### Alex's Adventures in Numberland

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.