Saturday, June 01, 2019 ... //

Wolfram on Gell-Mann

I got a permission to post a very interesting text by Stephen Wolfram so if you're thirsty for some intellectual adrenaline and if you can survive without tons of writers' humility ;-), keep on reading.

Remembering Murray Gell-Mann (1929–2019), Inventor of Quarks
Guest blog by Stephen Wolfram

First Encounters

In the mid-1970s, particle physics was hot. Quarks were in. Group theory was in. Field theory was in. And so much progress was being made that it seemed like the fundamental theory of physics might be close at hand.

Right in the middle of all this was Murray Gell-Mann—responsible for not one, but most of the leaps of intuition that had brought particle physics to where it was. There’d been other theories, but Murray’s—with their somewhat elaborate and abstract mathematics—were always the ones that seemed to carry the day.

It was the spring of 1978 and I was 18 years old. I’d been publishing papers on particle physics for a few years, and had gotten quite known around the international particle physics community (and, yes, it took decades to live down my teenage-particle-physicist persona). I was in England, but planned to soon go to graduate school in the US, and was choosing between Caltech and Princeton. And one weekend afternoon when I was about to go out, the phone rang. In those days, it was obvious if it was an international call. “This is Murray Gell-Mann”, the caller said, then launched into a monologue about why Caltech was the center of the universe for particle physics at the time.

Perhaps not as starstruck as I should have been, I asked a few practical questions, which Murray dismissed. The call ended with something like, “Well, we’d like to have you at Caltech”.

A few months later I was indeed at Caltech. I remember the evening I arrived, wandering around the empty 4th floor of Lauritsen Lab—the home of Caltech theoretical particle physics. There were all sorts of names I recognized on office doors, and there were two offices that were obviously the largest: “M. Gell-Mann” and “R. Feynman”. (In between them was a small office labeled “H. Tuck”—which by the next day I’d realized was occupied by Helen Tuck, the lively longtime departmental assistant.)

There was a regular Friday lunch in the theoretical physics group, and as soon as a Friday came around, I met Murray Gell-Mann there. The first thing he said to me was, “It must be a culture shock coming here from England”. Then he looked me up and down. There I was in an unreasonably bright yellow shirt and sandals—looking, in fact, quite Californian. Murray seemed embarrassed, mumbled some pleasantry, then turned away.

With Murray at Caltech

I never worked directly with Murray (though he would later describe me to others as “our student”). But I interacted with him frequently while I was at Caltech. He was a strange mixture of gracious and gregarious, together with austere and combative. He had an expressive face, which would wrinkle up if he didn’t approve of what was being said.

Murray always had people and things he approved of, and ones he didn’t—to which he would often give disparaging nicknames. (He would always refer to solid-state physics as “squalid-state physics”.) Sometimes he would pretend that things he did not like simply did not exist. I remember once talking to him about something in quantum field theory called the beta function. His face showed no recognition of what I was talking about, and I was getting slightly exasperated. Eventually I blurted out, “But, Murray, didn’t you invent this?” “Oh”, he said, suddenly much more charming, “You mean g times the psi function. Why didn’t you just say that? Now I understand”. Of course, he had understood all along, but was being difficult about me using the “beta function” term, even though it had by then been standard for years.

I could never quite figure out what it was that made Murray impressed by some people and not others. He would routinely disparage physicists who were destined for great success, and would vigorously promote ones who didn’t seem so promising, and didn’t in fact do well. So when he promoted me, I was on the one hand flattered, but on the other hand concerned about what his endorsement might really mean.

The interaction between Murray Gell-Mann and Richard Feynman was an interesting thing to behold. Both came from New York, but Feynman relished his “working-class” New York accent, while Gell-Mann affected the best pronunciation of words from any language. Both would make surprisingly childish comments about the other.

