字幕列表 影片播放 列印所有字幕 列印翻譯字幕 列印英文字幕 Today I want to talk to you about the mathematics of love. 今天我想要和大家談談關於愛情的數學。 Now, I think that we can all agree 我想大家都同意 that mathematicians are famously excellent at finding love. 數學家在尋找真愛上特別在行。 But it's not just because of our dashing personalities, 但那並不只是因為我們精力充沛的性格、 superior conversational skills and excellent pencil cases. 超凡的對話技巧，和炫麗的筆盒。 It's also because we've actually done an awful lot of work into the maths 也是因為我們真的花了許多時間精力在數學上， of how to find the perfect partner. 計算如何找到完美的伴侶。 Now, in my favorite paper on the subject, which is entitled, 現在，在此學科中我最愛的論文，名為 "Why I Don't Have a Girlfriend" -- (Laughter) -- 「為甚麼我沒有女友」（笑聲） Peter Backus tries to rate his chances of finding love. Peter Backus 試著計算他尋得真愛的機會。 Now, Peter's not a very greedy man. 現在，Peter 不是一個非常貪心的人。 Of all of the available women in the U.K., 在英國所有適宜的女性對象中， all Peter's looking for is somebody who lives near him, Peter 所看的，就只是那個住在他附近的對象、 somebody in the right age range, 某個處於適宜的年齡階段的女人、 somebody with a university degree, 某個擁有大學文憑、 somebody he's likely to get on well with, 某個他很有可能相處地不錯的對象、 somebody who's likely to be attractive, 某個有魅力的女子， somebody who's likely to find him attractive. 以及......某個認為他也富有魅力的對象。 (Laughter) （笑聲） And comes up with an estimate of 26 women in the whole of the UK. 結果他估計在全英國大概有 26 位此類女性。 It's not looking very good, is it Peter? 這看來很不妙，不是嗎，Peter？ Now, just to put that into perspective, 我們好好思考一下這件事， that's about 400 times fewer than the best estimates 在無數聰明外星生命形式存在的情況下， of how many intelligent extraterrestrial life forms there are. 那是少於 400 倍數的估計呀。 And it also gives Peter a 1 in 285,000 chance 那也給了 Peter 一個 of bumping into any one of these special ladies 在某晚遇見一個特別的女子 on a given night out. 28 萬 5 千之 1 的機會。 I'd like to think that's why mathematicians 我想，那就是為什麼數學家 don't really bother going on nights out anymore. 不再怎麼想晚上出去約會了的原因了吧。 The thing is that I personally 重點是，我個人其實並不同意 don't subscribe to such a pessimistic view. 這種悲觀的看法， Because I know, just as well as all of you do, 因為我知道，如同你們所有所知道的， that love doesn't really work like that. 愛情並不是這樣發生的。 Human emotion isn't neatly ordered and rational and easily predictable. 人類的情感不是那樣地秩序井然、乾淨利落、邏輯清晰，和容易預測。 But I also know that that doesn't mean 但我也知道那並不意謂著 that mathematics hasn't got something that it can offer us 數學無法提供幫助， because, love, as with most of life, is full of patterns 因為愛情，如同生命中多數的事物一般，充斥著許多規律， and mathematics is, ultimately, all about the study of patterns. 而數學最終就是那研究規律的學說。 Patterns from predicting the weather to the fluctuations in the stock market, 從預測天候，到預測股票市場的開高走低， to the movement of the planets or the growth of cities. 到星球的運轉，或都市的發展。 And if we're being honest, none of those things 如果我們對自己誠實的話，上述那些東西，沒有一個是 are exactly neatly ordered and easily predictable, either. 井然有序以及容易預測的。 Because I believe that mathematics is so powerful that it has the potential 因為我相信，數學的力量非常強大，以至於它讓我們得以以新方法 to offer us a new way of looking at almost anything. 重新看待任何事物。 Even something as mysterious as love. 就算是和愛情一般神秘的東西也是。 And so, to try to persuade you 為了試著說服你們 of how totally amazing, excellent and relevant mathematics is, 數學的神妙用處， I want to give you my top three mathematically verifiable tips for love. 