Category Archives: Genius

Freeman Dyson (1923-2020)

Source: Information Processing, Mar 2009

Dyson’s drawings as a child

The breakthrough came on summer trips Dyson made in 1948, traveling around America by Greyhound bus and also, for four days, in a car with Feynman. Feynman was driving to Albuquerque, and Dyson joined him just for the pleasure of riding alongside “a unique person who had such an amazing combination of gifts.”

The irrepressible Feynman and the “quiet and dignified English fellow,” as Feynman described Dyson, picked up gypsy hitchhikers; took shelter from an Oklahoma flood in the only available hotel they could find, a brothel, where Feynman pretended to sleep and heard Dyson relieve himself in their room sink rather than risk the common bathroom in the hall; spoke of Feynman’s realization that he had enjoyed military work on the Manhattan Project too much and therefore could do it no more; and talked about Feynman’s ideas in a way that made Dyson forever understand what the nature of true genius is.

Dyson wanted to unify one big theory; Feynman was out to unify all of physics. Inspired by this and by a mesmerizing sermon on nonviolence that Dyson happened to hear a traveling divinity student deliver in Berkeley, Dyson sat aboard his final Greyhound of the summer, heading East. He had no pencil or paper. He was thinking very hard. On a bumpy stretch of highway, long after dark, somewhere out in the middle of Nebraska, Dyson says, “Suddenly the physics problem became clear.” What Feynman, Schwinger and Tomonaga were doing was stylistically different, but it was all “fundamentally the same.”

Related Resources:

The Guardian, Mar 2020

The young Dyson reported that his happiest ever school holiday – from Winchester college – was spent working his way, from 6am to 10pm, through 700 problems in Piaggio’s Differential Equations. “I intended to speak the language of Einstein,” he said in his 1979 memoir Disturbing the Universe. “I was in love with mathematics and nothing else mattered.

NY Times, Feb 2020

Richard Feynman, a young professor at Cornell, had invented a novel method to describe the behavior of electrons and photons (and their antimatter equivalent, positrons). But two other physicists, Julian Schwinger and Sin-Itiro Tomonaga, had each independently devised a very different way. Each of these seemed to satisfy the requirements of both quantum mechanics and special relativity — two of nature’s acid tests. But which one was correct?

While crossing Nebraska on a Greyhound bus, Dr. Dyson was struck by an epiphany: The theories were mathematically equivalent — different ways of saying the same thing. The result was QED. Feynman called it “the jewel of physics — our proudest possession.”

Information Processing, Dec 2009

It’s been said that Quantum Electrodynamics or QED is the most successful theory science has ever produced, having been verified in some cases to an accuracy of 12 decimal places. It was worked out by two geniuses, Feynman and Schwinger, but their theories looked totally at odds—one used diagrams the other formal analysis.

In perhaps your most celebrated piece of physics, you showed they were equivalent. I’m curious, did Feynman and Schwinger grasp immediately what you had done?

Tim O’Reilly, Mar 2020

When I interviewed Freeman on stage at OSCON in 2004, along with his son George, the subject strayed to digital preservation. I lamented how much would be lost due to incompatible standards for information storage, and he said, “Oh no, forgetting is so important! It is what gives room for new ideas to come in.” This was such a typical Freeman moment: bringing a profoundly fresh perspective to any discussion.

Perhaps the most famous example is the paper he wrote in 1949 at the age of 25 making the case that the visualizations of Richard Feynman were mathematically equivalent to the calculations of the more conventional physicists Julian Schwinger and Shin’ichirō Tomonaga, a paper that led to Feynman, Schwinger, and Tomonaga receiving the 1965 Nobel Prize in Physics for the theory of quantum electrodynamics.

This talent Freeman had for seeing to the heart of things was apparent even earlier, when he was working as a statistician in the operations research section of the Royal Air Force Bomber Command during World War II. As recounted in the first of his numerous volumes of autobiography, Disturbing the Universe, he had been asked to study the pattern of bullet holes on the bombers returning to Britain from their forays overseas with an eye to reinforcing the areas with the most anti-aircraft damage.

