Transcription
I had long been interested in kind of, what fundamentally is there underneath physics? What is the sort of foundational things that create our physical universe? What rules could those be? I at first thought when the rules are simple enough, the behavior one will get will always be correspondingly simple. But I started doing actual computer experiments to find out what really happens. It's kind of like you get to take the computer like a telescope, turn it at the sky and see what you see. What I saw was really very remarkable. At first, I didn't quite believe it. Even when the rules by which you're operating are very simple, the behavior of the system can be very complicated. I'm Stephen Wolfram. I've been motivated for a long time by understanding the significance of the paradigm of computation, both in its practical applications in technology and its implications for kind of deep conceptual issues in thinking about the world.
- Chapter 1: The limits of theoretical physics
The story of 20th century physics was a story of discovering many different phenomena. And the question was, do all these phenomena fit together? And it hadn't been figured out how that could work. You know, in antiquity, people just sort of said we can think about how the universe works and we can conclude that it's made of atoms or everything flows or something like that. It's kind of a pure, we just think about it to see how it works. By the 1600s, people were starting to use kind of mathematical methods to understand the natural world and so on. They picked out certain aspects of the natural world that were amenable to analysis by mathematical methods. I I mean, you know, Newton, for example, was skilled in realizing that he should study mechanics of solid objects. You know, what is the trajectory of this thing? How does it move when acted on by forces? Had he studied fluids, which can behave in much more complicated ways and show turbulent random behavior, he wouldn't have been able to deduce these kind of simple laws of motion to kind of launch the whole Newtonian story about physics. But there was still at that time, people like, I don't know, Descartes was saying, you know, within 100 years, we'll just have understood everything. We will have managed to just decode how our universe works. That didn't happen. What seemed to happen was, as people discovered more kinds of phenomena, the theories got more complicated. And what happened in, well, going into the 20th century, I would say that an important sort of trend was the idea of formalization of things, which came to mathematics in the course of the 19th century, the idea that mathematics could be built up as an almost logical, structural kind of thing, rather than something which was kind of an almost empirical way of describing the world as we perceive it. That was something which coming into the 20th century, I think, influenced kind of thinking about physics. And the three big theories that have sort of dominated 20th century physics are general relativity, the theory of space-time and gravity, quantum mechanics, and statistical mechanics, where sort of the key insight is the second law of thermodynamics, the idea that there's a tendency for systems to kind of get more random in their behavior through time. Those are sort of the three big theories of 20th century physics. And they all come out of, they all rely on this kind of formalization that was a thing that had sort of emerged in the 19th century. You know, then the question is, okay, so we've got these general ideas about how things work. What specifically, how specifically is our universe built? And is there some underlying structure that is underneath those theories? Well, there were ideas like supersymmetry and string theory and so on, a whole collection of ideas which never really connected with the actual experimental observations that had been made. And there were still a lot of kind of things that seemed very arbitrary, like, you know, there are electrons and they have a certain mass. And then there are muons that are just like electrons, but they're 206 times heavier. Why does that exist? There were a lot of kind of mysterious, it just happens to be that way kinds of things. And there was sort of an attempt for a few decades to make that something that would be more explainable, but didn't work out. My own efforts really started from a different place. They started not from looking at kind of the world as it is and trying to reverse engineer using mathematical ideas to see how one could derive that world from mathematical ideas. Rather, what I was doing was something in a sense much more pedestrian, which was is to say, let's look at this computational universe of possibilities based on the operation of simple programs. Let's see what those things do. And maybe somehow we will see that those things behave in ways that are like the way that we observe our physical universe to behave. And the remarkable thing is that worked out. And it became clear to me that we're really being able to see kind of what is the fundamental machine code of our universe, what's sort of underneath all the physics we know? It's been a very exciting thing for me. And in fact, the methods that have come from that understanding of physics have turned out to also have a lot of implications for the foundations of mathematics, foundations of computation, foundations of machine learning, and foundations of biology. This notion that one can think about things kind of in computational terms seems like a lot of questions that have been around for a century or more, we're starting to be able to unlock.
