Wolfram Physics Project Launch

Well, hello everyone. Thank you for joining me here today. Let's talk about how to get to the fundamental theory of

physics

. I never expected this. If you had asked me even last fall, I would have said I have an idea, but I don't. I don't know if it's going to work and I'm very excited to say that it is working and I think we now have a real path to the fundamental theory of

physics

. I think we've come a long way, we haven't really reached the end. We're not there yet and I'm hopeful that together we can really finish this job, so I want to tell you here where we are so far.

I mean, it's been a long road for me. I became interested in physics almost 50 years ago and started doing physics when I was a child. I used to do physics for a living, but as many of you know, I've spent most of my life pursuing the idea of ​​computing, which is a really powerful idea and is actually what's leading us to the physics that we're going to talk about here today and I've spent my life alternating between doing science and doing technology with the idea of ​​computing and one of the things that happened like the result of this is that in the 1980s I started studying this type universe of simple shows and I discovered something surprising: even when the shows you're watching are very simple, even when the rules you set are very simple the behavior you can get can be incredibly complicated and that kind of discovery set me on a path that It led me to all kinds of things and made me wonder if maybe this is how physics works, maybe there is some very simple rule underneath everything that exists. in our universe that leads to everything we see and I had a definite idea about how this could work back in the 1990s and I started working on it and I actually wrote about a hundred pages about that idea and its consequences in this well.

They're here, this great book that I wrote for him in 2002, but in fact, in the end, as I realize now, I came very close to discovering what we've now discovered, but he didn't discover it then. and I ended up hibernating this idea for a long time doing things like mouth for open language and stuff and I always wanted to come back to this and I was always thinking about it um and then a little over a year ago I had a kind of little idea that gave me a little more and then two young physicists, Jonathan gorod and Max piss Knopf, who came to our annual summer school, got very excited about this and said: you have to work on this and we are going to help you do it and that's what we really It made me start over and we started really working on this last fall and it was a totally amazing experience because, like I say, I've been interested in physics for 50 years and there are all these things. about physics that I knew about quantum mechanics, about relativity, all this kind of stuff and suddenly everything started to fit together, everything started to make sense, we started to realize how everything really works and it was just great and I want to try it and tell you a little bit about that experience here today, really what I think is most spectacular is how beautiful everything is, how all these different pieces fit together in this really beautiful way and I have to say that what we have done would not be possible in any way without all the achievements of physics so far.

I mean, basically, what we're doing particularly takes advantage of the two great developments in 20th century physics, general relativity and quantum field theory, without which we wouldn't be possible. able to get to where we are and the other thing I want to say is that one of the things that has been really interesting is that there have been a lot of modern developments in physics and mathematics and it turns out that a lot of those seem to fit wonderfully with the things that we discover about physics and so it's not one of those cases where it's like something new is coming in, you throw out all the old stuff, not that we have some kind of new foundation, but all these other things that has been working they fit together beautifully and I think it will be something very, very wonderful to see well, so I want to tell you all about it here today and I hope to get your help to finish this job, of course.

The timing of this is totally strange because we are now in the middle of this terrible pandemic. I mean, our company has been doing data curation and modeling and helping where we can with pandemic kind of things, but I thought that, among other things, while we're all stuck at home, people can enjoy a little physics and this sort of thing. of strange historical resonance with all of us because back in 1665 there was also a plague and a guy called Isaac Newton had to leave Cambridge University and go hang out at home and while he was doing that, he discovered the basic ideas of calculus and its theory of gravity.

Well, we may not be able to match old Isaac, but while we're stuck in this pandemic, maybe we can all figure out physics, so let me. show you what we have so far, so what I'm going to do here is go over sort of a basic outline. There's a lot to say, but I'll go over a basic outline and then we'll have a quality check here. today and tomorrow we will do a more technical QA for physicists and mathematicians, followed by one that will talk about more philosophical implications, then on Thursday we will do a QA for the computer science people and then we will start a kind of live. realization flows of this

project

, we really want it to be as open a

project

as possible and as part of that we will be live streaming our kind of work sessions and our discussions with other people about this project and we hope that many of people can participate on them, okay, let me really start here, okay, yeah, you and start well, so let me start, this is the website and you can find most of the things that I'm going to talk about here today in the summer. this website um, there's probably about a thousand pages of material on this website, let me point out some parts of this that might be helpful.

First of all, there's an ad here, it's kind of the basic outline of what it was supposed to be. It's going to be a short ad, it turns out it's about 60 or 70 pages, but it's kind of a summary of what we're doing here. Oops, they tell me I won't show my spoon, so let's check if that's wrong. Wait, boom. there we go, well let's start that again, so I was, I was saying this is our main website that just went live, there's about a thousand pages of stuff here and I let myself go through a few pieces of it, um, here it is. something, um, okay, so there's something from our main announcement, there's another piece that I've written that's about the backstory of this project, how we got here, then there's kind of a technical introduction that I've written, describes with More detail on how the models we're discussing work, then there's an area for technical papers and related material including a couple of articles by Jonathan for people who are first-time equation readers. particularly professional physicists, I encourage you to check out some of Jonathan's work here.

So there's an area here of software tools. One of the things we're doing is creating all the tools to do the things that we've been doing completely. available, they're available today and you should be able to run them on the Wolfram Cloud or wherever you're running the Wolfram Language and that's one way we hope people can start using the bus as a beta. Miss, I will talk more about some. Of these other things later there is a record of notable universe models that we will talk about a little later. I would also like to point out quality control.

We have answered some of the ones that we consider the most obvious. questions here, as questions arise we will try to answer more, but I encourage you to check that out as well. Okay, let's get to the point. How do we think physics basically works well? Here's a sort of pictorial outline of things and this seems a little complicated. I suppose it could be because our universe is ultimately a bit complicated, but this is much simpler than that, this is shown far below our universe, so I'll talk about different parts. I'm going to talk about how we start from this type of very simple rule, how we build a structure that represents space in our universe, how we understand how time works, how we derive the properties of space and time, relativity, special relativity. general activity the theory of gravity.

I'm going to talk about how the different paths you can take when applying this rule correspond to the different paths that can occur in quantum mechanics and how you get this kind of entanglement of states. in quantum mechanics and how that arises in these models and in some sense one of the most spectacular things that happens is that it turns out that relativity and quantum mechanics are in some sense the same idea in these models there is a kind of complete unification of the notions of relativity and quantum mechanics, which is one of the most beautiful things that I think comes out of this, and in the middle of a lot of that stuff there are things about black holes and the quantum mechanics of black holes, um, let's see people.

They're asking me to zoom in a little bit here. I think, unfortunately, if I make an approach, I will. Okay, here we go. I encourage you to look at this for yourself on the web. This is below the visual summary on the website. Okay, let's summarize, let's get started. We know how this works, so what we're interested in is figuring out if there's a rule underneath the universe, what that rule might be like, and if the rule is going to be simple, we know that pretty well. nothing that we are familiar with in the universe will be immediately evident in that rule, we will not be able to see that the rule has a three for the number of dimensions of space that we will not be able to see. that the rule has some basis for some particular detail of the properties of the electron and so on, that rule has to be something that packages everything about the universe into a small package from which all the things we observe must emerge, so does that?

I realized a long time ago that we need that rule to be as minimal and unstructured as possible and we need to have something that allows for the possibility that everything we see in the universe now emerges, one of the things that more or less A characteristic basic of this rule is that we don't have any notion of space intrinsically in this rule and therefore we have to make space out of something and in the end one of the things that is kind of a first surprise is the idea that occurs in these models that space is a discrete thing, space is made up of a bunch of discrete points that are going to be joined together and traditionally for the last few thousand years people have assumed that space is somehow a continuous thing that you can just say I'm going to choose any position in space, it will be specified by a precise triple of numbers, for example, and that is how we define what we can do, that we can choose any possible position in space, what happens in these models, among other things, is that that is no longer possible and instead we are making space out of these discrete elements and one of the other things about these models that I said is that it is very minimal, very little that is placed from the beginning.

In a sense, everything is just space and all the features that we are familiar with about matter and elementary particles and all these kinds of things will eventually emerge as features of space. Okay, so let's talk about what are the rules for doing things in It might seem like okay, so what we're going to talk about are rules that we can represent as rules for hypergraphs or we'll talk about them in a minute, but we can think about them as rules for graphs or networks, etc. for example, we could start by saying let's imagine we have a structure like this and we have these elements, we just number them 1 2 3 4 and then we have some rule that says how are we going to update this using Just looking at the different element patterns here, what are we going to do?

What to do with this in the structure? It's a bit embarrassing to admit, but the basic idea of ​​how these rules work is something that is also the basis of the type. of symbolic programming which is the basis of the language and is actually the basis of almost all the practical things that I have done in computing for the last 40 years and the shameful thing is that I did not realize that kind of the essence of that idea Symbolic programming was exactly what was needed to understand how to build physics and I was working on a slightly different way of setting this up, but the essence of that idea comes from the essence of the idea.

It seems like we need it for physics, although it's just an example of a rule essentially. This is just kind of a more algebraic representation of what I was showing earlier, this rule that tells us how to replace one type of structure in our graph with another. structure well, so let's say we start with a graph that looks like this, then let's try to apply that rule a few times, this is what we get, at first then we apply the rule, we apply it again,again, again and finally I'm getting something like this, so this is kind of a story I first learned in the 1980s: even when the rule is very simple, the behavior and structure you get can be complicated, so that this is an example of what you should do by just running maybe ten steps or something like that with that particular underlying rule, so you can say what's going to happen at the end: We'll run this rule. maybe ten to four hundred times or a rule like this maybe ten to four hundred times and that's going to build our universe now.

I'll say right up front that we still don't know exactly what the correct underlying rule is that we have. It turns out that a lot of what appears in physics and this is one of the big surprises is quite generic and actually quite independent of the details of this underlying rule, so we can already derive a lot of physics without knowing this last ending. underlying rule one of the things we want to find is what that final underlying rule is, but you can, but if we ask ourselves carefully what kinds of things happen with different rules, here are just some examples of things that happen with some of the most common rules. simple possible and what we anticipate is that when we analyze enough rules eventually one of them will turn out to be the rule for our particular physical universe.

I'll make a little footnote on that. I'll explain later why, in a sense, there can be many different rules that represent our universe, but we'll get to that in more detail later. In a sense, I want to say that this is the kind of process of observing everything. these rules and seeing what happens is a very zoological thing, it's like you're looking at all these different possible creatures in the computational universe and you're trying to find the one that really corresponds to our physical universe, but then all kinds of different behaviors can occur and This is what we are interested in seeing.

Well, the first question is how do you get something like space as we know it? So the basic idea is that when you look at the kind of at the large-scale limit of one of these structures, after growing for a long time, you'll have something that, to a high degree of approximation, looks like the space that we're familiar with. , so it's kind of an analogy that one is very familiar with. We have known this for about 150 years, although it was not the case, it had been guessed even long before that something like a fluid like water, which seems continuous to us, seems to flow continuously, in reality we know that, ultimately, it consists of a lot. of discrete molecules bouncing around and I think the same thing is essentially what's happening in space, that space is just a bunch of discrete points, but on a large scale it looks like something continuous to us that we can apply mathematics like calculus etc., it's good.

So how can we see that more accurately? Let's take a look at a very simple particular rule. There is only one of these specific rules and these are the first steps of what it does. If you continue for a while longer, I will find that you start to see it here, it is like weaving this structure, continue for a while longer, you will find that it weaves a structure like this, continue, keep weaving this structure well, when we look at the structure, we can write it down. of making a reasonable assumption that in the end this will be something like an ordinary space, it will be like a plane that is just a mesh that corresponds to a kind of two-dimensional space and that is something so this particular case is very It's easy to see how the thing produces something resembling space, but things are not always so simple.

Here is an example of another other rule. This creates a structure like this. Understanding the limit of this is more complicated. Here's another one. This creates a structure. like this, which again we can recognize is something that looks a little bit like our kind of traditional mathematical object with a two-dimensional surface or something like that, if you project it in 3D and complete it, it will form a structure that looks like this, so What we have underneath is just this discrete collection of points and all we know is which point is attached to which point. We don't know, there's nothing that intrinsically tells us that things should be arranged in like a structure like this, all we know is a kind of connectivity information for this network.

I might mention one point, one point is that the real underlying thing we have here is something called a hypergraph, it's a generalization of a graph where instead of just having points joined by a point joined together by a connection, you can have a hyperedge on the that you have multiple points that are all joined together by a hyperedge which is just kind of a detail of how we're building things. but that is why we will refer to the structure that we believe bounds physical space as the spatial hypergraph. Well, let's say we want to analyze what is happening in a system like this.

How we do it? A question would arise. that we have a structure that looks like this and we look at it with a lot of points to what dimensional space it might correspond to. Well, there's actually a pretty simple way to determine that and its heart works as there's a little bit of math stuff going on, but it's not that bad, so if we think about a two-dimensional grid, let me tell you let's start at a point where the middle of this two-dimensional grid and let's continue towards two points that are one step away. on the grid from the points we already have, let's continue to grow that structure and see what we achieve.

One of the things you'll see here is if we count how many points we get to after we move forward, let's say our steps. we'll find that the number of points we got two is approximately R squared, so squared of R squared, two in R squared, two is what represents the fact that this behaves like a two-dimensional space. just a grid on a plane, if we do the same thing in 3d on a graph that is made to correspond to a 3d grid, we will discover that in the same way we do the same calculation, we will discover that the number of points we arrive at is approximately R al cube, in other words, and that is that cube is what tells us that we have something that behaves like a three-dimensional space.

Well, we can do exactly the same thing in one of these structures. Here we simply start from one point and continue moving forward by two points that are one step further in each of these, away from the points that we already have two and then we can ask the question if we do this, how many points do we reach after we have followed our steps right and we can start to map that out and we can, it's a little complicated because there's multiple things happening where we're evolving the structure, so the structure gets bigger and we're also asking for these kind of dot balls that we're watching, we wonder what happens as they grow, but anyway, when we do, we will discover that these are just curves that essentially represent the log difference of growth, well, their growth rate represents it in a way. of adjusting that exponent and then what we see here is that the exponent adjusts to approximately two point seven or something like that, what that means is that that structure that we had here in the limit is behaving approximately as two point seven dimensions. space is kind of like a not quite three-dimensional space, it's more the kind of thing you'd find with fractals and such, where it behaves like a fractional dimension space but it behaves like a space with a definite or fractional. number of dimensions, if we go back to something like this and do the same test, we will find that in that case, when we measure it, this thing behaves as if it were a two-dimensional space and if we do the same for something like a fractal we can measure it and we will find out which behaves like Oh, in that particular case of that particular fractal, this is an eight-dimensional space of one point five, okay, so this gives us an idea of ​​how we calculate the dimension of the space, well, another question would be fine, we have space, but our universe is not just space, it has many things, it has many particles like electrons and photons and all those kinds of things, etc. one question would be what are those things like as particles, so the basic picture is that there is a kind of background of activity in space where there is this thing bubbling and a lot of connections are changing here, but there are certain parts of it. network that has some stability at least locally and those things are the things that correspond to particles that we were familiar with, so as an analogy of that we can say imagine that this network was just cleaner, everything could just be distributed in the plane. but imagine that somewhere in that flat lattice there is a small piece that is not completely flat and that could correspond to something like a particle in that lattice;

It's something that's locally stable on the network and can move across the network and something like that. maintain your identity and that's how we think particles work, we haven't actually found specific, more complicated particles and rules here and that's one of the things we hope to start working on in the next few weeks, so first thing about space is to know what dimension it is and for our universe right now we want to know that that number is approximately three as we will talk about maybe one of the things that comes out of this theory is that the dimension of space might not be exactly three, there could be variations in the dimension of space that could be associated with phenomena and cosmology, it could be that in the early universe a mention of space was not exactly three, but it could have been much larger than three to talk about it. a little bit later, okay, so one feature of space that was discovered arises from the general activity invented by Einstein in 1915, is the idea that space is not just something flat and three-dimensional, it is something that also has curvature and, in fact, we can understand it. the phenomenon of curvature in these networks here are examples of networks that emerged from simple rules.

I mean, it makes some sense to me, since these networks are presented here, that there is some kind of curvature in space that corresponds to these networks, well, that criterion. I told you that to calculate the dimensions of space you can use a similar criterion to calculate curvature and just to mention how it works, you know when you might think that the area of ​​a circle is PI R squared, but if you draw that circle on a sphere its area is not exactly PI R squared there is a correction that depends on the fact that it is being drawn on a curved object and that is, um, we can introduce that correction so that we can solve for that when we do this of saying how big the ball, how many points we reach when we travel a certain distance in our system, that will end up not being something that on this graph looks like a kind of two-dimensional flat space. instead, this thing will have a variation and that variation corresponds to the coverage and will see all kinds of characteristics of that curvature.

