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  • Imagine an island where 100 people,


  • all perfect logicians, are imprisoned by a mad dictator.

    他們每一個都是優秀的邏輯學家, 卻被一位邪惡的獨裁者所監禁。

  • There's no escape, except for one strange rule.

    唯一能逃離島上的方法, 必須符合一條特殊的規則:

  • Any prisoner can approach the guards at night and ask to leave.

    所有人都可以在晚上去找守衛, 並要求離開島上,

  • If they have green eyes, they'll be released.

    只要這位居民擁有綠色眼睛, 就可以被釋放。

  • If not, they'll be tossed into the volcano.

    但如果不是綠色眼睛, 就要被丟進火山!

  • As it happens, all 100 prisoners have green eyes,


  • but they've lived there since birth,


  • and the dictator has ensured they can't learn their own eye color.

    獨裁者很確定,居民們都不知道 自己眼睛的顏色。

  • There are no reflective surfaces,

    島上沒有任何物品 能夠反射出自己的影像,

  • all water is in opaque containers,


  • and most importantly,


  • they're not allowed to communicate among themselves.


  • Though they do see each other during each morning's head count.

    雖然每天早上點名時, 他們會看到彼此,

  • Nevertheless, they all know no one would ever risk trying to leave

    不過他們都知道, 從來沒有人敢冒險嘗試離開,

  • without absolute certainty of success.


  • After much pressure from human rights groups,


  • the dictator reluctantly agrees to let you visit the island


  • and speak to the prisoners under the following conditions:

    你可以跟被監禁的居民談話, 但是必須符合以下的條件:

  • you may only make one statement,

    1. 你只能說一件事,

  • and you cannot tell them any new information.

    2. 而且不能告訴他們任何新的消息。

  • What can you say to help free the prisoners


  • without incurring the dictator's wrath?


  • After thinking long and hard,


  • you tell the crowd, "At least one of you has green eyes."


  • The dictator is suspicious


  • but reassures himself that your statement couldn't have changed anything.

    但依然告訴自己: 你說的話不會改變任何事情。

  • You leave, and life on the island seems to go on as before.

    然後你離開了, 島上的生活又變得和之前一樣。

  • But on the hundredth morning after your visit,


  • all the prisoners are gone,


  • each having asked to leave the previous night.

    每一位居民, 都在前一天晚上要求離開。

  • So how did you outsmart the dictator?


  • It might help to realize that the amount of prisoners is arbitrary.

    以下就來讓大家了解,為何所有的居民 都能下定決心要求離開?

  • Let's simplify things by imagining just two, Adria and Bill.

    讓我們先把情況簡化, 想像只有兩個居民 Adria 和 Bill。

  • Each sees one person with green eyes,


  • and for all they know, that could be the only one.

    所以他們都知道: 對方是可以離開島上的那一位。

  • For the first night, each stays put.


  • But when they see each other still there in the morning,

    但是到了隔天早上, 當他們看到彼此都還在,

  • they gain new information.


  • Adria realizes that if Bill had seen a non-green-eyed person next to him,

    Adria 的想法是: 如果 Bill 看到的人 (Adria) 沒有綠色眼睛,

  • he would have left the first night

    那 Bill 在第一天晚上就會要求離開。

  • after concluding the statement could only refer to himself.

    當他得到這個結論的時候, 就會推論出:自己有綠色眼睛。

  • Bill simultaneously realizes the same thing about Adria.

    而 Bill 也會得到相同的結論。

  • The fact that the other person waited


  • tells each prisoner his or her own eyes must be green.

    這個事實告訴每位居民: 他們自己的眼睛一定是綠色的。

  • And on the second morning, they're both gone.

    根據第二天早上的結果, 他們兩個都會要求離開。

  • Now imagine a third prisoner.


  • Adria, Bill and Carl each see two green-eyed people,

    Adria, Bill 和 Carl 都看到 其他兩位擁有綠色眼睛,

  • but aren't sure if each of the others is also seeing two green-eyed people,

    但無法確定其他兩位, 也同樣看到兩個綠眼的人,

  • or just one.


  • They wait out the first night as before,


  • but the next morning, they still can't be sure.


  • Carl thinks, "If I have non-green eyes,

    Carl 想: 「如果我不是綠眼睛,

  • Adria and Bill were just watching each other,

    Adria 和 Bill 只會互看彼此,

  • and will now both leave on the second night."


  • But when he sees both of them the third morning,

    但當 Carl 第三天早上看到其他兩人還在,

  • he realizes they must have been watching him, too.

    Carl 瞭解到一件事: 其他兩人知道 Carl 有綠色眼睛 。

  • Adria and Bill have each been going through the same process,

    而 Adria 和 Bill 也經過同樣的推理過程, (確認了自己有綠色眼睛)

  • and they all leave on the third night.


  • Using this sort of inductive reasoning,


  • we can see that the pattern will repeat no matter how many prisoners you add.


  • The key is the concept of common knowledge,


  • coined by philosopher David Lewis.

    哲學家 David Lewis 所提出的 「公開知識」這個哲學概念。

  • The new information was not contained in your statement itself,


  • but in telling it to everyone simultaneously.

    但是一旦告訴了每一個人, 就會產生新的訊息。

  • Now, besides knowing at least one of them has green eyes,

    現在,除了知道居民當中 至少一位有綠色眼睛,

  • each prisoner also knows that everyone else is keeping track


  • of all the green-eyed people they can see,


  • and that each of them also knows this, and so on.


  • What any given prisoner doesn't know


  • is whether they themselves are one of the green-eyed people


  • the others are keeping track of


  • until as many nights have passed as the number of prisoners on the island.

    一直要等到他們等待的夜晚天數, 和島上的居民數目一樣為止。

  • Of course, you could have spared the prisoners 98 days on the island

    當然,你可以幫這些居民 省下98天觀察等待的時間。

  • by telling them at least 99 of you have green eyes,

    方法就是直接告訴他們: 「你們當中至少有99位擁有綠色眼睛。」

  • but when mad dictators are involved, you're best off with a good headstart.

    但是別忘了還有獨裁者正在監視, 所以你還是小心一點比較好。

Imagine an island where 100 people,



影片操作 你可以在這邊進行「影片」的調整,以及「字幕」的顯示

A2 初級 中文 TED-Ed 居民 綠色 眼睛 獨裁 離開

【TED-Ed】著名的難點綠眼邏輯謎題--亞歷克斯-根德勒。 (【TED-Ed】The famously difficult green-eyed logic puzzle - Alex Gendler)

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    稲葉白兎 發佈於 2021 年 01 月 14 日