Why Is That Country Enormous on the Map? Area Is Showing Something Else

Shading countries or regions by a value is the usual way of mapping data, and it has a serious flaw, which is that the eye reads area as importance. A large sparsely populated region dominates the picture while a small dense one nearly disappears, so a map of votes, disease cases or wealth gives a visual impression driven by land area rather than by the quantity being shown. Resizing each territory so that its area is proportional to the quantity removes that problem directly, since the visual weight then matches the data by construction and a region with few people occupies little space.

Several approaches trade accuracy of shape against accuracy of area:

• •Continuous versions stretch and squeeze while keeping regions connected
• •Those preserve neighbours and topology at the cost of distorted shapes
• •Non-contiguous versions scale each region in place, leaving gaps between
• •Those keep shapes recognisable and lose the sense of a continuous surface
• •Grid versions replace each region with squares or hexagons
• •Dorling versions replace each region with a circle sized by the value

Resizing regions to exact areas while keeping them connected and recognisable is a genuinely difficult mathematical problem, since changing one region forces its neighbours to move and the constraints propagate everywhere. Early examples were made by hand over weeks. A method published in 2004 by Michael Gastner and Mark Newman treated the problem as physical diffusion, imagining the quantity as a density that flows outward until it is uniform and moving the boundaries along with that flow, which produces good results and is now widely used. A faster method published in 2018 by the same group made large datasets practical. Software implementing these is freely available, which is why the maps became common.

The technique is older than computing and several hand-drawn examples remain the best known. A German engineer produced maps in the 1930s resizing countries by population. An English geographer published a series in the 1970s that made the technique widely familiar, including a map of the world by population that startled readers by the size of China and India relative to Africa and Russia. Election maps resizing constituencies by electorate became common in the 2000s specifically to counter the impression given by large rural districts. A project mapping hundreds of global variables this way in the mid 2000s was widely reproduced and remains the most cited example of the form.

The technique has real limitations and they explain why it has not displaced the shaded map. Readers must recognise the underlying geography to interpret the distortion, so a map of an unfamiliar region communicates nothing. Severe distortion can leave a shape unrecognisable even to somebody who knows it well. Small territories can vanish entirely or balloon beyond usefulness. Comparing two of these maps is difficult, since both the shapes and the sizes differ. And the technique encodes exactly one variable in the area, so adding colour to show a second forces the reader to disentangle two distortions at once, which frequently produces a striking image that nobody can actually read.

The eye reads area as importance, so a shaded map is dominated by large empty regions, and resizing each territory to match the quantity fixes that by construction. Continuous versions keep neighbours and distort shapes, while separated, grid and circle versions trade the other way. A diffusion-based method published in 2004 made them practical to compute, and unfamiliar geography makes them unreadable.