First posted on theawl.com website.
Have you seen that episode of "The West Wing"? This is a Fun with Maps column, so you know which one I mean.* The one where it's Big Block of Cheese Day, and CJ meets with the Organization of Cartographers for Social Equality? If that's not ringing any bells, here's what happens: the organization is promoting an alternative to the Mercator projection, that is, the version of the world map with which you're probably most familiar—it's the one that has Greenland roughly the same size as Africa. The group would prefer the Peters projection be used, because it doesn't exaggerate the size of Europe and North America at the expense of non-Western nations, which appear proportionally a lot smaller the closer they are to the Equator.
* Hint: Episode 38: Somebody's Going to Emergency, Somebody's Going to Jail.
Well, the organization might be fictional, but itís an entirely real controversy. Arno Peters, a German historian, unveiled his eponymous map in 1973 with the goal of displaying all nations with accurate sizing. The Gall-Peters (sometimes just ‘the Peters,’ even though James Gall had created the same projection a full century before. Petersí unwillingness to credit Gallís contribution did not win him many fans in cartographic circles) preserves area all right, but the shapes of the continents are completely distorted, especially toward the poles.
Look at Russia—the area is technically correct, but the shape is elongated East-West and flattened. Closer to the equator, countries are drastically elongated North-South.
Map projections are just different ways of translating the dimensions of a globe onto a two dimensional surface. A sphere (or oblate spheriod, if you want to be fancy) can't be flattened without causing some kind of distortion, be it in scale, area, distance and/or direction. Distortions in scale mean that a linear inch from one section of the document may mean 1 mile in the middle while an inch measured from another place could be a completely different length on the ground. Distortions in area means that size is not consistent across the map, which is how you end up with Greenland and Africa looking like landmass equals. Distortions in distance are similar to scale, in a way. On a map made to conserve distance, you could place a dot on the map with a circle drawn around it, and all points on the circle would be equidistant from the original dot. The Azimuthal Equidistant is such a map. Look at it and see—the distance from the North Pole to Washington, DC is accurate. The distance from the North Pole to Warsaw, Poland is accurate. But the distance from Washington, DC to Warsaw, Poland? No way. Directional distortions have to be avoided on maps used for navigational purposes. On a map made to preserve direction, such as the Mercator, you can place your finger on Chignik, Alaska, and move it in a straight line south through the Pacific to hit Honolulu. But on something like the Goode homolosine, which doesn't preserve direction? That line would be kinda lumpy.
Projection methods fall into four category:
To figure out which map projection is right for you, channel your inner cartographer and combine a distortion you'd like to avoid with a method that will help you to avoid it.
The Mercator projection that we're familiar with was actually one of the first well-known map projections. It was developed in the 16th century by Gerardus Mercator, a Flemish cartographer and fan of floppy hats, in part to decrease shipwrecks, which can happen when youíre sailing without a trustworthy map. His Mercator projection is a straightforward cylindrical projection with the tangent at the equator, meaning that all latitude and longitude lines are at right angles to each other. The map preserves direction with rhumb lines and can be used for accurate navigation at sea. But the same grid that keeps direction standard distorts area and scale; see how, as mentioned before, Greenland and Africa look the same, right? Africa is, in actuality, 14 times larger than Greenland. The boxes formed by latitude and longitude lines are all technically the same size. But the stretching that occurs on his map closer to the poles greatly distorts the North-South distance as compared to the East-West distance, which stays the same regardless of where you are. You can see why this annoyed Arno Peters.
So you want a projection that preserves area? Good news! There are a lot of projections out there for you! And most of them have the helpful term “Equal-Area” right in the name. Letís review some options: here are azimuthal, conic and cylindrical projections that preserve area, published by the Swiss mathematician Johann Heinrich Lambert in 1772.
Lambert Equal Area Azimuthal and Equal Area Conic Projections
But look at those conic angles!
Lambert Equal Area Cylindrical Projection
… and look at that scale!
Or look at those angles and that scale! Siiiiigh.
Okay, so letís conserve distance. The Polar Azimuthal Equidistant projection, with which you may be familiar if you spend a lot of time staring at the UN emblem, uses the North Pole as the center point. Distance is correct, but youíve thrown area out the window. I mean, is Greenland really the same size as New Zealand? But it is useful for some things, like airline routing.
What if you want to just have a general map? A nice, inoffensive map that distorts everything, but just a little bit and an equal amount across the board? In 1989, seven individual societies of professional cartographers gathered to discuss tactics for educating the public on the effects of map distortion. They put forth a resolution to …
… strongly urge book and map publishers, the media and government agencies to cease using rectangular world maps for general purposes or artistic displays. Such maps promote serious, erroneous conceptions by severely distorting large sections of the world, by showing the round Earth as having straight edges and sharp corners, by representing most distances and direct routes incorrectly and by portraying the circular coordinate system as a squared grid. The most widely displayed rectangular world map is the Mercator (that is, a navigational diagram devised for nautical charts), but other rectangular world maps proposed as replacements for the Mercator also display a greatly distorted image of the spherical Earth.
So what should we use instead of the wildly distorted Mercator and Peters? The Robinson Projection was accepted by academics as an agreeable middleground map, one that distorted everything a little instead of preserving one aspect at the expense of all the others. Following the cartographer societies' lead, the National Geographic Society used the Robinson for official maps from 1989 until 1998, when it was replaced with the Winkle Tripel Projection, generally thought to be a more attractive and balanced view of the earth. I think it looks pinched, but my formative map years were spent gazing at the Robinson.
The Robinson and Winkel Tripel Projections
These aren't the only ways to show the world, of course, there are hundreds of projections out there. Here are three notable for their nonconformity:
Buckminster Fullerís Dymaxion map, a polyhedron that eliminates the cardinal directions.
The Peirce Quincunial, where the equator is a square and The Werner which, … awwwww.
And finally a gem, unearthed by Strange Maps, from the woefully short-lived Globehead! Journal of Extreme Cartography: Catherine Reevesí Equinational Projection, which allocates each nation the exact amount of space by reducing it to a simple square. If only it were that easy…
The Reeves Equinoctial Projection
Map images courtesy of Wikipedia.