Tim Harford: Trial, error and the God complex

譯者: Cheng-An Li 審譯者: Jenny Yang

It's the Second World War.

這是在第二次世界大戰時

A German prison camp.

德國的一個戰俘營

And this man,

而這位軍人

Archie Cochrane,

是已故英國臨床流行病學者亞契．柯克倫（Archie Cochrane）

is a prisoner of war and a doctor,

既是戰俘也是醫生,

and he has a problem.

他當時有個難題

The problem is that the men under his care

多名接受他治療的病人

are suffering

正飽受令人費解之病痛

from an excruciating and debilitating condition

這種病使患者感到劇烈疼痛, 渾身無力

that Archie doesn't really understand.

亞契苦思不得其解

The symptoms

他們的症狀

are this horrible swelling up of fluids under the skin.

是皮下嚴重水腫

But he doesn't know whether it's an infection, whether it's to do with malnutrition.

然而他無法確定水腫是由病菌所感染, 還是營養不良所引起

He doesn't know how to cure it.

那時，他遍尋不著良方

And he's operating in a hostile environment.

更何況那是在惡劣的環境之下

And people do terrible things in wars.

兵馬倥傯戰亂之中

The German camp guards, they've got bored.

德軍軍營守衛如果閒著無聊

They've taken to just firing into the prison camp at random

就對戰俘營裡恣意掃射

for fun.

打發時間並尋開心。

On one particular occasion,

某次

one of the guards threw a grenade into the prisoners' lavatory

一名警衛扔手榴彈

while it was full of prisoners.

到人滿為患的犯人廁所內。

He said he heard suspicious laughter.

守衛的理由是，他聽到可疑的笑聲。

And Archie Cochrane, as the camp doctor,

亞契．柯克倫 ，這名營區的醫生，

was one of the first men in

是首批進去收拾善後，

to clear up the mess.

處理慘狀的人之一。

And one more thing:

另外，

Archie was suffering from this illness himself.

亞契也身染該病。

So the situation seemed pretty desperate.

這千鈞一髮的情況下，

But Archie Cochrane

足智多謀的亞契

was a resourceful person.

想辦法取得資源

He'd already smuggled vitamin C into the camp,

悄悄地走私維他命C進去營區

and now he managed

而且當時

to get hold of supplies of marmite

他還設法換取

on the black market.

黑市裡的麴精

Now some of you will be wondering what marmite is.

在座的各位，也許正在猜想麴精是什麼？

Marmite is a breakfast spread beloved of the British.

其實那是英式早餐的一種麵包醬

It looks like crude oil.

外型看似未提煉的原油，黝黑色。

It tastes ...

嘗起來

zesty.

棒透了。

And importantly,

更重要的是，

it's a rich source

麵包裡富含

of vitamin B12.

維他命B12。

So Archie splits the men under his care as best he can

亞契將這群他苦心照料的病人

into two equal groups.

分成兩組。

He gives half of them vitamin C.

一組餵以維他命C。

He gives half of them vitamin B12.

另一組則以維他命B12。

He very carefully and meticulously notes his results

醫生鉅細靡遺地

in an exercise book.

在筆記簿上記下結果。

And after just a few days,

數日之後，

it becomes clear

一切撥雲見日。

that whatever is causing this illness,

無論病因為何，

marmite is the cure.

麵包醬就是解藥。

So Cochrane then goes to the Germans who are running the prison camp.

因此，柯克倫便去見德軍營長，

Now you've got to imagine at the moment --

在座的各位，試想在此時此刻--

forget this photo, imagine this guy

先把這張照片丟至九霄雲外，只要想像

with this long ginger beard and this shock of red hair.

一下巴剪不斷理還亂的鬍鬚，和一頭震懾人的紅髮

He hasn't been able to shave -- a sort of Billy Connolly figure.

