TEDxBinghamtonUniversity
Hannah Fry: The mathematics of love
漢娜．弗萊: 愛情數學
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尋得最好的伴侶談何容易，這事能夠透過數學來完成嗎？在這迷人的談話中，數學家漢娜．弗萊向我們展示了人們看待愛情的規律，並且揭露了三大秘訣（已經由數學驗證！）來幫助你尋得那最特別之人。
Hannah Fry - Complexity theorist
Hannah Fry researches the trends in our civilization and ways we can forecast its future. Full bio
Hannah Fry researches the trends in our civilization and ways we can forecast its future. Full bio
Double-click the English transcript below to play the video.
00:12
Today I want to talk to you
about the mathematics of love.
about the mathematics of love.
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今天我想要和大家談談
關於愛情的數學。
關於愛情的數學。
00:16
Now, I think that we can all agree
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我想大家都同意
00:18
that mathematicians
are famously excellent at finding love.
are famously excellent at finding love.
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數學家在尋找真愛上特別在行。
00:23
But it's not just
because of our dashing personalities,
because of our dashing personalities,
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但那並不只是因為我們
精力充沛的性格、
精力充沛的性格、
00:27
superior conversational skills
and excellent pencil cases.
and excellent pencil cases.
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超凡的對話技巧，
和炫麗的筆盒。
和炫麗的筆盒。
00:31
It's also because we've actually done
an awful lot of work into the maths
an awful lot of work into the maths
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也是因為我們真的
花了許多時間精力在數學上，
花了許多時間精力在數學上，
00:36
of how to find the perfect partner.
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計算如何找到完美的伴侶。
00:38
Now, in my favorite paper
on the subject, which is entitled,
on the subject, which is entitled,
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現在，在此學科中我最愛的論文，名為
00:41
"Why I Don't Have a Girlfriend" --
(Laughter) --
(Laughter) --
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「為甚麼我沒有女友」
（笑聲）
（笑聲）
00:45
Peter Backus tries to rate
his chances of finding love.
his chances of finding love.
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Peter Backus 試著
計算他尋得真愛的機會。
計算他尋得真愛的機會。
00:49
Now, Peter's not a very greedy man.
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現在，Peter 不是一個非常貪心的人。
00:51
Of all of the available women in the U.K.,
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在英國所有適宜的女性對象中，
00:53
all Peter's looking for
is somebody who lives near him,
is somebody who lives near him,
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Peter 所看的，
就只是那個住在他附近的對象、
就只是那個住在他附近的對象、
00:56
somebody in the right age range,
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某個處於適宜的年齡階段的女人、
00:58
somebody with a university degree,
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某個擁有大學文憑、
01:01
somebody he's likely to get on well with,
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某個他很有可能相處地不錯的對象、
01:03
somebody who's likely to be attractive,
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某個有魅力的女子，
01:05
somebody who's likely
to find him attractive.
to find him attractive.
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以及......某個認為
他也富有魅力的對象。
他也富有魅力的對象。
01:08
(Laughter)
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（笑聲）
01:11
And comes up with an estimate
of 26 women in the whole of the UK.
of 26 women in the whole of the UK.
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結果他估計在全英國
大概有 26 位此類女性。
大概有 26 位此類女性。
01:17
It's not looking very good,
is it Peter?
is it Peter?
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這看來很不妙，不是嗎，Peter？
01:19
Now, just to put that into perspective,
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我們好好思考一下這件事，
01:21
that's about 400 times fewer
than the best estimates
than the best estimates
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在無數聰明外星
生命形式存在的情況下，
生命形式存在的情況下，
01:24
of how many intelligent
extraterrestrial life forms there are.
extraterrestrial life forms there are.
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那是少於 400 倍數的估計呀。
01:28
And it also gives Peter
a 1 in 285,000 chance
a 1 in 285,000 chance
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那也給了 Peter 一個
在某晚遇見一個特別的女子
01:33
of bumping into any one
of these special ladies
of these special ladies
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28 萬 5 千之 1 的機會。
01:35
on a given night out.
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01:37
I'd like to think
that's why mathematicians
that's why mathematicians
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我想，那就是為什麼數學家
01:39
don't really bother
going on nights out anymore.
going on nights out anymore.
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不再怎麼想
晚上出去約會了的原因了吧。
晚上出去約會了的原因了吧。
01:42
The thing is that I personally
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重點是，我個人其實並不同意
01:44
don't subscribe
to such a pessimistic view.
to such a pessimistic view.
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這種悲觀的看法，
01:47
Because I know,
just as well as all of you do,
just as well as all of you do,
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因為我知道，如同你們所有所知道的，
01:49
that love doesn't really work like that.
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愛情並不是這樣發生的。
01:52
Human emotion isn't neatly ordered
and rational and easily predictable.
and rational and easily predictable.
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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。
乾淨利落、邏輯清晰，和容易預測。
01:57
But I also know that that doesn't mean
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但我也知道那並不意謂著
01:59
that mathematics hasn't got something
that it can offer us
that it can offer us
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數學無法提供幫助，
02:03
because, love, as with most of life,
is full of patterns
is full of patterns
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因為愛情，如同生命中多數的事物一般，
充斥著許多規律，
充斥著許多規律，
02:06
and mathematics is, ultimately,
all about the study of patterns.
all about the study of patterns.
