How useful are maps for understanding the world? Ever since the Mercator projection (1559): very. Topographic maps take us around cities and countries and the world; floor plans guide us in buildings; stylized maps help us take the right subway train; and so on. But if maps have generally achieved a high level of sophistication for the representation of spatial information, they are way less helpful when it comes to show and make sense of other variables such as, say, population, incidence of a disease, money flows, literacy, telephone usage, production and consumption, and any other data of statistical or human interest.
Many things have been done with maps to make them "talk" about these variables: color-coding, stylizing, stripping them of secondary details, modifying the coordinate axis. But the results are often misleading because the data are generally locked into geographic proportions (despite the fact that a figure like "one case in a thousand", for example, would mean something entirely different in Canada from what it means in Singapore).
To represent these variables convincingly, map makers have sought to construct cartograms, or density-equalizing maps: maps in which the size of regions appears in proportion to the given variable. But this has led to distortion and overlapping, and often resulted in maps that are difficult to read. A couple of years ago, borrowing the linear diffusion method from elementary physics, Michael Gastner and M.E.J. Newman at the University of Michigan did some theoretical work and put forth a series of mathematical formulas that, fed to a computer, can process data and turn them into "elegant, well-behaved and useful cartograms". That's what the Social and Spatial Inequalities Research Group at the University of Sheffield, in the UK, has done, producing a first set of maps, on many very different variables, that are very intuitive and very impactful.
For example, this would be the standard projection by land area:
If however we redesign the map according to the population, here is what we get:
For an example of what happens when other variables are represented, let's look at how people travel. This is the map by aircraft passengers:
Rail passengers are distributed rather differently:
And this is the distribution of passenger cars:
Immediately understandable - thanks also to the regional color-coding, which makes visual comparison even easier. There are some 92 maps already on the Worldmapper website (exports and imports, refugees flows, tourism flows, and so on) and more are being added. Each map is presented with basic related information, a downloadable "poster" in PDF, the excel file with the data used to create it, and associated technical notes.