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My wife and I have an ongoing lighthearted argument over the mowing of the lawn. We each have our way of doing it and have a hard time accepting the other s method. The last time I was mowing the lawn, I had to go in for a few moments. When I came back I found that she had grabbed the mower and was mowing it her way. I had to virtually beg, plead, cajole and bribe to get the mower back from her.

My wife s way of mowing is the grid pattern, which is the way I ve noticed most people mow. Up and down, back and forth, in linear fashion, continuing to follow the path they ve created. My method is more random, more chaotic. I mow this patch, then go diagonally and head in a different direction, then I may go circular, and when that ends I may zig zag.

I am convinced that my way saves more personal energy than the grid approach. I wouldn t know how to research this, but I m sure if I charted out my coordinates, I would be following a strange attractor trajectory. I feel a certain freedom when I mow the lawn my way, whereas I get bored very quickly when I do it the grid way. It may look chaotic, but there is truly a method to my madness: I m creating order out of chaos.

An interesting aspect of all this is my wife s and my relationship to mathematics. She hates math with a passion, and found it to be a horrible and intimidating realm while in school. I, on the other hand, had a love affair with math at one time in my life; furthermore, I found geometry to be incredibly exciting. So shouldn t it be the other way around: that the non-mathematician should relate to odd patterns and the math geek/geometer should be fascinated with grids? And add to that that my wife is a very talented artist, with a specialty in ceramics; thus she has an artist s temperament and perspective on things.

Perhaps it s the background in ceramics that has led her down the linear path. In studying ceramics, she had to learn some rudimentary chemistry, in order to understand and put recipes together for glazes. Maybe the little bit of chemistry she studied was enough to leave a lasting effect on her as to the seeming absoluteness of known chemical and natural laws, as understood and intuited by man. As the saying goes, a little bit of knowledge is dangerous.

Somehow all the years of being taught that Euclid s worldview was THE worldview did not stay cemented in my brain. Or maybe it was because of my training that I felt comfortable venturing beyond and feeling comfortable with nonlinear dynamics. My training showed me the limits of the linear world; worlds beyond were hinted at but were always shunted as being irrelevant. I was always fascinated by such transcendental concepts as infinity, negative numbers, imaginary numbers, and numbers that had no end, such as pi (which does not end at 3.1415925), or even the simple equation of 20 divided by three (6.666666666666666666666666666666 . etc., etc., etc.).

We often hear the term counterintuitive being used when some scientific principle appears that runs counter to common sense. But as Benoit Mandelbrot said, Intuition is not something that is given. I ve trained my intuition to accept as obvious shapes that were initially rejected as absurd, and I find everyone else can do the same (Mandelbrot, cited in Gleick, 1987, p. 102).

It s the shallow ideas that are easily assimilable; the ideas that require people to reorganize their picture of the world provoke hostility. It is because, as the various writers in the book The Metaphysical Foundations of Modern Science (Harman and Clark, 1994) point out, there are metaphysical underpinnings to our viewpoints of the world and the assumptions we make about it. And we consider these underpinnings our intuitive grasp of the world. So when something challenges our worldview, it becomes counterintuitive.

When Mitchell Feigenbaum was creating his theory of universality, he used numbers and functions as his subjects. In doing so, he needed to inquire into their behavior: he needed to create intuition (Gleick, 1987 p. 178). Or perhaps we could more precisely say he needed to create a new intuition, a more encompassing intuition.

Many mathematicians and scientists are not able to expand their intuitions, and are consequently left behind, never to fully comprehend the world of nonlinear dynamics. Engineers are most notorious for that. I know that firsthand, because there but for the grace of God go I.

My Uncle Paul, who I love dearly, is an engineer, and because of my early affinity for numbers, I was often compared to him and encouraged to look to him as a role model. Somewhere along the way our paths diverged. My Uncle Paul just ended 36 years of civil service to the Federal government, working in the patent office, using his expertise to study patent applications. He s 63, so he has a lot of years still ahead of him. I called him recently to congratulate him on his new life. We had a nice chat, he telling me he s looking forward to doing nothing for awhile. He implicitly reminded me that he still can t understand the path my life has taken and how I ve zigged and zagged from mathematics and veered off in directions he cannot comprehend. (Incidentally, he also can t understand his two nephews on his wife s side who live in California. They prefer surfing to anything else.)