I remember Feynman insisting on telling me the story of the origin of the word “quark”. He said he’d been talking to Murray one Friday about these hypothetical particles, and in their conversation they’d needed a name for them. Feynman told me he said (no doubt in his characteristic accent), “Let’s call them ‘quacks’”. The next Monday he said Murray came to him very excited and said he’d found the word “quark” in James Joyce. In telling this to me, Feynman then went into a long diatribe about how Murray always seemed to think the names for things were so important. “Having a name for something doesn’t tell you a damned thing”, Feynman said. (Having now spent so much of my life as a language designer, I might disagree). Feynman went on, mocking Murray’s concern for things like what different birds are called. (Murray was an avid bird watcher.)

Meanwhile, Feynman had worked on particles which seemed (and turned out to be) related to quarks. Feynman had called them “partons”. Murray insisted on always referring to them as “put-ons”.

Even though in terms of longstanding contributions to particle physics (if not physics in general) Murray was the clear winner, he always seemed to feel as if he was in the shadow of Feynman, particularly with Feynman’s showmanship. When Feynman died, Murray wrote a rather snarky obituary, saying of Feynman: “He surrounded himself with a cloud of myth, and he spent a great deal of time and energy generating anecdotes about himself”. I never quite understood why Murray—who could have gone to any university in the world—chose to work at Caltech for 33 years in an office two doors down from Feynman.

Murray cared a lot about what people thought of him, but would routinely (and maddeningly to watch) put himself in positions where he would look bad. He was very interested in—and I think very knowledgeable about—words and languages. And when he would meet someone, he would make a point of regaling them with information about the origin of their name (curiously—as I learned only years later—his own name, “Gell-Mann”, had been “upgraded” from “Gellmann”). Now, of course, if there’s one word people tend to know something about, it’s their own name. And, needless to say, Murray sometimes got its origins wrong—and was very embarrassed. (I remember he told a friend of mine named Nathan Isgur a long and elaborate story about the origin of the name “Isgur”, with Nathan eventually saying: “No, it was made up at Ellis Island!”.)

Murray wasn’t particularly good at reading other people. I remember in early 1982 sitting next to Murray in a limo in Chicago that had just picked up a bunch of scientists for some event. The driver was reading the names of the people he’d picked up over the radio. Many were complicated names, which the driver was admittedly butchering. But after each one, Murray would pipe up, and say “No, it’s said ____”. The driver was getting visibly annoyed, and eventually I said quietly to Murray that he should stop correcting him. When we arrived, Murray said to me: “Why did you say that?” He seemed upset that the driver didn’t care about getting the names right.

Occasionally I would ask Murray for advice, though he would rarely give it. When I was first working on one-dimensional cellular automata, I wanted to find a good name for them. (There had been several previous names for the 2D case, one of which—that I eventually settled on—was “cellular automata”.) I considered the name “polymones” (somehow reflecting Leibniz’s monad concept). But I asked Murray—given all his knowledge of words and languages—for a suggestion. He said he didn’t think polymones was much good, but didn’t have any other suggestion.

When I was working on SMP (a forerunner of Mathematica and the Wolfram Language) I asked Murray about it, though at the time I didn’t really understand as I do now the correspondences between human and computational languages. Murray was interested in trying out SMP, and had a computer terminal installed in his office. I kept on offering to show him some things, but he kept on putting it off. I later realized that—bizarrely to me—Murray was concerned about me seeing that he didn’t know how to type. (By the way, at the time, few people did—which is, for example, why SMP, like Unix, had cryptically short command names.)

But alongside the brush-offs and the strangeness, Murray could be personally very gracious. I remember him inviting me several times to his house. I never interacted with either of his kids (who were both not far from my age). But I did interact with his wife, Margaret, who was a very charming English woman. (As part of his dating advice to me, Feynman had explained that both he and Murray had married English women because “they could cope”.)