One thing I might mention from a mathematical point of view is that what immediately emerges in these models is what matters to the kind of growth rate of the number of points is something called Ricci scalar curvature, which turns out to be exactly something that appears in general, but one of the characteristics of curvature is that when a space is curved it means that the shortest distance between points is no longer an ordinary straight line, so if you were alone in this flat space, the shortest distance would be these straight lines on a sphere, the so-called gd6, the shortest distances curve like this, this is a negative curvature space where the jd6s flatten, well, we can, we can look at exactly this kind of thing in our systems and we can, and This is kind of like, by the way, in Einstein's idea of ​​general relativity, gravity is associated with the fact that when things travel like a laser beam, for example, they would travel in what you think is a straight line. , but because space is curved, that straight line is not really a straight line and that non-straightness is what it is. associated with the effect of gravity and we have exactly the same phenomenon and we can actually go ahead and solve the effective equations for these, for what happens with this jd6 and so on, and it turns out that the equations that are obtained for the limit of what What happens to the geodesics in our space is created only from these underlying rules that are applied to create this ever-larger spatial hypergraph.

It turns out that the equations that govern the behavior of these geodesics are exactly Einstein's equations. to start with a little more technicality to start what we're talking about so far is the vacuum Einstein's equations the equations that essentially govern the curvature and structure of space itself ok so we can ok so that's a little bit about how space works They work with each other, another great thing about our universe is time. I was describing this as these spatial hypergraphs just grow but they grow over time. How does that time thing work well? A feature of the traditional approach to physics is this idea. of space-time, the idea that somehow space andtime are in a certain sense the same type of things and that is an idea that has a lot of special relativity, it is very involved with space and time being more or less the same type of things, but in these models of space and time are not intrinsically the same kind of things and space is up to this point. time these models are fundamentally very different kinds of things, it will turn out, however, that the all the phenomena of space-time emerge and one gets all the standard results of relativity, etc., but at the intrinsic level, space and the time are not the same type of things in these models and if I had to choose one type of potential A wrong turn in the history of physics was probably about a hundred years ago when people started saying that space and time really are the same type of thing and without considering the possibility that they should be thought of differently, it is something that arose from a kind of our computational paradigm that time is something that corresponds to a kind of calculation process and space is something different, okay, let's talk about time, so when I showed this sequence of different steps in the evolution of this graph I was a little bit cheating because What I should have really shown is each individual little update that is applied by that underlying rule, so this is a possible set of updates that are shown in purple parts of the ones that were applied, so what it was actually showing with the kind of complete steps. after every update that could have been applied to this chart has been applied, but this is like looking underneath, looking at every possible update that could have been applied, so here the time progress is about the application of these updates. but now there is one very important thing and that is that this image is not the only image I could make of how these updates are applied when we are given the underlying rule.

There are many different places on this overall Canon B chart where the update could be applied. So how does that work? Actually, what we can think of is this complete graph of all the possible updates that could be applied, so here is the initial state. This is an update to hear a different update that actually looks. similar but the arrows will be different here we continue, we will reach these different structured states and if we continue again we will reach more states, okay, so, um, and maybe it's kind of a spoiler that this kind of branching will turn out to be what will give us quantum mechanics, but for current purposes, what I'm explaining is that the type of time progress is at the bottom of the page here and what we're seeing is that there will be a progression from one spatial hypergraph to another and that corresponds to the progression of time if we continue this graph longer, this is a version of this graph where we don't arrange it so that it somehow explicitly goes down the page, this is just showing the relationship between these different spatial hypergraphs, um , okay, let me explain how this works, so in a moment we'll get to what we call causal graphs, which are a very important concept and They're a little bit easier to explain, not in the context of spatial hypergraphs but in the context of just rewriting strings, so think of it as if you're in some kind of find/replace text editor and you have a big string of text and they tell you every time you see an egg, replace it with BBB.

Every time you see BB, you can replace it with an ok, so the question is what happens if you run your text editor in every possible way, so this is this. is what we call a multi-way graph of what happens, so we could start with an A that can only get BBB, but then BBB could give a possible transformation, as it gives to B, another transformation gives to B a and continue from there, okay? so we end up with this whole network of possibilities, okay, that's analogous to the network of possibilities that I was showing you before for special hypergraphs, but it's a little easier to see in the case of strings, okay, we can look.

In a little more detail, this shows what we can think of as update events, so it starts with an A and then this is the type of update event that says it goes to BBB and there are more update events, so that this is shown as the network of states and events that shows how things can progress through time and effect. Okay, now I'm going to make this a little more complicated because one of the big questions here is what can happen before what and we can think about. Of these update events as shown below, you can think of them as sort of really similar computing functions and they have certain inputs and a particular update event can only occur if all of its inputs already in some sense have this kind of order about what. can occur when, based on when your inputs are ready, so to speak, we can draw that here by adding these causal relationships, so they say this particular thing depends on this having happened because you need that to get your input and So.

Down here there could be something that needs this to have happened to get your information, etc., and all these orange lines represent the causal relationships, what you needed to have your information ready from something that happened before, so to speak, ok . so we can, let's get rid of the states and just talk about we can call the causal graph, which is the graph that represents the causal relationships between events, this says that an event here, this event here could only happen after this event here this event here it can only occur after this event here this is a graph of causal relationships okay and this will turn out to be something critical to understanding a lot of what happens, let me show you so if I continued a little further and didn't lay it out from the first event.

I might get something. This could be the causal graph of the relationships between different events, the threads of causality that link those events. Okay, now let me explain. There's a very important idea here, which is the idea of ​​what we call causal invariants, so one of the questions is that we've said that there are different types of updates that we could do and there are many different orderings that we can apply them to. updates, but it turns out that for many types of underlying rules it doesn't matter what order we use, as long as we respect this causal graph, we can do the updates in any order we want, okay, let's show an example of causal invariants. in action essentially what causal invariants this is for a particular rule which is a rule that takes our string of characters and only two at a time sorts them so it says that ba should become a B that's all it's doing and this is showing from BBB AAA, this shows all the possible ways that BBB AAA can be rewritten with that particular rule and we see these various events that can occur etc., okay, there are all kinds of different things that can happen and we can finish. with B a B a a B we can write with a be be a be a but in the end we will always get the same answer in the end we will always get an ordered string, no matter the sequence of the states we go through, we will always arrive at the same answer to the final and that is the essence of causal invariants.

It's actually a property that has been studied in mathematical logic and elsewhere, it's actually known by many different names, sometimes called. The confluence has a variety of different names, Church-Rosser property, all kinds of other things, there are slight technical differences between all these different things, but they are basically the same idea, how would you know this idea exists if you've done algebra? You may know that when you're doing something like expanding some polynomial, you can say, "Well, first I'll expand this set of terms in parentheses and then I'll do this one. I'll do it in the other order, but in the end, it doesn't matter what order I do it in." do, because that type of algebra has this property of confluence or causal invariance and some of these rules that we're looking at also have that property, so this particular classification rule has that property so, so what that means. is that there are different possible types of story paths, but it doesn't really matter in a sense which story path we choose, we're always going to get the same behavior in the end, okay, so, for example, for this particular thing, we can see what the causal graph is that it creates.

Its causal graph is actually very simple, it just looks like this, let's see how this works in a real kind of operation in the original chain, so here we have. quite a long string and each of these yellow boxes represents an event that represents a rewrite of ba and it becomes a B, so this is a particular choice on how we can do that sequence of rewrites that I can show. you know what the causal graph is associated with that particular set of rewrites, but there are many different causal graphs that I can use and what we'll notice here is that although the actual particular updates were done in different orders, if you look and just look at the structure of this causal graph, is always the same, so no matter what the underlying order of the updates is, you will always get the same causal graph, well, so here's the first big thing that comes out of this. we come to derive special relativity and that is special relativity that is generally not something that one imagines deriving, it is something that in some sense the ISM is a consequence of sort of axiomatic features of the way that physics establishes constancy of the speed of light independence of inertial frames this kind of thing, but in these models we come to derive special relativity, it may not be true in these models, but it is true, it is a consequence of causal invariance and of various types of limits and intrinsic randomness properties and things from these models that one gets special relativity, so let me show you roughly how it works, so let's look at a simple causal graph.

Here's a simple causal graph that has a bunch of events, two linked together in these simple ways, so let's imagine that the important thing to say is In special relativity, one of the great innovations was to be more realistic about what an observer The reality of the universe can tell it is happening, so if we look from outside the universe we could see all kinds of things, but as an observer embedded in the universe operating according to the same rules as the universe, there are limits to what we can see. we can say, for example, we, in the physical kind of case, we can't, things can only travel at the speed of light, so we can't.

I still can't be aware of things that happened further away than we've been able to see based on the information coming from them at the speed of light, so it begs the question of how we model that observer. How do we model an observer that is embedded within the system? And I might say that for the systems we're looking at here one of the things one might ask is whether the observer operates according to the same rules as the system itself. What consequences have allowed me to give you an example of a consequence that has come to fruition?

The strange consequence, let's say we were to set the universe so that only one place in the universe is updated at a particular time, then what will happen is kind. like a Turing machine in computing, you have this kind of head that spins around the universe updating different parts of the universe, you could say that can't possibly be the way the real universe works. I can clearly see that that is not what is happening. The problem is that if you start to think about it, you realize that you can't see anything until, in a sense, you've been updated, and as this head spins around trying to update different things, it's a kind of causal network. that is producing. one that actually looks might look something like this, where you can't tell if that thing over there has been updated or not until you've updated it yourself, so when you put all that together you realize that you get this kind of integrated causal graph in which, in some sense, things to you as an observer can appear to happen at the same time, although to something outside the universe you could imagine seeing this head spinning around doing different things. at different times, okay, so how do we kind of make a model of what that observer is like?

What an observer will do is say, okay, I'm going to decide what counts as successive moments in time for me and these are mathematical foliation of this causal graph and this says that these are the successive moments of time that I, as an observer, I'm going to decide to identify, since this is my definition of time, it will be the sequence of cuts like this, okay,Well. The important thing is let's see, I have a better image than that, oh yeah, here we are going very well, so let's imagine that the observer is not only stationary, but our observer is moving, okay, so this is now our observer in motion towards our moving observer. that that moving observer will choose his type of space-time foliation in a different way if then if we say well how this will be perceived by an observer he will realize that the type of perception for the observer is something like this where the observer will say okay, I'm just having this sequence of simultaneous things of a kind of simultaneity surfaces that in physics are called space as hypersurfaces that the sequence of space as hypersurfaces and then this and that when I do that transformation my causal graph will look like this, OK?

So what, what is that transformation of the causal graph turns out to be exactly the transformation that occurs in special relativity and, in fact, we can see that what is happening here is that, although we could start with this simple rule that operates according to this particular way, produces this causal graph once we have this causal graph, when we are entities that exist in this universe as part of this causal graph, we will end up perceiving that the functioning of the universe is exactly the way that special relativity He says it has to be like this.

One of the phenomena of special relativity is its time dilation and time dilation is kind of like we can see time dilation here in my other image, I probably don't know that term if you're moving around. in space, if you're exploring space faster, time will move slower for you and let's take a look at how that works in these systems, so let's say we have something like this, this is what time is like, events are something what happens at a certain rate if we now choose a different frame of reference if we are indeed traveling at a certain speed in space this is the underlying sequence of events that we will perceive and you will notice that this kind of thing takes longer to get to the final answer here that when we were somewhat stationary and we chose to choose our sequence of moments of time differently and that phenomenon is, in fact, exactly time dilation and special relativity and the reason is fine, so why does all this happen? work, the reason this works is because of causal invariants, what law invariance implies is that even when we choose this different frame of reference that corresponds to going at a different speed, even when we choose a frame of different reference, will continue to be the case. that the causal graph that we get from the system will be the same and that is a consequence of the Goslin variance and therefore causal invariance implies, but now the real relativity situation is a little more complicated than I have given you. shown. it's a little bit more realistic causal, it's still not as wild as it seems, but this is a kind of foliation of this is all this that is built from this spatial hypergraph time extension is just the Computational Progression type of the application of updating rules, it remains true that when we look at what we, as observers within that universe, perceive, what we perceive is the causal graph and when there are causal invariants, that has the consequence that what we see will satisfy the rules. of special relativity in a sense, causal invariance is what leads to the independence of the reference frames that special relativity talks about, so that was the first one.

I'm serious, I think it's a big problem. I knew it in the 1990s, in fact, from models like this it was possible to derive special relativity. Let me tell you something that I didn't know at the time, which is what things like energy are, one of these, and it's really amazing to me that it's possible to say this as simple as it is possible to say it, so I'll just say what the statement is. final: energy, it is the flow of causal edges through space as hypersurfaces and so what does that mean when we look at this image?

I made these cuts here, these are the so-called spatial hypersurfaces, these things here, these are the causal edges and the statement is energy, if we look at some region of the universe and ask how much energy is in it. In this region of the universe, the answer is going to be the amount of energy that's there, basically the density of these causal edges that cut through this space like hypersurfaces, and in fact, that's what's in this model that seems to be what the energy. corresponds to, for example, momentum corresponds to the flow of causal edges, not through space like hypersurfaces, these horizontal surfaces, but through what is called time, like hypersurfaces, which here are the type of orthogonal surfaces, so what the impulse corresponds to the flow of these. traverses time as hypersurfaces, well, one of the things that arises in relativity, that kind of assumption in relativity, is that space and time have the same relativistic transformation properties as the energy momentum in this model that is derived of a ball and it comes.

This is due to this fact that that energy represents these slices through space as hypersurfaces and slices through time as hypersurfaces. When you work it out, you'll discover that the term implies the same special relativistic transformation properties for energy momentum as it does for space and time, okay, so another big thing in the world is mass, and you can understand rest mass in terms of This too, the rest mass is a little more complicated to describe, but it is essentially the one that relates to the kind of part of the energy that does not correspond to the communication with different parts of the special hypergraph, it is the part of the energy that it has to do with a single part of the spatial hypergraph being rewritten instead, so to speak, that corresponds to mass, so actually I think I even mentioned it in the announcement post and I mentioned it in more detail in the whitepaper and I think Jonathan mentions in even more detail in his whitepaper what that means from those definitions of energy and mass etc., we can simply derive, for example, a MC equal to the square, which again is quite notable because that doesn't It's something that's been derived from a ball in physics before, it's something that really comes from the kind of axiomatic assumptions of relativity, but in this case, it's actually derived from a ball from sort of the underlying structure of these models, okay. , that's something, so I should mention something else, Einstein's equations for gravity, the way Einstein's equations work, they say this kind of version.

Oh, actually, there's a good to that. is a version of Einstein's equations that talks about the curvature of space, that's what's on the left side, it's equal to this here, the energy momentum tensor which has to do with the energy and momentum in the space, since we think we know what momentum is and we think we know what curvature is, we should be able to derive this equation, and in fact we can, and in fact this equation follows as a result of causal invariants. This equation is an inevitable consequence of causal invariants plus some other types of mathematical features of them.

In fact, the models to say how it works roughly, the other main assumption is that, at the microscopic level, the type of individual rewrites that are happening occur in a random way, but in reality they are not random at all, they are completely determined but when We look at one of these things and it seems random to us. It's the same thing that happens, I don't know, in the digits of pi. For example, the digits of pi have a completely determined sequence but when we look at those digits they seem, for all practical purposes, random and if we do statistics on those digits will appear as a random sequence in all our statistical tests;

Well, the same thing happens with points in space on a very small scale, points in space are completely determined where they work and how they are connected, but for all practical purposes they appear random and that randomness effect allows us to use various types of statistical arguments that allow us to derive a kind of continuity of space and so on and essentially we need that kind of generation of intrinsic randomness, we need another one, we need causal variants and we need another crucial fact and the other crucial fact is that the universe is of dimension finite, the universe is not zero-dimensional and it is not infinite-dimensional. and if we include those facts, then we can derive Einstein's equations and it is actually analogous.

The derivation is strikingly analogous to the derivation of equations for fluid flow from knowledge of the microscopic dynamics of individual molecules and for the same reasons. No matter what the individual molecules look like, you still get the same fluid equations, no matter the precise details of the underlying rule, you still get Einstein's equations here, so that's another great thing. I mean, I knew it well. I knew it. at least the left side of this in the 1990s was De Rivel for models like this, but since he didn't know how power-drive worked, he couldn't really get the right side right, so that's it. so let me talk a little bit about the other things in the universe, so to speak, and then I'm going to talk about quantum mechanics after that, so let's talk a little bit more about the universe, so one question is when do we look at the Well , okay, so, yeah, okay, so when we look at the spatial hypergraph and its evolution it can do all kinds of things.

This is one of the strangest things that can happen: a piece of the spatial hypergraph can break, it's like we have the universe. everything goes well and then a piece just breaks once it breaks it can never communicate again it's stuck it's something it's a piece disconnected from space-time okay well what does that remind us of black holes and In fact, in these models it is quite natural to form black holes. This is a causal graph and this causal graph says you start here and everyone communicates, everyone comes and goes, but then it splits and this part of the causal graph is separated from this. part of the causal graph this is the interior of a black hole this is a kind of exterior of a black hole so it becomes something natural that happens in these models the formulation for the formation of singularities and many of the phenomena essentially yes We are familiar with general activity, these causal graphs of ours are very similar to the causal diagrams of generality that are now derived from a much lower level if we look at, you know, what our universe might be like, these are just three examples. of different types of rules, this is one that forms many disconnected pieces and these pieces are not disconnected in space-time, but are causally disconnected, so they will act like black holes.

