Flatterland - Ian Stewart ***

Ian Stewart's Flatterland has been around since 2001, but I've only just come across it. It is, of course a sequel to the famous novella Flatland by Edwin Abbott Abbott dating back to 1884. The original Flatland is perhaps the archetype of a book that is based on a brilliant idea, but be distinctly dreary to read. So the key question here is whether Stewart escaped this limitation in his sequel.

We start here with the (literally, not metaphorically) two-dimensional characters familiar to anyone who has read Flatland. The original both explored the nature of existing in two dimensions (and how the inhabitants would see a three-dimensional object), and provided Victorian social commentary, with female Flatlanders both physically different to males (lines, rather than polygons) and limited in what they can do by society. Stewart only mentions the social side in passing, but instead focuses on mathematical experiences.

Guided by a space hopper (the 60s bouncy toy), the central character Victoria Line is taken out of Flatland to experience a wide range of different mathematical spaces. They start off with the conventional three-dimensional space Vicky's ancestor came across (the original book was supposedly written by A. Square, who Stewart tells us was Albert Square) but then go on to a whole range of different mathematical spaces, from fractal space to topological space, finishing off by straying into physics by bringing in Schrödinger's cat, Minkowski space and time travel via the special and general theories of relativity.

All the way through, Stewart seems to be trying to outdo Abbott's weak attempts at humour by piling on cultural references (we've seen a couple above) and resorting to often excruciating puns. This can be distinctly wearing for the reader, though there are occasional gems such as 'he was the black shape of the family'.

If you can cope with the barrage of irritating humour, some parts of the book work really well at introducing concepts such as topology - this section is based in part on the Mad Hatter's tea party in Alice's Adventures in Wonderland. In fact, Stewart clearly takes a significant lead from mathematician Lewis Carroll's approach, though unfortunately lacks Carroll's peak writing skills. This is more Sylvie and Bruno than Alice or Snark. Other parts of the book, though, fail to get the message across. We are dealing here with quite abstruse mathematical concepts and while the portrayal through various characters and their worlds make good use of those concepts in you already know them, they don't act as a useful introduction, leaving the reader potentially baffled.

Like the original Flatland, this is an interesting and innovative attempt. It has always seemed that fiction should be a good route to explain science or maths painlessly and entertainingly. But for me, the painful punning and the relentless jokiness was too much, while the exposition was often not clear enough to do the job. A for effort, though.

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Review by Brian Clegg