The wiki article is barely a stub, but this looks to be a useful article on the topic, for those with access to the full article (which I don’t have.) Also, this. (tl:dr, like with many science questions, it is complex and mathy.)
This reminds me of a minor mystery I encountered years back–while beach combing with my grandmother we happened on a spot where (aged, so no longer lettered) lettered olive shells were washing up with the waves. In a matter of minutes, from a patch of beach maybe 20 feet wide, between us we collected more than 500 of the shells as they washed up at our feet. Normally, you didn’t often find even one of them while walking along the wave line, with finds being at the upper beach as rain exposed them from sand dredged from off-shore and piped in during beach reclamation projects. I have no idea why so many old shells were concentrated in that one narrow location.
But you can extend the same argument regarding linear dimensions to three dimensions as well, so the area of a continent is even more infinite than its coastline!
The fractal infinite dimension of coastlines and English muffins is immaterial (heh) because the divisors are not symbolic points in a mathematical domain but physical objects with a discrete size. So you can safely measure the amount and call it quits without appeal to the infinite.
But the relevant dimension for erosion is the three-dimensional land surface, not the two-dimensional area conventionally considered, so it should take into account the vertical dimension. But in any case, they don’t measure coastlines using infinitely smaller measurements either. It’s a theoretical argument. (Notice the smiley in my post.)
