics journals. (Puthoff, 1989) Considerable experimental activity, largely through efforts to obtain macroscopic polarization, is going on outside the mainstream with reports of success being published in various forms. (King, 1984) But in the absence of any noteworthy technological breakthroughs (to our knowledge), it is best to heed the advice of Puthoff (*Puthoff, 1990?, p.247), "...the prudent scientist, while generally keeping an open mind as to the possibility of vacuum energy extraction, must of course approach any particular device claim or theoretical proposal with the utmost rigor with regard to verification and validation." Our model would suggest that the extraction of vacuum energy could be sensitive to the patterns beyond space-time and, hence, to mental patterns. This would effect the "reproducibility" of such experiments.


THE UNIFICATION PROGRAM

Returning to our mathematical journey via quantum theory to the bottom of space-time, we have uncovered a troublesome impasse in physical theories as well as shown the reasonableness of positing a higher dimensional setting for the topology of space-time. To make our case more convincing we will now show that physics can resolve the impasse by introducing a different kind of topological structure for space-time. One which, it turns out, just happens to harmonize nicely with our model.

The solution to the problem of quantum gravity, which is what this impasse is all about, is a culmination of a dream of Albert Einstein, who believed that the various forces of physics could eventually be unified into one comprehensive theory. Until his death in 1955 he continued to work on unitary field theories but without making a great deal of headway. Others took up the challenge armed with more powerful theoretical tools. Then, in the early 1970's, the first major success was achieved with a theory and experimental verification of the unification of electromagnetism with the weak force.

Today, the effort continues in the high-energy physics community to apply the same techniques that worked for the "electroweak" unification to the strong nuclear force with the objective of achieving a "grand unification theory" (GUT). The ultimate goal, of course, is to be able to include gravity which would then result in the "theory of everything." This term, which is often abbreviated as TOE, appears frequently in popularized accounts of theoretical physics research. (Barrow, 1991) It is taken seriously by some, but for most physicists it is a tongue-in-cheek expression because the "everything" is limited only to inanimate matter. We will use the term in a metaphorical sense, referring to the goal of the unification program, but not implying in any way that we accept the notion that any theory can ever encompass "everything."

Nevertheless,the achievement of a "theory of everything" in physics would represent a tremendous advance in human intellectual understanding, and its pursuit is certainly as daring and exciting as would be an expedition to Mars. Barrow (Barrow, 1991) and Peat (Peat, 1988) have captured some of the flavor and spirit of this adventure.

There are three principle approaches being undertaken to the "theory of everything" which are potentially capable of providing mathematical pictures of "the other side" of space-time. All are based on novel topologies for the substrate of matter. These are called superstring theory, knot theory, and twistor theory. Superstring theories (there are a number being proposed) arise out of a 1970 proposal that elementary particles are not points but vibrating, rotating strings. (Peat, 1988) These are abstract one-dimensional objects having a length comparable to the Planck length and an energy spectrum which resembles that of ordinary particles in quantum field theory. The theories all require more than three dimensions of space. (An early version had as many as 26 dimensions!) One of the big problems with this approach is how to make the "extra" dimensions shrink into invisibility. In spite of this and other rather formidable problems, many theoreticians are investing a lot of their energies into superstrings.

Knot theory is a more recent arrival (Kauffman, 1987) and has fewer advocates who are, nevertheless, persuaded that their theory has more going for it than does superstring theory. Space-time, in knot theory, is like a medieval coat of chain mail, with tiny little loops of Planck length dimensions all linked together in a 3-dimensional lattice. (Waldrop, 1990) In knot theory (as in superstrings) there are no "points" on a continuous manifold to create the infinities that were such a bother in conventional, relativistic space-time.

The theory we wish to elaborate upon in connection with our model is twistor theory, a creation of Roger Penrose, mathematician and theoretical physicist at Oxford and author of the highly acclaimed book The Emperor's New Mind. (Penrose, 1989) For reasons which are partly aesthetic and partly technical we feel that twistors provide a better picture of what is going on down there in the "sponge" region of space-time.

A fuller accounting of the "twistor connection" will be given later when we get into the details of our model. The reader should recognize that the discussion of the unification program is really only tangential to our main purpose. The objective of the discussion was to establish the fact that mainstream physics is now ready to accept a radical topology for the space-time manifold if achievement of the unification is convincing, i.e., both astrophysical and accelerator data are comprehended by the theory. Furthermore, although only a small fraction of the physics community is directly involved in this effort, the concept of unification is a very powerful one that continually motivates both scientists and sages. (Weber, 1986) It is a goal which we believe will eventually be reached.


PATTERNS IN THE PHYSICAL WORLD

Throughout this paper we will be using the term "pattern" to represent a form or configuration in the cosmos. The term serves as a unifying concept for our discussion of the realms of Mind and matter. This section will focus upon patterns in our world of matter and relate it to issues in quantum physics. In later sections of the paper we will discuss the relationship of patterns to the spaceless-timeless realm.

Figure 5 is a picture of the atoms in mullite which is composed of the oxides of aluminum and silicon. (LBL Research Review, 1989) This is a photograph of atoms taken using the Atomic Resolution Microscope at the Lawrence Berkeley Laboratory. What one sees is a pattern that looks like the close weaving in a rug. The inserts represent computer modeling of the arrangement of the atoms and one can see the close relationship. Looking at more of the patterns in the universe let's move from atoms to a large molecule. The Figure on the cover of this issue of Subtle Energies is a molecule of DNA and is a completely computer generated model done by the Computer Graphics Laboratory of the University of California, San Francisco.

These patterns of nature can also be considered as sound or music. Dr. David Deamer, a molecular cell biologist at the University of California at Davis has decoded and translated the DNA molecule into music. The genetic material in all of life and its various forms is made up of only four base molecules -- adenine, thymine, guanine, and cytosine. These are paired up in various combinations (or sequences) along the DNA double helix structure. Dr. Deamer assigned musical notes to each of the four bases with the ground rule that another molecular biologist must be able to look at the music and decode it into the original sequences. The interesting musical sounds obtained vary and depend upon the source of the DNA -- some very meditative type of music resulted from the patterns. (Deamer, 1985)

Susan Alexjander, a composer, took a different approach. Since the four DNA bases are crystalline molecular structures, she investigated the light frequencies that would "ring these crystalline chimes," i.e., the infrared light waves that would resonate with the DNA base molecules. Scientists call this the infrared absorption spectra. By transposing this spectra into the audible range, four nonlinear musical scales were created. Using the four "DNA musical scales," Susan tuned instruments and composed music that was issued as the recording Sequencia (Alexjander, 1990). The beautiful harmonious nature of this "music of life" is astonishing.

Having considered patterns created by particles and noting the effect of light on those patterns, we will next consider the patterns generated by electromagnetic waves like light when they interact with each other. Figure 6 shows the patterns created when one takes a flat surface, punches patterns of holes, and then shines light at the surface. What you get when the light goes through the holes are interference or diffraction patterns that look very much like mandalas. (Harburn, et al, 1975)

Holography is a "quantum leap" in the science of image-making which makes use of the interference patterns from waves of light to create images in time and space. It has spawned a new art form of three dimensional light sculptures that are becoming increasingly better simulations of our perceived reality. "The hologram does not merely represent space, it is spatial." (Berner, 1980)

In order to regard the entire Mind-matter continuum as a realm of patterns we need to raise the question of whether there is an inherent difference between the patterns of matter and the patterns of waves of light? In quantum physics "light" is accorded equal status with matter and both treated dualistically by the mathematics as either wave or particle. However, only when one wants the physical representation of the mathematics does there arise a question regarding the patterns of matter or waves. In quantum physics this issue is known as the measurement problem: the shifting border between waves and particles. Where does this division occur between the world that must be described by waves and the world that must be described by particles? Where does this boundary lie?

