BOOK REVIEW

# Newton's Rational Mechanics

*Newton's Gift: How Sir Isaac Newton Unlocked the System of the World*. David Berlinski. xviii + 217 pp. The Free Press, 2000. $24.

In his new book on Sir Isaac Newton, David Berlinski writes that "In creating the science of rational mechanics, Newton determined the goals of mathematical physics as well as its methods. A subject that had been a tale became a quest." The subject was, in Newton's words, the System of the World.

By the time Newton was born, Kepler had provided in his three laws fairly accurate descriptions of the motions of the planets, and Galileo had effectively explained how material bodies moved near the surface of the Earth. Newton's great idea was that these descriptions?indeed, all descriptions of the various parts of the physical world?follow from universal principles through logic and mathematics. He articulated these principles and created the mathematics from which the descriptions of Kepler and Galileo could be deduced; all this and much more is contained in his *Mathematical Principles of Natural Philosophy*, known universally as the *Principia*.

As astonishing as this accomplishment is, the gift of Newton is in the very conception of a deductive science. "By showing that a mathematical investigation of the physical world was possible," Berlinski observes, "he made that investigation inevitable." The remarkably complete system of the world laid out by Newton in the* Principia *most importantly has provided the framework and methodology for continued investigation into the physical world for the three centuries since Newton. This is the quest, and gift, to which Berlinski refers.

This book is about the nature and meaning of Newton's investigations leading up to the *Principia*, and how he came to undertake them. Although Newton was 44 years old when he wrote the first version of the *Principia*, the genesis of his principal ideas, both mathematical and physical, took place in a two-year period when he was in his twenties. The first third of *Newton's Gift* discusses the development of his ideas during this period. The great leaps of understanding he achieved in this relatively short time seem unfathomable, particularly given that he left little in the way of a record of his thoughts. Nevertheless, Berlinski does a masterful job of providing a plausible scenario for the development of these ideas and methods.

The architecture of Newton's physics is laid out here clearly and sharply: The three Laws of Motion, the Law of Universal Gravitation and the existence of absolute space and time are central. Newton's refutation of the idea of centrifugal force in favor of forces of attraction that continually curve the planet in motion toward the Sun is explained. The reader is also made to understand how Newton's deep belief in a rational Creator naturally led him to reject the relativity implied by the Third Law of Motion and to postulate absolute space and time.

Berlinski does less well in actually explaining these ideas. The text is engrossing and perceptive in its discussions of Newton's way through the science but is hyperactive to the point of distraction in its elaboration of that science. For example, in Chapter 9, Berlinski quite correctly tells us that to best understand Newton's ideas, it is necessary for us to think in terms of vectors. However, the thread of this argument is obscured by Berlinski's florid linguistic embellishments in explaining Newton's development of vectors.

However, this is a minor criticism. Given the thesis of this book, what is important is the structure of Newton's rational mechanics, not the details of it, and Berlinski's exposition of that structure is excellent.*?Hugo Rossi, Mathematics, University of Utah
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