by James Gleick
Carl showed an early gift for science, to Feynman’s immense delight. When he was twelve, Feynman showed him an odd-looking photograph he had brought home from a Canadian laboratory and Carl guessed—correctly—that it was “probably a diffraction pattern from a laser from a regular pattern of square holes,” and Feynman could not help boasting to a friend, “I could have killed him—I was afraid to ask him for the focal length of the lens used!” He tried not to prod too clumsily, and he told himself that he would be happy with any careers his children chose (“trumpet playing—social worker—zygophalatelist—or whatever,” he wrote Carl), as long as they were happy and good at what they did. When Carl reached college, however—MIT—he found the one career ambition guaranteed to break his father’s equilibrium. “Well,” Feynman wrote, “after much effort at understanding I have gradually begun to accept your decision to become a philosopher.” But he hadn’t. He felt as betrayed and put upon as a business executive whose child wants to be a poet.
I find myself asking, “How can you be a good philosopher?” I see now that, like the poet son who never thinks of money (because he expects his old man to pay) you have chosen philosophy, over clear thought (and so your old man goes on with his clear thoughts) so that you can fly above common sense to far higher and more beautiful aspects of the intellect.
“Well,” he added sarcastically, “it must be wonderful to be able to do that.” Educating his children made him think again about the elements of teaching and about the lessons his own father had taught. By the time Carl was four, Feynman was actively lobbying against a first-grade science book proposed for California schools. It began with pictures of a mechanical wind-up dog, a real dog, and a motorcycle, and for each the same question: “What makes it move?” The proposed answer—“Energy makes it move”—enraged him.
That was tautology, he argued—empty definition. Feynman, having made a career of understanding the deep abstractions of energy, said it would be better to begin a science course by taking apart a toy dog, revealing the cleverness of the gears and ratchets. To tell a first-grader that “energy makes it move” would be no more helpful, he said, than saying “God makes it move” or “moveability makes it move.” He proposed a simple test for whether one is teaching ideas or mere definitions:
You say, “Without using the new word which you have just learned, try to rephrase what you have just learned in your own language. Without using the word energy, tell me what you know now about the dog’s motion.”
Other standard explanations were just as hollow: gravity makes it fall, or friction makes it wear out. Having tried to impart fundamental knowledge to Caltech freshmen, he also believed it was possible to teach real knowledge to first-graders. “Shoe leather wears out because it rubs against the sidewalk and the little notches and bumps on the sidewalk grab pieces and pull them off.” That is knowledge. “To simply say, ‘It is because of friction,’ is sad, because it’s not science.”
Feynman taught thirty-four formal courses during his Caltech career, roughly one a year. Most were graduate seminars called Advanced Quantum Mechanics or Topics in Theoretical Physics. That often meant his current research interest: graduate students sometimes heard, without realizing it, the first and last report of substantial work that another physicist would have published. For almost two decades he also taught a course, listed in no catalog, known as Physics X: one afternoon a week, undergraduates would gather to pose any scientific question they wished, and Feynman would improvise. His effect on these students was immense; they often left the Lauritsen Laboratory basement feeling that they had had a private pipeline to an oracle with an earthy kind of omniscience. He believed—in the face of the increasing esotericism of his own subject—that true understanding implied a kind of clarity. A physicist once asked him to explain in simple terms a standard item of the dogma, why spin-one-half particles obey Fermi-Dirac statistics. Feynman promised to prepare a freshman lecture on it. For once, he failed. “I couldn’t reduce it to the freshman level,” he said a few days later, and added, “That means we really don’t understand it.”
It was his own children, however, who crystallized many of his attitudes toward teaching. In 1964 he had made the rare decision to serve on a public commission, responsible for choosing mathematics textbooks for California’s grade schools. Traditionally this commissionership was a sinecure that brought various small perquisites under the table from textbook publishers. Few commissioners—as Feynman discovered—read many textbooks, but he determined to read them all, and had scores of them delivered to his house. This was the era of the so-called new mathematics in children’s education: the much-debated effort to modernize the teaching of mathematics by introducing such high-level concepts as set theory and nondecimal number systems. New math swept the nation’s schools startlingly fast, in the face of parental nervousness that was captured in a New Yorker cartoon: “You see, Daddy,” a little girl explains, “this set equals all the dollars you earned; your expenses are a sub-set within it. A sub-set of that is your deductions.”
Feynman did not take the side of the modernizers. Instead, he poked a blade into the new-math bubble. He argued to his fellow commissioners that sets, as presented in the reformers’ textbooks, were an example of the most insidious pedantry: new definitions for the sake of definition, a perfect case of introducing words without introducing ideas. A proposed primer instructed first-graders: “Find out if the set of the lollipops is equal in number to the set of the girls.” Feynman described this as a disease. It removed clarity without adding any precision to the normal sentence: “Find out if there are just enough lollipops for the girls.” Specialized language should wait until it is needed, he said, and the peculiar language of set theory never is needed. He found that the new textbooks did not reach the areas in which set theory does begin to contribute content beyond the definitions: the understanding of different degrees of infinity, for example.
