“我的心真的是冰冰的了”

今天，一张网传截图引爆微博热搜，该截图显示，知名主持人王冰冰‍疑似在朋友圈官宣与游泳名将徐嘉余的恋情。

还有网传徐嘉余的朋友圈签名是：“一寸光阴一寸金，寸金难买寸光阴，心无旁骛，唯有冰冰。”

网友纷纷表示：冰冰恋爱了，新郎不是我。我的心真的是冰冰的了......

目前，双方还未对此事进行回应。

借（cèng）此（gè）机（rè）会（diǎn），我们来看一个有趣的话题，爱情与数学，世界那么大，如何“科学地”找到唯一的真爱？找到唯一真爱的概率有多大？

看完你的心，是冰冰凉凉还是暖暖的？

无注释原文：

A theoretical physicist reassures the lovelorn

What are your chances of finding your one and only?

February 13, 2017

Science Daily

In 1990, Marilyn vos Savant, a columnist for Parade magazine, received the following reader question, a restatement of a famous puzzle called the Monty Hall problem:

Suppose you're on a game show, and you're given the choice of three doors. Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what's behind the doors, opens another door, say No. 3, which has a goat. He says to you, "Do you want to pick door No. 2?" Is it to your advantage to switch your choice of doors?

She said yes, triggering an avalanche of angry and insulting letters from readers claiming she was wrong. But, as further investigation showed, the answer she gave -- although counter-intuitive -- was correct.

People are not natural statisticians and often make the wrong decisions when faced with probabilities rather than certainties. Experiments with probabilistic problems have consistently shown that we have built-in biases that lead us astray. Even statisticians misjudge probability problems, which are often exploited to probe the foibles of the mind.

One of our leading foibles is we feel far more certain than we should about our judgment in cases like this: Hence, the angry tone of many of the letters sent to vos Savant.

The Monty Hall problem, named after the former television game-show host, was one of 13 paradoxes described this fall in a lecture to new Compton Fellows by Carl Bender, the Wilfred R. and Ann Lee Konneker Distinguished Professor of Physics at Washington University in St. Louis.

Here, in celebration of Valentine's Day, we present another of the paradoxes, sometimes called the Picky Suitor problem: Can you guess the odds that you will find your one and only among the 7.4 billion people on the planet?

The paradox reduces the problem to a numerical game: what are the odds of picking the biggest number out of a box of numbers? Each time you pick a slip you have to say whether the number is the biggest or not, and the first time you guess wrong, the game ends and you lose. If you correctly identify the biggest number, the game ends and you win. So what are the odds of winning?

The game, of course, is not a perfect analogy for the problem of picking a partner or spouse. For one thing, numbers can be unequivocally ranked from smallest to largest, whereas many a hapless seeker has ended up trying to decide between potential partners who have no clear rank order. For these and other reasons, the Picky Suitor problem is not meant to be a guide to the perplexed so much as to pique curiosity and arouse doubt.

On the other hand, experimental psychologists who have studied the decision behavior of people in such situations as the fussy suitor problem have shown that people tend to stop searching too soon. It may just be that the cost of continuing the search outweighs the cost of making a decision that is less than optimal.

"I enjoyed giving this lecture," Bender said, "because probabilistic problems can be so surprising and that makes them fun. "

He also said, by the way, that he met his wife while studying in the Cornell University library and not thinking about finding a spouse.

- ◆ -

注：中文文本为机器翻译仅供参考，并非一一对应

含注释全文：

A theoretical physicist reassures the lovelorn

What are your chances of finding your one and only?

February 13, 2017

Science Daily

In 1990, Marilyn vos Savant, a columnist for Parade magazine, received the following reader question, a restatement of a famous puzzle called the Monty Hall problem:

1990年，美国《Parade》杂志的专栏作家玛丽莲·沃斯·莎凡特（Marilyn vos Savant）收到了以下读者问题，这是对一个名为蒙提·霍尔问题（Monty Hall problem，即三门问题）的著名谜题的重述：

表示“（报纸、杂志的）专栏作家”，英文解释为“someone who writes a regular article for a newspaper or magazine”如：a gossip/sports columnist 漫谈/体育专栏作家。

1）表示“令人费解的情况；难题；谜”，英文解释为“a situation that is difficult to understand”举个🌰：

Scientists have been trying to solve this puzzle for years.