Whenever a measurement is made on a quantum system it is done with ordinary apparatus in this classical world - a world without waves, a world of particles. However, it is possible to treat the measuring apparatus itself as a quantum system, in which case the wave equation of quantum mechanics must be used, and the apparatus then becomes wave-like rather than particle-like. But now this second quantum measuring apparatus must be observed by a classical system. In other words, to get a quantum mechanical answer to a quantum question is essentially impossible because it requires an infinite regress of quantum and classical systems. Therefore, it is necessary to step outside of the classical world of particles entirely in order to comprehend the quantum world. In effect, we must change our "frame of reference" to another realm -- a realm of "archetypal" patterns which we will discuss later.

Hence, trying to decide where the waves really are and where the particles really are represents a shifting boundary. Everything physical can be described by the mathematics of quantum wave mechanics, yet the particles only manifest when a measurement is made. In a practical application this process terminates at some point when the measurement is accurate enough for the purposes at hand. Thus, in practice the shifting border between waves and particles doesn't matter. However, it does matter in principle, and we take the position that the boundary has been extended to where the physical universe can be considered to consist of only waves or holographic patterns. (Bell, 1988)







SECTION III: THE REALITY BEYOND SPACE-TIME


JUNG, PAULI, AND ARCHETYPES

The principle focus of the development so far has been to examine the mind-matter boundary of space-time from the side that physics is concerned about, being careful to point out that we are using a tool of the mind -- mathematics -- in the process. We have seen that the boundary is permeable, more like a sponge than the solid wall that conventional science has believed in for so long. It is appropriate at this juncture to take a look from the other side, realizing, of course, that this time we have very little scientific tradition on which to base our argument that Mind has any connection at all to space-time. It is therefore incumbent upon us to build the case by the logical use of evidence. And just as is done in the courtroom, the individual strands of evidence, while unconvincing alone, when skillfully braided together become highly persuasive.

Hence, what can be said about what lies beyond space-time and its relationship to our lives in everyday "physical reality?" In exploring this question we encountered an interesting connection between one of the important contributors to quantum physics in its developing stages, Wolfgang Pauli, and the founder of depth psychology, Carl Jung. {Footnote: Werner Heisenberg announced his discovery of quantum theory in 1925. Later in his life, Heisenberg claimed "that his most important influence had not been university professors or textbooks, but his discussions with Pauli," his friend and fellow student. (Peat, 1990, p. 31)} Pauli's quest was very similar to ours, namely, the relationship between mind and matter. Working together with Carl Jung he perceived parallelism between quantum physics and Jung's depth psychology and eventually published a joint book on aspects of their ideas (Jung & Pauli, 1955).

Jung, as early as 1919, had developed the theory of archetypes, the ordering factors in the collective unconscious, i.e., in the mental realm. In the following decades, Jung constantly deepened and broadened the theory. Pauli's contribution was that he considered it necessary to include in any unified conception of the cosmos both the world of physics and the "ordering operators," i.e., the archetypal patterns of the mental realm. Jung was profoundly influenced by Pauli's formulation and finally came to view archetypes as the ordering factors of both mind and matter. Jung applied the term unus mundus to denote a spaceless-timeless realm that encompasses the physical. Jung stated that his idea of an unus mundus is founded "on the assumption that the multiplicity of the empirical world rests on an underlying unity, and that not two or more fundamentally different worlds exist side by side." (von Franz, 1974, p.p. 8-9).

From the 1920's on Jung had been impressed by the many instances of synchronicity in his own and his patients' lives. He defined synchronicity as "the meaningful coincidence or equivalence of a psychic and a physical state that has no causal relationship to one another." (Jung, 1963, p.388) As time went on, and with the urging of his colleague, C. A. Meier, he came to view this kind of notable event as only a particular instance of a general "acausal orderedness" in nature. (Meier, 1988). These insights were of great consequence in the further development of Jung's theories.

Connection had now been made with the phenomena of quantum physics, especially the phenomena of non-locality, and with the theory of archetypes. Jung had found that archetypes were regularly activated in synchronistic events and accounted for their meaningfulness. So it was evident that archetypes reach across the boundary (or what we have called the "sponge") between the mental realm and the sphere of matter. In our model it is the feedback linkage across the "sponge" that creates the dynamism of the whole.

The possibility was raised by Jung and Pauli that there exists an ordering process beyond space-time (von Franz, 1981). We, too, assume that the archetypes represent units of ordering in this spaceless-timeless reality and that new orderings result in acts of creation in space-time. This latter point has been addressed by quantum physicist, Dr. Henry Stapp who presents a process formulation of quantum theory. He has called the ordering in the spaceless-timeless reality "process time." He distinguishes it from the ordering in space-time which he refers to the "Einstein time" of today's physics. "Process time" is "the time associated with a cumulative process whereby things gradually become fixed and settled." Thus, this "allows quantum theory to be regarded as a theory describing the actual unfolding or development of the universe itself." (Stapp, 1984) However, there is no a priori requirement that the sequence of the ordering in the spaceless-timeless reality map be a linear time sequence of events in our space-time reality.

We are assuming that there exists a hierarchical structuring of patterns at the archetypal level in a nested mode similar to the hierarchical structuring of patterns in the physical world. Thus, in the physical world we are aware of the nested patterns of bodies, organs, cells, molecules, atoms, particles, etc. In a analogous manner we could ascribe in the spaceless-timeless realm of Mind a hierarchy of archetypes to mammals, primates, humans, male/female, race, culture, family, etc. Just as in the physical body there exists feedback among the nested hierarchy of parts, so too at the archetypal level we are assuming that there is a similar "horizontal" feedback among the nested parts.

We suggest that there may exist a similar "horizontal" hierarchy within the spaceless-timeless realm. Thus, archetypes could be considered fundamental "elements" -- akin to the atomic elements from which the physical world is built and derives its structural order. The fundamental archetypes represent units or elements of ordering in the spaceless-timeless realm and new orderings result in acts of creation in space-time. Late in his life Jung had the conviction that "natural integers contain the very element which regulates the unitary realm of psyche and matter." (von Franz, 1974, p. 27)

We agree with Jung, and assume that the symbols we use in our physical world that represent "number" evolve from (and thus are representations of) these most fundamental archetypes for the order beyond space-time. Hence, these representations of the "number" archetypes serve the role of mediator between the happening in the physical or outer reality and the mental or inner reality. Jung contended that "number serves as a special instrument for becoming conscious of such unitary patterns" beyond space-time. (von Franz, 1974, p.27). Pauli held similar beliefs and stated that the concept of archetype "should be understood in such a way as to include the ideas, among others, of the continuous series of whole numbers in arithmetic, and that of the continuum in geometry." (Pauli quoted in von Franz, 1974, p. 18)

The archetypal hypothesis developed by Jung and Pauli and its relation to number was extended by a colleague of Jung, Dr. Marie-Louise von Franz. (von Franz, 1974) Dr. von Franz was also one of Pauli's analysts and had great influence on his inner development. (van Erkelens, 1991, p. 43) Based upon von Franz's research this more general archetypal hypothesis has been summarized as follows:

1) All mental and physical phenomena are complementary aspects of the same unitary, transcendental reality.

2) At the basis of all physical and mental phenomena there exist certain fundamental dynamical forms or patterns of behavior called number archetypes.