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而數學最終就是
那研究規律的學說。
那研究規律的學說。
02:11
Patterns from predicting the weather
to the fluctuations in the stock market,
to the fluctuations in the stock market,
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從預測天候，到
預測股票市場的開高走低，
預測股票市場的開高走低，
02:15
to the movement of the planets
or the growth of cities.
or the growth of cities.
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到星球的運轉，或都市的發展。
02:18
And if we're being honest,
none of those things
none of those things
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如果我們對自己誠實的話，
上述那些東西，沒有一個是
上述那些東西，沒有一個是
02:21
are exactly neatly ordered
and easily predictable, either.
and easily predictable, either.
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井然有序以及容易預測的。
02:24
Because I believe that mathematics
is so powerful that it has the potential
is so powerful that it has the potential
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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
以至於它讓我們得以以新方法
02:29
to offer us a new way of looking
at almost anything.
at almost anything.
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重新看待任何事物。
02:33
Even something as mysterious as love.
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就算是和愛情一般神秘的東西也是。
02:37
And so, to try to persuade you
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為了試著說服你們
02:38
of how totally amazing, excellent
and relevant mathematics is,
and relevant mathematics is,
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數學的神妙用處，
02:43
I want to give you my top three
mathematically verifiable tips for love.
mathematically verifiable tips for love.
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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。
在數學上可以驗證的愛情秘訣。
02:51
Okay, so Top Tip #1:
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好，首先最重要的秘技一：
02:53
How to win at online dating.
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如何贏得線上交友的機會。
02:58
So my favorite online dating
website is OkCupid,
website is OkCupid,
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我最愛的線上交友網站是 OkCupid
（網站名：好吧，丘比特），
（網站名：好吧，丘比特），
03:02
not least because it was started
by a group of mathematicians.
by a group of mathematicians.
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這並不僅僅因為這網站
是由一群數學家所架設的。
是由一群數學家所架設的。
03:05
Now, because they're mathematicians,
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因為他們是數學家，
03:07
they have been collecting data
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他們已經蒐集了
03:09
on everybody who uses their site
for almost a decade.
for almost a decade.
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近乎這十年來所有
該網站使用者的資料。
該網站使用者的資料。
03:11
And they've been trying
to search for patterns
to search for patterns
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他們試著尋找
03:14
in the way that we talk about ourselves
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我們在線上
談論自己的方式的模式，
03:16
and the way that we
interact with each other
interact with each other
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以及我們和他人互動的模式。
03:18
on an online dating website.
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03:19
And they've come up with some
seriously interesting findings.
seriously interesting findings.
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他們發現了一些重要的有趣結果。
03:22
But my particular favorite
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但我特別喜歡的結果之一是
03:24
is that it turns out
that on an online dating website,
that on an online dating website,
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在線上交友網站上
03:27
how attractive you are
does not dictate how popular you are,
does not dictate how popular you are,
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你的魅力程度並無法
預測你的受歡迎程度，
預測你的受歡迎程度，
03:33
and actually, having people
think that you're ugly
think that you're ugly
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事實上，讓人們覺得你很醜
03:37
can work to your advantage.
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可以讓你擁有優勢。
03:40
Let me show you how this works.
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讓我向各位展示這是怎麼一回事。
03:42
In a thankfully voluntary
section of OkCupid,
section of OkCupid,
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在 OkCupid 的一個自願欄目中，
03:46
you are allowed to rate
how attractive you think people are
how attractive you think people are
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你可以評價人們的魅力值，
03:49
on a scale between 1 and 5.
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從 1 到 5 。
03:52
Now, if we compare this score,
the average score,
the average score,
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現在，如果我們比較這個分數，
平均分數，
平均分數，
03:55
to how many messages a
selection of people receive,
selection of people receive,
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有多少人收到訊息，
03:58
you can begin to get a sense
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你就可以開始理解
03:59
of how attractiveness links to popularity
on an online dating website.
on an online dating website.
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在一個線上約會網站上
魅力指數與受歡迎程度有關。
魅力指數與受歡迎程度有關。
04:03
This is the graph that the OkCupid guys
have come up with.
have come up with.
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這是 OkCupid 得到的圖表。
04:07
And the important thing to notice
is that it's not totally true
is that it's not totally true
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一件重要的值得注意的事是
04:10
that the more attractive you are,
the more messages you get.
the more messages you get.
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並不是越有魅力的人，
收到的訊息越多。
收到的訊息越多。
04:13
But the question arises then
of what is it about people up here
of what is it about people up here
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問題是，為什麼上面的這些人
比下面這些人要受歡迎得多，
04:16
who are so much more popular
than people down here,
than people down here,
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04:21
even though they have the
same score of attractiveness?
same score of attractiveness?
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即便他們都有相同的魅力值？
04:24
And the reason why is that it's not just
straightforward looks that are important.
straightforward looks that are important.