This is a strange universe where things don't communicate. a lot of each other, this is rather kind of too simple to be our real universe, but this is more like ordinary space, so now a question would be in the early universe, what would it have looked like and one of the things that What comes out of these models is the idea that the early universe could have had much higher dimensions than our current universe and that results in solving a lot of problems about inflation and cosmology, etc., the idea that you have a universe that It starts in very high dimensions so everything can communicate easily and then gradually becomes more three dimensional, by the way, now that I keep talking about changing dimensions and such, there isn't a lot of good math on how to do that.

Typical studies of the way things work are based on fixed-dimensional and typically integer-dimensional spaces, for example, essentially all computation is based on the idea that one is looking at sort of continuous integer-dimensional spaces and So, to really one of the things we need is to essentially figure out a generalization of calculus that works for these fractional dimensional spaces and that also works for spaces that can change their dimension and that can work for strange things like the It's possible to rephrase General Authority not in terms of curvature of space but in terms of dimensional change in space, so those are some of the kinds of strange things that can happen.

Let me mention something else as I speak. about the structure of space and let's talk a little bit about particles again so you know I've studied cellular automata a lot, this is an example of a cellular automata, a cellular automata and unlike the models that are used for physics now , where there's just a bunch of points that are all arbitrarily connected, a cellular automaton has a very rigid grid, it's just a rigid grid of cells, each cell is, for example, black or white and there's a rule that updates the color of each cell depending on itsneighbors, so it has a very rigid notion of space and time, it doesn't have an emergent dynamic space in time, you just put it in from the beginning and then see what happens, but it's easier to see for running simulations etc. , there is a particular cellular automaton rule 110 and one of the characteristics of this cellular automaton is that you can see that it has these kinds of persistent localized structures that develop in the cellular automaton and behave very much like particles with which They interact, they have various rules for colliding, etc, etc, etc., this is a kind of analogue of the particles that we could see in these networks and, as I mentioned before, we still don't know in detail how it works.

There's an I. I've been interested in this stuff for a long time and I've asked, for example, some of the leading graph theorists in the world about how we can understand things about how localized structures might work in graphs and I think a good example quote was Let's go back in a hundred years and we can know more about how it works. My hope is that one of the things we can do now is because we can actually simulate these things and we can actually build. our intuition in doing things with computers we could speed up a lot those hundred years and that's just um So one thing I could mention about particles is something we hope is that eventually we can derive from these underlying rules what particles should exist in the universe and the fact that your poor electrons and muons and leptons and gluons and photons and all that kind of stuff, let's talk a little bit about that, although one of the problems is that just because you know the underlying rule doesn't mean you immediately know its consequences, there is a phenomenon which I call computational irreducibility and which I started studying a lot in the 1980s. that basically says that the process of knowing what will happen even in a system like this can be irreducible can be something that requires an irreducible amount of computation, you could say God , I don't need the rule it's so simple that I can just jump ahead and say this is what's going to happen and a million steps in the future, well it turns out that you can prove that you can't do that, essentially the reason is that it's the that whatever you're going to use to move forward is itself like a computer and this thing behaves like a computer and those two things are essentially computers of equal power.

There's what I call the computational equivalence principle that says that and we have more and more evidence of that and that means that we just don't get to Jumping forward is an irreducible process of knowing what will happen and that's one of the things where , if we have this underlying rule for the universe to know its consequences, it requires a kind of irreducible quantity of calculation and, among other things, to, for example, know its consequences. because, you know, whatever it is, in the 14 billion years that our universe has existed, we would essentially have to run the calculation that corresponds to all those steps of the evolution of our universe that we can't do in the universe and we don't We can't really speed it up much due to computational irreducibility.

Now the good news about computational irreducibility is that whenever there is computational irreducibility there are always pockets of reduced capacity, there are always pockets of places where you can make progress and those are the pockets that we have to live with when we try to understand how the physics of our universe arises. from these underlying rules. In fact, I should say that one of those spectacular things that I really don't expect at all is that in these models involving these hypergraphs and so on, it turns out that there is some kind of reducibility layer that sits on top of this kind of underlying computational irreducible, let's say, and that layer of reducibility is precisely what allows us to derive things like general relativity and will allow us to derive quantum mechanics is the fact that in these models, for reasons that I didn't expect, although it is somewhat obvious after the fact, there are things in them that are generic and don't depend on the precise details of the underlying rules and we're not trapped by this kind of irreducible difficulty of computation or disability, so that's an important part of why it's been possible to do this project so far and We don't know exactly how far computational reducibility is. is going to go and we don't know, for example, if it will allow us to derive things like features from local gauge invariants.

I'm hoping that's the case and we don't know if he'll go as far as telling us things. just like particle masses, I'm guessing that won't be the case and that they will be specific to particular rules, but anyway, so we can start trying to figure these things out, I'll just mention one thing: we know that certain particles have been discovered by accelerators. of particles. and all this kind of stuff, we have a kind of mystery in the universe that seems like a large fraction of the matter in the universe is dark matter that we don't know what it is yet, so the search has been thinking about what it could be. that in our models, there are many that there is a kind of question about what the spectrum of particles could be like, so one characteristic that I will talk about a little later is that it turns out that an electron, which is a kind of particle of different mass of zero lighter, except for neutrinos, which have a strange way of having mass that we know of, but in our models, for reasons that I will try to explain, there is reason to think that there could be particles incredibly much lighter than the electron that are between 10 and 20 times lighter than the electron, but not of zero non-zero mass, but very light compared to the electron and that is something interesting because it is a potential candidate for things like dark matter.

I have called these things Allah gongs, the reason I call them is because it comes from the Greek word allah gas which means phew and I call them that because they are things that involve their particles that involve few hyperedges in the spatial hypergraph etc. That's one of the things that kind of predicts this model is the expectation that we don't know exactly where those particles will be, but there will be very light particles compared to the electron that will exist. Well, then someone asks what. They've captured this image, this is rule 110, so an automaton, okay, let's keep talking about quantum mechanics, um, let me see what I have here, oh, okay, one thing, quantum mechanics is that weird.

A feature of physics that was originally discovered around 1900 was the first hint of it and it really came of age in the 1920s and my friend Dick Feynman always used to say that no one really understands quantum mechanics and I know they certainly don't. He understood quantum mechanics. mechanics before very recently um and there's still more to discover about it, but one of the characteristics of these models is that quantum mechanics is not an add-on, it's not something where you say oh, there's physics that we understand, classical physics that we understand that there are certain laws of motion and things like that, oh, now we have to add quantum mechanics, that's another, you know, another physics course that has to be added, so to speak, that's not how it works, it's absolutely inevitable in these Models. that one has to have quantum mechanics and then the reason that arises is what I was talking about before that there are these rules and there is not just one way that the rule can be applied, there are many ways that the rule can be applied and it What we think about is applying the rules in all the possible ways and, in a sense, in all these different possible ways.

So a key feature of quantum mechanics is that it is not the case that one always says that something definite happens in some sort of In classical physics it is said that you know that the ball moves in this trajectory and it is definite. In quantum mechanics it is said that the photon can go in this direction or it can go in that direction and there can be two differences between these different directions that it goes and everything is something. where one traditionally simply says that there is a certain probability of measuring it being this or that, then there are many paths of history that are followed and we can only sample the aggregate results of those different parts of history. and that's exactly what's happening here now, so this would be kind of a classic version, you just have that sequence of strings.

I'm looking at strings instead of hypergraphs here because it's a little easier to do, okay? How does quantum mechanics work well? These different possible things correspond to the states talked about in quantum mechanics. own states. Pure states. Anything that is talked about in quantum mechanics. Well, here's your kind of A great history of quantum mechanics results in the quantum mechanics that one should think about and think about this is the kind of multidirectional system with all the possible things that can happen in quantum mechanics. Now imagine that we are an observer also embedded in this multi. path system by looking at it and we are trying to make sense of what is happening in all these different paths that are happening in the different paths that are happening within us and so on, we are trying to make sense of all of this. we'll end up doing something very similar to what we did in space-time, we'll do this kind of foliation quantum observation frames.

There's sort of a new idea about how to think about quantum mechanics. This idea of ​​thinking about it in terms of sort of frames of reference, a little bit like relativity. One of the things that happens in quantum mechanics. Is this the idea that a measurement is made in quantum mechanics? There are all these different possible things that are happening, but at some point you say, "I'm going to find out if the electron went in that direction or in this direction." I have made the measurement, it is final, it will never change, that will be the result of that measurement.

Now, one of the things that's been very mysterious in quantum mechanics is the fact that since there are all these different parts of what can happen, how can it be the case that different observers, different measurements, are consistent? How can there be some kind of objective reality in quantum mechanics, even when what's coming out is just saying that there are all these different paths and all these probabilities, four paths and so on? and so this model of ours explains that and it turns out that the origin of the type of objectivity in quantum mechanics, the fact that there is a defined reality in quantum mechanics, is precisely the same phenomenon of causal invariants, although there are different ways in which one can make measurements, although there are different types of quantum observation frameworks one can use, one still ends up with a consistent view of reality and that is a consequence, just as in relativity, of the fact that we got the same laws of physics regardless of whether we were moving at different speeds and that corresponds to different reference frames in relativity, so here these different quantum observation frames correspond to different types of portions of visual reality, but nevertheless, of course, due to variation.

Ultimately, they all correspond to the same reality, so what I'm showing here is a kind of cartoon version of a quantum measurement. What happens here is what you say when you say okay, the quantum system is evolving and then what happens here is the observer decides. to do a foliation where they're essentially freezing time, they're saying, I think this is how things came about and I'm sticking to that, so I'm basically making all of these successive time steps group together here now again. a little complicated what's going on here I'll make an analogy this is what happens so this is analogous to what happens in a coordinate singularity in general relativity in spacetime it's actually analogous to what happens in the event horizon of a black hole effectively what is happening is that you are freezing time now in this case you are simply freezing time by convention.

The observer is choosing this way of configuring time, they are choosing to decide that time is not going to change for them after they get to this state and it turns out that when they do those things to maintain coherence, they are a kind of region that then freezes for them will get bigger and bigger and that corresponds to quantum decoherence. and to deal with state entanglement in quantum mechanics, okay, this is a super simple case, this is a little more complicated case, the real case is much more complicated than this, but this gives an idea of ​​how you can freeze time. foliation and this well, it turns out that when people do quantum computing they really want to freeze the state of a particular qubit, they want it to remain as a pure state, they say this is the state, I want it to remain like this and essentially what they are.

What we are doing is forming a black hole inthis multi-way space, so what you have to understand and a very beautiful kind of analogy, I think, is that we talk about space-time, we talk about how there is a causal graph in the space-time that we are now in. talking about the multi-way graph and this is what there is and we are talking about the z-foliation-- of the multi-way graph and those foliation czars, as I was mentioning, directly analogous to the z-foliation-- that we do in space- time, so one question you can ask is: are we okay, if when we looked at something like this again, this was a foliation of a causal graph, the cuts here when we look at these cuts and say what are the states associated with these cuts? these slices correspond to instantaneous spatial states, so they correspond to spatial hypergraphs at a particular moment in time, that is what the foliation of the causal graph corresponds to and space-time is a spatial hypergraph, what is the foliation of a multidirectional system, what does that correspond to?

Well, we can think of what it turns out to be like something we call the space of branching fields. Sorry, my British accent probably ruins that word, but it will branch, it um, it will branch. She, um, unfortunate Jonathan also has a British accent and we're the ones who've been talking about this a lot, so we don't really know if this works in America, but that's the word we're using. So in this, the cuts here correspond to what we call branch field space. If we take that slice and look to the side, we will discover that these successive steps correspond to the way that defining multi-way graph worked. connections between different states in the cold branch space and those connections correspond that they are essentially a map of quantum entanglements, this is essentially a map of quantum entanglements in the space of quantum states and so that is so, so we can analyze in a certain way in tank the entanglement of quantum states, so again there is space-time with this notion of extension in space in the multi-way graph, different nodes in the multi-way graph correspond to different quantum states and there is a notion of a space of different quantum states and there It is in this way that we can unite these different states using not positions in space but entanglements in branching field space and so it is, so what we have is this notion of gill space corresponding to the analogue of de physical space but in quantum state space, okay, so now we can start asking questions, so we have a complete configuration, it's a little bit like the generality that we have because we have some that we have, a little bit like relativity, we have these foliations , the quantum state space, then we can ask if there is an analogue of general relativity in branched real space and it turns out that there is, and essentially what is happening is when we look at gd6 the shortest. paths in the real space branch, those that we can, we can ask a question like if we want to go from this quantum state to this other quantum state, what is the geodesic that goes from one quantum state to another quantum state and we can ask what are those geodesics. affected by the presence of other quantum states and sure enough what ends up happening is that the gd6 in the real space branch is gone when you want to get from a place in the cold space branch a quantum state which is a kind of position of the space branch. to another you go through this gd6 and the geodesics are deformed by the presence of other quantum states and that defamation well the presence of other quantum states okay, I have to mention another thing that I mentioned that in space-time the energy corresponds to the flow of edges causal graphs across space like hypersurfaces, well we can do and it's something a little more complicated, just like we can make a causal graph in space-time, we can also make a causal graph in multiple residues only on one branch. in the multi-way graph and this is something called multi-way causal graph and causal invariance implies that the multi-way causal graph can essentially be decomposed into a collection of identical causal graphs corresponding to each different path that the multi-way system , but Basically, this multi-path causal graph is a representation of causal relationships, not only across space, but also across branching space, it is a representation of causal relationships that occur between events that occur in different places in the world. space and at different places in the quantum state space.

Well, now it turns out that we can use exactly the same definition of energy for the multi-way causal graph as for the ordinary causal graph. There is still a flow of causal edges. Now, in the details of the way physics works, it's always like this. It's been a bit of a mystery how the energy of classical mechanics and particular statistical mechanics relates to the energy that appears in quantum mechanics in this configuration, the way it works is that they are both causal edge flows, they are both flows, Of course, it is claimed that in sense decompose in the same way, but one of them can be considered part of it as an edge flow and the multi-way causal graph, the other and the ordinary causal graph is okay, a little complicated, but that means that when we ask about jd6 and Branchville space, what we like in physical space, the gd6, the shortest paths are affected by the presence of energy.

The same thing happens in Branch Hill space, in other words, the gd6 that determines the type of path that allows you to get from one quantum state to another is affected by the presence essentially of energy in the system represented by a multi-way causal graph feature. Well, then what's big? What do Weinstein's analog equations effectively say about the deformation of this gd6 tells you that the presence of energy deforms which makes the gd6 spin and that's okay, in a little more sophisticated physics, when you talk about energy and momentum , there's a relativistic invariant quantity called the Lagrangian, which is kind of a combination of those things and it turns out that what really matters here is the Lagrangian density and that's what really turns gd6 into Branchville space.

Well, the spin of gd6 in the real space of the branch gives you the equations of motion of quantum mechanics and that is the most direct way. Think about that, my friend Dick Fineman, one of his great achievements was this thing called the path under the poles in quantum mechanics, which is the mathematical formalism that underpins most modern ways of approaching quantum mechanics, the path integral. says that you are Looking between one quantum state and another, the type of world can take many paths, but each path is weighted by a particular quantity e to the one over h-bar um and in this configuration we get exactly the path integral, in other words when you look at these geodesics on the defamation of these geo d-6, the way these geodesics deform is precisely the way they spin corresponds exactly to this e to the I s that we're thinking of and it was spinning in Branch Hill space, you can equivalently think of them in terms of complex numbers, but we're effectively thinking of them as vectors in real branch space.

The branch field spaces are white, so I think it's a big deal that it's possible to derive the path integral from this underlying structure of a multi-way graph and the multi-way causal graph, etc., it's also cool that the fundamental fact of quantum mechanics is the same as the fundamental fact of space-time and is essentially analogous to Einstein's. The equations are the path integral, so we might wonder what branched real space is actually like. The branching real space is very complicated, while the physical space is nice and tame and appears to be approximately three-dimensional. Branched real space is much more complicated and probably exponential dimension is like some kind of projective Hilbert space or something, it's kind of complicated and we need to understand more about it, but we can already say things like this aggregate data about gd6 and about the integral route without knowing more details about branch field space, but to really understand branch field space we need to go and do more there.

I should mention that the analogy between quantum mechanics and general relativity has another interesting piece, so for example, some might know the uncertainty principle in quantum mechanics that if you do a for example if you do a position measurement and then you make a measurement of moment that one measurement affects the other or effectively that if you and that corresponds to the formalism of quantum mechanics the non-commutation of the operators that represent the operation of making the measurement of the position you are making the measurement of the momentum, so essentially what you're saying is that you position instead of momentum and that's not the same as doing momentum and then positioning well, so it turns out mathematically that it's a statement that these traders don't commute well, well, on general relativity we have something analogous, we have the so-called covariant derivatives, we take paths in space, so you can say let's start, let's go horizontally, let's go vertically, let's go horizontally, let's go vertically and when you're in a curved space, you know, come back to the point starting again and that is a consequence of the curvature, it is represented by the Riemann tensor in standard differential geometry and in space-time studies, it turns out that exactly the same phenomenon occurs in the branch.