No, no, Freeman argued, reinforcement may be more effective in areas that show little damage in returning planes, because hits to the most vital regions will have caused the planes to be lost! The essential information was to be found in what was missing.

immediately struck by how differently the world appears to someone so deeply mathematical. We see the world through the lens of our received ideas, but for most of us, words predominate. Freeman had a gift for seeing with both words and numbers, and for throwing both away when needed, to see the world afresh.

Before I met Feynman, I had published a number of mathematical papers, full of clever tricks but totally lacking in importance. When I met Feynman, I knew at once that I had entered another world. He was not interested in publishing pretty papers. He was struggling, more intensely than I had ever seen anyone struggle, to understand the workings of nature by rebuilding physics from the bottom up….I seized every opportunity to listen to Feynman talk, to learn to swim in the deluge of his ideas. He loved to talk, and he welcomed me as a listener. So we became friends for life.

For a year I watched as Feynman perfected his way of describing nature with pictures and diagrams, until he had tied down the loose ends and removed the inconsistencies. Then he began to calculate numbers, using his diagrams as a guide. With astonishing speed he was able to calculate physical quantities that could be compared directly with experiment.

During the same year when I was walking and talking with Feynman, I was also studying the work of the physicists Schwinger and Tomonaga, who were following more conventional paths and arriving at similar results.

Schwinger and Tomonaga had independently succeeded, using more laborious and complicated methods, in calculating the same quantities that Feynman could derive directly from his diagrams.

Schwinger and Tomonaga did not rebuild physics. They took physics as they found it, and only introduced new mathematical methods to extract numbers from the physics. When it became clear that the results of their calculations agreed with Feynman, I knew that I had been given a unique opportunity to bring the three theories together…. My paper was published in the Physical Review in 1949, and launched my professional career as decisively as “Every Man in His Humour” launched Jonson’s.

I knew in my heart that Feynman was the greatest of the three and that the main purpose of my paper was to make his revolutionary ideas accessible to physicists around the world. 

Genius

Source: Paul Graham blog, Nov 2019

The paths that lead to new ideas tend to look unpromising. If they looked promising, other people would already have explored them. How do the people who do great work discover these paths that others overlook? The popular story is that they simply have better vision: because they’re so talented, they see paths that others miss. But if you look at the way great discoveries are made, that’s not what happens. Darwin didn’t pay closer attention to individual species than other people because he saw that this would lead to great discoveries, and they didn’t. He was just really, really interested in such things.

Darwin couldn’t turn it off. Neither could Ramanujan. They didn’t discover the hidden paths that they did because they seemed promising, but because they couldn’t help it. That’s what allowed them to follow paths that someone who was merely ambitious would have ignored.

what matters? You can never be sure. It’s precisely because no one can tell in advance which paths are promising that you can discover new ideas by working on what you’re interested in.

But there are some heuristics you can use to guess whether an obsession might be one that matters. For example, it’s more promising if you’re creating something, rather than just consuming something someone else creates.

It’s more promising if something you’re interested in is difficult, especially if it’s more difficult for other people than it is for you. And the obsessions of talented people are more likely to be promising. When talented people become interested in random things, they’re not truly random.

But you can never be sure. In fact, here’s an interesting idea that’s also rather alarming if it’s true: it may be that to do great work, you also have to waste a lot of time.

… a way to avoid slowing down as you get older. Perhaps the reason people have fewer new ideas as they get older is not simply that they’re losing their edge. It may also be because once you become established, you can no longer mess about with irresponsible side projects the way you could when you were young and no one cared what you did.

The solution to that is obvious: remain irresponsible. It will be hard, though, because the apparently random projects you take up to stave off decline will read to outsiders as evidence of it. And you yourself won’t know for sure that they’re wrong. But it will at least be more fun to work on what you want.

 There is so much more to learn about how to do great work. As old as human civilization feels, it’s really still very young if we haven’t nailed something so basic. It’s exciting to think there are still discoveries to make about discovery. If that’s the sort of thing you’re interested in.

Feynman’s Courageous Creativity

Source: Chicago Tribune, Nov 1992

Feynman reformulated quantum mechanics, the all-embracing law of physics capable of describing the interaction of particles and radiation on a scale so small that Newton`s laws do not apply.

His new theory included the idea that the path a particle takes is based on the sum of every possible path it could take-a fundamental insight into modern physics.

