Paradise Lost - Migdal, Polyakov, and Landau

This is a placeholder for a longer post I hope to expand on in the future, based on this essay: 

Paradise Lost - Alexander Migdal 

Migdal and Polyakov were two of the great Soviet physicists of their generation. Polyakov is on the upper left and Migdal the lower right.

Wikipedia: Migdal, Polyakov. 

The essay describes their education as young physicists. They were examined by Landau himself at age 15, and by age 19 had written a paper anticipating the Higgs Mechanism and the role of spontaneous symmetry breaking in gauge theory.

Migdal: Khalat was a genius of political intrigue. Being married into Inner Circle of the Soviet System (his wife Valya is the daughter of a legendary Revolution hero), he used all his connections and all the means to achieve his secret goal — assemble the best brains and let them Think Freely. 

On the surface, his pitch to the Party went as follows. “The West is attacking us for anti-Semitism. The best way to counter this slander is to create an Institute, where Jews are accepted, allowed to travel abroad and generally look happy. This can be a very small Institute, by standards of Atomic Project, it will have no secret military research, it will cost you very little, but it will help “Rasryadka” (Détente). These Jews will be so happy, they will tell all their Jewish friends in the West how well they live. And if they won’t –it is after all, us who decide which one goes abroad and which one stays home. They are smart kids, they will figure out which side of the toast is buttered.” 

As I put it, Khalat sold half of his soul to Devil and used the money to save another half. I truly respect him for that, now once I learned what it takes to create a startup and try to protect it against hostile world. 

As many crazy plans before it, this plan really worked. Best brains were assembled in Landau Institute, they were given a chance to happily solve problems without being forced to eat political shit like the whole country and – yes, they sometimes traveled abroad and made friends in the West. 

In a way the plan worked too well — we became so worldly and so free that we could no longer be controlled. And, needless to say, our friends in the West became closer to us that our curators in KGB.

I was in the 1990s generation of American physicists who had to contend on the job market with a stream of great theorists from the former Soviet Union. Both Migdal and Polyakov ended up at Princeton, and there were many others in their wake, closer to my age.

Adventures of a Mathematician: Ulam, von Karman, Wiener, and the Golem

 

Ulam's Adventures of a Mathematician was recently made into a motion picture -- see trailer above. 

I have an old copy purchased from the Caltech bookstore. When I flip through the book it never fails to reward with a wonderful anecdote from an era of giants.

[Ulam] ... In Israel many years later, while I was visiting the town of Safed with von Kárman, an old Orthodox Jewish guide with earlocks showed me the tomb of Caro in an old graveyard. When I told him that I was related to a Caro, he fell on his knees... Aunt Caro was directly related to the famous Rabbi Loew of sixteenth-century Prague, who, the legend says, made the Golem — the earthen giant who was protector of the Jews. (Once, when I mentioned this connection with the Golem to Norbert Wiener, he said, alluding to my involvement with Los Alamos and with the H-bomb, "It is still in the family!")

See also von Neumann: "If only people could keep pace with what they create"

One night in early 1945, just back from Los Alamos, vN woke in a state of alarm in the middle of the night and told his wife Klari: 

"... we are creating ... a monster whose influence is going to change history ... this is only the beginning! The energy source which is now being made available will make scientists the most hated and most wanted citizens in any country. The world could be conquered, but this nation of puritans will not grab its chance; we will be able to go into space way beyond the moon if only people could keep pace with what they create ..." 

He then predicted the future indispensable role of automation, becoming so agitated that he had to be put to sleep by a strong drink and sleeping pills. 

In his obituary for John von Neumann, Ulam recalled a conversation with vN about the 

"... ever accelerating progress of technology and changes in the mode of human life, which gives the appearance of approaching some essential singularity in the history of the race beyond which human affairs, as we know them, could not continue." 

This is the origin of the concept of technological singularity. Perhaps we can even trace it to that night in 1945 :-)

More Ulam from this blog, including:

[p.107] I told Banach about an expression Johnny had used with me in Princeton before stating some non-Jewish mathematician's result, "Die Goim haben den folgenden satz beweisen" (The goys have proved the following theorem). Banach, who was pure goy, thought it was one of the funniest sayings he had ever heard. He was enchanted by its implication that if the goys could do it, then Johnny and I ought to be able to do it better. Johnny did not invent this joke, but he liked it and we started using it.

PRC Hypersonic Missiles, FOBS, and Qian Xuesen

There are deep connections between the images above and below. Qian Xuesen proposed the boost glide trajectory while still at Caltech.

Background on recent PRC test of FOBS/glider hypersonic missile/vehicle. More from Air Force Secretary Frank Kendall. Detailed report on PRC hypersonic systems development. Reuters: Rocket failure mars U.S. hypersonic weapon test (10/21/21)

The situation today is radically different from when Qian first returned to China. In a decade or two China may have ~10x as many highly able scientists and engineers as the US, comparable to the entire world (ex-China) combined [1]. Already the depth of human capital in PRC is apparent to anyone closely watching their rate of progress (first derivative) in space (Mars/lunar lander, space station, LEO), advanced weapons systems (stealth jets, radar, missiles, jet engines), AI/ML, alternative energy, materials science, nuclear energy, fundamental and applied physics, consumer electronics, drones, advanced manufacturing, robotics, etc. etc. The development of a broad infrastructure base for advanced manufacturing and R&D also contributes to this progress, of course.

[1] It is trivial to obtain this ~10x estimate: PRC population is ~4x US population, a larger fraction of PRC students pursue STEM degrees, and a larger proportion of PRC students reach elite levels of math proficiency, e.g., PISA Level 6.

See also One hundred thousand brains and Bezos on the Big Brains. 

Post from 2009: Qian Xuesen, father of Chinese missile program and of JPL, dies at 98

"It was the stupidest thing this country ever did," former Navy Secretary Dan Kimball later said, according to Aviation Week. "He was no more a Communist than I was, and we forced him to go." ... 

Qian Xuesen, a former Caltech rocket scientist who helped establish the Jet Propulsion Laboratory before being deported in 1955 on suspicion of being a Communist and who became known as the father of China's space and missile programs, has died. He was 98. ... 

Qian, a Chinese-born aeronautical engineer educated at Caltech and the Massachusetts Institute of Technology, was a protege of Caltech's eminent professor Theodore von Karman, who recognized him as an outstanding mathematician and "undisputed genius."

Below, a documentary on Qian and a movie-length biopic (English subtitles).

Leo Szilard, the Intellectual Bumblebee (lecture by William Lanouette)

 

This is a nice lecture on Leo Szilard by his biographer William Lanouette. See also ‘An Intellectual Bumblebee’ by Max Perutz.

