斯蒂芬·沃尔夫朗谈数学、哲学及其他

大家好，我是劳伦斯·克劳斯，欢迎收听《起源播客》。本期嘉宾是位极具魅力的人物——斯蒂芬·沃尔夫勒姆，他拥有多重职业身份。斯蒂芬最初是位少年科学家，非常年轻，基本靠自学成才，没怎么拿学位就直接去加州理工学院攻读博士，我记得他21岁就获得博士学位，还曾与理查德·费曼共事。之后他继续从事物理研究，去过普林斯顿高等研究院等地，但决定拓展新领域。他向来是个打破常规的人，认为世界需要一种在计算机上进行数学运算的新方法。

Hi, I'm Lawrence Krauss and welcome to the Origins Podcast. This episode is with a fascinating individual, Stephen Wolfram, who's had many different careers. Stephen began as a young scientist, a very young scientist, self educated, basically did without many degrees and went on to do a PhD at Caltech after educating himself and I think got it when he was 21 and was working with Richard Feynman. Then he went on to continue to do physics and went to the Institute for Advanced Study among other places, but decided to branch out. He's always been kind of an iconoclastic individual and decided that what the world needed was a new way of doing mathematics on computers.

他创造了最早的符号运算程序之一，不仅能进行数字计算，还能实现符号运算和代数处理。他创立的Mathematica软件及其公司，如今已成为绝大多数科学家（至少物理学家）处理复杂代数运算的主要工具，其功能远不止于此。但斯蒂芬并未满足于Mathematica的成就，期间他始终在研究如何通过细胞自动机等概念探索基础物理学的新理解途径。

And he created what was one of the first symbolic manipulation programs, something that allowed you to do not just number crunch with computers, but actually do symbolic manipulation, do algebra. And Mathematica, the program he created and the company he leads, became really the prime way that most scientists, most physicists at least now, do complex algebra. They use mathematics to do it, as well as much more. But Stephen didn't rest on his laurels of just doing Mathematica. During that time, he's always in doing research and following up on ideas of something called cellular automata to think about new ways of trying to understand fundamental physics.

他对自己提出的新科学方法在物理学领域的潜力做出重大断言，声称通过符号运算和细胞自动机理论能重现所有基础物理现象。这正是我想与他探讨的，我们也确实深入讨论了这点。我们聊了他的早期物理学生涯，谈到诸多话题——包括打字技能的重要性，这场精彩对话希望你们喜欢。若在YouTube观看，请考虑订阅我们的频道，这对双方都有益：既支持我们，也能及时获取新节目。若想无广告收听，欢迎在Patreon订阅支持本播客背后的非营利组织——起源项目基金会。

He's made great claims about what his new way of doing science as he talks about it might do for understanding physics. Claims in fact that he can really reproduce all of fundamental physics with his symbolic manipulation and the cellular automata ideas and I wanted to talk to him about that and we did. We talked about that, we talked about his early history in physics, we talked about many things including how important it is to know how to type, and it was a fascinating conversation that I hope you'll enjoy. If you're watching this on YouTube, hope you'll consider subscribing to us on YouTube because it'll help us, but it'll also help you because you'll learn about new episodes. If you want to watch this without advertisements, hope you'll consider subscribing to our podcast on Patreon, which will help support the foundation that runs this podcast, the nonprofit foundation, the Origins Project Foundation.

Patreon的资助是维持基金会运作和节目制作的关键。希望您能考虑通过这种方式加入我们的社区。无论您以何种形式收听，都愿您享受本期内容，我相信定会如此。保重。那么斯蒂芬，非常感谢你参与这次播客录制。

The funds from Patreon help it continue to exist and do the programs it does. So I hope you'll consider becoming a member of our community that way. Either way, no matter how you watch it or listen to it, I hope you enjoy this episode and I'm pretty sure you will. Take care. Well, Stephen, thanks a lot for coming to do this podcast with me.

虽然我们许久未见，但见到你总是令人愉快。

It's been a while since we've seen each other, but it's always good to see you.

是啊，很高兴见到你——至少是以虚拟形式。

Yep. Nice to see you and at least in virtual form.

以虚拟形式相见。

In virtual form.

自从我们上次见面，肯定得有十年了吧

It have been it must be like a decade since we actually

面对面的话。面对面。虽然据我理解——我们稍后会谈到——虚拟与现实其实没有区别，如果我能领会你部分研究的话，不过这个暂且放一边。但至少十年了，我们相识更久，追溯起来。我试着回忆，实际上我们得追溯到四十年前。

Physically. Physically. Although it's from what I understand, and we'll get to it, that there's really no difference between the virtual and the real, if I can understand some of your work, but we'll get to that. But it's been at least a decade, but we go back, we go back. I was trying to think we go back forty years actually.

差不多。对。对。而且，是的。

Probably. Yeah. Yeah. And, yeah.

那时候你...我们都从事粒子物理研究。

Well, you were you were we were both in the particle physics business.

我们确实都从事粒子物理研究。我会...你知道的，我会回溯那段时光，但既然这是起源播客，我想追溯得更远些。我想从你的出身谈起，这很有趣。我又了解到一些新情况。

We Yeah. Were both in the particle physics business. I'll, you know, I'll go back there, but I want to go back even further as we as we delve since it's the origins podcast. I wanted to, I wanted to begin with your origins and, which are interesting. And I learned a little bit more.

我原本知道一些关于你的事，但在斯蒂芬·威尔霍普的传闻中，我又了解到更多——也许部分属实。有件事我很感兴趣：你父母...我一直在试图...我总喜欢探究人们科学兴趣的源头。你母亲是牛津大学的哲学研究员对吧？她获得博士学位了吗？

I knew, I knew some things about you already, but in the, in the lore of Stephen Willhope from I've Learned Some More, maybe some of it's true. One thing that's interested me, so your parents were I was trying to, I always like to figure out where people might've gotten their interest in science or things. Your mother was a philosophy fellow at Oxford, right? Yeah. Does she have a PhD?

用美式说法就是哲学教授。

Translated into American, it will be philosophy professor.

是啊，是啊。他们没这么称呼

Yeah, yeah. They didn't call

他们。在牛津，他们称其为哲学导师。

them that. They call them philosophy dons in Oxford.

对，完全正确。那她有没有提到自己拥有哲学博士学位？她真的有博士学位吗？

Yeah, absolutely. So did she have an answer that she had a PhD in philosophy? Did she have a PhD?

她的博士学位其实是人类学的，因为那时候他们并不真正授予哲学博士学位。颇具讽刺意味的是，哲学被认为是一个无法成为哲学博士的领域。

A PhD was in anthropology because they didn't actually do philosophy PhDs back in those days. Philosophy was thought to be a field in which you couldn't get to be a doctor of philosophy ironically enough.

没错，确实如此。这可能是个好主意。是的，这很可能是个非常好的主意。所以是人类学。我首先好奇她对哲学的兴趣是否可能是形式逻辑那一类，但也许不是。

Yeah, that's right. Was probably a good idea actually. Yeah, that's probably a very good idea. So it was anthropology. I wonder first whether her interest in philosophy might've been formal logic and that end of philosophy, but perhaps not.

实际上她写过一本相当有名的哲学逻辑教科书，这与形式逻辑不同。所以她不是一个数学倾向的人。她更像是语言哲学那一类的人。她在这些方面做了很多工作。我是说，不，我对科学的兴趣来自于与我父母所做之事正交的方向。

She wrote actually a reasonably well known textbook on philosophical logic, which is different from formal logic. So she was not a mathematically oriented person. She was more of a kind of linguistic philosophy kind of person. And she worked a bunch on those kinds of things. She, I mean, no, my interest in science came from being orthogonal to what my parents did.

实际上有两个来源，一是与我父母的事业方向垂直，二是来自太空计划，那是我成长的上世纪60年代的大事，你知道，我那时还小，对未来充满兴趣。未来似乎就是像太空计划那样的事物。

Actually two things that came from, it came from being orthogonal to my parents and it came from the space program, which was kind of the big thing in the 1960s when I was growing up was kind of, you know, I was young, I was interested in the future. The future seemed like it was things like the space program.

当然。

Sure.

所以这让我产生了兴趣。我的意思是，有一位哲学教授母亲确实有些有趣的体验，比如向她的哲学界朋友解释某些科学概念时——虽然她对科学了解不多——他们总会反问‘你怎么能确定这个？’。啊，对了，我记得小时候大约10、11岁时，曾与一位后来才知道是著名时间哲学家的女士有过激烈争论。

And so that's, you know, it got me interested. I mean, having a philosophy professor as a mother has interesting features like, you know, it's like you explain something, not that she knew much about science, but I would explain something to particularly to friends of philosophy, friends of hers. And they would always say, well, how can you know that? Oh, great. I actually, there was a, I remember a philosopher of time that I remember when I was a young lad, probably, I don't know, 10, 11 years old.

当时我坚持说‘我理解相对论，事情就必须是这样运作的’等等。她反问道：‘你如何证明生物体也会经历时间膨胀？’——就像你能用时钟验证那样。我当时只能回答‘它就必须是这样’，其实并不完全明白原理。直到五十年后的现在，我才真正理解了原因。

I remember this big argument with this woman who was a quite well known philosopher of time as it turned out. And I was like, look, I understand relativity. This is how things have to work, etcetera, etcetera, etcetera. She was like, so one of the things that came up there was I'm like, okay, there's this time dilation, all that kind of thing. And she's like, how do you know that a human, a biological thing is going to actually show time dilation?

后来研究GPS卫星时我突然想到：天啊，我们终于有办法观测时间膨胀了！就用GPS卫星...哦等等，它们已经自动校正了时间膨胀效应。

It's like, okay, you can figure it out for a clock, etcetera, etcetera, etcetera. And I was like, but it just has to work that way. I didn't really quite know why. Now I think I do finally know why, but that's fifty years later or something. But I was kind of, and then later on when I was like thinking about that and I was learning about GPS satellites and things, I was thinking, gosh, we finally have a way to actually see time dilation.

让我们用GPS卫星来验证——哎呀，它们已经反向校正了时间膨胀。

Let's use the GPS satellites. Whoops, they back correct for time dilation.

这正是关键所在。如果不校正，我们连最近的剧院都定位不到。

That's the whole point. If they didn't, we wouldn't be able to get to the nearest theater or anything else.

这其实很耐人寻味——为什么GPS卫星不受时间膨胀影响？那么乘坐飞船的老鼠或人类，凭什么就该比卫星更遵循时间膨胀呢？四十年前那场对话让我后来有点尴尬：当年那个固执的、崇尚科学的10岁小孩坚持‘事情就该这样运作’，其实真相要更微妙些。

It's kind of amazing amazing. That they don't obey time dilation. And the question is the rat or the human going in the spaceship, why should they any more obey time dilation than the GPS satellite? So that's an example of my kind of, I felt a bit silly, you know, forty years after that conversation realizing that to the insistent young, you know, science oriented 10 or 11 year old was like, no, no, that's how it has to work. Actually it's a little bit more subtle than that.

嗯，你知道，当你谈到时间哲学家这个概念时很有趣，这对我来说是个惊人的概念，但后来我突然想到，在某种意义上，至少从你最近的一些文章来看，你在某种程度上已经成为这样的人了，至少你部分地成为了一位哲学家。

Well, is, you know, it's funny when you talked about a philosopher of time, which is an amazing concept to me, but then occurred to me that in some sense, at least reading some of your recent stuff, that's kind of sort of what you become in a way, at least part of what you've become is a philosopher.

是的，我正在更多地了解时间究竟是什么。

Yeah, I'm learning a bit more about what time actually is.

我们最终会谈到这个的。你会向我解释，因为...是的，虽然我读过你的文章，但我不确定自己是否完全理解，不过我相信这种理解是可以加深的。但很高兴你们有过那些讨论，有趣的是索希更偏向语言学，而你父亲，你说他成为了一名小说家。正如你所说，他们两人都完全不擅长数学。

And we'll get to that eventually. And you'll explain to me because I because yeah, I haven't think I understand having read your stuff, but I'm sure I could be that understanding could be approved upon. But it was nice that you had those discussions, but it is interesting that Soshie was more linguistic and your father, you said became a novelist. Neither of them, as you say, were mathematical at all.

不，不，我父亲主要是商人，写小说算是种爱好。你看，我是长子，有个比我小十岁的弟弟，但实际上我就像独生子，而且可能是个古怪的孩子。

No, no, My father was, I mean, mostly a businessman and wrote novels as a kind of a hobby. That was, you know, they were, look, I was a first child, I have a younger brother who's ten years younger than me, but I was effectively an only child and probably a strange child at best.

我猜也是。但如果你真的在11岁就有那些对话，那确实是件很有益的事。因为当被问到'你怎么知道这个？'时，这种提问至少会促进某种科学思维的形成。我是说，你具体是怎么知道的？

I suspect. But the fact that if you really had those conversations at age 11, if it was really those, I mean, that's kind of a useful thing because asking, if they ask you questions, how do you know that? That kind of promotes at least a kind of scientific thinking. I mean, how operationally do know that?

我那时常举的例子是：看吧，哲学就是疯子的学问。你们怎么能就同样的问题争论两千年？这根本就是个愚蠢的领域。

One example that I would always say at the time, it's like, look, philosophy is just crazy. You know, how can you guys have been debating the same questions for two thousand years? This is just a stupid field.

我确实，我有很大的...

I I do, I have great

科学，我们推动进步。

Science, we make progress.

嗯，我过去也这么说过，为此收到了不少骂我的邮件，不过。

Well, that's what I've said in the past and I've got a lot of hate mail for that, but.

我认为这是个微妙的问题。实际上，最近让我大为惊讶的是，通过自己的科研工作，我终于理解了哲学家们试图表达的许多观点——他们往往在用超前千年的术语描述事物。所以他们的言论在今天听来有些古怪。但当你真正从科学角度理解这些观点的真实性时，它们就显得没那么荒谬了。

Well, I think it's a subtle issue. And I think one of the things that's been a big surprise to me actually in recent times is from science that I've done, I finally understand a bunch of what philosophers were trying to say often in terms that they didn't have. They trying to describe things in terms that were a thousand years after their time, so to speak. And so what they sound, what they say sounds kind of goofy to us today. But as you actually understand what really seems to be true scientifically, it starts to seem a bit less goofy.

记得小时候有次参加聚会，大概五岁左右，满屋子大人就我一个孩子，在场有很多哲学家。一位白发苍苍的哲学家走过来——就像我现在可能也会这么做——他说'和这孩子聊天可能比跟这些中年人有意思多了'。

But you know, I'm kind of one of my early memories or something from sort of the, what will you do when you're grown up type question. Probably was about five or something. And I was at some party with a bunch of adults with, and I was probably the one kid at the party and there was a bunch of philosophers. And so some old white haired philosopher comes over to me as I would do probably in the current time and says, the kid's probably more interesting to talk to than a bunch of these middle aged adults.

是啊，当然。

Yeah, sure.

我和那位老先生聊了很久，具体内容记不清了。临走时他自言自语地嘟囔着，我听见他说：'总有一天那孩子会成为哲学家，或许需要些时日'。

So I have this long conversation with this guy. I forget about what, and then he's walking away and he kind of mumbles to himself. I can hear him sort of mumbling, you know, one day that child will be a philosopher. It may take a while.

我想那算是种赞美。挺好的。

I suppose that was a compliment. That's very good.

是的，我想是的。五十年后或更久，也许更准确些，可能是这样。

Yeah, I suppose, yes. Fifty years later or something, it's more, maybe that's right.

顺便说一句，你比我小五岁，我想。所以阿波罗登月时你可能还太小，但——

Well, by the way, you're five years younger than me, I think. So you would have been a little young for the Apollo landings, but-

哦，我看了那些。我看了那些。熬夜直到——

Oh, I watched those. I watched those. Stayed up until-

哦，你也是。我熬了一整夜。我在楼下地下室建了个小指挥中心，然后——

Oh, you too. I stayed up all night long. I had a little command center downstairs in the basement and-

哦，好吧。对我来说，大概是凌晨两点。英国时间凌晨两点踏上月球。是的，我确实看了。实际上，我以前非常密切关注这些。

Oh, okay. Well, for me, it was like two in the morning, I think. The setting foot on the moon was two in the morning British time. Yes, I did watch that. In fact, I used to keep very close track of that.

