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%. 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. Africa and South America are draped over the edge, like a sheet over a clothesline, but they’re continuous.” “If you’re an ant, you can crawl from one side of this ‘phonograph record’ to the other,” Gott said. 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. Either way, this is a map with no boundary cuts. 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. In a recent paper, Gott began considering “envelope polyhedra,” with regular shapes glued together back-to-back, which led to the breakthrough idea for the double-sided map. Imagery courtesy NASA’s Earth Observatory, with modifications by Mapthematics LLC Polyhedral maps are nothing new - in 1943, Buckminster Fuller broke the world into regular shapes, and provided instructions for how to fold it up and assemble it as a polyhedral globe - but while he could protect the shapes of continents, Fuller shredded the oceans and increased many distances, such as between Australia and Antarctica. The inspiration came from Gott’s work on polyhedra - solid figures with many faces. We’re proposing a radically different kind of map, and we beat Winkel Tripel on each and every one of the six errors.” “We’re doing this to break a record, to make the flat map with the least error possible. He set a new record and won a gold medal, and high jumpers have jumped backwards ever since. Gott drew a comparison to Olympic high jumpers: In 1968, Dick Fosbury shocked sports fans by arching his back and jumping over the bar backwards. Strebe via Wikimedia CommonsĬlearly, a completely new approach was needed. “A map that is good at one thing may not be good at depicting other things.” The Mercator projection, popular on classroom walls and used as the basis for Google maps, is excellent at depicting local shapes, but it distorts surface areas so badly near the North and South Poles that polar regions are usually simply chopped off. “One can’t make everything perfect,” said Gott, who is also a 1973 graduate alumnus of Princeton. The lower the score, the better: a globe would have a score of 0.0. 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). “This is a map you can hold in your hand,” Gott said. 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. Like many radical developments, it seems obvious in hindsight. Their new map is two-sided and round, like a phonograph record or vinyl LP. 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. 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, Robert Vanderbei and David Goldberg How do you flatten a sphere?įor centuries, mapmakers have agonized over how to accurately display our round planet on anything other than a globe.
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