Coding the Cosmos: Does Reality Emerge From Simple Computations?

Hello everyone, welcome to this live discussion presented by the World Science Festival. I'm Brian Green. I come to you live from my office in the physics department at Columbia University, the center for theoretical physics, and our discussion today will be with Steph Wolfram. a name that many of you are familiar with thanks to so many contributions from Mathematica that has had such a profound influence on the types of science we can do well since alpha the Wolfram language, of course Stephen is a physicist at heart, there it is where His initial training began and our conversation will focus on some of the work that He has been doing recently to try to give us a perhaps different way of thinking about the fundamental laws and before we continue I just want to quickly say look, you know those.

Of you who have followed physics and science in general, perhaps through World Science Festival events or books, your own studio view, you know that our goal, which was actually articulated perhaps most succinctly by Albert Einstein, is trying to discover the fundamental laws of the universe. As Einstein said, did God have any choice in the creation of the universe? And he was not talking about God in any conventional sense. What Einstein meant is: is there any freedom in the way the laws of the universe are constructed in the form they take? Or is there some principle that we are still struggling to find that would inevitably lead us to a single description of physical

reality

and that is an important question because we have developed over the course of the 20th century the quantum mechanics of 21st century general relativity?

Quantum field theory Much more speculative string theory of course, but I can't help but mix it up and as we get deeper and deeper into understanding the fundamental laws of fundamental mathematical equations in the way we normally frame those laws, Two questions arise. that come to the four number one: we have the fundamental laws, of course, that is vital and we all agree that it is a continuous search, a continuous process, no one would say that the laws of today are the laws, but even if in some time in the future we would have them. fundamental laws a key question will be why those laws and not other laws and whether we can show that there is a unique set of laws that meets a very basic set of criteria that would certainly help answer that question or perhaps we will be forced to do so . go in the other direction and say well that's not why this law instead of that law maybe all possible laws in some sense are out there and we as particular observers of the world only have access to or are only aware of a certain portion of

reality

that is okay. described by the particular laws that we have developed, that is one possible direction that all of this will go and Stephen Wlfr has been developing ideas that perhaps it is fair to say that intertwine and intertwine all of those interesting scientific and philosophical ideas and our goal today will be Find out exactly where Steph Wilf's show is right now and where it might be headed, so let me bring in Stephen Wolfram.

Hi St, how are you doing, great to see you, nice to see you too and where you are physically at the moment. Concord Massachusetts, oh, are you home, yeah, great, um, so I've been working from home your whole life for years, yeah, long before it was cool, you know, speaking of which, I just have one question. Quick completely irrelevant to our conversation, but someone asked me the other day and I didn't know the answer to all your efforts, Wolf of Research Mathematica and how many people work with you. I mean, what is your total employee base?

Yes, it's about 800 people, a pretty small operation. Yeah, and it's, my basic principle has been to automate as much as possible, so we've been doing that over the years, you know, what we can do with just 800 people is, you know, a lot of leverage from a lot of automation. and it's You know, I built the tools that we've been developing for so long partly because I wanted to use them myself and it turns out that you know, I've managed to switch between doing basic science and building technology about five times in my life so far and it's pretty interesting. because you know you build a lot of science, you see what tools can be built, you build the tools and that allows you to build another level of science and exemplify the things that I've been doing recently in physics. they are the result of multiple rounds of this kind of science and technology iteration, so to speak, it would be fair to say when it comes to the beginning of your career and, again, maybe I'm not framing it the way you, please, would feel free to correct, but would you say that your goal at some point was to delve deeper into computing and find the fundamental ingredients that underlie all computing in some universal way that would allow you to create a system like Mathematica that would be widely applicable because you weren't trapped in no particular computational framework, but rather the ER was the basis for all calculations.

Yeah, I mean, you know, what I thought I was doing at the time I did it, is not what I understood I was doing for decades. later, but you know, projecting back, uh, when you knew that I had studied physics when I was a teenager, etc., and uh, partial physics and cosmology and things like that, and you know, one of the things that's always a challenge there. is doing the calculations and I wanted to automate that and then at some point, it was late 1979, back in the day, yeah, I thought I wanted to make it as automatic as possible to do the types of calculations that I and other people want. do and the question was how do you do that and I suppose, from my life in the Natural Sciences, the most obvious thing was to try to find The Primitives, the underlying type of atomic elements of computation, but what I mean is projecting backwards For Speaking, one of the things that is a challenge is that what is computationally possible is much broader than what matters to us humans, yes, so, what you know, the first step is how to represent what is computationally possible , that's actually pretty easy, much more challenging is building the bridge. from the way we think about things to what is computationally possible and that has been one of the activities of my life: to build a computational language, a notation for computing that is convenient for us humans and that can take advantage of this type of reserve power in the computational universe and that's how it has been, that would be my way in modern times of explaining what I've been doing for the last 40 years, yes, I'm sure you know that.

I think a lot of people are watching this or will see this. Subsequently, they've made use of the tools that you've created, but maybe for one or two in the audience who maybe haven't let me point out, from a personal perspective, it's not just about the tools that you've provided. of mathematics in particular allows us to do things more easily, allows us to do calculations that we wouldn't have the audacity to even contemplate doing without having the tool in place and I'm thinking specifically about years ago when I was working on string theory. that was trying to use something that I fortunately played a role in developing called mirror symmetry to compute what is known as a series of rational curves on certain cabial manifolds.

The calculations we could set up, but without a tool like Mathematica it would be virtually impossible to go ahead with them, but you know, with what we had we could set it up and press a button and sit down and the machine would just spit out number after number after number calculating exactly what we were doing. looking for, so more, yes, yes, yes, it is but the beautiful thing is that what you are willing to try to undertake can be profoundly affected by the tools at your disposal. It's a very non-linear process between the two. Yeah, I mean, the way I look at what I'm trying to do is give. people have a way of thinking computationally about things, it's kind of like analog in mathematics was before like 500 years ago or something like that, when you wanted to talk about mathematics you just used natural language words, yeah, and then people started to invent the mathematical notation of plus signs and equal signs and stuff and then everything became very simplified and you could start to have a mathematical language in which to think mathematically and that is, you know, you have algebra and calculus and then all the mathematical sciences and so on, and I know what I see as our mission is to provide that kind of computational notation, that kind of computational language for thinking about things computationally and I think when we say what it means to think computationally about things, it's kind.

That is, we define rules about how things work and then we look at the consequences of those rules and that is a very general type of activity and the question of what types of rules are the ones that, for example, relate to the types of things that We humans care, that's kind of the art of Designing a computational language is being able to represent those kinds of things, I mean, but can you imagine, we'll get into this when we move on to physics in just a moment, but just talking more generally, you know at some point we have a conversation with some extraterrestrial civilization and we ask them about, do you know how you go about trying to quantify or think more deeply about the nature of the challenges that reality presents to you?

I think we have the same computational foundation as us or it's just a quirk of our evolutionary process that we think about the world in a particular way and that gives us a slice of the computational universe. Yeah, I mean, this is a broader conversation. but I think this whole kind of idea about, you know, can you think about the world being built out of rules? I think it is a very general idea. I think the way you package those rules and the way you perceive them and think about them. in terms of those rules, that's pretty specific and my tendency is to say, for example, if you say well, we're talking about aliens, you know the alien intelligences, etc., my feeling is that there are alien intelligences around us, you know the climate of famous way.

It's supposed to have a mind of its own and I think in many real senses it

does

, it's just that that mind is not well aligned with the kind of mind we have if we look at the neural activations in our brains. Following physical laws, they are doing what they do, if we look at the fluid dynamics in the atmosphere, they are following physical laws, they are doing what they do and the question is: can we say that what happens in our brains is, in some fundamental meaning? more sophisticated than what happens in the atmosphere, I don't think so.

I think the problem is that what happens in our brains is a kind of perception of this notion of intelligence, it's aligned in a particular direction, it's different from the alignment of you know fluid dynamics in the atmosphere or anything else. , so I tend to think that this question you ask, will aliens, so to speak, have the same vision of computing? I think at the lowest level it's kind of things work according to rules, if you ask what it would be like what is the internal narrative of the aliens, the internal narrative of the climate, the internal narrative of our brains, those are different and you know That this is the essence of what we do when we do science is we try to take the natural world as it is out there and we try to put it into a narrative that humans can understand.

I mean, that's what we say when we say we're making a theory for something. You know, what's out there just

does

what it does, the question is do we have a way to manage it within our minds, within our way of thinking about things, to talk about what it's doing, so to speak, but um, but in that sense. I can't help and I hope you're willing to sit for a while because I'd like to continue with this just for a moment and then get to the real topic of our conversation here because I don't think they're separating I actually think there's a deep connection between all of this, but you talk about internal representation or internal experience and I think that for most people that is what distinguishes our type of calculation from the calculation of time, right, I don't think most people.

I mean, Thomas Nagel had this famous phrase that if you want to describe Consciousness you should ask yourself what it's like to be that thing, you know what it's like to be human, we have a reasonably good understanding of that because they're in that category, what's it like to be a bat? Does a bat have a world of inner consciousness? And we can certainly imagine that the answer to that question is yes, although it is very difficult to put ourselves in the mind of a bat, but when it comes to the weather, I think most people would resist the idea that there is a what it is like. the weather.

Do you think there is a what the weather is like? Yeah, I mean, I think you know if Look, all any of us know are our own personal internal experiences, yeah, even extrapolating to experiencesharsh words from another human being is just an empathetic extrapolation, and by the way, when you imagine what it's like to be a human being with a different personality coming from a different time in their history or with a different kind of educational or cultural background, etc., it's not completely trivial to take your internal thought patterns and project them and you know, if you start thinking about, you know what it's like to be. a computer, you know, you start to think about what the experience of a computer is from the moment it starts up to the moment it crashes is like a human life, it remembers certain things, it has certain experiences, maybe someone you know plugs in a peripheral to some port, it has all kinds of horrible things like this. is that, as you trace it, it's a striking external description and strangely similar to the kind of things we feel and I think it's one of those things where, for example, you talk about the laws of physics and there's this question .

We're projecting what's really happening in the world onto our particular kind of internal representation of what's happening and you know you were talking about the inevitability or not of the laws of physics, one of the things that's been a big surprise. for me in recent years is that, as far as I can tell, there is in some sense a complete inevitability of the fundamental laws of 20th century physics for observers like us, in other words, if we were not the way we are, if we had different characteristics, we would believe that the world has different laws than we think it has, but what has been a big surprise to me is that it turns out that, you know, you could say well, it depends on the fact that? we have two eyes it depends on this it depends on that it depends on two very big things and a subsidiary thing depends on the fact that we are computationally limited observers of the universe that is, there are all these calculations happening in the universe, but to get it into our finite Minds we need simplify it a lot, that's one thing and the other thing is that we believe that we are persistent over time, that is, even in you know, we will talk about it.