我一直是大量文字材料的创作者。所以我至今还保留着关于那些航天器精确事件的所有笔记，虽然我不太明白为何如此着迷，但这有点像，嗯，关乎未来的事情。谢天谢地我没有一直专注于太空，否则我可能要在休眠中等待五十年，直到人们重新重视它。但后来，大约11岁左右，我开始对设计航天器产生兴趣。

I was always a producer of lots of written material. So I still have all of the kind of notes that I took about the precise things that happened in all those spacecraft, which was, I don't quite know why I was so into it, but it was kind of a, well, was a kind of, this is something about the future. Now, thank goodness I didn't sort of stay concentrated on space because then I would have been hibernated for fifty years until people actually started taking it seriously again. But no, mean, I started kind of, oh, I guess I got interested around probably age 11 or so in 10, 11, something like that. I'd been sort of in this, I'm gonna design spacecraft.

我不确定那具体意味着什么。于是我想，那我得学物理。后来我真的迷上了物理，12岁时还在网上发布过一份物理简明指南之类的东西，始终离不开物理。

I'm not clear what that meant. And so then it was like, then I have to learn physics, I guess. And then I got really interested in physics and I started doing things like I have this artifact that somewhere on the web from when I was like 12 of this kind of concise directory of physics, which is always physics.

我看了你的小剪贴簿。今天一直在翻阅它，深入探索。真是太棒了。

I looked at your little scrapbook. I've been going through it today, delving into it. It's amazing.

作为一个观察人类行为的人，我觉得有趣的是，你看到的是一堆物理事实和数据表格之类的东西。而我看着Wolfram Alpha，心想，天哪，我这辈子一直在做同样的事。实际上，当我重新翻出12岁时的那些记录时，第一反应就是把其中一些数字输入Wolfram Alpha，看看会有什么结果。是的，

Well, what's kind of funny about that to me as an observer of the human condition is, you look at that, it's a bunch of facts about physics and tables of data and things like that. And it's like, and I look at Wolfram Alpha and it's like, oh my gosh, I've been doing the same thing all my life. It's kind of, and actually when I kind of resurfaced that thing from when I was 12, sort of one of my first instincts was take some of those numbers, type them into Wolf and Alpha, see what was Yeah,

这种联系我完全能理解。事实上，以我对你的了解，回顾那些内容让我感到非常着迷。我并不感到惊讶，但没想到你是个如此严谨的记录者。我认识的人里只有我朋友艾伦·古斯会这么做，他基本上每晚都会记录当天发生的所有事情。

know that connection was not lost on me. In fact, it's been fascinating for me to look back at some of that knowing you as I do and see some of that. I didn't, I'm not surprised, but I didn't realize that you were so prestigious and notetaker and recorder of things. The only person I know who does that with my friend, Alan Guth, basically every night, more or less records everything that's happened during the day. I

我不知道他有这个习惯。

didn't know that about him.

嗯，我猜他现在还在这么做。我们共事时他总是这样，这很了不起，但有时也让人沮丧，因为他常常因为要记录每件事而进度落后。

Well, I I assume he still does. When we worked together, it was always that way and it was remarkable and sometimes frustrating because he'd often be behind because he was trying to keep track of every single thing. And it's

我记录的大部分内容，可能比任何人都更详细地收集了自己的个人分析数据。

Most of what I keep track of, I've recorded probably more sort of personal analytics data on myself than I think anybody else.

真是令人震惊。

Was shocked.

这一切都是被动的。我的意思是，如果我需要动手去做，虽然我确实会抬起手指敲击键盘，但这些动作只是被被动记录下来的。好吧。这不是那种需要我主动去做的事情，否则免谈，根本不可能实现。

All of it is passive. I mean, if I had to lift a finger to do it, I mean, I lift my fingers and type keystrokes, but they're just passively recorded. Okay. It's not, you know, if I actively did it, forget it, not gonna happen.

是啊，那样你就不会说这些了。顺便问一下，日志里有什么？以防有人好奇，你记录了你一生中敲击了多少次键盘。不知道你是否——

Yeah, then you wouldn't tell this. By the way, what's the log? Just in case people wondered, you've recorded how many keystrokes you've typed in your entire life. Don't know if you

已经度过了相当完整的一生，

have a quite entire life,

但——差不多吧。不过你屏幕左上角有没有显示什么小东西？那是——

but- Almost. But did you have a little thing on the upper left hand corner of your screen or anything? What's

具体数字我其实不知道。这是个有趣的想法。我没有那个功能。不过每天敲击的键数我是知道的。比如昨天，我记得昨天敲了五万次键盘。

the I number don't know that actually. It's an interesting idea. I don't have that. Every day, I do know how many keystrokes I've typed each day. So for example, I think yesterday, yesterday was a 50,000 keystroke day.

所以还算不错。那是个相当可观的数字

So that was okay. That was a decent Is

这对你来说是平均水平吗？五万次还是——

that an average day for you? 50,000 or a

不，实际上比平均水平要高。我当时在写一些东西，然后——

good No, it's actually higher than average. I was writing some stuff and-

你写作时确实从不敷衍了事，让我这么说吧。

You do write in, do write, when you write, it's never a sound bite. Let me put it that way.

嗯，我知道，我知道。我希望自己能写得更简洁些。十年前我写《一种新科学》时，那本书虽然厚达1200页，但从某种意义上说，它是最精简的——每一页我都尽可能压缩内容。后来我意识到这种优化方式不对，也不想再花十年隐居写作。所以现在我写作时更倾向于自然输出。

Well, know, I know, I know. I wish I could write shorter. Was, know, when I was working on my New Kind of Science book for a decade, that book is in a sense, even though it's a big book, 1,200 pages long, it is sort of a minimal length book in the sense that every page it's kind of compressed as much as I can compress it. I kind of decided that wasn't the right optimization and I didn't want to spend another ten years as a hermit writing things. So now when I write stuff, I write at sort of output.

我边思考边写，想到什么就写什么。虽然可能压缩四分之三的内容，但我觉得写得详尽些更好。反正内容会更丰富，而且这样能真正完成，而不是说'明年完成'却永远搁置。

I write it as I think about it and I write whatever I'm gonna write. And I can probably compress it by a factor of four or something, but I figure it's better to write it at more length. There's probably more stuff in there anyway. And then I'm actually gonna get it done rather than saying, well, one year I'll get it done and never get it

是啊，众所周知，写简短内容反而更耗时。就像那句名言'如果有更多时间，这封信会更短'。忘了是哪位英国名人说的，肯定会有人提醒我。我在想你对物理的兴趣是怎么产生的，早期是对数学有兴趣吧？

Yeah, it takes, you know, as everyone knows, it takes a lot more time to write something shorter. As you know, there's that famous letter, if I'd had more time, this letter would be shorter. Yeah. I forget one of the British, someone famous said that, and I'll no doubt someone will let me know who said it. It was, I was trying to think where the interest in physics came in, there was an early interest in math.

你说过自己算术不好，但我查过你的成绩单，其实还不错。虽然据说你当时背乘法表有点困难——现在用计算器就能解决这个问题。那么到底是什么让你迷上数学的呢？

Now there's this, you know, you said somewhere, Oh, I wasn't very good in arithmetic. I actually looked at your grades there in one of your things. They weren't too bad actually. I mean, it was said, you know, you were having trouble with your times tables or something like that, which now of course can be done passively too, because mathematical I'll give you that. What turned you on to mathematics then?

是因为...

Was it I the

什么都不需要。什么都不需要。因为我对物理学感兴趣。数学某种程度上只是做物理不得不面对的麻烦。

need nothing. Nothing. Because I interested in physics. Mathematics was sort of a necessary evil for doing physics.

没错，正是这样。我就在想这个问题。你需要用物理做什么，所以基本上你就学了它。

Yeah, exactly. That's what I was wondering. What you needed to do physics, so you learned it basically.

对。我是说，其实我并不喜欢学数学，所以我才让计算机替我算。但后来发生的是，我开始对事物的本质产生了兴趣？什么是最根本的抽象概念？由此，我深深陷入了数学的高级领域及其抽象性等等。

Right. I mean, I actually didn't like learning it and that's why I got computers to do it for me. And that's kind of the But subsequently, what has happened is that I got interested in kind of what is the essence of things? What is the sort of ultimate abstractions of things? And from that, I've gotten very deeply pulled into sort of advanced areas of mathematics and kind of abstraction of mathematics and so on.

事实上，我目前的一个项目就是最终理解数学究竟是什么。我们或许可以稍后讨论这个。好的，

In fact, one of my current projects is finally to understand what mathematics is. We can maybe come to that. Okay,

我会把这个放在最后。

I'll put that at the end there.

我认为不，我是说，对我来说，我从来不是，你知道，我觉得学校教数学的方式，至少在我那个年代的英国学校，充斥着大量数学技巧的把戏，而我对此毫无兴趣。就像，有这么一个特定的积分，你可以用某种巧妙技巧解出来。而我后来在做积分时（因为物理需要），学会了使用这些大型工业机器般的解法。比如把积分转换成乘积，现在可能是梅耶尔G函数，但那时是多重对数之类的奇特函数。你基本上构建了一个极其枯燥但高效的工业机器来碾过所有积分。

I think the No, mean, for me, I was never, you know, I think the way one gets taught mathematics in school and so on, at least in British schools of the time, it was an awful lot of math trickery, which I was never really into. It's like, there's this particular integral and you can do this particular one because there's this cool trick for doing it. And what I learned at some point in like doing integrals, because I want to do them for physics, was these big industrial machines. Like you turn an integral into a product of, well, nowadays it will be Mayer G functions, but then it was like polylogarithms and other such things, all these kinds of exotic functions. And you basically make a completely boring to implement industrial machine that will grind through all these integrals.

这些方法主要是为便于计算机计算设计的，但手工也能操作。回想那时，我甚至——要知道，我勉强通过了物理本科第一年的课程。考试还拿了第一，但这更多归功于考试本身而非我，因为那时我已经能处理专业级的物理问题了。唯一的问题是，如果你用完全另类的方法得出答案，这算数吗？因为我显然无法用那些——你知道的——针对特定积分的巧妙换元法解题，这完全不是我的风格。

And mostly that was set up to be easy to do on a computer, but even by hand, would do those things. And I think back in those days, well, even did, you know, I sort of made it through my sort of first year of physics undergraduate type thing. And I think I even came top in the exams, a tribute to the exams more so than to me, would say, because it's, I mean, by that point, I was kind of able to do sort of professional grade physics stuff. And the only question was, you know, if you could get to the answer, but using completely alien methods, was that okay? Because I certainly couldn't get to the answer using the, you know, there's this trick for doing a trick substitution of this and that kind, and it just happens to work for this integral, not my kind of thing at all.

你这么说很有意思。我要提前插一句，因为我实在忍不住——你那位老友理查德·费曼，我也认识他，不仅认识，我还为他写过传记。他以发明积分技巧著称，事实上他提出的费曼图在粒子物理计算中是核心工具。为了运用这些图表，他不得不开发了大量计算技巧。

Interesting that you say that. I'm gonna jump ahead, because I can't resist because your old pal who I knew as well, Richard Feynman, and you know, not only knew him, I wrote a book about him. He was famous for developing tricks to do integrals. One of the things he in fact is essential part of, in some sense, Feynman diagrams to understand, to calculate in particle physics. In order to use them, he had to develop a lot of tricks to do them.

是吗？

Did you?

嗯，我和他深入讨论过这个问题。当时我正在开发SMP系统（算是Mathematica的前身或工作语言），那段时间我们频繁交流。他不断告诉我'你应该这样做'、'该用这个方法'。他的技巧其实超越了普通技巧的范畴——那是成体系的方法论，比如对参数进行微分之类的系统操作。记得几年前在他家时，他拿出些关于费曼图积分的笔记，说是五十年代末整理的。

Well, I talked to him a bunch about that because when I was working on SMP, which was kind of for honor of Mathematica or working language and so on, he was, you know, I was talking to him a lot at that time and he kept on telling me, you should do this, you should use this method. You should have And his tricks were a little bit more general than tricks. I mean, he had definite methods of, you you would take this general thing and differentiate with respect to a parameter and this, and the other. I mean, I noticed a few years ago, one time I was at his house and he said, I got these notes about how to do integrals for Feynman diagrams. And he said, they were made sometime late fifties, I think.

他说'这些对你比对我更有用'，就把笔记给了我。当然我说以后会归还，不过现在还在我手里。

Said they'll be more used to you than to me. So he gives them to me and it's like, well, I give them back sometime. I still have them of course.

那是自然。

Of course.

说来有趣，从某种角度看他是位非常'低科技'的数学家——那些笔记全是关于多重对数函数之类的内容。如今多重对数理论已发展得花里胡哨，但这完全不是他的风格。

I mean, it's kind of the, but it's interesting because that was, he was a very, in a sense, he was a very low tech mathematician in the sense that those notes, they're really about polylogarithms and things like that. And there's all kinds of fancy theory of polylogarithms now. That wasn't his thing at all.

不不，他的风格是——用工具取得结果。

No, no, was his thing. Using them to get results.

而且他对数学的处理方式可以说是19世纪最强大的数学方法。他确实不太信任20世纪的数学。

But also his approach to mathematics was very much the most powerful nineteenth century mathematics, so to speak. He really didn't trust twentieth century mathematics.

有意思。

Interesting.

但我觉得他...不，我是说，我们曾多次尝试合作。实际上我们在1980年就研究过量子计算，这总是段有趣的经历。他会计算自旋链之类的东西，而我完全不明白结果为何正确。当我用计算机计算并展示给他时，他又会说他也搞不懂为什么这个结果是对的。

But I think that his, no, he was, I mean, I was always, you know, we tried to do some work together various times. We worked on quantum computing actually back in 1980 it was always an interesting experience because he would do these calculations of, you know, spin chains and this and that and the other. And I'm like, I have no idea why that result is correct. And I would do some computer calculation and show it to him. And he says, I have no idea why that result is correct.

所以当时沟通有点困难，但最让我佩服的是，他总能通过手算得出正确答案。

And so it was a little bit challenging to communicate there, but it was, no, he was, I mean, the most impressive thing as far as I'm concerned is, he would go through and he would calculate stuff and he would actually get the right answer.

是啊，是啊。

Yeah, yeah. Which

对我来说，不用计算机的话根本不可能，我肯定会算得晕头转向。但费曼的矛盾之处在于，他完成计算后总会说'这没什么了不起，谁都会算'——当然这不是事实。然后他会说'我必须想出些震撼的直观解释来打动人们'。

for me, without kind of, I can get a computer to get the right answer. For me by hand, no way, I'm gonna get lost in some whatever. But then the thing that was always a sort of paradox of Dick Feynman was that he would come up with this calculation, then he would say, that's not impressive. Everybody can calculate stuff, which isn't true, of course. And he would say, I've got to come up with some grand intuitive explanation that's really going to impress people.

我记得在部分子模型和场论方面，他告诉我他推导出了标量场论中部分子如何运作的全部理论。但他只对人说'这些部分子就是点粒子，运作原理显而易见'。当人们追问原理时，他从未透露过自己已经建立了完整理论。

And I remember like with the parton model and field theory and so on, I remember, you know, he told me he'd worked out all this stuff about scalar field theories and how these partons would work in scalar field theory. And he just tells people, oh, there are these partons and there are these point particles and so on. And it's all obvious how it works. And people are like, why does it work that way? And he never told anybody that he worked out this whole theory.

是的，费曼的这一点很出名。他喜欢让事情看起来像魔术一样完成。但当你回头查看他的笔记，会发现他写了三万页的笔记，所有东西都是他精心推演出来的。对我来说，他最令人惊叹的地方在于——这也正是他拥有如此惊人知识储备的原因——那些看似凭空变出的东西，其实并非无中生有。

Yeah, I mean, that's famous about Feynman. He loved to appear to do things by magic. But then you go back and you look at the notes, there was 30,000 pages of notes he'd done, he'd worked it all out. And that's to me, one of the more amazing things about him is that he'd, and that's why he had this incredible arsenal. It looked like he was pulling things out of thin air, but they weren't pulled out of thin air.

