Chaos: Making a New Science - James Gleick (1988)

Afterword

EVEN NOW, CHAOS THEORY sounds like a bit of an oxymoron. In the 1980s, “chaos” and “theory” were words that didn’t seem to belong in the same room, let alone the same sentence. When friends heard that I was researching a book about chaos—and that it was to do with science—there were quizzical looks and raised eyebrows. Much later, one told me she had thought I was writing about “gas.” As it says in the subtitle, chaos was a new science—strange and alien-sounding, exciting and hard to accept.

What a difference twenty years make. The ideas of chaos have been adopted and internalized, not just by mainstream science but also by the culture at large. Still, even now, plenty of scientists find chaos to be strange and alien-sounding, exciting and hard to accept.

We’ve all now heard of chaos, at least a little. “I’m still not clear on chaos,” says Laura Dern’s character in the 1993 film Jurassic Park, so that Jeff Goldblum’s character—who announces himself as a “chaotician”—can explain flirtatiously, “It simply deals with unpredictability in complex systems…. A butterfly can flap its wings in Peking, and in Central Park you get rain instead of sunshine.” By then the Butterfly Effect was well on its way to becoming a pop-culture cliché: inspiring at least two movies, an entry in Bartlett’s Quotations, a music video, and a thousand Web sites and blogs. (Only the place names keep changing: the butterfly flaps its wings in Brazil, Peru, China, California, Tahiti, and South America, and the rain/hurricane/tornado/storm arrives in Texas, Florida, New York, Nebraska, Kansas, and Central Park.) After the big hurricanes of 2006, Physics Today published an article titled “Battling the Butterfly Effect,” whimsically blaming butterflies in battalions: “Visions of Lepidoptera terrorist training camps spring suddenly to mind.”

Aspects of chaos—different aspects, usually—have been taken up by modern management theorists on the one hand, and postmodern literary theorists on the other. Both camps have found use for phrases like “orderly disorder,” especially popular in dissertation titles. Compelling literary characters, such as Shakespeare’s Cleopatra, are seen to be “strange attractors.” So are chart patterns in the financial markets. Meanwhile, painters as well as sculptors have found inspiration in both the words and the images of fractal geometry. For my money, the most powerful artistic incarnation of these ideas came in 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.” Stoppard goes beyond orderly disorder to the tension between the formal English garden and the wilderness, between the classical and the Romantic. He is channeling the voices in this book, and to quote him here is to engage in loopy feedback, but I can’t help it. He captures the exhilaration of so many young researchers at the discovery of chaos. He sees the opening door and the vista beyond.

The ordinary-sized stuff which is our lives, the things people write poetry aboutcloudsdaffodilswaterfallsand what happens in a cup of coffee when the cream goes inthese 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.

The door is open more than a crack now, and a new generation of scientists has come along, armed with a more robust set of assumptions about how nature works. They know that a complex dynamical system can get freaky. They know, when it does that, that you can still look it in the eye and take its measure. Meetings across disciplinary lines to share methodologies on scaling patterns or network behaviors are now, if not the rule, at least no longer the exception.

By and large, the pioneers of chaos came in from the wilderness and took their places in the scientific establishment. Edward Lorenz, as a much-honored professor emeritus at M.I.T., was still seen coming to work in his nineties and watching the weather from his office high up in Building 54. Mitchell Feigenbaum joined Rockefeller University and created a mathematical physics laboratory there. Robert May became president of the Royal Society and chief scientific adviser to the government of the U.K. and, in 2001, was created Baron May of Oxford. As for Benoit Mandelbrot, a “Vita” he published on his Yale Web page in 2006 listed twenty-four awards, prizes, and medals, two decorations, nineteen “diplomas, honoris causa & the like,” twelve memberships in scientific societies, fifteen memberships on editorial boards and committees, and a variety of items bearing his name, including a “Tree along the Nobel Lane” in Balantonfüred, Hungary, a laboratory in China, and an asteroid.

The principles they discovered and the concepts they invented have continued to evolve—beginning with the word “chaos” itself. Already by the mid–1980s the word was being defined rather narrowly (see here) by many scientists, who applied it to a special subset of the phenomena covered by more general terms such as “complex systems.” Astute readers, though, could tell that I preferred Joe Ford’s more freewheeling “cornucopia” style of definition—“Dynamics freed at last from the shackles of order and predictability…”—and still do. But everything evolves in the direction of specialization, and strictly speaking, “chaos” is now a very particular thing. When Yaneer Bar-Yam wrote a kilopage textbook, Dynamics of Complex Systems, in 2003, he took care of chaos proper in the first section of the first chapter. (“The first chapter, I have to admit, is 300 pages, okay?” he says.) Then came Stochastic Processes, Modeling Simulation, Cellular Automata, Computation Theory and Information Theory, Scaling, Renormalization, and Fractals, Neural Networks, Attractor Networks, Homogenous Systems, Inhomogenous Systems, and so on.

