sentence-transformers/parallel-sentences-talks

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It can identify gaps in knowledge and logical inconsistencies and can help guide us as to where we should keep looking and where there may be a dead end.	它能夠辨視出知識的落差、邏輯的不一致，能引導我們應該持續探索的方向，指出哪裡可能是死胡同。
In other words: mathematical modeling can help us answer questions that directly affect people's health -- that affect each person's health, actually -- because mathematical modeling will be key to propelling personalized medicine.	換言之，數學建模能協助我們回答直接影響人們健康的問題，其實會影響每個人的健康，因為數學建模將會是推進個人化醫學的關鍵。
And it all comes down to asking the right question and translating it to the right equation ...	而這全都涉及到：要問對問題，要將問題翻譯成對的方程式，
and back.	和再翻譯回來。
(Music) Sun shining up above down here it's 10 below I'm moving on to a place now where the streets are paved with gold There'll be two trains running -- running side by side Some trains are going out Two trains running -- running side by side I'm going to catch that fast express train to my reward in the sky Many rooms in my father's house now -- Oh Lord there's one for you and me Many rooms in my father's house now -- Oh there's one for you and me No blues and no trouble Oh my Lord sweet Jesus victory There's one glory from the moon -- Lord another, oh another from the sun Oh one glory from the moon and another from the sun Behind I'll leave this earthly body when my Lord king Jesus comes Thank you very much.	（音樂）太陽在天上照耀著，地面這裡則不到十度。我現在要前往一個地方，在那裡，街道是用黃金鋪成的。將會有兩列火車在行駛—— 肩併肩地行駛。有些火車要出發。兩列火車在行駛—— 肩併肩地行駛。我要趕上那列特快車，通往我在天上的獎賞。現在，我父親的房子裡有許多房間—— 噢，主，有一間是給祢和我的。現在，我父親的房子裡有許多房間—— 噢，有一間是給祢和我的。沒有沮喪沒有麻煩。噢，我主耶穌甜蜜得勝！有來自月亮的一項榮耀—— 主啊，還有另一項，另一項來自太陽。噢，來自月亮的一項榮耀，以及另一項來自太陽。我會把這塵世的身體抛下，當我的上主耶穌來臨時。非常謝謝你。
For as long as I remember, I've loved mathematics.	在我的記憶當中，我一直都熱愛數學。
Actually, it's not 100 percent true.	其實，這句話並非百分之百是對的。
I've loved mathematics for all but a two-week period in senior high school.	我一直都熱愛數學，除了一段兩星期的時間，發生在高中時期。
(Laughter) I was top of my class, and we were about to start the Extension Maths course.	（笑聲）我在班上名列前茅，我們即將要開始一門叫做延伸數學的課，
I was really excited about this brand new topic coming up, complex numbers.	我對於這個將要學到的新主題感到十分興奮：複數。（註：直譯為複雜數字）
I like complex.	我喜歡複雜。
My teacher was priming us for the concepts with some questions about square roots.	我的老師先給我們一些觀念，問到關於平方根的問題。
Square of nine -- three; square of 256 -- sixteen.	9 的平方根是 3； 256 的平方根是 16；
Too easy.	太簡單了。
Then she asked the trick question: What about the square root of negative one?	接著她問了一個腦筋急轉彎的問題：那麼 -1 的平方根呢？
Of course, we were all over it -- "Come on, Miss!	當然，我們熱切地嘮叨著：「少來了，老師！
We all know you can't take the square root of a negative."	我們都知道負數不能開平方根。」
"That's true in the real world," she said.	她說：「在真實世界是如此，
"But in the complex world, the square root of negative one is the imaginary number i."	但在複數的世界裡， -1 的平方根就是『虛數』 i。」（註：照字面譯是「想像的數字」）
(Laughter) That day, my entire mathematical world came crashing down on me.	（笑聲）那一天，我的整個數學世界垮在我身上。
(Laughter) "Imaginary numbers?	（笑聲）「虛數？
Seriously?	當真嗎？
