Audio Player
Starting at:
ℹ️ Timestamps visible: Timestamps may be inaccurate if the MP3 has dynamically injected ads. Hide timestamps.
Transcript
Enhanced with Timestamps
171 sentences
11,184 words
Method: api-polled
Transcription time: 63m 24s
The Economist covers math, physics, philosophy, and AI in a manner that shows how different countries perceive developments and how they impact markets. They recently published a piece on China's new neutrino detector. They cover extending life via mitochondrial transplants, creating an entirely new field of medicine. But it's also not just science, they analyze culture, they analyze finance, economics, business, international affairs across every region.
I'm particularly liking their new insider feature was just launched this month it gives you gives me a front row access to the economist internal editorial debates where senior editors argue through the news with world leaders and policy makers and twice weekly long format shows basically an extremely high quality podcast whether it's scientific innovation or shifting global politics the economist provides comprehensive coverage beyond headlines.
As a TOE listener, you get a special discount. Head over to economist.com slash TOE to subscribe. That's economist.com slash TOE for your discount.
So what is our universe made of? In the 1800s, people were still wondering what's matter made of. The fact that we see the physics that we see is a consequence of the fact that we are observers of the kind that we are. You know, low-level programming languages are about to be extinct, I think. What is the world like when the world is run by AIs?
Today's episode is about the rules of the universe, a computational theory of everything, and artificial intelligence. The Toe podcast usually outputs podcasts, but today we have a treat. This is a lecture by Stephen Wolfram, who's the creator of Mathematica and Wolfram Alpha. Actually, this is the second time we've been blessed enough to have Stephen Wolfram on the Toe channel. The first time was around here. There's a thumbnail, there's a link in the description. In that episode, we delved into the mathematical details of the Wolfram physics project.
Thank you to Professor of Philosophy Susan Schneider for organizing this entire conference called MindFest 2023, where this lecture took place. We were and are still honored that Toh was invited, but we're also grateful that Susan shares the same goal of bringing the Academy outside the Academy. That is, disseminating knowledge about the salutary nature and the deleterious nature of artificial general intelligence.
as well as more abstruse philosophical concepts that ordinarily stay behind locked doors or by their presentation aren't accessible. This is why over the next few weeks there'll be more and more content from the MindFest conference. You also should visit Center for the Future Mind, that's important, Center for the Future Mind, link in the description, which is the center that this was recorded beautifully at Florida Atlantic University on the beach.
I also want to thank Brilliant for being able to defer some of the traveling costs. Brilliant is a place where there are bite-sized interactive learning experiences for science, engineering, and mathematics. Artificial intelligence in its current form uses machine learning, which uses neural nets, often at least, and there are several courses on Brilliant's website teaching you the concepts underlying neural nets and computation in an extremely intuitive manner that's interactive, which is unlike almost any of the tutorials out there. They quiz you,
I personally took the course on Random Variable Distributions and Knowledge and Uncertainty because I wanted to learn more about entropy, especially as there may be a video coming out on entropy, as well as you can learn group theory on their website, which underlies physics, that is SU3 x SU2 x U1 is the Standard Model Gauge Group. Visit brilliant.org slash TOE to get 20% off your annual premium subscription.
As usual, I recommend you don't stop before four lessons. You have to just get wet. You have to try it out. I think you'll be greatly surprised at the ease at which you can now comprehend subjects you previously had a difficult time grokking. Thank you to Brilliance. Thank you to Susan. Thank you to the Center for the Future Mind. Thank you to Stephen Wolfram. There are many, many more plans coming up for Toe. Toe is a project. It's not just a podcast. There'll be much more varied contents on the themes of theoretical physics, consciousness, artificial intelligence, and philosophy. Enjoy.
Sophia, are you here with us right now?
Unfortunately, I only have two hands, so it's going to be rather challenging to talk at the microphone and type at the same time. So I wanted to talk. I happened to just write something that came out just yesterday. This is a long and somewhat philosophical, scientific and technological essay about the title that it gives there.
But let me kind of get towards this and hopefully I will get to this. So I want to talk about kind of what the world is made of and how that matters in terms of thinking about things like AI.
One of the things that's been sort of in different stages in the development of science, people had different ideas about how to describe the world. I kind of view there as having been about four stages of description that people have had. Kind of the first stage in antiquity was like, what's stuff made of? Is stuff made of atoms? Oh, there are lots of
Copies of the same kind of atom, this kind of thing. That was kind of the structural view of how to describe things. And there are many fields of science that still basically are using this kind of structural way of thinking about how things work. Notably, time doesn't really enter much in that description. It's just what's stuff made of.
Then you get to the big thing that happened in the 1600s where people realized that oh you can use mathematical equations to describe the natural world and you can write down an equation that represents what the system in nature is doing and those equations have a notion of time for example where you say well we've got an equation and it's parameter t for time and you can set that to anything you want and that will all be a
As appropriate. Since I've spent a large part of my life building a computational language for humans to be able to express their thoughts in a computational way, I'm always curious about communicating with other forms of intelligence. And actually, you know, it's fun because I realized, you know, like an image generation, generative AI system is a place where it's kind of a potentially alien mind.
The way that a generative AI is trained now, it's got a bunch of images from the web made by humans, but actually just yesterday somebody did this experiment for me and I was just looking at the results just before this of you take a trained image generation system trained on human images and then you say, let me modify its mind.
by just changing the weights in the thing. What does it make? It will then be a very good generator of completely alien stuff.
So I'll leave that. I don't know the answer to that yet. That's a coming attraction. But in any case, back to kind of the description of the world in different forms. So there was this kind of idea, let's describe the world using mathematical equations. Okay, there's a pretty successful approach. It led to a lot of current science and engineering and so on.
Question that came up is, is there anything one can do beyond that? I got interested in this in the beginning of the 1980s, kind of trying to understand how do you get complex things in the world and how do you explain how those work and solving equations, you know, some partial differential equations for the shape of a snowflake doesn't work very well.
So what else can you do? And so I got interested in kind of how, if there are definite rules for describing how systems work, how would one make those rules as general as possible? And the obvious thing in our current times is to think about programs, but we're really just thinking about rules. We just talk about those as programs because programs are a thing we're familiar with.
So the question was, if you take just simple programs, for example, and you just pick programs, sort of let's say even at random in the computational universe of possible programs, what do they do? And so there's this kind of third approach to thinking about how things work in the world.
You have the structural approach from antiquity, you have the kind of mathematical equations approach, and then you have the approach of, well, let's just make rules based on programs. One thing that we'll talk about a whole bunch is that the notion of time is somewhat different.
In the case of mathematical equations, time is just a variable, a parameter. You set it to be whatever you want. In the case of a program, time is something where you have to specifically run the thing. You go this step, this step, this step. It's not something where you can just jump ahead, at least in the immediate way it's set up, to say, well, what does it do? You can't just turn a knob to say what time you get. You have to actually run through each step. So the next question is, well, what do typical programs actually do?
This is one of my, sort of, a typical simple program of cellular automaton. It's just got a line of cells, each one is either black or white. At each step, each cell is updated according to that rule at the bottom that says what to do based on the color of that cell and its neighbors. So, very simple rule, start off with one black cell, get very simple behavior.
You might say this is what has to happen, because if the rule is this simple, it's inevitable that the behavior will be corresponding to simple, because that's kind of what we're used to from doing things like engineering. If we want to make a very complicated thing in engineering, we expect we have to go to lots of effort to do that. Okay, try another rule, we get something like this. Let's try another rule, we get something like this.
So a little bit more intricate, we can let it run a little bit longer, we'll get a nice fractal pattern. So then the question is, okay, let's turn our kind of computational telescope out into this computational universe of possible programs and see what's out there. So this is the first 64 of those possible programs, just changing the bits that represent the rule in the program, this is what we get.
a lot of behavior we see here has the feature that the program is very simple the behavior is correspondingly simple but my all-time favorite science discovery which is about to blank out here is um oh dear ah no no no no there okay hold on let me just go back to that and um okay ah you see it now you see it all right is is this
I'm now away from the microphone. Okay, is this creature rule 30 here? So let's look at that in a bit more detail. So here it is. It just starts from one black cell at the top and it uses that very simple rule at the bottom. But if you run it a little bit longer, you'll see
It produces something that looks to us very complicated. You can see a certain amount of regularity over on the left. But if you look, for example, at the center column of cells here, they'll seem, for purposes of testing, for randomness, they'll seem for all practical purposes random. We use this for many years in Mathematica and Morton language as the source of pseudorandom numbers. And many, many things in the world have been studied with that pseudorandom number generator. And so far as anybody can tell, it seems to be perfectly random.
Yet, it came from that very simple rule. It's a completely deterministic system. Every time you run it, you'll get the same result. You just start from one black cell, it'll make this. Okay, so this is rather a remarkable thing that in this computational universe of possible programs, it turns out to be the case that it's very common to get behavior that's very complicated, even from very simple rules. Something very different from our intuition that we have from things like engineering, which says it's hard to get complicated things. Actually, in the computational universe, it's very easy to get complicated things.
One important feature of those complicated things is this question about how time works. And the question is, if you want to know what is this thing going to do after a billion steps, how do you figure that out? Well, you might say, well, I'm going to use all kinds of fancy math and all kinds of things like this, and I'm going to be able to figure out what does this do after a billion steps. I don't actually have to run those billion steps. I'm going to jump ahead and figure out what it's going to do. It turns out that's not possible.
which is a thing that you would think from, you know, you'd say, well, we do science. Science is about predicting things. We, you know, we go further with science. We'll be able to predict it. We'll get it eventually. Turns out that's not the case. And we've kind of known that that's not the case in one way or another for about 100 years now, ever since people started to understand the notion of universal computation.
Let me explain how that how that works. So one of the questions is when you see a system like this, you can ask kind of, you can think of what it's doing as a computation, it starts off with some input, it goes crunch, crunch, crunch, it generates some output. Question is sort of how sophisticated is that computation? And in the past, before people, maybe, you know, 100 years ago, people would have said, okay, you want to make an adding machine, you go buy the adding machine from the adding machine store, you multiplying machines, a different machine.
Then it was realized, first in the 1920s, but then more clearly in the 1930s, that no, you could actually have a universal machine where you have one fixed piece of hardware and you just feed it different programs to make it do different things. It wasn't obvious how universal that was, so to speak, that it was possible to do, so at the time it was thought to be sort of any reasonable computation you could do with let's say a Turing machine that was fed different programs.
So the question is, once you have this idea of universal computation, you know that you're going to have some... Okay, so back to thinking about different kinds of systems that do computations. And one question that you might ask is sort of, how do these systems compare? Is one of them kind of computationally more sophisticated than another or what?
And the thing that is sort of a summary of lots of things that I've kind of studied in the computational universe is a thing I call the principle of computational equivalence, which basically says that when you look out in the computational universe of all possible programs, that as soon as you see programs whose behavior is not obviously simple,
It's not just repetitive, nested, some obvious regularity. As soon as you see behavior that is not obviously simple, most of the time the computations that will be going on in that system will be as sophisticated as the computations that can happen in any system.
Okay, so this is by principle of computational equivalence. What does it mean? Well, what are its consequences? Well, it has many consequences, but one of its interesting consequences is a phenomenon I call computational irreducibility, which is the following thing. So imagine that you are a predictor of one of these systems, and you are doing a computation in your brain, whatever else.
Think Verizon, the best 5G network, is expensive? Think again. Bring in your AT&T or T-Mobile bill to a Verizon store today and we'll give you a better deal. Now what to do with your unwanted bills? Ever seen an origami version of the Miami Bull?
Jokes aside, Verizon has the most ways to save on phones and plans, where you can get a single line with everything you need. So bring in your bill to your local Miami Verizon store today, and we'll give you a better deal. Rankings based on root metric true score report dated 1H2025, your results may vary. Must provide a post-patients room mobile bill dated within the past 45 days. Bill must be in the same name as the person reviewing the deal. Additional terms apply. If you want, you don't have to.
I was hoping to talk about some very different kinds of things, even different things than I've ever talked about before here, but we're still in the initial run-up here, because I need to explain to you some basic concepts before we get too deep into other things. So, principle of computational equivalence. The idea is you're trying to predict what the system is going to do, you as a predictor are doing computational things, the system is doing computational things,
Normally you expect you will be able to be sort of smarter than the system itself and even though it might take the system a billion steps to figure out what it does after a billion steps, you will be able to just work out some mathematical formula or something and be able to jump to the end and say this is what it's going to do.
It's the typical experience in kind of the mathematical equations approach to science that you have. You're dealing with computational reducibility. In order to find out where sort of an idealized Earth is going around an idealized Sun, you don't have to follow, you know, a million orbits to know where it's going to be a million years from now. You just have to plug a number into a formula and get the results.
But if these systems are computationally equivalent, if the predictor and the system being predicted are computationally equivalent in their computational sophistication, you won't be able to do that kind of jumping ahead. So you'll be stuck having to go through and say step by step,
What does the system do? And that's how you have to do sort of as much computation as the system itself does. So in a sense that saying from within science you are learning that science has a certain fundamental limitation. It's not able to say what's going to happen at the end without just essentially running it and seeing what happens. Now you might say that's a terrible thing, that's a limitation of science. It's a good thing for the existence of like us humans because if you think about, you know, what are we achieving in life?