- Chapter 2: A computational understanding of the world
Okay, so what is computation? The way I see computation, it's the following of rules and seeing what happens. So we used to computers. Computers have certain built-in machine instructions. We write programs that apply those machine instructions, and the computational process is seeing the consequences of applying those rules. So for me, computation at its heart is the consequences of applying rules. And those rules can be very simple. They can be more elaborate. That is what computation is, is the application of simple rules. In fact, for me, the field of study that has to do with looking at simple rules and seeing what their consequences are, I've tended in recent years to call that ruliology, the study of rules and their consequences. Computation is a metaphor that is very useful because we're familiar with computers and how they work. Ruliology is really the core basic science about simple rules and how they behave. So those rules might be the rules of arithmetic. And the computation might be working out some arithmetic calculation, those rules might be something that says you've got a collection of black and white cells in a line, and you're determining the of the cell as you go down the page, for example, according to a rule that depends on the color of the cells next to that particular cell on the row before. You state a rule for how things should work, and the computation is the result of applying those rules. So, for example, when we think about the whole universe, our current picture is that there's this kind of network of atoms of space, and the computation that the universe is doing is progressively rewriting that network of atoms of space, and doing that by saying, whenever there's a piece of network that looks like this, replace it by one that looks like that, and so on. When one's interested in kind of exploring the computational universe, there's kind of a question of what types of computations are most easily understood. And the one that I was sort of lucky enough to come upon at the beginning of the 1980s are some things that had, a slightly different version of them had been called cellular automata, and I kind of took that historical name. A cellular automaton is a row of cells. Each cell can be either black or white, for example, and the thing progresses, kind of making a picture down the page, line by line, and each successive line is formed from the one above it by taking each cell and asking, what were the colors of that cell and the two neighbors of that cell, for example, on the step before, and then looking up some table to how that cell should be colored on the next step. The idea of a cellular automaton could easily have existed in antiquity. And I've been kind of waiting for the time when some archaeological artifact will be unearthed that is a cellular automaton image. It's a very simple idea. The remarkable thing about it is just taking those very simple rules and applying them can lead to very complicated patterns, can lead to patterns that are in some sense as complicated as anything can be. That's the very remarkable discovery and observation that even very simple rules can lead to sort of arbitrarily complex behavior. Cellular automata are convenient because they have a very immediate visual aspect. You can kind of see the computation they do. There are plenty of other models of computation. There are Turing machines invented by Alan Turing in 1936. Those are things where there's kind of a tape with a bunch of ones and zeros, for example, on it. And you have this head that's moving back and forth according to certain rules. There are things called combinators, which were actually invented in 1920 by a chap called Moses Schönfinkel, they were actually the very first example of a sort of complete computational system, but they're incredibly obscure. And even to this day, they're very hard to understand. I wrote a book about combinators recently at the centenary of combinators. And I have to say that they're very hard for us to wrap our minds around. Then there are kind of approaches like so-called register machines, which are kind of very simple idealization of the way that practical computers work. There's a whole collection of these things. The remarkable thing is, even though at first, all these different kind of models of computation seem very different. They're talking about cells, they're talking about numbers, they're talking about sort of symbolic operations and things. They seem very different. One of the remarkable things is that they all, in fact, are equivalent. You can emulate a Turing machine with a cellular automaton. You can emulate a cellular automaton with a Turing machine. You can use combinators to emulate a register machine and so on. It's something that we have some familiarity with because we know that we can buy different kinds of computers, different kinds of computer hardware, and yet we can run the same software on those different computers. The details of the program are different, but the operation of the program when we're using it is the same on those different computers. That turns out to be a much more general phenomenon. Something that was understood by the 1940s and so on was that these different models of computation had this kind of equivalence. What was not clear is whether that equivalence extended to the physical world. It's very easy to just start saying, what are all the possible programs that you can make, let's say, with black and white cells and nearest neighbor rules and things like this. You can just enumerate them. For cellular automata, the very simplest class, I tended to call elementary cellular automata, there are 256 of those. And over the last 45 years or so, pretty much every one of those 256 rules has ended up being useful as a model of something. It's kind of a strange thing. what happens when you get sort of very fundamental kinds of models. They end up having applications in lots of different areas. My kind of all-time favorite is Rule 30, which has the feature that it's just that all of these rules are very tiny and very simple. The numbers kind of just come from taking the number 30 and writing it out in binary, and that's a representation of what this rule actually does. In terms of black and white cells