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• This video is made possible by brilliant.org.

• The first 755 people to sign up with "Brilliant", will get 20% off their premium subscription.

• So, here's the problem that this video is going to be talking about.

• If you look at any map and see America, you might think that it's easy

• Just measure the outline of the country and you have your answer.

• Several people and organisations have already tried this though.

• Like the Congressional Research Institute, that calculated it to be

• A second study from them that changed it to

• The CIA puts it at

• and a study from "NOAA" calculated the shoreline to be

• You may have noticed that all of these numbers are different.

• Which is weird, because they're all just measuring the same coastline.

• So, what's going on?

• Well, let's move over to a smaller country like, the United Kingdom

• and measure the coastline of Great Britain

• to get a clearer picture.

• Obviously, the coast of Britain isn't straight

• Every time you look closer at a line that looks straight

• you'll see more curves & bends

• So, how do you measure the length of the coast

• if, every time you look more closely, it never actually becomes straight

• You end up using the smallest measurement unit feasible.

• So, if you were to measure the British coast, using length of 100km

• you'd end up using 28 of them and get an answer of

• but if you shortend your measuring units down to 50km's

• you'd end up using 68 of them and get an answer of

• which is, 600 kms longer than your first measurement was!

• This is called

• and anybody's answer to how long a coastline is

• depends on what size of measurement they're using

• first observed by a guy named

• Lewis Fry Richardson

• back in 1951, as a way to explain how Portugal and Spain

• had come up with totally different answers to their mutual border length.

• The coastline paradox has been annoying cartographers ever since

• Basicaly, the smaller a unit measurement you use to measure a coastline

• the longer your answer will become

• You could, theoretically, go all the way down to the molecular level for your measurement unit

• but if you do that, the length of the coast seems to approach infinity

• it doesn't seem to make any sense that you can have a defined space

• with a finite area, like Great Britain

• be surrounded by an infinitely long perimeter

• but there is a similar concept that can be found in mathematics called

• A "Koch Snowflake", is probably the easiest way to visualise this concept

• So, imagine a triangle, with equal sides of one

• put another triangle of each side with equal lengths of one third

• you can keep repeating this process forever

• and if you zoom into a snowflake it essentially goes on forever.

• when you zoom back out to the original starting point

• you're left with a shape that has a finite area

• but an infinitely long perimeter

• A lot of coastlines across the world has similar properties to this

• so, you can keep zooming in and zooming in on the coast of Britain

• and the coastline will continue to look roughly the same

• No matter how far down the rabbit hole you go

• as mentioned previously, you'll eventually hit the molecular level, if you zoom in far enough

• and you'll be measuring a beach by counting atoms

• if you did this forever, you'd find the coast of Britain to be probably millions of km's in length

• which, just isn't very practical or easy to understand

• There's also the minor problem, that coastlines tend to change all the time, with erosion

• every time a wave crashes on a beach, it's shape it changed by a little

• and that is really hard to accurately pin down

• on top of this, sea levels are rising around the world

• which can drastically alter the way a coastline looks

• in extreme case, like what might happen to the maldives in a few decades

• entire land masses may become completely swallowed

• on the other hand, there's the dutch

• who have been adding land to their coastline now for over 700 years.

• The point is, Earth is constantly evolving. So good luck going out to a coast with a microscope

• and measuring the length that way.

• Every number you see online or in a book for how long a coastline is,

• is basically just a

• The true value is impossible to know, and that is the

• Just take a look at this list from the CIA world factbook

• on the countries with the longest coastline for a few surprises

• According to them, Canada is first, which kind of makes sense

• but the really surprising one is Norway, in second place

• at a first glance Norway's coast doesn't seem too long

• especially when compared with countries such as Russia or The United States

• but when you zoom in closer, Norway's coast

• get's pretty wild

• Just look at all these nooks and crannies and islands and fjords

• The CIA puts the total length of this coast at

• which, if you stretch that out all in a vertical line

• would circle the entire Earth at the equator almost one and a half times

• if you want to kill your entire weekend and see the coastline paradox in action

• try measuring the Norwegian coast from the south all the way to the border with Russia

• and put a comment down below comparing your answer with everyone else's

• of course if you want to do this, or any other coastal measurement.

• You'll need an understanding of Geometry, Algebra and Fractals

• Numbers and concepts like these are confusing for a lot of people

• including myself

• It was confusing for me, at least, until I tried Brilliant.org

• rather than telling you how to do algebra problems by memorising things

• they start by teaching the intuitive ideas behind algebra

• by playing through their puzzles, you get to understand, how algebra works

• Brilliant also has tons of other really interesting courses on topics like astronomy.

• Solar energy

• Computer memory

• and special relativity, which similarly, guide you along as you build your core knowledge

• You can take as many of these incredibly designed courses as you want

• with their premium subscription

• which, by being one of the first 755 to click on the link in the description

• you can get for 20% off

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B1 coastline coast measurement length measuring algebra

# The Coastline Paradox Explained

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林宜悉 posted on 2021/02/27
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