Holiday reading: Gorge on the mistakes of others

• Book information
• Brilliant Blunders by Mario Livio
• Published by: Simon & Schuster
• Price: ?18.99/$26

Enrico Fermi's fiasco: alpha male making an alpha mistake (Image: American Institute of Physics/SPL)

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HE IS known as one of the greatest physicists of the 20th century. A Nobel prizewinner who coined the term "neutrino", Enrico Fermi's mind was so sharp, and his work so infallible, that colleagues called him "the pope".

Yet this reputation came back to bite him. Embarrassingly for Fermi, he was once photographed in front of a blackboard on which he had written several important equations relating to quantum mechanics (see picture), one of which ? the equation for alpha ? contained a mistake. Unfortunately for Fermi, it escaped the eyes of designers at the US post office, who used the photograph on a stamp to commemorate the 100th anniversary of his birth. The story, as well as the photograph, has gone down in history.

As Fermi showed, when it comes to human error even great scientists are far from immune. But whether you are doing theoretical physics or number crunching, it is painfully easy for the wrong digit to slip into a calculation. In Magnificent Mistakes in Mathematics, Alfred Posamentier and Ingmar Lehmann relate the story of William Shanks, a 19th-century British mathematician who spent 15 years calculating the value of pi to a record 707 places.

Shanks was long dead when, in 1946, an error was discovered in the 528th digit. Unfortunately that was too late for the owners of the Palais de la D?couverte in Paris, who had immortalised Shanks's number in large wooden digits on the domed ceiling of their building's cupola.

But for me it is the mathematical gaffes the rest of us are more likely to fall for that make Posamentier and Lehmann's book interesting. My favourites are the proofs that involve dividing by zero, leading to results such as 1=2.

Mario Livio takes a grander view of mistakes. In Brilliant Blunders, Livio uses the errors of great scientists as a prism through which to explore some of science's most important episodes. The result is a sideways look at some well-known stories. But it's hard not to stumble over Livio's criteria for blunders. One of the more significant early criticisms of Darwin's theory of evolution, for example, involved the idea of blended inheritance: that an advantageous characteristic would inevitably be diluted in the next generation, further diluted in the one beyond and so on, as in the mixing of paints.

According to Livio, Darwin blundered by failing to anticipate that the mechanism of natural selection simply does not work under this assumption. That seems harsh since Darwin had doubts over blended inheritance, and had already taken a huge theoretical leap in understanding heredity at the time.

Then there is Lord Kelvin, who calculated Earth's age by measuring the rate at which the planet is cooling and comparing this to the heat generated by the various chemical processes. Kelvin settled on the youthful figure of 98 million years old, because he was unaware of the heat that nuclear processes can generate. We now know the real figure is some 4.5 billion years. But characterising Kelvin's work as stupid or careless seems a blunder in itself given that his approach changed the way we think about our world and established geology as a mainstream science.

Livio is insightful in other ways, though, not least in showing that, however you wish to define it, fallibility exists in even great scientists and their work.

Oscar Wilde once wrote that "experience is the name everyone gives to their mistakes". These books remind us that these experiences can prove edifying and entertaining for others.

This article appeared in print under the headline "Mistakes worth taking"

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