Flatterland (2001), by Ian Stewart, is the long-awaited sequel to Edwin Abbott’s Flatland (written in 1884!) — an imaginary story about two-dimensional beings living in a two-dimensional world. I’ve not read the original Flatland, but I have it on good authority that Flatterland is much better.

This book is essentially a mash-up of an easy-going children’s story with hard-core mathematical concepts that will stretch your mind. Flatland is a 2-dimensional world where females are lines with razor-sharp end-points; males are two-dimensional shapes; browsing the interline is always wireless because otherwise you’d be trapped inside a network of cables with no way to get out; meat comes mainly from oxagons – hexagons crossed with octagons; and books come as long lines rolled up into a spiral.

Vikki, a line from Flatland, is taken on a tour of different worlds by her guide, a space-hopper. On the way, they explore 3-dimensional space, 4-dimensional space, higher-dimensions, fractional dimensions, and more.

Although the story is fictional, the facts and concepts are most certainly not fictional. They explain the concepts of Hamming distance and error-detecting/error-correcting encodings in a way that is remarkably clearer than my university lectures on information theory! They visit topological worlds where doughnuts and two-holed doughnuts turn into teacups and teapots respectively. The milk comes from a one-sided cow named moobius, whose tail is joined to its nose with a twist; oh, and the milk is served in Klein bottles.

The book is full of incredibly witty puns, which are highly amusing for the scientifically-minded reader who has come across some of these mathematical concepts, and enjoys geeky jokes. One example: Moobius, the one-sided cow, has a loud marching band playing from within – this music cannot be stopped because that would be incredibly “orienting”, and besides, he is nothing without his “band”. (Geeky-pun explanation: A Möbius strip is a single-sided non-orientable two-dimensional surface embedded in three dimensions, and can be constructed by taking a band of paper and gluing its ends together with a twist.)

A non-technical reader can just ignore all the incredible puns and still enjoy the book, with all its challenging thought experiments and odd situations, written in an easy-to-read style.