How do you flatten a sphere?
For centuries, mapmakers have agonized over how to accurately display our round planet on anything other than a globe.
Now, a fundamental re-imagining of how maps can work has resulted in the most accurate flat map ever made, from a trio of map experts: J. Richard Gott, an emeritus professor of astrophysics at Princeton and creator of a logarithmic map of the universe once described as “arguably the most mind-bending map to date”; Robert Vanderbei, a professor of operations research and financial engineering who created the “Purple America” map of election results; and David Goldberg, a professor of physics at Drexel University.
Their new map is two-sided and round, like a phonograph record or vinyl LP. Like many radical developments, it seems obvious in hindsight. Why not have a two-sided map that shows both sides of the globe? It breaks away from the limits of two dimensions without losing any of the logistical convenience—storage and manufacture—of a flat map.
“This is a map you can hold in your hand,” Gott said.
In 2007, Goldberg and Gott invented a system to score existing maps, quantifying the six types of distortions that flat maps can introduce: local shapes, areas, distances, flexion (bending), skewness (lopsidedness) and boundary cuts (continuity gaps). The lower the score, the better: a globe would have a score of 0.0.
It can be displayed with the Eastern and Western Hemispheres on the two sides, or in Gott’s preferred orientation, the Northern and Southern Hemispheres, which conveniently allows the equator to run around the edge. Either way, this is a map with no boundary cuts. To measure distances from one side to the other, you can use string or measuring tape reaching from one side of the disk to the other, he suggested.
“If you’re an ant, you can crawl from one side of this ‘phonograph record’ to the other,” Gott said. “We have continuity over the equator. African and South America are draped over the edge, like a sheet over a clothesline, but they’re continuous.”
This double-sided map has smaller distance errors than any single-sided flat map—the previous record-holder being a 2007 map by Gott with Charles Mugnolo, a 2005 Princeton alumnus. In fact, this map is remarkable in having an upper boundary on distance errors: It is impossible for distances to be off by more than ± 22.2%. By comparison, in the Mercator and Winkel Tripel projections, as well as others, distance errors become enormous approaching the poles and essentially infinite from the left to the right margins (which are far apart on the map but directly adjacent on the globe). In addition, areas at the edge are only 1.57 times larger than at the center.