But mathematics is a source of truth, please don't go abstract on me.	但數學是個真相的來源，拜託別跟我來抽象的這一套。
I would have studied art if I wanted to play with imaginary numbers."	如果我想要玩「想像的」數字，早就去學藝術了。」
(Laughter) "This is Extension Maths, let's get back with our program!"	（笑聲）「這是延伸數學，咱們回來上我們的課吧！」
She didn't, and over the next couple of weeks, I reluctantly performed meaningless calculations, (Laughter) finding imaginary solutions to quadratic equations.	她沒有，在接下來的幾週，我很不情願地做無意義的計算，（笑聲）針對四次方程式，找出虛數解。
(Laughter) But then something amazing happened.	（笑聲）但接著，驚人的事發生了。
We began finding elegant solutions to real-world problems we previously had no answers to, starting with the complex world of imaginary numbers.	對於以前無解的真實世界問題，我們開始找到漂亮的答案，答案就從複數世界的虛數開始。
So some mathematician 500 years ago decides to have some fun and make up these imaginary numbers, and because of that we can now derive these amazing identities with applications in the real world, in fields like electrical engineering.	所以，五百年前的一些數學家想要找點樂子，所以編造出了這些虛數，正因如此，我們現在才能導出這些驚人的恆等式，在真實世界中應用，用到像是電子工程的領域上。
Wow!	哇！
I gained a whole new level of appreciation for mathematics.	我對數學的欣賞又再上了一層樓。
And after my brief mistrust, I was now in love with the subject more than ever.	在我那段短暫的不信任之後，我現在對這個科目的熱愛又更勝於過去。
Francis Su, the mathematician, sums it up beautifully when he says, "We study mathematics for play, for beauty, for truth, for justice and for love."	數學家法蘭西斯蘇用以下的說法，做了很漂亮的總結：「我們研究數學的目的是樂趣、美麗、真相、正義，和愛。」
But if you ask a student today, you'll probably hear a different story.	但如果你去問現在的學生，聽到的回應可能大不相同。
You might hear "difficult" and "boring."	你可能會聽到「困難」及「無聊」。
And they might be right about difficult.	說「困難」可能沒錯。
But it's certainly not boring.	但它絕對不無聊。
In fact, I'd say being difficult to master is part of what makes it beautiful.	事實上，我認為它之所以美麗，部分原因是因為它很難精通。
Because nothing worth doing is easy.	因為，值得做的事都不容易。
So we need students to stick around long enough through the difficult parts to appreciate the beauty when it all ties together.	所以我們需要學生能夠撐久一點，撐過困難的部分，才能在一切結合起來時欣賞它的美麗。
Much like I did for that brief couple of weeks in high school.	就像我在高中時那短短幾週的情況。
Unfortunately, our school systems -- we move students through mathematics in a lockstep process.	不幸的是，我們的學校體系—— 我們讓學生用密集連鎖步伐的過程來學數學。
So those who fall a little behind find it near impossible to ever catch up and appreciate that beauty.	所以，稍微落後一點的人，就會覺得要趕上並欣賞數學之美是幾乎不可能的。
But why is this a problem?	這為什麼是個問題？
Well today, more than ever, our world needs every citizen to be skilled in mathematics.	比起過去，現今，我們的世界更需要每位公民都具有數學技能。
With the advent of artificial intelligence and automation, many of the jobs we see today will either not exist or be transformed to require less routine work and more analysis and application of expertise.	隨著人工智慧和自動化的出現，現今的許多工作在將來不會繼續存在，或是會被轉變成比較不需要例行性的工作，需要更多分析與專門知識的應用。
But we're not producing the extra mathematics students to fill these new roles.	但我們並未產出額外的數學學生來補這些新角色。
This graph shows the number of students taking Standard Mathematics and Advanced Mathematics over a period of 20 years in Australia.	這張圖上的是學生數目，有修基礎數學的學生，及有修進階數學的學生，時間是過去二十年，地點是澳洲。