In the real models of physics that we are in, you know, our models are made up of different atoms of space at each moment in time, but we believe that we have a single thread of experience that passes through time and there is a third thing in reality that is We are of a certain size in relation to the underlying things in the universe, surely you know that we are not, and the fact that, for example, to give an example close to the type of things that I think you have thought about . You have long known that our notion of time and space depends a lot on how big we are.

That's the fact that you know we look around and see that you're 10,100 meters away and the light comes to us from that distance. quite fast and that means that in a microSC a millionth of a second we will have seen what is around us, our brain processes things on time scales of more like milliseconds, so for us we see the world as a series of types of frames This is what space is like, we say it's out there because we see it all at once, but right, if we were, for example, if we thought a million times faster we would replace our brain, the brain hardware with, ya You know, digital electronics.

We will think a million times faster, we would have a different point of view because then you will know that the scene we are in, if we were in a scene of the same size, would reach us in a shorter time compared to time. it takes us to process it we think of space more as time presumably if yes, yes, I mean, it's like that, I mean, there are these aspects of the way we are as observers that make us perceive the world the way we perceive it. For me, the big surprise in the world has been the very technical fact that the great laws of 20th century physics, statistical mechanics, second thermodynamics, you know, general relativity and quantum mechanics, as far as we know, do not they seem optional; are inevitable characteristics of observers like us, this is what observers like us will have to see as they try to understand what is in the world, which to me is remarkable.

I mean, maybe we'll talk more about this, but you already know the idea that it's conceivable. not simply introduce the laws of physics as if it were so, but to be able to say that at least for observers like us the laws of physics as we have discovered them are inevitable now, in that sense, again and again, enter into some of the details, but to characterize the phrase, observers like us have made reference to some qualities, yes, they have made reference to computational limits, they have made reference to the time scales on which we process information, for example, being very slow.

Compared to saying the speed of light, that seems very general to me, it's almost hard for me to imagine a non-computationally limited observer. I'm not sure what that Watcher is. Now I would say that this, of course, is a limitation of I guess I'm a computationally limited observer, but can you imagine what a computationally non-limited observer would be like? Well, entire universe. I mean, is it the universe has me? No. I'll give you an example, yes, so you know on this. room there's air there's a bunch of gas molecules a bunch of gas molecules they're all bouncing around essentially they're all calculating what they're going to do next they've got these ions there's a little calculation going on for us there's no way we can I can imagine following all those gas molecules, of course, because we are computationally limited.

If we weren't computationally limited, we would say: I have all those gas molecules. I know what they're going to do. I know it in 5 seconds. this particular collection of gas molecules that were here will end up there. I'm able to do it and then I wouldn't say, for example, oh, it's just a gas with a certain pressure, etc., I would say, I say, my friend, this gas molecule is going to do this particular thing well, but we might be computationally limited. and still be able to do it, it's just that the limit of our computational processing would have to be much higher than it currently is. that was the right distinction, I mean you don't need to be computationally unlimited to do that, you just need to be able to assimilate a type of data set that is beyond our ability, well no, but you know you can and this is where of this becomes m, but you know, if you start thinking as you increase the size of what you're looking at as you increase the amount of time that passes and so on, very quickly you find yourself in a situation where if you agree any limited size, you will explode your abilities, so to speak, so this is the question of whether it is like that, for example, if we look at the long-term future of the universe, you know one thing that sometimes disappoints people is, oh , you already know. eventually there will be a heat death in the universe, you know, all these processes, all these organized things that are happening in the universe, everything will just come down to random, random heat, you know, a kind of movement of molecules that are completely people say that's terrible, that's the end of everything one can care about in this kind of random soup in the universe, but if you weren't computationally limited, you wouldn't think that, of course, you'd say that every molecule I know where it is. it has all the history that you can read aloud, so that's an example of what it would be like to not be computationally limited.

You would surely have a very different vision. Now you know something that What I find very challenging is to think about what it's like to not be like us, so to speak, yeah, and you know, I've tried, for example, these days. You know, we have AIS that are well aligned with the way we humans think about things. You know, I did an experiment recently. You take an AI that has been trained on a few billion images that we humans have posted on the web and it can generate images. So you say you know, show me a picture of a cat and a party hat, yeah. and it will generate something that is typical of what we humans would consider to be a cat and a party hat, let's say, okay, that's what a concept that we humans understand now, let's move into a kind of conceptual space that we can do within .

This AI you can say, let's move the conceptual space away from the cat and party hat concept, let's move to what I called interc conceptual space, the space between the concepts that we humans have named, what's out there, well, you can have the AI simply. Generate an image of what is out there. What's out there is something that looks like an image. What does it mean for us? Yes, right now, practically nothing. They are just some elaborate patterns. A complicated image. What is it? Well, we can talk about it. a little bit, but it doesn't really resonate with us and if we go beyond that and say let's modify the AI, let's change its mind so to speak, let's change the way its mind is built and say what it thinks, then a cat thinks and a hat for the body it seems like you get these weird images that are very non-human, they're very, like they start to show us a little bit what it's like to be a mind that's not like a human mind, yeah, right, and and it's, you know , it is for me, it is a great exercise of imagination that I don't think I have managed to master.

I will say one thing though about the kind of concept of interconnected space, you know, one of the things. That's actually very interesting, it's even the most basic way of exploring conceptual space. The concepts that humans have come up with represent one part in a trillion trillion trillion trillion trillion trillion. I have to go on with a bunch of trillions of what is possible, yes, and then we wonder: will we ever get there? And what we realize is that that's what the progress of science and the kind of arc of intellectual history is all about. We are gradually expanding our domain in a kind of space. of Concepts, we are gradually expanding the paradigms that we think in, etc., it is a slow process, but that is the journey that we can think of as the Journey of Science and Mathematics, and these other types of areas, yeah, sure, look when I started as a physicist and since then I have changed, changed or matured.

I don't know what the right word is, but when I started life as a physicist I thought that what I was engaging in was a search for the abstract, objective laws that govern star formation, Big Bang black holes, and things like that. , and many of my colleagues still talk that way and feel deeply that that's the burden of Being a physicist or scientist in general is about I've shifted to a place where it feels much closer to what you're saying. I've shifted to a place where I see what I do, you and my colleagues as trying. describe in the conceptual space in the language that makes sense to us as human beings what is happening out there, I no longer feel that the equations we write for general relativity and quantum mechanics are operating there, which is certainly the bias what i think had when I was a younger person, if I understand correctly, you're saying something pretty

simple

: the goal of what we do as scientists is to find the description that makes sense to us, as these computationally limited observers with brains that operate on time scales say. much shorter than the speed of light and so on to describe what's out there, but do you think there's something out there that's operating?

According to some laws, rules, whatever we want to describe, that is in operation, of course, we are part of what is out there, so I don't mean to put the two out that way, but is there some fundamental set of rules that Is it really working or is it about finding the set of rules that do a good job of describing your perceptions well? so I think there is something that exists out there we call it a ruad and it is something strange and very abstract, it is not surprising that it is something abstract because it is something very conceptually big, what is it, is it essentially this object? the interleaved limit of all possible calculations, that's a very strange kind of concept because you usually say what a calculation is, well, you set up these rules, they could be the rules for the way your computer's microprocessor works, you enter some input What do you leave? the thing goes crunchy, crunchy, crunchy for a while and then you get the result which is essentially the process of a single calculation.

One of the things we can ask is well, let's say we change the rules for the calculation and we do the same thing we feed some input we get an output we have different things happening let's imagine we can see what happens with all the possible rules all the possible inputs one Of the things you say right, how could you conclude anything from that thing? It has a rich structure, especially since two very different inputs and maybe even two very different ways of calculating slide rules can end up producing the same thing, so you get this complicated interlocking object that represents all the possible calculations that are executed, let's say even from infinite time and looking at the kind of interlocking structure of allthese possible calculations, it is a very abstract thing, one thing is that there is only one, it is unique, it is the case that, in a certain sense, once you have this idea of ​​describing things according to rules you inevitably get this object, it is the limit of describing everything in terms of rules, so it's not like you can say oh, I'll have ruad number one, no, actually I'll choose ruad. the number seven on the other hand said that there is only one and it is as inevitable as you know once you have defined what you know are two and two and the pluses, etc., it is inevitable that 2 plus 2 equals 4, it is not a thing where you get to say you know it could be that way it could be a different has to be the way it is so just do I understand that space well enough and maybe how it relates to things that have been articulated before, you know. , when he was a student of Robert, a philosopher at Harvard, he had this idea.

What he was developing at that time was called the fertility principle, you know, it was like all realities were out there in some way. I don't know if he framed it precisely enough to draw a relationship, but um, max tegmark, you should know. at MIT had this idea that the larger reality is all the possible mathematical structures, they're just out there and we're aware that a small portion of it is your ruad according to those ideas, who knows, I mean, I know what the ruad and it's a very nice and precise thing, I have to say you know it's interesting because one of the things that happened is that we got to this place doing computing, physics, science, etc., and we ended up with these constructions and concepts that are deeply philosophical, almost theological in some ways, and in many cases, they kind of come out, you know, in the last 300 years or so, science has been at the forefront, but some of the things that they end up talking about are things that that theologians have talked about for centuries, but they have been immersed in modern science, so you know what happens with what we build with the ruad is that it is a nice, precise, very well-defined thing, so how do you related to?

I mean, people have asked me. U, the individual, let's see. I mean, I have to keep inventory of all the things people ask about. Is it related to XYZ? Because by the time you have this object, it's meant to be the underlying thing of all possible reality, so to speak, it better be related to a lot of things, but the answer is no, I don't really have a great way to approach that, I think the the concept, I mean the thing that, um uh, you know you're asking what's out there and one of the things you have to realize is that this is kind of a brain twist, since you were alluding to that no exit. there we are, yes, it is everything and we are part of it, so the question is really how an observer within the ruad is made of the same material that makes the ruad, what does that observer perceive about the ruad and what is the answer.