Wikipedia: Leo Szilard was a Hungarian-American physicist and inventor. He conceived the nuclear chain reaction in 1933, patented the idea of a nuclear fission reactor in 1934, and in late 1939 wrote the letter for Albert Einstein's signature that resulted in the Manhattan Project that built the atomic bomb.

How Alexander Sachs, acting on behalf of Szilard and Einstein, narrowly convinced FDR to initiate the atomic bomb project: Contingency, History, and the Atomic Bomb. 

Szilard wrote children's stories and science fiction. His short story My Trial as a War Criminal begins after the USSR has defeated the US using biological weapons.

I was just about to lock the door of my hotel room and go to bed when there was a knock on the door and there stood a Russian officer and a young Russian civilian. I had expected something of this sort ever since the President signed the terms of unconditional surrender and the Russians landed a token occupation force in New York. The officer handed me something that looked like a warrant and said that I was under arrest as a war criminal on the basis of my activities during the Second World War in connection with the atomic bomb. There was a car waiting outside and they told me that they were going to take me to the Brookhaven National Laboratory on Long Island. Apparently, they were rounding up all the scientists who had ever worked in the field of atomic energy ...

This story was translated into Russian and it had a large impact on Andrei Sakharov, who showed it to his colleague Victor Adamsky:

A number of us discussed it. It was about a war between the USSR and the USA, a very devastating one, which brought victory to the USSR. Szilard and a number of other physicists are put under arrest and then face the court as war criminals for having created weapons of mass destruction. Neither they nor their lawyers could make up a cogent proof of their innocence. We were amazed by this paradox. You can’t get away from the fact that we were developing weapons of mass destruction. We thought it was necessary. Such was our inner conviction. But still the moral aspect of it would not let Andrei Dmitrievich and some of us live in peace.

See also The Many Worlds of Leo Szilard (APS symposium). Slides for Richard Garwin's excellent summary of Szilard's work, including nuclear physics, refrigeration, and Maxwell's Demon. One of Garwin's anecdotes:

Ted Puck was a distinguished biologist, originally trained in physics. ‘With the greatest possible reluctance I have come to the conclusion that it is not possible for me personally to work with you scientifically,’ he wrote Szilard. ‘Your mind is so much more powerful than mine that I find it impossible when I am with you to resist the tremendous polarizing forces of your ideas and outlook.’ Puck feared his ‘own flow of ideas would slow up & productivity suffer if we were to become continuously associated working in the same place and the same general kind of field.’ Puck said, ‘There is no living scientist whose intellect I respect more. But your tremendous intellectual force is a strain on a limited person like myself.’

Puck was a pioneer in single cell cloning, aided in part by Szilard:

When Szilard saw in 1954 that biologists Philip Marcus and Theodore Puck were having trouble growing individual cells into colonies, he concluded that “since cells grow with high efficiency when they have many neighbors, you should not let a single cell know it’s alone”. This was no flippant excursion into psychobiology. Rather, Szilard’s idea to use a layered feeder dish worked, while the open dish had not (Lanouette, 1992: 396–397).

After the war Szilard worked in molecular biology. This photo of Jacques Monod and Szilard is in the seminar room at Cold Spring Harbor Lab. Monod credits Szilard for the negative-feedback idea behind his 1965 Nobel prize.

“I have … recorded” in my Nobel lecture, said Monod, “how it was Szilard who decisively reconciled me with the idea (repulsive to me, until then) that enzyme induction reflected an anti-repressive effect, rather than the reverse, as I tried, unduly, to stick to.”

 

Farewell, Big Steve

Steven Weinberg, a giant of theoretical physics, passed on July 23, 2021 -- he was 88 years old. His best known work, for which he received the Nobel prize, proposed the unification of electromagnetic and weak forces, and formed a key component of the Standard Model of particle physics. But his lifetime of work ranged from cosmology to gravitation to quantum field theory to foundations of quantum mechanics. A brief autobiography.

Wikipedia: It is a story widely told that Steven Weinberg, who inherited Schwinger's paneled office in Lyman Laboratory (Harvard Physics department), there found a pair of old shoes, with the implied message, "think you can fill these?"

Indeed, it is true that almost no one on the planet could have filled Schwinger's shoes. But Big Steve did, and more.

 

Below I've reproduced a post from 2017, Steven Weinberg: What's the matter with quantum mechanics? 

The video of Weinberg's talk is from 2016, when he would have been 83 or so.

In this public lecture Weinberg explains the problems with the two predominant interpretations of quantum mechanics, which he refers to as Instrumentalist (e.g., Copenhagen) and Realist (e.g., Many Worlds). The term "interpretation" may be misleading because what is ultimately at stake is the nature of physical reality. Both interpretations have serious problems, but the problem with Realism (in Weinberg's view, and my own) is not the quantum multiverse, but rather the origin of probability within deterministic Schrodinger evolution. Instrumentalism is, of course, ill-defined nutty mysticism 8-)

Physicists will probably want to watch this at 1.5x or 2x speed. The essential discussion is at roughly 22-40min, so it's only a 10 minute investment of your time. These slides explain in pictures.

See also Weinberg on Quantum Foundations, where I wrote:

It is a shame that very few working physicists, even theoreticians, have thought carefully and deeply about quantum foundations. Perhaps Weinberg's fine summary will stimulate greater awareness of this greatest of all unresolved problems in science.

and quoted Weinberg:

... today there is no interpretation of quantum mechanics that does not have serious flaws. 

Posts on this blog related to the Born Rule, etc., and two of my papers:

The measure problem in many worlds quantum mechanics

On the origin of probability in quantum mechanics

Dynamical theories of wavefunction collapse are necessarily non-linear generalizations of Schrodinger evolution, which lead to problems with locality.

Among those who take the Realist position seriously: Feynman and Gell-Mann, Schwinger, Hawking, and many more.

John von Neumann, 1966 Documentary

 

This 1966 documentary on von Neumann was produced by the Mathematical Association of America. It includes interviews with Wigner, Ulam, Halmos, Goldstine, and others. 

At ~34m Bethe (leader of the Los Alamos theory division) gives primary credit to vN for the implosion method in fission bombs. While vN's previous work on shock waves and explosive lenses is often acknowledged as important for solving the implosion problem, this is the first time I have seen him given credit for the idea itself. Seth Neddermeyer's Enrico Fermi Award citation gives him credit for "invention of the implosion technique" and the original solid core design was referred to as the "Christy gadget" after Robert Christy. As usual, history is much more complicated than the simplified narrative that becomes conventional.

Teller: He could and did talk to my three-year-old son on his own terms and I sometimes wondered whether his relations to the rest of us were a little bit similar.

A recent application of vN's Quantum Ergodic Theorem: Macroscopic Superposition States in Isolated Quantum Systems.

