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试验、排除错误和万能神力

Tim Harford: Trial, error and the God complex

这是二战期间,
It’s the Second World War.
一个德国集中营,
A German prison camp.
这个人,
And this man,
阿奇·卡克伦,
Archie Cochrane,
是战俘也是一名医生,
is a prisoner of war and a doctor,
他遇到了一个问题,
and he has a problem.
这个问题是他看护的人们
The problem is that the men under his care
正在承受
are suffering
病痛和衰弱的煎熬。
from an excruciating and debilitating condition
阿奇不明白是怎么回事。
that Archie doesn’t really understand.
这种症状是
The symptoms
皮肤下面有可怕水肿。
are this horrible swelling up of fluids under the skin.
他不知道这是一种感染,还是营养不良造成的。
But he doesn’t know whether it’s an infection, whether it’s to do with malnutrition.
他不知道怎样提供治疗。
He doesn’t know how to cure it.
他是在一个充满敌意的环境里工作。
And he’s operating in a hostile environment.
而人们常常在战争期间做可怕的事情。
And people do terrible things in wars.
德国集中营的守卫无聊的时候。
The German camp guards, they’ve got bored.
他们会对着集中营随意扫射
They’ve taken to just firing into the prison camp at random
来寻开心。
for fun.
特别是有一次,
On one particular occasion,
一个守卫朝犯人的厕所里扔了枚手榴弹,
one of the guards threw a grenade into the prisoners’ lavatory
里面满是犯人。
while it was full of prisoners.
他说他听到了可疑的笑声。
He said he heard suspicious laughter.
而阿奇·卡克伦,作为集中营的医生,
And Archie Cochrane, as the camp doctor,
是第一个进去
was one of the first men in
处理惨状的人。
to clear up the mess.
另外,
And one more thing:
阿奇自己也受着这个疾病的困扰,
Archie was suffering from this illness himself.
所以情况是非常危急。
So the situation seemed pretty desperate.
但是阿奇·卡克伦
But Archie Cochrane
是一个足智多谋的人。
was a resourceful person.
他已经将维生素C带到了集中营,
He’d already smuggled vitamin C into the camp,
现在他又想办法
and now he managed
从黑市上弄到了
to get hold of supplies of marmite
一些马麦。
on the black market.
你们中的一些人也许会问马麦是什么,
Now some of you will be wondering what marmite is.
马麦英国人热爱的早餐面包酱,
Marmite is a breakfast spread beloved of the British.
它看上去象天然油。
It looks like crude oil.
味道
It tastes …
很浓
zesty.
更重要的是,
And importantly,
它含有丰富的
it’s a rich source
维他命B12。
of vitamin B12.
所以阿奇就把他的病人平分
So Archie splits the men under his care as best he can
成两组人。
into two equal groups.
他给其中的一半维他命C。
He gives half of them vitamin C.
他给另一半维他命B12。
He gives half of them vitamin B12.
他非常小心谨慎把他的结果
He very carefully and meticulously notes his results
记录在一个练习簿上。
in an exercise book.
几天以后
And after just a few days,
结果显然表明
it becomes clear
不管是病因是什么
that whatever is causing this illness,
马麦能帮助治愈这个病。
marmite is the cure.
所以卡克伦跑去跟管理集中营的德国人说。
So Cochrane then goes to the Germans who are running the prison camp.
你想象一下那一刻,
Now you’ve got to imagine at the moment —
别看这张照片, 你想象一下这个家伙
forget this photo, imagine this guy
一下巴淡黄色大胡子,一头刺眼的红发
with this long ginger beard and this shock of red hair.
他好久没有修面,有点象比利·康诺利那个样子
He hasn’t been able to shave — a sort of Billy Connolly figure.
卡克伦开始数落那些德国人,
Cochrane, he starts ranting at these Germans
带着苏格兰口音,
in this Scottish accent —
其实他讲着一口流利的德语,只是带点苏格兰口音
in fluent German, by the way, but in a Scottish accent —
他对他们说他无法理解
and explains to them how German culture was the culture
能够为世界带来席勒和歌德的
that gave Schiller and Goethe to the world.
德国文化怎么可以容忍
And he can’t understand
如此的野蛮。
how this barbarism can be tolerated,
他发了一通牢骚
and he vents his frustrations.
然后就回到了他的住处,
And then he goes back to his quarters,
倒头哭泣
breaks down and weeps
因为他认为这个状况无可救药。
because he’s convinced that the situation is hopeless.
