Theories of Everything with Curt Jaimungal - Stephen Wolfram on Crypto, Aliens, Blackholes, Infinity, Consciousness, and his Theory of Everything

Episode Date: June 8, 2021

YouTube link: https://youtu.be/1sXrRc3BhrsStephen Wolfram is at his jovial peak in this technical interview regarding the Wolfram Physics project (theory of everything). Sponsors: https://brilliant.org/TOE for 20% off. http://algo.com for supply chain AI.Link to the Wolfram project: https://www.wolframphysics.org/Patreon for conversations on Theories of Everything, Consciousness, Free Will, and God: https://patreon.com/curtjaimungal Crypto (anonymous): https://tinyurl.com/cryptoTOE PayPal: https://tinyurl.com/paypalTOE Twitter: https://twitter.com/TOEwithCurt Discord Invite: https://discord.com/invite/kBcnfNVwqs iTunes: https://podcasts.apple.com/ca/podcast/better-left-unsaid-with-curt-jaimungal/id1521758802 Pandora: https://pdora.co/33b9lfP Spotify: https://open.spotify.com/show/4gL14b92xAErofYQA7bU4e Subreddit r/TheoriesOfEverything: https://reddit.com/r/theoriesofeverythingTIMESTAMPS: 00:00:00 Introduction 00:02:26 Behind the scenes 00:04:00 Wolfram critiques are from people who haven't read the papers (generally) 00:10:39 The Wolfram Model (Theory of Everything) overview in under 20 minutes 00:29:35 Causal graph vs. multiway graph 00:39:42 Global confluence and causal invariance 00:44:06 Rulial space 00:49:05 How to build your own Theory of Everything 00:54:00 Computational reducibility and irreducibility 00:59:14 Speaking to aliens / communication with other life forms 01:06:06 Extra-terrestrials could be all around us, and we'd never see it 01:10:03 Is the universe conscious? What is "intelligence"? 01:13:03 Do photons experience time? (in the Wolfram model) 01:15:07 "Speed of light" in rulial space 01:16:37 Principle of computational equivalence 01:21:13 Irreducibility vs undecidability and computational equivalence 01:23:47 Is infinity "real"? 01:28:08 Discrete vs continuous space 01:33:40 Testing discrete space with the cosmic background radiation (CMB) 01:34:35 Multiple dimensions of time 01:36:12 Defining "beauty" in mathematics, as geodesics in proof space 01:37:29 Particles are "black holes" in branchial space 01:39:44 New Feynman stories about his abjuring of woo woo 01:43:52 Holographic principle / AdS CFT correspondence, and particles as black holes 01:46:38 Wolfram's view on cryptocurrencies, and how his company trades in crypto [Amjad Hussain] 01:57:38 Einstein field equations in economics 02:03:04 How to revolutionize a field of study as a beginner 02:04:50 Bonus section of Curt's thoughts and questions* * *Just wrapped (April 2021) a documentary called Better Left Unsaid http://betterleftunsaidfilm.com on the topic of "when does the left go too far?" Visit that site if you'd like to watch it.

Stephen Wolfram is one of the most inventive and prolific people on the planet. He's the rare trifecta of a computer scientist, a physicist, and a business person, who founded Wolfram Research Designed Mathematica, which is a program that almost each mathematician-slash-physicist uses, especially engineers, as well as Wolfram Alpha, which powers Siri. This may be the most wide-ranging interview with Stephen that exists. We talk about aliens or alien life and the communication with them,

cryptocurrency, the nature of infinity and the reality to infinity. He even gives a template as to how to build your own theory of everything, which separates him from others because most of the time people are proposing their own theory of everything. Keep in mind that the podcasts on theories of everything

tend to be a bit more abstruse and technical. If you don't follow some of the jargon, that's okay. The point is that you stick through anyway till the end to get an overview and then it's in the rewatching that the actual information is gleaned. This was a live stream which is now reposted with better video and audio. And while I was live streaming at the end,

I gave some of my thoughts which I've included at the end of this as well. They include objections that I may have or questions that I'd like you to explore, and perhaps you can give me your thoughts, your answers in the Discord, or leave them in the comments section below. The sponsor of today's podcast is Algo. Algo is an end-to-end supply chain optimization software company with software that helps business users optimize sales and operations, planning to avoid stockouts, reduce returns and inventory write-downs while reducing inventory investment.

It's a supply chain AI that drives smart IOI headed by a bright individual by the name of Amjad Hussain. Another supporter of the podcast is Brilliant. You can subscribe to brilliant.org slash toe, T-O-E, if you'd like 20% off their annual subscription. And I'll be speaking more on that later. If you'd like to% off their annual subscription, and I'll be speaking more on that later If you'd like to hear more conversations like this, then please do consider supporting at patreon.com slash Kurt

Jai Mungle. I've also recently opened up a crypto account and a PayPal account and if you like you can donate there I plan on having many more conversations like this at the end of August There's going to be Yosha Bach and Donald Hoffman coming. At the end of this month, I'm speaking to Chris Langan. He's the person who has reportedly the highest IQ in America, and has a theory of everything called the Cognitive Theoretic Model of the Universe. There's also a Discord with the link in the description. If you'd like to discuss the topics in this podcast or other podcasts in real time to chat with other people who are like yourself. Thank you so much and enjoy. I like your colored background. That's very stylish. Oh, thank you. I appreciate that. So tell me just before we get started here, just give me a sense of who your viewers are.

Sure, sure, sure. They're generally mathematicians and physicists, as well as amateur mathematicians and physicists, people who are interested in consciousness as well. So we'll talk a bit about consciousness. So how long have you been doing this podcast? I've been doing it for almost a year, and I'm surprised that I was super excited that it's growing the way it is. Well, I just hope people continue to be interested in these intellectual things when they're not locked at home with the pandemic. Yeah, that's right. That's right. If I look around, I'm just focused on you. I have notes here.

Don't worry about it. Don't worry about it. You won't distract me. Great, great, of you, of what you've done is difficult to overstate with regard to the tools you provided mathematicians and engineers, physicists. You've not only provided concrete computational tools, but also, I don't know if you've heard of this concept called psychotechnologies. Language is a psychotechnology. It's what changes the way that you communicate and think. It's a good term. I haven't heard of heard that term so that's an interesting term great sounds a little

bit sinister though well i don't intend to be sinister it is important to give people frameworks to think within but uh uh yeah much of the critiques that i've read of yours are ad hominins they're not from people who have read your work. And I find that frustrating because as I'm researching, firstly, just so you know, I've gone through the Jonathan Gerard archive papers, almost each of them, as well as your bulletins. And it's so tricky. At least I find it frustrating because people who are commenting on you are commenting at an extremely high level at what they perceive you're doing or what they perceive you think you're doing with what you're doing.

And I'm curious if you get frustrated as well. One feature of, you know, I do what I do because I'm interested in doing what I do, so to speak. I'm not really doing it because I'm, you know, trying to convince other people that what we're doing is incredibly clever or whatever. And, you know, so the kind of, if I had spent my life kind of saying, what do other people think about what I'm doing? I wouldn't have done most of the things I've ever done. And I think, as a matter of fact, the thing that's been actually a surprise to me is how very positive so many people, particularly in the physics community, are being about the project that we're doing.

