I’m going to have to cut it open.

In order to get this to look anything like a rectangle.

I've had to cut it in places. I've had to stretch it so that the countries look all wonky.

And even still, it's almost impossible to get it to lie flat.

And that right there is the eternal dilemma of map makers: The surface of a sphere cannot

be represented as a plane without some form of distortion.

This guy proved that with math a long time ago.

Since around 1500s, mathematicians have set about creating algorithms that would translate

the globe into something flat.

To do this, they use a process called projection.

Popular rectangular maps use a cylindrical projections.

Imagine putting a theoretical cylinder over the globe and projecting each point of the

sphere onto the cylinder’s surface.

Unroll the cylinder, and you have a flat, rectangular map.

But you could also project the globe onto other objects, and how exactly a map maker

projects the globe will affect what the map looks like once it’s all flattened out.

And here’s the big problem: Every one of these projections comes with trade offs in

shape, distance, direction and land area.

Certain map projections can be either misleading or very helpful depending on what you are

using them for.

Here’s an example.

This map is called the Mercator projection.

If you’re American, you probably studied it in school.

It’s the projection Google Maps uses.

Mercator projection is popular for a couple of reasons.

First, it generally preserves the shape of the countries.

Brazil on the globe has the same shape as Brazil on the Mercator projection.

But the real purpose of the Mercator projection was navigation -- it preserves direction,

which is a big deal if you are trying to navigate the ocean with only a compass.

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

angle to follow on a compass to travel between those points.

If we go back into a globe, you can see that this line is not shortest route.

But it provides a simple, reliable way to navigate across oceans.

Gerardus Mercator, who created the projection in the 16th century, was able to preserve

direction by varying the distance between latitude lines while also making them straight,

creating a grid of right angles..

But that created other problems.

Where mercator fails is its representation of size.

Look at the size of Africa as compared to Greenland.

On the mercator map they look about the same size.

But look at a globe for Greenland’s true size, and you’ll see it’s way smaller

than Africa.

By a factor of 14 in fact.

If we put some dot that are all the same size on a globe, then we projected as a mercator

map, we would end up with this.

The circles retain their shape but are enlarged the closer you get the poles.

One modern critique is that this distortion perpetuates imperialist attitudes of European

domination over the southern hemisphere

"The Mercator projection has fostered imperialist attitudes for centuries

and created a ethnic bias against the third world."

"Really?"

If you want to see a map that more accurately displays size, you can use the Gall-Peters

projection, which is called an equal-area map.

Look at Greenland and Africa.

The size comparison is now accurate.

Much better than the mercator.

but it’s obvious that the country shapes are now stretched.

Here are the dots again so you can see how the projection preserves area

while totally distorting shape.

Something happened in the late 60s that would change the whole purpose of mapping and the

way we think about projections.

Satellites orbiting our planet started sending location and navigation data to little receiver

units all over the world.

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

both the sea and the sky.

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

and presentation.

The mercator map, that vital tool of pre-GPS navigation, was shunned by cartographers who

now saw it as misleading.

But most web mapping tools like Google maps still use the mercator.

According to Google this is because the Mercator’s ability to preserve shape and angles makes

close-up views of cities more accurate -- a 90 degree left turn on the map is a 90degree

left turn on the street you’re driving down.

But when trying to display something on a world map, cartographers rarely use the mercator.

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

split the difference between totally distorting either size or shape.

In 1998 The National Geographic Society adopted The Winkel tripel projection because of it’s

a pleasant balance between size and shape accuracy.

But the fact remains, that there is no one right projection.

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

a new perspective on the planet.

The best way to see what the earth really looks like is to look at a globe.

But as long we use flat maps, we will deal with the tradeoffs of projections, Just remember:

there’s no right answer.