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Most of the world maps that you have seen in your life are past their prime. The Mercator was designed by a Flemish cartographer in 1569. The Winkel Tripel, the style of map favored by National Geographic, dates from 1921. And the Dymaxion map, hyped by architect Buckminster Fuller, debuted in an issue of 1943 from Life.
Enter a brash new world map vying for world domination. Like sports, the mapping game can sometimes become obsolete when the best competitors are stuck on the same old strategy, said J. Richard Gott, an astrophysicist at Princeton who previously mapped the entire universe. But then comes an innovator: Think of the Golden State Warriors’ Stephen Curry, splashing 3 points in areas of the court that the rest of basketball didn’t think was worth keeping.
“We were kind of reaching the limit of what you could do,” Dr. Gott said. “If you wanted a meaningful breakthrough, you had to use a new idea.”
Dr. Gott’s version of Steph Curry’s wait-you-could-shoot-from-there 3? Also use the back of the page. Make the world map into a double-sided circle, like a vinyl record. You can put the northern hemisphere on top and the southern hemisphere on the bottom, or vice versa. Or to put it another way: you can deflate the 3D Earth in two dimensions. And if you did, you could blow the accuracy of previous maps out of the water.
No flat map of our round world can be perfect, of course. First you need to peel off the skin from the Earth, then fix it. This mathematical taxidermy introduces distortions. If you have a Mercator projection on your classroom walls, for example, you may grow up thinking that Greenland is the size of Africa (not even close) or that Alaska is larger than Mexico (no. more). This distorted view of the world might even make you subconsciously undervalue most developing countries.
Shapes also change in map projections. Distances vary. Curve of straight lines. Some projections, like Mercator, aim to excel at one of these concerns, making other mistakes worse. Other cards compromise, like the Winkel Tripel, so named because it attempts to strike a balance between three types of distortion.
Starting in 2006, Dr Gott and David Goldberg, a cosmologist at Drexel University in Philadelphia, developed a scoring system that could summarize these different types of errors. The Winkel Tripel beat other big contenders. But a great source of distortion persisted: a mathematical incision, often going from pole to pole in the Pacific. The resulting shape can never again be stretched and pulled back into the unbroken surface of a sphere. “It makes violence in the world,” said Dr Gott.
His new type of double-sided card, designed with Dr Goldberg and Robert Vanderbei, a mathematician at Princeton, completely avoids topological violence. The card simply continues on the edge. You can stretch a string on the side; an ant could walk there. Without any cuts, the card’s Goldberg-Gott Distortion Score pushes all other cards currently in use out of the water, the team reports in a study project.
Cartographers who regularly study maps of the world – perhaps fewer than 10 people – will now have time to react. “I never thought it could be done this way,” said Krisztián Kerkovits, a Hungarian cartographer working to develop his own projections.
But while the new card excels at dealing with warp, Dr Kerkovits said it introduces a new weakness as well. You can only see half the planet at a time, unlike the Winkel Tripel and Mercator. This undermines the basic principle of skinning the entire world for inspection on one page or one screen.
For Dr. Gott, this is no different from the 3-D globe itself. But Dr. Kerkovits isn’t entirely sure: after all, you can always rotate a globe slightly to see neighbors from any point you choose. But in the double-sided card you may have to flip everything.
Ultimately, the success of a card depends on the applications it is used for and how its popularity grows over time. Dr. Gott, whose article also features two-sided projections of Jupiter and other worlds, envisions the new map style as a physical object to return to your hands.
You can cut one out of a magazine or store an entire stack in a thin sleeve, showing different planets or different layers of data. And he hopes you might be tempted to try printing and creating your own using the appendix to his article.
“Tape it back to back with double-stick tape – I think it’s better than Elmer’s glue, but you can use glue,” Dr Gott said. Then cut it out. “Maybe use card stock,” he added.
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