The following is a conversation with Stephen Wolfram, 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's 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. It made

me fall in love with the mathematical beauty and power of cellular automata.

It is true that perhaps one of the criticisms of Stephen is on a human level, that he has a big

ego, which prevents some researchers from fully enjoying the content of his ideas.

We talk about this point in this conversation. To me, ego can lead you astray but can also be

a superpower, one that fuels bold, innovative thinking that refuses to surrender to the cautious

ways of academic institutions. And here, especially, I ask you to join me in looking

past the peculiarities of human nature and opening your mind to the beauty of ideas in Stephen's work

and in this conversation. I believe Stephen Wolfram is one of the most original minds of our time

and, at the core, is a kind, curious, and brilliant human being. This conversation was recorded in

November 2019 when the Wolfram Physics Project was underway but not yet ready for public

exploration as it is now. We now agreed to talk again, probably multiple times in the near future,

so this is round one, and stay tuned for round two soon.

This is the Artificial Intelligence Podcast. If you enjoy it, subscribe on YouTube,

review it with 5 Stars and Apple Podcast, support it on Patreon, or simply connect with me on Twitter

at Lex Friedman spelled F R I D M A N. As usual, I'll do a few minutes of ads now and never any

ads in the middle that can break the flow of the conversation. I hope that works for you and

doesn't hurt the listening experience. Quick summary of the ads. Two sponsors,

ExpressVPN and Cash App. Please consider supporting the podcast by getting ExpressVPN

at expressvpn.com slash lexpod and downloading Cash App and using code lexpodcast.

This show is presented by Cash App, the number one finance app in the App Store. When you get it,

use code lexpodcast. Cash App lets you send money to friends, buy Bitcoin, and invest in the stock

market with as little as one dollar. Since Cash App does fractional share trading, let me mention

that the order execution algorithm that works behind the scenes to create the abstraction of

fractional orders is an algorithmic marvel. So big props to the Cash App engineers for

solving a hard problem that in the end provides an easy interface that takes a step up to the

next layer of abstraction over the stock market. This makes trading more accessible for new

investors and diversification much easier. So again, if you get Cash App from the App Store,

Google Play, and use the code lexpodcast, you get ten dollars and Cash App will also donate

ten dollars to FIRST, an organization that is helping to advance robotics and STEM education

for young people around the world. This show is presented by ExpressVPN. Get it at expressvpn.com

slash lexpod to get a discount and to support this podcast. I've been using ExpressVPN for many years.

I love it. It's really easy to use. Press the big power on button and your privacy is protected.

And if you like, you can make it look like your location is anywhere else in the world.

This has a large number of obvious benefits. Certainly, it allows you to access international

versions of streaming websites like the Japanese Netflix or the UK Hulu. ExpressVPN works on any

device you can imagine. I use it on Linux. Shout out to Ubuntu. New version coming out soon actually.

Windows, Android, but it's available anywhere else too. Once again, get it at expressvpn.com

slash lexpod to get a discount and to support this podcast. And now here's my conversation

with Stephen Wolfram. You and your son Christopher helped create the alien language in the movie

Arrival. So let me ask maybe a bit of a crazy question, but if aliens were to visit us on earth,

do you think we would be able to find a common language?

Well, by the time we're saying aliens are visiting us, we've already prejudiced the whole story

because the concept of an alien actually visiting, so to speak, we already know they're kind of

things that make sense to talk about visiting. So we already know they exist in the same kind

of physical setup that we do. It's not just radio signals. It's an actual thing that shows up and so

on. So I think in terms of can one find ways to communicate? Well, the best example we have of

this right now is AI. I mean, that's our first sort of example of alien intelligence. And the

question is, how well do we communicate with AI? If you were in the middle of a neural network,

a neural net, and you open it up and it's like, what are you thinking? Can you discuss things

with it? It's not easy, but it's not absolutely impossible. So I think by the time, given the

setup of your question, aliens visiting, I think the answer is yes, one will be able to find some

form of communication, whatever communication means. Communication requires notions of purpose

and things like this. It's a kind of philosophical quagmire.

So if AI is a kind of alien life form, what do you think visiting looks like? So if we look at

aliens visiting, and we'll get to discuss computation and the world of computation,

but if you were to imagine, you said you already prejudiced something by saying you visit,

but how would aliens visit?

By visit, there's kind of an implication. And here we're using the imprecision of human language,

you know, in a world of the future. And if that's represented in computational language,

we might be able to take the concept visit and go look in the documentation, basically,

and find out exactly what does that mean, what properties does it have, and so on.

But by visit, in ordinary human language, I'm kind of taking it to be there's something,

a physical embodiment that shows up in a spacecraft, since we kind of know that that's

necessary. We're not imagining it's just, you know, photons showing up in a radio signal that,

you know, photons in some very elaborate pattern, we're imagining it's physical

things made of atoms and so on, that show up.

Can it be photons in a pattern?

Well, that's a good question. I mean, whether there is the possibility,

you know, what counts as intelligence? Good question. I mean, it's, you know, and I

used to think there was sort of a, oh, there'll be, you know, it'll be clear what it means to

find extraterrestrial intelligence, et cetera, et cetera, et cetera. I've increasingly realized,

as a result of science that I've done, that there really isn't a bright line between

the intelligent and the merely computational, so to speak.

So, you know, in our kind of everyday sort of discussion, we'll say things like, you know,

the weather has a mind of its own. Well, let's unpack that question. You know, we realize

that there are computational processes that go on that determine the fluid dynamics of this and

that and the atmosphere, et cetera, et cetera, et cetera. How do we distinguish that from

the processes that go on in our brains of, you know, the physical processes that go on in our

brains? How do we separate those? How do we say the physical processes going on that represent

sophisticated computations in the weather, oh, that's not the same as the physical processes

that go on that represent sophisticated computations in our brains? The answer is,

I don't think there is a fundamental distinction. I think the distinction for us is that there's

kind of a thread of history and so on that connects kind of what happens in different brains

to each other, so to speak. And it's a, you know, what happens in the weather is something which is

not connected by sort of a thread of civilizational history, so to speak, to what we're used to.

SL. In the stories that the human brains told us, but maybe the weather has its own stories.

MG. Absolutely. Absolutely. And that's where we run into trouble thinking about extraterrestrial

intelligence because, you know, it's like that pulsar magnetosphere that's generating these very

elaborate radio signals. You know, is that something that we should think of as being this

whole civilization that's developed over the last however long, you know, millions of years of

processes going on in the neutron star or whatever versus what, you know, what we're used to in human

intelligence? I mean, I think in the end, you know, when people talk about extraterrestrial

intelligence and where is it and the whole, you know, Fermi paradox of how come there's no other

signs of intelligence in the universe, my guess is that we've got sort of two alien forms of

intelligence that we're dealing with, artificial intelligence and sort of physical or extraterrestrial

intelligence. And my guess is people will sort of get comfortable with the fact that both of these

have been achieved around the same time. And in other words, people will say, well, yes, we're

used to computers, things we've created, digital things we've created, being sort of intelligent

like we are. And they'll say, oh, we're kind of also used to the idea that there are things around

the universe that are kind of intelligent like we are, except they don't share the sort of

civilizational history that we have. And so they're a different branch. I mean, it's similar to when

you talk about life, for instance. I mean, you kind of said life form, I think almost synonymously

with intelligence, which I don't think is, you know, the AIs would be upset to hear you equate

those two things. Because I really probably implied biological life. But you're saying,

I mean, we'll explore this more, but you're saying it's really a spectrum and it's all just

a kind of computation. And so it's a full spectrum and we just make ourselves special by weaving a

narrative around our particular kinds of computation. Yes. I mean, the thing that I think I've kind of

come to realize is, you know, at some level, it's a little depressing to realize that there's so

little or liberating. Well, yeah, but I mean, it's, you know, it's the story of science,

right? And, you know, from Copernicus on, it's like, you know, first we were like,

convinced our planets at the center of the universe. No, that's not true. Well, then we

were convinced there's something very special about the chemistry that we have as biological

organisms. That's not really true. And then we're still holding out that hope. Oh, this intelligence

thing we have, that's really special. I don't think it is. However, in a sense, as you say,

it's kind of liberating for the following reason, that you realize that what's special is the

details of us, not some abstract attribute that, you know, we could wonder, oh, is something else

going to come along and, you know, also have that abstract attribute? Well, yes, every abstract

attribute we have, something else has it. But the full details of our kind of history of our

civilization and so on, nothing else has that. That's what, you know, that's our story, so to

speak. And that's sort of almost by definition, special. So I view it as not being such a, I mean,

initially I was like, this is bad. This is kind of, you know, how can we have self respect about

the things that we do? Then I realized the details of the things we do, they are the story.

Everything else is kind of a blank canvas. So maybe on a small tangent, you just made me

think of it, but what do you make of the monoliths in 2001 Space Odyssey in terms of

aliens communicating with us and sparking the kind of particular intelligent computation that

we humans have? Is there anything interesting to get from that sci fi? Yeah, I mean, I think what's

fun about that is, you know, the monoliths are these, you know, one to four to nine perfect

cuboid things. And in the Earth a million years ago, whatever they were portraying with a bunch

of apes and so on, a thing that has that level of perfection seems out of place. It seems very kind

of constructed, very engineered. So that's an interesting question. What is the, you know,

what's the techno signature, so to speak? What is it that you see it somewhere and you say,

my gosh, that had to be engineered. Now, the fact is we see crystals, which are also very perfect.

And, you know, the perfect ones are very perfect. They're nice polyhedral or whatever.

And so in that sense, if you say, well, it's a sign of sort of it's a techno signature that

it's a perfect polygonal shape, polyhedral shape. That's not true. And so then it's an interesting

question. What is the right signature? I mean, like, you know, Gauss, famous mathematician,

you know, he had this idea, you should cut down the Siberian forest in the shape of sort of a

typical image of the proof of the Pythagorean theorem on the grounds that it was a kind of

cool idea, didn't get done. But, you know, it's on the grounds that the Martians would see that and

realize, gosh, there are mathematicians out there. It's kind of, you know, in his theory of the world,

that was probably the best advertisement for the cultural achievements of our species.

But, you know, it's a reasonable question. What do you, what can you send or create that is a sign

of intelligence in its creation or even intention in its creation? You talk about if we were to send

a beacon. Can you what should we send? Is math our greatest creation? Is what is our greatest

creation? I think I think it's a it's a philosophically doomed issue. I mean, in other

words, you send something, you think it's fantastic, but it's kind of like we are part of

the universe. We make things that are, you know, things that happen in the universe.

Computation, which is sort of the thing that we are in some abstract sense using to create all

these elaborate things we create, is surprisingly ubiquitous. In other words, we might have thought

that, you know, we've built this whole giant engineering stack that's led us to microprocessors,

that's led us to be able to do elaborate computations. But this idea that computations

are happening all over the place. The only question is whether whether there's a thread that connects

our human intentions to what those computations are. And so I think I think this question of what

do you send to kind of show off our civilization in the best possible way? I think any kind of

almost random slab of stuff we've produced is about equivalent to everything else. I think

it's one of these things where it's a non romantic way of phrasing it. I just started to interrupt,

but I just talked to Andrew in who's the wife of Carl Sagan. And so I don't know if you're

familiar with the Voyager. I mean, she was part of sending, I think, brainwaves of, you know,

wasn't it hers? Her brainwaves when she was first falling in love with Carl Sagan. It's

this beautiful story that perhaps you would shut down the power of that by saying we might

as well send anything else. And that's interesting. All of it is kind of an interesting, peculiar

thing. Yeah, yeah, right. Well, I mean, I think it's kind of interesting to see on the Voyager,

you know, golden record thing. One of the things that's kind of cute about that is, you know,

it was made when was it in the late 70s, early 80s. And, you know, one of the things, it's a

phonograph record. Okay. And it has a diagram of how to play a phonograph record. And, you know,

it's kind of like it's shocking that in just 30 years, if you show that to a random kid of today,

and you show them that diagram, I've tried this experiment, they're like, I don't know what the

heck this is. And the best anybody can think of is, you know, take the whole record, forget the

fact that it has some kind of helical track in it, just image the whole thing and see what's there.

That's what we would do today. In only 30 years, our technology has kind of advanced to the point

where the playing of a helical, you know, mechanical track on a phonograph record is now

something bizarre. So, you know, it's a cautionary tale, I would say, in terms of the ability to make

something that in detail sort of leads by the nose, some, you know, the aliens or whatever,

to do something. It's like, no, you know, best you can do, as I say, if we were doing this today,

we would not build a helical scan thing with a needle. We would just take some high resolution

imaging system and get all the bits off it and say, oh, it's a big nuisance that they put in a

helix, you know, in a spiral. Let's just unravel the spiral and start from there.

SL. Do you think, and this will get into trying to figure out interpretability of AI,

interpretability of computation, being able to communicate with various kinds of computations,

do you think we'd be able to, if you put your alien hat on, figure out this record,

how to play this record?

MG. Well, it's a question of what one wants to do. I mean,

SL. Understand what the other party was trying to communicate or understand anything about the

other party.

