The mathematics of love

愛的數(shù)學(xué)

by Hannah Fry

Today I want to talk to you about the mathematics of love. Now, I think that we can all agree that mathematicians are famously excellent at finding love. But it's not just because of our dashing personalities, superior conversational skills and excellent pencil cases. It's also because we've actually done an awful lot of work into the maths of how to find the perfect partner.

今天我想和你談?wù)勱P(guān)于愛的數(shù)學(xué)∏牙澹現(xiàn)在矮冬，我想我們都可以同意，數(shù)學(xué)家在尋找愛情方面是非常出色的蚕断。但這不只是因?yàn)槲覀兊膫€(gè)性欢伏，優(yōu)越的談話技巧和優(yōu)秀的鉛筆盒。這也是因?yàn)槲覀冊(cè)跀?shù)學(xué)上做了大量的工作來尋找完美的伴侶亿乳。

Now, in my favorite paper on the subject, which is entitled, "Why I Don't Have a Girlfriend" -- (Laughter) -- Peter Backus tries to rate his chances of finding love. Now, Peter's not a very greedy man. Of all of the available women in the U.K., all Peter's looking for is somebody who lives near him, somebody in the right age range, somebody with a university degree, somebody he's likely to get on well with, somebody who's likely to be attractive, somebody who's likely to find him attractive. (Laughter) And comes up with an estimate of 26 women in the whole of the UK. It's not looking very good, is it Peter? Now, just to put that into perspective, that's about 400 times fewer than the best estimates of how many intelligent extraterrestrial life forms there are. And it also gives Peter a 1 in 285,000 chance of bumping into any one of these special ladies on a given night out. I'd like to think that's why mathematicians don't really bother going on nights out anymore.

現(xiàn)在硝拧，在我最喜歡的題為“為什么我沒有女朋友”的文章中（笑聲）彼得?巴克斯試圖評(píng)價(jià)他找到愛情的機(jī)會(huì)。現(xiàn)在葛假，彼得不是一個(gè)很貪婪的人障陶。在英國所有的女性中，所有的彼得都在尋找一個(gè)生活在他身邊的人聊训，一個(gè)合適的年齡段的人抱究，一個(gè)擁有大學(xué)學(xué)位的人继准，一個(gè)他很可能會(huì)相處融洽的人轿塔，有人可能會(huì)有吸引力模捂，有人可能會(huì)發(fā)現(xiàn)他有吸引力（笑聲）法梯，并提出了一個(gè)估計(jì)，26名女性在整個(gè)英國妈候。它看起來不太好敢靡，是彼得嗎？現(xiàn)在苦银，只需要把這一點(diǎn)放在一個(gè)角度來看啸胧，這大約是對(duì)外星生命形式的最好估計(jì)的400倍。而且它也給了彼得一個(gè)285000的機(jī)會(huì)幔虏，在一個(gè)特定的晚上撞上任何一個(gè)特別的女士纺念。我想這就是為什么數(shù)學(xué)家們?cè)僖膊粫?huì)在夜晚外出的原因了。

The thing is that I personally don't subscribe to such a pessimistic view. Because I know, just as well as all of you do, that love doesn't really work like that. Human emotion isn't neatly ordered and rational and easily predictable. But I also know that that doesn't mean that mathematics hasn't got something that it can offer us because, love, as with most of life, is full of patterns and mathematics is, ultimately, all about the study of patterns. Patterns from predicting the weather to the fluctuations in the stock market, to the movement of the planets or the growth of cities. And if we're being honest, none of those things are exactly neatly ordered and easily predictable, either. Because I believe that mathematics is so powerful that it has the potential to offer us a new way of looking at almost anything. Even something as mysterious as love. And so, to try to persuade you of how totally amazing, excellent and relevant mathematics is, I want to give you my top three mathematically verifiable tips for love.