許久未能整理儀容，猶如比利康諾利的柯克倫

Cochrane, he starts ranting at these Germans

朝著這些德國人咆哮

in this Scottish accent --

帶著蘇格蘭口音

in fluent German, by the way, but in a Scottish accent --

卻極其流利的德文

and explains to them how German culture was the culture

數落對方，坐擁孕育世界偉人席勒和歌德

that gave Schiller and Goethe to the world.

的偉大文化

And he can't understand

竟能容忍這些野蠻行徑。

how this barbarism can be tolerated,

他完全無法理解這些德國人。

and he vents his frustrations.

他發完這頓牢騷之後，

And then he goes back to his quarters,

踱步回房。

breaks down and weeps

情緒失控，落下男兒淚。

because he's convinced that the situation is hopeless.

畢竟他認為情況陷入絕望，束手無策。

But a young German doctor

此時，一名年輕的德軍軍醫

picks up Archie Cochrane's exercise book

拾起亞契．科克倫的筆記簿

and says to his colleagues,

對同僚說：

"This evidence is incontrovertible.

「事實擺在眼前，

If we don't supply vitamins to the prisoners,

倘若我們再不提供戰俘維他命，

it's a war crime."

會有違人道。」

And the next morning,

於是，翌日清晨，

supplies of vitamin B12 are delivered to the camp,

營區便提供維他命B12補給

and the prisoners begin to recover.

而戰俘便逐漸好轉。

Now I'm not telling you this story

我敘述這個故事的原因

because I think Archie Cochrane is a dude,

並非因為我視亞契．柯克倫為堂堂漢子

although Archie Cochrane is a dude.

雖然他的確也是。

I'm not even telling you the story

講這個故事的理由是

because I think we should be running

我們都該更

more carefully controlled randomized trials

小心去掌控公共政策的所有層面

in all aspects of public policy,

下的隨機試驗。

although I think that would also be completely awesome.

即便，個人淺見，隨機試驗本身其實很棒。

I'm telling you this story

向各位闡述故事是為了

because Archie Cochrane, all his life,

解釋亞契． 柯克倫，

fought against a terrible affliction,

終其一生與苦難對抗

and he realized it was debilitating to individuals

而他明瞭，苦難對個體的蠶食

and it was corrosive to societies.

對整個社會的鯨吞。

And he had a name for it.

他將此命名為：

He called it the God complex.

上帝情結。

Now I can describe the symptoms of the God complex very, very easily.

接下來，為各位簡述上帝情結的症狀。

So the symptoms of the complex

這些症狀就像是

are, no matter how complicated the problem,

無論遭遇的問題有多錯綜複雜

you have an absolutely overwhelming belief

你總是有無與倫比的信心

that you are infallibly right in your solution.

總而言之，你認為你的解決之道正確且毋庸置疑

Now Archie was a doctor,

身為一名醫生，

so he hung around with doctors a lot.

亞契與醫生為伍

And doctors suffer from the God complex a lot.

醫生很容易有上帝情結。

Now I'm an economist, I'm not a doctor,

而我是一名經濟學家，並非醫生，

but I see the God complex around me all the time

在我眼裡，患有上帝情結的經濟學者，

in my fellow economists.

比比皆是。

I see it in our business leaders.

舉凡企業頭子、

I see it in the politicians we vote for --

甚至是我們票選出的政治人物。

people who, in the face of an incredibly complicated world,

這些人，身處在複雜程度難以置信的世界裡，

are nevertheless absolutely convinced

卻百分百相信

that they understand the way that the world works.

世界的運轉，自己瞭若指掌

And you know, with the future billions that we've been hearing about,

在座各位也曉得，我們將與未來的數十億人口共存，

the world is simply far too complex

如果還是用老法子去思考，

to understand in that way.

是難以理解這複雜的世界。

Well let me give you an example.

讓我為各位舉個例子。

Imagine for a moment

花幾秒想像一下

that, instead of Tim Harford in front of you,

站在台上的人不是我，

there was Hans Rosling presenting his graphs.

