and I was one of the founders of OK Cupid.

我是 OK Cupid 的創辦者之一

It's now one of the biggest dating sites in the United States.

現在它是美國最大的交友網站之一

Like almost everyone at the site,

跟這網站的其它負責人一樣

I was a math major, and, as you might expect,

我主修數學，而就如你所預期的

we're known for the analytic approach

我們較為人知的是

we have taken to love.

用分析方式研究戀愛行為

We call it our matching algorithm.

我們把它叫做「速配演算法」

Basically OK Cupid's matching algorithm helps us decide whether two people should go on a date.

基本上，OK Cupid 的速配演算法幫助我們決定某兩個人該不該去約會

We built our entire business around it.

這是我們事業的技術核心

Now, algorithm is a fancy word,

演算法聽起來很花俏

and people like to drop it like it's this big thing,

而人們放棄搞懂因為它太複雜了

but, really, an algorithm is just a systematic,

但說真的，演算法只是一個有系統的

step-by-step way to solve a problem.

一步一步解決問題的方法

It doesn't have to be fancy at all.

完全不必要是花俏的

Here, in this lesson, I'm going to explain

這個課程裡，我將會解釋

how we arrived at our particular algorithm

我們是怎麼設計我們的演算法

so you can see how it's done.

來讓你理解它是如何運作的

Now, why are algorithms even important?

為什麼演算法如此重要

Why does this lesson even exist?

又為什麼要有這個課程

Well, notice one very significant phrase I used above:

這個，請注意我剛剛用的那個非常具暗示性的詞彙：

they are a "step-by-step" way to solve a problem,

演算法是「一步一步」解決問題的方法

and, as you probably know,

而就像你可能知道的

computers excel at step-by-step processes.

電腦很擅長做這種一步一步規劃好的程序

A computer without an algorithm

一臺沒有演算法的電腦

is basically an expensive paperweight.

基本上只是一個很貴的紙鎮而已

And since computers are such a pervasive part of everyday life, algorithms are everywhere.

由於電腦在日常生活中已經非常普及，所以演算法也是無所不在

The math behind OK Cupid's matching algorithm

而 OK Cupid 演算法背後的數學

is surprisingly simple.

其實異常地簡單

It's just some addition,

只是一些加法

multiplication,

乘法

a little bit of square roots.

還有一些些開根號

The tricky part in designing it, though,

然而要設計它比較麻煩的部份

was figuring out how to take something mysterious,

反而是要想辦法把一些神秘的東西

human attraction,

例如人類的吸引力

and break it into components that a computer can work with.

把它變成電腦可以運算的東西

Well, the first thing we needed to match people up was data,

那麼，要將人們配對，我們首先需要的是數據

something for the algorithm to work with.

也就是要讓演算法能夠計算的東西

The best way to get data quickly from people

要快速取得人們資料的最好方法

is to just ask for it.

就是直接問他

So, we decided that OK Cupid should ask users questions,

所以，我們決定 OK Cupid 應該要問使用者一些問題

stuff like, "Do you want to have kids one day?"

像是：「你未來希望有小孩嗎？」

and "How often do you brush your teeth?",

還有「你多常刷牙？」

"Do you like scary movies?"

「你喜歡恐怖片嗎？」

and big stuff like "Do you believe in God?"

以及較大的問題，像是「你相信神嗎？」

Now, a lot of the questions are good

而很多問題都有助於

for matching like with like,

將有相同喜好的人配在一起

that is when both people answer the same way.

這是當雙方都回答了相同答案的情況

For example, two people who are both into scary movies are probably a better match than one person who is and one person who isn't.

舉例來說，兩個都喜歡恐怖片的人也許就是不錯的配對，這比起將喜歡和不喜歡的人配在一起好

But what about a question like,

但如果是像這樣的問題：

"Do you like to be the center of attention?"

「你喜歡成為眾人的焦點嗎？」

If both people in a relationship are saying yes to this,

如果一對情侶的兩個人都說「喜歡」

then they are going to have massive problems.

那麼他們就有大問題了

We realized this early on,

我們很早就知道這點

and so we decided we needed

所以我們決定

a bit more data from each question.

每個問題都需要再多一點資訊

We had to ask people to specify not only their own answer,

我們要求使用者不只回答問題本身

but the answer they wanted from someone else.

同時也回答他們對別人的期望

That worked really well,

這效果真的很好

but we needed one more dimension.

但我們還須要另一個衡量的維度

Some questions tell you more about a person than others.

有一些問題比起其它問題，更能提供一個人的個性

For example, a question about politics, something like,

比如說政治議題如：

"Which is worse: book burning or flag burning?"