While I was at Caltech, Margaret got very sick with cancer, and Murray threw himself into trying to find a cure. (He blamed himself for not having made sure Margaret had had more checkups.) It wasn’t long before Margaret died. Murray invited me to the memorial service. But somehow I didn’t feel I could go; even though by then I was on the faculty at Caltech, I just felt too young and junior. I think Murray was upset I didn’t come, and I’ve felt guilty and embarrassed about it ever since.

Murray did me quite a few favors. He was an original board member of the MacArthur Foundation, and I think was instrumental in getting me a MacArthur Fellowship in the very first batch. Later, when I ran into trouble with intellectual property issues at Caltech, Murray went to bat for me—attempting to intercede with his longtime friend Murph Goldberger, who was by then president of Caltech (and who, before Caltech, had been a professor at Princeton, and had encouraged me to go to graduate school there).

I don’t know if I would call Murray a friend, though, for example, after Margaret died, he and I would sometimes have dinner together, at random restaurants around Pasadena. It wasn’t so much that I felt of a different generation from him (which of course I was). It was more that he exuded a certain aloof tension, that made one not feel very sure about what the relationship really was.

A Great Time in Physics

At the end of World War II, the Manhattan Project had just happened, the best and the brightest were going into physics, and “subatomic particles” were a major topic. Protons, neutrons, electrons and photons were known, and together with a couple of hypothesized particles (neutrinos and pions), it seemed possible that the story of elementary particles might be complete.

But then, first in cosmic rays, and later in particle accelerators, new particles started showing up. There was the muon, then the mesons (pions and kaons), and the hyperons (Λ, Σ, Ξ). All were unstable. The muon—which basically nobody understands even today—was like a heavy electron, interacting mainly through electromagnetic forces. But the others were subject to the strong nuclear force—the one that binds nuclei together. And it was observed that this force could generate these particles, though always together (Λ with K, for example). But, mysteriously, the particles could only decay through so-called weak interactions (of the kind involved in radioactive beta decay, or the decay of the muon).

For a while, nobody could figure out why this could be. But then around 1953, Murray Gell-Mann came up with an explanation. Just as particles have “quantum numbers” like spin and charge, he hypothesized that they could have a new quantum number that he called strangeness. Protons, neutrons and pions would have zero strangeness. But the Λ would have strangeness –1, the (positive) kaon strangeness +1, and so on. And total strangeness, he suggested, might be conserved in strong (and electromagnetic) interactions, but not in weak interactions. To suggest a fundamentally new property of particles was a bold thing to do. But it was correct: and immediately Murray was able to explain lots of things that had been observed.

But how did the weak interaction that was—among other things—responsible for the decay of Murray’s “strange particles” actually work? In 1957, in their one piece of collaboration in all their years together at Caltech, Feynman and Gell-Mann introduced the so-called V-A theory of the weak interaction—and, once again, despite initial experimental evidence to the contrary, it turned out to be correct. (The theory basically implies that neutrinos can only have left-handed helicity, and that weak interactions involve parity conservation and parity violation in equal amounts.)

As soon as the quantum mechanics of electrons and other particles was formulated in the 1920s, people started wondering about the quantum theory of fields, particularly the electromagnetic field. There were issues with infinities, but in the late 1940s—in Feynman’s big contribution—these were handled through the concept of renormalization. The result was that it was possible to start computing things using quantum electrodynamics (QED)—and soon all sorts of spectacular agreements with experiment had been found.

But all these computations worked by looking at just the first few terms in a series expansion in powers of the interaction strength parameter α≃1/137. In 1954, during his brief time at the University of Illinois (from which he went to the University of Chicago, and then Caltech), Murray, together with Francis Low, wrote a paper entitled “Quantum Electrodynamics at Small Distances” which was an attempt to explore QED to all orders in α. In many ways this paper was ahead of its time—and 20 years later, the “renormalization group” that it implicitly defined became very important (and the psi function that it discussed was replaced by the beta function).