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原因是，並不是直觀的外貌是重要的。
04:28
So let me try to illustrate their
findings with an example.
findings with an example.
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讓我來談談他們的發現，
以一個案例說明。
以一個案例說明。
如果你拿 Portia de Rossi 為例，
04:31
So if you take someone like
Portia de Rossi, for example,
Portia de Rossi, for example,
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04:35
everybody agrees that Portia de Rossi
is a very beautiful woman.
is a very beautiful woman.
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每個人都同意 Portia de Rossi
是個非常美麗的女人，
是個非常美麗的女人，
04:40
Nobody thinks that she's ugly,
but she's not a supermodel, either.
but she's not a supermodel, either.
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沒有人覺得她醜，但她也不是超級名模。
04:43
If you compare Portia de Rossi
to someone like Sarah Jessica Parker,
to someone like Sarah Jessica Parker,
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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
Sarah Jessica Parker
（譯注：慾望城市女主角）來和她比較
04:48
now, a lot of people,
myself included, I should say,
myself included, I should say,
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許多人，包括我自己，我應該會說，
04:51
think that Sarah Jessica Parker
is seriously fabulous
is seriously fabulous
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Sarah Jessica Parker 魅力極為出眾，
04:56
and possibly one of the
most beautiful creatures
most beautiful creatures
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有可能是地表上
04:58
to have ever have walked
on the face of the Earth.
on the face of the Earth.
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最美麗的物種之一。
05:01
But some other people,
i.e., most of the Internet,
i.e., most of the Internet,
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但許多其他人，比如，大多數的網友
05:07
seem to think that she looks
a bit like a horse. (Laughter)
a bit like a horse. (Laughter)
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似乎都認為她看起來像馬。（笑聲）
05:13
Now, I think that if you ask people
how attractive they thought
how attractive they thought
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如果你問人們他們覺得自己有多美，
05:17
Sarah Jessica Parker
or Portia de Rossi were,
or Portia de Rossi were,
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Sarah Jessica Parker
或 Portia de Rossi
或 Portia de Rossi
05:19
and you ask them to give
them a score between 1 and 5,
them a score between 1 and 5,
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你要他們給自己打分，從 1 到 5，
05:22
I reckon that they'd average out
to have roughly the same score.
to have roughly the same score.
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我猜他們也會大約給一個
和大家都差不多的數字。
和大家都差不多的數字。
05:25
But the way that people would vote
would be very different.
would be very different.
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但是人們投票的方式各自不同。
05:27
So Portia's scores would
all be clustered around the 4
all be clustered around the 4
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因此 Portia 的分數會聚集在 4 分左右，
05:30
because everybody agrees
that she's very beautiful,
that she's very beautiful,
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因為所有人都同意，她非常美麗，
05:32
whereas Sarah Jessica Parker
completely divides opinion.
completely divides opinion.
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然而人們對 Sarah Jessica Parker
卻有截然不同的意見。
卻有截然不同的意見。
05:35
There'd be a huge spread in her scores.
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她的分差懸殊很大。
05:38
And actually it's this spread that counts.
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然而事實上，就是那分差別具意義，
05:40
It's this spread
that makes you more popular
that makes you more popular
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那差異讓你
05:42
on an online Internet dating website.
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在交友網站上受歡迎。
05:45
So what that means then
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所以那意味著
05:46
is that if some people
think that you're attractive,
think that you're attractive,
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如果有些人認為你別具魅力，
05:48
you're actually better off
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你最好有其他人認為
05:50
having some other people
think that you're a massive minger.
think that you're a massive minger.
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你很醜。
05:55
That's much better
than everybody just thinking
than everybody just thinking
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那遠優於所有人認為
05:58
that you're the cute girl next door.
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你是鄰家的可愛女孩。
05:59
Now, I think this begins
makes a bit more sense
makes a bit more sense
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當你們開始思考一下
這些寄送訊息的人的話，
這些寄送訊息的人的話，
06:02
when you think in terms of the people
who are sending these messages.
who are sending these messages.
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這開始變得合理些了。
06:05
So let's say that you think
somebody's attractive,
somebody's attractive,
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這麼說吧，假設你認為那個人很美，
06:07
but you suspect that other people
won't necessarily be that interested.
won't necessarily be that interested.
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但你同時猜想其他人並不會
和你有同樣的審美觀。
和你有同樣的審美觀。
06:11
That means there's
less competition for you
less competition for you
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那就意味著，你的競爭對手略少，
06:14
and it's an extra incentive
for you to get in touch.
for you to get in touch.
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這就給你增加了額外的動機
去與他/她認識。
去與他/她認識。
06:16
Whereas compare that
to if you think somebody is attractive
to if you think somebody is attractive
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與之相對的情況是，
你認為某人很有吸引力，
你認為某人很有吸引力，
06:19
but you suspect that everybody
is going to think they're attractive.
is going to think they're attractive.
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但你猜想所有其他的人
都認為那人很有吸引力，
都認為那人很有吸引力，
06:23
Well, why would you bother
humiliating yourself, let's be honest?
humiliating yourself, let's be honest?
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嗯，讓我們面對事實
為什麼要自取其辱呢？
為什麼要自取其辱呢？
06:26
Here's where the really
interesting part comes.
interesting part comes.
