Four stories about young Feynman

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I recently finished John Gribbin’s biography of Richard Feynman. It contains a bunch of remarkable anecdotes about his scientific process, and details about his life I did not know (such as that he was subjected to anti-Semitism throughout his life, including being rejected from Bell Labs several times likely due to it). 

I’ll maybe write more about his adult life in some future post. This one contains four stories about high schooler Feynman.

Fake knowledge

Feynman’s dad, Melville, played a significant role in getting young Richard interested in science. (He reportedly declared before Richard was born: “If it’s a boy, he’s going to be a scientist.”) For example, when he used to read the Encyclopedia Britannica to his son, it wouldn’t do to just say, “This dinosaur is twenty-five feet high and its head is six feet across,” and move on. From What Do You Care What Other People Think?:

My father would stop reading and say, “Now, let’s see what that means. That would mean that if he stood in our front yard, he would be tall enough to put his head through our window up here.” (We were on the second floor.) “But his head would be too wide to fit in the window.” Everything he read to me he would translate as best he could into some reality.

During summers, families from New York used to retreat to the Catskill Mountains. But the fathers still had to work on the weekdays. On weekends, Melville would take Richard on long walks in the woods and tell him about “interesting things that were going on” there. The mothers saw this prodded their husbands to take their kids on such walks too.

The next Monday, when the fathers were all back at work, we kids were playing in a field. One kid says to me, “See that bird? What kind of bird is that?”

I said, “I haven’t the slightest idea what kind of a bird it is.”

He says, “It’s a brown-throated thrush. Your father doesn’t teach you anything!”

But it was the opposite. He had already taught me: “See that bird?” he says. “It’s a Spencer’s warbler.” (I knew he didn’t know the real name.) “Well, in Italian, it’s a Chutto Lapittida. In Portuguese, it’s a Bom da Peida. In Chinese, it’s a Chung-long-tah, and in Japanese, it’s a Katano Tekeda. You can know the name of that bird in all the languages of the world, but when  you’re finished, you’ll know absolutely nothing whatever about the bird. You’ll only know about humans in different places, and what they call the bird. So let’s look at the bird and see what it’s doing—that’s what counts.”

So Richard learned at a young age, in his words, “the difference between knowing the name of something and knowing something”. 

When he taught himself math, he used his own symbols. From Surely You’re Joking, Mr Feynman!:

While I was doing all this trigonometry, I didn’t like the symbols for sine, cosine, tangent, and so on. To me, “sin f” looked like s times i times n times f! So I invented another symbol, like a square root sign, that was a sigma with a long arm sticking out of it, and I put the f underneath. For the tangent it was a tau with the top of the tau extended, and for the cosine I made a kind of gamma, but it looked a little bit like the square root sign.

Now the inverse sine was the same sigma, but left-to-right reflected so that it started with the horizontal line with the value underneath, and then the sigma. That was the inverse sine, NOT sin^-1 f—that was crazy! They had that in books! To me, sin^-1 meant 1/sine, the reciprocal. So my symbols were better. …

I thought my symbols were just as good, if not better, than the regular symbols—it doesn’t make any difference what symbols you use.

It’s not that difficult to find ways in which mathematical notation falls short!

Inertia

Once, when playing with an express wagon, Richard noticed the odd behavior of a ball in it. When he pulled the wagon, the ball rolled to the front of the wagon, and when he pushed it, the ball rolled to the back. He asked Melville why this was, and got this answer:

That, nobody knows. The general principle is that things which are moving tend to keep on moving, and things which are standing still tend to stand still, unless you push them hard. This tendency is called ‘inertia,’ but nobody knows why it’s true.

Honestly, I felt a bit bad after reading this — if a child asked me the same question, I couldn’t have come up with an answer as good as this one. As it turns out, though, the jury is out on the degree to which the stories Feynman recounts in interviews and memoirs are true, even if there is no doubt that they’re broadly true. As Gribbin writes:

Richard Feynman’s own stories should always be understood in this spirit – that as long as the underlying message is correct, the details and emphasis can be adjusted to improve the impact of the story. Joan Feynman’s brother didn’t lie, but as a great showman he presented his stories in the best possible light. As he said of his father’s stories, “I knew that they weren’t quite accurate, and yet they were utterly accurate, if you see what I mean, in the character of the story he was trying to tell me.” We could say the same about his own stories, especially when, for example, he quotes childhood conversations with his father verbatim, as if he had total recall, when in fact he was making up dialogue to match what he remembered of the occasion.

So, maybe Melville’s answer to the inertia question wasn’t exactly as elegant as the one Feynman remembers!

Feynman dabbled in art; this sketch sold on Sotheby’s for about 19,000 USD. His famous bongo drums sold for about 44,000 USD, and his pueblo for about a fourth that.

When Feynman realized he was different

Feynman’s high school algebra class was taught mechanically — subtract a constant from one side, then pool the unknowns, then divide by the coefficient, etc. So, when the teacher asked the class to solve a new kind of equation, 2^x = 32, “nobody could make head or tail of it”:

They didn’t have a set of rules for solving that kind of problem. But Richard didn’t need a set of rules; he saw straight away that the solution is x = 5, because 5 twos multiplied together is 32. This kind of thing was self-evident to Richard, and the fact that nobody else in the class felt the same way was one of the first indications he had that he really was different from the other students.

What math is like for mere people

Feynman had learned how to solve simultaneous equations before leaving elementary school. From Calculus Made Easy and Calculus for the Practical Man, he taught himself calculus towards the beginning of high school. He would solve problems students brought him from advanced geometry classes — “not because he was trying to ingratiate himself with the older boys,” Gribbin writes, “but because he couldn’t resist the challenge.” In the Interschool Algebra League, he would “[write] down his number and ostentatiously [draw]a circle around it, often on an otherwise blank piece of paper, usually before the other competitors had really got to grips with it at all”. 

Gribbin describes the time Feynman got a “glimpse of mathematical mortality”:

Richard was introduced to solid geometry, the study of shapes in three dimensions, in high school. He was completely thrown, and couldn’t understand what the teacher was getting at at all, although he could use the rules the teacher gave in order to carry through calculations properly. For once, he was in the same position as students who used the rules of algebra to solve equations without understanding what was going on. Then, the penny dropped. After a couple of weeks, he realized that the mess of lines being drawn on the blackboard was indeed meant to represent three-dimensional objects, not some crazy pattern in two dimensions. Everything came into focus, and he never had any trouble with the subject again. As far as science was concerned, “it was my only experience of how it must feel to the ordinary human being”, he later said.