杏吧原创

THE long-awaited study of Isaac Newton鈥檚 Principia by the 1983 Nobel prizewinner Subrahmanyan Chandrasekhar was published in early June. While in many ways magnificent, the work, given its overall intent, is sadly flawed.

A stunning jacket turns Chandrasekhar鈥檚 labour of love into a work of art. Inside, 24 chapters are devoted to rederiving 150 propositions used in Newton鈥檚 discovery of the law of gravity and its many consequences, while the final four chapters address other topics.

For the main part, Chandrasekhar wields his mighty analytical skills 鈥� as who else can? 鈥� to trace again the path to our first understanding of the gravitating Universe. His book is not for the mathematically faint-hearted 鈥� it will hardly sell like hot cakes on the railway newsstands. Those equipped to follow the truly superb modern derivations would still do well to pause and marvel, with Chandrasekhar, at the beauty, clarity and breathtaking economy of Newton鈥檚 own methods.

Chandrasekhar describes how he read the statements of the propositions, produced his own independent proofs, and then 鈥渃arefully follow[ed] Newton鈥檚 own demonstrations鈥�. His own proofs often precede his account of Newton鈥檚, the latter presented 鈥渨ithout the encumbrances of style and language of the original鈥�.

There is, however, a danger inherent in this method. Newton must be read with exceptional care. Particularly at the foundational level, the most important points are easily missed because they are often contained in unemphasised corollaries, rather than in the leading statements of lemmas or propositions; a mind in the thrall of its own proofs may even fail to recognise the key issues. Unfortunately, Chandrasekhar misunderstands some of Newton鈥檚 basic tools as well as some fairly elementary matters more accessible to 鈥渢he common reader鈥�.

This is not the place for technical accounts, but one elementary example from the penultimate page typifies the problems of translating and unravelling Newton鈥檚 meaning even in a simple context. Drawing on the Principia鈥檚 first edition, Chandrasekhar tells us that an 8-inch pendulum has a period of 鈥�28戮 min鈥�. There are three errors here: the length should be 9 inches, it鈥檚 a half-period (Newton鈥檚 usual convention), and it鈥檚 28戮 sixtieths of a second. The third mistake is quite instructive. The complete Latin phrase is minutorum tertiorum; despite its seductive look to our modern eyes, the term minutum is not 鈥渁 minute鈥� but rather 鈥渁 subdivision鈥�. The unit used by Newton is the third subdivision (of the hour), by 60 each time.

Nor does one have to wait till the end of the book to encounter such problems. There is a corresponding but more significant pair of gaffes on page 5, when Chandrasekhar tries to verify Newton鈥檚 original apparent mismatch of the Moon鈥檚 acceleration with the requirements of the inverse square law. While his superb modern mathematical derivations may be unexcelled, it is sad to see this tiger, who has burned so bright, frame his otherwise mighty work in such flawed symmetry.