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The Proof of the Packing books and arts more subtle and effective is needed. Overall, this book is a useful contribution to the literature, and one can hardly disagree with the conclusion that overfishing is “a pri- mary cause of ecosystem disruption”. It has some excellent images;in particular fig- ure 17 (shown overleaf), which is a graphic illustration of what it means to fish down the food web, and deserves to be widely repro- THE MARINERS’ MUSEUM/CORBIS duced. But I found the book’s structure awk- ward: it has no less than 30 pages of prefaces, and another 30 pages of endnotes, including some substantial discussions of important issues (such as whaling and international institutions),running to several pages each. Those who work in the field will find that the book is a bold attempt to create an ocean-wide overview that complements the more conventional stock-by-stock reductionist methods. General readers will find a broad, and in places passionate, account of the state of a whole ocean and its resources that is both accurate and infor- mative. One can only hope that it will help to motivate more strenuous and effective efforts to deal with the problems so clearly identified,which is,I am sure,what its authors intend. ■ John Shepherd is at the Southampton Oceanography Centre, Empress Dock, University of Southampton, Packing them in: cannon balls stored in a pyramid are stacked together as densely as possible. Southampton SO14 3ZH, UK. linear programming and Lord Kelvin’s soap- More on fisheries film problem. Handbook of Fish Biology and The proof of The book is a mixture of mathematics, Fisheries, Vols 1 and 2 history and anecdotes. In his research, the edited by Paul J. B. Hart & John D. Reynolds the packing author has found many good stories to retell. Blackwell, £130 Kepler’s Conjecture: How Some Even people familiar with the subject will of the Greatest Minds in History find new anecdotes here, and it seems that Helped Solve One of the Oldest most of them are more-or-less true, New in paperback Math Problems in the World although one might quibble with the details. by George G. Szpiro Did John Conway’s father really teach chem- I Have Landed Wiley: 2003. 304 pp. £18.50, $24.95, €24.95 istry to two of the Beatles? Well,sort of. Stephen Jay Gould Neil Sloane The tone of the remarks is sometimes Vintage, £7.99 derisive, which some readers may find The classical sphere-packing problem is to offensive rather than humorous. Young The Constants of Nature determine how densely a large number of Carl Friedrich Gauss is described as a “little by John Barrow identical spheres (such as ball-bearings) can squirt”, ‘wrangler’ is “one of those esoteric Vintage, £8.00 be packed together in a finite space. In 1611 blue-ribbon signs of esteem… reserved for “Barrow discusses the role of constants of the German astronomer Johannes Kepler British overachievers’’, and sheaf theory is a nature, the historical quest to understand stated that no packing could be denser than “major bore”. And after a rather harsh dis- them, the role of the anthropic principle as a that of the face-centred cubic (f.c.c.) lattice cussion of the attempts of the great Hungari- guiding philosophy and some recent evidence arrangement favoured by grocers for stack- an geometer László Fejes Tóth (his name is suggesting that some of the constants of ing oranges, which fills about 0.7405 of consistently misspelled in the book) to prove nature are probably not constants at all.” the available space. It took mathematicians the dodecahedral conjecture, Szpiro writes: Thanu Padmanabhan Nature 419, 780 (2002). some 400 years to prove him right. “One might come away from this chapter Kepler’s Conjecture gives an entertaining with the impression that Fejes-Tóth was The Borderlands of Science: Where Sense and readable account of the history of the a bumbling dreamer whose work mostly Meets Nonsense problem and the attempts to solve it, culmi- contained unfulfilled promises and unproven by Michael Shermer nating with Thomas Hales’ successful proof, hypotheses. This does not represent the Oxford University Press, £9.99 announced in 1998. George Szpiro also dis- whole picture.”Indeed not. cusses a large number of peripherally related The mathematical content is less satis- The Way of the Cell: Molecules, Organisms topics, including David Hilbert’s list of 23 factory than the historical part. As William and the Order of Life unsolved mathematical problems from 1900 Barlow described in Nature in 1883 (29, by Harold M. Franklin (Kepler’s conjecture is part of problem 18), 186–188),the f.c.c.packing can be built