3) Any specific process, physical or mental, is a particular representation of certain of these archetypes.

4) In particular, the number archetypes provide the basis for all possible symbolic expression.

5) Therefore, it is possible that a neutral language constructed from abstract symbolic representations of the number archetypes may provide highly unified, although not unique, descriptions of all mental or physical phenomena. (Card, 1991, p. 33)

Many different symbols and formats of symbols can be used to access and describe a given archetype. The primary archetypes have been represented by the symbols for numbers (Arabic, Roman, words, etc.) and by letters (Hebrew, Greek, Arabic, etc.)as we will discuss in a later section. Thus, one can envision symbols for archetypes 1) as one dimensional such as strings of numbers or of letters as in sacred texts, 2) as two dimensional such as the matrices of quantum physics or the Chinese matrices used to represent "the total archetypal order of the unus mundus and all its conceivable contents" (von Franz, 1974, p. 141), and 3) as three dimensional such as the knots of knot theory. Any pattern such as geometric figures, mandalas, sound/music, or language can be transposed into a number format as is evident from our compact disks and computer technologies. Therefore, art, music, and poetry are representations of levels of complexity in archetypal forms beyond space-time.

Both Western science and the ancient cultures used matrices, rectangular arrays of numbers, as representations of an aspect of reality. A matrix is a generalization of the concept of "number" in the sense that an ordinary number is a 1 x 1 matrix and is therefore a special case of a general n x m matrix. Matrices are a representation of the abstract group which is the mathematical theory of symmetry and are of critical importance to Heisenberg's formulation of quantum mechanics. A very significant difference between matrices and simple numbers is that matrix multiplication is in general non-commutative, i.e., a x b _\ b x a. In fact, Heisenberg's uncertainty principle "follows quite logically once matrices are chosen as the natural language for quantum physics." (Peat, 1990, p.39)

However, there exists a basic difference on how "numbers" are viewed when used by Western scientists versus ancient "scientists." In Western science, the numbers that make up the matrices are each considered only to represent a quantity. This is not true for the ancients. For example, in a Chinese matrix like the Lo-shu, each single element of the matrix is regarded as a quality of a "field." (von Franz, 1974, p. 26) with each number functioning as a hierarchically regulating element. "The single numbers of the matrices are not subdivisions but illustrations of the 'phases of transformation' that form the time-bound aspects of the whole." (von Franz, 1974, p. 42)

If we accept Pauli's contention that certain mathematical structures rest on an archetypal basis, then the observed isomorphism of mathematics with certain outer-world phenomena is not so surprising as we have already noted. (von Franz, 1974, p. 19) This view is also supported by Bertram Russell in his Introduction to Mathematical Philosophy where he denies number's aspect as a mere "quantity" and describes it, rather, as an ordering factor. (London, 1956, p. 213; from von Franz, 1974, footnote p. 40) Thus, modern science may work because it is unconsciously making use of the same patterns of order, the number archetypes, that the ancients recognized as being revealed by the "gods," i.e., originating beyond our space-time reality.

Over the centuries, symbols have been used extensively throughout all of human culture and have had specific qualities associated with them. (Cirlot, 1971) It is our premise that the patterns for all symbols in space-time have their base in archetypical patterns that are beyond space-time. Thus, symbols can be considered archetypical representations in the physical world.

Every symbol has potential meaning for an individual. Through relationships that we will discuss later, the accompanying emotion can release energy stored in the body. The meaning and hence the amount of potential energy to be released is individualized, i.e., it is different for each person and under different circumstances can be different for the same person. The amount of potential energy associated with a given symbol depends upon one's past experiences including culture, family, and individual experiences. To release this potential energy one need only focus attention upon a relevant symbol. The act of attention connects one to the corresponding archetypical pattern existing in the spaceless-timeless realm. Because of the way our brains function, the sharper the focus of attention and the longer its duration, the greater depth into a given hierarchical structure of the archetypical pattern one can penetrate.

When an archetype is activated from the physical space-time level by an individual, there is a "horizontal" feedback connection to its next more encompassing level, i.e., to a wholeness greater than the original archetype. This new level of "wholeness," in turn, manifests as "vertical" feedback from the spaceless-timeless realm to the physical space-time realm. It is experienced in the individual's body as emotions and feelings to which we ascribe meaning. The emotions are a person's internal releases of energy - releases of energy stored in the body - whereas the feelings are our judgments about something and can be without emotion.

In his discussion of archetypes, Carl Jung uses the term "numinosity" where "numen" means godlike or a characteristic of or befitting a deity. Jung states: "I must stress one aspect of the archetypes which will be obvious to anybody who has practical experience of these matters. That is, the archetypes have, when they appear, a distinctly numinous character which can only be described as 'spiritual,' if 'magical' is too strong a word. Consequently this phenomenon is of the utmost significance for the psychology of religion. In its effects it is anything but unambiguous. It can be healing or destructive, but never indifferent, provided of course that it has attained a certain degree of clarity." At another point he states: "The archetypes have about them a certain effulgence or quasi-consciousness, and that numinosity entails luminosity." (Jung, 1973/1960)

Normally we are unaware of the existence and effects of archetypes in our everyday life. However, when an individual undergoes a major disruption due to a loss of a loved one, a life's job, a near death experience, etc., there appear changes at the archetypical level that reflect to the physical. The person may undergo a period of transition from one stable state via chaos towards a new stable state. These inner messages from the spaceless-timeless reality of the unconscious can be received directly as dreams or can be made accessible through one's expressions in art, dance, music, poetry, etc. often with the help of persons skilled in such therapy. A pattern emerges as these symbolic messages unfold over time. When deeply understood and empowered by personal energy, the result is a restructuring of the person's psyche and a restoration of balance between body, mind and spirit. Failure to successfully make the transition can lead to dis-ease and sometimes death.

Our quantum linkage model would predict that the fundamental "number" archetypes permeate every level of the physical and mental hierarchies. To better appreciate the concept of "number" archetypes, let's explore how they might be operating in the pervasive attraction between "opposites" that characterizes much of the phenomena of matter and mind. At the most basic level of matter is the attraction between negatively and positively charged particles. Then on up through the hierarchy -- the attraction of adenine for thymine and guanine for cytosine in the DNA molecule. It's as if they have to find each other and marry. Then the attraction of the sperm and the ovum. Why does that sperm go on an incredible hero's journey to reach the ovum? Then all through the animal world there are unbelievably complicated ritual approaches necessitated by the attraction between the female and the male. Of course, look what happens to us human beings when we are overtaken by the force of attraction! Even in the human mind the opposites are in constant play.

Both the ancient literature and the work of Jung and Von Franz are in good agreement on the "qualities" inherent in the first five "number" archetypes. (von Franz, 1974; Hall, 1988, p. LXXII) The first numeral, one, is unity -- an archetype and attribute of God. The first distinction breaks it into opposites -- the inside and the outside. This is how a "one" gets to know itself and why self-reference and feedback permeate the universe. The even numbers represent archetypes that can be divided into two equal parts and have the female attribute of receptiveness. The odd numbers are masculine, active and disharmonic. Five is the union of an odd and even number. To the ancients it symbolized light, health, and vitality and a connection to the spiritual realms -- to the spaceless-timeless realms. This connection energizes a new archetype that results in a manifestation or creation in space-time -- in the physical.

