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Stephen Wolfram is a computer scientist, mathematician, and theoretical physicist who is the founder and CEO of Wolfram Research, a company behind Mathematica, Wolfram Alpha, Wolfram Language, and the new Wolfram Physics project. He is the author of several books including A New Kind of Science, which on a personal note was one of the most influential books in my journey in computer science and artificial intelligence.

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When you were at Caltech, did you get to interact with Richard Feynman at all?

We worked together quite a bit, actually.

In fact, both when I was at Caltech and after I left Caltech, we were both consultants at this company called Thinking Machines Corporation, which was just down the street from here, actually.

It was ultimately ill-fated company, but I used to say this company is not gonna work with the strategy they have, and Dick Feynman always used to say, what do we know about running companies?

But anyway, he was not into that kind of thing and he always thought that my interest in doing things like running companies was a distraction, so to speak.

And for me, it's a mechanism to have a more effective machine for actually getting things, figuring things out and getting things to happen.

Did he think of it, because essentially what you used, you did with the company, I don't know if you were thinking of it that way, but you're creating tools to empower the exploration of the university.

I think not as well as he might have done.

I mean, I think that, but, you know, he was actually my first company, which was also involved with, well, was involved with more mathematical computation kinds of things.

You know, he was quite, he had lots of advice about the technical side of what we should do and so on.

Do you have examples, memories, or thoughts that?

Oh yeah, yeah, he had all kinds of, look, in the business of doing sort of, you know, 1 of the hard things in math is doing integrals and so on, right?

And so he had his own elaborate ways to do integrals and so on.

He had his own ways of thinking about sort of getting intuition about how math works.

And so his sort of meta idea was take those intuitional methods and make a computer follow those intuitional methods.

Now it turns out, for the most part, like when we do integrals and things, what we do is we build this kind of bizarre industrial machine that turns every integral into, you know, products of mere G functions and generates this very elaborate thing.

And actually the big problem is turning the results into something a human will understand.

And actually Feynman did understand that to some extent.

And I am embarrassed to say, He once gave me this big pile of, you know, calculational methods for particle physics that he worked out in the 50s.

And he said, you know, it's more used to you than to me type thing.

And I was like, I've intended to look at it and give it back and I still have my files now.

So it's, But that's what happens when it's finiteness of human lives.

It's, you know, maybe if he'd lived another 20 years, I would have remembered to give it back.

But I think it's, you know, that was his attempt to systematize the ways that 1 does integrals that show up in particle physics and so on.

Turns out the way we've actually done it is very different from that way.

What do you make of that difference, Eugene?

So Feynman was actually quite remarkable at creating sort of intuitive, like diving in, you know, creating intuitive frameworks for understanding difficult concepts

I'm smiling because, you know, the funny thing about him was that the thing he was really, really, really good at is calculating stuff.

But he thought that was easy because he was really good at it.

And so he would do these things where he would calculate some, do some complicated calculation in quantum field theory, for example, come out with a result.

Wouldn't tell anybody about the complicated calculation because he thought that was easy.

He thought the really impressive thing was to have the simple intuition about how everything works.

And because he'd done this calculation and knew how it worked, it was a lot easier.

It's a lot easier to have good intuition when you know what the answer is.

And then he would just not tell anybody about these calculations.

And he wasn't meaning that maliciously, so to speak.

And that led to areas where people were just completely mystified and they kind of followed his intuition, but nobody could tell why it worked.

Because actually the reason it worked was because he'd done all these calculations and he knew that it would work.

And you know, he and I worked a bit on quantum computers actually back in

before anybody had heard of those things.

And the typical mode of, I mean, he always used to say, and I now think about this, because I'm about the age that he was when I worked with him, and I see that people are 1 third my age, so to speak.

And he was always complaining that I was 1 third his age and therefore various things.

But he would do some calculation by hand, blackboard and things, come up with some answer.

I do something with a computer and he'd say, I don't understand this.

So there'd be some big argument about what was going on, but it was always, and I think actually, many of the things that we sort of realized about quantum computing that were sort of issues that have to do particularly with the measurement process are kind of still issues today.

It's a funny thing in science that these, you know, that there's a remarkable, it happens in technology too, there's a remarkable sort of repetition of history that ends up occurring.

Eventually things really get nailed down, but it often takes a while and it often things come back decades later.

Well, for example, I could tell a story actually happened right down the street from here.