He was one of three scientists who independently of each other developed quantum electrodynamics, the modern description of light interacting with matter that is widely considered the most precise scientific theory humans have ever developed.

The three shared the Nobel Prize. But while the others used complex mathematical formulas that many physicists could not understand, Feynman invented a way of diagramming interactions between particles. Feynman diagrams have become a standard language of physics.

To Drasko Jovanovic, a senior scientist at Fermi National Accelerator Laboratory in Batavia who attended a number of lectures by Feynman, there is something in a mind like Feynman`s that is unknowable.

”We are not able to discern people`s intelligence, particularly people who are smarter than we are,” Jovanovic said.

”It is like climbing a mountain. You can see below you, but above, you can`t. Something can be thousands of meters above you, or hundreds; you don`t know. To me, he was a genius, in the clouds; I cannot penetrate it.”

But while the source of Feynman`s way of thinking may be impenetrable, Jovanovic said, his ideas themselves are extraordinarily accessible-further evidence to Jovanovic of his genius.

”Everything he has written is absolutely understandable,” he said. ”It is so simple I give lectures to high school students, and they understand it. It almost resonates with your own mind.”

Sachs said, scientific creativity does have a certain inexplicable quality.

When studying a problem, he said, ”You suffer miserably. What I feel I`m doing is bouncing around in my brain like I had a whole collection of computers talking back and forth to each other, trying to match things somehow so some coherence between these things will show up.

”Then, suddenly, things fall into place. That is the inspirational moment of creativity. It`s all been there somewhere, but I don`t think anybody can tell you just what happened at that moment it came together.”

`These are driven people`

Ken Hope, who for 10 years directed the MacArthur Fellowships program, known popularly as ”genius grants,” also tried to define the magic. He concluded that it involved far more than intelligence.

”I think it has to do with a certain courageousness,” he said. ”When someone like Feynman is trying to understand in a fundamental and deep way what the nature of science is, that`s kind of a bold program.”

The greatest scientists, he said, tend to think and speak in contradictions, as in Niels Bohr`s contention that light cannot be considered either a wave or a particle, but is simultaneously both and neither.

”It`s not that they reject logic entirely, but they realize that there is something beyond logic,” Simonton said.

”Einstein insisted that you need intuition-that once your intuition got the answer, you used logic in order to convince other people you were right.

”A number of physicists talk about how they actually imagine themselves to be an electron, and what an electron would do if it were heading toward a neutron,” he said. ”Einstein imagined what would happen if he were inside an elevator in free fall.”

Feynman seemed to have a particularly strong physical intuition about the way things worked, Gleick found, an ability to use all his senses to imagine the way tiny particles of matter interact.

He seemed permeated by mathematics.

”Feynman was constantly waving his hands and making geometric shapes,”

said Robert W. Wilson, a Nobel Prize-winning physicist, during a recent visit to Fermilab. ”I think his mind must have worked geometrically.

It all adds up to genius

For Gleick, the essence of genius seems to be part intelligence, part myth, part lucky timing and maybe part magic.

Related Resources:

Michigan State website, Nov 2013

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.

University of Melbourne, Oct 2017

Feynman also dabbled in biology. In the summer of 1960, he began working in the laboratory of the geneticist Max Delbrück on the rII mutation of the bacteriophage T4.

There he chanced upon a new phenomenon of mutual suppression of mutations within the same gene, dubbed the “Feyntrons” by his colleagues in the laboratory. Keen to go back to his quantum theory of gravity, however, Feynman did not publish the work. It was later discovered independently and is now known as intragenic suppression.

 

Feynman: No Ordinary Genius

Source: Wikiquote, date indeterminate

In science, as well as in other fields of human endeavor, there are two kinds of geniuses: the “ordinary” and the “magicians.”

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 he has 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. They seldom, if ever, have students because they cannot be emulated and it must be terribly frustrating for a brilliant young mind to cope with the mysterious ways in which the magician’s mind works.

Richard Feynman is a magician of the highest caliber. Hans Bethe, whom Dyson considers to be his teacher, is an “ordinary genius”; so much so that one may gain the erroneous impression that he is not a genius at all. But it was Feynman, only slightly older than Dyson, who captured the young man’s imagination.