It's clear that while we have demand for mathematics skills rapidly increasing, supply is in steady decline.	很顯然，雖然我們對於數學技能的需求正在快速增加，供應卻在穩定地下降。
To put things in perspective, half of the students completing high school today in Australia are not prepared to understand any argument about rates of change in data.	正確地說，在澳洲，有一半的高中畢業生都沒有準備好了解任何關於資料改變率的論點。
In this digital age where fake news can influence election results, this is very concerning.	在這個數位時代，連假新聞都能夠影響選舉結果，這點很讓人憂心。
Let me give you a concrete example.	讓我舉個具體的例子。
Let's take a closer look at that graph.	咱們更仔細看一下那張圖。
Can everyone see what I've done there to stress my point?	有沒有人看得出來，我做了什麼來強調我的重點？
If you can't, let me show you now, with the vertical axis starting at zero, where it should be.	如果沒有，我現在做給各位看。如果縱軸的起始點是零，原本看起來應該像這樣。
There, you see it now, right?	你們現在看見了，對嗎？
It's the exact same data but I've manipulated the representation to influence you.	資料都沒有變，但我調整了呈現方式，來影響你們。
And that's cool, that's my job up here.	那很酷，那是我在台上的工作。
(Laughter) But in all seriousness, unless we do something to drastically improve student engagement with mathematics, we'll not only have a huge skills shortage crisis but a fickle population, easily manipulated by whoever can get the most air time.	（笑聲）但，說正經的，除非我們採取行動來大大改善學生對於數學的投入，不然，我們不僅會有技能短缺的大危機，還會有會動搖的人民，很容易被取得最多播送時間的人給操弄。
So what's the solution?	所以，怎麼解決？
There are a lot of things we have to do.	我們需要做的事情很多。
We need curriculum reform.	我們需要課程改革。
We need our best and brightest encouraged to become teachers.	我們需要鼓勵最好和最聰明的人去當老師。
We need to put an end to high-stakes tests and instead follow a mastery-based learning approach.	我們得停止用考試結果為補助依據，改成使用以精通為基礎的學習方法。
But all these things take time.	但這些都要花時間。
And I'm impatient.	我不是有耐心的人。
See, I've been thinking about this for eight years now.	我過去八年都在想這件事。
Ever since I left my job as a derivative trader to build a web application to help students learn mathematics.	自從我辭掉衍生產品交易員的工作，去建立網路應用程式來協助學生學習數學，就開始想了。
Today, our app is used by schools across the globe.	現今，全球都有學校在用我們的應用程式。
And we're seeing big improvements for students who use the program regularly.	我們看到經常使用這個程式的學生進步很大。
But here's the thing -- we're only seeing it for students who use the program regularly.	但，重點是只有常用這個程式的學生才有進步。
And most of them don't.	而大部分學生並不常用。
So after years of developing and refining the application, our biggest challenge was not so much product related, our biggest challenge was motivating students to want to work on their gaps in understanding.	所以，在花了數年時間發展和改善這個應用程式之後，我們最大的挑戰竟然和產品沒有很大的關係，我們最大的挑戰是要鼓勵學生，讓他們「想要」去改善他們在了解上的不足。
You can imagine in today's attention economy, we're competing against Facebook, Snapchat and PlayStation to try and get these students' time.	你們可以想像，在現今的注意力經濟當中，我們的競爭對手是臉書、 Snapchat、PlayStation 遊戲，跟它們搶學生的時間。
So we went back to the drawing board and started to think about how we could make it worthwhile for students to spend some of their "attention budget" on their education.	所以，我們回到計畫階段，開始思考，我們要如何讓學生覺得值得花一些他們的「注意力預算」在他們的教育上。