MG. What does understanding mean? I mean, that's the issue. The issue is, it's like when people

were trying to do natural language understanding for computers, right? So people tried to do that

for years. It wasn't clear what it meant. In other words, you take your piece of English or whatever,

and you say, gosh, my computer has understood this. Okay, that's nice. What can you do with that?

Well, so for example, when we built WolfMalpha, one of the things was it's doing question answering

and so on, and it needs to do natural language understanding. The reason that I realized after

the fact, the reason we were able to do natural language understanding quite well, and people

hadn't before, the number one thing was we had an actual objective for the natural language

understanding. We were trying to turn the natural language into this computational language

that we could then do things with. Now, similarly, when you imagine your alien, you say,

okay, we're playing them the record. Did they understand it? Well, it depends what you mean.

If there's a representation that they have, if it converts to some representation where we can say,

oh yes, that's a representation that we can recognize is represents understanding, then all

well and good. But actually, the only ones that I think we can say would represent understanding

are ones that will then do things that we humans kind of recognize as being useful to us.

Maybe you're trying to understand, quantify how technologically advanced this particular

civilization is. So are they a threat to us from a military perspective? That's probably the

first kind of understanding they'll be interested in. Gosh, that's so hard. That's like in the

Arrival movie, that was one of the key questions is, why are you here, so to speak? Are you going

to hurt us? But even that, it's very unclear. It's like, are you going to hurt us? That comes

back to a lot of interesting AI ethics questions, because we might make an AI that says, well,

take autonomous cars, for instance. Are you going to hurt us? Well, let's make sure you only drive

at precisely the speed limit, because we want to make sure we don't hurt you, so to speak.

But you say, but actually, that means I'm going to be really late for this thing, and

that sort of hurts me in some way. So it's hard to know. Even the definition of what it means to

hurt someone is unclear. And as we start thinking about things about AI ethics and so on, that's

something one has to address. There's always tradeoffs, and that's the annoying thing about

ethics. Yeah, well, right. And I think ethics, like these other things we're talking about,

is a deeply human thing. There's no abstract, let's write down the theorem that proves that

this is ethically correct. That's a meaningless idea. You have to have a ground truth, so to

speak, that's ultimately what humans want, and they don't all want the same thing. So that gives

one all kinds of additional complexity in thinking about that. One convenient thing in terms of

turning ethics into computation, you can ask the question of what maximizes the likelihood of the

survival of the species. That's a good existential issue. But then when you say survival of the

species, you might say, you might, for example, let's say, forget about technology, just hang out

and be happy, live our lives, go on to the next generation, go through many, many generations

where, in a sense, nothing is happening. Is that okay? Is that not okay? Hard to know. In terms of

the attempt to do elaborate things and the attempt to might be counterproductive for the survival of

the species. It's also a little bit hard to know, so okay, let's take that as a sort of thought

experiment. You can say, well, what are the threats that we might have to survive? The

super volcano, the asteroid impact, all these kinds of things. Okay, so now we inventory these

possible threats and we say, let's make our species as robust as possible relative to all

these threats. I think in the end, it's sort of an unknowable thing what it takes. So given that

you've got this AI and you've told it, maximize the long term. What does long term mean? Does

long term mean until the sun burns out? That's not going to work. Does long term mean next thousand

years? Okay, they're probably optimizations for the next thousand years. It's like if you're

running a company, you can make a company be very stable for a certain period of time.

Like if your company gets bought by some private investment group, then you can run a company just

fine for five years by just taking what it does and removing all R&D and the company will burn

out after a while, but it'll run just fine for a little while. So if you tell the AI, keep the

humans okay for a thousand years, there's probably a certain set of things that one would do to

optimize that, many of which one might say, well, that would be a pretty big shame for the future of

history, so to speak, for that to be what happens. But I think in the end, as you start thinking

about that question, what you realize is there's a whole sort of raft of undecidability, computational

irreducibility. In other words, one of the good things about what our civilization has gone

through and what we humans go through is that there's a certain computational irreducibility

to it in the sense that it isn't the case that you can look from the outside and just say,

the answer is going to be this. At the end of the day, this is what's going to happen.

You actually have to go through the process to find out. And I think that feels better in the

sense that something is achieved by going through all of this process. But it also means

that telling the AI, go figure out what will be the best outcome. Well, unfortunately, it's going

to come back and say, it's kind of undecidable what to do. We'd have to run all of those scenarios

to see what happens. And if we want it for the infinite future, we're thrown immediately into

sort of standard issues of kind of infinite computation and so on. So yeah, even if you

get that the answer to the universe and everything is 42, you still have to actually run the universe.

Yes, to figure out the question, I guess, or the journey is the point.

Right. Well, I think it's saying to summarize, this is the result of the universe. If that is

possible, it tells us, I mean, the whole sort of structure of thinking about computation and so on

and thinking about how stuff works. If it's possible to say, and the answer is such and such,

you're basically saying there's a way of going outside the universe. And you're getting yourself

into something of a sort of paradox because you're saying, if it's knowable what the answer is, then

there's a way to know it that is beyond what the universe provides. But if we can know it, then

something that we're dealing with is beyond the universe. So then the universe isn't the universe,

so to speak. And in general, as we'll talk about, at least for our small human brains, it's

hard to show the result of a sufficiently complex computation. I mean, it's probably impossible,

right, on this side ability. And the universe appears by at least the poets to be sufficiently

complex. They won't be able to predict what the heck it's all going to. Well, we better not be

able to, because if we can, it kind of denies. I mean, it's you know, we're part of the universe.

Yeah. So what does it mean for us to predict? It means that we that our little part of the universe

is able to jump ahead of the whole universe. And this this quickly winds up. I mean, that it is

conceivable. The only way we'd be able to predict is if we are so special in the universe, we are

the one place where there is computation more special, more sophisticated than anything else

that exists in the universe. That's the only way we would have the ability to sort of the almost

theological ability, so to speak, to predict what happens in the universe is to say somehow we're

better than everything else in the universe, which I don't think is the case. Yeah, perhaps we can

detect a large number of looping patterns that reoccur throughout the universe and fully describe

them. And therefore, but then it still becomes exceptionally difficult to see how those patterns

interact and what kind of well, look, the most remarkable thing about the universe is that it's

has regularity at all. Might not be the case. If you just have regularity, do you? Absolutely.

That fits full of I mean, physics is successful. You know, it's full of of laws that tell us a lot

of detail about how the universe works. I mean, it could be the case that, you know, the 10 to the

90th particles in the universe, they will do their own thing, but they don't. They all follow. We

already know they all follow basically physical, the same physical laws. And that's something

that's a very profound fact about the universe. What conclusion you draw from that is unclear. I

mean, in the, you know, the early early theologians, that was, you know, exhibit number one for the

existence of God. Now, you know, people have different conclusions about it. But the fact is,

you know, right now, I mean, I happen to be interested, actually, I've just restarted a

long running kind of interest of mine about fundamental physics. I'm kind of like, come on,

I'm on a bit of a quest, which I'm about to make more public, to see if I can actually find the

fundamental theory of physics. Excellent. We'll come to that. And I just had a lot of conversations

with quantum mechanics folks with so I'm really excited on your take, because I think you have a

fascinating take on the the fundamental nature of our reality from a physics perspective. So

and what might be underlying the kind of physics as we think of it today. Okay, let's take a step

back. What is computation? It's a good question. Operationally, computation is following rules.

That's kind of it. I mean, computation is the result is the process of systematically following

rules. And it is the thing that happens when you do that. So taking initial conditions are taking

inputs and following rules. I mean, what are you following rules on? So there has to be some data,

some unnecessarily, it can be something where there's a, you know, very simple input. And then

you're following these rules. And you'd say there's not really much data going into this.

It's you could actually pack the initial conditions into the rule, if you want to. So I think the

question is, is there a robust notion of computation? That is, what does robust mean?

What I mean by that is something like this. So So one of the things in a different in another

physics, something like energy, okay, the different forms of energy, there's, but somehow energy is a

robust concept that doesn't, isn't particular to kinetic energy, or, you know, nuclear energy,

or whatever else, there's a robust idea of energy. So one of the things you might ask is,

is the robust idea of computation? Or does it matter that this computation is running in a

Turing machine? This computation is running in a, you know, CMOS, silicon, CPU, this computation is

running in a fluid system in the weather, those kinds of things? Or is there a robust idea of

computation that transcends the sort of detailed framework that it's running in? Okay. And is there?

Yes. I mean, it wasn't obvious that there was. So it's worth understanding the history and how we

got to where we are right now. Because, you know, to say that there is, is a statement in part about

our universe. It's not a statement about what is mathematically conceivable. It's about what

actually can exist for us. Maybe you can also comment because energy, as a concept is robust.

But there's also its intricate, complicated relationship with matter, with mass, is very

interesting, of particles that carry force and particles that sort of particles that carry force

and particles that have mass. These kinds of ideas, they seem to map to each other, at least

in the mathematical sense. Is there a connection between energy and mass and computation? Or are

these completely disjoint ideas? We don't know yet. The things that I'm trying to do about fundamental

physics may well lead to such a connection, but there is no known connection at this time.

So can you elaborate a little bit more on what, how do you think about computation? What is

computation? What is computation? Yeah. So I mean, let's, let's tell a little bit of a historical

story. Okay. So, you know, back, go back 150 years, people were making mechanical calculators of

various kinds. And, you know, the typical thing was you want an adding machine, you go to the

adding machine store, basically, you want a multiplying machine, you go to the multiplying

machine store, they're different pieces of hardware. And so that means that, at least at the

level of that kind of computation, and those kinds of pieces of hardware, there isn't a robust notion

of computation, there's the adding machine kind of computation, there's the multiplying machine

notion of computation, and they're disjoint. So what happened in around 1900, people started

imagining, particularly in the context of mathematical logic, could you have something

which would be represent any reasonable function, right? And they came up with things, this idea of

primitive recursion was one of the early ideas. And it didn't work. There were reasonable functions

that people could come up with that were not represented using the primitives of primitive

recursion. Okay, so then, then along comes 1931, and Godel's theorem, and so on. And as in looking

back, one can see that as part of the process of establishing Godel's theorem, Godel basically

showed how you could compile arithmetic, how you could basically compile logical statements like

this statement is unprovable into arithmetic. So what he essentially did was to show that

arithmetic can be a computer in a sense that's capable of representing all kinds of other things.

And then Turing came along 1936, came up with Turing machines. Meanwhile, Alonzo Church had

come up with lambda calculus. And the surprising thing that was established very quickly is the

Turing machine idea about what might be what computation might be is exactly the same as the

lambda calculus idea of what computation might be. And so, and then there started to be other ideas,

you know, register machines, other kinds of other kinds of representations of computation.

And the big surprise was, they all turned out to be equivalent. So in other words, it might have

been the case, like those old adding machines and multiplying machines, that, you know, Turing had

his idea of computation, Church had his idea of computation, and they were just different. But it

isn't true. They're actually all equivalent. So then by, I would say the 1970s or so in sort of

the computation, computer science, computation theory area, people had sort of said, oh,

Turing machines are kind of what computation is. Physicists were still holding out saying, no,

no, no, that's just not how the universe works. We've got all these differential equations.

We've got all these real numbers that have infinite numbers of digits.

The universe is not a Turing machine.

Right. The, you know, the Turing machines are a small subset of the things that we make in

microprocessors and engineering structures and so on. So probably actually through my work in the

1980s about sort of the relationship between computation and models of physics, it became a

little less clear that there would be, that there was this big sort of dichotomy between what can

happen in physics and what happens in things like Turing machines. And I think probably by now people

would mostly think, and by the way, brains were another kind of element of this. I mean, you know,

Gödel didn't think that his notion of computation or what amounted to his notion of computation

would cover brains. And Turing wasn't sure either. But although he was a little bit,

he got to be a little bit more convinced that it should cover brains. But I would say by probably

sometime in the 1980s, there was beginning to be sort of a general belief that yes, this notion

of computation that could be captured by things like Turing machines was reasonably robust.

Now, the next question is, okay, you can have a universal Turing machine that's capable of

being programmed to do anything that any Turing machine can do. And, you know, this idea of

universal computation, it's an important idea, this idea that you can have one piece of hardware

and program it with different pieces of software. You know, that's kind of the idea that launched

most modern technology. I mean, that's kind of, that's the idea that launched computer revolution

software, etc. So important idea. But the thing that's still kind of holding out from that idea

is, okay, there is this universal computation thing, but seems hard to get to. It seems like

you want to make a universal computer, you have to kind of have a microprocessor with, you know,

a million gates in it, and you have to go to a lot of trouble to make something that achieves that

level of computational sophistication. Okay, so the surprise for me was that stuff that I discovered

in the early 80s, looking at these things called cellular automata, which are really simple

computational systems, the thing that was a big surprise to me was that even when their rules were

very, very simple, they were doing things that were as sophisticated as they did when their rules

were much more complicated. So it didn't look like, you know, this idea, oh, to get sophisticated

computation, you have to build something with very sophisticated rules. That idea didn't seem to pan

out. And instead, it seemed to be the case that sophisticated computation was completely ubiquitous,

even in systems with incredibly simple rules. And so that led to this thing that I call the

principle of computational equivalence, which basically says, when you have a system that

follows rules of any kind, then whenever the system isn't doing things that are, in some sense,

obviously simple, then the computation that the behavior of the system corresponds to is of

equivalence sophistication. So that means that when you kind of go from the very, very, very

simplest things you can imagine, then quite quickly, you hit this kind of threshold above

which everything is equivalent in its computational sophistication. Not obvious that would be the case.