My uncle, bless his heart, epitomizes the engineer s belief in a deterministic, linear viewpoint. The greatest lesson he probably learned in his schooling, and I know it well because it got drummed in my head also, is that the shortest path between two points is a straight line that is part of Euclid s legacy.

That notion has shown itself to be not just quaint, but totally untrue. We have to thank the 20th century s three great revolutions in the physical sciences for overturning that. The three, relativity, quantum mechanics, and chaos theory each have shown that this concept epitomizes the concept of counterintuitive.

Relativity showed that the totality of space-time is curved, thus the shortest path between two points is a curved line. Quantum mechanics then showed that the path between the two points is uncertain, and that there are only possibilities of what the exact path taken is. And chaos theory has shown that this path is infinite within a finite space, and that its trajectory follows certain guidelines, that of a strange attractor.

Chaos is here to stay, although the truth is that it s always been here. Its world of fractal geometry, strange attractors, and sensitive dependence on initial conditions (AKA the butterfly effect) is now a legitimate scientific discipline that cuts across boundaries, attracting mathematicians, physicists, computer scientists, biologists, ecologists, chemists, psychologists, physiologists, and others (including a few engineers).

Chaos can also be seen as the intermediate process between the quantum world of particles/forces and the world of tangible structure (Slater, 1995, p. 212). It can be seen as the bridge between the classical scientific world of the macroscopic, and the quantum world of the microscopic and subatomic. It may be that to make a more complete science we have to marry quantum mechanics and chaos theory together to form the field of quantum chaos.

In his book The Quark and the Jaguar, author Murray Gell-Mann makes a partial case for this. Quantum research led to the discovery of the quark, which represents the simple and universal. Yet Gell-Mann believes it to be a reductionistic science, and incapable of coming up with answers to adequately explain deeper riddles. But, he argues, if we see the quark leading in an unbroken chain to the complex, as symbolized by the elusive jaguar, the answers can then be forthcoming.

Gell-Mann feels that the complement of reductionism and complexity theory can lead to an understanding of what he calls the complex adaptive system, which acquires information about its environment and identifies regularities in that information. These are then condensed into a model that is not static; instead the system continually evolves as conditions change (Crawford, 1995, p. 68).

To help expound on these understandings of complex adaptive systems, Gell-Mann helped found the Santa Fe Institute, which is one of the leading institutes in the field.

Another well-known scientist/author, Fritjof Capra, has taken it one step farther and declared that physics is no longer capable of answering the fundamental questions of life; instead systems thinking has taken over the mantle. He writes: Physics has now lost its role as the science providing the most fundamental description of reality Scientists as well as nonscientists frequently retain the popular belief that if you really want to know the ultimate explanation, you have to ask a physicist, which is clearly a Cartesian fallacy. Today the paradigm shift in science, at its deepest level, implies a shift from physics to the life sciences (Capra, 1996, p. 13).

To help expound on his theories, Capra has set up the Center for Ecoliteracy in Berkeley, California. One of the projects he has worked on with his Center is developing an organic food/agriculture project in the Berkeley public schools.

I am not ready to throw out the baby with the bath water. I believe quantum mechanics and chaos theory are two interdependent theories that fit together as components of the new scientific paradigm. The reason some are willing to forget about the quantum realm when embracing the world of chaos and complexity is that they believe that quantum mechanics has no place for chaos.

Chaos is a classical feature associated with the trajectory of a particle, and is well understood within the context of classical Newtonian physics. Chaos is not supposed to exist on the quantum level, where motion is not measured by trajectories but by the evolution of a wave function. Mitchell Feigenbaum says this about it:

When you look at a room you see junk sitting over there and a person sitting over here and doors over there you re supposed to take the elementary principles of matter and write down the wave functions to describe them. Well, this is not a feasible thought. Maybe God could do it, but no analytic thought exists for understanding such a problem (Feigenbaum, cited in Gleick, 1987, p.185).

Yet as Joseph Ford of Georgia Tech says, Quantum mechanics is supposed to be our universal theory of nature. It had better have chaos (Pool, 1989, p. 893).

To compare quantum mechanical behavior and the nonlinear chaos of classical behavior may be talking apples and oranges. Each of these worlds has their own behavioral patterns, imagery and language. Yet at the same time there is a relationship between the two. Quantum life is a world where electrons swirl in a surreal manner, in clouds of possibilities. We are unsure where they are until a measurement is made; until then they are everywhere and nowhere.