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這就是最有趣的部分。
06:28
Because when people choose the pictures
that they use on an online dating website,
that they use on an online dating website,
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因為當人們去選擇他們
在交友網站上使用的照片時，
在交友網站上使用的照片時，
06:33
they often try to minimize the things
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他們總是試圖最小化
06:35
that they think some people
will find unattractive.
will find unattractive.
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其他人認為不吸引人之處的可能性。
06:39
The classic example is people
who are, perhaps, a little bit overweight
who are, perhaps, a little bit overweight
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最經典的例子是，
那些體重略重的人
那些體重略重的人
06:43
deliberately choosing
a very cropped photo,
a very cropped photo,
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故意選擇一個
剪裁非常不正確的照片，
剪裁非常不正確的照片，
06:46
or bald men, for example,
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例如那些禿頭的男士，
06:48
deliberately choosing pictures
where they're wearing hats.
where they're wearing hats.
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故意去選擇他們帶著帽子的照片。
06:51
But actually this is the opposite
of what you should do
of what you should do
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但你的行為是與你的目標相悖的，
06:54
if you want to be successful.
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如果你想要在網上交友成功。
06:55
You should really, instead, play up to
whatever it is that makes you different,
whatever it is that makes you different,
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你真的應該，去選擇
讓你看起來與眾不同的照片，
讓你看起來與眾不同的照片，
07:00
even if you think that some people
will find it unattractive.
will find it unattractive.
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即便你認為某些人會對此失去興趣。
07:04
Because the people who fancy you
are just going to fancy you anyway,
are just going to fancy you anyway,
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因為那些喜歡你的人
無論如何都會去喜歡你，
無論如何都會去喜歡你，
07:07
and the unimportant losers who don't,
well, they only play up to your advantage.
well, they only play up to your advantage.
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而那些不重要的路人
只是渲染你的優勢。
只是渲染你的優勢。
07:12
Okay, Top Tip #2:
How to pick the perfect partner.
How to pick the perfect partner.
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好了，最高秘訣 2 號：
如何選擇完美的伴侶。
如何選擇完美的伴侶。
07:14
So let's imagine then
that you're a roaring success
that you're a roaring success
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讓我們想像你的約會
07:17
on the dating scene.
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精彩成功，
07:19
But the question arises
of how do you then convert that success
of how do you then convert that success
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但問題來了
你如何將那成功的約會
你如何將那成功的約會
07:23
into longer-term happiness
and in particular,
and in particular,
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轉變成長期的幸福，尤其是，
07:27
how do you decide
when is the right time to settle down?
when is the right time to settle down?
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你要如何選擇
在哪個時刻安定下來？
在哪個時刻安定下來？
07:31
Now generally,
it's not advisable to just cash in
it's not advisable to just cash in
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一般來說，
並不建議人們立刻
並不建議人們立刻
07:34
and marry the first person
who comes along
who comes along
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與第一個出現
07:36
and shows you any interest at all.
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對你表達好感的人結婚。
07:38
But, equally, you don't really
want to leave it too long
want to leave it too long
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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，
最大化你未來數十年幸福婚姻的機會，
07:41
if you want to maximize your
chance of long-term happiness.
chance of long-term happiness.
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你也不願等待太久。
07:44
As my favorite author,
Jane Austen, puts it,
Jane Austen, puts it,
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我最喜歡的作家珍．奧斯汀這樣說：
07:47
"An unmarried woman of seven and twenty
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「一個未婚的 27 歲女子
07:50
can never hope to feel or
inspire affection again."
inspire affection again."
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就別指望再能感受或觸動愛情了。」
07:53
(Laughter)
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（笑聲）
07:55
Thanks a lot, Jane.
What do you know about love?
What do you know about love?
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這太嚴重了，珍，
你對愛瞭解多少呢？
你對愛瞭解多少呢？
07:59
So the question is then,
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那麼問題來了，
08:01
how do you know when
is the right time to settle down
is the right time to settle down
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你怎麼知道哪個時刻
是該要安定下來的時刻，
是該要安定下來的時刻，
08:03
given all the people
that you can date in your lifetime?
that you can date in your lifetime?
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畢竟生命中你有很多可能的對象？
08:06
Thankfully, there's a rather delicious bit
of mathematics that we can use
of mathematics that we can use
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幸好，我們可以運用一點數學
08:10
to help us out here, called
optimal stopping theory.
optimal stopping theory.
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來幫助我們計算解決這個問題，
這理論名叫 「最優停止理論」。
這理論名叫 「最優停止理論」。
08:12
So let's imagine then,
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那麼讓我們來想像一下，
08:14
that you start dating when you're 15
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你在 15 歲的時候開始交往，
08:17
and ideally, you'd like to be married
by the time that you're 35.
by the time that you're 35.
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理想狀態下，你在 35 歲的時候會結婚。
08:21
And there's a number of people
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你的人生中
08:22
that you could potentially
date across your lifetime,
date across your lifetime,
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有很多潛在的約會對象，
08:25
and they'll be at varying
levels of goodness.
levels of goodness.