而是漢斯．羅史齡，在展示圖表。

You know Hans:

各位眼中的漢斯：

the Mick Jagger of TED.

就好比TED集團的米克．傑格。

(Laughter)

（笑聲）

And he'd be showing you these amazing statistics,

他會秀出這些驚人的數據，

these amazing animations.

讚為觀止的動畫。

And they are brilliant; it's wonderful work.

這挺棒的！

But a typical Hans Rosling graph:

一個典型的漢斯．羅史齡會用的圖表：

think for a moment, not what it shows,

試想圖表除了本身，

but think instead about what it leaves out.

還喻含的意義。

So it'll show you GDP per capita,

各位將會看到國內生產毛額、

population, longevity,

人口、壽命，

that's about it.

大概就是這些東西。

So three pieces of data for each country --

若每個國家都

three pieces of data.

列舉三種資訊

Three pieces of data is nothing.

才三種並沒有什麼。

I mean, have a look at this graph.

且讓我們看一下該表。

This is produced by the physicist Cesar Hidalgo.

我指的是這個物理學家所作的表。

He's at MIT.

凱薩．荷德果 畢業於MIT(麻省理工)。

Now you won't be able to understand a word of it,

目前各位可能一點也看不懂這個表。

but this is what it looks like.

但看起來像是這樣子。

Cesar has trolled the database

凱薩把逾5000多筆的產品的資料庫

of over 5,000 different products,

提取分析。

and he's used techniques of network analysis

利用網路分析的技術

to interrogate this database

藉此整合資料庫，

and to graph relationships between the different products.

並將不同結果間的關係視覺圖像化。

And it's wonderful, wonderful work.

創出這件傑出的作品，

You show all these interconnections, all these interrelations.

所有的互動、交互關聯一目了然。

And I think it'll be profoundly useful

欲瞭解經濟如何成長，

in understanding how it is that economies grow.

看這個圖表便能略知一二。

Brilliant work.

真是傑作。

Cesar and I tried to write a piece for The New York Times Magazine

凱薩和我試圖替紐時雜誌撰寫一篇文章，

explaining how this works.

藉此解釋運作方式。

And what we learned

從中，我們習得的是

is Cesar's work is far too good to explain

僅一篇的篇幅，不夠解釋

in The New York Times Magazine.

凱薩的傑作。

Five thousand products --

5000筆結果

that's still nothing.

不費吹灰之力。

Five thousand products --

5000筆結果耶！

imagine counting every product category

試想算出每個

in Cesar Hidalgo's data.

在資料庫裡的分類

Imagine you had one second

一秒鐘

per product category.

能算出的分類結果。

In about the length of this session,

同個時間範圍內，

you would have counted all 5,000.

各位會得到5000筆。

Now imagine doing the same thing

如果，如法炮製到

for every different type of product on sale in Walmart.

沃爾瑪超市內特價的各種商品

There are 100,000 there. It would take you all day.

那裡有十萬種商品，數完要花上一整天的時間。

Now imagine trying to count

試想，

every different specific product and service

在一個主要的經濟體內，像是在東京、倫敦或紐約

on sale in a major economy

計算在打折的

such as Tokyo, London or New York.

每種不同的產品和服務。

It's even more difficult in Edinburgh

算愛丁堡內的甚至會難上加難，

because you have to count all the whisky and the tartan.

因為還得加算威士忌和格子呢。

If you wanted to count every product and service

假設想算出每種

on offer in New York --

在紐約所提供的不同的產品和服務--

there are 10 billion of them --

答案將會是100億個

it would take you 317 years.

各位得花317年才算得出來

This is how complex the economy we've created is.

這就是人類所孕育出，無比複雜的經濟。

And I'm just counting toasters here.

而我不過就是在這裡算吐司麵包。

I'm not trying to solve the Middle East problem.

並不想解決中東問題。

The complexity here is unbelievable.