While QED could be investigated through a series expansion in the small parameter α≃1/137, no such program seemed possible for the strong interaction (where the effective expansion parameter would be ≃1). So in the 1950s there was an attempt to take a more holistic approach, based on looking at the whole so-called S-matrix defining overall scattering amplitudes. Various properties of the S-matrix were known—notably analyticity with respect to values of particle momenta, and so-called crossing symmetry associated with exchanging particles and antiparticles.

But were these sufficient to understand the properties of strong interactions? Throughout the 1960s, attempts involving more and more elaborate mathematics were made. But things kept on going wrong. The proton-proton total interaction probability was supposed to rise with energy. But experimentally it was seen to level off. So a new idea (the pomeron) was introduced. But then the interaction probability was found to start rising again. So another phenomenon (multiparticle “cuts”) had to be introduced. And so on. (Ironically enough, early string theory spun off from these attempts—and today, after decades of disuse, S-matrix theory is coming back into vogue.)

But meanwhile, there was another direction being explored—in which Murray Gell-Mann was centrally involved. It all had to do with the group-theory-meets-calculus concept of Lie groups. An example of a Lie group is the 3D rotation group, known in Lie group theory as SO(3). A central issue in Lie group theory is to find representations of groups: finite collections, say of matrices, that operate like elements of the group.

Representations of the rotation group had been used in atomic physics to deduce from rotational symmetry a characterization of possible spectral lines. But what Gell-Mann did was to say, in effect, “Let’s just imagine that in the world of elementary particles there’s some kind of internal symmetry associated with the Lie group SU(3). Now use representation theory to characterize what particles will exist”.

And in 1961, he published his eightfold way (named after Buddha’s Eightfold Way) in which he proposed—periodic-table style—that there should be 8+1 types of mesons, and 10+8 types of baryons (hyperons plus nucleons, such as proton and neutron). For the physics of the time, the mathematics involved in this was quite exotic. But the known particles organized nicely into Gell-Mann’s structure. And Gell-Mann made a prediction: that there should be one additional type of hyperon, that he called the Ω, with strangeness –3, and certain mass and decay characteristics.

And—sure enough—in 1964, the was observed, and Gell-Mann was on his way to the Nobel Prize, which he received in 1969.

At first the SU(3) symmetry idea was just about what particles should exist. But Gell-Mann wanted also to characterize interactions associated with particles, and for this he introduced what he called current algebra. And, by 1964, from his work on current algebra, he’d realized something else: that his SU(3) symmetry could be interpreted as meaning that things like protons were actually composed of something more fundamental—that he called quarks.

What exactly were the quarks? In his first paper on the subject, Gell-Mann called them “mathematical entities”, although he admitted that, just maybe, they could actually be particles themselves. There were problems with this, though. First, it was thought that electric charge was quantized in units of the electron charge, but quarks would have to have charges of 2/3 and –1/3. But even more seriously, one would have to explain why no free quarks had ever been seen.

It so happened that right when Gell-Mann was writing this, a student at Caltech named George Zweig was thinking of something very similar. Zweig (who was at the time visiting CERN) took a mathematically less elaborate approach, observing that the existing particles could be explained as built from three kinds of “aces”, as he called them, with the same properties as Gell-Mann’s quarks.

Zweig became a professor at Caltech—and I’ve personally been friends with him for more than 40 years. But he never got as much credit for his aces idea as he should (though in 1977 Feynman proposed him for a Nobel Prize), and after a few years he left particle physics and started studying the neurobiology of the ear—and now, in his eighties, has started a quant hedge fund.

Meanwhile, Gell-Mann continued pursuing the theory of quarks, refining his ideas about current algebras. But starting in 1968, there was something new: particle accelerators able to collide high-energy electrons with protons (“deep inelastic scattering”) observed that sometimes the electrons could suffer large deflections. There were lots of details, particularly associated with relativistic kinematics, but in 1969 Feynman proposed his parton (or, as Gell-Mann called it, “put-on”) model, in which the proton contained point-like “parton” particles.

