On the crucial question of the effect of temperature on O-ring safety, NASA had made an obvious statistical blunder. Seven flights had shown evidence of damage. The most damage had occurred on the coldest flight—at a still-mild 53 degrees Fahrenheit—but no general correlation could be seen between temperature and damage. Serious damage had occurred at 75 degrees, for example.
The error was to ignore the flights on which no damage had occurred, on the basis that they were irrelevant. When these were plotted—seventeen flights at temperatures from 66 to 81 degrees—the effect of temperature suddenly stood out plainly. Damage was strongly associated with cold. It was as if, to weigh the proposition that California cities tend to be in the westernmost United States, someone made a map of California—omitting the non-California cities that would make the tendency apparent. A team of statisticians formed by the National Research Council to follow up the commission report analyzed the same data and estimated a “gambling probability” of 14 percent for a catastrophic O-ring failure at a temperature of 31 degrees.
Feynman discovered that some engineers had a relatively realistic view of the probabilities involved—guessing that a disaster might occur on one flight in two hundred, for example. Yet managers had adopted fantastic estimates on the order of one in a hundred thousand. They were fooling themselves, he said. They cobbled together such numbers by multiplying absurd guesses—that the chance of a turbine pipe bursting was one in ten million, for example.
He concluded his personal report by saying, “For a successful technology, reality must take precedence over public relations, for nature cannot be fooled.” He joined his fellow commissioners for a ceremony at the White House Rose Garden. Then he returned home, as he now knew, to die.
EPILOGUE
God forbid that we should give out a dream of our own imagination for a pattern of the world.
— Francis Bacon
Nothing is certain. Werner Heisenberg wrote this message in the twentieth century’s consciousness. The mathematician Kurt Gödel followed with a famous proof that no logical system can ever be consistent and complete. The possibilities of true knowledge seemed to fade.
Heisenberg formulated his uncertainty principle narrowly: A particle cannot have both a definite place and a definite momentum. Still, philosophers took note. The implications seemed to cover a broader territory than the atom and its interior. Yet Feynman scorned philosophers (“rather than embarrass them, we shall just call them ‘cocktail-party philosophers’”) who overinterpreted the laws of physics by saying, for example,
“That all is relative is a consequence of Einstein, and it has profound influences on our ideas.” In addition, they say, “It has been demonstrated in physics that phenomena depend upon your frame of reference.” We hear that a great deal, but it is difficult to find out what it means… . After all, that things depend upon one’s point of view is so simple an idea that it certainly cannot have been necessary to go to all the trouble of the physical relativity theory in order to discover it.
Einstein’s relativity did not speak to human values. Those were, or were not, relative for reasons unrelated to the physics of objects moving at near-light speed. Borrowing metaphors from the technical sciences could be a dangerous practice. Did the uncertainty principle impose its inevitable fuzziness on any description of nature? Perhaps. But Feynman parted company with many of his colleagues. They looked to quantum uncertainty for an explanation of the many kinds of unpredictability that arise in the everyday, human-scale world: unpredictability in the weather, or indeterminacy in human behavior. Perhaps, some speculated, quantum unpredictability was the microscopic loophole through which free will and human consciousness entered the universe.
Stephen Hawking, typically, wrote: “The uncertainty principle signaled an end to Laplace’s dream of a theory of science, a model of the universe that would be completely deterministic… . Quantum mechanics therefore introduces an unavoidable element of unpredictability or randomness into science.” Feynman’s view was different. Even in the 1960s he anticipated the understanding that would emerge in the modern study of chaotic phenomena: that unpredictability was already a feature of the classical world. He believed that a universe without a quantum uncertainty principle would behave—on the scales of planetary storm systems and human brains—just as erratically and freely as our own.
It is usually thought that this indeterminacy, that we cannot predict the future, is a quantum-mechanical thing, and this is said to explain the behavior of the mind, feelings of free will, etc. But if the world were classical—if the laws of mechanics were classical—it is not quite obvious that the mind would not feel more or less the same.
Why? Because tiny errors, tiny gaps in our knowledge, are amplified by the interactions of complex systems until they reach large scales.
If water falls over a dam, it splashes. If we stand nearby, every now and then a drop will land on our nose. This appears to be completely random… . The tiniest irregularities are magnified in falling, so that we get complete randomness… .
Speaking more precisely, given an arbitrary accuracy, no matter how precise, one can find a time long enough that we cannot make predictions valid for that long a time. Now the point is that this length of time is not very large… . It turns out that in only a very, very tiny time we lose all our information… . We can no longer predict what is going to happen! It is therefore not fair to say that from the apparent freedom and indeterminacy of the human mind, we should have realized that classical “deterministic” physics could not ever hope to understand it, and to welcome quantum mechanics as a release from a “completely mechanistic” universe.
This discrepancy in beliefs—this subtle disagreement with the more standard viewpoint of physicists like Hawking—was no quibble. It formed a fulcrum on which turned, as the century neared its close, an essential disagreement about the achievements and the future of physics.