這裡的複雜性令人難以置信。

And just a piece of context --

只要一小塊人腦

the societies in which our brains evolved

所創造出的社會

had about 300 products and services.

就擁有逾300樣的產品與服務。

You could count them in five minutes.

卻只消五分鐘便算完了。

So this is the complexity of the world that surrounds us.

這就是我們周遭複雜的世界

This perhaps is why

也許

we find the God complex so tempting.

這就是為何上帝情結誘人。

We tend to retreat and say, "We can draw a picture,

我們嘗試要撤退並聲明「我們可以畫圖，

we can post some graphs,

我們可以張貼圖表，

we get it, we understand how this works."

我們全盤瞭解世界的遊戲規則。」

And we don't.

然而，事實並非如此。

We never do.

我們的能力從未所及。

Now I'm not trying to deliver a nihilistic message here.

我並無要散播虛無主義的用意

I'm not trying to say we can't solve

也不是暗指我們無法解決

complicated problems in a complicated world.

複雜世界裡的複雜問題。

We clearly can.

顯然，我們能。

But the way we solve them

但是用的是

is with humility --

謙虛--

to abandon the God complex

放棄上帝情結

and to actually use a problem-solving technique that works.

找出真正解決之道

And we have a problem-solving technique that works.

我們的確擁有有效的解決之道

Now you show me

假設在座的各位

a successful complex system,

拿給我一個成功且複雜的系統

and I will show you a system

那我會還給你們

that has evolved through trial and error.

一個經過試驗和錯誤失敗中重生的系統

Here's an example.

舉個例子。

This baby was produced through trial and error.

經過測試，這個寶寶出生了。

I realize that's an ambiguous statement.

我的說法有點模稜兩可

Maybe I should clarify it.

也許我該修飾一下

This baby is a human body: it evolved.

這是進化過的人類嬰兒

What is evolution?

何謂進化？

Over millions of years, variation and selection,

歷經數百萬年的

variation and selection --

演進天擇，

trial and error,

測試和

trial and error.

從錯誤中修正。

And it's not just biological systems

這不僅是從試驗和錯誤中

that produce miracles through trial and error.

產下的奇蹟。

You could use it in an industrial context.

若放到工業的框架下

So let's say you wanted to make detergent.

假設各位要製造清潔劑

Let's say you're Unilever

設想我們是聯合利華股份有限公司

and you want to make detergent in a factory near Liverpool.

想在利物浦附近的工廠生產清潔劑

How do you do it?

該如何下手？

Well you have this great big tank full of liquid detergent.

目前有滿滿的一大桶清潔液

You pump it at a high pressure through a nozzle.

先利用高壓將清潔液從管口抽出。

You create a spray of detergent.

然後把清潔液灑成霧狀

Then the spray dries. It turns into powder.

待噴霧乾凅，便轉成粉末。

It falls to the floor.

落到地面。

You scoop it up. You put it in cardboard boxes.

用勺子取出，放置到紙盒。

You sell it at a supermarket.

拿到超市販售。

You make lots of money.

錢財滾滾來。

How do you design that nozzle?

高壓管該如何設計？

It turns out to be very important.

這個很重要。

Now if you ascribe to the God complex,

倘若當下，各位患了上帝情結的大頭症

what you do is you find yourself a little God.

你們可能誤以為，自己跟上帝也相去不遠。

You find yourself a mathematician; you find yourself a physicist --

自以為是數學家、物理學家，

somebody who understands the dynamics of this fluid.

或是理解液體動學的某人

And he will, or she will,

然後就會

calculate the optimal design of the nozzle.

計算出最佳的噴管設計

Now Unilever did this and it didn't work --

不過，聯合利華也這麼做，卻沒效

too complicated.

因為太複雜了。

Even this problem, too complicated.

就連這樣的問題，都複雜。

But the geneticist Professor Steve Jones

基因學者史帝芬．瓊斯

describes how Unilever actually did solve this problem --

描述聯合利華是如何解決問題

trial and error,

經由試驗和錯誤，

variation and selection.

