Information Processing

Professor James Cline (McGill University) recently posted a set of lecture notes from Feynman's last Caltech course, on quantum chromodynamics. Cline, then a graduate student, was one of the course TAs and the notes were meant to be assembled into a monograph. Thanks to Tim Raben for pointing these out to me. The image below is from some of Feynman's handwritten notes (in this case, about the Gribov ambiguity in Fadeev-Popov gauge fixing) that Cline included in the manuscript. There are also links to audio from some of the lectures. As in some earlier notebooks, Feynman sometimes writes "guage" instead of gauge.

Thanks to a reader for sending the video to me. The first clip is of Feynman discussing AI, taken from the longer 1985 lecture in the second video.

There is not much to disagree with in his remarks on AI. He was remarkably well calibrated and would not have been very surprised by what has happened in the following 35 years, except that he did not anticipate (at least, does not explicitly predict) the success that neural nets and deep learning would have for the problem that he describes several times as "pattern recognition" (face recognition, fingerprint recognition, gait recognition). Feynman was well aware of early work on neural nets, through his colleague John Hopfield. [1] [2] [3]

I was at Caltech in 1985 and this is Feynman as I remember him. To me, still a teen ager, he seemed ancient. But his mind was marvelously active! As you can see from the talk he was following the fields of AI and computation rather closely.

Of course, he and other Manhattan project physicists were present at the creation. They had to use crude early contraptions for mechanical calculation in bomb design computations. Thus, the habit of reducing a complex problem (whether in physics or machine learning) to primitive operations was second nature. Already for kids of my generation it was not second nature -- we grew up with early "home computers" like the Apple II and Commodore, so there was a black box magic aspect already to programming in high level languages. Machine language was useful for speeding up video games, but not everyone learned it. The problem is even worse today: children first encounter computers as phones or tablets that already seem like magic. The highly advanced nature of these devices discourages them from trying to grasp the underlying first principles.

If I am not mistaken the t-shirt he is wearing is from the startup Thinking Machines, which built early parallel supercomputers.

Just three years later he was gone. The finely tuned neural connections in his brain -- which allowed him to reason with such acuity and communicate with such clarity still in 1985 -- were lost forever.

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I received this message over the weekend.

Dear Dr. Hsu,

With great interest I regularly read your excellent Information Processing Blog. With regard to your assessment of Dom Cummings' achievements I am at variance with yours. But I guess you will like the anecdote referring to Feynman.

I tried to comment directly on your blog but the whole procedure was somewhat cumbersome, so I mail my comment directly to you. Please feel free to post it at the comment section under my full name. See the comment attached.

I am a retired psychology prof from University of Mannheim, Germany specializing in intelligence research, research methodology, assessment and evaluation research.

Best regards
Werner W. Wittmann

The letter:

IQ makes the difference

If you want to learn more about what kind of difference differences in IQ make read the research of Dave Lubinski and Camilla Benbow what differences highly gifted youngsters accomplish after several decades. Dave makes their publications available at https://my.vanderbilt.edu/smpy/publications/david-lubinski/

But let me turn to a funnier anecdote for physicists like Steve Hsu

A 35 year gap:

Physicists are among the smartest high IQ people, there is no doubt. If you want a single case example take Richard Feynman. If we could have lured him to psychology an important concept probably would have been published 35 years earlier.

In 1939 Feynman as a graduate student at Princeton experimented just for fun together with his friend John Tukey (who later became the famous statistician) to assess the ability of measuring time by counting.(Gleick,1992) They run stairs up and down to accelerate their heartbeats and trained themselves at the same time to count seconds and steps. Feynman’s performance deteriorated when he talked but not when he read. Tukey instead performed well when he recited poems aloud and worse when he read. So both have detected what is now known as the two slave systems of working memory, namely the phonological loop and the visuo-spatial sketchpad. Now you get a feeling how much more psychology would have been advanced if brains like theirs had been invested in my discipline at that time.

As a true and convinced European I am really sorry that the English left us, the Scots and the Northern-Irish didn’t want it and maybe one day the fame of tearing the United Kingdom into parts goes to Cummings as well?

What I would say to Cummings:

“If a thing is not worth doing, it is not worth doing well.” ― John W. Tukey

But he did it and now…

Boris Johnson probably to Cummings: “The moor has pled guilty the moor can go” ?

References:

Gleick,J.(1992) Genius. The life and science of Richard Feynman. New York: Pantheon Books.

Lubinski, D., Benbow, C.P., & Kell, H.J. (2014). Life paths and accomplishments of mathematically precocious males and females four decades later. Psychological Science, 25, 2217–2232.

From Wikipedia about Working Memory

In 1974, Baddeley and Hitch[11] introduced the multicomponent model of working memory. The theory proposed a model containing three components: the central executive, the phonological loop, and the visuospatial sketchpad with the central executive functioning as a control center of sorts, directing info between the phonological and visuospatial components.[12] The central executive is responsible inter alia for directing attention to relevant information, suppressing irrelevant information and inappropriate actions, and coordinating cognitive processes when more than one task is simultaneously performed. A "central executive" is responsible for supervising the integration of information and for coordinating "slave systems" that are responsible for the short-term maintenance of information. One slave system, the phonological loop (PL), stores phonological information (that is, the sound of language) and prevents its decay by continuously refreshing it in a rehearsal loop. It can, for example, maintain a seven-digit telephone number for as long as one repeats the number to oneself again and again.[13] The other slave system, the visuospatial sketchpad, stores visual and spatial information. It can be used, for example, for constructing and manipulating visual images and for representing mental maps. The sketchpad can be further broken down into a visual subsystem (dealing with such phenomena as shape, colour, and texture), and a spatial subsystem (dealing with location).