它们建立在年复一年的计算基础上，这些计算被他发展、保留，并能运用那惊人的知识储备让事情显得神奇。当我写关于他的书时，了解这些细节真的很有趣。不过他确实热爱魔术效果，热衷于制造这种表象。我记得有个关于他的著名故事，就放在书的开头部分。

They were based on years and years of calculations, which he developed and retained and could use that incredible arsenal to make things appear magical. And it was, yeah, when I was writing the book about him, it was really interesting to learn those details. And, but he certainly loved the magic. He certainly loved to appear. I mean, you know, there's, I think it's a famous story about him, but you know, it was one of the things I put at the beginning of the book.

这让我想起件事。你可能听过——小时候他靠修收音机赚钱。知道这个故事吗？

He just reminded me of it. You probably know this story, but he's a kid and would make money by fixing radios. Do you know the story?

我不知道。

I don't know.

这故事太典型了，简直就是年轻的迪克·费曼的缩影。那还是电子管时代，没有晶体管之类的固态电路。有人拿来一台发出可怕噪音的收音机...

It's just perfect. It's a perfect It was Dick Feynman emerging right then. So he would It was back in the days of tubes before they had, you know, pansysters and stuff. And so he, or solid state circuitry. And someone brought this radio in that was making this awful noise.

当时他还是个孩子。他来回踱步，仰望天空沉思，然后调换了两根电子管，噪音就消失了。其实他当时立即就明白了问题所在，但他就是要让解决过程看起来像突然获得了魔法般的顿悟。他从一开始就是个表演者，但与其他表演者不同的是，他的表演背后有着远超表象的非凡实力。有意思的是，你们对计算方式至少有两种截然不同的理解。

He was a little kid, right? And he walked around, he walked around, he walked around, pondered, looked out to the sky pondered and then switched two tubes and the noise stopped. And, you know, he knew he'd known right as he said, he'd known immediately what the problem was, but the whole idea was to make it appear as if this magical insight came to him and he was a showman from the beginning, but the difference between him and many showmen is that he had, it was more than just show and remarkable. But it's interesting to me that you had two very different ways of thinking about at least how to do calculations. Right.

就是平面

Which is flat

我认为费曼的一个特点是，他真心不觉得自己能完成这些计算有什么了不起。我知道这是我生活中慢慢领悟到的一些事情，就像，那很简单。那并不令人印象深刻。我不会告诉别人这件事。那很简单。

think that one thing about Feynman that is he genuinely didn't think it was impressive that he could do these calculations. I know it's something I've slowly learned about some things in my life where it's like, that's easy. That's not impressive. I'm not gonna tell people about that. That's easy.

结果多年后你才发现，实际上大多数人根本做不到。我是说，几天前我才意识到这一点，关于某些我一直以为理所当然的事情。好吧，我从未真正思考过它。我从未想过为什么这很难？这个问题我可以描述为，就像你多年后回顾时，但在研究复杂性和类似问题时，为事物建立模型。

And it turns out, years later you realize actually, most people can't do that at all. I mean, I just realized that actually about something just a few days ago, about something that I kind of had always assumed. Well, I'd never really thought about it. I'd never thought why is this hard? And the issue I can describe it's like when you were jumping years later, but studying complexity and things like this, making models of things.

我意识到总存在这样一种元建模的过程。你对某事物有一个模型，你会问，这个模型背后的本质是什么？当我用这些简单的程序作为事物的模型等等时，很多情况下你会说，有一个可能相当精确详细的模型，但那里发生的本质是什么？我有点意识到，我是说，这是我自然感兴趣并发现的事情，但后来我意识到实际上这与计算语言设计中所做的是同一件事，你必须深入事物的本质。对我来说，这只是我自然而然地喜欢并最终在做的事情。

And it's always, I realized there's this kind of process of meta modeling. You have a model of something, you say, what is the underlying essence of what's there in this model? And that's something, when I worked on these simple programs as models of things and so on, a lot of what's going on there is you say, there's a model which may be a quite accurate detailed model, but what's the essence of what's happening there? And I kind of realized, I mean, that's something that I've sort of naturally been interested in and found, but then I realized actually that's the same thing one does in computational language design is you have to kind of drill down to the essence of things. And for me, that's just something I naturally like to do and end up doing.

你知道，我就想，为什么其他人不这么做？好吧，我已经花了四十年做这类事情。但对我来说，这是人们会做的显而易见的事情，但对其他人来说并不那么明显，因为这并不是他们所采取的模式。

And it's, you know, and I'm like, why do other people not do this? Well, I've just spent forty years doing that kind of thing. But it doesn't, but to me that's sort of an obvious thing one does and doesn't happen to be so obvious to other people because just hasn't been what the pattern they've taken.

是的，可以。但我想这就是为什么至少你和我早期会从事粒子物理学研究的一个原因。我是说，我对粒子物理学的兴趣，在于物理学是还原论的，而基础物理学在粒子物理学层面是还原论的。想法是一样的，你在寻找本质，你在寻找基本定律，这当然很有吸引力。这就是我成为粒子物理学家的原因。

Yes, can. But I guess that's one reason why you and I at least were doing particle physics, think early on. I mean, my interest in particle physics, I mean, to the sense that physics is reductionist and fundamental physics is reductionist at the level of particle physics. The idea is the same thing is that you're looking for the essence, you're looking for the fundamental laws and that was certainly attractive. That's why I became a particle physicist.

我想知道什么是本质的定律，自然的基本定律，基本规则。我怀疑我们有相同的——

I wanna know what were the essential laws, the fundamental laws of nature, the fundamental rules. And I suspect we had the same-

我有相同的兴趣。我是说，我现在所处的层次比粒子物理学还要底层，可以说是机器代码。但粒子物理学在它那个时代是好的。我是说，我实际上在12岁左右时意识到一件奇怪的事，那时我正在学习物理，我有这一套书，伯克利物理学课程的书。第五卷是关于统计力学的。

I had the same interest. I mean, what I've now, now I'm at a machine code way below particle physics, so to speak. But particle physics was good in its time. I mean, I realized actually one strange thing when I was like 12 years old, I was learning physics and I had this series of books, the Berkeley Physics Course books. And the volume five is about statistical mechanics.

在封面上，有一系列理想化台球碰撞的框架图示。这大概是为了阐释热力学第二定律，即熵增定律等等。出于某种原因，我对那些图片以及热力学第二定律的运作方式产生了浓厚兴趣。虽然时隔多年我已无法准确引用，但那本书在给出推导过程后会说：顺便一提，我们可以让这个推导过程时间反演进行。

And on the cover, has this series of frames of kind of collisions of, you know, idealized billiard ball type collisions. It's kind of supposed to be illustrating the second law of thermodynamics, the law of entropy increase and so on and so on and so on. So for whatever reason, I was really interested in those pictures and in how second law of thermodynamics works. And that book, I can't quote it after all these years, but it's one of these books where it says, here's the derivation. Then it says, oh, by the way, we can run this derivation in reverse time.

这个观点常常让学生感到困惑。可以说，我早期的一些计算机模拟尝试就是为了重现那些图示。多年后，我与制作那些图片的人交谈过——那些图片其实是伪造的，但这对我并不重要。

This point is often puzzling to the students, so to speak. Kind of like, know, some of my earliest sort of computer simulations were an effort to reproduce those pictures. I later, many, many years later, I talked to people who made those pictures. Those pictures were a fake, but it didn't matter to me.

伯克利系列教材很有趣，特别是它们居然用这些图片触动了你。那套物理教材非常出色，虽然因为难度过高并不总能成功教学。我最爱的可能还是埃德·珀塞尔的电磁学教材，它...

Well, were, you know, the Berkeley series, it's interesting that it got you that they had the pictures. Those were an amazing series of physics checks. They weren't always successful in teaching because they tended to be too hard for most students, but they're fantastic. My favorite is still probably Ed Purcell's, which is on electricity magnetism, which is

对，我记得那本。封面是橙色的，如果没记错的话。

Right, I remember that one. Orange cover as I recall.

我想是的。我在哈佛工作时，他就在那里。每次与他交谈——他是那种让人每次交流后都想成为物理学家的人，尽管我其实...确实如此。

I think so, yes. And it was an amazing I worked when I was at Harvard, he was there and every time He was one of those guys where every time I talked to him, wanted to grow up and be a physicist, even though I really Right, right.

但有趣的是，从某种意义上说，热力学第二定律以及如何从这类事物中获得连续行为？如何产生随机性？我最初研究这个，后来对粒子物理产生兴趣，因为1973-1974年间粒子物理是个热门领域。多年后，我又重新回到了...

Yeah, but what's funny is that that in a sense, second law of thermodynamics and how do you get sort of continuum behavior? How do you get randomness from these kinds of things? That to, you know, I started with that. I then got interested in particle physics because particle physics was kind of a happening area in 1973, And 1974, those kinds of then years later, I kind of got back

我正想说，某种程度上你现在的研究方向让我强烈联想到统计力学。关于宏观态与微观态的论述令我印象深刻。你在至少一篇文章中甚至直接指出——就像这个房间里的粒子可以处于无数微观构型，但温度压强保持不变。如果我们只能测量温度压强，就无需担忧所有微观状态。某种意义上，按你的说法，我们这些'计算能力有限'的存在者（这点稍后再谈）无法体验所有正在发生的不同可能性。

I was gonna say you right back to, in some sense, there's a lot of, when I read your stuff now about what you're trying to work on, it's very reminiscent of statistical mechanics. So the arguments of macrostates and microstates and I was struck by that. To some extent you even say that in at least one of the pieces I read by you and there can be many, you know, and I'm, again, I'm jumping way ahead, but just as the particles in this room could be in many different micro configurations, but there's still the same temperature and pressure. And if all I'm measuring is a temperature and pressure, I don't worry about all those configurations. And in some sense, if I get what you're saying that we who are quote computationally bounded and we'll get to that, can't experience all of the different things that are going on.

而我们将其解释为计算可约性的事实——你无法追踪所有粒子，而我们这种总结性的方式最终形成了我们对时间的理解。不过，我们会谈到这一点。总之，这些论点是，你知道，我试图消化内容并抓住你要表达的核心，但我们跳得太远了，不过没关系。

And we interpret the fact that that it's computationally reducible, you can't follow all the particles and that we sort of summarize things ends up being our view of time. Anyway, but we'll get to that. So, but the arguments are, you know, I was trying to trying to digest things and trying to get to the gist of what you were going to, but we're jumping way ahead, but that's okay.

对。回到起源问题。好的。

Right. Back to origins. Okay.

你知道，粒子物理学。所以我们在这方面有共同的兴趣。我本想问你为什么选择粒子物理，但我想我们已经回答了。你对粒子物理的兴趣和我一样，都是源于对本质的追求。

You know, particle physics. So we had the both the same interest in part. Was going to ask why particle physics, but I think we've already answered it. Your interest in particle physics was same as mine. It's the fundamental essence.

区别在于，应该说你在11、12或13岁时就知道什么是粒子物理了。而我肯定是在16岁左右，年纪更大时才真正了解粒子物理。我知道自己对本质问题感兴趣，但当时并不清楚这些本质问题具体是什么。说实话，我曾怀疑过你13、14岁时写的那些关于粒子物理不同方面的书——除非，我意思是，怀疑的我会说，也许你只是从某些教材上抄来的，但在我看来你确实理解了那些内容。

The difference was, I should say that you knew what particle physics was when you were 11, 12 or 13. And I certainly, I was probably 16, I was older before I really knew what particle physics was. Knew I was interested in fundamental things, but I didn't know what the fundamental things were. And I was, and to give you credit, did look, you know, cause I was skeptical at the books you wrote on various aspects of particle physics when you were 13 and 14. And unless, I mean, the skeptical one of me might say, well, maybe you were just copying things from some text, it looked to me like you actually understood it.

这非常令人印象深刻，斯蒂芬。你理解了弱相互作用，甚至量子场论。我本想问你是怎么学会的？不过在问之前，我想说，在我看来你似乎不擅长算术乘法表，但微积分——这个物理学的必备工具，却是你早期就掌握的。当然算术也有用，但如果我没理解错的话，这是你很早就抓住的东西。那么你是怎么学的，是什么引导你学习微积分，然后又是量子场论的？

And it's very impressive, Stephen. I was, you know, they're understanding the weak interactions and in fact, quantum field theory. I was gonna ask, how did you learn it? Now, before I get there, I wanted to say, it seemed to me that you weren't good at arithmetic times tables, but calculus, which is the essential tool that you kind of need for physics. I mean, arithmetic is useful too, but was something that you grasp onto early if I'm reading this And so how did you learn, what led you to learn calculus and then quantum field theory?

让我问问这个。

Let me ask that.

嗯，首先，我想第一个元发现大概是在10岁、11岁左右，就是你可以通过阅读书籍自学东西。这是个重要的元发现。我上过很好的学校，当时学习拉丁语、希腊语等等，有趣的是我当时觉得这些永远都用不上。而现在，你知道，我办公桌后面就放着拉丁语词典、希腊语词典，我总在尝试为事物创造新词等等。

Well, so, I mean, the first thing was the first meta discovery, I suppose, age, I don't know, 10, 11, something like that was you can just learn stuff by reading books. That's an important meta discovery. I went to very good schools and I learned, I suppose the things it's sort of interesting that, at the time I was learning Latin and Greek and God knows what else. And I was like, this is always gonna be useless to me. And now, you know, right behind my desk, I've got, know, Latin dictionary, Greek dictionary, and I'm always trying to make up words for things and so on.

但你知道，我虽然在学校学习，但所学内容很快与我感兴趣的业余物理活动分道扬镳了。我只是看书，我想其中一点是我从不做书中的练习题。我是说，书里有练习题，但我从不做。我总是想，嗯，我对这个问题感到好奇，我能解决这个问题吗？我能理解这个问题的答案吗？

But, you know, I was, but what I learned in school kind of rapidly diverged what I was interested in learning and sort of my kind of hobbyist physics activities, so to speak. And I just read books and I suppose one of the things was that I never did exercises in any book. I mean, books had exercises, I never did them. It was always like, well, I just wonder about this question and can I address this question? Can I understand the answer to this question?

这有点像，好吧，让我学这部分、那部分和其他部分。我确信，多年以来，在我学习物理和其他东西的过程中，有很多地方存在空白。我只是从不在意那些内容。所以，在很多很多年后，有时我会突然意识到自己对某些东西一无所知。因为，如果我接受标准的教育体系，我肯定会上过关于那个特定内容的课程，但这是到达前沿领域的一种非常高效的方式。

And it was kind of like, well, you know, let me learn this piece and that piece and the other piece. And I'm sure, you know, for years there were lots of places where I'd learned physics and other things where there were holes. I just never cared about that thing. And so that was, you know, in many, many, many years later, there would be situations where I would like realize I just don't know anything about that. And because, know, and if I'd gone through standard kind of schooling that would have been, you know, I would have necessarily done a class about that particular thing, but it was a very efficient way to kind of get to the frontiers.

如果你说，这就是我想达到的前沿领域。然后你学习所有能到达那个前沿的部分。

If you say, this is the frontier I want to get to. And then you learn all the pieces to get to that frontier. And

只学必要的部分，只学必要的部分，不是所有部分，而是必要的那些。

just the necessary pieces and just the necessary pieces, not all the pieces, but the necessary ones.

没错，没错。我是说，然后逐渐地填补空白，并利用这些知识。实际上，我最近在读我13岁左右时写的关于量子场的描述，其实并不糟糕。实际上我看起来...

That's right. That's right. I mean, and then, you know, and gradually it sort of fills out and you kind of make use of things. I think in, no, actually I was recently reading my description of quantum fields from when I don't know when I was 13 or something, actually wasn't terrible. It's actually I not some looked

我也看了，一点也不差。我印象深刻，因为我...

at it too, it wasn't bad at all. I was impressed because I

实际上为自己感到骄傲。

was actually proud of myself.