In real space you have the same, you do not return to the starting point in real space of the branch when you apply these two operators in two different orders and that is exactly the uncertainty principle. Then there are all kinds of other things you can spin off. in quantum mechanics and Jonathan has written a good article going into some of the mathematical details of that, but anyway, that's cool, so let me mention a couple of things here, and I'm getting closer to the end. I'm going to talk a little bit about some of this kind of what all this means and so on, but let's talk about this kind of analogy between spacetime and Branch Hill space, the space of quantum states, this is a very, very simplified representation of a multi-path causal graph in which essentially we're seeing types of edges that correspond to edges that correspond to this is a kind of direction of time and we're seeing that there is extension in space and there is extension in the space of Branch Hill.

Well, now we're looking at sort of physical space together and branching space most of the time, physical space and branching field space don't really come together much near black holes, they can come together and all kinds of fun things happen. . but let me mention another feature of this, so in spacetime one thing that happens is that there is a maximum speed at which information can propagate and that is the speed of light and we can see that in some of these models because in a causal graph the maximum rate of propagation of information here, let me show a causal graph here, information propagates going from one event to another and we can form light cones effectively by saying which events are in the future light cone from which events can this event be reached here and that you can only reach a certain cone of events in the future of that event and the width of that cone essentially corresponds to the speed of light and in some sense the conversion of an elementary time that goes down here to an elemental distance in the space that goes through that conversion factor is precisely the speed of light, okay, so in the real space branch the same kind of thing happens in the multi-way causal graph.

You can also make cones that are not light cones, what we now call Entanglement cones are cones that represent the maximum speed at which new quantum states can be entangled, so they represent a kind of limit for the measurement speed of more quantum degrees of freedom, such as in this case of the basses. represent the speed of light represents the maximum sampling rate of new parts of space, so the maximum rate of entanglement represents the maximum sampling rate of new parts of quantum space, new quantum states, okay, so that the maximum entanglement speed has some, well, all kinds of all kinds of consequences, let me mention one thing that relates to black holes, so in a black hole there is an event horizon and the event horizon is associated with the fact that, well, you can think of it as a black hole is something where the escape velocity of the black hole is more than the speed of light nothing can leave the event horizon around the holeblack that emerges that in our models that event horizon is associated with a separation a disconnection in the causal graph that corresponds to The effects that cannot propagate from one side of the event horizon to the other, so in addition to an event horizon physical associated with the spatio-temporal causal graph in our models, there is also an associated entanglement event horizon that can be thought of. of this also exceeds entanglement at the maximum entanglement speed that the effects would have to exceed the maximum entanglement speed and therefore all sorts of strange things happen, so there is an entanglement horizon that actually lies outside of the causal event horizon, so the entanglement horizon is not located in physical space, it is located in bronchial space, but it is something that is outside the spatiotemporal event horizon, so if you follow the theory of black holes, there has been something of an information paradox about black holes that has to do with where quantum rays originate. degrees of freedom that sort of reside between a black hole that starts out and a black hole that eventually evaporates into Hawking radiation and I think we now understand a way in which that works, which actually fits very well with a lot of of recent ideas about um.

That happened particularly in the CFT correspondence of the 80s and in the ER equivalent to the EPR work that has been done recently in black hole theory etc., but in one case in our image, what happens is that This intertwining that is felt arises. outside the causal event horizon and there may be some sort of quantum degrees of freedom that exist there and are conserved even when the black hole forms. Well, let me mention a strange thing: what happens in a black hole, I think in Russian black holes. They are called frozen stars and the reason for this is that if you look at a black hole from a great distance, it will never appear to form like that and what will happen is, for example, if you are looking at a spaceship that is falling. toward the black hole falling through the event horizon to you as an outside observer, time will appear to be freezing right at that event horizon, it will never appear to cross the event horizon to a distant observer, and In fact, that freezing of Atem time on the event horizon is exactly the same kind of thing that's happening here.

When you try to make a qubit in a quantum computer, what you are effectively doing is creating a black hole in Branch Hill space to try to freeze it. time around its qubit to prevent it from being affected by the rest of the universe the same thing happens, but now in the analysis of black holes, so in physical space, they are effectively freezing time as you pass through the event horizon causally, what happens is that you go through entanglement. event horizon, well, if you are an observer there and indeed something quite strange happens, oh, I should mention another thing when you go through the event horizon, when you enter a black hole, you get what is often technically called spaghettized, you get elongated a lot.

More or less by the tidal forces of gravitation, you spread out in space, well, the same thing happens: entanglement arises and you spread out in branching space and one of the consequences of all this is that you basically can't do it. a quantum measurement there it becomes infinitely difficult to make a definitive measurement so one way to think about this is at the entanglement horizon an observer can no longer form a classical thought no longer can reach a definitive conclusion about what is always happening. They will be trapped in a kind of quantum indeterminacy and that means, for example, if they ask you when they have a pair of particles like a pair of particles and you say: did the particle fall into the black hole or not the quantum one?

The observer stuck at the entanglement horizon will say oh I don't know, I can't form the definitive classical thought of whether the particle forms a black hole or not, that's just one of the weird things that happens at the entanglement horizon, which is one of the places, so let me show you something, one question is: I've talked about this structure of space and how it could be discrete, etc., let me, one question you could ask is how big are these, how big are these. little connections in space and I forgot to make a slide here, but I have to show you, actually, I might mention that in my more technical article there is a kind of table of what the different types of things that we know in physics correspond to. to things like local gauge invariants the expansion of the universe energy conservation microscopic reversibility all these kinds of things virtual particles all these kinds of things that one discusses in physics, by the way, we are trying to understand the analogue of those in our models Could To mention a great analogy in terms of cosmology, one of the mysteries of cosmology has been that when you try to mix quantum field theory with general activity, there is a kind of incompatibility in cosmology because quantum field theory says that there are a kind of uncertainty principle. about particles which says that in a quantum field you don't know how many particles there really are and there is a kind of infinite soup of virtual particles that are being produced and those virtual particles will have an energy density that is absolutely enormous and that energy density would roll according With them, if that energy density and Einstein's equations were applied, the universe would become a small ball.

Well, in our models, that doesn't happen and the reason that doesn't happen is because those virtual particles that are all of that type. bubbling in the quantum field is precisely what space does in our models because space is made of the same kind of material that particles are made of, and in fact, in a sense, space is making the particles, the particles. Particles are space. and then you don't get to that, that means it's not like the particles are adding to the space and then rolling up, the particles are creating the space, so you don't have the same kind of problem with zero point energy. and so on anyway, let me go down and show you something here, this is about how big these things are, what the elemental length is.

Well, one thing that people have often talked about is something called the Planck length, which is something that you get from dimensional analysis in traditional physics and the Planck length is something very involved in what we're talking about, but is not exactly what we're talking about, so we don't have a tremendously good way of estimating the elemental length but we do have a possible way of estimating the elemental length and let me tell you how that works out, so the best estimate we have of the elemental length is that it is 10 to the power of minus 93 meters, that is really small, the Planck.

The length is 10 to the minus 34 meters, so it's really small compared to the Planck length. Actually, 10, yes, 10 to the minus 35 meters, multiplied by this amount, so it's really small compared to the Planck length and roughly the reason this happens is that it's the trade-off between the multi-way causal graph and the ordinary causal graph and that the fact that what matters is the multi-way causal graph is what makes things much smaller than the Planck lengths, which means that elementary time is a 10 to minus 101 seconds in this estimate and, more importantly, the elemental energy is 10 to minus 30 electron volts in the case of Planck energy, the elemental energy in Planck's way of estimating things is actually 10 to 19 GeV, which corresponds to kind of the energy of a lightning bolt, it doesn't seem like a very small thing in the universe when you set this up in this model, the elemental energy is 10 to the power of minus 30 electron volts, which means how many elemental links there are throughout the universe approximately 10 to the power of one hundred and twenty how many elements are there in the spatial hypergraph approximately 10 to the power of 350 so these are big numbers um and do you know how many updates the universe has made so far ten to the power of one hundred and nineteen how many events of individual updates if you take into account all the different quantum degrees of freedom around 10 to the power of 500, then these are big numbers and when a woman worries about the limit of something, you know what I will get exactly, this is one I will get exactly a continuous space when it is 10 to the power of 500 events. 10 to the power of 500 is a very, very large number and that means that, to a very, very, very good approximation, you will get a continuous space.

These models are set up, it is possible that the numbers are even much larger than that, it is possible that there is a kind of continuous doubling, a kind of continuous increase in the number of elements in space that even goes beyond this. but with these estimates we can get things like the radius of an electron, so according to current physics the electron has zero radius, the intrinsic radius of an electron is zero, quantum quantum effects produce an effective radius, but the intrinsic radius of an electron is zero experimentally. We know that the radius of the electron must be less than 10 to the power of minus 22 meters in this theory, in this particular estimate we are saying that it is 10 to the power of minus 81 meters through a very small size, that means that although 10 minus 81 meters It's actually quite a bit. big compared to the true elemental length of 10 to minus 93 meters and that means that an electron is a big fluffy thing with like 10 to 35 elements in it and that's why when I talked about particles much lighter than the electron, that's why we suspect that they exist because there will be stable structures in the network that are much smaller than something like this, okay, so one of the consequences of all this is that we can estimate the maximum entanglement rate and the maximum entanglement rate corresponds to approximately remember it SATA, that is our analogue of seeing the speed of light is Zeta, the maximum speed in the real space branch and we can estimate that and it is a little big in this estimate, it is approximately 10 to 5 solar masses per second.

You could say that in the cold space branch in a The first approximation is that distances in physical space relative to times are measured by the speed of light, distances in cold space of the branches are approximately measured by the Planck's constant H bar, but when you look at all this multi-way stuff, etc., you find that what really matters is this maximum Zeta entanglement rate and, as I say, that maximum entanglement rate is, in this estimate, Pretty big, about 10 to 5 solar masses per second, so on our scale we don't usually find things that are like 10 to 5 solar masses. masses per second, but one can imagine that if, for example, there was a merger of black holes in the centers of galaxies, that would correspond to those kinds of masses doing things in a matter of seconds and then one would expect that this maximum speed of entanglement outside has a direct effect on what happens in that situation and what will produce different physical effects and I could mention that there are other physical consequences that we are talking about, for example one that we were looking at recently is what we can call frame creep in photons that are in orbit around black holes and we would expect that, as a result of the entanglement horizon, the correlations between said photons would be different than what would be expected, otherwise, there are other types of predictions that one can make, other than What's really strange is that one of the things we know about the universe is that on a very large scale it has some cosmic microwave background that gives us a kind of map of what the early universe was like.

Well, at least a hundred thousand years after the beginning of the universe it was seen in terms of where there was mass and where there was no mass and presumably that mass eventually seeded the galaxies that we have in our current universe, the question is what did it do though what did it do? Those initial density perturbations were good 100,000 years after the beginning of the universe is a lot of updates in our spatial hypergraph, so we don't really know if we can deduce anything based on some sort of early updates in the spatial hypergraph, but it's al It's less fun to think about the possibility that, for example, some kind of Sentri breakup associated with the first updates in the spatial hypergraph could actually have an effect on what we see in the Cosmic Microwave Background and I think one of the more In fact, I think it's science fiction because I don't think it's going to work this way, but we could imagine that that density perturbation is essentially a shadow of the first updates in the spatial hypergraph at the very beginning of the universe and so on.

Indeed, the rule for the universe is painted extremely large across the universe. I don't really thinkIt's going to work that way, but something like that could be true. Okay, then we'll come back. um, go ahead and come back here hmm, we don't have a visual summary in the navigation, okay, so I've given you a little tour of how things work in this physics model, from the underlying rule to all of these different possible updates to them. updates by making the spatial hypergraph whose boundary corresponds to space the way different updates have certain causal relations and the way those causal relations define space-time and the way different types of space-time foliation correspond to the reference frames of special relativity, etc., and then how this kind of multi-way graph of possible rewriting orders defines the different possibilities in quantum mechanics and then how this Branch Hill graph of entanglements between quantum states and how That allows one to make the analogue of relativity in a kind of quantum in the space of quantum states, so I just wanted to mention, wow, I wanted to mention, so what else can we say?

I think this is, you know, I'm really surprised at how far we've been able to go, like I said, I thought, among other things, that ultimately the underlying rule has a lot of computational irreducibility associated with it, but there's this layer of reducibility that I've discovered that that essentially gives us current physics and one thing that shouldn't make this so surprising is that we, as observers of the universe, would manage to make a coherent picture of what is happening in the universe if we were immediately pushed into a reducibility computational which was very difficult to do, we couldn't really tell much about what was going on in the universe, so in retrospect it's not surprising that there was a layer of computational reducibility that is essentially what we're entering when we're in sort of perceiving the universe and imagining and being able to make sense of what's going on in it, okay, so I'm going to mention one more thing: Tim is a bit of a complicated thing philosophically and one that we haven't solved as well as we have solved. the rest of what I've been talking about and it's the next question, so let's imagine we finally say great, we've managed to find the rule for the universe.

Well, what is the question in a sense? Why is that rule and why not another? What did we know? Isn't it strange that we have this rule or no other? For example, if it is a simple rule, we are in a very strange scientific position because if we look. In the infinity of all possible rules, most of them will not be simple, so to say that our universe has a simple rule is to say that we are very special in our universe, you know, since Copernicus, there has basically been a kind of en the science that You are not special, our Earth is not at the center of the universe, etc.

So how did our universe become one of the simple universes? How come it's that one and not another one? And I've been wondering about that for a while. a long time and the really strange thing is that I think we actually have a resolution to that question and it's something that Tim is so that's how it works so I've talked about how in each step you can apply different you can apply a particular rule for all these different to make all these different updates possible, the same rule, but there are different ways that rule can be applied in the spatial hypergraph.

Okay, so let's go crazy and say, well, we don't just have one rule, we have all the possible rules and we say we don't just get. To apply a particular rule in all possible ways, we can also apply all possible rules, which gives us a kind of ultra-multidirectional system, a multidirectional system where the branching is not just four different ways of applying a particular rule, but different rules. that we could apply. applies well, then we have this giant ultra-multidirectional system, so it turns out that it is basically inevitable that in that giant ultra-multidirectional system we have causal invariants and that means that there is a certain certainty that when we look at the consequences when we look at certain types of consequences of this rule type of the set of all possible rules that will actually end up finding that we get definitive answers for things that are guaranteed by causals and variants and then what happens is that We can define the foliation of this rule space basically and, in fact, well, I should say that causal invariants in the rule space imply a certain relativity of the rule space and we can define different foliations in the rule space of this rule of this multidirectional system of rules and what do those correspond to we said that, For example, different foliations in space-time correspond to different states of motion, different foliations x' in the multidirectional graph and the ordinary multidirectional graph correspond to different choices of measurement sequences. quantum, well the xin foliation in rural space correspond to essentially different ways of describing the universe, they are getting quite abstract, let me try and let me try to make a comment on this, so when we say we are trying to find the theory of the universe what do we really mean?

What we mean in the end is that we are trying to find a way to describe how the universe works in a way that humans can understand if we simply say what the universe does what we can look at the universe and see what it does, but say That we want a theory for fundamental physics is to say that we want something that we, as humans, can hold in our hands and, in a sense, understand and discover that does what the universe does now. Turns out I don't think humans can do that. I think it's a long way from what our brains are wired to do, but we have a good intermediary and the good intermediary is computers and computing and I think what we're seeing when we imagine a fundamental theory for physics is that we're seeing this kind of three-way situation where, on the one hand, we have humans trying to figure things out, on the other hand, we have the universe just doing it. the physics that does and on the other hand, I guess we are dealing with aliens here, we have them as this computational medium, this is a computing medium that is a form of a place where this process can occur and so I have spent much of it From my life as a language designer designing computational languages ​​for me, this is a kind of language design problem.

Can we design a language that can bridge these three things, human computing and the universe? Can we design a language that allows us? describe to make a description of those three different things and essentially what happens when we look at the zuv foliation rule space is that we are looking at different possible languages, each foliation corresponds to a different description language for the universe and what this is saying indeed then. is that in this type of ultra multidirectional system we are saying that the different foliations x' correspond to different ways of describing the universe, any particular foliation has a particular rule associated with it which will be the rule we use.

Works. with that description language, but another foliation will need a different rule with a different description language that will be the one you choose as a way to describe the universe, so one of the consequences that this has is that humans have a particular way of choose. to describe things we have a particular set of senses we have developed certain mathematics, etc., etc., so we are stuck in a particular foliation, it is not the only foliation and we can imagine that you know, I have had you often. I know I've talked about aliens and stuff like that and I've said it often, but at least they'll have the same physics as us, but then I realized that's not true because they may indeed be operating on a different foliation. the same kind of underlying universe, but it's a different foliation, a different description language, and that different description language may not just be a little bit different, but it may be completely strangely and incoherently different, so that the things we identify as features of the physical world are just like thrown into the dust on some other foliation that will have a completely different way of looking at the universe, so in the end I think the answer to why this rule or not is another one, it's actually all just up to us.

