Your maps are not lying to you

Or, your maps are lying to you but so would any other map.

A week or two ago [edit: by now, sometime last year] a journalist must have discovered thetruesize.com, a nifty site that lets you explore and discover how sizes of countries are distorted in the most common world map, and thus was born another wave of #content in the sea of web media.

Your maps are lying to you! They are WRONG! Everything you learned is wrong! They are instruments of imperial oppressors! All because of the “monstrosity” of a map projection, the Mercator projection.

Technically, all of that is more or less true. I love it when little nuggets of cartographic education make it into popular media, and this is no exception. However, those articles spend most of their time damning the Mercator projection, and relatively little on the larger point:

There are precisely zero ways to draw an accurate map on paper or a screen. Not a single one.

In any bizarro world where a different map is the standard, the internet is still abuzz with such articles. The only alternatives to that no-good, lying map of yours are other no-good, lying maps.

The problem with projection

The essential problem of map projections, illustrated by Mike Foster.

The earth is roughly a sphere, and there’s just no way to transform that to a two-dimensional representation without giving something up. Specifically, you have to mess up shapes, sizes, distances, or directions — or all of them at once. The way in which the round earth is transformed to a flat surface is a map projection (defined by a mathematical formula or algorithm), and Mercator is only one of many possible map projections.

There are some fun interactive ways to learn about map projections. One is to use different configurations of flat sheets around a globe, perhaps even lighted from the inside so as literally to project land onto the sheets.

“The map projection model”

Another is to draw the continents on fruits and vegetables and try to flatten them out. Watch this stop-motion film from 1947 (hat tip Sarah Cordivano), and then celebrate with a cool glass of turnip juice.

The Impossible Map, Evelyn Lambart (1947)

However you demonstrate it, you’ll find that no matter how hard you try, there’s no way to flatten that globe without getting something all out of whack. If sizes aren’t lying to you, something else is.

Choosing what to show and what to hide

Projections aren’t the only reason that no map can be 100% accurate. A map is not a reflection of reality; it is a representation of reality that cannot hope to show everything as it truly is. For one thing, there is simply too much stuff in the world. To fit it all on a map in perfectly precise detail, you’d basically need the world itself, as in a Lewis Carroll passage that cartographers like to trot out:

“That’s another thing we’ve learned from your Nation,” said Mein Herr, “map-making. But we’ve carried it much further than you. What do you consider the largest map that would be really useful?”
“About six inches to the mile.”
“Only six inches!” exclaimed Mein Herr. “We very soon got to six yards to the mile. Then we tried a hundred yards to the mile. And then came the grandest idea of all! We actually made a map of the country, on the scale of a mile to the mile!”
“Have you used it much?” I enquired.
“It has never been spread out, yet,” said Mein Herr: “the farmers objected: they said it would cover the whole country, and shut out the sunlight! So we now use the country itself, as its own map, and I assure you it does nearly as well.”

Maps only work because they are abstractions. They strip away those details that are irrelevant to the map’s purpose, and highlight (even exaggerate) those that are. Broadly, we call such processes generalization, and they include things from smoothing out jagged coastlines, to omitting small roads, to moving a river away from its actual location.

Some generalization operations, illustrated

It’s not only graphical (in)accuracy, though; it’s also that people make those design choices through the whole mapmaking process, starting with the decision to make a map in the first place. You can’t trust any map to show the objective truth. Every map reflects some choices and biases of its maker, be they benign or nefarious. Those choices include map projection.

Navigation and northern agendas

One of the complaints leveled at the Mercator projection, especially in the late 20th Century, is that it promotes a Eurocentric view of the world, as Europe’s (and North America’s) size is exaggerated relative to places like Africa. Perhaps that is indeed part of the reason the projection became so widespread in classrooms and publications. In recent news, Boston Public Schools replaced its Mercator maps with the controversial Peters projection for this very reason. But size exaggeration wasn’t the map’s original intent.

As you probably saw in the articles linked at the top of this one, Mercator developed his projection during an age of exploration, and it was useful for navigation. Its magical property is that rhumb lines (or loxodromes), which are lines of constant bearing, are straight lines on this map, making it easy to plot a course. What that means, for example, is that on the map I can measure that the angle between Boston and Cape Town is 133º (southeast), and if I sail out of Boston and keep my ship pointed at 133º on a compass the entire time, I should end up in Cape Town.

At any point along this path, the compass bearing to Cape Town is 133º, the same angle that’s measured on the map. On most other map projections, this path would not appear as a straight line.

It should be noted that this version of “straight line” is not the same as the shortest, straight line on a sphere, as I’ve tried to illustrate in odd ways before. But that didn’t matter: navigation this way is easier. The map’s lie was useful.

All this is at the expense of accurate sizes. Areas become extremely exaggerated as you approach the poles, with Greenland, somewhat famously, appearing to be about the same size as the more equatorial South America. As it happens, Europe occupies fairly high latitudes and thus is exaggerated in size. Hence the complaints about northern imperialism, or propaganda — Mark Monmonier points to a great example of using the projection to magnify the threat of the USSR — or that we all have a grossly distorted understanding of world geography.

Greenland is not the size of South America, as seen at thetruesize.com

Every map projection has some ideal purpose, and yeah, a simple map of countries isn’t Mercator’s best use case. But before you accept that it’s just the worst thing that ever happened to maps, remember that arguments against the Mercator projection also reflect choices and biases, and a set of priorities in which size accuracy is more important than other things. (I’ve struggled to find evidence that this actually matters, in terms of our grasp on geography.)

Conceivable headline: Your maps are LYING about how far north Maine is!

It’s also far from the only influence on our picture of the world. For all the surprise of learning that Greenland isn’t very big, as a kid I was just as surprised, after seeing enough US maps in the Albers projection, to learn that Maine is not farther north than Minnesota.


Digital epilogue

The Mercator projection saw a resurgence as digital maps came to age, as a version of it is the projection in the now-ubiquitous Google Maps and other similar map services. This caused a collective groan among professional cartographers, not simply because we thought Mercator had finally been supplanted by better general-purpose projections not so long ago, but largely because it led to widespread uses of the projection for purposes that actually do demand accurate representation of size.

The fact is that there are good technical reasons to use Mercator for web maps, and even besides those, our use of web (especially mobile) mapping has kind of arrived back at the projection’s ideal purpose: navigation. The preservation of angles means that “shape” is more or less correct. This projection is kind of amazing in that you can zoom into anywhere in the world, any city or neighborhood, and things will be in what you probably perceive as the correct arrangement. (Nothing looks squished, everything is in the right direction from everything else, etc.) When you’re staring at your phone and trying to find your way around, that’s important.

Be critical of ALL maps

There’s a lot more to a map than meets the eye — and we all look with different eyes. When you see a map, or someone else’s judgment of a map, think critically and to the best of your ability say to yourself some of the following:

  • No map is perfect truth.
  • This map can do some things accurately but must do other things inaccurately — but the same goes for any other map.
  • Who made this map, and why? What biases or agendas might it promote?
  • Who might say that this map is bad? What viewpoints would lead to that opinion?
  • What functions does this map enable that we’d lose if it were different? Do those functions suit the main purpose of the map?