Re: Brexit, see these remarks from Now it can be told: Dominic Cummings and the Conservative victory 2019

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.

The epistemically careful may end up like Zhou Enlai. When asked about consequences of the French Revolution, the late premier is reported to have said: Too early to tell. Be prepared to find that thoughtful people, pressed for an opinion, can disagree...

https://feynman100.caltech.edu

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 ..."

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Mathematician Peter Lax (awarded National Medal of Science, Wolf and Abel prizes), interviewed about his work on the Manhattan Project. His comments on von Neumann and Feynman:

Lax: ... Von Neumann was very deeply involved in Los Alamos. He realized that computers would be needed to carry out the calculations needed. So that was, I think, his initial impulse in developing computers. Of course, he realized that computing would be important for every highly technical project, not just atomic energy. He was the most remarkable man. I’m always utterly surprised that his name is not common, household.

It is a name that should be known to every American—in fact, every person in the world, just as the name of Einstein is. I am always utterly surprised how come he’s almost totally unknown. ... All people who had met him and interacted with him realized that his brain was more powerful than anyone’s they have ever encountered. I remember Hans Bethe even said, only half in jest, that von Neumann’s brain was a new development of the human brain. Only a slight exaggeration.

... People today have a hard time to imagine how brilliant von Neumann was. If you talked to him, after three words, he took over. He understood in an instant what the problem was and had ideas. Everybody wanted to talk to him.

...

Kelly: I think another person that you mention is Richard Feynman?

Lax: Yes, yes, he was perhaps the most brilliant of the people there. He was also somewhat eccentric. He played the bongo drums. But everybody admired his brilliance. [ vN was a consultant and only visited Los Alamos occasionally. ]

Full transcript. See also Another species, an evolution beyond man.

From Robert Jungk's Brighter than a Thousand Suns: A Personal History of the Atomic Scientists.

The H-bomb project:

... Immediately after the White House directive the Theoretical Division at Los Alamos had started calculations for the new bomb.

... There was a meeting in Teller's office with Fermi, von Neumann, and Feynman ... Many ideas were thrown back and forth and every few minutes Fermi or Teller would devise a quick numerical check and then they would spring into action. Feynman on the desk calculator, Fermi with the little slide rule he always had with him, and von Neumann, in his head. The head was usually first, and it is remarkable how close the three answers always checked.

The MANIAC:

... When von Neumann released his last invention for use, it aroused the admiration of all who worked with it. Carson Mark, head of the Theoretical Division at Los Alamos, recollects that 'a problem which would have otherwise kept three people busy for three months; could be solved by the aid of this computer, worked by the same three people, in about ten hours. The physicist who had set the task, instead of having to wait for a quarter of a year before he could get on, received the data he required for his further work the same evening. A whole series of such three months' calculations, narrowed down to a single working day, were needed for the production of the hydrogen bomb.

It was a calculating machine, therefore, which was the real hero of the work on the construction of the bomb. It had a name of its own, like all the other electronic brains. Von Neumann had always been fond of puns and practical jokes. When he introduced his machine to the Atomic Energy Commission under the high-sounding name of 'Mathematical Analyser, Numerical Integrator and Computer', no one noticed anything odd about this designation except that it was rather too ceremonious for everyday use. It was not until the initial letters of the six words were run together that those who used the miraculous new machine realized that the abbreviation spelled 'maniac'.

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Over the holiday I started digging through my mom's old albums and boxes of photos. I found some pictures I didn't know existed!

Richard Feynman and the 19 year old me at my Caltech graduation:



With my mom that morning -- hung-over, but very happy! I think those are some crazy old school Ray Bans :-)



Memories of Feynman: "Hey SHOE!", "Gee, you're a BIG GUY. Do you ever go to those HEALTH clubs?"

This is me at ~200 pounds, playing LB and RB back when Caltech still had a football team. Plenty of baby fat! I ran sprints for football but never longer distances. I dropped 10 or 15 pounds just by jogging a few times per week between senior year and grad school.




Here I am in graduate school. Note the Miami Vice look -- no socks!



Ten years after college graduation, as a Yale professor, competing in Judo and BJJ in the 80 kg (176 lbs) weight category. The jiujitsu guys thought it was pretty funny to have a professor on the mat! This photo was taken on the Kona coast of the big island in Hawaii. I had been training with Egan Inoue at Grappling Unlimited in Honolulu.



Baby me:

Radar and nuclear weapons could not have been developed without the big brains.

Feynman’s War: Modelling Weapons, Modelling Nature

Peter Galison*

What do I mean by understanding? Nothing deep or accurate—just to be able to see some of the qualitative consequences of the equations by some method other than solving them in detail. -- Feynman to Welton, 10 February 1947.


