Why all world maps are wrong

Making accurate maps is mathematically impossible

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Mercator tool: http://thetruesize.com/
Jason Bostock Map Transitions: http://bl.ocks.org/mbostock/3711652
Mercator Puzzle: http://hive.sewanee.edu/ldale/maps/10/06-LOCAL.html

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♪

Alright, here we go!

If I want to turn this globe
into a flat map,

I’m going to have to cut it open.

In order to get this globe to look
anything close to a rectangle lying flat,

I've had to cut it in several places.

I've had to stretch it so the
countries are starting to look all wonky.

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

That was mathematically proved,
by this guy, a long time ago.

Since around 1500s,

mathematicians have set about
creating algorithms that

would translate the globe
into something flat.

And 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 of the

points 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 the math used by map makers
to project the globe

Will effect 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
this map in school.

It’s the projection Google Maps uses.

The Mercator projection is popular
or 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.

[Ding]

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 to the globe, you can
see that this line is not shortest route.

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

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

was able to preserve direction
by varying the distance between

the latitude lines
and also making them straight.

Creating a grid of right angles.

But that created some 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 if you look at a globe for
Greenland’s true size,

you’ll see it’s way
smaller than Africa

By a factor of 14 in fact.

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

and then we projected that
onto the Mercator map

we would end up with this.

The circles retain their round shape,
but are enlarged

as they get closer to the poles.

One modern critique of this is that the
distortion perpetuates imperialist

attitudes of European domination
over the southern hemisphere

"The Mercator projection has fostered
European imperialist attitudes for centuries

and created a ethnic bias
against the third world."

"Really?"

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

you can use the Gall-Peters projection,

this is called an equal-area map.

Look at Greenland and Africa now.

The size comparison is accurate.

Much better than the Mercator.

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

Here are the dots again so we 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
around the world.

[Rocket blasting off]

"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."

This global positioning system
wiped out the need for paper maps

as a means of navigating

both the seas and the sky.

Map projection choices became less about
navigational imperatives and more about

aesthetics, design,and presentation

The Mercator map, that once vital tool of
pre-GPS navigation,

was shunned by cartographers who

now saw it as misleading.

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

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 90 degree left turn on
the street you’re driving down.

The distortion is minimal when
you are close up.

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

Most modern cartographers have
settled on a

variety of non-rectangular
projections that

split the difference between distorting
either size or shape.

In 1998 The National Geographic Society
adopted The Winkel-Tripel projection

because of it’s 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 with a new perspective on the planet.

And each useful for a different task.

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

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

of projections,

And just remember:

there’s no right answer.

If you yourself want to poke fun at
the Mercator projection

You can do so,
by going to thetruesize.com

Which is a fun tool that allows you to
drag around whatever country you want

around the map and see how it
is distorted depending on where it is.

I also want to say a big thanks,
to Mike Bostock

who's open source project
on map projections,

was a huge help in this video.

I'll put a link to both of those things
down in the description.