How long is the coastline of Britain? It depends on your ruler. Measure with a 200 km stick and you get about 2,400 km. Measure with a 50 km stick and you get 3,400 km. Shrink the ruler further and the answer keeps growing — apparently without bound.
Mandelbrot’s insight was that the coastline isn’t a curve of some hidden true length; it’s a fractal, and the rate at which the measured length grows is the meaningful number. Britain’s coast has a fractal dimension of roughly 1.25 — somewhere between a line and a plane.
I think about this whenever someone asks how long a project will take. The honest answer is: with which ruler? At the resolution of quarters, six months. At the resolution of days, an unbounded sum of small surprises.
Some questions don’t have answers; they have exponents.