Alwyn Scott is a professor in the Department of Mathematics at the University of Arizona and in the Department of Mathematical Modeling at the Technical University of Denmark. His most recent book is Nonlinear Science: Emergence and Dynamics of Coherent Structures, published by Oxford University Press in 1999. His previous book, entitled Stairway to the Mind, is being reprinted by Springer-Verlag (Copernicus) in 1999.
The Butterfly Effect
Some years ago on a fine March morning in Tucson, Arizona, I suddenly found myself flying through the air. This unexpected flight was neither a dream nor a virtual experience. No subjective impression deluded me nor was it a biochemical hallucination; I was quite literally flying. The air about was warm and sunny and full with the sweetly piquant perfume of lemon blossoms. Like spring butterflies, a few white clouds-so fresh and clean that one’s throat ached to see them-graced the brows of the Santa Catalina mountains to the north.
Why was I flying through the air? The short answer is that moments earlier my bicycle and I had been hit by a truck. But much more can be implied by this small question: Why? Depending on how one regards reality, there are several questions and many answers. From the instant that my eyes made contact with those of a frightened young driver (who was trying desperately to avoid a collision) until the sharp thump of the impact, the thought raced through my head: Why me? Surely this happens only to others!
Having studied Isaac Newton’s laws of motion, I knew of course that I flew because enough force had been applied to me and the bike in the proper direction for a sufficient length of time to provide our combined mass with the necessary momentum. But is that all there is to it? Why else? Was this collision merely an accident? Did the gods care? Did they even notice? Had I carelessly run a red light? Or neglected to touch iron that morning? Was someone out to get me? Or something? Did this event lie within or beyond the purview of science? Could I understand it? If so, how?
We often read in those extra sections of the Sunday papers about an exciting new branch of science called chaos studies, as part of which scientists are now “researching the unpredictable,” so we can be assured that all such happenstance events will soon be understood and cataloged in the journals of the world’s university libraries. And a standard item in these exercises of journalistic excess is a discussion of the recently formulated “butterfly effect,” a description of which often goes something like this
A single butterfly, by gently flapping its wings on the high plateau of the Gobi Desert in central Mongolia-scientists now know-can set in motion a train of events that could cause a tornado to form above the plains of Kansas and rip through a village, destroying all in its path.
A ”train of events”? From the perspectives of both aerodynamic science and common sense, this seems silly. If a Gobi butterfly could cause a Kansas tornado so also might a Greek grasshopper, an Indonesian firefly, perhaps even a Roman skylark. Not to mention someone fiddling with the Sunday paper, coughing at an outdoor concert, or yelling at the cat. None of these-one must admit-can be thought to cause a tornado. Reality, whatever it is, is not that simple. The relationships among causes and effects are more intricate, more involuted. Perhaps all of the above and umpteen billion more acting in concert might be blamed for carrying Dorothy and little Toto away to the Land of Oz, but what then happens to the idea of a cause? Should they all be dragged into court and forced to divide payment to Auntie Em?
And yet and yet. If a butterfly had landed on the handlebars of my bike that fateful March morning, I most certainly would have stopped to admire it. Several golden minutes would have passed, and the brakeless truck with its brainless driver would never have been near enough to hit me. I would not have known how close I came to becoming a permanent partial paraplegic.
But Tucson’s butterflies were busy with the citrus blossoms, and none landed on the bicycle. So I pedaled into an intersection from the east at the same instant that a white Ford truck entered it from the north, got hit, flew several yards through air, and landed in a heap, and this seemingly unpredictable and certainly unhappy accident set into motion a very predictable series of events. Passersby assembled, talking excitedly and wondering what to do. I tried to move my legs and found that they wouldn’t stir. Someone shouted: “Don’t touch him until the ambulance comes!” An ambulance soon arrived. Medics disentangled me from the twisted bicycle and laid me on a stretcher, which was carried gently into the ambulance. With lights flashing and sirens shrieking, the ambulance raced toward the emergency room of the University Medical Center. Upon being asked my name and the day of the week, I responded without hesitation. When we arrived at the hospital, several others asked for my name and the day of the week (giving the impression that these were the two questions of primary concern that day), and I was relieved to learn from a police officer that I had not, in a thoughtful daze, run a red light. At least there was no need to feel guilty! As medical science took control, the events of the afternoon began to unwind according to a practiced plan.
