Chapter 3. A Survey Of Contemporary Science

As I stated in the previous chapter, science and occultism are highly related in the sense that van der Leeuw describes. Science is an investigation into physical phenomena and occultism is an investigation into essentially nonphysical phenomena. We will discuss what it means to say that occultism is an investigation into nonphysical phenomena in the upcoming chapters. I have three intentions in this chapter. First, I would like to describe science in such a way as to set the stage for a unification or synthesis of scientific and occult ideas. What this means is that I will focus on concepts and notions from modern science that are particularly relevant in this regard. Yet, even though I am taking such a slant, I will do so within the context of all of the disciplines of science that are practiced today. Indeed, it is necessary to have at least some understanding of the relationship between the various disciplines of science in order to appreciate the relevance of occultism to science. My second intention is to convey to the reader the actual spirit and "feel" of what science really is to those who do it for a living; to show that science is a real activity that real people actually do. For I feel that science has become overly mystified in the popular mind, and that the average person sees scientists as somehow larger than life. Though scientists have done some great things, they are normal people like everyone else, and I want the reader to realize this. And third, I would like to describe science in such a way that it is seen in the greater scope (one among many) of activities with which human beings involve themselves. In this third regard, let us begin by looking briefly at the history of science.

What we call science today is an activity and approach to life that has its origins in the Renaissance period of Western European history1. It was during this time that Western Europe was climbing out of the Middle Ages through the discovery of the writings of the ancient Mediterranean civilizations which had been preserved by the Byzantine culture. The rediscovery of ancient Greek and Roman teachings, the works of Galen and Ptolemy and others, ushered in a new mentality for Western civilization. As well, this was the time of the crumbling of the Medieval feudalism and the early beginnings of secular nation-states and capitalistic economies. The 14th through 16th centuries was a period of great transition for Western civilization as it broke out of the shackled ignorance of the Middle Ages. The rise of modern science was the rise of a new attitude and a new civilization in Europe. The secular humanism which replaced the sacred traditions of the Church was an attitude that rejected the blinding faith required by the Church and replaced it with new and open eyes turned toward the marvels of Nature.

Initially, science did not exist as a separate branch of learning. Those who used science were scholars, physicians or magicians (alchemists and astrologers). In this period science was not distinguished from Natural Philosophy, but was a part of it and was seen as one approach to knowledge among many.

But over time, as physicians and magicians tried to apply the ancient learning, errors and discrepancies were discovered one after another. As a result, many began to branch out on their own and break away from the teachings of the ancients, usually quite violently , as the ancient teachings were the standards of learning to the respectable society of the day. This was a period of innovation that bred the likes of Paracelsus, Kepler, and Francis Bacon. It was at this period in history that Giordano Bruno was burned at the stake by the Roman Inquisition for his espousal of Copernicus' theories.

This was age of the beginning of the real innovative spirit behind modern science which scoffed at useless traditions and mocked the myths and old wives' tales of the past. The following quote in which Paracelsus is defending his teachings against those who would cling to the old ways conveys the spirit of the period nicely:

"You are not worthy that a dog shall lift his hind leg against you. Your Prince Galen is in hell, and if you knew what he wrote me from there you would make the sign of the cross and prepare to join him."2

The culmination of this period can be seen in the works and discoveries and very life of Galileo Galilie, armed with his crude telescope observing the moons of Jupiter (among other things) and overthrowing old dogmas for good. And as these bold innovators pressed on against the weight of worn out traditions, they left behind them an accumulation of new facts, new practices and techniques in medicine, astrology (which became astronomy), mathematics, navigation, physics and chemistry and every other field of endeavor they touched. And this accumulation began to take on an identity of its own and these things became known as "science".

And here we are today, 350 years after the death of Galileo, the inheritors of this science. A lot of water has gone under the bridge in this time. After the era of Galileo, science took on a definite form. First there was Newton with his mathematics and physics, Laplace the great French mathematician and physicist, Dalton and Lavoisier, the founders of chemistry. Then the nineteenth century saw Maxwell and his laws of electromagnetism, Darwin and his theory of evolution, Mendeléeff and the periodic table of the elements, Mendel and his laws of genetic inheritance. And as history entered the twentieth century even more bold and spectacular developments had taken place: Einstein's Theory of Relativity, The Quantum Mechanics of Plank, and Bohr, Heisenberg and Schrödinger, the discovery of the genetic code. And there is the work of thousands and thousands of others, whose names are not as familiar, who have left for us this heritage of knowledge and techniques that we call science.

Then, with the advent of quantum theory, the proverbial dam broke and the world transformed almost overnight. Today, a mere 60 years later, we live in a world of spaceships and computers, satellites and lasers, genetic engineering and, last but not least, nuclear bombs.

It is very easy to be intimidated by modern science, but the best way to overcome this intimidation is by knowing history, and understanding how science fits into history. For nuclear bombs and lasers did not come into existence overnight or out of the blue. They have their roots in Galileo's struggle with the Church, in Newton's calculus, in Maxwell's equations, in the philosophies of Nietzsche or Wittgenstein, in the lives of real people who lived and walked on the Earth like you and I. The rise of modern science is a courageous and inspiring story. What's important to realize about the people who created science is that they were in some respects driven. They were driven by an urge to understand; to understand truth, to understand Humanity, to understand Nature and to understand God, at all costs and no matter what their contemporaries believed. These were people with curiosity and animated minds, people who were obviously dissatisfied with the explanations of their day and so strove through creative work and effort to discover new explanations and new ways. And because they were driven, they left for mankind a trail of accumulation; more techniques, more explanations, more science.

It was only after World War II that science really became the enterprise it is today. That scientists could produce an atom bomb made the world stop and take notice. Governments and politicians became involved in the scientific enterprise to a much greater degree than they ever had before. And science, during the last fifty years or so, has become a multi-billion dollar enterprise, and the preoccupation of affluent nations. More scientists have lived since W.W.II than in all the past taken together.

Modern science is the way of life in the late Twentieth Century. Modern science, I think we can say in all fairness, is the official State Religion of contemporary civilization. No longer is science the activity of rebellious intellectual upstarts. Today it is the accepted way and practice, it is our tradition--a tradition that Max Weber called "rationalization"3. Science has definitively and finally ousted religion and replaced it as the ultimate dispensary of truth. And today we treat the proclamations of scientists as past ages treated the proclamations of priests.

