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海岸线到底有多长? – 译学馆
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海岸线到底有多长?

The Coastline Paradox Explained

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那么 本期视频我们要讨论的是:
So, here’s the problem that this video is going to be talking about.
美国的海岸有多长?
How long is the coast of the United States?
如果你看过美国的地图
If you look at any map and see America,
可能会觉得这个问题很简单
you might think that it’s easy.
只需测量一下美国的轮廓就能得到答案了
Just measure the outline of the country and you have your answer.
也有一些个人和组织已经这么试过了
Several people and organisations have already tried this though.
比如美国国会研究处测出美国的海岸长达12,383英里
Like the Congressional Research Institute, that calculated it to be 12,383 miles.
而他们的第二次研究将这个数字改成了29,093英里
A second study from them that changed it to 29,093 miles.
中央情报局测出的结果是19,924英里
The CIA puts it at 19,924 miles.
美国国家海洋和大气局的测量结果为95,471英里
And a study from “NOAA” calculated the shoreline to be 95,471 miles.
你可能注意到了 这些数字各不相同
You may have noticed that all of these numbers are different.
怪就怪在他们测的都是美国的海岸线
Which is weird, because they’re all just measuring the same coastline.
那么 到底是怎么回事呢?
So, what’s going on?
咱们先来看一个相对小的国家
Let’s move over to a smaller country like,
比如英国
the United Kingdom
我们来测一下英国的海岸线 测的时候删繁就简吧
and measure the coastline of Great Britain to get a clearer picture.
很明显 英国的海岸线不是直的
Obviously, the coast of Britain isn’t straight.
那些远看很直的线条 你离近了看
Every time you look closer at a line that looks straight
就会发现更多的弯弯曲曲
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,
反正这些线条总是不肯变直
it never actually becomes straight.
最后你可能会选择最小的可行测量单位
You end up using the smallest measurement unit feasible.
所以如果你测量英国的海岸时用的是100千米的单位
So, if you were to measure the British coast, using length of 100km
你就会测到28个100千米
you’d end up using 28 of them and
得出的结果也就是2800千米
get an answer of 2800km.
但是如果你将测量单位缩短至50千米
But if you shortend your measuring units down to 50km
你最终会得到68个50千米
you’d end up using 68 of them and
测出的结果就是3400千米
get an answer of 3400km.
而这个结果比第一次测的多出600千米
Which is, 600km longer than your first measurement was!
这就是我们说的“海岸线悖论”
This is called coastline paradox
即人们得出的海岸线的长度测量结果
and anybody’s answer to how long a coastline is
取决于他们所使用的测量单位
depends on what size of measurement they’re using.
1951年一个叫弗莱·理查森的男子首次注意到这种现象
First observed by a guy named Lewis Fry Richardson back in 1951,
因为当时葡萄牙和西班牙虽然共用一条边界
as a way to explain how Portugal and Spain
却得出了完全不同的边界长度结果
had come up with totally different answers to their mutual border length.
海岸线悖论一直让地图制作者非常恼火
The coastline paradox has been annoying cartographers ever since.
基本上 测量海岸线时你用的测量单位越小
Basicaly, the smaller a unit measurement you use to measure a coastline
得出的测量结果就越大
the longer your answer will become.
理论上说
You could, theoretically,
你可以将测量单位精确到以分子为单位
go all the way down to the molecular level for your measurement unit.
但如果你这样做了
But if you do that,
海岸线的长度就会接近无限大
the length of the coast seems to approach infinity.
你主观上将有限的区域变成无限大的空间
It doesn’t seem to make any sense
这样做好像没有任何意义
that you can have a defined space with a finite area
以悖论的测法测出英国的海岸线周长为无穷大有什么意义呢
like Great Britain be surrounded by an infinitely long perimeter.
但是这里有一个相似的概念
But there is a similar concept
就是数学上的“分形”
that can be found in mathematics called fractals.
“科赫雪花”可能是证明这个概念的最简单的例子
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
然后每个边上再放一个
put another triangle of each side
边长是原边长1/3的三角形
with equal lengths of one third.
你可以将这个过程一直重复下去
You can keep repeating this process forever
如果你放大了一片雪花 那它基本上就是无限大
and if you zoom into a snowflake it essentially goes on forever.
也就是说当你将镜头从初始点拉远
When you zoom back out to the original starting point
你就会得到一个有限大区域的形状 但它的周长是无穷大的
you’re left with a shape that has a finite area but an infinitely long perimeter.
世界上的很多海岸线都存在这种海岸线悖论
A lot of coastlines around the world have similar properties to this.
所以你可以将英国的海岸放大 再放大