... The fundamental problem facing theorists on the bomb project was this: in a limited time, they had to produce accurate, quantitative predictions of the efficiency and critical mass of the chain reaction in a wide variety of geometries. There was no time to devise detailed models for each configuration of fissile material and neutron-reflecting tampers, just as on the radar project physicists could not start calculating ab initio for each new arrangement of waveguides and junctions. At MIT, the radar physicists [ e.g., Julian Schwinger ] had to provide effective circuits for the various waveguides so the radio engineers could manipulate them. Similarly, for the Los Alamos physicists facing engineers, architects, and experimentalists, much rode on the theorists’ ability to modularise aspects of their work so it could be passed to non-theorists. They had to figure out ways of characterising the ‘neutronics’ using certain building blocks—whether those building blocks were standardised effective amplifiers or new theoretical techniques to model neutron diffusion.

Feynman learned from and contributed to this culture of modularity. Whether he was grappling with the human efficiency of crunching numbers using Marchant calculators, or inventing easily taught rules for tracking neutrons in tampers, Feynman developed highly movable theoretical modules. These simple, often visualisable mechanisms took complex human, physical and calculational configurations and sorted them into simpler parts that could be recombined in a myriad of ways to calculate rapid, approximate, yet reliable answers. It was a kind of theory particularly appropriate to the constantly rearranged devices they were to represent. ...

Note Feynman seems to spell Corollary as Coralary repeatedly. In other notebooks he often spelled gauge (as in gauge theory) as guage. These are commonly used words in physics. I always suspected that, as far as such constructs are well-defined, Feynman's mathematical ability was superior to his verbal ability. See Feynman's Cognitive Style.

The full text of The Feynman Lectures is now available online. These lectures were originally delivered to satisfy the physics requirement for first and second year students at Caltech. Legend has it that as the lectures went on, fewer and fewer undergraduates were seen in attendance, with their places taken by graduate students and even members of the faculty! In his epilogue, Feynman notes that only a few dozen students (out of a Caltech cohort of perhaps 200) were able to fully appreciate the material as it was delivered. Nevertheless, the lectures have been a resource for the physics community ever since.

When I was a high school student I took advanced physics courses at the local university. One of my professors suggested I look at the Feynman lectures for more challenging material. I ordered a set (paperback, with red covers) through the university bookstore -- I think they cost 30ドル in 1982. Years later I obtained a commemorative hardcover set (blue) which sits on my shelf even now.

Feynman's Epilogue

Well, I've been talking to you for two years and now I'm going to quit. In some ways I would like to apologize, and other ways not. I hope — in fact, I know — that two or three dozen of you have been able to follow everything with great excitement, and have had a good time with it. But I also know that “the powers of instruction are of very little efficacy except in those happy circumstances in which they are practically superfluous.” So, for the two or three dozen who have understood everything, may I say I have done nothing but shown you the things. For the others, if I have made you hate the subject, I'm sorry. I never taught elementary physics before, and I apologize. I just hope that I haven't caused a serious trouble to you, and that you do not leave this exciting business. I hope that someone else can teach it to you in a way that doesn't give you indigestion, and that you will find someday that, after all, it isn't as horrible as it looks.

Finally, may I add that the main purpose of my teaching has not been to prepare you for some examination—it was not even to prepare you to serve industry or the military. I wanted most to give you some appreciation of the wonderful world and the physicist's way of looking at it, which, I believe, is a major part of the true culture of modern times. (There are probably professors of other subjects who would object, but I believe that they are completely wrong.)

Perhaps you will not only have some appreciation of this culture; it is even possible that you may want to join in the greatest adventure that the human mind has ever begun.

What does Feynman mean by the true culture of modern times? Not mincing words, he refers to the greatest adventure that the human mind has ever begun! None can claim themselves an educated thinker or intellectual without mastery of a significant portion of the material in these lectures.


The figure below is from book III chapter 01: Quantum behavior

Lubos Motl seems to have taken offense at my last post: Feynman's Cognitive Style. This is a rather ironic outcome, given that I've been a "Feynman idolator" since I was in high school :-) In fact, I chose my college (Caltech), career, and even research specialization under his influence!

In the previous post, I noted that Feynman's cognitive profile was probably a bit lopsided -- he was stronger mathematically than verbally (these notions are ill-defined, but see the previous post and subsequent discussion). His research style was also influenced by an exceptional originality, creativity and stubborn streak of independence. Ultimately, this style may have led to greater contributions than if he had followed a more conventional path. But, it is nevertheless interesting to observe that his stubborn habit of ignoring the literature led to large gaps in his knowledge. (See earlier post for examples. Contrary to Lubos' impression I am not making fun of Feynman!) In Coleman's analysis below (taken from Gleick's Feynman biography -- the chapter on Genius), Feynman's refusal to read the literature is portrayed as a conscious choice, but I suspect it also had to do with cognitive profile, especially early in his career. Feynman often found it easier to invent his own solution to a problem than to understand someone else's published paper.

Lubos is upset that I might think that Schwinger was, at least in some ways, "smarter" than Feynman. Even so, Feynman is my hero, not Schwinger. Feynman had no rival in his generation when it came to originality and creativity. See also Success vs Ability and Out on the tail.

