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.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!’
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. This is a Great Circle, a circumference of the earth, and as shown on a globe it runs straight while rhumb lines curve. To flatten out the reality of the world inevitably distorts the proportion and size of its oceans and continents. Limiting this distortion is the map-maker’s art.
Both Mark Monmonnier and Andrew Taylor focus on the Rembrandt of cartography, Gerard Mercator, whose projection of the globe provided our most vivid images of what the earth looks like until pictures of it arrived from space. Since Taylor concentrates upon the man, and Monmonnier upon the cartography, they complement one another well, though individually each would have been the better for borrowing some of the other’s expertise.
Born near Antwerp in 1512, Mercator practised his craft during the desperate struggle of the Netherlands to escape the rule of imperial Spain. The danger was made explicit when he was suspected of Protestant sympathies in 1544 and imprisoned by the Inquis- ition, but the opportunities were equally great. He had the benefit of Flemish expertise in three crucial areas — mathematics (he was taught by Gemma Frisius, inventor of the modern method of surveying), technology (his home town of Louvain was a printing hothouse), and merchandising (Abraham Ortellius, successful publisher of the world’s first atlas, was his friend). Indeed religious strife fuelled the demand for maps, as Prot- estant and Catholic rulers struggled to establish the extent of their possessions both at home and, increasingly, across the Atlantic.
The projection first appeared in Mercator’s 1569 world map, and consisted of a grid made from vertical lines of longitude cutting across horizontal lines of latitude, precisely the conventions that so annoyed Carroll’s Snark-hunting crew. On a globe, lines of longitude converge as they approach the poles — at 60 degrees north, the distance between them is exactly half that at the equator — but on Mercator’s map they ran parallel. To compensate for this horizontal distortion, the grid was stretched vertically as it neared the North and South Poles by exactly the same proportion. For mariners who sailed by compass directions, the projection had the overwhelming advantage of allowing the rhumb lines to run straight, hugely simplifying navigation, but what made it an icon for the next four centuries was that it enabled everyone else to see at a glance the shape of lands and oceans around the world.
Taylor’s biography is readable and presents the historical context lucidly, but by limiting his scope to the life he misses the huge cultural impact of Mercator’s grid. Most people over the age of 50, for example, derived their fundamental idea of the British empire from Mercator-derived maps, and thus failed to appreciate India’s central importance because it appeared so small in relation to temperate zone countries like Canada and Australia. That was the cost of Mercator’s system — at 60 degrees north, seas and islands were stretched to twice their real width and height, so that Greenland appears as equal in size to South America although it covers one eighth the area.
Monmonnier does explore these consequences, unfortunately in waffling academic prose, but fails to appreciate that every map has some other end beyond accuracy. Thus he excoriates Arno Peters’ 1970s projection which tried unscientifically to redress the balance by stretching the tropics north and south, instead of examining why it was so popular. By contrast, The Map Book devotes itself entirely to the aesthetic pleasures of map-gazing without regard for accurate representation. Every one of its 160 illustrations, from an austere, eighth-century, Arab-influenced view of the Mediterranean to Harry Beck’s famous 1933 diagram of the London Underground, offers a combination of sensual delight and cultural insight that cannot be recommended too highly. It is proof of what every Snark-hunter knows, that all maps are as much art as science, and their appearance simply a convention that suits the times.
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