Posted on September 18, 2012
by Jack Kelly

Tags: readings

I’ve got a bit of a weakness for pop-maths books: the first make keeps giving them to me, and I keep reading them. At their most rigorous, they’ll have a sketch of a proof sketch and the rest of it is more about the mathematicians or intuitive understanding of the results. The latest book I’ve read in this vein is Alex Bellos’ Alex’s Adventures in Numberland, and it’s a decent one. Not great, but decent. (Normally I prefer to link to the author’s site, but in this case I’m getting warnings of malware coming from a .ru site, so it’s just an Amazon link.)

Bellos start with a discussion about numbers and the words used for them, starting that off with an anthropologist’s research into how isolated tribes perceive quantities and handle the concept of number. From there he wanders through a number of fields such as geometry, number theory, topology, puzzles and number systems. There’s interesting trivia throughout: in some Japanese abacus clubs, they teach advanced students to calculate with a visualised abacus instead of a real one. The most advanced students can use this mental abacus to add up fifteen numbers flashed in sequence on a screen for 0.2 seconds each, while playing a word game.

The section on Vedic mathematics was something I hadn’t seen mentioned before: the idea that there are mathematical truths hidden in ancient Hindu holy books. It sounds a bit fishy to me, but there’s a presentation of a faster long multiplication method which is pretty neat, wherever it came from. Bellos seems to have taken the “mystic mathematics” a bit far, and often goes on a bit of a quasi-mystic ramble near the end of a chapter. The results are interesting enough on their own, and don’t need embellishment.

The section on puzzles is a lot of fun and the tribute to Martin Gardner is heartwarming. There’s a section on calculating machines, covering everything from slide rules to the Chudnovsky’s home-made supercomputer, with a stop for the Curta, a hand-held mechanical calculator that produces results when you crank the handle. The section on crocheted approximations to hyperbolic surfaces is also quite cool, especially as it’s a hard area to set up useful intuitions. Overall, there’s a fair amount of interesting stuff in the book but it’s a little bit padded out.