The map that we grew up looking at doesn’t only show us locations of countries on Earth but also shapes our view of the world itself. But, let’s take an orange, peel it off delicately, and attempt to flatten all the peel out onto a tabletop. It wrinkles, rips, overlaps, or stretches. This simple experiment illustrates the problem of map-making from its beginning. The Earth is a curve, whereas paper is flat. One can cut and reassemble the peel, but cannot flatten it out completely without some modification. This phenomenon can be described in a reversed way, too: Try to cover an orange by a flat sheet of paper without distortion. Failure to do it doesn’t depend on the paper, but on geometry.
Nearly 200 years ago, in 1827, the legendary German mathematician Carl Friedrich Gauss offered a mathematical explanation to this problem by his Theorema Egregium. The curvature of the sphere is positive, and that of the plane is zero. Their geometrical natures are clearly different. Hence, while we project Earth, we have to give up something. We can keep form, area, some distance, or directions on our map. But we cannot keep all of them. There’s no ideal world map — that’s not a defect of cartography, but the effect of mathematics.
The map most of us use was invented by Gerardus Mercator in 1569. This map was extremely successful because of its practical uses — it was used for navigation as it preserved angles. In terms of its goal, it was an amazing creation. But Mercator has its noticeable drawback — sizes of objects become more and more exaggerated towards the poles. Take Greenland, which seems nearly the same size as Africa. It isn’t. Africa is actually 14 times larger. However, oddly enough, a projection intended for seafarers became the default map of the world in textbooks and also in practice.
An equal-area projection alters this perspective. Though, it doesn’t solve the problem from a mathematical standpoint. It just makes another kind of compromise. The Gall-Peters map preserves area but changes shape. Winkel Tripel tries to reduce multiple distortions. Though Goode Homolosine map projection maintains the proportion of sizes, the oceans have been split into pieces on the map. Equal Earth Projection was created by Tom Patterson, Bojan Savrič, and Bernhard Jenny in 2018. It retains relative size and maintains continent shape.
Which map, therefore, is the right one? Well, correct for what? A sailor would use one map, while a geographer would require another. A geography textbook will have yet another preference. Each map is an expression of the decision made on what to preserve and what to sacrifice.
However, each map is made with certain decisions in mind. Why is north at the top? Why is Europe in the middle? Why is the Pacific always shown on the margins? Nature doesn’t demand that “north” always be placed “up.” An upside-down map makes Australia appear at the top. Centre the Pacific, and the division between East and West starts looking like something completely different. The Earth remains the same. All that has changed is the frame around the picture. A map might begin geometrically, but it can become political.
Certainly one of the finest instances where humanity plays with the world is demonstrated in the movie The Great Dictator (1940) in which Charlie Chaplin played the Hitler-like character Adenoid Hynkel. In the film, Hynkel takes a globe, blows it up, and starts playing with it, throwing it up in the air. For a moment, the whole world is his toy. Then it bursts. While the sequence is comedic, there’s something strangely fitting about imagining the scene in relation to mapping. A globe keeps the curvature of the Earth; a map takes it away. Once the world is flattened, however, it becomes easier to reshape — shift boundaries, change centres, adjust scales. Maps have their own kind of power.
We shouldn’t, however, throw Mercator’s map in the dustbin of history. It still has its uses — for navigation and otherwise — wherever its attributes come in handy. Neither do we want to think that Equal Earth provides the solution. No map does so. Perhaps the truly honest answer is to appreciate the compromises in any map. This, perhaps, is the real message of the UN’s map debate. The earth will continue on just where it was before — round, huge, and completely unconcerned with the squabbles of the map-makers.
The writer is a professor of statistics, Indian Statistical Institute, Kolkata
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