Physicist Mitchell Feigenbaum died on June 30 at the age of 74. Trained as a particle physicist, he became a pioneer in the fields of chaos and complexity, which overlap so much that I call them “chaoplexity.” In the mid-1970s Feigenbaum discovered a hidden order, called period-doubling, underlying many nonlinear systems. Feigenbaum found that the period of some nonlinear systems--the time they take to return to their original state--keeps doubling as they evolve and therefore rapidly approaches infinity (or eternity). Period-doubling occurs in many real-world systems, such as faucets that progress from a steady drip to a turbulent gush. I interviewed Feigenbaum in 1994, and he turned out to be surprisingly skeptical of the claim that computers were creating a revolutionary “new science,” which could provide deep insights into complex systems, from brains to economies. This claim, a staple of chaoplexity hype, has been revived by proponents of “big data.” Below is an edited version of my portrait of Feigenbaum in The End of Science. --John Horgan
Mitchell Feigenbaum, when I met him at Rockefeller University, where he has a spacious office overlooking Manhattan's East River, looked like the genius he was said to be. With his magnificent, over-sized head and swept-back hair, he resembled Beethoven, though more handsome, less simian. Feigenbaum spoke clearly, precisely, with no accent, but with a strange kind of formality, as if English were a second language he had mastered through sheer brilliance. (The voice of string theorist Edward Witten has this same quality.) When amused, Feigenbaum did not smile so much as grimace. His already protuberant eyes bulged still further from their sockets, and his lips peeled back to expose twin rows of brown, peg-like teeth, stained by countless filter-less cigarettes and espressos (both of which he consumed during our meeting). His vocal cords, cured by decades of exposure to these toxins, yielded a voice as rich and resonant as a basso profundo's, and his laugh was a deep, villainous snicker.
Like many chaoplexologists, Feigenbaum could not resist ridiculing particle physicists for daring to think they could achieve a “final theory,” or “theory of everything.” It is quite possible, he said, that particle physicists might one day develop a theory that adequately accounts for all of nature’s forces, including gravity. But calling such a theory "final" is something else again. "A lot of my colleagues like the idea of final theories because they're religious. And they use it as a replacement for God, which they don't believe in. But they just created a substitute."
A unified theory of physics would obviously not answer all questions, Feigenbaum said. "If you really believe that this is a path of understanding the world, I can ask immediately: How do I write down in this formalism what you look like, with all the hairs on your head?" He stared at me until my scalp prickled. "Now, one answer is, that's not an interesting problem." Against my will, I felt slightly offended. "Another answer is, well it's okay, but we can't do it. The right answer is obviously an alloy of those two complements. We have very few tools. We can't solve problems like that."
Moreover, physicists are overly concerned with finding theories that are merely true, in the sense that they account for available data; the goal of science should be to generate "thoughts in your head" that "stand a high chance of being new or exciting," Feigenbaum explained. "That's the desideratum." He added: "There isn't any security by knowing that something is true, at least as far as I'm concerned. I'm thoroughly indifferent to that. I like to know that I have a way of thinking about things." I began to suspect that Feigenbaum, like David Bohm, had the soul of an artist, poet, even mystic: he sought not truth but revelation.
Feigenbaum noted that the methodology of particle physics--and physics generally--has been to examine the simplest aspects of reality, "where everything has been stripped away." The most extreme reductionists have suggested that looking at more complex phenomena is merely "engineering." But as a result of advances in chaos and complexity, he said, "some of these things that one relegated to engineering are now regarded as reasonable questions to ask from a more theoretical viewpoint. Not just to get the right answer but to understand something about how they work. And that you can even make sense out of that last comment flies in the face of what it means for a theory to be finished."
On the other hand, chaos, too, had generated too much hype. "It's a fraud to have named the subject 'chaos,'" he said. (The term was coined in the mid-1970s by mathematician James Yorke.) "Imagine one of my [particle-physics] colleagues has gone to a party and meets someone and the person is all bubbling over about chaos and tells him that this reductionist stuff is all bullshit. Well, it's infuriating, because it's completely stupid what the person has been told," Feigenbaum said. "I think it's regrettable that people are sloppy, and they end up serving as representatives."
Some of his colleagues at the Santa Fe Institute, Feigenbaum added, had too naïve a faith in the power of computers. "The proof is in the pudding," he said, and paused, as if considering how to proceed diplomatically. "It's very hard to see things in numerical experiments. That is, people want to have fancier and fancier computers to simulate fluids. There is something to be learned in simulating fluids, but unless you know what you're looking for, you're not going to see anything. Because after all, if I just look out the window, there's an overwhelmingly better simulation than I could ever do on a computer." He nodded toward his window, beyond which the leaden East River flowed. "I can't interrogate it quite as sharply, but there's so much stuff in that numerical simulation that if I don't know what to interrogate it about, I will have learned nothing."
