TED演讲：试验，排除错误和万能神力
It's the Second World War. A German prison camp.
这是二战期间，一个德国集中营。
And this man, Archie Cochrane, is a prisoner of war and a doctor, and he has a problem.
这个人，阿奇·卡克伦，是战俘也是一名医生，他遇到了一个问题。
The problem is that the men under his care are suffering from an excruciating and debilitating condition that Archie doesn't really understand.
这个问题是他看护的人们正在承受病痛和衰弱的煎熬。阿奇不明白是怎么回事。
The symptoms are this horrible swelling up of fluids under the skin.
这种症状是皮肤下面有可怕水肿。
But he doesn't know whether it's an infection, whether it's to do with malnutrition.
他不知道这是一种感染，还是营养不良造成的。
He doesn't know how to cure it. And he's operating in a hostile environment.
他不知道怎样提供治疗。他是在一个充满敌意的环境里工作。
And people do terrible things in wars. The German camp guards, they've got bored.
而人们常常在战争期间做可怕的事情。德国集中营的守卫无聊的时候。
They've taken to just firing into the prison camp at random for fun.
他们会对着集中营随意扫射，来寻开心。
On one particular occasion, one of the guards threw a grenade into the prisoners' lavatory while it was full of prisoners.
特别是有一次，一个守卫朝犯人的厕所里扔了枚手榴弹，里面满是犯人。
He said he heard suspicious laughter.
他说他听到了可疑的笑声。
And Archie Cochrane, as the camp doctor, was one of the first men in to clear up the mess.
而阿奇·卡克伦，作为集中营的医生，是第一个进去处理惨状的人。
And one more thing: Archie was suffering from this illness himself.
另外， 阿奇自己也受着这个疾病的困扰，
So the situation seemed pretty desperate.
所以情况是非常危急。
But Archie Cochrane was a resourceful person.
但是阿奇·卡克伦 是一个足智多谋的人。
He'd already smuggled vitamin C into the camp, and now he managed to get hold of supplies of marmite on the black market.
他已经将维生素C带到了集中营，现在他又想办法从黑市上弄到了一些马麦。
Now some of you will be wondering what marmite is.
你们中的一些人也许会问马麦是什么。
Marmite is a breakfast spread beloved of the British.
马麦是英国人热爱的早餐面包酱。
It looks like crude oil. It tastes ... zesty.
它看上去象天然油。味道很浓。
And importantly, it's a rich source of vitamin B12.
更重要的是，它含有丰富的维他命B12。
So Archie splits the men under his care as best he can into two equal groups.
所以阿奇就把他的病人平分成两组人。他给其中的一半维他命C。他给另一半维他命B12。
He gives half of them vitamin C. He gives half of them vitamin B12.
他给其中的一半维他命C。他给另一半维他命B12。
He very carefully and meticulously notes his results in an exercise book.
他非常小心谨慎把他的结果记录在一个练习簿上。
And after just a few days, it becomes clear that whatever is causing this illness, marmite is the cure.
几天以后，结果显然表明，不管病因是什么马麦能帮助治愈这个病。
So Cochrane then goes to the Germans who are running the prison camp.
所以卡克伦跑去跟管理集中营的德国人说。
Now you've got to imagine at the moment -- forget this photo, imagine this guy with this long ginger beard and this shock of red hair.
你想象一下那一刻，别看这张照片，你想象一下这个家伙，一下巴淡黄色大胡子，一头刺眼的红发。
He hasn't been able to shave -- a sort of Billy Connolly figure.
他好久没有修面——有点象比利·康诺利那个样子。
Cochrane, he starts ranting at these Germans in this Scottish accent -- in fluent German, by the way,
卡克伦开始数落那些德国人，带着苏格兰口音，其实他讲着一口流利的德语，
but in a Scottish accent -- and explains to them how German culture was the culture that gave Schiller and Goethe to the world.
只是带点苏格兰口音，他对他们说他无法理解，能够为世界带来席勒和歌德的德国文化。
And he can't understand how this barbarism can be tolerated, and he vents his frustrations.
怎么可以容忍如此的野蛮，他发了一通牢骚。
And then he goes back to his quarters, breaks down and weeps because he's convinced that the situation is hopeless.
然后就回到了他的住处，倒头哭泣，因为他认为这个状况无可救药。
But a young German doctor picks up Archie Cochrane's exercise book and says to his colleagues, "This evidence is incontrovertible.