I think it is important to realize the social reality of science today. Much of the popular image of the scientist as the lone seeker of truth is today but a myth of an image that died over 100 years ago. Today science is a very sober and rational enterprise, and it is a huge enterprise. Science is no longer an adversary to the legitimate powers. The scientist today is the right hand man to governments and huge multi-national corporations. Today's scientist is Merlin the magician of King Arthur's Court.

There is no facet of our modern life that is unaffected by modern science. The roads we drive on, the cars we drive in, the gasoline our cars use, the toothpaste we use, and the wine and soda pop we drink, our polyester underwear, all the medicine we take, our TVs, stereos and VCRs, the telephone and microwave oven; all of these are the products of modern science. Some like to make the distinction between science and technology, but this is a useless distinction. Technology is the physical product produced from science. Technology exists because we do science in a capitalistic free marketplace.

And as well as the physical products of science, our whole image of who and what we are is grounded in modern science. We see ourselves through science's eyes, through the ideas and notions that make up modern science. Through the eyes of science, we know the Earth is a globe spinning about a vast nuclear fire-ball called the Sun, and that our Sun is but one of billions of similar entities that we see as stars in the night sky. And we know that the human race is but one species among millions here on the face of the Earth, and that great processes of evolution over long ages have created life as we know it today. We think of our bodies as complex arrangements of chemicals, and TV commercials sell us on the cholesterol content of their products. Science has defined for us what and who we are. Science is the myth maker of the modern world.

Since everybody uses technology, and most everybody is exposed at least to some degree to the mythology of science, then, in these respects, everybody uses science as well. But there are certain people who use science more than others; people who use science on the job, you might say. These people are not only scientists, but engineers, and doctors, teachers and even philosophers and businessmen. These are the people who make their living by doing science today. The man (or woman) on the street has a different image of science than the man (or woman) who does science. In the media, science is displayed in a sensationalist fashion that is nothing at all like the reality of doing science. The popular image of science and the ideas used by scientists in their day-to-day endeavors are two totally different things. The reality of doing science on the job can range from the monotony of testing the quality of a piece of equipment over and over again to the excitement of winning the Nobel Prize.

Most of the excitement in science today is not with the thrill of discovery, but with the prestige of discovery4. In the day-to-day activity of science though, there is little discovery, it is mostly application of what is known. So the engineer programs well known equations into his computer, the medical technologist analyzes blood samples, the graduate student sequences yet another gene. When new facts are discovered they are but incremental steps in a direction that is clearly laid out and anticipated. The bulk of modern science has little to do with the penetration of Nature's profound mysteries. There have been recently discoveries in modern science that are deep penetrations into Nature's mysteries, and I am referring to the new science of Chaos and the new mathematics called fractal geometry (which will be discussed below). But such steps are rare. Usually it's just more of the same old thing; a new pill, a better engine, a biodegradable plastic bag.

At this point there are some notions I would like to discuss that will make it easier to understand the nature of scientific knowledge and the relationships between the various theories in science. Also, the following discussion will be critical for understanding the relationship between science and occultism.

A philosopher named Thomas Kuhn published a ground breaking book in the 1950s entitled The Structure Of Scientific Revolutions5. Kuhn's concern as a philosopher was to develop an understanding of how scientific theories change, and how science as a whole evolves. Kuhn put forward the theory that, in any particular branch of science at any given time, there exists a guiding intellectual framework that Kuhn refers to as a "paradigm". A paradigm is a model of how the world works, it is a set of ideas that defines what is and what is not real to the scientist who uses that paradigm. A paradigm is like a road map that the scientist uses to make sense out of Nature. Kuhn actually likens a paradigm to a puzzle, and likens the scientists who use the paradigm to puzzle-solvers. Thus, the popular image of a scientist as a discoverer is wrong in Kuhn's account of science. The only "discoverer" is the person who created the paradigm initially; the rare Newton or Einstein. The creator of the paradigm was the one who recognized and expressed a new way to view the world, a new truth, a new definition of what is and what is not real.

But the new paradigm is very nebulous, there are a lot of holes in it. What happens though is that other scientists will begin to accept the paradigm, incomplete though it may be, and see reality within its light. A prime example of this situation occurred when Charles Darwin expounded his theory of evolution by natural selection. When he originally stated this theory, he had no actual mechanism to account for the process of natural selection. Yet this did not stop scientists from accepting Darwin's theory as a "road-map" to explain biological life as we see it. The fact that this theory could not really explain how natural selection occurred was simply overlooked, and it was trusted that this mechanism would eventually be found. Forty or so years later, Mendel's laws of inheritance were rediscovered, and it was eventually realized and accepted that the "gene" postulated by Mendel was indeed the actual physical basis for evolution by natural selection. Thus, a paradigm is far from complete, or even consistent, at the time of its inception.

The scientists who come to accept a new paradigm are then what Kuhn calls the "puzzle solvers", for they have been given a incomplete picture of the world, and it is up to them to fill in the details. The puzzle solving scientist does not discover anything, he simply fills in the blanks of the paradigm and gives it more detail and makes it richer in particulars. But even though there are more details, the essential definition of what is and what is not real is still the same. This is why I said above that most discoveries in science are but incremental steps in a clearly anticipated direction. Really, in Kuhn's context, these are not discoveries but puzzles that have been successfully solved. And Kuhn, using examples from science's history, shows that paradigm creators are rare and the vast bulk of scientists are actually those who are the puzzle solvers.

Now there is more to Kuhn's theory that pertains to how scientists change from an old to a new paradigm. To say that a paradigm defines what is and what is not real to a scientist is very important. What this means is that the scientist only accepts the facts that the paradigm will allow him to accept. If the scientist encounters a fact that does not fit into the paradigm then the scientist will either ignore it or attempt to bend the paradigm to fit the fact. However, sometimes the paradigm simply cannot bend to fit certain facts. In this case other, usually younger, scientists will come along and create new paradigms to try to explain the anomalous facts. What results then is the competition between paradigms for the right to define reality in the scientists' eyes. This is what Kuhn called a "scientific revolution". The outcome of such a scientific revolution, according to Kuhn, has little to do with "truth" or with an understanding of Nature. Kuhn likens a scientific revolution to Darwin's notion of the "survival of the fittest". That is, what happens during a scientific revolution is literally a competition between different groups of scientists for the right to define reality. And the stronger group wins, perhaps by political means, and in spite of what may or not may be "truth". Often, scientific revolutions are hostile and bitter affairs amongst scientists of competing camps. The new paradigm only comes to prominence when the exponents of the old paradigm die. That is, when all of the scientists who believed in the old paradigm die, and all that is left are the younger scientists who use the new paradigm, then the new paradigm will eventually take over in the eyes of the scientists. Thus, a scientific revolution comes to pass, and "facts" or "truth" have very little to do with the process.