You know, it's a surprise partly because 20 years ago, when I released my new kind of science book, it's, you know, I'm enough of a student of the history of science that I kind of understand a little bit about what happens when paradigm shifts, when sort of changes of thinking occur. And one is absolutely should expect that the benign thing that happens is people just keep doing what they were doing before and they completely ignore whatever the new paradigm is. The less benign thing is people get out their pitchforks and they say, we don't want a new paradigm. We're, you know, go away. We just want to keep doing what we've been doing.

And what I found when the new kind of science book came out 20 years ago, in pretty much every field other than fundamental physics, people were like, oh, this is kind of interesting. You know, we don't mind having a new paradigm. We've, you know, we're there, or maybe they said we don't care. But mostly they were, most fields, it was like this idea of using computation as a foundation for modeling. This seems interesting. This seems like something we should explore. And they did. One place where that was, where it was a lot of pitchforks was a little strange to me because

you know I used to be a professional theoretical physicist so to speak so I you know I knew that crowd of people and it was a bit surprising to me you know I said to many of them I'm surprised you care why do you care so much and they were like because what you're doing is going to destroy all the stuff we've been doing and it's like I don't think so you know if we're doing something it's complementary to what's what's being done elsewhere not not something that across purposes so okay so 20 years goes by and now for a whole variety of reasons, not the least being Jonathan Gorad and Max Piskunov and other people sort of saying, yes, we'll help you actually push this thing forward. I get started on the project again. Two things surprised me. paradigm that we've kind of built out is much more sort of much more not

complimentary but much more kind of supportive of a lot of existing mathematical physics than I had expected that's one thing that's an intellectual thing the biggest surprise is the sociological response has been basically positive. And, you know, it's not a trivial thing to introduce something which is sort of a significant change of a bunch of ideas in a field and have people feel like, yes, that's a good thing. It's something that people can get behind. So I'm sure there's all kinds of copping about all kinds of things. And I have to say, it's completely invisible to me. I don't read it. I don't know what's there.

I don't really care. I think one thing to realize about my kind of activities is, from my point of view, one of the things that I get, you know, personally most fulfilled by is thinking that the things that I build, whether they're practical technological tools, whether they're ideas, are things other people have fun with. To me, for whatever reason of, you know, personal peculiarity or whatever, I like that. That's really nice. I like feeling that way. I also recognize that, you know, anytime one has a degree of visibility in the world, one becomes kind of a thing that gets battered around by people of like, look, you know, I can use this person as an example of this point that I'm making about this. this or you know look I you know I need to hate this person because this and that and the other you know because it makes me look good for this group of people or whatever it is who knows what you know that's what you sign up for if you're doing things that have visibility in the world

and as far as I'm concerned you know it's insofar as I'm kind of the mascot of or the anti-mascot for this or that thing, it's like, okay, that's fine. It has very little to do with me, so to speak. So I would say that the thing that's been interesting is, you know, there are a lot of fields now where there's a pretty good sort of back and forth connection between the things that we've been doing with our physics project and the kinds of often quite sophisticated mathematical physics that people have been developing in those areas. And as far as I'm concerned, that's really cool.

I mean, it's really nice. these fields sometimes they're fields which have been a little bit marooned because they've been or a little bit sort of adrift because they're fields where there's a lot of interesting mathematical structure but they don't really know how it connects to the real world so to speak and now we're giving them a way to connect and often giving them a way to understand why their mathematical structure is more natural than they thought and so on and I think for me personally the fact that people in those fields are excited about this, that's really cool. I really like that. But perhaps I didn't, since I didn't hear all the words of the question you asked, maybe I wasn't answering them. I'm not used to this particular recording mechanism, so I can't be absolutely certain, but it looks right. Why don't you give

a three-minute synopsis, I know that's difficult, as to your theory for those who are unacquainted? Well, gosh. So I've been working on this for like 40 years, so it's a little bit hard to compress, but I suppose as gradually as one learns more about what one's talking about, it becomes easier to explain. All right, let's talk about physics and kind of what's the universe made of, so to speak. And I think one of the things that has been, the first question is, we think about things like space and time, and the traditional view of something like space has been,

it's this thing that you put things in. It isn't a thing itself it's just sort of a background and you get to specify a position here or there in space. That's been kind of the idea of space since Euclid and so on. So one of the basic points in kind of the models that we've developed is there's something, space is made of something, just like a fluid like water. You might think of it as just a continuous fluid where you can like put something anywhere in the fluid. Actually, you can't.

It's made of discrete molecules bouncing around. And so we think it is with space that sort of at the lowest level at very small scales space is just made of a whole collection of discrete elements we can think of them as like geometrical points but they're not points that have a known position in anything they're just discrete elements and the only thing we know about those elements is how they're connected to other elements so it's kind of like the uh the the points since that exist in the universe are sort of friends with other points and we build up this whole network of connections between points and so our our universe as it is today might have maybe 10 to the 400 of these uh of these sort of atoms

of space that make it up so sort of the first point is everything in the universe is just space so what uh all of the particles and electrons and quarks and all those kinds of things they're all just features of this details of the connections between these atoms of space so sort of the first thing is what's the universe made of it's made of space what space made of space is made of this giant network of of nodes giant network of discrete elements and we don't even from that know why is space three-dimensional the thing could be connected any way way it wants. What happens is that on a large scale something which is discreetly connected like that can behave as if it is for example a three-dimensional manifold on a large scale. And for example one thing that can happen and we think does happen in the early universe

is that the universe goes from being essentially an infinite dimensional network where things are everything sort of connected to everything else to this sort of more or less three-dimensional so far as we know right now perfectly three-dimensional though we suspect there are some dimension fluctuations that exists today so okay so that's sort of what space is then what's time well the the the point is the idea is that there are these definite rules that will say, if there's a piece of network that looks like this, transform it into one that looks like that. And that's continually happening throughout this network that represents the structure of space and the content of the universe.

And so what we're seeing then is a sort of progression of all of these little updates of this network that represents space and that progress of all those updates corresponds to the progress of time. And one of the things that's unusual about that is for the last hundred years or so in physics, people have kind of assumed space and time as sort of the same kind of thing. One knows about relativity, one knows that sort of there's processes that kind of trade off space with time yet in our theory space is this extension of this this as it is turns out to be a hypergraph this network basically and time is the progressive sort of inexorable computation of the next configuration of the network based on rewriting the previous configuration

so one of the things that is sort of an early thing to realize in our models is this question of, so how does something like relativity arise? Well, the answer is, if you are an entity embedded within this network, it turns out that the only thing you are ever sensitive to is kind of the network of causal relationships between updating events. And it turns out, there's a few more steps here, but it turns out that with certain conditions on the way those updatings work, it is the case that basically special relativity comes out of that. We can talk in more detail about how that works. So the next thing that happens is this space just made up from this network,

it's sort of the continuum limit of this network in the sense it's like you've got these atoms of space underneath, and then on a large scale space is like kind of a fluid made up of lots of atoms that behaves in the continuous way that we're used to perceiving it. And then it turns out that you can get space in any of the dimensions, you can get space with different kinds of curvature. One of the big results is that you can get the way the curvature arises in space is exactly the way that Einstein's equations for gravity say curvature should arise. Roughly,

the way that Einstein's equations for gravity say curvature should arise. Roughly, energy, momentum, mass, these are all associated with levels of activity in the network. And roughly, levels of activity in the network produce curvature in the network, in just the way that Einstein's equations say that energy momentum in physical space-time should produce curvature in space. So that's a pretty important thing. I actually knew that back in the 1990s that these models could reproduce general relativity, reproduce Einstein's equations.