We tinkered with gamification elements like points, badges and avatars, and we'd see a temporary spike in engagement but things would go back to normal as soon as the novelty wore off.	我們補上遊戲化的元素，比如點數、徽章、頭像，在參與度上有出現暫時性的提升，但新鮮度不再時，馬上又回到原狀。
Then one day, my cofounder, Alvin, came across a study of students in Chicago led by the behavioral economist, Steven Levitt, where they paid students who improved on their test scores.	有一天，我的共同創辦人艾文看到一篇關於芝加哥學生的研究，主導研究的是行為經濟學家史帝芬萊維特（Steven Levitt），在研究中，他們付錢給學生，要他們改善考試分數。
He started telling me about some of the things they tested for and the interesting findings they had.	他開始告訴我研究做的一些測試，以及有趣的發現。
For instance, they found that incentivizing students for inputs, like effort, worked a lot better than incentivizing for outputs, like test scores.	比如，他們發現獎勵學生的投入，比如努力，效果大大優於獎勵他們的結果，如考試成績。
They found that for younger students, you could win them over with a trophy but for older students, you really needed cash.	他們發現，對年輕學生，用獎品可以贏得他們的心，但對較年長的學生，他們要的是現金。
(Laughter) And the amount of cash mattered -- 10 dollars was good, 20 dollars -- even better.	（笑聲）且現金的金額也很重要，$10 很好， $20 更好。
But perhaps most importantly, they found that the rewards had to be instant rather than promised at a later date.	但也許，最重要的是，他們發現，獎賞要「即時」，不能向他們保證晚一點再給。
They went as far as to give the students 20 dollars and say, "Touch it, feel it, smell it --" (Sniffing) "It's all yours.	他們做到這種程度—— 給學生 $20，然後說：「觸摸它，感受到，聞聞它。」（鼻吸）「這全是你的。
But if you fail, I'm going to take it back."	但若你失敗了，我會把它收回來。」
And that worked really well.	那樣做得效果非常好。
I immediately got excited about the possibilities of implementing this in our program.	我馬上就很興奮，心想有可能把這個點子導入我們的程式中。
But once the excitement settled down, there were a few concerns that crept in our minds.	但等興奮感平靜下來之後，我們慢慢想到了一些考量。
Firstly, was this ethical?	首先，這樣合乎道德嗎？
(Laughter) Secondly, how would we fund this thing?	（笑聲）第二，我們哪來的資金？
(Laughter) And finally, would the results be sustained if the students were no longer paid?	（笑聲）最後，如果不再付錢給學生，結果會維持下去嗎？
Now, let's look at the ethical part first.	先來看看道德的部分。
I'm a bit of a mathematical purist.	我有點算是數學純粹主義者。
So I'd be one of the first people to say that we should study mathematics for the sake of mathematics.	我會是最先說我們應該要為了數學而學數學的人之一。
Remember -- for play, for beauty, for truth, for justice and for love!	記得嗎？目的是為了樂趣、美麗、真相、正義，和愛！
Not for money!	不是為了錢！
(Laughter) As I struggled with this, I came to see that, while it's a way I look at mathematics now, it's only because I studied it long enough to appreciate it.	（笑聲）我為此掙扎時，漸漸理解到，雖然那是我現在看數學的一種方式，也只是因為我研究數學夠久，讓我能欣賞它。
It's very difficult to tell a student struggling with mathematics today to work hard for a payoff in the distant future.	很難告訴一個現在正在因為數學而掙扎的學生，只要努力，在遙遠的未來會有回報。
And it's not so much bribery that's at work here, because I could bribe students by telling them about my big bonuses in my derivative trading days as a reward for doing well at maths.	這裡其實還算不上有什麼行賄，因為我可以賄賂學生，告訴他們我還在當衍生產品交易員的日子，因為數學做得好而得到高額獎金。
But it doesn't pay off for a very long time.	但在很長一段時間內沒有回報。
So it's practically naught.	所以，它其實是零。