但是另一个年轻的德国医生拿起了阿奇·卡克伦的练习簿，对他的同僚说：“这个证据是不容质疑的。
If we don't supply vitamins to the prisoners, it's a war crime."
如果我们不给犯人提供维生素，这是战争犯罪。”
And the next morning, supplies of vitamin B12 are delivered to the camp, and the prisoners begin to recover.
第二天早上，含维他命B12的物资被送到了集中营，犯人开始恢复。
Now I'm not telling you this story because I think Archie Cochrane is a dude, although Archie Cochrane is a dude.
我现在跟你们讲这个故事，不是因为我认为阿奇·卡克伦是个人物，虽然阿奇·卡克伦的确是个人物。
I'm not even telling you the story because I think we should be running more carefully controlled randomized trials in all aspects of public policy,
我跟你说这个故事也不是因为我认为，我们在公共政策的各个方面，做随机抽样试验时，应该更小心，
although I think that would also be completely awesome.
虽然我觉得这样做真的很好。
I'm telling you this story because Archie Cochrane, all his life, fought against a terrible affliction,
我告诉你这个故事是因为阿奇·卡克伦的一生， 都在与一种可怕的痛苦做斗争。
and he realized it was debilitating to individuals and it was corrosive to societies.
而且他认识到这是一种削弱个人和腐蚀社会的东西。
And he had a name for it. He called it the God complex.
他为它取了个名字，他把它称为“万能神力”。
Now I can describe the symptoms of the God complex very, very easily.
现在我可以来描述一下“万能神力”的症状，非常非常简单。
So the symptoms of the complex are, no matter how complicated the problem,
“万能神力”的症状是：无论问题多么复杂，
you have an absolutely overwhelming belief that you are infallibly right in your solution.
你还是绝对彻底地相信，你的解决方案是准确无误的。
Now Archie was a doctor, so he hung around with doctors a lot.
阿奇是个医生，他一直和医生们在一起。
And doctors suffer from the God complex a lot.
医生就常常患有这种毛病。
Now I'm an economist, I'm not a doctor, but I see the God complex around me all the time in my fellow economists.
我是个经济学家，我不是医生，我身边的经济学家们，也经常会出现这种“万能神力”的症状。
I see it in our business leaders.
我看见它存在于我们的商业领袖身上。
I see it in the politicians we vote for -- people who, in the face of an incredibly complicated world,
我们看见它存在于我们推选的政客身上——这些人面对这及其复杂的情况时，
are nevertheless absolutely convinced that they understand the way that the world works.
仍然绝对坚信，他们知道这个世界是怎样运转的。
And you know, with the future billions that we've been hearing about, the world is simply far too complex to understand in that way.
而你们知道，我们在这里听到的未来的数十亿人的种种，用那种方法来理解这个复杂的世界显然是太简单化了。
Well let me give you an example.
让我来给你们一个例子。
Imagine for a moment that, instead of Tim Harford in front of you, there was Hans Rosling presenting his graphs.
你们想象一下，现在如果站在你们面前的不是我，而是汉斯·罗斯林在展示他的图表。
You know Hans: the Mick Jagger of TED.
你们知道汉斯：TED的米克·贾格尔。
And he'd be showing you these amazing statistics, these amazing animations.
他给你们展示了这些神奇的数据，神奇的动画。
And they are brilliant; it's wonderful work.
它们很出色，很棒的研究结果
But a typical Hans Rosling graph: think for a moment, not what it shows, but think instead about what it leaves out.
但是汉斯的图表：想一下，不是那些已经展示的，而是想一下那些没有被展示的。
So it'll show you GDP per capita, population, longevity, that's about it.
是，里面包括了人均国内生产总值，人口，寿命，就这些。
So three pieces of data for each country -- three pieces of data.
每个国家三个数据——三个数据。
Three pieces of data is nothing. I mean, have a look at this graph.
三个数据什么都不是，我是说，请看一下这张图。
This is produced by the physicist Cesar Hidalgo. He's at MIT.
这张图是物理学家塞萨尔·伊达尔戈制作的，他在麻省理工工作。
Now you won't be able to understand a word of it, but this is what it looks like.
你一个字也不懂，但是它看上去是这个样子的。
Cesar has trolled the database of over 5,000 different products,
塞萨尔用数据库搜索 5000个不同的产品，
and he's used techniques of network analysis to interrogate this database and to graph relationships between the different products.