It is because we exist in this particular foliation, we explore this particular foliation of this type of ultra multidirectional system and that is the experience that we have of the universe and that is when we say that we are going to find the fundamental. The theory of physics is what manages to establish this three-way connection between our computing as humans and the real universe and that is the goal here, so what Tim is what we are trying to do so is something That's right, I've told you given a sort of outline of what we know now.

The problem is: can we finish this? Can we just let me get back to if I can figure this out? Well, that's the story and that's kind of As far as we have a lot more technical details, I'm very happy to talk about it, everything is accessible on the website that we have also created, as I mentioned, all the tools that we have been using for this research are available, so if you go For example, in my technical introduction and click on any image, you will get the Wolfram language code. You can just run it in a notebook and you should get the same image I got.

I might take some pictures, take a lot of time on the computer. others don't, um, but we hope that this is kind of a foundation upon which we can go and try to find the rule for the universe, so to speak, and we can try to understand how all of this connects to the things that are already understood in physics, I mean, I could say you know, pick some idea like string theory or tornado theory or causal dynamical triangulations or tapas theory or a bunch of other names of mathematical theories that have been developed in physics.

I thought, my goodness, this is not going to be relevant to the way we are thinking about doing physics, but I was wrong, it seems that many, many of these theories talk about limits and mathematical analogies of what we are doing. And I think what we learn from those theories is going to be very relevant to what's being done here, and I think one of the first efforts is to try to make all these connections between what we've discovered. and what people have discovered with a variety of mathematical formalisms and these different types of theories. You could also say that from the point of view of mathematics this is a very rich hunting ground because basically, as is unfortunately very typical of physicists, we have worked our way through many fine details of mathematics to find out how we can obtain answers and when it comes to limits where the parameter is 10 to the power of 500, there is a lot of hacking, that's fine. because that's a very large number, um, but there are a lot of questions about what multidirectional causal mass actually is, is it really an analogue of Twister space?

What is the continuous limit of each of these things? What type of mathematical structure is it? There are a lot of very interesting questions there, but anyway, this is kind of an introduction to what we're trying to do and we're planning to livestream a bunch of working sessions that we have on this, I would say. that in the realization of this project that we really started in earnest in about October and November of last year, it has been a remarkably fast project. um, in the making of this project we started at some point when it seemed like it was actually let's go to work we said God, we're having a really interesting conversation, let's record them, so we actually have 430 hours of work sessions that we recorded and we'll put them on line soon is also about Tim, how many were there?

There are around 1,200 workbooks. Those are kind of the scrap paper, so to speak, of this project that actually goes back to 1994 when I really started working on this and we put them all online today. They should all be somewhat surprising as the language has often been nice and compatible so you can run code from 1994, so I guess that's all I had to say for now and I'm happy to try and answer questions. I think today will probably be addressed mostly more general types of questions and people who are going to ask really technical questions will probably be a better time tomorrow and I think Jonathan Gorod will help tomorrow and maybe also today if people ask questions that I don't know the answer to, so let's see.

I saw that I can't connect with two questions here if people have them, so as a question that came up a moment ago, what is the meaning of Planck units in this model? I think I sort of answered that Planck units establish thegeneral scale. but there is an additional quantity that we call capital science, my favorite obscure Greek letter, which essentially represents the parallelism of a multi-way space and which gives results that are numerically very different from Planck units. Well, there's a question here. Do you think this methodology can help us study the emergence of life?

You know we're way below things like living systems when we study the things that our length scales gave from 10 to minus 90 meters, etc., we're really We're very deeply immersed in a kind of micromachine code of physics, so which is quite a long way from that to living systems. That said, the mathematical structures that have emerged in this physics model turn out to be As is often the case, if you have a simple enough model, it will be applicable to a lot of things, and in fact, I think it will be applicable to a lot of questions that They have nothing to do with the application of physics, only with the mathematical structures that we build.

I think it will end up being applicable in many other places and I think one of the places is possibly a theory of evolution. I think that rule of spatial relativity I was talking about could actually have a big impact. a lot to do with that when you look at these different possible rules, it's a little bit like looking at the different possible genomes that can exist and therefore there can be an essentially mathematical analogy, not structural, but simply mathematical, between what we are seeing in physics and what we're looking at as a sort of workable theory of evolution, that's something I mean even more strangely, we were looking at it as part of sort of helping with endemic problems, we were looking at digital contact tracing and we realized that the reconstruction of essentially if you know, whose phone interacted with which phone, that gives you elements in a causal graph and the space-time reconstruction, which is kind of like who was, where , when, since the causal graph of which phone interacted with which phone is eerily similar again. to the mathematics of what's going on in this theory of physics, so I think we're going to see a lot of applications of structural theory here in addition to applications to fundamental physics itself and I might also mention that what we're doing here is essentially a great story of parallel computing.

I mean, essentially what's happening is that in the workings of the universe, so to speak, we're saying there's massively parallel computing. In fact, one of the things that probably kept me from doing this project for a while I just couldn't believe that the universe was as wasteful of calculations as it actually seems to be with all these different paths followed and so on, but following all those different parts is really a story that is like parallel calculus and, in fact, this notion of Koslow invariants, these ideas of foliation, etc., I think are potentially very applicable to approaches to parallel calculus and I think there will be an interaction very interesting among what one learns, I mean causally.

A graph is a partially ordered set and what you're essentially doing is like the universe is doing a breadth search and respecting this partial order of the partially ordered set and you can think of it in a very computational way like that, I mean in In a rather strange sense, the universe is like evaluating an expression and the entire operation, the entire history of the universe is the evaluation of an expression, if you think about it in terms of lambda expressions, there are lambda-free variables and essentially everything in our universe is a bunch of free lambda escape variables and this in this in this image okay, let's continue here um ah, how long is this project?

I'm not sure what that word means, the work will be published after peer review, well, yes, I mean, this is what we are going to publish today and it will be my giant 450 page document, let's say I hope a lot of people read it I hope a lot of reviewers read it um and then Jonathan will appear, some of Jonathan's articles, as I say, are much more suitable for early readers of equations and They will go through the same process. This is a pretty complicated conceptual structure we built here and it may take a little time to absorb well.

Okay, what is a node and what is a line here? Alright. What we are thinking about is calling them elements and relationships, nodes are just abstract elements, the only thing we know about them is that they exist and that they are different from each other, those are the only things we know about them. We can call them one, two, three, we can call them are saying these elements are related in some way and a hyperedge like a ternary hyperedge would be a relationship between three of those elements and the way this model is set up in detail, the order of those elements matters in the relationships, you probably don't need be a work that way, but that's the way we're doing it, it's very general, so that's what it is, it's just elements and relationships.

Now we can represent the elements and the relationships if the relationships are just binary relationships, that's what happens in a graph where there are nodes. in a graph and the nodes in the graph are connected by edges and there are nodes at each end of the edge which is like a binary relationship, that's how we build the graph but as far as we are concerned they are just elements and relationships. They don't have that, that's what everything is made of, but it's not really something we can talk about beyond just saying what these elements and relationships are.

You have a path to replicate the laws of thermodynamics. Yes, in fact, I think so. I discovered the laws of thermodynamics and in the 1990s, um, how it works, so the main thing that is mysterious, so the second law of thermodynamics is the most worrying, it is the law of increase in entropy, it is the law which tells when that typically occurs. you think that what you start is very ordered, like the movement of molecules, eventually it becomes a very disordered movement of molecules, that's what we call heat, you start from a very structured order, somewhat orderly, the molecules bounce around the molecules, they eventually organize themselves in a way that seems completely random, so people had been doing this for a long time, so back in the 1870s, I think Boltzmann proved something called the eh theorem which says that, based on microscopic collisions of molecules, it can be shown that entropy increases.

The problem with that is that you also showed that entropy decreases because the way we think microscopic laws work is, for all practical purposes, what matters to them is that the laws are reversible in the sense that any collision that may occur forward in time can also occur backward in time, a little footnote on that, but it's not relevant. during thermodynamics, okay, so there is microscopic reversibility, but macroscopically, once things become heat, they never come back from heat spontaneously once you have that kind of randomness, you never spontaneously have order again, how can that work well?

Actually, it is and it really wasn't very clear if it worked. I think in the end let me see if I can get something out to show here. Wait a second. If I can do this correctly, it's difficult. I don't see what I would expect to see on my thing here. well maybe maybe I'll go there, okay, show you something about this, this is my big book, there's a section on irreversibility and the second law of thermodynamics and the main thing to understand is that you can have even a reversible system And what happens. is that at some point you can have a simple beer, perhaps in a simple state, but only as a result of the computational irreducibility of evolution will the thing effectively encrypt that initial state into something that appears random for all practical purposes, so that the origin of the second law is essentially that, as observers with limited computational ability, we see things ranging from more ordered states of lower entropy to disordered states of higher entropy, so essentially the second law of thermodynamics is a consequence of the computational limitation of observers in the physical world and that's how it works, I think, and for the purposes of that way of setting things up that's important in this theory of physics because that's what allows us to take these continuous limits to get ordinary space-time and things like that, but it's quite a separate thing. which I think the origin of the second law is essentially computational irreducibility which essentially leads to the encryption of initial conditions for the purposes of computationally limited observers.

Look here, can you talk more about the relationship between physical particles, virtual particles and space itself? I think what we really are when we talk about particles, let me show you another example that I can also find in the undamned dollar, I think let's see where they are, here is a good example, yeah, so this is this is that. rule 110 of the cellular automaton that I was showing you and this is just an analogy in the case of spatial hypergraphs, it is more complicated, but here we can simply place the particles, we already know how to place the particles in space-time, so Here There are some particles that are propagating and this is, you know, these are collisions of particles.

Here there are two particles that collide forming another particle, so it is typical that we can catalog the particles. Here are a lot of particles that we can catalog and when those. particles propagate for an infinite time, it's like a real particle, like an electron in the language of particle physics, and it's in the mass shell of its own shell, particle that has something that has physics that you already know , p squared is equal to m squared, for momentum squared. equal to mass squared, something where the particle can propagate without using some kind of quantum mechanics to exist now in quantum field theory there is this notion of virtual particles that exist only for a short time, that kind of principle of uncertainty for the particles makes that Possible and virtual particles depend on quantum mechanics to exist and virtual particles are in this.

We don't know all the details of how that works in our models, but roughly what's going to happen is that those are particles that don't propagate. forever in the special hypergraph and not only that, they are also particles that have a kind of entanglement in the direction of the branch field and therefore they are there, they are virtual particles that exist as things that are not completely mental, since that they don't. They don't have an absolutely defined structure, they have a structure that extends in Branch Hill space and can last only a certain amount of time in physical space and in space-time and that is the rough picture. of how virtual particles work, but we have more to discover, in fact, one of the first live students will probably talk about quantum spin and talk about it, so that's one of the parts of what we need to understand. how particles work and we're going to talk about something called the spin statistics theorem, we don't know how to derive it yet, that's why we know, that's why we're going to try to solve it and that's going to be related to a lot of questions about how particles work, so the question of the relationship with space is like you can see this kind of pattern background here, which is kind of space in this very simple cellular automaton and the particles are just following exactly the same rules as the background space, but they have this localized form and it's the same kind of thing that we think of in the spatial hypergraph, but the background space is a little more random, essentially what these particles will be is some kind of topologically stable structure. in this background space, just like its small vortices and water, you can see that they have some stability and are not affected even by, for example, some turbulence in the water, similarly here there will be some kind of topological structure , although it is not. actually, topology in the ordinary sense of topology because we don't have certain data, we only have this connectivity data, we don't have more data about faces and things that are needed to form an ordinary topology, but it is something analogous to topology, um, okay, oh.

I could mention another thing, which is that you could ask all these particles running through space, how important are they to space? Well, I think all real particles, that is, virtual particles, are a different story, but all real particles in the universe could represent somewhere between ten and a hundred and twenty of what is really happening in space hypergraphs, so which, in other words, everythingWhat we know about particles, the vast majority, is a little piece of fluff on top of all this activity that basically maintains the structure. of space, so you know ten to a hundred and twenty, you know things that maintain the structure of space in relation to a thing, do something with the particle, that gives you an idea of ​​most of the activity of the universe in this type of configuration and with this parameter estimation it is involved in maintaining space and the existence of particles is just a small twist on top of that, okay, let's see, okay, if we find the model for the universe and run the code, would it be computationally equivalent? or actually equivalent to something like the Big Bang, yes absolutely, if you get some kind of final rule and we know its final initial conditions, by the way, you don't have to distinguish between rules and initial conditions, you can always construct the initial conditions which is part of the rule um if we have that and we just run it and we run this giant multi-way graph according to this theory we will get everything in our universe um and that's um that's what we get have and a kind of expansion of the universe is associated with the expansion of this space hydrograph, etc., okay, Justin's question, what predictions have you made that you think will be easier to verify empirically?

So in a sense, the first thing is theoretical verification, what do I mean by that? Well, there are studies emerging of things like black holes, etc., that have made various non-trivial inferences from existing physical theories, the fact that we can directly. Coming to those inferences from this theory is important now, anything that has to do with black holes will be something theoretical, we know from the detection of gravitational waves that we know some characteristics of black holes, but when we are talking about a kind of The Quantum effects around black holes are theoretical, but there are already theoretical predictions that can be verified in the context of the theories that have been developing over the last few decades around that kind of thing, so that's the first first kind of things, the second, the second.

The kind of things we can do are things like this, if you wish, these very light particles, we don't know exactly what their mass will be, but the kind of strong suggestion from these models is that it is very likely that very light particles exist in a way similar some of these things about the early universe similarly this maximum entanglement speed we just don't know the numerical value you know is exactly ten at five solar masses per second or is it ten at four solar masses ten at six solar masses per second we don't know exactly um and to really know for sure we have to find the real rule, but we can, there is a suggestion of things to look for although we can't pinpoint the real parameter and as I mentioned things like these correlations in photons orbiting black holes, things like that, I guess there are things to consider in quantum computing as well.

This theory has definite implications for quantum computing. It has more theoretical implications than it is in principle. possible in quantum computing because low invariance implies certain limits on what is possible in quantum computing and this maximum entanglement speed does as well, but those things may be very far from what is experimentally II accessible or may be possible to organize things very cleverly in quantum computing so that you can actually see some of these effects, like the maximum entanglement speed. I'm not sure yet. I think it's going to take a lot of work to figure out the details of what those predictions might look like once you know if we can find them. a defined rule then it's actually going to be much easier to get very defined predictions because we're going to know the exact scales of things and so on.

I would say that in terms of finding the rule, there are probably five attributes that we think are The final rule has to have among them, you know, eventually giving a three-dimensional space that has certain properties about causal invariants, etc. We have individual rules that have each of those probably five attributes, but we don't have a single rule that has all of them. of those attributes and it's a matter of finding that I mean, actually you know, I think I mentioned before that we have this record, let me show you this, we have this, look at this record, am I sharing my screen?

Yeah, I have this record of notable universes and you'll see here um, let's see that these were some calculated properties of this particular universe, you know, the embarrassing thing is that it might be that in our record, you already have our physical universe with our description language, but we don't know yet, so, but this is something we have to go explore, okay, it's a question about the renormalization group and this framework, I think internalization. The group is alive and well in this framework. I think how about we do that. If we want to talk more about the realization group, let's talk about it tomorrow and our physicists and mathematicians Q&A, because I think that's going to get pretty technical pretty quickly, um, thoughts on Leonard.

Susskind's ideas about the complexity of entanglement, let's see, Jonathan is online here, maybe Jonathan would like to take that. Yes, I'm here, if you continue, you want it, you want it, you read these articles a lot more than I do, right, like this, like this. It turns out that, in fact, the geometry that is induced in the space of the branching eel as Stephen was talking seems to be remarkably similar to many of the geometric ideas that Susskind has been talking about in the context of things like the ER equals conjecture. EPR. and things like that, one possibility is that well effectively what happens is that different points in real branch space their natural distance metric can be expressed in terms of something like an entanglement entropy and then things like conjecture ER equals EPR, which is What Susskind is interested in can be formulated in terms of correspondences between the multidirectional evolution graph and the multidirectional causal graph, but as Stephen said before, we should probably address this in more detail and, Alex, Well, we'll talk about it in its entirety. correct technical detail, correct, but the short answer is yes, it is definitely related, so, okay, the next questions about string theory, um, and the question is, is this related to string theory?

We still don't know for sure. You know I was writing my kind of technical introduction to this and I wanted to talk about the analogy with string substitution systems and I was thinking about the title of that section, you know, the string case and I thought, oh my gosh, this it's going to confuse all the physicists because they'll think I'm talking about string theory um and then I started thinking, well, actually there's an analogy, but between these string substitution systems in string theory and you know, it starts like a play on words that if you make these strings longer and longer and you're It's like looking at the continuous limit of an infinite number of symbols and the strings.

What is that theory? And the absolutely strange thing is that that play on words can turn into physics. It may turn out that the continuous limit of string substitution systems is string theory or more. precisely string field theory, we still don't know for sure, but it is an interesting possibility and it is something that is good, I hope that some string theorists will analyze it and see how the analogy is established between what is happening in this in this theory and in string theory, my guess is that string theory is kind of will end up being some kind of simplified limit of some part of this theory, that would be my guess, they don't know for sure yet and possibly even this limit.

