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Fun book for the science minded
Feynman's Lost Lecture: the Motion of Planets Around the Sun, by David and Judith Goodstein, is a truly remarkable little book. I am squarely in the target audience for a book like this, but if anything, I enjoyed it EVEN MORE than I expected to.
Several years after he taught what would be published as The Feynman Lectures on Physics, the good Dr. Feynman was brought back in to teach a single undergraduate class on the last day of a term. For his topic, he chose to prove Kepler's First Law: That the planets travel around the sun in an elliptical orbit. But the journey from this description to the finished book product takes many delightful turns.
First is the method of proof. Feynman chooses to use only plane geometry, the kind you learned in high school and promptly forgot, straight edges and compasses, Euclid and Pythagoras, and off you go. He is largely following Newton's argument, down to exactly copying diagrams and the first part of his argument straight from the Principia; he uses Newton's first two laws as givens, and uses them to demonstrate and prove Kepler's other two laws en route to his proof of the Law of Ellipses. He calls it an "elementary demonstration", by which he means you only need to know a small amount of things to understand it, but you must have a great deal of ingenuity and imagination.
A funny thing happens next. Feynman bemoans that Newton and his contemporaries were superbly talented with conic sections and their obscure properties, and he can't make head nor tail of it. So he invents his own second half of the proof, still keeping to plane geometry as the method. Hold that thought. After the class, as was usual, a transcript of the talk made its way into the Cal Tech archives, but there was a big flaw; in order to understand the proof, you would need to know the sequence and composition of (looking at the one picture that survives) 8 or 10 or more blackboards filled top to bottom with diagrams. Enter the authors, who laboriously recreated the argument, and the diagrams, and filled the middle section of the book (after a historical overview of Brahe, Kepler, and Newton) with a detailed explanation of Feynman's proof. In a lovely bit of recursion, the Goodstein's encounter a piece of Feynman's explanation that is very obscure, so they invent their own!
To close his lecture, "since [he had] some time left over" Feynman abandons the strict geometrical method, but uses the same basic arguments to explain Rutherford's scattering theorem, which led directly to the proof of the atomic nucleus, which caused a line of scientific inquiry that eventually led to the creation of quantum mechanics, which replaced Newtonian mechanics. Got that? Using Newton's laws, right down to copying the Principia, to support an argument that showed Newton was wrong (at least, wrong for the specific context of particle mechanics).
The resulting book has a strange structure; the explication of the proof by the Goodstein's is 2 or 3 times as long as the transcript of the speech itself :) As friend T. comments "That is one workable definition of art: it is its own shortest expression of itself". And make no mistake, once it's all done, the proof is absurdly elegant. Finally, this is a book plus audio tape package. So you get to hear the man work, goofy Brooklyn accent and all, and you get the question and answer session at the end of the lecture to cap the whole thing off.
Highly recommended!
Several years after he taught what would be published as The Feynman Lectures on Physics, the good Dr. Feynman was brought back in to teach a single undergraduate class on the last day of a term. For his topic, he chose to prove Kepler's First Law: That the planets travel around the sun in an elliptical orbit. But the journey from this description to the finished book product takes many delightful turns.
First is the method of proof. Feynman chooses to use only plane geometry, the kind you learned in high school and promptly forgot, straight edges and compasses, Euclid and Pythagoras, and off you go. He is largely following Newton's argument, down to exactly copying diagrams and the first part of his argument straight from the Principia; he uses Newton's first two laws as givens, and uses them to demonstrate and prove Kepler's other two laws en route to his proof of the Law of Ellipses. He calls it an "elementary demonstration", by which he means you only need to know a small amount of things to understand it, but you must have a great deal of ingenuity and imagination.
A funny thing happens next. Feynman bemoans that Newton and his contemporaries were superbly talented with conic sections and their obscure properties, and he can't make head nor tail of it. So he invents his own second half of the proof, still keeping to plane geometry as the method. Hold that thought. After the class, as was usual, a transcript of the talk made its way into the Cal Tech archives, but there was a big flaw; in order to understand the proof, you would need to know the sequence and composition of (looking at the one picture that survives) 8 or 10 or more blackboards filled top to bottom with diagrams. Enter the authors, who laboriously recreated the argument, and the diagrams, and filled the middle section of the book (after a historical overview of Brahe, Kepler, and Newton) with a detailed explanation of Feynman's proof. In a lovely bit of recursion, the Goodstein's encounter a piece of Feynman's explanation that is very obscure, so they invent their own!
To close his lecture, "since [he had] some time left over" Feynman abandons the strict geometrical method, but uses the same basic arguments to explain Rutherford's scattering theorem, which led directly to the proof of the atomic nucleus, which caused a line of scientific inquiry that eventually led to the creation of quantum mechanics, which replaced Newtonian mechanics. Got that? Using Newton's laws, right down to copying the Principia, to support an argument that showed Newton was wrong (at least, wrong for the specific context of particle mechanics).
The resulting book has a strange structure; the explication of the proof by the Goodstein's is 2 or 3 times as long as the transcript of the speech itself :) As friend T. comments "That is one workable definition of art: it is its own shortest expression of itself". And make no mistake, once it's all done, the proof is absurdly elegant. Finally, this is a book plus audio tape package. So you get to hear the man work, goofy Brooklyn accent and all, and you get the question and answer session at the end of the lecture to cap the whole thing off.
Highly recommended!
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(On a somewhat-related note, a fellow Stony Brook student is working at NIST over the summer, and they have an apple tree grown from a clipping from Newton's original. She's going to make an offering to it my name).
Using Newton's laws, right down to copying the Principia, to support an argument that showed Newton was wrong
There's at least one more way in which the quantum lurks within the classical... although I haven't seen the proof myself (and am probably not ready for it yet), it is apparently possible to derive Schrodinger's equation straight from the representations of the Galillei Group, that is, the group of symmetries in Newtonian mechanics!
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Did you see this article on prime numbers and the Reimann function? The main thrust of the article is curious enough, but the intro contains a comment, from Freeman Dyson's 1972 paper Missed Opportunities, that suggests that if only the mathematicans of the time had spoken with the physicists who were working with Maxwell's equations, they would have discovered relativity 40 years earlier. Leaving Einstein with only two Nobel-quality papers in 1905, not three, I suppose :)
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WishliX0Red.
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thanks a bunch for this