1089 and All That by David Acheson, Oxford University Press, 拢12.99, ISBN 0198516231 The Curvature of Spacetime: Newton, Einstein and gravitation by Harald Fritzsch, Columbia University Press, 拢20/$29.95, ISBN 0231118201 Reviewed by Ian Stewart
ONE of the happier effects of the explosion in popular science books is that every so often an author presents scientific ideas in a new way. These books exemplify two of them: the snappy illustrated miscellany, and the dramatic dialogue.
1089 and All That is one of those small, quirky illustrated books that often arrive a few months before Christmas. It aims to inform as well as amuse, and manages to do both with good humour and much sense. The title refers to a party piece that goes like this. Take any three-digit number whose first and last digits differ by 2 or more. Reverse it, and subtract the smaller number from the bigger. Add the result to its own reversal. The answer will be 1089, always.
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Starting from such minimalist material, David Acheson works his way up to chaos and catastrophe. Not a page passes without at least one intriguing insight. Even the 1089 trick is used later to justify the importance of algebra, and the necessity for proof is made crystal clear. This is a clever book, and anything but trivial. Anyone who is baffled by mathematics should buy it. And all mathematicians should buy at least a dozen copies to hand out to people they meet at parties. My enthusiasm for it knows no bounds.
I鈥檓 more ambivalent about The Curvature of Spacetime, which is a sequel to An Equation That Changed the World. The first book was about special relativity, whereas this one goes on to discuss general relativity. Both take the form of imaginary conversations between Albert Einstein, Isaac Newton and a fictitious Swiss physicist. The dialogue approach permits informed discussion of different viewpoints, and here it leads the reader rapidly to grapple with the frontiers of today鈥檚 cosmology, with definite success.
But Newton gives in all too readily to Einstein, because the author loads the conversational dice. So when Einstein blandly announces that 90 per cent of the mass in the Universe is dark matter, Newton accepts this without demur. The context here is omega, the ratio of the mass of the Universe to the mass at which its expansion will just halt. Visible matter suggests that omega is about 0.1. If 90 per cent of the Universe is dark matter, omega rises to about 1, which is the point that Einstein makes. What he doesn鈥檛 tell us is that the main evidence for the 90 per cent figure is that it makes omega equal to
Newton does remark, 鈥淭hat is really unbelievable!鈥� He should have pressed harder. And the dialogue should have made more effort to fully convey the difficulties of current cosmology, as well as its triumphs. Well worth reading, anyway.