Review Article

"Chaos" -- A New Science?

By I. M. Oderberg

Distinguished scientists David Bohm and F. David Peat in their stimulating book on the "creative roots of science and life," state that quite recently the "whole topic of chance and randomness has become the focus of a new mathematical development called chaos theory" [Science, Order, and Creativity, Bantam Books, 1987; 280 pages, illus., index]. Indeed, a new science is emerging to account for what appear to be random events in nature. Physicists are probing phenomena previously classified as inexplicable because they appear to be outside the range of orderly analysis.

The "science of chaos" sounds like a contradiction in terms, evoking memories of the strong disagreement between Einstein and Bohr on the behavior -- whether orderly or random -- of individual atoms and subatomic particles. A stream or flow of them can be predicted to behave in a certain way under experimental conditions, but which ones will comply and which will pursue individual courses of action, is unpredictable. Although he was one of the founding fathers of quantum theory, Einstein did not yield his position that if orderliness prevails in the large field of the universe, or macrocosmos, then it must do so also in the smaller, or microcosmos. Not enough evidence had come in to draw definitive conclusions.

With all the sophisticated instrumentation available these days, some scientists propose that there may be "layers" of orderliness and randomness; that pattern underlies the seeming haphazardness of changes in the weather, fibrillations of the human heart, the sudden whorls of wind twisting desert sands, and so on. In other words, what appear to be erratic occurrences -- chaos -- turn out to be responses to a previously unsuspected pattern that operates somehow behind the scenes or within the phenomena [Dr. Douglas Hofstadter expresses the thought succinctly: "It turns out that an eerie type of chaos can lurk just behind a facade of order -- and yet, deep inside the chaos lurks an even eerier type of order."]. While the common opinion has long been that the functions of the mind are reducible to physical and chemical processes, that is to say, that "consciousness is an epiphenomenon of the brain," Bohm and Peat advance an alternative view:

the notion that reality is inexhaustible and whatever we say a thing is, it is something more and also something different. Hence, for example, if we say that consciousness is a material process, this may well be fairly accurate up to a point. But it is also more. Its ground is in the infinite depths of the implicate and generative orders, going from the relatively manifest on to ever greater subtlety. -- p. 210

One application of chaos theory is to motion, an example of which is the seemingly chaotic breaking of the ocean on rocks near the shore.

At first sight this seems to be totally irregular, yet closer inspection shows many suborders of swirls, flows, and vortices. The word chaotic provides a good description for the order of such a movement. Within the context of order that is visible to the eye of a close observer, this motion contains a number of suborders and is far from random. Nevertheless, to a more distant viewer these suborders become so fine that they are no longer visible to the eye and the order would be called random. -- p. 126

Similarly, the scurrying of ants upon the ground may seem unguided or chancy. But could we enter into the realm of the ant world, we might find there is method behind the seeming lack of direction. This applies equally to other entities and occurrences in the small, compared to which a human being is a giant, operating in a time cycle that spans immensity. Can we imagine a "thinking" molecule or atom in our physical body moving along the bloodstream and after its "long ages" discovering a "deity" -- the human heart -- that sends it forth again and again? What could it possibly conceive that would even approximate the reality of our self-conscious, creative mind? What if we are like cells in the solar cosmos?

The authors speculate on the possibility of there being an infinite range of subtlety that cannot be classified as random; that what we call randomness may very well be but one aspect

of a general spectrum of order. At one end of the spectrum are the simple orders of low degree. At the other are the random orders, and in between is a whole world of complex and subtle order, including language and music as well as other examples that could be drawn from art, architecture, games of all kinds, social structures, and rituals. But this discussion need not be limited to human activities alone. Clearly life itself is such an infinite and subtle order. pp. 130-1

What this book presents to us is the idea that design is the underlying basis of the entities and processes animating our segment of the universe. The gorgeous colors and patterns of the wings of butterflies reveal even more stunning aspects of nature's creativity when these wings are seen through a microscope! Minute coordination extends deep into the microworld beyond the range of normal vision, and strongly suggests powerful and subtle intelligence directing these and other phenomena.

The same year another remarkable book appeared. CHAOS: Making a New Science [Viking Press, 1987; 354 pages, illus., index] by James Gleick, New York Times editor and reporter, is a collation of data, theories, and examples offered by researchers across many scientific disciplines. Wherever possible Gleick uses the scientists' own words and presents an understandable "translation" of scientific, mathematical terminology, even taking up children's questions such as "how do clouds form?" and "how does water in a stream make eddies?"