It was immediately guessed that partons might be quarks, and within a couple of years this had been established. But the question remained of why the quarks should be confined inside particles such as protons. To avoid some inconsistencies associated with the exclusion principle, it had already been suggested that quarks might come in three “colors”. Then in 1973, Gell-Mann and his collaborators suggested that associated with these colors, quarks might have “color charges” analogous to electric charge.

Electromagnetism can be thought of as a gauge field theory associated with the Lie group U(1). Now Gell-Mann suggested that there might be a gauge field theory associated with an SU(3) color group (yes, SU(3) again, but a different application than in the eightfold way, etc.). This theory became known as quantum chromodynamics, or QCD. And, in analogy to the photon, it involves particles called gluons.

Unlike photons, however, gluons directly interact with each other, leading to a much more complex theory. But in direct analogy to Gell-Mann and Low’s 1954 renormalization group computation for QED, in 1973 the beta function (AKA g times psi function) for QCD was computed, and was found to show the phenomenon of asymptotic freedom—essentially that QCD interactions get progressively weaker at shorter distances.

This immediately explained the success of the parton model, but also suggested that if quarks get further apart, the QCD interactions between them get stronger, potentially explaining confinement. (And, yes, this is surely the correct intuition about confinement, although even to this day, there is no formal proof of quark confinement—and I suspect it may have issues of undecidability.)

Through much of the 1960s, S-matrix theory had been the dominant approach to particle physics. But it was having trouble, and the discovery of asymptotic freedom in QCD in 1973 brought field theory back to the fore, and, with it, lots of optimism about what might be possible in particle physics.

Murray Gell-Mann had had an amazing run. For 20 years he had made a series of bold conjectures about how nature might work—strangeness, V-A theory, SU(3), quarks, QCD—and in each case he had been correct, while others had been wrong. He had had one of the more remarkable records of repeated correct intuition in the whole history of science.

He tried to go on. He talked about “grand unification being in the air”, and (along with many other physicists) discussed the possibility that QCD and the theory of weak interactions might be unified in models based on groups like SU(5) and SO(10). He considered supersymmetry—in which there would be particles that are crosses between things like neutrinos and things like gluons. But quick validations of these theories didn’t work out—though even now it’s still conceivable that some version of them might be correct.

But regardless, the mid-1970s were a period of intense activity for particle physics. In 1974, the
J/ψ particle was discovered, which turned out to be associated with a fourth kind of quark (charm quark). In 1978, evidence of a fifth quark was seen. Lots was figured out about how QCD works. And a consistent theory of weak interactions emerged that, together with QED and QCD, defined what by the early 1980s had become the modern Standard Model of particle physics that exists today.

I myself got seriously interested in particle physics in 1972, when I was 12 years old. I used to carry around a copy of the little Particle Properties booklet—and all the various kinds of particles became, in a sense, my personal friends. I knew by heart the mass of the Λ, the lifetime of the π0, and a zillion other things about particles. (And, yes, amazingly, I still seem to remember almost all of them—though now they’re all known to much greater accuracy.)

At the time, it seemed to me like the most important discoveries ever were being made: fundamental facts about the fundamental particles that exist in our universe. And I think I assumed that before long everyone would know these things, just as people know that there are atoms and protons and electrons.

But I’m shocked today that almost nobody has, for example, even heard of muons—even though we’re continually bombarded with them from cosmic rays. Talk about strangeness, or the omega-minus, and one gets blank stares. Quarks more people have heard of, though mostly because of their name, with its various uses for brands, etc.

To me it feels a bit tragic. It’s not hard to show Gell-Mann’s eightfold way pictures, and to explain how the particles in them can be made from quarks. It’s at least as easy to explain that there are 6 known types of quarks as to explain about chemical elements or DNA bases. But for some reason—in most countries—all these triumphs of particle physics have never made it into school science curriculums.

