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So, here’s the problem that this video is going to be talking about.
How long is the coast of the United States?
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 12,383 miles.
A second study from them that changed it to 29,093 miles.
The CIA puts it at 19,924 miles.
And a study from “NOAA” calculated the shoreline to be 95,471 miles.
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?
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.
所以如果仔细观察 非要较真的话 如何测量海岸线的长度呢
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 2800km.
But if you shortend your measuring units down to 50km
you’d end up using 68 of them and
get an answer of 3400km.
Which is, 600km longer than your first measurement was!
This is called coastline paradox
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 fractals.
A “Koch Snowflake”, is probably the easiest way to visualise this concept.
那么 想象一个三角形 等边三角形
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 around the world have 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 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 guess or estimation.
The true value is impossible to know, and that is the coastline paradox.
Just take a look at this list
from the CIA world factbook
on the countries with the longest coastline for a few surprises.
根据他们的统计 加拿大的海岸线最长 有道理
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 like Russia or the United States.
But when you zoom in closer, Norway’s coast
get’s pretty wild.
Just look at all these nooks
裂隙 岛屿 峡湾丛生
and crannies and islands and fjords.
The CIA puts the total length of this coast at 58133km,
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 comparing your answer with everyone else’s.
当然了 如果你真的想去测挪威海岸 或者其它海岸
Of course if you want to do this, or any other coastal measurement,
你需要掌握几何学 代数学 分形的相关知识
you’ll need an understanding of Geometry, Algebra and Fractals.
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