These are the essential notions we need for understanding science and for understanding the relationship between science and occultism. First, in terms of understanding modern science, one needs to realize that each of the fields of science is a paradigm. Thus the understanding of the different disciplines in science amounts to understanding the paradigms that define the disciplines. Second, with respect to discussing occult and scientific ideas and the relationship between them, we must realize: 1. occultism and science are different and competing paradigms, and 2. that to attempt to show a relationship between scientific and occult ideas amounts to no more than a scientific revolution. Claiming that occultism and science are related is almost a declaration of war on the paradigms that currently make up modern science because none of these paradigms accept occult facts.

3.1 The "Hard" And The "Soft" Sciences

There are a few different notions by which to understand modern science. One was already mentioned; "pure" verses "applied" science. What these terms mean is that "pure" science is science that is done with the intent of "knowledge for knowledge's sake" and "applied" science is science that is done for some definite application. Within this distinction, an example of pure science would be a researcher studying migratory patterns of birds simply because she wants to understand the phenomena. A perfect example of applied research involved scientists figuring out how to separate the isotopes of uranium to build the atom bomb. In this case, they did not separate these isotopes to just know how to do it, they had a particular application in mind. But there are some examples of research that don't fit easily into this distinction, like AIDS research. One would think this would be a case of applied research, but it is not. Much "pure" knowledge is needed, in this case about the immune system and about how the AIDS virus interacts with the immune system. When the distinction of pure verses applied knowledge is closely scrutinized it turns out to be an ambiguous distinction, and thus, one not well suited for characterizing the scientific enterprise.

Another distinction made among scientists is the issue of the "hard" verses the "soft" sciences. In this case the "hard" sciences are those that are grounded in mathematical theories such as physics and chemistry. "Soft" sciences are those that use little mathematics and are primarily descriptive and qualitative, such as psychology or sociology. This is a fairly good distinction to make though the terms are somewhat misleading in their implications. What I mean by this is that, for example, the study of a chemical reaction is easy compared to say, the study of human psychology which is hard. But this is not what scientists mean. They use the term "hard" to denote that these sciences are on a firm mathematical basis, whereas the "soft" sciences are wishy-washy (or soft) in this respect. What does it mean to say that a science is on a firm mathematical basis? This means that the essence of the paradigm the scientist uses is defined by a mathematical theory. In some respects this distinction is a leftover from the hey day of positivism's influence on modern science.

Yet this is a useful distinction because the "hard" sciences, those that are firmly rooted in mathematical theories, are usually more reliable. That is to say, a "hard" scientist understands and can predict his phenomena better than a "soft" scientists can understand and predict her phenomena (I use the pronouns that way to make a joke on the male chauvinist scientists and their terminology). Let me elaborate on this in a clearer fashion.

What we must realize about modern science is that the paradigms that define the "hard" sciences are all interrelated in terms of concepts and definitions, experimental analysis and the like. The paradigms of the hard sciences are very interchangeable amongst each other. The paradigms of the "soft" sciences, on the other hand, are very fragmented and terms and definitions cannot be interchanged. And most importantly, the "soft" sciences exist in a vacuum relative to the hard sciences. Another way to say this is that the "hard" sciences form one big happy family, but the "soft" sciences do not, and neither do they fit into the family of "hard" sciences. That the "soft" sciences should or should not fit in with the "hard" sciences is a philosophical issue. I believe they should because I believe in the unity of Nature, in spite of the paradoxical need for many languages to describe Nature's unity. And, as we shall see, the relationship between science and occultism has an incredible bearing on the present state of dissociation between the "hard" and "soft" sciences.

Now, examples of the "hard" sciences are the general fields of mathematics, physics, chemistry, and biochemistry. Each of these disciplines has a myriad of specialties but they need not concern us here. Now in the actual education of these scientists, a mathematician does not need to learn physics, chemistry or biochemistry. A physicist needs to know mathematics, but not chemistry or biochemistry. A chemist need to know math and physics but not biochemistry. And a biochemists need to learn the most: math, physics and chemistry. That is, these science are cumulative. Generally speaking, especially in terms of actual university curricula, this is true, although each progressively broader discipline gets a less detailed education of the more basic disciplines. Thus chemists or biochemists do not know math as well as physicists and mathematicians, for example. But in actual professional practice, since all of these disciplines speak the same language, and that language is mathematics, you will find physicists doing biochemistry (Francis Crick, the co-discoverer of the structure of DNA was one of these), or biochemists doing math, for example. Mathematicians used to stay mostly in their own academic world. But now, with the advent of computers, mathematicians are coming out of their holes more and participating in physics, chemistry and biochemistry.

We can generally carry this cumulative chain of disciplines into biology and physiology (and their respective sub-specialties), and also into the field of medicine. But in the actual education for these specialties, only the most cursory overview is provided of the more basic sciences such as math, physics and chemistry.

This situation in the "hard" sciences may seem complicated (and it is) but it stands in stark contrast to the situation in the "soft" sciences. Here we have sciences such as psychology, anthropology, and sociology and the myriad sub-disciplines of each of these. Now, unlike the "hard" sciences, the "soft" sciences are not all interrelated. For example, within psychology alone are many competing schools of thought and paradigms; Freudian psychoanalysis, Jungian psychology, behaviorism, Maslow's transpersonal psychology, the newer cognitive psychology, physiological psychology, medical psychiatry, only to name a few. Similar lists could be drawn up for the other "soft" sciences. Whereas a chemist, physicist and biologist all agree to the meaning of terms such as "work", "pressure", "energy" and other common terms they use, it would be a miracle if Freudian, Jungian and behaviorist psychologists could agree on the meaning of terms such as "personality", "cognition", "consciousness" and other terms that a psychologist may use.

In Kuhn's terms, the "hard" sciences are very mature to have come to a state where there is an established consensus of many standard definitions of phenomena; this implies a very stable set of paradigms (in this case, a set of paradigms that pertain to the nature of physical phenomena). The "soft" sciences, on the other hand, are very immature in their development as sciences precisely because they consist of many competing paradigms with no common consensus or standard definitions of the phenomena they claim to study (that being the study of the many levels of human behavior).

