What Is Cartography? Every Map Is an Argument

A sphere cannot be flattened without distortion, a result Gauss proved formally in 1827 and which means there is no correct projection, only projections that preserve different things. A conformal projection preserves local angles and shapes, which is what Mercator does, at the cost of grossly inflating area away from the equator, so Greenland appears comparable to Africa while being about a fourteenth of its size. An equal-area projection preserves area and distorts shape, which is what Gall-Peters, Mollweide and Equal Earth do. Equidistant projections preserve distance from a point or along particular lines. Compromise projections such as Robinson and Winkel Tripel distort everything slightly rather than anything badly, which is why atlases favour them for world maps. The right choice follows from the purpose: Mercator persists in web mapping because it is conformal, so shapes and angles are locally correct at any zoom, which is exactly what someone navigating a street wants, and it is a poor choice for comparing the sizes of countries.

Reducing the world to a readable sheet requires systematic simplification, and the operations have names because they are done deliberately:

• •Selection, deciding which features appear at all, which at small scales means most do not
• •Simplification, removing detail from lines so a coastline drawn with a million points becomes one drawn with a thousand without changing its character
• •Smoothing, removing minor irregularities
• •Aggregation, merging several small features into one, such as a cluster of buildings becoming an urban area
• •Displacement, moving features apart so symbols do not overlap, which is why a road, a river and a railway in a narrow valley are shown further apart on a map than they are on the ground
• •Exaggeration, drawing a feature larger than scale because it matters, which is why a road on a national map might represent a corridor a kilometre wide

Cartographic design has a body of theory about how marks convey meaning, much of it systematised by Jacques Bertin in 1967 as the visual variables: position, size, shape, value, colour hue, orientation and texture. Each suits different data, and the mismatches are the commonest errors on published maps. Size and value convey ordered quantities well, hue conveys categories but not order, so using a rainbow scale for a continuous quantity forces the reader to consult a legend constantly and hides patterns. A choropleth map, shading administrative areas by a value, must use a rate rather than a raw count, because otherwise it simply shows where the population is, and its appearance can be altered substantially by choosing different class breaks for the same data. Visual hierarchy determines what the eye reaches first, and a map that gives equal weight to everything communicates nothing. Typography carries information too, with conventions for italic labels on water features and letter spacing indicating extent.

Because every map selects and emphasises, it can persuade, and the history of cartography is full of maps made to do exactly that. Colonial maps rendered inhabited territory empty in order to present it as available. Boundary depiction remains actively contested, and mapping companies produce different editions for different countries showing disputed regions differently, because publishing a single version would be illegal in one market or another. Projections have been promoted for political reasons on both sides, with the Peters projection marketed in the 1970s as a corrective to Eurocentrism using an equal-area construction that had existed since 1855, prompting an unusually heated professional dispute. More prosaic distortions are everywhere: the election map shaded by area rather than population, the scale chosen so a trend appears steep, the omitted category. The cartographer Mark Monmonier's argument in How to Lie with Maps is not that maps are untrustworthy but that distortion is intrinsic, so the reader's defence is knowing what was chosen and why.

Cartography is the practice of deciding what a map shows and how, since a curved earth cannot be flattened without distortion and no projection preserves shape, area and distance at once. Mercator preserves local shape and badly inflates high-latitude area, which suits navigation and misleads size comparison. Readability requires deliberate generalisation, including selecting, simplifying, merging, displacing and exaggerating features. Because selection is unavoidable, maps argue, and reading one well means knowing what was left out.