I mean, that's a science fact. Well, no, hold on a second. So this you've opened with a new kind

of science. I mean, I remember it was a huge eye opener that such simple things can create such

complexity. And yes, there's an equivalence, but it's not a fact. It just appears to, I mean,

it's as much as a fact as sort of these theories are so elegant that it seems to be the way things

are. But let me ask sort of, you just brought up previously, kind of like the communities of

computer scientists with their Turing machines, the physicists with their universe, and whoever

the heck, maybe neuroscientists looking at the brain. What's your sense in the equivalence?

You've shown through your work that simple rules can create equivalently complex Turing machine

systems, right? Is the universe equivalent to the kinds of Turing machines? Is the human brain

a kind of Turing machine? Do you see those things basically blending together? Or is there still a

mystery about how disjoint they are? Well, my guess is that they all blend together, but we don't know

that for sure yet. I mean, this, you know, I should say, I said rather glibly that the principle of

computational equivalence is sort of a science fact. And I was using air quotes for the science fact,

because when you, it is a, I mean, just to talk about that for a second. The thing is that it has

a complicated epistemological character, similar to things like the second law of thermodynamics,

the law of entropy increase. What is the second law of thermodynamics? Is it a law of nature? Is

it a thing that is true of the physical world? Is it something which is mathematically provable? Is

it something which happens to be true of the systems that we see in the world? Is it, in some

sense, a definition of heat, perhaps? Well, it's a combination of those things. And it's the same

thing with the principle of computational equivalence. And in some sense, the principle

of computational equivalence is at the heart of the definition of computation, because it's telling

you there is a thing, there is a robust notion that is equivalent across all these systems and

doesn't depend on the details of each individual system. And that's why we can meaningfully talk

about a thing called computation. And we're not stuck talking about, oh, there's computation in

Turing machine number 3785, and et cetera, et cetera, et cetera. That's why there is a robust

notion like that. Now, on the other hand, can we prove the principle of computational equivalence?

Can we prove it as a mathematical result? Well, the answer is, actually, we've got some nice results

along those lines that say, throw me a random system with very simple rules. Well, in a couple

of cases, we now know that even the very simplest rules we can imagine of a certain type are

universal and do follow what you would expect from the principle of computational equivalence. So

that's a nice piece of sort of mathematical evidence for the principle of computational equivalence.

Just to link on that point, the simple rules creating sort of these complex behaviors. But

is there a way to mathematically say that this behavior is complex? That you've mentioned that

you cross a threshold. Right. So there are various indicators. So, for example, one thing would be,

is it capable of universal computation? That is, given the system, do there exist initial

conditions for the system that can be set up to essentially represent programs to do anything you

want, to compute primes, to compute pi, to do whatever you want? Right. So that's an indicator.

So we know in a couple of examples that, yes, the simplest candidates that could conceivably have

that property do have that property. And that's what the principle of computational equivalence

might suggest. But this principle of computational equivalence, one question about it is, is it true

for the physical world? It might be true for all these things we come up with, the Turing machines,

the cellular automata, whatever else. Is it true for our actual physical world? Is it true for the

brains, which are an element of the physical world? We don't know for sure. And that's not the

type of question that we will have a definitive answer to, because there's a sort of scientific

induction issue. You can say, well, it's true for all these brains, but this person over here is

really special, and it's not true for them. And the only way that that cannot be what happens is

if we finally nail it and actually get a fundamental theory for physics, and it turns out

to correspond to, let's say, a simple program. If that is the case, then we will basically have

reduced physics to a branch of mathematics, in the sense that we will not be, you know,

right now with physics, we're like, well, this is the theory that, you know, this is the rules that

apply here. But in the middle of that, you know, right by that black hole, maybe these rules don't

apply and something else applies. And there may be another piece of the onion that we have to peel

back. But if we can get to the point where we actually have, this is the fundamental theory of

physics, here it is, it's this program, run this program, and you will get our universe, then we've

kind of reduced the problem of figuring out things in physics to a problem of doing some, what turns

out to be very difficult, irreducibly difficult, mathematical problems. But it no longer is the

case that we can say that somebody can come in and say, whoops, you know, you will write about

all these things about Turing machines, but you're wrong about the physical universe, we know

there's sort of ground truth about what's happening in the physical universe. Now, I happen to think,

I mean, you asked me at an interesting time, because I'm just in the middle of starting to

to re energize my, my project to kind of study fundamental theory of physics. As of today, I'm

very optimistic that we're actually going to find something and that it's going to be possible to

to see that the universe really is computational in that sense. But I don't know, because we're

betting against, you know, we're betting against the universe, so to speak. And I didn't, you know,

it's not like, you know, when I spend a lot of my life building technology, and then I know what

what's in there, right? And it's there may be, it may have unexpected behavior, may have bugs,

things like that. But fundamentally, I know what's in there for the universe. I'm not in

that position, so to speak. What kind of computation do you think the fundamental laws of

physics might emerge from? Just to clarify, so you've done a lot of fascinating work with kind

of discrete kinds of computation that, you know, you can sell your automata, and we'll talk about

it, have this very clean structures, it's such a nice way to demonstrate that simple rules

can create immense complexity. But what kind, you know, is that actually, are cellular automata

sufficiently general to describe the kinds of computation that might create the laws of physics?

Just to give, can you give a sense of what kind of computation do you think would create?

Well, so this is a slightly complicated issue, because as soon as you have universal

computation, you can, in principle, simulate anything with anything.

Right. But it is not a natural thing to do. And if you're asking, were you to try to find our

physical universe by looking at possible programs in the computational universe of all possible

programs, would the ones that correspond to our universe be small and simple enough that we might

find them by searching that computational universe? We got to have the right basis, so to speak. We

have to have the right language, in effect, for describing computation for that to be feasible.

So the thing that I've been interested in for a long time is, what are the most structuralist

structures that we can create with computation? So in other words, if you say a cellular automaton,

it has a bunch of cells that are arrayed on a grid, and it's very, you know, and every cell is

updated in synchrony at a particular, you know, when there's a click of a clock, so to speak,

and it goes a tick of a clock, and every cell gets updated at the same time. That's a very specific

very rigid kind of thing. But my guess is that when we look at physics, and we look at things

like space and time, that what's underneath space and time is something as structuralist as possible,

that what we see, what emerges for us as physical space, for example, comes from something that is

sort of arbitrarily unstructured underneath. And so I've been for a long time interested in kind

of what are the most structuralist structures that we can set up. And actually, what I had thought

about for ages is using graphs, networks, where essentially, so let's talk about space, for

example. So what is space? It's a kind of a question one might ask. Back in the early days

of quantum mechanics, for example, people said, oh, for sure, space is going to be discrete,

because all these other things we're finding are discrete. But that never worked out in physics.

And so space in physics today is always treated as this continuous thing, just like Euclid

imagined it. I mean, the very first thing Euclid says in his sort of common notions is,

you know, a point is something which has no part. In other words, there are points that are

arbitrarily small, and there's a continuum of possible positions of points. And the question

is, is that true? And so for example, if we look at, I don't know, fluid like air or water,

we might say, oh, it's a continuous fluid. We can pour it, we can do all kinds of things continuously.

But actually, we know, because we know the physics of it, that it consists of a bunch

of discrete molecules bouncing around, and only in the aggregate is it behaving like a continuum.

And so the possibility exists that that's true of space too. People haven't managed to make that

work with existing frameworks in physics. But I've been interested in whether one can imagine that

underneath space, and also underneath time, is something more structureless. And the question is,

is it computational? So there are a couple of possibilities. It could be computational,

somehow fundamentally equivalent to a Turing machine, or it could be fundamentally not. So

how could it not be? It could not be, so a Turing machine essentially deals with integers, whole

numbers, at some level. And you know, it can do things like it can add one to a number, it can do

things like this. And it can also store whatever the heck it did. Yes, it has an infinite storage.

But when one thinks about doing physics, or sort of idealized physics, or idealized mathematics,

one can deal with real numbers, numbers with an infinite number of digits, numbers which are

absolutely precise. And one can say, we can take this number and we can multiply it by itself.

Are you comfortable with infinity?

In this context? Are you comfortable in the context of computation? Do you think infinity

plays a part? I think that the role of infinity is complicated. Infinity is useful in conceptualizing

things. It's not actualizable. Almost by definition, it's not actualizable. But do you

think infinity is part of the thing that might underlie the laws of physics? I think that no.

I think there are many questions that you ask about, you might ask about physics, which inevitably

involve infinity. Like when you say, you know, is faster than light travel possible? You could say,

given the laws of physics, can you make something even arbitrarily large, even quote, infinitely

large, that will make faster than light travel possible? Then you're thrown into dealing with

infinity as a kind of theoretical question. But I mean, talking about sort of what's underneath

space and time and how one can make a computational infrastructure, one possibility is that you can't

make a computational infrastructure in a Turing machine sense, that you really have to be dealing

with precise real numbers. You're dealing with partial differential equations, which have

precise real numbers at arbitrarily closely separated points. You have a continuum for

everything. Could be that that's what happens, that there's sort of a continuum for everything

and precise real numbers for everything. And then the things I'm thinking about are wrong.

And that's the risk you take if you're trying to sort of do things about nature,

is you might just be wrong. For me personally, it's kind of a strange thing. I've spent a lot

of my life building technology where you can do something that nobody cares about,

but you can't be sort of wrong in that sense, in the sense you build your technology and it does

what it does. But I think this question of what the sort of underlying computational

infrastructure for the universe might be, it's sort of inevitable it's going to be fairly abstract,

because if you're going to get all these things like there are three dimensions of space,

there are electrons, there are muons, there are quarks, there are this, you don't get to,

if the model for the universe is simple, you don't get to have sort of a line of code for

each of those things. You don't get to have sort of the muon case, the tau lepton case and so on.

Because they all have to be emergent somehow, something deeper.

Right. So that means it's sort of inevitable, it's a little hard to talk about

what the sort of underlying structuralist structure actually is.

Do you think human beings have the cognitive capacity to understand, if we're to discover it,

to understand the kinds of simple structure from which these laws can emerge?

Like, do you think that's a good question?

Well, here's what I think. I think that, I mean, I'm right in the middle of this right now.

Right.

I'm telling you that I think this, yeah, I mean, this human has a hard time understanding,

you know, a bunch of the things that are going on. But what happens in understanding is

one builds waypoints. I mean, if you said understand modern 21st century mathematics,

starting from, you know, counting back in, you know, whenever counting was invented 50,000 years

ago, whatever it was, right, that would be really difficult. But what happens is we build waypoints

that allow us to get to higher levels of understanding. And we see the same thing

happening in language. You know, when we invent a word for something, it provides kind of a cognitive

anchor, a kind of a waypoint that lets us, you know, like a podcast or something. You could be

explaining, well, it's a thing which works this way, that way, the other way. But as soon as you

have the word podcast and people kind of societally understand it, you start to be able to build on

top of that. And so I think that's kind of the story of science actually, too. I mean, science

is about building these kind of waypoints where we find this sort of cognitive mechanism for

understanding something, then we can build on top of it. You know, we have the idea of, I don't

know, differential equations we can build on top of that. We have this idea, that idea. So my hope

is that if it is the case that we have to go all the way sort of from the sand to the computer,

and there's no waypoints in between, then we're toast. We won't be able to do that.

Well, eventually we might. So if we're as clever apes are good enough at building those abstract

abstractions, eventually from sand we'll get to the computer, right? And it just might be a longer

journey. The question is whether it is something that you asked, whether our human brains will

quote, understand what's going on. And that's a different question because for that, it requires

steps from which we can construct a human understandable narrative. And that's something that

I think I am somewhat hopeful that that will be possible. Although, you know, as of literally

today, if you ask me, I'm confronted with things that I don't understand very well.

So this is a small pattern in a computation trying to understand the rules under which the

computation functions. And it's an interesting possibility under which kinds of computations

such a creature can understand itself.

My guess is that within, so we didn't talk much about computational irreducibility,

but it's a consequence of this principle of computational equivalence. And it's sort of a

core idea that one has to understand, I think, which is question is, you're doing a computation,

you can figure out what happens in the computation just by running every step in the computation and

seeing what happens. Or you can say, let me jump ahead and figure out, you know, have something

smarter that figures out what's going to happen before it actually happens. And a lot of traditional

science has been about that act of computational reducibility. It's like, we've got these equations,

and we can just solve them, and we can figure out what's going to happen. We don't have to trace

all of those steps, we just jump ahead because we solve these equations.

