New York City’s Rockaway Beach, like most beaches, looks out onto a seemingly endless stretch of blue water. Standing at the edge of the sand and peering outward, it’s hard to say what’s beyond the horizon. From NYC, one might guess a ship sailing a straight path would first hit Spain, or perhaps Portugal.

But in fact, getting from A to B in a “straight” line is a much trickier proposition than you might think. Standing perpendicular to the ocean at Rockaway Beach, you’re actually looking toward parts of Venezuela; while the first beach you’d hit, sailing from Nahant, Massachusetts, would be somewhere around Western Sahara. “The Boston region mostly faces Africa or Australia, if it gets past the cape at all,” says Andy Woodruff. Woodruff is a cartographer with Axis Maps and the designer of a new set of mind-bending maps that show what lies directly across the ocean from any given beach, if you take into account our planet’s round shape and wonky coastlines.

Screen-Shot-2016-03-28-at-111.jpgAndy Woodruff

Woodruff’s fascination with this idea began with a question. He wondered if it was possible to sail around the earth on the trajectory of a great circle, without hitting another landmass. It turned out that’s impossible, but it led him to another idea. “Say you are on land and were to look or sail straight out, what would you run into,” he asks. He wanted to find out. Woodruff had found inspiration in a series of maps, published in 2014 and 2015, which visualized the countries that lie due east and west of various points along the coasts of the Americas. Those maps neatly organize the world into color-coded common latitudes, i.e. how far north or south a location is of the equator. But Woodruff’s map doesn’t visualize latitudes, exactly. His is a stricter interpretation of “straight.”

To figure out what’s across the ocean from a coastline, Woodruff had to first know what direction the coastline was facing. “I spend a lot of time in summers at Jersey Shore,” he explains. “It’s the East Coast, so you think, oh, it faces East, but really a lot of where we are faces southeast, and if you get a particularly rugged piece of coast it faces every which way.” To determine what lies straight across the ocean from a given coastal point, says Woodruff, “we need to see what direction the coast faces at that point, then draw a great circle in that direction and see what it runs into.”

In cartographer-speak, the term “great circle” refers to the ring that’s formed when you trace a “line” along the surface of a sphere, starting and ending at the same point. Likewise, a “great circle route” is the shortest path between two points on the surface of a sphere. Woodruff charted great circle routes between dozens of coastlines around the world by picking coastal points around the globe, tracing imaginary sailing routes perpendicular to each shoreline, and seeing what he bumped into. It’s the digital equivalent of laying a piece of string across two coastal points on a globe’s surface, and pulling it taut.

Woodruff then transposed these routes onto maps. Problem is, 2-D projections are notorious for distorting geographic metrics like distance, size, shape, and location. As a result, most direct paths, as traced on a sphere, look wonky when translated into 2-D form. “If you were to project that straight line back onto a more normal looking map, it turns out to be this curved path.” Woodruff’s maps use the so-called Robinson projection, a style of map that preserves geographic measurements near the equator, but becomes more distorted toward the poles. This is why the paths on Woodruff’s maps curve most dramatically at extreme latitudes.

The brighter tip of each of Woodruff’s routes indicates the coastline of origin, the one from which the other continent can be “seen.” Woodruff explains that his maps (which use Natural Earth data) only account for routes that lead from one continent to another; not those routes that lead to the same continent. So in that sense, it’s not a perfectly representative map. When you break it down, the polar region is the recipient of the most lines. “Asia and specifically Russia (Siberia) win big largely because of the Arctic area, where the north edges of North America, Europe, and Asia look across at each other,” he says. Thought South America has a good showing, too.

Projects like these always tend to blow people’s minds because it’s nearly impossible to get this kind of perspective otherwise. Maps with their distortions of size, location and distance, inherently skew our points of view. Even Woodruff, who is a trained cartographer, says it was a learning process. “It was fun for me as a general geography lesson,” he says. “I found it revealing about the roundness of the earth, even as a cartographer I don’t necessarily visualize very well.” Geography lesson aside, sometimes it’s just nice to remember that a half a world away isn’t always as far as you think it is.

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Maps of What’s Across the Horizon From the World’s Beaches