The problem with projections

Ian Delaney
London 51° 30' 23.112" N, -0° 7' 37.956" E

A map projection is an attempt to portray the world’s surface in two dimensions – such as for a wall chart or an atlas.

So why is that a problem? Because the world is (approximately) round. If you peel the paper off a globe and lay it out on a table, it will look a bit like this:

800px-Waldseemüller-Globus

This example is from one of the world’s earliest globes to include America (sort-of). It was made in 1507, though the same techniques are still used today. Those double-arc shapes are called ‘gores’. The same principle is used to make other spherical objects, such as hot-air balloons.

As you can easily see, while those gores join together to make an accurate globe (or it would be, if we knew more about the world in 1507!), it’s not very useful when it’s flattened out. Countries and continents get split into segments. You can’t use it to plan a trip or easily understand the size and position of countries.

So geographers invented the idea of projections. They ‘project’ the surface of the sphere onto a flat surface. They make sure that the countries and continents are joined together, as they are on the ground. And then they fill in the gaps with either white space, decorations or ‘extra’ sea.

The trouble is, however you decide to make this projection, it’s going to distort the reality of the globe in some way.

Geographers have to choose between:

  • Straight lines for latitude and longitude;
  • Correct surface area for countries;
  • Correct distances between places;
  • Correct shapes, and several other possible requirements.

Sadly, it’s actually mathematically impossible to have all of those things on a 2D world map.

The most frequently seen projection was originally invented by the Flemish geographer Gerardus Mercator in 1569. If you imagine putting an illuminated globe inside a tube of photosensitive paper, then the Mercator projection is roughly what you’d end up with when you unroll that piece of paper.

Here is Wikipedia’s version of this projection:

1061px-Mercator_projection_SW

Because it’s so very familiar, it’s hard to immediately understand the problems. Basically, everything close to the equator is the right size. As you get further north and south, countries and continents get stretched out. (Imagine the light cast by that illuminated globe inside the tube of paper to understand why).

So Europe and North America are massive compared to their actual size. Africa, South East Asia and Latin America? Not so much.

Greenland is not the same size as Africa, people are sometimes astonished to learn. In fact, it’s around one-third the size of Australia. Nor is Antarctica larger than the rest of the continents. And as we’ve noted before, in reality, you could fit much of the rest of the world inside the vast expanses of Africa.

The Mercator projection was useful for navigation, though. The straight lines ‘worked’ when you were travelling on the high seas. If you leave Lisbon in your caravel and head west, then you will hit Delaware. And so it caught on, and has stuck with us ever since.

The straight lines approach is so useful for travel that the Mercator projection has also made its way onto the most popular digital maps websites. When people search for places or plan routes with map apps the area shown is usually relatively small enough to be unaffected by any distortion. It’s the same reason why at human scale, earth may seem flat.

 

For many people, by this point, this projection just looks ‘normal’.

But it quite clearly has a political bias, as well as the issue of it being incorrect in terms of country sizes. The US and Europe, not coincidentally the dominant world powers during the period this projection was most popular, got a much better deal than the rest.

Many efforts have been made to make a more politically fair map. A couple of weeks ago, we drew attention to the Peters Map, popularised by German film maker Arno Peters in 1967 (though the idea had been invented more than a century before by James Gall, a Scottish clergyman). This projection attempts to redress the political balance by making the size of countries true to their surface area. It has the added bonus of retaining the correct directions along straight lines from the Mercator projection.

1200px-Gall–Peters_projection_SW

As with so many things, US drama series West Wing nailed the differences:

 

 

This, more fair, representation of the world’s countries has actually proven very popular, though it’s not without its flaws. The shape of countries in the tropics and near the poles gets distorted. As tomsnq pointed out in our comments section, “Australia is actually wider than it is tall- but not according to [the] Peters projection.”

There have been many, many attempts to make fairer or more accurate projections. This one – the two point equidistant projection – concentrates on making the distances between points on the earth’s surface accurate.

1146px-Two-point_equidistant_projection_SW

That’s definitely a useful property for a map to have, of course. But this isn’t a very complete ‘world map’, as American, African and Australasian readers will probably have already noted.

So where does that leave us? For general use, the answer might be a compromise. A world map that isn’t quite right when it comes to any individual criteria, but isn’t as terribly wrong in any of them, either, as other formulae used to create projections.

1200px-Winkel_triple_projection_SW

This is the Winkel tripel projection, invented in 1921. While it’s not totally accurate on shapes, distances, directions or surface area, it’s nonetheless regarded by many, including the National Geographic Society, as one of the leading maps in terms of having the smallest degree of distortion overall.

The other answer is to choose a projection based on what you’re going to use it for. If you’re planning a trip, then correct distances and directions between countries are important. If you’re making political decisions, then surface area ought to count for something. If you’re actually on the ground in a country, then the right shape is going to be more of a priority.

Or maybe you should just buy a globe.

image credits: Wikimedia Commons

Topics: Cartography, Features

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