但是另一个年轻的德国医生
But a young German doctor
拿起了阿奇·卡克伦的练习簿
picks up Archie Cochrane’s exercise book
对他的同僚说
and says to his colleagues,
“这个证据是不用质疑的
“This evidence is incontrovertible.
“如果我们不给犯人提供维生素
If we don’t supply vitamins to the prisoners,
这是战争犯罪”。
it’s a war crime.”
第二天早上,
And the next morning,
含维他命B12的物资被送到了集中营,
supplies of vitamin B12 are delivered to the camp,
犯人开始恢复。
and the prisoners begin to recover.
我现在跟你们讲这个故事,
Now I’m not telling you this story
不是因为我认为阿奇·卡克伦是个人物,
because I think Archie Cochrane is a dude,
虽然阿奇·卡克伦本来就是个人物。
although Archie Cochrane is a dude.
我跟你说这个故事也不是
I’m not even telling you the story
因为我认为我们应该更小心地
because I think we should be running
随机抽样试验。
more carefully controlled randomized trials
在公共政策的各个方面
in all aspects of public policy,
虽然我觉得这样做完全会很好。
although I think that would also be completely awesome.
我告诉你这个故事
I’m telling you this story
是因为阿奇·卡克伦的一生,
because Archie Cochrane, all his life,
都在与一种可怕的痛苦做斗争。
fought against a terrible affliction,
而且他认识到这是一种削弱个人
and he realized it was debilitating to individuals
和腐蚀社会的东西。
and it was corrosive to societies.
他为它取了个名字,
And he had a name for it.
他把它称为:万能神力(自以为有能力解决复杂问题的本事)
He called it the God complex.
现在我可以来描述万能神力的症状
Now I can describe the symptoms of the God complex very, very easily.
它的症状是:
So the symptoms of the complex
无论问题多么复杂
are, no matter how complicated the problem,
你还是绝对彻底相信
you have an absolutely overwhelming belief
你的解决方案是准确无误的
that you are infallibly right in your solution.
阿奇是个医生
Now Archie was a doctor,
他一直和医生们在一起
so he hung around with doctors a lot.
医生就常常患有这种毛病
And doctors suffer from the God complex a lot.
我是个经济学家, 我不是医生
Now I’m an economist, I’m not a doctor,
我在我周围也一直看到这种“万能神力”的症状
but I see the God complex around me all the time
出现在我的经济学家伙伴中
in my fellow economists.
我看见它存在于我们的商业领袖身上
I see it in our business leaders.
我们看见它存在于我们推选的政客身上。
I see it in the politicians we vote for —
这些人面对这及其复杂的世界
people who, in the face of an incredibly complicated world,
仍然绝对坚信
are nevertheless absolutely convinced
他们知道这个世界是怎样运作的
that they understand the way that the world works.
而你们知道,我们在这里听到的未来的数十亿人的种种
And you know, with the future billions that we’ve been hearing about,
用那种方法来理解这个复杂
the world is simply far too complex
的世界显然是太简单化了
to understand in that way.
让我来给你们一个例子
Well let me give you an example.
你们想象一下
Imagine for a moment
现在如果站在你们面前的不是我
that, instead of Tim Harford in front of you,
而是汉斯·罗斯林在展示他的图表
there was Hans Rosling presenting his graphs.
你们知道汉斯:
You know Hans:
TED的米克·贾格尔
the Mick Jagger of TED.
(笑声)
(Laughter)
他给你们展示了这些神奇的数据
And he’d be showing you these amazing statistics,
神奇的动画
these amazing animations.
它们很出色,很棒的研究结果
And they are brilliant; it’s wonderful work.
但是汉斯的图表:
But a typical Hans Rosling graph:
想一下,不是那些已经展示的
think for a moment, not what it shows,
而是想一下那些没有被展示的。
but think instead about what it leaves out.
是,里面包括了人均国内生产总值
So it’ll show you GDP per capita,
人口,寿命
population, longevity,
就这些
that’s about it.
每个国家三个数据
So three pieces of data for each country —
三个数据
three pieces of data.
三个数据什么都不是
Three pieces of data is nothing.
我是说,请看一下这张图
I mean, have a look at this graph.
这张图是物理学家塞萨尔·伊达尔戈制作的
This is produced by the physicist Cesar Hidalgo.
他在麻省理工工作
He’s at MIT.
你一个字也不懂
Now you won’t be able to understand a word of it,
但是它看上去是这个样子的
but this is what it looks like.
