Katya Walter has written an interesting and insightful book linking the concepts of chaos to the double helix of genetics to the I Ching of ancient Chinese culture. Along the way she provides some of the best explanations of chaos and fractals I've read.
She begins her journey with a section called Beyond Linear Limits that I'm going to quote from extensively:
“Late one Saturday afternoon in Austin, Texas, I faced a showdown between my left and right brains. Shoot-out time. It was June 8, 1985, and it happened at the East-West Center when Diana Latham urged me to try the I Ching, just once. So reluctantly, I did ... with a lackadaisical and dubious query. But the response bowled me over! It was devastatingly appropriate-and poetic. Sheer chance, of course.
But when I tried it again later out of curiosity, it worked again. Moreover, the old Chinese oracle's answer again touched some deep chord in me that logic alone didn't reach. A response to wisdom, a welcoming hosanna of "Yes, that's it!"
I was confronted with the notion that this absurd old oracle might actually work, odd as that seemed to my logical mind. Irrational. So strange in fact that I ignored it for awhile. I could not admit the possibility ... so it chewed just underneath. After all, I was modern savvy, educated past superstition. A Ph.D. teaching at the University of Texas. Wasn't I? Logic shot the I Ching..down. Didn't it?
But I couldn't quite dismiss it. How in heaven's name could that abstract and ancient oracle mesh in such an amazing way with the events in my own modernday life? Rationality said, "Impossible Chance! Gullibility!"
But the simple fact remained: it had told me apt wisdom, pointed and calm, like a grandparent whispering in my ear. So I decided to explore in rational terms if such a thing might possibly be.”
Later in that section, she goes on to explain the I Ching:
“But I have slowly learned that the I Ching reveals the pattern. Not the specifics of an event, but its underlying pattern. It works through the dynamics of chaos theory, which can predict a trend without specifying its exact details. Discovering this huge hidden intelligence that rests deep in the weave of nature, even learning to communicate with it, can be disconcerting, frightening .. , until it becomes wonderful.
The discovery reveals a deeper truth beyond the limits of what we call normal reality. It exhibits an underlying coherent pattern in the dynamic chaos of nature itself. More eerily, it exhibits a tappable caring that's nestled in the very fabric of spacetine-mattergy, This huge pattern knits the Cosmos together in physics and metaphysics. It unites the objective and the subjective, the quantitative and qualitative, the alpha and omega. Its vast dynamic shapes us, body and soul.
But even now, despite extensive experience, I still understand why people fear such a possibility lurking beyond the sensory reality. What is this strange domain of power? It sounds rather like superstitious enslavement to some bogey of the imagination…and that is worthy of fear.
Fear is a reasonable response, It sees the psychic loss in giving oneself up to superstition and voodoo rites, in relinquishing personal power to brutal gods with canny, greedy priests, to wizards, healers, or gurus only too willing to manipulate their followers if given a chance, It fears an abandonment into destructive and orgiastic fantasy, a letting-go of choices, a precipitous lapsing away from logic to become lost in the enchantment of the deep. The descent looks too dangerous into the primal power of raw archetypes. It seems the epitome of romantic release to Dionysius, where one fears and yet follows a blind pull into the passionate unknown.
In here is an emotional powerhouse. In here, people "lose control" and argue or rape or fall blindly in love or seek the grail. They kill others in holy war or devote the rest of a short lifetime to the cure of AIDS or become inspired to paint a masterpiece. Moments or years later, a person can say bemusedly, "I don't know what came over me," or "Something possessed me," or "I felt driven!" or "The devil made me do it," or "I followed my bliss and it has blessed me."
This mysterious domain is not logical. It has it own reasons that reason does not know. To quote a bewildered Woody Allen, "The heart wants what it wants." But a passionate vision can so easily lead to bitter disillusion, to mob violence, to some idiosyncratic utopia where a demagogue-religious or social or political-holds sway and demands blind faith of spellbound followers who do battle for the cause. Some cause. It can idealize a saint or a demagogue to follow, fix upon some vile enemy to conquer, so that half of its huge polarized energy is projected away into the outer world to become wooed or defeated, driving us without free will.