So then the next big sort of pillar of 20th century physics is quantum mechanics. They're really probably two or maybe three pillars of 20th century physics. General relativity, the theory of gravity, quantum mechanics and also to some extent statistical mechanics which also sort of comes out from the formalism of these models but maybe it's not the first thing to explain here. So how does quantum mechanics arise?

Well first thing is what is quantum mechanics? What is the important feature of quantum mechanics? Basically in classical physics before the 1920s or so people thought that in physics there were definite equations of motion. Things behave in definite ways. You throw a ball it goes in a definite trajectory. When what quantum mechanics says is no that isn't what happens, instead there are many possible histories that develop and the universe has many possible histories and all we get to be sensitive to is some kind of aggregated probability of what happens, not knowing specifically what the history of the universe is.

Well it turns out in our models that's something that inevitably works that way and what happens is we're talking about sort of the rewriting of this big network and the point is that there isn't just one possible rewrite that happens at any given time. There are many possible rewrites and each of those different possible rewrites represents essentially taking the universe in a different path of history. But the critical fact is that just as there might be two possible rewrites that could happen and they produce a branching of two paths of history, so also it will turn out when there are other rewritings that can happen later that actually these branches can merge. So you end up with something which is this whole graph of possible histories we call it a multi-way graph and in this multi-way graph there is both branching and merging of histories and that process of branching and merging of histories

that ends up being the story of quantum mechanics basically. And one of the things that sort of a thing to think about is when we look at, they have this whole multi-way graph of all these branching histories of the universe. And we say, let's imagine that we are observing that. We are, it's a little bit hard to imagine because what's happening is we, our brains, our minds are themselves embedded in this multi-way graph. So just as the universe is breaking into all these different paths of history, so too are our brains breaking into all these different paths of history. So in a sense what's happening is it's a branching brain observing a branching universe.

You have to kind of think about how does our mind make sense of that universe? And what you realize is that you're kind of defining what we might call reference frames, kind of quantum reference frames. They're analogous to the reference frames that we think about in relativity, where reference frames, typical inertial frames are things like you are at rest, you're traveling at a certain velocity, et cetera, et cetera etc., etc. There's kind of a quantum analog of those. And that's the way that we perceive this multi-way graph of possible histories. And so when we say, let's pick a particular quantum reference frame, corresponds to more or less a particular time. And let's then ask, what is the sort of slice of this multi-way graph defined by this quantum

reference frame. What we have is all these different possible histories and they're all kind of laid out in some sense. Histories can be close to each other if they had common ancestors recently. Histories can be further away from each other if they didn't have a common ancestor for a long time and so on. All these histories are kind of laid out in some kind of space. We call that branchial space, the space of branches, the space of quantum branches. And that branchial space, it's

not like physical space, it's not like something where you have ordinary motion from one place to another, but in branchial space there is, it's a layout of possible histories, possible states of the universe effectively. So one of the things that I find really neat is that you can talk about motion in physical space. You can talk about, for example, you know, even ever since Newton, we've kind of had this principle that if things aren't acted on by a force, they will keep going in a state of uniform motion. So it's kind of like things go in straight lines if you leave them by themselves and kind of Einstein's big idea in general relativity

was to think that yes things do go in kind of straight lines in the sense that their shortest paths geodesic paths but space can be curved and then what might be to the thing, kind of its straight line path, to the outside is a curved path, and because that curvature is associated with energy momentum, that is what leads to the effect of gravity, so to speak. So in physical space, that's how things work. Turns out in branchial space, they work in essentially exactly the same way, except now, in terms of the equations of of gravity we have the equations of quantum mechanics and quantum field theory and essentially what's happening is that there are sort of paths in branchial space that are being followed and we are seeing deflections of those paths actually

associated also with energy momentum and the way those deflections work exactly gives one the path integral of quantum mechanics. So the thing that's really pretty neat is, I mean, one of many very neat things. But one thing that I just found really was a very wow moment about a year and a bit ago now. Gosh, I can't believe it's so long. Congratulations, by the way. Yeah, well, time inexorably moves forward, right? So it's, but I think that, you know, sort of a wow moment was realizing

that the Einstein equations of physical space are basically the same thing as the Feynman path integral in branchial space. So in a sense general relativity and quantum mechanics are the same theory just played out in these different kinds of space and that has a lot of implications because it kind of shows one how there are correspondences between general relativity and quantum and quantum mechanics and they're sort of the sort of I don't know intersectional cases when one's dealing with black holes and so on.

But so that's at least one level of the story of our models of physics. And there's a lot of detail and a lot of things that are now, it's now clear, yes, we really can reproduce exactly what happens in black hole mergers. We can reproduce what happens in quantum computing. we can reproduce all these other kinds of things and we're starting to have kind of ideas about uh you know a lot of i know a lot of experimental physicists who keep on saying to me when are you going to give us actual experiments to do and we're getting closer you know it's no point in telling them there's a lot of actual physics and astrophysics and so on to be done to work out exactly what to look for but I mean another direction here that that is well there's there's several directions I mean one is kind of understanding I've had sort of in the last few months kind of a deeper understanding of what kind of observers of the universe we

actually are and how consciousness relates to what kinds of things we do and don't observe about the universe and what consequences that has for the kinds of laws the kinds of physical laws that we believe are going on in the universe that's one direction another direction is trying to understand if we can say yes we have this simple rule that's updating this hypergraph and so on and then you say why is it that simple rule not another one what I've realized recently what we realized a while ago but it's become a lot crisper now is this idea that actually there is the in some sense the universe can be running all possible rules and we are we are seeing some kind of reference frame not in physical space or in branchial space but in this thing we call ruleal space the space of all possible rules we are essentially picking

a particular description language a particular reference frame with which to understand the universe and so this sort of paradox of why or this the sort of conundrum of why does one why does the universe follow one particular rule and not others turns out the answer is it follows all possible rules and we are just at some place in ruleal space observing it in a particular way and that has the big surprise to me recently last month or so has been realizing that I actually think we can get a serious answer to a question like why does the universe exist? And as a matter of fact, the thing that comes out of that is the realization that as soon as we say the universe exists, and as soon as we give that argument,

we are forced into a position that mathematics in some sense fundamentally exists too which is something you know people like Plato have said but something very different from the way that people have assumed the foundations of mathematics work. So you asked me for a three minute I'm sure that wasn't three minutes but summary but that's I mean I have not talked about a lot of the intuitional underpinnings that are necessary for this theory of physics. Concepts like the principle of computational equivalence, computational irreducibility, and so on. I mean, what's basically happened in the building of this theory is it's sort of the result of, well, I guess it's now 40 years of my activities that in the first,

the first layer is probably, you know, I used to do sort of traditional quantum field theory, general relativity, particle physics kinds of things. So I know that stuff fairly well, although it's kind of, it's a Rip Van Winkle type situation for me because that was 40 years ago. And I'm now kind of, it hasn't changed as much as you might have thought a field might change. Like if I look at biology over that period of time, you know, there were all these things in biology

where it's like I learned stuff about cells 40 years ago, 45 years ago, whatever. And it was like, that's an organelle of unknown function. And now there's a whole, you know, vast journals devoted to exactly what, you know, the Golgi complex does or something, something like this. So in a sense, that field has advanced a lot more than physics over that period of time. But I think the, you know, sort of that layer, then there's the layer that I've spent years building practical technology for actually computing things.