塞萨尔用数据库搜索
Cesar has trolled the database
5000个不同的产品,
of over 5,000 different products,
他用网络分析的技术
and he’s used techniques of network analysis
提取分析数据
to interrogate this database
并用图表来表示不同产品间的关系
and to graph relationships between the different products.
那是非常非常好的工作
And it’s wonderful, wonderful work.
展示了所有这些互相的关系和链接
You show all these interconnections, all these interrelations.
我想这些对理解经济怎样增长
And I think it’ll be profoundly useful
是极其有用的
in understanding how it is that economies grow.
是杰作
Brilliant work.
塞萨尔和我试着想要给纽约时代杂志
Cesar and I tried to write a piece for The New York Times Magazine
写一篇稿子描述这个工作
explaining how this works.
我们发现
And what we learned
塞萨尔的研究成果远不是一篇
is Cesar’s work is far too good to explain
纽约时代杂志的文章可以描述得清楚的
in The New York Times Magazine.
5000个产品
Five thousand products —
这还没什么
that’s still nothing.
5000个产品
Five thousand products —
想象我们来数塞萨尔·伊达尔戈数据
imagine counting every product category
中的每个产品的目录
in Cesar Hidalgo’s data.
想象你每一秒钟
Imagine you had one second
听到一个产品种类的名字
per product category.
大约用这段会议的时间
In about the length of this session,
你可以数完5000个产品
you would have counted all 5,000.
现在你再想象去数各种
Now imagine doing the same thing
不同的在沃尔玛销售的产品
for every different type of product on sale in Walmart.
那有10万种, 那大概需要一天才能数完
There are 100,000 there. It would take you all day.
现在你想象去数
Now imagine trying to count
在主要经济体中销售的
every different specific product and service
每种不同的特殊产品和服务
on sale in a major economy
比如,东京, 伦敦,或者纽约
such as Tokyo, London or New York.
在爱丁堡就更难了
It’s even more difficult in Edinburgh
因为你得数所有的威士忌和格子呢绒
because you have to count all the whisky and the tartan.
如果你要数在纽约提供的
If you wanted to count every product and service
产品和服务
on offer in New York —
那就有100亿种
there are 10 billion of them —
你得数317年
it would take you 317 years.
这就是我们创造的复杂的经济体
This is how complex the economy we’ve created is.
而我这只是在这里数烤面包机而已
And I’m just counting toasters here.
我没想去解决中东问题
I’m not trying to solve the Middle East problem.
所以问题的复杂性是不可思议的
The complexity here is unbelievable.
我再提供一个背景数据
And just a piece of context —
我们大脑演变的社会
the societies in which our brains evolved
具有300多种产品和服务
had about 300 products and services.
你可以在5分钟里数完他们
You could count them in five minutes.
所以这就是我们所处的环境的复杂性
So this is the complexity of the world that surrounds us.
这也许也是为什么
This perhaps is why
我们发现“万能神力”很有吸引力
we find the God complex so tempting.
我们喜欢退一步说:“我们可以来画一个图,
We tend to retreat and say, “We can draw a picture,
我们可以贴一些图表,
we can post some graphs,
我们知道这是怎么运作的。”
we get it, we understand how this works.”
但是我们不知道
And we don’t.
我们从来都不知道。
We never do.
我不是要在这里传递一个虚无主义的信息
Now I’m not trying to deliver a nihilistic message here.
我不是想说我们不能在
I’m not trying to say we can’t solve
复杂的世界里解决复杂的问题
complicated problems in a complicated world.
我们显然是可以的
We clearly can.
但是我们需要用一种
But the way we solve them
谦逊的态度来解决问题
is with humility —
要抛弃“万能神力”的态度
to abandon the God complex
而是用一个实际可行的解决问题的手法。
and to actually use a problem-solving technique that works.
我们有一个实际可行的解决问题的手法
And we have a problem-solving technique that works.
你给我举一个
Now you show me
成功的复杂系统
a successful complex system,
我就能显示给你看
and I will show you a system
这个系统是如何在试验和排除错误中不断演进的。
that has evolved through trial and error.
这里有一个例子
Here’s an example.
这个孩子是通过试验和排除错误而产生的
This baby was produced through trial and error.
我知道这是一个模糊的说法
I realize that’s an ambiguous statement.
也许我应该澄清
Maybe I should clarify it.
这个孩子是人类的身体:它进化了。
This baby is a human body: it evolved.
什么是进化?
What is evolution?
经历了几百万年的变种和选择
Over millions of years, variation and selection,
变种和选择
variation and selection —
试验和排除错误
trial and error,
试验和排除错误
trial and error.