他用网络分析的技术，提取分析数据，并用图表来表示不同产品间的关系。
And it's wonderful, wonderful work. You show all these interconnections, all these interrelations.
那是非常非常好的工作，展示了所有这些互相的关系和链接。
And I think it'll be profoundly useful in understanding how it is that economies grow. Brilliant work.
我想这些对理解经济怎样增长，是极其有用的，是杰作。
Cesar and I tried to write a piece for The New York Times Magazine explaining how this works.
塞萨尔和我试着想要给纽约时代杂志，写一篇稿子描述这个工作。
And what we learned is Cesar's work is far too good to explain in The New York Times Magazine.
我们发现 塞萨尔的研究成果远不是一篇，纽约时代杂志的文章可以描述得清楚的。
Five thousand products -- that's still nothing.
5000个产品，这还没什么。
Five thousand products -- imagine counting every product category in Cesar Hidalgo's data.
5000个产品，想象我们来数塞萨尔·伊达尔戈数据中的每个产品的目录。
Imagine you had one second per product category.
想象你每一秒钟，听到一个产品种类的名字
In about the length of this session, you would have counted all 5,000.
大约用这段会议的时间，你可以数完5000个产品
Now imagine doing the same thing for every different type of product on sale in Walmart.
现在你再想象去数各种，不同的在沃尔玛销售的产品。
There are 100,000 there. It would take you all day.
那有10万种，那大概需要一天才能数完。
Now imagine trying to count every different specific product and service on sale in a major economy such as Tokyo,
现在你想象去数，在主要经济体中销售的每种不同的特殊产品和服务。
London or New York. It's even more difficult in Edinburgh because you have to count all the whisky and the tartan.
比如，东京，伦敦或者纽约，在爱丁堡就更难了，因为你得数所有的威士忌和格子呢绒。
If you wanted to count every product and service on offer in New York -- there are 10 billion of them -- it would take you 317 years.
如果你要数在纽约提供的产品和服务，那就有100亿种，你得数317年。
This is how complex the economy we've created is.
这就是我们创造的复杂的经济体。
And I'm just counting toasters here.
而我这只是在这里数烤面包机而已。
I'm not trying to solve the Middle East problem.
我没想去解决中东问题。
The complexity here is unbelievable.
所以问题的复杂性是不可思议的。
And just a piece of context -- the societies in which our brains evolved had about 300 products and services.
我再提供一个背景数据，我们大脑演变的社会具有300多种产品和服务。
You could count them in five minutes.
你可以在5分钟里数完他们。
So this is the complexity of the world that surrounds us.
所以这就是我们所处环境的复杂性。
This perhaps is why we find the God complex so tempting.
这也许正是为什么我们发现“万能神力”这么有吸引力的原因。
We tend to retreat and say, "We can draw a picture, we can post some graphs, we get it, we understand how this works."
我们喜欢退一步说：“我们可以来画一张图，我们可以贴出图表，我们知道这是怎么运作的。”
And we don't. We never do. Now I'm not trying to deliver a nihilistic message here.
但是我们不知道，我们从来都不知道。我不是要在这里传递一个虚无主义的信息。
I'm not trying to say we can't solve complicated problems in a complicated world. We clearly can.
我不是想说我们不能在复杂的世界里解决复杂的问题。我们显然是可以的。
But the way we solve them is with humility -- to abandon the God complex and to actually use a problem-solving technique that works.
但我们需要用一种谦逊的态度来解决问题。要抛弃“万能神力”的态度。
And we have a problem-solving technique that works.
我们要用实际可行的问题解决方法。
Now you show me a successful complex system, and I will show you a system that has evolved through trial and error.
你给我举一个成功的复杂系统，我能展示给你看，看看这个系统是如何在试验和排除错误中不断演进的。
Here's an example. This baby was produced through trial and error.
这里有一个例子。这个孩子是通过试验和排除错误产生的。
I realize that's an ambiguous statement. Maybe I should clarify it.
我知道这是一个模糊的说法，也许我应该澄清。
This baby is a human body: it evolved. What is evolution?
这个孩子是人类个体，他进化了。什么是进化？
Over millions of years, variation and selection, variation and selection -- trial and error, trial and error.
