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这个著名的绿眼逻辑问题你能解开吗? – 译学馆
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这个著名的绿眼逻辑问题你能解开吗?

Can you solve the famously difficult green-eyed logic puzzle? - Alex Gendler

想象一座岛上有100个思维缜密的逻辑学家
Imagine an island where 100 people,
他们被一个疯狂的独裁者囚禁着
all perfect logicians,are imprisoned by a mad dictator.
他们无处可逃 除非符合一条奇怪的规则
There’s no escape,except for one strange rule.
任何一名犯人都可以在夜间接近守卫 请求出去
Any prisoner can approach the guards at night and ask to leave.
如果他们的眼睛是绿的 就能获得释放
If they have green eyes,they’ll be released.
否则 就会被扔进火山
If not, they’ll be tossedinto the volcano.
恰巧 这100名囚犯全部是绿眼睛
As it happens,all 100 prisoners have green eyes,
但他们自出生起就被囚禁在这
but they’ve lived there since birth,
独裁者确信他们无法得知自己眼睛的颜色
and the dictator has ensured they can’t learn their own eye color.
这里没有镜面 水也是装在不透明容器中
There are no reflective surfaces, all water is in opaque containers,
最重要的是 彼此不许交流
and most importantly, they’re not allowedto communicate among themselves.
不过每日早晨点名时 他们都能看到对方
Though they do see each otherduring each morning’s head count.
然而 他们都知道
Nevertheless, they all know no
在没有对成功十足的把握时
one would ever risk trying to leave
他们都不会冒险请求离开
without absolute certainty of success.
在受到来自人权组织的巨大压力后
After much pressurefrom human rights groups,
独裁者勉强同意让你访问该岛
the dictator reluctantly agreesto let you visit the island
并在遵守下列规则前提下与囚犯对话:
and speak to the prisonersunder the following conditions:
你只能说一句话
you may only make one statement,
而且还不能告诉他们任何新的信息
and you cannot tell themany new information.
你要怎样说才能不激怒独裁者
What can you sayto help free the prisoners
并帮助囚犯们获得自由?
without incurring the dictator’s wrath?
在一番漫长而艰难的思考后
After thinking long and hard,
你告诉人群“你们中至少有一人眼睛是绿的”
you tell the crowd,”At least one of you has green eyes.”
独裁者有些起疑心
The dictator is suspicious but reassures himself
但他安慰自己 你的话改变不了什么
that your statement couldn’t have changed anything.
你离开了 岛上的生活似乎如往常一样继续
You leave, and life on the island seems to go on as before.
但在你访问后的第100天清晨
But on the hundredth morningafter your visit,
所有犯人都不见了
all the prisoners are gone,
他们都在前一晚请求离开了
each having asked to leavethe previous night.
那么 你是如何智取独裁者的呢?
So how did you outsmart the dictator?
囚犯数量可以任意调整 意识到这点可能有助于解决问题
It might help to realize that the amount of prisoners is arbitrary.
让我们简化一下 设想只有两人 阿德利亚和比尔
Let’s simplify thingsby imagining just two, Adria and Bill.
他们每人都能看到一个绿眼睛的人
Each sees one person with green eyes,
他们所知道的也就是这个了
and for all they know,that could be the only one.
第一晚 他们都在等待
For the first night, each stays put.
但当第二日早晨 他们见到彼此时
But when they see each otherstill there in the morning,
他们又获得了一条新信息
they gain new information.
阿德利亚意识到
Adria realizes that
如果比尔看到的旁边人不是绿眼睛
if Bill had seen a non-green-eyed person next to him,
他会在第一晚就离开
he would have left the first night
因为叙述中指的人只能是他
after concluding the statement could only refer to himself.
同时 比尔也意识到和阿德利亚相同的事
Bill simultaneously realizesthe same thing about Adria.
对方在等待的这个事实
The fact that the other person waited
表明每一个人 他或她自己的眼睛也必定是绿色的
tells each prisoner hisor her own eyes must be green.
所以第二日早晨 他们都离开了
And on the second morning,they’re both gone.
现在设想加入第三人
Now imagine a third prisoner.
阿德利亚 比尔和卡尔 各自都能看到两个绿眼睛的人
Adria, Bill and Carl each seetwo green-eyed people,
但他们都不能确定
but aren’t sure
对方眼中是否也看到了两个绿眼睛
if each of the others is also seeing two green-eyed people,
或是仅有一个
or just one.
如之前一样 第一天夜晚他们在等待
They wait out the first night as before,
但第二天早晨 他们仍然没有十足把握
but the next morning,they still can’t be sure.
卡尔想“如果我的眼睛不是绿的”
Carl thinks,”If I have non-green eyes,
“阿德利亚和比尔会盯着对方”
Adria and Bill were justwatching each other,
“然后在今晚双双离开”
and will now both leaveon the second night.”
但当他在第三天早晨又看到这两人时
But when he sees bothof them the third morning,
他意识到 这两人也一定在盯着自己
he realizes they musthave been watching him, too.
阿德利亚和比尔也经历了同样的推理过程
Adria and Bill have eachbeen going through the same process,
接着他们都在第三天晚上离开了
and they all leave on the third night.
使用这种归纳推理法
Using this sort of inductive reasoning,
无论你往其中加入多少犯人
we can see that the pattern will repeat
同样的模式会不断重复
no matter how many prisoners you add.
其核心是哲学家大卫·刘易斯提出的
The key is the conceptof common knowledge,
“共同知识”这一概念
coined by philosopher David Lewis.
新信息不在你说的话中
The new information was not containedin your statement itself,
而存在于你将其同一时间公布给所有人这一行为中
but in telling it to everyonesimultaneously.
除了得知他们中至少一人是绿眼睛外
Now, besides knowing at least oneof them has green eyes,
每个囚犯也知道 现在其它所有人
each prisoner also knowsthat everyone else is keeping track
都在留意着他们看到的绿眼睛的人
of all the green-eyed people they can see,
并且各自也知道其它人都拥有相同的想法 以此类推
and that each of themalso knows this, and so on.
而囚犯不知道的是
What any given prisoner doesn’t know
他们自己是否是
is whether they themselves are oneof the green-eyed people
他人留意的绿眼睛中的一员
the others are keeping track of
直到度过的夜晚数量与岛上犯人的数量相等
until as many nights have passed as the number of prisoners on the island.
当然
Of course, you could have
你也可以帮囚犯们节省98天时间
spared the prisoners 98 days on the island
直接告诉他们“你们中至少99个人是绿眼睛”
by telling them at least 99 of youhave green eyes,
但由于独裁者的存在
but when mad dictators are involved,
开个好头才是最佳选择
you’re best off with a good headstart.

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著名逻辑难题,让你脑洞大开

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视频来源

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