問題是我個(gè)人并不贊同這種悲觀看法想括。因?yàn)槲抑老萜祝拖衲銈兯腥艘粯樱瑦鄄⒉皇钦嬲墓ぷ髦麟省Ｈ祟惖那楦胁⒉皇钦R有序叭首、理性和容易預(yù)測的。但我也知道踪栋，這并不意味著數(shù)學(xué)沒有它能提供給我們的東西焙格，因?yàn)椋瑦垡亩迹痛蠖鄶?shù)生活一樣眷唉，充滿了模式和數(shù)學(xué)，最終囤官，所有關(guān)于模式的研究冬阳。從天氣預(yù)報(bào)模式到股市的波動(dòng)，到行星的運(yùn)動(dòng)或城市的發(fā)展党饮。如果我們誠實(shí)的話肝陪，這些東西沒有一個(gè)是整齊有序的，也很容易被預(yù)測刑顺。因?yàn)槲蚁嘈艛?shù)學(xué)是如此強(qiáng)大氯窍，它有潛力為我們提供一種新的方式來看待幾乎任何事物。甚至像愛一樣神秘的東西蹲堂。所以狼讨，我想試著說服你，你的數(shù)學(xué)是多么的驚人柒竞，優(yōu)秀和相關(guān)政供，我想給你我的前三個(gè)Mathematica愛的可靠提示。

Okay, so Top Tip #1: How to win at online dating. So my favorite online dating website is OkCupid, not least because it was started by a group of mathematicians. Now, because they're mathematicians, they have been collecting data on everybody who uses their site for almost a decade. And they've been trying to search for patterns in the way that we talk about ourselves and the way that we interact with each other on an online dating website. And they've come up with some seriously interesting findings. But my particular favorite is that it turns out that on an online dating website, how attractive you are does not dictate how popular you are, and actually, having people think that you're ugly can work to your advantage. Let me show you how this works. In a thankfully voluntary section of OkCupid, you are allowed to rate how attractive you think people are on a scale between 1 and 5. Now, if we compare this score, the average score, to how many messages a selection of people receive, you can begin to get a sense of how attractiveness links to popularity on an online dating website.

好吧，那么TOP的第一個(gè)問題是：如何在網(wǎng)上約會(huì)中獲勝布隔。所以我最喜歡的網(wǎng)上交友網(wǎng)站是okcupid离陶，特別是因?yàn)樗怯梢蝗簲?shù)學(xué)家開始的。現(xiàn)在衅檀，因?yàn)樗麄兪菙?shù)學(xué)家枕磁，他們已經(jīng)收集了每個(gè)人使用他們的網(wǎng)站近十年的數(shù)據(jù)。他們一直在尋找我們談?wù)撟约旱姆绞绞趿撸约拔覀冊(cè)诰W(wǎng)上交友網(wǎng)站上相互交流的方式。他們提出了一些非常有趣的發(fā)現(xiàn)茸苇。但我特別喜歡的是排苍，在一個(gè)網(wǎng)上交友網(wǎng)站上，你的魅力并沒有決定你有多受歡迎学密，事實(shí)上淘衙，有人認(rèn)為你的丑陋可以發(fā)揮你的優(yōu)勢。讓我來告訴你這是怎么回事腻暮。在Okcupid的一個(gè)令人欣慰的自愿性部分彤守，你可以評(píng)估你認(rèn)為人們?cè)?到5之間的比例有多大。現(xiàn)在哭靖，如果我們比較一下這個(gè)分?jǐn)?shù)具垫，平均分，一個(gè)選擇的人收到多少信息试幽，你可以開始了解在網(wǎng)上交友網(wǎng)站上筝蚕，吸引力是如何與人氣聯(lián)系起來的。