Okay, so one of the things that is a consequence of the principle of computational equivalence is

you don't always get to do that. Many, many systems will be computationally irreducible,

in the sense that the only way to find out what they do is just follow each step and see what

happens. Why is that? Well, if you're saying, well, we, with our brains, we're a lot smarter,

we don't have to mess around like the little cellular automaton going through and updating

all those cells. We can just use the power of our brains to jump ahead. But if the principle

of computational equivalence is right, that's not going to be correct, because it means that

there's us doing our computation in our brains, there's a little cellular automaton doing its

computation, and the principle of computational equivalence says these two computations are

fundamentally equivalent. So that means we don't get to say we're a lot smarter than the cellular

automaton and jump ahead, because we're just doing computation that's of the same sophistication as

the cellular automaton itself. That's computational reducibility. It's fascinating. And that's a

really powerful idea. I think that's both depressing and humbling and so on, that we're all,

we and the cellular automaton are the same. But the question we're talking about, the fundamental

laws of physics, is kind of the reverse question. You're not predicting what's going to happen. You

have to run the universe for that. But saying, can I understand what rules likely generated me?

I understand. But the problem is, to know whether you're right, you have to have some

computational reducibility, because we are embedded in the universe. If the only way to know whether

we get the universe is just to run the universe, we don't get to do that, because it just ran for

14.6 billion years or whatever. And we can't rerun it, so to speak. So we have to hope that

there are pockets of computational reducibility sufficient to be able to say, yes, I can recognize

those are electrons there. And I think that it's a feature of computational irreducibility. It's

sort of a mathematical feature that there are always an infinite collection of pockets of

reducibility. The question of whether they land in the right place and whether we can sort of build

a theory based on them is unclear. But to this point about whether we as observers in the universe

built out of the same stuff as the universe can figure out the universe, so to speak, that relies

on these pockets of reducibility. Without the pockets of reducibility, it won't work, can't work.

But I think this question about how observers operate, it's one of the features of science over

the last 100 years particularly, has been that every time we get more realistic about observers,

we learn a bit more about science. So for example, relativity was all about observers don't get to

say what's simultaneous with what. They have to just wait for the light signal to arrive to decide

what's simultaneous. Or for example, in thermodynamics, observers don't get to say the

position of every single molecule in a gas. They can only see the kind of large scale features,

and that's why the second law of thermodynamics, the law of entropy increase, and so on works.

If you could see every individual molecule, you wouldn't conclude something about thermodynamics.

You would conclude, oh, these molecules are just all doing these particular things. You wouldn't

be able to see this aggregate fact. So I strongly expect that, and in fact, in the theories that I

have, that one has to be more realistic about the computation and other aspects of observers

in order to actually make a correspondence between what we experience. In fact,

my little team and I have a little theory right now about how quantum mechanics may work, which is

a very wonderfully bizarre idea about how the sort of thread of human consciousness

relates to what we observe in the universe. But there's several steps to explain what that's

about. What do you make of the mess of the observer at the lower level of quantum mechanics,

sort of the textbook definition with quantum mechanics kind of says that there's some,

there's two worlds. One is the world that actually is, and the other is that's observed.

What do you make sense of that? Well, I think actually the ideas we've recently had might

actually give away into this. I don't know yet. I think it's a mess. The fact is,

one of the things that's interesting, and when people look at these models that I

started talking about 30 years ago now, they say, oh no, that can't possibly be right.

What about quantum mechanics? You say, okay, tell me what is the essence of quantum mechanics? What

do you want me to be able to reproduce to know that I've got quantum mechanics, so to speak?

Well, and that question comes up. It comes up very operationally actually, because we've been

doing a bunch of stuff with quantum computing. And there are all these companies that say,

we have a quantum computer. And we say, let's connect to your API and let's actually run it.

And they're like, well, maybe you shouldn't do that yet. We're not quite ready yet.

And one of the questions that I've been curious about is, if I have five minutes with a quantum

computer, how can I tell if it's really a quantum computer or whether it's a simulator at the other

end? And it turns out it's really hard. It's like a lot of these questions about what is

intelligence? What's life? It's like, are you really a quantum computer? Yes, exactly. Is it

just a simulation or is it really a quantum computer? Same issue all over again. So this

whole issue about the sort of mathematical structure of quantum mechanics and the completely

separate thing that is our experience in which we think definite things happen, whereas quantum

mechanics doesn't say definite things ever happen. Quantum mechanics is all about the amplitudes for

different things to happen, but yet our thread of consciousness operates as if definite things

are happening. Dilinga, on the point, you've kind of mentioned the structure that could

underlie everything and this idea that it could perhaps have something like a structure of a graph.

Can you elaborate why your intuition is that there's a graph structure of nodes and edges

and what it might represent? Right. Okay. So the question is, what is, in a sense,

the most structuralist structure you can imagine, right? And in fact, what I've recently realized

in the last year or so, I have a new most structuralist structure. By the way, the question

itself is a beautiful one and a powerful one in itself. So even without an answer, just the

question is a really strong question. Right. But what's your new idea? Well, it has to do with

hypergraphs. Essentially, what is interesting about the sort of model I have now is it's a

little bit like what happened with computation. Everything that I think of as, oh, well, maybe

the model is this, I discover it's equivalent. And that's quite encouraging because it's like

I could say, well, I'm going to look at trivalent graphs with three edges for each node and so on,

or I could look at this special kind of graph, or I could look at this kind of algebraic structure.

And turns out that the things I'm now looking at, everything that I've imagined that is a plausible

type of structuralist structure is equivalent to this. So what is it? Well, a typical way to think

about it is, well, so you might have some collection of tuples, collection of, let's say,

numbers. So you might have one, three, five, two, three, four, just collections of numbers,

triples of numbers, let's say, quadruples of numbers, pairs of numbers, whatever.

And you have all these sort of floating little tuples. They're not in any particular order.

And that sort of floating collection of tuples, and I told you this was abstract,

represents the whole universe. The only thing that relates them is when a symbol is the same,

it's the same, so to speak. So if you have two tuples and they contain the same symbol,

let's say at the same position of the tuple, at the first element of the tuple,

then that represents a relation. So let me try and peel this back.

Wow. Okay.

I told you it's abstract, but this is the...

So the relationship is formed by some aspect of sameness.

Right. But so think about it in terms of a graph. So a graph, a bunch of nodes,

let's say you number each node, then what is a graph? A graph is a set of pairs that say

this node has an edge connecting it to this other node. And a graph is just a collection

of those pairs that say this node connects to this other node. So this is a generalization of that,

in which instead of having pairs, you have arbitrary n tuples. That's it. That's the

whole story. And now the question is, okay, so that might represent the state of the universe.

How does the universe evolve? What does the universe do? And so the answer is

that what I'm looking at is a transformation rules on these hypergraphs. In other words,

you say this, whenever you see a piece of this hypergraph that looks like this,

turn it into a piece of hypergraph that looks like this. So on a graph, it might be when you

see the subgraph, when you see this thing with a bunch of edges hanging out in this particular way,

then rewrite it as this other graph. Okay. And so that's the whole story. So the question is

what, uh, so now you say, I mean, as I say, this is quite abstract. And one of the questions is,

uh, where do you do those updating? So you've got this giant graph. What triggers the updating,

like what's the, what's the ripple effect of it? Is it, uh, and I suspect everything's discreet

even in time. So, okay. So the question is where do you do the updates? And the answer is the rule

is you do them wherever they apply. And you do them, you do them. The order in which the updates

is done is not defined. That is the, you can do them. So there may be many possible orderings

for these updates. Now, the point is if imagine you're an observer in this universe. So, and you

say, did something get updated? Well, you don't in any sense know until you yourself have been

updated. Right. So in fact, all that you can be sensitive to is essentially the causal network

of how an event over there affects an event that's in you. That doesn't even feel like

observation. That's like, that's something else. You're just part of the whole thing.

Yes, you're part of it. But, but even to have, so the end result of that is all you're sensitive to

is this causal network of what event affects what other event. I'm not making a big statement about

sort of the structure of the observer. I'm simply saying, I'm simply making the argument that

what happens, the microscopic order of these rewrites is not something that any observer,

any conceivable observer in this universe can be affected by. Because the only thing the observer

can be affected by is this causal network of how the events in the observer are affected

by other events that happen in the universe. So the only thing you have to look at is the

causal network. You don't really have to look at this microscopic rewriting that's happening. So

these rewrites are happening wherever they, they happen wherever they feel like.

Causal network. Is there, you said that there's not really, so the idea would be an undefined,

like what gets updated? The, the sequence of things is undefined. It's a, yes. That's what

you mean by the causal network, but then the call, no, the causal network is given that an

update has happened. That's an event. Then the question is, is that event causally related to,

does that event, if that event didn't happen, then some future event couldn't happen yet.

Gotcha.

And so you build up this network of what affects what. Okay. And so what that does,

so when you build up that network, that's kind of the observable aspect of the universe in some

sense. And so then you can ask questions about, you know, how robust is that observable network

of the, what's happening in the universe. Okay. So here's where it starts getting kind of

interesting. So for certain kinds of microscopic rewriting rules, the order of rewrites does not

matter to the causal network. And so this is, okay, mathematical logic moment. This is equivalent

to the Church Rosser property or the confluence property of rewrite rules. And it's the same

reason that if you're simplifying an algebraic expression, for example, you can say, oh, let me

expand those terms out. Let me factor those pieces. Doesn't matter what order you do that in,

you'll always get the same answer. And that's, it's the same fundamental phenomenon that causes

for certain kinds of microscopic rewrite rules that causes the causal network to be independent

of the microscopic order of rewritings.

Why is that property important?

Because it implies special relativity. I mean, the reason it's important is that that property,

special relativity says you can look at these sort of, you can look at different reference frames.

You can have different, you can be looking at your notion of what space and what's time

can be different depending on whether you're traveling at a certain speed, depending on

whether you're doing this, that, and the other. But nevertheless, the laws of physics are the

same. That's what the principle of special relativity says, is the laws of physics are

the same independent of your reference frame. Well, turns out this sort of change of the

microscopic rewriting order is essentially equivalent to a change of reference frame,

or at least there's a sub part of how that works that's equivalent to change a reference frame.

So, somewhat surprisingly, and sort of for the first time in forever,

it's possible for an underlying microscopic theory to imply special relativity, to be able to derive

it. It's not something you put in as a, this is a, it's something where this other property,

causal invariance, which is also the property that implies that there's a single thread of time

in the universe. It might not be the case that that's what would lead to the possibility of an

observer thinking that definite stuff happens. Otherwise, you've got all these possible rewriting

orders, and who's to say which one occurred. But with this causal invariance property,

there's a notion of a definite thread of time. It sounds like that kind of idea of time,

even space, would be emergent from the system. Oh, yeah. No, I mean, it's not a fundamental part

of the system. No, no, it's a fundamental level. All you've got is a bunch of nodes connected by

hyper edges or whatever. So there's no time, there's no space. That's right. And

but the thing is that it's just like imagining, imagine you're just dealing with a graph. And

imagine you have something like a, you know, like a honeycomb graph, or you have a hexagon,

a bunch of hexagons. You know, that graph at a microscopic level, it's just a bunch of nodes

connected to other nodes. But at a macroscopic level, you say that looks like a honeycomb,

you know, lattice, it looks like a two dimensional, you know, manifold of some kind, it looks like a

two dimensional thing. If you connect it differently, if you just connect all the

nodes one, one to another, and kind of a sort of linked list type structure, then you'd say,

well, that looks like a one dimensional space. But at the microscopic level, all these are just

networks with nodes, the macroscopic level, they look like something that's like one of our sort

of familiar kinds of space. And it's the same thing with these hyper graphs. Now, if you ask me,

have I found one that gives me three dimensional space? The answer is not yet. So we don't know.

This is one of these things we're kind of betting against nature, so to speak. And I have no way to

know. And so there are many other properties of this kind of system that are very beautiful,

actually, and very suggestive. And it will be very elegant if this turns out to be right,

because it's very clean. I mean, you start with nothing. And everything gets built up,

everything about space, everything about time, everything about matter. It's all just emergent

from the properties of this extremely low level system. And that, that will be pretty cool if

that's the way our universe works. Now, do I on the other hand, the thing that that I find very

confusing is, let's say we succeed, let's say we can say this particular sort of hypergraph rewriting

rule gives the universe just run that hypergraph rewriting rule for enough times, and you'll get

everything, you'll get this conversation we're having, you'll get everything. It's that if we

get to that point, and we look at what is this thing, what is this rule that we just have,

that is giving us our whole universe, how do we think about that thing? Let's say, turns out the

minimal version of this, and this is kind of cool thing for a language designer like me,

the minimal version of this model is actually a single line of orphan language code.

So that's, which I wasn't sure was going to happen that way, but it's, it's a, that's, it's kind of,

no, we don't know what, we don't know what that's, that's just the framework to know the actual

particular hypergraph that might be a longer, the specification of the rules might be slightly

longer. How does that help you accept marveling in the beauty and the elegance of the simplicity

that creates the universe? That does that help us predict anything in the universe?

That does that help us predict anything? Not really because of the irreducibility.

That's correct. That's correct. But so the thing that is really strange to me,

and I haven't wrapped my, my brain around this yet is, you know, one is one keeps on realizing

that we're not special in the sense that, you know, we don't live at the center of the universe.