Of these string substitution systems which are not really the same as spatial hypergraphs, hybrid spatial graphs are in a sense much cleaner and have much less intrinsic structure than strings, they still have no notion of ordering and things like that in them. but that's at least my guess right now as to how that might correspond. Can this model explain weak nuclear forces? So the answer is certainly it is better that we know that the weak nuclear force is associated with the cross su 2 u 1. local gauge invariance that exists in the physical world and here there is a question that local gauge invariance is something like that we can think of a kind of rotation invariants, since things are the same when rotated, which are the same independent laws of physics. which way you are rotated, so to speak, and there is a more local version of that, you can rotate locally and give the case that you can match things in such a way that you still get the same laws of physics.

There is an analogy of that rotating in a kind of internal space that corresponds to the space of the so-called gauge groups and, in fact, in our models it exists. I think we strongly suspect that local gauge invariance can arise quite easily in our models. and essentially the way it comes out is that when you're doing updates, when you're applying these updates on different terms, you can apply these updates in different ways at a particular place in the spatial hypergraph and there are multiple ways to apply these updates. which essentially correspond to a kind of rotation in the spatial hypergraph and that rotation in the spatial hypergraph is like the operations on the gauge group and when you look at the sequences of those things we think that the limit of the type of equivalences between different updates that the limits of that set of equivalences will correspond to the continuous group of the lis group which corresponds to a local gauge group, so that just as the limitation of the spatial hypergraph itself is to a variety, something like ordinary space, the assumption is that the limitation of local equivalences rewriting rules around a particular point in the spatial hypergraph will end up corresponding, that the limit of those things will end up corresponding to a group lis that will correspond to local gauge invariants in the system and that will be what will lead to knowledge of the local caliber. invariants and you know it's part of its 2 cross V 1 is what gives you the W boson and the Z boson and the weak nuclear forces and you know I have to tell you that when I was a kid the weak nuclear force was my favorite thing and Even when I was about 13, I wrote this book with a long description of weak interactions that was about that, so that was before gauge groups were really important, but I'm a big weak interaction enthusiast. in physics and it is, but we can actually already take advantage of what has been done in the standard model of particle physics to know that if we can get the standard model, we have weak interactions that allow you to make all the generative rules produce objects similar to curvatures. emergently, then the problem is what is curvature and what is dimension, that's really the big part of the story, so we talked about measuring dimension by looking at the growth rate of these balls in the spatial hypergraph.

The curvature is and therefore the dimension is kind. of the leading term is the exponent of the leading term in that curvature of the growth rate is a correction of that, so for example, it is R raised to D times 1 minus R squared times the Ricci scalar curvature over 6 plus D plus 6 times D plus 2 and so on but in other words, the existence of curvature changes the growth rate of the number of elements in these so-called Gd SiC balls, so it's a complicated interaction between curvature and dimension once you say that there will be a finite dimension, so all the corrections to that once you fix the dimension the corrections correspond to the culture exactly what the interaction between curvature and dimension may be there may be some little surprises in terms of things that are dimension mixtures of curvature that we don't do I still don't understand it because all the calculus that we have built is in an integer dimensional space, we don't really know what the analogue of curvature is in a fractional dimensional space and that is what we have to be able to understand and understand that The interaction, let's see, is there. an equivalent graph with unordered edges to a given graph with ordered edges, yes, there is.

I talked about that in a section of my technical introduction, actually what I was studying in the 1990s involved unordered graphs rather than these ordered hypergraph constructions and the frustrating thing is that at the end of the day, after doing everything This works with this whole fancy system with elements and relationships etc., you can essentially get exactly the same results with trivalent graphs, the only thing that's different is the rule enumeration. is different, so if you say I want to find a simple rule that does this or that, the order in which you can list those rules can be completely different for graphstrivalents as it is for these ordered hypergraphs, so there is a difference there. and I think ordered hypergraphs are a cleaner way of enumerating what's going on, but it's a consequence of having models that have a sort of calculation in isolation that eventually they all end up being in some sense equivalent to each other and The frustrating thing is that I was very close to solving this in the 1990s, but you know, I should have tried a little harder to get there, but I didn't and so I languished for many years, okay, let's see, okay.

There's a question from Steve here on the live stream about a destroyer. I've been talking a little bit most of the time. I have been talking about a single rule that applies at a time when a single rule applies. increases the size of the hypergraph, you absolutely can also have rules that decrease the size of the hypergraph and yes, you can have a dynamic balance between rules that increase the size of the hypergraph and decrease the size of the hypergraph. I do not do it. I know if that will end up being important. I'll tell you a kind of allegory or something when Einstein invented the Einstein equations for general activity in 1915, one of the things that the simplest equations that he wrote predicted is that the universe expands and he said, but of course, the universe is not expanding, we can see we know that, so I am going to add this called cosmological term to solve the problem that the universe would expand according to his equations and Later he said that the cosmological term was the biggest mistake of his life, so to speak, because it turned out that another fifteen years later turned out well, the universe is actually expanding.

Now there is a lot of discussion about how big the cosmological term really is and Now we think there could be a cosmological term, a long and complicated story related to virtual particles and zero point energy etc., but in general, Attila T Einstein made the mistake of saying that the natural thing is that space expands the universe. it expands, but I'm going to put this trick in there to prevent it from expanding, so I'm trying to avoid making the exact same mistake. It is certainly possible to have in these rules a dynamic equilibrium where you have a kind of limited expansion rate because there is also contraction or you can have rules that simply expand Li unlimitedly.

I don't know what's really right and we need to look at that, but I think saying well, we obviously need rules that decrease size is making exactly Einstein's mistake and I don't want to do that, so could this answer the mystery of dark energy? and dark matter, so did I mention dark matter? My best guess is that these things that I call all Egan's, these very light particles, much lighter than the electron, could be related. Regarding dark matter, the main problem with elegans is the question of how hot they are, how fast they go, whether they go slow enough to get trapped in the gravity wells of galaxies and so on, or not, That's essentially a question of if polygons were produced in the early universe, how do they do it?

They get to the point where they interact so weakly that they only feel the force of gravity, they don't feel any other forces, and as a result, as the universe expands, they have now effectively cooled down. particularly if they occurred at a time before the dimensionality of space ended up being 3 and before we had a kind of inflationary period in the evolution of the universe, I think there is good reason to think that they will be very, very cold, but there will be very low energy and therefore will be caused by the gravitational worlds of galaxies, meaning they are reasonable candidates for dark matter now that their interaction with anything other than gravity would be extremely weak, so which is a challenge in terms. to detect them and that is one of the questions is whether specific models can be made and trying to do experiments around that dark energy is a slightly different story that has to do with the acceleration in the expansion of the universe and that I believe that It's more about whether it exists and whether that really is acceleration, it really plays out that way, it's more of a story of the exact structure of this, part of the way that the spatial hypergraph works and effectively in the derivation, as if Jonathan had a good referral. from Einstein's equations in which essentially the cosmological constant, which is what leads to dark energy etc., increases is an integration constant in certain equations and therefore we cannot determine from our derivation further immediate what that constant of integration is when we have With more knowledge about what the underlying rule is, we should be able to determine that and that will tell us if this type of spatial hypergraph, if the structure of the spatial hypergraph can add a dark energy term to the equations of Einstein, then the next question is.

What does this tell us about the nature of time? Is there physics in these models? Time is essentially associated with this kind of inexorable higher calculation, so the universe progresses through all these different rules that apply and it's the aggregate. of the progression of the application of those rules is the passage of time and one thing that must be mentioned is that in ordinary physics there are several different types of time, there is cosmological time, the time that defines the expansion of the universe, there is a kind of thermodynamic time. the time that defines the integration of entropy and the formation of heat, etc.

Perhaps there is psychological time for us humans to perceive what is happening in the universe in this model. One of the good things is that all of those types of time are aligned and they have to be aligned because now they are all associated with this underlying type of computational process. What happens is that we know a lot about how time works and based on I am your artillery and so on. What happens, as I was talking about before, is that in these models all that type of structure emerges as a consequence of the type of large scale operation of the model, well, what you put in the model is time as a calculation, what comes out of the model It is time in space, time, time as it operates in quantum mechanics, time in the way we are familiar with it in physics, but what? time in these models is the calculus of the program, that the passage of time is the operation of an irreducible calculus and it is a kind of satisfactory answer because it means that as time passes, something irreducible is happening, it's not like we can look at our universe and just say oh you don't need to control the universe, you don't need to exist for all these billions of years, we can just skip to the end and the answer is 42 or something like that.

What this says is in this model. We're explaining that no, it can't really be done, that there is irreducible computation involved in the progression of the universe, that's what time is, it's this irreducible progression of computation and, in a sense, that irreducible progression of computation. it really means something that cannot be done in any way. There's one more way than just going through the universe and seeing what it does, we can't jump ahead and immediately say this is the result. How sure are we that we will find the rule? It's a good question, you already met him last fall.

When we restarted this project, I didn't think we would get as far as we have. I thought we'd be caught up in computational irreducibility almost immediately and we'll be watching, you know, maybe we can get the first one. 10 to minus 100 seconds into the evolution of the universe, but we won't know if it really connects to the universe as it exists today. It has worked much better than I expected because there is this layer of computational reuse that we have discovered in these in these models now looking for the rule, the rule that corresponds to our description language, etc.

I don't know how difficult that will be. I really don't know and I don't know if you know I was going to do it. I don't know if we are going to find it this month of this year of the century. um, it's not easy to predict that because we just don't know if essentially what the question is: how good is the description language that I have. I've been telling you today how close this is to aligning between us humans and the physical universe and computing as we know it. How successful have we been in aligning those things?

If we are successful enough, the rule will turn out to be something very simple. expressed in that language um and we just don't know how successful we are at doing that, so we just can't say how difficult it will be to find the rule. I mean, we're going to do everything. types of searches, hopefully other people will too. It is not trivial to establish criteria. One of the things that happens when you look for the kind of computational universe of possible rules. My little mantra is that computational animals are always smarter than you anytime you set it. a trap for them every time you say I'm going to use this criteria to decide which ones are interesting, you will find those who somehow manage to get around that trap, they do things that you didn't expect at all, so it's a little difficult. doing these systematic searches, but you know we're going to do a lot of these and hopefully other people will help do it and that will help guide things and then we'll have to think a lot about it, let's see if we talk about emergent effective differential geometry from fundamental computational rules absolutely absolutely the differential geometry that emerges from that that's exactly what we're doing, we're saying that when a finite dimensional space emerges it has certain properties that have certain characteristic differential geometries that correspond to Einstein's equations when you end up with something whose limit is the entire dimensional space you can go to town with differential with traditional differential geometry you can define the Riemann tensor like you can talk about Christoffel symbols you can look at you Know the deviation equations all these all these things just work, they are more elaborate and less defined in fractional dimensional spaces, that's kind of a mathematical question that still needs to be solved, let's look at a standard science fiction question, can you go faster? light is possible to travel in time, okay, they can go fast and with complicated light because in the real space branch you are reaching that is something a little complicated, you can have entanglements as if you were doing quantum mechanics, but the cone of light is It adds up and depends on how wild the structure of spacetime is, you can have wild wormholes and things like this, but they will work pretty much the same way as in general relativity.

I think that's the story, the story about faster-than-light travel. More or less it's going to be the same as general relativity, a story about time travel, closed time curves. Yes, you can have rules that provide closed time curves and the multi-way graph, for example, but those rules do not support the possibility of foliation. z-- which are a kind of consistent temporal foliation z-- so again, closed temporal curves end up being like a consistency condition between different parts of the system and they have kind of a problem in terms of well, they have problems with invariants causes they have.

Basically the cause of variation says that you can't have closed time curves, um, so it's not understood, but time travel is a complicated concept anyway and the basic answer is that you can't take it into account. these types of models, antimatter problems. So the question about the universe is that there is matter and antimatter. By the way, we still don't know in our model how antimatter works for each particle. You can apply this charge conjugation operation that goes from one particle to each particle. like an electron to its antiparticle, the positron, and there's a question about how that's going to work in these models, we don't know for sure, the first thing we're hoping to get is something called the cpt theorem which says that if you charge conjugation parity that space reversal and time investment that the result of all those three things is guaranteed in traditional physics Lorentz invariants relativistic invariance guarantees that cpt invariance is an invariance of any theory that we have not yet proven in our theory, but not I don't expect it to be so difficult to prove that and that will at least give us an idea of ​​how antiparticles work and how they are actually obtained.

As I think about it, I have an idea of ​​how that might work, which I already have. We haven't thought about that yet. We've been in the last few weeks, as we've been preparing this to be able to present things and a website, etc., we've had a kind of no science policy because we know that if we start doing more science there will be a never-ending process to get to the Finally, it actually reminds me of Zeno's paradox and I have to mention something I forgot to mention. I was talking about that. I mentioned time dilation.

In relativity, relativistic time dilation, it turns out that there is a phenomenonSimilar in quantum mechanics, it's called the quantum Zeno effect, which basically says that if you measure too often you won't see things change, so essentially time dilates if you make too many measurements and in our theory that comes out very beautiful basically. It says that as you move in Branchville space, the motion and space of the branching field gives you time dilation and that's the quantum Zeno effect, but we were worried about a Zeno effect for this project anyway, yeah we do it too. A lot of science, if we keep doing science, will never finish the project, so to speak, so anyway one of the things we should talk about is charge conjugation and I had an idea of ​​how that might work, and I think the But about antimatter in general, one of the mysteries of the universe is that there doesn't seem to be much antimatter in the current universe.

It seems that there is and we could have thought that in the early universe it would be symmetrical between matter and antimatter. Actually, I worked. In that problem back in 1980, we tried to figure out why there is more matter than antimatter in the universe and we came up with a definitive theory about that that we still don't know if it's right or wrong because it involves some particles much heavier than things we've been able to see. so far: the central phenomenon that leads to the possibility of matter being compared to antimatter is the violation of CP invariants, so the universe appears to be invariant with respect to rotations, for example, but if you make a space inversion if you simply negate all coordinates, the so-called parity transformation, the universe is not invariant according to weak interactions, for example, well, actually, the most obvious thing is that neutrinos are each neutrino is almost exactly left-handed in the sense of which is its direction of motion and its spin are always arranged in a sort of counterclockwise shape with respect to its direction of motion and that means that the spatial inversion the universe is not symmetrical under the spatial inversion and the universe is also symmetrical, as I mentioned, the universe is invariant under the combination of charge conjugation parity, that space reversal and time reversal seems to be invariant under that, but individually it is not invariant under any of them and it is also not invariant under parity and charge conjugation CPE or equivalently under time inversion and that in equivalence At least in the theory I talked about around 1980, that is what leads to excess matter or antimatter when you combine it with the expansion of the universe, but we don't know how that will work that in our models and for example, There is a small amount of CP violation that is seen in particle physics and being able to reproduce that and our models will be really cool, we still don't know for sure how to do it, we may have or not to start building things that represent. particles like quarks and so on to be able to obtain that or it can be something more generic.

I have a sneaking suspicion that it might be more generic, making it possible to solve it without knowing the definitive rule, let's see here is the model consistent with Ian's many worlds theory, how about we send it to Jonathon? Evolution, the way we have constructed it, and the connection we conjecture it has to quantum mechanics is very reminiscent of the many-worlds interpretation of quantum mechanics, so it is the simplest version of the always Rezian interpretation in which there is no interaction. branches of quantum evolution that effectively correspond to the special case where you have just a multi-way evolution graph where everything branches and you don't get convergence between states in the more sophisticated type of Doshi and the version of the interpretation where you get an interaction between parallel branches of evolutionary history that correspond to our notion of a kind of multidirectional fusion and this notion that Stephen was talking about before of a kind of isolation of states within a kind of event horizons of quantum observation frames and things that are there.

We can go into more details, but we should probably save it for tomorrow. Well, David's question. Here we are saying that the universe is deterministic. The answer is simple. The answer is yes. However, it is a little more nuanced because we say there is. is this multi-way graph that has all these different stories of evolution, but we as observers of that graph are basically slicing different of these stories, but the entire multi-way graph is absolutely deterministic and our perception of it may not seem deterministic, but the actual progress of all those possible branches is completely deterministic if you ask questions like well, what does that mean for free will?

Well, that's all about computational irreducibility. Computational irreducibility is what gives us an impression of free will because even though everything is determined, you can I don't know what is going to happen effectively and more efficiently than just running it by running the calculation, so you can't know, oh no it's like you know that the 50s style sci-fi robot works according to logical rules and therefore you can predict what it's going to do, it doesn't work that way because of computational irreducibility, you're kind of stuck. When having to track the progress of time to know what is going to happen, how do you measure whether the rules you have are successful? a good question and that depends on this whole question of computational irreducibility versus computational reducibility in other words, you know, the fundamental question is whether we reproduce the parameters that we know in the universe, we reproduce that there are three dimensions of space, we reproduce that the relationship The electron mass of the muon is 206.

