Calculated to inspire delight

No book with the wonderful opening sentence It is a truth universally acknowledged that a single man in possession of a good fortune must be in want of a wife can possibly fail. Though it is a very different work from its classic predecessor, this one should be no exception.

Its content may be characterised as lucid musing, a kind of free association, based on the numbers one to nine. Mathematics and theoretical physics are its main subjects, but it ranges widely through literature, music, philosophy, politics and whatever else occurs to its author, in a charmingly scholarly and entertaining way. The genre is popular writing about, and popularisation of, mathematics. But the author uses it to display a great range of interests: in mathematics from the very pure to the wholeheartedly applied; in physics from the mundane to the most modern and (to a non-physicist) far-fetched; in music from classical to pop.

A great strength of the book is its power to evoke vast numerical ranges. Physics, for example, deals with the unimaginably tiny numbers associated with quantum-mechanical constants that describe, on a scale developed from human experience, how subatomic particles behave; using that same scale it deals also with the astronomical numbers associated with cosmological theories. Thus the Planck length 10 33cm measures particles, one thousand million million million million million of which, if laid end to end, might just reach across one's fingernail, while the cosmological radius 1028cm is such that ten thousand million million million million fingernails laid side by side would be needed to stretch from here to the end of the world. The one number is 1061 times as large as the other, yet even this is tiny in comparison with some that mathematics can treat and which Andrew Hodges helps his readers find delightful ways to comprehend.

Einstein's famous equation E=mc2 relating energy to mass and the (enormous) speed of light is illustrated in several ways. For example, the dust settling every day in a 10sq m room, if converted to energy, would be comparable to that of the explosion of 1,000 tons of TNT or of an earth tremor measuring 4 on the Richter scale; measured in calories it would produce a thousand million of them, enough to feed 400,000 people or power a similar number of light bulbs for the day.

The book is evidence of the author's pride in learning and knowledge; not only his own, but that of the human race. It shows mastery of a huge range of intellectual endeavour. Whether the book can be read so as to transmit any of that learning from writer to reader is perhaps doubtful. There is so much here, and it is treated mostly - though with notable exceptions - at such an impressionistic level, that the reader is unlikely to be able to retain what he or she learns, or acquire that deep understanding which is what real knowledge is. But, although it is sprinkled with charming and well-judged exercises presented as challenges and rated (like sudoku, which is one of its many leitmotifs) easy, gentle, moderate, tricky, difficult or fiendish, the book was never written to be a textbook: it was written to be a joyous read.

And it is a joyous read - mostly. The exceptions are the passages, mercifully rare, where prejudice against school mathematics and, by implication, school teaching of mathematics, strikes a sadly discordant note. Those passages aside, the book can be strongly recommended to all who value C. P. Snow's "two cultures" and the myriad connections between them.

Peter M. Neumann is fellow and tutor, The Queen's College, Oxford.