NYTimes: ... The generation coming up behind him, with the advantage of hindsight, still found nothing predictable in the paths of his thinking. If anything he seemed perversely and dangerously bent on disregarding standard methods. "I think if he had not been so quick people would have treated him as a brilliant quasi crank, because he did spend a substantial amount of time going down what later turned out to be dead ends," said Sidney Coleman, a theorist who first knew Feynman at Caltech in the 50's.

"There are lots of people who are too original for their own good, and had Feynman not been as smart as he was, I think he would have been too original for his own good," Coleman continued. "There was always an element of showboating in his character. He was like the guy that climbs Mont Blanc barefoot just to show that it can be done."

Feynman continued to refuse to read the current literature, and he chided graduate students who would begin their work on a problem in the normal way, by checking what had already been done. That way, he told them, they would give up chances to find something original.

"I suspect that Einstein had some of the same character," Coleman said. "I'm sure Dick thought of that as a virtue, as noble. I don't think it's so. I think it's kidding yourself. Those other guys are not all a collection of yo-yos. Sometimes it would be better to take the recent machinery they have built and not try to rebuild it, like reinventing the wheel. Dick could get away with a lot because he was so goddamn smart. He really could climb Mont Blanc barefoot."

Coleman chose not to study with Feynman directly. Watching Feynman work, he said, was like going to the Chinese opera. "When he was doing work he was doing it in a way that was just -- absolutely out of the grasp of understanding. You didn't know where it was going, where it had gone so far, where to push it, what was the next step. With Dick the next step would somehow come out of -- divine revelation."

The characterization below is one of my favorites. We all stand in awe of the magicians!

"There are two kinds of geniuses, the 'ordinary' and the 'magicians,' " wrote the mathematician Mark Kac. "An ordinary genius is a fellow that you and I would be just as good as, if we were only many times better. There is no mystery as to how his mind works. Once we understand what they have done, we feel certain that we, too, could have done it. It is different with the magicians. They are, to use mathematical jargon, in the orthogonal complement of where we are and the working of their minds is for all intents and purposes incomprehensible. Even after we understand what they have done, the process by which they have done it is completely dark. Richard Feynman is a magician of the highest caliber."

Some interesting finds in this 1966 AIP oral history interview with Feynman.

I have always felt that Feynman was cognitively a bit "lopsided" -- much stronger mathematically than verbally. This might be partially responsible for his way of learning -- it was often easier for him to invent his own solution than to read through someone else's lengthy paper. (Personality factors such as his independent streak, and his strong creativity, also play a role.) But this sometimes left him with gaping holes in knowledge. In contrast, Schwinger had at age 17 an encyclopedic understanding of what was known about quantum electrodynamics -- he had read and mastered all of the literature as a high school kid!

This excerpt reveals that Feynman did not understand the conventional formulation of QED even after Dyson's paper proving the equivalence of the Feynman and Schwinger methods. (When someone explained the action of a creation operator on the vacuum, Feynman reportedly objected "How can you create an electon? It disagrees with conservation of charge!" :-)

... I was struggling gradually to learn. I mean, I had to learn something to prove the connection between my thing and the same thing. Dyson had done a great deal in that direction. That didn’t satisfy me because I couldn’t follow that. Dyson told me, when he wrote his paper, “Don’t bother to read it, there’s nothing in it that you don’t know, except that it proves it’s the same as what everybody else knows, but it doesn’t say anything different or do anything different than is in your paper. Nothing more in it,” he told me.

... Yeah, because I remember him telling me not to worry about the paper. It hadn’t anything in it, you see. ... But then I thought I had to understand the connection, for publication purposes and others. And I had a good opportunity, because Case sent me his theorem — the manuscript of a big paper that he was going to publish in the Physical Review, which had all the steps of the theorem. Now, I argued in the meantime with myself, in my usual physical way of arguing, and concluded for several physical reasons, by some examples and other things — simpler examples that weren’t so elaborate as the calculations I made — that it couldn’t be true that the two methods would give the same result. ... I prepared a letter in which I wrote the physical arguments. Then I decided, that isn’t going to convince him. Nobody pays any attention to physical arguments, no matter how good they are. I’ve got to find a mistake in the proof. But the proof has creation and annihilation operators and all kinds of stuff. So I went to some students, in particular Mr. Scalator who was only fair, but he understood. He had learned in a pedestrian way what it all meant, and he explained to me what the symbols meant. So I learned like a little child what all this was about, so I understood what the symbols that he was using in the paper meant, and I tried to follow the proof, and I learned enough to be able to do that kind of mathematics, see — for the first time. So I followed the whole thing through, and I found a mistake, a very simple algebraic error, in the proof. He commuted some things that didn’t commute and so on.