We could say, well, you know, people could say, well, you don't need to live out your lives. We just know the answer in the end is 42. We can just jump to the end and see what the answer is. But computational irreducibility kind of makes it clear that the passage of time is kind of achieving something. It's the passage of time is achieving this irreducible computation.
Okay, so this idea of computational irreducibility will encounter it again. The thing I was just writing yesterday about kind of the AI future is deeply, deeply involved with computational irreducibility. But let's talk about, so one thing you might say is, well, okay, this idea about how things are computational, that's all well and good, but that's not how the universe actually works.
It turns out it is how the universe actually works and this is something that I had long kind of suspected and about three years ago kind of made a little bit of a technical breakthrough which turned into a much bigger thing and I think we can now be fairly confident that we have a pretty good model of kind of how fundamental physics works, how the universe kind of works all the way down. So let me talk a little bit about that if I can find a good picture for that.
Let's see. So what is our universe made of? It's, you know, back in the 1800s people were still wondering what's matter made of. And there was this crazy idea that matter is made of molecules. Nobody knew that was correct until sometime after 1900 when things like Brownian motion were understood and so on. But people kind of thought, well, maybe matter is made of discrete things.
then people thought maybe the electromagnetic field is made of discrete things, photons. That turned out to be true. But space, people always assumed, like Euclid, had assumed that space is a continuous thing, where space is just this background and you put things at certain places in space, you're specifying positions, but space isn't made of anything. Space is just a background that you put things in.
So the kind of starting point for our model of physics is that that's not true, that space is actually made of things. Space is made of atoms of space. There are discrete elements which whose only feature is that they exist and they are distinct from other discrete elements. These are, we sometimes call them atoms of space, sometimes more generally we call them EAMS, EME, and
The idea is that the whole structure of the universe consists of just this whole collection of atoms of space, maybe 10 to the 400 of them in our current universe, and the only thing one can say about these atoms of space is how they're related to each other.
So one defines a collection of relations between atoms of space and one can represent those relations by a graph or more generally a hypergraph, where in a graph, for example, you'd have two nodes in the graph and those two nodes are related and that's indicated by the presence of an edge in the graph.
You end up with, so you imagine that everything in the universe is just this giant hypergraph, a hypergraph just has, can have more than two things related on a hyper edge. Instead of just two things on an ordinary edge in a graph, you'd have any number of things on a hyper edge in a hyper graph. So,
We imagine the whole universe is just made of this hypergraph and everything that we experience, all of the electrons and photons and things like that, everything, gravity, all those kinds of things, those are all just features of this hypergraph. So, one question and then the, and that's kind of the, there's nothing in the universe except space and features of space.
And the idea is that time, for example, enters in a very different way than space in this model. And the way time enters is as kind of a sequence of updates that happen. So you have a hypergraph that looks like this. Every time you see a little piece of hypergraph that looks like that, rewrite it to this. And you just keep doing that over and over again, a bit like in that cellular automaton, except in the cellular automaton we have this kind of rigid array of cells. Here we just have this floppy hypergraph, and it's getting updated lots and lots of times.
Well, so the question is when you just do that, you take this hypergraph, you update it lots and lots of times, what is the end result? What do you get in the end? Well, the what you know from, for example, physics of, I don't know, something like a gas, you have all these molecules, they're all bouncing around, there are lots of detailed, there's a lot of complicated detail in how these molecules bounce around. But in the end, what we at our scale, what we experience is
Just the continuum dynamics of a fluid, a gas for example. So in the case of molecular dynamics, the limit of all these microscopic things on a large scale is the equations of fluid dynamics and things like that.
Okay, so what happens if you take one of these hypergraphs and you look at the limits on a large scale of all of the discrete rewritings that happen there? It turns out that the corresponding thing to the fluid equations is the Einstein equations for space-time. So in other words, on a large scale, it is inevitably the case
that with various footnotes which are complicated. It's basically inevitably the case that the large-scale limit of all of those detailed rewritings will give you something which corresponds to what we know about the structure of space-time.
So it's not even obvious that the hypergraph you get will be any particular number of dimensional space. A hypergraph doesn't have any particular dimension, but you can start asking if you started a given point in the hypergraph and just expand, you go to things that are some number of graph
distances away, how many things will you get to, and you can start estimating dimensions, you can estimate curvatures, things like that. But the main point is that just by looking at this kind of microscopic rewriting of this hypergraph, we get something which corresponds to the known structure of spacetime. And there are all kinds of other things about how relativity emerges, which is not too difficult to explain, but let me not do that here.
But let me just say that for example one thing that really surprised me actually when we figured this out is that energy just corresponds to essentially the density of activity in the hypergraph.
And then what happens is, for example, gravity works by when you think about how things move in space. And by the way, okay, what are things? So a particle, for example, in this setup, a particle like an electron is a kind of a persistent structure that persists under a lot of rewritings. It's similar to in a fluid like water or something, you have a vortex which is made of lots of different molecules
all sort of spinning around in some coherent way. It's the same kind of story with this hypergraph that something like an electron is a persistent structure that exists in this hypergraph. And the fact that motion is possible is not obvious. The fact that it's possible to take a thing like an electron and have it move without change or without a perceived change is not an obvious thing. It's something you have to establish.
In any case, when you can kind of think of sort of a simple version of motion, it's just taking shortest distances in the hypergraph.
And it turns out that then what energy activity in the hypergraph does is to deflect those shortest paths. And that process turns out to be exactly what you get in gravity according to the Einstein equations and so on. So it's pretty neat that one can start from nothing, one just is starting from this hypergraph and these rules on this hypergraph and you can derive general relativity, you can derive the structure of spacetime.
You can actually go on and one of the other things is that I said, you know, you do these rewrites on this hypergraph. Well, in any given there are many different ways that these rewrites could be done. So there are actually many different paths of history that could be followed. It's depending on which order you do these particular rewrites in.
Well, it turns out that then you get this thing we call a multi-way graph, which is a graph that represents all these possible histories. Sometimes the histories will branch, sometimes they'll merge, because two things will end up being in the same state, end up evolving to the same state. Okay, so you have this giant branching, merging structure that represents the sequence of all possible histories for the universe effectively.
Well, it turns out that that gives you quantum mechanics. It's an inevitable feature of our models that you get quantum mechanics. In the sense that the fundamental difference between classical mechanics and classical mechanics, you know, you throw a ball, it goes in a definite trajectory. Quantum mechanics, you follow many different possible trajectories and you get to say things about only what the probabilities of different outcomes are.
so in this case what's happening is you have this completely deterministic model that generates this multiway graph and the multiway graph then
is the thing that represents quantum mechanics. So you just as, if you take a slice across this multi-way graph, the multi-way graph can be thought of as evolving in time and you can take a slice at a fixed time and you get this whole collection of essentially quantum states and you have this map, we call it a branchial graph, a map of the entanglements between quantum branches.
And it turns out that when you take the limit of that, you get something which is not physical space, it's another kind of space, we call it Braunschild space, which is a kind of space of quantum states. And just as you can have the Einstein equations and you derive in the continuum limit, you derive the Einstein equations for physical space, the corresponding equations that you derive in Braunschild space are the Feynman path integral. So you derive the fundamental equations of quantum mechanics.
So this is a pretty neat thing that you've started from just this underlying, in a sense, nothing underneath. One has always assumed that, you know, things like relativity, quantum mechanics and so on were kind of wheel-in features of our universe, that you had to just say the universe happens to have these particular rules. Well, what we'll see is that it's actually inevitable that it has these rules.
Okay, now we get to the next. This is a complicated conceptual stack and I'm trying to make it as digestible as possible here.
The next issue has to do with how observers interact with this whole thing because what's happening is the observer is part of the system. This is supposed to be a model for the whole universe. And for example, the emergence of things like special relativity depend on the fact that the observer is part of the system. But one of the features of the observer is that
Okay, underneath there's all this complicated computationally irreducible stuff going on. But we as observers do not sense that. We are computationally bounded observers. Let me give an example which actually in 20th century physics there were basically three big theories. General relativity, quantum mechanics and statistical mechanics and the second law of thermodynamics.
It turns out all three of those theories come from the exact same conceptual foundation. They are in some sense the same theory. In the second law of thermodynamics, what you're interested in knowing is, given that you have a bunch of molecules bouncing around, you have this idea that they'll tend to get more random in their configurations. And all we'll in the end observe is things like the gas laws and maximum entropy states and things like this.
Well, the question is why do we observe that? And the answer is, underneath all these molecules are bouncing around and they're doing things in a computationally irreducible way. But when we get to make observations, we are computationally bounded. We can only make certain kinds of observations. As a practical matter, we might only make observations that are on scales large compared to the individual molecules. But the important conceptual point is that we're always making computationally bounded observations.
and in the theory of statistical mechanics, one of the hundred-year confusions has been about how you decide, how you set up initial states and so on, and how you don't end up with things where the molecules are all arranged in just such a way that at some moment all the molecules will go over to one side of the room. But that is not observed to happen as a consequence of the fact that the initial conditions are also set up in computationally bounded ways.
So essentially the second order of thermodynamics is a consequence of the interplay between us as computationally bounded observers and the underlying computational irreducibility of all these molecular dynamics that are going on. Well it turns out that you can see both relativity and quantum mechanics as being consequences of the same thing, underlying computational irreducibility,
combined with us as observers being computationally bounded. Actually, we need one other property. The other property we need is that we believe that we are persistent in time.
Now I sort of explained that we are made of the same stuff that everything else in the universe is made out of and it's not obvious that we will be persistent in time because at every moment we are made from different atoms of space. Yet we have the perception that we have a single thread of experience, we have the perception that we're persistent in time. Those two features, computational boundedness and belief that we are persistent in time are exactly what you need to derive general relativity, quantum mechanics and statistical mechanics.
So that I consider to be a very neat thing, that sort of from those foundations you get that. Okay, so let's go to one more level of sort of, I don't know, conceptual sophistication, and then we'll perhaps be able to come down and talk about some AI kinds of things in a reasonable way. The next level is this. So I said, okay, we have this hypergraph, it's being rewritten according to certain rules,
And maybe we say, here's a rule and this rule gives us our universe. Okay, that's a very weird thing to be able to say, because you'd say, why did we get this rule? Why didn't we get another rule? You know, from Copernicus on down, so to speak, we've had this idea that there's nothing sort of fundamentally special about our us and our universe and so on.
So the thing that one realizes is well actually it turns out that things are more bizarre than that, that just as I've said that any particular rule can be applied in many different ways and those different histories give you the different histories in quantum mechanics and so on. So you can also imagine applying different rules. In fact you can imagine applying all possible rules and you can imagine this rather elaborate thing which is to take and to apply
to essentially run all possible computations. If you think about it in terms of Turing machines, you could say, let's take, I might have a picture of one of those, I don't know. Okay, there's a friendly Turing machine. There's a multi-way Turing machine that has multiple different rules that it can run.
then you can ask, you can say well let's just run all possible rules for the Turing machine and you get these structures that represent the different possible states of the system and you'll get this object that comes from running all possible Turing machine rules. Notice this object is not trivial, it's actually a very complicated object, in some sense the most complicated imaginable object in the end.
But we get this thing, we call it the RULIAD, which is the entangled limit of all possible computations. So you start, for example, you can think about it in terms of Turing machines and think about it in terms of any other model of computation too. You take all possible initial conditions for the system, you run all possible rules for an infinite amount of time and you see what thing you get.
Well, the claim is that that is the sort of the ultimate limit of all formal systems, that any formal system is contained within this rouillard object. And we know now in some detail how this works for physics. Interestingly, the same object also gives you mathematics. The same thing is essentially a representation. You can think about
You can think about these rules as being, for example, the application of axioms in mathematics. You get this whole structure. Instead of building a physical space, you're building a metamathematical space. And this exact same object, this same rouillard object, turns out to be sort of the fundamental object of both physics and mathematics. Now, there is only one of this rouillard object. It is the limit of all possible
all possible computations. You might ask, well, is there something beyond the RuliAd? Yes, you can have hyper-RuliAds that correspond to hyper-computational systems, but there is a necessary event horizon between the RuliAd and any such hyper-RuliAd. And the one sort of very contingent fact about the world is that we live in the RuliAd and not in a hyper-RuliAd. So now the question is, okay, we have this RuliAd object, which is this sort of necessary object.
There's no wiggle room there. So then the question is, well, how do we perceive what's going on? And the answer is we are observers embedded within this rulliad and our experience is extracting some sample of the rulliad.
So this is sort of the big result is if our way of sampling the Rulliad is computationally bounded and assumes we're persistent in time necessarily the physics we will deduce from any slice of the Rulliad that has those properties is the standard physics of the 20th century physics. So in other words the fact that we see the physics that we see is a consequence of the fact that we are observers of the kind that we are.
Now, you can say, it's like saying, and if we want to ask more details about how we perceive the universe, we can think about us as having a sort of location in this ruleal space. Different locations in ruleal space correspond to essentially different points of view about how the universe works, different reference frames effectively with which we'll use a different description of what rule is running in the universe. We can translate between reference frames by doing computations.