And both the level of understanding of how formal systems work that has come with the process of designing Wolfram language and Mathematica and so on, that has been really critical to what we built. And then the very practicalities of, you know, so we actually have an environment in which to do experiments. We can, you know, do graph theory easily and things like this. And then the whole new kind of science development of what simple programs do, understanding principles of that and so on. And I realized there's a, there's in the end, a fairly tall tower that we've ended up relying on to, to kind of construct this theory. And I, you know, to me, is this funny feeling, because, you know, I'm really excited that we managed to get this done. And it's gone a lot better than I expected it would go. But it almost didn't happen. I mean, it very, very nearly didn't

happen. And, you know, the question that I might ask myself is, if it hadn't happened, when would it have happened otherwise? And the answer is, I don't know, 50 years, 100 years, I don't know. It wasn't a thing where, it wasn't like all the stars were lined up for everybody, so to speak. It was a particular series of things that are kind of the story of my life and then people like Jonathan who had their own things that they bring into this you know it's kind of a an unexpected and unusual alignment plus it turned out we managed to get a lot further than we ever expected to get so it's anyway that's a little bit of an outline of kind of where we are I suppose I mean there's a lot more to an outline of kind of where we are, I suppose. I mean, there's a lot more to say about the details of what's happening with the models

and how we compute things from them and so on. But you asked for a basic introduction. That's my attempt at a basic introduction. What's the difference between the causal graph and the multi-way graph? Is one a transitive reduction of the other, or are they the same? No, no, they're different kinds of things so so you have this prop okay so that there are many kinds of graphs oh look there we go there's a nice this is a multi-way or a causal that's a causal graph that that thing is a causal graph so okay sorry there are lots of kinds of graphs running around.

Yeah, that's fine. And each one of these nodes represents a hypergraph in and of itself, and then these lines represent updating rules? That's a causal graph. No, each one of those nodes represents an event, an updating event. So what happens is, okay, let's go through the kinds of graphs. So first kind of graph is the spatial hypergraph that represents the structure of space. Its nodes are atoms of space. Its hyperedges are relations between atoms of space. And at any moment in time, you can imagine that you've taken a slice representing the current moment in time there is a spatial hypergraph that represents the structure

of the universe okay so that's first first level of graph the second thing is that graph then evolves and it evolves by events that take a particular set of hyper edges combine them together and produce another set of hyper edges combine them together and produce another set of hyper edges or another some set of atoms of space that produce another set of atoms of space so it's like a you're running all these little functions you've got you've got this the spatial hypergraph and it's got all these all this it's like a big data structure with lots of lots of pieces in it and there are these functions that are running on particular parts of that data structure to produce pieces of a new data structure.

Every update event, that's an event. So the causal graph is the network of causal relationships between those updating events. So why are those updating events connected? those updating events. So why are those updating events connected? Well, the reason they're connected is because a particular updating event needs something as input. It needs to use certain hyper-edges, certain atoms of space as its input. And the question is, are those hyper-edges up to date? And so there's a set of causal relationships between these updating events where one updating event can, it has a causal dependence on a previous updating event. So you get this graph that connects, that represents the causal relationships between updating events. That's a directed graph.

If you go from one event and you follow its arrows, you're basically going into events that are in the future. So those arrows represent a time-like path. Just following those arrows is a possible time-like path. So you can also ask, two events, could they happen at the same time? So there are events that couldn't possibly happen at the same time because they are in a chain, one following from another in a time-like sequence. So those couldn't possibly happen at the same time. There's no reference frame.

There's no assignment of simultaneity which will allow those things to happen at the same time. So what can occur is that, but in this, it's a partially ordered set of updating events and in that post set there are things where you can have two updating events which can be considered to happen at the same time. You can have a reference frame where those two updating events could happen, you say they happen at the same time. you couldn't do that if they were in

a chain one after the other but you can do that if they're in what in post-set language is an anti-chain yeah do they correspond to the different lines that are separating which i imagine they're separating into quote-unquote branchial space possible that's a possible foliation of that causal graph so what that means is that that is a possible choice of what updating events should be considered simultaneous to what other ones and just like in relativity theory there are multiple different possible foliations of space time so there are multiple different choices of what you consider to be simultaneous so to speak and that that's the so the causal graph okay the the ordinary causal graph is the network of causal relationships between updating events in space or in space time now, okay, so that's one level of graph.

The other, the next thing that we can talk about is the multi-way graph. And then, not to sound too confusing, but there's also a multi-way causal graph. Ah, okay, okay. And the multi-way causal graph is... Just so you know, Stephen, I read virtually each one of the archive papers,

and for some reason, this is a sticking point for me. What's the causal graph versus the multi-way graph? Are they the same? Well, they're defined in the same document. So it'd be unlikely. I wrote this kind of technical introduction to our project where I have an appendix that simply lists all the different kinds of graphs because I knew people. And one of the things that was, you know, there's a practicality of doing a big project

like this. You know, there was a funny moment when we did the colors for all these graphs, because what we realized is, you know, you're just drawing all these graphs and you see one of these graphs. And it's like, what on earth is this? And we realized if we have consistent coloring of these different graphs, at least as soon as you see a graph, you say, I mean, we kind of joke that there's this color we call branchial pink, which is the color of our branchial graphs, which is yet another kind of graph we haven't even talked about yet. But, you know, the causal graph we have, you know, the events are in yellow, the edges are in brown, the spatial graph, it's all sort of blue. And the multi-way graph, well, let's talk and the multi-way graph well let's talk about the multi-way graph so the multi-way graph in the simplest form the nodes of the multi-way graph are complete states of the universe so the paths in the multi-way graph correspond to possible histories for the

whole universe now that's what we might call the global multi-way graph. There's been a big effort, Max Piskunov has been the main one, sort of pushing this to have these things we can call local multi-way graphs. They're hard to understand but they're important and they will help us to understand quantum field theory a lot. But the global multi-way graph, every node is a complete state of the universe and so so then the multi-way causal graph is asking of those complete states of the universe what are the causal relationships between between those those states of the universe and that gives us the multi-way causal graph and the

ordinary causal graph is a kind of a slice of the multi-way causal graph. So the multi-way causal graph represents the set of causal relationships including both things that could happen at different places in space and things that can happen on different branches of history. So one talks about events being time-like separated, that is one they follow from each other in time. Another possibility is that they're space-like separated, that is those events correspond could correspond to the same time but they are separated in space. There's a third possibility which is they can be branch-like separated which means that they are occurring on different branches of quantum history.

And so there's all three of those time-like separation, space-like separation, branch-like separation. In the multi-way causal graph all three kinds of separation occur and the question of which one you know any two events can be both space-like separated and branch-like separated, or they can be just branch-like separated, and so on. And that's a, that object, the multi-way causal graph, okay, so for the spatial hypergraph, we believe that its continuum limit, when you look at a large number of nodes, is like ordinary space. It's like a manifold. It's like, for the uh for the multi for the ordinary causal graph it's the same kind of thing it's like a minkowski space it's like the space you

probably know that that ordinary you know something like euclidean space has this feature that you can move one way you can move back you know every every path you can go down you can you can reverse it and go the other way right that's a feature of ordinary space i can move this way i can move back, you know, every path you can go down, you can reverse it and go the other way. That's a feature of ordinary space. I can move this way, I can move that way. In space-time, that's not how it works. We get to go forwards in time, we don't get to go backwards in time. And so that corresponds to the limit. The limiting structure is not a Euclidean space, but a Minkowski space. And so that's the same kind of thing with our causal graph the limiting structure is a Minkowski signature space that is it can be in

general a curved space just like in general relativity the multi-way causal graph we don't understand very well yet what its continuum limit is it's a it's a weird kind of Minkowski-like Hilbert space. Interesting. And a special case of it is probably Twister space, which is this idea that's this kind of neat trick with complex numbers that Roger Penrose invented back in the 1960s as a way to understand, well, to think about sort of quantum mechanics and space-time and so on. But that seems to be a special case of the multivariate causal graph.