In addition to Newton’s dynamics, I am also familiar with the mathematics behind a machine called a CAT scan. Computer assisted tomography is a means for assembling many bits of x-ray data into a vivid image of the brain or the lumbar region of the spine. Surgeons need such pictures before they begin to cut, and with a back injury there is little time to be lost. The swelling from broken blood vessels kills spinal neurons, and once gone these cannot be replaced. While understanding the scientific principles upon which the machine is based and the neurological implications of unnecessary delay, I had not known until that afternoon how frightful it feels to be inside a CAT machine, laid out like Roderick Usher for seemingly endless hours in a tube somewhat smaller than a coffin. Medical science has little to tell of one’s emotions in such a place at such a time, being instead concerned with the
INDICATIONS FOR PROCEDURE: Patient sustained a burst fracture of his first lumbar vertebra with a retropulsed fragment into the spinal canal. He had a partial paraplegia with sparing of motor fibers to L2 or L3 and sparing of sensation down to L4. It was felt that since his lesion was partial and there was an obvious fragment in the spinal canal that emergency decompression was warranted.
As preparation for surgery progressed throughout the long afternoon, I edged ever closer to an abyss of panic. Near the nadir, when I was collapsing like an old rag doll spilling her sawdust out onto the floor, a seemingly simple interaction helped to sustain my spirits. A young man-I never knew who it was-looked into my eyes and touched my arm for a few moments. Just that. No word was spoken, but I experienced a rush of . . . What? Comfort? Human contact? Love? Spiritual grace? Faith healing? Contact with some universal consciousness? Since science has no place for such ephemerals, this seemingly trivial event went unrecorded in the hospital’s
DESCRIPTION OF TECHNIQUE: The patient was taken to the operating room and anesthesia was induced while he was on a gurney on a backboard. He was turned carefully onto a Wilson frame in the prone position. Foley catheter had been placed previously and TED hose were placed on his legs. The left knee was aspirated just prior to turning him and 50 cc of blood with fat globules were taken out. His left lower extremity was placed in a posterior ankle splint prior to bringing him to the operating room. He had a large abrasion on his left buttock in the ischial region. When he was turned over a palpable defect could be felt between L1 and T12 in the region of the interspinous ligament.
The skin over his back and iliac crest was prep’d and draped in a sterile manner. The incision was made from about T9 to L4. It was carried through the subcutaneous tissue. Prior to the incision the area had been injected with a solution of 1:500,000 epinephrine. The fascia was divided from the spinous processes leaving the interspinous ligament intact with the exception of the portion that had already torn between T12 and L1. The soft tissue was then stripped from spinous processes and the lamina.
And so on and on for several hours until
the patient was flipped onto the ICU bed very gently using careful technique so as not to torque his spine. He was awakened from his anesthetic and taken to the recovery room and eventually to the surgical intensive care unit in satisfactory condition and extubated.
In learning to deal with a major disability over the following months, there was much to fill my days, but for many nights I experienced the same vivid dream, in which I was crawling up a deep well with green and slimy walls that disgusted me and wore my fingers to the quick. The upward climb was difficult because at the beginning of each dream I seemed to have lost the previous night’s progress, slipping back toward the darkness below. After some weeks of intense effort, however, I finally gained the top of the well, where, expecting the ordeal to be over, it was vastly disappointing to look out and see a desert. Not a fertile desert filled with the rich variety of flora and fauna surrounding Tucson, but a real desert, a barren waste of gypsum like that northwest of Alamogordo in New Mexico or on the surface of Mars, baked and cracking under a fierce sun and devoid of life. No cacti or lizards or scorpions graced this forbidding land; only minerals with their atoms neatly arranged in regular patterns by chemical forces were able to endure. It was a “full desertness,” in Mrs. Browning’s words,
Under the blanching vertical eye-glare
Of the absolute heavens.
Most like a monumental statue set
In everlasting watch and ceaseless woe.
Touch it. The marble eyelids are not wet.
If it could weep, it could arise and go.
Strangely, it was the smug rows and layers of atoms that filled me with the deepest sense of horror.
To help me survive as I began to crawl across this desert toward some mountains half hidden in the distant haze, there came many with information and advice. The high level practitioners of allopathic medicine were ever crisp and sure of themselves, making ex cathedra pronouncements that were often in conflict with those of other experts. Many seemed unduly concerned with filling out insurance forms, and all were very busy. One morning, when the young resident who had ably assisted at the surgery stopped by to remove the stitches from my back, I set caution aside and asked, “What’s your worst case estimate of my situation?” “You’ll be flat on your back for the rest of your life,” he responded matter-of-factly while examining the scar. Since there seemed nothing more to say, I lay flat on my back, silently watching gray clouds form over the mountains as a mixture of dark pain and hot panic rose within my gut and oozed out across the world. It was on that afternoon that I began to dream of putting a loaded pistol against my temple and slowly squeezing the trigger.