是啊，是啊，史蒂文，我当时是持怀疑态度的。我是说，我了解你也欣赏你，但我还是觉得，你知道，我听说过你年轻时做的那些不同的事情。我想，好吧，有很多年轻人认为自己做了些了不起的事，那些描述听起来确实不错。不过你说的一些话，我确信那不是他本意。我们走着瞧吧。

Yeah, yeah, I was skeptical, Steven. I mean, I know you and I appreciate you, but I still figured out well, you know, I'd heard these different things you've done when you're younger. And I thought, okay, well, there are lot of young kids who think they've done something good, they were really good descriptions. But you said something though that I'm sure I don't think it came out the way he meant it. So we'll see.

你没做那些练习题，但再次引用费曼的话，他曾说‘无所作为者一无所知’。你可能没做书上的习题，但物理不能被动学习。你不能只是读教材而不动手演算，因为只有当你亲自推导时——所以虽然不一定是书上的习题，但你必须通过演算来弄明白

You didn't do the exercises, but again, quoting Feynman who once said he who can do nothing knows nothing. You may not have done the exercise in the book, but you can't learn the physics passively. You can't just read the textbook and not at least work some things out because you're only when you work it out. So it may not have been the exercises in the book, but you had to work out things in order to figure

我当时读书也很糟糕。我做的只是，这是我想弄明白的问题。现在让我试着解决它。我会阅读书中需要理解这部分的内容。

out I how to do was terrible at reading the books as well. All I was doing was, this is a thing I want to figure out. Now let me try and figure this out. I'll read the parts of the book I need to figure that out.

然后你就会付诸实践。进行数学推导。

And then you'll do the work. Do the math.

对，对，对。我是说，1974年发生的事，比如J/ψ粒子的发现，正负电子湮灭截面上升这类现象，在那个年代我觉得特别激动人心。于是我开始尝试构建理论来解释这个现象，最终提出了这个关于强相互作用电子的理论。

Right, right, right. I mean, so what happened is like 1974 was when the japesi particle was discovered and it was when a plusminus annihilation cross section was going up and all these kinds of things that in those days I thought were exciting. So I started trying to figure out, could I have some theory about this? And eventually I came up with this theory about strongly interacting electrons.

我读过那篇论文，顺便说一句，只是粗略

I read that paper by the way, just looked

看了下，那是篇很蹩脚的论文。

It at was a lame paper.

是啊，一篇蹩脚的论文，但对年轻人来说。

Yeah, a lame paper, but for a young person.

对于一个14岁的孩子来说，它并不算太差，但从宏观角度看确实有点蹩脚。不过，就像我最近注意到的，我当时在讨论电子的大小可能是10的负18次方米。现在我说电子的大小可能是10的负81次方米。所以这有点像，再次说明细节真的会改变。不，我认为，写那篇论文的过程挺有趣的，因为我读过很多类似的论文。

For a 14 year old, it wasn't quite so lame, but it's on a grand scale it was kind of lame. Although, as I noticed recently, there I was talking about, maybe electrons have a size of 10 to the minus 18 meters. Now I'm saying maybe electrons have a size of 10 to the minus 81 meters. So it's kind of like, it's again, really changes, but the details. No, I think, and it was the process of writing that paper was kind of interesting because it was like, I'd seen a bunch of these papers.

我读过很多物理期刊上的论文。我过去常常骑自行车去当地大学图书馆查阅物理论文。

I'd read a bunch of papers in physics journals. I used to bicycle to the local university library and go look up physics papers.

你能这样做真是太好了。

That's great that you could do that.

没错，那时候，随便一个13岁左右的孩子出现在大学图书馆，没人管，你知道，那时候没什么严格的安保措施。我不认为有人会在意。所以我读了很多这类东西，然后想，嗯，我有些有趣的观点可以试着写下来。我对学术体系和那些规矩一无所知。就像你看着期刊，能清楚地看到投稿地址，寄出去后就会收到愚蠢的审稿意见，这可能会让我直接放弃。但我觉得，不，这太蠢了。

Right, well, was, in those days random 13 year old or so showing up at the university library, nobody, you know, there was no kind of grand security or anything. I don't think anybody, but I think that in, you know, that was so, you know, I read a bunch of these things and I thought, well, I've got some interesting things to say when I try writing something about it. And I had no idea about, you know, the academic system and the whole whatever. And it's just like, you look at the journal, you can see, you know, I can plainly see this is the address you send it to off you send it and steadily it gets, you get back stupid referee reports and then you kind of, which might've caused me to just say, forget it, I give up. But it was like, no, this is just dumb.

我要继续推进，可以说。那是个过程，我的论文逐渐变得更好。

I'm gonna keep pushing forward, so to speak. That was a, and my papers steadily got better, I would say. Did

你在写论文时有没有模仿，因为我有过很多学生，你得训练他们如何写科学论文。但一种方法是看科学论文并尝试模仿其风格，至少避免写得像高中作文，或者意识到科学论文中不要把你所知道的全写进去。那么你有没有模仿你读过的论文风格呢？

you follow, did you, in writing the papers, I mean, again, because I've had a lot of students and you have to sort of train people how to write scientific papers. But again, one way to do it is look at the scientific papers and try and mimic the style at least to, you know, so you don't write something that sounds like a high school composition or you realize that in a scientific paper, don't put everything you know. And so did you mimic the style of the papers you read or not?

有一点吧。我是说，你知道，在学校时写作算是我做得不算差的事情之一。然后我... 是的，你的

A little bit. I mean, you know, one of the things I, you know, I guess I was always, you know, in school writing was one of my sort of, one of the things I didn't do badly and then I was Yeah, your

早期成绩非常优秀。知道。

early grades were very good. Know.

对，没错。所以我觉得科学论文的有趣之处在于它的写作风格与其他类型截然不同。确实。但一旦掌握了基本要领，写起来就不那么困难了。我记得大概十七八岁时写过一篇关于宇宙学和粒子物理的论文。

Yeah, right. So I mean, was interesting about scientific papers is a very different style from writing other kinds of things. Sure. But once I got kind of the basic idea, it wasn't so hard to do that. I mean, actually I remember one paper I wrote must have been when I was 18 or 17 or so was about cosmology and particle physics.

好的。你说得对，不必把所有知道的都写进去。那篇论文对宇宙学和粒子物理做了相当不错的综述。完整版最终没能发表。当然。

Okay. And you say, you don't put everything you know. Well, gave a pretty good summary of cosmology and particle physics. The big version of that paper was never published. Sure.

因为期刊说'这些都是常识'之类的。实际上那些内容根本不为人熟知，它清晰阐述了粒子在早期宇宙中的运行机制等等。后来我发表了精简版，但那个删节版确实比完整版乏味得多。

Because the journal said, oh, this is all well known, blah, blah, blah. Actually it wasn't well known at all. It was a pretty clean description of how things work with particles in the early universe and so on. And I published a shorter version of that paper. I've seen that That for was much less interesting really than the full version.

因为完整版还包含了许多关于宇宙膨胀和粒子相互作用背后原理的思考，这些在精简版里都消失了。这就是那种毫无价值的学术反馈案例之一。

Cause the full version also had a bunch of things about kind of the intuition behind expanding universes and particle interactions and so on, was gone in the small paper. So it was a piece of, one of those pieces of academic feedback that was hopeless.

唉，期刊就是这样运作的，必须精简内容。可惜很多深刻见解无法呈现——不过论文里应该可以保留。有意思的是，我读到你那篇论文的时候，正好在哈佛研究类似课题，当时我已转向粒子天体物理领域，思考着... 这不正是粒子宇宙学吗？关于早期宇宙相互作用、残余粒子预测等问题，与你早年那篇论文有很多共通之处。

Well, I mean, that's just the way it is though in journals, you have to be tourists and you can't put in, it's a shame that probably many of the insights. Well, I guess you put them in a thesis. It's interesting that, that was the year I read it because at that time or shortly around then at Harvard, I was working on some similar things. I'd already moved into particle astrophysics and was thinking about, well, wasn't that because particle cosmology, thinking about interactions in the early universe and what particles and how you could predict what particles might be left over. There's a lot of similarities to that early paper of yours.

但这么早就对它产生兴趣确实很，嗯，难得。让我问你，你说他上了好学校。什么是龙校？

But it's still very, yeah, to be interested in it that early. Let me ask you, you said he went to good schools. What's the dragon school?

那是一所小学。

It's an elementary school.

是私立还是...我是说，我了解那边的制度。在英格兰公立学校其实就是私立的。我不清楚...

It's a private or, I mean, I know how things are done. Public schools are private in England. I don't know what-

对，没错。那是牛津的一所私立小学。当时它只是牛津当地一所不错的学校。后来因为出了不少知名校友才声名鹊起。但就我在校那年来说，可能被列出的校友大概就是我和一个叫休·劳瑞的演员。

Yeah, right. It's a private elementary school in Oxford. At the time it was just a good local school in Oxford. It's become much more famous because it had a bunch of famous alumni since that time. But I think for the year I was there, the ones that are probably listed in the, it's probably me and a chap called Hugh Laurie, who's an actor.

我们八岁左右是朋友。说起来很有趣，因为我完全不知道他的近况。我通常都会追踪小学和幼儿园同学的去向，但对休·劳瑞，我只隐约知道他当了演员，没想到成了大明星。后来发现他主演了美剧《豪斯医生》。

We were friends when we were like eight years old or something. And I actually, it was really funny because I had no idea what happened to him. And I have kept track of what happened to most people I knew when I was in elementary school and kindergarten and so on. And with Hugh Laurie, I kind of knew he'd become an actor, but I didn't know he'd become a particularly famous actor. And so then I find out he's become a famous actor and he's doing this show and it's called House, it was an American television show.

好剧。

Great show.

于是我想得看看这部剧。打开电视就看到他歪着头的样子——这和他八岁时的习惯动作一模一样。人在某些本质特征上不会改变。那所学校有意思的是，即使在幼儿园时期，牛津的孩子群体就给人印象深刻。

And so I say, okay, I better watch a little fragment of this. So I switch it on and there he is, He's got his head cocked to one side and I'm remembering that's exactly what he did when he was eight years old. He walked around just like that. People don't change at that level, but no, was a school. One thing that was interesting about going to school in Oxford and even when I was in kindergarten, it was an impressive group of kids.

如果你知道他们现在的成就，就会发现他们做了各种令人印象深刻的事，大多是学术方面的。我想这就是你能得到的——和一群教授的孩子一起上学。很长一段时间里，我常说，我认识的最聪明的一群人就是我幼儿园时期认识的那些人。

If you know what they've done now, it's kind of like, they've done all kinds of impressive, mostly academic types of things. And that's what you get, I guess. You get to go to school with a bunch of professors' kids. For me, for a long time, I used to say, the smartest group of people I knew were the group of people I knew in kindergarten.

但我经常告诉后来的孩子们，关键在于你的同龄人。无论是在大学还是其他地方，你都能在任何地方接受良好或糟糕的教育。但如果可以选择，尽量选择一个至少能让你被同龄人挑战的地方，因为那才是你真正学习的地方。当然幼儿园未必如此，但有趣的是，当我与某些人交谈时，总会因我们背景的巨大差异而感到惊讶——我父母都没读完高中，而我有个在温哥华当物理学家朋友。

But often, I mean, I tell kids at a later stage that it's your peers, you know, when you're at university or anywhere else on the whole that you can get a good education anywhere, a bad education anywhere. But if you're gonna choose, try and choose a place where your peers are gonna challenge you at least. And because that's where you'll do a lot of your learning. Obviously in kindergarten, it's not necessarily that, but it is interesting to me to think how different I'm always amazed when I talk to some people because our backgrounds are so different because neither of my parents sort of finished high school. I have a friend of mine who's a physicist in Vancouver.

他叫伊恩·阿弗莱克。他给我看过他幼儿园时写的诗，里面说'长大后我要当哲学博士'。我当时想，哇，我完全不知道哲学博士是什么——我们的成长环境如此不同。

Well, I put his name Ian Affleck, but he showed me a poem he wrote when he was in, I think in kindergarten. And he said, when I grow up, I want to be a doctor of philosophy. And I thought, wow, I had no idea what a doctor of philosophy was probably from so many years. So such a different upbringing,

那你是在哪里长大的？具体是哪里？

Where did now you grow up? Where did you grow up?

我在多伦多长大。虽然出生在纽约，但成长于加拿大多伦多。读的都是公立中小学。加拿大或许有些私立学校，但我并不了解，也从未想过要去美国上学。

I grew up in Toronto. I was born in New York, but I grew up in Toronto in Canada. And, you know, went to public school and high school. You know, and there were maybe some private schools in Canada, but I wasn't really aware of them. And, and I never even thought of going to The United States to school.

这些念头从未出现在我脑海里。因为我父母没上过大学，加上犹太背景，我母亲希望我当医生，我弟弟当律师——后来弟弟确实成了律师。很多年里，母亲都对我没成为医生耿耿于怀。不过这就是——

It was these things never, never occurred to me. My parents wanted because they hadn't gone to school and because think because I had a Jewish background, my mother wanted me to be a doctor and my and my brother to be a lawyer my brother became a lawyer. My mother was for many years, not happy that I wasn't a doctor. But anyway, that's- So

你现在也算是某种博士了。

you're some kind of doctor.

是的，你知道，那不是她想要的那种。不过她已经释怀了。但龙校是你为数不多真正毕业的学校之一，对吧？

Yeah, know, it wasn't the kind she wanted. But yeah, no, she's gotten over that. But Dragon School was one of the few schools you actually graduated from. Is that right?

在英格兰，他们没有毕业的概念。是的，我读完了所有学年，然后我注意到

In England, they don't have the notion of graduation. Yes, went through all the years of it and then I noticed

我在阅读时，不知道是维基百科还是其他资料，总是提到，斯蒂芬提前离开了。所以你提前离开了伊顿公学？

when I was reading, I don't know whether it was Wikipedia or some other thing, it always says, and Stephen prematurely left. So you left Eton early?

是的，

Yes,

是的。意思是，

yes. Mean,

那实际上是，我去了伊顿公学，这所学校在哥伦布到达美洲之前就成立了。但说实话，我在那里的时候它是一所好学校。我是说，它经历过一些疯狂的阶段，但我在那里的时候，它算是...我申请那里是因为它有最好的奖学金。我其实并不那么需要经济上的资助，但那些获得奖学金的孩子们组成了一个非常友好有趣的群体。那是个很小的群体，你知道，看看他们的结局，要么非常成功，要么彻底失败。是的，是的。

that was really what, I went to Eaton, which is sort of this school that was founded before Columbus came to America, so to But it was a good school actually when I was there. I mean, I think it had gone through phases when it was kind of crazy, but at the time when I was there, it was kind of, you know, I applied there because it sort of had the best scholarships. I didn't really financially that much need a scholarship, but it was of a, it was this very nice, interesting group of people who were the scholarship kids at Eton. And it's kind of a very small group and it's, you know, if you look at what happens to them, they either go spectacularly or they crash and burn. Yeah, yeah.

但你知道，那是个有趣的群体。我在那里时，一边做着各种物理研究，学习相关知识，逐渐变得相当熟练。所以到了16岁左右，当时在英格兰，如果你获得了牛津或剑桥的奖学金，就可以免去参加所有政府标准化考试等等。我就是这么做的。当时有人给了我一个有趣但糟糕的建议，说你不该提前上大学。

And it's the, but you know, it was an interesting group and, but you know, went there and I was kind of doing the sort of side thing of doing a bunch of physics and learning about those kinds of things. And I got reasonably proficient at that. And so by the time I was like 16, it was like in England at the time, you could have this, if you got a scholarship to Oxford or Cambridge, you could avoid doing the whole standardized government exams, etcetera. So that's what I did. And that was my kind of, you know, people told me at the time, one of the things which was sort of interesting piece of bad advice was, you know, Oh, you shouldn't go to college early.

你会处于极大的社交劣势，等等等等，这某种程度上是一种——关于你知道能做什么和不能做什么的认知。多年后，我花了很多时间创办公司之类的事情。回顾童年时我意识到，自己一直都是那个组织者角色。所以那些'你会因不与人互动而处于劣势'的说法其实不太准确。细究起来，更像是——我总在组织其他孩子做这做那的那个孩子。

You'll be so socially disadvantaged, etcetera, etcetera, etcetera, which was kind of a, in the, what do you know how to do and not know how to do? Years later, I've spent a bunch of time starting companies and stuff like this. And I realized looking back when I was a kid, I was always the organizing kid. And so it was kind of, this, oh, you'll be so disadvantaged and not interacting with people and things, not really quite right. If you look in more detail, it was kind of a, you know, I was the kid who was organizing the group of kids to do this and that and the other.