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他們都有各自的優點。
08:27
Now the rules are that once
you cash in and get married,
you cash in and get married,
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規則是，你一旦跳進婚姻，
08:30
you can't look ahead to see
what you could have had,
what you could have had,
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你就不能繼續前進尋找
你可能可以有的對象，
你可能可以有的對象，
08:32
and equally, you can't go back
and change your mind.
and change your mind.
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你也不能回頭來改變你的主意。
08:35
In my experience at least,
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我個人的經驗看來，
08:37
I find that typically people don't
much like being recalled
much like being recalled
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一般人們不希望
在被拒絕又過了多年後被找回來，
也許只有我這樣想。
也許只有我這樣想。
08:39
years after being passed up
for somebody else, or that's just me.
for somebody else, or that's just me.
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08:45
So the math says then
that what you should do
that what you should do
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數學告訴我們
08:48
in the first 37 percent
of your dating window,
of your dating window,
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你應該拒絕認為會和
在你人生約會週期
在你人生約會週期
08:51
you should just reject everybody
as serious marriage potential.
as serious marriage potential.
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前 37% 時段出現的任何人
有嚴肅認真的婚姻關係。
有嚴肅認真的婚姻關係。
08:55
(Laughter)
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（笑聲）
08:57
And then, you should pick the
next person that comes along
next person that comes along
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接著，你要選擇下一個人，
09:01
that is better than everybody
that you've seen before.
that you've seen before.
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那個比你以前約會對象都好的人。
09:04
So here's the example.
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這裡舉個例子。
09:05
Now if you do this, it can be
mathematically proven, in fact,
mathematically proven, in fact,
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如果你這麼做，從數學證明來看
可以認為，事實上
可以認為，事實上
09:08
that this is the best possible way
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這可能是最好的選擇
09:10
of maximizing your chances
of finding the perfect partner.
of finding the perfect partner.
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來最大化你找到完美伴侶的機會。
09:15
Now unfortunately, I have to tell you that
this method does come with some risks.
this method does come with some risks.
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現在不幸的是，我必須告訴你
這個方法也是有風險的。
這個方法也是有風險的。
09:20
For instance, imagine if
your perfect partner appeared
your perfect partner appeared
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比如，想像一下，假設你的完美伴侶
09:25
during your first 37 percent.
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出現在你約會歷程的前 37%
09:28
Now, unfortunately,
you'd have to reject them.
you'd have to reject them.
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那就很不幸了，
你會拒絕他們。
你會拒絕他們。
09:30
(Laughter)
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（笑聲）
09:33
Now, if you're following the maths,
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如果你相信數學，
09:35
I'm afraid no one else comes along
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恐怕你不會再找到
09:37
that's better than anyone
you've seen before,
you've seen before,
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比你以往見過更好的對象，
09:39
so you have to go on
rejecting everyone and die alone.
rejecting everyone and die alone.
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你就會持續拒絕每個人
然後孤獨終老。
然後孤獨終老。
09:44
(Laughter)
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（笑聲）
09:46
Probably surrounded by cats
nibbling at your remains.
nibbling at your remains.
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可能會被貓咪包圍
一點點啃食你的遺骸。
一點點啃食你的遺骸。
09:51
Okay, another risk is,
let's imagine, instead,
let's imagine, instead,
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好，另一個風險是，
讓我們想像，相反的，
讓我們想像，相反的，
09:55
that the first people that you dated
in your first 37 percent
in your first 37 percent
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你約會歷程前 37% 裡第一個對象
09:58
are just incredibly dull,
boring, terrible people.
boring, terrible people.
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極度愚蠢、無聊又很糟糕。
10:02
Now, that's okay, because
you're in your rejection phase,
you're in your rejection phase,
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沒關係，因為你還處於拒絕對象的階段，
10:05
so thats fine,
you can reject them.
you can reject them.
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沒問題，你可以拒絕他們。
10:07
But then imagine, the next
person to come along
person to come along
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但想像一下，下一個出現的人
10:10
is just marginally less boring,
dull and terrible
dull and terrible
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4338
只是沒那麼無聊、愚蠢，
10:14
than everybody that you've seen before.
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1882
比你以前的對象都略好那麼一點。
10:16
Now, if you are following the maths,
I'm afraid you have to marry them
I'm afraid you have to marry them
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如果你遵循數學，
恐怕你要和他們結婚
恐怕你要和他們結婚
10:20
and end up in a relationship
which is, frankly, suboptimal.
which is, frankly, suboptimal.
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然後沈浸在一段，
實話說，次優的關係中。
實話說，次優的關係中。
10:24
Sorry about that.
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很抱歉。
10:25
But I do think that there's
an opportunity here
an opportunity here
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2200
但我認為，機會還是有的
10:27
for Hallmark to cash in on
and really cater for this market.
and really cater for this market.
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賀曼公司迎合市場需求
10:30
A Valentine's Day card like this.
(Laughter)
(Laughter)
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出售這樣的情人節賀卡。
（笑聲）
（笑聲）
10:32
"My darling husband, you
are marginally less terrible
are marginally less terrible
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「我親愛的丈夫，你沒有
我約會歷程中前 37% 的男士
那麼糟糕。」
那麼糟糕。」
10:36
than the first 37 percent
of people I dated."
of people I dated."