This is the graph that the OkCupid guys have come up with. And the important thing to notice is that it's not totally true that the more attractive you are, the more messages you get. But the question arises then of what is it about people up here who are so much more popular than people down here, even though they have the same score of attractiveness? And the reason why is that it's not just straightforward looks that are important. So let me try to illustrate their findings with an example. So if you take someone like Portia de Rossi, for example, everybody agrees that Portia de Rossi is a very beautiful woman. Nobody thinks that she's ugly, but she's not a supermodel, either. If you compare Portia de Rossi to someone like Sarah Jessica Parker, now, a lot of people, myself included, I should say, think that Sarah Jessica Parker is seriously fabulous and possibly one of the most beautiful creatures to have ever have walked on the face of the Earth. But some other people, i.e., most of the Internet, seem to think that she looks a bit like a horse. (Laughter) Now, I think that if you ask people how attractive they thought Sarah Jessica Parker or Portia de Rossi were, and you ask them to give them a score between 1 and 5, I reckon that they'd average out to have roughly the same score. But the way that people would vote would be very different. So Portia's scores would all be clustered around the 4 because everybody agrees that she's very beautiful, whereas Sarah Jessica Parker completely divides opinion. There'd be a huge spread in her scores. And actually it's this spread that counts. It's this spread that makes you more popular on an online Internet dating website. So what that means then is that if some people think that you're attractive, you're actually better off having some other people think that you're a massive minger. That's much better than everybody just thinking that you're the cute girl next door.

這是Okcupid的家伙想出的圖表铺坞。重要的是要注意的是起宽，你越有吸引力，你得到的信息就越多济榨。但問題是坯沪，這里的人比這里的人更受歡迎，盡管他們的吸引力是一樣的擒滑。原因是腐晾，這不僅僅是簡單的外表，也很重要橘忱。所以讓我用一個(gè)例子來說明他們的發(fā)現(xiàn)赴魁。所以，如果你選擇像波西亞·德羅西這樣的人钝诚，每個(gè)人都認(rèn)為波蒂亞·德羅西是一個(gè)非常漂亮的女人颖御。沒有人認(rèn)為她丑，但她也不是超級(jí)名模。如果你把波西亞·德·羅西和莎拉·杰西卡·帕克這樣的人比較一下潘拱，現(xiàn)在疹鳄，很多人，包括我自己芦岂，我應(yīng)該說瘪弓，認(rèn)為莎拉·杰西卡·帕克是一個(gè)非常出色的人，可能是世界上最美麗的生物之一禽最。但有些人腺怯，也就是說，大多數(shù)人互聯(lián)網(wǎng)川无，似乎認(rèn)為她看起來有點(diǎn)像馬呛占。（笑聲）現(xiàn)在，我認(rèn)為懦趋，如果你問人們?nèi)绾斡形α缆牵麄冋J(rèn)為莎拉杰西卡帕克或波西亞德羅西，你要求他們給他們1分和5分的分?jǐn)?shù)仅叫，我估計(jì)他們的平均分?jǐn)?shù)大致相同帜篇。但是人們投票的方式會(huì)有很大的不同。因此诫咱，波西亞的分?jǐn)?shù)都會(huì)聚集在4周圍笙隙，因?yàn)榇蠹叶颊J(rèn)為她很漂亮，而莎拉·杰西卡·帕克則完全區(qū)分了意見遂跟。她的分?jǐn)?shù)會(huì)有很大的變化逃沿。事實(shí)上正是這種傳播才有意義。正是這種傳播使你在網(wǎng)上交友網(wǎng)站上更受歡迎幻锁。那么這意味著凯亮，如果有人認(rèn)為你很有吸引力，那么你最好讓其他人認(rèn)為你是個(gè)大人物哄尔。比每個(gè)人都認(rèn)為你是隔壁可愛的女孩要好得多假消。

Now, I think this begins makes a bit more sense when you think in terms of the people who are sending these messages. So let's say that you think somebody's attractive, but you suspect that other people won't necessarily be that interested. That means there's less competition for you and it's an extra incentive for you to get in touch. Whereas compare that to if you think somebody is attractive but you suspect that everybody is going to think they're attractive. Well, why would you bother humiliating yourself, let's be honest? Here's where the really interesting part comes. Because when people choose the pictures that they use on an online dating website, they often try to minimize the things that they think some people will find unattractive. The classic example is people who are, perhaps, a little bit overweight deliberately choosing a very cropped photo, or bald men, for example, deliberately choosing pictures where they're wearing hats. But actually this is the opposite of what you should do if you want to be successful. You should really, instead, play up to whatever it is that makes you different, even if you think that some people will find it unattractive. Because the people who fancy you are just going to fancy you anyway, and the unimportant losers who don't, well, they only play up to your advantage.