He refers to the discovery of the "Butterfly Effect" found by distinguished weather scientist Edward Lorenz in changes in the weather thought to be unpredictable. This relates to "the notion that a butterfly stirring the air today in Peking can transform storm systems next month in New York" (p. 8). He found that predictions of weather changes could never be accurate because measurements can never be "perfect." Winds and other features of the weather, while seeming to be repetitions, "were never quite exact. There was pattern, with disturbances. An orderly disorder" (p. 15).

Because errors in calculation are often very small there is a tendency to overlook them as having no significance upon a result embracing large parameters. So there has come about an unexpressed "law" that one can calculate only the approximation of anything. One scientist used to tell his students that a leaf falling on a planet somewhere far out in space need not affect a billiard ball rolling on a table here on earth. Yet Einstein found that what is surprising about the universe is its fundamental simplicity, for the macrocosmos seems to function very well on the laws that govern the microcosmos.

Such differences as seem to apply may be ascribed to the conditions of observation. We are geared to dimensions of a "middle" range: the time cycles of the very small flow so rapidly to our senses we cannot differentiate their components. A whole era of development could be encompassed in just one of our minutes! At the other end of the spectrum, the universe that surrounds us has cycles commensurate with its size, and a millennium of our years would compare to the wink of a cosmic eye!

The Orphics of ancient Greece viewed Chaos metaphysically, as the Mother Night out of which emerged the new world. Now, as Gleick remarks, "to some physicists chaos is a science of process rather than state, of becoming rather than being" (p. 5). When stars grow old and die, their substance and energy are recycled in the birth and evolution of new star-systems. Because of this some astrophysicists propose a series of "big bangs" rather than a one-time birth of the cosmos. This is not a new idea by any means, for it was expressed by the ancient Hindus in their scriptures, and also by the astronomer E. J. Opik in The Oscillating Universe, published in 1960.

Of course, much more has come to light in the realm of astrophysics since then. For instance, Engineering and Science, Spring 1988, published at the California Institute of Technology, summarizes a lecture "Why Do Galaxies Exist?" delivered last January by Professor Martin Rees [Director of the Institute of Astronomy at Cambridge University]. He comments: "Each atom on earth can be traced back to stars that died before the solar system formed" (p. 12). "The dynamics of the early universe must have been finely tuned" to allow stars and galaxies to form in the permitted range. "Had it recollapsed sooner, there would have been no time for stellar evolution." If it had exploded much faster, "the kinetic energy would have overwhelmed gravity, and the clouds that developed into galaxies wouldn't have been able to pull themselves together" (p. 19).

Dr. Rees asks interesting questions: "Why was the universe set up to expand in this rather special way? . . . why does the universe contain small-scale initial fluctuations that are necessary as 'seeds' for galaxy formation, while still remaining so homogeneous overall?" The "small-scale initial fluctuations" in cosmos could relate to the "randomness" seen from a great distance, which actually hides a number of internal activities in the organism being studied.

In the same issue of Engineering and Science is an address delivered before the Caltech Associates on October 1, 1987, by Nobel Laureate Murray GellMann, "Simplicity and Complexity in the Description of Nature." He presented some pictures of "fractals" -- a term used in the new geometric system and language devised by Benoit B. Mandelbrot to cover his concept of "self-similarity," which demonstrates that "gross structure is composed of structures of the same kind in Miniature" (p. 3). Professor Gell-Mann asks whether "this fractal is a simple system or a complex one," echoing the question posed by Mandelbrot himself.

It so happens that Bohm and Peat in their book have an interesting section on the subject of fractals summarizing the view of Mandelbrot that "the geometry of fractals lies much closer to the forms of nature than do the circles, triangles, and rectangles of Greek geometry" (p. 154). They comment further: "While the fractal figures . . . appear quite complex, they could hardly be called disordered, for they are composed of a quite simple order involving a single similar difference that is repeated at constantly decreasing scale" (p. 156).

Mandelbrot himself used the example of a coastline with its various shapes, indentations, etc., while the concept of fractals has also been applied to mathematics, and other areas such as music, electrical noise, geology, and forms of chaotic behavior.

The homogeneity of the cosmos gives us a clue to the nature of manifested life, indeed of the essence of Life itself! Our physical body obviously is an organic whole, a "homogeneity" of interrelated parts and processes, yet consists of trillions of individual entities, each with its own identity, which collaborate to form and maintain the organism. Since all the processes observed in the macroworld indicate an interlocking of all systems such as planets, solar systems, galaxies, and so forth, it is surely safe to assume that what we perceive in space applies equally to the simple yet complex microcosms of Earth. We are among the components of the great universe, and from it we derive the urge to express ever more the potentialities in the "formless" fields of the life-forces. As astronomer Harlow Shapley stated years ago, we, Mother Earth and all her children, are made of "star-stuff."

(From Sunrise magazine, October/November 1988; copyright © 1988 Theosophical University Press)

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