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10:39
It's actually more romantic
than I normally manage.
than I normally manage.
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這比一般的賀卡浪漫很多。
10:45
Okay, so this method doesn't give
you a 100 percent success rate,
you a 100 percent success rate,
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這個數學方法不能保證
100% 的成功率，
100% 的成功率，
10:50
but there's no other possible
strategy that can do any better.
strategy that can do any better.
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3303
但也沒有更好的策略了。
10:53
And actually, in the wild,
there are certain types
there are certain types
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事實上，在動物界，
某個特定種類的魚
某個特定種類的魚
遵循使用這樣的策略。
10:56
of fish which follow and
employ this exact strategy.
employ this exact strategy.
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3713
10:59
So they reject every possible
suitor that turns up
suitor that turns up
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在交配期，牠們拒絕
11:02
in the first 37 percent
of the mating season,
of the mating season,
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出現在前 37% 的每個求婚者，
11:05
and then they pick the next fish
that comes along after that window
that comes along after that window
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3531
接著牠們選擇 37% 後出現的下一個
11:08
that's, I don't know, bigger and burlier
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2056
比所見過的魚
11:11
than all of the fish
that they've seen before.
that they've seen before.
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體型更加龐大，更加結實的魚。
11:13
I also think that subconsciously,
humans, we do sort of do this anyway.
humans, we do sort of do this anyway.
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我想作為人類
我們潛意識裡也在做同樣的選擇。
我們潛意識裡也在做同樣的選擇。
11:18
We give ourselves a little bit of time
to play the field,
to play the field,
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我們給自己更多時間尋找，
11:21
get a feel for the marketplace
or whatever when we're young.
or whatever when we're young.
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3502
在我們年輕的時候
感受婚戀市場。
感受婚戀市場。
11:25
And then we only start looking seriously
at potential marriage candidates
at potential marriage candidates
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4908
我們只有在 20 歲年齡段的中後期
11:30
once we hit our mid-to-late 20s.
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1890
才會很真尋找潛在的結婚對象。
11:31
I think this is conclusive proof,
if ever it were needed,
if ever it were needed,
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我想這證明了，
即使不確定是否需要，
即使不確定是否需要，
11:34
that everybody's brains are prewired
to be just a little bit mathematical.
to be just a little bit mathematical.
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4506
每個人的大腦
都預配了點數學能力。
都預配了點數學能力。
11:39
Okay, so that was Top Tip #2.
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687616
1861
好，上述就是最高秘訣 2 號。
11:41
Now, Top Tip #3: How to avoid divorce.
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3253
現在，最高秘訣 3 號：如何避免離婚。
11:44
Okay, so let's imagine then
that you picked your perfect partner
that you picked your perfect partner
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3138
好的，讓我們想像一下
你找到了你的完美對象，
你找到了你的完美對象，
11:47
and you're settling into
a lifelong relationship with them.
a lifelong relationship with them.
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你和他/她進入了一生的婚姻關係。
11:52
Now, I like to think that everybody
would ideally like to avoid divorce,
would ideally like to avoid divorce,
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我假設每個人都不希望離婚，
11:56
apart from, I don't know,
Piers Morgan's wife, maybe?
Piers Morgan's wife, maybe?
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4366
當然，也許除了 Piers Morgan 的太太？
12:02
But it's a sad fact of modern life
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2290
可是，現代婚姻一個悲傷的事實
12:04
that 1 in 2 marriages in the
States ends in divorce,
States ends in divorce,
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3809
就是美國離婚率高達 50%，
12:08
with the rest of the world
not being far behind.
not being far behind.
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3301
世界其他國家也離這個數據不遠。
12:11
Now, you can be forgiven, perhaps
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2099
當然，你可以認為
12:13
for thinking that the arguments
that precede a marital breakup
that precede a marital breakup
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婚姻破裂的原因
12:17
are not an ideal candidate
for mathematical investigation.
for mathematical investigation.
230
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3533
不是數學運算理想的數據源。
12:20
For one thing, it's very hard to know
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1900
一方面來說，很難瞭解到
12:22
what you should be measuring
or what you should be quantifying.
or what you should be quantifying.
232
730777
3057
你該去測量什麼
或者是你該去量化什麼。
或者是你該去量化什麼。
12:25
But this didn't stop a psychologist,
John Gottman, who did exactly that.
John Gottman, who did exactly that.
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6573
但這並沒有阻止心理學家
John Gottman 做這樣的研究。
John Gottman 做這樣的研究。
12:32
Gottman observed hundreds of couples
having a conversation
having a conversation
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5195
Gottman 觀察了數百對夫婦的對談
12:37
and recorded, well,
everything you can think of.
everything you can think of.