現(xiàn)在，我認(rèn)為當(dāng)你考慮發(fā)送這些信息的人時(shí)岭接，這開始有點(diǎn)意義富拗。所以，讓我們說鸣戴，你認(rèn)為某人的吸引力啃沪，但你懷疑其他人不一定會(huì)有興趣。這意味著你的競爭會(huì)減少窄锅，這是你獲得聯(lián)系的額外動(dòng)力创千。相比之下，如果你認(rèn)為某人是有吸引力的，但你懷疑每個(gè)人都會(huì)認(rèn)為他們是有吸引力的追驴。好吧械哟，你為什么要去羞辱你自己，讓我們誠實(shí)點(diǎn)殿雪？這里是真正有趣的部分暇咆。因?yàn)楫?dāng)人們選擇他們?cè)诰W(wǎng)上交友網(wǎng)站上使用的圖片時(shí)，他們往往會(huì)盡量減少他們認(rèn)為一些人會(huì)覺得沒有吸引力的東西丙曙。典型的例子是人們爸业，也許是有點(diǎn)超重，故意選擇一張裁剪得很好的照片亏镰，或者禿頭的男人沃呢，比如故意選擇他們戴著帽子的照片。但事實(shí)上這與你的相反如果你想成功拆挥，就應(yīng)該做。事實(shí)上某抓，你應(yīng)該去迎合那些讓你與眾不同的東西纸兔，即使你認(rèn)為有些人會(huì)覺得它不吸引人。因?yàn)槟切┗孟肽愕娜藭?huì)喜歡你否副，而那些不重要的失敗者汉矿，他們只會(huì)發(fā)揮你的優(yōu)勢。

Okay, Top Tip #2: How to pick the perfect partner. So let's imagine then that you're a roaring success on the dating scene. But the question arises of how do you then convert that success into longer-term happiness and in particular, how do you decide when is the right time to settle down? Now generally, it's not advisable to just cash in and marry the first person who comes along and shows you any interest at all. But, equally, you don't really want to leave it too long if you want to maximize your chance of long-term happiness. As my favorite author, Jane Austen, puts it, "An unmarried woman of seven and twenty can never hope to feel or inspire affection again." (Laughter) Thanks a lot, Jane. What do you know about love?

好的备禀，頂級(jí)的：如何挑選完美的伴侶洲拇。所以，讓我們想象一下曲尸，你在約會(huì)現(xiàn)場是一個(gè)巨大的成功赋续。但問題是，你如何將成功轉(zhuǎn)化為更長期的幸福另患，尤其是你如何決定何時(shí)才是安頓下來的合適時(shí)間纽乱？現(xiàn)在一般來說，只需現(xiàn)金和結(jié)婚的第一人誰來昆箕，并顯示您的任何興趣是不可取的鸦列。但是，同樣地鹏倘，如果你想最大化你長期幸福的機(jī)會(huì)薯嗤，你也不想太久。正如我最喜歡的作家簡·奧斯汀所說的那樣纤泵，“一個(gè)七歲和二十歲的未婚女子再也不能指望能感受到或激發(fā)出愛了骆姐。”（笑聲）謝謝，簡诲锹。你知道什么是愛繁仁？

So the question is then, how do you know when is the right time to settle down given all the people that you can date in your lifetime? Thankfully, there's a rather delicious bit of mathematics that we can use to help us out here, called optimal stopping theory. So let's imagine then, that you start dating when you're 15 and ideally, you'd like to be married by the time that you're 35. And there's a number of people that you could potentially date across your lifetime, and they'll be at varying levels of goodness. Now the rules are that once you cash in and get married, you can't look ahead to see what you could have had, and equally, you can't go back and change your mind. In my experience at least, I find that typically people don't much like being recalled years after being passed up for somebody else, or that's just me.