我想要給大家三個最重要的在數學上可以驗證的愛情秘訣。 Okay, so Top Tip #1: 好，首先最重要的秘技一： How to win at online dating. 如何贏得線上交友的機會。 So my favorite online dating website is OkCupid, 我最愛的線上交友網站是 OkCupid（網站名：好吧，丘比特）， not least because it was started by a group of mathematicians. 這並不僅僅因為這網站是由一群數學家所架設的。 Now, because they're mathematicians, 因為他們是數學家， they have been collecting data 他們已經蒐集了 on everybody who uses their site for almost a decade. 近乎這十年來所有該網站使用者的資料。 And they've been trying to search for patterns 他們試著尋找 in the way that we talk about ourselves 我們在線上 and the way that we interact with each other 談論自己的方式的模式， on an online dating website. 以及我們和他人互動的模式。 And they've come up with some seriously interesting findings. 他們發現了一些重要的有趣結果。 But my particular favorite 但我特別喜歡的結果之一是 is that it turns out that on an online dating website, 在線上交友網站上 how attractive you are does not dictate how popular you are, 你的魅力程度並無法預測你的受歡迎程度， and actually, having people think that you're ugly 事實上，讓人們覺得你很醜 can work to your advantage. 可以讓你擁有優勢。 Let me show you how this works. 讓我向各位展示這是怎麼一回事。 In a thankfully voluntary section of OkCupid, 在 OkCupid 的一個自願欄目中， you are allowed to rate how attractive you think people are 你可以評價人們的魅力值， on a scale between 1 and 5. 從 1 到 5 。 Now, if we compare this score, the average score, 現在，如果我們比較這個分數，平均分數， to how many messages a selection of people receive, 有多少人收到訊息， you can begin to get a sense 你就可以開始理解 of how attractiveness links to popularity on an online dating website. 在一個線上約會網站上魅力指數與受歡迎程度有關。 This is the graph that the OkCupid guys have come up with. 這是 OkCupid 得到的圖表。 And the important thing to notice is that it's not totally true 一件重要的值得注意的事是 that the more attractive you are, the more messages you get. 並不是越有魅力的人，收到的訊息越多。 But the question arises then of what is it about people up here 問題是，為什麼上面的這些人 who are so much more popular than people down here, 比下面這些人要受歡迎得多， even though they have the same score of attractiveness? 即便他們都有相同的魅力值？ And the reason why is that it's not just straightforward looks that are important. 原因是，並不是直觀的外貌是重要的。 So let me try to illustrate their findings with an example. 讓我來談談他們的發現，以一個案例說明。 So if you take someone like Portia de Rossi, for example, 如果你拿 Portia de Rossi 為例， everybody agrees that Portia de Rossi is a very beautiful woman. 每個人都同意 Portia de Rossi 是個非常美麗的女人， Nobody thinks that she's ugly, but she's not a supermodel, either. 沒有人覺得她醜，但她也不是超級名模。 If you compare Portia de Rossi to someone like Sarah Jessica Parker, 如果你拿某個人，比如Sarah Jessica Parker（譯注：慾望城市女主角）來和她比較 now, a lot of people, myself included, I should say, 許多人，包括我自己，我應該會說， think that Sarah Jessica Parker is seriously fabulous Sarah Jessica Parker 魅力極為出眾， and possibly one of the most beautiful creatures 有可能是地表上 to have ever have walked on the face of the Earth. 最美麗的物種之一。 But some other people, i.e., most of the Internet, 但許多其他人，比如，大多數的網友 seem to think that she looks a bit like a horse. (Laughter) 似乎都認為她看起來像馬。