  • Mark Kac, in his introduction to Enigmas of Chance: An Autobiography (1985), p. xxv

An honest men, the outstanding intuitionist of our age, and a prime example of what may lie in store for anyone who dares to follow the beat of a different drum.

Several conversations that Feynman and I had involved the remarkable abilities of other physicists. In one of these conversations, I remarked to Feynman that I was impressed by Stephen Hawking‘s ability to do path integration in his head. “Ahh, that’s not so great”, Feynman replied. “It’s much more interesting to come up with the technique like I did, rather than to be able to do the mechanics in your head.” Feynman wasn’t being immodest, he was quite right. The true secret to genius is in creativity, not in technical mechanics.

Related Resource: Michigan State website, Nov 2013

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.

Chicago Tribune, Nov 1992

Feynman reformulated quantum mechanics, the all-embracing law of physics capable of describing the interaction of particles and radiation on a scale so small that Newton`s laws do not apply.

His new theory included the idea that the path a particle takes is based on the sum of every possible path it could take-a fundamental insight into modern physics.

He was one of three scientists who independently of each other developed quantum electrodynamics, the modern description of light interacting with matter that is widely considered the most precise scientific theory humans have ever developed.

The three shared the Nobel Prize. But while the others used complex mathematical formulas that many physicists could not understand, Feynman invented a way of diagramming interactions between particles. Feynman diagrams have become a standard language of physics.

To Drasko Jovanovic, a senior scientist at Fermi National Accelerator Laboratory in Batavia who attended a number of lectures by Feynman, there is something in a mind like Feynman`s that is unknowable.

”We are not able to discern people`s intelligence, particularly people who are smarter than we are,” Jovanovic said.

”It is like climbing a mountain. You can see below you, but above, you can`t. Something can be thousands of meters above you, or hundreds; you don`t know. To me, he was a genius, in the clouds; I cannot penetrate it.”

But while the source of Feynman`s way of thinking may be impenetrable, Jovanovic said, his ideas themselves are extraordinarily accessible-further evidence to Jovanovic of his genius.

”Everything he has written is absolutely understandable,” he said. ”It is so simple I give lectures to high school students, and they understand it. It almost resonates with your own mind.”

Sachs said, scientific creativity does have a certain inexplicable quality.

When studying a problem, he said, ”You suffer miserably. What I feel I`m doing is bouncing around in my brain like I had a whole collection of computers talking back and forth to each other, trying to match things somehow so some coherence between these things will show up.

”Then, suddenly, things fall into place. That is the inspirational moment of creativity. It`s all been there somewhere, but I don`t think anybody can tell you just what happened at that moment it came together.”

`These are driven people`

Ken Hope, who for 10 years directed the MacArthur Fellowships program, known popularly as ”genius grants,” also tried to define the magic. He concluded that it involved far more than intelligence.

”I think it has to do with a certain courageousness,” he said. ”When someone like Feynman is trying to understand in a fundamental and deep way what the nature of science is, that`s kind of a bold program.”

The Genius Famine

Source: VDare, Jun 2017

… geniuses are a distinct psychological type.

They have extremely high intelligence, meaning they excel at quickly solving cognitive problems. This strongly predicts socioeconomic, educational and even social success. But geniuses combine this with relatively low conscientiousness and low empathy. They also tend to be uninterested in worldly things—money, sex, power—focused intensely on the intellectual pursuit of solving whatever seemingly unsolvable problem has come to obsess them. New ideas always break established rules and offend vested interests, but the genius couldn’t care less, claim Dutton and Charlton. This is why it is the genius who is able to make original, fantastic breakthroughs.

These kinds of people are fundamental to the growth and survival of civilization, the authors maintain. They are behind all major innovations. But, frighteningly, levels of genius have been in decline during the twentieth century. Measured from 1455 to 2004, macro-inventions—those that really changed the course of history—peaked in the nineteenth century and are now in on the slide. So, what has happened? Why is genius dying-out?

Based on representative samples, the authors show that reaction times are getting longer and have been getting longer since about 1900. Between 1900 and 2000, IQ—using this proxy—seems to have gone down by about 15 points. This means that the doctors of today are the high school science teachers of 1900. The result of this is that for purely genetic reasons there would be a far smaller percentage of Turing-types today.