The fact that there is something reasonable that one can say about it I consider remarkable and the point is that, you know, to an arbitrary observer there is not much you can say, except to an observer with these limitations that we seem to have because it is the way there are a lot of things you can say and what's really exciting is that the things you can say seem to line up almost perfectly with the great things we read B to say in 20th century physics, which is super amazing? I mean, it's not what I thought. was going to happen and I think that, you know, this question of how you perceive a thing when you're in that thing is something that we've been lucky with thanks to mathematics. physics we basically have some of the necessary tools to talk about it we understand things like the frameworks of relativity we understand a lot of things about measurement quantum mechanics these are the things that are a kind of raw material that gives us a kind of hope to turn what would otherwise be a sort of vague philosophical concept, you know, into something we can actually do hard science with, so I'd love to get into some of the details, but I wonder if we could really set expectations at the beginning , my expectations perhaps more than anything.

I mean the reason I think it's not even the right word. The reason I have confidence in quantum mechanics, of course, is that I know how to sit down with basic mathematics and if given enough time and computation. power I know how to calculate things like a scattering amplitude or the anomalous dipole moment of the electron, you know, I can calculate things and I know that when those calculations are done correctly they match fantastically accurately with things that we actually observe in the world. I know how to sit down with general relativity and calculate the bending of starlight by the sun just to go back to 1919, so where is your program before we get into the details?

Can you calculate like the anomalous magnetic moment of the electron no, it's not that, but what we know, this is where we are, we can uh, in the case of Well, then we have these three areas statistical mechanics general relativity quantum mechanics statistical mechanics is actually the easiest to talk about maybe We'll talk about that later, but what's the easiest statistical mechanic to talk about. It has um uh, just but, in general relativity, for example, we can calculate, for example, now we have a good calculation of the fusion of two blacks. holes and it seems to agree well with the predictions of general relativity, in fact, it seems to agree quite well with that the method that we have for calculating uh so so normally as you well know when you are calculating something like the merger of two black holes that you are studying , like all these differential equations that represent the kind of curvature of spacetime and so on, and when you actually do it on a computer after you've probably preprocessed it with Mathematica, but then you finally try it and discretize the SpaceTime so you can put it on a computer digital.

Yes, in our methods and we will talk about this in more detail. We start from the discrete underlying structure of SpaceTime and then add to it to see what consequences. that's on a large scale and it turns out that what we've built seems to be a very good way to just calculate what happens in general periods of a day, so, for example, could you calculate? Do you know gravitational waves that say ligo? observed saying from the beginning it seems like yeah, it seems like it's very convenient that black holes oh yeah, we have a nice little video there that that, um, yeah, come on, we can show this, yeah, that's what we're looking at, we're seeing two. very, very small little black holes, close in size to the elemental length in the universe and there they merged and if you analyze this a little bit you will find that there were gravitational waves that arose in that merger and, uh, uh, you know it looks good.

In terms of agreeing with what is predicted from general relativity and what is observed, do you mean that the surface area of ​​the merged black hole is not decreasing? That kind of deal, but you can also look down at the actual ring, uh, and you can look. in and it seems correct and you know, I think this is something that is now being validated much more precisely because people really want to use our models as a scheme for doing numerical relativity. I mean, it's kind of funny because people who say this is a good scheme for doing numerical relativity and for them, if numerical relativity doesn't agree with standard relativity, it's a really bad thing for us, that's really exciting because it gives us a kind of crack through which to see things like the discretion of the space, so in the case of the General activity, we are in very good shape, we have a good agreement with what would be expected of the domains in which an agreement with General is expected and we have many strange effects that we have not yet been able to calculate, what their magnitude should be, how they work, they depend on a parameter whose value we do not know, but we have a lot of original things from the that we will talk. about that, things like dimension fluctuations in the universe, the universe before going there, etc., in the image you showed, yes, you mentioned that the size of black holes was on par with the elemental size, so These are small black holes. little black holes, what sets the scale, over and over again for the audience, you know, in general relativity, you know, we have several numbers that come in Newton's constant, if we include the speed of light, that's a useful number.

If we're doing something that has quantum aspects, we bring in the h-bar from quantum mechanics, put them together, and we get a fundamental length scale called the table length, about 10 to the power of minus 33 cm, a fundamental energy scale, the mass of the table is about 10 to 19 times the mass of a proton, a fundamental time scale, you know, 10 to minus 43 seconds, the iron time, so where does all that come in? Well, I mean, all that goes into, I mean, we, we. probably let me give you a little bit of the status report because you asked for it and then let's start explaining how the model actually works because I think it's, so, you know, general relativity, good check mark, we really have, you know we can.

I really see how things line up with General, but how do those little black holes radiate? Hawking oh, that's a good question, we're, we're just working on it, it looks very promising, but now you're asking and again I have to explain a lot more because what you saw there was a classic image, yeah, right, we actually have kind of a full quantum version, but you know, for the universe, that's the calculation that the universe does for us, it's very difficult to do that calculation, it's a lot of calculation. but yes, in our models there is absolutely what I mean, we still can't say that we get the Hawking temperature and all that kind of stuff.

It is quite promising that we get er equals epr, which we can explain. it's um, it's very clear how the CFT correspondence of ads works in our models, things like that, um, again, you know technical things, we can get to them, how about the singularity, how about the black hole? Singularity, do you have any idea about that? yeah, I mean, well, we should, we should, let's get into it because I mean, you know, because we have discrete spacetime, the world of singularities is a little bit different than it is in the spacetime continuum, so that, for example, topology change is very easy in discrete spacetime and we absolutely see it, so, but, let us know just in terms of where we are, so, overall, in pretty good shape, uh, In quantum mechanics, we can do a good job of reproducing some kind of standard quantum information.

Quantum circuits. quantum mechanics type and in fact you can even take a quantum circuit and you can compile it into our models, do calculations at that level and you actually get somewhat better and more efficient ways of optimizing quantum circuits than we've had before, so that works fine. Quantum field theory, wait, you can make particles in a box? I'm wondering, I mean, can you do the basics? Well, the only thing I understood is that particles are difficult for us, we don't know it yet and we will explain it. how this works, but for us the particles are like if you have a fluid like water or something, you can have a little Eddie on the surface of the water and those are kind of what we think the particles are in our models and figuring out. what is the spectrum of particles such as electrons, photons, quarks, etc. in our models.

No, we haven't been able to do it yet. We know the way to do it, but it's technically complicated and we're just working towards it. um, I guess what I mean is that one of the amazing things about these models is that you usually make a model for something and compare it to experimental data. Oh wow, that part of the model doesn't quite work, let me modify the model. to fix that and so on, now we're in, you know, three and a half years from now and we have no adjustments, I mean, there's not a single thing where we've said, wow, you know the model doesn't agree with this. , let's change the model, it's a very hard job to go from the underlying model to the actual observable features of physics, but what's just amazing as far as I'm concerned is that, as I say, we're at zero adjustments, yeah, you know , there's no oh wow!

You know, the thing predicts that we have a different number of dimensions than we do, etc., etc., there aren't any. I mean, having said that we don't know why the universe seems to us right now to have three dimensions, we can't derive the number three or three or big three dimensions maybe what that is, yeah, big three dimensions, right, and we know that we can talk about what the issue is, so one of the things that has happened is a lot of different approaches in mathematical physics like you know, causal set theory, spin networks, high triangulations, I guess so, dynamical triangulations, all of these are things that we can see are limits of our models, the one that still exists is string theory, which I am quitesure that it is also a limit of our models, but that mathematical physics has simply not been done, it will be very nice when it is finished and the really interesting thing about seeing this correspondence with the existing work in mathematical physics is that you know that they have been achieved a lot of things there and So we can connect the things that have been achieved and learn more about our models and also provide interesting foundations for what has been done in other areas of mathematical physics.

I mean, for example, in causal set theory, for example, people would just say, oh, there are events that happen in different places in spacetime, it's always been a little confusing why relativity would work given that there are events randoms in different places in space-time in our models, there are events in different places in space-time, but they are kind of algorithmic generation and the way they are generated inevitably gives relativity, so you can talk about things using the type of theory of the coal set machinery, but now you have a basis that says there is not the big problem that they used to be and you can know how to work from there.

Briefly, you were about to. say something about quantum field theory, so could you finish that? Yes Yes. I mean, as I say, we can... the next challenge that we're working on now is to do the same kind of thing for quantum field theory that I've been able to do for general relativity, which is to start from the underlying model and just do a lot of calculations and being able to reproduce features of quantum field theory and it's pretty clear what the roadmap is to do that. It is technically difficult. I ask you a quick question about that and again we're going a little non-linear here, but that's okay, our audience is used to that.

To me, quantum mechanics is quantum field theory in dimensions 0 plus one and quantum field theory as you normally describe it. so just quantum mechanics in let's say a signature n comma a reality that you know n more1 Dimensions why do you know from what I understand you're going to describe dimensionality? It's so fluid in your approach. I would have thought that starting from quantum mechanics. to quantum field theory it's like there's no problem, so this is what happens and now we're definitely jumping around here, there's a there when we think about quantum mechanics, we're thinking about these many possible paths of history and that is.

The defining characteristic of quantum mechanics is that no definite things happen, but rather there are many parts of the story and we can simply observe certain aggregates of those parts of the story, so in our models the

simple

st case corresponding to a species minimal type of quantum information, quantum mechanics looks at these different paths of history and simply says: take the entire universe and say there is this path of history for the entire universe, take the entire universe, this kind of thing, it's Well, that's a waste. way of representing things and it doesn't have to do with the spatial degrees of freedom of what's happening if you try to do that in a less wasteful way and say no, I don't just mean there's a complete, you know, complete state. of the universe and it branches off to another whole state of the universe, but you want to go in there and say well, it's actually just this little piece of the universe that's different between these two branches and you're dealing with space, which is the thing.

You already know that, what is happening is that most of the space has not changed, there is only a small part of the space that has changed, it is technically more difficult to do that and that is why there is a distinction between the type of mechanics quantum in the kind of quantum information style of doing quantum mechanics and this, you know, quantum field theory, where there's a spatial extent that you have to deal with and, actually, we're talking about scattering processes and particles that are moving. I mean, for example, in our models, maybe we get to this. the idea that movement is possible is not trivial;

In other words, the fact that you can take a thing and move it somewhere else and it will still be the same thing isn't obvious, is it? I mean, you know, in traditional general relativity, if you're near a space-time singularity, you know that any material object you try to move there will be destroyed and probably not the same, but in our models the possibility of movement is something that you have to derive and therefore we can derive it for things like black holes, we need to figure out what other things we can define it for and those other things that we can define it for, those are particles basically because particles are the identity carriers that They survive through time and through space, right, and that's it, but, you know, finding what they are is just, you know, technically difficult, so, so, can you now take us further back to the beginning?

