Agreed that the fact it's continuously changing is an additional issue, but I don't see the "eventually you start working with curves" argument. Where are these

Agreed that the fact it's continuously changing is an additional issue, but I don't see the "eventually you start working with curves" argument. Where are these curves on a typical coastline? If you're measuring the coastline on a map, that argument holds, but the map is only one representation of the reality, and they've already made decisions regarding minimum feature size implicit in the construction of the map. But yes, also agreed that measuring rivers should be fine, because you can represent it as a one-dimensional line along the 'centre of mass' of each segment of the river, which should give well-defined values regardless of what the 'edges' of the river look like.