And as I stated, there are as yet no paradigms in the "soft" sciences that are related to the paradigms of the "hard" sciences. "Hard" scientists and "soft" scientists are educated into completely different paradigms; they speak vastly different languages. What this means is that the study of physical matter is unrelated to the study of human behavior in very fundamental ways. There are no stated principles in modern science that tie together the behavior of atoms and humans. Or another way to say this is that modern science does not provide a unified description of the world. Again, this is because the sciences that study human behavior are unrelated to the sciences that study physical events. About the only attempt made in this direction is in the newer field of cognitive psychology, in which an eclectic sampling of paradigms from computer science, artificial intelligence and other sources are applied to human behavior. Yet it is unlikely that the cognitive psychology paradigm will produce the type of synthesis of "hard" and "soft" sciences which will allow for the discovery of general principles between Humankind and Nature because the cognitive psychology framework is still too intimately involved with addressing traditionally "soft" scientific concerns. But there is also another avenue in modern science that points to fundamental principles operating both in physical matter and human behavior and this involves the new science of chaos and the new fractal geometry. I will go into this point in more detail below and in other chapters.

For an initial look at all of the disciplines that make up modern science, this distinction of "hard" verses "soft" sciences is useful. However, in actual practice, there is much more overlap than these terms imply. For example, a science known as psychopharmacology--which is the study of the effects of drugs on behavior and the mind--draws heavily on both biochemistry and physiological psychology, as well as medicine. Furthermore, it is very important for the reader to realize that modern science is constantly changing in terms of the paradigms that define it and the relationship between these paradigms. Thus, any generalizations about science as a whole must be taken with a grain of salt.

So keeping this overlap and dynamism of paradigms in mind, the important thing I want the reader to realize with this "hard"/"soft" distinction in science is that the "hard" sciences are grounded in a relatively unified theoretical framework which is, in general, not shared with the "soft" sciences. To anticipate a bit, perhaps it is possible to develop an approach to the "soft" sciences (which in essence are the sciences of human behavior) which is fundamentally grounded in the same paradigms as the "hard" sciences. I will suggest that this can be accomplished by introducing occult notions into science and coupling these notions with the new paradigms provided by theories of chaos and fractal geometry, as well as with the paradigms of quantum mechanics. This contention will serve as the subject of the following chapters.

There is another point I would like to make about the difference between the "hard" and "soft" sciences and this was alluded to above when I said that the "hard" sciences were better at predicting and understanding phenomena than the "soft" sciences. The reason this situation exists rests primarily on the nature of the paradigms each uses. In general, in the "hard" sciences the paradigms used provide a mechanistic explanation of the phenomena being studied. Here I am not talking about the mechanistic philosophy of Newton's clock-work universe. What I mean here is that the paradigms and models used in the "hard" science provide detailed mechanisms of cause and effect to explain the phenomena they study. It is because "hard" sciences understand, explain, and describe the mechanisms of the processes they study that these sciences have been so successful at elucidating Nature's secrets.

On the other hand, there are no mechanistic explanations in the "soft" sciences in general. Usually the paradigms of the "soft" sciences amount to little more than philosophical opinions concerning the nature of human behavior (Marxist sociology, for example, or behaviorist psychology), and are usually broad sweeping generalizations. Such generalizations usually do nothing to suggest actual mechanisms in human behavior. Thus this dichotomy also explains in part the relative strength of the "hard" sciences over the "soft" sciences.

However, there are fundamental scientific reasons why there is no substantial overlap between the "hard" and "soft" sciences and this involves the respective content of the "hard" and "soft" sciences.

First there is the issue of complexity. The subjects studied in the "soft" sciences (i.e. the operation of the brain, large-scale social behavior, personality development) are extremely complex systems from the "hard" science point of view. Thus, "hard" science approaches fall apart at these levels of complexity if they are applied literally. An example here would be trying to understand the behavior of the brain in quantum mechanical terms--this is simply impossible. Furthermore, in terms of the analysis of complex systems, the "hard" sciences usually cannot adequately deal with systems that seem to be in their domain. A prime example here is that the behavior of biological systems cannot be adequately described using present theories from chemistry and physics. These theories provide partial windows of understanding into say, the behavior of enzymes or cells, but there are still fundamental behaviors observed in these systems that cannot be adequately explained in "hard" science terms, such as enzyme biogenesis, gene behavior or cell division (and ultimately the development of biological organization).

The second fundamental scientific factor that separates the "hard" from the "soft" science is one of observational methodology. "Hard" scientists operate under a reductionistic methodology in which they isolate a system from its natural environment in the laboratory and then dissect it into its component parts. This is a methodology that, though it is attempted, cannot really be applied to human systems. We cannot put human societies in a laboratory and then manipulate them to see what are the controlling variables. The study of human systems generally requires an observational methodology akin to what biologists, ethologists and ecologists use to study animals in their natural settings. Thus, the "soft" scientist's hands are tied, so to speak, relative to the "hard" scientist in that the "soft" scientists simply cannot manipulate the systems they study to obtain the type of information that "hard" scientists routinely use.

There is a third scientific factor as well which separates the "hard" and "soft" sciences, aside from complexity and observational methodology, and this is the issue of time. Time, as we all know in our everyday experience, always goes forward. Physicists call this property of time "irreversibility". Irreversibility is intimately connected with two seemingly contradictory observations in Nature: first, that natural complex systems seem to get more complex over time, as with biological or cultural evolution, second, that some natural systems seem to "run down" over time. This is the idea of "entropy"; ultimately that disorder wins (or entropy becomes a maximum). Thus, biological organisms die, species and cultures go extinct, or the universe dies in a heat death.

The notion of time leads to these two seemingly contradictory notions; systems get more complex over time or systems run down over time. This is a great problem in modern physics for the relationship between these two seemingly contradictory aspects of time is not understood on any fundamental basis. That is, entropy and evolution are not built into the supposedly fundamental theories of modern physics, for example relativity or quantum mechanics. Yet these notions play a vital role in the study of the systems that "soft" scientists use, such as the evolution of cultures or the development of personalities.

Along with chaos, fractals and quantum theory, this issue of time and irreversibility will also be another scientific theme that will thread through this book. What we shall see is that occult views offer some novel approaches to this particular problem that are relevant not only in a "hard" science context, but as well in the context of relating the "hard" and "soft" sciences.

Thus, to summarize, the "hard" sciences and "soft" sciences presently are unrelated because of the following factors: 1. the relative maturity of the paradigms, 2. the use of mechanistic explanations in the "hard" but not the "soft" sciences, 3. the complexity of the systems being studied, 4. observational methodologies, and 5. the role played by time and irreversibility in our theoretical understanding of natural systems.

