One of the reasons I enjoy meetups with other geographers is because I can always count on a warm audience for my many merry rants about maps that poor, non-cartographically inclined plebeians are sharing on Twitter.

Take this gem floating around Facebook in late October of 2017.

Available by mail outside of Japan for about 30 bucks in a nifty lil’ kit.

This gorgeous map is called AuthoGraph and it is the work of Hajime Narukawa. It was recently published, won some design awards and has been circulating the internet mostly because it’s not Mercator Projection.

Mercator. Admit it, you feel your blood boiling already.

Becoming a #MercatorHater is the first step in learning about geomatics. For the uninitiated: Mercator distorts the poles and makes equatorial regions look smaller and inflates the size of colonial powers which often are located in northern latitudes. Subconsciously we equate size with importance so Mercator perpetuates colonialist, top-down attitudes of the world. It is the world’s most popular self portrait and has been for hundreds of years. You recognize it.

Narukawa’s map is not Mercator. It has much smaller distortions in actual size (it’s still being reworked into a true equal-area map) and while it monkeys with shape a little, it is a big improvement into showing us the true proportions of the earth. For perspective, every world map that you see has converted a 3D planet into a 2D picture so it is inevitable that shape, area, direction and distance be compromised in some unique combination. Moral of the story? No world map on a page or a flat screen can be made without compromise.

But look at the strategic compromises Narukawa made: You can’t navigate by this map because a straight line drawn across the earth’s surface would be shown bent on the map. The shape of landmasses is off by a bit and the distances between features varies from very accurate to very inaccurate. That said, unlike most equal area maps, this one has done a good job of preserving the area of oceans and it actually shows Antarctica as a complete landmass instead of a massive sliver along the bottom. Pacific Island nations have long been cut in half by most maps which break through the international date line in the Pacific and this map shows the relationship between them for once. AuthaGraph has many of the same problems that other maps have. It solves some, it creates others. All maps lie and carry the subjective baggage of the artist. Surely a Japanese designer didn’t win a Japanese design competition with a map that shows Japan dead center by coincidence. This map has been adopted as the official world map in all Japanese schools and I doubt it was because of a great national love of area fidelity. This map is not going to cure imperialism but it is still a very cool map though for much more brain bendingly awesome reasons.

AuthaGraph takes advantage of a sophisticated understanding of folding and tesselating.

R. Buckminster Fuller published his Dymaxion Map in 1943. It’s cool for a lot of the reasons that the AuthaGraph map is cool. It shows continents connected and it helps us think about the world in a very different and equally valid way that shows land masses close to the sizes that they are relative to each other. While other maps transform a round planet into a flat rectangle with a lot of stretching and pulling, the Dymaxion map simply folds up into a icosohedron with 20 triangle faces. You can print this image, cut it out and fold it into a neat little globe. No distortion required.

This is the kind of map you get from a guy who made his career on his lack of visual acuity.

Well, a little distortion at least. Each one of the triangular faces is HUGE and the earth curves noticeably beneath each one. The flat face is a best approximation of the land underneath it so each face has the same problems as the Mercator map we looked at earlier, just much smaller.

Image: By Jack van Wijk, Eindhoven University of Technology

The more pixels you have in a photograph, the higher the resolution you can get in an image. So too, the smaller the extent of the map, the less distortion from the curvature of the earth you have to worry about. The reason that people fight over the projections on world maps and not county maps is because projection is nearly irrelevant for maps with small extents.

OMG that would make an awesome map

To get better precision you would simply make the flat faces smaller and smaller and smaller until they were indistinguishable from a sphere. This will probably give you flashbacks to your calculus class.

Just looking around at the world from our meager human perspective, the world looks pretty flat but the more you zoom out, the more apparent it is that the world does in fact curve.

AuthaGraph isn’t broken up into many more tiny triangles than the Dymaxion map and it folds like this:

The other cool thing about AuthaGraph is tesselation. Tesselation is when you have a pattern made up of interlocking shapes that can continue on and on without gaps. Like this:

I wonder if MC Escher ever thought about hexbin maps.

The left and right edges of a Mercator Map line up so that you can tape them together and form a continuous cylinder. If you think about it, Mercator Projection is like a sidescrolling arcade game like Asteroids where if you move the cursor too far to the left it pops up again on the right side. If you cut out the AuthaGraph map and print out a bunch of copies, you can stack them all together and get one continuous map.

For another much older example of this, there’s the Peirce Quincuncial projection which would make a very nice tiled floor. That’s not super useful but it’s interesting.

My main problem with bashing Mercator is that it implies that the only thing a map is useful for is showing the entire planet at once. In the kind of mapping I do, I’m not interested in showing the whole planet. I’m rarely interested in showing an entire county. If you’re making an infographic about what country grows the most yams or which countries drive on the left side of the road, sure, you’re going to want to use a projection that shows the whole planet in a way that represents size accurately. Distorting size will confuse your audience into being more impressed with higher latitudes than they ought to be.

The Authograph and Mercator are two tools designed to solve different problems. There are times when Authograph is the best solution and there will be times when Mercator is the best and the fact that we still find a four hundred year old cartographic trick useful today says something about its utility. We do not live in a world with one perfect solution to this problem- instead we must remember that we have a glorious tool box chock-full of different solutions that we can select for different use cases. Authograph is cool and new but it is not the end.

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