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罢颈尘辞迟丑测听搁别惫别濒濒

EVER wondered about the best angle from which to view Nelson鈥檚 column? To work out the answer, you will need a whit of logic and some basic calculus. Don鈥檛 panic if your mathematical muscles appear to have withered away (or you never truly cracked differentiation), David Acheson鈥檚 The Calculus Story could be just the thing.

For a book hardly bigger than a phablet, its size may trick you into thinking that it is some sort of pocket guide. Wrong. It is a roller-coaster read, constantly climbing and diving through the wonderful world of calculus.

There鈥檚 something for everyone, from the inexperienced integrator to seasoned solver of equations. Before the end of page 11, Acheson has already proven Pythagoras鈥檚 theorem and shown how Iranian scholar Al-Biruni approximated the radius of Earth in 1019 to within 1 per cent of today鈥檚 best measurements. A few pages later we learn how an infinite sum like 1/4 + 1/4² +1/4³ +鈥� can have a finite total. Add up all the terms and you get 1/3. Take that, Zeno!

Acheson sets the book鈥檚 trajectory on a steep gradient to calculus: if you鈥檙e not already hooked, luckily explaining the old-school favourites of differentiation and integration soon reveals how to get the most out of a trip to Trafalgar Square.

His enthusiasm for calculus is almost palpable. And while merely teaching the reader the tools of the trade would be an admirable goal in itself, Acheson is far more ambitious 鈥� he wants you to appreciate just how useful calculus is.

Understanding how the planets move, guitar strings vibrate and planes fly depends on a knowledge of calculus. Acheson even touches on quantum mechanics and chaos theory, as well as who gets the most crust when cutting equal-width slices from a spherical loaf of bread. (Answer: everyone!)

This book is small enough to fit in the old Christmas stocking, but the ideas are big enough to melt your mind. And if this isn鈥檛 the time of year for mind-melting mathematics, when is?

Simon Ings

PUBLIC buildings embody the scientific fashions and values of their day. In 1834, two years after the Great Reform Act was passed, the old Palace of Westminster burned down, and Britain needed a new parliament building to convey continuity and modernity, as well as science and sentiment.

The building was to be 鈥渁 powerful machine, of nicest force,鈥� according to the utilitarian writer Arthur Symonds, 鈥渁djusted to a thousand special functions, yet combining for the production of one grand general effect鈥�.

It didn鈥檛 quite work out that way. Chemical tests convinced the architect Charles Barry that magnesian limestone would be the best building material. Seven years later, with the stone showing signs of decay, Charles Dickens called it 鈥渢he worst ever used in the metropolis鈥�. David Boswell Reid used the new building as an experiment to study air chemistry. MPs, alternately sweating and shivering in the 鈥渋mproved鈥� building, were inclined to agree with The Times鈥榮 comment about such specialists that there was 鈥渘ot upon the face of the civilised earth a more impracticable set of people than the savans鈥�.

There was even a mordant note sounded over George Biddell Airy鈥檚 great clock (a late addition to the project) when its iconic bell, Big Ben, cracked shortly after its recasting in 1858.

It鈥檚 easy to take cheap shots: Gillin, on the contrary, celebrates the moment experimental science discovered, in full public view, what it could and could not do.

Mary Halton

POPULAR science books often set out to tackle expansive themes, but the idea of wonder itself as a unifying topic is an unusual choice. This is the adventure that Caspar Henderson leads readers on in A New Map of Wonders, a veritable canter through biology, psychology, cartography and physics, and a quick brush with astronomy.

Dividing his exploration into seven 鈥渨onders鈥�, Henderson also peers through unusual lenses. For example, he explores the complexity of life through snowflake patterns, and our understanding of geography via the star maps of Australia鈥檚 Yolngu people. The range of chapters is wide, with those devoted to relatively tidier subjects, such as the heart, giving way to messier concepts like light.

Matched with a tone that wanders from barraging readers with facts to wryly suggesting they look up online videos of animal mating rituals, Map of Wonders is the kind of reading characteristic of a winter holiday. This kind of writing occupies the hinterland between personal essay and popular science, and readers may warm to it more readily if it is about topics that already interest them.

Henderson鈥檚 own sense of wonder at phenomena both natural and manufactured is pervasive, from marvelling at a murmuration of starlings to admiring advances in solar power. Wonder, we then conclude, is a very personal experience, while scientific fact is often presented as a very universal one.

The book is peppered with quotes in the margins. Designed to be evocative rather than explanatory, at times this can make for a true marriage of the poetic and the analytical.

鈥淗enderson has a refreshing optimism about humanity鈥檚 potential that other authors lack鈥�

The book really hits its stride, though, in chapters like 鈥淔uture Wonders鈥�, where the possibilities of energy technology and astronomy show that, although the scope of human knowledge is already astounding, the vastness of what we have yet to understand verges on the overwhelming.

Henderson鈥檚 approach fares best where questions remain unanswered. He has a refreshing optimism about humanity鈥檚 potential that other authors, perhaps more cautious, lack. This is coupled with a concern for the moral consequences, rather than simply the capabilities, of human ingenuity. Where, he asks, will future wonder lead us? And should we follow?

Liz Else

I HAVE often wondered what would happen (in detail, that is) if the cable broke and the lift I was in hurtled to the ground. Cody Cassidy and Paul Doherty have taken a cool-headed look at this and other disasters: what happens if you lose your head, or stow away on the next moon mission are also good fodder for your inner catastrophile.

Back in the lift. Free-falling from 170 storeys, the authors say you hit ground at 305 kilometres an hour. With luck, the lift fits the shaft snugly, so air trapped below it cushions the fall. But not enough to really reduce g-forces: around 40 g over a few seconds appears to be the survivable limit.

My plan was to jump up and down. That knocks a fraction off but only if you are in the air at impact. If not, your organs 鈥渂reak from their arterial moorings鈥�. Enough. I鈥檓 taking the stairs.

Liz Else

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CHARLES DARWIN was not one for memorable sound bites. Even the one for which he is best known, about the survival of the fittest, was coined by Herbert Spencer, his contemporary, a philosopher and a biologist.

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That could have been a bit of a headache for the author of a book called The Quotable Darwin. But no. This book works because his own words paint an unexpectedly complete and truthful picture of the man (brilliance, wit, sickness), his times 鈥� and limitations.

Try these: 鈥淗e who understand baboon would do more towards metaphysics than Locke鈥�, and (on marriage) 鈥淥nly picture to yourself a nice soft wife on a sofa鈥︹��

This article appeared in print under the headline 鈥淭he gift of reading鈥