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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.

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

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