and so on. Well, Rule 30 has this feature that you start it off from just one cell and it produces this extremely complicated pattern. Some aspects of the pattern, it's kind of regular on one side, but if you look, for example, at the center column of this triangular kind of pattern, the center column, for all practical purposes, looks completely random. You can't predict it in any way. The only way you can find out what it's going to be, it seems, is by running Rule 30 and seeing what happens. kind of a little bit like what you get in something like the digits of pi. It's easy to say what pi is. It's the ratio of the circumference diameter of a circle. There are methods for computing pi, but once you've computed it, you know, 3.14159, etc., the digits of pi look completely random. And it's the same kind of thing with Rule 30, except Rule 30 is a much simpler kind of setup and one that is much closer to the kinds of things that you can expect to see in the natural world. So what are some examples of natural systems that kind of can be described easily in terms of programs? One example, snowflake growth. Snowflakes grow by aggregating pieces of ice onto a growing structure. And there are very simple rules that describe the way in which a snowflake grows arms and then the arms grow arms and so on. That's something that is very easy to describe in simple computational terms. Another example, in biology, lots of growth processes are fundamentally computationally quite simple. Whether it's the way that a mollusk shell kind of grows in a spiral, or whether it's the way the pigmentation on mollusk shells work, whether it's kind of just a row of cells and they're each either producing pigment or not, and it's actually exactly one of these cellular automata where you have either you get the pigment or you don't get the pigment in each cell at each step and the result is this kind of elaborate pattern on the shell of the mollusk Biology has traditionally not been a theoretical science. Biology has been a science where you just observe, this is how organisms work, this is how molecular biology works, and so on. It's not been something where one anticipates that there will be some theoretical basis. Really, there are basically two basic theories in biology. One is natural natural selection, theory of biological evolution, and the other is kind of the molecular nature of biology and particularly the nature of DNA and so on. Those have been kind of all we've had in terms of thinking about biology sort of at a theoretical level. Now, when it comes to even biological evolution, It's not been completely clear why it works. Why doesn't it get stuck? Why can biological evolution go on and produce more and more elaborate forms? You know, Darwin, I think, believed, I think the last sentence of Origin of Species talks about how, you know, as the Earth goes circling around the sun, according to the fixed law of gravity, so sort of more and more complex organisms are being produced. He thought that there would be some kind of abstract law or kind of law like the laws of physics that would determine the progress of biological evolution. But nobody found that. I came back to that a couple of years ago and tried to understand sort of in computational terms, how does biological evolution work? And I had one very important new data point, which was machine learning and the fact that machine learning works. You know, I had played around the neural nets and kind of the foundations of machine learning back in the early 1980s. I'd never managed to get neural nets to do anything interesting. What was discovered in the 2010s was the surprising fact that if you take a neural net and you just bash it really, really hard, eventually it will learn stuff. And so I thought, well, let's try that same idea. for thinking about biological evolution. Biological evolution and machine learning turn out to be extremely related kinds of things. And so I did try that. And to my considerable surprise, yes, these simple computational systems could kind of evolve to get more and more complex forms to achieve more and more elaborate fitness objectives and so on. One of the things that is always remarkable about studying sort of rules, systems out there in the computational universe, it's a very humbling experience because you typically have some hypothesis about what you're going to see. You do some big search for things, you explore things, you kind of are observing things through your computational telescope, and always the things do something different than you expected. Yes, it really is the case that there's this kind of thing that is probably the secret that nature uses to make all this complexity that it makes, which is that in the computational universe of possible programs, even a very simple program can produce extremely complicated behavior. And that kind of led me to this concept of computational irreducibility that's been an important one for a lot of what I've done. Kind of this question of when you have a simple program, if you want to know what it does, one thing you can do is just run it step by step. Let's say you want to know what it's going to do after a million steps, where you can run those million steps and see what it does. The question is, can you jump ahead and work out what it's going to do without having to go through all those steps? One had had the view that came from kind of the success of mathematical science and physics and so on, that in some sense, everything was computationally reducible. Whatever was going on in the world, you would be able to sort of be smarter than those things and say, I know how it's going to work out, predict what's going to happen. And that's the thing, you know, in the tradition of the exact sciences, the idea that you can predict things, that you can say, I don't need to follow a million orbits of the Earth around the sun or some idealized sun. I can just use a formula and jump ahead and say what's going to happen. One of the things that has come out of what I've studied that is the result of this idea of computational irreducibility is that, no, science isn't that powerful. Science is not able to make statements, in many cases, about what will happen. The only way to find out what will happen is basically just to run the system and see what