多年来科学家们一直试图解开这个谜。

2）表示“测验智力的游戏（或玩具）”，英文解释为“a game or toy in which you have to fit separate pieces together, or a problem or question that you have to answer by using your skill or knowledge”如：a jigsaw puzzle 智力拼图玩具。

Suppose you're on a game show, and you're given the choice of three doors. Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what's behind the doors, opens another door, say No. 3, which has a goat. He says to you, "Do you want to pick door No. 2?" Is it to your advantage to switch your choice of doors?

假设你在参加一个游戏节目，你可以选择三扇门中的一扇。一扇门后面是一辆汽车，其他的门后面是山羊。当你选了一扇门，比如说1号门，而主持人知道门后面是什么，他打开了另一扇门，比如说3号门，里面有一只山羊。他对你说，“你想换选2号门吗？”改变你选择的门对你有利吗？

She said yes, triggering an avalanche of angry and insulting letters from readers claiming she was wrong. But, as further investigation showed, the answer she gave -- although counter-intuitive -- was correct.

她同意了换选，引发了大量愤怒和侮辱性的读者来信，声称她选错了。但是，进一步的调查显示，她给出的答案——尽管是反直觉的——却是正确的。

1）作动词，除了表示“发动；引起；触发”，英文解释为“to make sth happen suddenly”举个🌰：

Nuts can trigger off a violent allergic reaction.

坚果可以引起严重的过敏反应。

2）作名词，表示“扳机”，英文解释为“The trigger of a gun is a small lever which you pull to fire it.”举个🌰：

A man pointed a gun at them and pulled the trigger.

一个男人用枪指着他们，扣动了扳机。

类似的还有：

📍stir表示“激发，激起（强烈的感情）；引起（强烈的反应）”，英文解释为“to make someone have a strong feeling or reaction”，举个🌰：

The poem succeeds in stirring the imagination.

这首诗能够激发起想象力。

📍provoke也表示“激起，引起”，英文解释为“to cause a reaction or feeling, especially a sudden one”，如：provoke debate/discussion 激起辩论/讨论。

📍spur 鼓动；激励；鞭策；刺激；鼓舞”，英文解释为“If one thing spurs you to do another, it encourages you to do it.”举个🌰：

It's the money that spurs these fishermen to risk a long ocean journey in their flimsy boats.

是金钱驱使这些渔民驾驶单薄的小船冒险出海远航。

🎬电影《龙之心3：巫师的诅咒》（Dragonheart 3: The Sorcerer's Curse）中的台词提到：To spur the clans to war. 激励部族发起战争。

avalanche /ˈævəˌlɑːntʃ/ 1）表示“雪崩，山崩”，英文解释为“a large mass of snow, ice, and rocks that falls down the side of a mountain”

2）表示“大量；突然到来的一大批”，英文解释为“too many things that arrive or happen at the same time”举个🌰：

We were swamped by an avalanche of letters/phone calls/complaints.

大批的来信/电话/投诉让我们疲于应付。

We received an avalanche of letters in reply to our advertisement.

我们在登出广告后收到了雪片般飞来的大批答复信件。

insult作动词，表示“侮辱，辱骂”，英文解释为“to say or do something to someone that is rude or offensive”举个🌰：

First he drank all my wine and then he insulted all my friends.

他先喝光了我的酒，然后又辱骂了我所有的朋友。

📍insulting作形容词，表示“侮辱的，有冒犯性的，无礼的”（rude or offensive）。

1）表示“获得；赢得；取得”，英文解释为“to gain, win or achieve sth”举个🌰：

She has finally claimed a place on the team.

她终于成了那支队的队员。

2）表示“声称；宣称；断言；主张”，英文解释为“to say that something is true or is a fact, although you cannot prove it and other people might not believe it”举个🌰：

The company claims (that) it is not responsible for the pollution in the river.

