文本选自：Scientific American（科学美国人）
作者：Manon Bischoff
原文标题：Why the ‘Sleeping Beauty Problem’ Is Keeping Mathematicians Awake
原文发布时间：10 May 2023
Why the 'Sleeping Beauty Problem' Is Keeping Mathematicians Awake
Usually, there are clear answers in mathematics—especially if the tasks are not too complicated. But when it comes to the Sleeping Beauty problem, which became popular in 2000, there is still no universal consensus. Experts in philosophy and mathematics split into two camps and ceaselessly cite—often quite convincingly—arguments for their respective side. More than 100 technical publications exist on this puzzle, and almost every person who hears about the Sleeping Beauty thought experiment develops their own strong opinion.
The problem vexing the minds of experts is as follows: Sleeping Beauty agrees to participate in an experiment. On Sunday she is given a sleeping pill and falls asleep. One of the experimenters then tosses a coin. If "heads" comes up, the scientists awaken Sleeping Beauty on Monday. Afterward, they administer another sleeping pill. If "tails" comes up, they wake Sleeping Beauty up on Monday, put her back to sleep and wake her up again on Tuesday. Then they give her another sleeping pill. In both cases, they wake her up again on Wednesday, and the experiment ends.
The important thing here is that because of the sleeping drug, Sleeping Beauty has no memory of whether she was woken up before. So when she wakes up, she cannot distinguish whether it is Monday or Tuesday. The experimenters do not tell Sleeping Beauty either the outcome of the coin toss nor the day. They ask her one question after each time she awakens, however: What is the probability that the coin shows heads?
为什么“睡美人问题”让数学家睡不着觉
精听党背景导读
我们都玩过抛硬币的游戏，几乎谁都知道，正面和反面的出现的概率各为50%，但实际的情况是，你有时可能连续抛出十几次都是正面，以至于你感觉这似乎违反了概率原理。可是只要你有足够的耐心继续抛下去，正面及反面的数量总会差不多。即便你连续抛出1000次正面，但只要你继续抛，反面的数量总会慢慢追上，这造成一种假象，好像硬币自己知道已经抛接的情况，并对后面的结果进行修正。
文本选自：Scientific American（科学美国人）作者：Manon Bischoff原文标题：Why the ‘Sleeping Beauty Problem’ Is Keeping Mathematicians Awake原文发布时间：10 May 2023关键词：睡美人 难题 概率
精听党带着问题听
1.“睡美人”问题是什么时候开始流行的？2. 如何理解第二段中的“tails”？3.“明辨是非”用英语可以怎么表达？
精听党选段赏析
标题解读
Why the ‘Sleeping Beauty Problem’ Is Keeping Mathematicians Awake
为什么“睡美人问题”让数学家睡不着觉
mathematician n. 数学家；1. mathematics n. 数学；数学运算；
awake adj. 醒着的（尤指入睡前或刚醒时）；1. The noise was keeping everyone awake. 喧闹声吵得大家都睡不着。
段一
Usually, there are clear answers in mathematics—especially if the tasks are not too complicated. But when it comes to the Sleeping Beauty problem, which became popular in 2000, there is still no universal consensus. Experts in philosophy and mathematics split into two camps and ceaselessly cite—often quite convincingly—arguments for their respective side. More than 100 technical publications exist on this puzzle, and almost every person who hears about the Sleeping Beauty thought experiment develops their own strong opinion.
complicated adj. 复杂的，难处理的；1. The instructions look very complicated. 这说明书看起来很难懂。
when it comes to 当提到…；1. When it comes to music, I'm a complete ignoramus. 说到音乐，我完全是个门外汉。
universal adj. 普遍的，全体的，全世界的；通用的，万能的；
consensus n. 一致看法，共识；1. The consensus among the world's scientists is that the world is likely to warm up over the next few decades. 全世界科学家的共识是地球可能在未来几十年中变暖。
split into 分开，使分开（成为几个部分）；1. She split the class into groups of four. 她按四人一组把全班分成若干小组。
camp n. 营地；兵营，军营；度假营；阵营，集团；
ceaselessly adv. 不停地；
convincingly adv. 令人信服地；有说服力地；1. convincing adj. 令人信服的；有说服力的；
a convincing argument/explanation 有说服力的论点/解释；
respective adj. 分别的；各自的；1. They are each recognized specialists in their respective fields. 他们在各自的领域都被视为专家。
puzzle n. 令人费解的人（或事物），难题；
参考译文
通常，数学中都有明确的答案——尤其是在任务不是太复杂的情况下。但是，对于2000年开始流行的“睡美人”问题，人们仍然没有达成普遍共识。哲学和数学方面的专家分裂成两个阵营，不断地为各自的观点引证——往往相当有说服力。关于这个谜题的技术出版物有100多种，几乎每个听说过睡美人思维实验的人都有自己有力的观点。
段二
The problem vexing the minds of experts is as follows: Sleeping Beauty agrees to participate in an experiment. On Sunday she is given a sleeping pill and falls asleep. One of the experimenters then tosses a coin. If “heads” comes up, the scientists awaken Sleeping Beauty on Monday. Afterward, they administer another sleeping pill. If “tails” comes up, they wake Sleeping Beauty up on Monday, put her back to sleep and wake her up again on Tuesday. Then they give her another sleeping pill. In both cases, they wake her up again on Wednesday, and the experiment ends.