We don't blah, blah, blah. And yet if we produce a rule for the universe and it's quite simple,

and we can write it down and a couple of lines or something that feels very special.

How did we come to get a simple universe when many of the available universes, so to speak,

are incredibly complicated? It might be, you know, a quintillion characters long.

Why did we get one of the ones that's simple? And so I haven't wrapped my brain around that

issue yet. If indeed we are in such a simple, the universe is such a simple rule. Is it possible

that there is something outside of this that we are in a kind of what people call the simulation,

right? That we're just part of a computation that's being explored by a graduate student

in alternate universe. Well, you know, the problem is we don't get to say much about

what's outside our universe because by definition, our universe is what we exist within. Now,

can we make a sort of almost theological conclusion from being able to know how our

particular universe works? Interesting question. I don't think that if you ask the question,

could we, and it relates again to this question about extraterrestrial intelligence, you know,

we've got the rule for the universe. Was it built in on purpose? Hard to say. That's the same thing

as saying we see a signal from, you know, that we're receiving from some random star somewhere,

and it's a series of pulses. And, you know, it's a periodic series of pulses, let's say.

Was that done on purpose? Can we conclude something about the origin of that series of

pulses? Just because it's elegant does not necessarily mean that somebody created it or

that we can even comprehend. Yeah. I think it's the ultimate version of the sort of identification

of the techno signature question. It's the ultimate version of that is was our universe

a piece of technology, so to speak, and how on earth would we know? But I mean, in the kind of

crazy science fiction thing you could imagine, you could say, oh, there's going to be a signature

there. It's going to be made by so and so. But there's no way we could understand that,

so to speak, and it's not clear what that would mean. Because the universe simply,

you know, if we find a rule for the universe, we're simply saying that rule represents what

our universe does. We're not saying that that rule is something running on a big computer

and making our universe. It's just saying that represents what our universe does in the same

sense that, you know, laws of classical mechanics, differential equations, whatever they are,

represent what mechanical systems do. It's not that the mechanical systems are somehow running

solutions to those differential equations. Those differential equations are just representing the

behavior of those systems. So what's the gap in your sense to linger on the fascinating,

perhaps slightly sci fi question? What's the gap between understanding the fundamental rules that

create a universe and engineering a system, actually creating a simulation ourselves?

So you've talked about sort of, you've talked about, you know, nano engineering kind of ideas

that are kind of exciting, actually creating some ideas of computation in the physical space. How

hard is it as an engineering problem to create the universe once you know the rules that create it?

Well, that's an interesting question. I think the substrate on which the universe is operating is

not a substrate that we have access to. I mean, the only substrate we have is that same substrate

that the universe is operating in. So if the universe is a bunch of hypergraphs being rewritten,

then we get to attach ourselves to those same hypergraphs being rewritten. We don't get to,

and if you ask the question, you know, is the code clean? You know, can we write nice,

elegant code with efficient algorithms and so on? Well, that's an interesting question.

That's this question of how much computational reducibility there is in the system.

But I've seen some beautiful cellular automata that basically create copies of itself within

itself, right? So that's the question whether it's possible to create, like whether you need

to understand the substrate or whether you can. Yeah, well, right. I mean, so one of the things

that is sort of one of my slightly sci fi thoughts about the future, so to speak, is, you know,

right now, if you poll typical people, you say, do you think it's important to find the fundamental

theory of physics? You get, because I've done this poll informally, at least, it's curious,

actually, you get a decent fraction of people saying, oh, yeah, that would be pretty interesting.

I think that's becoming, surprisingly enough, more, I mean, a lot of people are interested

in physics in a way that like, without understanding it, just kind of watching

scientists, a very small number of them struggle to understand the nature of our reality.

Right. I mean, I think that's somewhat true. And in fact, in this project that I'm launching into

to try and find fundamental theory of physics, I'm going to do it as a very public project. I mean,

it's going to be live streamed and all this kind of stuff. And I don't know what will happen. It'll

be kind of fun. I mean, I think that it's the interface to the world of this project. I mean,

I figure one feature of this project is, you know, unlike technology projects that basically are what

they are, this is a project that might simply fail, because it might be the case that it generates

all kinds of elegant mathematics that has absolutely nothing to do with the physical

universe that we happen to live in. Okay, so we're talking about kind of the quest to find

the fundamental theory of physics. First point is, you know, it's turned out it's kind of hard

to find the fundamental theory of physics. People weren't sure that that would be the case. Back in

the early days of applying mathematics to science, 1600s and so on, people were like, oh, in 100 years

we'll know everything there is to know about how the universe works. Turned out to be harder than

that. And people got kind of humble at some level, because every time we got to sort of a greater

level of smallness and studying the universe, it seemed like the math got more complicated and

everything got harder. When I was a kid, basically, I started doing particle physics. And when I was

doing particle physics, I always thought finding the fundamental, fundamental theory of physics,

that's a kooky business, we'll never be able to do that. But we can operate within these

frameworks that we built for doing quantum field theory and general relativity and things like this.

And it's all good. And we can figure out a lot of stuff. Did you even at that time have a sense

that there's something behind that? Sure, I just didn't expect that. I thought in some rather un,

it's actually kind of crazy and thinking back on it, because it's kind of like there was this long

period in civilization where people thought the ancients had it all figured out, and we'll never

figure out anything new. And to some extent, that's the way I felt about physics when I was

in the middle of doing it, so to speak, was, you know, we've got quantum field theory, it's the

foundation of what we're doing. And there's, you know, yes, there's probably something underneath

this, but we'll sort of never figure it out. But then I started studying simple programs in the

computational universe, things like cellular automata and so on. And I discovered that

they do all kinds of things that were completely at odds with the intuition that I had had.

And so after that, after you see this tiny little program that does all this amazingly complicated

stuff, then you start feeling a bit more ambitious about physics and saying, maybe we could do this

for physics too. And so that got me started years ago now in this kind of idea of could we actually

find what's underneath all of these frameworks, like quantum field theory and general relativity

and so on. And people perhaps don't realize as clearly as they might that, you know, the

frameworks we're using for physics, which is basically these two things, quantum field theory,

sort of the theory of small stuff and general relativity, theory of gravitation and large stuff.

Those are the two basic theories. And they're 100 years old. I mean, general relativity was 1915,

quantum field theory, well, 1920s. So basically 100 years old. And it's been a good run. There's

a lot of stuff been figured out. But what's interesting is the foundations haven't changed

in all that period of time, even though the foundations had changed several times before

that in the 200 years earlier than that. And I think the kinds of things that I'm thinking about,

which are sort of really informed by thinking about computation and the computational universe,

it's a different foundation. It's a different set of foundations. And might be wrong. But it is at

least, you know, we have a shot. And I think it's, you know, to me, it's, you know, my personal

calculation for myself is, is, you know, if it turns out that the finding the fundamental theory

of physics, it's kind of low hanging fruit, so to speak, it'd be a shame if we just didn't think to

do it. You know, if people just said, Oh, you'll never figure that stuff out. Let's, you know,

and it takes another 200 years before anybody gets around to doing it. You know, I think it's,

I don't know how low hanging this fruit actually is. It may be, you know, it may be that it's kind

of the wrong century to do this project. I mean, I think the cautionary tale for me, you know,

I think about things that I've tried to do in technology, where people thought about doing them

a lot earlier. And my favorite example is probably Leibniz, who, who thought about making essentially

encapsulating the world's knowledge in a computational form in the late 1600s, and did a

lot of things towards that. And basically, you know, we finally managed to do this. But he was

300 years too early. And that's the that's kind of the in terms of life planning. It's kind of like,

avoid things that can't be done in your in your century, so to speak.

Yeah, timing. Timing is everything. So you think if we kind of figure out the underlying rules

that can create from which quantum field theory and general relativity can emerge,

do you think they'll help us unify it at that level of abstraction?

Oh, we'll know it completely. We'll know how that all fits together. Yes, without a question.

And I mean, it's already even the things I've already done. There are very, you know, it's very,

very elegant, actually, how things seem to be fitting together. Now, you know, is it right?

I don't know yet. It's awfully suggestive. If it isn't right, it's then the designer of the universe

should feel embarrassed, so to speak, because it's a really good way to do it.

And your intuition in terms of design universe, does God play dice? Is there is there randomness

in this thing? Or is it deterministic? So the kind of

That's a little bit of a complicated question. Because when you're dealing with these things

that involve these rewrites that have, okay, even randomness is an emergent phenomenon, perhaps.

Yes, yes. I mean, it's a yeah, well, randomness, in many of these systems,

pseudo randomness and randomness are hard to distinguish. In this particular case,

the current idea that we have about some measurement in quantum mechanics

is something very bizarre and very abstract. And I don't think I can yet

explain it without kind of yakking about very technical things. Eventually, I will be able to.

But if that's right, it's kind of a it's a weird thing, because it slices between determinism and

randomness in a weird way that hasn't been sliced before, so to speak. So like many of these

questions that come up in science, where it's like, is it this or is it that? Turns out the

real answer is it's neither of those things. It's something kind of different and sort of orthogonal

to those categories. And so that's the current, you know, this week's idea about how that might

work. But, you know, we'll see how that unfolds. I mean, there's this question about a field like

physics and sort of the quest for fundamental theory and so on. And there's both the science

of what happens and there's the sort of the social aspect of what happens. Because, you know,

in a field that is basically as old as physics, we're at, I don't know what it is, fourth generation,

I don't know, fifth generation, I don't know what generation it is of physicists. And like,

I was one of these, so to speak. And for me, the foundations were like the pyramid, so to speak,

you know, it was that way. And it was always that way. It is difficult in an old field to go back to

the foundations and think about rewriting them. It's a lot easier in young fields where you're

still dealing with the first generation of people who invented the field. And it tends to be the

case, you know, that the nature of what happens in science tends to be, you know, you'll get,

typically the pattern is some methodological advance occurs. And then there's a period of five

years, 10 years, maybe a little bit longer than that, where there's lots of things that are now

made possible by that methodological advance, whether it's, you know, I don't know, telescopes,

or whether that's some mathematical method or something. Something happens, a tool gets built,

and then you can do a bunch of stuff. And there's a bunch of low hanging fruit to be picked. And

that takes a certain amount of time. After all that low hanging fruit is picked, then it's a hard

slog for the next however many decades or century or more to get to the next sort of level at which

one could do something. And it's kind of a, and it tends to be the case that in fields that are in

that kind of, I wouldn't say cruise mode, because it's really hard work, but it's very hard work for

very incremental progress. And then in your career and some of the things you've taken on,

it feels like you're not, you haven't been afraid of the hard slog. Yeah, that's true. So it's quite

interesting, especially on the engineering, on the engineering side. On a small tangent, 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. 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 an ill fated company. But I used

to say this company is not going to 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.

Did he think of it, because essentially what 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...

I think not as well as he might have done. I mean, I think that... But he was actually my

first company, which was also involved with, well, was involved with more mathematical computation

kinds of things. 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... One of the hard things in math is doing

integrals and so on. 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 products of major 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, quote,

doing the integral. And actually, Feynman did understand that to some extent. And I'm 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, yeah, 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'm still on my files now. But that's

what happens when it's finiteness of human lives. Maybe if he'd live another 20 years, I would have

remembered to give it back. But I think that was his attempt to systematize the ways that one 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 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 this simple intuition about how

everything works. So he invented that at the end. And, you know, 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 and then he would just not tell anybody about these calculations

that he wasn't meaning that maliciously, so to speak. It's just he thought that was easy.

And and that's, you know, 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 was

would work. And, you know, when I he and I worked a bit on quantum computers actually back in 1980,

81, before anybody had heard of those things. And, you know, the typical mode of I mean,

he was used to say, and I now think about this, because I'm about the age that he was when I

worked with him. And, you know, I see the people who are one third my age, so to speak.

And he was always complaining that I was one third his age, and therefore various things. But, but,

you know, he would do some calculation by by hand, you know, blackboard and things come up with some

answer. I'd say, I don't understand this. You know, I do something with a computer. And he'd say,

you know, I don't understand this. So there'd be some big argument about what was, you know,

what was going on, but but it was always some. And I think, actually, we many of the things that we

sort of realized about quantum computing, that was 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, there's a remarkable happens

in technology to 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 thinking machines, I had been working on this particular

cellular automaton, who rule 30, that has this feature that it 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 same kind

of printer that people use to make layouts microprocessors. So one 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, you know, 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 one thing 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, you know, 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. You know, I thought you had some intuition that he didn't have

that would let one. I said, No, no, no, no intuition, just experimental science.

TK Oh, that's such a beautiful sort of dichotomy there of that's exactly you showed is you really

can't have an intuition about an irreducible. I mean, you have to run it.

MG Yes, that's right.

TK 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. MG Yes, yes. 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 a little bit 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 one 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 going to ignore that case,

because whatever. And how did you have an open mind enough? Because you're essentially the same

person as you should find, 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?

MG 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, you know, 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 so it was sort of interesting for me, because from doing science,

where you're just thrown in 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, 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 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, you know,

this is kind of a brain, right? And it's well, it's it's or telescope, or you know, it's a tool,

it's it lets you let's you see stuff, but there's something fundamentally different

between a computer and a telescope. I mean, it just, yeah, I'm hoping to romanticize the notion,

but it's more general, the computer is more general. And it's, 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 the distance between, you know, the building the paradigm that allows you to

actually understand stuff or allows one to be open to seeing what's going on. That's really hard.