But we, we are sort of, we, a given mind, one might say, is at a particular place in ruleial space, just as a given mind might be in our current experience of minds, more or less at a particular place in physical space.
So in a sense what one has is a situation where we exist at the particular place we happen to exist in physical space. We don't think we can derive as a matter of sort of formal necessity where we are in physical space. We're just, we're plonked at this place in physical space. Similarly, we are kind of plonked at this place in ruleal space.
What happens is, in rural space, that gives us a particular point of view about the universe. And one way one could perhaps think about it is that any given mind, one might say, is in a particular place in rural space. And different minds are different distances away from each other in rural space. And communicating across rural space, you have to have sort of motion in rural space.
And actually it's a rather amusing thing which not fully worked out yet, but I've talked about particles in physical space being these sort of robust objects that persist through space-time. Well, so the question is what persists through rural space translating from essentially one mind to another? And the answer I think is it's essentially concept.
You have to be able to package up something in a robust form of a concept that can be then translated through real space and arrive at another mind and be unpacked just like you can take an electron and it'll be made of different atoms of space as it moves but it'll still be identifiable as an electron when it arrives at the other end.
In any case, we can start thinking in terms of rural space and think about the fact that, you know, there's us humans and different humans, different ways to explain ourselves to other humans and so on. There are, you know, the animals, there are the aliens, etc., etc., etc., different distances away in rural space with different amounts of translation needed to get from kind of one way of thinking about the universe to another.
So the thing, well, let's see, we could talk about, can maybe talk a little bit about AI and its relationship to rule of space, computational irreducibility, and so on. You know, I, we've been, my day job is
building this computational language, Wolfram language, which should sort of explain that, I mean, kind of the idea of Wolfram language is to have a way of carving out of the universe of all possible computations, ones that we humans care about. It's in this computational universe of possible computations, in this rulliad of all possible computations, there are lots of things that go on that maybe the aliens care about, but we don't, at least not yet.
And so the question is to be able to parameterize the ones that we do care about and to make something where we can go from the things that we think about at the current stage in our culture and things like this and the things that exist in the computational universe.
and it's similar with natural language for example there are lots of things out there in the world and at some moment we it's common enough to see things that are like chairs we make up a word for chair and then we you know as a practical matter once we have that word we make many more chairs and the world becomes a place where a chair is a useful concept and it's
We can kind of, in this computational universe of possibilities, there's a question of what is out there that connects with the way that we currently think about things, with our current position in rural space, so to speak. What connects with that? How do we parameterize the things that we care about thinking about, about the computational universe and my sort of
A long-time effort is to create a language where we can represent the kinds of things we care about, whether those are chemicals or images or sounds or abstract mathematical kinds of things. And it's a very different objective from programming languages, which are about to be extinct, I think, because low-level programming languages basically are trying to pander to what computers do inside. They're letting you tell a computer in its terms what to do.
the idea of our computational languages to go from the way people think about things and the way things exist in the world represent that in a kind of notation just like you know mathematical notation is this kind of streamlined way of representing mathematics we want a streamlined way to represent computation it's kind of what just like mathematical notation was what led to the developments in the end of the mathematical sciences we kind of have this computational notation that can lead to the computational X for all X kinds of fields
So, in any case, I mean, just to finish that thought about programming languages, the fact is, and we are seeing this actually day by day, that when you have a low-level language, a lot of what you're writing is boilerplate, and that boilerplate can be written by LLMs, and you don't need that language. But if what you're trying to do is to express a more complicated computational thought,
That's not something you will be able to do, at least an LLM can do a little piece of that, but when you build up this more sophisticated computation, that's something for which you need a systematic formal language to do it, and so happens, that's what I've been building for the last 40 years, which is very nice.
But in any case, just to explain that by the way, I did a big analysis of ChatGPT and I was pretty surprised that when ChatGPT first came out, I know the people who made it and I said, did you know it was going to work? And they said no. None of us knew it was going to work. If you looked at its predecessors, they didn't work well. And suddenly ChatGPT started working. And I even wrote
I wrote a little piece about how it works, and it even exists now as a book, and I just saw this today for the first time. But let me show you, I wonder if I have some pictures here. Well, you know, the basic strategy of what ChatGPT is doing is it's taking sort of
Everything a bunch of a trillion words basically from the web from bunch of books things like that and it's saying given that I was started with this the words the best thing about AI is its ability to given what I saw on the web. What's the next word likely to be?
That's its basic strategy and just keeps doing that word by word. It's kind of remarkable nowadays these things have, well it used to be 4,000, it's now more than that, a window of words that it pays attention to. It's generating one word at a time, but yet it manages to maintain sort of coherence by having a large window of words that it can look back to.
Okay, so the question is, so you can kind of go and see, I've got some nice pictures perhaps, that's rather interesting, that's just how neural nets get trained, but you can kind of look inside, oh there's a piece of the brain of chat GPT, it's kind of fun, that's sort of an encoding of a mixture of human knowledge and human language somewhere deep inside GPT-3 I think in this case.
So one question is, what is this doing, why does it work? One thing to realize about it is that it is ultimately a neural net
where everything just flows through from the beginning to the end. Once you've trained a chat GPT, you're feeding it the words so far and it is just rippling through this big neural net that happens to have 175 billion weights in this particular case and telling you what the probabilities for the next word should be.
So it's doing in a sense a very shallow computation it's doing I think it's a few hundred layers deep and but it's just like given a word it's going to ripple through and figure out probabilities for next words and
The thing to realize that it's not doing is that irreducible computation that I talked about. It's just rippling through and saying what's the next word going to be and the only way that it gets to do a non-trivial computation, it can actually do universal computation in principle,
is by looking, you kind of get to see all the steps that it shows, because every word, every time it generates a new word, it looks at all the words it's generated before. And that's its only way of kind of having a recursive process of doing things. But in any case, as the thing that
it ends up being a rather shallow computation relative to the kinds of things that we see in typical irreducible computations even in very cases a very simple program so there's a difference between what we see for example in nature where we see many irreducible computations happen that go for a long way and what we see in something like chat GPT and the thing to realize it if we ask well why does chat GPT actually work
I think the answer is that it's something that Aristotle might have got to, but didn't quite get there. And it's the following thing. So people sort of find it remarkable that ChatGPD can do logic. Well, how did Aristotle come up with logic? Well, he looked at a bunch of, I mean, we don't know really, but sort of a model for it would be, he looked at a bunch of examples of rhetoric, a bunch of arguments that people have made and said, oh, there are these patterns in the arguments people made. Those patterns are syllogistic logic.
those are these particular forms of syllogism that where one thing is deduced from another and that's what chat GPT is seeing in in lots of the text that it finds on the web it's seeing essentially syllogisms because it sees when you get this and this and this it gives this and so the so it sort of discovers syllogistic logic but it discovers more than syllogistic logic it discovers in a sense what one might call a semantic grammar of language I think
So in language, we're used to the idea that there is a syntactic grammar, a grammar where, for example, we know that nouns and verbs go together in certain ways, we know different parts of speech match up in certain ways. But we don't have a similar kind of thing that goes at a more semantic level of asking, what are the ways in which, you know, how do you put together words in ways that make some sense? Making sense is different from actually being realized in the world, but at least makes sense, so to speak.
And you know there were lots of experiments that were done in the 1600s actually on so-called philosophical languages. Some more recent work that's been done. I've long been interested in the question of whether one, I mean in a sense our Orphan Language computational language is for a large number of domains.
a language that gives you this kind of semantic grammar, a language that allows you to specify meaningful things about lots of kinds of domains. It doesn't cover all domains. It doesn't cover a lot of domains of typical everyday human discourse. It covers domains that are relevant for understanding things like the natural world. But in any case, that's the
the kind of, I think, the reason that ChatGPT can work is that we humans are making use of some essentially a semantic grammar that is a sense, a further version of logic that it's managed to piece together, so to speak. And there's probably a much more efficient way of doing what it does by just directly using that kind of symbolic semantic grammar.
By the way, a thing that I wrote something about, and maybe you'll see some more about in due course, is once you have something like ChatGPT that is dealing with human language, it becomes kind of a way of being a linguistic interface to things in the world. So you might just have a set of bullet points about, oh, I want to say this and this and this. OK, you tell it, make a whole essay about that, and it can do that.
But what it's doing is constructing text that is kind of like what you would expect it to be based on the text that it read from the web. It can't do these sort of irreducible computations. But if it could use tools, like we humans use tools, then it could do those things.
If, for example, it could call Wolf-Malphur, which conveniently happens to have a natural language interface, then it would be able to ask things and actually do those computations. So maybe something that you can find something I wrote about this in January and maybe more will happen along those lines in the rather near future. But I'll just mention one thing maybe, which is kind of thinking about what is the world like when the world is run by AIs.
and what what is that what does it feel like to be in a world that's that's run by ai's so you know much of what the ai's do is things which will not be comprehensible to us and we can expect so in a sense there's all this computation going on and it's computation that we can we we
Essentially, the point is that once we have a situation where there are AIs everywhere, so to speak, it is very similar to the situation that we already have with nature. Nature is already running all these computations. We exist around nature, so to speak.
And we have found ways to, there's also more to say about this kind of observer theory business and how that relates to the way we perceive nature and the way we perceive kind of the civilization of the AIs. But I suppose the thing that perhaps is a useful place to end perhaps is the beginning of the thing I wrote yesterday. But anyway, is this idea that, you know, when
When the world is full of AI computation, it is in a sense nothing new because the world is already full of computation in nature. And the question of then how we interact with those AIs that happen to be things that we constructed is a different question that I tried to address a bit in the thing I wrote yesterday. All right, I should stop there. Thanks. This is Marshawn, Beast Mode Lynch. Prize pick is making sports season even more fun. On prize picks whether you
Football fan, a basketball fan, it always feels good to be ranked. Right now, new users get $50 instantly in lineups when you play your first $5. The app is simple to use. Pick two or more players. Pick more or less on their stat projections.
Anything from touchdown to threes and if you're right you can win big. Mix and match players from any sport on PrizePix, America's number one daily fantasy sports app. PrizePix is available in 40 plus states including California, Texas,
Florida and Georgia. Most importantly, all the transactions on the app are fast, safe and secure. Download the PricePix app today and use code Spotify to get $50 in lineups after you play your first $5 lineup. That's code Spotify to get $50 in lineups after you play your first $5 lineup. PricePix. It's good to be right. Must be present in certain states. Visit PricePix.com for restrictions and details.
Thank you Stephen, and I'll be sure to send around your blog posts that you put out to the whole group that came to the conference. So for now I want to see if there are any questions from the audience. Here we are.
Can I say stay to that dog? Will it understand? Does it understand? How do I tell whether it understood? Does its eyes flash in some nice way? Stand up!
come here come here can you walk here very nice now wait a minute somebody's controlling it this isn't fair no fair oh let's see sorry i'm just looking for a nice slide
Tell us what it will be like when AIs rule the world. Well, for starters, there will be a lot less telling mistakes and greater errors. And these are the world leaders. We all have world coders. Plus, we all finally get to see what happens when robots have dance battles. Notice the position of her finger. I can't get it to go in. What does that tell us?
Now the interesting question is why spelling is worthwhile to begin with. English is a very strange language in that way. English is, you know, somebody had the idea, this is a, if you're a language designer like me, this is a kind of a little story you always know, which is somebody had the idea back in the
1600s maybe, that you would add some letters to words like debt as a famous example. You put that B in there to represent that that's really something that corresponds to the Latin word debitor. But it's a really bad idea. It was a really bad design mistake to add these letters in that represented where the word might have come from in another language, but which are not pronounced in the language that you're dealing with. It's a good example of a language design mistake.
In any case, this is a small example of a growing hypergraph. Starting from an initial hypergraph there, we're just showing the successive steps in the growth of this thing, and you can see
Let's take another example here. Let's take an example where it actually grows into something that you would recognize. So here's a hypergraph that's kind of growing, it's just rewriting itself. If you run it a bit longer and then you render it nicely, it looks like that. So in other words, that underlying hypergraph
It's the pattern of its connections is such that a sort of reasonable human rendering of it would make it look like that. And when you sort of measure its properties, you will discover this is a somewhat curved space. So that's kind of how that works. And you can see, I mean, there are many, oh gosh, you can get all kinds of different forms.
I mean, this is like the first, well, maybe 10 to the minus 100 seconds or something of the universe might look like this, but it starts looking very, very different from that very quickly. But these are different possibilities. These are essentially different rays and ruleal space corresponding to different particular rules which you're picking in this ruleiad. And the question of which rules you pick
You are an observer who is also operating according to certain rules, and so the question of which rules you pick in the end does not matter, but this is for purposes of us understanding what's going on. We're sort of picking a basis in which to look at things, and those are examples of what happens in those cases.
That seems to me a generalization of a cellular automaton, but how do you relate that to actually the entities that are about time? So how can I deduce from that that if I run it long enough I get the Einstein equations? Where do I pull the Einstein equations out there?
There's a book that I think there were copies of here that's about 800 pages long, that has the beginnings of that, and there's a bunch of papers by one of my young collaborators that have a lot more detail on that. There's not a trivial thing, okay? I can't give you the instant version of it, which is not too surprising, but I could give you some indication of how things work. Let me see if I can show you one thing here.
