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  • 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