So, you can keep zooming in and zooming in on the coast of Britain
而对海岸线来说 不管你的观察位置的远近
and the coastline will continue to look roughly the same
它将一直具有自我相似性
no matter how far down the rabbit hole you go.
之前提到过 如果你将物体放至足够大
As mentioned previously, you’ll eventually hit the molecular level
你最终会遇到分子单位
if you zoom in far enough,
然后你就要通过计算原子的数量来测量海滩
and you’ll be measuring a beach by counting atoms.
如果你一直测量下去
If you did this forever,
你可能会发现英国的海岸线变成了无穷长
you’d find the coast of Britain to be probably millions of km in length,
这种方法操作起来有难度 理解起来也有难度
which just isn’t very practical or easy to understand.
还存在一个次要的问题
There’s also the minor problem,
由于侵蚀作用 海岸总在不停地改变
that coastlines tend to change all the time, with erosion.
由于海浪的拍打
Every time a wave crashes on a beach,
海滩会逐渐被塑型 改变
it’s shape it changed by a little
真的很难准确测定
and that is really hard to accurately pin down.
除此之外 世界范围内的海平面正在上升
On top of this, sea levels are rising around the world
这将彻底地改变海岸线的原貌
which can drastically alter the way a coastline looks.
在极端情况下
In extreme case,
几十年内像马尔代夫这种小岛会发生什么呢
like what might happen to the maldives in a few decades,
它们的整个大陆块会被完全吞没
entire land masses may become completely swallowed.
还有 荷兰这个国家
On the other hand, there’s the dutch
已经往他们的海岸线那里运了700多年的土了
who have been adding land to their coastline now for over 700 years.
问题在于 地球是在不断进化的
The point is, Earth is constantly evolving.
所以如果你是拿着显微镜去计算海岸线的长度
So good luck going out to a coast with a microscope
那就祝你好运吧
and measuring the length that way.
网络上 书中列举的
Every number you see online or in a book
所有海岸线的长度
for how long a coastline is,
基本上都是推测或者估算的
is basically just a guess or estimation.
真值是不可能得到的 这就是海岸线悖论
The true value is impossible to know, and that is the coastline paradox.
不信咱们来看这个图表
Just take a look at this list
这张表来自《世界概况》
from the CIA world factbook
是关于最长海岸线国家的排行榜
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
但是不可思议的是挪威竟然位居第二
but the really surprising one is Norway, in second place.
我们大眼一撇就能看出挪威的海岸并不长
At a first glance Norway’s coast doesn’t seem too long
特别是和俄国 美国相比之下
especially when compared with countries like Russia or the United States.
但是当你将挪威逐渐放大
But when you zoom in closer, Norway’s coast
你会发现它长得相当肆意
get’s pretty wild.
不信你看它的边边角角
Just look at all these nooks
裂隙 岛屿 峡湾丛生
and crannies and islands and fjords.
中央情报局算出的海岸线总长度为58,133千米
The CIA puts the total length of this coast at 58133km,
如果你将这个长度垂直展开
which, if you stretch that out all in a vertical line
它将沿着赤道
would circle the entire Earth
环绕整个地球1.5周
at the equator almost one and a half times.
如果你们的周末闲得发霉 就去实践一下海岸线悖论吧
If you want to kill your entire weekend and see the coastline paradox in action
去试着测测挪威的海岸
try measuring the Norwegian coast
从南部一直测到俄罗斯边境
from the south all the way to the border with Russia
然后到我们的评论区和大家分享一下
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.
数字和概念让很多人晕头转向 包括我在内
Numbers and concepts like these are confusing for a lot of people including myself.
我真的对这些不在行
It was confusing for me,
至少 我主持Brilliant.org之前对这些东西完全不敏感
at least, until I tried Brilliant.org.
Brilliant不会叫你
Rather than telling you how to
靠死记硬背来解决代数问题
do algebra problems by memorising things,
他们会向你解释代数学背后的直观想法
they start by teaching the intuitive ideas behind algebra.
通过玩他们的智力游戏
By playing through their puzzles,
你就能轻松理解代数学的原理
you get to understand how algebra works.
Brilliant还有许多其它有趣的课程
Brilliant also has tons of other really interesting courses on topics like astronomy,
包括天文学 太阳能 计算机存储器
solar energy, computer memory
狭义相对论
and special relativity, which similarly,
还有 它会引导你建立自己的核心知识
guide you along as you build your core knowledge.
你可以在这里随心所欲地上非常棒的设计课
You can take as many of these incredibly designed courses as you want
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视频概述

本视频介绍了关于海岸线悖论的一些解释。

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视频来源

https://www.youtube.com/watch?v=kFjq8PX6F7I

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