When we were both at thinking machines, I had been working on this particular cellular automaton called Rule 30 that has this feature that from very simple initial conditions, it makes really complicated behavior.

So, and actually of all silly physical things, using this big parallel computer called the connection machine that that company was making, I generated this giant printout of Rule 30 on very, on actually on the same kind of printer that people use to make layouts for microprocessors.

So 1 of these big, you know, large format printers with high resolution and so on.

So, okay, so print this out, lots of very tiny cells.

And so there was sort of a question of how, some features of that pattern.

And so it was very much a physical, on the floor with meter rules trying to measure different things.

We've been doing that for a little while and takes me aside and he says, I just want to know this 1 thing.

He says, I want to know, how did you know that this rule 30 thing would produce all this really complicated behavior that is so complicated that we're going around with this big printout and so on.

I just enumerated all the possible rules and then observed that that's what happened.

I thought you had some intuition that he didn't have that would let 1.

I said, no, no, no, no intuition, just experimental science.

So that's such a beautiful sort of dichotomy there of that's exactly what you showed is you really can't have an intuition about an irreducible, I mean, you have to run it.

That's so hard for us humans, and especially brilliant physicists like Feynman to say that you can't have a compressed, clean intuition about how the whole thing works.

No, he was, I mean, I think he was sort of on the edge of understanding that point about computation.

And I think he found that, I think he always found computation interesting.

I mean, that intuition, you know, the difficulty of discovering things, like even you say, oh, you know, you just enumerate all the cases and just find 1 that does something interesting, right?

Turns out, like, I missed it when I first saw it because I had kind of an intuition that said it shouldn't be there.

So I had kind of arguments, oh, I'm gonna ignore that case because whatever.

Because you're essentially the same person as Richard Feynman, like the same kind of physics type of thinking.

How did you find yourself having a sufficiently open mind to be open to watching rules and them revealing complexity?

Yeah, I think that's an interesting question.

I've wondered about that myself because it's kind of like, you know, you live through these things, and then you say, what was the historical story?

And sometimes the historical story that you realize after the fact was not what you lived through, so to speak.

And so, you know, what I realized is, I think what happened is, you know, I did physics kind of like reductionistic physics where you're thrown in the universe and you're told go figure out what's going on inside it.

And then I started building computer tools and I started building my first computer language, for example.

And computer language is not like, it's sort of like physics in the sense that you have to take all those computations people want to do and kind of drill down and find the primitives that they can all be made of.

But then you do something that's really different because you're just saying, okay, these are the primitives.

Now, hopefully they'll be useful to people.

So you're essentially building an artificial universe in a sense, where you make this language, you've got these primitives, you're just building whatever you feel like building.

And that's, and so it was sort of interesting for me because from doing science where you're just throwing the universe as the universe is, to then just being told, you know, you can make up any universe you want.

And so I think that experience of making a computer language, which is essentially building your own universe, so to speak, is, you know, that's kind of the, that's what gave me a somewhat different attitude towards what might be possible.

It's like, let's just explore what can be done in these artificial universes rather than thinking the natural science way of let's be constrained by how the universe actually is.

being able to program, essentially, you've, as opposed to being limited to just your mind and a pen, you now have, you've basically built another brain that you can use to explore the universe by, computer program is a kind of a brain.

Right, well it's, or a telescope, or it's a tool.

But there's something fundamentally different between a computer and a telescope.

I mean, it just, I'm hoping not to romanticize the notion, but it's more general,

the computer is more general than the telescope.

And it's, I think, I mean, this point about, you know, People say, oh, such and such a thing was almost discovered at such and such a time.

The distance between, the building the paradigm that allows you to actually understand stuff or allows 1 to be open to seeing what's going on, That's really hard.

And I think I've been fortunate in my life that I've spent a lot of my time building computational language, and that's an activity that in a sense works by sort of having to kind of create another level of abstraction and kind of be open to different kinds of structures.

But, you know, it's always, I mean, I'm fully aware of, I suppose, the fact that I have seen it a bunch of times of how easy it is to miss the obvious, so to speak.

That at least is factored into my attempt to not miss the obvious, although it may not succeed.


Speaker 0: When you were at Caltech, did you get to interact with Richard Feynman at all? Do you have any memories of Richard? We worked together quite a bit, actually.