The "two" represents polarity; it has to exist, but Nature did not intend it to exist forever. The division appears necessary to establish a limited power of discrimination -- an ability to learn. "The individual creations must of themselves search out their reunion. Creation is a process of division within unity, and evolution is finally a uniting of separated parts." (Hall, 1984) Hence, every part of duality must labor to restore unity -- this attraction would seem an inherent quality of the "number" archetypes. Another name for the unity is love -- and is why love has such great power to heal.

In summary we assume that 1) there exists a reality beyond space-time to which everything in the physical world is linked, resulting in a connectiveness that negates the apparent separateness of our space-time reality, 2) there exists an ordering principle or process in this spaceless-timeless reality that affects processes and patterns in our space-time reality via a downward causation, 3) there is a fundamental or lowest level of ordering that reflects a universally recurring, common motion of patterns for both mental and physical energy, and 4) because of the linkage, humans interact in a feedback manner with the reality beyond space-time and thus, can alter aspects of the ordering process while seeking balance with the whole.

The feedback process between the patterns of the space-time physical world and the archetypical patterns of the spaceless-timeless world of Mind and can be viewed as a mirroring or self-referencing process in both directions. The process results in a cosmos that can be considered as a self-organizing system of continuous creation -- a "Living Cosmos." (Elgin, 1988)


MATHEMATICS AND THE MENTAL REALM

Mathematics is the study of pure patterns. Since everything in the cosmos can be considered a kind of pattern, mathematics is the study of this language of nature (Rucker, 1987). A preliminary step will be to elaborate further on Assumption 3 where we stated that the contents of the mental realm are essentially patterns -- archetypical patterns that include those that are accessed by mathematical symbols.

That mathematics is a mental activity seems self-evident, but where is the locus of the objects that mathematicians work with? The mathematician, Dr. Morris Kline, after quoting a number of mathematicians on the objectivity of mathematical material, concludes:

These assertions about the existence of an objective, unique body of mathematics do not explain where mathematics resides. They say merely that mathematics exists in some extrahuman world, a castle in the air, and is merely detected by humans. The axioms and theorems are not purely human creations; instead, they are like riches in a mine that have to be brought to the surface by patient digging. Yet their existence is as independent of man as the planets appear to be. (Kline, 1985, p. 200)

If this testimony from practicing mathematicians strongly suggests that the mathematical "landscape" is there to be explored by anyone so inclined, then the story of the Indian genius, Ramanujan, should be even more convincing. (Kanigel, 1991) This young man's dramatic emergence into mathematical prominence in 1915 was preceded by only the barest exposure to elementary mathematical concepts in his very limited formal schooling. Yet his formulas and theorems went far beyond the ability of advanced mathematicians of his day to prove and are only now being proved using methods completely unknown to Ramanujan.

His biographer makes this comment on Ramanujan's philosophy regarding mathematical reality:

In the West, there was an old debate as to whether mathematical reality was made by mathematicians or, existing independently, was merely discovered by them. Ramanujan was squarely in the latter camp; for him, numbers and their mathematical relationships fairly threw off clues to how the universe fit together. Each new theorem was one more piece of the Infinite unfathomed. (Kanigel, 1991, p 66)

How can the individual mind explore this landscape which gives every indication of being "public?" Penrose suggested that one's consciousness breaks through into this world of ideas and mathematical concepts and makes direct contact with it. He also felt that even though different mathematicians may come out with different mental images, they are able to communicate with each other about them because they had been in contact with the same externally existing world. (Penrose, 1989, p. 428)

It is clear that both Penrose and Kline have refrained from going as far as we have in our model in which we propose that the phenomenon of mathematics, described so clearly by these writers, is possible because the mathematical "public landscape" and the "private mind" of the mathematician are both aspects of one and the same Mind or mental realm. No journey to an "extrahuman world" or a "castle in the air" is required. The entire landscape is present and available to each and every mind that is disposed to explore it, because that mind is in the landscape and the landscape is in that mind.

Einstein once said, "The most incomprehensible thing about the universe is that it is comprehensible." We now have a basis for explaining this "puzzling comprehensibility": Matter, and thus the universe, is a manifestation of basic mathematical patterns. The human mind is capable of apprehending these patterns because it shares the same realm. Therefore, humans "understand" nature by experiencing it through those mathematical structures which harmonize or "resonate" with the patterns of nature.

The language of nature may be mathematics but it is the job of the scientist or engineer to write the script, i.e., to understand the constraints of the system. By the term "constraints" we refer to those parts of a system which represent an energy barrier which would have to be overcome to modify the behavior of the system. Once these constraints are put into mathematical form, we can determine how nature's patterns unfold over time. Mathematics then becomes a true representation of reality. This is why discoveries in mathematics have enabled us to predict and learn to use radio and TV waves which our normal senses do not perceive; and to discover particles too small to be "seen" by any existing technology.


LANGUAGE AND THE MENTAL REALM

Numbers and letters are intimately connected. For the Hebrews, Arabs, and Greeks, the letters of the alphabets were also the symbols for numbers. Thus, these languages and their alphabets are particularly intertwined with the numerical, mathematical and algorithmic thought of these ancient peoples. In addition, ancient cultures claim a universality or sacred status for traditional alphabets (Sanskrit, Islamic Arabic, Hebrew, Greek, Tibetan, etc.). In studies of the Norse people's Runic characters and the Celtic symbols, anthropologists find that the symbols of alphabets appear to have served sacred and mystical purposes hundreds of years before they find evidence of their application as a written language for the general society (Branston, 1980).

We are suggesting that the "hidden meaning" of the letter/number symbols of the ancients is really the fact that the ancients knew that numbers/letters were symbols linked to an aspect of a universal idea or quality beyond the physical, i.e., connected to "number" archetypes in the spaceless-timeless realm. Thus, numbers/letters could be used as elements in a hyperdimensional map of that higher reality. These symbols for universal patterns -- whether we see them, hear them, or feel them -- are received by our sensory system and are mapped upon our brain. In the brain a comparison process and feedback to the mental realm occurs. There exists a filtering process. PET scans of the brain show that when we receive words or near words the brain "lights up" in recognition. However, when symbols or sequences of letters that are not "relevant" to a person are received by the brain, there is no indication that an active mental process occurs. (Petersen, et. al., 1990)


EXAMPLE 1: READWARE

What evidence do we have that letters/numbers are symbols that connect us to fundamental archetypes associated with a universal idea or quality? We have not found such evidence in mainstream linguistic but rather in a commercial computer software application. The application is based upon a new linguistic and cognitive theory named READWARE invented by Dr. Tom Adi of Management Information Technologies, Inc., who developed the theoretical foundation from study of the Arabic text of the Holy Quran (Adi & Ewell, 1987; Ewell & Adi, 1987).

Although this theory remains controversial, the underlying hypothesis is that the letter symbols have inherent meaning and "that each letter acts on our mind in a way that is different from every other letter." (Adi & Ewell, 1991) Thus, letter semantics is founded on the principle that every word of a natural language is a combination of alphabetic letters, every single letter is a message in itself, and every way of combining letters is a more sophisticated message. By analogy letters could be considered particles, whereas words are more like molecules, yet both serve as symbols for linking us to the archetypes of the spaceless-timeless realm. The universe helps us "discover" letters and words. An "egg" could never be called a "horse" -- it just wouldn't resonate right in that feedback process between our brain and the mental realm -- and it would soon drop out of our vocabulary. (Adi & Ewell, 1987)
Based upon the this theory, a U. S. Patent was granted in 1989 and then commercial software was marketed. (Adi, 1989, Fellows, 1991) The first application, "The Research Assistant," is being marketed as computer software for the IBM-PC. The software performs an Idea Search in contrast to a Keyword Search. It is the first software program that understands human languages without dictionaries, synonym lists, thesauruses, indexes or the programmer's rules and strict query protocols typical of artificial intelligence (AI) text retrieval programs. Letters are converted to binary numbers in the computer. The computer program then uses two algorithms, one that computes the content of information about reality from the letters of a word, and another that computes the amount of common information content between two arbitrary words.

