Where in the world are we? A brief exploration of cartography

Setting foot inside Boston Public Library’s Norman B. Leventhal map collection is like stepping into a condensed vignette of human exploration, or perhaps an extra-detailed version of high school history. The library houses 200,000 maps from all corners of the globe (if you’ll pardon the expression); myriad records spanning—and illustrating—history. The sheer number is testament to the 2,000-plus year pursuit to develop a more accurate two-dimensional representation of our 3-dimensional planet. Much to cartographers’ chagrin, however, a wholly accurate projection is as elusive as the mythical sea monsters gracing many of the library’s oldest maps. Cartography is not a field for perfectionists. It has long been conceded that the perfect projection is a mathematical impossibility: try flattening an eggshell, and you’ll quickly discover there’s no way to precisely represent a spherical surface in two dimensions.

Every global map projection introduces flaws, or distortions, to the representation of the planet. “If you have a rectangular map, there’s no way that it can not be distorted,” said Eric Bullock, a Ph.D. remote sensing student at Boston University, “that’s just not the way a globe unfolds.” Any global map you have ever seen is necessarily inaccurate—some prodigiously so. Perhaps the most common map projection—the Mercator—is also among the most egregiously distorted, primarily at the north and south poles. If the only map you’ve seen is a Mercator, chances are you didn’t know Greenland is not the same size as Africa—in fact, its land area is 14 times smaller than Africa’s. “The public at large—unless they have some sort of geographical education—are not particularly aware of the power of maps to give a distorted image of the world,” said Dr. Michael Jones, an emeritus professor of geography at Norwegian University of Science and Technology. Many of us spend our lives literally unaware of the true shape of our world.

Check out truesize.com to see just how unaware we can be when it comes to the size of countries. 

Consider Google Maps. The ubiquitous cartographic tool has largely replaced the classic dog-eared tome of roadmaps that used to ride shotgun in every family’s minivan. Google Maps and other cartographic apps tend to hone in on an utterly local scale, a scale at which distortions are naturally minimized. The complications with projections increase as scale does—this is why full global projections have caused the most headaches through the ages. Think back to the eggshell: you can take a shard and make it relatively flat—but try laying out the whole thing in shards and it’ll be hopelessly fragmented.

Like Google Maps, most classrooms in the United States display and use the notorious Mercator projection, which was developed (in an admittedly primitive form) in 1569 by the German-Dutch cartographer, Gerardus Mercator, and used primarily for navigation by sea. In this it excels, because it overlays a grid on the world, allowing seafarers to navigate the globe using just the map and compass angles. In Mercator’s projection, latitude and longitude always meet at 90 degree angles, meaning the shapes of continents are preserved in the transition from globe to map, but their sizes become increasingly distorted the further one looks from the equator. Because the lines of latitude have no curvature, they all sit the same distance apart across the board. The corresponding lines of longitude must then move increasingly farther apart as they step away from the equator. The size of continents and oceans maintain fidelity in a narrow band along the equator, but the dimensions of other regions become increasingly distorted as we move nearer to the poles on a Mercator map. “Many world projections—not least the Mercator projection—are favoring the global north,” said Jones. Mercator’s distortion of the poles has taken flak for promoting an imperialist view—by making the global north appear larger relative to its southern neighbors, some suggest the projection implies that the former regions are superior in some way to the latter.

Image of a Mercator map projection

The Mercator projection intentionally emphasizes straight angles of latitude and longitude, unintentionally emphasizing landmasses by the poles (Photo by Wikimedia Commons user Jecowa (CC BY-SA 3.0)).

In contrast—intentionally so—is the Gall-Peters equal area projection, first introduced in Germany in 1974. A Gall-Peters projection distorts the shape of countries in favor of preserving their sizes. The resulting map is a distinctly stretched and gangly interpretation of the world. The competing projection wouldn’t face judgment for fostering imperialism, but it depicted a strange world hosting a squat, wide Greenland and a thin, stretched Africa. Their sizes were corrected, but at the cost of their true shapes. Arthur Robinson, an American cartographer, once described the Gall-Peters projection disparagingly as looking like “wet, ragged long underwear hanging on the line to dry,” in the words of Jones.

Robinson’s own projection—a compromise model that sacrifices a little of both shape and size—arguably fared better, being the map of choice for the National Geographic Society for nearly a decade between 1988 and 1995. In Robinson’s depiction of the world, distortions are largely hidden from the untrained eye because the model tweaks both size and shape rather than favoring one over the other. It has since been replaced by the Winkel Tripel—another compromise projection, and now the norm in general reference maps. Distortions in compromise projections are less visually noticeable, because they’ve been distributed between the vectors of shape and size.

Image showing how distortion occurs in three common map projections.

Tissot’s Indicatrix shows how a Mercator projection (left) distorts size at the poles, the Gall-Peters projection (center) distorts shape, and a Robinson projection (right) slightly distorts both (Images by Wikimedia Commons user Eric Gaba (CC BY 1.0)).

Two millennia and several hundred projections since mathematicians first set out to map the globe, cartographers continue the quest—if not for the perfect map, at least the ideal one. Just this year, Dr. Hajime Narukawa, a Japanese cartographer and professor, won Japan’s prestigious Good Design Award for his design of the much-lauded AuthaGraph projection. Narukawa’s model is so accurate that the map, divided into 96 equal-area triangles, can be folded into a passable globe. The projection’s secret? Transferring distortions to the oceans, where they are little noticed by terrestrial beings such as ourselves. AuthaGraph is also intentionally non-politicized: the only thing given prominence in its center is the Pacific Ocean. Such a perspective of the world is so foreign to anyone viewing it that Dr. Jason VanHorn, a geography professor at Calvin College, suspects it won’t be easily adopted. “It’s not a traditional view, and it’s a very odd projection,” he said. “I feel like most people will look at it and say, ‘well, that’s great—but I don’t really like it.’” It is perhaps disorienting to see the earth arranged around the Pacific Ocean, continents tipped drunkenly askew by the chosen angle.

Whatever the case with accuracy or lack thereof, every projection was designed with a specific rationale—without Mercator’s representation, for example, early seafaring would have been even more challenging than it was made by complications like scurvy. Compromise projections may be the way to go for a better idea of the world’s true shape, but even they, strictly speaking, can’t claim accuracy in any plane. AuthaGraph presents the world in an ostensibly truthful light, but no well-equipped sea vessel would consider taking it on board. “The complaints people have about different projections aren’t necessarily problems with the projection itself—it’s a matter of the projection being misused for its purpose,” said Evan Thornberry, a reference and geospatial librarian at the Norman B. Leventhal Map Center. “Maps tell stories,” he said. “You really have to learn to read between the lines.”

Perhaps the ultimate example of using maps to tell stories is the cartogram: a representation of the earth in which countries are intentionally distorted according to a specific variable. A population cartogram, for example, beefs up the size of the United States and Mexico, shrinks Canada, Russia, and Australia to a shadow of their Mercator-selves, and absolutely balloons up China and India. “They’re powerful, powerful pieces of visual data representation,” said VanHorn. “They’re phenomenal education pieces.” The recent election in the United States has spurred cartographers to produce cartograms demonstrating just how divided the country really is along political lines.

Any map can be an educational tool—even as a cautionary tale about mistaken human perceptions or a lesson in mathematical impossibilities. “No map is absolutely perfect,” VanHorn said. “It’s just a metaphor for reality. The weight that we give it as an authority in our lives should be massaged with that knowledge.”

Comic about map projections.

xkcd courtesy Randall Munroe (CC A-NC 2.5).

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