Elliptical Thinking

Following on from last night's post and my encomia to Richard Feynman and Captain Beefheart of the ninth inst., my newly bought copy of 'Feynman's Lost Lecture' [pictured] arrived yesterday in the post from World of Books. A paperback edition in decent nick for a measly three or four quid, and I only had to wait a few days for it, in the end. Although the transcript of the lecture was never actually 'lost' as such, the diagrams that he used to illustrate his proof were photographed from his blackboards as usual, but those photographs were lost to history for some reason. However, his pencilled notes, including his sketches of his diagrammatic representations turned up years later in his personal papers, allowing the substance of the lecture and his proof to be reconstructed in the 1990s.

His motivation for this particular exposition was to present a proof of the motions of the planets around the sun in as simple terms as possible: the lecture was delivered to freshman and sophomore students at Caltech in 1964. His aim was to use no more complex a mathematical proof of the observations of Kepler, first formalised by Isaac Newton, regarding the elliptical orbits of celestial objects due to the effects of gravity, than simple plane geometry itself. What followed was an exercise in the purest reductive mathematical thinking imaginable: a proof that pretty much anyone with basic high-school geometry could readily understand. A proof of such power and simplicity that it overshadowed the colossus that was Isaac Newton's thinking on that very subject: in the course of a single university lecture, he posited a proof of such beauty and simplicity that even today, sixty-two years on, seems magical in its purity of thought.