happens. It's a fundamental limitation of science that comes from within science. I mean, kind of in historical lineage, it's kind of a descendant of things like Gödel's Theorem in mathematics, but it's, more directly it's a consequence of the principle of computational equivalence and computational irreducibility. So that's been one of the things that has been sort of an important thing for me to understand, that there are sort of certain fundamental limitations to the traditional scientific paradigm. One of the questions in biology is what's special about life? Even if you just take a piece of living tissue. What kind of a thing is that? Is a piece of living tissue liquid? Well, it's kind of gooey often. Is it solid? Well, it's kind of has some, you know, maintains its structure in some way. It's really not those things. When you look at it microscopically, so that the big discovery of molecular biology, I suppose, in the last few decades has been that things are very orchestrated. Molecules, are sort of specifically and actively transported from here to there. This thing fits exactly into that, which then opens up to do this and so on. There's this question of how are all these pieces kind of orchestrated together to do the things that happen in biology? And this notion of sort of bulk orchestration that we're full of tons of molecules, but they're all doing things in this very kind of orchestrated way. That's a phenomenon that seems to be sort of an essential phenomenon of life. It's sort of the result of this big technology stack that's been built up through the course of biological evolution. It's one where the pieces are sort of like these kind of lumps of computational irreducibility that have been fit together to make, in the end, something which achieves the purposes that biological organisms achieve. The analogy is the organism is trying to do something like build a wall. Well, if we were doing that by engineering, we would make bricks that are nice shapes and we would arrange them in some simple pattern. But what's happening in biology, and by the way, also in machine learning, is that one is picking up these kind of random lumps of irreducible computation. They're kind of like rocks lying around on the ground. And one's fitting those in and saying, well, this one happens to fit this way and this way. And eventually you build up this wall. And the reason that biological evolution works is that the fitness objectives that exist for biological organisms are computationally very simple compared to sort of the power of this underlying irreducible computation. I mean, it's sort of unsurprising if every organism, as soon as it was born, had to be able to solve some elaborate mathematical problem, no organisms would survive. It's because the sort of fitness objectives are computationally quite simple, particularly relative to sort of the power of these underlying computational elements, that biological evolution is possible and can work, so to speak. If we look at the history of science and thinking in general, a lot of that history has to do with formalizing things. From the earliest days of human natural language, It's kind of like one could just be pointing at different kinds of things, but then one sort of formalized the idea of a rock. And then one just has to say the word rock, and one knows that corresponds to any of those things that we might have explicitly pointed at before. And then we get things like logic, which are another sort of formalization in that case of the structure of arguments. And then later on, we get mathematics, which is a kind of a formalization of certain aspects of how the world works or certain aspects of how we think about things abstractly. Computation is another formalization, is a broader formalization of things in the world and abstract things. sort of the great paradigm of the 21st century, is how do we think about things in computational terms? It's a way of structuring our thinking. It's a way of allowing us to kind of build towers of consequences because we have something that is formal and structured. And one of the things that's been a big activity of my life is trying to see, how do we represent different kinds of things in the world in computational terms? How do we eventually have a computational language for describing the world? That's what technology I built, Wolfram Language and so on, is all about, is finding computational ways to describe the world. Now you say, well, what can we not describe in computational terms? It's a good question. It's, you know, there keep on being things where I'm like, I don't know how this is going to work. And then you start looking at it and you realize, well, actually, this is something you can very much describe in computational terms, and it's very useful to do that. So at this point, I think it's fair to say this is sort of the paradigm that allows one to formalize things. This idea that things operate according to rules, and then you're looking at their consequence, that's a very general and very powerful idea. I mean, if you ask sort of what are the bigger sort of philosophical consequences of this and of knowing, for example, that our whole universe is kind of computational all the way down, what difference does it make to sort of in common life that we now believe that sort of we can describe the universe even at its most fundamental level in computational terms? I think sort of an analogy to what we're seeing now is kind of what happened in sort of the Copernican story, where the fact that, you know, one had believed. that one could understand the world just by common sense. It's obvious the earth is standing still and the sun is going around in the sky, so to speak, because that's what we feel. And then what became clear was, well, actually, the math says you can think about it differently. And then it's like, trust the math. Don't trust your everyday senses. That was kind of, in a sense, the lesson of the Copernican Revolution. I think what we're seeing now is this idea that, you know, you can really think about things in a structured computational way. That's the thing we're learning. And sort of things are computational all the way down. So it makes sense to think about things using this kind of way of structuring one's thinking in terms of computation.