This is a nice chaotic summary, although it may have been due to my randomness. you ask and I apologize for that, but if we take a step back now, where does it begin? I've done some but certainly not fully read up on the topic, but presumably it starts with just a collection of nodes. and Rule, yeah, go ahead, what is it? Do you know what the universe is made of, so to speak? Yeah, and you know that's been something that people have discussed since ancient times and you know if it's made of discrete atoms, is it something continuous?

That was something. There has been much debate, what is matter made of? Well, we discovered years ago that it's made of discrete molecules. We definitely know that light the same way. You know, we can think of it as being made of photons. Space, on the other hand, we have tended. To assume that it is continuous, we have assumed that space is just some background and that we can put things anywhere we want in space. The starting point for our models is that space is not just something in the background. Space is actually made of things and fact.

Everything in the universe we can think of as features of space, and in fact there are many equivalent ways of thinking about this because it's a deeply abstract thing, but I think it's the kindest way we talk about it. about what the role of science is, you know, turning what's in the world into narratives understandable to humans, the best one I know to explain this is the following to just say what space is made of, it's kind of discrete atoms of space, which are things that the only thing you can say about them is that they have an identity, they are distinct from each other, and then the other thing you can say is how those atoms of space relate to each other, so In other words, we can say that this space atom is related to these other two space atoms.

What do we get when we have this whole great collection of relationships? We can represent that as a kind of graph where we say it's like a friend network what is the friend network of space atoms, so to speak, and maybe in our current universe there may be 10 to 400 space atoms, we're not sure, but it's a very large number you're talking about in the observable universe. presumably in the observable universe and the entire path is much larger than that, yes, the universe as we have sliced ​​it and so on, but then, we have this giant network that has, you know, these.

These atoms of space are related in these ways and so, and that's what we think that everything in the universe is made of and, for example, the particles are these black holes, for example, they are particular regions that have certain characteristics that correspond to the The way black holes work, particles are these things that are like topologically knotted pieces of that Web, we think they have some kind of continuous identity, so that's the idea of ​​what the universe is made of. I find it interesting as a historical matter that, in the early 20th century, many people believed that space was discrete.

In fact, I keep discovering that a lot of those famous physicists that we both know, you know, I keep discovering. you know, Heisenberg thought that space was discrete B thought that space was discrete Einstein thought that space was discrete, it was um 1916 Einstein has this nice letter where he says that in the end it will turn out that space is really discrete, but we don't know it yet . you have the tools necessary to see how that works, uh, I mean, I would understand it well for all the other luminaries that you referenced, because the discretion of reality was emerging with a vengeance through quantum mechanics studies.

The Einstein Photoelectric Effect 2. I know about discrete natural life, but I had no idea that he really thought that when it came to SpaceTime, I would love to watch it offline. I'll get the reference, yeah, yeah, sure, no, it's a um uh, but, you know, so what. What happened at that time was that no one could get their discrete models of space to agree with relativity, yeah, and um, you know, and I'm not surprised, given what we know now, that it required a few more layers of thinking. paradigmatic, so to talk to be able to achieve something that would not be difficult to achieve, but okay, in our models what is in the universe is this giant network that represents a kind of state, state of the universe, state of space, everything in the universe it is a characteristic of space, so the question is what happens with time? and you know, one of the things that was kind of like, you know, people have tended to say that space and time are the same kind of things and I think Einstein actually thought that Minkovski was who he was, but accepted Minkowski's opinion quite quickly and quite rightly, but it was Makovski who said that we can create this SpaceTime object and it has very nice mathematical properties etc. but but then I don't think space and time are the same kind of things.

I think they are very different types of things. I think we can think of time as a kind of inexorable progress of computing, so time is this thing. where we are applying the rules and we continue to apply them, we continue to apply them that successive application of rules which is the progress of time and then, in the case of these models, what happens is that you have this giant network and you have these rules that say that if you have a little piece of network that looks like this, rewrite it into a piece of network that looks like this, you just keep doing it over and over again and the time is defined by those progressive rewrites now that so then the question is when do you do that for a very large network and you do it over a very long period of time, many rewrites, what is the aggregate, what do you see in the aggregate, it's like asking, you know, these molecules are bouncing around. on a microscopic scale what will be the type of large scale behavior of the system and we know that in the case of molecules that bounce, they are fluids like water, etc., that is what you get from this type of large scale structure, so The question is, what do you get from this graph?

It's actually a hypergraph that we tend to use, um, and you know these rewriting rules, etc., what do you get? What is the large scale limit? Well, with several footnotes we can talk about, the answer is grand scale. The limit is Einstein's equations for space-time and are you talking about the vacuum equations? No, no, it's the full equations, but you have to say what's right, so just to complete that, I mean, remember I'm saying everything in the universe. is made of space, so when we get energy, for example, and matter, they are just features of space and we have to characterize what it means to have a portion of space that represents matter, energy and mass, etc., and it turns out that this is Something really surprised me: energy turns out to be basically the density of updates that occur on this network.

I mean, there's a slightly more formal definition which is a flow of causal edges through space like hypersurfaces, but basically it's the number of updates that happen in the network. characterizes the energy density associated with that part of the network and then we ask questions like, okay, here's an example of something you can ask, that is, let's talk about gravity, how does gravity work well, so you know we can . Talk about if in the absence of gravity you know that things move along shorter paths, so you know we have gd6 shorter paths from here to there on a graph.

It's pretty easy to define what the shortest path is because it's just from each node you have. You follow one edge until you reach another edge, so you have this the shortest path. Now you ask in this model what happens when there is a lot of activity in the network and it turns out that this diverts the shortest paths by which the gd6 are changed. This activity in the network and the way they change is exactly according to Einstein's equations according to the standard laws of gravity and that is so. Can you abuse me with a couple of concerns that immediately come to mind?

So worry. Number one is again, you know, we'll talk about various levels of sophistication, so I hope the audience will bear with us, but you know, in general relativity, as many in the audience know, we describe spacetime continually asa manifold in which there is a distance function. the so-called metric, yes, and normally, as we describe it, we try to solve Einstein's equations to find out what the metric is, the distance function in that space, but of course we could always say that any metric is a solution to the Einstein's equation simply. by defining the right side and as what comes out of the Einstein tensor for the given metric that you put in a metric as trivial as a solution to the Einstein equation from that perspective, the only time it stops being trivial is if you have a independent definition. on the left and right side, but if for you everything is a SpaceTime feature, do you have a separate definition on the left and right side or is it just a correct topology?

So the fact that I'm describing what energy that independence is, so to speak, and also the fact that, for example, in that black hole simulation, those are vacuum solutions to Einstein's equations, there's not a kind separate from separate place where we are identifying, I mean, you know where, subject to particular. boundary conditions exactly yes, that had to be set up with very particular boundary conditions, but I mean to give a kind of sketch of how things

emerge

, so we have this giant network and the question is how do you extract something that looks like space from that? continuous.

Well, the first thing you have to do is this network. It just tells how all the atoms in space are related. It doesn't tell you, for example, where. the atoms of space are not anywhere yet, so the first thing you have to do is start defining, you know what the effective dimension of space is that this represents, so you can do that by saying start at a particular position in this lattice, go to all the nodes that are a distance one away from that in terms of just following an edge on the graph, oh, and calculate the volume or something like that, calculate the volume of the basic GD ball, the volume you get to if you go R steps to the right and as it grows, if the parent term is R, the power D, then you can identify d as the dimension, well, then you look at the subparent term and there is a correction in the art of D growth and that correction It's proportional to Richie.

Scala curvature, that tells you that that correction tells you that you know a measure of the curvature of space correctly, so by doing things like that you can see how to unravel this ultimately very discrete structure that you can unravel. It's kind of like the standard Continuum stuff and you get to um, you know, Richie's turnbuckle, for example, comes out in a nice way. Again, it's a little more complicated because you're dealing with a space-time Richie tensor. We're dealing with these cones of light that you have to build in this kind of space as a function of time and so on, so you know there's something technical now just to explain the technical complexity of this when you talk about a variety. it's a kind of representation of geometry where you look at it microscopically microscopically it's just geometry in the way that uid defined geometry it's the British space uh in our case you look at it microscopically microscopically there's just a hypergraph down there there's no underlying Ukian space and that's why we wrote We have to build our own new version of Geometry, we call it for now infr geometry, where we start from this underlying structure and we have to build the features of differential geometry from that and we're kind of like Midway.

By doing a pretty rigorous kind of development of what it's like, you know what the geometry is like when it's not based on a manifold based on UK space, and by the way, that answers questions like what's the curvature tensor like on three and a. semi-dimensional space nobody there is no literature I I I would love it if you told me that there is literature on this, we don't find literature on the subject, I mean, this is not something that people have ever had, you know, had reasons or ability to explore. Yes, analytical, we can continue analytically.

You know, sometimes it's necessary to do that when certain integrals aren't well defined, but I don't think we've ever really dealt with it. No, I'm talking about quantum field theory. You know, we do a little bit of dimensional. you know four minus dimensions of Epsilon and so on, but in the case of differential geometry that is not what has been explored, here is work number two, if not, yes, yes, please move on, so Einstein spent 10 years writing. down or find out what Einstein's field equations ultimately gave to the world in November 1915 when we look back at what Einstein wrote in retrospect, of course, it's pretty obvious that it had to be once, once that you're dealing with curvature and once you're dealing with the energy boost as described by this particular symmetric two tensor, there's only so many things you can put on the left side, so you could actually put them all there and just label them Because of the number of derivatives they have, they keep the ones that have the least number of derivatives, then they simply impose some conservation equation and that takes you to Einstein's equation, so what I'm worried about is taking those equations out, maybe I'll find it less impressive. than it should. be and maybe you can get me to the point of being really impressed because there's not much that could have been because presumably you're looking for the lower order part, we could talk about higher order fixes as well, but there's not much to say. it could have been besides armuu minus half gunu r on the left side, yes you're right, what we didn't know is how to go from a level lower than that, in other words, it's like saying, you look at the fluid equations, you know What are a bunch of gas molecules or liquid molecules or something like that, what is the aggregate behavior of those things, in that case there isn't much else either, it could be the Navia Stokes equations are somewhat inevitable given certain characteristics, but in that case case was not trivial, even given the Navia Stokes equations, they were known long before we knew molecules existed, but knowing that what is underneath is a bunch of molecules bouncing around, is something worth knowing and that is all. you're right that to me also Einstein's equations seem obvious um you know, it's kind of uh um and in fact the same thing happens with quantum mechanics in our models.