But there needs to be a generalization of that made to be able to see what that continuum limit looks like. And we can keep going, and things get wilder. I mean, we start talking about, oh, well, I mean, yeah. I mean, there are a lot of kinds of graphs running around here. Does causal invariance apply to one of the graphs and not the others or all the graphs? Causal invariance is a feature of causal graphs. And what it is telling you is that, well, it's also a feature of multi-way graphs.

Let me be specific. There's the condition placed of causal invariance. Is that one placed on the causal graph? Or is that one placed on the multi-way graph? It applies to both of them. It has consequences for both of them. They're different consequences. The consequence of the multi-way graph is it implies that in a simple sense, which isn't completely correct,

it says every time there's a branch, there's also a merge. Every time the paths of history diverge, they will also converge in the future. That's confluence, correct? That's confluence. That's right. And causal invariance is a generalization of that that also applies to the infinite time case. Right. Okay. So one of the conditions for causal invariance implies global confluence. What else is necessary for causal invariance? So one of the conditions for causal invariance implies global confluence. What else is necessary for causal invariance? So one of the conditions is global confluence.

Yes, I mean, it's its own separate condition. I mean, it's a condition. What it implies is that the multi-way causal graph breaks down into a whole collection of individual non multi-way single-way causal graphs that is given a particular branch of history there is a causal graph and that causal graph is independent of the of the microscopic order of updates so in other words the the whole idea of causal invariance which was sort of a concept that I I up with in the 1990s was this idea of okay so you have all these updates and you can say well what order should I do these updates in

okay and you can look at from the outside of the system you do these updates in different orders you'll get different results. The interesting fact is when certain properties hold the causal graph not the individual sequence of updatings that you can change the order of those but the causal graph that connects those different updates that gives the causal relationships between those updates that is the same for systems that are causal invariant. That's the importance of causal invariance, is that the causal graph remains the same, and that's what pretty directly leads to special relativity. So it's a feature of...

That's a feature that the causal graph is a unique causal graph. It could be the case that as you do different updating orders for things, that you end up with different causal graphs, but you don't. And so that's the feature of causal invariance that gives you a unique causal graph. And that's why, sort of played in the relativity situation, that's why different choices of reference frames give you the same physics. That's the sort of underlying cause of that of that effect now you know what we've understood in more recently is causal invariance can be an effective causal invariance

that can be a kind of trickle-down effect from something much more well again it's kind of complicated because this is an idea of Jonathan's is sort of to induce causal invariance through what are called completions in the multi-way graph and in any case one of the things that I think is becoming clear is that we had thought oh there are all these possible rules, only some of them will be causal invariant. But it turns out that by the time we're looking at kind of the trickle down from this sort of universal possible rules, there is an inevitable effect of causal invariance there. So we don't have to worry about, oh, can we find a particular rule that has these causal

invariance features this this is a bit complicated and I'm skipping many steps in talking about this but I'm trying to give a sense that that causal invariance which we had thought was a kind of a special property it's like you know be a prime number rather than just be a number it's kind of an inevitable the level of causal invariance needed is sort of an inevitable consequence of this sort of trickle down from thinking about all possible rules for the universe. This is a detail, but never mind this. Never mind this.

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If you use that code, you'll get two years worth of blades for free. Just make sure to add them to the cart. Plus 100 free blades when you head to h-e-n-s-o-n-s-h-a-v-i-n-g.com slash everything and use the code everything. What I haven't seen much of an exploration of in the archive papers is Rulio Space, and that could just be because I haven't read the right ones. Okay, so I wrote one piece about Rulio Space, investigating a particular example of it for Turing machines and you know it's a very junior version of the universe so to speak to imagine

the universe is just a Turing machine so you know a Turing machine it just has this tape where there's symbols written on the tape ones or zeros for example and there's the Turing machine has this head that's walking up and down the tape and according to fixed rules so an ordinary Turing machine just has a fixed set of rules so it sees a particular symbol on the tape it looks up its sort of table for what it should do it moves to the left or the right. It writes a different symbol on the tape. That's what an ordinary Turing machine does. You can also have a multi-way Turing machine where, just like all these other multi-way systems, instead of it doing a definite thing at every step, it has multiple things that it can do at each step. And so you then end up getting this multi-way graph of possible histories of Turing machines. Yeah. Okay. So then what you can do is you can say, well, let me consider all possible Turing machines. Interesting.

So that then is ruleal space. That's in this particular example, with this particular coordination, that is a ruleal space of Turing machines where you're looking at the maximally sort of non-deterministic Turing machine, the Turing machine where it can do any possible thing. And so one of the things that is interesting is you might say, well, if it can do any possible thing, how come there's any structure to the space? The reason there's a structure to the space is the following. You're saying, I'm starting off all possible Turing machines,

and they do all possible things. But the point is that two Turing machines that start the same and then branch into two different states it can be the case that those Turing machines can also merge that is those two different states can both end up being being transformed to the same state. So that phenomenon, that when you have many possible states and you apply many possible rules, you can end up with something where there's sort of this entanglement

between states induced by the use of these rules. So in a sense, it's the fact that identical states merge that leads to a kind of entanglement in this multi-way graph and that's what makes space non-trivial. And so then the question is what is this limit of you know when you have when you have this limit of all possible rules being applied what is the thing you get from this limit of all possible rules being applied, what is the thing you get from this limit of all possible rules being applied? And that object is this ruleal multi-way graph.

And that's kind of the object that represents kind of the universe of all possible universes, so to speak. So, I mean, this gets fairly abstract. And it's, you know, you can understand this. these are this gets fairly abstract and it's it's you know you can understand this I mean the the there's a whole kind of world of higher category theory and so on which provides a framework for thinking about these kinds of things that I think is useful I think a bunch has been done it's one of these places of sort of mathematical physics mathematics kind of area where um you know a lot has been built and it turns out that um um the um um uh a lot that has been built turns out to be useful for our project you know i'm extremely impressed with this model both its its simplicity and its power i don't

like to give my opinions usually when i'm interviewing someone because the audience doesn't particularly care about what i think and in some ways it detracts but i i find i find plenty of it to be fun in the sense that there are these elemental elements, these novelties. Then you're wondering, well, okay, so we have these hypergraphs, we have updating rules and so on, and we have our laws of physics. Okay, how can this limit to that? And I imagine much of the working sessions, I've only watched a couple, imagine them that

they're quite enjoyable. Oh, yeah, I do this because it's fun. I mean, it's as simple as that. But, you know, one thing I would like to say about this, you've got a model over here, you've got physics that we know over here. One of the things that is an important kind of intuitional thing to realize is

don't reverse engineer from the physics we think we know. That is a tremendous tendency of people to do that. And it's a tremendous, you know, we know all this stuff. So let's figure out that must mean that underneath it is this, this, and this. That's not how this was built. This was given this, you know, very simple framework. What consequences does it have? Now, is it going to intersect with actual physics

