Over the last few years I’ve seen an increasing number of cartograms used to display single dimensional country by country statistics such as GDP, carbon emissions, electoral college votes etc with varying degrees of success. My team has been involved with production of a few too (1. 2).

Below, for those of you not already asleep, are some of my thoughts on them:

Cartograms, are certainly eye catching visualizations their effect can be as powerful as seeing the Peters projection for the first time after a life of Mercator. The power comes from taking something familiar and exposing us to our assumptions about it. In the Peters/ Mercator example it’s the assumption that maps are perfect reflections of a fixed reality rather than imperfect approximations which inevitably compromise some aspects of their depiction in order to maximise some other utility (the ability to draw perfect straight lines across a map for navigation vs true area representation).

The problem comes when you’re trying to use cartograms for looking deeper into data. I’ve packed up my Tufte books so I can’t quote the numbers but he shows how area representation is perceptually tricky. You can get an idea of how slippy our intuitions about quantities in more than one dimension are by looking at equal amounts of chocolate milkshake in a tall thin glass and a short fat one, whilst you can say they’re the same amount you only do so by overriding your intuition that the taller one has more in it. The problem is even more pronounced when confronted with the twisted fractal boundaries between nations on a cartogram.

But that’s not even the worst of it! No, as I see it the main problem is that when we read a cartogram we’re so familiar with the original map that what we actually end up reading as the primary variable is the change of size. An illustration; imagine we want to show military spending China vs Great Britain, we decide to do this by scaling the countries so that their area is proportional to this value. Now I’m not sure what the actual numbers are but I’m pretty sure China spends more than the UK but the thing is that what a proportional representation will actually show is the spatial density of military spending (in itself this may be interesting but it’s not what we’re intending to show), because China has a much bigger area it may infact be smaller in the proportional representation than it is in ‘real life’ and the UK may be bigger so because of our familiarity with the map of the world we’ll perceive UK military spending as being high and Chinese spending being low, we’ll be reading the change in sizes rather than the absolute sizes. Because of the aforementioned weird shapes that countries have found themselves in, even sitting down and applying a close critical eye to the visualization is likely to yield little decent information about the data. The same problem is true if you use per capita data too. Whilst undoubtedly less striking a simple histogram or a kind of heat map where depth of colour is keyed to values are both more useful approaches.

A great example of this is the afforelinked BBC piece we all know that American per capita emissions of CO2 are way high right? Then why does America shrivel up when we click on that view? It’s because whilst the US does indeed have massive per capita emissions they also have more space than average per capita so their country shrinks, in this case the effect is emphasised by the tumulescent Saudi Arabia whose heroic per capita emissions dwarf even the bold attempts of the US and completely skew the scale.

So the moral of the story is be careful out there kids.

This post was inspired by this set of cartograms linked from boing boing. Ignoring problems with the data set I think this is a classic “look at me” example of cartograms with very little utility.

Right, now I really am going on holliday.