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盡可能錄下來所有資訊。
12:40
So he recorded what was said
in the conversation,
in the conversation,
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2487
記錄了對話的內容、
12:42
he recorded their skin conductivity,
237
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皮膚的傳導性、
12:44
he recorded their facial expressions,
238
752614
1920
面部表情、
12:46
their heart rates, their blood pressure,
239
754534
2340
心跳、血壓，
12:48
basically everything apart from whether
or not the wife was actually always right,
or not the wife was actually always right,
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6450
基本上除了「太太永遠是對的」
以外的所有東西，
以外的所有東西，
12:55
which incidentally she totally is.
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3024
當然，太太永遠是對的。
12:58
But what Gottman and his team found
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766348
2920
但是，Gottman 和他的團隊發現
13:01
was that one of the
most important predictors
most important predictors
243
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2504
最能夠準確預測
13:03
for whether or not a couple
is going to get divorced
is going to get divorced
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2150
這對夫妻是否未來會離婚的
13:05
was how positive or negative each
partner was being in the conversation.
partner was being in the conversation.
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5100
是雙方在對話過程中
積極還是消極。
積極還是消極。
13:11
Now, couples that were very low-risk
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2612
那些離婚風險很低的夫妻
13:13
scored a lot more positive points
on Gottman's scale than negative.
on Gottman's scale than negative.
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4227
在 Gottman 的測試中得到了
更多正面而不是負面的分數。
更多正面而不是負面的分數。
13:17
Whereas bad relationships,
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相反的，在糟糕的關係中，
13:20
by which I mean, probably
going to get divorced,
going to get divorced,
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我是指那些可能離婚的夫妻，
13:22
they found themselves getting
into a spiral of negativity.
into a spiral of negativity.
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他們發現自己沈浸在消極的漩渦中。
13:27
Now just by using these very simple ideas,
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就用這些非常簡單的方法，
13:29
Gottman and his group were able to predict
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Gottman 和他的團隊能夠準確預測
13:32
whether a given couple
was going to get divorced
was going to get divorced
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一對夫妻是否會離婚,
13:35
with a 90 percent accuracy.
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準確率高達 90%。
13:37
But it wasn't until he teamed up
with a mathematician, James Murray,
with a mathematician, James Murray,
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但是，直到他與
數學家 James Murray 聯手，
數學家 James Murray 聯手，
13:41
that they really started to understand
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他們才真正找出
13:43
what causes these negativity spirals
and how they occur.
and how they occur.
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那些消極漩渦是
如何產生，為什麼產生的。
如何產生，為什麼產生的。
13:47
And the results that they found
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結果是他們發現
13:49
I think are just incredibly
impressively simple and interesting.
impressively simple and interesting.
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我認為不可思議太令人驚嘆
的簡單而有趣。
的簡單而有趣。
13:53
So these equations, they predict how
the wife or husband is going to respond
the wife or husband is going to respond
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這些算式，他們用來預測
妻子或是丈夫是如何去回應
妻子或是丈夫是如何去回應
13:58
in their next turn of the conversation,
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他們下一段對話，
13:59
how positive or negative
they're going to be.
they're going to be.
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他們的積極或消極程度是多少。
14:02
And these equations, they depend on
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這些算式，取決於
14:03
the mood of the person
when they're on their own,
when they're on their own,
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當他們獨處時各自的情緒，
14:06
the mood of the person when
they're with their partner,
they're with their partner,
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當他們和伴侶在一起時候的情緒，
14:08
but most importantly, they depend on
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但最重要的是，
14:10
how much the husband and wife
influence one another.
influence one another.
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取決於丈夫和妻子相互間的影響。
14:13
Now, I think it's important
to point out at this stage,
to point out at this stage,
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在這個階段我認為最重要的是，
14:16
that these exact equations
have also been shown
have also been shown
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這個一模一樣的算式
14:19
to be perfectly able at describing
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同時也可以完美預測
14:22
what happens between two
countries in an arms race.
countries in an arms race.
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兩個國家是否會開戰。
14:26
(Laughter)
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（笑聲）
14:30
So that -- an arguing couple
spiraling into negativity
spiraling into negativity
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因此，對沈浸於消極情緒
14:33
and teetering on the brink of divorce --
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在離婚邊緣搖擺的夫妻──
14:35
is actually mathematically equivalent to
the beginning of a nuclear war.
the beginning of a nuclear war.
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實際在數學上等同於
即將開始一場核戰爭。
即將開始一場核戰爭。
14:40
(Laughter)
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（笑聲）
14:42
But the really important term
in this equation
in this equation
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事實上，這個算式最重要的部分
14:45
is the influence that people
have on one another,
have on one another,
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是人們給對方帶來的影響，
14:47
and in particular, something called
the negativity threshold.
the negativity threshold.
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尤其是消極閾值。
14:50
Now, the negativity threshold,
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消極閾值，
14:52
you can think of as
how annoying the husband can be
how annoying the husband can be
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你可以認為它指的是
丈夫討厭到什麼程度
丈夫討厭到什麼程度
14:57
before the wife starts to get
really pissed off, and vice versa.
really pissed off, and vice versa.
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就能惹到妻子真的暴怒，
或者是相反。
或者是相反。
15:01
Now, I always thought that good marriages
were about compromise and understanding
were about compromise and understanding
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我一直認為美好的婚姻
是基於妥協和理解
是基於妥協和理解
15:06
and allowing the person to
have the space to be themselves.
have the space to be themselves.
