Can you solve the famously difficult green-eyed logic puzzle? - Alex Gendler
15,573,584 views ・ 2015-06-16
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翻译人员: Rebecca Wang
校对人员: Zhuo Wang
00:06
Imagine an island where 100 people,
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想象在一个岛上,
00:09
all perfect logicians,
are imprisoned by a mad dictator.
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一个疯狂的独裁者囚禁了100个完美的逻辑家
00:14
There's no escape,
except for one strange rule.
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他们没办法逃离,除了一个奇怪的规则
00:18
Any prisoner can approach the guards
at night and ask to leave.
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在晚上任何囚犯都可以请求警卫放他走
00:23
If they have green eyes,
they'll be released.
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若他有绿眼睛,他就会被释放
00:26
If not, they'll be tossed
into the volcano.
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若不是,他就会被扔进火山口
00:30
As it happens,
all 100 prisoners have green eyes,
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实际上,那一百个逻辑家都有绿眼睛
00:34
but they've lived there since birth,
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但他们从出生起就住在那儿
00:36
and the dictator has ensured
they can't learn their own eye color.
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而且独裁者确保他们不会知道自己眼睛什么颜色
00:41
There are no reflective surfaces,
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那儿也没有反光表面
00:43
all water is in opaque containers,
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所有水都装在不透明的容器里
00:46
and most importantly,
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而且最重要的
00:47
they're not allowed
to communicate among themselves.
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他们不能互相交流
00:50
Though they do see each other
during each morning's head count.
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尽管他们每天早上点人数时都能看到彼此
00:54
Nevertheless, they all know no one would
ever risk trying to leave
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不仅如此,他们都知道
若没有绝对的把握会成功
00:59
without absolute certainty of success.
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没人会尝试离开
01:02
After much pressure
from human rights groups,
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在人权组织的压力下
01:05
the dictator reluctantly agrees
to let you visit the island
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那个独裁者勉强允许你访问那个岛
01:09
and speak to the prisoners
under the following conditions:
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并且和犯人说话时 要遵从以下条件:
01:12
you may only make one statement,
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你只可陈述一个声明
01:14
and you cannot tell them
any new information.
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你不能告诉他们新的信息
01:17
What can you say
to help free the prisoners
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你说什么才能帮助这些犯人获得自由
01:20
without incurring the dictator's wrath?
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而不激怒这位独裁者呢?
01:24
After thinking long and hard,
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经过深思熟虑
01:25
you tell the crowd,
"At least one of you has green eyes."
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你告诉人群:你们当中
至少有一个人有绿眼睛
01:31
The dictator is suspicious
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独裁者持有怀疑的态度
01:33
but reassures himself that your statement
couldn't have changed anything.
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但还是告诉自己你的言论不会改变任何事情
01:37
You leave, and life on the island
seems to go on as before.
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你离开了,岛上的生活依然照旧
01:42
But on the hundredth morning
after your visit,
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但在你访问后的第一百天早上
01:44
all the prisoners are gone,
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所有的犯人都不见了
01:47
each having asked to leave
the previous night.
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每一个人都在前天晚上要求离开
01:50
So how did you outsmart the dictator?
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所以你是如何智胜独裁者的?
01:53
It might help to realize that the amount
of prisoners is arbitrary.
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意识到犯人的数量不固定也许能帮到你
01:59
Let's simplify things
by imagining just two, Adria and Bill.
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我们来把这个问题简化一下,
假设只有两个犯人,小红和小明
02:04
Each sees one person with green eyes,
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彼此都能看到对方的绿眼睛
02:06
and for all they know,
that could be the only one.
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他们心里清楚 也许只有对方有绿眼睛
02:09
For the first night, each stays put.
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所以第一天,谁也没轻举妄动
02:12
But when they see each other
still there in the morning,
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但当他们第二天早上又看到对方时
02:15
they gain new information.
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他们得到了新的信息
02:17
Adria realizes that if Bill had seen
a non-green-eyed person next to him,
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小红意识到如果小明看到了一个“非绿眼睛”的人在他旁边
02:22
he would have left the first night
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他就知道自己拥有绿眼睛
02:24
after concluding the statement
could only refer to himself.
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第一天就会离开
02:28
Bill simultaneously realizes
the same thing about Adria.
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小明也同一时间想到了同样的事情
02:32
The fact that the other person waited
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两个人都在等这个事实
02:34
tells each prisoner his
or her own eyes must be green.
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告诉她或他的眼睛一定是绿色的
02:39
And on the second morning,
they're both gone.
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之后的那天早上,他俩都走了
02:42
Now imagine a third prisoner.
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现在想象第三个犯人
02:44
Adria, Bill and Carl each see
two green-eyed people,
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小红小明和小刚各看到两个绿眼睛的人
02:48
but aren't sure if each of the others
is also seeing two green-eyed people,
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但不确定另外两人是不是也看到了
02:53
or just one.
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一个或者两个绿眼睛的人
02:55
They wait out the first night as before,
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他们第一天也和之前一样等着
02:57
but the next morning,
they still can't be sure.
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到了第二天,他们还是不确定
03:01
Carl thinks, "If I have non-green eyes,
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小刚想:如果我没有绿眼睛
03:03
Adria and Bill were just
watching each other,
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小红和小明只是看着彼此
03:06
and will now both leave
on the second night."
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那他们第二天早上就会都走了
03:09
But when he sees both
of them the third morning,
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但当他第三天早上看到另外两人时
03:12
he realizes they must
have been watching him, too.
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他意识到那两人肯定也在观察他
03:16
Adria and Bill have each
been going through the same process,
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小红和小明在想同样的事情
03:19
and they all leave on the third night.
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然后他们三人在第三天晚上都走了
03:22
Using this sort of inductive reasoning,
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用这种归纳性推理
03:24
we can see that the pattern will repeat
no matter how many prisoners you add.
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我们可以看出这种模式会一直重复,
不论犯人的数量多少
03:28
The key is the concept
of common knowledge,
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关键点是公识的概念
03:31
coined by philosopher David Lewis.
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来自哲学家David Lewis的创造
03:34
The new information was not contained
in your statement itself,
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新知识不在你的陈述里
03:38
but in telling it to everyone
simultaneously.
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而在于你的声明同时陈述给了所有人
03:42
Now, besides knowing at least one
of them has green eyes,
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现在呢,每个犯人除了知道他们中至少一个有绿眼睛
03:46
each prisoner also knows
that everyone else is keeping track
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也知道其他人都在观察记录
03:51
of all the green-eyed people they can see,
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他们能看到的所有绿眼睛的人
03:54
and that each of them
also knows this, and so on.
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而且所有人都知道每个人都是这么想的
03:58
What any given prisoner doesn't know
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每个犯人不知道的是
04:00
is whether they themselves are one
of the green-eyed people
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他们自己是不是别人观察记录的
04:04
the others are keeping track of
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绿眼睛的人中的一员
04:06
until as many nights have passed
as the number of prisoners on the island.
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直到和犯人数量同等的夜数过去了才能确定
04:12
Of course, you could have spared
the prisoners 98 days on the island
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当然啦,你也可以让犯人早98天离开这岛
04:17
by telling them at least 99 of you
have green eyes,
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告诉他们至少99个人有绿眼睛
04:21
but when mad dictators are involved,
you're best off with a good headstart.
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但当疯狂独裁者在的时候,你最好做出明智的选择
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