Coastline Paradox Explained

I was searching around on youtube when I found an interesting question: how long is the United States’ Coastline? The CIA says that it is 18,924 miles, the Countries with the Longest Coastline quiz lists 69,500 miles, and NOAA says that it is 95,471 miles. So, which is right?

The short answer is that they are all wrong. But to understand this, let’s use a smaller example. I choose New Guinea. Let’s start measuring New Guinea’s coast with sticks of about 310 miles (500 km). When you do this, you will use six of these sticks, making it about 1865 mi. But, it looks nothing like the actual shape of New Guinea. Let’s try using a smaller unit, cutting it in half. By this count, there are 15 sticks, a total of 2330 miles, more than 450 more than the first measure. Next, let’s cut it in half again, with 33 sticks at about 2560 mi. 1865, 2330, and 2560 are completely different numbers. You can see that with smaller and smaller units, the length gets longer and longer. But why?

To understand this, we will need to understand a mathematical shape called a fractal. A fractal is a shape that has another of that shape inside, and so on. The same thing is with the coastline. We could go down to the atom, triggering more problems. There will be near-infinite atoms, which will mean that the length is infinity. But as we all know, some islands’ coastlines must be smaller than others, like Canada and Iran, or Indonesia and Japan. So, how do you measure coastlines? Leave your thoughts in the comments!