Feynman never carefully read either Schwinger or Tomonaga's work:

Weiner: How about Tomonaga’s work? When did you first hear of it?
Feynman: I don’t know when I first heard of it. The work itself, I never knew exactly what it was, and I don’t yet know precisely what it was.
Weiner: You read his paper?
Feynman: No.
Weiner: I mean, there’s one paper that is often cited —
Feynman: No. No. I don’t think I read the paper. But this must be understood — I don’t mean anything disparaging. If Schwinger hadn’t been in the front yard at Pocono, or next to me, I wouldn’t have known what he did either. I got the same as everybody else. If you can do it yourself, why learn how somebody else does it? So I don’t know precisely what the relation of Tomonaga’s and Schwinger’s work is or the relation of his and mine. I think the relation of Tomonaga’s work to my work is very small. I mean, I think he’s gone around much closer the direction that Schwinger went.
Weiner: I think it’s the general impression.
Feynman: But I don’t know the precise relationship of their work. But I believe, if I’m not mistaken, although you’ll have to ask Schwinger, that everything that Schwinger did he did without knowledge of what Tomonaga did. I hear, but I don’t know, that Tomonaga did a very great deal, and did essentially what Schwinger did, except perhaps for working on certain practical problems. I don’t know. That’s what I hear. But I don’t know. I’m sorry, that sounds stupid, but I have never looked into it, and I never read Schwinger’s paper in a comprehensible way. I don’t know what’s in that paper of Schwinger’s.
Weiner: Haven’t tried to read it?
Feynman: Never. Tried in the sense that I looked at it and I flipped the pages, because it’s too hard. I read it at a time when I didn’t even know what a creation-annihilation operator was. I read it — you probably can prove that by the fact that I refer to it in various places, and get certain formulas out of it — I read it in the same way that I talk to him. When something looks like something, I know that’s it, you know? But I didn’t follow all the steps. I never followed all the steps.
Weiner: But you did know, when you talked to him at Pocono, and then —
Feynman: I know Schwinger — that’s what I say, I must have read it in pieces and bits. I know what Schwinger did; I know more or less how he did it. ...

Feynman: Yes, because we talked together, we had the physical idea of what starts it, but there’s a difference from that and checking all the equations, ... I don’t know whether he really read mine in detail or not. But he knows what’s in it, and I know what’s in his, but I can’t tell you. Perhaps if I look at his paper carefully, I can see that I really did read it, you know? I mean, I’d have to have it and look at it and see if I did read it. That’s a good way to look. I doubt that I read it in detail. I doubt that I looked at all of the various complicated sub-things that he had to worry about, like what to do with the longitudinal waves — because I don’t think there’s any problem with the longitudinal waves. I couldn’t pay attention to such a thing, see? So I doubt that I’ve ever read the paper in any careful way like a student would try to learn it. I don’t believe I’ve ever done that.

Finally, an interesting conversation between Feynman and Oppenheimer concerning the covariant propagator and positrons as electrons moving backwards in time:

So I went to the Physics Society and gave this paper, and I wanted Professor Oppenheimer to hear it, and other people like that. I particularly wanted Oppenheimer to hear it because he often said that there wasn’t anything to it. He understood Schwinger’s and he didn’t understand mine. And I thought he would be at the meeting. I’d kind of half thought about him when I prepared it. When I went to the meeting, he wasn’t there, but I gave the paper, and then Weisskopf got up and said, “This paper is so important and unusual” and so on “that we ought to give the man more time to express his ideas.” ... Then I stepped down, and just at that moment, Oppenheimer came in and sat down in the chair just ahead of me. And he turned around and said, “What did you talk about?” I said, “The idea of electrons going backwards,” meaning positrons. He said, “Oh, I heard all that. Oh, yes,” he said, “I heard that stuff, right? That stuff I heard.” I said, “Yeah, you’ve heard it, but you’ve never understood it.” Now, the response to that was an invitation I found in the mail when I got back to Cornell, to come to Princeton to the Institute and explain all my ideas, in as many lectures as I wished, two a week, as long a time as I wanted, expenses to be paid by the Institute, and so on. He’s a very great man, I know. I mean, I understand him. We’re good friends. You know. I mean, it’s not enemies. I said that because I was trying to get something across to him, that he didn’t understand it. That was honest. He knew that if I were driven to say that that was true — you know what I mean — and it was worth learning. So I said that, and his response was very generous — any length of time I want, any conditions. So I went to the Institute of Advanced Study.

In his eulogy, Schwinger described Feynman as "... the outstanding intuitionist of our age ..." :-)

Note added: I recalled another anecdote related to this post. At his Pocono talk Feynman was repeatedly asked by Dirac "Is it unitary?" (referring to Feynman's diagram method deduced from the path integral). Unfortunately, Feynman did not seem sure what "unitary" meant and responded "perhaps it will become clear as we proceed..." (a trick he learned from an earlier Schwinger talk). Feynman also did not seem to know what an S-matrix was!

But is it unitary? :-)

See follow up post: Feynman and the secret of magic.

Another historical letter sent by a reader. My understanding is that Feynman was not appointed at Berkeley because of Birge's anti-semitism: "One Jew (Oppenheimer) is enough," he is reported to have said.

CONFIDENTIAL

November 4, 1943

Professor R. T. Birge
Chairman, Department of Physics
University of California
Berkeley, California

Dear Professor Birge:

In these war times it is not always easy to think constructively about the peace that is to follow, even in such relatively small things as the welfare of our department. I would like to make one suggestion to you which concerns that, and about which I have myself a very sure and strong conviction.

