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  • Imagine an island where 100 people,


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

    100人の完璧に論理的な人々が 独裁者によって幽閉されています

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

    しかし 不思議なルールが1つあり そこから逃げることができます

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

    どの囚人も夜間 守衛のところへ行くことが許され

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

    囚人が緑色の瞳ならば 解放されますが

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

    そうでない場合は 火山の噴火口に投げ込まれてしまいます

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

    実は 囚人達は100人とも 緑色の瞳なのですが

  • but they've lived there since birth,


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

    独裁者のせいで 自分の瞳の色を知らないのです

  • There are no reflective surfaces,


  • all water is in opaque containers,


  • and most importantly,


  • they're not allowed to communicate among themselves.

    お互いに口をきくことは 禁じられているのです

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

    しかし 毎朝の点呼の時に お互いの姿を確認できます

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

    しかし 成功を完全に確信できるまでは

  • without absolute certainty of success.


  • After much pressure from human rights groups,


  • the dictator reluctantly agrees to let you visit the island

    独裁者はしぶしぶと あなたの訪問を受け入れ

  • and speak to the prisoners under the following conditions:

    囚人達に次の条件で 話しかけることを許しました

  • you may only make one statement,


  • and you cannot tell them any new information.


  • What can you say to help free the prisoners

    どうすれば 独裁者を怒らせることなく

  • without incurring the dictator's wrath?


  • After thinking long and hard,


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

    「少なくとも1人は緑色の瞳だ」と 全員に呼びかけました

  • The dictator is suspicious


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

    これでは何も変化は 起こらないはずだと考え 安心します

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

    あなたは島を離れ そこでの生活に変化はなさそうです

  • But on the hundredth morning after your visit,

    しかし あなたが訪問した100日後の朝

  • all the prisoners are gone,


  • each having asked to leave the previous night.


  • So how did you outsmart the dictator?

    さて どうやって独裁者を 出し抜いたのでしょうか?

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

    囚人の数は任意であるといえば 分かりやすくなるでしょう

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

    アドリアとビルの2人だけだったと 話を単純化しましょう

  • Each sees one person with green eyes,


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

    緑色なのは 1人だけかもしれないと考えます

  • For the first night, each stays put.


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

    しかし 翌朝2人とも島に残っていたため

  • they gain new information.


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

    アドリアはビルと一緒にいる相手が 緑色の瞳でなければ

  • he would have left the first night


  • after concluding the statement could only refer to himself.

    最初の晩に逃げ出しただろうと 気づきます

  • Bill simultaneously realizes the same thing about Adria.

    同時にビルもアドリアについて 同じことに気づきます

  • The fact that the other person waited


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


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

    2日目の朝には 2人とも脱出しています

  • Now imagine a third prisoner.


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

    アドリア、ビル、カールはそれぞれ 他の2人が緑色の瞳である事に気づきます

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

    しかし 他の人も同様に 緑色の瞳は2人だと気付いているか

  • or just one.

    それとも1人だけなのか 確信を持てません

  • 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,


  • Adria and Bill were just watching each other,


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

    2晩目に2人とも逃げてしまうだろう」と 考えます

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

    しかし 3日目の朝に両方とも残っていた場合

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


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


  • 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,

    ここで大切なのは 共有知識という概念で

  • coined by philosopher David Lewis.

    哲学者デイヴィド・ルイスが 導入しました

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

    あなたの発言自体には 何ら新しい情報は含まれていませんが

  • but in telling it to everyone simultaneously.


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

    すると 少なくとも1人は 緑色の瞳であることに加えて

  • each prisoner also knows that everyone else is keeping track

    囚人はそれぞれ 緑色の瞳の人の姿を

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


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

    そして各自が そのことを理解しています

  • What any given prisoner doesn't know


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

    緑色の瞳であるかどうかは 分からないので

  • the others are keeping track of


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

    島にいる囚人と同じ数の夜だけ 待つ必要があります

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

    もちろん 「少なくとも99人は 緑色の瞳だ」と言えば

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

    時間を98日間 短縮する事もできます

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

    でも 独裁者のことを考えて 穏やかに切り出すべきですね

Imagine an island where 100 people,



動画の操作 ここで「動画」の調整と「字幕」の表示を設定することができます

A2 初級 日本語 TED-Ed 囚人 アドリア 独裁 ビル カール

TED-ED】有名な難解な緑目のロジックパズル - アレックス・ゲンドラー (【TED-Ed】The famously difficult green-eyed logic puzzle - Alex Gendler)

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    稲葉白兎 に公開 2021 年 01 月 14 日