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

前755名註冊 "輝煌 "的用戶，可享受高級訂閱8折優惠。

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

所以，這就是這個視頻要講的問題。

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

如果你看任何一張地圖，看到美國，你可能會覺得這很容易

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

只要測量一下國家的輪廓，就有了答案。

Several people and organisations have already tried this though.

不過已經有幾個人和組織嘗試過了。

Like the Congressional Research Institute, that calculated it to be

像國會研究所，計算出的是。

A second study from them that changed it to

他們的第二項研究，將其改為

The CIA puts it at

中情局的說法是

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

和 "NOAA "的研究計算出的海岸線是。

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

你可能已經注意到，這些數字都是不同的。

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

這很奇怪，因為他們都只是在測量相同的海岸線。

So, what's going on?

那麼，這是怎麼回事呢？

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

好吧，讓我們轉移到一個較小的國家，如，英國。

and measure the coastline of Great Britain

丈量大不列顛的海岸線

to get a clearer picture.

以獲得更清晰的畫面。

Obviously, the coast of Britain isn't straight

很明顯，英國的海岸線並不平坦。

Every time you look closer at a line that looks straight

每當你仔細觀察一條看起來很直的線時

you'll see more curves & bends

你會看到更多的曲線和彎曲。

So, how do you measure the length of the coast

那麼，如何測量海岸的長度呢？

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

如果每次仔細看，都不會真的變成直的。

You end up using the smallest measurement unit feasible.

你最終使用的是可行的最小測量組織、部門。

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

所以，如果你要測量英國的海岸，用100公里的長度。

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

你最終會使用28個，得到的答案是......。

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

但如果你把測量組織、部門縮短到50公里的話

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

你最終會使用其中的68個，並得到一個答案。

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

也就是比你第一次測量的距離長了600公里!

This is called

這就是所謂的

and anybody's answer to how long a coastline is

誰能告訴我海岸線有多長？

depends on what size of measurement they're using

取決於他們所使用的測量尺寸。

first observed by a guy named

首先由一個叫

Lewis Fry Richardson

Lewis Fry Richardson

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

早在1951年，作為一種解釋葡萄牙和西班牙的方式

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

已經得出了完全不同的答案，他們的相互邊界長度。

The coastline paradox has been annoying cartographers ever since

自從海岸線悖論開始，就一直困擾著製圖師。

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

基本上，你用越小的組織、部門測量來測量海岸線

the longer your answer will become

越長越好

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

理論上，你可以一直到分子水準的測量組織、部門。

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

但是，如果你這樣做，海岸的長度似乎接近無窮大。

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

這似乎沒有任何意義，你可以有一個定義的空間。

with a finite area, like Great Britain

有限地區，如英國

be surrounded by an infinitely long perimeter

四通八達

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

但在數學中也有一個類似的概念，叫做

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

"科赫雪花"，可能是將這一概念形象化的最簡單方式。

So, imagine a triangle, with equal sides of one

所以，想象一個三角形，邊長相等的一

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

再放一個邊長相等的三角形。

you can keep repeating this process forever

循環往復

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

如果你把雪花放大，它基本上就會永遠消失。

when you zoom back out to the original starting point

當你放大到原點時

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

你剩下的形狀有一個有限的面積。

but an infinitely long perimeter

惟有無限長的周長

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

世界上很多海岸線都有類似的特性。

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

所以，你可以繼續放大和放大在英國的沿海地區

and the coastline will continue to look roughly the same

而海岸線將繼續保持大致相同的面貌。

No matter how far down the rabbit hole you go

無論你在兔子洞裡走了多遠的路

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

如前所述，如果你放大到足夠遠的地方，你最終會達到分子水準。

and you'll be measuring a beach by counting atoms

而你將通過計算原子來測量海灘的大小

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

如果你永遠這樣做，你會發現英國的海岸大概有幾百萬公里的長度

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

這，就是不太實用，也不太容易理解。

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

還有一個小問題，海岸線往往會隨時變化，會受到侵蝕

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

每當海浪衝上沙灘，它的形狀就會改變一點點

and that is really hard to accurately pin down

而這真的很難準確地確定

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

除此之外，世界各地的海平面都在上升

which can drastically alter the way a coastline looks

這可以極大地改變海岸線的外觀。

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

極端情況下，就像幾十年後馬爾地夫可能發生的情況一樣。

entire land masses may become completely swallowed

滿目瘡痍

on the other hand, there's the dutch

反之

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

迄今已有700多年的歷史，他們一直在為自己的海岸線增加土地。

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

重點是，地球是不斷進化的。所以，祝你帶著顯微鏡到海邊去吧

and measuring the length that way.

並以這種方式測量長度。

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

你在網上或書上看到的每一個數字，都是海岸線有多長。

is basically just a

基本上只是一個

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

真正的價值是不可能知道的，這就是。

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

看看中情局世界實錄中的這份名單吧。

on the countries with the longest coastline for a few surprises

在擁有最長海岸線的國家上，有一些意外的驚喜

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

根據他們的說法，加拿大是第一，這也是有道理的。

but the really surprising one is Norway, in second place

但真正令人驚訝的是挪威，排在第二位

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

乍看之下，挪威的海岸線似乎並不漫長

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

特別是與俄羅斯、美國等國相比

but when you zoom in closer, Norway's coast

但當你放大到近處時，挪威的海岸。

get's pretty wild

喪心病狂

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

看看這些犄角旮旯 島嶼和峽灣。

The CIA puts the total length of this coast at

中情局認為，這條海岸線的總長度為：

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

如果你把它拉長到一條垂直線上

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

將在赤道上繞整個地球一圈，幾乎是其1.5倍。

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

如果你想打發你的整個週末，並看到海岸線悖論的行動。

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

試著測量一下挪威海岸，從南邊一直到俄羅斯的邊界。

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

並在下面留言，將你的答案與大家的答案進行比較。

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

當然，如果你想做這個，或者其他沿海測量。

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

你需要了解幾何、代數和分形。

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

這樣的數字和概念對很多人來說都是混亂的。

including myself

包括我在內

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

至少在我嘗試Brilliant.org之前，它對我來說是混亂的。

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

而不是告訴你如何通過記憶的東西來做代數題

they start by teaching the intuitive ideas behind algebra

他們從代數的直觀概念開始教起。

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

通過玩他們的謎題，你會明白，代數是如何工作的。

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

Brilliant還有大量其他非常有趣的課程，如天文學等主題。

Solar energy

太陽能

Computer memory

計算機內存

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

和狹義相對論，同樣，在你構建核心知識的過程中，引導你走下去

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

您可以隨意選擇這些設計精美的課程。

with their premium subscription

與他們的高級訂閱

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

其中，通過成為第一批點擊描述中的鏈接的755人之一。

you can get for 20% off

你可以得到8折

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