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WHERE CHAOS BEGINS, classical science stops.
Chaos poses problems that defy accepted ways of working in science.
The most passionate advocates of the new science go so far as to say that twentieth-century science will be remembered for just three things: relativity, quantum mechanics, and chaos. Chaos, they contend, has become the century’s third great revolution in the physical sciences.
“Relativity eliminated the Newtonian illusion of absolute space and time; quantum theory eliminated the Newtonian dream of a controllable measurement process; and chaos eliminates the Laplacian fantasy of deterministic predictability.”
The simplest systems are now seen to create extraordinarily difficult problems of predictability. Yet order arises spontaneously in those systems—chaos and order together.
Implicitly, the mission of many twentieth-century scientists—biologists, neurologists, economists—has been to break their universes down into the simplest atoms that will obey scientific rules. In all these sciences, a kind of Newtonian determinism has been brought to bear.
LORENZ’S DISCOVERY WAS AN ACCIDENT, one more in a line stretching back to Archimedes and his bathtub.
Under normal conditions the research scientist is not an innovator but a solver of puzzles, and the puzzles upon which he concentrates are just those which he believes can be both stated and solved within the existing scientific tradition,” Kuhn wrote. Then there are revolutions. A new science arises out of one that has reached a dead end. Often a revolution has an interdisciplinary character—its central discoveries often come from people straying outside the normal bounds of their specialties.
FAST Agile
Every scientist who turned to chaos early had a story to tell of discouragement or open hostility.
Shallow ideas can be assimilated; ideas that require people to reorganize their picture of the world provoke hostility.
Tolstoy: “I know that most men, including those at ease with problems of the greatest complexity, can seldom accept even the simplest and most obvious truth if it be such as would oblige them to admit the falsity of conclusions which they have delighted in explaining to colleagues, which they have proudly taught to others, and which they have woven, thread by thread, into the fabric of their lives.”
The spot is a self-organizing system, created and regulated by the same nonlinear twists that create the unpredictable turmoil around it. It is stable chaos.
Feedback can get out of hand, as it does when sound from a loudspeaker feeds back through a microphone and is rapidly amplified to an unbearable shriek. Or feedback can produce stability, as a thermostat does in regulating the temperature of a house: any temperature above a fixed point leads to cooling, and any temperature below it leads to heating.
PEOPLE WOULD SAY that James Yorke had discovered Lorenz and given the science of chaos its name. The second part was actually true.
physicists had learned not to see chaos.
as have agilists...
When people stumbled across such things—and people did—all their training argued for dismissing them as aberrations. Only a few were able to remember that the solvable, orderly, linear systems were the aberrations. Only a few, that is, understood how nonlinear nature is in its soul.
Enrico Fermi once exclaimed, “It does not say in the Bible that all laws of nature are expressible linearly!”
This was the discovery that came as an “electric shock” to physicists like Freeman Dyson. It was so contrary to intuition.
Yorke had offered more than a mathematical result. He had sent a message to physicists: Chaos is ubiquitous; it is stable; it is structured.
Clouds are not spheres, Mandelbrot is fond of saying. Mountains are not cones. Lightning does not travel in a straight line. The new geometry mirrors a universe that is rough, not rounded, scabrous, not smooth. It is a geometry of the pitted, pocked, and broken up, the twisted, tangled, and intertwined.
Over and over again, the world displays a regular irregularity.
The old intuition was misleading.
“Intuition is not something that is given. I’ve trained my intuition to accept as obvious shapes which were initially rejected as absurd, and I find everyone else can do the same.” Mandelbrot
Simple shapes are inhuman. They fail to resonate with the way nature organizes itself or with the way human perception sees the world.
The answer seems to me, even if somewhat speculative, to follow from the new insights into dynamical systems. Our feeling for beauty is inspired by the harmonious arrangement of order and disorder as it occurs in natural objects—in clouds, trees, mountain ranges, or snow crystals. The shapes of all these are dynamical processes jelled into physical forms, and particular combinations of order and disorder are typical for them.”
“If the image is complicated, the rules will be complicated,” Barnsley said. “On the other hand, if the object has a hidden fractal order to it—
much of nature does have this hidden order—then it will be possible with a few rules to decode it.
as soon as nature began organizing itself by means of simple physical laws, repeated with infinite patience and everywhere the same.
Schrödinger’s view was unusual. That life was both orderly and complex was a truism;
Simple systems behave in simple ways.
Complex behavior implies complex causes.
In the intervening twenty years, physicists, mathematicians, biologists, and astronomers have created an alternative set of ideas. Simple systems give rise to complex behavior. Complex systems give rise to simple behavior. And most important, the laws of complexity hold universally, caring not at all for the details of a system’s constituent atoms.
chaos was the end of the reductionist program in science.
Uncomprehension; resistance; anger; acceptance. Those who had promoted chaos longest saw all of these.
Ford, self-proclaimed evangelist of chaos: Dynamics freed at last from the shackles of order and predictability…. Systems liberated to randomly explore their every dynamical possibility…. Exciting variety, richness of choice, a cornucopia of opportunity.
Chaos was the set of ideas persuading all these scientists that they were members of a shared enterprise. Physicist or biologist or mathematician, they believed that simple, deterministic systems could breed complexity; that systems too complex for traditional mathematics could yet obey simple laws; and that, whatever their particular field, their task was to understand complexity itself.
In our world, complexity flourishes, and those looking to science for a general understanding of nature’s habits will be better served by the laws of chaos. Somehow, after all, as the universe ebbs toward its final equilibrium in the featureless heat bath of maximum entropy, it manages to create interesting structures. Thoughtful physicists concerned with the workings of thermodynamics realize how disturbing is the question of, as one put it, “how a purposeless flow of energy can wash life and consciousness into the world.”
the essence of chaos: a delicate balance between forces of stability and forces of instability;
“Evolution is chaos with feedback,” Joseph Ford said. The universe is randomness and dissipation, yes. But randomness with direction can produce surprising complexity.
“I’m still not clear on chaos,” says Laura Dern’s character in the 1993 film Jurassic Park,
Tom Stoppard’s play Arcadia, which opened in London a few months before Jurassic Park. It, too, features a mathematician reveling in chaos: “The freaky stuff,” he says, “is turning out to be the mathematics of the natural world.”
The ordinary-sized stuff which is our lives, the things people write poetry about—clouds—daffodils—waterfalls—and what happens in a cup of coffee when the cream goes in—these things are full of mystery, as mysterious to us as the heavens were to the Greeks…. The future is disorder. A door like this has cracked open five or six times since we got up on our hind legs. It’s the best possible time to be alive, when almost everything you thought you knew was wrong.
IN THE HEADY early days, researchers described chaos as the century’s third revolution in the physical sciences, after relativity and quantum mechanics.
The fundamental equations of general relativity are nonlinear—already a signal, we know by now, that chaos lurks.
Chaos is a creator of information—another apparent paradox. This thread connects with something Bernardo Hubemian said: that he was seeing complex behaviors emerge unexpectedly in information networks. Something was dawning, and we’re finally starting to see what it is.