It can identify gaps in knowledge and logical inconsistencies and can help guide us as to where we should keep looking and where there may be a dead end.

它能夠辨視出知識的落差、邏輯的不一致，能引導我們應該持續探索的方向，指出哪裡可能是死胡同。

In other words: mathematical modeling can help us answer questions that directly affect people's health -- that affect each person's health, actually -- because mathematical modeling will be key to propelling personalized medicine.

換言之，數學建模能協助我們回答直接影響人們健康的問題，其實會影響每個人的健康，因為數學建模將會是推進個人化醫學的關鍵。

And it all comes down to asking the right question and translating it to the right equation ...

而這全都涉及到：要問對問題，要將問題翻譯成對的方程式，

and back.

和再翻譯回來。

(Music) Sun shining up above down here it's 10 below I'm moving on to a place now where the streets are paved with gold There'll be two trains running -- running side by side Some trains are going out Two trains running -- running side by side I'm going to catch that fast express train to my reward in the sky Many rooms in my father's house now -- Oh Lord there's one for you and me Many rooms in my father's house now -- Oh there's one for you and me No blues and no trouble Oh my Lord sweet Jesus victory There's one glory from the moon -- Lord another, oh another from the sun Oh one glory from the moon and another from the sun Behind I'll leave this earthly body when my Lord king Jesus comes Thank you very much.

（音樂）太陽在天上照耀著，地面這裡則不到十度。我現在要前往一個地方，在那裡，街道是用黃金鋪成的。將會有兩列火車在行駛—— 肩併肩地行駛。有些火車要出發。兩列火車在行駛—— 肩併肩地行駛。我要趕上那列特快車，通往我在天上的獎賞。現在，我父親的房子裡有許多房間—— 噢，主，有一間是給祢和我的。現在，我父親的房子裡有許多房間—— 噢，有一間是給祢和我的。沒有沮喪沒有麻煩。噢，我主耶穌甜蜜得勝！有來自月亮的一項榮耀—— 主啊，還有另一項，另一項來自太陽。噢，來自月亮的一項榮耀，以及另一項來自太陽。我會把這塵世的身體抛下，當我的上主耶穌來臨時。非常謝謝你。

For as long as I remember, I've loved mathematics.

在我的記憶當中，我一直都熱愛數學。

Actually, it's not 100 percent true.

其實，這句話並非百分之百是對的。

I've loved mathematics for all but a two-week period in senior high school.

我一直都熱愛數學，除了一段兩星期的時間，發生在高中時期。

(Laughter) I was top of my class, and we were about to start the Extension Maths course.

（笑聲）我在班上名列前茅，我們即將要開始一門叫做延伸數學的課，

I was really excited about this brand new topic coming up, complex numbers.

我對於這個將要學到的新主題感到十分興奮：複數。（註：直譯為複雜數字）

I like complex.

我喜歡複雜。

My teacher was priming us for the concepts with some questions about square roots.

我的老師先給我們一些觀念，問到關於平方根的問題。

Square of nine -- three; square of 256 -- sixteen.

9 的平方根是 3； 256 的平方根是 16；

Too easy.

太簡單了。

Then she asked the trick question: What about the square root of negative one?

接著她問了一個腦筋急轉彎的問題：那麼 -1 的平方根呢？

Of course, we were all over it -- "Come on, Miss!

當然，我們熱切地嘮叨著：「少來了，老師！

We all know you can't take the square root of a negative."

我們都知道負數不能開平方根。」

"That's true in the real world," she said.

她說：「在真實世界是如此，

"But in the complex world, the square root of negative one is the imaginary number i."

但在複數的世界裡， -1 的平方根就是『虛數』 i。」（註：照字面譯是「想像的數字」）

(Laughter) That day, my entire mathematical world came crashing down on me.

（笑聲）那一天，我的整個數學世界垮在我身上。

(Laughter) "Imaginary numbers?