It is an example of the use of words, new definitions of new words, but in this particular case a most extreme example because no facts whatever are given… . It will perhaps surprise most people who have studied this textbook to discover that the symbol ? or ? representing union and intersection of sets … all the elaborate notation for sets that is given in these books, almost never appear in any writings in theoretical physics, in engineering, business, arithmetic, computer design, or other places where mathematics is being used.
Feynman could not make his real point without drifting into philosophy. It was crucial, he argued, to distinguish clear language from precise language. The textbooks placed a new emphasis on precise language: distinguishing “number” from “numeral,” for example, and separating the symbol from the real object in the modern critical fashion—pilpul for schoolchildren, it seemed to Feynman. He objected to a book that tried to teach a distinction between a ball and a picture of a ball—the book insisting on such language as “color the picture of the ball red.”
“I doubt that any child would make an error in this particular direction,” Feynman said dryly.
As a matter of fact, it is impossible to be precise … whereas before there was no difficulty. The picture of a ball includes a circle and includes a background. Should we color the entire square area in which the ball image appears all red? … Precision has only been pedantically increased in one particular corner when there was originally no doubt and no difficulty in the idea.
In the real world, he pointed out once again, absolute precision is an ideal that can never be reached. Nice distinctions should be reserved for the times when doubt arises.
Feynman had his own ideas for reforming the teaching of mathematics to children. He proposed that first-graders learn to add and subtract more or less the way he worked out complicated integrals—free to select any method that seems suitable for the problem at hand. A modern-sounding notion was, The answer isn’t what matters, so long as you use the right method. To Feynman no educational philosophy could have been more wrong. The an
swer is all that does matter, he said. He listed some of the techniques available to a child making the transition from being able to count to being able to add. A child can combine two groups into one and simply count the combined group: to add 5 ducks and 3 ducks, one counts 8 ducks. The child can use fingers or count mentally: 6, 7, 8. One can memorize the standard combinations. Larger numbers can be handled by making piles—one groups pennies into fives, for example—and counting the piles. One can mark numbers on a line and count off the spaces—a method that becomes useful, Feynman noted, in understanding measurement and fractions. One can write larger numbers in columns and carry sums larger than 10.
To Feynman the standard texts seemed too rigid. The problem 29 + 3 was considered a third-grade problem, because it required the advanced technique of carrying; yet Feynman pointed out that a first-grader could handle it by thinking 30, 31, 32. Why should children not be given simple algebra problems (2 times what plus 3 is 7?) and encouraged to solve them by trial and error? That is how real scientists work.
We must remove the rigidity of thought… . We must leave freedom for the mind to wander about in trying to solve the problems… . The successful user of mathematics is practically an inventor of new ways of obtaining answers in given situations. Even if the ways are well known, it is usually much easier for him to invent his own way—a new way or an old way—than it is to try to find it by looking it up.
Better to have a jumbled bag of tricks than any one orthodox method. That was how he taught his own children at homework time. Michelle learned that he had a thousand shortcuts; also that they tended to get her into trouble with her arithmetic teachers.
Do You Think You Can Last On Forever?
Although he had never liked athletic activity, he tried to stay fit. After he broke a kneecap falling over a Chicago curb, he took up jogging. He ran almost daily up and down the steep paths above his house in the Altadena hills. He owned a wet suit and swam often at the beachfront house in Mexico that he had bought with his Nobel Prize money. (It had been a shambles when he and Gweneth first saw it. He told her that they did not want it. She looked at the glass wall facing the warm currents sweeping up from the Tropic of Cancer and replied, “Oh yes, we do.”)
Traveling in the Swiss Alps in the summer of 1977, he frightened Gweneth by suddenly running to the bathroom of their cabin and vomiting—something he never did as an adult. Later that day he passed out in the téléphérique. Twice that year his physician diagnosed “fever of undetermined origin.” It was not until October 1978 that cancer was discovered: a tumor that had grown to the size of a melon, weighing six pounds, in the back of his abdomen. A bulge was visible at his waistline when he stood straight. He had ignored the symptoms for too long. He had had other worries: just months before, Gweneth had herself undergone surgery for cancer. Feynman’s tumor pushed his intestines aside and destroyed his left kidney, his left adrenal gland, and his spleen.
It was a rare cancer of the soft fat and connective tissue, a myxoid liposarcoma. After difficult surgery, he left the hospital looking gaunt and began a search of the medical literature. There he found no shortage of probabilistic estimates. The likelihood of a recurrent tumor was high, though his had appeared well encapsulated. He read a series of individual case studies, none with a tumor as large as his. “Five-year survival rates,” one journal said in summary, “have been reported from 0% to 11%, with one report of 41%.” Almost no one survived ten years.
He returned to work. “You are old, Father Feynman,” wrote a young friend in a mocking bit of verse,
“And your hair has turned visibly gray;
And yet you keep tossing ideas around—
At your age, a disgraceful display!”
“In my youth,” said the Master, as he shook his long locks,
“I took a great fancy to sketching;
I drew many diagrams, which most thought profound
While others thought just merely fetching.”
“Yes, I know,” said the youth, interrupting the sage,
“That you once were so awfully clever;
But now is the time for quark sausage with chrome.