An independent evaluation of the software's performance recently was featured in the Library Software Review. (Urr, 1991) The reviewer noted that "The Research Assistant (RA)... offers a genuinely distinctive free-text retrieval program that uses neither the Boolean text-string methods nor any type of AI approach." After discussing the "letter semantics" theory, the reviewer commented: "This may all sound rather abstract, but I can attest that, even if you do not fully understand the theory behind this program, it does seem to work, often very well." The reviewer then went on to discuss "one of the most interesting or perhaps magical results" that occurred when he tested the program. "The program successfully found a highly relevant passage even though none of the words pertaining to the specific issue at hand, included in the search statement, appear in the text retrieved. No conventional text-retrieval program could have found the text RA did using the search terms employed in this exercise." The principle caveat the reviewer had was that the program pulled up a large proportion of apparently "utterly irrelevant items."

Because letters, or the sounds they represent, have meanings, the process may be applied to the words of all alphabetical languages, without the need for translation. (Adi, 1989, p.15). Thus, in the current software the query can be in one language, and the text to be searched can be in any of eight languages (Arabic, English, French, German, Hebrew, Russian, Spanish, Swedish) (Helgerson, 1988). In theory, the number of languages can be increased to include all alphabetic languages. In fact, Ken Ewell, President of Management Information Technologies, Inc., states that "There is no reason to believe that it couldn't also be applied to the Chinese language and its derivatives. We need only determine which of the Chinese symbols are elementary, in the same sense as in the Indo-European and other Western languages." (Ewell, 1990)


EXAMPLE 2: MERU

There is other evidence, again not mainstream, that purports to be the discovery of a mathematical relationship between a sacred alphabet and the sequence of letters in a sacred text. The research of Stan Tenen and the MERU Foundation is exploring the relationship between the Hebrew alphabet, the Biblical text and three dimensional geometrical forms (Tenen & Gough, 1989). What has been discovered is a mathematical relationship between a sacred alphabet (Hebrew) and the sequence of letters in a sacred text (Genesis). The letters of the Hebrew alphabet have been recreated by projecting two dimensional shadows from a three dimensional form as shown in Figure 7. Using a rotational algorithm, some of the letters even emerge in their appropriate order. From the same form letters of the Islamic Arabic alphabet have also been produced. Thus, according to this research, the sequence of letters in Genesis is just as determinable as the sequence of numbers in pi!

But how can any predetermined sequence of letter symbols yield the beauty, the poetry, of say the King James version of Genesis? Recall that each letter/number symbol has associated with it qualities of a "number" archetype in the spaceless-timeless realm that provide it meaning. Short sequences of letters will carry the more sophisticated meaning of words. In effect, the predetermined text of symbols is writing its own story -- a message from beyond space-time -- the "word of God!"

The MERU research has not been subjected to wide review or criticism, therefore, its value is untested. However, it is suggesting that the ancients were accessing the spaceless-timeless reality and expressing their discoveries via their sacred alphabets and texts. This was probably accomplished by mental processes such as meditation and prayer. Hence, the Hebrew alphabet and Bible could represent a sequence of letter/number symbols that relate to the archetypes of the spaceless-timeless realm. Thus, they may provide even deeper insights about the nature of the universe then is generally believed and may even model the life process. (Tenen, 1989, 1990, 1991).

The reconstructed model of the ancients that has emerged from the MERU research presents a theory of creation from a spaceless-timeless realm, that is both continuous and self-organizing. There is an "unfurlment" of space-time and the "things" or patterns that fill space-time. The system is open, and it is hierarchical and self-embedding. The MERU model predicts a feedback linkage between the physical and mental realms. This feedback in the MERU model is between a 3D physical world and a 6D mental universe and is via a helical (rotational) form. In complex space, the linkage can be visualized as geometric shapes that evolve from 3D towards 4D by a process of symmetry breaking. The MERU model of the ancients has considerable similarities with our quantum linkage model. We believe that the MERU work could become an important element in developing the long sought bridge between science and religion.


SECTION IV: THE MECHANISM FOR LINKING MIND AND MATTER


THE PROPOSED MODEL -- THE DETAILS

The approach thus far has been to focus attention on the two "sides" of the mind-matter connection in order to illustrate that they are, indeed, parts of a continuum. Now we will examine the connection itself in more detail with the objective of making plausible our contention that it can be understood within the framework of conventional physics and mathematics.

A brief review is needed to re-set the stage for this section. We have pointed out that the foundation for all the mathematical structures which so accurately describe the world of matter is the 4-dimensional manifold of space-time. The section on the Unification Program demonstrated that the classical picture of this manifold as the continuous, non-permeable boundary of all that is real is flawed and that physics is prepared to accept a new and richer topology for its foundation. Three candidates for this new topology were mentioned briefly, each having its own set of attractive aspects as well as potential drawbacks. We have selected twistor theory to describe in more detail based upon its several unique features that happen to fit in nicely with our model.

First, a disclaimer is in order. Twistor theory is an extremely abstruse mathematical subject, as one glance at the Twistor Newsletter (Twistor Newsletter, 1991) will prove, and we make no claim to being experts in it. Accordingly, we have benefited greatly from the work of other scientists who have been able to provide more readable interpretations of the highly technical writings of Penrose and his colleagues. (Ward & Wells, 1990; Gardner, 1990; Peat, 1988)

Penrose invented twistors almost a quarter of a century ago. They were created for the express purpose of replacing space-time with a new kind of topology of 4 complex dimensions (an 8-dimensional space) called twistor space. Twistors combine the spin or twist of angular momentum with an axial component of linear momentum. It is possible to visualize a twistor if it is projected to a space of 3 dimensions. Figure 8 is taken from the cover of the Twistor Newsletter; Robert Forward's verbal description is also helpful:

One way of trying to visualize the geometric view of a twistor is to imagine a small hunk of complex space shaped like a twisted rope ring that travels along its axis at the speed of light. If the twistor has a lot of energy, then it is a tiny, tightly wound, localized loop of thread. If the energy is low, then it is a bloated hawser whose influence extends for a considerable range. ... From a geometrical point of view, a twistor can be thought of as a "fuzzy" particle. (Forward, 1980, pp 40-49)
These are the entities that make up twistor space. To go over to space-time one uses the Penrose transform to take data from one space to the other. (Ward and Wells, 1990) Even though twistors are discrete as opposed to continuous, they are effective in representing space-time, because, at Planck-length dimensions, a point "fuzzes out" in twistor space as a result of the uncertainty principle.

Twistor theory has other features which help make it a serious contender in the race toward the Theory of Everything, and these are described by Peat (Peat, 1988) and Gardner (Gardner, 1990). For our purposes several need to be mentioned briefly: (1) Twistors can be combined in pairs, triads, etc., to model the properties of the elementary particles including their internal symmetries. (2) Twistors have a built-in asymmetry both in time and helicity (twist) which may be important in explaining why such asymmetries manifest at macroscopic and even cosmological scales. (3) Twistors are inherently non-local. This is such a significant property from the standpoint of our model that it needs to be discussed in a separate section below.