（笑聲）「虛數？

Seriously?

當真嗎？

But mathematics is a source of truth, please don't go abstract on me.

但數學是個真相的來源，拜託別跟我來抽象的這一套。

I would have studied art if I wanted to play with imaginary numbers."

如果我想要玩「想像的」數字，早就去學藝術了。」

(Laughter) "This is Extension Maths, let's get back with our program!"

（笑聲）「這是延伸數學，咱們回來上我們的課吧！」

She didn't, and over the next couple of weeks, I reluctantly performed meaningless calculations, (Laughter) finding imaginary solutions to quadratic equations.

她沒有，在接下來的幾週，我很不情願地做無意義的計算，（笑聲）針對四次方程式，找出虛數解。

(Laughter) But then something amazing happened.

（笑聲）但接著，驚人的事發生了。

We began finding elegant solutions to real-world problems we previously had no answers to, starting with the complex world of imaginary numbers.

對於以前無解的真實世界問題，我們開始找到漂亮的答案，答案就從複數世界的虛數開始。

So some mathematician 500 years ago decides to have some fun and make up these imaginary numbers, and because of that we can now derive these amazing identities with applications in the real world, in fields like electrical engineering.

所以，五百年前的一些數學家想要找點樂子，所以編造出了這些虛數，正因如此，我們現在才能導出這些驚人的恆等式，在真實世界中應用，用到像是電子工程的領域上。

Wow!

哇！

I gained a whole new level of appreciation for mathematics.

我對數學的欣賞又再上了一層樓。

And after my brief mistrust, I was now in love with the subject more than ever.

在我那段短暫的不信任之後，我現在對這個科目的熱愛又更勝於過去。

Francis Su, the mathematician, sums it up beautifully when he says, "We study mathematics for play, for beauty, for truth, for justice and for love."

數學家法蘭西斯蘇用以下的說法，做了很漂亮的總結：「我們研究數學的目的是樂趣、美麗、真相、正義，和愛。」

But if you ask a student today, you'll probably hear a different story.

但如果你去問現在的學生，聽到的回應可能大不相同。

You might hear "difficult" and "boring."

你可能會聽到「困難」及「無聊」。

And they might be right about difficult.

說「困難」可能沒錯。

But it's certainly not boring.

但它絕對不無聊。

In fact, I'd say being difficult to master is part of what makes it beautiful.

事實上，我認為它之所以美麗，部分原因是因為它很難精通。

Because nothing worth doing is easy.

因為，值得做的事都不容易。

So we need students to stick around long enough through the difficult parts to appreciate the beauty when it all ties together.

所以我們需要學生能夠撐久一點，撐過困難的部分，才能在一切結合起來時欣賞它的美麗。

Much like I did for that brief couple of weeks in high school.

就像我在高中時那短短幾週的情況。

Unfortunately, our school systems -- we move students through mathematics in a lockstep process.

不幸的是，我們的學校體系—— 我們讓學生用密集連鎖步伐的過程來學數學。

So those who fall a little behind find it near impossible to ever catch up and appreciate that beauty.

所以，稍微落後一點的人，就會覺得要趕上並欣賞數學之美是幾乎不可能的。

But why is this a problem?

這為什麼是個問題？

Well today, more than ever, our world needs every citizen to be skilled in mathematics.

比起過去，現今，我們的世界更需要每位公民都具有數學技能。

With the advent of artificial intelligence and automation, many of the jobs we see today will either not exist or be transformed to require less routine work and more analysis and application of expertise.

隨著人工智慧和自動化的出現，現今的許多工作在將來不會繼續存在，或是會被轉變成比較不需要例行性的工作，需要更多分析與專門知識的應用。

But we're not producing the extra mathematics students to fill these new roles.

但我們並未產出額外的數學學生來補這些新角色。

This graph shows the number of students taking Standard Mathematics and Advanced Mathematics over a period of 20 years in Australia.