or did we just miss completely? And is this a model of nothing in particular? It's very important that you build up from the simple model and then you see where you build. And it so happens that the amazing thing that was really the big surprise of a year and a bit ago is the thing we built is physics, basically. And that's the thing, that was was really the big surprise of a year and a bit ago is, you know, the thing we built is physics, basically. And that's the thing that was that was sort of the big surprise. It might not have been, you know, as it's turning out. OK, I now realize that I should have realized years ago that it's sort of inevitable that this has to be physics. But that wasn't obvious to me as we were building it and it's it's the thing that's

been really interesting to me is the realization that not only is it a model of physics it's also a model of a whole bunch of other things and that you know I had the experience with cellular automata that I worked on for many years so cellular automata are just these extremely simple programs where you just have a line of cells, let's say each one is either black or white, and then in a series of steps you update the color of a cell according to the color of the cell above it and to its left and right, let's say. You might have thought that a simple rule like that would always lead to simple patterns of behavior, but the big discovery that I made in the early 1980s is that that's not true that you can

get very complicated behavior even from very simple rules and the thing that happened with cellular automata is they're very minimal models they're just you have a line of cells or you have a array of cells or whatever and you're applying these local rules and you're updating the thing very minimal model so then you roll the clock forward a few decades and you realize oh gosh there are models that use cellular automata for zillions of different things from you know road traffic flow to you know the way leaves work to the way that um i don't know catalysts and and surfaces work to the way all kinds of different things all kinds of to mollusk pigmentation patterns whatever all kinds of different things and so in a sense you've had

this very minimal model which in that particular case assumes a certain structure of space and time but you have a very minimal model and that model ends up being a model of lots of kinds of things so in a sense it's unsurprising that this much more flexible model that we have that we built for physics ends up looking like it's going to be a really I mean a you know a very powerful model for the foundations of a whole bunch of other fields as well and the thing that's really interesting about that is you know so I've been doing a whole bunch of work on metamathematics the kind of overall structure of mathematics where where the nodes are not atoms of space, but the nodes are mathematical theorems and the relationships between them are proofs

of one theorem from another. Well, you might say, what on earth does that have to do with the structure of the physical universe? But it turns out that it looks like the formalistic structure of that is the same as the structure of the physical universe. And that's something that's both surprising. And the most important thing for me is it means that you get to have this kind of cross-connection of the ideas from metamathematics and the ideas from physics. So in physics, we've learned a lot of stuff about how general relativity works,

how all these kinds of things work. So now we get to import those ideas into metamathematics and we get to import the ideas of mathematical logic into physics. And so by realizing that the underlying formalism is the same, we get to make that kind of conversion. And this formalism also seems to be really the right formalism to think about distributed computing. It may very well be the right formalism to think about systems biology. And the one that I've been poking at a lot recently is economics. And it may well be the right formalism to think about that. In each of these applications, the details of what the corresponding, what the thing that's like the atoms of space is are different.

And the details of how it works is different. But the point is that the overall structure, the overall formalism seems to carry over. And that allows you to use sort of big ideas from one field in another field. So that's been, you know, it's a more global theory than I ever imagined it could possibly be. more global theory than I ever imagined it could possibly be. And I've realized that the fundamental sort of struggle in a sense for these theories is the following. You have a simple rule underneath but that simple rule just like in my cellular automata the simple rule leads to very complicated behavior. It leads to behavior that is computationally irreducible in the sense

it's complicated enough you can't tell what's going to happen without basically just running the rule and seeing what happens. So then the thing which I should have been able to figure out but didn't is in assume that there's a simple underlying rule for the universe there's computational irreducibility that produces immense complexity in the behavior of the universe. computational irreducibility. That produces immense complexity in the behavior of the universe. How come we can figure out anything about the universe? How come we can even say the universe follows definite laws? How come we can predict what's going to happen at all? Why isn't it just a whole mass of irreducibility? And what you realize is within any computational irreducible system, there are always these pockets of reducibility. There are always pockets. Yeah, there are always pockets of reducibility

It's it's a there is no way to construct a system. That's computationally irreducible that has no pockets of reducibility I believe that to be correct but I mean that no, I mean that's a To fully formalize that notion would be quite interesting I suspect that you can get some formalization through speed-up theorems in computation theory, but I think it is intuitively fairly obvious, but as you try and nail it down, there will be, you know, I think the speed-up theorems are the way to think about that in a somewhat more formal way. But so in any case the thing that one realizes is so there are these pockets of reducibility that exist and the thing that is sort of the big

surprise is those pockets correspond to the big theories of physics. Each one has probed some pocket. Now the next question is are there other pockets that have never been discovered that are theories of physics that we just don't know that are complete global theories like general relativity like quantum mechanics but we don't know them and what i realized recently is that the the kind of the you know the reason that we know those theories is because there are certain attributes that we as observers of the universe have and those attributes lead us to those theories so the attributes are things like that we have a computationally bounded way of understanding the universe that's one of them Another one is that we have a definite

thread of experience and time. We are not operating with many, many, many threads of experience. We have a definite sort of thread of consciousness that we follow. We're not, and that, and in fact, the thing I realized just in the last week, actually, And in fact, the thing I realized just in the last week, actually, is one of the things that is non-trivial in our models is the notion of maintaining your identity, so to speak. So in this hypergraph, every atom of space is being destroyed, a new one is being created all the time. So the question is, how come you and me seem like we sort of exist through time? Turns out our atoms of space are being destroyed and recreated, you know, whatever it is, 10 to the 100 times per second. So in other words, how come we are a thing, we maintain our identity?

That is a non-trivial fact about us as observers that we consider ourselves to maintain our identity and through time. The thing I realized just recently is there's a similar way in which we do that in space. It is not obvious that there would be a pure notion of motion. That is that you could move, you know, as I move from here to there, the atoms of space that are in me are different. And yet me, I have an identity that I think I can carry around. I can carry it through time. I carry it around in space. The assumption that I maintain that identity is what ends up being sort of a tail that wags eventually that gives us the laws of physics that we know in other words if we did not have that assumption about ourselves we would have

different laws of physics and if we didn't have for example the the notion that oh I don't know there's quantum measurements occur the notion that that we collapse all these different paths of history into a single definite outcome, that is directly related to the fact that we imagine that we maintain a definite identity through time. That, in other words, if we just said, oh, I don't care about that, I'm not going to maintain a definite identity through time, I'm perfectly happy to have myself branched a zillion times then you no longer get this idea that we imagine about quantum mechanics that there are somewhat there are definite outcomes that occur so in other words it's it's our our way of constructing ourselves and the way we think about ourselves and the way we kind of perceive

the universe that drives the structure of the laws of physics that we know. So one of the things that that obviously leads to is well maybe there are completely other laws of physics and a completely other sort of plane of existence that we are utterly unfamiliar with and I think that's almost undeniably the case that that exists. And that's probably one of the reasons why, you know, when you say, what about other intelligence in the universe? Why haven't we met all the aliens and so on? Well, because actually their sort of perception of the universe may be so different from ours. It's kind of incoherently different. And it's not something where our narrative about how the universe

works kind of carries over to those those those kinds of places so it's it's a it's in a sense it's a rather humbling experience because you're realizing that that you know all the stuff we built in physics and so on is all we built it because that's the way that we parse the universe so to speak and were we to parse the universe differently we would have completely different views of physics and I mean I think the thing that has been well this is this week's issue is thinking about that in terms of mathematics insofar as we believe that there is this kind of object that represents the mathematics of all possible mathematics is and that we are merely

