Feynman Illuminates Newton

In 1684, the great English astronomer Edmond Halley journeyed to Cambridge to speak with Isaac Newton about the motion of the planets. At that time, Kepler's law stating that a planet travels around the sun in an elliptical orbit with the sun at a focus of the ellipse was well-known and accepted in scientific circles. Kepler had deduced it 70 years prior from careful analysis of Tycho Brahe's exquisite observations of the planets, particularly Mars. While nobody really knew why the planets behaved this way, an idea was floating about that the observed planetary motion might result from a force towards the sun that diminished as the inverse square of the distance between the sun and the planet.

Mr. Halley was keen to discuss these issues with the celebrated mathematician Mr. Newton, in the hopes that an analytical solution could be found that would describe the mechanics behind Kepler's Laws. To Halley's surprise and delight, Mr. Newton claimed to have already worked out a proof of the connection between an inverse-square force and the observed elliptical motion of planets. However, he was unable to put his hands on it immediately and promised to re-create it for Halley shortly. Sure enough, a short time later, Halley received a treatise containing the promised proof. It was brilliant - and it changed the world.

Now leap forward 280 years to March 13th, 1964. On that day, the great 20th-century physicist Richard Feynman presented a lecture to a freshman audience at the California Institute of Technology (CalTech) in which he re-created that very same proof of Kepler's laws of planetary motion. The lecture was recorded and Feyman's notes archived, but somehow they were lost until Judith Goodstein, a CalTech archivist, discovered them in the 1980s. Unfortunately, the records were incomplete, requiring the re-creation of some of Feynman's work by David Goodstein, another CalTech physicist. The book is the result of the Goodsteins' efforts and the circuitous turn of events that culminated in its publication are as interesting as the proof, itself. For those details, do not skip the preface and introduction.

Beyond the details of the proof, the book spins out a personal drama that I found most interesting. Here is one of the most creative scientific geniuses of the 20th century speaking frankly of his own struggles with a proof that for him was "elementary but very hard". In this case, what Feynman means by "elementary" is that the proof does not require any exceptional or arcane knowledge to understand. A simple facility with high school geometry is sufficient. Nonetheless, the proof is "hard" because it demands the creative application of geometry through a protracted series of connected steps. Indeed, the book dedicates 80 pages to carefully elaborate it, complete with dozens of detailed figures. Overall, I found it required a concerted effort to fully grasp the sweep of it. I found myself returning to sections several times to work it all out.

Feynman himself admits that he struggled to follow Newton's original arguments, since Newton approached the problem using obscure properties and theorems of conic sections that are not often used in contemporary mathematics. Undaunted, Feynman successfully developed his own solution to several parts of the proof, simultaneously demonstrating his own creative brilliance, as well as that of Isaac Newton. There are modern solutions to the planetary motion problem that are far easier to construct using higher-order mathematics. But it is Feynman's determination to re-create Newton's proof using only geometric concepts that makes the entire story compelling - and such a fitting glimpse into the inner workings of a legendary modern-day physicist.

The detailed proof itself is accompanied by introductory chapters which describe the relevant history leading up to Newton's great achievement, a brief and poignantly personal biography of Feynman and, finally, the complete transcript of his CalTech lecture - as reproduced on the companion CD.

It's not often we're privileged to witness one genius illuminating the pivotal work of another. So I consider myself lucky to have stumbled across this delightful book. Hats off to the Goodsteins for their personal commitment (and considerable effort) to bring this fascinating story to the rest of us.