因此，問題是归园，你怎么知道什么時(shí)候是適當(dāng)?shù)臅r(shí)間來解決所有的人黄虱，你可以約會(huì)在你的一生？值得慶幸的是庸诱，有一個(gè)相當(dāng)美味的數(shù)學(xué)捻浦，我們可以用來幫助我們?cè)谶@里，所謂的最佳停止理論桥爽。所以讓我們想象一下朱灿，當(dāng)你15歲的時(shí)候開始約會(huì)，理想的時(shí)候钠四，你想在35歲的時(shí)候結(jié)婚盗扒。還有一些人，你可能會(huì)在你的一生中約會(huì)缀去，他們會(huì)在不同程度的善良÷略睿現(xiàn)在的規(guī)則是，一旦你的現(xiàn)金和結(jié)婚缕碎，你不能向前看褥影，看看你可以有什么，同樣咏雌，你不能回去凡怎，改變你的想法。至少在我的經(jīng)歷中赊抖，我發(fā)現(xiàn)典型的人不太喜歡被別人追憶统倒，或者僅僅是我。

So the math says then that what you should do in the first 37 percent of your dating window, you should just reject everybody as serious marriage potential. (Laughter) And then, you should pick the next person that comes along that is better than everybody that you've seen before. So here's the example. Now if you do this, it can be mathematically proven, in fact, that this is the best possible way of maximizing your chances of finding the perfect partner. Now unfortunately, I have to tell you that this method does come with some risks. For instance, imagine if your perfect partner appeared during your first 37 percent. Now, unfortunately, you'd have to reject them. (Laughter) Now, if you're following the maths, I'm afraid no one else comes along that's better than anyone you've seen before, so you have to go on rejecting everyone and die alone. (Laughter) Probably surrounded by cats nibbling at your remains.

因此氛雪，數(shù)學(xué)上說檐薯，在你的約會(huì)窗口的第一個(gè)37%，你應(yīng)該做的是注暗，你應(yīng)該拒絕所有人的婚姻潛力坛缕。（笑聲）然后，你應(yīng)該挑選下一個(gè)比你以前見過的人更好的人捆昏。這里有一個(gè)例子∽現(xiàn)在，如果你這樣做骗卜，它可以在數(shù)學(xué)上證明宠页，事實(shí)上左胞，這是最好的方式最大化你的機(jī)會(huì)找到完美的合作伙伴。不幸的是举户，我不得不告訴你烤宙，這種方法確實(shí)帶來了一些風(fēng)險(xiǎn)。例如俭嘁，想象一下躺枕，如果你的完美伴侶出現(xiàn)在你的第一個(gè)37%。現(xiàn)在供填，不幸的是拐云，你不得不拒絕他們。（笑聲）現(xiàn)在近她，如果你在學(xué)數(shù)學(xué)叉瘩，恐怕沒有人會(huì)比你以前見過的任何人都好，所以你必須繼續(xù)拒絕所有人粘捎，獨(dú)自死去薇缅。（笑聲）可能被貓?jiān)谀愕倪z體上啃咬。

Okay, another risk is, let's imagine, instead, that the first people that you dated in your first 37 percent are just incredibly dull, boring, terrible people. Now, that's okay, because you're in your rejection phase, so thats fine, you can reject them. But then imagine, the next person to come along is just marginally less boring, dull and terrible than everybody that you've seen before. Now, if you are following the maths, I'm afraid you have to marry them and end up in a relationship which is, frankly, suboptimal. Sorry about that. But I do think that there's an opportunity here for Hallmark to cash in on and really cater for this market. A Valentine's Day card like this. (Laughter) "My darling husband, you are marginally less terrible than the first 37 percent of people I dated." It's actually more romantic than I normally manage.

好吧攒磨，另一個(gè)風(fēng)險(xiǎn)是捅暴，讓我們想象一下，你第一次約會(huì)的人咧纠，你的第一個(gè)37%是令人難以置信的無聊，無聊泻骤，可怕的人∑岣幔現(xiàn)在，沒關(guān)系狱掂，因?yàn)槟闾幵谀愕木芙^階段演痒，所以很好，你可以拒絕他們趋惨。但是想象一下鸟顺，下一個(gè)跟你一起走的人比你以前見過的每個(gè)人都要少一些無聊、無聊和可怕∑飨海現(xiàn)在讯嫂，如果你在學(xué)數(shù)學(xué)，恐怕你必須要和他們結(jié)婚兆沙，然后在一段關(guān)系中結(jié)束欧芽，坦率地說，這是不理想的葛圃。對(duì)不起千扔。但我認(rèn)為有一個(gè)機(jī)會(huì)在這里的Hallmark現(xiàn)金憎妙，并真正迎合這個(gè)市場。像這樣的情人節(jié)賀卡（笑聲）“我親愛的丈夫曲楚，你比我約會(huì)過的37%的人稍微差一點(diǎn)厘唾。”實(shí)際上它比我通常管理的更浪漫龙誊。