這張圖上的是學生數目，有修基礎數學的學生，及有修進階數學的學生，時間是過去二十年，地點是澳洲。

It's clear that while we have demand for mathematics skills rapidly increasing, supply is in steady decline.

很顯然，雖然我們對於數學技能的需求正在快速增加，供應卻在穩定地下降。

To put things in perspective, half of the students completing high school today in Australia are not prepared to understand any argument about rates of change in data.

正確地說，在澳洲，有一半的高中畢業生都沒有準備好了解任何關於資料改變率的論點。

In this digital age where fake news can influence election results, this is very concerning.

在這個數位時代，連假新聞都能夠影響選舉結果，這點很讓人憂心。

Let me give you a concrete example.

讓我舉個具體的例子。

Let's take a closer look at that graph.

咱們更仔細看一下那張圖。

Can everyone see what I've done there to stress my point?

有沒有人看得出來，我做了什麼來強調我的重點？

If you can't, let me show you now, with the vertical axis starting at zero, where it should be.

如果沒有，我現在做給各位看。如果縱軸的起始點是零，原本看起來應該像這樣。

There, you see it now, right?

你們現在看見了，對嗎？

It's the exact same data but I've manipulated the representation to influence you.

資料都沒有變，但我調整了呈現方式，來影響你們。

And that's cool, that's my job up here.

那很酷，那是我在台上的工作。

(Laughter) But in all seriousness, unless we do something to drastically improve student engagement with mathematics, we'll not only have a huge skills shortage crisis but a fickle population, easily manipulated by whoever can get the most air time.

（笑聲）但，說正經的，除非我們採取行動來大大改善學生對於數學的投入，不然，我們不僅會有技能短缺的大危機，還會有會動搖的人民，很容易被取得最多播送時間的人給操弄。

So what's the solution?

所以，怎麼解決？

There are a lot of things we have to do.

我們需要做的事情很多。

We need curriculum reform.

我們需要課程改革。

We need our best and brightest encouraged to become teachers.

我們需要鼓勵最好和最聰明的人去當老師。

We need to put an end to high-stakes tests and instead follow a mastery-based learning approach.

我們得停止用考試結果為補助依據，改成使用以精通為基礎的學習方法。

But all these things take time.

但這些都要花時間。

And I'm impatient.

我不是有耐心的人。

See, I've been thinking about this for eight years now.

我過去八年都在想這件事。

Ever since I left my job as a derivative trader to build a web application to help students learn mathematics.

自從我辭掉衍生產品交易員的工作，去建立網路應用程式來協助學生學習數學，就開始想了。

Today, our app is used by schools across the globe.

現今，全球都有學校在用我們的應用程式。

And we're seeing big improvements for students who use the program regularly.

我們看到經常使用這個程式的學生進步很大。

But here's the thing -- we're only seeing it for students who use the program regularly.

但，重點是只有常用這個程式的學生才有進步。

And most of them don't.

而大部分學生並不常用。

So after years of developing and refining the application, our biggest challenge was not so much product related, our biggest challenge was motivating students to want to work on their gaps in understanding.

所以，在花了數年時間發展和改善這個應用程式之後，我們最大的挑戰竟然和產品沒有很大的關係，我們最大的挑戰是要鼓勵學生，讓他們「想要」去改善他們在了解上的不足。

You can imagine in today's attention economy, we're competing against Facebook, Snapchat and PlayStation to try and get these students' time.

你們可以想像，在現今的注意力經濟當中，我們的競爭對手是臉書、 Snapchat、PlayStation 遊戲，跟它們搶學生的時間。

So we went back to the drawing board and started to think about how we could make it worthwhile for students to spend some of their "attention budget" on their education.

所以，我們回到計畫階段，開始思考，我們要如何讓學生覺得值得花一些他們的「注意力預算」在他們的教育上。

We tinkered with gamification elements like points, badges and avatars, and we'd see a temporary spike in engagement but things would go back to normal as soon as the novelty wore off.