实际上有件趣事，看到当年被我组织做事的那些孩子，后来有些人从事的职业竟与我当年安排他们做的小项目类似，这种感觉很奇妙。

Actually one of my, yeah, it's always fun to see some of the people who I sort of organized as kids to do things. Some of their later professions ended up being kind of what I organized them to do in some little project of mine, which is kind of nice to see.

这很有意思。人们通常认为社交方面...虽然你们当时年纪尚小，但我觉得英国的情况会完全不同。英国的导师制更鼓励独立思考和社会独立性。美国的大班授课制度确实难以培养这种独立性。即使存在青春期等社交年龄问题，在一个为自主学习设计的体系里，这些可能并不明显。在英国的体系里，如果你能独立学习和工作，可能会发展得更好。你觉得呢？

Well, that's interesting. Know, one tends to think that socially, well, were a little young, you didn't find so I think it's different in England than it would have been a very different experience for you in England than The US because in England, with the tutorial system, can be more independent minded and more independent socially too. I mean, The United States where it's all with large classes and everything else, really can't, you're not encouraged to be so independent. And so even if there were social age issues having to do with puberty and everything else, I mean, it may not have been so noticeable in a system where, which was designed for, if you could learn on your own and if you could work on your own, you could probably flourish more in an English system. Do you think that's right

或者说...不，我认为美国大学确实走的是全方位服务路线，所有资源都集中在大学里。英国的情况并非如此，可能至今仍保留差异。以牛津体系为例，实际上你只需要参加年终考试就行。

or am I? No, I mean, I think that The US has definitely gone for the full service university. Everything is at the university. I think that was less so and probably even still less so in The UK. Mean, look, for example, the way that the Oxford system worked, I went to college in Oxford was that, all you actually had to do was the exams at the end of the year.

我曾尝试听些讲座，但觉得索然无味就不再去了。倒是参加过几次研究生讲座，有些确实不错。我还和一群实验粒子物理学家达成协议：我可以用他们的计算机和ARPANET网络连接，作为交换帮他们做些数据分析。这笔交易很划算——而且那间机房是全英国我唯一知道有空调的地方。

And I tried going to some lectures and I didn't find them at all interesting and I stopped going to them. And I went to a few graduate lectures that were some of them are pretty good actually. And I had kind of made this deal with this group of experimental particle physicists that I would use their computers and all their ARPANET connections and things, and in return for me doing some data analysis for them. And so that was a pretty good deal. It also the only place that I knew of in The UK where there was air conditioning, was in the computer room.

啊，那真是太棒了。

Ah, so that's great. That

算是额外福利吧。

was an added benefit.

我们马上要谈到计算机了，这几乎是个很好的过渡。但你说到考试这件事让我很感兴趣，因为在我自己的生活中，我能理解这一点。我本科时曾与教授达成协议跳过某些环节，但在MIT读博时真正欣赏的一点（不知他们现在是否还这样做）是，你必须完成所有这些关卡——研究生诊断考试、资格考等等。按规定你需要修两年课程才能参加，而我当时赌自己能自学通过，结果第一学期就完成并合格了。

Well, we're gonna get to computers in just a second, it's almost good segue. But the interesting thing you say about that, that it's intriguing to me that the exam thing, because you know, that in my own life, I can appreciate that because the only time, I mean, I had deals with professors and undergraduate where I could skip things, but the one thing I really liked about doing my PhD at MIT, and I don't know if they still do it, was that, you know, there are all these hoops you have to jump through and there are all these graduate diagnostic exams and graduate qualifying exams and etcetera. And you're supposed to take courses for two years to take them. And at the time I gambled that I could learn enough on my own. And I did them in my first term and pass them.

当然这意味着像你可能经历过的知识缺口，但也让我提前达到了原则上可以毕业的阶段。之后我实际上浪费了一年左右时间，不过这挺好。至少你明白了通过关卡是一回事，而能做出成果是另一回事。通过考试对通过考试有用，但某种意义上真正重要的是之后你能做什么。

And it'll allow And now of course it meant that there were gaps like they probably were with you, but it meant that I was at a stage where in principle I have been taken off early. What I did was then waste time for a year or so, it's a nice thing. At least you get understanding that getting through the hoops, is one thing and then being able to do other things is something else. Passing the exams is useful for passing the exams, but really what's important is what you do after that in some sense.

确实如此。你看，我在物理考试中表现不错，但放在现代可能就行不通了。这让我想起个趣事——我14岁左右参加政府O水准标准化物理考试时，完全没做任何准备，连教学大纲都不清楚。

Well, yeah, right. No, I think, I mean, look, was the fact that I did well in the physics exams, as I say, I'm sure in modern times it wouldn't even work because again, it's kind of like, actually one of my favorite, okay, I have to, this is just one of these crazy stories. When I was doing this was when I was probably 14 or something like that, I was supposed to do some standardized government O level, standardized exam type thing. Was doing on physics. So I'd done absolutely no preparation for this and I had no idea what the syllabus was and so on.

考试中有道题问：列举电场和磁场对电子作用的两个区别。我当时想：好吧，电场力是电荷乘E，磁场力是电荷乘V叉乘B，这是一个区别。但第二个呢？

So I go do this exam. And one of the questions on the exam is name two differences between the effect of electric and magnetic fields on electrons. Okay. So I'm like, okay, you know, it's E times, you know, charge times electric field, it's, you know, charge times V cross B, that's one difference. What on earth?

后来灵光一现，我写道：电子具有磁偶极矩但没有电偶极矩。还补了句：这大概不是你们想考察的知识点吧？

And I realized, I knew at the time, so I wrote down something, I said, well, electrons have magnetic dipole moments, but they don't have electric dipole moments. And I said, Probably not what you were looking for, more Did or

他们给分了吗？你后来——

they grade you on that? Did you-

不清楚。虽然整体成绩不错，但这是个典型案例——掌握宏观知识框架未必能帮你通过考试。现在很多考试可能更看重你是否按课程要求学习，而非真正掌握知识。

I have no idea. I mean, I got a fine grade on the whole exams, I don't know, but I was just, it was one of those cases where, you know, it's not clear that knowing the big story, so to speak, actually helps you in passing the exams. I think in some of these things, probably in more recent times, would be more like, well, did you do the course the way the course was supposed to be done rather than do you know the material, so to speak?

是的，不，这很有趣。确实很有趣。每个人在某个时刻... 确切地说，学生在某个阶段必须完成从擅长课程作业到真正理解事物、自主学习的转变。我是说，你发现了这个元认知——原来通过阅读书籍确实能学到东西，但当然，所有最终成为学者或研究生的人都明白，真正重要的是你自主习得的知识，这意味着你不必依赖课堂、论文或文章。能够做到这一点... 这是种截然不同的学习转型。你能早期领悟这点很棒。

Yeah, no, that's an interesting Yeah, it's interesting. At some point everyone Well, at some point students have to make the transition from doing well in coursework to understanding things and to learning themselves. I mean, you made that meta discovery that you can actually learn things by reading books, but of course that's a discovery that everyone who then becomes an academic, a graduate student has learned that ultimately what's important is what you learn yourself, which means you're not going to class and the way you get it, well, or paper or articles. To be able to That's a very different kind of transition to learning. It's great that you learned it early on.

根据我和学生们的经验，对于那些长期通过课堂表现优异、突然需要转向阅读论文并以不同方式学习的学生来说，这种转型并不容易。这是种完全不同的体验。

My experience, both for myself and students is that that transition is not so easy for students who have excelled most of the time by going through classes and then get to a point where they suddenly have to read papers and learn things in a different way. It's a very different experience.

确实如此。这需要不同的技能组合。可悲的是，在当前教育体系中，你必须通过某种特定的'准直器'（打个比方）才能获得从事研究型工作的资格，许多人可能在这之前就已经失去热情了——即便他们本可能擅长于此。我本人很可能就是这样的例子。

Well, right. And it's a different set of skills. And unfortunately, of the issues is, in an education system where you have to go through this particular sort of collimator, so to speak, to get to the point where you're allowed to do the kind of more research kind of thing. People will kind of die on the vine before they get to that point, even if they would have been good at that. And probably that would have happened to me.

我很庆幸自己快速通过了教育体系，否则我怀疑自己能否坚持下来。关于个人擅长领域与自我认知的问题... 回想起来，我很早就习惯思考'我想提出什么问题'，并且在这方面其实相当擅长。我过去总认为这是理所当然的——'大家不都这样吗？'但实际上并非如此。

I mean, I'm very glad I got through the education system as quickly as I did because I'm not sure I would have survived it otherwise. I mean, the other thing in the kind of what one's good at and what one knows one's good at. It's like, I think early on I was always like, well, let me figure out what question I want to ask. And I got, in retrospect, I was pretty good at that figuring out questions to ask. I always thought that was kind of like, oh, that's obvious.

事实上，在学术研究中，尤其是成功的学术研究，我认为更大的决定性因素在于：你是否能解决正确的问题？而不是解决问题的技术细节。

Everybody does that. But in fact they don't. And in fact, in academic research and sort of successful academic research to my mind that tends to be the bigger determinant real successes. Can you actually solve the right problem? Not, what about the mechanics of solving the problem?

现行教育体系最让我失望的一点是，它完全缺乏'研究策略'的培养——因为这不是人们教授的内容。他们教的是既定技能：'你要完成这个特定任务'。而关于'在这个广阔领域中，什么样的问题可能值得探索'这种思维方式，往往被忽视。我曾以为这是微不足道的事，直到多年后才明白，这其实是我毕生都在实践的核心能力——它效果非凡，但远没有想象中那么容易掌握。

And one of the things I've always been disappointed about in a lot of the education system is the fact that that strategy of what to study is absolutely not there because that's not what people teach. People are teaching there is a trade, you're going to do this particular thing and this idea of you know well actually there's this general area what's a question that might be interesting is tends to not be, tends to not be taught. And I, you know, again, I always thought that was a kind of triviality except that it turns out, you know, that's the thing I've been doing all my life, so to speak. And it's worked rather well, but it wasn't, you know, it only in many later years did it become obvious to me that that wasn't quite as easy a skill as one might think.

这是学者极其重要的素养。常听我演讲的人都知道，我反复强调：教育的最大败笔就是没有教会孩子通过提问来学习。我们应该教授提问的方法，鼓励这种思维方式——包括教师也要学习如何回应这些问题。培养提问能力才是关键。

Well, it's a very important scholar. You know, anyone who's listening to me talk on these things will have heard me said, and I've answered this question a lot that to me, all of education comes in. The one and the biggest disappointment in education is that we don't get kids to ask by asking questions. Questioning is what we should be teaching, how to ask questions and encouraging that kind of thing and encouraging not knowing by the way, including being a teacher and finding out how to answer those questions. But learning how to ask questions is vital.

这一点我同意你的看法。在我看来，这是教育领域最大的缺陷之一。

It's one, I agree with you. It's one of the biggest shortcomings in education in my opinion.

但这确实是个难题。我从事这方面工作多年，经常组织孩子们参与这类活动，比如让他们随意提问科学问题等等。去年开始我还尝试了直播这种形式。最让我惊讶的是孩子们的提问——第一个问题往往是标准的高中物理知识范畴。

But it's a tough business. I've done this thing. For years I've done these things with groups of kids and so on, it'll be like, ask me anything about science or whatever. I started doing that live streaming that as well in last year or so. One of the things that's always striking about that with kids is there'll be some question and question number one, it's like, okay, that's standard high school physics or whatever.

我能轻松解答。第二个问题可能恰好是我知道答案的前沿物理研究课题，因为我认识这个领域的顶尖专家，最近还碰巧与他们交流过。但紧接着就会出现第三个问题——我清楚地知道目前全人类都尚未找到答案，因为我自己也曾好奇并深入研究过。

I can answer that. Question number two, it's like, well, I happen to know the answer. That's a frontier physics, frontier research question. I know the person who is the world expert and I happen to run into them recently and I know the answer to that. And then there'll be another question where it's like, I know nobody knows the answer to that question because I've been curious myself and I've looked into it and nobody knows the answer.

我认为这需要具备相当深厚的知识储备才能分辨。虽然互联网让这类甄别变得容易些，但对孩子来说仍然很困难。举个真实例子：我有个学生在很小时候就问过'恐龙时代的地球可能拥有两颗月亮吗？'

And I think that's really, you have to know a lot to be able to parse those things out. I mean, it's gotten easier with the web and all that kind of thing, but it's still a, it's surprising for a kid. Like a good example, actually this was one of my kids asked this question when he was pretty young was, know, when there were dinosaurs, could the earth have had two moons?

明白了。

Okay.

是的。

Okay.

这是个绝妙的问题。

It's a great question.

没错，这是个非常不简单的问题。答案大概是否定的，但多年来我询问过许多精通天体力学的人，最初他们都说我们真的不知道。而最近得到的反馈是，已有模拟实验进行了深入探索。

Right, and it's very non trivial question. Yeah. Answer is probably no, but I asked a bunch of people who know about celestial mechanics and so on over the course of years and at the beginning of asking that question, they were like, we just don't know. And then more recently it's like, well there are simulations that have gone far

足够深入...要让两个这样的卫星保持稳定轨道运行周期非常困难。不过无论如何，我认为...

enough It'd hard go into to the have a stable orbit like rotational period with two moons like that. But anyway, I would think

对对，其实要看卫星的大小。对了，最近真有孩子问我为什么月球没有卫星？这个我知道答案——因为不存在稳定轨道。

Right, right. Well, mean, depends how big the moons are Yeah, and of course. Depends on one that some kid asked me actually recently is why does the moon not have moons? I know the answer to that one. There aren't stable orbits.

事实上，就连航天器都很难在月球周围稳定运行。

Fact, even hard to get a spacecraft to orbit stably around the moon.

还有个可能不太实用的解释：如果它有卫星，那它就不是卫星了，而是行星。关键在于...它要有卫星就必须在引力影响上主导周围环境。否则就像你说的会出现不稳定。这其实也是行星的定义之一——在其区域内具有引力主导地位。

There's another answer which is perhaps not as useful answer. If it did, it wouldn't be a moon because then it'd be a planet. The is the thing that well, would be the only way it could have moons is if it dominated the gravitational influence in its surroundings. Otherwise, as you say, there'd be instabilities. And that's one of the definition of a planet, I suppose, is that it dominates the gravitational influence in the region.

所以卫星并不能...

So moons don't just- But

别忘了，月球勘测轨道器就是月球的卫星啊。

remember, the Lunar Reconnaissance Orbiter is a moon of the moon.

是啊是啊，确实如此。不过——

Yeah, yeah, it's true. But it's-

所以事实证明它并不能持续数十亿年。对，对。我们走偏了，而且偏得离谱。我们陷入了一种——

So it just doesn't happen to last for billions of years as it turns out. Yeah. Yeah. We're off in a very different way. We're off in a It's

好吧，我原本不知道话题会转向哪里。我正要说——哦对了，其实我想问这个。我东拉西扯了半天，但最终会回到正题。不过我希望明确两点：一是既然你孩子问起恐龙时代的事，你在笔记里写道（我又要回溯了）——

alright, I didn't know where we're gonna go. I was about to Oh yes, actually I'm gonna ask this. I'm going all over the place and we will eventually get to where I want to get. But, I hope, two things though. One that you, since your kid asked about the time when there were dinosaurs, you wrote, I'm going way back again.

记得你六七岁时，有幅剑龙背上长刺的图画，你自己在旁边标注'理性的黎明'，因为当时你自问'究竟有多少根刺？'能解释下为什么称其为理性黎明吗？

Think when you were six or seven, there's a picture of spikes on a stegosaurus of drawing you wrote yourself and over that you put the dawn of reason because you asked yourself how many spikes are there? Do you wanna explain why that was the dawn of reason?