Cloning vN (science fiction): short story, longer (AI vs genetic engineering).

Yuri Milner interviews Donaldson, Kontsevich, Lurie, Tao, and Taylor (2015 Breakthrough Prize)

 

I came across this panel discussion recently, with Yuri Milner (former theoretical physicist, internet billionaire, and sponsor of the Breakthrough Prize) as interlocutor and panelists Simon Donaldson, Maxim Kontsevich, Jacob Lurie, Terence Tao, and Richard Taylor. 

Among the topics covered: the nature of mathematics, the simulation question, AGI and automated proof, human-machine collaboration in mathematics. Kontsevich marvels at the crystalline form of quantum mechanics: why linearity? why a vector space structure? 

Highly recommended!

See also 

The Quantum Simulation Hypothesis: Do we live in a quantum multiverse simulation? 

Locality and Nonlinear Quantum Mechanics

Pure State Quantum Thermalization: from von Neumann to the Lab

Perhaps the most fundamental question in thermodynamics and statistical mechanics is: Why do systems tend to evolve toward thermal equilibrium? Equivalently, why does entropy tend to increase? Because Nature is quantum mechanical, a satisfactory answer to this question has to arise within quantum mechanics itself. The answer was given already in a 1929 paper by von Neumann. However, the ideas were not absorbed (were in fact misunderstood) by the physics community and only rediscovered in the 21st century! General awareness of these results is still rather limited.

See this 2011 post: Classics on the arxiv: von Neumann and the foundations of quantum statistical mechanics.

In modern language, we would say something to the effect that "typical" quantum pure states are highly entangled, and the density matrix describing any small sub-system (obtained by tracing over the rest of the pure state) is very close to micro-canonical (i.e., thermal). Under dynamical (Schrodinger) evolution, all systems (even those that are initially far from typical) spend nearly all of their time in a typical state (modulo some weak conditions on the Hamiltonian). Typicality of states is related to concentration of measure in high dimensional Hilbert spaces. One could even claim that the origin of thermodynamics lies in the geometry of Hilbert space itself.

[ It's worth noting that vN's paper does more than just demonstrate these results. It also gives an explicit construction of macroscopic classical (commuting) observables arising in a large Hilbert space. This construction would be a nice thing to include in textbooks for students trying to connect the classical and quantum worlds. ]

Recently I came across an experimental realization of these theoretical results, using cold atoms in an optical lattice (Greiner lab at Harvard):

Quantum thermalization through entanglement in an isolated many-body system

Science 353, 794-800 (2016)    arXiv:1603.04409v3

The concept of entropy is fundamental to thermalization, yet appears at odds with basic principles in quantum mechanics. Statistical mechanics relies on the maximization of entropy for a system at thermal equilibrium. However, an isolated many-body system initialized in a pure state will remain pure during Schrodinger evolution, and in this sense has static, zero entropy. The underlying role of quantum mechanics in many-body physics is then seemingly antithetical to the success of statistical mechanics in a large variety of systems. Here we experimentally study the emergence of statistical mechanics in a quantum state, and observe the fundamental role of quantum entanglement in facilitating this emergence. We perform microscopy on an evolving quantum system, and we see thermalization occur on a local scale, while we measure that the full quantum state remains pure. We directly measure entanglement entropy and observe how it assumes the role of the thermal entropy in thermalization. Although the full state remains measurably pure, entanglement creates local entropy that validates the use of statistical physics for local observables. In combination with number-resolved, single-site imaging, we demonstrate how our measurements of a pure quantum state agree with the Eigenstate Thermalization Hypothesis and thermal ensembles in the presence of a near-volume law in the entanglement entropy.

Note, given the original vN results I think the Eigenstate Thermalization Hypothesis is only of limited interest. [ But see comments for more discussion... ] The point is that this is a laboratory demonstration of pure state thermalization, anticipated in 1929 by vN.

Another aspect of quantum thermalization that is still not very well appreciated is that approach to equilibrium can have a very different character than what students are taught in statistical mechanics. The physical picture behind the Boltzmann equation is semi-classical: collisions between atoms happen in serial as two gases equilibrate. But Schrodinger evolution of the pure state (all the degrees of freedom together) toward typicality can take advantage of quantum parallelism: all possible collisions take place on different parts of the quantum superposition state. Consequently, the timescale for quantum thermalization can be much shorter than in the semi-classical Boltzmann description.

In 2015 my postdoc C.M. Ho (now director of an AI lab in Silicon Valley) and I pointed out that quantum thermalization was likely already realized in heavy ion collisions at RHIC and CERN, and that the quantum nature of the process was responsible for the surprisingly short time required to approach equilibrium (equivalently, to generate large amounts of entanglement entropy).

Entanglement and fast thermalization in heavy ion collisions (see also slides here).

Entanglement and Fast Quantum Thermalization in Heavy Ion Collisions (arXiv:1506.03696)

Chiu Man Ho, Stephen D. H. Hsu

Let A be subsystem of a larger system A∪B, and ψ be a typical state from the subspace of the Hilbert space H_AB satisfying an energy constraint. Then ρ_A(ψ)=Tr_B |ψ⟩⟨ψ| is nearly thermal. We discuss how this observation is related to fast thermalization of the central region (≈A) in heavy ion collisions, where B represents other degrees of freedom (soft modes, hard jets, co-linear particles) outside of A. Entanglement between the modes in A and B plays a central role; the entanglement entropy S_A increases rapidly in the collision. In gauge-gravity duality, S_A is related to the area of extremal surfaces in the bulk, which can be studied using gravitational duals.

An earlier blog post Ulam on physical intuition and visualization mentioned the difference between intuition for familiar semiclassical (incoherent) particle phenomena, versus for intrinsically quantum mechanical (coherent) phenomena such as the spread of entanglement and its relation to thermalization.

[Ulam:] ... Most of the physics at Los Alamos could be reduced to the study of assemblies of particles interacting with each other, hitting each other, scattering, sometimes giving rise to new particles. Strangely enough, the actual working problems did not involve much of the mathematical apparatus of quantum theory although it lay at the base of the phenomena, but rather dynamics of a more classical kind—kinematics, statistical mechanics, large-scale motion problems, hydrodynamics, behavior of radiation, and the like. In fact, compared to quantum theory the project work was like applied mathematics as compared with abstract mathematics. If one is good at solving differential equations or using asymptotic series, one need not necessarily know the foundations of function space language. It is needed for a more fundamental understanding, of course. In the same way, quantum theory is necessary in many instances to explain the data and to explain the values of cross sections. But it was not crucial, once one understood the ideas and then the facts of events involving neutrons reacting with other nuclei.

This "dynamics of a more classical kind" did not require intuition for entanglement or high dimensional Hilbert spaces. But see von Neumann and the foundations of quantum statistical mechanics for examples of the latter.

