Customer Reviews

Huygens & Barrow, Newton & Hooke

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Entertaining and opinionated survey of the history of the origins of mechanics, post-Galileo, Kepler and Descartes, by the greatest living theorist of classical mechanics. Arnol'd shows sympathy for Hooke and argues that Hooke, not Newton, should be given credit for the inverse square law of gravity. However, I find Newton's approach to be more convincing. Arnol'd praises Newton's geometric insight and reminds us that Leibnitz mechanized the rules of calculus so that (fortunately, I would say) it can be taught to idiots. Interesting and highly entertaining descriptions of the nonsense of the extreme formalization of simple mathematical problems (in the hands of the Bourbaki school of math, e.g.) can be found in the footnotes.

A note to students: classical mechanics, in most texts, is taught in totally unphysical postulational style, divorced from experiment/observation. This is an anachronism. If you ask the typical physics professor "What, exactly, is the origin of the inverse square law of gravity, how was it discovered?", then he/she will not be able to explain it. Textbooks, blindly present a postulatory exposition (bad physics!) and merely plug an assumed force law (where did it come from!?) into The Second Law and derive Kepler's orbits, but this is not an explanation how Newton arrived at "1/r^2" in the first place. Hooke's explanation can be found in the monograph reviewed here. Newton's original "inverse solution" can be found in my book "Classical Mechanics", where the connection of apples with the discovery of the law of gravity is also explained, following "Principia".

Having written all that, I strongly recommend this beautifully-written little monograph for both enlightenment and entertainment.

Chapter 1 is on the inverse square law of gravitation. The presentation is structured by the Newton-Hooke correspondence on experimental verification of the rotation of the earth, which provides impetus for the law while containing missteps that are fun to correct once the law is in place. Chapter 2 is a polemic account of the creation of the calculus if there ever was one: Newton understands everything better than anyone, while Leibniz is "clumsy" at best. Then Arnol'd loses his head in chapter 3: Huygens studied evolvents (involutes), but Arnol'd thinks that evolvents should be though of as discriminants of groups generated by reflections, so the study of quasicrystals is really "the completion of the research begun be Huygens". Chapter 4 is a hodgepodge of celestial mechanics fun-facts. Arnol'd is his usual provocative self again in chapter 5, arguing that the Principia contains "an astonishingly modern topological proof of a remarkable theorem on the transcendence of abelian integrals".