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A graph of a chaotic function called the Lorenz attractor, by User:Wikimol, User:Dschwen [GFDL, CC-BY-SA-3.0, via Wikimedia Commons (, and Blue Morpho butterfly ( [CC0 1.0]

A graph of a chaotic function called the Lorenz attractor, by User:Wikimol, User:Dschwen [GFDL,CC-BY-SA-3.0, via Wikimedia Commons, and Blue Morpho butterfly [CC0 1.0]. The Lorenz attractor is a set of chaotic solutions of the Lorenz system which, when plotted, resemble a butterfly. The term “butterfly effect” was coined by Edward Lorenz.

Agreat plane falls from the sky and takes 230 lives. The newspapers fill with stories of fate’s quirks. Thunderstorms kept another plane on the ground for four hours in Chicago. One of its passengers had a ticket on the doomed plane, which she missed by a few minutes. “Thank God,” she told a reporter. An unfortunate young man arranged to fly a package to Europe as a courier. He planned to visit his sweetheart in London. Joyful at his free ticket and filled with delicious anticipation, he met his death. What does it mean that destiny chose one to survive and the other to die?

Television and the press fill with stories responding to our fascination and horror at life’s uncertainties. What made TWA Flight 800 a target? Why did fate draw these particular people to their common destiny? Literature, great and otherwise, often treats of fate’s powers. The ancients believed that fate worked upon human character to produce inevitable tragedy. Thus honorable Oedipus seeks the truth to save his city and discovers the awful facts of parricide and incest. We moderns are more likely to think that fate strikes us random blows. In The Bridge of San Luis Rey, Thornton Wilder sought the common threads that placed certain people on a collapsing bridge. In Kurt Vonnegut’s novels, fate is a prankster, while John Barth’s novels portray predestined malevolence.

For some centuries the progress of modern science has created the feeling that we, at last, were gaining some control over the unpredictable forces of nature. Ancient scourges, such as smallpox, are gone. The water is safe to drink. We have been secure from war on our soil, and we survive even natural disasters. Even so, many of us believe that our parents and grandparents led safer lives, and we fear that the future will only bring deterioration and danger.

Until recently science, at least, had the reputation for unceasingly improving our ability to anticipate and mold the future. Now scientific discoveries themselves seem to undermine science’s credibility. Chaos theory, sensitive dependence on initial conditions, bizarre strange attractors, and the notorious butterfly effect afflict us. Scientists tell us that the tiniest disturbances in nature lead to wildly unpredictable outcomes. The foundations of physics, the most certain of all the sciences, settle in the liquefied soil of nonlinear systems.

A California butterfly flutters this way instead of that. A tiny parcel of unstable air bubbles skyward. But for the butterfly it would have stayed in its place. Soon a cloud appears. Beneath the cloud the ground cools in the shade while the southwestern sun sizzles the rest. Large swirls of warm air lift soaring birds and draw cooler air from the nearby sea. Each effect is the predictable consequence of its cause, but the result changes the weather sweeping eastward around the globe. As the unpredictable consequence, a great storm douses Rangoon. Are the world’s workings a Newtonian clock or a Rube Goldberg machine?

New Agers triumphantly crow that the human spirit is free and science is dead. They once proclaimed the salvation of free will in the probabilities of quantum mechanics. Now they announce that if physics itself cannot predict the future, then anything may be possible. In a paradox, they believe that the end of scientific predictability offers an answer to the questions of human destiny. The traditional answers, once discredited by the pronouncements of science, now fill hearts with hope. Astrology, faith healing, feats of mind over matter, meditation, and prayer comfort many.

Just as we must know what we are looking at to see it, so we must have the proper language to think about the natural world.

The situation is worse than you have imagined. I here announce an important, if disquieting, discovery. I call it the Butterball Effect. If a small butterfly can cause torrents on the other side of the globe, imagine the disasters that may arise as a turkey desperately flaps to escape the Thanksgiving ax. Is this why winter in the northern hemisphere comes after November’s feasts while the rest of the globe basks in beautiful summer? The evidence is strong that winter always follows Thanksgiving. You object, “But snow sometimes blankets the ground before November 25.” Do not forget that those turkeys meet their ax long before our holiday. Not one of those closed minded establishment scientists has yet investigated this question. Do not fear. It is not too late for us to act. We, and we alone, can save the world from the evils of technology. We must immediately clip the wings of every genetically enhanced, factory-grown turkey.

If the world is so unpredictable, why have scientists discovered this fact so recently? Has the development of chaos theory undermined the premises of science? Does principle or anarchy govern the world? Can we understand the world or will it remain forever unknown? The answers are: They have known for a long time. It has not. It does. We can and it won’t.