Particle physicists were awed by the effectiveness of their theories. They adopted a rhetoric of the “grand unified theory,” a concept with its own acronym, GUT. Progress in science had long meant unification of phenomena that previously had been treated separately: Maxwell’s electrodynamics had begun to unify electricity and light, for example. Steven Weinberg and Abdus Salam had unified the realms of electromagnetic and weak interactions with their (inevitably so-called) electroweak theory; however, this latter unification of such distant realms seemed more a mathematical tour de force than a demonstration that the two realms were two sides of one simple coin. Quantum chromodynamics attempted to embrace the strong interactions as well; however, experimental support seemed remote. Physicists now talked as though they could extend unification to cover everything, as though they could conceive of a time when physics would be able to close shop, its work complete. They could imagine—they could almost see—“the ultimate theory of the universe”; “nothing less than a complete description of the universe we live in”; “a complete unified theory of everything.” The inflation of rhetoric accompanied a noticeable reversal of the physicists’ political stature. The aura that had come with the success of the atomic bomb project was fading. To carry out increasingly high-energy experiments, physicists needed exponentially more-expensive machinery, and the question of financing such projects became politically divisive among scientists.
In the year of Feynman’s death, a pair of experimental physicists introduced a text with the simple declaration, “Fifty years of particle physics research has produced an elegant and concise theory of particle interactions at the subnuclear level.” Particle-physics outsiders could be less generous. Elegant and concise? Why, then, did so many particle masses and other specific numerical parameters have to be fed into the theory, rather than read out? Why so many overlapping fields, so many symmetries broken—it seemed—as necessary to fit the data? Quantum numbers such as color and charm might be elegant simplifications, or they might be last-minute rubber bands applied to joints that had threatened to spri
ng loose. And if theorists explained quark confinement, justifying a kind of particle that could never stand on its own, they surely could explain anything. Was the theory rigged—as one critic put it provocatively, “a contrived intellectual structure, more an assembly of successful explanatory tricks and gadgets … than a coherently expressed understanding of experience”?Although each piece of the theory might have been tested against experiment, the whole theory—the style of theory making—had become resistant to disproof. It was hard to imagine phenomena that could not be explained with a new symmetry breaking, a new quantum number, or a few extra spatial dimensions. Perhaps the spare-parts department of modern physics was so well stocked with ingenious devices that a serviceable engine could now be devised to handle any data the particle accelerators could offer.
This was a harsh critique—not Feynman’s. Still, in another time, Feynman had spoken of the search for the fundamental laws of nature. No longer:
People say to me, “Are you looking for the ultimate laws of physics?” No, I’m not… . If it turns out there is a simple ultimate law which explains everything, so be it—that would be very nice to discover. If it turns out it’s like an onion with millions of layers … then that’s the way it is.
He believed that his colleagues were claiming more success at unification than they had achieved—that disparate theories had been pasted together tenuously. When Hawking said, “We may now be near the end of the search for the ultimate laws of nature,” many particle physicists agreed. But Feynman did not. “I’ve had a lifetime of that,” he said on another occasion. “I’ve had a lifetime of people who believe that the answer is just around the corner.”
But again and again it’s been a failure. Eddington who thought that with the theory of electrons and quantum mechanics everything was going to be simple … Einstein, who thought that he had a unified theory just around the corner but didn’t know anything about nuclei and was unable of course to guess it… . People think they’re very close to the answer, but I don’t think so… .
Whether or not nature has an ultimate, simple, unified, beautiful form is an open question, and I don’t want to say either way.
In the 1980s a mathematically powerful and experimentally untestable attempt at unification emerged in the form of string theory, using stringlike entities wrapped through many dimensions as their fundamental objects. The extra dimensions are supposed to fold themselves out of the way in a kind of symmetry breaking given the name compactification. String theory relies on Feynman’s sum-over-histories method as an essential underlying principle; the theory views particle events as topological surfaces and computes probability amplitudes by summing over all possible surfaces. Feynman kept his distance, sometimes saying that perhaps he was too old to appreciate the new fashion. String theory seemed too far from experiment. He suspected that the string theorists were not trying hard enough to prove themselves wrong. In the meantime he never adopted the rhetoric of GUT’s. It made him uncomfortable. He retreated into the stance that he himself merely solved problems as they came along.
When a historian of particle physics pressed him on the question of unification in his Caltech office, he resisted. “Your career spans the period of the construction of the standard model,” the interviewer said.
“‘The standard model,’” Feynman repeated dubiously.
“SU(1) × SU(2) × U(1). From renormalization to quantum electrodynamics to now?”
“The standard model, standard model,” Feynman said. “The standard model—is that the one that says that we have electrodynamics, we have weak interaction, and we have strong interaction? Okay. Yes.”
The interviewer said, “That was quite an achievement, putting them together.”
“They’re not put together.”
“Linked together in a single theoretical package?”
“No.”