经历了几百万年的变种和选择，变种和选择，试验和排除错误，试验和排除错误。
And it's not just biological systems that produce miracles through trial and error.
不只是生物系统，在试验和排除错误中缔造神奇。
You could use it in an industrial context.
你可以把它用于产业环境中。
So let's say you wanted to make detergent.
比如你要生产清洁剂。
Let's say you're Unilever and you want to make detergent in a factory near Liverpool.
比如你是联合利华，你要在利物浦旁边的一家工厂生产清洁剂。
How do you do it? Well you have this great big tank full of liquid detergent.
你怎么做呢？你有这么一大池子的液体清洁剂。
You pump it at a high pressure through a nozzle. You create a spray of detergent.
你用高压将它压过一个喷嘴，你制造了清洁剂喷雾。
Then the spray dries. It turns into powder. It falls to the floor.
喷雾干燥后就成了粉末，掉在地板上。
You scoop it up. You put it in cardboard boxes. You sell it at a supermarket.
你将它铲起，放入一个纸板盒子里。你到超市去卖。
You make lots of money. How do you design that nozzle? It turns out to be very important.
你可以赚好多钱。你怎么设计喷嘴，结果这个很重要。
Now if you ascribe to the God complex, what you do is you find yourself a little God.
如果你倾向于用万能神力来解决这个问题。
You find yourself a mathematician; you find yourself a physicist -- somebody who understands the dynamics of this fluid.
你会觉得自己是个小上帝，你会发现自己是个数学家，物理学家，是一个懂得液体动态的专家。
And he will, or she will, calculate the optimal design of the nozzle.
他或者她会计算管口的最佳设计方案。
Now Unilever did this and it didn't work -- too complicated. Even this problem, too complicated.
联合利华这么做了，但是失败了，太复杂了。即使是这样的问题，也太复杂了。
But the geneticist Professor Steve Jones describes how Unilever actually did solve this problem -- trial and error, variation and selection.
但是遗传学家史蒂文琼斯教授，讲述了联合利华其实是怎样解决这个问题的。
You take a nozzle and you create 10 random variations on the nozzle.
试验和失败，改变和选择，你拿一个管口，你随机地做出10个不同的管口。
You try out all 10; you keep the one that works best.
你测试这10个管口，你把最好的那个保留下来。
You create 10 variations on that one. 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，你测试这10个，你把最好的保留下来。
You try out 10 variations on that one. You see how this works, right?
你再这个基础上测试10个，你知道这是怎么做出来的了吧？
And after 45 generations, you have this incredible nozzle.
经过45轮测试后，你们就得到了这个很好的喷嘴管口。
It looks a bit like a chess piece -- functions absolutely brilliantly.
这个看上去有点象国际象棋棋子——工作起来绝对高效。
We have no idea why it works, no idea at all.
我们不知道，为什么它那么高效，根本不知道。
And the moment you step back from the God complex -- let's just try to have a bunch of stuff;
当你不再认为自己有万能神力——而是开始尝试一些东西；
let's have a systematic way of determining what's working and what's not -- you can solve your problem.
用一个系统的办法来决定什么办法行什么办法不行，你就能解决你的问题。
Now this process of trial and error is actually far more common in successful institutions than we care to recognize.
这个过程就是试验和排除错误的过程，事实上这是成功机构的一个很大的共性，只是我们认识得很不够。
And we've heard a lot about how economies function.
我们听过很多经济是如何运作的言论。
The U.S. economy is still the world's greatest economy.
美国的经济仍然是世界上最好的经济体。
How did it become the world's greatest economy?
它怎么变成世界上最好的经济体的呢？
I could give you all kinds of facts and figures about the U.S. economy,
我可以给你很多事实和数字，关于美国经济的。
but I think the most salient one is this: ten percent of American businesses disappear every year.
但是我想最突出的是这点：每年10%的美国企业会消失。
That is a huge failure rate. It's far higher than the failure rate of, say, Americans.
这是很高的失败率。这个失败率比美国人的失败率要高。
Ten percent of Americans don't disappear every year.
美国人并没有以10%的比率每年消失。
Which leads us to conclude American businesses fail faster than Americans, and therefore American businesses are evolving faster than Americans.
所以我们可以总结说，美国企业比美国人消失得更快。因此，美国企业比美国人进化得要快。
And eventually, they'll have evolved to such a high peak of perfection that they will make us all their pets --
而最终，他们进化到了完美的顶端，他们会把我们都变成他们的宠物——
if, of course, they haven't already done so. I sometimes wonder.