Farewell Freeman Dyson

He was 96 when he passed last Friday, one of the last giants who participated in the creation of Quantum Electrodynamics and modern quantum field theory.

He has appeared many times on this blog. Below are a few links.

The intestinal fortitude of Freeman Dyson: an account of his visit to the University of Oregon.

The evening began ominously. Dyson had a stomach bug -- he declined to eat anything at dinner, and made several emergency trips to the bathroom. After dinner he fell asleep on a couch in the physics building. Facing a packed auditorium, with people sitting in the aisles and filling an adjoining overflow room with video monitor, the other organizers and I decided that we'd offer Freeman the chance to call the whole thing off when we woke him up. Luckily for everyone, he felt much better after the nap, and was obviously energized by the large and enthusiastic crowd. After we finished the Q&A, he turned to me and said "Well, your questions cured my bug!"

Profile in The Atlantic (2010)

The prodigy in question, Freeman Dyson, now middle-aged, stared ahead, his incessant concentration on the road unbroken. ... I asked him whether as a boy he had speculated much about his gift. Had he asked himself why he had this special power? Why he was so bright?

Dyson is almost infallibly a modest and self-effacing man, but tonight his eyes were blank with fatigue, and his answer was uncharacteristic.

“That’s not how the question phrases itself,” he said. “The question is: why is everyone else so stupid?”

I want to emphasize that Dyson was a lovely and gentle person. The answer above is indeed uncharacterstic. But it is true...

Profile in NYTimes Magazine (2009). Below is a sample of work produced by Dyson between the ages of 5 and 9.

From Disturbing the Universe, one of my favorite scientific memoirs. It describes dramatic events of Dyson's early life: childhood in England, the war, QED, Feynman and Oppenheimer.

... In that spring of 1948 there was another memorable event. Hans [Bethe] received a small package from Japan containing the first two issues of a new physics journal. Progress of Theoretical Physics, published in Kyoto. The two issues were printed in English on brownish paper of poor quality. They contained a total of six short articles. The first article in issue No. 2 was called "On a Relativistically Invariant Formulation of the Quantum Theory of Wave Fields," by S. Tomonaga of Tokyo University. Underneath it was a footnote saying, "Translated from the paper . . . (1943) appeared originally in Japanese." Hans gave me the article to read. It contained, set out simply and lucidly without any mathematical elaboration, the central idea of Julian Schwinger's theory. The implications of this were astonishing. Somehow or other, amid the ruin and turmoil of the war, totally isolated from the rest of the world, Tomonaga had maintained in Japan a school of research in theoretical physics that was in some respects ahead of anything existing anywhere else at that time. He had pushed on alone and laid the foundations of the new quantum electrodynamics, five years before Schwinger and without any help from the Columbia experiments. He had not, in 1943, completed the theory and developed it as a practical tool. To Schwinger rightly belongs the credit for making the theory into a coherent mathematical structure. But Tomonaga had taken the first essential Step. There he was, in the spring of 1948, sitting amid the ashes and rubble of Tokyo and sending us that pathetic little package. It came to us as a voice out of the deep.

A few weeks later, Oppy received a personal letter from Tomonaga describing the more recent work of the Japanese physicists. They had been moving ahead fast in the same direction as Schwinger. Regular communications were soon established. Oppy invited Tomonaga to visit Princeton, and a succession of Tomonaga's students later came to work with us at Princeton and at Cornell. When I met Tomonaga for the first time, a letter to my parents recorded my immediate impression of him "He is more able than either Schwinger or Feynman to talk about ideas other than his own. And he has enough of his own too. He is an exceptionally unselfish person." On his table among the physics journals was a copy of the New Testament.

Rest in Peace, Freeman Dyson.

Happy New Year 2020

It's been a wonderful year and a wonderful decade. All the best to everyone :-)

Be of good cheer -- we will prevail !!!


A New Year's present to you, the documentary: Bill Evans Time Remembered.

"Truth and Beauty .. forget the rest."



You can watch the whole thing on Amazon Prime.


Bonus: from 1966, The Universal Mind of Bill Evans. I originally posted this video as a 2012 Christmas present to readers.

Best introspective bits about his development, improvisational ability, intellectual / analytical approach versus raw talent @30 min and thereafter.

Not bad for a heroin junkie (like Chet Baker: see earlier post Time After Time).

All About Jazz: ... He played an equal role with Miles Davis in composing Kind Of Blue, the top-selling jazz album ever, yet the association proved disastrous as Evans' shyness and pressures of the stage fed a drug addiction that led to his death in 1980. His intelligence allowed him to surpass other players with more raw talent and he inspired a rare cult-like following, but also endured critics who saw him as a fraudulent lightweight.

Evans is generally acknowledged as the most influential pianist since Bud Powell, and a primary influence on players such as Keith Jarrett and Chick Corea. Many consider his Sunday At The Village Vanguard the best piano trio album ever and compositions such as "Waltz For Debby" are all-time standards. He is also credited with advancing harmonic and voicing structures, and pioneering modern trio format elements such as giving sidemen equal interplay during improvisations.

His career peaked early during the late 1950s and early 1960s, then went through a series of peaks and valleys for the rest of his life. The best of those latter periods were probably during the early 1970s and right before his death, although neither reached the pinnacle of his early days.

Landau, Sakharov, and thermonuclear instabilities

Above, Lev Landau. See also F > L > P > S and Out on the Tail.

An incredible story from The World of Andrei Sakharov:

... Nonetheless, in the early 1950s, Landau worked on Sakharov’s assignments. True enough, that work was in computational mathematics, not theoretical physics. Odd “material evidence” of this appears in Landau’s Collected Works: placed between the 1958 article about fermions and the 1959 article about quantum field theory is the lecture “Numerical Methods of an Integration of Partial Equations by a Method of Grids.” It was published in 1958 but, as it indicates, describes the methods developed in 1951–1952.

When you look at the article’s unexciting formulas, it’s difficult to imagine what’s behind them. What’s behind them, among other things, is the first thermonuclear bomb in the world and the suicide of the head of the security department. ...

Landau’s group did the calculations for the 1949 A-bomb, for which he received an Order of Lenin and a Stalin Prize of the Second Degree.

Landau’s contribution to the hydrogen bomb was even greater, judging by the fact that he was awarded the title of Hero of Socialist Labor and a Stalin Prize of the First Degree. Landau’s group managed to complete the Sloyka calculations “by hand”; it was the problem akin to the one the Americans postponed until computers appeared. This required devising an entirely new method of calculation.