As you know, we have quite a number of physicists here, and I have run into a few who are young and whose qualities I had not known before. Of these there is one who is in every way so outstanding and so clearly recognized as such, that I think it appropriate to call his name to your attention, with the urgent request that you consider him for a position in the department at the earliest time that that is possible. You may remember the name because he once applied for a fellowship in Berkeley: it is Richard Feynman. He is by all odds the most brilliant young physicist here, and everyone knows this. He is a man of thoroughly engaging character and personality, extremely clear, extremely normal in all respects, and an excellent teacher with a warm feeling for physics in all its aspects. He has the best possible relations both with the theoretical people of whom he is one, and with the experimental people with whom he works in very close harmony.

The reason for telling you about him now is that his excellence is so well known, both at Princeton where he worked before he came here, and to a not inconsiderable number of "big shots" on this project, that he has already been offered a position for the post war period, and will most certainly be offered others. I feel that he would be a great strength for our department, tending to tie together its teaching, its research and its experimental and theoretical aspects. I may give you two quotations from men with whom he has worked. Bethe has said that he would rather lose any two other men than Feyman from this present job, and Wigner said, "He is a second Dirac, only this time human."

Of course, there are several people here whose recommendation you might want; in the first instance Professors Brode and McMillan. I hope you will not mind my calling this matter to your attention, but I feel that if we can follow the suggestion I have made, all of us will be very happy and proud about it in the future. I cannot too strongly emphasize Feynman's remarkable personal qualities which have been generally recognized by officers, scientists and laity in this community.

With every good wish,

Robert Oppenheimer

Murray Gell-Mann on his relationship with Feynman.

[フレーム]

See also Gell-Mann, Feynman, Everett.

I had only one memorable encounter with Murray while I was a student at Caltech. On the other hand I have quite a few memories of Feynman, who enjoyed interacting with students. I don't really blame Murray for not being particularly interested in students. The gap between him and us must have been (and still is) quite vast :-)

Hawking was on campus and was giving a kind of "secret" (not advertised) seminar in the medium sized lecture room on the second floor of Lauritsen. In those days Hawking could sort of talk, although only people who had worked closely with him could understand what he was saying. Nick Warner, at that time a postdoc at Caltech, was Hawking's interpreter. Hawking would gurgle briefly, and Nick would translate (decompress?) the message as Consider a 4-manifold endowed with a metric ... drawing a blob on the blackboard and even writing equations. I could never figure out how this communication worked because what Nick said was so much more elaborate than the brief gurgle from Hawking. Perhaps the gurgle messages were something like Give the setup for the no-boundary wavefunction on a Euclidean 4-manifold!

They were filming the lecture for a documentary. A statuesque blonde woman in a tank top and jeans was holding a boom mike (microphone attached to long white plastic tube), standing in the aisle next to my seat. To keep the mike off camera she had both arms extended above her head with her chest thrust forward in a dramatic posture. Murray was seated directly ahead of me, and he couldn't keep his eyes on the lecture. He spent the first 15 minutes craning his neck to look at the chest display of boom mike girl. But he must have been half listening because at some point he got agitated about what Nick was saying and jumped up to disagree. He ran to the blackboard and hijacked the lecture from the postdoc and the guy in a wheelchair to explain his ideas about the wavefunction of the universe. After holding the speaker, interpreter and audience hostage for about 10 minutes, he relinquished the chalk and sat back down to resume peeking over his shoulder. That's my most vivid memory of Murray.

Feynman had that on his final blackboard. Crazy? Even for Feynman? An admirable ambition, nonetheless.

At what point did this become impossible for even the smartest human alive? What if we amend it to Learn to solve every important problem that has been solved? (For some threshold of importance...)




Feynman's TO LEARN list:

Bethe Ansatz, Kondo Effect, 2-D Hall Effect, "accel. temp" = Unruh Effect?, Non-linear classical Hydrodynamics

Do I know anyone well-acquainted with all of these topics? I can think of a few people who come close ...

While it may be impossible to achieve Feynman's goal, I'm surprised that more people don't attempt the importance-threshold modified version. Suppose we set the importance bar really, really high: what are the most important results that everyone should try to understand? Here's a very biased partial list: basic physics and mathematics (e.g., to the level of the Feynman Lectures); quantitative theory of genetics and evolution; information, entropy and probability; basic ideas about logic and computation (Godel and Turing?); ... What else? Dynamics of markets? Complex Systems? Psychometrics? Descriptive biology? Organic chemistry?

This site is a treasure trove of interesting video interviews -- including with Francis Crick, Freeman Dyson, Sydney Brenner, Marvin Minsky, Hans Bethe, Donald Knuth, and others. Many of the interviews have transcripts, which are much faster to read than listening to the interviews themselves.

Here's what Murray Gell-Mann has to say about quantum foundations:

In '63…'64 I worked on trying to understand quantum mechanics, and I brought in Felix Villars and for a while some comments... there were some comments by Dick Feynman who was nearby. And we all agreed on a rough understanding of quantum mechanics and the second law of thermodynamics and so on and so on, that was not really very different from what I'd been working on in the last ten or fifteen years.

