Ink Tea Stone Leaf

Recently, the U.N. General Assembly voted to endorse a version of the world map that more accurately depicts the relative size of the Earth’s landmasses. As usual when this issue pops up, the discourse has focused on the apparent size of Africa, an enormous continent which appears to be suspiciously modest on some common types of world maps, including those that use the Mercator projection. The vote in the General Assembly, by the way, was 164 in favor to one against, with six countries casting no vote. The United States was of course the only member country to oppose this non-binding endorsement so much as to actually cast a vote against it, which could easily have been anticipated from our perversely comical tradition of voting against overwhelmingly popular non-binding resolutions on seemingly every conceivable subject. This tradition does extend much further back in history than our present era of humiliation, in which Donald Trump embarassingly embodies and literalizes every historical criticism of our foreign policy, and that really makes it sadder if you think about it. But I’m not here to condemn the administration today, though it is appropriate to do so every day. I’m here to idly muse about maps and their projections.

For those who don’t know much about maps or why they need to be projected, here is a brief explanation. Maps of the world displayed in various settings (classrooms, for instance) are typically displayed as rectangles, like most other pictures. Earth is not a rectangle, and any child who has not been deeply indoctrinated in flat-Earth ideology understands that if you were to travel across the map from east to west, you would loop around back to the eastern side. However, they may not have considered that the geometrical implications of depicting the complete and entire surface of an approximate sphere within the borders of a rectangle are as challenging as they really are. If you were to peel an orange (also an approximate sphere) while keeping the whole skin intact, and press the skin flat on a table, it would not form a rectangle. To make it fill a rectangular frame, you would have to stretch or compress it around the edges, which is exactly what all flat world maps must do to their depictions of the world’s surface.

This process is called “projection,” and there are several approaches to it, but all of them necessarily introduce inaccuracies into the map, because the core premise that the surface of our planet is rectangular is itself inaccurate. In choosing or designing a projection, therefore, you have to decide how you wish to be inaccurate. This choice ultimately depends on what you intend to use your map for. The Mercator projection, developed originally by Flemish mapmaker Geert Kremer (better known by his Latinized alias, Gerardus Mercator) in the sixteenth century, was intended as an aid to navigation by ships on the ocean, and it is very useful for that purpose. If you look at a straight line passing through any two locations on a Mercator map (let’s say Lisbon to Rio de Janeiro), you will see that the line crosses every line of longitude (the vertical, north-to-south lines) at the same angle; if you were setting a course on your ship with the aid of a north-pointing compass, then following the lines on a Mercator projection would surely lead you to your destination.

The only way to accomplish this, however, is to depict lines of longitude as parallel with one another. They are not, in fact, parallel with one another—they bend toward each other as you travel north or south from the equator, and ultimately converge at the poles. Mercator solved this problem by inflating the earth’s surface at its extremes. If the North (or South) Pole is actually a single point, then on a classic Mercator map it is essentially depicted as a line that is the same length as the equator. Every landmass that lies close to the North (or South) Pole stretches along with this line, so that the closer an area of land lies to either pole, the larger it will appear to be. A lot of Mercator maps omit all or most of Antarctica, but those that do not easily demonstrate how extreme the distortion becomes.

If you are not a navigator, and you primarily use a map to get an idea of what the world looks like, the Mercator projection is not very good. It’s actually pretty deceptive. It leaves many a child wondering why Australia ranks among the continents and Greenland does not, when Greenland is obviously so much bigger (Greenland could easily fit inside Australia, in fact). It also presents Africa, which happens to lie on the equator and therefore has minimal Mercator stretching, as if it were much smaller than North America, which extends quite close to the North Pole.

You may wonder why this matters. I’m not always sure that it does matter, but then again, I understand how map projections work. A lot of people don’t, and in their naïve supposition that any given map of the world is reasonably accurate, they may fall victim to a quaint and simple cognitive bias that is common to humanity, namely that bigger things are more important than smaller things. They are a bigger deal, you might say. And if North America and Europe—both of which are more northerly than any continent is southerly (except Antarctica)—are made to look larger than they really are, one might conclude that the Global North is quite a big deal indeed, while the Global South (anything south of the Tropic of Cancer, more or less) is a lesser, even a less consequential deal.

Some people will speak of the Mercator as though it were the product of a conspiracy to hoodwink the world with exactly this misconception, in service of Western imperialism and white supremacy. I think that’s overstating things—Mercator’s map is a tool with a specific purpose, which is still useful to people even centuries past the Age of Sail. Anybody who wants to understand what the Earth really looks like, and what are the relative sizes of things, has access to a superior tool for that purpose—a globe. Take a look at Africa on a decent globe, and you may be astonished by how much space it occupies. Or you may already know, and you’ll just nod, sagely.

You can’t look at both sides of a globe simultaneously, though. You can’t display its entire surface on a computer screen, or a classroom wall, or even a page in a book. The globe works best as a tool that one person can hold in their hands and manipulate, which has unfortunate pedagogical consequences (but also some fortunate opportunities, if you can afford sufficient quantities of globes). For other purposes, you need a flat map. Therefore, you have to pick your poison, and sacrifice some component of what most people would regard as “accuracy.”

There are basically three sacrifices you can make when designing a flat map: you can distort the size of some areas, you can distort the shapes of some areas, and you can use something other than a rectangle. Many maps mitigate the rectangle problem by depicting places like Alaska in both the northwest and northeast extremes of the image (to demonstrate the “wrap-around” reality of the planet), while others are so extreme as to break the surface up into disjointed pieces. The Dymaxion map does not clearly communicate Earth’s spherical nature to a casual observer, but by gum it will show you all the landmasses in essentially their correct proportions.

The map projection favored by the African Union and endorsed by the U.N. is called the Equal Earth projection, which does a pretty good job of balancing the competing compromises required of any map. The sizes are realistic, the shapes are pretty accurate, and it’s rounded at the corners instead of rectangular. This last part helps avoid the problems of the famous Gall-Peters projection, which is often cited as a progressive rival to Mercator and is sort of its philosophical opposite—it relentlessly pursues correct sizes while allowing for highly noticeable distortions of shape. Presumably, a Gall-Peters map might have gotten a sixteenth century navigator and his crew killed, but that’s not exactly our most pressing concern today.

Anyway, we shouldn’t have just one map for all purposes, because no map projection serves all purposes equally well. In my opinion, particularly as relates to classroom applications and education, we need three things:

• A diversity of types of maps.
• Comprehensive lessons on how maps are made and what they do.
• Way, way more globes for people to hold and study.

In my classroom I used to display a world map called “What’s Up? South!” and gleefully field questions about why I had my map “upside down.” My point in using this map, of course, was to illustrate that the equation of North with “up” on maps was merely a convention, having absolutely no basis in physics or any absolute standard of any kind. There are things I dislike about the map—it omits Antarctica and most of the Arctic ocean, and it has much more Mercator-like size distortion than I would have liked to put in front of my students every day. But it also has along the bottom a series of informational panels on different types of projections, so that any person who wants to understand what is going on with this unconventional depiction will be exposed to more alternatives than they might have imagined there were.

Of all the things that a map can accomplish,  I believe that inspiring curiosity is the most important. Earth is too great to be contained by any single depiction, even on a globe. Real education comes with understanding what it is that our limited means can represent of the true shape (and size) of our world.