Yet there is also fear of no passion. Cool Apollonian logic can survey this universe with a despairing sense that it is caught in some limitless, endless, mindless design that also leaves no room for free will. Sartre showed us the architecture of this existential prison with no exit from a godless hell of cold linear logic. It locks us into a gray, chilly, basement whose flat expanse of pointless concrete data cannot conceal the futile bones buried beneath. Here is dead-end living,
Both extremes - passionate romantic or cool logician - reveal a paucity of perspective in the West for more than 2,500 years. It has split us into romantic versus classic, liberal versus conservative, left versus right, heart versus head. But it is possible to encompass both poles within a larger, transcendental third stance. This paradigm is cradled in chaos theory, that amazing new science of the 20th century. It reveals the I Ching is a model of chaos patterning in microcosm. It even connects science to spirit.”
She tells of the loss of spiritual depth in our society to the rise of drugs. “ …habituating drugs can only offer a road away from, not to. The escape into addiction is triggered by our search for psychic release from the data-mad mire of ordinary life.”
Walters discusses the difficulty of comprehending the Tao.
“Laotse opens his Tao Te Ching this way: 'The Tao that can be spoken is not the Tao.'”
And, she summarizes her way through this enigma. “By discovering that the I Ching is merely a spiritual version of DNA, and both of them are merely subprograms of a deeper, even universal order called complementary chaos. For the scientific mind, this allows the security of an explanation. For the mystical soul, it opens an endless vista on wordless beauty charged with transcendent connection.”
In an article written by Katya Walter reprinted in Future Positive in 2004, she explained the concept of patterned chaos:
“My book Tao of Chaos discusses in detail the ability of both DNA and the I Ching to combine fractal analog and binary functions. It is based on modern chaos theory, which can predict a trend without specifying its exact details. Chaos patterning is determined because it can predict an overall pattern, but also chaotic because it cannot specify any exact point of its next manifestation. The mathematician can determine its general form but not the exact contents. Patterned chaos has its own special signature:
• Order in the midst of apparent disorder.
• Cycling that repeats with continual slight variation.
• Scaling that fits one level into another like nesting boxes
• Universal applicability. “
This an extremely import concept for it allows her to connect patterned chaos to fractal geometry.
Patterned chaos is also linking many disciplines together.
“The universal import of this odd new science is even tending to heal the ever-dividing rift of disciplines that fragmented the past centuries into splinter groups specializing ever more narrowly in describing more and more about less and less. But now cardiac specialists stockbrokers, psychologists, and turbulence physicists can all meet in joint conference on chaos patterning. A recent conference held in Florida sponsored papers on chaos patterns in physiology, biophysics, gestalt psychology, chemical systems, mathematics, physics, communication theory and linguistics. Such unity within diversity was unheard of not so long ago. Here indeed is interdisciplinary reunion. Patterned chaos can find shared meaning in areas as wide-ranging as plasma physics, genetic coding, perceptual psychology, coffee prices, weather reports, the body's living ductwork of blood vessels, airways, and nerve impulses.”
The author then spends several chapters relating patterned chaos to fractal geometry, which provides much needed insight into the application of the new geometry to the science of chaos.
One of the other powerful concepts in this book is the concept of complementary chaos (or co-chaos, sometimes cochaos).
We are all probably familiar with digital doubling: 20 = 1, 21 = 2, 22 = 4, 23 = 8, etc. Fewer people are probably less familiar with analog doubling in an example like the logistic map. The logistic map is the result of repeated application of the rather simple looking logistic function:
xn+1 = rxn(1-xn),
where n is the iteration number and r is a constant. Repeated application of this equation produces the complicated graph below (Wikipedia)
You can observe the digital doubling effect by looking at the branches: 1, 2, 4 and 8. But, beyond that, the logistic map becomes “random”. At eight branches, called period 3, the state of the logistics map is very close to wild fluctuations.
Complementary chaos results from the counterpoise of two period 3 systems. Walters uses this model to draw analogies with the double helix genetic code and the I Ching.
I am not in any position to verify these assertions. But the theory offers a tantalizing hint of a unification of East and West, and the unification of several sciences in the Western tradition.
In any case, I'll close with the advice of Buddha:
"Chaos is inherent in all compounded things. Strive on with diligence." - Buddha
The Tao of Chaos
Kairos Center, 1994, 287 p
You can find more information about Katya Walter and her work on her web site, The Double Bubble Universe