Some idea of the scope of the efforts of Penrose and his co-workers can be seen in the "Twistor Program" as reported by Peat (Peat, 1988, p 213):

o Extending the earlier ideas of spin networks and generating a space-time out of twistor relationships alone.
o Expressing the elementary particles, their internal structures and symmetries in terms of twistors.
o Using the complex analytic properties of twistor space to understand the various fields of physics.
o Exploring the implications of quantum theory for the twistor picture and speculating on ways in which quantum theory may be transformed.
o Understanding how space-time curvature enters via twistor space and giving a rigorous treatment of quantum gravity.

This glimpse into the intricacies as well as the power of twistor theory is to help drive home the point that there are a considerable number of physicists who are working intently on a theory, one objective of which is to show that continuous space-time is, at best, an approximation. In addition, it is possible to understand how working from the very small up to the large may be more productive for creating the TOE than the more usual large to small approach. Twistors, as well as superstrings and knots, are all capable of generating particle-like structures, and, with suitable additions (see below), the force fields responsible for their interaction.


FIBER BUNDLES

There is one more link in the chain that needs to be discussed in connection with the details of the model. This remaining link bridges the gap between twistor space and still higher dimensional spaces that we choose to identify as sub-levels of Mind. The needed connection is provided by fiber bundle theory, a branch of pure mathematics called differential geometry. Bergmann provides this description of these geometrical structures:

Given a manifold, such as space-time, called the base manifold, one attaches new manifolds to each point. These attached manifolds, all identical, are the fibers. They may have any dimensionality, not necessarily that of the base manifold. Each fiber can be subjected to mappings, or transformations on itself, which maintain the fiber's essential properties. ... Given a fiber and its permitted self-mappings, one may introduce a connection that establishes 'corresponding' points on fibers at nearby points. (Bergmann, 1979, p.44)

Fiber bundles fit into twistor theory in an essential way. Ward (Ward & Wells, 1990) has shown that, while adequate for certain of the internal symmetries of elementary particles, twistor space is not general enough to handle the quantum forces that operate between the particles. He has, therefore, introduced fiber connections at each point of twistor space, giving it a much richer geometrical structure. Although we did not bring up the subject before since it would have required additional explanation not germane to our model, it turns out that there is an intimate mathematical relationship between the force fields (the so-called "gauge fields") of physics and fiber bundles. (Bernstein & Phillips, 1981, pp 123-137) The Nobel laureate, C.N. Yang tells the following story about this relationship which is germane to our model. He is relating a conversation with the mathematician, Shiing-Shen Chern:

I said I found it amazing that gauge fields are exactly connections on fiber bundles, which the mathematicians developed without reference to the physical world. I added, "this is both thrilling and puzzling, since you mathematicians dreamed up these concepts out of nowhere." He (Chern) immediately protested, "No, no. These concepts were not dreamed up. They were natural and real." (Yang, 1980, p 42)

Figure 9 summarizes this detailed description of the model. It shows explicitly how mathematical links connect the two realms of Mind and matter. Two caveats are needed, however: (1) Twistor theory and the Penrose transform may not be the final form of the "Theory of Everything." Some mixture of strings, knots, loops, and twistors may ultimately be necessary to provide the best foundation for the Unification Program. But we are confident that whatever eventual form the theory takes, continuous, 4-dimensional space-time will no longer be regarded as a firm foundation for physics; it will, instead, be considered as an approximation. (2) The identification of higher-dimensional manifolds (hyperspaces) with sub-levels of Mind is unique to this model and would not be regarded as orthodox mathematics. (If it were, this paper would not be necessary!) We believe, however, that the evidence and arguments arrayed here are sufficient to counter this objection.


NON-LOCALITY:

Our model evolved from the science of inanimate small structures and is based upon quantum theory. Quantum theory has been firmly established, and however bizarre its predictions, no exceptions to the theory have been found. A key point that we wish to emphasize in this model is one particular aspect of quantum theory -- the issue of non-locality. Erwin Schroedinger called non-locality "quantum theory's most distinctive feature, the place where it differs most from classical expectations." Unlike all conventional interactions which drop off with distance and cannot travel faster than light, the quantum linkage due to non-locality is as strong at a million miles as at a millimeter, and its changes are transmitted instantaneously - considerably faster than the speed of light. (Herbert, 1988a, p. 58)

In 1964 John Stewart Bell proposed a crucial test between the predictions of quantum theory of non-locality and those of any theory based on the concept of local reality. This test, known as Bell's Theorem, did not propose an experimental situation in which non-local interactions are directly observed. Instead, Bell invented a simple argument that could be tested experimentally that would indirectly demonstrate the necessary existence of non-local connections. (Herbert, 1988b, p. 318)

Local reality means that effects that are strong within a given region of space fall off outside, so that it makes sense to divide the world into separate, self-contained systems that interact by forces and signals that fall off rapidly with distance. Thus, the idea of non-locality is shocking, because for hundred of years scientists have said that if anything moved it was because something else acted on it. Non-locality suggests that distant systems can be connected in a totally new way -- a way in which distance no longer seems to matter.

The experimental results are now in and most physicists are well satisfied that quantum theory has been confirmed and local reality has been ruled out. The tests of Bell's theorem demonstrate that the quantum linkage is real and that, whether we like it or not, nature has chosen to include this instantaneous linkage into her creation of reality. (Herbert, 1988a, p. 60) These careful experiments were carried out by Alain Aspect and others and have shown that quantum systems are correlated in ways that defy explanation in terms of any connections, interactions, fields, pushes, or pulls that would have any meaning in conventional physics. Today, the only possibility for continuing to believe in a local-reality theory is to suppose that the Bell correlations are somehow the result of a physical interaction or signal that passes between the detectors at a speed that is faster than light! (Peat, 1990).
Normally, we think locally -- that's how we divide reality. We divide it into separate self-contained systems where the interaction between systems decreases with distance of separation. Indeed, even physicists do not possess a single description of the world. They alternate between two modes of speaking about things - a classical language and a quantum language - depending on whether an object is being observed or not. The majority of physicists dismiss the quantum linkage of non-locality as a philosophical question not a phenomenon applicable to everyday life. (Herbert, 1988a p. 57) However, macroscopic quantum effects have been observed in superconductivity and superfluids. (Shimony, 1988; Leggett, 1986) What we are suggesting is that you consider in your concept of reality that such phenomena just might exist on a macroscopic scale -- even though the physics experimental data was developed on a microscopic scale.

However, not all scientists are avoiding the implication of the question of non-locality in quantum theory. Various scientists are developing ways to address the issue -- David Bohm and his Implicate Orders, Roger Penrose and his twistor theory, and Edward Witten and his knot physics (Peterson, 1990). Much of this work is seeking a generalization of geometry that lies beyond the space-time of general relativity and the non-Euclidean geometry used by Einstein.

We believe that non-locality at the quantum level underlies all phenomena and that the world is filled with innumerable non-local influences. Thus, we agree with John Stewart Bell, Nick Herbert, and others who state that these instantaneous linkages underlie everyday reality. (Herbert, 1988b, p. 319) According to Bells' theorem our knowledge via quantum connections at every level is non-local and instantly linked to everything we have previously "touched." Thus, we may ask, that if a quantum connection of some kind is established by every interaction, then why aren't all human beings experiencing this unity? One reason for this apparent absence of unity might be that, although the strength of the quantum linkage does not diminish with distance, there appears to be a form of "coupling coefficient" associated with each connection. Where coupling is defined as an interaction between systems, or between properties of a system. When there is little interaction, the coupling is said to be loose; with considerable interaction, it is called tight.