Okay, so this method doesn't give you a 100 percent success rate, but there's no other possible strategy that can do any better. And actually, in the wild, there are certain types of fish which follow and employ this exact strategy. So they reject every possible suitor that turns up in the first 37 percent of the mating season, and then they pick the next fish that comes along after that window that's, I don't know, bigger and burlier than all of the fish that they've seen before. I also think that subconsciously, humans, we do sort of do this anyway. We give ourselves a little bit of time to play the field, get a feel for the marketplace or whatever when we're young. And then we only start looking seriously at potential marriage candidates once we hit our mid-to-late 20s. I think this is conclusive proof, if ever it were needed, that everybody's brains are prewired to be just a little bit mathematical.

好的抚垃，所以這個(gè)方法不會(huì)給你100%的成功率，但是沒有其他可能的策略可以做得更好载迄。事實(shí)上讯柔，在野外，有某些種類的魚遵循和使用這種精確的策略护昧。因此魂迄，他們拒絕所有可能的求婚者，在交配季節(jié)的前37%惋耙，然后他們挑選下一條在那扇窗戶之后的魚捣炬，我不知道，比他們以前見過的魚更大更大绽榛。我也認(rèn)為湿酸，在潛意識(shí)里，人類灭美，我們無論如何都會(huì)這樣做推溃。我們給自己一點(diǎn)時(shí)間去玩這個(gè)領(lǐng)域，在我們年輕的時(shí)候有一個(gè)市場的感覺届腐。然后铁坎，我們才開始認(rèn)真對(duì)待潛在的結(jié)婚候選人，一旦我們打到我們的中到20歲左右犁苏。我認(rèn)為這是一個(gè)確鑿的證據(jù)硬萍，如果需要的話，每個(gè)人的大腦都是天生的围详，只是一點(diǎn)點(diǎn)數(shù)學(xué)朴乖。

Okay, so that was Top Tip #2. Now, Top Tip #3: How to avoid divorce. Okay, so let's imagine then that you picked your perfect partner and you're settling into a lifelong relationship with them. Now, I like to think that everybody would ideally like to avoid divorce, apart from, I don't know, Piers Morgan's wife, maybe? But it's a sad fact of modern life that 1 in 2 marriages in the States ends in divorce, with the rest of the world not being far behind. Now, you can be forgiven, perhaps for thinking that the arguments that precede a marital breakup are not an ideal candidate for mathematical investigation. For one thing, it's very hard to know what you should be measuring or what you should be quantifying. But this didn't stop a psychologist, John Gottman, who did exactly that. Gottman observed hundreds of couples having a conversation and recorded, well, everything you can think of. So he recorded what was said in the conversation, he recorded their skin conductivity, he recorded their facial expressions, their heart rates, their blood pressure, basically everything apart from whether or not the wife was actually always right, which incidentally she totally is. But what Gottman and his team found was that one of the most important predictors for whether or not a couple is going to get divorced was how positive or negative each partner was being in the conversation.