The processes of a thermonuclear explosion are much more complicated than an atomic one, if only because it includes the atomic one as its first step. Numerical calculations using old methods would have taken years, but the problem had to be solved in months, which ensured a new method needed to be found. However, while developing it at the Institute for Physical Problems, theorists found a serious mathematical problem—the stability of the calculations. Without solving it, they couldn’t be sure that the calculations, no matter how precise, would actually have any relationship to physical reality. The new method solved this problem. But the mathematics group directed by Andrei Tikhonov, which had been created in parallel as a failsafe, denied the problem’s very existence.

Dissent and discussion are common in science, but in this case the science was top secret and super-urgent. Beria could not wait for the problem to be resolved in a free exchange of ideas, so a meeting was convened under the chairmanship of Mstislav Keldysh, the future president of the Academy of Sciences. It lasted for several days and the discussions ended in an unusual way: based on Keldysh’s opinion, the top leadership gave the order regarding which interpretation was to be considered scientific truth—the top leadership was Nikolai Pavlov, the KGB general in charge of nuclear weapons development. And Tikhonov’s group switched to the new method of calculation.

The assignment for the Sloyka calculations sent to the Landau group was “a piece of graph paper, handwritten on both sides in green-blue ink, and it contained all the geometry and data of the first hydrogen bomb.”

[[ Sloyka = "layer cake" = early thermonuclear bomb design. ]]

This was possibly the most secret document in the Soviet project—and it could not be entrusted to any typist. After a mathematical assignment was prepared on the basis of this document at the Institute of Physical Problems, it was sent on to the Institute of Applied Mathematics where Tikhonov’s group worked. And the page disappeared there. Perhaps it was mistaken for a rough draft—it was a single handwritten page—and it was destroyed along with other drafts. But this action was not recorded, which is what led to the tragedy Sakharov describes:

The head of the Security Department from the Ministry—a man whose mere physical appearance, his stare from under drooping eyelids, elicited physical dread in me—came to investigate the extraordinary incident. Former head of Leningrad State Security during the so-called “Leningrad Affair,” when about 700 top leaders were executed there, he spent nearly an hour on Saturday with the head of Institute Security. The Institute official spent the next day, Sunday, with his family; they say he was cheerful and very affectionate with his children. He came to work on Monday 15 minutes early and shot himself before his co-workers arrived.

Andrei Sakharov with daughter, 1948.

Physicists can do stuff.

Now it can be told: Dominic Cummings and the Conservative victory 2019

Dominic Cummings has done it again!

The scale of ... triumph cannot be exaggerated. He ... had brought about a complete transformation of the European international order. He had told those who would listen what he intended to do, how he intended to do it, and he did it. He achieved this incredible feat without commanding an army, and without the ability to give an order to the humblest common soldier, without control of a large party, without public support, indeed, in the face of almost universal hostility, without a majority in parliament, without control of his cabinet, and without a loyal following in the bureaucracy. -- Brexit: victory over the Hollow Men

A few remarks. As you know I am a Rationalist and a Realist: epistemology, proper calibration of beliefs, accuracy of prediction, Bayesian reasoning, update of priors, etc. etc.

I can tell you that Dom prepared for this outcome as far back as summer 2019, before he joined No 10 Downing Street. They were deadly serious about Brexit. If they could have gotten it done in the fall, they would have. But the larger goal was positioning to win a general election. People vs Parliament, Betrayal of Democracy, Get Brexit Done. Those were the themes carefully prepared in every tactical decision along the way.

There were difficult times in the last months. I was amazed by his courage and quiet stoicism. Look up the Finnish term, Sisu. Familiar to those that attempt something great against difficult odds.

I watched the media report on UK politics, while simultaneously having some knowledge of what was really happening -- prorogation of Parliament, negotiations with the EU, Farage and the Brexit Party. My opinion of the UK and US media cannot be lower. All noise, little signal -- much of what is stated at high confidence is simply not true. (More evidence? Read the latest IG report and compare to what is said about it in national media...)

Everything is in Dom's blog. Out in the open to be read by anyone with enough intelligence to understand him. How many did? Almost none.

Dominic Cummings: You guys should get outside London and go to talk to people who are not rich remainers.

What does he want? Why is he doing this? Not for money, not for fame. For love of country and human progress and civilization. Dom's dream is to make the UK a global center for science, technology, and education. He may succeed, he may fail. But he will get his chance to further shape the history -- the future -- of his homeland. Don't bet against him.

On election night, I was told that Dom's small team of physicists / data scientists had called the results more accurately than anyone else ;-)

See also

How Brexit was won, and the unreasonable effectiveness of physicists
Brexit in the Multiverse: Dominic Cummings on the Vote Leave campaign
Dept. of Physicists Can Do Stuff: Brexit!

Added: This article is reasonably accurate, as far as I can tell:

We’re all living in Dominic Cummings’ world now (Politico.eu)


Some Remarks on Brexit: I don't know enough to have a high confidence or high conviction opinion concerning Brexit. Intelligent and thoughtful people disagree strongly over whether it is a good idea or a potential disaster.

Nevertheless, I can admire Dom's effectiveness as a political strategist and chief advisor to the Prime Minister. I do know him well enough to state with high confidence that his intentions are idealistic, not selfish, and that he (someone who has spent decades thinking about UK government, foreign policy, relations with Europe) sincerely thinks Brexit is in the best interests of the British people. Dom has deeper insights and better intuition about these issues than I do!

Being a rationalist, Dom has pointed out on his own blog that it is impossible to know with high confidence what the future implications of most political decisions are... In that sphere one cannot avoid decision making under extreme uncertainty.


Brexit: Down to the Wire (October 2019):

Get ready for the general election!

Over the summer I was at the Tallinn Digital Summit in Estonia. At dinner, sitting across from a UN official, I expressed to his initial incredulity that the victory of Vote Leave three years ago was a triumph of the human spirit: a small team of talented individuals defeated overwhelmingly powerful forces arrayed against them -- the UK government, the media, the elites. After some discussion, he came to understand my perspective. ...

Ulam on von Neumann, Godel, and Einstein

Ulam expresses so much in a few sentences! From his memoir, Adventures of a Mathematician. Above: Einstein and Godel. Bottom: von Neumann, Feynman, Ulam.

When it came to other scientists, the person for whom he [vN] had a deep admiration was Kurt Gödel. This was mingled with a feeling of disappointment at not having himself thought of "undecidability." For years Gödel was not a professor at Princeton, merely a visiting fellow, I think it was called. Apparently there was someone on the faculty who was against him and managed to prevent his promotion to a professorship. Johnny would say to me, "How can any of us be called professor when Gödel is not?" ...

As for Gödel, he valued Johnny very highly and was much interested in his views. I believe knowing the importance of his own discovery did not prevent Gödel from a gnawing uncertainty that maybe all he had discovered was another paradox à la Burali Forte or Russell. But it is much, much more. It is a revolutionary discovery which changed both the philosophical and the technical aspects of mathematics.