Scientists have known for a long time. It is the essence of science to look beyond the frontier, but not too far. All of us, not just scientists, can ask important questions the answers to which are beyond our grasp. Part of the essential talent of a productive scientist is to recognize problems that are solvable. In the middle of the last century, James Clerk Maxwell, the famous physicist, lectured about sensitive dependence on initial conditions and other aspects of modern chaos theory. Beyond identifying these limitations of the physics of his day, he could make no progress. Henri Poincaré, the French mathematician and contemporary of Albert Einstein, pondered and wrote about unstable mechanical systems at the century’s beginning.

Chaos theory does not undermine the premises of science. Chaos theory is a triumph of science. Chaos theory is the extension of principle to what had been only confusion. Chaos theory has taught us the proper language and the principles that govern many previously lawless and unpredictable phenomena. The flapping flag, the dripping faucet, a fibrillating heart all defy detailed predictions, but hidden beneath the apparently random behavior is a strange attractor. These colorfully named mathematical objects label those hidden properties that otherwise differing natural phenomena hold in common.

It is not a failure of natural science when we find that our current theories do not fit every case. As more of nature comes within our understanding, our theories both explain and define their subjects. Newton taught us that, insofar as motion is concerned, we need only consider masses and forces, and he gave us clear definitions of these terms. Quantum theory taught us that it makes no sense to ask what a microscopic object is doing when it is not interacting with the world. Now chaos theory has educated us and added meaningful terms to our vocabulary. We have abandoned the hope, if we ever held it, of predicting the weather on August 1, 2096, until a few days before that date. At the same time our new ideas have taught us the proper time to discharge electricity to reset the functioning of a fluttering heart.

Just as we must know what we are looking at to see it, so we must have the proper language to think about the natural world. Galileo’s notebooks show that the first person to see Saturn’s rings saw handles like a teacup’s, extra moons, earlike extensions, until after several weeks he saw thin flat rings. We have struggled to know what is knowable about randomness. Chaos theory tells us how to think and what to say about unpredictable, fluttery events.

In truth, it is not necessary to eat all the turkeys nor to poison all the butterflies. We must, however, learn to accept the now more understandable randomness of the world. Theodicy is the ancient and unsolved problem of how an infinitely beneficent God can allow evil and random disasters. Thinkers have proposed many answers. In the biblical Book of Job, God makes a wager with Satan. Job loses his wife and family, his health and his wealth. Even a sheltering tree withers. He calls on God for an explanation. Without any evidence of shame, God tells Job to mind his own business. The modern Rabbi Kusher, in his thoughtful book,When Bad Things Happen to Good People, says that God is not omnipotent. He would save us if he could. He does not wish for babies to die of AIDS, but even He has limitations.

My contribution is this. We still find our future mysterious. It is, however, much less mysterious than it has ever been. Scholars tell us that from ancient times until well into the last century, the fraction of people alive in one year who were still alive in the next was small. From birth, the number of survivors plummeted on a path like a child’s slide. Scientists call this curve exponential. They know that total, absolute randomness is the governing law of any phenomenon that produces an exponential curve. This curve describes the decay of radioactive atoms.

Skeptic magazine 4.3

This article appeared inSkeptic magazine 4.3 (1996)

Imagine, if you can, what it would mean that death would take, say, one in 10 individuals—a literal decimation— in any one year. It would not matter what their station in life, their efforts to save themselves, their age, sex, or religion. Death by disease, by infection, by injury, in childbirth, by accidents, war, and natural disaster was commonplace. In a world without scientific knowledge filled with such desperate uncertainty, it is no wonder that so many sought the future in auguries, fortune-telling, or astrology.

Today with modern public health and medicine the situation is radically different. If we survive infancy, we are likely to survive to become elderly. During that long period of youth and adulthood, 98 or 99 of a 100 will survive from one year to the next. As before, death chooses its victims randomly. The poor die on the streets from guns and drugs. The rich break their necks falling from their horses. Life still has its imponderables, and the hopes and plans cut short by the TWA disaster are a loss to us all. Still, few of us face untimely death. Let us resolve to face the uncertainties that remain with courage, integrity, compassion, and love. END

About the Author

Dr. Bernard Leikind is a Senior Editor of Skepticmagazine and a plasma physicist familiar to skeptics for his pioneering work in explaining the physics of firewalking, as well as his personal participation in dozens of firewalks. Dr. Leikind has also lectured for skeptics on “strange and unusual atmospheric phenomena,” as well as on the physics of sports, dance, and ballet. He has taught physics and researched at the University of Maryland, UCLA, the Lawrence Livermore Laboratory, and General Atomics. He may be the only sensible firewalker, although some consider this an oxymoron.


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