Do you think you can last on forever?”
Younger physicists, including Gell-Mann, had already stepped aside from the research frontier, but Feynman turned to problems in quantum chromodynamics—the latest synthesis of field theories, so named because of the central role of quark color. With a postdoctoral student, Richard Field, he studied the very-high-energy details of quark jets. Other theorists had realized that the reason quarks never emerged freely was that they were confined by a force unlike those with which physics was familiar. Most forces diminished with distance—gravity and magnetism, for example. It seemed obvious that this must be so, but the opposite was true for quarks. When they were close together, the force between them was negligible; when they were drawn apart, the force grew extremely strong. Jets, as Feynman and Field understood them, were a by-product. In a high-energy collision, before a quark could be broken free of these bonds, the force would become so great that it would create new particles, pulling them into existence out of the vacuum in a burst traveling in the same direction—a jet.
At first Field met with Feynman one afternoon a week. Feynman did not realize that Field was spending almost every waking hour preparing for their meeting. Their work took the form of predictions in a language well suited to experimenters. It was not abstruse theory but a realistic guide to what experimenters should see. Feynman insisted that they calculate only experiments that had not yet been performed; otherwise, he said, they would not be able to trust themselves. Gradually they found that they were able to stay a few months ahead of the experiments and provide a useful framework. As the accelerators reached higher energies, jets of the kind Feynman and Field had described came into existence.
Theorists meanwhile continued to struggle with their understanding of quark confinement: whether quarks must always be confined under every circumstance and whether confinement could be derived naturally from the theory. Victor Weisskopf urged Feynman to work on this, too, by saying that all he could see in the literature was formal mathematics. “I don’t get any physics out of it. Why don’t you attack the problem? You are just the right guy for it and you would find the essential physical reasons why QCD confines the quarks.” Feynman made an original effort in 1981 to solve this problem analytically in a toy model of two dimensions. Quantum chromodynamics, as he noted, had become a theory of such internal complexity that usually even the fastest supercomputers could not generate specific predictions to compare with experiments. “QCD field theory with six flavors of quarks with three colors, each represented by a Dirac spinor of four components, and with eight four-vector gluons, is a quantum theory of amplitudes for configurations each of which is 104 numbers at each point in space and time,” he wrote. “To visualize all this qualitatively is too difficult.” So he tried removing a dimension. This turned out to be a blind alley, although the freshness of his approach kept the work on some theorists’ reading lists long after they had passed by its conclusions.
In September 1981 a tumor recurred, this time entwined about Feynman’s intestines. The doctors tried a combination of doxorubicin, radiation treatment, and heat therapy. Then he underwent his second major surgery. The radiation had left his tissues spongy. The surgery lasted fourteen and a half hours and involved what the physicians described euphemistically as a “vascular incident”—his aorta split. An emergency request for blood went out at Caltech and the Jet Propulsion Laboratory, and donors lined up. Feynman needed seventy-eight pints. When Caltech’s president, Marvin Goldberger, entered his hospital room afterward, Feynman said, “I’d rather be where I am than where you are” and added that he still was not going to do anything Goldberger asked. In visible pain, he entertained his hospital visitors with new stories. Before the operation, the surgeon, Donald Morton of the UCLA Medical Center, had appeared with a halo of residents and nurses. Feynman asked what
his chances were. “It’s impossible to talk about the probability of a single event,” he recounted the surgeon as saying, and he replied, “From one professor to another, it is possible if it’s a future event.”
Caltech’s influence in physics had waned. It drew the same extraordinary collection of bright, naïve, gangly undergraduates, all assuming that they would be taking graduate courses by their junior years. The best graduate students, however, went elsewhere. The physics colloquium remained an institution—Feynman usually sitting like a magnet in the front row, capable of dominating every session, visitors knew, entertainingly or ruthlessly. He could reduce an unwary speaker to tears. He shocked colleagues by tearing the flesh off an elderly Werner Heisenberg, made the young relativist Kip Thorne physically ill—the stories reminded older physicists of Pauli (“ganz falsch”). Douglas Hofstadter, a pioneer in artificial intelligence, gave an unusual talk on the slippery uses of analogy. He began by asking the audience to name the First Lady of England, looking for such answers as Margaret Thatcher, Queen Elizabeth, or Denis Thatcher. “My wife,” came the cry from the front row. Why? “Because she’s English and she’s great.” Through the rest of his talk, it seemed to Hofstadter that Feynman continued heckling in the manner of the village idiot. He was no less an institution than ever, but the center of gravity of elementary particle physics had drifted eastward again, toward Harvard and Princeton and other universities. A combined theory of electromagnetism and weak interactions had led to the gauge theories that brought together the strong interactions under the same quantum-chromodynamical umbrella. This resurgence of quantum theory also brought a new appreciation of Feynman’s path integrals, because path integrals proved essential in quantizing the gauge theories. Feynman’s discovery now seemed not just a useful tool but an organizing principle at nature’s deepest levels. Yet he did not pursue the new implications of path integrals himself. At the forefront were such theorists as Steven Weinberg,