这不只是生物系统
And it’s not just biological systems
在试验和排除错误中缔造神奇
that produce miracles through trial and error.
你可以把它用于产业环境中
You could use it in an industrial context.
比如你要生产清洁剂
So let’s say you wanted to make detergent.
你是联合利华
Let’s say you’re Unilever
你要在利物浦旁边的一家工厂生产清洁剂
and you want to make detergent in a factory near Liverpool.
你怎么做呢?
How do you do it?
你有这么一大池子的液体清洁剂
Well you have this great big tank full of liquid detergent.
你用高压将它压过一个喷嘴
You pump it at a high pressure through a nozzle.
你制造了清洁剂喷雾
You create a spray of detergent.
喷雾干燥后就成了粉末
Then the spray dries. It turns into powder.
掉在地板上,
It falls to the floor.
你将它铲起,放入一个纸板盒子里。
You scoop it up. You put it in cardboard boxes.
你到超市去卖,
You sell it at a supermarket.
你可以赚好多钱。
You make lots of money.
你怎么设计喷嘴
How do you design that nozzle?
结果这个很重要
It turns out to be very important.
如果你倾向于用万能神力来解决这个问题
Now if you ascribe to the God complex,
你会觉得自己是个小上帝
what you do is you find yourself a little God.
你会发现自己是个数学家,物理学家
You find yourself a mathematician; you find yourself a physicist —
是一个懂得液体动态的专家
somebody who understands the dynamics of this fluid.
他或者她会
And he will, or she will,
计算管口的最佳设计方案
calculate the optimal design of the nozzle.
联合利华这么做了,但是失败了
Now Unilever did this and it didn’t work —
太复杂了
too complicated.
即使是这样的问题,也太复杂了
Even this problem, too complicated.
但是遗传学家史蒂文琼斯教授
But the geneticist Professor Steve Jones
讲述了联合利华其实是怎样解决这个问题的
describes how Unilever actually did solve this problem —
试验和失败
trial and error,
改变和选择
variation and selection.
你拿一个管口
You take a nozzle
你随机地做出10个不同的管口
and you create 10 random variations on the nozzle.
你测试这10个管口,你把最好的那个保留下来
You try out all 10; you keep the one that works best.
你再拿这个做基础再做10个不同的管口
You create 10 variations on that one.
你测试这10个,你把最好的保留下来
You try out all 10. You keep the one that works best.
你再这个基础上测试10个
You try out 10 variations on that one.
你知道这是怎么做出来的了吧?
You see how this works, right?
经过45轮测试后
And after 45 generations,
你们就得到了这个很好的喷嘴管口
you have this incredible nozzle.
这个看上去有点象国际象棋棋子
It looks a bit like a chess piece —
工作起来绝对高效
functions absolutely brilliantly.
我们不知道
We have no idea
为什么它那么高效
why it works,
根本不知道
no idea at all.
当你不再认为自己有万能神力
And the moment you step back from the God complex —
而是开始尝试一些东西
let’s just try to have a bunch of stuff;
用一个系统的办法来决定什么办法行什么办法不行
let’s have a systematic way of determining what’s working and what’s not —
你就能解决你的问题
you can solve your problem.
这个过程就是试验和排除错误的过程
Now this process of trial and error
事实上这是成功机构的一个很大的共性
is actually far more common in successful institutions
只是我们认识得很不够
than we care to recognize.
我们听过很多经济是如何运作的言论
And we’ve heard a lot about how economies function.
美国的经济仍然是世界上最好的经济体
The U.S. economy is still the world’s greatest economy.
它怎么变成世界上最好的经济体的呢?
How did it become the world’s greatest economy?
我可以给你很多事实和数字
I could give you all kinds of facts and figures
关于美国经济的
about the U.S. economy,
但是我想最突出的是这点:
but I think the most salient one is this:
每年10%的美国企业
ten percent of American businesses
会消失
disappear every year.
这是很高的失败率
That is a huge failure rate.
这个失败率比美国人的失败率要高
It’s far higher than the failure rate of, say, Americans.
美国人并没有以10%的比率每年消失
Ten percent of Americans don’t disappear every year.
所以我们可以总结说
Which leads us to conclude
美国企业比美国人消失得更快
American businesses fail faster than Americans,
因此美国企业比美国人进化得要快
and therefore American businesses are evolving faster than Americans.