- Chapter 3: A new kind of theory of everything
When we start thinking about the world in computational terms, there's a question of sort of what does that mean? People will say things like, if the world is computational, where's the computer that it's running on? is a confusion. Models are a way of representing what the natural world does. They're not mechanistically what the natural world is doing. When we imagine that there's an equation that governs the motion of the Earth around the sun, for example, we're not imagining that inside the Earth there's a little piece of software of the kind that I build, so to speak, that's calculating those mathematical equations. It's just the mathematical equations are a way of describing the way the natural world works. And so it is, as we start thinking about sort of a computational model of what is underneath physics, that is a representation of what is happening in the world. It's not that the machinery of the world is set up to work the way that we imagine a computation should be done. So at a more fundamental level, you can ask questions like, what goes from sort of an abstract model of the world to the actuality of the world? That's a complicated philosophical question. It's something people have been asking for a long time. You know, why does the universe exist? You know, there are versions of this, I think Spinoza had some line, you know, the universe is the thoughts of God actualized. That was sort of a version of how to think about that question. Now, I think we have a very interesting way of thinking about that question. This is a deep rabbit hole, but let's go into it. Let's start off with physics. And what is the physical world made of? We start back in antiquity, people arguing is the universe discrete or continuous. We learn by the end of the 19th century that matter is discrete, kind of the realization that we've had in recent times, that's sort of the foundation of the things I've done, is that we can think of space as also discrete. And so we think, what's in the universe? What's the universe made of? Well, we think of it as a bunch of discrete atoms of space. They're not atoms in the sense of chemical atoms. They're atoms in the sense of being indivisible units. There are atoms of space, and the only thing one can say about the atoms of space are how they are related to each other. And we can represent that by a network where we say this atom of space is kind of connected, related to these other atoms. of space. So we represent the whole universe just as a graph, a network. And we imagine that the universe and space and everything in it is just features of that network. What there ultimately is, is just this network that represents space and everything in it. Well, another question is, well, what does this network do? You know, that might be in sort of technological terms, the data structure of the universe. But what now is the algorithm of the universe, so to speak? And for that, what we imagine is that this network, we look at little pieces of this network and we say there are a collection of rules that say whenever you see a little piece of network that looks like this, it gets rewritten to a piece of network that looks like that. And this just keeps on happening. And that process of the rewriting of the network, that is the progress of time. That is, the time is kind of corresponds to this progressive computational process of the rewriting of this network. And one thing one can ask is, well, what's the large-scale effect of that? If there are, you know, 10 to the 400 of these atoms of space, and they're all getting rewritten in all these ways, what does that do in the aggregate? And sort of an analogous situation is what happens in a fluid, where we know what happens at the level of individual molecules colliding and bouncing off each other and so on. But then the question is, what is the aggregate effect of that when we look at zillions of molecules together? And we know in that case that what emerges is fluid mechanics. Well, in the case of these networks and atoms of space and so on, what seems to emerge is general relativity, the theory of gravity, Einstein's equations, and so on. That's the thing that is the aggregate effect of all these microscopic processes associated with the structure of this network. Well, then what happens is there are all these different sort of ways that the network can get rewritten, but there are all these different parts of the network that can be rewritten separately. There isn't sort of a single thread of history that says the network is in this form and then in this form and then in this form. There are lots of different possible threads of history that correspond to different possible orders in which these little pieces of rewriting can be done. And that possibility of all these different paths of history is what leads to quantum mechanics in our models. What's characteristic for quantum mechanics is that whereas in kind of classical physics, the notion is sort of definite things happen, things follow definite trajectories. In quantum mechanics, it's like there are many, many paths that are followed, and we only get to be able to look at sort of the aggregate effect represented in terms of probabilities of all those paths. So kind of the picture here is what there ultimately is in the universe is this network of atoms of space. And there are many different sort of paths of history of those atoms of that network. And that's what kind of leads to physics as we know it. And we're getting sort of more and more detail about how physics as we know it emerges from that very simple underlying structure. But there's one thing that confused me for a long time, which is with this picture, it's like there's a particular rule for updating this graph, this network and so on. Why did our universe get that particular rule and not another one. How do we understand that? And of all the infinitely many possible rules, why do we get this particular one? And what I realized in the end is actually we didn't get a particular one. Actually, all possible rules are being used. What's happening is just as there are different paths of history, associated with the different applications of a particular rule, so there are different parts of history associated with the application of different rules. And in the end, the way to think about things is that what one has is this object that represents all possible computations. I call it the ruliad. What is the ruliad? It is the entangled limit of all possible computations. The ruliad is a very abstract thing. It's a unique thing. Imagine that you have all possible machines that can do computation, all possible abstract systems that can do computation. You start them all running. They are entangled because two different machines may produce the same result. And that kind of weaves together the different pieces, the structure of the ruliad. So the ruliad is this very abstract thing. You can imagine a notion of rulial space. So as you move around the ruliad, it's as if you are using different kind of computational devices to figure out what will happen in the world. And in a sense, you can even think that different minds are embedded in