Speaker 1: In fact, both when I was at Caltech and after I left Caltech, we were both consultants at this company called Thinking Machines Corporation, which was just down the street from here, actually. It was ultimately ill-fated company, but I used to say this company is not gonna work with the strategy they have, and Dick Feynman always used to say, what do we know about running companies? Just let them run their company. But anyway, he was not into that kind of thing and he always thought that my interest in doing things like running companies was a distraction, so to speak. And for me, it's a mechanism to have a more effective machine for actually getting things, figuring things out and getting things to happen.

Speaker 2: Did he think of it, because essentially what you used, you did with the company, I don't know if you were thinking of it that way, but you're creating tools to empower the exploration of the university. Do you think, did he? Did he understand that point? The point of tools of?

Speaker 1: I think not as well as he might have done. I mean, I think that, but, you know, he was actually my first company, which was also involved with, well, was involved with more mathematical computation kinds of things. You know, he was quite, he had lots of advice about the technical side of what we should do and so on. Do you have examples, memories, or thoughts that? Oh yeah, yeah, he had all kinds of, look, in the business of doing sort of, you know, 1 of the hard things in math is doing integrals and so on, right?

And so he had his own elaborate ways to do integrals and so on. He had his own ways of thinking about sort of getting intuition about how math works. And so his sort of meta idea was take those intuitional methods and make a computer follow those intuitional methods. Now it turns out, for the most part, like when we do integrals and things, what we do is we build this kind of bizarre industrial machine that turns every integral into, you know, products of mere G functions and generates this very elaborate thing. And actually the big problem is turning the results into something a human will understand.

It's not quotes doing the integral. And actually Feynman did understand that to some extent. And I am embarrassed to say, He once gave me this big pile of, you know, calculational methods for particle physics that he worked out in the 50s. And he said, you know, it's more used to you than to me type thing. And I was like, I've intended to look at it and give it back and I still have my files now.

So it's, But that's what happens when it's finiteness of human lives. It's, you know, maybe if he'd lived another 20 years, I would have remembered to give it back. But I think it's, you know, that was his attempt to systematize the ways that 1 does integrals that show up in particle physics and so on. Turns out the way we've actually done it is very different from that way.

Speaker 2: What do you make of that difference, Eugene? So Feynman was actually quite remarkable at creating sort of intuitive, like diving in, you know, creating intuitive frameworks for understanding difficult concepts

Speaker 1: is. I'm smiling because, you know, the funny thing about him was that the thing he was really, really, really good at is calculating stuff. But he thought that was easy because he was really good at it. And so he would do these things where he would calculate some, do some complicated calculation in quantum field theory, for example, come out with a result. Wouldn't tell anybody about the complicated calculation because he thought that was easy.

He thought the really impressive thing was to have the simple intuition about how everything works. So he invented that at the end. And because he'd done this calculation and knew how it worked, it was a lot easier. It's a lot easier to have good intuition when you know what the answer is. And then he would just not tell anybody about these calculations.

And he wasn't meaning that maliciously, so to speak. It's just he thought that was easy. And that led to areas where people were just completely mystified and they kind of followed his intuition, but nobody could tell why it worked. Because actually the reason it worked was because he'd done all these calculations and he knew that it would work. And you know, he and I worked a bit on quantum computers actually back in

Speaker 0: 1980, 81,

Speaker 1: before anybody had heard of those things. And the typical mode of, I mean, he always used to say, and I now think about this, because I'm about the age that he was when I worked with him, and I see that people are 1 third my age, so to speak. And he was always complaining that I was 1 third his age and therefore various things. But he would do some calculation by hand, blackboard and things, come up with some answer. I'd say, I don't understand this.

I do something with a computer and he'd say, I don't understand this. So there'd be some big argument about what was going on, but it was always, and I think actually, many of the things that we sort of realized about quantum computing that were sort of issues that have to do particularly with the measurement process are kind of still issues today. And I kind of find it interesting. It's a funny thing in science that these, you know, that there's a remarkable, it happens in technology too, there's a remarkable sort of repetition of history that ends up occurring. Eventually things really get nailed down, but it often takes a while and it often things come back decades later.

Well, for example, I could tell a story actually happened right down the street from here. When we were both at thinking machines, I had been working on this particular cellular automaton called Rule 30 that has this feature that from very simple initial conditions, it makes really complicated behavior. Okay? So, and actually of all silly physical things, using this big parallel computer called the connection machine that that company was making, I generated this giant printout of Rule 30 on very, on actually on the same kind of printer that people use to make layouts for microprocessors. So 1 of these big, you know, large format printers with high resolution and so on.