When we talked about Einstein, Johnny would express the usual admiration for his epochal discoveries which had come to him so effortlessly, for the improbable luck of his formulations, and for his four papers on relativity, on the Brownian motion, and on the photo-electric quantum effect. How implausible it is that the velocity of light should be the same emanating from a moving object, whether it is coming toward you or whether it is receding. But his admiration seemed mixed with some reservations, as if he thought, "Well, here he is, so very great," yet knowing his limitations. He was surprised at Einstein's attitude in his debates with Niels Bohr—at his qualms about quantum theory in general. My own feeling has always been that the last word has not been said and that a new "super quantum theory" might reconcile the different premises.

Manifold Show, episode 3: Noor Siddiqui on Stanford and Silicon Valley

Show Page    YouTube Channel

Noor Siddiqui, Thiel Fellow, on Stanford and Silicon Valley – Episode #3

Corey and Steve interview Noor Siddiqui, a student at Stanford studying AI, Machine Learning, and Genomics. She was previously a Thiel Fellow, and founded a medical collaboration technology startup after high school. The conversation covers topics like college admissions, Tiger parenting, Millennials, Stanford, Silicon Valley startup culture, innovation in the US healthcare industry, and Simplicity and Genius.


man·i·fold /ˈmanəˌfōld/ many and various.

In mathematics, a manifold is a topological space that locally
resembles Euclidean space near each point.

Steve Hsu and Corey Washington have been friends for almost 30 years, and between them hold PhDs in Neuroscience, Philosophy, and Theoretical Physics. Join them for wide ranging and unfiltered conversations with leading writers, scientists, technologists, academics, entrepreneurs, investors, and more.

Steve Hsu is VP for Research and Professor of Theoretical Physics at Michigan State University. He is also a researcher in computational genomics and founder of several Silicon Valley startups, ranging from information security to biotech. Educated at Caltech and Berkeley, he was a Harvard Junior Fellow and held faculty positions at Yale and the University of Oregon before joining MSU.

Corey Washington is Director of Analytics in the Office of Research and Innovation at Michigan State University. He was educated at Amherst College and MIT before receiving a PhD in Philosophy from Stanford and a PhD in a Neuroscience from Columbia. He held faculty positions at the University Washington and the University of Maryland. Prior to MSU, Corey worked as a biotech consultant and is founder of a medical diagnostics startup.

Music and Mathematics: Noam Elkies

Dinner with two old Harvard friends -- mathematician Noam Elkies and MSU physicist Dean Lee. Noam is in town this week to give a lecture, a colloquium, and perform a piano recital.

At 26 Noam became the youngest full professor in Harvard history, and the youngest to ever receive tenure. He has an amazing Wikipedia entry :-)

In 1981, at age 14, he was awarded a gold medal at the 22nd International Mathematical Olympiad, receiving a perfect score of 42 and becoming one of just 26 participants to attain this score,[3] and one of the youngest ever to do so. Elkies graduated from Stuyvesant High School in 1982[4][5] and went on to Columbia University, where he won the Putnam competition at the age of sixteen years and four months, making him one of the youngest Putnam Fellows in history.[6] He was a Putnam Fellow two more times during his undergraduate years. After graduating as valedictorian at age 18 with a summa cum laude in Mathematics and Music, he earned his Ph.D. at the age 20 under the supervision of Benedict Gross and Barry Mazur at Harvard University.[7]

From 1987 to 1990 he was a junior fellow of the Harvard Society of Fellows.[8]

In 1987, he proved that an elliptic curve over the rational numbers is supersingular at infinitely many primes. In 1988, he found a counterexample to Euler's sum of powers conjecture for fourth powers.[9] His work on these and other problems won him recognition and a position as an associate professor at Harvard in 1990.[4] In 1993, he was made a full, tenured professor at the age of 26. This made him the youngest full professor in the history of Harvard.[10] Along with A. O. L. Atkin he extended Schoof's algorithm to create the Schoof–Elkies–Atkin algorithm.

Noam, Dean, and I are all veterans of the Malkin Athletic Center weight room, when it was old-school and gritty :-)

Here's an earlier version of the talk Noam gave tonight. Video should start with him constructing a canon from thin air!

The French Way: Alain Connes interview

I came across this interview with Fields Medalist Alain Connes (excerpt below) via an essay by Dominic Cummings (see his blog here).

Dom's essay is also highly recommended. He has spent considerable effort to understand the history of highly effective scientific / research organizations. There is a good chance that his insights will someday be put to use in service of the UK. Dom helped create a UK variant of Kolmogorov's School for Physics and Mathematics.

On the referendum and on Expertise: the ARPA/PARC ‘Dream Machine’, science funding, high performance, and UK national strategy


Topics discussed by Connes: CNRS as a model for nurturing talent, materialism and hedonic treadmill as the enemy to intellectual development, string theory (pro and con!), US, French, and Soviet systems for science / mathematics, his entry into Ecole Normale and the '68 Paris convulsions.

France and Ecole Normale produce great mathematicians far in excess of their population size.

Connes: I believe that the most successful systems so far were these big institutes in the Soviet union, like the Landau institute, the Steklov institute, etc. Money did not play any role there, the job was just to talk about science. It is a dream to gather many young people in an institute and make sure that their basic activity is to talk about science without getting corrupted by thinking about buying a car, getting more money, having a plan for career etc. ... Of course in the former Soviet Union there were no such things as cars to buy etc. so the problem did not arise. In fact CNRS comes quite close to that dream too, provided one avoids all interference from our society which nowadays unfortunately tends to become more and more money oriented.


Q: You were criticizing the US way of doing research and approach to science but they have been very successful too, right? You have to work hard to get tenure, and research grants. Their system is very unified in the sense they have very few institutes like Institute for Advanced Studies but otherwise the system is modeled after universities. So you become first an assistant professor and so on. You are always worried about your raise but in spite of all these hazards the system is working.


Connes: I don’t really agree. The system does not function as a closed system. The US are successful mostly because they import very bright scientists from abroad. For instance they have imported all of the Russian mathematicians at some point.


Q: But the system is big enough to accommodate all these people this is also a good point.