（笑聲） Now, I think that if you ask people how attractive they thought 如果你問人們他們覺得自己有多美， Sarah Jessica Parker or Portia de Rossi were, Sarah Jessica Parker 或 Portia de Rossi and you ask them to give them a score between 1 and 5, 你要他們給自己打分，從 1 到 5， I reckon that they'd average out to have roughly the same score. 我猜他們也會大約給一個和大家都差不多的數字。 But the way that people would vote would be very different. 但是人們投票的方式各自不同。 So Portia's scores would all be clustered around the 4 因此 Portia 的分數會聚集在 4 分左右， because everybody agrees that she's very beautiful, 因為所有人都同意，她非常美麗， whereas Sarah Jessica Parker completely divides opinion. 然而人們對 Sarah Jessica Parker卻有截然不同的意見。 There'd be a huge spread in her scores. 她的分差懸殊很大。 And actually it's this spread that counts. 然而事實上，就是那分差別具意義， It's this spread that makes you more popular 那差異讓你 on an online Internet dating website. 在交友網站上受歡迎。 So what that means then 所以那意味著 is that if some people think that you're attractive, 如果有些人認為你別具魅力， you're actually better off 你最好有其他人認為 having some other people think that you're a massive minger. 你很醜。 That's much better than everybody just thinking 那遠優於所有人認為 that you're the cute girl next door. 你是鄰家的可愛女孩。 Now, I think this begins makes a bit more sense 當你們開始思考一下這些寄送訊息的人的話， when you think in terms of the people who are sending these messages. 這開始變得合理些了。 So let's say that you think somebody's attractive, 這麼說吧，假設你認為那個人很美， but you suspect that other people won't necessarily be that interested. 但你同時猜想其他人並不會和你有同樣的審美觀。 That means there's less competition for you 那就意味著，你的競爭對手略少， and it's an extra incentive for you to get in touch. 這就給你增加了額外的動機去與他/她認識。 Whereas compare that to if you think somebody is attractive 與之相對的情況是，你認為某人很有吸引力， but you suspect that everybody is going to think they're attractive. 但你猜想所有其他的人都認為那人很有吸引力， Well, why would you bother humiliating yourself, let's be honest? 嗯，讓我們面對事實為什麼要自取其辱呢？ Here's where the really interesting part comes. 這就是最有趣的部分。 Because when people choose the pictures that they use on an online dating website, 因為當人們去選擇他們在交友網站上使用的照片時， they often try to minimize the things 他們總是試圖最小化 that they think some people will find unattractive. 其他人認為不吸引人之處的可能性。 The classic example is people who are, perhaps, a little bit overweight 最經典的例子是，那些體重略重的人 deliberately choosing a very cropped photo, 故意選擇一個剪裁非常不正確的照片， or bald men, for example, 例如那些禿頭的男士， deliberately choosing pictures where they're wearing hats. 故意去選擇他們帶著帽子的照片。 But actually this is the opposite of what you should do 但你的行為是與你的目標相悖的， if you want to be successful. 如果你想要在網上交友成功。 You should really, instead, play up to whatever it is that makes you different, 你真的應該，去選擇讓你看起來與眾不同的照片， even if you think that some people will find it unattractive. 即便你認為某些人會對此失去興趣。 Because the people who fancy you are just going to fancy you anyway, 因為那些喜歡你的人無論如何都會去喜歡你， and the unimportant losers who don't, well, they only play up to your advantage. 而那些不重要的路人只是渲染你的優勢。 Okay, Top Tip #2: How to pick the perfect partner. 好了，最高秘訣 2 號：如何選擇完美的伴侶。 So let's imagine then that you're a roaring success 讓我們想像你的約會 on the dating scene. 精彩成功， But the question arises of how do you then convert that success 但問題來了你如何將那成功的約會 into longer-term happiness and in particular, 轉變成長期的幸福，尤其是， how do you decide when is the right time to settle down? 