The infinite coastline paradox

How unexpected difficulties in a practical measurement problem challenged fundamental conceptions of length and led to a new theory of dimension, while revealing monsters lurking at small scales.

A century ago Lewis Fry Richardson (1881–1953), noted polymath with prizes now named in his honor in metereology and scientific peace research, had a mathematical theory for predicting the likelihood of war between two countries based in part on the length and nature of their common border.

Aiming to test his theory, he looked into the details of variou…