Do we reproduce that neutrinos are mainly left-handed? All that kind of stuff, um, that's what will ultimately determine if we find the rule, but we can already say that it's one thing if the rule is simple and then as soon as we get three dimensions of space and you know, electrons and electrons and muons and Torr lap tones and things. I would be surprised if it wasn't actually the rule because the distance between a simple rule and the neighboring simple rule will be enormous with respect to its effect on the universe, so going from one rule to the nearest neighbor rule, you will go from space infinite exponential space and something you know wildly different, as soon as you have the basic parameters of the universe you can really be, I think I'm very confident that everything else will fall into place, but that's the best hope and how difficult will be what parameters we will find first.

I don't know, for example, I have a I suspect that the local gauge group is going to be a direct window to the underlying rule that is going to greatly restrict the underlying rule in a way that I think dimension space doesn't. I think the dimension of spaces is emerging towards larger places. a scale in space and time to make it equally useful. I suspect the local gauge group will be a much better constraint, but we'll have to see, do we see the possibility of new ways to manipulate space? Oh, that's a good question, I don't know.

I mean, of course, all of these things are operating at length scales of like 10 to minus 93 meters, which is incredibly far from what we have now. If you have a pet black hole in your backyard, then there is a lot more that can be done, but we don't have favorite black holes, probably for the better. The question is whether by doing some kind of quantum measurement process and by doing some iterative quantum measurement process, it could have some strange effect on this whole process. branchial field space thing is conceivable it is conceivable that there could be some way to teleport by sliding through space in some elaborate way making use of some feature of the branchial space.

I don't know at the moment, it seems very far away, but I'm not sure, I mean, it's worth remembering that in particle physics we still don't have a single kind of practical application of anything beyond ordinary particles, there are no particles strange, for example, that they are particles, whatever they are. reduced to practicing even relativity, you know, it's a hundred years old, we're still just at the beginning of having things that actually matter in practice in practical things that we measure, are used in engineering, etc. in gaps and neutrinos how many lights do neutrinos have will be fine we don't know we know the neutrino mass matrix we know we don't know the individual rest mass of neutrinos but we know that neutrinos that mix with other neutrinos have certain velocities I'm trying to remember the limits of neutrino masses at this time.

The point is that we still have sort of 30 orders of magnitude between the absolute minimum masses of particles because there is an elementary element. Another thing I should say, you know, in standard physics right now, space and time are continuous and energy is also continuous and mass is also continuous, there is no quantization of mass and energy, and space and time , this quantification of angular momentum, there is quantification of all kinds of others. things, but there is no quantization of the momentum and mass of space-time energy in these models, those things are quantized, but the individual quantum units are really small and the point is that I suppose you can have particles that are a number small of quantum units of mass and those are really tiny, twenty or thirty orders of magnitude smaller than the current limits on neutrino masses, but that doesn't mean there can't be a whole spectrum of particles living in that space, much lighter. that neutrinos are much lighter than all these other types of things.

I mean, neutrinos have very weak interactions, that's part of why they have low masses, but there may be other reasons. It's a bit complicated, it's not directly related to that, but you know this possibility. It had never really occurred to me, at least, that there could be, you know, 20 orders of magnitude or 30 orders of magnitude of lighter particles that I've never really considered and I think that's kind of interesting even when we don't. I don't know the full parameters to start considering the next one. How is the graph stored? 10 to 500 steps requires a good amount of memory.

Yes, it requires all the memory in the universe. It's the universe. I mean, this is one of those philosophical questions. That comes up when you start saying that the universe operates according to a rule, it's a kind of computational rule, people start saying, well, what does that rule run on? Do you know where the computer that runs this rule is? Well it doesn't work that way, the rule is simply a description of how the universe works it's like when we know that the motion of the planets is governed by differential equations we don't believe that the planets have little mathematics within them solving those differential equations simply We are saying that differential equations are a way of describing how the planets move and it is exactly the same thing here we are saying that these rules are a way of describing what the universe does the universe is equivalent to performing these calculations it is not that the universe somehow it is performing these calculations externally it is just the The real thing that the universe is is the performance of these calculations and that means that the data structure of the universe is the universe, the computer of the universe is the universe itself, it is running itself , so to speak, and by the way, I mean it's It's interesting to see all these things about computing, all these ideas about computing, like the tradeoffs between space and time, and computing that's actually physical, the Tradeoff between space and time is related to relativity and similar spins and things like this. question, I mean, you know by turning what you've done into a theory like this, once you combine three things, once you combine calculus physics and mathematics, really, ultimately, they're all the same. kind of thing, so you know math is a thing. where you start with sort of axioms and then you say, well, what are the deductions you can make from the fact that physics has always been this empirical theory? where you say, well, the world works more or less like this and this is an approximation, but this means that In fact, we can find the rule precisely, like an ax in mathematics, where by simply calculating the consequences of that rule, by Just as we calculate the accident of mathematics, we know exactly what the universe does, of course, this computational reducibility, so it is irreducibly difficult to understand. do it, but from a conceptual point of view this will reduce physics to mathematics and similarly, in a sense, it is reducing physics to computation and it is providing a kind of and we can actually think about computation, so this is the universe , it's just an example of a Parallel calculation and the laws of physics will also be laws that will apply to these parallel calculations, so we can start talking about thingsrelativistic and I haven't discovered it yet.

This is another good thing we should talk about: analog. of time dilation for space-time offsets in parallel computing, but I think that all that formalism can be interconverted. Is there any application of this in the short term for the average person? My theory is there. We're not average people, but anyway, it's kind of like I think about it, you know, there will be technology that operates on the basis of elemental lengths of 10 to minus 93 meters, not in the short term, um, I think that's the main thing. The meaning of this is probably conceptual. I mean, I would say that a slight analogy can be drawn with what Copernicus did in 1500, more or less.

People had always thought they knew that the Sun revolves around the Earth. all that kind of stuff there was this whole theory of, you know, Ptolemy's theory of epicycles, all that kind of stuff works very well to predict the motion of the planets, even today, when we know that a eclipse, we're basically using the computational analogue of tens of thousands of epicycles, but what Copernicus did was show that there was actually a mathematical theory that could be established that didn't follow what we perceived through our senses that the Earth is stationary and the Sun is moving around it, but that was actually saying well, no, that's not really the case.

This mathematical theory shows that you can have the Sun at rest and the Earth moving around it, but the theory was a little complicated and had a lot of technical details and you know. I don't know how many people cared about the theory, but the consequence of the theory was that science and mathematics can tell you things that were not obvious to the everyday senses, to the ordinary senses, and that started a great progression of types of thinking. scientist who said he just solved the science, right? The fact that it cannot be solved by pure thought, by pure reasoning, is not really the important thing.

Science can solve it well. I think what we do. What we're seeing here is that we're seeing a kind of basis for physics for our understanding of the physical world that has its roots in computing and once we really believe in the fact that what computing is all about, once We really believe in all this, it is a kind of computing. Until the end, that has consequences and, for example, one of its important consequences is the phenomenon of computational irreducibility. There is simply no way out of computational irreducibility. Once things are computational, you will have computational irreducibility, and computational irreducibility has everyday consequences.

That is the question. that tells you that you can't just figure out what's going to happen by just thinking about it it's what it tells you that you can't know if a program is going to have an error without running it it's what it tells you when you have an algorithm to decide what content should being on a news feed and some AI-based algorithm for which you can't know what the consequences will be without running it effectively, is what limits the effectiveness of science to make sort of global predictions is one way in which Science is an interesting term, for example in the case of Copernicus, which was simply trusting science, it will discover everything we are saying. is that when things are rooted in computation, there are inevitable limitations of science that arise simply by nature, simply by the logical structure of the way that science is built from computation and those central to it. computational irreducibility and that implies certain limits on the way in which we think about science and I think that from an everyday point of view what I would say is that it is a different way of understanding the world and you know, since the time of Newton and Galileo and people like that we have concepts like momentum and force, etc., and those concepts were originally physics concepts, but we've been able to apply them to our general thinking about many kinds of things in the world that we talk about, you know, momentum. some product that isn't the physical movement of the product, presumably it's something more conceptual and we think about those things in a conceptual way and I think knowing that things are rooted in computing gives us a way to think conceptually about the world with concepts as computational? computational equivalence irreducibility principle undecidability those kinds of things that I think will have general applicability to how we think about the world far beyond the specific details of how the physical universe works.

Well, the question was: universal simulation. I think we can fairly say that that question really doesn't make any sense and let's see that Jonathan and I just worked on it. You know, this is one of those questions that always takes me a little while to unravel philosophically and Jonathan and I just worked on a In a nice succinct answer to that, let me see if I can find that here it is in the quality control section from the website and I think we might be okay here we go so okay so actually I guess I wrote this was Jonathan. somehow involved in this, then I want to say that the first point is that if there is a defined rule for the universe, it means that everything in the universe is determined from that rule, there are no external miracles in the universe, there is only this rule that determines how the universe works. works and then to say that the universe is a simulation would be to say that there is something intentional about this rule, there is someone, something set up this rule in the way that is right, so there is a, there is a notion of someone, some programmer. programmed this rule on purpose to be like this, well we already get into trouble trying to take intentionality outside the domain of humans, maybe even with animals we have problems, but when dealing with AIS we have a lot of problems and In the At the time we are dealing with you, you know other systems in nature, as you know, we could say that the weather has a mind of its own.

What is the weather trying to do today? Is the weather trying to get us wet? Do you know what you're trying to do? Is there a way to transfer our notion of intentionality to these other kinds of things? That is already very difficult to do. In this case, what we would be doing is transferring intentionality to the entire universe and saying that in some sense it was something external. the universe intentionally putting this rule, okay, that's the first problem, the second problem, which in a sense is an even worse problem, is that it is innocent, this rule, the idea of ​​spatial relativity implies that all the possible rules for the universe are, in some sense, equivalent to the rule that we who identify ourselves in our type of foliation of the universe is the one that corresponds to our particular way of understanding the universe, our language of particular description of the universe, so It really doesn't make any sense to say that you know someone can decide. in a rule, but any possible rule would work, the rule we consider is the one that is working and the one that fits into the description language we can create, so it's not something you can really insert from the outside, so I think I think that we're really pretty unraveled in terms of being able to say simulation university.

I think that's really not a sensible thing to say. I think I'll add an odd footnote. What in the end one could say about the universe after eliminating all this, all these different possible rules, all these different possible description languages, the only thing that shines is that the universe is a universal computer, nothing more than a universal computer, So people have asked me, do you know if the universe is capable? Know? When we have all the computers we can build as far as we know, they are all ultimately equivalent. We can program a computer to behave like any other computer.

We can make a Turing machine something like this. we can model any type of computer, we can emulate any type of computer that we build, whether it is the computer on our CPU chip or whether it is the computer that corresponds to some physical process, all of these things can be emulated, well, we know we can do it. This is because of the things we normally think of as calculations, but the question implied by this model is that the only absolutely certain thing we can say about the universe is that the universe is just a universal computer and nothing more than, for example, can you?

Let's say, well, what could be more than the universal computer? Well, here's an example, a Turing machine, for example, might be necessary, might just keep going, might keep going, you say, does the Turing machine ever stop even after infinite time? Well, we will know. which is something computationally irreducible, so you might have to spend infinite time to figure it out, but you can imagine building some kind of super Turing machine, a hypercomputer that could immediately answer the question and just say yes, this Turing. The machine you have after infinite time will stop or never keep up even after infinite time so a hypercomputer is something you can imagine but the question is can we build a hypercomputer in our physical universe and this model says?

No, you can't build a hypercomputer in our physical universe, and in fact, this kind of spatial relativity of rules implies that even if there were a hypercomputer that was something like our universe, even if there were rules for our universe that were possible. that, corresponding to hypercomputing, there was essentially a cosmological event horizon that would prevent us from communicating with those rules that correspond to hypercomputing, then there really isn't much room for a programmer in this whole story, well, let's see. Okay, so this question about an approximation of how big the bits are and the underlying rule, we have a way of estimating that I think is a little shaky, but the estimate we have is 10 to the minus 93 meters, which is really little one, let's see.

Okay, if we compute very finely grained, we should be able to converge to something that looks continuous, it's a way of doing continuous calculus. Well, the answer is that, um, what we're saying here, sorry, I'm a little confused by my my screen here, yeah, what we're saying here is that ultimately things are discrete, but at 10 raised to minus 93 meters that is actually very small and therefore to a very high degree of approximation we still see things that look continuous as a continuous space, this doesn't really give us any more way to do continuous calculus than it did then.

I mean, we're still doing the computation in the universe, so we start building the computational elements from things in the universe. I think this could give us some interesting things. ideas about how we could do some sort of massively parallel computation, but I think it's a different kind of story. A question about why there are four fundamental forces is related to this question about local gauge invariants. The four fundamental forces of the well that the standard model deals with. three of those in particle physics, well, four fundamental forces: gravity, the strong nuclear force, the weak nuclear force and electromagnetism.

Gravity has always been the odd-odd force in that sequence. In our models we explain how gravity works. The other three forces. we can see how those forces could arise they are all related to quantum mechanics, but the real test of those forces is that they are known to be associated with local gauge invariants and if we can reproduce local gauge invariants we will reproduce the possibility of those forces. but we haven't done it yet, we have an idea of ​​how it might work. Okay, let's say you have a rule for making useful descriptions of large-scale phenomena.

You would need to run the simulation due to computational irreducibility. Ultimately, yes. to find out that I'm doing this live broadcast right now from the original of the underlying rule for the universe and the initial condition for the universe, we would have to run that rule for whatever, 10 to 500 steps to get to this point and Unfortunately computational irreducibility means that we would probably have to basically execute those 10 to 500 steps and that's something we can't do in our universe. Our universe just did it, but we can't do it. Now in our universe the hope is that there are pockets of computational reducibility that allow us to make general statements without having to run all those irreducible calculations and one of the big surprises in this project is how thick the layer of computational reducibility is that allows us to derive Einstein's equations a Rive Schrodinger's equation deriving the path integral all these kinds of things that don't seem to fit with computational irreducibility are detailed parameters the detailed characteristics of the particles may well fit them, but These general characteristics of thePhysics don't intertwine in those things, so we can derive them, so to what extent is the limit of reducibility, we don't know, I mean realization after the fact.

Do we know that they are a somewhat thick layer of reducibility because that is why we humans can make any sense of the world? If everything in the world were immediately pushed into computational readability, we wouldn't be able to make any kind of general statement about how the world works, we wouldn't think that there is some kind of coherent functioning of the universe, everything would be trapped in this kind of very high-speed computational irreducibility. low level, let's see how the observer effect fits into this theory. Which means that a lot of what we're talking about is the interaction between the observer as part of the system and the system itself, the fact that when we try to analyze the system we are analyzing it in terms of causal graphs that represent causal relationships between events and what we're analyzing in terms of this foliation, the causal graph, etc., it's about trying to effectively model the way in which an observer who is embedded within the system interacts with the system that can be understood by the observer effect.

I mean things like the uncertainty principle that I talked about a little bit earlier about the well, again, it's all related to the observer as something embedded within the system, but that's also related to the geometry of branch field space and some others. kinds of things, but I'm not entirely sure what that means, Hi Jonathan, do you have a better idea on that? Yeah, yeah, okay, maybe I can add something so that when people talk about the observer effect in quantum mechanics, like you say, they normally do. that is, a kind of effect that the observer can have on the results of certain types with certain kinds of quantum measurements and effectively, in our model, this boils down to what Stephen was talking about before about these quantum observation frameworks that drank , where just as in relativity, when you have different relativistic observers, they can see different orderings of space, as separate updating events, in the case of quantum mechanics, where you are in the graph of multidirectional evolution of different quantum observers or depending on the identity of the quantum observer can see different branches as orderings of measurement events effectively how it works and again, this is probably something we can address in more detail later.

Oh, good answer. Thanks, okay, let's see if it increases the amount of computation in the universe. Over time, as it grows in richness and complexity, it is possible to quantify how well the clock speed of the universe is doing, so the odds of that being yes, the amount of computing that is happening in some sense increases. over time, because well, in less time as we perceive it because the way we are foliated in time, the way we decide what counts as the next moment in time, we are imagining that moments in time traverse everything the universe, so assuming we use the sort of way of measuring time, which is the typical way we think of measuring time, then the answer is that the spatial hypergraph increases in size as the universe evolves further. and we, and that is, or yes, it is basically certain that the spatial hypergraph is increasing in size probably related to the expansion of the universe and that means that, in a sense, for each new step of time in this type of time foliation , more pieces, more underlying nodes in the hypergraph, you have more underlying relationships. it must be updated to get to the next thing we consider at the next moment in time, so in that sense, yes, the amount of computation increases as we go through the evolution of the universe, what is the clock speed of which do we really have an estimate? that leaves me just looking up because I'm forgetting what I shouldn't be doing that Tim let me just see here um see I should I should know all this right away but I don't think these estimates either and they're still solid um come on look, okay, yeah, so the estimate for elemental time is 10 to the power of minus 101 seconds, so that would be the clock speed of the universe, i.e. the time elapsed between two update events on a single causal edge between two update events where we tend to - 101 seconds and in this estimate and that would be in a sense the clock speed um and this question then there is an interesting feature in the rules space there is also the notion of a maximum speed in rural space and that maximum speed is related and we don't understand that this is still essentially related to a maximum speed of translation between different description languages, so I think what that is going to do is link algorithmic information theory that talks about the complexity of the sizes of the programs with characteristics of physics and I think that just as we have the speed of light as a fundamental constant of the universe, I think we have another fundamental constant which is the maximum entanglement speed that I'm going to Zeta, I think there is another fundamental constant of nature which is the maximum speed and the space of rules that we call Rho and that maximum speed and the space of rules is essentially the maximum speed at which translations can occur between description languages ​​and which, as I say, is somehow related with a gives a scale for the size of the program that is just as the speed of light is translated from elementary time to length, the maximum entanglement speed is translated from elementary time to essentially quantum units, essentially h-bar, it translates in a kind of quantum extensions in branched space, so there is a translation of elementary time to distance in rule space and that distance in rule space is somehow related to the duration of the program, so that there is a way, I think, to connect the duration of the program, which has always been something quite abstract with something like physicality.