噢，我也不清楚。那只是我随手加的标注——其实我当时正在快速给这些图片配文。但某种程度上，你知道，这是我找到的最早关于定量思考的证据。回顾自己的教育经历总是很有趣，特别是像我这样参与过教育工作的人。我有四个孩子，见识过各种教育现象。这让我不禁反思自己当年的学习过程。

Oh, I don't know. That was just me, me captioning or actually I think I was going through quickly captioning these pictures but it was kind of, you know, it's the first piece of evidence of actually kind of thinking about things quantitatively that I could find. I mean, had, it was some, I had a, you know, it's always interesting to look back on one's own education as one, know, I've been sort of involved in education. I have four kids, I've, you know, kind of seen a bunch of things that go on. It's some, and then I think back to my own kind of education.

当我观察现在遇到的年轻人时，也会追溯他们的发展轨迹。我意识到自己六七岁时的某些行为，天哪，居然和现在做的事如出一辙。比如有次我发现把两把尺子相对滑动就能做成简易加法计算尺——当然那时我根本不懂这个。这其实是我算术学不好的众多原因之一，老师可能很疑惑为什么我桌上总放着两把尺子？因为这能让我...

And I also think back as I look at people that I meet who are now young, you know, sort of what's the trajectory, so to speak. And I realized there are things that I would do when I was, you know, six, seven, eight years old, which it's like, oh my gosh, that's the same kind of thing that I'm doing today. Like I remember the realization that you could take two rulers and you could run one against the other and you could make an addition slide rule. I mean, I didn't know what, and this was kind of my, this was one of the many ways that I failed to learn arithmetic was that, you know, teachers are probably wondering why does he have two rulers on his desk? Because that would allow

不用实际运算就能解决问题。我明白了。不过——

you to do things without having to do things. I see, yes. But

然后这就形成了一种趋势，因为，你知道，我一生中大部分时间都在构建工具，让人们能够不费人力地完成事情，可以这么说。

then there's a trend because, you know, then I've spent a large part of my life building tools to let one do stuff, you know, without putting in human effort, so to speak to do it.

现在我们有了很好的过渡，因为那个Steggy的事情是个题外话，但我忍不住要提，你看，我正试图为人们构建一些东西。也许它现在没什么用，因为我们的话题很分散，但我想谈谈你所做和正在做的事情的背景。这里有三个组成部分：物理学、数学，另一个就是计算机。我想知道你是什么时候、因为什么对计算机产生兴趣的。我在你的剪贴簿里看到了一些线索，我记得有一张你年轻时和计算机磁带在一起的照片。

Now we have the good segue because that Steggy thing was an aside, but I couldn't resist, but see, I'm trying to build for people. Maybe if it's not useful because we're all over the place, but I want to talk about the context of what you've done and what you're doing now. And so there's three components. There's physics, there's mathematics, but the other component is computers. And I wanna find out when you got, what got you interested in computers and when I know I saw an inkling of that because I think I saw a computer tape in one of your scrapbooks there as a young person.

所以，到底是什么让你对计算机产生了兴趣，又是什么时候？让我来问这个问题。

So you were clearly what got you interested in computers and when? Let me ask that question.

好的。我第一次见到计算机是在大约10岁的时候，那是一台远处的大型主机。12岁上中学时，我才真正近距离接触计算机，因为我的中学有一台计算机——那是一台疯狂的英国计算机，有桌子那么大，用纸带编程，使用非常晦涩的机器码等等。实际上，我尝试用计算机做的第一件正经事，是模拟物理课本封面上那些四处弹跳的气体分子。

Okay. So I first saw a computer when I was like 10 years old. It was a big mainframe computer at a distance. I first got exposed to a computer close-up when I was 12 years old, when I went to high school because my high school had a computer, which was a thing of the crazy British computer that was the size of a desk and you programmed it with paper tape and it had a very arcane machine code and so on. And then the question was, actually the first really serious thing I tried to do with computers was to simulate that bunch of gas molecules bouncing around on the cover of the physics book.

我当时想，让我写个程序来做这个吧。但那台计算机没有浮点运算功能，缺少很多东西。讽刺的是，我写的程序基本上是一个元胞自动机程序，也就是我多年后研究的那种简单程序。要不是因为一些不变性的巧合之类，我本可以——如果当时知道自己在寻找什么——发现许多我在十年后才发现的成果，那还是我13岁左右第一次做这个的时候。

And I was like, let me write a piece of a program to do this. Well, that computer didn't have floating point arithmetic. It didn't have lots of things. The real irony is the program that I wrote was basically a cellular automaton program, which is, you know, this kind of simple program that I investigated years later. But for a little coincidence of invariances and things like this, would have discovered, well, if I'd known what I was looking for, I would have discovered tons of things that I discovered like a decade later, right back when I was first doing this when I was 13 or so.

但你知道，我开始使用计算机是想做这类物理模拟，后来却因为计算机本身相当原始，我开始为它编写实用程序之类的东西。我特别为我的纸带加载器感到自豪——纸带会通过这个光学阅读器快速运行，最后卷进一个木箱里，你得倒带再重新运行。如果纸带上沾了一小片碎屑堵住了某个孔，就会把错误数据读入计算机内存。那么问题来了：怎么解决这个问题？

But, you know, I started using computers. I wanted to do this kind of physics simulations, but then I got into actually doing things with the computer for its own sake because it was a quite primitive creature and I was trying to write utility programs and so on. I was very proud of my paper tape loader, which was a, so the paper tape would run through this optical reader and it would run pretty fast and it was, and it would wind up in a wooden bin and you would rewind the tape and then run it through again. If that paper tape ever picked up a little piece of confetti that would kind of fill in one of its holes, then it would just get the wrong data into the memory of the computer. And so the question was, how do you deal with that?

现在回想起来，我当时发明了一种纠错代码，能在读取时积累数据，通过校验位等机制发现问题。它真的会把纸带倒回阅读器重新读取，自我重新同步等等。那可以说是我编写的第一个系统软件。

And so I was in retrospect, I ended up inventing some error correcting code that would figure out as the thing was reading, you know, would accumulate data to figure out that it would have checked digits and things. I was very proud of that. It would was, literally pull the tape back in the tape reader and it would start reading again. It would resynchronize itself and so on. But that was my first piece of system software, so to speak.

哦，好的。那是什么时候的事？

Oh, okay. And when was that?

大概在1973或1974年，那时我十三四岁。

Probably in 1973, 1974, when I was 13, 14 years old.

那个

That

是的，实际上这件事是这样的，那只是我写的一个东西。我想其他人会用到它。这可能是我开发的第一个软件工具，后来还积累了一些用户，虽然用户群体可能不大。

was, and actually it was one of these things where, yeah, I mean, that was just something I wrote. I guess other people would use it to that point. And it was probably my first piece of software. Now that I think about it, it's probably my first piece of software tooling that ended up getting a user base, so to speak. Probably not a very big user base.

我之所以想深入探讨这个，是因为你现在做的事情与编程如此紧密相关。事实上，宇宙本身就像一个程序，我真的很想多理解一些。根据之前的讨论，我最初假设你会被计算机吸引是因为它们能帮你完成不喜欢做的事。但真正让你着迷的是计算机的什么特质？具体是什么吸引了你？

The reason I want to really go into this because what you're trying to do now is so integrated to programming. In fact, the universe is a program that I really want to try and understand this a little bit more. My first assumption based on earlier discussions that you would have been fascinated by computers because they would allow you to do things that you didn't like to do. But was it that that intrigued you about computers? What was it in particular?

是它的力量吗？我记得它们有多迷人。我小时候学校还在用打孔卡，能看到这个机器给出你原本得不到的答案——甚至不知道它是怎么算出来的——这种感觉很奇妙。你还记得当时最吸引你的是什么吗？

Was it the power? I mean, I remember how seductive they were. We had punch cards when I was a kid in school and it was neat to be able to see that you could make this thing come up with answers that you might not have gotten otherwise, and maybe not even know how it did it. But do you remember what it was that was so seductive to you about it?

嗯，我觉得科技...我喜欢未来，而科技是未来的一部分。这是我喜欢计算机的一个原因。我对计算机感兴趣还因为我想做物理这类事情。不过那时候，我的第一台计算机根本做不了复杂的数学运算，那种机器太简陋了。

Well, mean, like technology and technology was kind of, I liked the future and technology was part of the future. And that was one reason why I liked computers. I liked computers because it was, I was interested in doing these things like physics. Now at the time, my very first computer, I couldn't do serious mathematical computations on that computer. That would have been way too difficult on that kind of machine.

但我认为那种纯粹为了计算机而计算机的事情，嗯，我做过一些类似的事，比如我说过我是个组织能力强的孩子对吧？学校会举办开放日之类的活动。我总是负责组织计算机展览。所以我写了一些小电脑游戏之类的东西。人们会进来参观，要知道那是1973、1974年，这些家长和其他人进来后会说'哇，是计算机'，他们以前从没见过电脑，反应非常新奇。

But I think that sort of computers for their own sake, well, I did things like, okay, I said I was an organizer kid, right? They would have like open days at the school and things. And so I would always organize the computer exhibit for the And open so I wrote a bunch of little computer games and things like that. The people would come in, you know, this was 1973, 1974, and all these various parents and so on would come in and say, Oh, it's a computer. And they would, you know, it was very, they'd never seen a computer before.

他们当然也从未...我有些游戏其实是这样的：有一个会在电传打字机上打印出两个字母，然后你必须根据字母表顺序按下对应按钮。

And they certainly never, you know, I had some games that were actually, here's one that was, would print out on teleprinter. It would print out two letters and then you would have to press a button depending on which letter was earlier in the alphabet.

它

It

结果发现如果运行速度够快，人们正确率会系统性低于50%，至少这是我13岁左右做的实验心理学观察。所以这可能是我计算机展览中最得意的作品。

turns out if you run that fast, people get it right less than 50% of the time, systematically get it wrong. At least that was my experimental psychology observation of age 13 or something. And so that was my, the sort of my, probably my proudest exhibit for the computer.

听起来其实像个科学展览项目。

Sounds like a science fair project actually.

确实像。嗯，我可能收集了很多好数据。可惜当时没有真正记录数据的方法，更多只是观察人们的表现。

Sounds like right. Well, I probably got a lot of good data. I did. Unfortunately, I didn't really have a way to collect that data at the time. It was more just observing what people did.

你知道这很有趣，因为现在我们要谈到一个交汇点——虽然你可能不记得这事，但我得说，我获得哈佛博士学位后发表的第一篇正式科学论文其实是关于计算的。用的是HP-15C计算器做数值积分。当时同事都能用大型计算机，但我发现可以用计算器完成——虽然要运算整晚，但我不需要三十秒出结果。直到很久之后我才重新用回大型计算机，那是我...（提及第一台电脑时被打断）

Well, you know, it's interesting because I wanna now we'll talk about when one thing we converge, because I'm proud of this, although you may not have the same memory of me, but I will say by the way, my very first real science paper after I got my PhD when I was at Harvard was actually done on computations. It was numerical integrations using a HP 15C. All of my colleagues had access to mainframes, but I realized I could do this numerical integration. It would take a night for the calculator to do it, but I didn't have any, you know, I didn't need it in thirty seconds. And so it took me a long while before I made it back to larger scale computers and what, and my first computer.

我之所以提起这件事，是因为我确实记得读过你记录过自己用鼠标的里程数。好吧。但我相信，难道不是我把Macintosh介绍给你的吗？记得我在哈佛时拥有第一批Mac电脑，你来参观时非常怀疑，是我带你见识的。那台机器算是便携式的，因为重达23磅，就放在我的办公室里。你进来时，我记得你对它充满怀疑，毕竟那时我已经用上了鼠标等全套设备。

And the reason I wanna bring this up is I do believe I've read that you've logged how many mouse miles you've also done. Okay. But I believe I, is this not true that I introduced you to the Macintosh? You remember I at had the one, the first Macs at Harvard, you came visiting and you were very skeptical and I brought you down. I had a, cause it was like a portable because it was 23 pounds and I had in my office and I think, and you came in and I think you were very skeptical of it because I had the mouse and everything.

但我坚信是我向你介绍了Mac电脑，这一点我绝不退让。

But I believe that I introduced you to the Mac and I'm gonna stand That by

这很可能属实。不过要说明的是，那时我主要在使用Sun工作站计算机。

very well be true. I'll tell you by that time, I was mostly using these Sun workstation computers.

之前

Before

在1988年Mathematica软件问世前，我从未真正深度使用过个人电脑。虽然拥有个人工作站电脑，但即便在Mathematica发布后——尽管它支持Mac平台——我也从未在Mac上使用过。演示时会用Mac展示，但实际工作都在工作站上完成。不过这是个有趣的故事，确实有可能。

Mathematica came out in 1988, I had never really used a personal computer in a serious way. I had had personal workstation computers, but you know, and really even at that time when after Mathematica came out, it ran on the Mac, but I never used it on the Mac. I would use it for demos on a Mac, but I would actually use it on some workstation. But that's an interesting story. It's plausible.

推算时间的话，Mac是1984年推出的，所以那应该是...应该是1984年底吧。

Mean, must have been, well, Mac came out in 1984, so that must have been- that must have been late. 1984,

我明白了。我是在1984年1月后不久拿到第一台的，属于首批用户。当时需要通过抽签购买，因为需求太火爆了。记得我告诉朋友Shelly Glaschow这件事时，因为太渴望拥有而焦虑不已。

I got it. Well, I got one in Jan, a little after January '4. Was one of the first, there was a lottery because there's so many people who wanted it. And I wanted, I remember I told my friend who was Shelly Glaschow about it. And it really upset me because I really want it.

我说，有个抽奖活动。他说，真的吗？然后他报名了。他排到了第一名，得到了奖品，我不知道他怎么处理的。他用了吗？

I said, there's a lottery. And he said, oh really? And he put his name in. He got to be like number one and he got, I don't know what he did with it. Did he use it?

不，不。正是这点让我很恼火，因为我真的很想要那个奖品。但我刚作为重力研究中心的专家赢得了一个奖项。金额恰好，我当时正琢磨怎么买那台Mac电脑。奖金数额和Mac的价格一模一样。

No, no. That's what pissed me off because I really wanted it. But I, and I just won a prize as the gravity research center experts. It was exactly, I was trying to figure out how I could buy it. And it was exactly the same amount as the Mac.

所以我真的中了奖，我...我...我...我把支票兑了现。大概四月或五月中的奖，之后不久你来哈佛找我的时候，我特别自豪。实际上我大部分时间都在炫耀，人们总想进我办公室玩这台电脑，因为它和其他电脑很不一样。你进来后你...

And so I literally won the prize and I, and I, and I, and I, and I gave the check back in, but yeah, so I had won maybe by April or May, and you came shortly thereafter afterwards when I was in Harvard and, and, and I was very proud of it. In fact, I spent most of my time, people would want to come in my office and play and see it because it was very different than other computers. You came You in and you

做了个决定。这事我有点模糊印象。老一辈人，像谢利·格拉肖那代人，他们大多不会打字。比如默里·盖尔曼，我记得和他讨论电脑时，他从不愿让我看他打字，因为他根本不会。

made made a decision. This is vaguely coming back to me. It's a story. One of the things about the older generation, the Shelley Glashard generation and so on, most of them didn't know how to type. And I remember, like Marie Gell Mann, for example, I remember interacting with him about computers and things, and he never wanted me to see him type because he couldn't type.

很长一段时间里，我为自己从小就用打字机而感到骄傲。

For a long time, I was like proud of myself because I used a typewriter from when I was an early kid.

是啊，我能看出来，从你的论文就能看出。

Yeah, can read, I can see it in your papers.

对，没错。我打字速度很快，其实我最擅长的是二指打字，因为当时手指力度不够。后来学会了十指打字，成了速记员。我曾以为这是自己的巨大优势，结果这技能后来完全没用了。

Yeah, yeah, right. And I got pretty fast at typing and actually what I really got fast at doing was typing with two fingers because my fingers were not strong enough to do the full typewriter thing. And then at some moment I did the 10 finger thing and I was fast typist. And then I used to think that's a great advantage that I have in the world and then it all went away.

哇，我周围都没看到什么人。

Wow. I'm not seeing people that all around.

