““The length of the coastline, in a sense, is infinite.””
I don’t get it. The length of a coastline if measured from the mean high tide could be measured to be a known quantity.
Is the infinite description a relative term based on observation from different perspectives?
It’s the same paradox as you see in the following anecdote:
If a rabbit hops halfway from his position to a carrot in one second, then half the remaining distance in the next second and half the remaining distance in the next, etc., how long will it take the rabbit to reach the carrot? Answer: forever. His velocity approaches zero since the distance he covers approaches zero while the time remains constant.
If you define the coastline down to the individual grains of sand on the beach and even beyond that, to the very atomic level, it can be argued that the distance approaches infinity. But of course that is absurd, since APPROACHING infinity is not the same as infinity. 10 ^^ x is a very large number, depending on x, but it is still not infinite.
The length of the coastline is proportional to the scale of the measurement.
If you measure in miles, you get one value.
If you measure in yards and convert that to miles, you get a larger value because the number of bumps and indentations in the coastline you can measure and don't have to average around is larger.
If you measure in inches and convert that to miles, you get a larger value still because you can now measure around every pebble and crack in the rock.
Take your measurements down to an infinitely small scale and you get an infinitely long coastline.
Or... Just see post 6.
:o)