The nurses, on the other hand, were helpful in many unexpected ways, providing in addition to their professional knowledge and skill some serious attempts to deal with the desperate state of my spirit. Being far out of balance, I needed such help, for my soul seemed to stray untethered, like an unkempt beast, yards away from my body. Among the nurses was a big fellow who could pick me up with one hand and make it fun, and a handsome woman named Monica with deep brown eyes and black hair to frame her olive face, who brought morphine in the night and showed me how to use a catheter. There were physical therapists who taught me to handle a wheelchair and later to stagger about on crutches, occupational therapists who helped analyze the unexpected challenges of the home, a behavioral psychologist with whom I spent many hours learning how to resist the psychic demands of chronic pain and the ravages of suicidal depression, and a urologist who patiently tried to teach me to pee.
Toward the doctors, I felt, correctly or not, the need to be a good soldier (“How’re ya doin’, fella?” “Great Doc!”), but with some of the nurses it was possible to talk about what really concerned me. Especially Monica, who one morning rearranged her schedule so she could take me to lunch. As she wheeled me to a nearby Macdonald’s, the sense of breathing free air and mixing with ordinary people was intoxicating, and my head began to spin under the bright summer sun. Seeming to anticipate this, she laid her hand on my arm and looked into my eyes, reminding me of the young man whose touch had supported my spirits on that first afternoon. “Tell me how you are really doing,” she said, and merely by asking, she seemed to be helping me find a path out of the suicidal despair that had covered me under a leaden cloud.
I told her of the disappointment of climbing from the slimy well into a barren desert and of another vivid and recurring dream in which I could walk again, with ease and grace. Buoyed with pleasure and feeling close to the sky, I would tramp over the woods and mountains of Appalachia, which were keenly remembered from youthful rambles. Upon awaking, I would remain momentarily elated by the sense that my difficulties were gone and then become even more discouraged as the bitterness of reality crashed back into my fragile consciousness.
“Do you have other dreams?” she asked, looking at me intently, and in response I described being lost in a deep forest, almost a jungle, that was inhabited by shadowy figures who were armed with every sort of pistol and rifle while I had only a simple bow and arrow. As she listened, nodding without comment, my arm still glowed quietly from the touch of her hand. Although it was not possible to change some aspects of my present life, she told me on the way back to the hospital, I could alter the ways that I felt about them. I hung on her words, needing to believe.
A representative of some Christian church came by one morning and described the remarkable faith of a man named Job. All is written in God’s Book, he said, and all that happens is part of His Great Plan. Although a devout atheist since the age of thirteen, as most scientists are, I listened and wondered: Did God write the Book?
One Saturday evening I heard a radio personality named Garrison Keillor tell a story about a Minnesota man who is late in changing his storm windows. Deep in November, the ground is frozen with random patches of ice, and the man stands near the top of his longest ladder, holding a storm window by its bottom edge in gloveless hands, trying to reach the hooks under the very highest gable: an exercise I recall from living through a score of Wisconsin winters. Unknown to this frustrated man, the bottom of his ladder rests on a patch of ice and may slip at any moment. At this point, Keillor paused to advise his audience that as story teller he can choose the outcome. He can let the ladder slip and have the man and window tumble to the ground or he can allow its footing to hold. Listening alone in the night, I wondered: Is God a story teller?
On a very long afternoon and evening, I was visited by an enlightened friend from Santa Fe, a guru of sorts, who proposed to help me explore the spiritual dimensions of my plight from a New Age perspective. Starting with the concept of a universal consciousness-pervading reality and tying all that happens together-she searched to find the meaning behind my misfortune. Everything that occurs is part of the great unfolding pattern of existence, she claimed, which has been explored and understood for millennia by the Eastern sages. Since the possibility of events being meaningless was ruled out by assumption, she was forced to consider the relationship between my misfortune and the state of my mind at the time it occurred: the karma of the situation. At the end of the evening, she shared this insight: “You know, the thing is that you really wanted the accident to happen. At some level, you chose to be hit by that truck.” Gasping with disbelief at this lack of ordinary sensitivity, I was unable to reply. Is this where enlightenment leads? Is this all the sages have to offer? Does everyone rely on simple formulations? How can such nonsense be considered insightful? Needing to be alone, I clenched my teeth and told her that I had suddenly become very tired. Later, I wondered if my anger stemmed from a suspicion that her intuition might be correct.