如果，他们还没有这么做的话，我有时会想。
But it's this process of trial and error that explains this great divergence, this incredible performance of Western economies.
但是试验和排除错误的过程，解释了这巨大的差异，西方经济的出色的表现。
It didn't come because you put some incredibly smart person in charge. It's come through trial and error.
它的发生不是因为你让一些特别聪明的人掌管了一切。它是从试试验和排除错误中得来的。
Now I've been sort of banging on about this for the last couple of months,
在过去的几个月里，我反复在讨论这个问题，
and people sometimes say to me, "Well Tim, it's kind of obvious. Obviously trial and error is very important.
有时有人跟我说：“提姆，这不是很显然么，很显然试验和排除错误很重要，
Obviously experimentation is very important. Now why are you just wandering around saying this obvious thing?"
很显然尝试很重要。你为什么到处讲这个显而易见的事情呢？”
So I say, okay, fine. You think it's obvious?
所以我说，好啊，你认为这个很显然是吗？
I will admit it's obvious when schools start teaching children that there are some problems that don't have a correct answer.
当学校开始告诉孩子们，有时问题不总是有正确答案的时候，我会说这很显然。
Stop giving them lists of questions every single one of which has an answer.
不再给他们一堆问题，而每个问题都对应一个答案，
And there's an authority figure in the corner behind the teacher's desk who knows all the answers.
老师的桌子背后的角落里总是站着一个知道所有答案的权威。
And if you can't find the answers, you must be lazy or stupid.
如果你找不到答案，你不是懒惰就是愚蠢。
When schools stop doing that all the time, I will admit that, yes, it's obvious that trial and error is a good thing.
当学习停止这么做时，我愿意承认，试验和排除错误显然是好事。
When a politician stands up campaigning for elected office and says, "I want to fix our health system.
当政客们站出来，竞选公职时，他们说：“我想整顿我们的医疗体系。
I want to fix our education system. I have no idea how to do it.
我想整顿我们的教育体系。我还不知道怎么做。
I have half a dozen ideas. We're going to test them out.
但是我有很多想法，我们会测试这些想法。
They'll probably all fail. Then we'll test some other ideas out.
我们可能失败。然后我们会再测试其他想法。
We'll find some that work. We'll build on those. We'll get rid of the ones that don't."
我们会发现有些有效的办法，然后在那个基础上继续建设。我们会抛弃那些无效的做法。
-- when a politician campaigns on that platform, and more importantly,
当政治家在那样的平台上竞选，更重要的是，
when voters like you and me are willing to vote for that kind of politician,
像你我这样的选举人，愿意投票给这样的政治家，
then I will admit that it is obvious that trial and error works, and that -- thank you.
那我就承认，测试和排除错误显然是有效的，而那时，我会对你们说：谢谢。
Until then, until then I'm going to keep banging on about trial and error and why we should abandon the God complex.
到那时候，到那时候，我会继续讨论测试和排除错误这个话题，以及为什么我们需要抛弃“万能神力”的态度。
Because it's so hard to admit our own fallibility. It's so uncomfortable.
因为我们很难承认我们自己是很容易犯错的。这令人感到很不舒服。
And Archie Cochrane understood this as well as anybody.
阿奇·卡克伦和其他人一样理解这一点。
There's this one trial he ran many years after World War II.
这是二战后多年，他做的一个试验。
He wanted to test out the question of, where is it that patients should recover from heart attacks?
他想要测试出，病人心脏病发作后，应该在哪里康复？
Should they recover in a specialized cardiac unit in hospital, or should they recover at home?
他们是应该在医院的心脏科康复，还是在家康复？
All the cardiac doctors tried to shut him down. They had the God complex in spades.
所有心脏科医生都想要把他挡在门外。他们完全摆出一副拥有万能神力的样子。
They knew that their hospitals were the right place for patients,
他们知道医院才是病人康复的地方，
and they knew it was very unethical to run any kind of trial or experiment.
他们觉得做任何试验都是不道德的。
Nevertheless, Archie managed to get permission to do this. He ran his trial.
无论如何，阿奇得到了试验的许可。
And after the trial had been running for a little while, he gathered together all his colleagues around his table,
他进行了试验，试验进行了一阵后， 他把他所有的同事召集到他桌旁，
and he said, "Well, gentlemen, we have some preliminary results.