你要如何選擇在哪個時刻安定下來？ Now generally, it's not advisable to just cash in 一般來說，並不建議人們立刻 and marry the first person who comes along 與第一個出現 and shows you any interest at all. 對你表達好感的人結婚。 But, equally, you don't really want to leave it too long 但是，一般來說，如果你想要最大化你未來數十年幸福婚姻的機會， if you want to maximize your chance of long-term happiness. 你也不願等待太久。 As my favorite author, Jane Austen, puts it, 我最喜歡的作家珍．奧斯汀這樣說： "An unmarried woman of seven and twenty 「一個未婚的 27 歲女子 can never hope to feel or inspire affection again." 就別指望再能感受或觸動愛情了。」 (Laughter) （笑聲） Thanks a lot, Jane. What do you know about love? 這太嚴重了，珍，你對愛瞭解多少呢？ So the question is then, 那麼問題來了， how do you know when is the right time to settle down 你怎麼知道哪個時刻是該要安定下來的時刻， given all the people that you can date in your lifetime? 畢竟生命中你有很多可能的對象？ Thankfully, there's a rather delicious bit of mathematics that we can use 幸好，我們可以運用一點數學 to help us out here, called optimal stopping theory. 來幫助我們計算解決這個問題，這理論名叫 「最優停止理論」。 So let's imagine then, 那麼讓我們來想像一下， that you start dating when you're 15 你在 15 歲的時候開始交往， and ideally, you'd like to be married by the time that you're 35. 理想狀態下，你在 35 歲的時候會結婚。 And there's a number of people 你的人生中 that you could potentially date across your lifetime, 有很多潛在的約會對象， and they'll be at varying levels of goodness. 他們都有各自的優點。 Now the rules are that once you cash in and get married, 規則是，你一旦跳進婚姻， you can't look ahead to see what you could have had, 你就不能繼續前進尋找你可能可以有的對象， and equally, you can't go back and change your mind. 你也不能回頭來改變你的主意。 In my experience at least, 我個人的經驗看來， I find that typically people don't much like being recalled 一般人們不希望 years after being passed up for somebody else, or that's just me. 在被拒絕又過了多年後被找回來，也許只有我這樣想。 So the math says then that what you should do 數學告訴我們 in the first 37 percent of your dating window, 你應該拒絕認為會和在你人生約會週期 you should just reject everybody as serious marriage potential. 前 37% 時段出現的任何人有嚴肅認真的婚姻關係。 (Laughter) （笑聲） And then, you should pick the next person that comes along 接著，你要選擇下一個人， that is better than everybody that you've seen before. 那個比你以前約會對象都好的人。 So here's the example. 這裡舉個例子。 Now if you do this, it can be mathematically proven, in fact, 如果你這麼做，從數學證明來看可以認為，事實上 that this is the best possible way 這可能是最好的選擇 of maximizing your chances of finding the perfect partner. 來最大化你找到完美伴侶的機會。 Now unfortunately, I have to tell you that this method does come with some risks. 現在不幸的是，我必須告訴你這個方法也是有風險的。 For instance, imagine if your perfect partner appeared 比如，想像一下，假設你的完美伴侶 during your first 37 percent. 出現在你約會歷程的前 37% Now, unfortunately, you'd have to reject them. 那就很不幸了，你會拒絕他們。 (Laughter) （笑聲） Now, if you're following the maths, 如果你相信數學， I'm afraid no one else comes along 恐怕你不會再找到 that's better than anyone you've seen before, 比你以往見過更好的對象， so you have to go on rejecting everyone and die alone. 你就會持續拒絕每個人然後孤獨終老。 (Laughter) （笑聲） Probably surrounded by cats nibbling at your remains. 可能會被貓咪包圍一點點啃食你的遺骸。 Okay, another risk is, let's imagine, instead, 好，另一個風險是，讓我們想像，相反的， that the first people that you dated in your first 37 percent 你約會歷程前 37% 裡第一個對象 are just incredibly dull, boring, terrible people. 