And, you know, I think, in I've been fortunate in my life that I 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, 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. What do you think is the role

of ego in the history of math and science? And more sort of, you know, a book title is something

like a new kind of science. You've accomplished a huge amount. In fact, somebody said that Newton

didn't have an ego, and I looked into it and he had a huge ego. Yeah, but from an outsider's

perspective, some have said that you have a bit of an ego as well. Do you see it that way? Does

ego get in the way? Is it empowering? Is it both? So it's, it's, it's complicated and necessary. I

mean, you know, I've had, look, I've spent more than half my life CEO in a tech company. Right.

Okay. And, you know, that is a, I think it's actually very, it means that one's ego is not

a distant thing. It's a thing that one encounters every day, so to speak, because it's, it's all

tied up with leadership and with how one, you know, develops an organization and all these

kinds of things. So, you know, it may be that if I'd been an academic, for example, I could have

sort of, you know, check the ego, put it on, put on a shelf somewhere and ignore its characteristics,

but you're reminded of it quite often in the context of running a company. Sure. I mean,

that's what it's about. It's, it's about leadership and, you know, leadership is intimately tied to

ego. Now, what does it mean? I mean, what, what is the, you know, for me, I've been fortunate that I

think I have reasonable intellectual confidence, so to speak. That is, you know, I, I'm one of

these people who at this point, if somebody tells me something and I just don't understand it,

my conclusion isn't that means I'm dumb. That my conclusion is there's something wrong with

what I'm being told. And that was actually Dick Feynman used to have that, that that feature too,

he never really believed in. He actually believed in experts much less than I believe in experts.

So. Wow. So that's a fun, that's a, that's a fundamentally powerful property of ego and saying,

like, not that I am wrong, but that the, the world is wrong. And, and tell me, like, when confronted

with the fact that doesn't fit the thing that you've really thought through sort of both the

negative and the positive of ego, do you see the negative of that get in the way sort of being

sure of the mistakes I've made that are the results of, I'm pretty sure I'm right. And

turns out I'm not. I mean, that's, that's the, you know, but, but the thing is that the, the,

the idea that one tries to do things that, so for example, you know, one question is if people have

tried hard to do something and then one thinks, maybe I should try doing this myself. Uh, if one

does not have a certain degree of intellectual confidence, one just says, well, people have been

trying to do this for a hundred years. How am I going to be able to do this? Yeah. And, you know,

I was fortunate in the sense that I happened to start having some degree of success in science

and things when I was really young. And so that developed a certain amount of sort of intellectual

confidence. I don't think I otherwise would have had. Um, and you know, in a sense, I mean,

I was fortunate that I was working in a field, particle physics during its sort of golden age

of rapid progress. And that, that's kind of gives one a false sense of, uh, achievement because

it's kind of, kind of easy to discover stuff that's going to survive. If you happen to be,

you know, picking the low hanging fruit of a rapidly expanding field.

I mean, the reason I totally, I totally immediately understood the ego behind a new

kind of science to me, let me sort of just try to express my feelings on the whole thing,

is that if you don't allow that kind of ego, then you would never write that book.

That you would say, well, people must have done this. There's not, you would not dig.

You would not keep digging. And I think that was, I think you have to take that ego and,

and ride it and see where it takes you. And that's how you create exceptional work.

But I think the other point about that book was it was a non trivial question,

how to take a bunch of ideas that are, I think, reasonably big ideas. They might,

they might, you know, their importance is determined by what happens historically.

One can't tell how important they are. One can tell sort of the scope of them.

And the scope is fairly big and they're very different from things that have come before.

And the question is, how do you explain that stuff to people? And so I had had the experience

of sort of saying, well, there are these things, there's a cellular automaton. It does this,

it does that. And people are like, oh, it must be just like this. It must be just like that.

So no, it isn't. It's something different. Right. And so I could have done sort of,

I'm really glad you did what you did, but you could have done sort of academically,

just published, keep publishing small papers here and there. And then you would just keep

getting this kind of resistance, right? You would get like, yeah, it's supposed to just

dropping a thing that says, here it is, here's the full, the full thing.

No, I mean, that was my calculation is that basically, you know, you could introduce

little pieces. It's like, you know, one possibility is like, it's the secret weapon,

so to speak. It's this, you know, I keep on discovering these things in all these different

areas. Where'd they come from? Nobody knows. But I decided that, you know, in the interests of one

only has one life to lead and, you know, writing that book took me a decade anyway. There's not a

lot of wiggle room, so to speak. One can't be wrong by a factor of three, so to speak, in how long

it's going to take. That I, you know, I thought the best thing to do, the thing that is most sort

of, that most respects the intellectual content, so to speak, is you just put it out with as much

force as you can, because it's not something where, and, you know, it's an interesting thing.

You talk about ego and it's, you know, for example, I run a company which has my name on it,

right? I thought about starting a club for people whose companies have their names on them. And

it's a funny group because we're not a bunch of egomaniacs. That's not what it's about,

so to speak. It's about basically sort of taking responsibility for what one's doing.

And, you know, in a sense, any of these things where you're sort of putting yourself on the line,

it's kind of a funny, it's a funny dynamic because, in a sense, my company is sort of

something that happens to have my name on it, but it's kind of bigger than me and I'm kind of just

its mascot at some level. I mean, I also happen to be a pretty, you know, strong leader of it.

LW. But it's basically showing a deep, inextricable sort of investment. Your name,

like Steve Jobs's name wasn't on Apple, but he was Apple. Elon Musk's name is not on Tesla,

but he is Tesla. So it's like, it meaning emotionally. If a company succeeds or fails,

he would just that emotionally would suffer through that. And so that's, that's a beautiful

recognizing that fact. And also Wolfram is a pretty good branding name, so that works out.

LW. Yeah, right. Exactly. I think Steve had it had a bad deal there.

LR. Yeah. So you made up for it with the last name. Okay. So in 2002, you published

A New Kind of Science, to which sort of on a personal level, I can credit my love for

cellular automata and computation in general. I think a lot of others can as well. Can you

briefly describe the vision, the hope, the main idea presented in this 1200 page book?

LW. Sure. Although it took 1200 pages to say in the book. So no, the real idea, it's kind of

a good way to get into it is to look at sort of the arc of history and to look at what's happened

in kind of the development of science. I mean, there was this sort of big idea in science about

300 years ago, that was, let's use mathematical equations to try and describe things in the world.

Let's use sort of the formal idea of mathematical equations to describe what might be happening in

the world, rather than, for example, just using sort of logical augmentation and so on. Let's have

a formal theory about that. And so there'd been this 300 year run of using mathematical equations

to describe the natural world, which had worked pretty well. But I got interested in how one could

generalize that notion. There is a formal theory, there are definite rules, but what structure could

those rules have? And so what I got interested in was let's generalize beyond the sort of purely

mathematical rules. And we now have this sort of notion of programming and computing and so on.

Let's use the kinds of rules that can be embodied in programs as a sort of generalization of the

ones that can exist in mathematics as a way to describe the world. And so my kind of favorite

version of these kinds of simple rules are these things called cellular automata. And so typical

case... So wait, what are cellular automata? Fair enough. So typical case of a cellular automaton,

it's an array of cells. It's just a line of discrete cells. Each cell is either black or white.

And in a series of steps that you can represent as lines going down a page, you're updating the

color of each cell according to a rule that depends on the color of the cell above it and

to its left and right. So it's really simple. So a thing might be if the cell and its right neighbor

are not the same or the cell on the left is black or something, then make it black on the next step.

And if not, make it white. Typical rule. That rule, I'm not sure I said it exactly right,

but a rule very much like what I just said, has the feature that if you started off from just one

black cell at the top, it makes this extremely complicated pattern. So some rules you get a very

simple pattern. Some rules, the rule is simple. You start them off from a sort of simple seed.

You just get this very simple pattern. But other rules, and this was the big surprise when I

started actually just doing the simple computer experiments to find out what happens, is that they

produce very complicated patterns of behavior. So for example, this rule 30 rule has the feature

you start off from just one black cell at the top, makes this very random pattern. If you look

like at the center column of cells, you get a series of values. It goes black, white, black,

black, whatever it is. That sequence seems for all practical purposes random. So it's kind of like

in math, you compute the digits of pi, 3.1415926, whatever. Those digits once computed, I mean,

the scheme for computing pi, it's the ratio of the circumference to the diameter of a circle,

very well defined. But yet, once you've generated those digits, they seem for all practical

purposes completely random. And so it is with rule 30, that even though the rule is very simple,

much simpler, much more sort of computationally obvious than the rule for generating digits of pi,

even with a rule that simple, you're still generating immensely complicated behavior.

Yeah. So if we could just pause on that, I think you probably have said it and looked at it so long,

you forgot the magic of it, or perhaps you don't, you still feel the magic. But to me,

if you've never seen sort of, I would say, what is it? A one dimensional, essentially,

cellular automata, right? And you were to guess what you would see if you have some

sort of cells that only respond to its neighbors. Right. If you were to guess what kind of things

you would see, like my initial guess, like even when I first like opened your book,

A New Kind of Science, right? My initial guess is you would see, I mean, it would be a very simple

stuff. Right. And I think it's a magical experience to realize the kind of complexity,

you mentioned rule 30, still your favorite cellular automaton? Still my favorite rule. Yes.

You get complexity, immense complexity, you get arbitrary complexity. Yes. And when you say

randomness down the middle column, that's just one cool way to say that there's incredible complexity.

And that's just, I mean, that's a magical idea. However, you start to interpret it,

all the reducibility discussions, all that. But it's just, I think that has profound philosophical

kind of notions around it, too. It's not just, I mean, it's transformational about how you see the

world. I think for me it was transformational. I don't know, we can have all kinds of discussion

about computation and so on, but just, you know, I sometimes think if I were on a desert island

and was, I don't know, maybe it was some psychedelics or something, but if I had to take

one book, I mean, you kind of science would be it because you could just enjoy that notion. For some

reason, it's a deeply profound notion, at least to me. I find it that way. Yeah. I mean, look, it's

been, it was a very intuition breaking thing to discover. I mean, it's kind of like, you know,

you point the computational telescope out the window and you're like, okay, I'm going to

point the computational telescope out there. And suddenly you see, I don't know, you know,

in the past, it's kind of like, you know, moons of Jupiter or something, but suddenly you see

something that's kind of very unexpected and rule 30 was very unexpected for me. And the big

challenge at a personal level was to not ignore it. I mean, people, you know, in other words,

you might say, you know, it's a bug. What would you say? Yeah. Well, yeah. I mean, I,

what are we looking at by the way? Oh, well, I was just generating here. I'll actually generate

a rule 30 pattern. So that's the rule for, for rule 30. And it says, for example, it says here,

if you have a black cell in the middle and black cell to the left and white cell to the right,

then the cell on the next step will be white. And so here's the actual pattern that you get

starting off from a single black cell at the top there. And then that's the initial state initial

condition. That's the initial thing. You just start off from that and then you're going down

the page and at every, at every step, you're just applying this rule to find out the new value that

you get. And so you might think rule that simple, you got to get the, there's got to be some trace

of that simplicity here. Okay. We'll run it. Let's say for 400 steps. Um, so what it does,

it's kind of aliasing a bit on the screen there, but, but, um, you can see there's a little bit

of regularity over on the left, but there's a lot of stuff here that just looks very complicated,

very random. And, uh, that's a big sort of shock to was a big shock to my intuition, at least

that that's possible. The mind immediately starts. Is there a pattern? There must be a repetitive

pattern. There must be. So I spent, so indeed, that's what I thought at first. And I thought,

I thought, well, this is kind of interesting, but you know, if we run it long enough, we'll see,

you know, something we'll resolve into something simple. And, uh, uh, you know, I did all kinds of

analysis of using mathematics, statistics, cryptography, whatever, whatever to try and crack

it. Um, and I never succeeded. And after I hadn't succeeded for a while, I started thinking maybe

there's a real phenomenon here. That is the reason I'm not succeeding. Maybe. I mean, the thing that

for me was sort of a motivating factor was looking at the natural world and seeing all this complexity

that exists in the natural world. The question is, where does it come from? You know, what secret

does nature have that lets it make all this complexity that we humans, when we engineer

things typically are not making, we're typically making things that at least look quite simple to

us. And so the shock here was even from something very simple, you're making something that complex.

Uh, maybe this is getting at sort of the secret that nature has that allows it to make really

complex things, even though its underlying rules may not be that complex. How did it make you feel

if we, if we look at the Newton apple, was there, was it, was there a, you know, you took a walk

and, and something it profoundly hit you or was this a gradual thing, a lobster being boiled?