As days wore on, I spent much time in the hospital library and came across a book by another handicapped scientist, named Stephen Hawking, on the roles that black holes and brown holes and curved space and quantum gravity have played throughout the history of time in the universe. When physicists finally come to understand the fundamental laws of physics, Hawking confidently asserted, they will know the “mind of God.” Nearby was a modest book by an amateur naturalist and writer named Annie Dillard entitled Pilgrim at Tinker Creek, in which she described a year spent living on Virginia’s Blue Ridge above the Shenandoah Valley, where I had often hiked as a young man, watching and recording with both wonder and dismay the intricate harmonies and cruel excesses of the biological world. What sort of deity would permit-not to say encourage-the careless carnage and pain running rampant through the animal kingdom? Upon finishing this book, I stared out into the blue desert sky above the Santa Catalina mountains beyond my hospital window, my aching soul asking with hers: Is God a maniac?
For better or worse, the attempt to recover from spinal cord injury provides opportunities to relive some aspects of one’s past. Just as one year old, having discovered that those arms and legs belong to him, must learn to manipulate them in useful ways by imitating the people around him and pulling himself toward that cookie on the table, the fledgling paraplegic must work with the remaining muscles, which have no idea what to do. To emphasize the nature of this task, the walls of the physical therapy room were covered with pictures of babies learning locomotion, first pushing themselves up, then crawling, later sitting, standing, and walking: all skills that we battered patrons needed somehow to relearn. From another perspective, injury to nerves around the second lumbar vertebra broadcasts confusion in the crotch, adding the many uncertainties of puberty to a full plate of problems.
While being knocked like a shuttlecock between the poles of hope and despair as week followed weary week-one day striving to relearn some basic skill and the next consumed by an envious amazement that legs and ankles could function at all, never mind trying to comprehend the mystery of their perfection-I managed to wonder about the appearance of life in the universe and of my small place within that sphere of life.
Central to this effort was the discovery of a little book on the philosophy of human existence by Erwin Schrödinger—the Austrian philosopher and quantum theorist-cum-biophysicist—entitled My View of the World. First published in Germany in 1961 (under the title Meine Weltansicht ), this curious little volume comprises two parts: the first having been written in the autumn of 1925, just before the annus mirabilis, which carried him to the fore of twentieth century science, and the second in 1960, a year before his death. Why was this book so influential for me? Perhaps because Schrödinger approached his existence, both early and late, with a sense of wonder. “What is real?” he asked with a passion that was refreshingly unacademic. How can it be “that anything is experienced and encountered at all?” “Which material events are directly associated with consciousness?” “What is human consciousness, and how is it related to the phenomena of our existence?” Although not always in agreement with Schrödinger’s answers, it was stirring to share with him the conviction—in this age of shallow queries and slick replies—that deeper questions need to be asked.
How deep is the mystery of mind? About a year after that sudden and unhappy flight through the air, I found myself sitting alone in the garden of a small restaurant. The air was soft and warm and full with the perfume of citrus blossoms, and small white clouds again graced the brow of the northern mountains. The little garden rested within a wall of bamboo, reminding me at first of the Orient and then of an incident that had happened quite unexpectedly in a Javanese garden some years before.
In the hills above Surabaya, I was reading a book by the Judaic scholar Martin Buber that told of an Eastern philosopher who awoke from dreaming that he had been a butterfly to ask himself: “Am I a man who has just dreamt he was a butterfly, or am I a butterfly now dreaming she is a man?” At the moment I read these words, a butterfly landed on the page. The hair on the back of my neck arose, and the butterfly stood quite deliberately on the very words I had been reading, digging the tips of her little feet into the surface of the paper so the moving air could not blow her away. For some minutes I sat in a trance, feeling with the little creature the emotions of her struggle and seeming to share in her life. The rest of the day was spent trying to express the experience in a rambling poem (which I won’t inflict upon you), but upon recalling that half forgotten morning, I seemed suddenly to awaken from an ugly dream. Scales fell from my eyes as I looked about with wonder, again seeing the white clouds near the brow of the mountains and feeling the warmth of the afternoon sunshine and smelling the crisp sweetness of the lemon blossoms. It was as if Elizabeth Barrett’s statue had arisen, and a wall within my soul had cracked and crumbled away, disintegrating into dust before me. Long hidden waves of raw emotion boiled from under the soles of my feet, surging upward through my legs and gut, bursting into my chest and pouring out in aching sobs, washed with floods of tears.
In that moment I recovered, as Buber has described it, an intimate association—an Ich und du relationship—with my surroundings. All the problems and pains of paraplegia were with me still, but I had managed to cross the sulfate sands of despair and reach into the sweet waters of the mountains beyond. As if it were a gift from God (or was it the butterfly?), I had rediscovered a sense of joy.
Copyright © by Alwyn C. Scott 1998. All rights reserved.