This coupling coefficient can be reduced by subsequent irrelevant interaction or reinforced by repeated interactions of the same connections. The fact that the quantum linkage can be diluted by irrelevant interactions means that to keep the connection intact, the quantum linkage may need to be protected from outside influence. It also implies that frequent direct contact is an effective way of strengthening the quantum linkage. Our suggestion is that mental thoughts/intentions can alter the coupling coefficient for a quantum linkage -- in people/people, people/matter, and matter/matter interactions.

This could be why clarity of intent, i.e., choice of a clear-cut linkage, and sharp focus of attention, i.e., removal of outside influences, are key to successful use of subtle energy in healing. In fact in all human relationships, one could speculate that any intense emotional process would initiate a persistent quantum linkage between people. Thus, forever after, their union is, in the words of Nick Herbert, "unmediated, unmitigated, and immediate" on the many levels of experience due do the quantum linkages. (Herbert, 1985, p. 214)

Also, in metaphysical traditions some of the admonitions in the practices have greater meaning if we assume that they involve quantum linkages, i.e., linkages to the spaceless-timeless reality of Mind. For example, the stressing of secrecy in the ancient traditions could reflect a recognition that the effectiveness of the process would be diluted by irrelevant or hostile mental interactions at the mental and emotional level. The emphasis on daily meditative practice could be a recognition of the need to maintain and strengthen the quantum linkage.

One could also speculate about certain types of scientific experiments. If a quantum linkage were to be a key element in an experiment, one would expect non-repeatability to rear its ugly head when there was a decrease in focus of attention or a negative outside influence. This may be at the root of some of the repeatability problems discussed in parapsychology literature. It also might be considered as a contributing factor to the strange reports of non-reproducibility in areas such as "cold fusion." (Close, 1991) However, we should avoid the temptation of attempting to explain away all mysteries by resorting to quantum non-locality -- nevertheless, non-locality is a phenomenon of nature that exists.

We will discuss later our speculation that non-local effects participate in our brain's functioning. We will also discuss how non-local effect relate to the ideas of Carl Jung and Wolfgang Pauli and the theory of synchronicity, i.e., that meaningful patterns in the universe are generated through acausal connections from beyond space-time. (Peat, 1987)


TWISTORS AND NON-LOCALITY

Bell's theorem and the requirement of non-local reality have not had nearly the impact on physics that one might imagine, given the startling implications of the theorem and its experimental tests. Ballentine has charted the annual citations of Bell's paper showing a gradual rise to about 33 over 2 decades (Ballentine, 1987). This "ho-hum" response is easily explained by realizing that to the great bulk of practicing physicists quantum mechanics is a calculational tool that works exceedingly well for certain kinds of problems, but as a guide for the formation of a philosophy or worldview it may be subject to too many differing interpretations (Herbert, 1985).

Nevertheless, to those having philosophy as a passion and who see quantum mechanics as the window to the basic structure of the universe, Bell's theorem may indeed be "the most profound discovery of science" (Stapp, 1975). Those working in this area, in particular those concerned with developing some kind of TOE, are faced with one of the most baffling problems in physics. How can a theory be formulated that incorporates the demands of Bell's theorem and still be compatible with all the other "good" theories of physics which are based on local realism? Herbert states the case rather forcefully (Herbert, 1985, p. 214):

Despite physicists' traditional rejection of non-local interactions, despite the fact that all known forces are incontestably local, despite Einstein's prohibition against superluminal connections, and despite the fact that no experiment has ever shown a single case of unmediated faster-than-light communication, Bell maintains that the world is filled with innumerable non-local influences. Furthermore these unmediated connections are present not only in rare and exotic circumstances, but underlie all the events of everyday life. Non-local connections are ubiquitous because reality itself is non-local.

It may be only coincidence that Roger Penrose was developing the beginnings of twistor theory about the same time that Bell published his famous theorem. But over the two and a half decades since that time twistors have received even less public notice than has Bell. For example, Barrow's 1991 book makes no mention of twistors while giving considerable coverage to superstrings (Barrow, 1991). This apparent neglect could be attributed to the somewhat radical approach that Penrose and his colleagues have taken as well as the difficult mathematics that must be mastered in order to deal with twistor space (Ward and Wells, 1990). The latter problem may be responsible for the dearth of literature on twistor theory for physicists who want to explore its features without too many mathematical accouterments. Fortunately, Peat (Peat, 1988) has helped fill part of this gap with a non-mathematical survey of twistors, and we have relied heavily on his work in order to provide this brief description of how they relate to the non-locality issue.

We have noted above that twistors are inherently non-local in their structure. This is because they are designed not to embody spacelike dimensional qualities; instead they combine quantum mechanical angular momentum (spin) and relativistic linear momentum (speed of light). As a result twistor space, which is made up of these objects, has the property of defining direction but not separation or distance. Non-locality is therefore an intrinsic and natural property of twistor space.

However, space-time is where we live, and it is also the abode of the conventional fields and formulas of physics. In order to take advantage of the power of the twistor formalism, the physics of space-time can be taken over into twistor space (and vice versa) by means of a set of mathematical rules called the Penrose transform (Ward and Wells, 1990). When the transform is applied to the space-time manifold it turns out that a "null line" or ray of light in this manifold corresponds to a point in twistor space. In other words, the points of twistor space can be thought of as encoding global or large-scale information about space-time. Bell's quantum connection, therefore, finds a natural home in twistor space. The deeper structures of reality do indeed lie outside of space-time.

But the "baffling problem" alluded to above still remains: How can it be that our space-time world of experience, which is dominated by four forces propagating at the finite speed of light, be coupled to a non-local reality in which connections are immediate and unmediated? This paradoxical situation, we believe, can be resolved within the context of our model. Our explanation utilizes two rather specialized subjects in physics which we have not needed to discuss up to now. The following two paragraphs will help set the stage.

Alfred North Whitehead (1861-1947), philosopher and mathematician, has proposed a "process" model of the world which is regarded as one of the major philosophical works of modern times (Whitehead, 1929). Stapp (Stapp, 1979) has argued that this model provides a natural theoretical setting for quantum theory. "The basic elements of the model are events that actualize, or bring into existence, certain definite relationships from among a realm of possibilities or potentialities inhering in the set of prior events." The model is also in accord with the idea that "actualization" is brought about by mind or consciousness as part of a feedback loop.

The Unification Program for the forces of physics is driven by the belief that the forces are "gauge fields" (mentioned above under Fiber Bundles) and have their roots in an underlying "gauge symmetry" in abstract mathematical spaces (Barrow, 1991, p. 74) (which our model places in the mental realm). The common velocity (of light) that the forces have in physical space can be attributed to a common origin in a pattern outside of space-time.

Putting these two ideas together produces a picture of the physical world continuously "unfolding" out of the non-local realm of patterns at the finite rate of the speed of light. (This picture is not unlike that proposed by David Bohm (Bohm, 1980, 1985) with his implicate and explicate orders.) Thus quantum connectedness, which is intrinsic to the pattern realm, is compatible with the realm of matter with its universal speed limit. Since the Whitehead model provides for "actualization" via consciousness, this picture also suggests an interesting relationship between consciousness and light.

An analogy may help illustrate this point. Consider a loom which has a human operator watching the pattern unfold. The machinery of the loom runs at a fixed speed, but the operator has the ability to change the pattern at any time so that it conforms better to what she has in mind. Thus there is continuous feedback between what is unfolding and what has already been created. The weaving of the fabric of reality involves this continuous back and forth exchange between space-time and the higher realms.