The issues of complexity and observational methodology resolve themselves into the philosophical issue of the reductionistic mentality of modern science; what are the limits and validity of this mentality? We shall see that occultism offers an alternative methodology, a holistic or ecological methodology to the study of natural systems. Thus, when we begin our scientific interpretation of occultism, we will begin to appreciate how a holistic mentality will allow us to approach the issues described above, for which the present reductionistic mentality has not been successful.

Also, the dichotomy between "hard" and "soft" sciences is a situation in transition for, as I said above, some "soft" sciences are beginning to overlap substantially with the "hard" sciences. As well, chaos theory and fractal geometry, coupled with occult notions, pave the way for true mechanistic explanations in the "soft" sciences.

3.2 Chaos, Fractals and Quantum Theory

What are fractal geometry and chaos theory and why are they relevant with regard to explaining human behavior? Furthermore, what does this have to do with occultism? This second question we will return to later. Let us now focus on the first question.

Both fractal geometry and chaos theory are new paradigms in modern science. Each is a new mathematical approach that, when applied to Nature, gives surprisingly accurate results with respect to understanding the mechanisms being studied. What one must realize with regard to these two new approaches is that before their time, most systems and phenomena studied with traditional mathematical approaches fell apart when it came to the accuracy of the traditional model in describing real world situations. That is, traditional physics and chemistry had many mathematical descriptions of natural processes, but always these models fell short of describing real situations in the real world and usually could only describe very limited events that occurred in the laboratory (a good example of this in physics is the mathematical theory of statistical mechanics). So physicists and chemists spoke of "ideal cases" and then twisted and contorted their mathematical models to fit real life. In a sense, this is like cheating. However, with the advent of chaos theories and fractal geometry, scientists no longer need to "cheat" in such a fashion when they describe the real world with mathematics because these new theories, when applied to real world situations, give real world answers.

Again, chaos theory is a mathematical approach to studying the world. It allows scientists to understand such diverse phenomena as a pot of boiling water, the distribution of a population of animals over time, weather patterns, and how the brain organizes sensory input. What underlies these diverse phenomena is the same mathematical principle. The mathematical principle that underlies chaos theories is that seemingly very complex behavior can be understood in very simple terms. In chaos theories, one takes a usually very simple nonlinear equation (a nonlinear equation is one that when graphed out does not give a straight line) and subjects it to a process known as iteration6. When one iterates a nonlinear equation, one gets a graph much different than one would obtain by plotting the equation by normal means. The graph produced by iterating the equation is very complex and shows very subtle behaviors. Such graphs define what scientists call attractors (also called "modes" or "orbits").

An attractor is a stable state to which the system represented by the graph will be attracted. For example, if we drop an apple to the floor, then the floor would be an attractor. Or if we were to roll a marble around the edge of a funnel, it would eventually roll down the side and come to rest at the neck of the funnel. In this case the neck of the funnel would be an attractor. Mathematically, these examples would be known as simple attractors. There are two more classes of attractors recognized by scientists and these are called periodic attractors and chaotic (or "strange") attractors.

An example of a periodic attractor would be the four seasons that repeat over and over again in the temperate climates. Here, over the year, the weather goes through four distinct phases: spring, summer, autumn and winter. These phases repeat over and over, and scientists would then say that the seasons form a periodic attractor with respect to the weather.

The final type of attractor is a chaotic attractor. The reason it is called a chaotic attractor is because it does not ever seem to repeat the same behavior. Here the system seems to jump around chaotically (thus the name "chaos theory") from one state to the next and makes no definite pattern. An example of a chaotic attractor is the day to day weather of a region. One day it may rain, the next day it may be sunny, then the following day it may be cloudy. There is no repeating pattern to day to day weather. In spite of the fact that over time there are large-scale or seasonal patterns to the weather, on a day to day basis, the weather is relatively unpredictable. This day to day unpredictability of the weather is called by scientists a chaotic attractor.

So the essence of chaos theories is the understanding of a phenomena in terms of what type of attractor behavior it exhibits. A system whose behavior may be very complex may actually be described by a simple nonlinear equation that is subject to iteration.

We can see how the ideas of chaos theory may be applied to human behavior. Consider our memories, for example. Each of us has many stable habits of thought; we remember our name, where we live, what our job is, the events of our past. In a sense these types of memories are periodic attractors; they are repeatable and stable states that our minds will go to. Likewise, we have our daily social routines such as getting up, going to work, coming home and eating dinner, going to sleep, then getting up the next day and repeating the process. So our daily social routines too can be thought of as periodic attractors.

But there are other aspects of our life that are repetitive, yet never repeat exactly. Whenever we learn anything it falls under this category. We repeat the learning process, but each time we get better, as for example when we learn and practice a musical instrument. The fact that our minds can adapt to new circumstances and that we can learn new things, even to old age, points to the presence of chaotic attractors in our psychology. For if we were locked only into periodic attractors, then our actual behavior would be totally inflexible, and we would be like automatons or robots. The flexibility of "trial and error" is in reality an indication of chaotic attractor states at some level in our psychology. The same is true with our daily social routines. They repeat on a broad level perhaps, but the day to day details are different each time around that they cycle indicating the presence of chaotic elements. Thus chaos theories may help to bring about a transformation in psychology and sociology and improve our understanding of the mind and human behavior, and as well serve as a point of relation between the "hard" and "soft" sciences.

Before I leave the topic of chaos theories, I would like to point out that there is a fundamental difference between chaotic behavior and random behavior. Something that is chaotic is not random; these are two completely different mathematical notions. The real difference here lies in the mathematics used to describe each type of behavior. Random behavior is described by a branch of mathematics that is known as probability theory. Here we talk about odds and one in one thousand chances. Randomness applies to rolling dice or winning the lottery. When we are dealing with randomness we predict the odds that a certain event will be realized. This is not the way a chaotic system works. As we saw, chaos is described by different mathematics, the iteration of nonlinear equations. The iteration of these equations produces attractor states, either simple, periodic or chaotic attractors. Because of these mathematical differences, chaos is predetermined (or "deterministic' in the jargon of mathematics), but randomness, by definition, is not. Furthermore, and what is important to scientists, is that when we find the attractor states of a phenomena by chaos theory, this points to definite cause and effect relationships between the variables we used in the nonlinear equations. There is no cause and effect relationship in probability mathematics. Thus, chaos theories allow scientists to make mechanistic models which could not be made by using probability theory. This distinction is important because, in the application of chaos theory to human behavior, events that we may have thought were mathematically random may actually be mathematically chaotic. Traditionally, statistical methods have been the only mathematical means utilized by psychologists, sociologists and other "soft" scientists. Thus, chaos theories may eventually provide a mathematical framework for the social sciences, bringing the social sciences much closer to being "hard" sciences.