as mathematicians so to speak we are merely observers observing some slice of that object what is the what is the analog of the constraints of consciousness in the physical world on the on sort of what is a mathematical consciousness so to speak that's my that's my that's my personal homework exercise for the week. That's interesting. So this consciousness that we have isn't necessarily that we can't communicate with any other being

because the laws of physics that they perceive is incoherent. Do they perceive coherent laws? Yes, I think so. I think so. I mean, but the way you think about it is this. In this kind of ruleal space, different points in ruleal space correspond to different description languages for the universe. So just like in physical space, we have a view of the universe that's based on the fact that we're sitting on the Earth,

you know, which is in some corner of some galaxy that's in some corner of the universe. We have a point of view on the universe based on where we are in physical space. So similarly in ruleal space, we have a point of view on the universe that's based on where we are in ruleal space. Now the question that we can ask is, just like we can ask for the extraterrestrials, do they live in Alpha Centauri or do they live in, you know, 25 light years away or whatever? Where do they live in physical space relative to us? We can also ask the question, where do they live in ruleal space relative to us? We've not mapped out ruleal space nearly as well as we mapped out physical space. So we don't really have a good sense of those distances and what that corresponds to. But that's kind of the way to think about it. And I would love to know, you know, how close is the nearest civilization in ruleal space? People say, you know, let's go check out the stars, you know, the nearby stars and, you know,

look at the ones with exoplanets and things like that. And, you know, but there's a different question, which is kind of in ruleal space, What's the closest you know, what's the closest thing we can recognize, so to speak? And I don't know the answer to this. And that's some. But I think to the observer themselves, I think it is almost tautological that things will seem coherent. So, for example, to do an an exercise let's consider two intelligences that aren't us. Okay so one that I'm always fond of mentioning is you know the weather has a mind of its own. It has you know it's doing these sophisticated computations but it doesn't have this kind of single thread of consciousness type thing. I mean we have in our brains we have actual you know structures in our brains

that lead us to have this sort of single thread of attention that kind of sequentializes all of our experiences. And when people sort of lose that, they become unconscious, so to speak. And you can still have plenty of neurons firing in your brain but not have consciousness you don't have this integration of of kind of the single thread of experience and the weather is sort of a bit like that it's got lots of not neurons but it's got lots of fluid processes sort of firing all over the planet and but it doesn't seem to have any kind of sort of single thread of experience that's going on so that's a sort of an example of, and if we say, can we communicate with the weather? Well, not any way that we know. I mean, we have something

where it's sort of an incoherently different experience of the universe than the one we have. Now, if we put ourselves in the mindset of the weather, does it have a coherent view of what's going on to itself probably tautologically yes maybe a better example that's maybe a little bit closer at hand which I have not thought through completely is sort of distributed AIs so in other words you've got an AI but it isn't just one AI it's a whole network of computers and it's like what is its experience of the of the world and what physics does it imagine is going on because for example you've got all these different AIs they've got all these sensors and they're seeing things that happen those sensors might be separated by distances that are quite large compared to you know that takes significant time

to for signals to travel between them you know what is its view of the universe so to speak it's very different from ours because we're we're localized at a particular point in space etc so it's kind of a good exercise to try and think through in fact I was I was sort of trying to inventory and I think it's a great setup for a piece of science fiction more difficult than I can than I can certainly muster, which is imagine all these different scenarios. Imagine you are an organism that spans a galaxy. How does the universe look to you? Imagine you're an organism that routinely ends up on different sides of the event horizons of black holes. What does the universe look to you? Imagine you're an organism so to speak that lives on photons that's associated with photons you know

where basically no time has passed from the last scattering surface a few hundred thousand years after the beginning of the universe and now if you're a photon. So it's kind of like what are these different views of the universe that you have if you are implemented in different ways and you know there are probably sort of implementation levels for the universe that involve kind of just recognizing different features of this whole network of atoms of space and so on completely different from the ones that we recognize in our analysis of the structure of the universe. So, I mean, that's kind of my way of thinking about this. It seems like there are two issues here about extraterrestrial life or intelligent life.

One is whether or not we can communicate with them. And the other is that we can perceive them. So when we're saying that we don't see extraterrestrial life, the argument you've given seems to be that we can't communicate or be extremely unlikely that we'd be able to communicate with it if we were to encounter it. But does that mean that we can't perceive it? We can see, for example, a whirlpool or a hurricane. Whether or not we can communicate with it is another issue. So, I mean, the first step is there's a level where we don't even see it because it's features of the structure of space that we are simply not paying any attention to.

You know, there's some detail. Like, for example, one of my guesses about, you know, I like to think about, you know, I like to think about history of science. I like to think about history of science. I like to think about how do people make mistakes in the past? How were things that became obvious later not seen before? And so a question about today's science is what is there in today's science that people will say, I can't believe that they didn't see this. And I'll give you an example of one that I suspect is one of those. So you look at a gas. It's got a bunch of molecules bouncing around. We say the gas has a

certain pressure. It has a certain temperature. But all those details about all the gas molecules bouncing around, we just say that's entropy. There's no detail there that we care about. It's just random. That's probably there's probably another you know whole pile of other properties that we should be thinking about there but we're just not paying attention to so to speak and so that's that's an example of of a place where sort of the extraterrestrials could be all around us and we just wouldn't know it because they are sort of their civilization so to speak lives in features of space that we are simply not paying attention to so that's one possibility another possibility is yes there are things that we can perceive but they just don't make any sense to us. It doesn't, you know, it's like the weather, for example,

where it doesn't, it makes, I mean, you know, it makes no sense. We don't have, you know, what would you talk to the weather about? You know, what is its experience? In order to, you know, what do we talk to animals about? Well, not a lot really because you know there's certain emotional kind of commonality that we have with animals at some level but mostly we can't really have a a philosophical discussion with your average bear so to speak um and uh the i think the reason uh you know that's something that it isn't you know that there's a separate level of issue

of sort of the sort of this beyond just perceiving that the thing is out there it's like why is it doing what it's doing do we have a story about why it's doing what it's doing do you know if we don't have any such understanding and even across time for our own species you know you look at archaeological remains from a few thousand years ago it's like what on earth were they thinking we have no idea you know what would be our communications we might be you know we put ourselves down a time machine which I don't think can exist but anyway imagine it you, and we say to some, you know, person from 3,000 years ago, you know, what are you doing? Oh, they give a whole explanation about, you know, they're pleasing the gods by doing this thing that does this, that does that.

And it's like, what the heck are you talking about? You know, we have no common framework for thinking about these kinds of things. So I think that that's, you know, the level at which communication is possible is pretty narrow. Is there a way in which this entire hypergraph or our entire universe is conscious? Much like you mentioned, we can have consciousness or different alien intelligence running through us in an ether that we can't interact with either either because computationally irreducible, so we don't discern it, or because, well, because whatever reason. sort of there's intelligence there's consciousness i think they're somewhat different so intelligent in any definition of that that is a generalization beyond the purely human i think in in any reasonable definition one would say the universe is intelligent

is it is yes it is okay the now conscious it's a little bit more tricky because it seems that consciousness is actually a step down from intelligence. That is, you can be, you know, all those individual neurons, all those, like our immune system might be something that is doing computations as sophisticated as our brains, for all we can tell. The immune system is, you know, has all these complicated interactions between cells and so on. but yet there's something a little different about the way the computations that our brains do from the ones our immune system does or there seems to be. And one of the differences is that we have this notion of a single thread of experience. And that's a feature of the kind of thing that our brains do that isn't an immediate

feature of the way that our, the way that these other computational processes that sort of seem like that have intelligent like behavior, it's not a feature of those. So consciousness I have come to think is a step down from intelligence. Consciousness is a specific thing that gets added on top of intelligence that is sort of this single thread of time story and also this computational boundedness, but that's kind of a necessary thing. But it's this idea of a single thread of time, I think, is sort of a critical feature that adds kind of, that's the layer that adds consciousness. So does the universe have that? Not really. The universe doesn't have that. In fact, the universe

in our models, it's got all these atoms of space that are doing all these things all over the universe. There's no single thread of time. there's no single thread of time there's no single thread of experience lots of different things are happening all over the universe lots of different space-like separated things are happening lots of different branch-like separated things are happening so there isn't that single thread type type experience so i think in that sense i would i would say that in that what seems to be the appropriate definition of consciousness, the appropriate generalization of consciousness beyond the merely human wouldn't encompass the universe. Intelligence would encompass the universe, consciousness would not.