Intelligence is correlated with a trait known as ‘Intellect’: being open to new ideas and fascinated by intellectual pursuit. Until the 1950s, this kind of attitude underpinned the British university and perhaps even the US one—the book focuses on the UK. Academics were under no pressure to regularly publish or obtain grants. They were expected to teach and were given vast amounts of time to think and research based on the hope that some would produce works of genius.

Religion was part of the reason that universities were created along these lines. Their purpose was to reach a greater understanding of God’s Creation. If this involved frittering away money—with most academics not publishing anything—this didn’t matter. Some things are more important than money, such as the glory of God.

Since the 1960s, the authors note, universities have become bureaucratic businesses. This reflects the anti-intellectual, anti-religious attitude that their purpose is to make money. Academics contribute to this by getting funding, publishing frequently, and attending conferences.

All of this is anathema to the genius, who wants to be left alone to solve his problem. He also won’t tick the bureaucratic boxes that get you an academic position—Francis Crick, discoverer of DNA, was rejected from Cambridge, failed to get a top mark in his bachelor’s degree, and dropped out of assorted PhDs. As such, universities are less likely to appoint genius types.

They will appoint what Dutton and Charlton call the ‘head girl’ (at UK schools)—quite intelligent, socially skilled, conscientious; absolutely not a genius.

This person will be excellent at playing the academic game and will make a great colleague. But they won’t innovate; won’t rock the boat. Once upon a time, they note, a ‘country vicar’ had lots of free time to research, but with the shrinking of the Church, the days of the Victorian ‘scholar-rector,’ are long gone as well. The genius has no institution to nurture him and his potential will not be fulfilled.

Dutton and Charlton’s book predicts that genius will continue to decline and civilization will collapse because it is ultimately underpinned by intelligence and genius. Technology will reach a peak, stagnate, and go backwards, as there are fewer and fewer people intelligent enough to maintain and eventually even use it.

Life will become harsher and simpler and, eventually, more religious. At the moment, it seems that there’s nothing we can do to stop this short of a horrendous reversion to pre-Industrial levels of child mortality. But if we could better nurture genius then somebody might come up with a solution before it is too late.

So, the authors ask, how can we help geniuses?

Firstly, we need to identify them.

The genius is likely to be highly intelligent but it will be a lop-sided kind of intelligence. Oxford University philosopher A. J. Ayer, for example, had such poor spatial intelligence that he never learnt to drive. The genius will combine this very narrow intelligence with very narrow interests. Thus, he might be rejected from a top university, like Francis Crick, and do brilliantly only on aspects of his degree. He’ll also be socially awkward and eccentric.

Secondly, we need to give them an environment in which they can flourish.

They tend to be useless at everyday things—Einstein had a tendency to get lost—so these need to be taken care of for them.

Thirdly, they are very fragile people and they are not usually interested in money.

They will work for the minimum they require as long as they are looked after and free to get on with problem solving. The mathematician Paul Erdos, note Dutton and Charlton, lived out of a suitcase and camped out with various math professors. They need long-term security so that they do not have to worry about ordinary things, which they not interested in and are no good at.

If we can make these changes, insist Dutton and Charlton, then in spite of declining intelligence, it is possible that a genius may be produced who can develop a solution to this problem.

JCR Licklider – Ideas for the Digital Age

Source: Wikipedia, Aug 2019

Licklider became interested in information technology early in his career. His ideas foretold of graphical computing, point-and-click interfaces, digital libraries, e-commerce, online banking, and software that would exist on a network and migrate wherever it was needed. Much like Vannevar Bush‘s, Licklider’s contribution to the development of the Internet consists of ideas, not inventions. He foresaw the need for networked computers with easy user interfaces.

Licklider was instrumental in conceiving, funding and managing the research that led to modern personal computers and the Internet. In 1960 his seminal paper on “Man-Computer Symbiosis[23] foreshadowed interactive computing, and he went on to fund early efforts in time-sharing and application development, most notably the work of Douglas Engelbart, who founded the Augmentation Research Center at Stanford Research Institute and created the famous On-Line System where the computer mouse was invented.

