How long is the coast of Britain? The answer depends entirely on your ruler
Measure a coastline with a 100-mile-long ruler, and you get one length. Measure the same coastline with a 1-mile ruler, tracing every bay and headland the longer ruler skipped over, and you get a noticeably bigger number. Keep shrinking the ruler and the measured length keeps growing, seemingly without limit. Does a coastline actually have a single, well-defined length at all?
Reveal the answer
Not in the usual sense. Mathematician Benoit Mandelbrot used this exact puzzle, first noticed by meteorologist Lewis Fry Richardson, to argue that coastlines behave as fractals: their measured length genuinely depends on the scale of measurement, with no limit as the ruler shrinks toward zero. Instead of a single length, a fractal dimension, somewhere between a one-dimensional line and a two-dimensional area, is the only number that stays stable no matter what scale you measure at.