In reply to Franco Cookson:
> Are you saying there's a way to definitively say one coastline is longer than another, without having to specify at what scale you're viewing the two coastlines?
It depends on the specific coastlines and the “Hausdorff dimension” of each, which says how their measured length scales with ruler size.
If both have the same characteristics ie the same Haussdorf dimension - meaning their measured length increases by the same fraction when you, say, halve the length of the measuring ruler, then if one is longer then the other for one particular measurement size, it’s definitively longer for all measurement scales.
If they scale differently - for example a coast made of straightish cliffs like near Saltburn vs the complex marshes of Foulness island, then there may be a critical ruler length for which one coast is longer for rulers smaller than the critical scale, and the other is longer for longer rulers.
For coastal counties in some given geographic region the way length scales with measure size is going to be pretty similar meaning that a ranking of coast lengths is going to be invariant over a wide range of measurement scales, so long as you take a fixed view on the inclusion or exclusion of tidal river sections across those scales.
Post edited at 20:22