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Einstein Year 2005

Measurement is a tricky business, and rarely leaves the thing measured unchanged, as Heisenberg's Uncertainty Principle states at the quantum level. But statistician David Hand has gone back to the foundations, examining measurement right across the various disciplines: psychology, medicine, physical sciences, economics, the social sciences and elsewhere. He must treat in a unified manner scales used to measure phenomena as different as pain, retail prices and magnetism.

This charming book is in its second edition (the first was published in 1994). It is about integers, with a short section for each number between 1 and 200, and a line for each between 201 and 999. There are "boxes" for interesting facts and definitions, such as "perfect number", and a few "large numbers" also make the cut, including 1729, the subject of a famous anecdote about Hardy and Ramanujan, and 10¹⁰⁰⁰, the googol.

Jose Munoz explains how engineering can allow you to explore the unknown, from understanding how mechanical structures bend to investigating the way genes affect the shape of embryos.

Did you know that you can't average averages? Or that Paris is rainier than London ... but it rains more in London than in Paris? Andrew Stickland explores the dangers that face the unwary when using a single number to summarise complex data.

Many people find no beauty and pleasure in maths - but, as Lewis Dartnell explains, our brains have evolved to take pleasure in rhythm, structure and pattern. Since these topics are fundamentally mathematical, it should be no surprise that mathematical methods can illuminate our aesthetic sense.

Mathematician and physicist John Baez declares himself fascinated by exceptions in mathematics. This interest has led him to study the octonions, and, through them, to find out more about the origins of complex numbers and quaternions. In the second of two articles, he talks about the characters of the different dimensions, beauty and utility in mathematics, and just why he likes dimension 8 so much.