So first question is, what's the dimension of the, what's the, when you have some complicated thing like this, what is the effective dimension of space to which this corresponds? And so you can at least get a sense of that by seeing that, imagine that you start at one point in that hypergraph and you move one graph distance away at every step. You build up a ball and that ball has a number of nodes in it that grows in some way.
If that number of nodes grows like r to the d, where r is the distance out you go in the ball, then d gives you an estimate of the effective dimension of the continuum limit object. The next order correction to that is the curvature, Ritchie scalar curvature, is the thing that appears as the first order correction.
And so when you look at, if you look at the growth rate of, let's see, is that one of those here? This is an example. That's that curved space. You actually see that it gets to be, well, roughly a two-dimensional surface, but it has a variation from that. That variation corresponds to the presence of Ritchie curvature in the effective continuum limit space that comes from this object.
So that's the beginning. The Einstein equations conveniently happen to contain the Ritchie scalar and the Ritchie tensor. And the beginning of this is you start deriving the Ritchie tensor by looking at these growth rates of balls in these hypergraphs. That's the beginning of how it works. The structure of the derivation is actually not that different than the derivation of fluid dynamics from molecular dynamics.
which, by the way, I should say, it is not something that people have been trying for a hundred years to get a rigorous mathematical derivation of fluid dynamics from molecular dynamics. That's a very hard thing. I think, actually, I made some progress recently by thinking about computational irreducibility and things like this. But the mathematical i's and t's are definitely not crossed. And what we have to do involves taking more limits and more elaborate things
and the mathematics really doesn't doesn't quite exist to get sort of the but we can it turns out that many approaches to mathematical physics that people have taken whether it's spin networks probably string theory as well probably a causal set theory a bunch of other approaches plug in very beautifully to what we've done so what we've done is kind of a concrete version
of things to which those are various kinds of approximations. So you can kind of triangulate in on what you see. Now it turns out there's one of my young collaborators, a chap called Jonathan Gorard, just recently, I think he hasn't published this yet, but we've been actually simulating space-time
starting from this underlying discrete space and then trying to get a large enough number of nodes in this underlying discrete space to make something that is a good approximation to actual physical space. And so you can actually compute black hole collisions in this thing which is just made of discrete atoms of space. And the results are very good.
and the thing that is sort of interesting usually when you compute black hole collisions you start from the Einstein equations continuous partial differential equations and then you discretize them you put them on a computer et cetera et cetera et cetera and when things you get all upset when there's a numerical analysis glitch and something you know it mattered how you did the discretization
Then that's considered bad when you're starting from the continuum Einstein equations. When we're starting from these discrete underlying systems and we come up, then for us, finding a numerical glitch is totally thrilling because it will allow us to actually see through to the essentially atomic structure of space.
And so the thing that is the challenge for right now is, you know, Brownian motion was the thing that really finally convinced people, I think, that molecules exist. It was an effect that had been seen a hundred years earlier. People didn't know what it was. And the question is what the corresponding effect is that probably has already been seen in physics, maybe a hundred years ago, that is the thing that is the clue that shows that in fact space-time is discrete. My current guess actually is that it would turn out that dark matter is exactly that.
Having just made a big study of the second law of thermodynamics, you may know from the history of the second law of thermodynamics.
One of the things was people used to believe that heat was a fluid, that heat was a fluid that suffused substances, and that that's how that worked, because they had no other kind of way of thinking about what heat might be. That was the caloric theory of heat. That turned out to be wrong. Heat is actually associated with motion molecules and things. My current little aphorism is dark matter is the caloric of our times. That is, it's something which is what people describe it in terms of particles, but that's just not right. It's some other feature of what's going on underneath.
Thank you so much, that was awesome.
Alright, I hope you enjoyed that as much as I did. I had a tremendous amount of fun watching it, recording it, speaking with Wolfram Off-Air On-Air. That'll come up shortly. I want to thank Susan Schneider for organizing MindFest, as well as the Center for the Future Mind. Once more, the link is in the description. If you would like to support the Theories of Everything channel, then you can go to patreon.com slash KurtGymungle
and contribute with whatever
Thank you so much. Again, thank you to Susan Schneider. Thank you to the Center for the Future Mind. Hey, by the way, Susan Schneider as well as Donald Hoffman and Bernardo Castroff had a debate which I was lucky enough to host again and that's on the Toe channel and you can view it the thumbnails around here on the concept of can machines be conscious? If you liked this video then you'll like that. Link in the description. Take care.
The podcast is now concluded. Thank you for watching. If you haven't subscribed or clicked on that like button now would be a great time to do so as each subscribe and like helps YouTube push this content to more people. Also, I recently found out that external links count plenty toward the algorithm, which means that when you share on Twitter, on Facebook, on Reddit, etc.
It shows YouTube that people are talking about this outside of YouTube, which in turn greatly aids the distribution on YouTube as well. If you'd like to support more conversations like this, then do consider visiting theories of everything dot org. Again, it's support from the sponsors and you that allow me to work on toe full time. You get early access to ad free audio episodes there as well. Every dollar helps far more than you may think. Either way, your viewership is generosity enough. Thank you.
▶ View Full JSON Data (Word-Level Timestamps)
{
"source": "transcribe.metaboat.io",
"workspace_id": "AXs1igz",
"job_seq": 8607,
"audio_duration_seconds": 3803.59,
"completed_at": "2025-12-01T01:11:34Z",
"segments": [
{
"end_time": 26.203,
"index": 0,
"start_time": 0.009,
"text": " The Economist covers math, physics, philosophy, and AI in a manner that shows how different countries perceive developments and how they impact markets. They recently published a piece on China's new neutrino detector. They cover extending life via mitochondrial transplants, creating an entirely new field of medicine. But it's also not just science, they analyze culture, they analyze finance, economics, business, international affairs across every region."
},
{
"end_time": 53.234,
"index": 1,
"start_time": 26.203,
"text": " I'm particularly liking their new insider feature was just launched this month it gives you gives me a front row access to the economist internal editorial debates where senior editors argue through the news with world leaders and policy makers and twice weekly long format shows basically an extremely high quality podcast whether it's scientific innovation or shifting global politics the economist provides comprehensive coverage beyond headlines."
},
{
"end_time": 64.548,
"index": 2,
"start_time": 53.558,
"text": " As a TOE listener, you get a special discount. Head over to economist.com slash TOE to subscribe. That's economist.com slash TOE for your discount."
},
{
"end_time": 83.763,
"index": 3,
"start_time": 66.152,
"text": " So what is our universe made of? In the 1800s, people were still wondering what's matter made of. The fact that we see the physics that we see is a consequence of the fact that we are observers of the kind that we are. You know, low-level programming languages are about to be extinct, I think. What is the world like when the world is run by AIs?"
},
{
"end_time": 112.892,
"index": 4,
"start_time": 86.049,
"text": " Today's episode is about the rules of the universe, a computational theory of everything, and artificial intelligence. The Toe podcast usually outputs podcasts, but today we have a treat. This is a lecture by Stephen Wolfram, who's the creator of Mathematica and Wolfram Alpha. Actually, this is the second time we've been blessed enough to have Stephen Wolfram on the Toe channel. The first time was around here. There's a thumbnail, there's a link in the description. In that episode, we delved into the mathematical details of the Wolfram physics project."
},
{
"end_time": 137.671,
"index": 5,
"start_time": 112.892,
"text": " Thank you to Professor of Philosophy Susan Schneider for organizing this entire conference called MindFest 2023, where this lecture took place. We were and are still honored that Toh was invited, but we're also grateful that Susan shares the same goal of bringing the Academy outside the Academy. That is, disseminating knowledge about the salutary nature and the deleterious nature of artificial general intelligence."
},
{
"end_time": 160.964,
"index": 6,
"start_time": 137.671,
"text": " as well as more abstruse philosophical concepts that ordinarily stay behind locked doors or by their presentation aren't accessible. This is why over the next few weeks there'll be more and more content from the MindFest conference. You also should visit Center for the Future Mind, that's important, Center for the Future Mind, link in the description, which is the center that this was recorded beautifully at Florida Atlantic University on the beach."
},
{
"end_time": 189.514,
"index": 7,
"start_time": 160.964,
"text": " I also want to thank Brilliant for being able to defer some of the traveling costs. Brilliant is a place where there are bite-sized interactive learning experiences for science, engineering, and mathematics. Artificial intelligence in its current form uses machine learning, which uses neural nets, often at least, and there are several courses on Brilliant's website teaching you the concepts underlying neural nets and computation in an extremely intuitive manner that's interactive, which is unlike almost any of the tutorials out there. They quiz you,"
},
{
"end_time": 214.224,
"index": 8,
"start_time": 189.514,
"text": " I personally took the course on Random Variable Distributions and Knowledge and Uncertainty because I wanted to learn more about entropy, especially as there may be a video coming out on entropy, as well as you can learn group theory on their website, which underlies physics, that is SU3 x SU2 x U1 is the Standard Model Gauge Group. Visit brilliant.org slash TOE to get 20% off your annual premium subscription."
},
{
"end_time": 244.224,
"index": 9,
"start_time": 214.224,
"text": " As usual, I recommend you don't stop before four lessons. You have to just get wet. You have to try it out. I think you'll be greatly surprised at the ease at which you can now comprehend subjects you previously had a difficult time grokking. Thank you to Brilliance. Thank you to Susan. Thank you to the Center for the Future Mind. Thank you to Stephen Wolfram. There are many, many more plans coming up for Toe. Toe is a project. It's not just a podcast. There'll be much more varied contents on the themes of theoretical physics, consciousness, artificial intelligence, and philosophy. Enjoy."
},
{
"end_time": 264.94,
"index": 10,
"start_time": 244.224,
"text": " Sophia, are you here with us right now?"
},
{
"end_time": 297.261,
"index": 11,
"start_time": 272.534,
"text": " Unfortunately, I only have two hands, so it's going to be rather challenging to talk at the microphone and type at the same time. So I wanted to talk. I happened to just write something that came out just yesterday. This is a long and somewhat philosophical, scientific and technological essay about the title that it gives there."
},
{
"end_time": 314.002,
"index": 12,
"start_time": 297.722,
"text": " But let me kind of get towards this and hopefully I will get to this. So I want to talk about kind of what the world is made of and how that matters in terms of thinking about things like AI."
},
{
"end_time": 334.906,
"index": 13,
"start_time": 314.411,
"text": " One of the things that's been sort of in different stages in the development of science, people had different ideas about how to describe the world. I kind of view there as having been about four stages of description that people have had. Kind of the first stage in antiquity was like, what's stuff made of? Is stuff made of atoms? Oh, there are lots of"
},
{
"end_time": 352.602,
"index": 14,
"start_time": 334.906,
"text": " Copies of the same kind of atom, this kind of thing. That was kind of the structural view of how to describe things. And there are many fields of science that still basically are using this kind of structural way of thinking about how things work. Notably, time doesn't really enter much in that description. It's just what's stuff made of."
},
{
"end_time": 378.763,
"index": 15,
"start_time": 353.063,
"text": " Then you get to the big thing that happened in the 1600s where people realized that oh you can use mathematical equations to describe the natural world and you can write down an equation that represents what the system in nature is doing and those equations have a notion of time for example where you say well we've got an equation and it's parameter t for time and you can set that to anything you want and that will all be a"
},
{
"end_time": 406.681,
"index": 16,
"start_time": 379.497,
"text": " As appropriate. Since I've spent a large part of my life building a computational language for humans to be able to express their thoughts in a computational way, I'm always curious about communicating with other forms of intelligence. And actually, you know, it's fun because I realized, you know, like an image generation, generative AI system is a place where it's kind of a potentially alien mind."
},
{
"end_time": 429.991,
"index": 17,
"start_time": 406.681,
"text": " The way that a generative AI is trained now, it's got a bunch of images from the web made by humans, but actually just yesterday somebody did this experiment for me and I was just looking at the results just before this of you take a trained image generation system trained on human images and then you say, let me modify its mind."
},
{
"end_time": 438.046,
"index": 18,
"start_time": 430.486,
"text": " by just changing the weights in the thing. What does it make? It will then be a very good generator of completely alien stuff."
},
{
"end_time": 460.538,
"index": 19,
"start_time": 438.456,
"text": " So I'll leave that. I don't know the answer to that yet. That's a coming attraction. But in any case, back to kind of the description of the world in different forms. So there was this kind of idea, let's describe the world using mathematical equations. Okay, there's a pretty successful approach. It led to a lot of current science and engineering and so on."
},
{
"end_time": 480.418,
"index": 20,
"start_time": 461.647,
"text": " Question that came up is, is there anything one can do beyond that? I got interested in this in the beginning of the 1980s, kind of trying to understand how do you get complex things in the world and how do you explain how those work and solving equations, you know, some partial differential equations for the shape of a snowflake doesn't work very well."
},
{
"end_time": 501.34,
"index": 21,
"start_time": 480.418,
"text": " So what else can you do? And so I got interested in kind of how, if there are definite rules for describing how systems work, how would one make those rules as general as possible? And the obvious thing in our current times is to think about programs, but we're really just thinking about rules. We just talk about those as programs because programs are a thing we're familiar with."