Connes: If the Soviet Union had not collapsed there would still be a great school of mathematics there with no pressure for money, no grants and they would be more successful than the US. In some sense once they migrated in the US they survived and did very well but I believed they would have bloomed better if not transplanted. By doing well they give the appearance that the US system is very successful but it is not on its own by any means. The constant pressure for producing reduces the “time unit” of most young people there. Beginners have little choice but to find an adviser that is sociologically well implanted (so that at a later stage he or she will be able to write the relevant recommendation letters and get a position for the student) and then write a technical thesis showing that they have good muscles, and all this in a limited amount of time which prevents them from learning stuff that requires several years of hard work. We badly need good technicians, of course, but it is only a fraction of what generates progress in research. It reminds me of an anecdote about Andre Weil who at some point had some problems with elliptic operators so he invited a great expert in the field and he gave him the problem. The expert sat at the kitchen table and solved the problem after several hours. To thank him, Andre Weil said “when I have a problem with electricity I call an electrician, when I have a problem with ellipticity I use an elliptician”.

From my point of view the actual system in the US really discourages people who are truly original thinkers, which often goes with a slow maturation at the technical level. Also the way the young people get their position on the market creates “feudalities” namely a few fields well implanted in key universities which reproduce themselves leaving no room for new fields.

....

Q: So you were in Paris [ Ecole Normale ] in the best place and in the best time.

Connes: Yes it was a good time. I think it was ideal that we were a small group of people and our only motivation was pure thought and no talking about careers. We couldn’t care the less and our main occupation was just discussing mathematics and challenging each other with problems. I don’t mean ”puzzles” but problems which required a lot of thought, time or speed was not a factor, we just had all the time we needed. If you could give that to gifted young people it would be perfect.

See also Defining Merit:

... As a parting shot, Wilson could not resist accusing Ford of anti-intellectualism; citing Ford's desire to change Harvard's image, Wilson asked bluntly: "What's wrong with Harvard being regarded as an egghead college? Isn't it right that a country the size of the United States should be able to afford one university in which intellectual achievement is the most important consideration?"

E. Bright Wilson was Harvard professor of chemistry and member of the National Academy of Sciences, later a recipient of the National Medal of Science. The last quote from Wilson could easily have come from anyone who went to Caltech! Indeed, both E. Bright Wilson and his son, Nobel Laureate Ken Wilson (theoretical physics), earned their doctorates at Caltech (the father under Linus Pauling, the son under Murray Gell-Mann).

Where Nobel winners get their start (Nature):

Top Nobel-producing undergraduate institutions

Rank School                Country               Nobelists per capita (UG alumni)
1 École Normale Supérieure France       0.00135
2 Caltech                               US             0.00067
3 Harvard University            US             0.00032
4 Swarthmore College          US             0.00027
5 Cambridge University       UK             0.00025
6 École Polytechnique          France       0.00025
7 MIT                                   US              0.00025
8 Columbia University         US              0.00021
9 Amherst College               US              0.00019
10 University of Chicago     US              0.00017

Stephen Hawking (1942-2018)

Roger Penrose writes in the Guardian, providing a scientifically precise summary of Hawking's accomplishments as a physicist (worth reading in full at the link). Penrose and Hawking collaborated to produce important singularity theorems in general relativity in the late 1960s.

Here is a nice BBC feature: A Brief History of Stephen Hawking. The photo above was taken at Hawking's Oxford graduation in 1962.

Stephen Hawking – obituary by Roger Penrose

... This radiation coming from black holes that Hawking predicted is now, very appropriately, referred to as Hawking radiation. For any black hole that is expected to arise in normal astrophysical processes, however, the Hawking radiation would be exceedingly tiny, and certainly unobservable directly by any techniques known today. But he argued that very tiny black holes could have been produced in the big bang itself, and the Hawking radiation from such holes would build up into a final explosion that might be observed. There appears to be no evidence for such explosions, showing that the big bang was not so accommodating as Hawking wished, and this was a great disappointment to him.

These achievements were certainly important on the theoretical side. They established the theory of black-hole thermodynamics: by combining the procedures of quantum (field) theory with those of general relativity, Hawking established that it is necessary also to bring in a third subject, thermodynamics. They are generally regarded as Hawking’s greatest contributions. That they have deep implications for future theories of fundamental physics is undeniable, but the detailed nature of these implications is still a matter of much heated debate.

... He also provided reasons for suspecting that the very rules of quantum mechanics might need modification, a viewpoint that he seemed originally to favour. But later (unfortunately, in my own opinion) he came to a different view, and at the Dublin international conference on gravity in July 2004, he publicly announced a change of mind (thereby conceding a bet with the Caltech physicist John Preskill) concerning his originally predicted “information loss” inside black holes.

Notwithstanding Hawking's premature 2004 capitulation to Preskill, information loss in black hole evaporation remains an open question in fundamental physics, nearly a half century after Hawking first recognized the problem in 1975. I read this paper as a graduate student, but with little understanding. I am embarrassed to say that I did not know a single person (student or faculty member) at Berkeley at the time (late 1980s) who was familiar with Hawking's arguments and who appreciated the deep implications of the results. This was true of most of theoretical physics -- despite the fact that even Hawking's popular book A Brief History of Time (1988) gives a simple version of the paradox. The importance of Hawking's observation only became clear to the broader community somewhat later, perhaps largely due to people like John Preskill and Lenny Susskind.

I have only two minor recollections to share about Hawking. The first, from my undergraduate days, is really more about Gell-Mann: Gell-Mann, Feynman, Hawking. The second is from a small meeting on the black hole information problem, at Institut Henri Poincare in Paris in 2008. (My slides.) At the conference dinner I helped to carry Hawking and his motorized chair -- very heavy! -- into a fancy Paris restaurant (which are not, by and large, handicapped accessible). Over dinner I met Hawking's engineer -- the man who maintained the chair and its computer voice / controller system. He traveled everywhere with Hawking's entourage and had many interesting stories to tell. For example, Hawking's computer system was quite antiquated but he refused to upgrade to something more advanced because he had grown used to it. The entourage required to keep Hawking going was rather large (nurses, engineer, driver, spouse), expensive, and, as you can imagine, had its own internal dramas.

Big Ed

Today I came across a recent interview with Ed Witten in Quanta Magazine. The article has some nice photos like the one above. I was struck by the following quote from Witten ("It from Qubit!"):

When I was a beginning grad student, they had a series of lectures by faculty members to the new students about theoretical research, and one of the people who gave such a lecture was Wheeler. He drew a picture on the blackboard of the universe visualized as an eye looking at itself. I had no idea what he was talking about. It’s obvious to me in hindsight that he was explaining what it meant to talk about quantum mechanics when the observer is part of the quantum system. I imagine there is something we don’t understand about that.  [ Italics mine ]

The picture he refers to is reproduced below.

This question has been of interest to me since I was first exposed to quantum mechanics, although I put it off for a long time because quantum foundations is not considered a respectable area by most physicists! Of course it should be obvious that if quantum mechanics is to be a universal theory of nature, then observers like ourselves can't help but be part of the (big) quantum system.

See related posts Feynman and Everett, Schwinger on Quantum Foundations, Gell-Man on Quantum Foundations, and Weinberg on Quantum Foundations.

