Why doesn't a coastline have a true length?

A coastline has no true length because the answer depends on the size of your ruler. Measure a coast with a long ruler and you skip over every bay and headland smaller than the ruler. Use a shorter ruler and you follow more of those wiggles, so the total grows. And coasts have wiggles at every scale, from giant bays down to rocks, pebbles and grains of sand. There is no obvious point at which to stop, so measuring in finer detail never settles on an answer; it just keeps adding to the total. This is called the coastline paradox.

The person who noticed it was Lewis Fry Richardson, an English Quaker and pacifist who had served in an ambulance unit in World War I. Later he wondered whether countries with longer shared borders were more likely to go to war, so he collected border lengths. He found a strange mismatch: Portugal said its border with Spain was 987 kilometres long, while Spain said 1,214. Neither was lying. They had simply measured with different rulers.

At the time, scientists ignored him. Years later, in 1967, the mathematician Benoit Mandelbrot built on Richardson's work in a paper called "How Long Is the Coast of Britain?". Coastlines, he argued, behave like shapes that look similar at every magnification, the kind of shape he would later name a fractal.

So when an atlas tells you how long a coast is, it is really telling you how carefully somebody chose to measure it.