All Maps Are Wrong But Many Are Useful

It is an inarguable mathematical fact that every map is a lie.

- Evelyn Lamb

Well, a map is not a lie in the sense of a statement intended to deceive someone. Maps do give us useful information about the world. But every map is a compromise. Statistician George Box famously said, “All models are wrong.” He was pointing out that no simplified mathematical formulation can perfectly capture the complicated reality of the world. He followed it up, though, with, “But some are useful.” Even models that are incomplete can help us understand the world, as long as we understand their strengths and limitations. The same is true of maps.

Mathematical Impossibility

In the 1820s, German mathematician Carl Friedrich Gauss proved the theorema egregium, which is Latin for “remarkable theorem.” (A theorem is a mathematical statement that can be proved using a chain of logical reasoning that starts with some basic assumptions.) One consequence of this theorem is the fact that there is no way to draw a flat map of the spherical Earth without some distortions. Of course, if you’ve ever peeled an orange or clementine and tried to press the peel completely flat, you might have figured that out already. It always tears somewhere.

Mathematical impossibility is no match for the convenience of a flat representation of the world, though. Geography textbooks and magazine pages just can’t accommodate tiny globes. So until virtual reality, holographic, or replication technology improves significantly and we can have accurate globes at our fingertips whenever we want, humans will keep drawing 2D maps despite Gauss’s theorem.

Compromise, Compromise, Compromise

Some maps distort area, some distort shapes, some distort directions and distances. Different situations call for maps with different strengths. For hundreds of years, cartographers have been creating maps that work the best for particular situations.