yego.me
💡 Stop wasting time. Read Youtube instead of watch. Download Chrome Extension

What Is The Coastline Paradox?


2m read
·Nov 10, 2024

I've been driving along Australia's famous Great Ocean Road. And I'm stopped here near the Twelve Apostles, which are these big sandstone bluffs. Actually, there's only eight of them left because the others have eroded over time. And erosion is really what's given us this coastline the way it looks now.

So that brings to mind a question for me. Which is, "How long is the Australian coastline?" Well, if you were to measure it out in lengths of 500 kilometers, you would find that it's about 12 and a half thousand kilometers long. But the CIA World Factbook puts the figure at more than double that: over 25,700 kilometers.

But how can it be that we have two different estimates for the length of the same coastline? Well, this is called "The Coastline Paradox." The answer is, it depends on the length of measuring stick that you use. So, if you connect up the dots from cliff to cliff to cliff, you get a shorter length of coastline than if you measure with a smaller measuring stick and measure into every inlet.

So what length of measuring stick should we use? Well, in theory, you can go all the way down to the size of a water molecule. And if you do that, then the length of Australia's coast is virtually infinite. Do you believe me that you could have a finite area object like Australia bounded by an infinite perimeter? It doesn't seem to make sense.

But I can give you another example of this: it's called the Koch snowflake. So what you do is you take a triangle with sides of length 1 and then on each side add another triangle with sides of length a third. Continue doing that again and again forever. What you end up with is a shape which is a finite area but an infinite perimeter.

Shapes like these are called fractals, and many coastlines have the same fractal structure, which means they have some sort of self-similarity on many different scales. So you can zoom in and zoom in, and the coastline looks roughly the same.

So if you want to know the length of a coastline, you need to first specify the length of your measuring stick because that's what the answer depends on.

More Articles

View All
Seeing Inside a Thermite Reaction
[Derek] This is the first in a series of videos about a chemical reaction discovered over 125 years ago. It releases a tremendous amount of heat. Oh no, the GoPro. Liquefying metal. It is so hot. It is not an explosive, but it can cause explosions. That i…
Catch of the Week - Hundred-Incher | Wicked Tuna
[Music] Oh nice, Mark. [Music] Dude, we’re on! It’s a big one! Go to work! Yes, sir! Thank God that Drake freed us from the anchor line earlier, or we wouldn’t be able to chase this fish down. Get him, get him, get him! Get some, baby! Get some! Nice wor…
Bill Belichick & Ray Dalio on Identifying and Addressing Mistakes: Part 2
So we do, uh, some of the things, we actually video everything that’s going on, and then you could look at the video and then reflect on it. One of the things I found is that, um, some people, when they look at their, uh, mistakes, react differently than …
I Am Associated With Red Straps Now #shorts
Are there any watches where you think you shouldn’t put a red strap on? I own a 5711 in its mintage form. I wear it; the bracelet for that is part of the heritage of the piece. But it means it can’t take the journey with me onto television because I’m ass…
New Zealand's Stunning Landscapes | National Geographic
First thing you’re struck by is the landscape, like it’s absolutely stunning the entire way. The landscape changes so quickly from one amazing vista to the next. As a photographer, like you can’t really ask for anything else. There’s a lot of inspiring pl…
Environmental change and adaptation in Galápagos finches | Middle school biology | Khan Academy
This here is a picture of the ground finch of the Galapagos Islands, and one of its primary sources of food is seeds that it finds on the ground. If we go back to 1976, we can look at the distribution of beak depths, and these beak depths I would assume a…