这是怎么回事，你

This is what, you

我的两个

My two

手指操作随着手机回归了。现在能告诉别人这个技巧很有用。哦对了，

finger thing came back with phones. Now is useful to be able to tell people. Oh yeah,

没错。不过现在通常用大拇指而不是四根手指。

that's right. But now with thumbs rather than four fingers generally, however.

是啊，我从来没用过大拇指。这是我早期养成的毛病。用的是食指

Well, right, I'd never got into the thumbs. This a disease from my early time. It's index

其实我还是用食指，单手操作。是的。但我要说我母亲——虽然我告诉过你父母没上过大学——她坚持让我学会打字，因为她说你将来要写论文。所以我上了打字课，那本是选修课。

Actually, still use the index finger, hold one hand and do it. Yeah. But I will say my mother, again, I told you my parents didn't go to college, but the one thing she insisted I learn how to do was type because she said, you'll have essays. So I took typing class. It was optional.

是的，我一直觉得她给我的最大恩赐之一就是让我早早学会了打字。确实。现在很多人已经不会这项技能了。总之，看，我们现在已经拼凑出了引导你走到今天的所有线索。

Yeah, and I've always felt it was one of the great gifts she did me that I learned how to type early on. Yeah. Yeah. A lot of people don't know how to do that now. Anyway, look, wanna get Well, we've now put together the pieces that will lead you to where you are.

我正想说，容我直言——虽然现在不想深究——你并未完成伊顿公学的学业。之后你去了牛津，记录显示你也提前离开了那里。所以你不断提前离开学校，我想是因为你觉得已经从中获得了所需。后来你去了加州理工，终于在那里取得了学位，尽管过程相当...

I was gonna say, let me just say, and I don't wanna go into this now. You didn't complete Eton. Then you went to Oxford and it says you also left that prematurely as well. And so you keep leaving schools prematurely because you've, I guess, felt you'd gotten out of them what you did. And then you went to Caltech and actually did get a degree there finally, although in a very

简短...其实情况很容易解释。当时我已经在写一堆物理论文，就觉得：既然我都能写物理论文了，那上大学学物理的意义何在？

short Well, what happened was, it's easy to describe. Mean, got to the point I was writing a bunch of physics papers and it's like, okay, I can go to college and do physics, but I'm writing physics papers. So what's the point here?

而且

And

这就像把进程加速到极致，让我能尽快结束教育流程。实际上效果相当不错，确实很...

it was kind of like accelerate things to the point where I'm done with the education process as quickly as possible. And that worked rather well actually. Worked

非常成功。但前提是要遇到识才之人，比如那些在你物理考试中给出高分的人。加州理工有什么特别？其他很多院校——我猜多数研究生院——应该都要求更正规的学历。是因为学校规模小所以能破例，还是...

really well. It only works well if you have people who recognize it, the people who happen to give you the good grades in that physics test. What was it about Caltech? I mean, there are a lot of places that would have required, I assume there are a lot of graduate schools that might have required more formal degree. Is it because Caltech was so small that they were able to What was it allowed to

这个嘛...到那时，有件事既是优势也是负担：我十五六岁时就开始出现在牛津各类物理研讨会上，逐渐成为国际物理学界熟面孔。后来我在英国卢瑟福实验室工作过，又去了美国阿贡国家实验室实习等等。可以说我早已卷入物理学界的漩涡——事实证明这在某些方面简直是灾难，因为那些见过我的人...虽然我不算特别，但确实是个莽撞的十六七岁少年。当你以莽撞少年形象混迹国际学术界，三十年过去后，人们记忆中的你依然是个莽撞的十六岁...

get Oh, to look, by that point, one of the things that was both a good thing and a bad thing is by the time I was like 15, 16 years old, I was showing up at all these physics seminars in Oxford and things, and I became a sort of known fixture on the international physics scene. And then I worked at the Rutherford Lab in England, and then I worked at Argonne National Lab in The US for a summer and so on. So I kind of was in the swirl of the kind of physics world, which is actually, it turns out it's kind of disastrous in some ways because there are all these people, I a, I don't think I was a particularly, but I was a somewhat brash 16, 17 year old. And when you're in sort of the international community and you're a brash 16, 17 year old, you turn the clock thirty years later and people still think of you as a brash 16, You

17岁时我也很莽撞，但后来人们就不觉得那么莽撞了。当你年纪大了，说着和年轻时同样的话，大家反而不会认为那是莽撞。

17 year were very brash when I first met you too, but yeah. The good is afterwards people don't think it's brash so much when you're older and you say the same kind of things as when you're younger.

嗯，也许确实如此吧？不，我是这么想的。当时的情况是，我联系了几所不同的学校，和哈佛、普林斯顿以及加州理工的人谈过。哈佛说，如果你没有大学学位就不能来读研究生。普林斯顿说没问题，加州理工也说没问题。我当时已经参观过普林斯顿，但还没去过加州理工。

Well, perhaps that's true, right? No, I think that, but, you know, so what happened, so I was, I talked to people at these different schools and I was talking to Harvard and Princeton and Caltech. And Harvard said, Oh, if you don't have a college degree, you can't come as a graduate student. Princeton said, Fine, Caltech said, Fine. I decided I'd visited Princeton, I hadn't visited Caltech.

所以我决定去那个我还没怎么参观过的地方。

And so I figured I'll go to the place I haven't visited more or less.

或多或少...不是因为天气吧？我是说，两地的天气差异很大...不，

More or Wasn't the weather, was it at all? Was it, I mean, which is very different No,

特别是天气，我当时没太在意。我觉得加州理工的制度也更灵活些，普林斯顿要求必须修这些课程之类的。而我就想，我不想也不需要这么做。加州理工在这方面相当灵活。后来我去听了迪克·费曼的一门课，结果没过多久他就跟我说，以后别来上这门课了。

particular the weather, I wasn't really paying attention. I think Caltech also had a slightly, Princeton had a more structured, oh, you have to do these courses and all that kind of And I was like, I don't I don't wanna do this and I don't really need to do this. And Caltech was quite flexible about that. So it was, and I did, I went to a, I tried to go to a course that Dick Feynman was teaching. And actually he told me after a little while, please don't come to this course anymore.

真的吗？

Really?

所以那就是——

So that was-

为什么？是你在提问还是

Why? Were you asking questions or did

不，我认为当时的情况是合适的。是的，我是说，我并没有特别冒犯，但我记得我给他写了些关于温伯格角持续时间的内容。然后他就说，别再上我的课了。

you No, think it was appropriate for was Yes, I mean, I wasn't being particularly brash, but it was like, I remember I wrote him up something about the duration of the Weinberg angle. And he was like, don't come to my course anymore.

哦，他说你

Oh, says you

别用

don't use

它。它没用。好吧。嗯，那件事其实挺好的。我是说，如果他早知道的话，他也不会举行什么仪式之类的。

it. It's not useful. Okay. Well, and that was great about fine. Mean, he would have not held a ceremony or anything like that if he knew.

没错，就是这样。好老师的一个优点就是知道孩子们需要了解什么，不需要了解什么。好了，听着，我们已经绕开了一些话题。

Yeah, exactly. That's a good thing. Quality of good teachers to know what kids need to know and what they don't know, need to know. Okay. Look, we've, we've skirted around things.

我们已经讨论过基础物理学和你的兴趣所在。正如我之前所说，我们初次见面时，差不多就在你的生活发生转变的时候。在我看来，大约是83、84年，你突然从那种标准的、通过数学量子场论理解基本定律的基础物理学，转向了——我想你已经去了高等研究院，我们第一次在哈佛见面时你刚从那儿过来，然后你确实——你发现了，我不确定是不是那时你发现了细胞自动机，但即使在那时，远距离了解你就已经改变了你，改变了你的生活。据我所见，它改变了你的方向，改变了你对世界的整个思考方式。

We've already talked about fundamental physics and your, and your interest. And that's when we, as I said, when we first met almost was right around, we met at the time when your life was changing. It seems to me was around '83, '84 suddenly went from the kind of what the standard kind of fundamental physics, understanding the fundamental laws by mathematical quantum field theory to suddenly, I guess you'd already gone to the Institute for Advanced Study, I guess when I first met you at Harvard and you came up from there and then you did sell your, you discover, I don't know whether it was then you discovered cellular automaton, that it was even then it was knowing you at a distance that changed you and changed your life. As far as I can see, it changed your direction. It changed everything about the way that you thought about the world as far as I could see.

确实如此。我是说，看，事情是这样的。我在1979年获得博士学位之前，一直在从事粒子物理研究。就在那之后的一周，我开始思考未来的规划。

That's true. I mean, look, the sequence was this. I mean, I've been doing particle physics up until basically I got my PhD in 1979. Right. A week after that, I was like, okay, let me plan the future type thing.

于是我意识到，虽然一直在使用各种计算机系统进行数学计算，但它们无法满足我的需求。怎样才能得到真正想要的东西呢？如果你真心想要，就得自己动手。于是我开始构建一个名为SMP的系统。

And so I realized, I've been using all of these computer systems for doing sort of mathematical computation. I realized these don't do what I want. How am I going to get something that does what I want? Well, if you really want it, you should just do it yourself. So I started building this thing called SMP.

接下来的几年里，虽然仍做些物理学相关的工作，但主要精力都投入到了这个软件系统的开发上。

And so I spent a couple of years, you know, I was still doing some physics kinds of things at that time, but I was mostly working on building this software system.

请允许我向观众说明——鉴于讨论已相当深入——SMP在当时堪称革命性。计算机本擅长数值计算，你编程后它们就能执行浮点运算。但没人用它们进行纸上那种代数或微积分符号运算，而SMP实现了这点。我至今仍清晰记得它的实用性，以及对其可行性感到的震撼。

Let me interject for the public who, I mean, we've already gone so deep that people may have lost us anyway, SMP, I mean, it was in my mind at the time revolutionary. There may have been other people doing it, but computers were fine for doing calculations. Know, you plug, you'd program them and then they work with desk floating point arithmetic. But you didn't use them for symbolic when you sat on a piece of paper and did algebraic or calculus calculations, those were symbolic and computers just didn't do that. And I do remember vividly the utility and also being amazed that it was possible to do.

SMP是首个（我猜代表符号处理程序）能让计算机真正做数学而不仅是数值运算的系统。它能协助进行真正的数学——符号数学，这令我震惊。记得同事们开始讨论其价值，特别是在费曼图计算这种容易迷失于符号操作的领域——这或许正是你开发它的初衷。

SMP was the first that stands, I assume for symbolic manipulation program. Was that what it I stood think that And the idea that computers could actually do mathematics instead of just churning numbers. Could actually do mathematical and help you do math, real mathematics, symbolic mathematics was shocking to me. I remember my colleagues began to say, this can be useful because of course the one area where, and maybe this is the reason I guess you got into it. The one area where you really, where you can get lost in this symbolic manipulations is the calculation of what are called Feynman diagrams, which I know you did.

所以这就是推动你开发SMP的原因吗？还是说...

And so, and that I assume is that's what drove you to wanna do SMP is is there a No more

差不多吧。早期也有计算机代数系统，但它们都只能在其开发者指导下使用，就像需要保姆照看一样。

or less, I mean, had been earlier computer algebra systems, but they were always, they basically had the feature that they could only be used for the babysitter. That is they could only be used with the help of the people who'd originally created the

系统。没错。

system. Exactly.

还有人们，我的意思是，令我惊讶的是，这再次印证了你永远无法预知什么是真正困难的、什么是容易的。我掌握了足够的计算机知识，能够独立使用这些系统，可以说不再需要‘保姆’了。后来我用它们完成了一些有用的事情，逐渐超出了它们的能力范围。因此我不得不开发SMP系统。现在回想起来，SMP最有趣的地方在于它蕴含了一种根本的计算理念——本质上是一种符号化思维，甚至比纯粹的数学运算更具符号性。

And also people, I mean, was surprising to me the extent to which, again, it's one of these things where you never know what's actually hard and what's easy. I learned enough about computers that I could successfully use these systems without a babysitter, so to speak. Then I used them to do useful things and I kind of outgrew them. And so I had to build SMP. I mean, what was in retrospect pretty interesting about SMP is it has a sort of a fundamental idea about how to compute that is sort of fundamentally symbolic, more symbolic even than just doing mathematics.

它真正关注的是符号表达式及其转换规则。实际上就在最近几个月，我终于明白了如何将当年试图解决的问题进行推广。当年开发SMP时，关于系统如何评估内容、如何转换表达式直到无法继续转换的过程充满谜团。这种‘转换至无法继续’的机制，以及当存在多种转换路径时会发生什么？

It's really about symbolic expressions and transformation rules for symbolic expressions. And actually very recently, like the last few months, I finally understood how to generalize the things I tried to figure out. So back when I was working on SMP, there were all kinds of mysteries about how you, it sort of evaluates things, it transforms things until it can't transform them anymore. And that process of transforming until you can't transform anymore. And what about if there are different paths for transforming things?

这整套问题涉及极其复杂的计算数学概念。颇具讽刺意味的是，当我为SMP思考这些问题时，同时也在研究规范场理论。现在我才意识到，SMP的求值过程与规范场理论中不同操作路径的问题本质上是相同的——但这个认知足足耗费了四十年时间。

That is a whole tangle of difficult kind of ideas, computational mathematical ideas. And what's sort of ironic is that at the time when I was thinking about those kinds of things for SMP, I was also thinking about gauge field theories. And it turns out that what I now realized is that the issues about all the different ways to do things between evaluation processes and SMP and gauge field theories are exactly the same problem. But it took another forty years to realize that.

好的，我们会讨论这个，因为我知道你一直在强调这些定律——规范场理论作为核心对称性，是理解所有基本定律的关键方式。我知道你对其衍生机制有很多主张...

Okay, we'll get to that because I know you keep talking about how you can basically get these laws that we mean, gauge field theory is a central symmetry and the central way of understanding all fundamental laws. I know there are lots of claims you make about them coming out of doing

目前还无法完全掌握规范场。虽然我们大致知道理论框架，但数学实现非常困难。

Can't quite yet get gauge field. Although we kind of know how we think it's gonna work. The math is hard.

稍后我想就此提出一些质疑，但首先让我们保持学术友好——我必须公正地说，确实有人在做相关研究。比如阿诺德·图夫和特尼·韦尔特曼开发了一个（我本想说‘帆船’）程序，用于对费曼图进行符号运算，这最终帮助他们完成了获得诺贝尔奖的物理研究。所以确实有先行者，你是对的。

I wanna challenge you on some of that in a moment, but first let me be more collegial and then we'll challenge. And I should say to not do short shrift, you're right. There were people, for example, I think Arnaud Tuft and teeny Veltman developed a schooner. I mean a program to do symbolic, some symbolic manipulation of Feynman diagrams in order for them to be able to do the kind of physics, which eventually led them to the Nobel Prize. So there were people working on it, but you're right.

它们必须是专业化的，没有那种随便一个像我这样的外行都能直接上手使用的东西。

They had to be, they were specialized. There was no one who developed something that some Bozo like me could come along and just use.

没错。SMP真正的核心理念，最终至关重要的，是关于符号表达式转换的思想——这是计算领域非常普适的理念。我的意思是，即便四十年后的今天，人们仍未完全消化这个抽象概念，但它正是我们整个Wolfen语言及Mathematica技术栈的根基。不过从发展轨迹来看，那次经历确实非常有趣，因为构建软件系统与做物理研究截然不同——物理世界里万物自有其规律。

Right, no. The real idea of SMP, the important idea in the end was this idea of transformations for symbolic expressions, which is a very general idea about computing. That's, I mean, it's kind of an abstract idea that I think people haven't fully absorbed even now forty years later, but it's also the core idea that our whole Wolfen language mathematica stack is based on. But I mean, that was anyway, but in terms of the sort of the trajectory, it was, yes, I did It was a very interesting experience because building a software system is very different from doing physics. Because in physics, it's like the world is the way it is.