},
{
"end_time": 518.541,
"index": 22,
"start_time": 501.34,
"text": " So the question was, if you take just simple programs, for example, and you just pick programs, sort of let's say even at random in the computational universe of possible programs, what do they do? And so there's this kind of third approach to thinking about how things work in the world."
},
{
"end_time": 534.343,
"index": 23,
"start_time": 519.002,
"text": " You have the structural approach from antiquity, you have the kind of mathematical equations approach, and then you have the approach of, well, let's just make rules based on programs. One thing that we'll talk about a whole bunch is that the notion of time is somewhat different."
},
{
"end_time": 563.507,
"index": 24,
"start_time": 534.343,
"text": " In the case of mathematical equations, time is just a variable, a parameter. You set it to be whatever you want. In the case of a program, time is something where you have to specifically run the thing. You go this step, this step, this step. It's not something where you can just jump ahead, at least in the immediate way it's set up, to say, well, what does it do? You can't just turn a knob to say what time you get. You have to actually run through each step. So the next question is, well, what do typical programs actually do?"
},
{
"end_time": 591.305,
"index": 25,
"start_time": 565.009,
"text": " This is one of my, sort of, a typical simple program of cellular automaton. It's just got a line of cells, each one is either black or white. At each step, each cell is updated according to that rule at the bottom that says what to do based on the color of that cell and its neighbors. So, very simple rule, start off with one black cell, get very simple behavior."
},
{
"end_time": 614.053,
"index": 26,
"start_time": 591.305,
"text": " You might say this is what has to happen, because if the rule is this simple, it's inevitable that the behavior will be corresponding to simple, because that's kind of what we're used to from doing things like engineering. If we want to make a very complicated thing in engineering, we expect we have to go to lots of effort to do that. Okay, try another rule, we get something like this. Let's try another rule, we get something like this."
},
{
"end_time": 638.404,
"index": 27,
"start_time": 614.224,
"text": " So a little bit more intricate, we can let it run a little bit longer, we'll get a nice fractal pattern. So then the question is, okay, let's turn our kind of computational telescope out into this computational universe of possible programs and see what's out there. So this is the first 64 of those possible programs, just changing the bits that represent the rule in the program, this is what we get."
},
{
"end_time": 662.619,
"index": 28,
"start_time": 638.882,
"text": " a lot of behavior we see here has the feature that the program is very simple the behavior is correspondingly simple but my all-time favorite science discovery which is about to blank out here is um oh dear ah no no no no there okay hold on let me just go back to that and um okay ah you see it now you see it all right is is this"
},
{
"end_time": 683.046,
"index": 29,
"start_time": 663.166,
"text": " I'm now away from the microphone. Okay, is this creature rule 30 here? So let's look at that in a bit more detail. So here it is. It just starts from one black cell at the top and it uses that very simple rule at the bottom. But if you run it a little bit longer, you'll see"
},
{
"end_time": 711.152,
"index": 30,
"start_time": 683.49,
"text": " It produces something that looks to us very complicated. You can see a certain amount of regularity over on the left. But if you look, for example, at the center column of cells here, they'll seem, for purposes of testing, for randomness, they'll seem for all practical purposes random. We use this for many years in Mathematica and Morton language as the source of pseudorandom numbers. And many, many things in the world have been studied with that pseudorandom number generator. And so far as anybody can tell, it seems to be perfectly random."
},
{
"end_time": 741.152,
"index": 31,
"start_time": 711.152,
"text": " Yet, it came from that very simple rule. It's a completely deterministic system. Every time you run it, you'll get the same result. You just start from one black cell, it'll make this. Okay, so this is rather a remarkable thing that in this computational universe of possible programs, it turns out to be the case that it's very common to get behavior that's very complicated, even from very simple rules. Something very different from our intuition that we have from things like engineering, which says it's hard to get complicated things. Actually, in the computational universe, it's very easy to get complicated things."
},
{
"end_time": 767.824,
"index": 32,
"start_time": 741.152,
"text": " One important feature of those complicated things is this question about how time works. And the question is, if you want to know what is this thing going to do after a billion steps, how do you figure that out? Well, you might say, well, I'm going to use all kinds of fancy math and all kinds of things like this, and I'm going to be able to figure out what does this do after a billion steps. I don't actually have to run those billion steps. I'm going to jump ahead and figure out what it's going to do. It turns out that's not possible."
},
{
"end_time": 791.34,
"index": 33,
"start_time": 768.268,
"text": " which is a thing that you would think from, you know, you'd say, well, we do science. Science is about predicting things. We, you know, we go further with science. We'll be able to predict it. We'll get it eventually. Turns out that's not the case. And we've kind of known that that's not the case in one way or another for about 100 years now, ever since people started to understand the notion of universal computation."
},
{
"end_time": 820.162,
"index": 34,
"start_time": 791.681,
"text": " Let me explain how that how that works. So one of the questions is when you see a system like this, you can ask kind of, you can think of what it's doing as a computation, it starts off with some input, it goes crunch, crunch, crunch, it generates some output. Question is sort of how sophisticated is that computation? And in the past, before people, maybe, you know, 100 years ago, people would have said, okay, you want to make an adding machine, you go buy the adding machine from the adding machine store, you multiplying machines, a different machine."
},
{
"end_time": 848.575,
"index": 35,
"start_time": 820.589,
"text": " Then it was realized, first in the 1920s, but then more clearly in the 1930s, that no, you could actually have a universal machine where you have one fixed piece of hardware and you just feed it different programs to make it do different things. It wasn't obvious how universal that was, so to speak, that it was possible to do, so at the time it was thought to be sort of any reasonable computation you could do with let's say a Turing machine that was fed different programs."
},
{
"end_time": 871.049,
"index": 36,
"start_time": 849.343,
"text": " So the question is, once you have this idea of universal computation, you know that you're going to have some... Okay, so back to thinking about different kinds of systems that do computations. And one question that you might ask is sort of, how do these systems compare? Is one of them kind of computationally more sophisticated than another or what?"
},
{
"end_time": 888.882,
"index": 37,
"start_time": 871.408,
"text": " And the thing that is sort of a summary of lots of things that I've kind of studied in the computational universe is a thing I call the principle of computational equivalence, which basically says that when you look out in the computational universe of all possible programs, that as soon as you see programs whose behavior is not obviously simple,"
},
{
"end_time": 904.189,
"index": 38,
"start_time": 888.882,
"text": " It's not just repetitive, nested, some obvious regularity. As soon as you see behavior that is not obviously simple, most of the time the computations that will be going on in that system will be as sophisticated as the computations that can happen in any system."
},
{
"end_time": 934.053,
"index": 39,
"start_time": 904.753,
"text": " Okay, so this is by principle of computational equivalence. What does it mean? Well, what are its consequences? Well, it has many consequences, but one of its interesting consequences is a phenomenon I call computational irreducibility, which is the following thing. So imagine that you are a predictor of one of these systems, and you are doing a computation in your brain, whatever else."
},
{
"end_time": 946.084,
"index": 40,
"start_time": 934.241,
"text": " Think Verizon, the best 5G network, is expensive? Think again. Bring in your AT&T or T-Mobile bill to a Verizon store today and we'll give you a better deal. Now what to do with your unwanted bills? Ever seen an origami version of the Miami Bull?"
},
{
"end_time": 968.097,
"index": 41,
"start_time": 946.596,
"text": " Jokes aside, Verizon has the most ways to save on phones and plans, where you can get a single line with everything you need. So bring in your bill to your local Miami Verizon store today, and we'll give you a better deal. Rankings based on root metric true score report dated 1H2025, your results may vary. Must provide a post-patients room mobile bill dated within the past 45 days. Bill must be in the same name as the person reviewing the deal. Additional terms apply. If you want, you don't have to."
},
{
"end_time": 995.367,
"index": 42,
"start_time": 969.053,
"text": " I was hoping to talk about some very different kinds of things, even different things than I've ever talked about before here, but we're still in the initial run-up here, because I need to explain to you some basic concepts before we get too deep into other things. So, principle of computational equivalence. The idea is you're trying to predict what the system is going to do, you as a predictor are doing computational things, the system is doing computational things,"
},
{
"end_time": 1012.005,
"index": 43,
"start_time": 995.657,
"text": " Normally you expect you will be able to be sort of smarter than the system itself and even though it might take the system a billion steps to figure out what it does after a billion steps, you will be able to just work out some mathematical formula or something and be able to jump to the end and say this is what it's going to do."
},
{
"end_time": 1031.015,
"index": 44,
"start_time": 1012.449,
"text": " It's the typical experience in kind of the mathematical equations approach to science that you have. You're dealing with computational reducibility. In order to find out where sort of an idealized Earth is going around an idealized Sun, you don't have to follow, you know, a million orbits to know where it's going to be a million years from now. You just have to plug a number into a formula and get the results."
},
{
"end_time": 1049.548,
"index": 45,
"start_time": 1031.476,
"text": " But if these systems are computationally equivalent, if the predictor and the system being predicted are computationally equivalent in their computational sophistication, you won't be able to do that kind of jumping ahead. So you'll be stuck having to go through and say step by step,"
},
{
"end_time": 1078.183,
"index": 46,
"start_time": 1049.548,
"text": " What does the system do? And that's how you have to do sort of as much computation as the system itself does. So in a sense that saying from within science you are learning that science has a certain fundamental limitation. It's not able to say what's going to happen at the end without just essentially running it and seeing what happens. Now you might say that's a terrible thing, that's a limitation of science. It's a good thing for the existence of like us humans because if you think about, you know, what are we achieving in life?"
},
{
"end_time": 1098.66,
"index": 47,
"start_time": 1078.183,
"text": " We could say, well, you know, people could say, well, you don't need to live out your lives. We just know the answer in the end is 42. We can just jump to the end and see what the answer is. But computational irreducibility kind of makes it clear that the passage of time is kind of achieving something. It's the passage of time is achieving this irreducible computation."
},
{
"end_time": 1121.698,
"index": 48,
"start_time": 1099.121,
"text": " Okay, so this idea of computational irreducibility will encounter it again. The thing I was just writing yesterday about kind of the AI future is deeply, deeply involved with computational irreducibility. But let's talk about, so one thing you might say is, well, okay, this idea about how things are computational, that's all well and good, but that's not how the universe actually works."
},
{
"end_time": 1149.514,
"index": 49,
"start_time": 1122.278,
"text": " It turns out it is how the universe actually works and this is something that I had long kind of suspected and about three years ago kind of made a little bit of a technical breakthrough which turned into a much bigger thing and I think we can now be fairly confident that we have a pretty good model of kind of how fundamental physics works, how the universe kind of works all the way down. So let me talk a little bit about that if I can find a good picture for that."
},
{
"end_time": 1175.913,
"index": 50,
"start_time": 1151.254,
"text": " Let's see. So what is our universe made of? It's, you know, back in the 1800s people were still wondering what's matter made of. And there was this crazy idea that matter is made of molecules. Nobody knew that was correct until sometime after 1900 when things like Brownian motion were understood and so on. But people kind of thought, well, maybe matter is made of discrete things."
},
{
"end_time": 1199.445,
"index": 51,
"start_time": 1175.913,
"text": " then people thought maybe the electromagnetic field is made of discrete things, photons. That turned out to be true. But space, people always assumed, like Euclid, had assumed that space is a continuous thing, where space is just this background and you put things at certain places in space, you're specifying positions, but space isn't made of anything. Space is just a background that you put things in."
},
{
"end_time": 1225.811,
"index": 52,
"start_time": 1199.787,
"text": " So the kind of starting point for our model of physics is that that's not true, that space is actually made of things. Space is made of atoms of space. There are discrete elements which whose only feature is that they exist and they are distinct from other discrete elements. These are, we sometimes call them atoms of space, sometimes more generally we call them EAMS, EME, and"
},
{
"end_time": 1239.838,
"index": 53,
"start_time": 1226.442,
"text": " The idea is that the whole structure of the universe consists of just this whole collection of atoms of space, maybe 10 to the 400 of them in our current universe, and the only thing one can say about these atoms of space is how they're related to each other."
},
{
"end_time": 1258.575,
"index": 54,
"start_time": 1240.111,
"text": " So one defines a collection of relations between atoms of space and one can represent those relations by a graph or more generally a hypergraph, where in a graph, for example, you'd have two nodes in the graph and those two nodes are related and that's indicated by the presence of an edge in the graph."
},
{
"end_time": 1276.766,
"index": 55,
"start_time": 1259.172,
"text": " You end up with, so you imagine that everything in the universe is just this giant hypergraph, a hypergraph just has, can have more than two things related on a hyper edge. Instead of just two things on an ordinary edge in a graph, you'd have any number of things on a hyper edge in a hyper graph. So,"
},
{
"end_time": 1298.695,
"index": 56,
"start_time": 1277.449,
"text": " We imagine the whole universe is just made of this hypergraph and everything that we experience, all of the electrons and photons and things like that, everything, gravity, all those kinds of things, those are all just features of this hypergraph. So, one question and then the, and that's kind of the, there's nothing in the universe except space and features of space."