Quantum mechanics also seems obvious, but the fact is that uh you know the fact that it has been possible to derive this from something, first of all, from a lower level, just this kind of discrete machine code and, even more so, this ruad object, which is a necessary thing, the fact that it is possible to derive these things from That to me is quite remarkable, yes, and let me explain a little bit about how to think about this. Let's talk about what I said was going to be the easiest of the big three. 20th century theories of physics, that is, statistical mechanics, okay, so you know, the big result of statistical mechanics is the second law of thermodynamics, the law of entropy, increases the rule that says the law which says that if you start systems in a sort of ordered state they will tend to degrade to disorder or you know if you have a bunch of molecules and they are all going in the same direction and doing mechanical work pushing in the same direction, things are likely to happen. are randomized and hot-spinned, yeah, and that's right, that's the second law and people have asked, could you derive the second law?

In fact, Einstein, interestingly enough, something I just found out, you may have known for a long time in 1905. Einstein wrote these three amazing papers that established you know, the quantum mechanics of relativity and Brownian motion, yeah, um, uh, and the size, the size of Adam's moon, but it's actually four. I like to count the four, but anyway, go ahead, okay, that's interesting. The question is what were the articles that Einstein wrote in the three years prior to that moment in 1905, the answer is that Einstein wrote articles trying to prove the second Ro of therapeutics and the articles were wrong, they were philosophically interesting, they were still largely measure to Boltzman, who had been sort of the person who was originally pushing the idea of ​​a sort of molecular theory of gases, early derivations of the second law and so on, yeah, and Einstein thought he could derive the second law, no. was successful, it used the same kind of almost philosophical approaches. to science and applied them in these other areas and you know surprising results, so to speak, that's just a footnote to the story, yes, but you know people believe that the Second Law would be derivable, that is, If you knew the mechanics of molecules they would do it.

It would be inevitable that you would have this tendency towards randomization. It's very confusing, like if Boltzman, for example, had his theorem uh H. H, I'm sure he said, oh, well, if you have these molecules bouncing around this amount H, which is good, basically, the entropy will increase. over time, well, H will decrease over time, the entropy will increase over time, but the problem is that you put the input and the output if you look at it more closely, of course, yeah, right, exactly, I mean, you know how mysterious it is. This is that if you look at the individual collisions of molecules, they are reversible in time, yes, there is nothing you know, you look at the little movie of the billiard balls bouncing, you could run it backwards, you wouldn't know the difference, yes, of course, but taken together, when you look at all those gas molecules, you can absolutely say that things go from ordered initial states to disordered final states, yes, and the question is why do we believe that and and the answer is because we are observers of the kind that we are and and That's how to think about it.

I think it's because we are computationally limited observers, although in principle there is something we can think of as a kind of encryption process. We start with the simple initial condition and then do everything. this calculation and that is mashing that initial condition into something that seems encrypted and random to us, if we were computationally sophisticated enough we could say, hey, I understand what that is. I can reverse it and see that it comes from that simple initial. condition, but since we are computationally limited we cannot do that and, in fact, the second law phenomenon is a consequence of something very computational, it is a consequence, okay, so there is one more piece that I have to explain, but before get to that detail and I hope I don't mislead you, but there is something that is confusing in what you just said, maybe you can clarify it in half a second, so I agree with you that this being that did it does not suffer the limitations that we have, would see all the molecules and all the trajectories and would be able to immediately reverse it and recognize where it came from and so on, but that being would also have the ability to say hey, there's a more useful way to think about this too.

I'm not going to erase my ability to see all the molecules in their trajectories, but coarse grain seems to be a useful tool to be able to have a language that talks about molecules. simply fill the room rather than the trajectory of each individual molecule and for some discourses it is useful to have that approximation of what course the being would still be able to take and that would not necessarily be linked to the level of detail that would place the second law of Thermodynamics is out of business, that's true, but they know the problem and this relates to the march of the paradigm, so to speak, there are things that now we would say oh, it's obvious that you describe this aspect of the world. this way, but you know, looked at with different instruments, you know, looked at without a telescope, looked at without whatever, we would just describe the world differently, yeah, and you know, I think that's the saying that, oh yeah, you could add this and say, oh, well.

This is more or less what happens, the computationally unlimited being could tell why you would want to do that. I can discover everything. Why would I need to look at this added thing that is irrelevant? It's like there are a lot of situations where you know. as you know, in the practical world, where we get more and more data about things that one could have said, oh, I don't know, take some medicine, you know, and find out that you know you could have said, oh, you know, you you look pale today. okay that we can convert that in modern times to this is the precise metabolomics that we can measure of this and that and the other and you know and then the oh you look pale today doesn't seem like the most relevant thing to say. to speak and I think it's hard to project that you're absolutely right, there's nothing stopping an entity that can do this unlimited calculation from deciding to add things like that, on the other hand, it's, you know, it's The fact that we're taken adding things the way we do is a consequence of the way we are for sure, but you know, I should explain another very important piece, which is this phenomenon that I call computational irreducibility, which is something that, I mean, I started to discover in the early 1980s, actually, and it's this, one of the insights that you get from mathematical physics is that once you have the equation, you've solved the problem. more or less true, I wantTo say that the equation is like I have it now and I can calculate all the consequences of that when you're in the computational world, that's no longer true in the same sense that you have some rules. you start running the rules, you say because running the rules will take so long that you can't do it faster than running the rules correctly and this is the fact that you can't go ahead and say and the answer is it's going to be X, you have to run every step and see what happens.

It is a new feature of the computational world, a little different from what we have ever understood in the mathematical world. I mean, by the way, it's not like people haven't done it. I understood this intuitively, I mean, you know Newton, for example, he famously said, "You know, um uh, when you talk about a lot of planets in the solar system, you know he says that now he has the equations, but he has to calculate the movement of all these". planets is, I think he said, if I'm not mistaken, beyond the capacity of any human mind, he thought God could do it, but no human mind could do it, so he already had this idea of ​​a kind of irreducible computational difficulty of working out the consequences of things, but we see it much more extreme in these computational environments and that's because of the In some ways, that's what time is, that's the difficult aspect of time, so to speak, that time, the passage of time means something because it's an irreducible calculation, you know, we can live our lives and do all the things we do and we can't just jump ahead and say and the answer will be 47 or something like that.

We have to live the time to... It means something to live the time, so to speak, so that we can lack free will, but we never can. predicting what we are going to do so that everything turns out well, yes, exactly, I think that is correct, but, in this case of the second law, what is very critical is this underlying computational irreducibility, if that were the case. But for the fact that it's hard to figure out what happened, if it were still easy, then there wouldn't be any, we wouldn't say oh, it seems random, we'd just say, oh, it's obvious, you know, I can, I can see.

It's this, it's this interaction between the computational irreducibility of what's going on underneath and our computational limitations in our ability to observe things and that's what gives us in this case the second law, now you know that once you've understood those principles. It's pretty obvious that the Second Law has to work well, but before you understand those things, I mean, if you read, I spent a lot of effort unraveling the history of the Second Law and the incredible confusions that developed because people didn't do it. did. understand these kinds of essentially computational principles because it was 100 years too early to understand those things and yeah, you know what's cool and you always know it's very encouraging when you have some model and you figure things out and so on if you can keep going Come back to the end and You say it was obvious, it's a big victory, you know?

If you say, no, you know, you have to stack all these stones and exactly this way and then eventually you'll get this big tower that's a lot less. more satisfying than if you say well, I should have been able to see it a long time ago, for sure, and that's more the situation we're in now, having said that you know when you ask what the experimental implications are, etc. You know what dimensional flu is, the consequence of dimensional fluctuations, that's a lot of hard physics work, so let me give you an example of how it works, so in our models the universe probably started in an infinite dimension and gradually became smaller. it was cooling.

To be effectively three-dimensional, it's like we had this initial network where everything was connected to everything and then gradually it became more like three dimensions, where you know things can be very far apart, so to speak, but when you say early, just kind. have an idea here, do you imagine from the beginning that there is like a primordial node or is there some primordial configuration? How does it start? Oh yeah, well that's a funny thing in street life because, um, okay, so yeah we're okay. there is a ruad in a sense it has no beginning but in a sense it is that you have to talk about it the object itself is just uh, what can I say? it's like a circle where the beginning of the circle is, it's like we're actually I'm going to draw the circle on a piece of paper, so there's a beginning, but conceptually there's no beginning, yeah, it's just it's and it's the same thing here. and where we need to understand something about this is that we as observers embedded in this street, we can be in different positions on the street, so let's talk about that in terms of ordinary space, so we have physical space and we have a certain vision of what what is happening in the universe, our view of what is happening. in the universe it depends on where we are, you know we are on this planet in this galaxy, etc., etc., if we were somewhere else, we would have a different view of what is happening now more abstractly on the street, we have a mind, so to speak. is somewhere on the street different minds are indeed in different places on the street Different minds attribute in some sense different sets of rules to what happened in the universe there is a notion of movement in the street just as there is movement in the physical space just like when we move to a different place we remain the same there is a similar kind of concept of movement on the street we can say there is this entity and there is another entity nearby and these two entities will have a kind of correspondence points of view of what's happening, you know, when we talk about some kind of extraterrestrial intelligence, we can think of that as more distant things, things on the street, it's like all the humans are grouped together in this little one, just like we we're crammed together on this little planet, so to speak. we are also grouped in a small region of the ruad, all our minds are concentrated in the small region of the ruad when we go to meet your cat or dog or something, it is a little further away as we go to the weather for example .

It's much further away and communicating across the street translating from one place in Ral space to another is not as easy and so you know there's not a good alignment between these different things, yeah, but I think in uh. uh, let's see, you were asking about the beginning of things, yes, so if we stick to the physical space for a moment, can you describe for us how in your approach a space similar to ours can be constructed? And I and I saw an animation that that can help give people yeah, yeah, sure, we can look, let's see what this was, this was number one, you can try it, so tell us what we're looking at here, okay, so this is just a possible beginning of our universe, so if we start it again from the beginning, we will start from a single node and it will keep rewriting itself by building new nodes and new nodes etc., and this is, you know, a number ridiculously small of effectively the time at the beginning of the universe, so to speak, and there is a very simple rule for starting with a node and what exactly to do next, and you continue long enough and you will get revenge for this particular rule, you will get something which has A kind of set that looks like a continuous space, like if we had enough molecules bouncing around, it would look like a continuous fluid and here you can apply your technique to work on the dimensionality of space like you. you're saying you started giving it a node, consider all of them one edge move or two edge moves, look at the volume of the space you fill and that way you get a notion of dimensionality, so in this particular case the answer is approximately 2.6. and then do you imagine you know?

