The ways of the wave

From ocean waves and sound waves, to the “muscular waves” of human heartbeats and Mexican waves that sweep across a stadium, it is easy to see how this ubiquitous phenomenon grabbed the attention of author Gavin Pretor-Pinney. He decided to write The Wavewatcher’s Companion after spending an afternoon at the Cornish seaside with his daughter – although the prospect of a “research trip” to Hawaii may have helped, too, Pretor-Pinney admits. One of the most interesting wave narratives concerns the German scientist Hans Berger, who conducted the first ever electroencephalograph (EEG) test, apparently on his 15-year-old son, Klaus. Berger carried out further experiments on his daughter as she completed her homework, on toddlers and even on a dying dog; the last of these experiments allowed him to see the EEG trace flatline. As Pretor-Pinney wryly observes, Berger “was clearly unable to restrain himself from hooking up anyone he came across”. Other sections of the book deal with sonar, “nasty waves” such as shock waves and even “sexy waves” such as mating calls and husky human voices. Yet despite these attempts at organization – there are nine “wave types” in total, plus an introduction – the book’s individual sections lack distinct structure. The author’s attention seems to ebb and flow between largely unrelated phenomena, and while his prose is charming in places, a few of his attempts at humour seem tone-deaf. There is one particularly grating reference to “the type of broad who drinks, smokes, doesn’t hold back and is up for anything and everything” in the “sexy waves” chapter. Overall, The Wavewatcher’s Companion reads like the first draft of what could have been a really good book, and it is difficult to understand why it won the 2011 Royal Society Winton Prize for Science Books. While some readers might – like the Winton Prize judges – be inclined to “go with the flow”, it is certainly not for everyone.

• 2011 Bloomsbury £8.99pb 336pp

A real puzzler

Can you prove that there are at least two people in the city of Tokyo with the same number of hairs on their heads? What about demonstrating that if you take at least one aspirin a day (and 45 aspirin in total) during the month of April, there must be a stretch of consecutive days over which you take precisely 14 aspirin? Or maybe you would prefer to show that if you select 16 integers between 1 and 30, at least two of those integers must differ by exactly 3? All three puzzles are examples of the so-called pigeonhole principle in action, and if they appeal to you, then The Puzzler’s Dilemma will be your ticket to a pleasantly diverting afternoon. In this slim volume, mathematician and New York Times crossword setter Derrick Niederman leads readers through 11 classes of conundrum, offering sample problems and sketching out some of the general principles for solving them. The pigeonhole principle, for example, is discussed in a chapter on turning complex conundrums into simpler ones; other chapters explore such topics as probability theory, induction errors and puzzles that seem easy but are actually impossible. There is even a chapter devoted to “kangaroo puzzles”, where the statement of the puzzle contains a clue to the solution, like a joey in a mother kangaroo’s pouch. Kangaroos notwithstanding, Niederman’s prose certainly hops along nicely, making the book a fairly effortless read – unless, of course, you stop to solve the puzzles before he reveals their solutions.

• 2012 Duckworth Overlook £14.99hb 216pp

Analogy failure

Analogies are tricky things. A good one will only take you so far, and a bad one can be worse than useless. This lesson was brought home to your reviewer several years ago when, as an undergraduate, a classmate asked a mathematics lecturer to give the class a physically intuitive explanation of curl, ∇ × F. “That’s a tough one,” the lecturer replied. “Can you imagine an infinitely small paddle wheel spinning in the middle of a river?” Unfortunately, the class could not, and the lecturer never tried again. Authors Brian Cox and Jeff Forshaw are made of sterner stuff, however, and in their new book The Quantum Universe: Everything That Can Happen Does Happen they work much harder to bridge the gap between analogy and physics. After a promising start, though, they are soon off into infinitesimal paddle-wheel territory. In their analogy, quantum fields are replaced by an infinite array of clocks, in which the length (squared, of course) of the individual clock hands represents the probability that a particle will be found in a particular spot, and particles deposit additional clocks as they move from place to place. Sometimes, the clocks have to shrink in size for the maths to work out. This is scarcely simpler than the actual physics, and will confuse experts more than it reassures novices. Setting aside the clock analogy for a moment, though, the amount of mathematical detail is fairly high for a popularly oriented book, which should please those who felt that Cox’s Wonders series for BBC television lacked rigour. The authors are not afraid of the occasional equation, and the overall level is similar to that of Feynman’s QED: the Strange Theory of Light and Matter (a fact that Cox and Forshaw acknowledge in the “further reading” section at the end of the book). If you can get past the tortuous clock analogy, you will find the book a real treat. If not, well, there is always the option of watching Cox’s television documentaries instead.

• 2011 Allen Lane £20.00hb 256pp