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並且給對方留足獨處空間。
15:09
So I would have thought that perhaps
the most successful relationships
the most successful relationships
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我會想，最成功的關係是
15:12
were ones where there was
a really high negativity threshold.
a really high negativity threshold.
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當那裡有非常高的消極閾值時
15:16
Where couples let things go
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夫妻共同選擇不去理會這些問題。
15:17
and only brought things up if
they really were a big deal.
they really were a big deal.
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只有在非常嚴重的時候
才會嚴肅討論。
才會嚴肅討論。
15:20
But actually, the mathematics
and subsequent findings by the team
and subsequent findings by the team
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事實上，團隊得出的
數學運算結果和後續研究成果顯示
數學運算結果和後續研究成果顯示
15:24
have shown the exact opposite is true.
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完全相反的結果。
15:27
The best couples,
or the most successful couples,
or the most successful couples,
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最完美的夫妻，
最成功的夫妻，
最成功的夫妻，
15:29
are the ones with a really low
negativity threshold.
negativity threshold.
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有著很低的消極閾值。
15:33
These are the couples that don't
let anything go unnoticed
let anything go unnoticed
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這些夫妻不會忽視矛盾
15:37
and allow each other
some room to complain.
some room to complain.
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給對方抱怨的空間。
15:40
These are the couples that are continually
trying to repair their own relationship,
trying to repair their own relationship,
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這些夫妻持續努力
修復他們的關係，
修復他們的關係，
15:45
that have a much more positive
outlook on their marriage.
outlook on their marriage.
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他們對自己的婚姻
有著非常積極的預期。
有著非常積極的預期。
15:48
Couples that don't let things go
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他們不會忽略矛盾，
15:50
and couples that don't let trivial things
end up being a really big deal.
end up being a really big deal.
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他們不會讓一件件瑣碎的小事
堆積成為巨大的問題。
堆積成為巨大的問題。
15:56
Now of course, it takes bit more than
just a low negativity threshold
just a low negativity threshold
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當然，這不僅僅是
一個低消極閾值
一個低消極閾值
16:02
and not compromising to
have a successful relationship.
have a successful relationship.
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和對成功關係毫不妥協的態度。
16:06
But I think that it's quite interesting
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但我認為，很有趣的是
16:08
to know that there is really
mathematical evidence
mathematical evidence
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真的有數學證據
16:11
to say that you should never
let the sun go down on your anger.
let the sun go down on your anger.
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來證明你永遠不該長時間
積攢憤怒，太陽要下山了。
（譯注：這句話出自聖經）
積攢憤怒，太陽要下山了。
（譯注：這句話出自聖經）
16:14
So those are my top three tips
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上述就是我的三條最高秘訣，
16:16
of how maths can help you
with love and relationships.
with love and relationships.
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有關數學如何讓你有
更美好的愛情和關係。
更美好的愛情和關係。
16:19
But I hope
that aside from their use as tips,
that aside from their use as tips,
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我希望，除了作為愛情秘訣，
16:21
they also give you a little bit of insight
into the power of mathematics.
into the power of mathematics.
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它們也展示了數學的力量。
16:25
Because for me, equations
and symbols aren't just a thing.
and symbols aren't just a thing.
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對我來說，算式和符號
不僅僅是一樣東西。
不僅僅是一樣東西。
16:30
They're a voice that speaks out
about the incredible richness of nature
about the incredible richness of nature
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它們表達出
自然令人贊嘆的豐富性
自然令人贊嘆的豐富性
16:35
and the startling simplicity
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以及簡化
16:36
in the patterns that twist and turn
and warp and evolve all around us,
and warp and evolve all around us,
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那些我們身邊
扭曲、旋轉、包圍、進化的事物，
扭曲、旋轉、包圍、進化的事物，
16:41
from how the world works to how we behave.
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從世界是如何運作的，
到人類行為舉止。
到人類行為舉止。
16:44
So I hope that perhaps,
for just a couple of you,
for just a couple of you,
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我希望，也許你們中的一部分人
16:46
a little bit of insight into
the mathematics of love
the mathematics of love
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能夠瞭解一些
愛的數學運算，
愛的數學運算，
16:48
can persuade you to have
a little bit more love for mathematics.
a little bit more love for mathematics.
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能夠讓你愛數學稍微多一點。
16:52
Thank you.
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謝謝。
16:53
(Applause)
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（鼓掌）
ABOUT THE SPEAKER
Hannah Fry - Complexity theoristHannah Fry researches the trends in our civilization and ways we can forecast its future.
Why you should listen
Hannah Fry completed her PhD in fluid dynamics in early 2011 with an emphasis on how liquid droplets move. Then, after working as an aerodynamicist in the motorsport industry, she began work on an interdisciplinary project in complexity sciences at University College London. Hannah’s current research focusses on discovering new connections between mathematically described systems and human interaction at the largest scale.
Fry is the author of the TED Book, The Mathematics of Love: Patterns, Proofs, and the Search for the Ultimate Equation.
Hannah Fry | Speaker | TED.com