For these reasons "a lot of work at Santa Fe has not led to answers. The reason for that is, these are truly hard problems, and one doesn't have any tools. And the job should really be to do those insightful calculations which require some piece of faith and good luck as well. People don't know how to begin doing these problems."
I admitted that I was often confused by the rhetoric of people in chaos and complexity. Sometimes they seemed to be delineating the limits of science—such as the butterfly effect--and sometimes they implied that they could transcend those limits.
"We are building tools!" Feigenbaum cried, his eyes bulging alarmingly. "We don't know how to do these problems. They are truly hard. Every now and then we get a little pocket where we know how to do it, and then we try to puff it out as far as it can go. And when it reaches the border of where it is going, then people wallow for a while, and then they stop doing it. And then one waits for some new piece of insight. But it is literally the business of enlarging the borders of what falls under the suzerainty of science. It is not being done from an engineering viewpoint. It isn't just to give you the answer to some approximation."
"I want to know why," he continued, still staring at me hard. "Why does the thing do this?"
Was it possible that this enterprise could, well, fail? "Of course!" Feigenbaum bellowed, and he laughed maniacally. He confessed that he had been stymied himself of late. Up through the late 1980s he had sought to refine a method for describing how a fractal object, such as a cloud, might evolve over time when perturbed by various forces. He wrote two long papers on the topic that were published in 1988 in relatively obscure physics journals [see here and here]. "I have no idea how well they've been read," Feigenbaum said defiantly. "In fact, I've never been able to give a talk on them." The problem, he suggested, might be that no one can understand him. (Feigenbaum was renowned for obscurity as well as brilliance.) Since then, he added, "I haven't had a further better idea to know how to proceed in this."
In the meantime, Feigenbaum had turned to applied science. Engineering. He had helped a map company develop software for automatically constructing maps with minimal spatial distortion and maximum aesthetic appeal. He belonged to a committee that was redesigning U.S. currency to make it less susceptible to counterfeiting. (Feigenbaum proposed using fractal patterns that blur when xeroxed.) I noted that these sounded like what would be, for most scientists, fascinating and worthy projects. But people familiar with Feigenbaum's former incarnation as a leader of chaos theory, if they heard he now worked on maps and currency, might think...
"He's not doing serious things anymore," Feigenbaum said quietly, as if to himself. Not only that, I added. People might think that if someone who is arguably the most gifted person in the field of chaos could not proceed further, then perhaps the field had run its course. "There's some truth to that," he replied. He acknowledged that he hadn't really had any good ideas about how to extend chaos theory since 1989. "One is on the lookout for things that are substantial, and at the moment..." He paused. "I don't have a thought. I don't know..." He turned his large, luminous eyes once again toward the river beyond his window, as if seeking a sign.
Feeling guilty, I told Feigenbaum that I would love to see his last papers on chaos. Did he have reprints? In response, he thrust himself from his chair and careened wildly toward a row of filing cabinets on the far side of his office. En route, he cracked his shin against a low-lying table. Wincing, teeth clenched, Feigenbaum limped onward, wounded by his collision with the world. The scene was a grotesque inversion of Samuel Johnson's famous stone-kicking episode. The coffee table seemed to be gloating: "I refute Feigenbaum thus."
My meeting with Feigenbaum convinced me that chaoplexity will never live up to its hype. Chaoplexologists have created potent metaphors: the butterfly effect, strange attractors, fractals, artificial life, the edge of chaos, self-organized criticality. They have slightly extended the borders of knowledge in certain areas and more sharply delineated the borders elsewhere. But they have not told us anything about the world both concrete and truly surprising.
Feigenbaum was right, computers are tools, not magic wands. No matter how powerful they become, they cannot help us achieve any great insights into nature--certainly none comparable to Darwin's theory of evolution or quantum mechanics. They will not force any significant revisions in our map of reality or narrative of creation. They will not reveal what Murray Gell-Mann calls “something else,” such as an anti-entropy force postulated by Stuart Kauffman.
In fact, by giving scientists the power to simulate natural phenomena in many different ways, computers may undermine our faith that any given theory is True, exclusively and absolutely true. Computers may, if anything, accelerate the proliferation of ironic science and hasten the end of empirical science.