up by Oxford University Press, £12.95 the kissing-number problem (how many layers.Put down a layer of spheres arranged in balls can touch another ball of the same size), a triangular lattice — the arrangement used 126 © 2003 Nature Publishing Group NATURE | VOL 425 | 11 SEPTEMBER 2003 | www.nature.com/nature books and arts when racking billiard balls — and place globe”. However, the correct answer is not different, these books have much in com- another layer on top, and repeat. There are 400,000,000,but 5. mon. Both are insiders’ views of the subject, two ways to place subsequent layers. Viewed One can only admire Szpiro’s valiant both are highly original because the subject from above, there are three different posi- attempts to explain the different approaches matter is seen from the perspective of the tions for the centres of the spheres in any used by Richard Buckminster Fuller, Wu-Yi authors’ own research, and both include a one layer, say A, B and C. If the layers follow Hsiang and Hales in their attacks on the lot of autobiographical material. the order A, B, C, A, B, C, …, then the f.c.c. problem (although the serious reader would Few scientists are capable of putting their packing is obtained. If they follow the order do better to read Hales’ own descriptions). understanding and experiences into words A,B,A,B,A,B,…,then an equally dense pack- Szpiro’s discussion of the arguments as effectively as these two, so publishers have ing known as the hexagonal close packing between the protagonists is certainly enter- instead enlisted professional writers to look (h.c.p.) is obtained. taining. He illustrates them with a quotation at the subject from the outside. A science Kepler’s conjecture is that there are no from Henry Kissinger, who “was once journalist may not have as deep an under- packings that are denser than the f.c.c. or the asked why departmental fights are so violent, standing of the technicalities as a research h.c.p. packings (or any one of the infinite why back-stabbing is so common among scientist, but may be more experienced at number of different packings obtained by academic colleagues. His answer was short writing for the general public and conse- varying the order of the layers).The f.c.c.and and to the point: ‘Because the stakes are so quently better at getting the basic ideas h.c.p. packings have the same density, but small’.” Typically, not quite relevant, but a across.Particularly successful examples of this they are different: one is a lattice, the other is good story. genre are The Whole Shebang by Timothy not. Spiro claims that the f.c.c. and the h.c.p. As long as readers skip over the tech- Ferris (Weidenfeld & Nicolson/Simon & are “the exact same packing, viewed from nical sections,the book can be recommend- Schuster, 1997) and, more recently, Bill different angles’’.They are not. ed as a readable and informative account Bryson’s A Short History of Nearly Everything Another distraction in the mathematical of a fascinating chapter in the history of (reviewed in Nature 424, 725; 2003), which discussions (which fortunately are set in a geometry. both demonstrate that winners need not different typeface, so they can — and should Neil Sloane is at the AT&T Shannon Laboratory, necessarily be on the inside track. Sadly, — be skipped by the casual reader) is the 180 Park Avenue, Florham Park, New Jersey Alpha and Omega by Charles Seife is not author’s misuse of the word ‘surface’.Several 07932-0971, USA. among the medal positions. times he writes of the surface of an object, The book starts promisingly enough, if when he means its area,or even its volume. you can forgive the pseudo-religious over- One of the oldest theorems about sphere tones of the title (a reference to the Book packing was proved by Gauss in 1831, when of Revelations). The suggested emphasis on he showed that the f.c.c. is the densest lattice The rise and fall both the beginning and the end seems a good packing of spheres.Szpiro attempts to repro- idea,as there are many books about the birth duce Gauss’s proof, but makes a mess of it. of the Universe of the Universe but relatively few about its For example, on page 255 the determinant Alpha and Omega: The Search for death. Unfortunately, despite the claims needs to be negated, and denoted by a new the Beginning and the End of the made on the jacket, this theme isn’t really ǵ symbol, , say. Then six occurrences of the Universe taken up by the book itself, except for a few letter D on that page need to be changed to ǵ. by Charles Seife comments in the final chapter. Similar repairs are needed on the next page.
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