SECTION V: DYNAMICS OF THE MODEL


THE ISSUE OF DYNAMICS

Up to this point we have focussed on the static features of the model, making only occasional references to the processes that occur in relating the parts of the system on the two sides of the space-time boundary. In this section we wish to elaborate upon the dynamics which apparently exist in this relationship. It is like describing how a telephone system works. First we show the wiring and other hardware and the interconnections. Then comes the electrical part in which the voltages and currents play their role in carrying information in both directions leading finally to meaning.

Our task is made somewhat more difficult because we do not have nearly as good a science of Mind as we do a science of matter. Physics and mathematics have evolved categories of thought which have made it possible for us to describe in conventional terms our proposed model of the connection between Mind and matter. But terminology for the mental realm is not as convenient. Although many different disciplines and ancient traditions have developed vocabularies for discussing the contents of Mind, there is not the degree of consensus on terminology that prevails in the natural sciences. Nevertheless, we have attempted to describe these dynamic processes in Western scientific terms with the hope that the reader will recognize that this effort is of a tentative nature.


SELF-REFERENCE AND FEEDBACK

In order to appreciate the dynamical nature of the quantum linkage model, it is helpful to recall one of its basic assumptions. We have assumed that the cosmos is an interconnected unity in which a hierarchy of levels are arranged in a "Chinese box" configuration with consciousness common to all levels. In effect such an interconnected unity represents a cosmos that is learning; therefore, in such a cosmos there must be self-reference, i.e., feedback processes must abound.

Indeed, feedback is an inherent aspect of how we learn about ourselves. For example, in our bodies the difference between the voluntary and the autonomic systems is the presence or absence of feedback to the brain. Once conscious feedback is achieved, voluntary control over an autonomic process is gained. This has been strikingly demonstrated through biofeedback research and training (Green, 1989). But we also receive feedback and guidance from the spaceless-timeless realm. This feedback appears as dreams and the inner voice, visions, feelings of the sixth sense which are often expressed by a person through dancing, drawing, painting, modeling, music, or poetry.

The combination of the two feedback processes, one from the body senses, the other from the mental realm, merge in the brain and cause one to experience "a strong double life on the borderland between the earthly and the divine, the temporal and eternal, nature and dream." (Jaffe, 1971, p. 88) According to Jaffe, through this combined feedback process the body, mind, and higher levels (spirit) can be balanced. Whenever this balanced condition exists there is a realization of self, and an individual becomes self-fulfilled with the emergence of an aura of authenticity. (Jaffe, 1971, p. 79)

There is a tremendous difference whether the human race recognizes and accepts the fact that there are these two distinct kinds of feedback, one in space-time, the other in the spaceless-timeless realm. This is what allows us to span the immeasurable distance between the polarities of divinity and humanity, eternity and history, dream and reality. If we do act on the basis of our dual nature, human potential is essentially unlimited (or at least we are in no position to set any bounds). If this does not occur then we can expect to continue to experience imbalance and dis-ease, both as individuals and in the society as a whole.

In addition to the self-referential aspects of the human being, all of nature seems to display these feedback properties, with mathematics supplying us with clues as to how it might be taking place. Feedback and self-reference are related to fractals -- all can be expressed as mathematical recursive forms (Kauffman, 1987). The unimaginably detailed structures created by fractal geometry have been found to succinctly describe complex natural objects and processes (Peitgen & Saupe, 1988). A fractal model of a fern produced completely through mathematics by the use of an appropriate set of parameters is shown in Figure 10. Even a landscape with all its complexity can be generated with fractal mathematics, this method being commonly used in computer animated movies.


FRACTALS AND SCALING

The idea of the "dimension" of a space was defined in an earlier section, but we need to reconsider it in the light of fractals. The dimension of a "smooth" manifold (one with no holes) is the integer representing the number of coordinates for a point on the manifold. This integer is a "topological invariant," meaning that the manifold can be stretched and deformed (but not ripped) without altering its dimensionality. Consider, however, the relation between the perimeter of a snowflake and a circle. One would think they are topologically equivalent with dimension equal to one. But the snowflake's perimeter is infinite (theoretically) and cannot be put into the same class of manifold as the circle. It is regarded as a fractal. Dimensionality, for fractals, is therefore based upon metric properties rather than topological properties, i.e., properties analogous to distance. The result is that the dimension of a fractal can be a fractional value, such as 1.4427. (Stewart, 1987, pp 180-191).

Since fractals cannot be represented on a smooth manifold, their fractional dimensionality reflects "scaling properties" and results in self-similarity among scales. This means, for example, that one can take a section of coastline (a fractal) and magnify it, obtaining a result that is equally plausible as a stretch of coastline. Similarly, the fern of Figure 10 can be magnified indefinitely and still be a fern. Hence, for patterns in the physical world that can be represented as fractals, their coupling to the archetypal counterparts in the spaceless-timeless realm would appear to be independent of their physical size. In other words, for feedback from an appropriate archetype, it makes no difference if the physical pattern is on the scale of the solar system, a mountain range, a tree, a crystal, the DNA molecule, or the spin structure of an atomic nucleus. However, in addition to the effects of the archetypal patterns, the system is affected by other systems within the "horizontal" hierarchy of physical space-time thereby "bootstrapping" the infinite diversity we experience in the space-time world from a finite set of archetypes.

Thus, the mathematics of fractals gives us a form of "holographic" universe in which every pattern regardless of size can be thought of as linked in a feedback manner beyond space-time. This could represent a key organizing principle in nature. Such an organizing principle is supported by Michael Talbot's recent book, The Holographic Universe. (Talbot, 1991)


COMPLEX NUMBERS

Another branch of mathematics provides a glimpse at an additional possible dynamic relationship between Mind and matter. The complex number system with its "imaginary" square root of -1 was invented to accommodate the needs of mathematicians but soon found a host of applications in physics and engineering. Imaginary numbers serve as a kind of "rotator" which moves a quantity into another "realm." The very names for the two kinds of numbers ("real" and "imaginary") suggest this sort of action. Thus, in relativity theory, time is wedded to space by making it imaginary. Also in applications involving time-varying quantities, such as electromagnetic theory, fluid mechanics, aerodynamics, and waves, complex numbers play a major role in simplifying the mathematics. But for our purposes the most interesting feature is shown by Kauffman (Kauffman, 1987) to be the fact that the self-reference process is precisely mirrored by the formalism of complex numbers.
A curious contrast exists between the roles that complex numbers play in classical physics and in modern physics (relativity and quantum mechanics). In the former, as indicated above, complex numbers greatly simplify the mathematics, although the theories could be expressed in terms of "real" variables. But in modern physics, particularly quantum mechanics, complex numbers are vital to the correct formulation of the theories. It is almost as if modern physics is inviting us to move out of the "real world." Indeed, in Wolfgang Pauli's quest for a bridge between mind and matter, he received a very provocative response through his dreams about complex numbers. A Chinese lady presents him with a mathematical symbol -- the ring i, which corresponds to the complex unit circle. "As a mathematical element the complex unit circle is simplicity itself, but as a symbol it is as profound as the cross in Christianity. Its subtlety consists primarily in that it represents a marriage of two dimensions, the real and the imaginary." (van Erkelens, 1991)


MATRICES

The development of quantum mechanics in the mid-1920's proceeded along two distinct lines. One was Schroedinger's wave mechanics; the other was Heisenberg's matrix mechanics. It was eventually proved that both approaches were mathematically equivalent, even though the starting points were radically different. This fact suggests that we take another look at matrices and their applications even though we have already explored their connection to archetypes. Perhaps more light might be shed on the inner workings of the mental realm.

In addition to its esoteric use by the ancient Chinese discussed