Now let us turn to fractal geometry. Fractal geometry is a new branch of mathematics that gives us a new way to describe shapes. The shapes described by fractal geometry are called, not surprisingly, "fractals". Fractal shapes are extremely life-like compared to the circles, triangles and parabolas of traditional geometry. Fractal shapes look exactly like real clouds and real trees and real landscapes. Plates 5, 6 and 13, and Figure 9 show examples of fractal shapes and also illustrate some of the properties of fractals. Fractal curves, like the equations in chaos theories, are produced by the iteration of simple nonlinear functions. Actually, most chaotic attractors are fractals as well. Figure 9 illustrates a "chaotic fractal"7.

Aside from the very organic and life-like appearance of fractal shapes, as seen in the illustrations, the main property exhibited by fractals that sets them apart from traditional geometric shapes is a property called "self-similarity". Self-similarity means that the same pattern repeats at different scales or levels of resolution within the picture. That is, if we take a fractal curve and enlarge and magnify some small region of it then this small region will appear to look like the whole fractal curve. We can see this property very clearly in Plates 5 and 6, and Figure 9 in that the main pattern of each of these fractals is made up of ever smaller copies of itself. The founder of fractal geometry, Benoit Mandelbrot, proposes the following definition of fractals based upon their property of self-similarity: "A fractal is a shape made of parts similar to the whole in some way"8. We shall see that this definition will make it very easy for us to equate occult and fractal concepts in upcoming discussions.

If we look at Plate 13, we see a subtler example of self-similarity. Plate 13 illustrates what is called a "fractal zoom". The fractal in Plate 13 is very important and is called the "Mandelbrot Set", named after its discoverer Benoit Mandelbrot. In frame a of Plate 13, we see the beetle-like shape of the Mandelbrot Set. Frames b-h are progressive magnifications, or blow-ups, of the boundary of this set. What we will notice though, is that in frame g, we find another beetle-like Mandelbrot Set repeated in the depths of our original set. This is a subtler example of self-similarity in which we eventually come across our original pattern, instead of having the fractal simply being made up of ever smaller copies of itself. I will discuss more about these plates later when it is necessary to introduce fractal concepts in an occult context.

This notion of self-similarity of fractal curves is very important in terms of understanding the relationship between science and occultism and we will return to it again and again throughout this book.

Implied in the concept of self-similarity is another important concept in fractal geometry and that is the notion of levels of resolution. Here we are referring to the nesting of pattern within pattern within pattern. Ultimately, this nesting of patterns within patterns goes on to infinity. This was Ezekiel's vision of circles within circles within circles. The importance of this notion is that we begin to realize that any phenomena is in turn made up of other phenomena, these in turn being made up of other phenomena.

A real life example of nested levels of resolution is found to be ourselves and the world we live in; our bodies have nested within them the various organs (hearts, livers, kidneys, brains, etc.), in turn the organs have nested within them cells, the cells in turn have nested in them what are called organelles (these are such things as mitochondria, nuclei, ribosomes, etc.), nested in the organelles are molecules like proteins and DNA, RNA and other biological molecules, nested within these molecules are atoms such as carbon, nitrogen, oxygen and others, nested within the atoms are subatomic particles like protons and electrons and neutrons, nested inside the subatomic particles are things called quarks, and it is not known today in science if there is anything nested inside of quarks (we will see, however, that occultism teaches that there are particles nested inside of quarks. These are called "Ultimate Physical Atoms" and are illustrated in Figure 4. These will be discussed in chapter 6, section 6.2.4).

Now if these patterns of nesting inward seem complex, well we can go the other way too; we humans are nested inside of our societies, our societies are nested in the biosphere of the Earth, the Earth is nested inside of the solar system with the other planets, our solar system is nested inside of the Milky Way Galaxy along with billions of other stars, and it is known that the Milky Way Galaxy is nested inside a cluster of other galaxies in what is called "the local cluster", and this cluster is part of a larger cluster, and on and on it goes beyond our ability to perceive. Thus, that our very lives are made up of all of these nested levels of resolution points to the fact that reality, or the world, or the universe, or what ever you want to call it (later in the book, what I am here referring to I will call the "physical plane") is in some sense a vast and living fractal shape. However, to consider the entire structure of the physical world to be a fractal will require that we utilize the notion of self-similarity in a very subtle fashion which will be provided by occult concepts.

Thus, as well as being a new way to deal with shapes, fractals provide us with a new conceptual means of organizing the reality of our experience.

Now, with some understanding of what chaos theories and fractal geometry are, I would like to spell out why these are important to my purposes in this book. First, as I said earlier, both of these theories are new-comers to modern science, neither being any more than twenty years old. Both have their roots in the 1960s (though fractals have ancestors that extend to the late nineteenth century, and chaos has attracted the attention of thinkers for centuries, most notably Leonardo da Vinci), and both were only really recognized in the 1970s9. Thus, these developments represent new paradigms in modern science. In spite of the enormous popularity of these new disciplines, their effects have barely begun to be felt in modern science. Together, these new paradigms introduce into science notions that will eventually transform the entirety of modern science, and thus our technology and how we view ourselves. The new and important notions these two disciplines introduce into modern science are:

1. Complex phenomena can be understood by simple mathematics. That is, things that were previously seen to be random, such as day to day weather or learning, are now realized to be chaotic processes.

2. Natural phenomena exist as a hierarchy of nested levels of resolution.

3. Natural phenomena can display self-similarity.

In many respects, the really important new conceptual element for modern science is that the notions of fractals and chaos provide completely new means of understanding how Nature can be organized. Fractals and chaos represent organizing principles that have until now remained unrecognized by modern science. As I will discuss and illustrate in upcoming chapters, the organizing principle of self-similarity as embodied in fractal geometry has long been recognized in occult teachings in what is known as the "Hermetic Axiom". The Hermetic Axiom is stated "As Above, So Below". As is very clear from the context in which the Hermetic Axiom is used in occult writings, occultists have always viewed Nature in a fractal form. And the organizing principle behind chaos is that seemingly complex and random behaviors can be easily understood in terms of attractor states, ideas which have been foreshadowed by occultism.