vex vt. 使恼火；使烦恼；使忧虑；
as follows 如下；1. Briefly, the argument is as follows… 简言之，理由如下…；
toss vt.（轻轻地或随意地）扔，抛，掷；
administer vt. 给予，施用（药物等）；1. Police believe his wife could not have administered the poison. 警方认为他的妻子不可能下毒。
tails n. 硬币的反面；
参考译文
困扰专家们的问题是这样的：睡美人同意参加一项实验。星期天，医生给她吃了一片安眠药，她就睡着了。然后其中一名实验者抛硬币。如果“正面”出现，科学家们将在周一唤醒睡美人。之后，他们给睡美人服用另一颗安眠药。如果出现“反面”，他们会在周一叫醒睡美人，让她继续睡觉，周二再叫醒她。然后他们给她另一颗安眠药。在这两种情况下，他们在周三再次叫醒她，实验结束。
段三
The important thing here is that because of the sleeping drug, Sleeping Beauty has no memory of whether she was woken up before. So when she wakes up, she cannot distinguish whether it is Monday or Tuesday. The experimenters do not tell Sleeping Beauty either the outcome of the coin toss nor the day. They ask her one question after each time she awakens, however: What is the probability that the coin shows heads?
distinguish vt. 使有别于；看清，认出；区别，分清；1. distinguish right from wrong 明辨是非；
neither…nor… 既不…也不…；1. I neither knew nor cared what had happened to him. 我既不知道也不关心他出了什么事。2. either…or… 要么…要么…；不是…就是…；
outcome n. 结果，效果；1. The outcome was still in doubt. 结果仍不确定。
probability n. 可能性，或然性；可能发生的事，可能真实的事；（数）概率，几率；1. Without a transfusion, the victim's probability of dying was 100%. 不输血的话，该患者的死亡概率是100%。
参考译文
重要的是，由于服用了安眠药，睡美人不记得自己之前是否被叫醒过。所以当她醒来时，她分不清今天是星期一还是星期二。实验人员既没有告诉睡美人抛硬币的结果，也没有告诉她是哪一天。然而，每次她醒来后，他们都会问她一个问题：硬币正面朝上的概率是多少?
精听党每日单词
mathematician
/ˌmæθəməˈtɪʃn/ n. 数学家；
awake
/əˈweɪk/ adj. 醒着的（尤指入睡前或刚醒时）；
complicated
/ˈkɑːmplɪkeɪtɪd/ adj. 复杂的，难处理的；
when it comes to
当提到…；
universal
/ˌjuːnɪˈvɜːrs(ə)l/ adj. 普遍的，全体的，全世界的；通用的，万能的；
consensus
/kənˈsensəs/ n. 一致看法，共识；
split into
分开，使分开（成为几个部分）；
ceaselessly
/ˈsiːsləsli/ adv. 不停地；
camp
/kæmp/ n. 营地；兵营，军营；度假营；阵营，集团；
convincingly
/kənˈvɪnsɪŋli/ adv. 令人信服地；有说服力地；
respective
/rɪˈspektɪv/ adj. 分别的；各自的；
puzzle
/ˈpʌz(ə)l/ n. 令人费解的人（或事物），难题；
vex
/veks/ vt. 使恼火；使烦恼；使忧虑；
as follows
如下；
toss
/tɔːs/ vt.（轻轻地或随意地）扔，抛，掷；
administer
/ədˈmɪnɪstər/ vt. 给予，施用（药物等）；
tails
/teɪlz/ n. 硬币的反面；
distinguish
/dɪˈstɪŋɡwɪʃ/ vt. 使有别于；看清，认出；区别，分清；
neither…nor…
既不…也不…；
outcome
/ˈaʊtkʌm/ n. 结果，效果；
probability
/ˌprɑːbəˈbɪləti/ n. 可能性，或然性；可能发生的事，可能真实的事；（数）概率，几率；
精听党文化拓展
抛硬币的最早记载可追溯至罗马时期，当时人们认为抛出正面或反面的机率为神性意志的展现。虽然直至今日已经没有那么严肃，但抛硬币仍被认为是做决定或解决争端的公平方式。在某些体育赛事中，抛硬币用于决定队伍的进攻方向，或者在平局时选出获胜者。但抛硬币究竟有多随机呢？曾为职业魔术师的佩尔西·戴康尼斯（Persi Diaconis）后来成为了史丹佛大学的数学和统计学家，由于职业的原因，他对这个问题的答案很感兴趣。2007年，戴康尼斯和来自史丹佛与加利福尼亚大学圣克鲁兹分校的研究伙伴们进行了实验，包括抛掷一枚系着丝带的硬币，借由解开硬币上的丝带来确定硬币旋转的次数。为了消除抛硬币过程中不希望出现的人为变数，抛硬币的初始条件必须一致，因此他们委托哈佛大学制作抛硬币机来进行实验。此外，他们还使用高速摄像机捕捉每次抛硬币的慢动作照片，以精确的角度测量硬币的翻转方向。
进动（或者说旋进）硬币的座标结果发现，当初始条件完全相同时，抛硬币能产生相同的结果，这意味着抛硬币的随机性很可能是由于每个人的抛掷方式不同（抛掷的速度和高度、接硬币时的角度和翻转程度等等）所造成。尽管用手抛硬币看似具有不可预测性，但仍然存在固有的偏差：如果硬币一开始是正面，那么最后有51％的可能性硬币会落在同一面，而不是反面。也就是说，原本应该是一半一半的机率产生了偏差，变成了51%对49％。
精听党每日美句
One thorn of experience is worth a whole wilderness of warning.
一次痛苦的经验抵得上千百次的告诫。