「哪一個比較糟：燒書或是燒國旗？」

might reveal more about someone than their taste in movies.

比起對電影的品味，這可能透露更多這個人的個性

And it doesn't make sense to weigh all things equally,

而每個人看事情的輕重大小都不同

so we added one final data point.

所以我們加入了最後一個資料點

For everything that OK Cupid asks you,

每一個 OK Cupid 問你的問題

you have a chance to tell us

你都可以告訴我們

the role it plays in your life,

它在你生活中扮演的角色

and this ranges from irrelevant to mandatory.

而選項是從「不相關」到「極重要」

So now, for every question,

所以現在，每一個問題

we have three things for our algorithm:

我們都有三筆資訊可以給我們的演算法：

first, your answer;

第一，你的答案

second, how you want someone else,

第二，你對別人答案的期望

your potential match,

也就是對於可能會跟你配對的人

to answer;

的答案的期望

and three, how important the question is to you at all.

第三，這問題究竟對你有多重要

With all this information,

有了全部的這些資訊

OK Cupid can figure out how well two people will get along.

OK Cupid 就可以算出這兩個人相處會多融洽

The algorithm crunches the numbers and gives us a result.

演算法會在數值運算後，給我們一個答案

As a practical example,

舉一個實際的例子

let's look at how we'd match you with another person,

讓我們來看看你和另一個人有多速配

let's call him, "B".

姑且叫他 B

Your match percentage with B is based on

你和 B 的速配指數是基於

questions you've both answered.

你們雙方都回答過的問題

Let's call that set of common questions, "s".

這些問題的集合叫做 s

As a very simple example, we use a small set "s"

舉一個非常簡單的例子， 我們用很小的集合 s

with just two questions in common

只包含兩個雙方都回答過的問題

and compute a match from that.

然後由它算出速配程度

Here are our two example questions.

舉例來說，他們回答了這兩個問題

The first one, let's say, is, "How messy are you?"

第一個，比如說：「你有多不愛乾淨？」

and the answer possibilities are

而可能的答案是

very messy,

「很髒亂」

average,

「普通」

and very organized.

及「很愛乾淨」

And let's say you answered "very organized,"

假設你的答案是「很愛乾淨」

and you'd like someone else to answer "very organized,"

而你期望別人也回答「很愛乾淨」

and the question is very important to you.

並且這問題對你來說「非常重要」

Basically you are a neat freak.

基本上你有潔癖

You're neat,

你愛乾淨

you want someone else to be neat,

你也希望別人愛乾淨

and that's it.

這是你的結果

And let's say B is a little bit different.

又假設 B 的回答有點不一樣

He answered very organized for himself,

他回答自己「很愛乾淨」

but average is OK with him

但別人回答「普通」

as an answer from someone else,

對他來說就可以了

and the question is only a little important to him.

而且這問題對他只有「些許重要」

Let's look at the second question,

接著我們來看第二個問題

it's the one from our previous example:

是我們先前說過的例子：

"Do you like to be the center of attention?"

「你喜歡成為眾人的焦點嗎？」

The answers are just yes and no.

而答案只有「是」或「否」

Now you've answered "no,"

假設你的答案是「否」

how you want someone else to answer is "no,"

而你希望對方回答「否」

and the questions is only a little important to you.

並且這問題對你只有「些許重要」

Now B, he's answered "yes,"

換 B，他回答「是」

he wants someone else to answer "no,"

而他希望對方回答「否」

because he wants the spotlight on him,

因為他希望焦點是在他身上

and the question is somewhat important to him.

而這問題對他「蠻重要的」

So, let's try to compute all of this.

好，讓我們試著來算看看

Our first step is,

我們的第一個步驟是

since we use computers to do this,

因為要用電腦計算

we need to assign numerical values

我們必須對不同答案如「蠻重要的」和「非常重要」

to ideas like "somewhat important" and "very important"

賦予相對應的數字

because computers need everything in numbers.

因為電腦必須透過數字才能運算

We at OK Cupid decided on the following scale:

在 OK Cupid 裡我們訂定了這樣的量表：

irrelevant is worth 0,

「不相關」是 0

a little important is worth 1,

「些許重要」是 1

somewhat important is worth 10,

「蠻重要的」是 10

very important is 50,

「非常重要」是 50

and absolutely mandatory is 250.

而「極重要」是 250

Next, the algorithm makes two simple calculations.

接著，演算法會進行兩個簡單的運算

The first is how much did B's answers satisfy you,

第一是 B 的答案有多符合你的期望

that is, how many possible points did B score on your scale?

