In 1967, the mathematician Benoit Mandelbrot published a paper with a deceptively simple title: 'How Long Is the Coast of Britain?' His answer was uncomfortable. The question has no fixed answer.

If you measure with a 200-kilometer ruler, you get one length — say, 2,400 kilometers. Use a 100-kilometer ruler instead, and your shorter ruler captures inlets the longer one stepped over. The total grows. Use a 1-kilometer ruler, and you measure every cove, every spit, every rocky promontory. The total grows again. Use a meter stick, and you measure individual boulders. Use a centimeter, and you measure pebbles.

The coastline gets longer as your measuring stick shrinks. It does not converge. There is no 'true' length to which the measurements settle. As the ruler approaches zero, the measured coastline approaches infinity.

This is the defining property of a fractal: a shape that has more detail at every smaller scale, never smoothing out. Mandelbrot showed that coastlines, mountains, lightning bolts, river networks, broccoli florets, lung passages, and the patterns of capillaries in your tissue are all fractals. They have a fractal dimension — a number between 1 and 2 for line-like things — that quantifies how rough they are. The British coastline has a fractal dimension of about 1.25.

Real-world measurement of coasts therefore depends on resolution. The CIA World Factbook says Britain's coastline is 12,429 kilometers. Other sources give 19,491. Both are right at their respective scales.

Mandelbrot's insight reshaped geometry, computer graphics, finance, geology, and biology. The mathematics of natural shapes turns out to require fractals.

There is no exact length to your country's coastline. There can't be.