你需要不断深挖试图理解底层原理。而设计计算机语言时，你会先定义这些基础元素，然后思考能构建出什么。这更像是从某些任意起点开始向上搭建，不像物理学中世界本就存在，你需要逆向解析其运行机制。

You have to kind of drill down and try and figure out what's underneath it. When you build a computer language, you're like, let me write down these primitives. Now what can be built from those? It's kind of very much a more sort of, start from something, it's like you start from these arbitrary things and then you build up from there rather than in physics, you kind of, the world is the way it is. And you have to try and figure out you have to sort of reverse Now engineer what's going

你的解释让我豁然开朗，这个观点非常关键——虽然我对你转向的领域持保留意见，但显然细胞自动机吸引你的原因变得清晰了。你主张的这种新科学，正是通过简单规则探索可能性，这与你的软件开发经历完美呼应，这个关联我过去从未意识到。

you've explained everything to me because it's now it all comes to clearly to me because that's a very important statement because it's clear that what you switch to and it's an area where I'm not sure I agree with you with, but it's what you've switched to is it's so natural to understand where cellular automata appealed to you. And ultimately this new kind of science is you're now claiming, and then with cellular automaton, it's some simple rules and what can you do with them? It's exactly, so that's what it's clear why that appealed to you because you'd been developing software that had never hit me before.

确实。追溯个人历史总是令人尴尬，我自己也花了十年才明白这个联系。我长期关注的核心问题是：世界如何产生复杂现象？早期研究统计力学时，我尝试反应扩散方程等方法都失败了，于是决定回归本质——

Right. Well, actually, it's always embarrassing when one tries to understand one's personal history, because it took me a decade before I realized that connection myself. But yes, that's the So what happened is I was, the big thing that I've been interested in for a long time and my early interest in statistical mechanics and so on was how does complex stuff happen in the world? So it was like I was studying reaction diffusion equations and I was studying these other kinds of mathematical approaches to that and they just didn't work. And so I was like, let me see what's the fundamental thing.

我要深挖基础，找出构成现象的基本单元。这引导我最初尝试建模自引力气体和神经网络时思考：介于两者之间的是什么？最终发现了这些黑白格子的细胞自动机，它们仅靠简单的局部规则运作。

Let me drill down. Let me understand what are the primitives from which I can build up that phenomenon. And that's what led me to, I mean, originally I was trying to model, I was actually looking at self gravitating gases and neural networks. It was like, what's in between these two? And I came up with these simple cellular automata, which are just these rows of black and white cells, which have simple local rules.

细胞自动机虽擅长许多事，但对自引力气体和神经网络这两类问题却完全不适用。有趣的是当时竟从这两个领域切入...

And cellular automata are good for many things. Self gravitating gases and neural nets are two things they are profoundly not good for. So it was kind of interesting that that was in Let those

让我暂停一下，因为我确实想，我是说，我们还没有为那些必须跟进的人定义太多内容，你大致定义了细胞自动机，但我想把它讲得非常清楚。它们之所以诱人且有趣，是因为它们本质上是一组黑白方格。当你有一个黑格和一个白格相邻时，存在一条规则决定下一行会是什么。如果两个白格相邻，或者两个黑格，甚至可能是连续四个同色格子，都有一套简单的规则告诉你结果，然后你就可以一步步推进下去。

me just stop for one second because I do wanna, I mean, we haven't tried to define a lot for people who've had to follow through, you sort of define cellular automata, but I wanna make it quite clear. They're seductive and interesting because they are that they're basically a set of squares, blacks and whites. And there's a rule when you have, let's say a black and a white together, there's a rule for what the next role will be. And we have two whites together, there'll be, or two blacks or maybe four of them in a row. So it's just a simple set of rules that tells you, and then you proceed from one step to the other.

令人惊讶且引人入胜的是——虽然我不确定是否如你所想的那般深刻，这点我们稍后再讨论——从几条简单的规则（比如当这两个东西相邻时会发生什么，可能就三条规则），你就能产生这些极其复杂的图案。我只是想让人们了解什么是细胞自动机。我注意到在你的剪贴簿里，好像是《自然》杂志的封面吧，有些早期通过简单规则生成的美丽复杂图案，这些肯定对你产生了深远影响，因为

And what is surprising and seductive, but I'm not sure as profound as you think, but we'll have to discuss that. What is surprising and seductive is it from a very simple rule of what happens if these two things are together, maybe three rules, you produce these incredibly complex patterns. So I just wanted to let people know what cellular automata are. And I guess I did notice in your scrapbook, I guess it was a cover of nature or something, but some of the early beautiful complex patterns you can get from these simple set of rules, which must have profoundly affected you because

核心问题是：自然界究竟藏着什么秘密，能创造出所有这些复杂事物？而这就是...好吧，可能是直觉，我的直觉一直认为，要制造复杂的东西，你需要付出巨大努力，需要以非常复杂的方式设置条件。但这个例子中，你只是随机选择这些极其简单的规则，运行它们，就能自动产生惊人的复杂性。

The of big question was what secret does nature have that lets it make all this complicated stuff? And this was, well, it might be, one's intuition, my intuition have been, you wanna make complicated stuff, you need to go to a lot of effort. You need to set things up in a very complicated way. This was a thing where you just randomly pick these rules, very, very simple rules. You run them and you kind of automatically get this amazing complexity.

起初我觉得这根本不可能是对的。实际上，我记得费曼还就此与他有过一场有趣的对话，因为这个30号规则——一个特别简单的规则——产生了在许多方面看似完全随机的模式。记得当时我们都在波士顿一家叫'思维机器公司'的计算机企业当顾问。

First I was like, this can't possibly be right. In fact, I remember Feynman actually had an interesting sort of exchange with him about this because this rule 30 rule, which is a particular simple rule that produces this seemingly completely random in many ways pattern. And I remember when we both that, we were both consultants at a computer company in Boston called Thinking Machines Corporation.

那时候啊，

Way back then,

我当时打印了这份巨大的30号规则输出图，其中某些特征呈现出规律性等等。我们正趴在地上用尺子测量各种数据。费曼把我拉到一边说：听着，我就问你一件事，你怎么知道这条规则会产生所有这些真正复杂的东西？我回答说：我完全不知道。

And I had produced this big printout of rule 30 and there was certain features of it that had some regularities and so on. We're kind of crawling around to measure a bunch of things with meter rules and so on. And Feynman takes me aside and he says, look, I just want to ask you one thing. How did you know that this rule was gonna make all this really complicated stuff? And I said, I didn't have any idea.

我只是做了实验，结果就这样出现了。他说：哦，这下我感觉好多了。我还以为你有什么特殊直觉能预知这个。我说：不不不，在那个层面上，我充其量只是个实验科学家罢了。

I just ran the experiment and that's what happened. And he said, Oh, I feel much better now. I thought you had some kind of intuition that would let you figure this out. And I said, No, no, no. I'm just experimental scientist, so to speak at that level.

但令我惊讶的是，这是一种非常强烈的现象。这种现象表明简单规则能产生极其复杂的行为。我在各种可能的简单规则世界中都能观察到这种现象。当你回溯历史时会问，难道人们之前不知道这个吗？答案是，某种程度上确实知道。

But I think what was surprising to me, it's a very strong phenomenon. It's a phenomenon where simple rules can do very complicated things. It's a phenomenon that I've seen all over the kind of world of possible simple rules. When you go back and look and you say, didn't people already know this? And the answer is, well, did kind of.

比如圆周率π的数字3.14159等，生成这些数字有既定规则，但一旦生成后，它们在实际应用中看起来完全是随机的。质数序列也是同样的情况——质数序列中存在大量随机性。但人们尚未真正理解的是，这种现象意味着什么？我花了很长时间才想明白。

I mean, like the digits of pi, for example, 3.14159, etcetera. There's a rule for producing those digits, but once you produce them, they seem for all practical purposes random. Sequence of primes, same type of thing. There's a bunch of randomness and sequence of primes. But what people hadn't kind of gotten onto and it took me a while to get into was, so what does it mean?

简单规则能产生如此复杂的行为。以质数为例，几个世纪以来人们研究的是其中可被发现的规律性。整体上存在大量随机性这个事实并不重要，重要的是那些能用传统数学方法处理的规律。因此《一种新科学》这本书本质上探讨的是：当我们真正专注于计算规则可能产生的现象时，会得到什么样的科学？

So there's this simple rule and it generates this very complicated behavior. For example, in the case of the primes, people spent centuries studying what regularities you can work out. The fact that the overall story is there's lots of randomness, that was not relevant. What was relevant was the stuff that could be attacked with kind of traditional mathematical approaches and things of saying, what are the regularities? So in a sense, ended up with this book called New Kind of Science is what science do you get if you are really concentrating on this phenomenon of what can happen with computational rules?

这类现象可以说我们根本不在乎。人们观察到这些现象时总说'这只是噪音'。我们只关注那些非常规律的特例，这本质上取决于你的研究兴趣所在。

And that's kind of the thing that you can say, we just don't care. And people had seen these phenomena and they just said, oh, it's just noise. We don't care. We're concentrating on this particular thing, which is very regular that we're looking for. And, you know, it's a question of what you're interested in.

比如热力学第二定律：开始时气体分子在箱子里排列非常规则，经过一段时间后变得完全随机分布。问题是这其中真正发生了什么？因为微观相互作用是可逆的，理论上从有序到无序的过程完全可以逆向运行。

For example, talk about the second law of thermodynamics. The second law of thermodynamics is the story of you start off a bunch of gas molecules and they're all in a very regular arrangement of a box and then you let them run for a while and then they're all randomized in the box. And the question is, what's really going on there? Because among other things, the microscopic interactions are reversible. So whatever process could happen that goes from that simple configuration to the apparently random configuration could also run-in reverse.

为什么逆向不发生？最终正是这种基础的计算现象解释了其中的原理。

Why does that not happen? And this, in the end, it's this kind of fundamental computational phenomenon that explains how that works.

确实，玻尔兹曼花了很长时间研究这个，最终因此自杀。我是说，他试图理解为什么会出现这种情况。

Well, yeah, though I think Boltzmann spent a long time, eventually killed himself because of it. But I mean, trying to understand why that happened that way.

人们没有——我想我最终在1990年代弄明白了这是如何运作的。当时我理解这一点时，我觉得已经没人在意了。我其实没有——我是说，故事是这样的，还挺有趣的。想象这些气体分子在一个盒子里四处弹跳。

People didn't I think I finally figured this out in the 1990s, how this works. And I think people haven't At the time when I figured it out, I don't think anybody cared anymore. And I haven't really I mean, here's the story. It's kind of an interesting story. So you've got these gas molecules, they're bouncing around in a box.

它们处于某种构型中，从最终构型出发，原则上总能回溯并发现，哦，这个最终构型源自盒子里分子的简单排列模式，而另一个则不是。为什么我们不会遇到分子突然神奇重组、让打散的鸡蛋复原这样的情况？我认为答案在于我称之为‘计算不可约性’的现象，这个我们还没详细讨论过。

They are in some configuration where from that final configuration, you can always in principle go backwards and figure out, oh, this final configuration was one that came from the simple pattern of molecules in the box. This other one was one that didn't come from a simple pattern of molecules in the box. Why is it the case that we don't, for example, end up with some configuration of molecules that will magically reassemble itself and unscramble the egg and things? And so the answer I think is this phenomenon that I call computational irreducibility, which we didn't really talk about yet.

我们马上会讲到。你可以——对，开始谈谈这个吧

We're gonna get there. You can Yeah, start talking about it

好。比如这个‘规则30’现象。其中关键在于一个简单规则，它一步步告诉你如何生成模式，但这个模式本身很复杂。

right. Mean, so take this rule 30 phenomenon. So one of the things that you have is simple rule. The simple rule tells you step, step, step, you work out what the pattern is. The pattern is complicated.

你可能会说，我们是科学家，我们要预测事物，让我们预测规则30会产生什么。于是你搬出所有高级数学工具，宣称要破解它，弄清它的行为。实际上，理查德·费曼曾花时间尝试破解规则30。

So you might say, we're scientists here, we predict things, let's go predict what is rule 30 gonna do. And so you might say, you wheel in all of your sophisticated mathematical apparatus and so on and say, we're gonna crack it. We're gonna figure out what it's gonna do. And you try doing that. Actually Dick Feynman spent a while trying to do that for rule 30.

他最后说，好吧，你确实发现了什么。我破解了。问题在于：能否做到科学训练所要求的——做出预测？比如二体系统，地球绕太阳转，从牛顿时代起，我们就能用数学算出位置，无需追踪每段轨道。那么对规则30能做到吗？答案是不能。

And he finally said, okay, think you are onto something. I crack it. The way that, so there's this question of, can you do what one has been trained is sort of the effort in science? Can you make a prediction? Can you say, you've got a two body system, earth going around sun, from Newton onwards, it was kind of like, we can just use math to figure out where this is gonna be.

换句话说，要计算它的行为所需的工作量，你必须投入相当于——嗯，差不多就是那么多

We don't have to trace every orbit. So the question is, can you do that for rule 30? And the answer is, well, no, you can't. And we have, in other words, it's something where the computations that you have to do to work out what it's gonna do, you have to kind of spend as Yeah, much as it's

就我所知，计算可约性是你必须弄清楚事情本质的关键。你基本上需要重现整个过程。没有更简单的方法。除了让粒子自行实验外，没有更简单的预测方式。信息无法被压缩——这就是所谓的计算不可约性。我花了一段时间才理解这一点。

computations, as far as I can tell, computational reducibility is the thing you have to, you know, to figure out what's going on. You have to basically do what's going on. Can't, there's no simpler way. There's no simpler way to predict other than to just do the experiment to let the particles do it. There's no compactification of information that That's you what you call a It took me a while to get that, but computationally reducibility is why.

这就是为什么我认为它像是哥德尔定理的更精细版本，以及其他一系列观点的延伸——它揭示了计算世界的根本事实。在我看来，它源自更深层的原理，我称之为计算等价性原则。这涉及到以下内容：当你选取一组规则并运行它们时，就会执行某种计算。你可能会想对这些计算进行分级...

That's why think it's something that is kind of a, it's sort of a finer version of things like Godel's theorem and a bunch of other ideas that have a sort of, it's a kind of fundamental fact about computational world. It derives from an even deeper principle as far as I'm concerned, which is the thing I call the principle of computational equivalence. And that has to do with the following things. So you take some set of rules and you say that set of rules when I run them, it will do some computation. And you might say, well, let me rank these computations.

哪些计算最复杂？哪些最简单？令人震惊的是，一旦超出那些产生简单重复模式的范畴，根据计算等价性原则，所有系统的计算复杂度都是等价的。这是个重大论断——从规则30到人类大脑，再到物理学的诸多现象，它们的计算能力本质上没有高下之分。正是这个论断引出了计算不可约性的概念。

Which one is doing the most sophisticated computation, the least sophisticated computation? The big surprise is as soon as you get out of a domain of ones that do obviously simple things, that just make simple repeating patterns and things like that. The claim of the principle of computational equivalence is as soon as you're out of that zone, they're all equivalent in the sophistication of computation they can do. And that ends up being a big claim because it says that from rule 30 to our brains, to lots of things in physics, it's all equivalent in terms of the sophistication of the computations it can do. That claim is what leads to this idea of computational irreducibility.

因为如果你试图预测规则30的行为，就相当于宣称人脑比规则30更聪明——你能跳过步骤直接预知结果。但计算等价性原则指出这是不可能的，从而推导出计算不可约性的结论。

Because if you're going to figure out what's rule 30 gonna do, what you're basically saying is my brain is smarter than rule 30. I can jump ahead. It has to go through all its steps, but I can jump ahead. And that's what this principle of computational equivalence says you can't do. So that's what leads to this idea of computational irreducibility.

好的，我们稍后会讨论计算不可约性。坦白说，你在新科学著作和物理项目中基于计算不可约性和有限计算提出的观点很有趣——它们解释了世界为何如此运作。但核心问题是：物理学的本质是预测世界运行规律。在我看来，那些关于世界普遍特性的诱人论断，与实际预测操作之间存在巨大鸿沟。

Okay, well we're gonna get to computational irreducibility. I mean, because the interesting thing I found frankly with the writing you've been doing and the statements about new kinds of science and the physics project that you've been working on is one makes interesting claims based on computational irreducibility and bounded computation about why the world may be the way it is. But the quick question is, but what physics does is predict how the world operates. And so there's a big gulf as far as I can see between general statements that are tempting and seductive about that may make some, that may seem plausible about general qualities of the world, but that's a big difference than doing things.