也就是，B 在你的量表上會得到幾分？

Well, you indicated that B's answer

嗯，你在第一個愛乾淨的問題中

to the first question about messiness

表示 B 的答案

was very important to you.

對你非常重要

It's worth 50 points and B got that right.

它佔 50 分而 B 正好符合

The second question is worth only 1

而第二個問題只佔 1 分

because you said it was only a little important,

因為你說它只有些許重要

and B got that wrong.

而 B 答得不對

So B's answers were 50 out of 51 possible points.

所以 B 的答案在總分 51 分裡得到 50 分

That's 98% satisfactory.

這樣是 98% 的滿意度

It's pretty good.

相當不錯

And, the second question of the algorithm looks at

而演算法第二步要做的是

is how much did you satisfy B.

你有多符合 B 的要求

Well, B placed 1 point on your answer

嗯，B 認為你對整潔問題

to the messiness question

的答案佔 1 分

and 10 on your answer to the second.

而第二個問題的答案佔 10 分

Of those, 11, that's 1 plus 10,

總共是 11 分，也就是 1 + 10

you earned 10,

你得到 10 分

you guys satisfied each other on the second question.

你們雙方在第二個問題符合兩方的條件

So your answers were 10 out of 11

所以你的答案是 11 分裡得 10 分

equals 91% satisfactory to B.

也就是對於 B 來說 91% 的滿意度

That's not bad.

也是不錯

The final step is to take these two match percentages

而最後一步， 是把這兩個數字

and get one number for the both of you.

變成你們兩個速配指數

To do this, the algorithm multiplies your scores,

要完成這件事， 演算法會把你們的分數乘起來

then takes the nth root,

然後開 n 次方根

where n is the number of questions.

這裡 n 是問題的數目

Because s, which is the number of questions,

因為在我們例子的 s 裡

in this sample, is only 2,

問題數只有 2

we have match percentage equals

我們就算出速配指數

the square root of 98% times 91%.

是 98% 乘 91% 的開根號

That equals 94%.

也就是 94%

That 94% is your match percentage with B.

這 94% 就是你和 B 的速配指數

It's a mathematical expression

這是我們基於對於你們的了解

of how happy you'd be with each other

透過數學算式

based on what we know.

來表現出你們在一起會多快樂的方式

Now, why does the algorithm multiply as opposed to, say,

而，為什麼演算法要用相乘的

average the two match scores together

而不用相加的

and do the square-root business?

並且要取平方根呢？

In general, this formula is called the geometric mean,

一般來說，這個公式叫作幾何平均數

which is a great way to combine values

它是將範圍很廣

that have wide ranges

並表達不同特性的數據合在一起的

and represent very different properties.

一種很棒的方法

In other words, it's perfect for romantic matching.

也就是說，它對浪漫的配對來說是很完美的

You've got wide ranges

你會有很廣的數據

and you've got tons of different data points,

你也許多不一樣的資訊

like I said, about movies,

比如說，關於電影

about politics,

關於政治

about religion,

關於信仰

about everything.

關於所有事

Intuitively, too, this makes sense.

直覺來說，這也合理

Two people satisfying each other 50%

兩個人互相有 50% 的滿意度

should be a better match

應該會比

than two others who satisfy 0 and 100,

一人是 0% 另一人是 100% 來得好

because affection needs to be mutual.

因為感情是互相的

After adding a little correction for margin of error,

再加上一些邊界錯誤的修正

in the case when we have a very small number of questions,

就是說當問題數很少的時候的修正

like we do in this example,

像是我們這個例子

we're good to go.

我們就完成了

Any time OK Cupid matches two people,

每一次 OK Cupid 在幫兩人配對時

it goes through the steps we just outlined.

都經過了我們所講的那些步驟

First it collects data about your answers,

首先從你的答案收集資訊

then it compares your choices and preferences

然後用簡潔的數學方法

to other people in simple, mathematical ways.

來將你和其它人的偏好作比較

This, the ability to take real world phenomena and make them something a microchip can understand, is, I think, the most important skill anyone can have these days.

這樣把真實世界的現象變成微晶片能運作的一種能力，我認為是我們現今可以擁有最重要的技能

Like you use sentences to tell a story to a person,

就像是你用句子來向別人說故事一樣

you use algorithms to tell a story to a computer.

你會用演算法來對電腦說故事

If you learn the language,

如果你學會這種語言

you can go out and tell your stories.

你就可以把你的故事告訴別人

I hope this will help you do that.

這就是我希望幫助你達成的事情