我們補上遊戲化的元素，比如點數、徽章、頭像，在參與度上有出現暫時性的提升，但新鮮度不再時，馬上又回到原狀。

Then one day, my cofounder, Alvin, came across a study of students in Chicago led by the behavioral economist, Steven Levitt, where they paid students who improved on their test scores.

有一天，我的共同創辦人艾文看到一篇關於芝加哥學生的研究，主導研究的是行為經濟學家史帝芬萊維特（Steven Levitt），在研究中，他們付錢給學生，要他們改善考試分數。

He started telling me about some of the things they tested for and the interesting findings they had.

他開始告訴我研究做的一些測試，以及有趣的發現。

For instance, they found that incentivizing students for inputs, like effort, worked a lot better than incentivizing for outputs, like test scores.

比如，他們發現獎勵學生的投入，比如努力，效果大大優於獎勵他們的結果，如考試成績。

They found that for younger students, you could win them over with a trophy but for older students, you really needed cash.

他們發現，對年輕學生，用獎品可以贏得他們的心，但對較年長的學生，他們要的是現金。

(Laughter) And the amount of cash mattered -- 10 dollars was good, 20 dollars -- even better.

（笑聲）且現金的金額也很重要，$10 很好， $20 更好。

But perhaps most importantly, they found that the rewards had to be instant rather than promised at a later date.

但也許，最重要的是，他們發現，獎賞要「即時」，不能向他們保證晚一點再給。

They went as far as to give the students 20 dollars and say, "Touch it, feel it, smell it --" (Sniffing) "It's all yours.

他們做到這種程度—— 給學生 $20，然後說：「觸摸它，感受到，聞聞它。」（鼻吸）「這全是你的。

But if you fail, I'm going to take it back."

但若你失敗了，我會把它收回來。」

And that worked really well.

那樣做得效果非常好。

I immediately got excited about the possibilities of implementing this in our program.

我馬上就很興奮，心想有可能把這個點子導入我們的程式中。

But once the excitement settled down, there were a few concerns that crept in our minds.

但等興奮感平靜下來之後，我們慢慢想到了一些考量。

Firstly, was this ethical?

首先，這樣合乎道德嗎？

(Laughter) Secondly, how would we fund this thing?

（笑聲）第二，我們哪來的資金？

(Laughter) And finally, would the results be sustained if the students were no longer paid?

（笑聲）最後，如果不再付錢給學生，結果會維持下去嗎？

Now, let's look at the ethical part first.

先來看看道德的部分。

I'm a bit of a mathematical purist.

我有點算是數學純粹主義者。

So I'd be one of the first people to say that we should study mathematics for the sake of mathematics.

我會是最先說我們應該要為了數學而學數學的人之一。

Remember -- for play, for beauty, for truth, for justice and for love!

記得嗎？目的是為了樂趣、美麗、真相、正義，和愛！

Not for money!

不是為了錢！

(Laughter) As I struggled with this, I came to see that, while it's a way I look at mathematics now, it's only because I studied it long enough to appreciate it.

（笑聲）我為此掙扎時，漸漸理解到，雖然那是我現在看數學的一種方式，也只是因為我研究數學夠久，讓我能欣賞它。

It's very difficult to tell a student struggling with mathematics today to work hard for a payoff in the distant future.

很難告訴一個現在正在因為數學而掙扎的學生，只要努力，在遙遠的未來會有回報。

And it's not so much bribery that's at work here, because I could bribe students by telling them about my big bonuses in my derivative trading days as a reward for doing well at maths.

這裡其實還算不上有什麼行賄，因為我可以賄賂學生，告訴他們我還在當衍生產品交易員的日子，因為數學做得好而得到高額獎金。

But it doesn't pay off for a very long time.

但在很長一段時間內沒有回報。

So it's practically naught.

所以，它其實是零。