The false dichotomy that took over Popular Cartography

In March 2017, public schools in Boston changed their standard map projection from the ubiquitous “Mercator Projection”, in which Greenland is displayed bigger than Africa, to the “Peters Projection”, where the areas of landmasses appear proportionate to their actual areas. This received a lot of praise, including an article in the Guardian saying the move “cut the developing world down to size”. However, the Peters Projection is far from the ideal solution to the Mercator Projection’s distortion problems.

The hard problem of cartography

Maps are flat, but Earth is (unless you belong to certain strange subcultures)round. That is the essence of what could be considered that hard problem of cartography. It follows that it is impossible to perfectly represent the surface of Earth on a flat surface.

So when you design a map of the world (or the moon or the cosmic microwave background or anything else that’s round), you have to compromise. You have to favour one thing at the expense of the other. You can go all out for preserving relative areas, but you’re going to end up distorting shapes. You can preserve directions, but you’re going to fuck up all the relative areas. You can compromise and try to sacrifice a bit of one benefit to get a bit of another. There’s all sorts you can do, which is why people have made so many different map projections over the years.

The Mercator Projection

One such ”projection”, and probably the best-known, was developed by the Flemish cartographer Gerardus Mercator in 1569, with one crucial selling-point: a constant bearing is a straight line. For reasons that should be obvious, this is very useful for maritime navigation (and during the Age of Discovery, when the Mercator Projection was created, this was the main thing people used maps for). You can draw a line on the map showing your route, and at any point on that line, it’s going to make an angle with the vertical which is the same as the angle at which your compass should be pointing.

The problem, though, is that when you’ve gone all out to make a constant bearing a straight line, you end up with areas being enormously inflated towards the poles (and even going to infinity at the poles themselves). The classic example is the way Greenland appears a similar size to Africa, then there’s also the way Scandinavia appears to be the size of India, and the islands of the Canadian Arctic appear to dwarf the much larger islands of Madagascar, Borneo and New Guinea. An interesting curiosity I once stumbled across is that the Lena River, in North-Eastern Siberia, has the distinction of looking like the longest river in the world in the Mercator Projection.

But, for whatever bizarre reason, the Mercator Projection has ended up as the classic image of ”what the world looks like”.

Peters’ solution

Needless to say, this is far from ideal, and that is what the German historian and filmmaker Arno Peters exploited when he announced, in 1973, that he had developed a ”new” projection, which preserved the relative areas of landmasses.

Peters argued that the equatorial regions compressed by the Mercator Projection are generally poor and marginalised, compared to Europe and North America, which the Mercator Projection stretches.  According to Peters, this led to people’s perception of the world being skewed, and excessive emphasis being placed on these areas.

An equal-areas projection, according to Peters, would help to fix this skewed perception.

In fairness to Peters, the Mercator Projection does inflate the size of Europe while diminishing that of Africa, South Asia, and Latin America, and it’s reasonable to suggest that the ubiquity of the Mercator image of Earth could lead people to place a disproportionate psychological emphasis on the inflated regions. Some credit’s due to Peters for pushing that idea into the mainstream. The problem, though, is that the projection doesn’t actually have half the qualities he claimed as its advantages.

Peters claimed that the projection has “no distortion”. It quite clearly does, as any map projection does. It is a trade-off between different types of distortion, like any other projection. Relative areas are shown accurately, but the shapes of things are all over the place (for example, Africa comes out very long). There is distortion of shapes everywhere except along the standard parallels.

Perhaps worse than all of these is Peters’ claim that he was the first person to come up with the idea of an equal-area projection. Equal-area projections have been around for centuries, with the sinusoidal projection appearing in 1570, a year after the Mercator projection (although it looks very weird).  Cylindrical equal-area projections (formed by wrapping a cylinder around the Earth, projecting onto that, and then unwrapping it, giving you a rectangular map) have been around at least since the Lambert cylindrical projection, first described in 1772, where the standard parallel is the equator. Since then, many cartographers have put different standard parallels into the same formula to produce different projections. These included James Gall who, in 1855, published a cylindrical equal-area projection with standard parallels at 45° from the Equator, identical to the Peters projection.

In fairness to Peters, Gall’s projection was never well-known, and he had probably never heard of it. But even if he is not guilty of intentional plagiarism, his wilful ignorance of the whole history of equal-area projections and his anti-intellectual caricature of the cartographic community as some kind of weird Mercator cult was just straight-up arrogant and irresponsible.

Other projections

Peters projection propaganda typically presents the world of cartography in terms of a dichotomy between Mercator and Peters, with Mercator grossly distorted (it is), and the Peters projection as totally accurate (it isn’t). However, the ways of representing the world on a flat surface are so much more diverse than that. If you want equal areas, you’ve got sinusoidal (which is weird) or Mollweide (which I like because it doesn’t look like it’s meant to be flat). If, like Peters, you’re hung up on the idea that maps have to be rectangular (which actually makes sense if you’re looking for something to blu-tack to your classroom wall), you’ve still got a whole host of ‘cylindrical’ equal area projections (so named because they’re formed by wrapping a cylinder round the Earth, projecting the surface onto that, and then unwrapping it, giving you a rectangular map). In fact, you can make your own cylindrical equal area projection just by multiplying the longitude of a point by the cosine of the standard parallel (an arbitrarily chosen latitude where there is no distortion) to get the x coordinate of that point, and dividing the sine of the latitude by the cosine of the standard parallel to get its y coordinate. Just (unlike Arno Peters) make sure nobody’s already used your standard parallel.

So why do people like the Peters projection?

Most of the hype that has surrounded the Peters projection since the get-go simply comes down to the way it was marketed. Peters, a filmmaker-turned-historian with no background in cartography, did not go through the conventional method for presenting a new map projection. Instead of publishing it in a cartography journal, Peters went straight to the media, presenting to the general public his manifesto for the anti-Mercator revolution.

cylindrical equal areas
Some examples of cylindrical equal area projections, with the standard parallels and aspect ratios indicated, and with Tissot’s Indicatrices showing distortion at different locations. Image source: Wikimedia Commons, created by Eric Gaba.

And of course, actual experts in maps, with their acne, terrible personal hygiene and distinct lack of social skills proved no match in this arena for a sexy, charismatic Hollywood historian. Peters’ unashamedly anti-intellectual wokeness played very well with the general public who, as any cartography enthusiast is likely well-aware, aren’t generally that interested in map projections. It’s easy to see how, for someone unfamiliar with the 400 year pre-Peters history of people trying to come up with alternatives to the Mercator projection, the idea of some kind of cartographic cabal, wearing hooded robes and chanting in Latin while they sacrifice goats to Gerardus Mercator. People like to feel special, and like they know something the so-called “experts” don’t. As such, the Peters cult was able to quickly gain momentum, ending up with many NGOs, including UNESCO, adopting it as standard in an effort to be woke and address the problem of ‘cartographic imperialism’.

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