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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

  • [End Screen]

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B1 coastline coast measurement length measuring algebra

The Coastline Paradox Explained

  • 3 0
    林宜悉 posted on 2021/02/27
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