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If I want to turn this globe into a flat map, I'm going to have to cut it open.

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In order to get this globe to look anything close to a rectangle lying flat, I've had

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to cut it in several places, I've had to stretch it so that the countries are starting to look

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all wonky. And even still, it's almost impossible to get it to lay flat.

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And that right there is the eternal dilemma of mapmakers. The surface of a sphere cannot

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be represented as a plane without some form of distortion. That was mathematically proved

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by this guy a long time ago. Since around the 1500s, mathematicians have set about creating

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algorithms that would translate the globe into something flat. And to do this, they

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use a process called projection. Popular rectangular maps use a cylindrical projection. Imagine

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putting a theoretical cylinder over the globe and projecting each of the points of the sphere

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onto the cylinder's surface. Unroll the cylinder and you have a flat rectangular map. But you

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could also project the globe onto other objects. And the math used by map makers to project

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the globe will affect the way the map looks once it's all flattened out. And here's the

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big problem. Every one of these projections comes with trade-offs in shape, distance, direction,

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and land area. Certain map projections can either be misleading or very helpful depending on what

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you're using them for. Here's an example. This map is called the Mercator Projection. If you're

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American, you've probably studied this map in school. It's also the projection that Google Maps

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uses. The Mercator Projection is popular for a couple of reasons. First, it generally preserves

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the shape of countries. Brazil on the globe has the same shape as Brazil on the Mercator

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projection. But the original purpose of the Mercator projection was navigation. It preserves

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direction, which is a big deal if you're trying to navigate the ocean with only a compass.

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It was designed so that a line drawn between two points on the map would provide the exact

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angle to follow on a compass to travel between those two points. If we go back to the globe,

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you can see that this line is not the shortest route, but at least it provides a simple,

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reliable way to navigate across the ocean.

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Girardus Mercator, who created the projection in the 16th century,

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was able to preserve direction by varying the distance between the latitude lines,

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and also making them straight, creating a grid of right angles.

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But that created some other problems.

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Where the Mercator fails is its representation of size.

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Look at the size of Africa as compared to Greenland.

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On the Mercator map, they look about the same size.

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But if you look at a globe for Greenland's true size,

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you'll see that it's way smaller than Africa.

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by a factor of 14, in fact.

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If we put a bunch of dots onto the globe that are all the same size

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and then project that onto the Mercator map, we will end up with this.

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The circles retain their round shape but are enlarged as they get closer to the poles.

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One modern critique of this is that the distortion perpetuates

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imperialist attitude of European domination over the southern hemisphere.

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The Mercator projection has fostered European imperialist attitudes for centuries

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and created an ethnic bias against the third world.

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Really?

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So if you want to see a map that more accurately displays land area,

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you can use the Gall-Peters projection.

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This is called an equal area map.

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Look at Greenland and Africa now.

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The size comparison is accurate, much better than the Mercator.

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But it's obvious now that the country shapes are totally distorted.

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Here are those dots again so that we can see how the projection preserves area

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while totally distorting shape.

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Something happened in the late 60s that would change the whole purpose of mapping and the way that we think about projections.

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Satellites orbiting our planet started sending location and navigation data to little receiver units all around the world.

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Today, orbiting satellites of the Navy Navigation Satellite System provide round-the-clock, ultra-precise position fixes from space to units everywhere in any kind of weather.

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This global positioning system wiped out the need for paper maps as a means of navigating

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both the sea and the sky.

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Map projection choices became less about navigational imperatives and more about aesthetic, design,

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and presentation.

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The Mercator projection, that once vital tool of pre-GPS navigation, was shunned by cartographers

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who now saw it as misleading.

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But even still, most web mapping tools, like Google Maps, use the Mercator.

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This is because the Mercator's ability to preserve shape and angles makes close-up views

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of cities more accurate.

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A 90 degree left turn on the map is a 90 degree left turn on the street that you're driving

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down.

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The distortion is minimal when you're close up.

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But on a world map scale, cartographers rarely use the Mercator.

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Most modern cartographers have settled on a variety of non-rectangular projections that

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split the difference between distorting either size or shape.

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In 1998, the National Geographic Society adopted the Winkle Triple Projection because of its

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pleasant balance between size and shape accuracy.

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But the fact remains that there's no right projection.

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Cartographers and mathematicians have created a huge library of available projections, each

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with a new perspective on the planet, and each useful for a different task.

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The best way to see the Earth is to look at a globe.

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But as long as we use flat maps, we'll have to deal with the trade-offs of projections.

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And just remember, there's no right answer.