Science operates according to a law of conservation of difficulty. The simplest questions have the hardest answers; to get an easier answer, you need to ask a more complicated question. The four-color theorem in math is a particularly egregious case. Are four colors enough to identify the countries on a planar map, so that two bordering countries (not counting those that meet at a point) never have the same color? The answer is yes, but the proof took a century to develop and filled a 50-page article plus hundreds of pages of supplementary material.
More complicated versions of the theorem are easier to prove. For instance, it takes a single page to show that a map on a torus requires at most seven colors. The latest example of unconventional cartography comes from philosopher Hud Hudson of Western Washington University in a forthcoming American Mathematical Monthly paper. He presents a hypothetical rectangular island with six countries. Four occupy the corners, and two are buffer states that zigzag across the island. The twist is that the zigs and zags change in size and spacing as they go from the outskirts toward the middle of the island: each zigzag is half the width of the previous one. As the zigzags narrow to nothingness, an infinite number of them get squeezed in.
This article was originally published with the title Color Madness.