The interviewer was having trouble getting his question onto the table. “What do you call SU(×3)SU(2)×U(1)?”
“Three theories,” Feynman said. “Strong interactions, weak interactions, and electromagnetic… . The theories are linked because they seem to have similar characteristics… . Where does it go together? Only if you add some stuff that we don’t know. There isn’t any theory today that has SU(3) × SU(2) × U(1)—whatever the hell it is—that we know is right, that has any experimental check… . Now, these guys are all trying to put all this together. They’re trying to. But they haven’t. Okay?”
Particle physicists were his community. They were the elite who revered him, who passed along his legend, who lent him so much of his prestige. He rarely dissented publicly from their standard dogma. For the past two decades, he had worked on their problems: try though he might to disregard, in the end he had accepted their agenda.
“So we aren’t any closer to unification than we were in Einstein’s time?” the historian asked.
Feynman grew angry. “It’s a crazy question! … We’re certainly closer. We know more. And if there’s a finite amount to be known, we obviously must be closer to having the knowledge, okay? I don’t know how to make this into a sensible question… . It’s all so stupid. All these interviews are always so damned useless.”
He rose from his desk and walked out the door and down the corridor, drumming his knuckles along the wall. The writer heard him shout, just before he disappeared: “It’s goddamned useless to talk about these things! It’s a complete waste of time! The history of these things is nonsense! You’re trying to make something difficult and complicated out of something that’s simple and beautiful.”
Across the hall Murray Gell-Mann looked out of his office. “I see you’ve met Dick,” he said.
Feynman had always set high standards for fundamental work, although he meant something broader by the word than many particle physicists did. Liquid helium and other solid-state problems had seemed to him as fundamental as the smallest-scale particle interactions. He believed that fundamentalness, like beauty or intelligence, was a multidimensional quality. He had tried to understand turbulence and quantum gravity. Throughout his career he had suffered painful periods of malaise, when he could not find a suitable problem. In later years he and his colleagues had seen their crowded field thin: bright young students, looking for fundamental issues on their own terms, often turned to biology, computation, or the new study of chaos and complexity. When his son, Carl, ended his flirtation with philosophy and took up computer science, Feynman, too, looked again at the field he had helped pioneer at Los Alamos. He joined two Caltech authorities on computation, John Hopfield and Carver Mead, in constructing a course on issues from brain analogues and pattern recognition to error correction and uncomputability. For several summers he worked with the founders of Thinking Machines Corporation, near MIT, creating a radical approach to parallel processing; he served as a high-class technician, applying differential equations to the circuit diagrams, and as an occasional wise man among the young entrepreneurs (“Forget all that ‘local minima’ stuff—just say there’s a bubble caught in the crystal and you have to shake it out”). And he began to produce maverick research at the intersection of computing and physics: on how small computers could be; on entropy and the uncertainty principle in computing; on simulating quantum physics and probabilistic behavior; and on the possibility of building a quantum-mechanical computer, with packets of spin waves roaming ballistically back and forth through the logic gates.
His own community had largely left behind questions with the spirit that first drove him toward physics. An intellectual distance had opened between the subatomic particle universe and the realm of ordinary phenomena—the magic that nature reveals to children. In The Feynman Lectures he spoke allegorically of the beauty of a rainbow. Imagine a world in which scientists could not see a rainbow: they might discover it, but could they sense its beauty? The essence of a thing does not always lie in the microscopic details. He supposed that the blind scientists learned that, in some weathers, the intensity of radiation plot
ted against wavelength at a certain direction in the sky would show a bump, and the bump would shift from one wavelength to another as the angle of the instrument shifted. “Then one day,” he said, “the physical review of the blind men might publish a technical article with the title ‘The Intensity of Radiation as a Function of Angle under Certain Conditions of the Weather.’” Feynman had no quarrel with beauty—our human illusion, our projection of sentiment onto a reality of radiation phenomena.
“We are all reductionists today,” said Steven Weinberg—meaning that we seek the deepest explanatory principles in the elementary particles that underlie ordinary matter. He spoke for many particle physicists but not for Feynman. Understanding the principles at the lowest level of the hierarchy—the smallest length-scales—is not the same as understanding nature. So much lies outside the accelerators’ domain, even if it is in some sense reducible to elementary particles. Chaotic turbulence; the large-scale structures that emerge in complex systems; life itself: Feynman spoke of “the infinite variety and novelty of phenomena that can be generated from such simple principles”—phenomena that are “in the equations; we just haven’t found the way to get them out.”
The test of science is its ability to predict. Had you never visited the earth, could you predict the thunderstorms, the volcanoes, the ocean waves, the auroras, and the colorful sunset? …
The next great era of awakening of human intellect may well produce a method of understanding the qualitative content of equations. Today we cannot. Today we cannot see that the water-flow equations contain such things as the barber pole structure of turbulence that one sees between rotating cylinders. Today we cannot see whether Schrödinger’s equation contains frogs, musical composers, or morality—or whether it does not.