Lunch With Freeman Dyson, in 196,883 Dimensions

Lunchtime in the cafeteria at the Institute for Advanced Study in Princeton, N.J. — sometimes called the Institute for Advanced Dining — is a heady scene, and Freeman Dyson, who died last week at 96, was a regular fixture, arriving with reading material tucked under his arm.

One day about 10 years ago, Dr. Dyson put down his tray of food at the physics table and joined the conversation. Nima Arkani-Hamed, a professor in the institute’s School of Natural Sciences, was talking about recent research that had brought him into contact with some beautiful, elementary, albeit ancient, results in projective geometry. He was asking around to see if people knew of any decent books on the subject, since everything he could find was too abstract and fancy.

“Freeman sat down next to me and immediately agreed that all the new books were too highfalutin and that he himself had learned projective geometry in school, from a great little practical book,” Dr. Arkani-Hamed said recently. When Dr. Arkani-Hamed lamented that such books no longer existed, Dr. Dyson happily offered to pass along his own, dotted with his youthful jottings.

“So that’s how I came into possession of Freeman’s book on projective geometry,” Dr. Arkani-Hamed said. “I learned a bunch of stuff that I now daily use in my work. It really brings me tremendous pleasure to have it.”

Dr. Dyson — math whiz turned physicist, humanist, author and cosmic visionary — was one of a kind, a polymath with a kaleidoscopic line of inquiry. Best known for his revolutionary calculations describing the interaction of light and matter, he produced valuable contributions to numerous fields, including solid state physics, ferromagnetism, astrophysics, biology and applied mathematics.

Often he sat along the eastern side of the institute’s dining room at a table for two, with a companion, or alone with his reading. Whenever I was there as a visitor, researching and writing, I sought him out. On one occasion in 2010, he suggested by email that we meet on the early side, at 12:15 p.m., “so as to be ahead of the mob of mathematicians.” He invariably arrived looking spiffy, in a tweedy sports jacket, shirt and tie. He usually got an entree, maybe roast beef with natural jus and braised carrots and mashed potato.

Over lunch on more than one occasion, I asked him about his 1983 paper “Unfashionable Pursuits.” Notoriously contrarian, he sought to identify unfashionable ideas that might later emerge as essential for 21st-century physics. “We ought to seek out and encourage the rare individualists who do not fit into the prevailing pattern,” he wrote. But he acknowledged that communal interest in fashionable problems served a purpose: The news and the rumors, “every petty success and every ephemeral triumph,” could be shared with friends at the lunch table.

Dr. Dyson was an anti-reductionist who liked to build bridges. His “Unfashionable Pursuits” paper surveyed the history of mathematics, and then, sixth-eighths of the way in, arrived at “the monster and the moral”: an entity that exists within the mathematical realm of symmetry, in the field of group theory. The “monster group” had been predicted to exist, and mathematicians hunted for verifying clues. Eventually, this creature was proved to live — or, technically, to act — in 196,883 dimensions, and to possess 808 sexdecillion or so symmetries. Dr. Dyson suggested that these symmetries might be connected to the symmetries of the universe. The monster and its ilk might seem like “a pleasant backwater in the history of mathematics,” he said. “But we should not be too sure that there is no connection.”

Lunch with Dr. Dyson was never short of fascinating, fun or lengthy. He was a slow eater, and he did nearly all the talking. Listening, while trying to capture the last few peas of my salad, I’d realize that my lunch mate had made little progress with his meal; it was work, cutting and chewing the meat.

I’d try to fill airtime — and trigger his silent but shoulder-bobbing laugh — with trivial bits, like recounting a tale relayed by his son, George Dyson, an author and historian of technology, regarding an email the elder Dyson once received from a woman with a cleaning business. Subject line: “vacuum — unsatisfied.” Cindy had spent $500 on the DC14 model and had come to hate it with a passion, she explained in great detail. The suction on the rug was so strong that it threw “my shoulder out (NO LIE) having to push so hard.” She signed off, defeated: “I know that I will not hear from Dyson.”

Dr. Dyson, ever the reliable correspondent, hit Reply: “Thank you for the hate mail which I enjoy reading. I get quite a lot of it because my name is Dyson. But I am sorry to tell you that I am the wrong Dyson. My name is Freeman and not James. I suggest that you take the trouble to find James’s address and send the message to him. I wish you good luck and good health.”

Sara Seager, an astrophysicist and planetary scientist at M.I.T., lunched with Freeman when she was a long-term member of the institute. Sometimes, they talked about exoplanets and the underlying physics. Dr. Dyson was generous with his time and insight, she said: “He was kind even when he asked very tough questions!” And long after his lunches with other postdocs were over, she noticed, he would still be there, reading.

