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“Well,” he added sarcastically, “it must be wonderful to be able to do that.” Educating his children made him think again about the elements of teaching and about the lessons his own father had taught. By the time Carl was four, Feynman was actively lobbying against a first-grade science book proposed for California schools. It began with pictures of a mechanical wind-up dog, a real dog, and a motorcycle, and for each the same question: “What makes it move?” The proposed answer—“Energy makes it move”—enraged him.

That was tautology, he argued—empty definition. Feynman, having made a career of understanding the deep abstractions of energy, said it would be better to begin a science course by taking apart a toy dog, revealing the cleverness of the gears and ratchets. To tell a first-grader that “energy makes it move” would be no more helpful, he said, than saying “God makes it move” or “moveability makes it move.” He proposed a simple test for whether one is teaching ideas or mere definitions:

You say, “Without using the new word which you have just learned, try to rephrase what you have just learned in your own language. Without using the word energy, tell me what you know now about the dog’s motion.”

Other standard explanations were just as hollow: gravity makes it fall, or friction makes it wear out. Having tried to impart fundamental knowledge to Caltech freshmen, he also believed it was possible to teach real knowledge to first-graders. “Shoe leather wears out because it rubs against the sidewalk and the little notches and bumps on the sidewalk grab pieces and pull them off.” That is knowledge. “To simply say, ‘It is because of friction,’ is sad, because it’s not science.”

Feynman taught thirty-four formal courses during his Caltech career, roughly one a year. Most were graduate seminars called Advanced Quantum Mechanics or Topics in Theoretical Physics. That often meant his current research interest: graduate students sometimes heard, without realizing it, the first and last report of substantial work that another physicist would have published. For almost two decades he also taught a course, listed in no catalog, known as Physics X: one afternoon a week, undergraduates would gather to pose any scientific question they wished, and Feynman would improvise. His effect on these students was immense; they often left the Lauritsen Laboratory basement feeling that they had had a private pipeline to an oracle with an earthy kind of omniscience. He believed—in the face of the increasing esotericism of his own subject—that true understanding implied a kind of clarity. A physicist once asked him to explain in simple terms a standard item of the dogma, why spin-one-half particles obey Fermi-Dirac statistics. Feynman promised to prepare a freshman lecture on it. For once, he failed. “I couldn’t reduce it to the freshman level,” he said a few days later, and added, “That means we really don’t understand it.”

It was his own children, however, who crystallized many of his attitudes toward teaching. In 1964 he had made the rare decision to serve on a public commission, responsible for choosing mathematics textbooks for California’s grade schools. Traditionally this commissionership was a sinecure that brought various small perquisites under the table from textbook publishers. Few commissioners—as Feynman discovered—read many textbooks, but he determined to read them all, and had scores of them delivered to his house. This was the era of the so-called new mathematics in children’s education: the much-debated effort to modernize the teaching of mathematics by introducing such high-level concepts as set theory and nondecimal number systems. New math swept the nation’s schools startlingly fast, in the face of parental nervousness that was captured in a New Yorker cartoon: “You see, Daddy,” a little girl explains, “this set equals all the dollars you earned; your expenses are a sub-set within it. A sub-set of that is your