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Physicist David Goldberg Helps Create the Most Accurate Map of the World

By Gina Myers


March 23, 2021

How do you represent the world globe on a flat surface? Can it be done without distorting the sizes of countries and continents and the distances between places? What would it take to make an accurate flat map?

Professor of Physics David Goldberg, PhD, is part of a team that tackled these questions and struck upon what is now the most accurate flat map of the world: a double-sided circle that features the Northern Hemisphere on one side and the Southern Hemisphere on the other. Picture a vinyl record and flipping it over in your hands—the edge of the record would be the equator.

While cartography might not immediately seem a likely project for a physicist, Goldberg identifies this work as a natural outgrowth of his own core research on gravitational lensing.

“Gravitational lensing is an effect predicted by Einstein in which mass in the universe—galaxies and clusters of galaxies—warp space and distort the images of even more distant galaxies as we measure it in our telescopes,” he explains. “This shape distortion is very similar to the effects of taking a map of the earth and putting it on a flat piece of paper. There will be distortions.”

Goldberg uses the example of the border between the United States and Canada, which appears on maps as a straight line. However, if one were to try to walk that straight line, they would actually wind up walking entirely through Canada instead of along the border.

Goldberg first joined forces with J. Richard Gott, emeritus professor of astrophysics at Princeton University, in 2007 to identify the various ways that distortion in maps could be quantified. “We came up with six: area, isotropy (whether a circle on the earth is a circle on the map), distance (whether distant points on the map are also distant on the earth), boundary (how many times ‘typical’ pairs of points are interrupted by an edge), flexion (how bent large great circle paths look), and skewness (how uneven those paths look).”

flat circular map of the earth

Using these criteria, they measured and scored numerous maps. The lower the score means the more accurate the map, so a globe would score 0.0. At the time, they discovered the Winkel Tripel projection, which dates back to 1921, was the most accurate map, with a Goldberg-Gott score of 4.563. However, it still had distortions that could be improved upon.

Gott reached out to Goldberg about a year ago to explore the idea of using their previous research to create the new double-sided map. This time around the pair worked with Robert Vanderbei, professor of operations research and financial engineering at Princeton, who created the images and also applied this projection to look at other planets and moons.

Though they could not eliminate all distortions, their map greatly improves upon the Winkel Tripel projection and has a Goldberg-Gott score of 0.881. While some critics have pointed out that this new map allows one to see only half of the world at once, the same criticism can be applied to a globe. In a press statement, Gott said, “To see all of the globe, you have to rotate it; to see all of our new map, you simply have to flip it over.”

Easy to manufacture and store, the new round double-sided map opens up exciting possibilities for the classroom. Goldberg says, “It’s difficult for every grade school student to have a globe on their desk, but far easier to have a two-sided map that they can stash in their notebook. Also, unlike many traditional projections, continents aren’t going to be greatly distorted.”

Download and print your own round double-sided map. “Flat maps that improve on the Winkel Tripel,” by J. Richard Gott III, David M. Goldberg and Robert J. Vanderbei, was published on Arxiv on Feb. 15.