different places in the ruliad. Different minds have a different way of thinking about what's going to happen in the world. And you can represent that by saying those different minds are at different places in the ruliad. So minds that are very closely aligned will be close together in rulial space. You know, human minds might be all clumped together. You know, cats and dogs might be a bit further away. The weather with its mind of its own might be much further away. It's similar to physical space where we would have a different point of view about kind of what we see out there in the world. If we're standing very close together, we'll say we see the same things. If we're standing far apart, we'll say we see different things. There actually, in our model of physics, there actually are three different kinds of space that turn out to be important. Physical space is the kind we're used to experiencing, what we call branchial space, which is kind of the space of possible histories that's associated with quantum mechanics, and rulial space, which is this much more general thing that is these kind of different points of view about how the universe works. But the ruliad is a completely inevitable, necessary object. Given the idea of computation, there is no choice but to have the ruliad The ruliad is this limit of all possible computations. It's a unique, inevitable object. So then the question is, well, how do we fit into that? We are observers embedded within the ruliad made of the same stuff as the ruliad. And the question is, what is our perception of the ruliad given that setup? And what turns out to be crucial is that we are observers of a certain kind, and observers of the kind we are necessarily perceive the ruliad in certain ways. Let me try and give a simpler example first. When we're looking at molecules bouncing around, we can ask the question, what do you perceive about these molecules bouncing around? One feature of molecular processes is they're reversible. If you have a movie of molecules colliding, bouncing off, and so on, you can't tell whether the movie is being run in the forward direction or in reverse. The microscopic collisions all look the same. But yet, macroscopically, we know you smash a piece of glass, and what you get is something very different. It's a very different thing that you don't go backwards from that. We see the thing smashing. We don't see the thing assembling itself spontaneously from all the fragments. And so that's the phenomenon of irreversibility. That's the phenomenon of law of entropy increase, the second law of thermodynamics, and so on. Why does it happen? Well, it happens actually because of this phenomenon of computational irreducibility. What's happening is the original setup of the system is sort of being run forwards computationally. That computation is effectively encrypting whatever simplicity there was in the initial conditions, in the initial setup of the system. And then the issue is, well, what do we see from that initial setup? In principle, we can take whatever comes out and we could reverse it. But in practice, because we are observers who are computationally bounded, we can't do all that irreversible, irreducible computation to go and follow through all those steps. We're stuck just saying it looks random to us. If we could do sort of unbounded computation, we could always know this particular elaborate configuration of molecules, that came from the simple initial condition. But because we are computationally bounded, we have to just say it looks random to us, and we believe in the second law of thermodynamics. So the second law of thermodynamics is a consequence of our computational simplicity relative to the computational irreducibility of the underlying processes that are going on. So that's an example of a place where the nature of us as observers determines essentially the laws of physics that we perceive. And what seems to be the case is that that's actually a much more general phenomenon that in fact within the ruliad it is the case that observers like us, what does it mean to be like us? Well, the two characteristics I know for sure are being computationally bounded, having finite minds, not being able to do arbitrarily elaborate computation, being computationally bounded and believing that we are persistent in time. It is a surprising thing. Given that in these models, we're made of different atoms of space at every successive moment in time, yet we have the internal perception that we experience, we have a thread of experience that's persistent. And so that belief that we have about how things work, that belief and persistence that sort of maintenance of the single thread of experience combined with computational boundedness, those two characteristics of us as observers seem to be telling us what we have to perceived within the ruliad. The ruliad is full of irreducible computation, but it also, one feature of irreducible computation is within irreducible computation, there are always an infinite number of pockets of computational reducibility. In other words, even though you can't say everything about what's going to happen, you can always say a few specific things about what's going to happen. In fact, there's no limit to the number of specific things you can say about what will happen. And so what we're effectively doing is observers like us kind of are sampling particular pockets of reducibility. I have to say that if everything was purely irreducible, we wouldn't believe there were laws of nature. would just say everything about the universe is unpredictable. We just have to watch the universe unfold to see what's going to happen. But in fact, we know there are certain pieces of computational reducibility. There are places in which we know there are regularities in the universe, which we, with our finite minds, are capable of making use of to be able to say that's predictable. That's a law of nature. That's something that allows us to kind of reduce the complexity of the world to something that we can kind of tell a narrative about in our minds. So the question then is not why does the ruliad exist? The ruliad inevitably exists. It's an abstract thing that necessarily exists and is unique. The question that is less obvious is why do we exist? Why are there observers like us embedded within the ruliad? I think that is something which we are within sight of being able to sort of derive scientifically. mean, one feature of observers like us is that we tend to take huge amounts of input data. You You know, we're looking around the room and we're seeing all these pixels of data. And yet we take all that input and we decide we're going to say this word next. We're going to reduce all of that input. We're going to kind of crush it down. to at a very slow rate decide what we do next. That seems to be a feature of our brains. It seems to be an essential feature of the thing that we perceive as consciousness, so to speak, that we are getting the sort of single thread of experience that emerges from the sort of crushing down of all of this input. It's something that is different from the rest of the natural world. I mean, in my principle of computational equivalence, It's not that brains are