變異和選擇。

You take a nozzle

選個管子

and you create 10 random variations on the nozzle.

10種隨機變異製造的管子

You try out all 10; you keep the one that works best.

10種都試試看，然後留下最好用的那只。

You create 10 variations on that one.

以那只為基礎，繼續做出10種。

You try out all 10. You keep the one that works best.

全都測試。然後留下最棒的。

You try out 10 variations on that one.

再從屏雀中選的那一只，繼續測試。

You see how this works, right?

各位眼見為憑。

And after 45 generations,

在45輪的測試後，

you have this incredible nozzle.

擁有了這只無敵的噴管

It looks a bit like a chess piece --

外型看似西洋棋

functions absolutely brilliantly.

運作完美

We have no idea

我們對於為何它運作無礙

why it works,

毫無頭緒

no idea at all.

打破頭腦也想不出來

And the moment you step back from the God complex --

此時，各位回到上帝情結的大頭症

let's just try to have a bunch of stuff;

讓我們來測試這一堆

let's have a systematic way of determining what's working and what's not --

系統化精密計算過的管子

you can solve your problem.

一樣可以解決問題

Now this process of trial and error

但是經由測試和錯誤

is actually far more common in successful institutions

實際上成功率比較高，

than we care to recognize.

高過我們所認為的機率。

And we've heard a lot about how economies function.

我們時有所聞經濟如何運作的方式。

The U.S. economy is still the world's greatest economy.

美國的經濟體仍是世界的龍頭。

How did it become the world's greatest economy?

如何才能成為世界最大的經濟體呢？

I could give you all kinds of facts and figures

我可以提供各位五花八門的事實和數據

about the U.S. economy,

只要關於美國，應有盡有。

but I think the most salient one is this:

然而，個人所見，其中最重要的一點是；

ten percent of American businesses

每年，

disappear every year.

美國有10％的商業實體消失。

That is a huge failure rate.

這個數據意味著驚人的失敗率。

It's far higher than the failure rate of, say, Americans.

比起美國的人口數，高的太多。

Ten percent of Americans don't disappear every year.

美國人口不會每年遞減10％。

Which leads us to conclude

總結一句，

American businesses fail faster than Americans,

比起美國人，美國的企業太容易被淘汰，

and therefore American businesses are evolving faster than Americans.

因此美國的企業經營進化神速。

And eventually, they'll have evolved to such a high peak of perfection

以致於，經營模式演化至完美極致

that they will make us all their pets --

使我們都成為他們的搖擺狗。

(Laughter)

（笑聲）

if, of course, they haven't already done so.

如果，他們還沒這麼做的話。

I sometimes wonder.

我不時在想

But it's this process of trial and error

試驗和錯誤

that explains this great divergence,

解釋中間的巨大差異

this incredible performance of Western economies.

西方經濟表現出色，

It didn't come because you put some incredibly smart person in charge.

並非靠一群絕頂聰明之人掌權。

It's come through trial and error.

靠得是透過不斷試驗和從錯誤中學習。

Now I've been sort of banging on about this

過去的幾個月以來，

for the last couple of months,

我反覆思量這個概念。

and people sometimes say to me,

周遭的人們會對我說：「提姆，

"Well Tim, it's kind of obvious.

道理顯而易見，不需一直反覆述說。

Obviously trial and error is very important.

所有人都懂試驗和錯誤是非常重要。

Obviously experimentation is very important.

每個人也都理解，實驗的精神很重要。

Now why are you just wandering around saying this obvious thing?"

所以，為何要四處跑著宣傳這些常識呢？」

So I say, okay, fine.

於是，我回答: 「我懂你的意思。

You think it's obvious?

你認為這是常識？

I will admit it's obvious

我承認道理很簡單，

when schools

當學校開始

start teaching children

教學生

that there are some problems that don't have a correct answer.

有些問題並沒有所謂的正解時。

Stop giving them lists of questions

別再給他們一成串的問題，

every single one of which has an answer.

