The art of limiting distortion

He had bought a large map representing the sea, Without the least vestige of land: And the crew were much pleased when they found it to be A map they could all understand. ‘What’s the good of Mercator’s North Poles and Equators, Tropics, Zones, and Meridian Lines?’ So the Bellman would cry: and the crew would reply, ‘They are merely conventional signs!’

As The Hunting of the Snark suggests, what gives rise to a map is an absurd logic best appreciated by a mathematician like Lewis Carroll. The problem that cartography seeks to solve is also the one that drove painters to experiment with perspective and cubism: how best to represent three dimensions on a two-dimensional surface. As Peter Barber’s sumptuously illustrated book reveals, map-makers have been trying different styles to cope with the problem at least since the Babylonians in 1500 BC, but each involves some distortion.

On a two-dimensional map, for example, it may appear that the shortest distance between London and New York is straight across the Atlantic — in navigational terms, a rhumb line — but in three-dimensional reality, as any air traveller quickly notices, the shortest route actually passes close to Greenland.