# Is the coastline paradox only applicable to physical coastlines? **URL:** \ **Category:** Factual Questions\ **Created:** [June 22, 2021, 4:27pm UTC](https://boards.straightdope.com/t/is-the-coastline-paradox-only-applicable-to-physical-coastlines/944844 "2021-06-22T16:27:12Z")\ **Posts on this page:** 1\ **Showing post:** 118
**Author:** ![Dr.Winston\_OBoogie](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/dr.winston_oboogie/32/2945_2.png) [@Dr.Winston\_OBoogie](https://boards.straightdope.com/u/Dr.Winston_OBoogie)\ **Post date:** [June 25, 2021, 1:52pm UTC](https://boards.straightdope.com/t/is-the-coastline-paradox-only-applicable-to-physical-coastlines/944844/118 "2021-06-25T13:52:48Z")
> [@Chronos](#): > > Anyone have any problems with any of these points? A little bit. And, I think this is where the confusion comes in: > [@Chronos](#): > > 5: In any of these mathematically ideal shapes, as you look at smaller and smaller scales, the total length increases without bound. That is to say, if you pick any finite number, there is some measurement scale small enough such that, if you measure at that scale or smaller, the total length will exceed your chosen length. In other words, the length is greater than any finite number. I would throw more weasel words in there, like “there some theoretical measurement scale…” I think the whole confusion here comes from literalists saying “of course we can measure the coastline of Norway” because they are thinking of physically measuring the coastline with instruments that can be physically created vs. the mathematical fractal theory that says “using infinitely smaller rulers…” I suppose it would be possible to measure the coastline of Norway using electron microscopes; the mathematical theory assumes you can get 10X more accurate than that, and then you can get 10X more accurate than that, and then you can get 10X more accurate than that, and… The coastline paradox is a great mathematical question that in its raw statement has no application in the real world. OK, a very small application - the coastline of Norway can be calculated at roughly X if you sail around it; Y if you include the fjords; Z if you include going around the rock formations within the fjords. Past that, measuring coastlines is pretty useless. The mathematical theory, however, is useful in, well, mathematics and limit theory; probably useful in physics and astrophysics. It’s called theoretical mathematics for a reason - great and necessary for mathematics; limited application in every-day life. --- _[View the full topic](https://boards.straightdope.com/t/is-the-coastline-paradox-only-applicable-to-physical-coastlines/944844)._