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  • This video is made possible by brilliant.org.

    這個視頻是由 brilliant.org 提供的。

  • 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

  • [End Screen]

    [結束螢幕]

This video is made possible by brilliant.org.

這個視頻是由 brilliant.org 提供的。

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B1 中級 中文 海岸線 長度 單位 代數 挪威 放大

海岸線悖論解讀 (The Coastline Paradox Explained)

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    林宜悉 發佈於 2021 年 02 月 27 日
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