Most of the world maps you have seen in your life have passed their prime. The Mercator was designed by a Flemish cartographer in 1569. The Winkel Tripel, National Geographic’s preferred map style, dates back to 1921. And the Dymaxion map, hyped by architect Buckminster Fuller, appeared in a 1943 issue of Life.
Enter a new map of the world that vies for global supremacy. As with sports, the card game can get stale at times when top competitors stick to the same old strategy, said J. Richard Gott, a Princeton astrophysicist who previously mapped the entire universe. But then comes an innovator: think of Stephen Curry of the Golden State Warriors splashing 3-pointers out of areas of the court that the rest of basketball didn’t think were worth guarding.
“We have kind of reached the limit of what you can do,” said Dr. God. “If you wanted a major breakthrough, you had to use a new idea.”
Dr. God’s version of Steph Curry’s wait-you-could-shoot-from-there-3? Use the back of the page as well. Make the world map 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 could empty the 3D earth in two dimensions. And if you do, you can blow the accuracy of previous maps out of the water.
Of course, no flat map of our round world can be perfect. First you need to peel off the skin of the earth, and then nail it down. This mathematical taxidermy leads to distortions. For example, if you have a Mercator projection on the walls of your classroom, you might think Greenland is as big as Africa (not even close) or Alaska is bigger than Mexico (also no). This distorted worldview could even subconsciously lead you to underestimate most of the developing world.
Shapes also change in map projections. Distances vary. Straight curve. Some projections, such as Mercator, aim to solve one of these problems, which exacerbates other errors. Other cards compromise, like the Winkel Tripel, because it tries to strike a balance between three types of distortion.
From 2006, Dr. God and David Goldberg, a cosmologist at Drexel University in Philadelphia, developed a scoring system that can summarize these different types of errors. The Winkel Tripel beat out other main competitors. One major source of the distortion remained, however: a mathematical cut that often runs from pole to pole in the Pacific. The resulting shape can never again be stretched and retracted into the unbroken surface of a sphere. “This is what makes the world violent,” said Dr. God.
His new type of double-sided card featuring Dr. Goldberg and Robert Vanderbei, a mathematician at Princeton, completely skips topological violence. The card simply continues over the edge. You could stretch a string across the side; An ant could go there. In a study draft, the team reports in a draft study that the card’s Goldberg-God distortion value blows all other cards currently in use out of the water without any reduction.
Cartographers who regularly study world maps – perhaps fewer than 10 people – now have time to react. “It never crossed my mind that it could be done this way,” said Krisztián Kerkovits, a Hungarian cartographer who works on developing his own projections.
While the new card works great against distortion, Dr. Kerkovits also introduced a new weakness. In contrast to Winkel Tripel and Mercator, you can only see half of the planet at a time. This undermines the basic requirement to hide the whole world for inspection on a single page or screen.
For Dr. God is no different from the 3D globe itself. But Dr. Kerkovits is not entirely sure: after all, you can always easily rotate a globe to see the neighbors of any point. But in the double-sided card, you may have to flip the whole thing over.
Ultimately, the success of a card depends on what applications it is used for and how its popularity grows over time. Dr. God, whose article also features double-sided projections of Jupiter and other worlds, envisions the new map style as a physical object that you can flip over in your hands.
You could cut one out of a magazine or keep a whole stack of them in a thin case that shows different planets or different layers of data. And he hopes that you may be tempted to use the appendix to his paper to try to print out and make your own.
“Tape it back to back with double-sided tape – I think that’s better than Elmer’s Glue, but you can use glue,” said Dr. God. Then cut it out. “Maybe use card stock,” he added.