Between the lines

No more discoveries

A century ago, the fastest human on the planet could run 100 m in 10.6 s. Since then, times have dropped steadily – the current record is 9.58 s – but at some point, athletes must surely approach a fundamental limit, and progress will then slow to a halt. There is, after all, only so much that human bone and muscle can do. But are human brains fundamentally limited as well? And if they are, does that mean there are problems in science that are not only unsolved, but insoluble? In The End of Discovery, Open University physicist Russell Stannard answers both questions with a cautious “yes”. Although he does not claim that the age of significant discoveries has finished entirely, he does suggest that we may never know the answers to a couple of dozen current problems, from the existence of other universes to the validity of string theory. It is an intriguing premise for a book. However, after a brisk and promising start with consciousness and cosmology, it quickly lapses into extremely well-trodden territory – driven, we suspect, by the need to cater for readers who have never heard of quarks or Schrödinger’s cat. It is presumably those readers that Stannard has in mind when he spends 40 pages on Young’s double-slit experiment, wave–particle duality and the like before introducing the (interesting to physicists, and quite possibly insoluble) measurement problem in quantum mechanics. Still, Stannard does raise some interesting philosophical questions. “Suppose…that there were no triangles – no physical triangles because there was no physical world,” he writes in a chapter on the laws of nature. “Would there still be such a thing as Pythagoras’s theorem?”

• 2010 Oxford University Press £14.99/$24.95 hb 224pp

Consider a spherical piano…

Physicists like simplified models. Indeed, we like them so much that we sometimes forget the advice of Einstein, who observed that “everything should be made as simple as possible, but no simpler”. Yet when faced with a complex object such as a vibrating piano soundboard – a complete description of which requires 27 different elastic constants – is it any wonder that physicists seek solace in an ideal world of spherical cows and infinite, massless piano wires? In Physics of the Piano, Purdue University physicist Nicholas Giordano steers a middle course between the messy world of artisan piano-makers and the tidy one of simplifying physicists. His description of a piano hammer striking a string, for example, begins with the physics of an instantaneous elastic collision between a uniform hammer and an ideal string. In later sections, he peels away each of these assumptions, and examines the very different physics of what happens when real hammers of different weight and composition meet springy, massive strings. A similar de-simplifying process occurs when Giordano describes the sound produced in such collisions. The frequency spectra produced by single notes on a piano (and reproduced as graphs in the book) turn out to be nothing like the idealized single-frequency spikes found in many introductory physics books. Indeed, the spectrum of a piano’s lowest note, A0, contains almost no components at its “fundamental” frequency of 27.5 Hz. The fact that we still perceive this note as A0 despite the “missing fundamental” has attracted the attention of physicists (including Ohm and Helmholtz) for almost two centuries. All fascinating stuff, but be warned: aside from a few sections on the history of the piano, Physics of the Piano is not a quick or easy read. Rather, it is an excellent book for musicians and physicists who are serious about learning more about how real pianos work, and who are willing to engage with all the messy details that this requires.

• 2010 Oxford University Press £35.00/$59.95 hb 184pp

Little book, big ideas

String theory has a reputation for being complicated and confusing. But if the material in Stephen Gubser’s The Little Book of String Theory is any indication, the situation is not as bad as we thought – it is much, much worse. In fairness, this probably says as much about the current state of the field as it does about the author’s explanatory powers. As Gubser frequently acknowledges, string theory really needs a third “revolution” to bring new insights – and perhaps a bit of order – to the current chaos, in which dimensions, branes, dualities and even competing versions of string theory proliferate with abandon. But even in the introductory chapters, its explanations are often frustratingly incomplete. At one point, for example, Gubser implies that the temperature of a black hole is inversely related to its mass, but he does not give any physical reason for why this is the case. The problem worsens after the fifth chapter, when the difficulty of the material increases sharply. Like most writers of popular-science books, Gubser papers over the complexities of his subject by substituting analogies for formal mathematics. This is usually no bad thing: a good analogy can be worth 50 equations, especially for readers who need to have the metric system and exponential notation explained to them (as Gubser does in the first chapter). But while some of the author’s analogies are memorably vivid, they are seldom very informative. In one particularly baffling example, we are told that the S-duality in string theory relates one type of string or brane to another, and that this is like Fred Astaire dancing with a slimy alien. The connection, apparently, is that string-theory dualities relate things we understand well (Fred) with things we do not (slimy aliens). Enlightened? No, neither were we. On this evidence, string theorists have a lot of work to do before their theories can again be described as “elegant”.

• 2010 Princeton University Press £13.95/$19.95 hb 184pp