Skip to main content

Foolproof - Brian Hayes *****

The last time I enjoyed a popular maths book as much as this one was reading Martin Gardner’s Mathematical Puzzles and Diversions as a teenager. The trouble with a lot of ‘fun’ maths books is that they cover material that mathematicians consider fascinating, such as pairs of primes that are only two apart, which fail to raise much excitement in normal human beings. 

Here, all the articles have something a little more to them. So, even though Brian Hayes may be dealing with something fairly abstruse-sounding like the ratio of the volume of an n-dimensional hypersphere to the smallest hypercube that contains it, the article always has an interesting edge - in this case that although the ‘volume’ of the hypersphere grows up to the fifth dimension it gets smaller and smaller thereafter, becoming an almost undetectable part of the hypercube.

If that doesn’t grab you, many articles in this collection aren’t as abstruse, covering everything from random walks to a strange betting game. What's more, an extra delight for me is that Hayes throws in a lot of computing reflections, even including snippets of code as a way of explaining some processes. I particularly loved the exploration of pseudorandom and quasirandom numbers (not the same thing) and their implications for Monte Carlo methods.

The only times I felt Hayes loses it a bit is when he gets too heavily into research mode and gives us more detail than we need. For example, he digs into the origins of the story of the young Gauss adding up 1 to 100 almost instantaneously at school. His exploration of this mathematical legend is impressive, but he enumerates every possible source and route for the various versions of the legend to have originated, taking us to a level that feels unnecessarily complete. Similarly he lost me a bit when he tries to forensically examine why a Victorian mathematician who calculated pi to 707 places went wrong from the errors that he made in his calculations. But this kind of over-detailed analysis is rare.

I suspect the ideal reader is someone who has an aged physics, maths or computer science degree, who is still aware of (say) what Monte Carlo methods or eigenvalues are in a vague sense, but needs some gentle reminders. The essential, however, is to have a sense of wonder in discovery. For people like us it’s a brilliant book.


Hardback:  



Review by Brian Clegg

Comments

Popular posts from this blog

The Feed (SF) - Nick Clark Windo ****

Ever since The War of the Worlds, the post-apocalyptic disaster novel has been a firm fixture in the Science Fiction universe. What's more, such books are often among the few SF titles that are shown any interest by the literati, probably because many future disaster novels feature very little science. With a few exceptions, though (I'm thinking, for instance, The Chrysalids) they can make for pretty miserable reading unless you enjoy a diet of page after page of literary agonising.

The Feed is a real mixture. Large chunks of it are exactly that - page after page of self-examining misery with an occasional bit of action thrown in. But, there are parts where the writing really comes alive and shows its quality. This happens when we get the references back to pre-disaster, when we discover the Feed, which takes The Circle's premise to a whole new level with a mega-connected society where all human interaction is through directly-wired connections… until the whole thing fails …

The Bastard Legion (SF) - Gavin Smith *****

Science fiction has a long tradition of 'military in space' themes - and usually these books are uninspiring at best and verging on fascist at worst. From a serious SF viewpoint, it seemed that Joe Haldeman's magnificent The Forever War made the likes of Starship Troopers a mocked thing of the past, but sadly Hollywood seems to have rebooted the concept and we now see a lot of military SF on the shelves.

The bad news is that The Bastard Legion could not be classified as anything else - but the good news is that, just as Buffy the Vampire Slayer subverted the vampire genre, The Bastard Legion has so many twists on a straightforward 'marines in space' title that it does a brilliant job of subversion too.

The basic scenario is instantly different. Miska is heading up a mercenary legion, except they're all hardened criminals on a stolen prison ship, taking part because she has stolen the ship and fitted them all with explosive collars. Oh, and helping her train her &…

On the Moor - Richard Carter ****

There's much to enjoy in Richard Carter's pean to the frugal yet visceral delights of being one with England's Pennine moorland. If this were all there were to the book it would have made a good nature read, but Carter cleverly weaves in science at every opportunity, whether it's inspired by direct observations of birds and animals and plants - I confess I was ignorant of the peregrine falcon's 200 mile per hour dive - or spinning off from a trig point onto the geometric methods of surveying through history all the way up to GPS.

Carter is something of an expert on Darwin, and inevitably the great man comes into the story many times - yet his appearance never seems forced. It's hard to spend your time in a natural environment like this and not have Darwin repeatedly brought to mind.

I confess to a distinct love of these moors. Having spent my first 11 years in and around Littleborough, just the other side of Blackstone Edge from Carter's moor, the moorland…