而最终, 他们进化到了完美的顶端
And eventually, they’ll have evolved to such a high peak of perfection
他们会把我们都变成他们的宠物
that they will make us all their pets —
(笑声)
(Laughter)
如果,他们还没有这么做的话
if, of course, they haven’t already done so.
我有时会想
I sometimes wonder.
但是试验和排除错误的过程
But it’s this process of trial and error
解释了这巨大的差异
that explains this great divergence,
西方经济的出色的表现。
this incredible performance of Western economies.
它的发生不是因为你让一些特别聪明的人掌管了一切
It didn’t come because you put some incredibly smart person in charge.
它是从试试验和排除错误中得来的
It’s come through trial and error.
在过去的几个月里, 我反复
Now I’ve been sort of banging on about this
在讨论这个问题
for the last couple of months,
有人有时跟我说
and people sometimes say to me,
“提姆,这不是很显然么
“Well Tim, it’s kind of obvious.
很显然试验和排除错误很重要
Obviously trial and error is very important.
很显然尝试很重要
Obviously experimentation is very important.
你为什么到处讲这个显然的事情呢?”
Now why are you just wandering around saying this obvious thing?”
所以我说,好啊
So I say, okay, fine.
你认为这个很显然是吗?
You think it’s obvious?
我也会承认这个很显然
I will admit it’s obvious
当学校
when schools
开始告诉孩子们
start teaching children
有时问题不总是有正确答案的时候
that there are some problems that don’t have a correct answer.
不再给他们一系列问题
Stop giving them lists of questions
每个问题都有一个答案
every single one of which has an answer.
而老师的桌子背后的角落里总是站着
And there’s an authority figure in the corner
一个知道所有答案的权威
behind the teacher’s desk who knows all the answers.
如果你找不到答案
And if you can’t find the answers,
你不是懒惰就是愚蠢
you must be lazy or stupid.
当学习停止这么做时
When schools stop doing that all the time,
我愿意承认
I will admit that, yes,
试验和排除错误显然是好事
it’s obvious that trial and error is a good thing.
当政客们站出来
When a politician stands up
竞选公职时
campaigning for elected office
他们说:“我想治理我们的健康系统
and says, “I want to fix our health system.
我想治理我们的教育体系
I want to fix our education system.
我还不知道怎么做
I have no idea how to do it.
但是我又很多想法
I have half a dozen ideas.
我们会测试这些想法, 我们可能失败
We’re going to test them out. They’ll probably all fail.
然后我们会再测试其他想法
Then we’ll test some other ideas out.
我们会发现有些有效的办法,然后在那个基础上继续建设
We’ll find some that work. We’ll build on those.
我们会抛弃那些无效的做法。“
We’ll get rid of the ones that don’t.” —
当政治家在那样的平台上竞选
when a politician campaigns on that platform,
更重要的是,象你我这样的选举人
and more importantly, when voters like you and me
愿意投票给这样的政治家
are willing to vote for that kind of politician,
那我就承认
then I will admit
测试和排除错误显然是有效的,而那时, 我会对你们说:谢谢
that it is obvious that trial and error works, and that — thank you.
(掌声)
(Applause)
直到那个时候, 直到那个时候
Until then, until then
我会继续讨论测试和排除错误这个话题
I’m going to keep banging on about trial and error
和为什么我们需要抛弃“万能神力”态度
and why we should abandon the God complex.
因为我们很难
Because it’s so hard
我们自己是很容易犯错的
to admit our own fallibility.
这令人感到很不舒服
It’s so uncomfortable.
阿奇·卡克伦和其他人一样理解这一点
And Archie Cochrane understood this as well as anybody.
这是他做的一个试验
There’s this one trial he ran
那时在二战很多年后
many years after World War II.
他想要测试出
He wanted to test out
病人心脏病发作后
the question of, where is it
应该在哪里
that patients should recover
康复
from heart attacks?
他们是应该在医院的心脏科康复
Should they recover in a specialized cardiac unit in hospital,
还是在家康复
or should they recover at home?
所有心脏科医生都想要把他挡在门外
All the cardiac doctors tried to shut him down.
他们完全摆出拥有万能的神力的样子
They had the God complex in spades.
他们知道医院才是病人康复的地方
They knew that their hospitals were the right place for patients,
他们觉得做任何试验都是
and they knew it was very unethical
不道德的
to run any kind of trial or experiment.
无论如何,阿奇得到了试验的许可
Nevertheless, Archie managed to get permission to do this.
他进行了试验
He ran his trial.