Related Resources:

http://iae-pedia.org/J.C.R._Licklider, date indeterminate

Licklider at DARPA

DARPA (Department of Defense Advanced Research Projects Agency)has provided leadership and funding in a number of world-changing projects.

Quoting from http://www.nationmaster.com/encyclopedia/J.C.R.-Licklider:

In October 1962 Licklider was appointed head of the DARPA information processing office, part of the United States Department of Defense Advanced Research Projects Agency. He would then convince Ivan Sutherland, Bob Taylor, and Lawrence G. Roberts that an all-encompassing computer network was a very important concept.

When Licklider began his work at ARPA, there were no Ph.D. programs in computer science at American universities. ARPA began handing out grants to promising students, a practice that convinced MIT, Stanford, University of California at Berkeley, and Carnegie Mellon University to start their own graduate programs in computer science in 1965. This is certainly one of Lidlicker’s most lasting legacies.

SCIHI.Org, Mar 2019

During his active years in computer science, Licklider managed to conceive, manage, and research the fundamentals that led to modern computers and the Internet as we know it today.

His 1960 scientific paper on the Man-Computer Symbiosis was revolutionary and foreshadowed interactive computing. This inspired many other scientists to continue early efforts on time-sharing and application development. One of the scientists funded by Licklider’s efforts was the famous American computer scientist Douglas Engelbart, whose efforts led to the invention of the computer mouse.[4]

In August 1962, in a series of memos, Licklider described a global computer network that contained almost all the ideas that now characterize the Internet.

With a huge budget at his disposal, he hired the best computer scientists from Stanford University, MIT, UCLA, Berkeley and selected companies for his ARPA research. He jokingly described this approximately a dozen or so researchers, with whom he had a close exchange, as the “Intergalactic Computer Network“.

About six months after starting his work, he distributed an opinion in this unofficial panel, criticizing the problems of the proliferating multiplication of different programming languages, debugging programs and documentation procedures and initiating a discussion on standardization, as he saw this as a threat to a hypothetical, future computer network.

Asking Feynman: What Color is a Shadow?

Source: Nautilus, Jan 2019

I can remember a few times during my freshman year when I screwed up enough courage to say hello to Feynman before a seminar. Anything more would have been unimaginable at the time. But in my junior year, my roommate and I somehow summoned the nerve to knock on his office door to ask if he might consider teaching an unofficial course in which he would meet once a week with undergraduates like us to answer questions about anything we might ask. The whole thing would be informal, we told him. No homework, no tests, no grades, and no course credit. We knew he was an iconoclast with no patience for bureaucracy, and were hoping the lack of structure would appeal to him.

Feynman thought a moment and, much to our surprise, replied “Yes!” So every week for the next two years, my roommate and I joined dozens of other lucky students for a riveting and unforgettable afternoon with Dick Feynman.

Physics X always began with him entering the lecture hall and asking if anyone had any questions. Occasionally, someone wanted to ask about a topic on which Feynman was expert. Naturally, his answers to those questions were masterful.

In other cases, though, it was clear that Feynman had never thought about the question before. I always found those moments especially fascinating because I had the chance to watch how he engaged and struggled with a topic for the first time.

I vividly recall asking him something I considered intriguing, even though I was afraid he might think it trivial. “What color is a shadow?” I wanted to know.

After walking back and forth in front of the lecture room for a minute, Feynman grabbed on to the question with gusto. He launched into a discussion of the subtle gradations and variations in a shadow, then the nature of light, then the perception of color, then shadows on the moon, then earthshine on the moon, then the formation of the moon, and so on, and so on, and so on. I was spellbound.

One of the most important things Feynman ever taught me was that some of the most exciting scientific surprises can be discovered in everyday phenomena. All you need do is take the time to observe things carefully and ask yourself good questions.

He also influenced my belief that there is no reason to succumb to external pressures that try to force you to specialize in a single area of science, as many scientists do. Feynman showed me by example that it is acceptable to explore a diversity of fields if that is where your curiosity leads.

I also learned that “impossible,” when used by Feynman, did not necessarily mean “unachievable” or “ridiculous.” Sometimes it meant, “Wow! Here is something amazing that contradicts what we would normally expect to be true. This is worth understanding!”