So, okay, so print this out, lots of very tiny cells. And so there was sort of a question of how, some features of that pattern. And so it was very much a physical, on the floor with meter rules trying to measure different things. So, so Feynman kind of takes me aside. We've been doing that for a little while and takes me aside and he says, I just want to know this 1 thing.

He says, I want to know, how did you know that this rule 30 thing would produce all this really complicated behavior that is so complicated that we're going around with this big printout and so on. And I said, well, I didn't know. I just enumerated all the possible rules and then observed that that's what happened. He said, oh, I feel a lot better. I thought you had some intuition that he didn't have that would let 1.

I said, no, no, no, no intuition, just experimental science.

Speaker 2: So that's such a beautiful sort of dichotomy there of that's exactly what you showed is you really can't have an intuition about an irreducible, I mean, you have to run it. Yes, that's right. That's so hard for us humans, and especially brilliant physicists like Feynman to say that you can't have a compressed, clean intuition about how the whole thing works.

Speaker 0: Yes, yes.

Speaker 1: No, he was, I mean, I think he was sort of on the edge of understanding that point about computation. And I think he found that, I think he always found computation interesting. And I think that was sort of what he was

Speaker 0: a little bit

Speaker 1: poking at. I mean, that intuition, you know, the difficulty of discovering things, like even you say, oh, you know, you just enumerate all the cases and just find 1 that does something interesting, right? Sounds very easy. Turns out, like, I missed it when I first saw it because I had kind of an intuition that said it shouldn't be there. So I had kind of arguments, oh, I'm gonna ignore that case because whatever.

Speaker 2: How did you have an open mind enough? Because you're essentially the same person as Richard Feynman, like the same kind of physics type of thinking. How did you find yourself having a sufficiently open mind to be open to watching rules and them revealing complexity?

Speaker 1: Yeah, I think that's an interesting question. I've wondered about that myself because it's kind of like, you know, you live through these things, and then you say, what was the historical story? And sometimes the historical story that you realize after the fact was not what you lived through, so to speak. And so, you know, what I realized is, I think what happened is, you know, I did physics kind of like reductionistic physics where you're thrown in the universe and you're told go figure out what's going on inside it. And then I started building computer tools and I started building my first computer language, for example.

And computer language is not like, it's sort of like physics in the sense that you have to take all those computations people want to do and kind of drill down and find the primitives that they can all be made of. But then you do something that's really different because you're just saying, okay, these are the primitives. Now, hopefully they'll be useful to people. Let's build up from there. So you're essentially building an artificial universe in a sense, where you make this language, you've got these primitives, you're just building whatever you feel like building.

And that's, and so it was sort of interesting for me because from doing science where you're just throwing the universe as the universe is, to then just being told, you know, you can make up any universe you want. And so I think that experience of making a computer language, which is essentially building your own universe, so to speak, is, you know, that's kind of the, that's what gave me a somewhat different attitude towards what might be possible. It's like, let's just explore what can be done in these artificial universes rather than thinking the natural science way of let's be constrained by how the universe actually is. Yeah, by

Speaker 2: being able to program, essentially, you've, as opposed to being limited to just your mind and a pen, you now have, you've basically built another brain that you can use to explore the universe by, computer program is a kind of a brain.

Speaker 1: Right, well it's, or a telescope, or it's a tool. It lets you see stuff.

Speaker 2: But there's something fundamentally different between a computer and a telescope. I mean, it just, I'm hoping not to romanticize the notion, but it's more general,

Speaker 0: the computer is more general than the telescope.

Speaker 1: And it's, I think, I mean, this point about, you know, People say, oh, such and such a thing was almost discovered at such and such a time. The distance between, the building the paradigm that allows you to actually understand stuff or allows 1 to be open to seeing what's going on, That's really hard. And I think I've been fortunate in my life that I've spent a lot of my time building computational language, and that's an activity that in a sense works by sort of having to kind of create another level of abstraction and kind of be open to different kinds of structures. But, you know, it's always, I mean, I'm fully aware of, I suppose, the fact that I have seen it a bunch of times of how easy it is to miss the obvious, so to speak. That at least is factored into my attempt to not miss the obvious, although it may not succeed.

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Richard Feynman on Computation (Stephen Wolfram) | AI Podcast Clips