The truth of every sort of science discovery is it's not that gradual. I mean, I've spent,

I happen to be interested in scientific biography kinds of things. And so I've tried to track down,

you know, how did people come to figure out this or that thing? And there's always a long kind of,

uh, sort of preparatory, um, you know, there's a, there's a need to be prepared in a mindset

in which it's possible to see something. I mean, in the case of rule 30,

I was around June 1st, 1984 was, um, uh, kind of a silly story in some ways. I finally had

a high resolution laser printer. So I was able, so I thought I'm going to generate a bunch of

pictures of the cellular automata and I generate this one and I put it, I was on some plane flight

to Europe and they have this with me. And it's like, you know, I really should try to understand

this. And this is really, you know, this is, I really don't understand what's going on.

And, uh, that was kind of the, um, you know, slowly trying to, trying to see what was happening.

It was not, uh, it was depressingly unsubstantial, so to speak, in the sense that, um, a lot of these

ideas like principle of computational equivalence, for example, you know, I thought, well, that's a

possible thing. I didn't know if it's correct, still don't know for sure that it's correct.

Um, but it's sort of a gradual thing that these things gradually kind of become seem more important

than one thought. I mean, I think the whole idea of studying the computational universe of simple

programs, it took me probably a decade, decade and a half to kind of internalize that that was

really an important idea. Um, and I think, you know, if it turns out we find the whole universe

lurking out there in the computational universe, that's a good, uh, you know, it's a good brownie

point or something for the, uh, for the whole idea. But I think that the, um, the thing that's

strange in this whole question about, you know, finding this different raw material for making

models of things, um, what's been interesting sort of in the, in sort of arc of history is,

you know, for 300 years, it's kind of like the, the mathematical equations approach.

It was the winner. It was the thing, you know, you want to have a really good model for something

that's what you use. The thing that's been remarkable is just in the last decade or so,

I think one can see a transition to using not mathematical equations, but programs

as sort of the raw material for making models of stuff. And that's pretty neat. And it's kind of,

you know, as somebody who's kind of lived inside this paradigm shift, so to speak,

it is bizarre. I mean, no doubt in sort of the history of science that will be seen as an

instantaneous paradigm shift, but it sure isn't instantaneous when it's played out in one's actual

life. So to speak, it seems glacial. Um, um, and it's the kind of thing where, where it's sort of

interesting because in the dynamics of sort of the adoption of ideas like that into different fields,

the younger the field, the faster the adoption typically, because people are not kind of locked

in with the fifth generation of people who've studied this field and it is, it is the way it is

and it can never be any different. And I think that's been, um, you know, watching that process

has been interesting. I mean, I'm, I'm, I think I'm fortunate that I, I've, uh, uh, I, I do stuff

mainly cause I like doing it. And, um, uh, if I was, um, uh, that makes me kind of thick skinned

about the world's response to what I do. Um, and uh, but that's definitely, uh, you know, and anytime

you, you write a book called something like a new kind of science, um, it's kind of the, the pitch

forks will come out for the, for the old kind of science. And I was, it was interesting dynamics.

I think that the, um, um, uh, I have to say that I was fully aware of the fact that the, um, when

you see sort of incipient paradigm shifts in science, the vigor of the negative response

upon early introduction is a fantastic positive indicator of good longterm results. So in other

words, if people just don't care, it's, um, you know, that's not such a good sign. If they're

like, oh, this is great. That means you didn't really discover anything interesting. Um, what

fascinating properties of rule 30 have you discovered over the years? You've recently

announced the rule 30 prizes for solving three key problems. Can you maybe talk about interesting

properties that have been kind of revealed rule 30 or other cellular automata and what problems

are still before us? Like the three problems you've announced. Yeah. Yeah. Right. So, I mean,

the most interesting thing about cellular automata is that it's hard to figure stuff out about them.

And that's, um, uh, in a sense, every time you try and sort of, uh, uh, you try and bash them with

some other technique, you say, can I crack them? The answer is they seem to be uncrackable. They

seem to have the feature that they are, um, that they're sort of showing irreducible computation.

They're not, you're not able to say, oh, I know exactly what this is going to do. It's going to

do this or that, but there's specific formulations of that fact. Yes. Right. So, I mean, for example,

in, in rule 30, in the pattern you get just starting from a single black cell, you get this

sort of very, very sort of random looking pattern. And so one feature of that, just look at the

center column. And for example, we use that for a long time to generate randomness symbols and

language, um, just, you know, what rule 30 produces. Now the question is, can you prove

how random it is? So for example, one very simple question, can you prove that it'll never repeat?

We haven't been able to show that it will never repeat.

We know that if there are two adjacent columns, we know they can't both repeat,

but just knowing whether that center column can ever repeat, we still don't even know that. Um,

another problem that I sort of put in my collection of, you know, it's like $30,000 for

three, you know, for these three prizes for about rule 30. Um, I would say that this is not one of

those. There's one of those cases where the money is not the main point, but, um, it's just, uh,

you know, helps, um, uh, motivate somehow the, the investigation. So there's three problems

you propose to get $30,000 if you solve all three or maybe, you know, it's 10,000 for each for each.

Right. My, uh, the, the problems, that's right. Money's not the thing. The problems

themselves are just clean formulation. It's just, you know, will it ever become periodic?

Second problem is, are there an equal number of black and white cells down the middle column,

down the middle column. And the third problem is a little bit harder to state, which is essentially,

is there a way of figuring out what the color of a cell at position T down the center column is

in a, with a less computational effort than about T steps. So in other words, is there a way to jump

ahead and say, I know what this is going to do, you know, it's just some mathematical function

of T, um, or proving that there is no way or proving there is no way. Yes. But both, I mean,

you know, for any one of these, one could prove that, you know, one could discover, you know,

we know what rule 30 does for a billion steps, but, um, and maybe we'll know for a trillion steps

before too very long. Um, but maybe at a quadrillion steps, it suddenly becomes repetitive.

You might say, how could that possibly happen? But so when I was writing up these prizes,

I thought, and this is typical of what happens in the computational universe. I thought,

let me find an example where it looks like it's just going to be random forever,

but actually it becomes repetitive. And I found one and it's just, you know, I did a search,

I searched, I don't know, maybe a million different rules with some criterion. And this is

what's sort of interesting about that is I kind of have this thing that I say in a kind of silly

way about the computational universe, which is, you know, the animals are always smarter than you

are. That is, there's always some way. One of these computational systems is going to figure

out how to do something, even though I can't imagine how it's going to do it. And, you know,

I didn't think I would find one that, you know, you would think after all these years that when

I found sort of all possible things, uh, uh, uh, funky things that, um, uh, that I would have, uh,

that I would have gotten my intuition wrapped around the idea that, um, you know, these creatures

are always in the computational universe are always smarter than I'm going to be. But, uh,

well, they're equivalently as smart, right? That's correct. And that makes it,

that makes one feel very sort of, it's, it's, it's humbling every time because every time the thing

is, is, uh, you know, you think it's going to do this or it's not going to be possible to do this

and it turns out it finds a way. Of course, the promising thing is there's a lot of other rules

like rule 30. It's just rule 30 is, oh, it's my favorite cause I found it first. And that's right.

But the, the problems are focusing on rule 30. It's possible that rule 30

is, is repetitive after trillion steps and that doesn't prove anything about the other rules.

It does not. But this is a good sort of experiment of how you go about trying to prove something

about a particular rule. Yes. And it also, all these things help build intuition. That is if

it turned out that this was repetitive after a trillion steps, that's not what I would expect.

And so we learned something from that. The method to do that though, would reveal something

interesting about the, no doubt. No doubt. I mean, it's, although it's sometimes challenging,

like the, you know, I put out a prize in 2007 for, for a particular Turing machine that I,

there was the simplest candidate for being a universal Turing machine and the young chap in

England named Alex Smith, um, after a smallish number of months said, I've got a proof and

he did, you know, it took a little while to iterate, but he had a proof. Unfortunately,

the proof is very, it's, it's a lot of micro details. It's, it's not, it's not like you look

at it and you say, aha, there's a big new principle. The big new principle is the simplest

Turing machine that might have been universal actually is universal. And it's incredibly much

simpler than the Turing machines that people already knew were universal before that. And so

that intuitionally is important because it says computation universality is closer at hand than

you might've thought. Um, but the actual methods are not, uh, in that particular case,

we're not terribly illuminating. It would be nice if the methods would also be elegant.

That's true. Yeah. No, I mean, I think it's, it's one of these things where, I mean, it's,

it's like a lot of, we've talked about earlier kind of, um, you know, opening up AI's and machine

learning and things of what's going on inside and is it, is it just step by step or can you

sort of see the bigger picture more abstractly? It's unfortunate. I mean, with Fermat's last

theorem proof, it's unfortunate that the proof to such an elegant theorem is, um, is not, I mean,

it's, it's, it's not, it doesn't fit into the margins of a page. That's true. But there's no,

one of the things is that's another consequence of computational irreducibility. This, this fact

that there are even quite short results in mathematics whose proofs are arbitrarily long.

Yes. That's a, that's a consequence of all this stuff. And it's, it's a, it makes one wonder,

uh, you know, how come mathematics is possible at all? Right. Why is, you know, why is it the

case? How people managed to navigate doing mathematics through looking at things where

they're not just thrown into, it's all undecidable. Um, that's, that's its own own separate, separate

story. And that would be, that would, that would have a poetic beauty to it is if people were to

find something interesting about rule 30, because I mean, there's an emphasis to this particular

role. It wouldn't say anything about the broad irreducibility of all computations, but it would

nevertheless put a few smiles on people's faces of, uh, well, yeah. But to me, it's like in a

sense, establishing principle of computational equivalence, it's a little bit like doing

inductive science anywhere. That is the more examples you find, the more convinced you are

that it's generally true. I mean, we don't get to, you know, whenever we do natural science,

we, we say, well, it's true here that this or that happens. Can we, can we prove that it's true

everywhere in the universe? No, we can't. So, you know, it's the same thing here. We're exploring

the computational universe. We're establishing facts in the computational universe. And that's,

uh, that's sort of a way of, uh, of inductively concluding general things. Just to think through

this a little bit, we've touched on it a little bit before, but what's the difference between the

kind of computation, now that we're talking about cellular automata, what's the difference between

the kind of computation, biological systems, our mind, our bodies, the things we see before us that

emerged through the process of evolution and cellular automata? I mean, we've kind of implied

to the discussion of physics underlying everything, but we, we talked about the potential equivalents

of the fundamental laws of physics and the kind of computation going on in Turing machines.

But can you now connect that? Do you think there's something special or interesting about the kind

of computation that our bodies do? Right. Well, let's talk about brains primarily. I mean,

I think the, um, the most important thing about the things that our brains do are that we care

about them in the sense that there's a lot of computation going on out there in, you know,

cellular automata and, and, you know, physical systems and so on. And it just, it does what it

does. It follows those rules. It does what it does. The thing that's special about the computation in

our brains is that it's connected to our goals and our kind of whole societal story. And, you know,

I think that's the, that's, that's the special feature. And now the question then is when you

see this whole sort of ocean of computation out there, how do you connect that to the things that

we humans care about? And in a sense, a large part of my life has been involved in sort of the

technology of how to do that. And, you know, what I've been interested in is kind of building

computational language that allows that something that both we humans can understand and that can

be used to determine computations that are actually computations we care about. See, I think

when you look at something like one of these cellular automata and it does some complicated

thing, you say, that's fun, but why do I care? Well, you could say the same thing actually in

physics. You say, oh, I've got this material and it's a ferrite or something. Why do I care? You

know, it's some, has some magnetic properties. Why do I care? It's amusing, but why do I care?

Well, we end up caring because, you know, ferrite is what's used to make magnetic tape,

magnetic discs, whatever. Or, you know, we could use liquid crystals as made, used to make,

well, not actually increasingly not, but it has been used to make computer displays and so on.

But those are, so in a sense, we're mining these things that happen to exist in the physical

universe and making it be something that we care about because we sort of entrain it into

technology. And it's the same thing in the computational universe that a lot of what's

out there is stuff that's just happening, but sometimes we have some objective and we will

go and sort of mine the computational universe for something that's useful for some particular

objective. On a large scale, trying to do that, trying to sort of navigate the computational

universe to do useful things, you know, that's where computational language comes in. And, you

know, a lot of what I've spent time doing and building this thing we call Wolfram Language,

which I've been building for the last one third of a century now. And kind of the goal there is

to have a way to express kind of computational thinking, computational thoughts in a way that

both humans and machines can understand. So it's kind of like in the tradition of computer languages,

programming languages, that the tradition there has been more, let's take how computers are built

and let's specify, let's have a human way to specify, do this, do this, do this,

at the level of the way that computers are built. What I've been interested in is representing sort

of the whole world computationally and being able to talk about whether it's about cities or

chemicals or, you know, this kind of algorithm or that kind of algorithm, things that have come to

exist in our civilization and the sort of knowledge base of our civilization, being able to talk

directly about those in a computational language so that both we can understand it and computers

can understand it. I mean, the thing that I've been sort of excited about recently, which I had

only realized recently, which is kind of embarrassing, but it's kind of the arc of what

we've tried to do in building this kind of computational language is it's a similar kind of

arc of what happened when mathematical notation was invented. So go back 400 years, people were

trying to do math, they were always explaining their math in words, and it was pretty clunky.