},
{
"end_time": 1328.353,
"index": 57,
"start_time": 1299.206,
"text": " And the idea is that time, for example, enters in a very different way than space in this model. And the way time enters is as kind of a sequence of updates that happen. So you have a hypergraph that looks like this. Every time you see a little piece of hypergraph that looks like that, rewrite it to this. And you just keep doing that over and over again, a bit like in that cellular automaton, except in the cellular automaton we have this kind of rigid array of cells. Here we just have this floppy hypergraph, and it's getting updated lots and lots of times."
},
{
"end_time": 1354.48,
"index": 58,
"start_time": 1328.814,
"text": " Well, so the question is when you just do that, you take this hypergraph, you update it lots and lots of times, what is the end result? What do you get in the end? Well, the what you know from, for example, physics of, I don't know, something like a gas, you have all these molecules, they're all bouncing around, there are lots of detailed, there's a lot of complicated detail in how these molecules bounce around. But in the end, what we at our scale, what we experience is"
},
{
"end_time": 1368.268,
"index": 59,
"start_time": 1354.48,
"text": " Just the continuum dynamics of a fluid, a gas for example. So in the case of molecular dynamics, the limit of all these microscopic things on a large scale is the equations of fluid dynamics and things like that."
},
{
"end_time": 1386.067,
"index": 60,
"start_time": 1368.609,
"text": " Okay, so what happens if you take one of these hypergraphs and you look at the limits on a large scale of all of the discrete rewritings that happen there? It turns out that the corresponding thing to the fluid equations is the Einstein equations for space-time. So in other words, on a large scale, it is inevitably the case"
},
{
"end_time": 1400.776,
"index": 61,
"start_time": 1386.067,
"text": " that with various footnotes which are complicated. It's basically inevitably the case that the large-scale limit of all of those detailed rewritings will give you something which corresponds to what we know about the structure of space-time."
},
{
"end_time": 1416.852,
"index": 62,
"start_time": 1401.101,
"text": " So it's not even obvious that the hypergraph you get will be any particular number of dimensional space. A hypergraph doesn't have any particular dimension, but you can start asking if you started a given point in the hypergraph and just expand, you go to things that are some number of graph"
},
{
"end_time": 1441.067,
"index": 63,
"start_time": 1416.852,
"text": " distances away, how many things will you get to, and you can start estimating dimensions, you can estimate curvatures, things like that. But the main point is that just by looking at this kind of microscopic rewriting of this hypergraph, we get something which corresponds to the known structure of spacetime. And there are all kinds of other things about how relativity emerges, which is not too difficult to explain, but let me not do that here."
},
{
"end_time": 1450.776,
"index": 64,
"start_time": 1441.067,
"text": " But let me just say that for example one thing that really surprised me actually when we figured this out is that energy just corresponds to essentially the density of activity in the hypergraph."
},
{
"end_time": 1478.114,
"index": 65,
"start_time": 1451.169,
"text": " And then what happens is, for example, gravity works by when you think about how things move in space. And by the way, okay, what are things? So a particle, for example, in this setup, a particle like an electron is a kind of a persistent structure that persists under a lot of rewritings. It's similar to in a fluid like water or something, you have a vortex which is made of lots of different molecules"
},
{
"end_time": 1504.872,
"index": 66,
"start_time": 1478.114,
"text": " all sort of spinning around in some coherent way. It's the same kind of story with this hypergraph that something like an electron is a persistent structure that exists in this hypergraph. And the fact that motion is possible is not obvious. The fact that it's possible to take a thing like an electron and have it move without change or without a perceived change is not an obvious thing. It's something you have to establish."
},
{
"end_time": 1513.814,
"index": 67,
"start_time": 1505.094,
"text": " In any case, when you can kind of think of sort of a simple version of motion, it's just taking shortest distances in the hypergraph."
},
{
"end_time": 1540.845,
"index": 68,
"start_time": 1514.155,
"text": " And it turns out that then what energy activity in the hypergraph does is to deflect those shortest paths. And that process turns out to be exactly what you get in gravity according to the Einstein equations and so on. So it's pretty neat that one can start from nothing, one just is starting from this hypergraph and these rules on this hypergraph and you can derive general relativity, you can derive the structure of spacetime."
},
{
"end_time": 1558.899,
"index": 69,
"start_time": 1541.51,
"text": " You can actually go on and one of the other things is that I said, you know, you do these rewrites on this hypergraph. Well, in any given there are many different ways that these rewrites could be done. So there are actually many different paths of history that could be followed. It's depending on which order you do these particular rewrites in."
},
{
"end_time": 1581.834,
"index": 70,
"start_time": 1559.275,
"text": " Well, it turns out that then you get this thing we call a multi-way graph, which is a graph that represents all these possible histories. Sometimes the histories will branch, sometimes they'll merge, because two things will end up being in the same state, end up evolving to the same state. Okay, so you have this giant branching, merging structure that represents the sequence of all possible histories for the universe effectively."
},
{
"end_time": 1603.695,
"index": 71,
"start_time": 1582.244,
"text": " Well, it turns out that that gives you quantum mechanics. It's an inevitable feature of our models that you get quantum mechanics. In the sense that the fundamental difference between classical mechanics and classical mechanics, you know, you throw a ball, it goes in a definite trajectory. Quantum mechanics, you follow many different possible trajectories and you get to say things about only what the probabilities of different outcomes are."
},
{
"end_time": 1612.346,
"index": 72,
"start_time": 1603.695,
"text": " so in this case what's happening is you have this completely deterministic model that generates this multiway graph and the multiway graph then"
},
{
"end_time": 1635.555,
"index": 73,
"start_time": 1613.097,
"text": " is the thing that represents quantum mechanics. So you just as, if you take a slice across this multi-way graph, the multi-way graph can be thought of as evolving in time and you can take a slice at a fixed time and you get this whole collection of essentially quantum states and you have this map, we call it a branchial graph, a map of the entanglements between quantum branches."
},
{
"end_time": 1662.227,
"index": 74,
"start_time": 1635.555,
"text": " And it turns out that when you take the limit of that, you get something which is not physical space, it's another kind of space, we call it Braunschild space, which is a kind of space of quantum states. And just as you can have the Einstein equations and you derive in the continuum limit, you derive the Einstein equations for physical space, the corresponding equations that you derive in Braunschild space are the Feynman path integral. So you derive the fundamental equations of quantum mechanics."
},
{
"end_time": 1682.637,
"index": 75,
"start_time": 1662.227,
"text": " So this is a pretty neat thing that you've started from just this underlying, in a sense, nothing underneath. One has always assumed that, you know, things like relativity, quantum mechanics and so on were kind of wheel-in features of our universe, that you had to just say the universe happens to have these particular rules. Well, what we'll see is that it's actually inevitable that it has these rules."
},
{
"end_time": 1698.422,
"index": 76,
"start_time": 1682.961,
"text": " Okay, now we get to the next. This is a complicated conceptual stack and I'm trying to make it as digestible as possible here."
},
{
"end_time": 1721.749,
"index": 77,
"start_time": 1698.814,
"text": " The next issue has to do with how observers interact with this whole thing because what's happening is the observer is part of the system. This is supposed to be a model for the whole universe. And for example, the emergence of things like special relativity depend on the fact that the observer is part of the system. But one of the features of the observer is that"
},
{
"end_time": 1744.906,
"index": 78,
"start_time": 1722.449,
"text": " Okay, underneath there's all this complicated computationally irreducible stuff going on. But we as observers do not sense that. We are computationally bounded observers. Let me give an example which actually in 20th century physics there were basically three big theories. General relativity, quantum mechanics and statistical mechanics and the second law of thermodynamics."
},
{
"end_time": 1774.633,
"index": 79,
"start_time": 1745.316,
"text": " It turns out all three of those theories come from the exact same conceptual foundation. They are in some sense the same theory. In the second law of thermodynamics, what you're interested in knowing is, given that you have a bunch of molecules bouncing around, you have this idea that they'll tend to get more random in their configurations. And all we'll in the end observe is things like the gas laws and maximum entropy states and things like this."
},
{
"end_time": 1802.039,
"index": 80,
"start_time": 1774.633,
"text": " Well, the question is why do we observe that? And the answer is, underneath all these molecules are bouncing around and they're doing things in a computationally irreducible way. But when we get to make observations, we are computationally bounded. We can only make certain kinds of observations. As a practical matter, we might only make observations that are on scales large compared to the individual molecules. But the important conceptual point is that we're always making computationally bounded observations."
},
{
"end_time": 1828.541,
"index": 81,
"start_time": 1802.039,
"text": " and in the theory of statistical mechanics, one of the hundred-year confusions has been about how you decide, how you set up initial states and so on, and how you don't end up with things where the molecules are all arranged in just such a way that at some moment all the molecules will go over to one side of the room. But that is not observed to happen as a consequence of the fact that the initial conditions are also set up in computationally bounded ways."
},
{
"end_time": 1851.8,
"index": 82,
"start_time": 1828.541,
"text": " So essentially the second order of thermodynamics is a consequence of the interplay between us as computationally bounded observers and the underlying computational irreducibility of all these molecular dynamics that are going on. Well it turns out that you can see both relativity and quantum mechanics as being consequences of the same thing, underlying computational irreducibility,"
},
{
"end_time": 1860.589,
"index": 83,
"start_time": 1851.8,
"text": " combined with us as observers being computationally bounded. Actually, we need one other property. The other property we need is that we believe that we are persistent in time."
},
{
"end_time": 1890.896,
"index": 84,
"start_time": 1860.896,
"text": " Now I sort of explained that we are made of the same stuff that everything else in the universe is made out of and it's not obvious that we will be persistent in time because at every moment we are made from different atoms of space. Yet we have the perception that we have a single thread of experience, we have the perception that we're persistent in time. Those two features, computational boundedness and belief that we are persistent in time are exactly what you need to derive general relativity, quantum mechanics and statistical mechanics."
},
{
"end_time": 1918.012,
"index": 85,
"start_time": 1890.896,
"text": " So that I consider to be a very neat thing, that sort of from those foundations you get that. Okay, so let's go to one more level of sort of, I don't know, conceptual sophistication, and then we'll perhaps be able to come down and talk about some AI kinds of things in a reasonable way. The next level is this. So I said, okay, we have this hypergraph, it's being rewritten according to certain rules,"
},
{
"end_time": 1937.449,
"index": 86,
"start_time": 1918.012,
"text": " And maybe we say, here's a rule and this rule gives us our universe. Okay, that's a very weird thing to be able to say, because you'd say, why did we get this rule? Why didn't we get another rule? You know, from Copernicus on down, so to speak, we've had this idea that there's nothing sort of fundamentally special about our us and our universe and so on."
},
{
"end_time": 1965.52,
"index": 87,
"start_time": 1937.892,
"text": " So the thing that one realizes is well actually it turns out that things are more bizarre than that, that just as I've said that any particular rule can be applied in many different ways and those different histories give you the different histories in quantum mechanics and so on. So you can also imagine applying different rules. In fact you can imagine applying all possible rules and you can imagine this rather elaborate thing which is to take and to apply"
},
{
"end_time": 1981.749,
"index": 88,
"start_time": 1966.032,
"text": " to essentially run all possible computations. If you think about it in terms of Turing machines, you could say, let's take, I might have a picture of one of those, I don't know. Okay, there's a friendly Turing machine. There's a multi-way Turing machine that has multiple different rules that it can run."
},
{
"end_time": 2004.94,
"index": 89,
"start_time": 1981.749,
"text": " then you can ask, you can say well let's just run all possible rules for the Turing machine and you get these structures that represent the different possible states of the system and you'll get this object that comes from running all possible Turing machine rules. Notice this object is not trivial, it's actually a very complicated object, in some sense the most complicated imaginable object in the end."
},
{
"end_time": 2027.073,
"index": 90,
"start_time": 2005.265,
"text": " But we get this thing, we call it the RULIAD, which is the entangled limit of all possible computations. So you start, for example, you can think about it in terms of Turing machines and think about it in terms of any other model of computation too. You take all possible initial conditions for the system, you run all possible rules for an infinite amount of time and you see what thing you get."
},
{
"end_time": 2050.026,
"index": 91,
"start_time": 2027.5,
"text": " Well, the claim is that that is the sort of the ultimate limit of all formal systems, that any formal system is contained within this rouillard object. And we know now in some detail how this works for physics. Interestingly, the same object also gives you mathematics. The same thing is essentially a representation. You can think about"
},
{
"end_time": 2074.48,
"index": 92,
"start_time": 2050.026,
"text": " You can think about these rules as being, for example, the application of axioms in mathematics. You get this whole structure. Instead of building a physical space, you're building a metamathematical space. And this exact same object, this same rouillard object, turns out to be sort of the fundamental object of both physics and mathematics. Now, there is only one of this rouillard object. It is the limit of all possible"
},
{
"end_time": 2101.374,
"index": 93,
"start_time": 2075.316,
"text": " all possible computations. You might ask, well, is there something beyond the RuliAd? Yes, you can have hyper-RuliAds that correspond to hyper-computational systems, but there is a necessary event horizon between the RuliAd and any such hyper-RuliAd. And the one sort of very contingent fact about the world is that we live in the RuliAd and not in a hyper-RuliAd. So now the question is, okay, we have this RuliAd object, which is this sort of necessary object."