试验进行了一阵后
And after the trial had been running for a little while,
他把他所有的同事召集起来
he gathered together all his colleagues
在他的桌子旁,
around his table,
他说:“先生们,
and he said, “Well, gentlemen,
我们已经有了初步的结果。
we have some preliminary results.
这些数据在统计学上并不可观
They’re not statistically significant.
但是我们有了些数据
But we have something.
结果表明你们是正确的我是错的
And it turns out that you’re right and I’m wrong.
让心脏病人在家
It is dangerous for patients
康复是危险的
to recover from heart attacks at home.
他们应该留在医院里。 ”
They should be in hospital.”
这引起了一片吵嚷, 医生们开始拍桌子
And there’s this uproar, and all the doctors start pounding the table
说:“我们一直说阿奇你这样做是不道德的”
and saying, “We always said you were unethical, Archie.
你用你的临床试验在杀人,你应该现在就停止。
You’re killing people with your clinical trials. You need to shut it down now.
马上停止。“
Shut it down at once.”
阿奇等这一阵大声的吵嚷
And there’s this huge hubbub.
安静下来后
Archie lets it die down.
说:“先生们, 真是很有意思,
And then he says, “Well that’s very interesting, gentlemen,
因为当我给你们看结果的时候,
because when I gave you the table of results,
我互换了这两行资料
I swapped the two columns around.
其实结果证明你们的医院在杀人,
It turns out your hospitals are killing people,
病人应该在家恢复。
and they should be at home.
你们还想让我停止试验呢
Would you like to close down the trial now,
还是希望等我们得到更确切的结果?”
or should we wait until we have robust results?”
会议室如风滚草
Tumbleweed
卷过一般安静下来
rolls through the meeting room.
阿奇喜欢做这样的事情
But Cochrane would do that kind of thing.
他喜欢这么做的原因是
And the reason he would do that kind of thing
他知道
is because he understood
大家更喜欢
it feels so much better
站在那里说:
to stand there and say,
“ 在我的小世界里,
“Here in my own little world,
我是上帝, 我懂得一切
I am a god, I understand everything.
我不希望有人挑战我的观点。
I do not want to have my opinions challenged.
我不需要有人来测试我的结论。”
I do not want to have my conclusions tested.”
简单地定下法则
It feels so much more comfortable
然人感到很自在。
simply to lay down the law.
阿奇懂得
Cochrane understood
他们对那种不肯定的, 易错的
that uncertainty, that fallibility,
被挑战的感觉感到不爽
that being challenged, they hurt.
而有的时候我们需要把这种感觉震落掉
And you sometimes need to be shocked out of that.
我不想假装这是件容易的事情
Now I’m not going to pretend that this is easy.
这并不容易
It isn’t easy.
它会是个痛苦的过程
It’s incredibly painful.
当我开始谈论这个话题
And since I started talking about this subject
研究这个话题
and researching this subject,
我脑海里一直环绕着
I’ve been really haunted by something
一个日本数学家在这个话题上说的话
a Japanese mathematician said on the subject.
战争一结束
So shortly after the war,
这个年轻人,谷山丰
this young man, Yutaka Taniyama,
提出了惊人的推测
developed this amazing conjecture
谷山-志村猜想
called the Taniyama-Shimura Conjecture.
结果几十年后
It turned out to be absolutely instrumental
为证明费马最后定理
many decades later
奠定了基础
in proving Fermat’s Last Theorem.
事实,它和费马最后定理是
In fact, it turns out it’s equivalent
同等的
to proving Fermat’s Last Theorem.
你证明了一个,就证明了另一个
You prove one, you prove the other.
但是它只是一个猜想
But it was always a conjecture.
谷山丰试了一遍又一遍
Taniyama tried and tried and tried
但是他不能证明它是正确的
and he could never prove that it was true.
1958年他刚刚过了30岁后
And shortly before his 30th birthday in 1958,
谷山丰结束了自己的生命
Yutaka Taniyama killed himself.
他的朋友,志村五郎
His friend, Goro Shimura —
和他一起研究数学
who worked on the mathematics with him —
几十年后回顾谷山丰的生平时
many decades later, reflected on Taniyama’s life.
他说
He said,
“他不是一个很仔细的人
“He was not a very careful person
作为一个数学家
as a mathematician.
他犯了很多错误
He made a lot of mistakes.
但是他能朝好的方向犯错
But he made mistakes in a good direction.
我想效仿他
I tried to emulate him,
但是我发现
but I realized
能朝好的方向犯错
it is very difficult
很难。”
to make good mistakes.”
谢谢
Thank you.
(掌声)
(Applause)

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