说：“先生们，我们已经有了初步的结果。
They're not statistically significant. But we have something.
这些数据在统计学上并不可观。但是我们有了些数据。
And it turns out that you're right and I'm wrong.
结果表明你们是正确的我是错的。
It is dangerous for patients to recover from heart attacks at home.
让心脏病人在家康复是危险的。
They should be in hospital." And there's this uproar,
他们应该留在医院里。”这引起了一片哗然，
and all the doctors start pounding the table and saying, "We always said you were unethical, Archie.
医生们开始拍桌子，说道：“我们一直说阿奇，你这样做是不道德的。
You're killing people with your clinical trials. You need to shut it down now.
你在用临床试验杀人，你应该立刻停止。
Shut it down at once." And there's this huge hubbub. Archie lets it die down.
马上停止。” 阿奇等这一阵大吵大嚷平息后，
And then he says, "Well that's very interesting, gentlemen, because when I gave you the table of results,
说：“先生们，真是很有意思，因为当我给你们看结果的时候，
I swapped the two columns around. It turns out your hospitals are killing people, and they should be at home.
我互换了这两行资料，其实结果证明你们的医院在杀人，病人应该在家恢复。
Would you like to close down the trial now, or should we wait until we have robust results?"
你们还想让我停止试验呢，还是希望等我们得到更确切的结果？”
Tumbleweed rolls through the meeting room.
会议室安静下来。
But Cochrane would do that kind of thing.
阿奇喜欢做这样的事情。
And the reason he would do that kind of thing is because he understood it feels so much better to stand there and say,
他喜欢这么做的原因是，他知道大家更喜欢站在那里说：
"Here in my own little world, I am a god, I understand everything. I do not want to have my opinions challenged.
“在我的小世界里，我是上帝，我懂得一切，我不希望有人挑战我的观点。
I do not want to have my conclusions tested."
我不需要有人来测试我的结论。”
It feels so much more comfortable simply to lay down the law.
简单地定下法则，让人感到更自在。
Cochrane understood that uncertainty, that fallibility, that being challenged, they hurt.
阿奇懂得那种不肯定,不可靠以及被挑战的感觉，他们感到受伤。
And you sometimes need to be shocked out of that.
而有的时候我们需要把这种感觉抖掉。
Now I'm not going to pretend that this is easy. It isn't easy. It's incredibly painful.
现在我不想假装这是件容易的事情。这并不容易。这会是个痛苦的过程。
And since I started talking about this subject and researching this subject,
自从我开始谈论这个话题，研究这个话题，
I've been really haunted by something a Japanese mathematician said on the subject.
我的脑海里一直萦绕着，一个日本数学家在这个话题上说过的话。
So shortly after the war, this young man, Yutaka Taniyama,
战争一结束，这个年轻人，谷山丰，
developed this amazing conjecture called the Taniyama-Shimura Conjecture.
提出了惊人的推测，称作“谷山-志村猜想”。
It turned out to be absolutely instrumental many decades later in proving Fermat's Last Theorem.
结果为几十年后证明费马大定理，奠定了基础。
In fact, it turns out it's equivalent to proving Fermat's Last Theorem.
事实上，它和费马大定理是等效的。
You prove one, you prove the other. But it was always a conjecture.
你证明了一个，就证明了另一个。但是它只是一个猜想。
Taniyama tried and tried and tried and he could never prove that it was true.
谷山丰试了一遍又一遍，但是他无法证明它就是正确的。
And shortly before his 30th birthday in 1958, Yutaka Taniyama killed himself.
1958年的他，刚刚过了30岁生日，谷山丰结束了自己的生命。
His friend, Goro Shimura -- who worked on the mathematics with him -- many decades later, reflected on Taniyama's life.
他的朋友，和他一起研究数学的志村五郎——几十年后回顾谷山丰的生平时，
He said, "He was not a very careful person as a mathematician. He made a lot of mistakes.
他说：“他不是一个很仔细的人，作为一个数学家，他犯了很多错误。”
But he made mistakes in a good direction. I tried to emulate him,
但是他能朝好的方向犯错。我想效仿他，
but I realized it is very difficult to make good mistakes." Thank you.
但是我发现能朝好的方向犯错，很难。”谢谢
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