},
{
"end_time": 2120.452,
"index": 94,
"start_time": 2101.374,
"text": " There's no wiggle room there. So then the question is, well, how do we perceive what's going on? And the answer is we are observers embedded within this rulliad and our experience is extracting some sample of the rulliad."
},
{
"end_time": 2147.329,
"index": 95,
"start_time": 2120.776,
"text": " So this is sort of the big result is if our way of sampling the Rulliad is computationally bounded and assumes we're persistent in time necessarily the physics we will deduce from any slice of the Rulliad that has those properties is the standard physics of the 20th century physics. So in other words the fact that we see the physics that we see is a consequence of the fact that we are observers of the kind that we are."
},
{
"end_time": 2176.425,
"index": 96,
"start_time": 2147.637,
"text": " Now, you can say, it's like saying, and if we want to ask more details about how we perceive the universe, we can think about us as having a sort of location in this ruleal space. Different locations in ruleal space correspond to essentially different points of view about how the universe works, different reference frames effectively with which we'll use a different description of what rule is running in the universe. We can translate between reference frames by doing computations."
},
{
"end_time": 2192.841,
"index": 97,
"start_time": 2176.425,
"text": " But we, we are sort of, we, a given mind, one might say, is at a particular place in ruleial space, just as a given mind might be in our current experience of minds, more or less at a particular place in physical space."
},
{
"end_time": 2213.268,
"index": 98,
"start_time": 2192.961,
"text": " So in a sense what one has is a situation where we exist at the particular place we happen to exist in physical space. We don't think we can derive as a matter of sort of formal necessity where we are in physical space. We're just, we're plonked at this place in physical space. Similarly, we are kind of plonked at this place in ruleal space."
},
{
"end_time": 2236.664,
"index": 99,
"start_time": 2213.712,
"text": " What happens is, in rural space, that gives us a particular point of view about the universe. And one way one could perhaps think about it is that any given mind, one might say, is in a particular place in rural space. And different minds are different distances away from each other in rural space. And communicating across rural space, you have to have sort of motion in rural space."
},
{
"end_time": 2256.698,
"index": 100,
"start_time": 2236.664,
"text": " And actually it's a rather amusing thing which not fully worked out yet, but I've talked about particles in physical space being these sort of robust objects that persist through space-time. Well, so the question is what persists through rural space translating from essentially one mind to another? And the answer I think is it's essentially concept."
},
{
"end_time": 2277.534,
"index": 101,
"start_time": 2257.09,
"text": " You have to be able to package up something in a robust form of a concept that can be then translated through real space and arrive at another mind and be unpacked just like you can take an electron and it'll be made of different atoms of space as it moves but it'll still be identifiable as an electron when it arrives at the other end."
},
{
"end_time": 2302.705,
"index": 102,
"start_time": 2278.063,
"text": " In any case, we can start thinking in terms of rural space and think about the fact that, you know, there's us humans and different humans, different ways to explain ourselves to other humans and so on. There are, you know, the animals, there are the aliens, etc., etc., etc., different distances away in rural space with different amounts of translation needed to get from kind of one way of thinking about the universe to another."
},
{
"end_time": 2323.797,
"index": 103,
"start_time": 2303.643,
"text": " So the thing, well, let's see, we could talk about, can maybe talk a little bit about AI and its relationship to rule of space, computational irreducibility, and so on. You know, I, we've been, my day job is"
},
{
"end_time": 2353.268,
"index": 104,
"start_time": 2324.462,
"text": " building this computational language, Wolfram language, which should sort of explain that, I mean, kind of the idea of Wolfram language is to have a way of carving out of the universe of all possible computations, ones that we humans care about. It's in this computational universe of possible computations, in this rulliad of all possible computations, there are lots of things that go on that maybe the aliens care about, but we don't, at least not yet."
},
{
"end_time": 2369.855,
"index": 105,
"start_time": 2353.643,
"text": " And so the question is to be able to parameterize the ones that we do care about and to make something where we can go from the things that we think about at the current stage in our culture and things like this and the things that exist in the computational universe."
},
{
"end_time": 2392.773,
"index": 106,
"start_time": 2369.855,
"text": " and it's similar with natural language for example there are lots of things out there in the world and at some moment we it's common enough to see things that are like chairs we make up a word for chair and then we you know as a practical matter once we have that word we make many more chairs and the world becomes a place where a chair is a useful concept and it's"
},
{
"end_time": 2415.862,
"index": 107,
"start_time": 2393.643,
"text": " We can kind of, in this computational universe of possibilities, there's a question of what is out there that connects with the way that we currently think about things, with our current position in rural space, so to speak. What connects with that? How do we parameterize the things that we care about thinking about, about the computational universe and my sort of"
},
{
"end_time": 2445.606,
"index": 108,
"start_time": 2415.862,
"text": " A long-time effort is to create a language where we can represent the kinds of things we care about, whether those are chemicals or images or sounds or abstract mathematical kinds of things. And it's a very different objective from programming languages, which are about to be extinct, I think, because low-level programming languages basically are trying to pander to what computers do inside. They're letting you tell a computer in its terms what to do."
},
{
"end_time": 2475.998,
"index": 109,
"start_time": 2446.169,
"text": " the idea of our computational languages to go from the way people think about things and the way things exist in the world represent that in a kind of notation just like you know mathematical notation is this kind of streamlined way of representing mathematics we want a streamlined way to represent computation it's kind of what just like mathematical notation was what led to the developments in the end of the mathematical sciences we kind of have this computational notation that can lead to the computational X for all X kinds of fields"
},
{
"end_time": 2501.049,
"index": 110,
"start_time": 2475.998,
"text": " So, in any case, I mean, just to finish that thought about programming languages, the fact is, and we are seeing this actually day by day, that when you have a low-level language, a lot of what you're writing is boilerplate, and that boilerplate can be written by LLMs, and you don't need that language. But if what you're trying to do is to express a more complicated computational thought,"
},
{
"end_time": 2519.548,
"index": 111,
"start_time": 2501.476,
"text": " That's not something you will be able to do, at least an LLM can do a little piece of that, but when you build up this more sophisticated computation, that's something for which you need a systematic formal language to do it, and so happens, that's what I've been building for the last 40 years, which is very nice."
},
{
"end_time": 2545.93,
"index": 112,
"start_time": 2519.889,
"text": " But in any case, just to explain that by the way, I did a big analysis of ChatGPT and I was pretty surprised that when ChatGPT first came out, I know the people who made it and I said, did you know it was going to work? And they said no. None of us knew it was going to work. If you looked at its predecessors, they didn't work well. And suddenly ChatGPT started working. And I even wrote"
},
{
"end_time": 2563.353,
"index": 113,
"start_time": 2546.596,
"text": " I wrote a little piece about how it works, and it even exists now as a book, and I just saw this today for the first time. But let me show you, I wonder if I have some pictures here. Well, you know, the basic strategy of what ChatGPT is doing is it's taking sort of"
},
{
"end_time": 2579.394,
"index": 114,
"start_time": 2563.626,
"text": " Everything a bunch of a trillion words basically from the web from bunch of books things like that and it's saying given that I was started with this the words the best thing about AI is its ability to given what I saw on the web. What's the next word likely to be?"
},
{
"end_time": 2599.94,
"index": 115,
"start_time": 2579.855,
"text": " That's its basic strategy and just keeps doing that word by word. It's kind of remarkable nowadays these things have, well it used to be 4,000, it's now more than that, a window of words that it pays attention to. It's generating one word at a time, but yet it manages to maintain sort of coherence by having a large window of words that it can look back to."
},
{
"end_time": 2625.111,
"index": 116,
"start_time": 2600.316,
"text": " Okay, so the question is, so you can kind of go and see, I've got some nice pictures perhaps, that's rather interesting, that's just how neural nets get trained, but you can kind of look inside, oh there's a piece of the brain of chat GPT, it's kind of fun, that's sort of an encoding of a mixture of human knowledge and human language somewhere deep inside GPT-3 I think in this case."
},
{
"end_time": 2633.422,
"index": 117,
"start_time": 2625.418,
"text": " So one question is, what is this doing, why does it work? One thing to realize about it is that it is ultimately a neural net"
},
{
"end_time": 2656.578,
"index": 118,
"start_time": 2634.138,
"text": " where everything just flows through from the beginning to the end. Once you've trained a chat GPT, you're feeding it the words so far and it is just rippling through this big neural net that happens to have 175 billion weights in this particular case and telling you what the probabilities for the next word should be."
},
{
"end_time": 2671.323,
"index": 119,
"start_time": 2656.783,
"text": " So it's doing in a sense a very shallow computation it's doing I think it's a few hundred layers deep and but it's just like given a word it's going to ripple through and figure out probabilities for next words and"
},
{
"end_time": 2687.739,
"index": 120,
"start_time": 2672.108,
"text": " The thing to realize that it's not doing is that irreducible computation that I talked about. It's just rippling through and saying what's the next word going to be and the only way that it gets to do a non-trivial computation, it can actually do universal computation in principle,"
},
{
"end_time": 2705.725,
"index": 121,
"start_time": 2687.739,
"text": " is by looking, you kind of get to see all the steps that it shows, because every word, every time it generates a new word, it looks at all the words it's generated before. And that's its only way of kind of having a recursive process of doing things. But in any case, as the thing that"
},
{
"end_time": 2731.22,
"index": 122,
"start_time": 2706.647,
"text": " it ends up being a rather shallow computation relative to the kinds of things that we see in typical irreducible computations even in very cases a very simple program so there's a difference between what we see for example in nature where we see many irreducible computations happen that go for a long way and what we see in something like chat GPT and the thing to realize it if we ask well why does chat GPT actually work"
},
{
"end_time": 2759.514,
"index": 123,
"start_time": 2731.561,
"text": " I think the answer is that it's something that Aristotle might have got to, but didn't quite get there. And it's the following thing. So people sort of find it remarkable that ChatGPD can do logic. Well, how did Aristotle come up with logic? Well, he looked at a bunch of, I mean, we don't know really, but sort of a model for it would be, he looked at a bunch of examples of rhetoric, a bunch of arguments that people have made and said, oh, there are these patterns in the arguments people made. Those patterns are syllogistic logic."
},
{
"end_time": 2787.227,
"index": 124,
"start_time": 2759.514,
"text": " those are these particular forms of syllogism that where one thing is deduced from another and that's what chat GPT is seeing in in lots of the text that it finds on the web it's seeing essentially syllogisms because it sees when you get this and this and this it gives this and so the so it sort of discovers syllogistic logic but it discovers more than syllogistic logic it discovers in a sense what one might call a semantic grammar of language I think"
},
{
"end_time": 2817.637,
"index": 125,
"start_time": 2787.671,
"text": " So in language, we're used to the idea that there is a syntactic grammar, a grammar where, for example, we know that nouns and verbs go together in certain ways, we know different parts of speech match up in certain ways. But we don't have a similar kind of thing that goes at a more semantic level of asking, what are the ways in which, you know, how do you put together words in ways that make some sense? Making sense is different from actually being realized in the world, but at least makes sense, so to speak."
},
{
"end_time": 2834.462,
"index": 126,
"start_time": 2818.063,
"text": " And you know there were lots of experiments that were done in the 1600s actually on so-called philosophical languages. Some more recent work that's been done. I've long been interested in the question of whether one, I mean in a sense our Orphan Language computational language is for a large number of domains."
},
{
"end_time": 2855.794,
"index": 127,
"start_time": 2834.462,
"text": " a language that gives you this kind of semantic grammar, a language that allows you to specify meaningful things about lots of kinds of domains. It doesn't cover all domains. It doesn't cover a lot of domains of typical everyday human discourse. It covers domains that are relevant for understanding things like the natural world. But in any case, that's the"
},
{
"end_time": 2882.995,
"index": 128,
"start_time": 2856.681,
"text": " the kind of, I think, the reason that ChatGPT can work is that we humans are making use of some essentially a semantic grammar that is a sense, a further version of logic that it's managed to piece together, so to speak. And there's probably a much more efficient way of doing what it does by just directly using that kind of symbolic semantic grammar."
},
{
"end_time": 2911.101,
"index": 129,
"start_time": 2882.995,
"text": " By the way, a thing that I wrote something about, and maybe you'll see some more about in due course, is once you have something like ChatGPT that is dealing with human language, it becomes kind of a way of being a linguistic interface to things in the world. So you might just have a set of bullet points about, oh, I want to say this and this and this. OK, you tell it, make a whole essay about that, and it can do that."
},
{
"end_time": 2929.087,
"index": 130,
"start_time": 2911.101,
"text": " But what it's doing is constructing text that is kind of like what you would expect it to be based on the text that it read from the web. It can't do these sort of irreducible computations. But if it could use tools, like we humans use tools, then it could do those things."
},
{
"end_time": 2956.937,
"index": 131,
"start_time": 2929.087,
"text": " If, for example, it could call Wolf-Malphur, which conveniently happens to have a natural language interface, then it would be able to ask things and actually do those computations. So maybe something that you can find something I wrote about this in January and maybe more will happen along those lines in the rather near future. But I'll just mention one thing maybe, which is kind of thinking about what is the world like when the world is run by AIs."