而每個問題都有個固定答案。

And there's an authority figure in the corner

更別提，權威的主流思想

behind the teacher's desk who knows all the answers.

暗藏在老師的桌下，這些自識萬能的老師。

And if you can't find the answers,

學生如果找不到答案，

you must be lazy or stupid.

就會被視為天性懶惰或是天資駑鈍。

When schools stop doing that all the time,

學校一旦停止這般的教育時，

I will admit that, yes,

我會承認，

it's obvious that trial and error is a good thing.

試驗和錯誤會有所助益。

When a politician stands up

如果，當一名政客起身

campaigning for elected office

替選情登高一呼：

and says, "I want to fix our health system.

「我承諾當選後，會整頓醫療系統。

I want to fix our education system.

還有教育組織。

I have no idea how to do it.

不過我毫無頭續。

I have half a dozen ideas.

雖然腦子裡有半打的主意。

We're going to test them out. They'll probably all fail.

即便這些點子全都將陣亡，但是我們還是會一個一個測試。

Then we'll test some other ideas out.

然後，我們會繼續想出其他方法。

We'll find some that work. We'll build on those.

其中有些會有效。我們便可奠基於此。

We'll get rid of the ones that don't." --

剔除那些無效的方式。」

when a politician campaigns on that platform,

如同你我，選民聽到這般的牛肉，

and more importantly, when voters like you and me

從政客口中說出，

are willing to vote for that kind of politician,

會願意投他一票。

then I will admit

接下來，

that it is obvious that trial and error works, and that -- thank you.

我願意承認，試驗和錯誤這個常識有效。感謝。

(Applause)

（掌聲）

Until then, until then

在那時以前，

I'm going to keep banging on about trial and error

我將會繼續傳播我的思想，

and why we should abandon the God complex.

為何我們應禁絕上帝情結的大頭症。

Because it's so hard

因為，承認我們會失敗，

to admit our own fallibility.

是件困難事。

It's so uncomfortable.

還會令人渾身不對勁。

And Archie Cochrane understood this as well as anybody.

和各位一樣，亞契．科克倫體會到這點。

There's this one trial he ran

二次大戰結束的數年後，

many years after World War II.

他另外又做了個測試。

He wanted to test out

他想測出

the question of, where is it

心臟病發的患者

that patients should recover

該在何處較能

from heart attacks?

從病痛中康復？

Should they recover in a specialized cardiac unit in hospital,

如果醫院安排他們在特別的心臟治療區，會康復嗎？

or should they recover at home?

還是該讓他們在家靜養？

All the cardiac doctors tried to shut him down.

全部的心臟科醫生都不支持這項作法。

They had the God complex in spades.

他們都有大頭症。

They knew that their hospitals were the right place for patients,

認為醫院一定是最佳場所。

and they knew it was very unethical

他們也認為進行任何的測試

to run any kind of trial or experiment.

是有違人道。

Nevertheless, Archie managed to get permission to do this.

然而，亞契排除萬難

He ran his trial.

進行他的實驗。

And after the trial had been running for a little while,

實驗進行沒多久

he gathered together all his colleagues

他集合所有的同僚

around his table,

到他的桌前

and he said, "Well, gentlemen,

宣佈：「各位，

we have some preliminary results.

一些初步的結果已經出來了，

They're not statistically significant.

雖然數據上並不顯著，

But we have something.

但是

And it turns out that you're right and I'm wrong.

結果是我錯了。

It is dangerous for patients

在家靜養

to recover from heart attacks at home.

對病人風險太高。

They should be in hospital."

他們該待在醫院。」

And there's this uproar, and all the doctors start pounding the table

此時，一陣喧囂，所有的醫生都開始搥桌

and saying, "We always said you were unethical, Archie.

怒罵：「我們老早就警告過你了，亞契。

You're killing people with your clinical trials. You need to shut it down now.