And as I was writing this piece, I was shocked at how thin the information on “classic” particle physics is on the web. In fact, in trying to recall some of the history, the most extensive discussion I could find was in an unpublished book I myself wrote when I was 12 years old! (Yes, full of charming spelling mistakes, and a few physics mistakes.)

The Rest of the Story

When I first met Murray in 1978, his great run of intuition successes and his time defining almost everything that was important in particle physics was already behind him. I was never quite sure what he spent his time on. I know he traveled a lot, using physics meetings in far-flung places as excuses to absorb local culture and nature. I know he spent significant time with the JASON physicists-consult-for-the-military-and-get-paid-well-for-doing-so group. (It was a group that also tried to recruit me in the mid-1980s.) I know he taught classes at Caltech—though he had a reputation for being rather disorganized and unprepared, and I often saw him hurrying to class with giant piles of poorly collated handwritten notes.

Quite often I would see him huddled with more junior physicists that he had brought to Caltech with various temporary jobs. Often there were calculations being done on the blackboard, sometimes by Murray. Lots of algebra, usually festooned with tensor indices—with rarely a diagram in sight. What was it about? I think in those days it was most often supergravity—a merger of the idea of supersymmetry with an early form of string theory (itself derived from much earlier work on S-matrix theory).

This was the time when QCD, quark models and lots of other things that Murray had basically created were at their hottest. Yet Murray chose not to work on them—for example telling me after hearing a talk I gave on QCD that I should work on more worthwhile topics.

I’m guessing Murray somehow thought that his amazing run of intuition would continue, and that his new theories would be as successful as his old. But it didn’t work out that way. Though when I would see Murray, he would often tell me of some amazing physics that he was just about to crack, often using elaborate mathematical formalism that I didn’t recognize.

By the time I left Caltech in 1983, Murray was spending much of his time in New Mexico, around Santa Fe and Los Alamos—particularly getting involved in what would become the Santa Fe Institute. In 1984, I was invited to the inaugural workshop discussing what was then called the Rio Grande Institute might do. It was a strange event, at which I was by far the youngest participant. And as chance would have it, in connection with the republication of the proceedings of that event, I just recently wrote an account of what happened there, which I will soon post.

But in any case, Murray was co-chairing the event, and talking about his vision for a great interdisciplinary university, in which people would study things like the relations between physics and archaeology. He talked in grand flourishes about covering the arts and sciences, the simple and the complex, and linking them all together. It didn’t seem very practical to me—and at some point I asked what the Santa Fe Institute would actually concentrate on if it had to make a choice.

People asked what I would suggest, and I (somewhat reluctantly, because it seemed like everyone had been trying to promote their pet area) suggested “complex systems theory”, and my ideas about the emergence of complexity from things like simple programs. The audio of the event records some respectful exchanges between Murray and me, though more about organizational matters than content. But as it turned out, complex systems theory was indeed what the Santa Fe Institute ended up concentrating on. And Murray himself began to use “complexity” as a label for things he was thinking about.

I tried for years (starting when I first worked on such things, in 1981) to explain to Murray about cellular automata, and about my explorations of the computational universe. He would listen politely, and pay lip service to the relevance of computers and experiments with them. But—as I later realized—he never really understood much at all of what I was talking about.

By the late 1980s, I saw Murray only very rarely. I heard, though, that through an agent I know, Murray had got a big advance to write a book. Murray always found writing painful, and before long I heard that the book had gone through multiple editors (and publishers), and that Murray thought it responsible for a heart attack he had. I had hoped that the book would be an autobiography, though I suspected that Murray might not have the introspection to produce that. (Several years later, a New York Times writer named George Johnson wrote what I considered a very good biography of Murray, which Murray hated.)