Here's a similar figure, meant to represent the perspective of an observer inside the wavefunction of the universe (which evolves deterministically and unitarily; the degrees of freedom of the observer's mind are part of the Hilbert space of Psi; time runs vertically and Psi evolves into exp(-iHT) Psi while we are "inside" :-). The little person (observer) is watching particles collapse into a black hole, which then evaporates into Hawking radiation. The figure was drawn on the whiteboard of my University of Oregon office and persisted there for a year or more. I doubt any visitors (other than perhaps one special grad student) understood what it was about.

For some powerful Witten anecdotes like the one below, see here. (If you don't know who Ed Witten is this should clarify things a bit!)

I met him in Boston in 1977, when I was getting interested in the connection between physics and mathematics. I attended a meeting, and there was this young chap with the older guys. We started talking, and after a few minutes I realized that the younger guy was much smarter than the old guys. He understood all the mathematics I was talking about, so I started paying attention to him. That was Witten. And I’ve kept in touch with him ever since.

In 2001, he invited me to Caltech, where he was a visiting professor. I felt like a graduate student again. Every morning I would walk into the department, I’d go to see Witten, and we’d talk for an hour or so. He’d give me my homework. I’d go away and spend the next 23 hours trying to catch up. Meanwhile, he’d go off and do half a dozen other things. We had a very intense collaboration. It was an incredible experience because it was like working with a brilliant supervisor. I mean, he knew all the answers before I got them. If we ever argued, he was right and I was wrong. It was embarrassing!

(Fields Medalist Michael Atiyah, on what it was like to collaborate with Witten)

The closest thing I have read to a personal intellectual history of Witten is his essay Adventures in Physics and Math, which I highly recommend. The essay addresses some common questions, such as What was Ed like as a kid? How did he choose a career in Physics? How does he know so much Mathematics? For example,

At about age 11, I was presented with some relatively advanced math books. My father is a theoretical physicist and he introduced me to calculus. For a while, math was my passion. My parents, however, were reluctant to push me too far, too fast with math (as they saw it) and so it was a long time after that before I was exposed to any math that was really more advanced than basic calculus. I am not sure in hindsight whether their attitude was best or not.

A great video, suggested by a commenter:

Feynman, Schwinger, and Psychometrics

Slate Star Codex has a new post entitled Against Individual IQ Worries.

I write a lot about the importance of IQ research, and I try to debunk pseudoscientific claims that IQ “isn’t real” or “doesn’t matter” or “just shows how well you do on a test”. IQ is one of the best-studied ideas in psychology, one of our best predictors of job performance, future income, and various other forms of success, etc.

But every so often, I get comments/emails saying something like “Help! I just took an IQ test and learned that my IQ is x! This is much lower than I thought, and so obviously I will be a failure in everything I do in life. Can you direct me to the best cliff to jump off of?”

So I want to clarify: IQ is very useful and powerful for research purposes. It’s not nearly as interesting for you personally.

I agree with Scott's point that while g is useful as a crude measurement of cognitive ability, and a statistical predictor of life outcomes, one is better off adopting the so-called growth mindset. ("Individuals who believe their talents can be developed through hard work, good strategies, and input from others have a growth mindset.")

Inevitably the question of Feynman's IQ came up in the discussion. I wrote to Scott about this (slightly edited):

Dear Scott,

I enjoyed your most recent SSC post and I agree with you that g is better applied at a statistical level (e.g., by the Army to place recruits) than at an individual level.

I notice Feynman came up again in the discussion. I have written more on this topic (and have done more research as well). My conclusions are as follows:

1. There is no doubt Feynman would have scored near the top of any math-loaded test (and he did -- e.g., the Putnam).

2. I doubt Feynman would have scored near the ceiling on many verbally loaded tests. He often made grammatical mistakes, spelling mistakes (even of words commonly used in physics), etc. He occasionally did not know the *meanings* of terms used by other people around him (even words commonly used in physics).

3. By contrast, his contemporary and rival Julian Schwinger wrote and spoke in elegant, impeccable language. People often said that Schwinger "spoke in entire paragraphs" that emerged well-formed from his mouth. My guess is that Schwinger was a more balanced type for that level of cognitive ability. Feynman was verbally creative, colorful, a master communicator, etc. But his score on the old SAT-V might not have been above top few percentile.

More people know about Feynman than Schwinger, but not just because Feynman was more colorful and charismatic. In fact, very little that Schwinger ever said or wrote was comprehensible to people below a pretty high IQ threshold, whereas Feynman expressed himself simply and intuitively. I think this has a bit to do with their verbal IQs. Even really smart physics students have an easier time understanding Feynman's articles and lectures than Schwinger's!

Schwinger had read (and understood) all of the existing literature on quantum mechanics while still a HS student -- this loads on V, not just M. Feynman's development path was different, partially because he had trouble reading other people's papers.

Schwinger was one of the subjects in Anne Roe's study of top scientists. His verbal score was above +4 SD. I think it's extremely unlikely that Feynman would have scored that high.

See links below for more discussion, examples, etc.

Hope you are enjoying Berkeley!

Best,
Steve

Feynman's Cognitive Style

Feynman and the Secret of Magic

Feynman's War

Schwinger meets Rabi

Roe's Scientists

Here are some (accessible) Schwinger quotes I like.

The pressure for conformity is enormous. I have experienced it in editors’ rejection of submitted papers, based on venomous criticism of anonymous referees. The replacement of impartial reviewing by censorship will be the death of science.


Is the purpose of theoretical physics to be no more than a cataloging of all the things that can happen when particles interact with each other and separate? Or is it to be an understanding at a deeper level in which there are things that are not directly observable (as the underlying quantized fields are) but in terms of which we shall have a more fundamental understanding?


To me, the formalism of quantum mechanics is not just mathematics; rather it is a symbolic account of the realities of atomic measurements. That being so, no independent quantum theory of measurement is required -- it is part and parcel of the formalism.

[ ... recapitulates usual von Neumann formulation: unitary evolution of wavefunction under "normal" circumstances; non-unitary collapse due to measurement ... discusses paper hypothesizing stochastic (dynamical) wavefunction collapse ... ]

In my opinion, this is a desperate attempt to solve a non-existent problem, one that flows from a false premise, namely the vN dichotomization of quantum mechanics. Surely physicists can agree that a microscopic measurement is a physical process, to be described as would any physical process, that is distinguished only by the effective irreversibility produced by amplification to the macroscopic level. ...

(See Schwinger on Quantum Foundations ;-)

Schwinger survived both Feynman and Tomonaga, with whom he shared the Nobel prize for quantum electrodynamics. He began his eulogy for Feynman: "I am the last of the triumvirate ..."