# Can Geometry Be Racist?

I recently stumbled upon this article by the Daily Mail: “Why every world map you’re looking at is WRONG: Africa, China and India are distorted despite access to accurate satellite data.” The article’s main beef is with the Mercator projection, a map which you have definitely seen and which looks like this [from Wikipedia]: Here is a political map in the style of Mercator [source, with watermark]: The point of the Mercator projection is to preserve straight lines and compass orientation (i.e. very useful for navigation). For example, Atlanta and Los Angeles have roughly the same latitude, and are separated by 2173 miles. However, if you go up straight north from both cities, the distance starts getting smaller and smaller, until it eventually reaches zero when you’re at the north pole. To account for this change in distance, the Mercator projection exaggerates areas that are far from the equator. Here’s a visualization of this distance getting smaller as you go further from the equator [source; just focus on the triangle on the globe; the picture was demonstrating non-euclidean geometry where the angles of a triangle don’t have to add up to 180 degrees]: So what’s the point? Now that the geometry lesson is out of the way, here is the point of the Daily Mail article. If you look at the Mercator maps, you’ll note that Greenland looks at least as big as Africa, when it is actually 14 times smaller (836,000 sq miles vs 11,670,000 sq miles). It also notes that the Scandinavian countries look bigger than India, when, in fact, India is 3 times larger. These are all great points. However, one statement sounds strange: “It gives the right shapes of countries but at the cost of distorting sizes in favour of the wealthy lands to the north.” Another statement is, “Much of this is due to technical reasons, said Mr Wan, while other inconsistencies are caused by ideological assumptions that can change the way we see the world.” “The wealthy lands to the north”? Ideological assumptions? I’m not sure if the author is just using these phrases sensationally, but there is an issue here. The Mercator projection is not racist or imperialist or north-ist. It is simply a geometric application. In fact, it is physically and mathematically impossible for a 2-dimensional map to accurately portray the globe.

The author even concedes this point in the article: “The biggest challenge is that it is impossible to portray the reality of the spherical world on a flat map – a problem that has haunted cartographers for centuries.” Then hasn’t the author figured out the solution to the title? “Why every world map you’re looking at is WRONG: Africa, China and India are distorted despite access to accurate satellite data.” Answer: because of geometry, it is, has always been, and always will be, impossible. The only way to look at the globe truly accurately is via… a globe. Or Google Earth. So what then is the point of the Mail article? A refresher course on history?

Anyways, it is an interesting topic to think about; I just thought the implied arguments were severely flawed. Namely,  the statement that “other inconsistencies are caused by ideological assumptions that can change the way we see the world” implies that perhaps the Mercator projection causes us to think more of “big” countries far from the equator, which happen to be richer, and less of “little” countries nearer the equator, which happen to be poorer. Also, the fact that this pseudo-explanation is even implied seems to weaken the real answer to the question, why every world map is wrong. Look at the phrasing again: “Why every world map you’re looking at is WRONG: Africa, China and India are distorted despite access to accurate satellite data.” The northern racism explanation (latitude-ism?) makes it seem like we can make accurate maps because of accurate satellite data but we don’t because we want to perpetuate northern superiority and oppress the southerners. (Of course, the Mercator projection equally distorts southern countries, but most of Earth’s landmass is in the Northern hemisphere.)

Thus, the article is extremely misleading and is another example of taking some of the views of postmodernism too far while simultaneously discounting mathematical knowledge. The objective facts—the impossibility of accurately representing a sphere on a plane—are right there and we even see them, but some of us just choose to ignore them. Also, the comment section of the Mail article seems to share this sentiment of critique. Plenty of factors contribute to racism, but geometry is not one of them.