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