You can’t shrink the yardstick down to an infinitesimal size.
Coastlines are not well defined. They change in time with tides and waves. And even if you take a picture and try to measure that, you still have to decide at what point exactly the sea ends and the land starts.
If the criteria for that is “the line is where it would make a fractal” then sure, by that arbitrary decision, it is infinite. However, a way better way to answer the question “where is the line” is to just decide on a fixed resolution (or variable if you want to get fancy), which makes the distinction between sea and land clearer.
It is like saying that an electron is everywhere in the universe, because of Heisenberg’s uncertainty principle. While it is very technically true, just pick a resolution of 1mm^3 and you know exactly where the electron is.
You can’t shrink the yardstick down to an infinitesimal size.
Coastlines are not well defined. They change in time with tides and waves. And even if you take a picture and try to measure that, you still have to decide at what point exactly the sea ends and the land starts.
If the criteria for that is “the line is where it would make a fractal” then sure, by that arbitrary decision, it is infinite. However, a way better way to answer the question “where is the line” is to just decide on a fixed resolution (or variable if you want to get fancy), which makes the distinction between sea and land clearer.
It is like saying that an electron is everywhere in the universe, because of Heisenberg’s uncertainty principle. While it is very technically true, just pick a resolution of 1mm^3 and you know exactly where the electron is.