Leaving for the moment fractals and chaos theory, I also stated earlier that quantum mechanics will play a fundamental role in understanding the relationship between modern science and occultism. Here I would briefly like to discuss quantum mechanics so as to lay a basis for upcoming discussions. Again, quantum theory has been very well popularized10 so I will dwell on an interpretation that is relevant to my purposes here.

Quantum mechanics is a paradigm. The quantum mechanical approach to natural phenomena was a departure from the classical Newtonian approach to motion and energy. In Newton's paradigm, motion and energy were both seen to be continuous phenomena. That is, distances, times, and the values of energy that an object could have could take on any real number. Yet it was experimentally discovered that these ideas did not apply to our measurements of microscopic phenomena such as the behaviors of atoms, molecules, or electrons. It was found by Max Plank, J.J. Thomson, Ernest Rutherford, and others around the turn of the century that the microscopic behavior of these objects was discreet. That is, the energy of an atom could only take on certain discreet values and not any value. The difference between continuous and discreet is the difference between the real number line where we can express fractions and irrational numbers (like ) on the one hand, and the counting numbers (1,2,3,...) with no fractions in between on the other hand. Thus, the quantum mechanical paradigm came about to account for the discreetness of the microscopic events physicists measure.

To account for this discreetness, new mathematics had to be used in quantum mechanics that were not used in the Newtonian paradigm. The mathematics of discreteness used in quantum mechanics are in large part embodied in what is called the Schrödinger Wave Equation, introduced in 1926 by Erwin Schrödinger, and in an equivalent mathematical formulation known as the matrix mechanics put forth by Werner Heisenberg, Max Born, and Pascual Jordan at the same time. The technical details of this mathematics are far beyond the scope of this discussion, but the concepts that derive from this mathematics are highly relevant. As well, it is fair to point out that many mathematical refinements have been presented in quantum mechanics since the days of Schrödinger and Heisenberg, but these will not concern us until later discussions.

The essence of the Schrödinger wave equation is exactly what it says. This equation is an equation of a wave but it is applied to particles such as hydrogen atoms. Now the famous de Broglie relationship states that the momentum of a quantum particle is proportional to the wavelength of the particle. It is this de Broglie relationship that is the basis of the famous wave/particle duality in quantum physics. This relationship states that any quantum particle can literally be viewed as either a wave or a particle depending upon how it is measured11. I want to make a clear distinction between the wave/particle duality of the de Broglie relationship and the wave description of a particle embodied in the Schrödinger wave equation. This distinction is important because in the Schrödinger equation, a particle is literally viewed mathematically as a wave. To quote the text from which I learned quantum mechanics:

"Schrödinger, reasoning that electronic motions could be treated as waves, developed wave mechanics. In this treatment, he took over the great body of information from classical physics about wave motion and applied it to atomic and molecular motion. The stationary states that an atom or molecule might have were analogous to standing waves (such as occur on a violin string)..."12

What I am trying to do here is to explain the wave nature of matter differently from most popular accounts of the wave/particle duality of matter. The wave equation is in many respects conceptually similar to the type of equation used to describe a simple sound wave. We know that a simple tone, say one produced by striking middle C on the piano, is made up of a fundamental tone and its associated harmonics. The harmonics occur at discreet intervals of frequency over the fundamental tone. This situation is analogous to describing an atom using the Schrödinger wave equation. An atom can literally be thought of as a fundamental tone with its associated harmonics13. When we speak of the fundamental tone of an atom we call this the "ground state" of an atom. The harmonics of the atom are called "excited states". What is known as a "quantum transition" is when the electrons of the atom go from the ground state (fundamental tone) to one of the excited states (harmonics). A quantum transition is not as unfamiliar an idea as scientists and philosophers have led us to believe. The way a melody of a song moves discreetly from note to note is just like a quantum transition. That is, a quantum transition is a harmonic transition.

Thus, if we literally interpret the Schrödinger wave equation, then an atom is, in some fundamental sense, analogous to a sound wave (though there are technical differences of course). Normally, in the common interpretation of quantum theory, the fundamental tone and harmonics that define the atom are interpreted to be the probability of finding the atom at some location in space. Granted this accepted interpretation works perfectly well, as is attested by all of our modern quantum technology (such as semiconductor chips or lasers, or the variety of instruments used for experimental measurements). Yet one must ask what this accepted view (the Copenhagen Interpretation) provides for us: is it an accurate description of Nature, or merely a description of the technologies we have devised?

What I am saying here is that, instead of interpreting the equations of quantum theory to indicate the probability of finding a particle at some location in space14, we can instead interpret these equations to say that matter is literally a tone. As a tone is a wave propagating through the medium of air, an atom is a "tone" propagating through the medium of the quantum vacuum (the quantum vacuum is the sum of the energy fields of Nature: the weak and strong nuclear, electromagnetic and gravitational fields). Thus, physical matter, when viewed through the paradigm of quantum theory, can be thought of as a vast symphony of atomic tones.

That we can literally think of an atom as something akin to a musical tone is the main point I want to make in this discussion, and this is not something stressed in popular expositions of quantum theory. However, I want to stress here that I am not saying that atoms obey harmonic rules that are identical to the harmonic rules of combination of Western music theory, or any other human system of music theory. What I am saying is that atoms are analogous to any system of music theory in that atomic structure (and nuclear, sub-nuclear and molecular structures as well) defines for itself its own internal system of harmonic combination and interaction. Within such a system we can then think of the behavior of atoms, nuclei or molecules as songs or polyphonies.

If we begin to think of atoms being like musical notes, then we can understand that atoms will combine and form combinations that are like songs. This metaphor will make it very easy for us to understand how and why atoms behave as they do. Some atoms are more likely to combine with each other in just the same fashion that some tone combinations sound better together than others. Stable arrangements of atoms, which are called molecules, are very much like a polyphonic piece of music. Furthermore, this metaphor of thinking of an atom as a tone will allow us to understand the behavior of atoms much more intuitively. Atoms resonate, they resonate at certain frequencies, these frequencies being defined by the Schrödinger equation (or other similar formalisms or approximation methods). Atoms obey all of the properties tones do. If two atoms are "out of tune" with each other, that is they don't resonate in a harmonic combination, then they will push away from each other. This is the process of electrical repulsion, and it is a process much like tonal dissonance. If the atoms resonate in phase with each other, or form a harmonious combination, then they will be attracted to each other to the degree of their overlapping resonance. That is to say, electrical attraction is just like musical harmony. If the atoms resonate at frequencies far removed from one another, that is, there is a vast separation in their frequencies, then they will be invisible to each other, just the same way we cannot hear a tone that is outside of the ear's frequency range.