I was not aware, and I don't think Felix was aware either, of the work of Everett when he was a graduate student at Princeton and worked on this, what some people have called 'many worlds' idea, suggested more or less by Wheeler. Apparently Everett was, as we learned at the Massagon [sic] meeting, Everett was an interesting person. He… it wasn't that he was passionately interested in quantum mechanics; he just liked to solve problems, and trying to improve the understanding of quantum mechanics was just one problem that he happened to look at. He spent most of the rest of his life working for the Weapon System Evaluation Group in Washington, WSEG, on military problems. Apparently he didn't care much as long as he could solve some interesting problems! [Some of these points, concerning Everett's life and motivations, and Wheeler's role in MW, are historically incorrect.]

Anyway, I didn't know about Everett's work so we discovered our interpretation independent of Everett. Now maybe Feynman knew about… about Everett's work and when he was commenting maybe he was drawing upon his knowledge of Everett, I have no idea, but… but certainly Felix and I didn't know about it, so we recreated something related to it.

Now, as interpreted by some people, Everett's work has two peculiar features: one is that this talk about many worlds and equally… many worlds equally real, which has confused a lot of people, including some very scholarly students of quantum mechanics. What does it mean, 'equally real'? It doesn't really have any useful meaning. What the people mean is that there are many histories of the… many alternative histories of the universe, many alternative course-grained, decoherent histories of the universe, and the theory treats them all on an equal footing, except for their probabilities. Now if that's what you mean by equally real, okay, but that's all it means; that the theory treats them on an equal footing apart from their probabilities. Which one actually happens in our experience, is a different matter and it's determined only probabilistically. Anyway, there's considerable continuity between the thoughts of '63-'64 and the thoughts that, and… and maybe earlier in the ‘60s, and the thoughts that Jim Hartle and I have had more recently, starting around '84-'85.

Indeed, Feynman was familiar with Everett's work -- see here and here.

Where Murray says "it's determined only probabilistically" I would say there is a subjective probability which describes how surprised one is to find oneself on a particular decoherent branch or history of the overall wavefunction -- i.e., how likely or unlikely we regard the outcomes we have observed to have been. For more see here.

Murray against Copenhagen:

... although the so-called Copenhagen interpretation is perfectly correct for all laboratory physics, laboratory experiments and so on, it's too special otherwise to be fundamental and it sort of strains credulity. It's… it’s not a convincing fundamental presentation, correct though… though it is, and as far as quantum cosmology is concerned it's hopeless. We were just saying, we were just quoting that old saw: describe the universe and give three examples. Well, to apply the… the Copenhagen interpretation to quantum cosmology, you'd need a physicist outside the universe making repeated experiments, preferably on multiple copies of the universe and so on and so on. It's absurd. Clearly there is a definition to things happening independent of human observers. So I think that as this point of view is perfected it should be included in… in teaching fairly early, so that students aren't convinced that in order to understand quantum mechanics deeply they have to swallow some of this…very… some of these things that are very difficult to believe. But in the end of course, one can use the Copenhagen interpretations perfectly okay for experiments.

Von Neumann, Feynman and Ulam, back in the day. (Probably Santa Fe or Los Alamos.)

Some Ulam quotes from his autobiography Adventures of a Mathematician.

One of the luckiest accidents of my life happened the day G. D. Birkhoff came to tea at von Neumann's house while I was visiting there. We talked and, after some discussion of mathematical problems, he turned to me and said, “There is an organization at Harvard called the Society of Fellows. It has a vacancy. There is about one chance in four that if you were interested and applied you might receive this appointment."

I came to the Society of Fellows during its first few years of existence ... I was given a two-room suite in Adams House, next door to another new fellow in mathematics by the name of John Oxtoby ... He was interested in some of the same mathematics I was: in set theoretical topology, analysis, and real function theory.

... While l was at Harvard, Johnny came to see me a few times and I invited him to dinner at the Society of Fellows. We would also take automobile drives and trips together during which we discussed everything from mathematics to literature and talked without interruption while still paying attention to our surroundings. Johnny liked this kind of travel very much.

... Edward [Teller] took up my suggestions, hesitantly at first, but enthusiastically after a few hours. ... Teller lost no time in presenting these ideas ... at a ... meeting in Princeton which was to become quite famous because it marked the turning point in the development of the H-bomb.

... It seems to me this was the tragedy of Oppenheimer. He was more intelligent, receptive, and brilliantly critical than deeply original. ... Perhaps he exaggerated his role when he saw himself as the "Prince of Darkness, the destroyer of Universes." Johnny used to say, "Some people profess guilt to claim credit for the sin."

... Banach once told me, "Good mathematicians see analogies between theorems or theories, the very best ones see analogies between analogies." Gamow possessed this ability to see analogies between models for physical theories to an almost uncanny degree ... It was along the great lines of the foundations of physics in cosmology and in the recent discoveries in molecular biology that his ideas played an important role. His pioneering work in explaining the radioactive decay of atoms was followed by his theory of the explosive beginning of the universe, the “big bang" theory (he disliked the term by the way) and the subsequent formation of galaxies.

I found the excerpt below in the comments here.