極度愚蠢、無聊又很糟糕。 Now, that's okay, because you're in your rejection phase, 沒關係，因為你還處於拒絕對象的階段， so thats fine, you can reject them. 沒問題，你可以拒絕他們。 But then imagine, the next person to come along 但想像一下，下一個出現的人 is just marginally less boring, dull and terrible 只是沒那麼無聊、愚蠢， than everybody that you've seen before. 比你以前的對象都略好那麼一點。 Now, if you are following the maths, I'm afraid you have to marry them 如果你遵循數學，恐怕你要和他們結婚 and end up in a relationship which is, frankly, suboptimal. 然後沈浸在一段，實話說，次優的關係中。 Sorry about that. 很抱歉。 But I do think that there's an opportunity here 但我認為，機會還是有的 for Hallmark to cash in on and really cater for this market. 賀曼公司迎合市場需求 A Valentine's Day card like this. (Laughter) 出售這樣的情人節賀卡。（笑聲） "My darling husband, you are marginally less terrible 「我親愛的丈夫，你沒有 than the first 37 percent of people I dated." 我約會歷程中前 37% 的男士那麼糟糕。」 It's actually more romantic than I normally manage. 這比一般的賀卡浪漫很多。 Okay, so this method doesn't give you a 100 percent success rate, 這個數學方法不能保證100% 的成功率， but there's no other possible strategy that can do any better. 但也沒有更好的策略了。 And actually, in the wild, there are certain types 事實上，在動物界，某個特定種類的魚 of fish which follow and employ this exact strategy. 遵循使用這樣的策略。 So they reject every possible suitor that turns up 在交配期，牠們拒絕 in the first 37 percent of the mating season, 出現在前 37% 的每個求婚者， and then they pick the next fish that comes along after that window 接著牠們選擇 37% 後出現的下一個 that's, I don't know, bigger and burlier 比所見過的魚 than all of the fish that they've seen before. 體型更加龐大，更加結實的魚。 I also think that subconsciously, humans, or we do sort of do this anyway. 我想作為人類我們潛意識裡也在做同樣的選擇。 We have to give ourselves a little bit of time to play the field, 我們給自己更多時間尋找， get a feel for the marketplace or whatever when we're young. 在我們年輕的時候感受婚戀市場。 And then we only start looking seriously at potential marriage candidates 我們只有在 20 歲年齡段的中後期 once we hit our mid-to-late 20s. 才會很真尋找潛在的結婚對象。 I think this is conclusive proof, if ever it were needed, 我想這證明了，即使不確定是否需要， that everybody's brains are prewired to be just a little bit mathematical. 每個人的大腦都預配了點數學能力。 Okay, so that was Top Tip #2. 好，上述就是最高秘訣 2 號。 Now, Top Tip #3: How to avoid divorce. 現在，最高秘訣 3 號：如何避免離婚。 Okay, so let's imagine then that you picked your perfect partner 好的，讓我們想像一下你找到了你的完美對象， and you're settling into a lifelong relationship with them. 你和他/她進入了一生的婚姻關係。 Now, I like to think that everybody would ideally like to avoid divorce, 我假設每個人都不希望離婚， apart from, I don't know, Piers Morgan's wife, maybe? 當然，也許除了 Piers Morgan 的太太？ But it's a sad fact of modern life 可是，現代婚姻一個悲傷的事實 that 1 in 2 marriages in the States ends in divorce, 就是美國離婚率高達 50%， with the rest of the world not being far behind. 世界其他國家也離這個數據不遠。 Now, you can be forgiven, perhaps 當然，你可以認為 for thinking that the arguments that precede a marital breakup 婚姻破裂的原因 are not an ideal candidate for mathematical investigation. 不是數學運算理想的數據源。 For one thing, it's very hard to know 一方面來說，很難瞭解到 what you should be measuring or what you should be quantifying. 你該去測量什麼或者是你該去量化什麼。 But this didn't stop a psychologist, John Gottman, who did exactly that. 但這並沒有阻止心理學家John Gottman 做這樣的研究。