公司声称对该河流污染没有责任。

表示“（想法、提议等）违反常理的，反直觉的”，英文解释为“(of an idea, proposal, etc) seemingly contrary to common sense”；

📍intuitive本身表示“（出于）直觉的”（an intuitive idea is based on a feeling rather than on knowledge or facts），而前缀counter-表示“（用于构词）表示相反或相对”（Counter- is used to form words which refer to actions or activities that are intended to prevent other actions or activities or that respond to them.）如：counter-terrorism 反恐，counter-example 反面例子，counterproductive 产生相反效果的，适得其反的。

近义词对比：

📍instinctive表示“本能的；天性的；直觉的”（based on instinct and not involving thought）

People are not natural statisticians and often make the wrong decisions when faced with probabilities rather than certainties. Experiments with probabilistic problems have consistently shown that we have built-in biases that lead us astray. Even statisticians misjudge probability problems, which are often exploited to probe the foibles of the mind.

人们不是天生的统计学家，在面对概率性而不是确定性问题时，往往会做出错误的决定。有关概率问题的实验一直表明，我们有内在的偏见，导致我们误入歧途。甚至统计学家也会误判概率问题，这些问题经常被利用来探究心灵的弱点。

statistician /ˌstæt.ɪˈstɪʃ.ən/ 表示“统计学家；统计员”，英文解释为“someone who studies or is an expert in statistics”

表示“确定的事情；必然的事情”，英文解释为“something that cannot be doubted”举个🌰：

There are few absolute certainties in life.

世事无绝对。

表示“基于概率的”，英文解释为“based on or relating to how likely it is that something will happen ”举个🌰：

These examples illustrate the probabilistic rather than causal status of risk factors.

这些例子阐明了风险因素的概率性质，而不是因果性质。

1）表示“内嵌的；嵌入式的”，英文解释为“If a place or piece of equipment has built-in objects, they are permanently connected and cannot be easily removed.”如：built-in storage 嵌入式储物间。

2）表示“内在的；固有的”，英文解释为“A built-in quality is an original part of something or someone and cannot be separated from it, him, or her.”如：an built-in advantage/problem 内在的优势/固有的问题。

表示“偏见；偏心；偏向；偏差”，英文解释为“a strong feeling in favour of or against one group of people, or one side in an argument, often not based on fair judgement”举个🌰：

Employers must consider all candidates impartially and without bias.

雇主必须公平而毫无成见地考虑所有求职者。

astray /əˈstreɪ/ 表示“偏离正轨地；迷路地；离开正道地；误入歧途地”，英文解释为“away from the correct path or correct way of doing something”举个🌰：

The letter must have gone astray in the post.

这封信一定是在邮递过程中丢失了。

表示“错误地判断；对…判断不公；错看”，英文解释为“to form an opinion or idea about someone or something that is unfair or wrong”举个🌰：

I thought he wasn't going to support me, but I misjudged him.

我以为他不会支持我，其实我看错了他。

1）表示“利用；剥削（…为自己谋利）”，英文解释为“to treat a person or situation as an opportunity to gain an advantage for yourself”举个🌰：

He exploited his father's name to get himself a job.

他利用他父亲的名声为自己找到一份工作。

2）表示“开发，运用；利用；发挥”，英文解释为“to use sth well in order to gain as much from it as possible”举个🌰：

She fully exploits the humour of her role in the play.

她在剧中把她那个角色的幽默发挥得淋漓尽致。

🎬电影《惊天魔盗团》（Now You See Me）中的台词提到：What I hate is people who exploit other people. 我只是讨厌那些利用别人的人。

作动词，表示“盘问；追问；探究”，英文解释为“to try to discover information that other people do not want you to know, by asking questions carefully and not directly”举个🌰：

The interviewer probed deep into her private life.

采访者深入地打探她的私生活。

在恏渏 亾類哋夲能文中提到了probe作名词有“探索；探查；查究；调查”的意思，英文解释为“an attempt to discover information by asking a lot of questions”，如：an FBI probe into corruption 联邦调查局对腐败的调查；也可以指“（医生或科学家用的）探针”，英文解释为“a long thin metal instrument that doctors and scientists use to examine parts of the body”。

📍probe还可以解释为“探测器”，英文解释为：a device that is put inside something to test or record information. 如：a space probe 航天探测器/太空探测器。

🎬电影《像素大战》（Pixels）中的台词提到：That videotape will be placed in a space probe 录影带将放在太空探测器中。

foible /ˈfɔɪ.bəl/ 表示“（无伤大雅的）怪癖，小毛病，小缺点”，英文解释为“a strange habit or characteristic that is seen as not important and not harming anyone”举个🌰：

We all have our little foibles.