Linear dynamics would tell us that when the quantum world decoheres into the macroscopic world, density takes over and everything becomes deterministically predictable. Life follows grids and engineers rule. But the problem is that one of the mainstays of classical life is friction, and friction seems to gum up equations, leading to unpredictable and unsolvable problems.

Take the Tacoma Bridge. The film of the Tacoma Bridge is a thing of beauty; having been presented in science museums and to physics students. It was supposed to be an engineering marvel and was one of the first suspension bridges when it was built in the 1940 s. But because the engineers hadn t been taught how friction and air resistance can change equations, they didn t take it into account. So what happened was that they created a bridge that swayed and vibrated in the wind. And it swayed big time. People were assured it was safe, though, so commuters continued to use it. Until it collapsed, taking many innocent people to an early grave.

When decoherence occurs at the quantum level, the quantum version of uncertainty is replaced with a material version of uncertainty in the form of chaos. Gone is the infiniteness of the quantum realm, replaced with a specific finiteness that has parameters. Yet within this finiteness lies a certain infiniteness.

Turbulence, randomness, fractal behavior, aperiodic/strange trajectories, bifurcations, self-organization, and other behavior, once considered to be anomalous, now are understood to be the norm. This is the standard way nature behaves and operates at our level of being.

Quantum chaos, then, would be the science of understanding the relationship between the quantum world, the world of chaos, and the macroscopic world. To answer the question of what quantum chaos is, physicists and other scientists are exploring the border between classical and quantum physics (Pool, 1989, p. 893). What I believe they may eventually discover is based on my own speculations and hypotheses.

What I think occurs is a communication between the two realms, the microscopic and macroscopic, with chaos as the intermediary, residing in the mesoscopic. The root of the communication lies in the quantum world s intercommunication amongst its superpositions.

Biophysicist Mae-Wan Ho talks about this communication occurring via an uncorrelated network of space-time points which can be modulated instantaneously by certain signals (Mae-Wan Ho, in Harman and Clark, 1994, p. 201). All the superpositioned electrons, behaving independently yet interdependently, speaking to each other via nonlocal channels, provide instructions to one another through information pathways. Once the wave functions collapse and the superpositions decohere into one specific density, does that spell the end of the communication pathways? Linear dynamics would say yes.

I believe just because the superpositions have abandoned the infinite dimensions of the quantum realm and entered the four dimensional world of space-time that the communication pathways do not end. Quantum behavior is not forgotten just because the electrons have become citizens of a brave new world, just as an immigrant to America does not leave their cultural habits behind because they are in a new land. The quantum behavior remains, but in a new setting.

The communication goes on, with an innate and intrinsic desire to continue to be in a superpositioned, coherent state. But this is impossible, because decoherence has occurred and gravity and density now rule. So in the classical framework, the system will instead move chaotically and seemingly unpredictably, in a desire to spread out infinitely. But because of the limitations inherent in the classical world, the system does it within finite parameters. So the system finds happiness by doing the next best thing it can think of: a finite version of superpositioning.

Furthermore, a quantum system can go home again a quantum system is not irreversible and can retrace its tracks because it has the knowledge of where it has been (Pool, 1989, p. 894). A classical chaotic system cannot do this, again due to its loss of superposition. So it recreates this ability to the best of its capabilities: its random path has an order that is dictated by the center. It cannot return home, but it can organize itself in patterns that continually recreate itself, the self-organizing patterns of fractals. This is the order out of chaos that is seen in chaotic trajectories.

I know this is pure speculation. I am mixing philosophy and science to come up with my conclusions. To prove it would take the building of a mammoth supercollider, which seems like an obscene use of money. So instead we are left with the speculations, trying to get to the bottom of the mysteries of life. And my speculations show why we can t negate quantum theory as Capra would do, or even dismiss it as reductionistic and just a piece of the complexity puzzle, as Gell-Mann would do: the quantum world s role is highly significant!