I still don't fully understand it, but I think it's a coming attraction, so to speak, okay, Peter's next question, you know? Does the theory predict how the universe ends? No, we don't know, we strongly suspect that the universe will end. We will continue forever that corresponds to a calculation that will not be maintained. There's a lot of reasons to believe that in this kind of model, but we can't, we can't say that for sure, I mean, there's a possibility that this. the calculation will eventually reach a final state where it just says and the answer is 42 or whatever, but it seems very unlikely that this will be the case.

It's very difficult to make that consistent with causality and variance. It's hard to make it consistent with things we already know to be true about. the universe, but it is not absolutely ruled out by this type of model. Okay, if the experiment produced a Turing Oracle or a hypercomputer, that would disprove the theory. Yes, that would disprove this theory. Good luck hooking up such a hypercomputer, though. Anything that our senses can deal with because in everything we have done in science we have tried to reduce what we observe in science to an essentially symbolic representation and a symbolic representation is a finite symbolic representation and is incapable of representing the types of raw material . that you really need to interact with a hypercomputer, so even if we had a hypercomputer right under our noses we wouldn't know because we simply don't have a good way to interact with a hypercomputer due to the fact that our way of describing things and probably even thinking about things It's rooted in a kind of symbolic notion of doing things.

Someone asks: can we get a copy of the project book signed by Jonathan Max and I'm not sure I've been considering that? We thought about this project and tried to understand what things we could offer people in this project and how people could participate. I have to say, loot was at the top of the list and we kind of embraced the universe. of ideas from the registry is also something that some are on the list, so we hope to be able to provide some of those things, but above all we are very interested, I mean, we see this as a kind of a great intellectual adventure it's kind of if we can climb the highest possible scientific Mount Everest and you know, we don't know if we'll get to the top and we don't know if it'll take a century to get to the top, but we think it'll be fun to see what happens on the way up and We hope that other people will help in that climb, but we also hope that people will find it interesting to see what it entails. get there and see what you know in our efforts to do some kind of frontline science what actually goes into doing that, let's see, so a question here: do the hypergraph updates happen in parallel?

What happens in the case? of collisions, yes that's the point, there are many possible updates that can occur and the fact that those possible updates exist defines this multidirectional system that is the source of quantum mechanics and what it means that they operate. In parallel, well, there is a set of causal relations in which one thing has to have happened before another can happen, which defines the causal graph, defines a partial order of those types of update events and that is the story complete understanding of what possible types of total ordering are consistent with that partial order that translates into what we consider these types of successive steps of time in our universe, that's how it all works and it's this invariance of the order of what happens. when things happen in parallel, that corresponds to calling invariants, that implies special relativity, that implies a kind of objectivity in quantum mechanics, etc., so yes, it is something very critical that these things can happen in parallel and that the collisions in quotes are precisely the same. that the kind of things that lead to entanglement, so to speak, that happen in quantum mechanics, etc., can the nominal average type contribute to this project?

You know we are going to have a distributed computing mechanism where some small fragment can be executed. to search the universe on your computer, that's a good way to contribute. I would say that we don't know what kind of thinking it will take to figure out everything that needs to be solved here and there. many types of both, I mean, some aspects of this will be on the front lines of sort of quantum field theory, general activity, those kinds of things that need a PhD in physics knowledge to really be fully. involved in them, but there's a lot going on at a sort of computational level where you know we're really operating from scratch, we don't know anything yet.

I would say a lot of the work I did on a new type. of science, etc., explore different types of systems, there is a lot to do there and there is a lot of intuition to develop. You know, I mentioned using string substitution systems as a way to understand the multi-way graph, etc., there's a lot of it. More can be done in that sense and this is a very young field, so there is a lot that can be done without having a PhD in physics. There is a lot that can be done simply by doing computational experiments trying to draw conclusions from them. computational experiments trying to come up with some sort of general principles based on those experiments and I don't think anyone has much of an advantage in doing that.

I mean, I've been doing that kind of stuff for 40 years, so I've developed a certain amount of intuition about it and I can do these things at a certain speed, but in particular, you know the tools that we have in the Wolfram Language. Part of the reason I built the Wolfram Language was to have what I needed to be able to. doing those explorations so those tools are very well optimized for those types of explorations and as I mentioned, the dwarven language features and things to do evolution according to these hypergraph models etc. are all available from today through our features repository and you. you can get them through the website and so on and so you can you can explore these things and you know it's a real open field no one has explored these things you know we've just started we've just been picking on the edge of So I think exploring both complete hypergraph rewriting systems is a bit complicated, but exploring these analogues and string rewriting even in things like cellular automata is very useful and it's like, it's a very open field where there's a huge amount to do and I think my unique um, you know, one of the things that happened from my work in a new kind of science is that I really pushed this idea that you can make models for things in the world just for things.

In nature, things in the social sciences are based on programs rather than mathematical equations and it's actually quite an interesting thing that's happened in the last 20 or 15 years and I'm not saying it's all faultmine, so to speak, but I think the new kind of science book was, you know, that was really the idea that I really pushed in that book was this idea of ​​using programs to make models of things instead of using mathematical equations and Afterwards you know. Basically it's been a 300-year streak of people primarily using mathematical equations to model things. In the last 15 years there has been a pretty complete transition towards using programs to make models of things and that's quite interesting to see, it's something that to me is kind of It's a little ironic because a group of people, when it came out my book, they said it couldn't possibly work, that it would never be useful, that the programs would never be useful for anything, and now that's basically what everyone does, so it's a good thing, but it's the only area where they really It was like this.

What has not been advanced is in the study of fundamental physics, where the idea of ​​using programs to make models of things has not progressed is in the study of fundamental physics and I think that now we have solved the problem of seeing how they can be use computer programs and ideas. modeling fundamental physics, that's something I'm a little excited about, but I think, as I say, what are the best contributions that can be made, you know, if you really want to get into the intellectual essence of this study. Simple programs study what they do, whether it's the actual full hypergraph or these simplified cases, and try to develop principles about what happens and try to find phenomena.

You know you can find some weird kind of new singularity that corresponds to some weird kind of mixed quantum mechanics. relativistic black hole or something, you might find that just by studying these hypergraphs and the evolution of these hypergraphs, the trick in these things, like you always see some strange phenomenon on the screen, what's maddeningly difficult is understanding what that really means. but there's a lot that can be done just by saying in the simple cases just look at these cases do a systematic study describe what you see systematically and that's part of the basis that you can do science and that's what a lot of science is just good science is Try to do things systematically, be able to have a good presentation of what you find, etc.

I mean, I would say that in this project what's happened over the 40 or so years that I've been Choosing things in some way related to this, has been a kind of gradual understanding of more and more what the meaning of things is and a gradual understanding that, often, it's that thing that I kind of understood, that I kind of had seen, but I didn't really understand its meaning and then I progressively understood more and more of its meaning and that's typically the slow part, at least in my experience, okay, we should answer a few more questions and then probably wrap this up for today, let's see.

How much simulation is required before enough information can be found to compare the rule with existing theories? We don't fully know the answer I said, there are several times here, I mean, we just don't know, we don't know. um, about the universe in the record of notable universes. I don't think we're done. We were actually re-running the log last night and I think they didn't finish running, so I think we have about a thousand universes. Those are actually just. universes that emerged from various searches were based on various criteria seem to have some interest or another are really quite arbitrary I mean, that's just the universe that just doesn't do anything or makes this very simple tree those that don't for the record, this universe It's just that for one reason or another it's like, oh, that's kind of interesting, putting them in the registry, we're generating too many things for the registry in the hopes of capturing things that will be useful. examples to study and by talking about it you know what the average person does on this project you know what we haven't even looked at every page in that record we don't know what's there we don't know what there might be There are a lot of really strange and interesting phenomena that we don't even We haven't even seen it yet, so that would be a good place to start.

Let's look at the theory of whether a hot dog is a sandwich. You know, one of the things the theory says is. There's a lot about the way we perceive things that depends on how we perceive them, and so I don't think we have anything directly to say about it, other than that there are different description languages ​​for the world and that they are sort of equivalents between these different description languages ​​and does not answer your question. um, someone comments that he likes what Jonathan said. Me too. Jonathan has been a great contributor, as has Max, to this project as well and I hope.

Tomorrow Jonathan will be a big part of the more technical explanations we are giving. The question here is can we explain the principle of least action in the context of hypergraphs? The answer is basically yes, we can reproduce the quantum mechanical path integral from which. you can derive the mechanical principle of least action and the way it works like I was mentioning is a kind of analogy of things, a kind of analogy of Einstein's equations in real brass space instead of in physical space and that That's what Tim, that's what you can that's what leads to this, okay, there's a search that uses Turner and the integrity of the rules to do massive calculations using tiny structures in the network, that's how the universe is going. building for us, I think it's doing an I all the time.

I mean, one of the things that really took me a while to accept is that this universe is a waste of computation. I mean, there's incredible amounts of computing going on to maintain a small chunk of space and that's a very strange thing now. Can we leverage that calculation for something we think is useful? I think it's useful for maintaining space, but can we leverage calculus in a way that has some purpose for us? We don't know how to do it yet. That's obviously it. It's very interesting to think that the length scales that are involved here are actually very small, so it's a challenge, but there may be ways to do it, okay, low entropy at the Big Bang, yeah, I think I talked a little bit about that, what?

What I think is happening is that the initial conditions may be very simple, but essentially what is happening is that the evolution, the irreducible calculation that is happening in the evolution of the system, encrypts those initial conditions in such a way that for us, As sort of computationally limited observers, we can't figure that out and when we can't figure it out it seems random to us, so it looks like it has high entropy and that's that phenomenon that leads to the second law of thermodynamics and the apparent increase in entropy. and the low entropy of inertia, which means that we can start from this low entropy, this very simple initial condition and end with this higher entropy with the law of increase of entropy, etc., to receive comments from established physicists orally, oh yes, many.

It has been something interesting. We haven't had it partly because of the pandemic. They haven't communicated to us that much. There was really only one type of completely interactive session with a group of friends of mine who were established physicists. It was really funny because I said they were getting it, which is really good, and they said this is really cool, so that's good. I had been in the last 24 or 48 hours that we were sending out more or less draft versions of some of this stuff and I'm sure while I was on this live stream I've gotten a lot of other responses and you know what's interesting here is the methodology, the underlying methodology is a little strange, but as soon as we've reached the level of connection with things like quantum field theory and general relativity, it's actually quite familiar and, as I mentioned, one of the really interesting things is This correspondence with many types of theories that have particularly emerged. in the last decade or so in physics, particularly as we come out of the CFT surveys of the '80s and so on, and I think that really helps make this connection with the kind of, you know, I used to be an established physicist, so established physicists are probably the wrong description I think I'm part of that group although I've been out of the business for a long time but you know what happened it's kind of a fun time walk.

For me, because you know many people who have been outstanding physicists. Do you know friends, colleagues of mine when I did physics? I happen to be a bit younger than most of them because I started doing physics when I was pretty young and it's been very strange for me because I've been following physics all these years but haven't been very involved in it. It's interesting for me to go back and see what happened with this particular thing. One of the things that has actually happened in physics is that there have been many different streams of development and one of the things that has happened in the established physics kind of thing is that many of those streams have merged in different ways, so that things that would be in completely different articles will now be found as words in the same sentence and, in fact, that unification I think we can take much further with this theory and the fact that we have related to many things.

Of those things I think it's very useful to make a connection with physics, you know, one of the things that I'm really hopeful that we can take advantage of what people have already studied a lot. of the kind of technical work in string theory Twista Theory all these kinds of things will be fine, that means we can say this in this and this in addition to what we have been able to say and one of the things that we hope to do in our live broadcasts is to have conversations with some of the leaders in those various fields, many of whom I think I would consider friends of mine from the time when I used to do physics, and to be able to talk about how their theories and the mathematical developments of their theories relate particularly to what we are doing here.

How does this define a context-free grammar for physics? Okay, so these hypergraph rewriting rules are like graph rewriting rules. Typically context-free grammars operate on strings, just sequences of things. they're like graph grammars, the theory of graph grammars isn't particularly well developed, but you can think of these things like they're hypergraph grammars, except our goal is a little different from a typical grammar and the typical grammar you're trying for. What you have to do is say analyze this sentence in English, for example, or analyze this part of a programming language code or something like that and you are saying that you know how to decompose it, make a tree with it and you are doing it by saying that there are these rules. and I'm going to thin out the tree that could be used to generate it.

What we're doing instead is running that process in reverse and we're saying take this starting point and do our best to figure out what might happen and in a sense what we're doing is like running a graph grammar in reverse, running a graph grammar in reverse. hypergraphic in reverse and that's what's really happening here and we're. the intermediate our entire existence and the entire universe are the intermediate stages the non-terminal nodes effectively in the operation of that hypergraph grammar in reverse, is it possible to write unit tests that validate the presence of certain analogous physical characteristics when a particular rule is applied ? run hmm, my goodness, how to think that you know one of the well, let me try and take it this way, so one of the things about existing science, particularly experimental science, is the idea of ​​doing isolated experiments, so that in experimental science the typical thing I'm trying to do is say: I'm going to do an experiment on this part of this system and nothing else matters.

I'm going to be able to try to isolate the effects in this particular area of ​​the universe to just do an experiment on it. Well, that's something that's been really critical in experimental science. One of the characteristics of these models is that everything is really connected to each other, so it is actually more difficult to know, since we have been working on the study of these models. What we've often done is say, let's idealize everything, let's just make a sample of the old black hole and nothing else, well, it turns out you can't do that, you have to have all the other things around it, you can't just make this hole black isolated with nothing of the rest of the universe hanging around it and the least we have we don't think we can do that, so you know, we spend a lot of time trying to do these idealized experiments. based on a kind of separation, isolation of particular effects in the universe and being able to study them separately and that turned out to be quite difficult, in other words, everything comes together in this model of the universe, so it is possible to analyze it.

In these edge cases where you can do a sort of unit test and just test that feature onparticular without trying other features, it's quite difficult and that's one of the challenges to find ways that you can use some kind of computational reduction capability to cause. After those unit tests, you could say that there is a bit of humor here, that Max is a big unit testing enthusiast. Max is probably the biggest software engineer on our small team here and one of the things I've continually given. What's hard for him is that he insists on building with the fundamental code that we have that runs these models on setting up unit tests for every possible aspect and continuously integrating all of this code and I've been complaining. which, you know, we don't even know where certain aspects of this model are correct, so you know you shouldn't be doing all these precise unit tests, but I'm really glad that you did them because it means that we know that the code is actually doing what we think it's doing, but I'm a little amused that unit testing the question of unit testing the universe is reminiscent of unit testing universe models. which we have contributed greatly to in this project, so one question is: are there general methods to find out where the computational reducibility is?

It's a really interesting question. I don't know the answer, you know, machine learning could speed up what is essentially our human poking around at things and we've used machine learning. I've used machine learning a little bit to analyze some of these models, etc., but I don't have a really good answer for that, I guess that says. That guy is like the automated scientist, if you will, looking for computational reducibility. You know that reducibility is where you can make a scientific law, so asking to automate the finding of computational reducibility is like seeking to automate the process. of science so to speak and with a little bit of the ways to achieve it, but we don't know a really systematic way to do it.

Well, I think we should end here, so thank you all for coming. I am very excited to

launch

this project. I hope people decide to participate. I encourage you to check out all the things on the website and start playing with the real tools we provide. Give us your opinion. I bet they're a bunch of professionals. physicists in this live stream and mathematicians so I really hope there's stuff to dig into like I say tomorrow we plan to do two more Q&As 14 mainly more professional physicists and mathematicians where we'll really get into arbitrary levels of detail from other people .

You might find it funny, but I don't guarantee that we'll explain everything we're talking about there and then the QC will be a QC on the kind of philosophy of this, some of what it means to find the fundamental theory of physics in this. In some ways, then we plan to continue on Thursday with a QA session on computer science where we will talk about both types of this from a computer science point of view and the possible implications of this for thinking about the fundamentals of the theory of computation. calculation and so on, thank you all very much and we hope to see you all in another live broadcast another day, thank you