你這麼做只是拿病人的性命開玩笑，你得立刻停止這一切。

Shut it down at once."

馬上！」

And there's this huge hubbub.

接著又是一陣叫喊嘈雜。

Archie lets it die down.

亞契試著平息眾怒。

And then he says, "Well that's very interesting, gentlemen,

接著他對他們說：各位，

because when I gave you the table of results,

我會給你們一桌的報告，

I swapped the two columns around.

交換兩個專欄的版面，因為結果饒富趣味，

It turns out your hospitals are killing people,

你們的醫院事實上荼毒生靈，

and they should be at home.

病患其實該待在家中。

Would you like to close down the trial now,

所以，各位想立刻停止實驗，

or should we wait until we have robust results?"

還是想靜待有力證據出爐呢？

Tumbleweed

風吹但草不動。

rolls through the meeting room.

會議室一片靜默。

But Cochrane would do that kind of thing.

柯克倫會做這樣的事情

And the reason he would do that kind of thing

原因是

is because he understood

他瞭解

it feels so much better

他會因此感覺良好

to stand there and say,

並且能站出來並宣佈

"Here in my own little world,

：「此地，我為王。

I am a god, I understand everything.

我是上帝，瞭解萬物，

I do not want to have my opinions challenged.

不讓任何人挑戰我。

I do not want to have my conclusions tested."

不讓任何人檢視我的研究結果。」

It feels so much more comfortable

這種感覺無以倫比。

simply to lay down the law.

不過就是清楚地表明遊戲規則。

Cochrane understood

柯克倫懂

that uncertainty, that fallibility,

不確定性、錯誤性

that being challenged, they hurt.

會被挑戰，他們會失去江城。

And you sometimes need to be shocked out of that.

有時，會震驚。

Now I'm not going to pretend that this is easy.

我不會假裝，這一切看似容易。

It isn't easy.

其實一點也不。

It's incredibly painful.

極其痛苦。

And since I started talking about this subject

自從我討論這個主題，

and researching this subject,

研究它之後，

I've been really haunted by something

有個不知名的東西一直縈繞著我，

a Japanese mathematician said on the subject.

是日本的一名數學家說的話

So shortly after the war,

戰後不久後，

this young man, Yutaka Taniyama,

谷山豐（Yutaka Taniyama）那時還是個年輕人，

developed this amazing conjecture

他發明出這個

called the Taniyama-Shimura Conjecture.

稱為「谷山- 志村猜想」的理論。

It turned out to be absolutely instrumental

日後，該猜想地位重要。

many decades later

數十年後，

in proving Fermat's Last Theorem.

費馬大定理被證明。

In fact, it turns out it's equivalent

事實上，

to proving Fermat's Last Theorem.

谷山-志村猜想和費馬大定理並駕齊驅。

You prove one, you prove the other.

證明一者，亦證出另一者。

But it was always a conjecture.

但猜想永遠是猜想。

Taniyama tried and tried and tried

谷山試了又試，

and he could never prove that it was true.

從未能夠證明正確性。

And shortly before his 30th birthday in 1958,

1958年，在他30歲生日沒多久後，

Yutaka Taniyama killed himself.

谷山便自我了斷。

His friend, Goro Shimura --

身兼同事與友人的志村五郎（Goro Shimura ）

who worked on the mathematics with him --

和他一起研究數學，

many decades later, reflected on Taniyama's life.

在數十年後，

He said,

回憶起谷山的一生，

"He was not a very careful person

他說：「他不是個小心翼翼的數學家。

as a mathematician.

身為數學家

He made a lot of mistakes.

他犯了很多錯誤。

But he made mistakes in a good direction.

但都導向正確的道路。

I tried to emulate him,

我曾試著迎頭趕上，

but I realized

但終究

it is very difficult

我理解到，這極其困難。

to make good mistakes."

特別是犯良性錯誤。」

Thank you.

謝謝各位的聆聽。

(Applause)

（掌聲）