I don't even know if this is the right language in the approach you're taking, but if we think about the Big Bang, yeah, it starts with a No? I mean, what's good, like this, then? You can, that's why I started explaining about different places in Ral space etc, in standard relativity we're talking about different frames of reference, different ways of dividing up what counts as space, what counts as time etc. yeah, the same story in Ral space, so you can, it's the same kind of thing, there's a view of the universe where it starts with a node um and that view of the universe can be a useful view of the universe for a mind of one. particular person.

Well, it is not the only possible view of the universe, it is possible, it is a frame of reference essentially a Ral frame of reference, which is the coordination of the universe in that particular form, in that particular form of a kind of Ral space foliant of that particular way. of choosing frames of reference and that is reasonable. I think that's a reasonable way to start talking about things. It is not the only possible way, just as in relativity. You know, you could choose a different coordinate system, etc., and you would have. a different kind of narrative description of what's happening, although in an underlying sense it's the same thing that's happening, so it's a bit slippery that way now it seems again.

I have to admit that I am quite naive with the questions I am asking. So if you want to correct my questions, I'm perfectly fine with that, but from the image you showed us of the animation you showed us, it seems like the notion of expanding space seems quite visible and intuitive. It's a reasonable way. of of of of articulating in some crude sense of continuous geometry what we are seeing happening. I think so. I think so. I mean, I've been wondering about that kind of expansion of space and how to think about that and it certainly resonates.

To me, you know Einstein wrote down his equations and said, "My God, these equations imply that the Universe is expanding. I better add this cosmological term that you know as a correction to prevent that from happening, but in reality the universe is expanding." and you know that I." I have to say that we have the obvious conclusion that the universe is expanding because more nodes are created, but there is something stranger possible that is happening, which is that as time goes by you are generating. there are more and more nodes and in a sense the universe is getting finer and finer, our length scale is fixed but the universe is getting finer and finer and in fact one of the strangest possibilities when you ask is the discrete or continuous universe, for example one.

One of the strangest possibilities that we still can't exclude is that if you say, "Okay, I'm going to measure, I'm going to measure the elemental length, and I'm going to take a certain amount of time to measure the elemental length." It could be that by the time you've made that measurement, the universe has subdivided to the point where that measurement no longer makes sense, so we don't do it. I don't think we fully understand yet what you know. notion of the expansion of space and so on, to be a little more technical, one of the things that we have been very interested in, you know about standard relativity and cosmology, etc., you know Robertson Walker Freeman Robertson Walker, whatever Names have been added to that since I started studying lra L Matra deserves a place on that list.

I know it has a good story, right, but anyway, so, um uh, in any case, that's an aggregate description of the universe that simply says that the universe is about this big and we're not going to assume that everything in the universe is homogeneous. We'd really like to expand that to include Dimension as a dynamic parameter in addition to curvature. uh, size of the universe we want to include Dimension and I think we'll understand a lot more about how this works when we have that kind of aggregate Dimension change equation for the aggregate evolution of the universe, so presumably I'm you the quality of the dimension change stabilizes quite a bit quick, otherwise it's hard to imagine how we get stars and galaxies, at least in our little corner of this picture, yeah, yeah, well, I mean, okay, so one of the things I suspect right now is that the universe is only three-dimensional for observers like us and that, and I still don't know what attribute, you know, observers like us have all kinds of strange attributes, you know, we assume that we are, you know that we are persistent in time, we assume. that in some sense we are located in space, we assume things about free will, for example, we assume all kinds of things that seem so obvious to us that we don't even identify them as an assumption, but I suppose that some aspect of the way we We exist as observers, it makes us analyze the universe is three-dimensional.

I think I understand what you're saying, but of course we have all these very precise experimental results in terms of how the gravitational field decreases with distance and you know. and all of these are consistent with, you know, a three-dimensional space, but you would want me to interpret them as something that an observer like me would necessarily measure because of my own constitutional makeup, yeah, because you're measuring, you know, what are those measurements? those measurements assume things like okay, let me start taking those measurements apart, okay, you're right, you have material objects, distinct objects, you think you can put those objects in arbitrary positions.each other, that's an assumption about free will, you know.

There are a lot of assumptions being made and you know that the experiment you're doing is an experiment worth doing, but it's an experiment with all kinds of things that have been put into it and you know that in terms of what we expect. for the universe, you know that we expect there to be fluctuations in dimensions, that is, you know as a whole the universe, we do not know why there are three, but to observers like us the universe will appear three-dimensional, but we would expect that there will be fluctuations in places that will remain of the early Universe where the universe was about 3.01 dimensions, let's say, and gradually calmed down to being three-dimensional.

We don't know why it's three-dimensional, as I say, but a big question is how long do they last? Dimensional fluctuations last and we are starting to do simulations to try to find out. The obvious thing from a practical physics point of view is whether they lasted until the cosmic microwave background formed and whether we could detect them in aspects of the cosmic microwave background. Of course, we don't know the answer to that yet, but it certainly is and we don't even know what a dimensional fluctuation in the cosmic microwave background would look like. I mean, the most extreme it would be, yeah, this is a good physics question, right, this is where I know there's some sort of underlying model, but there's a whole big tower of real physics that needs to be built to connect it with experimental observations. and I know that one of the things that is a cautionary tale from history, you know if the bending of Light around the Sun in general was measured in 1616 in 1916, as it was originally, it could have been Einstein had the wrong results at the time and it was only later, so you know, 1914.

I guess he was probably right when the teams left. went out to measure the 1911 prediction or something like that, which had the wrong equations, they did the measurement, in fact, they arrested those astronomers when they went to Russia, that's why they confiscated their equipment, but you're right, if they had. measurement Einstein would have been in the awkward position of crying wolf in 19 a little later because his first prediction would have been false, true, but you always know that going from an underlying theory to a measurable prediction is always a challenge and you know, one of the things that is a bit of a strange possibility is the phenomenon of gravitational lensing, where you know you have something huge and you have a beam bent on either side and you can see, you know you can.

You know, you get these two different images of the same galaxy from different sides of the gravitational lens. Now the possibility is that if there was fractional dimension gravitational lensing, which could happen, we don't know if this happens, but it would be cool. If that were the case, the image of the Galaxy breaks up, so to speak, into many little fractal pieces and if we could get the transformation right, we would simply tell you that our friends at the Space Telescope take this image of the sky and apply this. Transform and you'll reconstruct those pixels and you'll get images of galaxies that would be kind of a fantasy version of what you know how you would detect a dimensional fluctuation and you know it's going to be like that.

It's going to be harder than that, right, but that's the kind of thing we like to be able to figure out now, you know, one of the questions that comes up in all of this is: are there a lot of parameters? Are there many knobs? and switches and so on in these models for our models there is only one which is the elemental length what is it? we have two space atoms and they have a relationship between them what is the translation between that distance defined by that relationship and the thing that we measure with metric rules, etc., I mean, it sounds very string theoretical in that sense, I mean, the The only parameter we have, of course, is that you can frame it in many ways, the tension of the string, the length of the string or the square root of alpha Prime however you want to frame it, but it's really this parameter that you put in the story and, for your particular case, I guess you just leave it as a free parameter, well, we've tried to estimate well, so I don't know, we have a very dumb estimate, that's how you got the 10 to 400 that you mentioned at the beginning because it seemed to me that it would have said more like 10 to 400. 200, if you were thinking about the lengths and volumes of the tables, the observable universe, yes, then our elemental length is certainly significantly smaller than the length of the tables, so you know more like 10 Theus 90 meters instead of 10 minus 34 meters, but why where in the world, do you even understand that I have the idea that that's pretty much what happens?

In our models there is a factor that occurs, which is the number of essentially parallel story threads that exist in the universe and that number is quite large, you know, maybe it's 10. to0 or something like that and essentially that number is that you end up dividing the table units, you know, for that kind of number and, for example, one of the mysteries in the table units is why the table energy is so large, you know the table energy is the energy from lightning or something that seems very little, you know. Elementary. I like to think of it as the dough of a Moe powder, but yes, I'm sure they are similar in some ways. in our models, elemental energy is actually very small and, you know, this question of how big is elemental length, elemental length, elemental time, elemental energy, they're all related by standard table units, so there's really only one parameter now you know that parameter, it's a question of are we going to be lucky that that parameter is something that can be measured in our lifetime, so to speak, you know, when people were talking about molecules, It might have been that, in theory, atoms and molecules exist, but you know that might not have been the case, that there was a phenomenon like Brownian motion that allowed people to say yes, we can actually see the effect under the microscope. those individual molecules because of the way Brownian motion was discovered, I think in the 1830s. long before its interpretation revealed the fact that it showed that individual molecules were crashing into safe things, so the real question now is, for example, can we detect an analogue of the Brownan motion in space?

Do you know what Brownan's sign is? movement of space that will be a kind of analogue of the discretion of space and I have a guess that is actually a very new guess, so it's a uh, it's still very fresh from um um and it leads me to a rather strange aphorism that was In the 19th century, when people were studying heat, no one knew what heat was, so people invented this idea of ​​caloric fluid. Sure, what was it, you know the heat must be this fluid, yeah, right, that would be what would flow from this place to that, okay, now we have a phenomenon that you know in gravity, which is things like dark matter, we have this, you know, something that causes gravity, but it's not matter that we can see, see what it is, so to speak, and then my My aphorism is: you know, dark matter is the caloric of our time and what I want What that means is that people say what dark matter could be.

What is matter? Matter is made of particles. We are going to look for particles that form this dark matter. In the 19th century people said what could be heat, it must be a fluid. Let's study the properties of this fluid. I guess my current assumption is a very new assumption, so it's like this is the first time I'm mentioning it. this assumption anywhere other than um uh, you know, so to speak, it's um uh. My current still unresolved assumption is that dark matter is the kind of spacetime analogue of heat and what do I mean by that?

This means that the structure of space, like heat, is actually the microscopic movement of molecules. In a sense, this thing that produces gravity but doesn't have the characteristics of standard matter is a characteristic of the structure of space and, in particular, when you look at, for example, that simulation of black holes, yes, what you could see in the The bottom line was the fabric of the fabric of space which was a bunch of space-time heat, space wouldn't exist if it weren't for The fact that all the atoms of space interact in these ways, etc., that's what makes it space be the question: is there an effective temperature, so to speak?