我们都有自己的小毛病。

One of our leading foibles is we feel far more certain than we should about our judgment in cases like this: Hence, the angry tone of many of the letters sent to vos Savant.

我们的一个主要弱点是，在这种情况下，我们过分盲目相信自己的判断了：因此，许多写给玛丽莲·沃斯·莎凡特的信的语气都很愤怒。

1）表示“风格；基调，格调；气氛”，英文解释为“the general mood or main qualities of something”举个🌰：

I didn't like the jokey tone of the article - I thought it was inappropriate.

我不喜欢这篇文章的搞笑风格——我觉得这不恰当。

2）表示“色调；明暗；影调”，英文解释为“a form or degree of a colour”，如：warm tones of brown and yellow 棕色和黄色这种暖色调。

3）表示“（常指对听话人的）语气，腔调，口吻”，英文解释为“a quality in the voice that expresses the speaker's feelings or thoughts, often towards the person being spoken to”举个🌰：

I tried to use a sympathetic tone of voice.

我试着用一种同情的语气说话。

The Monty Hall problem, named after the former television game-show host, was one of 13 paradoxes described this fall in a lecture to new Compton Fellows by Carl Bender, the Wilfred R. and Ann Lee Konneker Distinguished Professor of Physics at Washington University in St. Louis.

蒙提·霍尔问题（三门问题）以这位前电视游戏节目主持人的名字命名，是今年秋天圣路易斯华盛顿大学（Washington University in St. Louis）物理学教授卡尔·本德（Carl Bender）给新康普顿研究员的讲座中描述的13个悖论之一。

表示“以（某人或某物的名字）命名”，英文解释为“If you name someone or something after another person or thing, you give them the same name as that person or thing.”举个🌰：

Why haven't you named any of your sons after yourself?

为什么你没用你名字给你儿子中的任何一个命名？

paradox /ˈpærəˌdɒks/ 表示“自相矛盾的情况；似非而是的说法，悖论”，英文解释为“a situation or statement that seems impossible or is difficult to understand because it contains two opposite facts or characteristics”举个🌰：

It's a curious paradox that drinking a lot of water can often make you feel thirsty.

大量喝水经常会让人感觉口渴，这是看似矛盾而正确的奇怪说法。

Here, in celebration of Valentine's Day, we present another of the paradoxes, sometimes called the Picky Suitor problem: Can you guess the odds that you will find your one and only among the 7.4 billion people on the planet?

在这里，为了庆祝情人节（Valentine's Day），我们提出了另一个悖论，有时被称为“挑剔的求婚者问题”（the Picky Suitor problem）：你能猜到你在地球上74亿人中找到你的唯一真爱的概率吗？

在概率及博弈论上，称作秘书问题（Secretary problem），类似的名称有相亲问题、止步问题、见好就收问题、苏丹的嫁妆问题、挑剔的求婚者问题等，属于最佳停止问题。

📍内容是这样的：要聘请一名秘书，有 n 个应聘者。每次面试一人，面试后就要及时决定是否聘他，如果当时决定不聘他，他便不会回来。面试后总能清楚了解应聘者的合适程度，并能和之前的每个人做比较。问什么样的策略，才使最佳人选被选中的概率最大。

The secretary problem demonstrates a scenario involving optimal stopping theory that is studied extensively in the fields of applied probability, statistics, and decision theory. It is also known as the marriage problem, the sultan's dowry problem, the fussy suitor problem, the googol game, and the best choice problem.

表示“挑剔的”，英文解释为“Someone who is picky is very careful about choosing only what they like.”举个🌰：

The children are such picky eaters.

孩子们非常挑食。

表示“求婚者，追求者”，英文解释为“a man who wants to marry a particular woman”举个🌰：

It's the story of a young woman who can't make up her mind which of her many suitors she should marry.