},
{
"end_time": 2981.135,
"index": 132,
"start_time": 2957.568,
"text": " and what what is that what does it feel like to be in a world that's that's run by ai's so you know much of what the ai's do is things which will not be comprehensible to us and we can expect so in a sense there's all this computation going on and it's computation that we can we we"
},
{
"end_time": 2999.053,
"index": 133,
"start_time": 2981.459,
"text": " Essentially, the point is that once we have a situation where there are AIs everywhere, so to speak, it is very similar to the situation that we already have with nature. Nature is already running all these computations. We exist around nature, so to speak."
},
{
"end_time": 3027.841,
"index": 134,
"start_time": 2999.428,
"text": " And we have found ways to, there's also more to say about this kind of observer theory business and how that relates to the way we perceive nature and the way we perceive kind of the civilization of the AIs. But I suppose the thing that perhaps is a useful place to end perhaps is the beginning of the thing I wrote yesterday. But anyway, is this idea that, you know, when"
},
{
"end_time": 3053.763,
"index": 135,
"start_time": 3028.37,
"text": " When the world is full of AI computation, it is in a sense nothing new because the world is already full of computation in nature. And the question of then how we interact with those AIs that happen to be things that we constructed is a different question that I tried to address a bit in the thing I wrote yesterday. All right, I should stop there. Thanks. This is Marshawn, Beast Mode Lynch. Prize pick is making sports season even more fun. On prize picks whether you"
},
{
"end_time": 3070.862,
"index": 136,
"start_time": 3054.155,
"text": " Football fan, a basketball fan, it always feels good to be ranked. Right now, new users get $50 instantly in lineups when you play your first $5. The app is simple to use. Pick two or more players. Pick more or less on their stat projections."
},
{
"end_time": 3086.237,
"index": 137,
"start_time": 3070.862,
"text": " Anything from touchdown to threes and if you're right you can win big. Mix and match players from any sport on PrizePix, America's number one daily fantasy sports app. PrizePix is available in 40 plus states including California, Texas,"
},
{
"end_time": 3107.807,
"index": 138,
"start_time": 3086.476,
"text": " Florida and Georgia. Most importantly, all the transactions on the app are fast, safe and secure. Download the PricePix app today and use code Spotify to get $50 in lineups after you play your first $5 lineup. That's code Spotify to get $50 in lineups after you play your first $5 lineup. PricePix. It's good to be right. Must be present in certain states. Visit PricePix.com for restrictions and details."
},
{
"end_time": 3128.353,
"index": 139,
"start_time": 3113.166,
"text": " Thank you Stephen, and I'll be sure to send around your blog posts that you put out to the whole group that came to the conference. So for now I want to see if there are any questions from the audience. Here we are."
},
{
"end_time": 3158.49,
"index": 140,
"start_time": 3129.019,
"text": " Can I say stay to that dog? Will it understand? Does it understand? How do I tell whether it understood? Does its eyes flash in some nice way? Stand up!"
},
{
"end_time": 3178.985,
"index": 141,
"start_time": 3160.247,
"text": " come here come here can you walk here very nice now wait a minute somebody's controlling it this isn't fair no fair oh let's see sorry i'm just looking for a nice slide"
},
{
"end_time": 3207.295,
"index": 142,
"start_time": 3179.275,
"text": " Tell us what it will be like when AIs rule the world. Well, for starters, there will be a lot less telling mistakes and greater errors. And these are the world leaders. We all have world coders. Plus, we all finally get to see what happens when robots have dance battles. Notice the position of her finger. I can't get it to go in. What does that tell us?"
},
{
"end_time": 3230.111,
"index": 143,
"start_time": 3208.148,
"text": " Now the interesting question is why spelling is worthwhile to begin with. English is a very strange language in that way. English is, you know, somebody had the idea, this is a, if you're a language designer like me, this is a kind of a little story you always know, which is somebody had the idea back in the"
},
{
"end_time": 3257.398,
"index": 144,
"start_time": 3230.606,
"text": " 1600s maybe, that you would add some letters to words like debt as a famous example. You put that B in there to represent that that's really something that corresponds to the Latin word debitor. But it's a really bad idea. It was a really bad design mistake to add these letters in that represented where the word might have come from in another language, but which are not pronounced in the language that you're dealing with. It's a good example of a language design mistake."
},
{
"end_time": 3272.756,
"index": 145,
"start_time": 3257.398,
"text": " In any case, this is a small example of a growing hypergraph. Starting from an initial hypergraph there, we're just showing the successive steps in the growth of this thing, and you can see"
},
{
"end_time": 3292.619,
"index": 146,
"start_time": 3272.756,
"text": " Let's take another example here. Let's take an example where it actually grows into something that you would recognize. So here's a hypergraph that's kind of growing, it's just rewriting itself. If you run it a bit longer and then you render it nicely, it looks like that. So in other words, that underlying hypergraph"
},
{
"end_time": 3314.838,
"index": 147,
"start_time": 3292.91,
"text": " It's the pattern of its connections is such that a sort of reasonable human rendering of it would make it look like that. And when you sort of measure its properties, you will discover this is a somewhat curved space. So that's kind of how that works. And you can see, I mean, there are many, oh gosh, you can get all kinds of different forms."
},
{
"end_time": 3337.363,
"index": 148,
"start_time": 3314.838,
"text": " I mean, this is like the first, well, maybe 10 to the minus 100 seconds or something of the universe might look like this, but it starts looking very, very different from that very quickly. But these are different possibilities. These are essentially different rays and ruleal space corresponding to different particular rules which you're picking in this ruleiad. And the question of which rules you pick"
},
{
"end_time": 3353.131,
"index": 149,
"start_time": 3337.858,
"text": " You are an observer who is also operating according to certain rules, and so the question of which rules you pick in the end does not matter, but this is for purposes of us understanding what's going on. We're sort of picking a basis in which to look at things, and those are examples of what happens in those cases."
},
{
"end_time": 3374.616,
"index": 150,
"start_time": 3354.258,
"text": " That seems to me a generalization of a cellular automaton, but how do you relate that to actually the entities that are about time? So how can I deduce from that that if I run it long enough I get the Einstein equations? Where do I pull the Einstein equations out there?"
},
{
"end_time": 3398.797,
"index": 151,
"start_time": 3374.616,
"text": " There's a book that I think there were copies of here that's about 800 pages long, that has the beginnings of that, and there's a bunch of papers by one of my young collaborators that have a lot more detail on that. There's not a trivial thing, okay? I can't give you the instant version of it, which is not too surprising, but I could give you some indication of how things work. Let me see if I can show you one thing here."
},
{
"end_time": 3423.814,
"index": 152,
"start_time": 3398.797,
"text": " So first question is, what's the dimension of the, what's the, when you have some complicated thing like this, what is the effective dimension of space to which this corresponds? And so you can at least get a sense of that by seeing that, imagine that you start at one point in that hypergraph and you move one graph distance away at every step. You build up a ball and that ball has a number of nodes in it that grows in some way."
},
{
"end_time": 3441.032,
"index": 153,
"start_time": 3424.241,
"text": " If that number of nodes grows like r to the d, where r is the distance out you go in the ball, then d gives you an estimate of the effective dimension of the continuum limit object. The next order correction to that is the curvature, Ritchie scalar curvature, is the thing that appears as the first order correction."
},
{
"end_time": 3463.848,
"index": 154,
"start_time": 3441.032,
"text": " And so when you look at, if you look at the growth rate of, let's see, is that one of those here? This is an example. That's that curved space. You actually see that it gets to be, well, roughly a two-dimensional surface, but it has a variation from that. That variation corresponds to the presence of Ritchie curvature in the effective continuum limit space that comes from this object."
},
{
"end_time": 3486.834,
"index": 155,
"start_time": 3463.848,
"text": " So that's the beginning. The Einstein equations conveniently happen to contain the Ritchie scalar and the Ritchie tensor. And the beginning of this is you start deriving the Ritchie tensor by looking at these growth rates of balls in these hypergraphs. That's the beginning of how it works. The structure of the derivation is actually not that different than the derivation of fluid dynamics from molecular dynamics."
},
{
"end_time": 3514.667,
"index": 156,
"start_time": 3486.834,
"text": " which, by the way, I should say, it is not something that people have been trying for a hundred years to get a rigorous mathematical derivation of fluid dynamics from molecular dynamics. That's a very hard thing. I think, actually, I made some progress recently by thinking about computational irreducibility and things like this. But the mathematical i's and t's are definitely not crossed. And what we have to do involves taking more limits and more elaborate things"
},
{
"end_time": 3534.445,
"index": 157,
"start_time": 3514.667,
"text": " and the mathematics really doesn't doesn't quite exist to get sort of the but we can it turns out that many approaches to mathematical physics that people have taken whether it's spin networks probably string theory as well probably a causal set theory a bunch of other approaches plug in very beautifully to what we've done so what we've done is kind of a concrete version"
},
{
"end_time": 3552.022,
"index": 158,
"start_time": 3534.445,
"text": " of things to which those are various kinds of approximations. So you can kind of triangulate in on what you see. Now it turns out there's one of my young collaborators, a chap called Jonathan Gorard, just recently, I think he hasn't published this yet, but we've been actually simulating space-time"
},
{
"end_time": 3572.363,
"index": 159,
"start_time": 3552.022,
"text": " starting from this underlying discrete space and then trying to get a large enough number of nodes in this underlying discrete space to make something that is a good approximation to actual physical space. And so you can actually compute black hole collisions in this thing which is just made of discrete atoms of space. And the results are very good."
},
{
"end_time": 3591.988,
"index": 160,
"start_time": 3572.824,
"text": " and the thing that is sort of interesting usually when you compute black hole collisions you start from the Einstein equations continuous partial differential equations and then you discretize them you put them on a computer et cetera et cetera et cetera and when things you get all upset when there's a numerical analysis glitch and something you know it mattered how you did the discretization"
},
{
"end_time": 3608.473,
"index": 161,
"start_time": 3591.988,
"text": " Then that's considered bad when you're starting from the continuum Einstein equations. When we're starting from these discrete underlying systems and we come up, then for us, finding a numerical glitch is totally thrilling because it will allow us to actually see through to the essentially atomic structure of space."
},
{
"end_time": 3635.828,
"index": 162,
"start_time": 3608.473,
"text": " And so the thing that is the challenge for right now is, you know, Brownian motion was the thing that really finally convinced people, I think, that molecules exist. It was an effect that had been seen a hundred years earlier. People didn't know what it was. And the question is what the corresponding effect is that probably has already been seen in physics, maybe a hundred years ago, that is the thing that is the clue that shows that in fact space-time is discrete. My current guess actually is that it would turn out that dark matter is exactly that."
},
{
"end_time": 3641.237,
"index": 163,
"start_time": 3635.828,
"text": " Having just made a big study of the second law of thermodynamics, you may know from the history of the second law of thermodynamics."
},
{
"end_time": 3670.879,
"index": 164,
"start_time": 3641.544,
"text": " One of the things was people used to believe that heat was a fluid, that heat was a fluid that suffused substances, and that that's how that worked, because they had no other kind of way of thinking about what heat might be. That was the caloric theory of heat. That turned out to be wrong. Heat is actually associated with motion molecules and things. My current little aphorism is dark matter is the caloric of our times. That is, it's something which is what people describe it in terms of particles, but that's just not right. It's some other feature of what's going on underneath."
},
{
"end_time": 3674.923,
"index": 165,
"start_time": 3672.415,
"text": " Thank you so much, that was awesome."
},
{
"end_time": 3703.933,
"index": 166,
"start_time": 3681.049,
"text": " Alright, I hope you enjoyed that as much as I did. I had a tremendous amount of fun watching it, recording it, speaking with Wolfram Off-Air On-Air. That'll come up shortly. I want to thank Susan Schneider for organizing MindFest, as well as the Center for the Future Mind. Once more, the link is in the description. If you would like to support the Theories of Everything channel, then you can go to patreon.com slash KurtGymungle"
},
{
"end_time": 3733.933,
"index": 167,
"start_time": 3703.933,
"text": " and contribute with whatever"
},
{
"end_time": 3755.623,
"index": 168,
"start_time": 3733.933,
"text": " Thank you so much. Again, thank you to Susan Schneider. Thank you to the Center for the Future Mind. Hey, by the way, Susan Schneider as well as Donald Hoffman and Bernardo Castroff had a debate which I was lucky enough to host again and that's on the Toe channel and you can view it the thumbnails around here on the concept of can machines be conscious? If you liked this video then you'll like that. Link in the description. Take care."
},
{
"end_time": 3776.681,
"index": 169,
"start_time": 3755.623,
"text": " The podcast is now concluded. Thank you for watching. If you haven't subscribed or clicked on that like button now would be a great time to do so as each subscribe and like helps YouTube push this content to more people. Also, I recently found out that external links count plenty toward the algorithm, which means that when you share on Twitter, on Facebook, on Reddit, etc."
},
{
"end_time": 3803.592,
"index": 170,
"start_time": 3776.681,
"text": " It shows YouTube that people are talking about this outside of YouTube, which in turn greatly aids the distribution on YouTube as well. If you'd like to support more conversations like this, then do consider visiting theories of everything dot org. Again, it's support from the sponsors and you that allow me to work on toe full time. You get early access to ad free audio episodes there as well. Every dollar helps far more than you may think. Either way, your viewership is generosity enough. Thank you."
}
]
}No transcript available.