any more computationally sophisticated than random things in the world. You know, people would say sort of whimsically, the weather has a mind of its own. And the principle of computational equivalence says, actually, yes, all those fluid motions in the atmosphere, they're doing a computation that's just as sophisticated as the computation that happens with all the electrochemistry of neurons and brains. But the issue is that computation that's going on in the weather is very different in character. It's not aligned with the kinds of computations that we do in our brains. And it doesn't have the same feature of taking sort of all of its input data and crushing it down to a single sort of consensus next action. It seems that that, sort of, that feature is something that's very essential to our particular way of perceiving the universe. And it's relevant to what we perceive as the laws of physics. There are other features of this, like, for example, why do we believe in objective reality? You know, each one of us has an internal view of how things work and how we're thinking about things. But we believe that there is an outside world there that everybody sort of more or less agrees how it's set up. And I think what is surprising to me as well, that it seems like the emergence of sort of a reasonable notion of objective reality depends on the fact that there are lots of us. If there was just one of us, wouldn't have a clear notion of objective reality. It's because we can all extrapolate that our internal perceptions and feelings are similar in other people. And those other people, we're all observing, we're all sort of agreeing about how the universe, how the world works. And that's why we sort of believe in objective reality. It's sort of an interesting feature of that extends to lots of different things. Quantum mechanics, for example, is a place where it's been very confusing to understand why people think definite things happen in quantum mechanics. In quantum mechanics, you're always following these many possible paths of history. Why is it, then, people sort of say, yes, a definite thing happened and we agree about what that was? I think the answer to that is it's because, in a sense, we're all very close together in this thing I call branchial space, the space of possible quantum branches. It's similar to physical space. I mean, if you say, what's the night sky like? We'll all say, well, it looks roughly like this. It has these constellations in it and so on. But we all say, we all agree about what the night sky looks like because we're all sitting on this one planet. If we were spread throughout the galaxy, we absolutely would not agree. what the night sky was like. It's because we're sort of close together, we're many entities close together, that we have certain kinds of perceptions about the way the world works. But you can kind of keep going and try to understand the extent to which because we are the way we are, then it becomes inevitable that the science that we believe in, the laws of physics that we believe in, must be the way that they are, which is sort of a very surprising sort of metaphysical conclusion that I, for one, did not see coming at all.
- Chapter 4: If the universe is a program, what is the meaning of life?
I've been talking a bunch about abstract foundational ideas about how the world is put together and so on. What does that mean for each individual one of us? I think for me, the key takeaway is foundational knowledge is possible. That is, you can think foundationally about things. It's not obvious that you could. It might just be the world is the way it is. We'll never understand it. We'll never be able to think about the foundations of it. But we realize that we can. We can drill down and really get to the foundations of things. And certainly in my own sort of experience of life and discovering things and running companies and doing all those kinds of things. Foundational thinking has been a very key element of the way that I've approached things, that you can understand stuff. You can drill down and know what's really going on, know the primitives of what's happening. Now, the thing about the universe, it's like, how awesome is the universe, so to speak? And if we know the fundamental rules for the universe, does that mean the universe can't be awesome anymore? Does that mean we just got it? It's all over. The reason that, in fact, the universe can still be and necessarily will be sort of fundamentally awesome is this phenomenon of computational irreducibility. So in a sense, you might say computational irreducibility is a bad thing because it limits what we can do in science. It limits the extent to which we can predict what's going to happen. But in some sense, computational irreducibility is what gives us any richness in life. Because if we could always predict what was going to happen, nothing is sort of achieved by the actual passage of time and the actual living of our lives. The fact that there's computational irreducibility means that sort of the living of our lives adds up to something. We are executing that irreducible computation. There's no way that something can come from the outside and say, I know what's going to happen there. It's like you have to live the life to know what's going to happen, so to speak. Computational irreducibility has a ton of consequences, but one very direct one for us has to do with kind of our perception of free will. One might imagine that underneath there are definite rules that govern our behavior, that describe how, you know, the electrical signals in our nerve cells will operate and things like this. Given that there are those definite deterministic underlying rules, how can it be the case that the things we do somehow are the result of some kind of free will? Well, computational irreducibility kind of explains that because what it says is, yes, you know those underlying rules, but to know what the whole critter is going to do, you have to just follow those rules and see what happens. You can't say, oh, I know those rules, so therefore I know. the critter is going to stick its head up at just this moment or something. That is the thing. Computational irreducibility is what provides a sort of irreducible gap between the underlying deterministic rules and the actual behavior of a system. There will always be new things to discover. Within computational irreducibility, there are always an infinite number
of pockets of reducibility, and each one of those represents some discovery about how things work. Each one of those represents a surprise.
Now, you know, there are many, many consequences of computational irreducibility. If you start saying, you know, I'm going to build an AI and I want it only to think good thoughts and do good things. Well, the problem is, as soon as you build an AI that is actually making sort of deep use of computation, it's going to have computational irreducibility. And it's going to have this feature that it can always surprise us. It can always do things that are the result where you can tell what it does by just following through the steps and seeing what it does. But you can never say, I know you're never going to do the wrong thing or whatever else.