The name new science signifies many different fields that at times can be interrelated and at times not; yet all contain the common thread of a universe that is dynamic, vital, and interconnected. Some of the new sciences are in actuality part of the old sciences, cast in a new light. Thus, I would put under the new science rubric such fields as quantum mechanics, chaos theory, nonlinear dynamics, systems theory, particle physics, cosmology, relativity; I m sure I m leaving some out, but it s clear what I mean. Each of these is important in their own right; I don t believe one stands over the over in importance. And when synthesized, as I did with my speculations about quantum chaos, larger realities about the whole can then be seen: for as they taught me in geometry, the whole is greater than the sum of its parts. Now doesn t that sound like a nonlinear concept?

I often reflect on the name of the field that I m interested in, Quantum Medicine. I m not sure if the name does the field justice, because it s not just quantum theories I m integrating with medicine; it s all of the new sciences. But I haven t been able to figure out another name New Science Medicine, Complexity Medicine, Chaos Medicine, New Paradigm Medicine, Cosmology Medicine, Holographic Medicine, Quantum Chaos Medicine, Particle Physics Medicine, Systems Theory Medicine, Nonlinear Medicine, Fractal Medicine, Non-Euclidian Medicine; none of these has the right ring to it. So Quantum Medicine it is, even if the name only tells a part of the story. And the story is about seeing the body as a dynamic process that lives by the rules of quantum chaos.

I was reminded of this recently by a woman who came to see me. She was eight weeks pregnant and for the past 10 days had been experiencing uterine bleeding. Blood work showed that she was still pregnant. A visit to a high-risk pregnancy specialist showed that she had a sac of fluid in her uterus independent of the embryo. This was the origin of the blood. The specialist said there was no known medical reason for this sac being there, nor could he tell her what might happen. All he could do was monitor the situation to see how things progress. If it continued to build up and bleed, it could eventually lead to a miscarriage, although he could not say why. The only thing he could recommend to her was rest.

Although I could not give her a definitive answer as to why it was occurring, I could borrow from the new sciences to help her understand the nonlinear dynamics of the situation. I believe that all illness is part of a complex adaptive process of the body to try and maintain the viability of the whole at the expense of the part.

Complex adaptive systems have three properties that can be used to identify and define them:

1. They consist of relatively independent parts that are interconnected and interactive
2. They must be capable of forming and changing strategies
3. They alter the strength of their interaction with others in a way that maximizes the average fitness of the system (Schwab and Pienta, 1996, p. 236).

So for whatever reason, her body was self-adapting and self-organizing to maintain health overall. And perhaps it was doing this to maintain the health and viability of her baby, by filtering out substances that could be toxic to the baby.

Physiologist Ary Goldberger and associates have discovered that the heart and other physiological systems behave most erratically when they are young and healthy. Conversely, he has found that increasingly regular behavior sometimes accompanies aging and disease. What he has concluded is that irregularity and unpredictability are important features of health and that decreased variability and accentuated periodicities are associated with disease (Goldberger, Rigney and West, 1990, p. 44).

To use the quantum chaos analogy, we could say that perfect health is the quantum model, and illness is the classical model. The intermediary, the chaos model, attempts to work within the finiteness of the dense realm, our material body, to bring perfect health. Unfortunately it can never achieve that ultimate perfection of the quantum realm, because we live in a bag of bones that is subject to gravity. But through the movement and physiology of strange attractor trajectories, we can undergo a complex adaptive process that can help us maintain good health.

REFERENCES

Capra, Fritjof (1996). The Web of Life. New York: Anchor.

Crawford, Robert J. (November, 1995). Shedding light on complexity theory (Book review of Murray Gell-Mann s The Quark and the Jaguar). Technology Review. 98, (8), pp. 68-69.

Gleick, James (1987). Chaos, Making a New Science. New York: Penguin Books.

Goldberger, Ary L., Rigney, David R. and West, Bruce J. (February, 1990). Chaos and fractals in human physiology. Scientific American. Pp. 43-49.

Harman, Willis and Clark, Jane, editors (1994). New Metaphysical Foundations of Modern Science. Sausalito: Institute of Noetic Sciences.

Pool, Robert (February 17, 1989). Quantum chaos: Enigma wrapped in a mystery. Science. Pp. 893-895.

Schwab, E. D. and Pienta, K. J. (Sept. 1996). Cancer as a complex adaptive system. Medical Hypotheses. 47, (3), pp. 235-241.

Slater, Victoria E. (September, 1995). Toward an understanding of energetic healing. Journal of Holistic Nursing. 13, (3), pp. 209-224.