这个故事说的是一位年轻女子拿不定主意该嫁给众多追求者中的哪一个。

fussy /ˈfʌs.i/ 表示“过分挑剔的；难以满足的”，英文解释为“not easily satisfied, or having very high standards about particular things”举个🌰：

All children were fussy eaters.

所有的孩子都挑食。

1）表示“可能性，机会；几率，概率”，英文解释为“the probability (= how likely it is) that a particular thing will or will not happen”举个🌰：

The overall odds of winning a lottery prize are 1 in 10.

抽中彩票的几率是1/10。

2）表示“不利条件；掣肘的事情；逆境”，英文解释为“something that makes it seem impossible to do or achieve sth”举个🌰：

They secured a victory in the face of overwhelming odds.

尽管情况非常不利，他们仍得到了胜利。

📍奥巴马卸任后首次重返白宫 和拜登互开玩笑文中提到，奥巴马讲话：“Despite great odds, Joe and I were determined, because we met too many people on the campaign trail who shared their stories, and our own families had been touched by illness.”“尽管困难重重，乔和我还是下定决心，因为我们在竞选路上遇到了太多分享他们故事的人，我们自己的家庭也被疾病所影响。”

📍great odds 表示“困难重重，困难诸多”，相当于a lot of difficulties，举个🌰：

We believe that, despite great odds, we can achieve a peaceful settlement.

我们相信，尽管困难重重，我们还是能够实现和平解决。

表示“独一无二；唯一的”，英文解释为“the only person or thing of this type; unique; single (used for emphasis or as a designation of a celebrity).”

The paradox reduces the problem to a numerical game: what are the odds of picking the biggest number out of a box of numbers? Each time you pick a slip you have to say whether the number is the biggest or not, and the first time you guess wrong, the game ends and you lose. If you correctly identify the biggest number, the game ends and you win. So what are the odds of winning?

该悖论将这个问题简化为一个数字游戏：从一箱写有数字的纸条中选出一张纸条，恰好是最大数字的几率有多大？每次你选了一张纸条，你都必须说这个数字是不是最大的。一旦猜错了，游戏结束，你就输了。如果你正确地找出最大的数字，游戏结束，你就赢了。那么获胜的几率有多大呢？

表示“数字的；以数字表示的”，英文解释为“involving or expressed in numbers”如：a numerical calculation 数字运算。

作动词，表示“滑倒；滑跤；溜走”，也可以指“摆脱；挣脱；松开；放走”，英文解释为“to get free; to make sth/sb/yourself free from sth”举个🌰：

The ship had slipped its moorings in the night.

那艘船在夜间漂离了停泊处。

作名词，熟词僻义，表示“纸条；小纸片”，英文解释为“a small piece of paper”如：a slip of paper 一张纸条。

表示“认出，识别”，英文解释为“to recognize someone or something and say or prove who or what that person or thing is”举个🌰：

Even the smallest baby can identify its mother by her voice.

就连年龄最小的婴儿也能根据声音分辨出自己的妈妈。

2）表示“确定；发现”，英文解释为“to recognize a problem, need, fact, etc. and to show that it exists”举个🌰：

The research will be used to identify training needs.

该研究将用来确定培训的需求。

The game, of course, is not a perfect analogy for the problem of picking a partner or spouse. For one thing, numbers can be unequivocally ranked from smallest to largest, whereas many a hapless seeker has ended up trying to decide between potential partners who have no clear rank order. For these and other reasons, the Picky Suitor problem is not meant to be a guide to the perplexed so much as to pique curiosity and arouse doubt.

当然，这个游戏对于挑选伴侣或配偶的问题并不是完美的类比。首先，数字可以明确地从小到大排列，而许多运气不好的追求者最终试图在没有明确排名顺序的潜在伴侣之间做出决定。出于种种原因，“挑剔的求婚者问题”与其说是困惑者的指南，不如说是激起了人们的好奇心并让人疑惑。

analogy /əˈnælədʒɪ/ 表示“类似；类比；比拟；类推”，英文解释为“a comparison between things that have similar features, often used to help explain a principle or idea”举个🌰：

He drew an analogy between the brain and a vast computer.