And as soon as mathematical notation was invented, you could start defining things like algebra and

later calculus and so on. It all became much more streamlined. When we deal with computational

thinking about the world, there's a question of what is the notation? What is the kind of

formalism that we can use to talk about the world computationally? In a sense, that's what I've

spent the last third of a century trying to build. And we finally got to the point where

we have a pretty full scale computational language that sort of talks about the world.

And that's exciting because it means that just like having this mathematical notation, let us

talk about the world mathematically, and let us build up these kind of mathematical sciences.

Now we have a computational language which allows us to start talking about the world

computationally, and lets us, my view of it is it's kind of computational X for all X. All these

different fields of computational this, computational that. That's what we can now build.

Let's step back. So first of all, the mundane. What is Wolfram language in terms of,

I mean I can answer the question for you, but it's basically not the philosophical deep,

the profound, the impact of it. I'm talking about in terms of tools, in terms of things you can

download, in terms of stuff you can play with. What is it? What does it fit into the infrastructure?

What are the different ways to interact with it?

Right. So I mean the two big things that people have sort of perhaps heard of that come from

Wolfram language, one is Mathematica, the other is Wolfram Alpha. So Mathematica first came out

in 1988. It's this system that is basically an instance of Wolfram language, and it's used to do

computations, particularly in sort of technical areas. And the typical thing you're doing is

you're typing little pieces of computational language, and you're getting computations done.

It's very kind of, there's like a symbolic.

Yeah, it's a symbolic language.

It's a symbolic language. I mean I don't know how to cleanly express that, but that makes it very

distinct from how we think about sort of, I don't know, programming in a language like Python or

something.

Right. So the point is that in a traditional programming language, the raw material of the

programming language is just stuff that computers intrinsically do. And the point of Wolfram

language is that what the language is talking about is things that exist in the world or things

that we can imagine and construct. It's aimed to be an abstract language from the beginning.

And so for example, one feature it has is that it's a symbolic language, which means that the

thing called, you have an X, just type in X, and Wolfram language will just say, oh, that's X.

It won't say error, undefined thing. I don't know what it is, computation, in terms of computing.

Now that X could perfectly well be the city of Boston. That's a thing. That's a symbolic thing.

Or it could perfectly well be the trajectory of some spacecraft represented as a symbolic thing.

And that idea that one can work with, sort of computationally work with these different,

these kinds of things that exist in the world or describe the world, that's really powerful.

And when I started designing, well, when I designed the predecessor of what's now Wolfram

language, which is a thing called SMP, which was my first computer language, I kind of wanted to

have this sort of infrastructure for computation, which was as fundamental as possible. I mean,

this is what I got for having been a physicist and tried to find fundamental components of things

and wound up with this kind of idea of transformation rules for symbolic expressions

as being sort of the underlying stuff from which computation would be built.

And that's what we've been building from in Wolfram language. And operationally, what happens,

it's, I would say, by far the highest level computer language that exists. And it's really

been built in a very different direction from other languages. So other languages have been

about, there is a core language. It really is kind of wrapped around the operations that a

computer intrinsically does. Maybe people add libraries for this or that, but the goal of

Wolfram language is to have the language itself be able to cover this sort of very broad range

of things that show up in the world. And that means that there are 6,000 primitive functions

in the Wolfram language that cover things. I could probably pick a random here. I'm going to pick

just for fun, I'll pick, let's take a random sample of all the things that we have here.

So let's just say random sample of 10 of them and let's see what we get.

Wow. Okay. So these are really different things from functions. These are all functions,

Boolean convert. Okay. That's the thing for converting between different types of Boolean

expressions. So for people are just listening, uh, Stephen typed in random sample of names,

so this is sampling from all function. How many you said there might be 6,000 from 6,000 10 of

them. And there's a hilarious variety of them. Yeah, right. Well, we've got things about, um,

dollar requester address that has to do with interacting with, uh, uh, the, the world of the,

of the cloud and so on. Discrete wavelet data, spheroidal, graphical sort of window. Yeah. Yeah.

Window movable. That's the user interface kind of thing. I want to pick another 10 cause I think

this is some, okay. So yeah, there's a lot of infrastructure stuff here that you see. If you,

if you just start sampling at random, there's a lot of kind of infrastructural things. If you're

more, you know, if you more look at the, um, some of the exciting machine learning stuff you showed

off, is that also in this pool? Oh yeah. Yeah. I mean, you know, so one of those functions is

like image identify as a, as a function here where you just say image identify. I don't know. It's

always good to, let's do this. Let's say current image and let's pick up an image, hopefully.

Current image accessing the webcam, took a picture yourself.

Took a terrible picture. But anyway, we can say image identify, open square brackets, and then

we just paste that picture in there. Image identify function running on the picture.

Oh, and it says, Oh wow. It says I, it looked, I looked like a plunger because I got this great

big thing behind my classifies. So this image identify classifies the most likely object in,

in the image. So, so plunger. Okay. That's, that's a bit embarrassing. Let's see what it does.

And let's pick the top 10. Um, okay. Well, it thinks there's a, Oh, it thinks it's pretty

unlikely that it's a primate, a hominid, a person. 8% probability. 57 is a plunger.

Yeah. Well, hopefully we'll not give you an existential crisis. And then, uh,

8%, uh, I shouldn't say percent, but, uh, no, that's right. 8% that it's a hominid. Um, and,

uh, yeah. Okay. It's really, I'm going to do another one of these just cause I'm embarrassed

that it, um, I didn't see me at all. There we go. Let's try that. Let's see what that did.

Um, we took a picture with a little bit more of me and not just my bald head, so to speak.

Okay. 89% probability it's a person. So that, so then I would, um, but, uh, you know, so this is

image identify as an example of one of just one of them, just one function out of that part of the

that's like part of the language. Yes. And I mean, you know, something like, um, I could say,

I don't know, let's find the geo nearest, uh, what could we find? Um, let's find the nearest volcano.

Um, let's find the 10. I wonder where it thinks here is. Let's try finding the 10 volcanoes

nearest here. Okay. So geo nearest volcano here, 10 nearest volcanoes. Right. Let's find out where

those are. We can now, we've got a list of volcanoes out and I can say geo list plot that

and hopefully, okay, so there we go. So there's a map that shows the positions of those 10 volcanoes

of the East coast and the Midwest and well, no, we're okay. We're okay. There's not, it's not too

bad. Yeah. They're not very close to us. We could, we could measure how far away they are, but, um,

you know, the fact that right in the language, it knows about all the volcanoes in the world. It

knows, you know, computing what the nearest ones are. It knows all the maps of the world and so on.

It's a fundamentally different idea of what a language is. Yeah, right. That's why I like to

talk about is that, you know, a full scale computational language. That's, that's what

we've tried to do. And just if you can comment briefly, I mean, this kind of,

the Wolfram language along with Wolfram Alpha represents kind of what the dream of what AI is

supposed to be. There's now a sort of a craze of learning kind of idea that we can take raw data

and from that extract the, uh, the different hierarchies of abstractions in order to be able

to under, like in order to form the kind of things that Wolfram language operates with,

but we're very far from learning systems being able to form that.

Like the context of history of AI, if you could just comment on, there is a, you said computation

X and there's just some sense where in the eighties and nineties sort of expert systems

represented a very particular computation X. Yes. Right. And there's a kind of notion that

those efforts didn't pan out. Right. But then out of that emerges kind of Wolfram language,

Wolfram Alpha, which is the success. I mean, yeah, right. I think those are in some sense,

those efforts were too modest. That is they were, they were looking at particular areas

and you actually can't do it with a particular area. I mean, like, like even a problem like

natural language understanding, it's critical to have broad knowledge of the world. If you want to

do good natural language understanding and you kind of have to bite off the whole problem. If you,

if you say, we're just going to do the blocks world over here, so to speak, you don't really,

it's, it's, it's actually, it's one of these cases where it's easier to do the whole thing than it

is to do some piece of it. You know, what, one comment to make about sort of the relationship

between what we've tried to do and sort of the learning side of, of AI. You know, in a sense,

if you look at the development of knowledge in our civilization as a whole, there was kind of this

notion pre 300 years ago or so. Now you want to figure something out about the world. You can

reason it out. You can do things which are just use raw human thought. And then along came sort

of modern mathematical science. And we found ways to just sort of blast through that by in that case,

in that case, writing down equations. Now we also know we can do that with computation and so on.

And so that was kind of a different thing. So, so when we look at how do we sort of encode

knowledge and figure things out, one way we could do it is start from scratch, learn everything.

It's just a neural net figuring everything out. But in a sense that denies the sort of knowledge

based achievements of our civilization, because in our civilization, we have learned lots of stuff.

We've surveyed all the volcanoes in the world. We've done, you know, we figured out lots of

algorithms for this or that. Those are things that we can encode computationally. And that's what

we've tried to do. And we're not saying just, you don't have to start everything from scratch.

So in a sense, a big part of what we've done is to try and sort of capture the knowledge of the

world in computational form and computable form. Now there's also some pieces which, which were

for a long time, undoable by computers like image identification, where there's a really,

really useful module that we can add that is those things which actually were pretty easy

for humans to do that had been hard for computers to do. I think the thing that's interesting,

that's emerging now is the interplay between these things, between this kind of knowledge of the

world that is in a sense, very symbolic and this kind of sort of much more statistical kind of

things like image identification and so on. And putting those together by having this sort of

symbolic representation of image identification, that that's where things get really interesting

and where you can kind of symbolically represent patterns of things and images and so on. I think

that's, you know, that's kind of a part of the path forward, so to speak.

Yeah. So the dream of, so the machine learning is not in my view, I think the view of many people

is not anywhere close to building the kind of wide world of computable knowledge that will from

language of build. But because you have a kind of, you've done the incredibly hard work of building

this world, now machine learning can be, can serve as tools to help you explore that world.

Yeah, yeah.

And that's what you've added. I mean, with the version 12, right? You added a few,

I was seeing some demos, it looks amazing.

Right. I mean, I think, you know, this, it's sort of interesting to see the,

the sort of the, once it's computable, once it's in there, it's running in sort of a very efficient

computational way. But then there's sort of things like the interface of how do you get there? You

know, how do you do natural language understanding to get there? How do you, how do you pick out

entities in a big piece of text or something? That's I mean, actually a good example right now

is our NLP NLU loop, which is we've done a lot of stuff, natural language understanding using

essentially not learning based methods, using a lot of, you know, little algorithmic methods,

human curation methods and so on.

In terms of when people try to enter a query and then converting. So the process of converting

NLU defined beautifully as converting their query into a computational language,

which is a very well, first of all, super practical definition, very useful definition,

and then also a very clear definition of natural language understanding.

Right. I mean, a different thing is natural language processing, where it's like,

here's a big lump of text, go pick out all the cities in that text, for example.

And so a good example of, you know, so we do that, we're using, using modern machine learning

techniques. And it's actually kind of, kind of an interesting process that's going on right now.

It's this loop between what do we pick up with NLP using machine learning versus what do we pick up

with our more kind of precise computational methods in natural language understanding.

And so we've got this kind of loop going between those, which is improving both of them.

Yeah. And I think you have some of the state of the art transformers,

like you have BERT in there, I think.

Oh yeah.

So it's closely, you have, you have integrating all the models. I mean,

this is the hybrid thing that people have always dreamed about or talking about.

I'm actually just surprised, frankly, that Wolfram language is not more popular than it already is.

You know, that's a, it's a, it's a complicated issue because it's like, it involves, you know,

it involves ideas and ideas are absorbed slowly in the world. I mean, I think that's

And then there's sort of like what we're talking about, there's egos and personalities and some of

the, the absorption, absorption mechanisms of ideas have to do with personalities and the students of

personalities and the, and then a little social network. So it's, it's interesting how the spread

of ideas works.

You know, what's funny with Wolfram language is that we are, if you say, you know, what market

sort of market penetration, if you look at the, I would say very high end of R&D and sort of the,

the people where you say, wow, that's a really impressive, smart person. They're very often

users of Wolfram language, very, very often. If you look at the more sort of, it's a funny thing.

If you look at the more kind of, I would say people who are like, oh, we're just plodding

away doing what we do. They're often not yet Wolfram language users. And that dynamic,

it's kind of odd that there hasn't been more rapid trickle down because we really, you know,

the high end we've really been very successful in for a long time. And it's, it's, but with,

you know, that's partly, I think, a consequence of my fault in a sense, because it's kind of,

you know, I have a company which is really emphasizes sort of creating products and

building a sort of the best possible technical tower we can rather than sort of doing the

commercial side of things and pumping it out in sort of the most effective way.

And there's an interesting idea that, you know, perhaps you can make it more popular

by opening everything up, sort of the GitHub model. But there's an interesting,

I think I've heard you discuss this, that that turns out not to work in a lot of cases,

like in this particular case, that you want it, that when you deeply care about the integrity,

the quality of the knowledge that you're building, that, unfortunately, you can't,

you can't distribute that effort.

Yeah, it's not the nature of how things work. I mean, you know, what we're trying to do

is a thing that for better or worse, requires leadership. And it requires kind of maintaining

a coherent vision over a long period of time, and doing not only the cool vision related work,

but also the kind of mundane in the trenches make the thing actually work well, work.