You know, is there some kind of activity? level and so on and so on and I think you know this is the question what are the effective equations for the one you know for the structure of that kind of space-time heat, so this is a this is what you're hearing this is It's an idea very crude, although it is a crude idea, it is an interesting idea. I mean, obviously, one thing I would like to emphasize to the audience is that there are indirect signatures that Dark Matter follows the rules of matter, it just doesn't reflect light. or emit light, but I agree that we have been looking for Dark Matter particles for a long time and haven't really been able to find any that we can play by the rules of the matter.

What you are saying is that it is gravitational. effects yes, do you know that it has gravitational effects? Okay, I mean, it has inertia and stuff like that and the way it exerts or doesn't exert pressure seems to be consistent with our understanding of how ordinary matter exerts or doesn't exert pressure to For example, it's a little bit more than that, but yeah, I can't sit here and no one can say what dark matter is, but how would you distinguish dark matter and dark energy? So is dark energy also a feature of the structure of space probably I mean you know again this is what we have is kind of you know, we have a paradigmatically different way of thinking about space and knowing what the consequences are. that's not trivial um and uh you know I think one of the things that they gave, for example, that we had a paradigmatically different way of thinking about matter, that is, that it is made of molecules, so one had ideas like that the Heat could be a microscopic feature of the movement of molecules, etc., and so on.

Now that we have a different paradigmatic idea about the structure of space, we can ask all these questions and, for example, do you know what questions I guess are the most pressing as far as I'm concerned? Do you know how we can really Do you know how we know what we're talking about? Do you know how we get, for example, strange and completely unexpected phenomena that we go out looking for and they are actually there and that's it? Which is when you feel really good about theories is when I mean. What made me feel really good about this theory is that everything seems to line up, it seems to fall into place, it's like I don't understand how this thing works and Now, actually, one thing we should talk about is quantum mechanics because yeah, I'd love to get to that, but before we do, GNA puts a bit of pressure on you at that point, so a moment ago you showed us an animation starting with you.

I know a very simple structure like a node and presumably behind the scenes there was some rule to update it. Take this node and replace it with two nodes that are connected in some way, etc. Do you have a very specific rule for updating a graph? what is the rule that gives rise to, you know, features like general relativity on some aggregate scale, no, and that's the point in a sense, this is what I was wondering, okay, we're looking for the rule and then a day you could say God, we have the rule and we hold it up and say this is the rule for our universe and then the next question is why did we get this rule and not another rule and that really confused me for quite a while. until I understood this idea of ​​the ruad, which is the idea that all the possible rules are being used and that we are simply seeing a portion of that right, but I am saying that we beings, computationally limited beings whose processing is so slow compared to speed is There is a rule that we beings somehow focus on from the language you are using, yes, I mean, my assumption is that there is a class of such rules, so for example , let's make the analogy in fluid dynamics, yes, the fluid equations.

The dynamics works for both water and air, although the structure of water molecules and air molecules is completely different and that is the same, here there is, we already know, I mean, there are many different underlyings. rules that inevitably for observers like us have these characteristics, so now, if you ask, you know, depending on the type of question you ask, if you are asking questions about air and water, there are certain detailed questions that you could ask that will distinguish the molecular structure of those. two materials and similarly here's something where presumably as we become more precise about what kind of observer we are, we'll focus on saying oh, it's this rule that we're attributing the behavior of the universe to rather than that , but that's You know, I think what we've observed is that there are, you know, there are at least broad classes of rules that have thischaracteristic, just as there are statistical mechanics that lead to the type of behavior that we. that we expect to see, so to speak, for example, the rule for that image of emerging black holes is not the same rule that I used for that other image, a slightly different rule, but it's simple, they're both incredibly simple rules um and uh You know, the one about black hole mergers could have been the same rule, but then we would have had to do it, as you correctly note, setting the initial conditions for that is not trivial, since it is not trivial for Einstein's equations either. and it's just that you know the technical difficulty of doing it was made easier by choosing a particular rule to look at instead of that other rule, but again, so as not to get too far into the weeds, are there any particular rules that say? give it Einstein's equations and say a higher order derivative expansion where maybe you have curvature squared or curvature to the fourth term where another set of rules doesn't do that, I mean, it's that level of precision between eventually, yes, eventually you will . understand it as if you look at fluid flow and you look at, for example, hypersonic flow, eventually you see down to the molecules and then it matters what the molecules are like, but we can't distinguish them, you know, at a general level. relativity that we can't distinguish when we look at higher order corrections and that, um uh, you know that by the way, the disappointment about higher order corrections is the scale that determines the importance is the elemental length, yeah, when we look at you're looking at or elelemental energy or anything else, so if we're looking at something that's 100 orders of magnitude larger than the elemental length, those effects are pretty small, we kind of hope that in CRI iCal black holes, you know where it is the the effective kind, I hate to call it momentum because it's all, it's all so bogus about black holes, the spin of black holes, but you probably have a better way to explain this, but, um, you know the parameter that essentially determines. the rotation speed of black holes yeah, um, you know, at the critical point, uh, you know, at the J is equal to m critical point of the black hole, uh, what happened in our models, which is pretty nice , is that, um, essentially, a part of the universe is hanging. a causal thread to other parts of the universe, so if you went above that, you would essentially break a part of the Universe, um, and what happens right at that point is that the kind of part of the universe that could break is attached only by a small number of causal edges, so there is a possibility that there is a kind of discretion effect that will manifest itself in that case, for example, in a kind of clumps and the gravitational radiation emitted by black holes in that state. things like this, um, because it's like having a gravitational microscope where you've separated things to the point where you're seeing the underlying structure of space, but again, these are All you know is the question of when and when it comes to effects like that, yes, they absolutely depend on the specific rule you're using, yes, but when you look at the black hole in general, you know the merger. of two large black holes makes no difference, just as it makes no difference in the case of flow dynamics, right, um, so, after we've gotten past Einstein's equations in general relativity for a while, if we move on to quantum mechanics.

You know, quantum mechanics is, of course, in many ways a neglected or confusing topic compared to the pristine beauty of the general theory of relativity. It certainly took many hands over many years to put together what we are finally going to celebrate, I suppose. 100th anniversary in 2025 2026 you already know the Schrodinger equation Heisenberg matrix mechanics wherever you want to date it, but there are a lot of things in quantum mechanics today that many of us, well, I must say, some of us don't particularly feel comfortable, we have the problems of the measurement problem. In quantum mechanics we have the question of the interpretation of quantum mechanics, so when we talk about quantum mechanics, obviously I'm deeply interested in hearing your approach, but also maybe from the beginning you can tell us if that's the case. give us some idea of ​​the questions that are still rising between the eyebrows of quantum mechanics thinking about the foundations of quantum mechanics around the world.

Yes I think so. I mean, you know. I feel more comfortable with quantum mechanics. I almost think I understand quantum mechanics. A fanatic friend of Dick's who worked on quantum mechanics all his life, he was very fond of saying that no one understands quantum mechanics, yes, and I think so. I'm getting close to the point where I can say I really understand quantum mechanics, so let me explain. What I think I understand, I mean you know what we're talking about, you know what the universe is made of. It's made of this giant network and, uh, this network is being updated and little rewrites are happening, one of the things you can ask.

Is there a rule that says how to do these rewrites? The question is: is there a unique way these rewrites can occur given a particular state of the universe? And the answer is no. There are many possible arrangements, many different possible ones. You can say I am. I'm going to do this update from time to time I'm going to do this update I'm going to do that update first and so on there are many different orderings for those updates, yes, and each of those different orderings definitely finds a different microscopic story for the universe, so in a sense what you have is that you can have one state of the universe, you can have two different possibilities for how to update it, they lead to two different branches of History, something less obvious, it can also be something where you have two branches different. states of the universe and when you rewrite them they end up in the same state, so you can have this merging and branching structure that you get and we call these things multi-way graphs and in fact it turned out that after we discovered that they are relevant to physics, we have been finding multigraphs everywhere and, in fact, the very fact that they seem to describe some aspects of physics we have been able to export ideas from physics to many other fields such as metamathematics. like distributed computing, maybe like biology, all kinds of areas, so it's been really interesting to see this structure of so many things can happen.

Many things can happen. You have emerging branches. Give a very simple example: you play a game like Tic-tac-toe. and you start with a board in a particular state, now you can make a move or you can make another move and you can build this graph, this game graph of all the possible moves you can make in Tic-tac-toe and eventually I know someone wins , someone loses, but there is this graph and sometimes you can make different moves that end up with the same board state even though the moves were different, so it's kind of a picture of many branches of time that are happening in the universe and then the question about the idea of ​​quantum mechanics ends up being uh, you're looking at those many branches of history and when you ask a question like well, okay, so we can, we can go in different directions in quantum mechanics, but one question is what does the observer do in quantum mechanics, what does the observer do well, what you have to keep in mind is that the observer is embedded in the system, so the observer.

The mind of the observer is also branching and merging, so quantum mechanics becomes this strange story of what a branching and merging mind believes is happening in a branching and merging universe and this is where this idea that persistence over time becomes critical because if we were simply flowing through all those ramifications and fusions we would not have a vision of what we are, we would not have the idea that we have a defined experience over time, but as soon as we We claim that we are having a definite experience in time, we have to combine many of these branches of history and the fact that it is coherent to do so is not trivial, we have to show that that is the case and the extent to which we see the effects That there are many branches is essentially the essence of seeing that there are quantum effects, it is a very rough picture.

I mean, I can't help but chime in, as I suspect many of you watching this would also think and once again disabuse me, it feels like Everett, it feels like the many worlds of quantum mechanics is just that or is it something different, I don't think so. I think the biggest thing that those guys didn't have was fusion and I think fusion is really important, no, no, you can definitely merge, I mean, yeah. Do you know the double slit experiments and are you overlapping the different trajectories? I think the fusion is definitely part of that story too, but no, I think well, I don't know this, I'm always really bad, you know, okay.

My way of talking about other people's theories tends to be this: either I really do the story and try to understand in great detail what really happened or I think I have nothing to say and this is a case where I really haven't. history made. so I'm not really sure, but my impression is that the kind of popular many-worlds version tends to be the kind our Consciousness might flow into one of these possible branches and it's kind of arbitrary which branch we're on. and that's why we see things probabilistically, that's not the picture in um again, it may not be fruitful to analyze this, but I think many edans would say that our Consciousness itself divides and flows along different trajectories and , in a sense, the probabilities, which is a very subtle question, arise because in some way there is a greater measure, a greater weight placed on our Consciousness when observing one outcome versus another, there is great controversy about how that is defined. measured and we know how to really operationally make sense of the probabilities. in a universe where everything happens, but yes, I think that would be closer to the spirit of an Ever Edan, yes, but I think maybe the difference here is that we are talking about a kind of Observer as an extended object. in what we call gill space.