But then I heard that Murray’s book was actually going to be about his theory of complexity, whatever that might be. A few years went by, and, eventually, in 1994, to rather modest fanfare, Murray’s book The Quark and the Jaguar appeared. Looking through it, though, it didn’t seem to contain anything concrete that could be considered a theory of complexity. George Zweig told me he’d heard that Murray had left people like me and him out of the index to the book, so we’d have to read the whole book if we wanted to find out what he said about us.

At the time, I didn’t bother. But just now, in writing this piece, I was curious to find out what, if anything, Murray actually did say about me. In the printed book, the index goes straight from “Winos” to Woolfenden. But online I can find that there I am, on page 77 (and, bizarrely, I’m also in the online index): “As Stephen Wolfram has emphasized, [a theory] is a compressed package of information, applicable to many cases”. Yes, that’s true, but is that really all Murray got out of everything I told him? (George Zweig, by the way, isn’t mentioned in the book at all.)

In 2002, I’d finally finished my own decade-long basic science project, and I was getting ready to publish my book A New Kind of Science. In recognition of his early support, I’d mentioned Murray in my long list of acknowledgements in the book, and I thought I’d reach out to him and see if he’d like to write a back-cover blurb. (In the end, Steve Jobs convinced me not to have any back-cover blurbs: “Isaac Newton didn’t have blurbs on the Principia; nor should you on your book”.)

Murray responded politely: “It is exciting to know that your magnum opus, reflecting so much thought, research, and writing, will finally appear. I should, of course, be delighted to receive the book and peruse it, and I might be able to come up with an endorsement, especially since I expect to be impressed”. But he said, “I find it difficult to write things under any conditions, as you probably know”.

Murray followed up with an email: “It was good to talk with you. I found the exchange of ideas very interesting. We seem to have been thinking about many of the same things over the last few years, and apparently we agree on some of them and have quite divergent views on others”. He talked about the book, saying that “Obviously, I can’t, in a brief perusal, come to any deep conclusions about such an impressive tome. It is clear, however, that there are many ideas in it with which, if I understand them correctly, I disagree”.

Then he continued: “Also, my own work of the last decade or so is not mentioned anywhere, even though that work includes discussions of the meaning and significance of simplicity and complexity, the role of decoherent histories in the understanding of quantum mechanics, and other topics that play important roles in A New Kind of Science”. (Actually, I don’t think I discussed anything relevant to decoherent histories in quantum mechanics.) He explained that he didn’t want to write a blurb, and ended: “I’m sorry, and I hope that this matter does not present any threat to our friendship, which I hold dear”.

As it turned out, I never talked to Murray about science again. The last time I saw Murray was in 2012 at a peculiar event in New York City for promising high-school students. I said hello. Murray looked blank. I said my name, and held up my name tag. “Do I know you?”, he said. I repeated my name. Still blank. I couldn’t tell if it was a problem of age—or a repeat of the story of the beta function. But, with regret, I walked away.

I have often used Murray as an example of the challenges of managing the arc of a great career. From his twenties to his forties, Murray had the golden touch. His particular way of thinking had success after success, and in many ways, he defined physics for a generation. But by the time I knew him, the easy successes were over. Perhaps it was Murray; more likely, it was just that the easy pickings from his approach were now gone.

I think Murray always wanted to be respected as a scholar and statesman of science—and beyond. But—to his chagrin—he kept on putting himself in situations that played to his weaknesses. He tried to lead people, but usually ended up annoying them. He tried to become a literary-style author, but his perfectionism and insecurity got in the way. He tried to do important work in new fields, but ended up finding that his particular methods didn’t work there. To me, it felt in many ways tragic. He so wanted to succeed as he had before, but he never found a way to do it—and always bore the burden of his early success.

Still, with all his complexities, I am pleased to have known Murray. And though Murray is now gone, the physics he discovered will live on, defining an important chapter in the quest for our understanding of the fundamental structure of our universe.