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:

Using these links earns us commission at no cost to you

Review by Brian Clegg

Comments

The Decline and Fall of the Human Empire - Henry Gee ****

In his last book, Henry Gee impressed with his A (Very) Short History of Life on Earth - this time he zooms in on one very specific aspect of life on Earth - humans - and gives us not just a history, but a prediction of the future - our extinction. The book starts with an entertaining prologue, to an extent bemoaning our obsession with dinosaurs, a story that leads, inexorably towards extinction. This is a fate, Gee points out, that will occur for every species, including our own. We then cover three potential stages of the rise and fall of humanity (the book's title is purposely modelled on Gibbon) - Rise, Fall and Escape. Gee's speciality is palaeontology and in the first section he takes us back to explore as much as we can know from the extremely patchy fossil record of the origins of the human family, the genus Homo and the eventual dominance of Homo sapiens , pushing out any remaining members of other closely related species. As we move onto the Fall section, Gee gives ...

Pagans (SF) - James Alistair Henry *****

There's a fascinating sub-genre of science fiction known as alternate history. The idea is that at some point in the past, history diverged from reality, resulting in a different present. Perhaps the most acclaimed of these books is Kingsley Amis's The Alteration , set in a modern England where there had not been a reformation - but James Alistair Henry arguably does even better by giving us a present where Britain is a third world country, still divided between Celts in the west and Saxons in the East. Neither the Normans nor Christianity have any significant impact. In itself this is a clever idea, but what makes it absolutely excellent is mixing in a police procedural murder mystery, where the investigation is being undertaken by a Celtic DI, Drustan, who has to work in London alongside Aedith, a Saxon reeve of equivalent rank, who also happens to be daughter of the Earl of Mercia. While you could argue about a few historical aspects, it's effectively done and has a plot...

Amazing Worlds of Science Fiction and Science Fact: Keith Cooper ****

There's something appealing (for a reader like me) about a book that brings together science fiction and science fact. I had assumed that the 'Amazing Worlds' part of the title suggested a general overview of the interaction between the two, but Keith Cooper is being literal. This is an examination of exoplanets (planets that orbit a different star to the Sun) as pictured in science fiction and in our best current science, bearing in mind this is a field that is still in the early phases of development. It becomes obvious early on that Cooper, who is a science journalist in his day job, knows his stuff on the fiction side as well as the current science. Of course he brings in the well-known TV and movie tropes (we get a huge amount on Star Trek ), not to mention the likes of Dune, but his coverage of written science fiction goes into much wider picture. He also has consulted some well-known contemporary SF writers such as Alastair Reynolds and Paul McAuley, not just scient...

Search This Blog