他把大脑比作一台庞大的计算机。

表示“配偶”，英文解释为“a person's husband or wife”举个🌰：

In 60 percent of the households surveyed both spouses went out to work.

在60%的被调查家庭中，夫妻双方都外出工作。

形容词性 unequivocal /ˌʌn.ɪˈkwɪv.ə.kəl/表示“完全的；表达明确的；毫不含糊的”，英文解释为“total, or expressed in a clear and certain way”如：an unequivocal rejection 明确的拒绝。

hapless /ˈhæpləs/表示“倒运的；不幸的”，英文解释为“not lucky; unfortunate”如：the hapless victims of exploitation 受到剥削的不幸牺牲品。

作形容词，表示“困惑的；迷惑不解的”，英文解释为“confused and anxious because you are unable to understand sth; showing this”如：a perplexed expression 困惑的表情。

📍此处the+形容词，表示一类人，理解为困惑的人。

表示“与其说是…还不如说是…”，英文解释为“If you say that something is not so much one thing as something else, you mean it is more the second thing.”举个🌰：

They're not so much lovers as friends.

他们与其说是恋人，不如说是朋友。

pique /piːk/ 是“使生气；使愤恨；使恼怒”（a feeling of anger, especially caused by someone damaging your feeling of being proud of yourself）的意思。

此外，pique还可以表示“激起（某人）的好奇心／兴趣（等等）”如：pique sb's curiosity, interest, etc.  举个🌰：

The noise continued, piquing her curiosity.

那种声音没有停，激起了她的好奇心。

表示“引起；唤起；激起”，英文解释为“to cause someone to have a particular feeling”举个🌰：

It's a subject that has aroused a lot of interest.

这个话题引起了很多人的兴趣。

On the other hand, experimental psychologists who have studied the decision behavior of people in such situations as the fussy suitor problem have shown that people tend to stop searching too soon. It may just be that the cost of continuing the search outweighs the cost of making a decision that is less than optimal.

另一方面，研究人们在“挑剔的求婚者问题”等情况下的决策行为的实验心理学家表明，人们往往会过早地停止寻找。这可能只是继续探寻的成本超过了做出不太理想的决定的成本。

表示“（尤指科学方面）实验（性）的，试验（性）的，根据实验（试验）的”，英文解释为“relating to tests, especially scientific ones”举个🌰：

The drug is still at the experimental stage (= is still being tested).

这种药物仍处于试验阶段。

psychologist /saɪˈkɒl.ə.dʒɪst/ 表示“心理学家”，英文解释为“someone who studies the human mind and human emotions and behaviour, and how different situations have an effect on people”如：a child psychologist 儿童心理学家。

1）表示“（在重要性或意义上）超过”，英文解释为“If one thing outweighs another, the first thing is of greater importance, benefit, or significance than the second thing.”举个🌰：

The advantages of this deal largely outweigh the disadvantages. 

这笔交易的利远大于弊。

2）表示“比（某人）重”，英文解释为“If you outweigh someone, you are heavier than them.”举个🌰：

He outweighed her by about 20 kilograms. 

他比她重约20千克。

表示“最优的，最佳的；优化的”，英文解释为“best; most likely to bring success or advantage”举个🌰：

A mixture of selected funds is an optimal choice for future security and return on investment.

同时选择几种基金是确保未来投资安全和投资收益的最佳选择。

📍《经济学人》（The Economist）一篇讲述量化交易的文章中提到：It requires algorithms that first establish and then fine-tune the optimal period over which to do the sorting. 这需要通过算法来确定并微调出一个最优的筛选期。

"I enjoyed giving this lecture," Bender said, "because probabilistic problems can be so surprising and that makes them fun. "

“我很喜欢做这个讲座，”本德说，“因为概率问题会让人非常惊讶，这让它们很有趣。”

He also said, by the way, that he met his wife while studying in the Cornell University library and not thinking about finding a spouse.

他还顺便说了一句，他在康奈尔大学（Cornell University）图书馆学习时认识了他的妻子，当时并没有想到要找一个配偶。

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