It's a trade-off, actually. It's something that I think will be a feature of sort of societal decisions is do you go for computational reducibility or you go for computational irreducibility? We've had the experience sort of after the Industrial Revolution of having machines where we can kind of understand how they work. They've got gears and levers and things like this. Before the Industrial Revolution, lots of things we used, we didn't understand. You know, you ride a horse. The horse says, we know what we can do with the horse. don't know how the horse works inside. And then, you know, post Industrial Revolution, we did have sort of a way of understanding how our machines work. But that's something as we get into this sort of domain of computational machines, that's no longer the case.
And we can either say we insist on knowing how the machine works inside. It's got to be computationally reducible in its behavior. If it's computationally reducible, it will be very limited in what it can do. If we say, no, it can be computationally irreducible, then we can make use of its computational capabilities to the fullest extent. But then it has the problem that in principle, it can have, things can happen which will be surprises to us and which we can't foresee in advance. And sort of one can ask, what does that mean for sort of us coexisting with the AIs and so on?
I I mean, I think already we're in a situation where in addition to human civilization, there's a civilization of the AIs. And the question is, what is it like to have a world in which there's this alien civilization right in front of us doing all these things? Well, actually, we have a very common experience of that, which is nature. Nature is, we can think of it also like a sort of alien civilization that's doing things, that's computing all these different kinds of things. We've learned to coexist with nature. You know, we build houses that prevent it, you know, problems when it rains and things like this. I mean, that's the feature of kind of this sort of computationally irreducible technology, different from sort of of the traditional engineering tradition of saying, we build only things where we can foresee what they're going to do. As soon as we start really making use of the computational universe, we break away from, we're building only things where we can foresee what they will do.
One of the things that comes about by thinking about the ruliad and sort of everything that can be, everything that is, and so on is, one might have thought that science, the universe, is sort of a cold, inhuman kind of place. And I think what has come out from the science I've done is that an awful lot of science reflects back on us humans in very important ways. In other words, there's in a sense nothing to say if there isn't a human somewhere in the middle. In other words, without an observer, without an observer with definite characteristics, everything is kind of, there's only kind of very uniform things to say.
So when it comes to kind of when we talk about sort of AI and is there something sort of different and special about us humans, the answer is yes. The whole bundle of things that make up the human condition is unique. It is that whole bundle of things. And the AIs that don't have mortality or don't have certain kinds of sensory experiences or whatever, they are different in those ways from us humans.
Now, interesting question for us as humans. You might say at some point, enough is enough. You know, we in our technology, what is technology? Technology is kind of taking what exists in the world and applying it for human purposes. Finding that, you know, that magnetic material, we can use that to, you know, snap things together or make a compass. We can use those liquid crystals to make a display. We're taking things from the natural world and we're kind of applying them for human purposes. And this idea of computational irreducibility. and so on, tells us we're always going to be able to find more things that we can apply from the natural world. And the question is, well, at what point is sort of, are we done? At what point is, you know, between our computational systems and our AIs and our robotics and all that kind of thing, at what point have we got everything that we need to have?
I don't think that's the nature of us as biological organisms. I think we are, to some extent, we have the vestiges of natural selection, of the sort of struggle for life over the last three billion years. We are continually kind of seeking the new. That has been the that's been the experience to this point. So, you know, the idea that kind of we're done now is unlikely to be what will happen. But we don't need to be done. There's an infinite amount of things that can be discovered. It's not like every invention that can be made has already happened.
And then what becomes important is the sort of the human choice of which possibility to pursue. So within the computational universe, there's sort of lots of sort of infinite collection of things that can happen that one can study. The thing that is the role of us humans is to decide which particular things should we do and look at and so on. What should we choose to find interesting? I mean, it's something in ruliology as one studies sort of possible simple programs. It's a thing that is sort of a routine experience. You can pick a random simple program. You look at it, you say, that's really cool what it does. It makes a nice picture. I don't know what its significance is. It's not connected to things that are part of what my human experience, our collective human experience has led us to think about. It's just like in human language, you know, we have 50,000 words in typical languages. We've given words to certain kinds of things that we care about. There's a lot of other things that we can imagine in the abstract world, imagine in the ruliad etc. that we have not yet humanized. We've not yet thought that those things are things that is worth us discussing, that we should include as part of kind of the way we think about things in our lives.
And it's been a very exciting journey the last few years, kind of exploring those things. And I suppose from a philosophical point of view, one of the things that has most surprised me is that it looks as if, in some sense, we can derive the laws of physics. I had always assumed that the laws of physics that we get in our universe are kind of just things that get wheeled into the universe, that our universe happens to have the laws it does. There's this inevitability for observers like us that we must perceive the laws of physics as they are. If we were observers not like us, we might perceive different laws of physics. But actually what seems to be the case is that for entities like us, for observers like us, it is inevitable and derivable that the laws of must have the form that they do.