In actuality, the concept of an infinite fractal is not applicable to a coastline; as progressively more accurate measurement devices are used (with the measurement result growing every time), other, practical problems with measurement emerge.
- The sea is in constant motion, meaning there is no fixed “coastline”.
Even if the sea’s movement could be halted while measurement took place, there would be no way (beyond arbitrary decisions) to define where the coastline lies in terms of river outflow. A measurement including the entire banks of every river that extends into a landmass would conflict with many interpretations of a coastline, yet no established technique exists for selecting an arbitrary line where river becomes sea.
Even if the issue of rivers were overcome, it would still be impossible to decide which the boundary between land and water is, as land may be wet but not submerged.
Even if such a definition could be agreed upon, as increasingly accurate measurement is performed, the problem of measuring the boundary of an atom—which ultimately does not have a defined boundary—arises. Even in the classical model of an atom, which assumes atoms are composed of individual solid particles, most of an atom is made up of the space between these particles. This problem is further exacerbated when other, more modern models of the atom are considered.