Taking this approach to quantum theory is very valid and highly intuitive, and it illustrates a very important feature of the quantum mechanical paradigm. This is that physical matter is vibratory patterns. Again, we can liken the world that we know to be a combination of atoms to be a vast symphony of quantum resonances. Such an interpretation completely supersedes the mythos and mystique that surrounds the counter-intuitive aspects of trying to interpret the quantum mechanical paradigm in particle terms. Indeed, this is why the ancients required the study of music alongside the study of mathematics and Nature.

Likewise, we can view light in exactly the same fashion. Light (or more precisely, electromagnetic radiation) is also a vibratory pattern like matter, except that light vibrations are at a different type of frequency than atomic vibrations (in occult terms, light is a different, though related, type of matter from atoms as we shall discuss ahead). The same rules of harmony and dissonance apply with light and how it interacts with other frequencies of light, and how light reacts with matter. Light causes an object to be colored and the color you see represents the frequencies that the light and the matter do not have in common. The light reflected off an object contains the frequencies not absorbed by the object, that is, the frequencies of the light that the object does not resonate with and thus repels. That light will pass through a transparent window indicates that the light you see and the atoms that make up the window do not share any frequencies, thus the atoms are invisible to the light.

Incidentally, I do not think it is simply a coincidence that there are seven colors in the visible spectrum and seven tones to a musical scale. The rules of color combination using the three primary colors of red, blue and yellow have much in common with the music theoretician's rules of harmony combination using the first, fourth and fifth scale tones in a major scale. Both lead to an incredible plethora of variety on their respective levels.

This whole approach to quantum theory is essential for understanding how occult notions fit in with science, for occultists view the world as so many complex vibratory patterns and so do quantum physicists. And using the musical analogy I developed above will help make it obvious that occult and quantum descriptions of the world are identical. Furthermore, as I stated already, we shall see that occultists teach notions that are identical to those found in fractal geometry and chaotic systems theory. To foreshadow my conclusions somewhat, what I shall do for the rest of this section of the book and throughout the entire next section is support the claim that if we interpret occult concepts in terms of quantum theory, fractal geometry and chaos theory, we will find that occult notions are highly compatible with modern science. And second, we will see that, in general, occultism is a set of paradigms that can be interpreted as describing human behavior in quantum, fractal and chaotic terms. Thus my ultimate goal here is to show that we can unify the "hard" and "soft" sciences by interpreting occultism in terms of these three modern scientific theories.

Notes: Chapter 3

1One of the most excellent histories of science during this period I have read is Boas, (1962). This work is especially interesting because it is written in a fashion that stresses the fact that science and occultism used to be identical.

2Jaffe, (1960), page 25.

3The theory of social rationalization was created by the great German sociologist Max Weber. As defined by Weber, a "rational" form of social organization is to be distinguished from a "traditional" form of social organization. This distinction is based on the fact that the rules (norms and values) of a "traditional" society remain constant from generation to generation, but those of a "rational" society are always in a state of flux. For a development of this theory see Weber (1947). What I am doing here saying that the tradition of our Western civilization is "rational" is pointing out the paradoxical situation that the implicit and unchanging norm of our civilization is to seek to change its values.

4The classic book portraying the competitive image of modern science is Watson, (1969). This book was supposed to have created quite an uproar in the scientific community when it was initially published because it so blatantly made apparent the competitive mentality of modern science. This book did much to shatter the mythical image of scientists working together in harmony trying to unfold Nature's secrets. Incidentally, this book is fun and quick reading and is highly recommended.

5The full theory of paradigm transformation and scientific revolution is worked out in the now classic Kuhn, (1971).

6For the reader interested in obtaining knowledge of constructing iterated equations see Gliek, (1987), or Peitgen and Saupe, (1988), chapter 3.

7The mathematical reasons for calling this fractal "chaotic" are beyond the scope of this book. The interested reader may find details in Peitgen and Saupe, (1988).

8Feder, (1988). page 11.

9The concept of fractals and fractal geometry was introduced in Mandelbrot, (1977) and made wide-spread in Mandelbrot, (1982).

Chaos theories arose through many independent efforts. For a good history of chaos theories see Gliek, (1987). For a technical introduction to Chaos theories see Infeld and Rowlands (1990).

10For popular accounts of quantum mechanics, see for example: Gribbon, (1984), Hawking, (1988).

11I would suggest that a more accurate interpretation of this equation is not that particle and wave behavior are equivalent, but that under certain conditions, some wave patterns behave as if they were particles. The idea here is that Nature consists only of wave patterns but that under suitable conditions, such wave properties can be treated as particles. These would be standing waves, as Schrödinger's approach describes.

12Hanna, (1981), page 45.

13The standing wave patterns predicted by the various boundary conditions applied to the Schrödinger wave equation are conceptually identical to standing wave patterns generated by musical instruments. And such standing wave patterns correspond to the distribution of harmonics over the fundamental tone. Thus, the standing wave patterns generated by wave mechanics can be thought of as representing the harmonic distribution of atomic and electronic states. In other words, what I am saying is that we could theoretically design a musical instrument whose relative harmonic distribution is identical to, say, the exact solution of the hydrogen atom. Such an instrument would let us literally hear what a hydrogen atom sounds like in terms of the relative relationship of the harmonic distribution of hydrogen.

14The issue of the use of probability in quantum theory has always been in question. Einstein, for example, did not believe that this was a fundamental interpretation. One way out of such a dilemma is to substitute chaos theory for probability theory as we have seen is possible in other sciences (psychology, ecology, meteorology). Alternatively, we must realize that the use of probability theory in quantum mechanics is due to the use of noncommuting matricis in the description of quantum mechanical dynamic variables. This situation has come about because of the need of physicists to continue to attempt to conceptualize microscopic matter in particle terms. It is likely that, if the need to view matter in particle form is completely given up, and instead a musical or purely wave approach is adopted, then the use of probability could be superseded. That is, if microscopic dynamic behavior was thought of in terms of patterns that are analogous to musical patterns, then a more fundamental understanding of matter would result. This is precisely the occult view. This line of thinking is elaborated on in chapter 13.

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