Mega Questions for Renowned Psychologist Dr._Arthur R. Jensen - Interview by Christopher Michael Langan and Dr. Gina LoSasso and members of the Mega Foundation, Mega Society East and Ultranet

Question #1:

Christopher Langan for the Mega Foundation: It is reported that one of this century’s greatest physicists, Nobelist Richard Feynman, had an IQ of 125 or so. Yet, a careful reading of his work reveals amazing powers of concentration and analysis…powers of thought far in excess of those suggested by a z score of well under two standard deviations above the population mean. Could this be evidence that something might be wrong with the way intelligence is tested? Could it mean that early crystallization of intelligence, or specialization of intelligence in a specific set of (sub-g) factors – i.e., a narrow investment of g based on a lopsided combination of opportunity and proclivity - might put it beyond the reach of g-loaded tests weak in those specific factors, leading to deceptive results?

Arthur Jensen: I don’t take anecdotal report of the IQs of famous persons at all seriously. They are often fictitious and are used to make a point - typically a put-down of IQ test and the whole idea that individual differences in intelligence can be ranked or measured. James Watson once claimed an IQ of 115; the daughter of another very famous Nobelist claimed that her father would absolutely “flunk” any IQ test. It’s all ridiculous.

Furthermore, the outstanding feature of any famous and accomplished person, especially a reputed genius, such as Feynman, is never their level of g (or their IQ), but some special talent and some other traits (e.g., zeal, persistence). Outstanding achievements(s) depend on these other qualities besides high intelligence. The special talents, such as mathematical musical, artistic, literary, or any other of the various “multiple intelligences” that have been mentioned by Howard Gardner and others are more salient in the achievements of geniuses than is their typically high level of g. Most very high-IQ people, of course, are not recognized as geniuses, because they haven’t any very outstanding creative achievements to their credit. However, there is a threshold property of IQ, or g, below which few if any individuals are even able to develop high-level complex talents or become known for socially significant intellectual or artistic achievements. This bare minimum threshold is probably somewhere between about +1.5 sigma and +2 sigma from the population mean on highly g-loaded tests.

Childhood IQs that are at least above this threshold can also be misleading. There are two famous scientific geniuses, both Nobelists in physics, whose childhood IQs are very well authenticated to have been in the mid-130s. They are on record and were tested by none other than Lewis Terman himself, in his search for subjects in his well-known study of gifted children with IQs of 140 or above on the Stanford-Binet intelligence test. Although these two boys were brought to Terman’s attention because they were mathematical prodigies, they failed by a few IQ points to meet the one and only criterion (IQ > 139) for inclusion in Terman’s study. Although Terman was impressed by them, as a good scientist he had to exclude them from his sample of high-IQ kids. Yet none of the 1,500+ subjects in the study ever won a Nobel Prize or has a biography in the Encyclopedia Britannica as these two fellows did. Not only were they gifted mathematically, they had a combination of other traits without which they probably would not have become generally recognized as scientific and inventive geniuses. So-called intelligence tests, or IQ, are not intended to assess these special abilities unrelated to IQ or any other traits involved in outstanding achievement. It would be undesirable for IQ tests to attempt to do so, as it would be undesirable for a clinical thermometer to measure not just temperature but some combination of temperature, blood count, metabolic rate, etc. A good IQ test attempts to estimate the g factor, which isn’t a mixture, but a distillate of the one factor (i.e., a unitary source of individual differences variance) that is common to all cognitive tests, however diverse.

I have had personal encounters with three Nobelists in science, including Feynman, who attended a lecture I gave at Cal Tech and later discussed it with me. He, like the other two Nobelists I’ve known (Francis Crick and William Shockley), not only came across as extremely sharp, especially in mathematical reasoning, but they were also rather obsessive about making sure they thoroughly understood the topic under immediate discussion. They at times transformed my verbal statements into graphical or mathematical forms and relationships. Two of these men knew each other very well and often discussed problems with each other. Each thought the other was very smart. I got a chance to test one of these Nobelists with Terman’s Concept Mastery Test, which was developed to test the Terman gifted group as adults, and he obtained an exceptionally high score even compared to the Terman group all with IQ > 139 and a mean of 152.

I have written an essay relevant to this whole question: “Giftedness and genius: Crucial differences.” In C. P. Benbow & D. Lubinski (Eds.) Intellectual Talent: Psychometric and Social Issues, pp. 393-411. Baltimore: Johns Hopkins University Press.

See here for data relevant to this topic and the discussion in the comments.

In his PhD dissertation, Charles Misner, following a suggestion from his advisor John Wheeler, formulates quantum gravity in terms of the path integral. This article has a very clear explanation for why the Hamiltonian operator in GR is zero.

Rev. Mod. Phys. 29, 497–509 (1957): Feynman Quantization of General Relativity

Of course, in this kind of formulation the "wavefunction of the universe" plays a central role, and the universe is necessarily a closed system. There is no appealing to outside "observers" for help!

Misner was a contemporary of Everett, and played a role in the development of many worlds quantum mechanics. See here for Dieter Zeh's discussion of the 1957 Chapel Hill meeting where Everett's interpretation and quantum gravity were both discussed.

Feynman presents a thought experiment in which a macroscopic mass (source for the gravitational field) is placed in a superposition state. One of the central points is necessarily whether the wavefunction describing the macroscopic system must collapse, and if so exactly when. The discussion sheds some light on Feynman's (early) thoughts on many worlds and his exposure to Everett's ideas, which apparently occurred even before their publication (see below).