好吧，那是最高的小費(fèi)了≈蓿現(xiàn)在买羞，頂尖的“三好”：如何避免離婚。好吧雹食，那么讓我們想象一下哩都，你選擇了你的完美伴侶，你就和他們建立了一種終生的關(guān)系⊥衽牵現(xiàn)在漠嵌，我喜歡認(rèn)為每個(gè)人都希望避免離婚咐汞，除了，我不知道儒鹿，皮爾斯摩根的妻子化撕，也許？但現(xiàn)代生活中的一個(gè)可悲事實(shí)是约炎，在美國的2次婚姻中植阴，有1次婚姻以離婚告終，而世界上其他國家的婚姻卻沒有那么遙遠(yuǎn)』常現(xiàn)在掠手，你可以被原諒，也許是因?yàn)檎J(rèn)為在婚姻破裂之前的爭論并不是數(shù)學(xué)調(diào)查的理想人選狸捕。一方面喷鸽，很難知道你應(yīng)該測量什么，或者你應(yīng)該量化什么灸拍。但這并沒有阻止心理學(xué)家約翰·戈特曼做祝，他確實(shí)做到了這一點(diǎn)。戈特曼觀察到數(shù)百對(duì)夫婦進(jìn)行了交談并記錄下了所有你能想到的事情鸡岗。于是他錄下了談話中所說的話混槐，記錄了他們的皮膚導(dǎo)電性，他記錄下了R面部表情轩性，他們的心率声登，他們的血壓，基本上一切除了妻子是否真的總是正確的揣苏，順便說一句悯嗓，她完全是。但是Gottman和他的團(tuán)隊(duì)發(fā)現(xiàn)舒岸，一對(duì)夫婦是否要離婚的最重要的預(yù)測因素之一是雙方在談話中的積極性或消極性。

Now, couples that were very low-risk scored a lot more positive points on Gottman's scale than negative. Whereas bad relationships, by which I mean, probably going to get divorced, they found themselves getting into a spiral of negativity. Now just by using these very simple ideas, Gottman and his group were able to predict whether a given couple was going to get divorced with a 90 percent accuracy. But it wasn't until he teamed up with a mathematician, James Murray, that they really started to understand what causes these negativity spirals and how they occur. And the results that they found I think are just incredibly impressively simple and interesting. So these equations, they predict how the wife or husband is going to respond in their next turn of the conversation, how positive or negative they're going to be. And these equations, they depend on the mood of the person when they're on their own, the mood of the person when they're with their partner, but most importantly, they depend on how much the husband and wife influence one another.

現(xiàn)在芦圾，低風(fēng)險(xiǎn)的夫婦在Gottman的比例上得分比負(fù)的多蛾派。而壞的關(guān)系，我的意思是个少，可能會(huì)離婚洪乍，他們發(fā)現(xiàn)自己陷入了一個(gè)螺旋的消極。現(xiàn)在夜焦，只要使用這些簡單的想法壳澳，Gottman和他的小組就能夠預(yù)測一對(duì)夫婦是否會(huì)以90%的準(zhǔn)確率離婚。但直到他與一位數(shù)學(xué)家詹姆斯·默里合作茫经，他們才真正開始理解是什么導(dǎo)致了這些負(fù)性螺旋巷波，以及它們是如何發(fā)生的萎津。他們發(fā)現(xiàn)我認(rèn)為的結(jié)果是令人難以置信的簡單和有趣。因此抹镊，這些方程锉屈，他們預(yù)測妻子或丈夫?qū)⑷绾位貞?yīng)他們的下一輪對(duì)話，他們將如何積極或消極垮耳。而這些方程颈渊，取決于他們自己的情緒，當(dāng)他們和伴侶在一起時(shí)的心情终佛，但最重要的是俊嗽，他們丈夫和妻子之間的相互影響到底有多大。

Now, I think it's important to point out at this stage, that these exact equations have also been shown to be perfectly able at describing what happens between two countries in an arms race. (Laughter) So that -- an arguing couple spiraling into negativity and teetering on the brink of divorce -- is actually mathematically equivalent to the beginning of a nuclear war. (Laughter)

現(xiàn)在铃彰，我認(rèn)為在這個(gè)階段指出绍豁，這些精確的方程式也被證明能完美地描述兩個(gè)國家在軍備競賽中所發(fā)生的事情。（笑聲）這樣豌研，一對(duì)爭吵的夫妻陷入了消極情緒妹田，搖搖欲墜，瀕臨離婚鹃共。-實(shí)際上在數(shù)學(xué)上相當(dāng)于一場核戰(zhàn)爭的開始鬼佣。（笑聲）