The observer spans the individual mind encompasses many different branches of history and therefore it is not so and the individual mind that believes it has a single threat of experience spans many branches of history and is having to let you know is having to enforcing coherence conditions to say yes, it's really true that there's only one experience threat and it's not, it's not trivial to set up all those coherence conditions and make sure they work, so to speak, how? do that, I mean, how do you enforce that consistency? It's just from a rule from the outside where you say I need to impose an interesting question, okay, so this is um uh, we don't know all this, in fact, I'm just one thing.

What I'm writing now is about what I call Observer Theory, which is an attempt to have a sort of idealized version of what an observer does, just as things like touring machines are idealized versions of what computers do well. and the fundamental thing that what observers do is equivalence, you know that there is all the complexity of the world and the observer is taking a kind of summary of all that complexity in the world and putting it into a finite mind which is basically what you look at. all kinds of different observers and it's not trivial, so for example in the case of gases you can say that an observer could be a piston that is measuring the pressure in the gas and there are many different particular molecular impacts that could occur, but the only thing that matters to the piston is the sum of all those impacts and how the piston will be pushed and it is a matter of physics that the piston has a much more rigid object and, although every time a molecule hits it, it warps A little bit there, so you can, but the big idea of ​​observers is that they equate things and it's a little confusing because in quantum mechanics the big oh, I measured that bit, that qbit or whatever, it's a lot more.

There are different types of measurements, I really think of two types, one is things that add things and the other is things like scales where it's heavier on one side or heavier on the other side and a lot of what's done in the style of quantum information from quantum mechanics is more like scales than the kind of aggregate thing that people do when they extract the chemistry of quantum mechanics and say yes, we really have a water molecule that actually has this shape even though quantum mechanics talks about a lot of different ways, which is more of the aggregation type of measurement, yeah, this is the question of what, um, okay, what is the measurement dynamics? um, in our models, there's certainly an underlying Dynamics to measure measurement cost, so to speak, we don't really know how it works, but in fact, I'm literally in the section that's on my computer is called observation cost, so which is um uh the um um uh, but itum, you meet more people.

What we're doing is you know some of this is very paradigmatically similar to mathematical physics, some of it really. connects to mathematical physics, but a lot of it doesn't do it a lot it's more like distributed computing you know mathematical logic uh you just know computer experimentation things like this and it's something paradigmatically different um and and I would also say that you know, this is what It happens to me having spent 40 years building tools, the tools we have are nice, you know, LED optimized and efficient, and there are a lot of things where it's pretty easy for me, given those tools, to jump pretty far relative to what they are. people. they used to do in the kind of steps that they take when doing mathematical physics and so on, so that lets you know that there are a lot of extraterrestrial things that are possible because of that and I think that lets you know in a sense.

As time goes on, the tower we're building gets a little taller and it gets a little harder to know that when people get involved, we do summer school. and the winter school on this project and you know, it's becoming a challenge to fit what we know so far into a few weeks of master classes and that's, uh, you know, I think that's kind of it, but you know . You know, the more people we can get involved, the better at this point. I mean, one of the frustrating things is that there are a lot of experimental physicists who say we have a telescope, we have a particle accelerator, you know, we would like to look. for something unusual and interesting just tell us what to look for and we're still in the situation where we still don't know, hey we've been in that position in string theory for quite a while so you see but this is why that we need to make the right bridge to string theory because we want to make use of everything that you have discovered, maybe you will find what we have discovered useful.

I think one of the things that has excited me about this project is that, for example, I said there will be, you know, people said what are you working on, I say Fundamental Theory of Physics, people say, oh, that It doesn't sound very practical and I'm like, yeah, you. I know it could have applications 200 years from now, um and the surprise for me is that I was wrong in saying that there are applications for distributed computing now because the model that we have of the structure of space-time is basically a model that you can imagine . as events happen and so on, and that's, and thinking about that as big distributed computing, so the ways that we have to think about SpaceTime now become ways of thinking about ways of thinking about distributed computing, now we're starting to think about programming in a certain frame of reference, things like this, so we're importing, using the fact that we have a common formalism, we can start importing hits from physics into other areas, so for me Surprise, there actually seems to be some pretty short-term applications not so much on the physical side of this but the bridge that is made to physics from the kind of things we're doing, yeah, well I can make you a promise right now for what worth it, you calculate the electron to muon mass ratio correctly and I'll stop everything I'm doing and and the work that is GNA is challenging, give me something, you know, I have that, um, you know, the moment when we can see what , um, uh, um, you know, uh, it's, you know, getting 206 is, um, it's, uh, you know, I m I'm not counting on that being anytime soon.

I have to say that some things about these models have just fallen into place much more easily, like the idea of ​​what energy is. I thought it was going to be long. I thought all this was going to last. Maybe we could talk about what happens in the first 10 Theus 100 seconds of the universe, but we would never have things to say about the kinds of things that are most obviously connected to some kind of current. I think the other thing that has been. A very interesting surprise is the fact that the methods we are developing are practically useful for people who do things like numerical relativity.

That is something that is true. I didn't know that's true. I mean. the number yeah, yeah, yeah, that seems to be, I mean, I don't know, we've been Jonathan Gorard, who's one of the people working on this, who's been traveling around talking to numerical relativity groups that are starting to use the software that he's produced that is based on our models, so that's encouraging um and you know, I think that's um um, so yeah, electron muon mass ratio. I'm not counting on that anytime soon, you know? I could get you an E8. I think an E8 would already be pretty impressive, you know, because of the classification of the League's compact groups, again, the small number, in a sense, of truly distinct groups that exist.

I don't know if that would be okay as it might encompass others. but I can't help but make a comment: you noted that in your approach, Rel there may be a relationship between black holes and elementary particles, which would be interesting. I don't know if you're aware of it, but in a paper I wrote with Andy Strominger and Dave Morrison a few years ago, we found something exactly of the same kind that we found in string theory: if you have certain shapes, varieties for the extra dimensions, and you take a particular subspace within it, like a sphere, and collapsing it to a small enough size may look like a black hole for most of that motion, but when you actually collapse it down to zero there is a smoothing of the space in which that black hole settles. becomes an elementary particle, so there is a yes.

So there is a direct link that we found through certain types of warps of the Additional Dimensions that was a direct link between black holes and elementary particles, so again, if that has an incarnation in something that in your approaches, already You know, it certainly stood out. to me when you said that, yeah, that's cool, I didn't know that, I mean, I think, um um, it's um uh, it's funny because you know I knew 1980s physics pretty well, yeah, and then I've been in a kind of uh, you know, it's like a frozen cry for um where I was only partially paying attention for a long time, but no, I mean that kind of result is interesting and you know, that's exactly why one should try it. to make a better bridge between our models and string theory because one could see how that actually plays out in our models and then in string theory see how you actually know this, these additional dimensions. goes to I, I don't know, we'll see, but I think this idea that you're taking out of this hypergraph both a spatial direction and internal degrees of freedom, I think it's, you know, I don't know what their relationship is. that's it, but I think it's going to end up being, you know, I mean, it's just that there's a certain, I don't know, there's a certain tenderness or something to everything, um, you know, to that whole kind of way of thinking about things, But but.

I would like that to be my guess about how it's going to end up working out and that you actually know again you'll know if you know, like I say, I think that's what's really interesting to me because from my point of view, it's not like if you knew there's a kind of sense of where mathematical physics has gone and I just don't think there's been anything, I mean, it's kind of similar, I guess, to what happened in the beginning. days of computing where people had different models of computing and then the touring machines came along and that was a way to anchor a lot of different types of ideas and then you could take these models that have often been harder to understand and you had a pretty mechanistic way of thinking about them and you could build a lot of things out of that, so that's my qualitative view on what I think can happen and it's well, look, it's uh, it's something wonderfully exciting and I think as we all know, if you're going to shoot for the stars, you've got to be willing to fail miserably and therefore you've got to be bold and so you're certainly being bold and stuff.

It would be fascinating to see how this develops, so I'd love to check back at some point with an update on where things stand. I'm also hoping to talk today, but hopefully we'll postpone it for another conversation if you're willing to do the whole thing about AI and Consciousness and Free Will and all those wonderful ideas, but you know that when you have an opening in your schedule in the future , it would be great to connect again. I would be happy. to talk about that, I have this week's fun thought is quantum movies, there you go, okay, that's intriguing enough, so thank you very much for joining us and we'll talk again sometime in the no.

Future too distant, yes, charming to charming to talk. Great thanks. Okay, everyone who concludes this live session. Um, if I'm completely honest and too much information and I end up partly because I have to use the facilities and sit down. Continuing here will definitely be dangerous, but it's been a wild ride in this conversation with Stephen Wolfram, as we expected him to try to find the underlying computational structure of all the things we, as physicists, have been in love with for the last hundred years. . by statistical mechanics special relativity general relativity quantum mechanics Quantum field theory and who knows, I mean the idea that there might be some deeper underlying structure that allows us to understand where these laws come from and also tie them to the fact that we are the observer .

Users who know these laws, it's certainly very exciting, who knows if it will work, but that's the nature of being on The Cutting Edge, so thank you very much for joining us for this live conversation, subscribe to our YouTube channel or subscribe. at worldscience festival.com to stay updated on the various programs we are running about a week ago we launched a wonderful conversation on AI, some of you may have seen it, if you haven't you should check it out with Yan laon Sebastian bubic and Tristan Harris, where we actually describe the inner workings of some of the films that Steve Wolin just referenced and also discuss some of the potential dangers or how some on the show suggested the exaggerated view of the dangers of AI in the future .

We will launch it shortly. I think our next release will be a show on cosmology that we had at our live events in September and please stay tuned. We'll be posting a really wonderful conversation shortly about string theory, the state of string theory. We had at that event with David Gross Ed Whitten Andy Stromer and I really trying to give a sense of where we are, you know, here we are in 2023, these ideas started in 1968, where are we in the process of trying to realize the potential of the string theory? And that program will also be launched in the not-too-distant future.

Okay, I think that's it. In updates again, subscribe to our YouTube channel, go to worldscience festival.com, subscribe to our newsletter and we'll have one of these live. conversations in the future, but for now that's all here from Columbia University my office here in this world Science Festival Live Event Me Brian Green thanks for joining us