Most of the world maps you have seen in your life are past their prime. The Mercator was invented in 1569 by a Flemish cartographer. The Winkel Tripel, the map style preferred by National Geographic, dates from 1921. And the Dymaxion map, hyped by the architect Buckminster Fuller, debuted in Life in 1943.
Enter a brash new world map vying for world domination. Like sports, the card game can sometimes grow old when the best competitors are stuck with the same old strategy, said J. Richard Gott, an astrophysicist at Princeton who previously mapped the entire universe. But then comes an innovator: think Stephen Curry of the Golden State Warriors, who splashed three-pointers out of parts of the court that the rest of the basketball didn’t think were worth guarding.
“We were reaching the limit of what you could do,” said Dr. Gott. “If you wanted a major 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 a double-sided circle out of the world map, like a vinyl record. You could place the Northern Hemisphere on the top and the Southern Hemisphere on the bottom, or vice versa. Or to put it another way, you could deflate the 3D Earth in two dimensions. And if you did, you could blow the accuracy of previous maps out of the water.
Of course, no flat map of our circular world can be perfect. First you need to peel the skin from the earth, then pin it. This mathematical taxidermy introduces distortions. For example, if you have a Mercator projection on the walls of your classroom, you might think that Greenland is the size of Africa (not even close) or that Alaska is bigger than Mexico (also no). This distorted worldview could even unconsciously influence you to undervalue most of the developing world.
Shapes also change in map projections. Distances vary. Bending straight lines. Some projections, like Mercator, aim to excel at one of these concerns, exacerbating other mistakes. Other cards compromise, such as the Winkel Tripel, so called because it tries to balance three types of distortion.
Starting in 2006, Dr. Gott and David Goldberg, a cosmologist at Drexel University in Philadelphia, set up a scoring system that could sum up these different types of errors. De Winkel Tripel beat other big contenders. But one major source of deformation persisted: a mathematical incision, often from pole to pole along the Pacific Ocean. The resulting shape can never again be stretched and retracted into the continuous surface of a sphere. “This is violent for the entire world,” said Dr. Gott.
His new kind of double-sided card, made in collaboration with Dr. Goldberg and Robert Vanderbei, a mathematician at Princeton, completely skip topological violence. The map simply continues over the edge. You could stretch a string over the side; an ant could walk there. Without any cut, the map’s Goldberg-Gott distortion score blows all other maps currently in use out of the water, the team reports in a concept study.
Cartographers who regularly study world maps – perhaps less than 10 people – now have time to respond. “It never occurred to me that it could be done this way,” said Krisztián Kerkovits, a Hungarian cartographer who is working on developing his own projections.
But while the new card excels at addressing distortion, Dr. Kerkovits that he also introduced a new weakness. You can only see half of the planet at a time, unlike the Winkel Tripel and Mercator. That undermines the premise of skinning the entire world for inspection on a single page or screen.
For Dr. Gott, this is no different from the 3D globe itself. But Dr. Kerkovits is not entirely sure: after all, you can always rotate a globe a bit to see the neighbors of a chosen point. But in the double-sided card, you may have to turn the whole thing over.
The success of a card ultimately depends on the applications for which it is used and how its popularity grows over time. Dr. Gott, whose paper also presents double-sided projections of Jupiter and other worlds, envisions the new map style as a physical object that you can turn over in your hands.
You could cut one out of a magazine, or you could keep an entire stack in a thin sleeve, with different planets or different data layers. And he hopes you might be tempted to try printing them and make your own using the appendix to his paper.
“Glue it back to back with double-sided tape – I think that’s better than Elmer’s Glue, but you can also use glue,” said Dr. Gott. Then cut it out. “Maybe use cardboard,” he added.