But the really important term in this equation is the influence that people have on one another, and in particular, something called the negativity threshold. Now, the negativity threshold, you can think of as how annoying the husband can be before the wife starts to get really pissed off, and vice versa. Now, I always thought that good marriages were about compromise and understanding and allowing the person to have the space to be themselves. So I would have thought that perhaps the most successful relationships were ones where there was a really high negativity threshold. Where couples let things go and only brought things up if they really were a big deal. But actually, the mathematics and subsequent findings by the team have shown the exact opposite is true. The best couples, or the most successful couples, are the ones with a really low negativity threshold. These are the couples that don't let anything go unnoticed and allow each other some room to complain. These are the couples that are continually trying to repair their own relationship, that have a much more positive outlook on their marriage. Couples that don't let things go and couples that don't let trivial things end up being a really big deal.

但是這個(gè)等式中真正重要的一個(gè)詞是人們相互之間的影響，特別是所謂的負(fù)性閾值∷。現(xiàn)在晶衷，消極的門檻，你可以想到的是阴孟，在妻子開始真正生氣之前晌纫，丈夫是多么的煩人，反之亦然∮浪浚現(xiàn)在锹漱，我一直認(rèn)為，良好的婚姻是關(guān)于妥協(xié)和理解慕嚷，讓人有空間自己哥牍。所以我想，也許最成功的關(guān)系是那些有一個(gè)真正的高負(fù)門檻的關(guān)系喝检。如果情侶們讓事情發(fā)生嗅辣，如果他們真的是一個(gè)大問題，他們只會(huì)把事情提出來挠说。但事實(shí)上澡谭，該小組的數(shù)學(xué)和隨后的發(fā)現(xiàn)顯示出了完全相反的事實(shí)。最好的夫婦损俭，或最成功的夫婦蛙奖，都是一個(gè)真正的低負(fù)門檻潘酗。這些夫婦不讓任何事情不被注意，讓對(duì)方有抱怨的余地外永。這對(duì)夫婦他們一直在努力修復(fù)自己的關(guān)系崎脉，對(duì)他們的婚姻有更積極的看法。不讓事情發(fā)生的夫婦和那些不讓瑣碎事情發(fā)生的夫妻最終會(huì)成為一個(gè)大人物伯顶。

Now of course, it takes bit more than just a low negativity threshold and not compromising to have a successful relationship. But I think that it's quite interesting to know that there is really mathematical evidence to say that you should never let the sun go down on your anger.

當(dāng)然囚灼，它需要的不僅僅是一個(gè)低的消極的門檻，而不是妥協(xié)有一個(gè)成功的關(guān)系祭衩。但我認(rèn)為灶体，知道有真正的數(shù)學(xué)證據(jù)表明你永遠(yuǎn)不應(yīng)該讓太陽落在你的憤怒上，這是很有趣的掐暮。

So those are my top three tips of how maths can help you with love and relationships. But I hope that aside from their use as tips, they also give you a little bit of insight into the power of mathematics. Because for me, equations and symbols aren't just a thing. They're a voice that speaks out about the incredible richness of nature and the startling simplicity in the patterns that twist and turn and warp and evolve all around us, from how the world works to how we behave. So I hope that perhaps, for just a couple of you, a little bit of insight into the mathematics of love can persuade you to have a little bit more love for mathematics. Thank you. (Applause)

因此蝎抽，這些是我的三大秘訣：數(shù)學(xué)如何幫助你的愛情和人際關(guān)系。但我希望路克，除了他們的使用技巧樟结，他們也給你一點(diǎn)洞察到數(shù)學(xué)的力量。因?yàn)閷?duì)我來說精算，方程式和符號(hào)不只是一件事瓢宦。他們是一個(gè)聲音，講述了大自然的驚人的豐富和令人驚訝的簡單的模式灰羽，扭曲和扭曲驮履，并在我們周圍演變，從世界如何運(yùn)作廉嚼，我們的行為。所以我希望怠噪，也許，對(duì)于你們兩個(gè)傍念，一點(diǎn)點(diǎn)的了解愛的數(shù)學(xué)可以說服你對(duì)數(shù)學(xué)有一點(diǎn)點(diǎn)的愛。謝謝捂寿。（掌聲）