Bar-Yam, the son of a high-energy physicist, had studied condensed matter physics and become an engineering professor at Boston University, but he left in 1997 to found the New England Complex Systems Institute. He had been exposed to Stephen Wolfram’s work on cellular automata and Robert Devaney’s work in chaos and discovered that he was less interested in polymers and superconductors than in neural networks and—he says this with no sense of grandiosity—the nature of human civilization. “Thinking about civilization,” he says, “led me to think about complexity as an entity. How do you compare civilization to something else? Is it like brass? Is it like a frog? How do you answer that question? This is what motivates complex systems.”

In case you couldn’t tell, civilization is more like a frog than brass. For one thing, it evolves—evolutionary, adaptive processes being essential in the design and creation of anything so complex that it cannot effectively be decomposed into separate pieces. So-cioeconomic systems are like ecosystems. In fact, they are ecosystems. With computer modeling, Bar-Yam has been studying, among other things, global patterns of ethnic violence, trying to isolate patterns of population mixing and boundaries that trigger conflicts. At its core, this is research on pattern formation. That he can do this work at all illustrates the profound shift over the past two decades in the community’s understanding of what constitutes a legitimate scientific problem. “Let me diagram for you the process,” he says. He has a parable:

People are working to harvest fruit from an orchard, okay? Beautiful fruit were taken and brought to market, and then you harvest fruit that’s higher up in the trees. It’s a little bit harder to get to and maybe a little bit smaller and not as nice. And then you build ladders and you climb up the tree and you get to the higher fruit. And then you reward people for building the ladders.

My feeling of what I did is, I looked and I saw that there was a hedge, and beyond the hedge was another orchard, which had beautiful fruit on many, many trees. And here am, I find a fruit and I go back through the hedge and I show it to people. And they say, “That’s not a fruit!” They couldn’t recognize the fruit anymore.

Communication is better now, he feels. Disciplines across the scientific spectrum have learned to focus on understanding complexity and scale and patterns and the collective behavior that is associated with patterns. That’s fruit.

IN THE HEADY early days, researchers described chaos as the century’s third revolution in the physical sciences, after relativity and quantum mechanics. What has become clear now is that chaos is inextricablefrom relativity and quantum mechanics. There is only one physics.

The fundamental equations of general relativity are nonlinear—already a signal, we know by now, that chaos lurks. “People aren’t always well versed in its methods,” says Janna Levin, an astrophysicist and cosmologist at Barnard College of Columbia University. “Theoretical physics in particular is built on the notion of fundamental symmetries,” she notes. “For that reason, I think it’s been a difficult paradigm shift for theoretical physics to embrace.” Symmetries and symmetry groups tend to produce solvable equations—that’s why they work so well. When they work.

As a relativist, Levin deals in the biggest questions there are. (Is the universe infinite, for example, or just really big? Her work suggests big, or—if we want to be technical—topologically compact and multiconnected.) In studying the origin of the universe, Levin found herself dealing with chaos willy-nilly and ran into resistance. “When I first brought this work out, there was an insanely violent reaction against it,” she says. People thought chaos was fine “for complicated, grungy physical systems—not the pure, uncomplicated and virtual terrain of fundamental physics.”

We were working on chaos in pure general relativity without any grunge, and this was a tiny, tiny, little industryworking out chaos in a generic big bang, or collapse to a black hole, or in orbits around a black hole. People don’t think it’s a spooky word, but they’re surprised to see chaos play a role in something as ungrungyno atoms or junkas a purely relativistic system.

Astronomers had already found the fingerprints of chaos in violence on the sun’s surface, gaps in the asteroid belt, and the distribution of galaxies. Levin and her colleagues have found them in the exit from the big bang and in black holes. They predict that light trapped by a black hole can enter unstable chaotic orbits and be reemitted—making the black hole visible, if only briefly. Yes, chaos can light up black holes. “There are rational numbers to mine, fractal sets, and all kinds of truly beautiful consequences,” she says. “So on the one hand, people are horrified, on the other they’re mesmerized.” She does chaos in curved space-time. Einstein would be proud.

AS FOR ME, I never returned to chaos, but readers might spot seeds of all my later books in this one. I knew hardly anything about Richard Feynman, but he has a cameo here (see here). Isaac Newton has more than a cameo: he seems to be the antihero of chaos, or the god to be overthrown. I discovered only later, reading his notebooks and letters, how wrong I’d been about him. And for twenty years I’ve been pursuing a thread that began with something Rob Shaw told me, about chaos and information theory, as invented by Claude Shannon. 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.

James Gleick
Key West
February 2008