At our lunches, Dr. Dyson always bestowed something unexpected. One day it was a problem he was toying with, which he called “Rank, Crank and Prank.” It dated back to his undergraduate days and pertained to “partitions” — sums of all the positive integers that add up to a desired integer, for example 4, which has five partitions: 4, 2+2, 3 +1, 2 + 1 + 1 and 1 + 1 + 1 + 1. (The order of “summands” doesn’t matter.) “The Prank isn’t yet discovered,” he said. “The Rank exists and the Crank exists. The Prank is just a dream” — the prank was just his playing around with renewed investigations.

Another day, jumping off the question of truth versus beauty in science, he mentioned an essay he had just finished on a related dichotomy, “Is Science Mostly Driven by Ideas or by Tools?” The essay, published in 2012, marked the 50th anniversary of “The Structure of Scientific Revolutions,” by the theoretical physicist and historian Thomas Kuhn. Dr. Kuhn’s favorite word, Dr. Dyson reckoned, was “paradigm,” a system of ideas that dominate a scientific era. “A scientific revolution is a discontinuous shift from one paradigm to another,” he added. “The shift happens suddenly because new ideas explode with a barrage of new insights and new questions that push old ideas into oblivion.” As a counterpoint, Dr. Dyson mentioned Peter Galison, a physicist and historian at Harvard, whose work focused more on experiments and instruments. Dr. Galison had published “a fatter but equally illuminating book” called “Image and Logic” — a history dominated by tools, whereas Kuhn’s was a history dominated by ideas.

“Roughly speaking, Kuhn stands for beauty and Galison for truth,” Dr. Dyson said. “My answer is that we need them both.”

He also pointed me toward his essay “Birds and Frogs,” in which he described complementary species of mathematicians: “Some mathematicians are birds, others are frogs,” he wrote. “Birds fly high in the air and survey broad vistas of mathematics out to the far horizon. They delight in concepts that unify our thinking and bring together diverse problems from different parts of the landscape. Frogs live in the mud below and see only the flowers that grow nearby. They delight in the details of particular objects, and they solve problems one at a time. I happen to be a frog, but many of my best friends are birds.”

Some might disagree with Dyson’s assessment of himself. “Characteristically clever and self-deprecating,” the author James Gleick replied, when I posted that excerpt on Twitter. “I think he was a bird.”

He elaborated in an email. For a moment, Mr. Gleick said, in the case of quantum electrodynamics, Richard Feynman and Julian Schwinger were the frogs and only Dr. Dyson could see them both: “Schwinger had solved quantum electrodynamics with a difficult formalism that almost no one understood, and Feynman had solved quantum electrodynamics with his powerful diagrams — easy for physicists to use and compute with but still hard to understand — and it was Dyson who saw the thing whole, proving that Feynman’s and Schwinger’s solutions were mathematically equivalent.” He added that Dr. Dyson should have shared their Nobel Prize.

With the “monster group,” it again turned out that Dr. Dyson had a prescient bird’s-eye view. His prediction bore out later in the 1980s and ’90s, specifically with string theory and its proposed supersymmetries — which, granted, so far lack experimental verification. But as Dr. Dyson noted, “We have strong evidence that the creator of the universe loves symmetry, and if he loves symmetry, what lovelier symmetry could he find than the symmetry of the Monster?”

Last Tuesday, Dr. Dyson took a spill during lunch in the dining hall. It didn’t seem too serious at first. But his wife, Imme, drove him to the hospital (he refused a ride in the ambulance), and three days later he died — perhaps achieving the “Cosmic Unity of all souls” that, at 15, he firmly believed was possible. In his book “Disturbing the Universe,” he reflected on his mother’s decline and her favorite walk to a nearby graveyard. As they walked, he listened to her cheerfully talk about her approaching death.

“My mother did not like the phrase Cosmic Unity,” he wrote. “It was too pretentious. She preferred to call it a world soul. She imagined that she was herself a piece of the world soul that had been given freedom to grow and develop independently so long as she was alive. After death, she expected to merge back into the world soul, losing her personal identity but preserving her memories and her intelligence. Whatever knowledge and wisdom she had acquired during her life would add to the world soul’s store of knowledge and wisdom.

“‘But how do you know that the world soul will want you back?’ I said. ‘Perhaps, after all these years, the world soul will find you too tough and indigestible and won’t want to merge with you.’”

“‘Don’t worry about that,’ my mother replied. ‘It may take a little while, but I’ll find my way back. The world soul can do with a bit more brains.’”

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