You mentioned photons not having an experience of time. In your model, do you have a conceptualization of photons because it seems like there's different time steps and time is just the intellectable sequence of updating so what's a photon is it one that goes well we're not sure yet completely but um uh the possibility of something moving at the speed of light, the speed of light is defined in our models by you have one event and you say, how many other events does that event lead to? That's the light cone of what you produce. And so photons have to live on the at least close to the edges of that light cone. And so that's that's sort of what tells us something about the kind of structures that photons correspond to.

We don't know exactly what they are yet. I think the thing that one can realize is this notion about time passing versus distance gone. If you are an entity within our system, you are using computation to progress, so to speak. And you can use that computation. you are using computation to progress, so to speak. And you can use that computation, if you're just sitting still, all that computation gets used to actually move you forward in time.

All that computation gets used to figure out the next configuration that you have in time. If you're also moving, some of that computation has to be used up in recomputing what you're like at a different place in space. That's interesting. That's basically what leads to time dilation in relativity is that you're trading off the

use of, you know, you're trading off the computation used for motion with the computation used for time evolution. So if you are, if you have motion then you get to use less of that computation for time evolution and time effectively runs more slowly. And so for photons, there's presumably an extreme version of that, but we don't understand the details of that yet. When it comes to ruleal space, there's a quote. I believe I took it from one of your papers. It says, the principle of computational equivalence implies a fixed maximum speed row

in ruleal space. Now, is this principle taken as an axiom or is it derived? And how exactly do you derive that maximum speed without that axiom or can you? Okay. So the epistemology of science is more complicated than people often give it credit for. The principle of computational equivalence is it has a complicated epistemological status somewhat similar to the second law of thermodynamics somewhat similar to things like the church Turing thesis. They're all the same kind of thing. So the second law of thermodynamics is both a definition of heat and a statement about how systems in the universe tend to work and a mathematically provable thing. It is both all of those things and none of those things. So in other words the principle of computational equivalence if you is something for which

we actually have good evidence that, the principle of computational equivalence basically says if you have a system that operates according to rules, if the behavior that you see is not obviously simple, the behavior will correspond to a computation that is as sophisticated as anything. That's the basic statement. So it implies that your average thing,

even though its rules may be simple, so long as its behavior isn't obviously simple, will tend to be, for example, computation universal. To interrupt, sorry. What do you mean by isn't obviously simple? So can you give me an example of something that is computationally inequivalent? Yeah, yeah, right. So repetitive behavior is obviously simple. Nested fractal behavior is obviously simple. It's things where we can readily predict, where we can use a much simpler computation to jump ahead, where we can say, you know, you've shown me a few steps. Now I know what's going to happen. I can predict a billion steps in the future what's going to happen. Now all of these concepts there so that's what it means to be computationally that's what it means to be not you know to be to not seem like it has complicated behavior. Now as you start trying to I mean the thing that's interesting about all of these principles is that as you start trying to put stakes in the ground of what does this precisely mathematically mean, you realize that the thing is, it ends up being, you know, the principle of computational equivalence is at some level an abstract fact about rules. fact about rules. It's an abstract fact and it can be proved at least in certain examples as an abstract fact. But you might say that thing over there I don't see how it's simple so it must be

computationally as sophisticated as anything but then somebody can say oh you missed this particular way in which it was simple so you know and that's why it isn't as computationally sophisticated. But then you can say that's sort of tautological because if it's computationally sophisticated, that's basically the statement that it doesn't have any simple way to work out what it does. So it's the thing that's important about the principle of computational equivalence is that it is a conceptual framework for thinking about how things work. That is people had the idea, including me, that you have simple rules, you'll have simple behavior. It's not true. And this principle tells you that it is maximally not true. In other words, whenever it seems like it might not be the

case that the behavior is simple, it really isn't. And it is sort of as sophisticated as you can possibly get. So with respect to speed in ruleal space, that assumption of a maximum upper limit, I think you could derive it. Yeah, you could derive the upper limit from the church turing thesis which is a a sort of subset of the principle of computational equivalence so uh-huh the so i mean that particular thing is is not doesn't need pce i think i mean i think it needs um uh to derive the upper limit what what what is not obvious is that the typical light cone will have a surface that is like that in ruleal space. That needs PCE. So what it's saying is the Church-Turing

thesis would say that there exist things that go as fast as that, but not faster. What PCE says is your average light cone in ruleal space will in fact expand at that speed that's interesting so so okay so that then that maximum speed of of um uh so the maximum speed in ruleal space is essentially telling you something about the actual raw processing power of the universe. It's telling you, I mean it's, I was, I think I'd written somewhere in a, in kind of, you could, you could take it in any kind of computational units, but you can say, you know, number of Wolfram language tokens processed per second is, by the universe, is kind of one, one way

of measuring that something we realized recently is that coarse graining that is the process of not looking at every detail but looking only at a large scale which you use in statistical mechanics and so on coarse graining in real space is making a higher level description language so in other words you can make a description language that's really at the lowest level where you actually describing how every everything works

or you can have a higher level language which describes only more in in sort of higher level terms what's going on what's the relationship between computational irreducibility and undecidability, general undecidability? So, also the relationship between irreducibility and the principle of computational equivalence. Does one require the other? Can you imagine a world with one but not the other? So, principle of computational equivalence implies computational irreducibility.

And basically, they're really locked together. Because what happens is you have a system, it's computing what it's going to do next. You are an observer of that system. You're trying to predict what it's going to do next. The question is, can you jump ahead of it and figure out what it's going to do sort of more efficiently than it does it itself. Principle of computational equivalence says, sorry, you're stuck being just computationally equivalent to the system, and that's what leads to computational irreducibility. Undecidability is an infinite time limit of computational irreducibility. Computational irreducibility is a, if you say, what's the system going to do in the end after an infinite amount of time?

The answer can be, well, in order, if it's computationally irreducible, the only way to find that out is to wait for a potentially infinite amount of time. So if you say, I really want to know to know infinite time what's the system going to do the answer is sorry it's computationally irreducible the only way to know that infinite time answer is to wait an infinite time so that that's the reason that term so those you know computational irreducibility implies undecidability could undecidability exist? I don't think so. I think it might be associated with some things called intermediate degrees which are an idea that you can have a system which has undecidability without computation universality

which I tend to think is not a real thing. It's something people imagine can happen in systems universality which I tend to think is not really it's not a real thing it's a it's something people imagine can happen in systems but I don't think it will actually end up happening it's something where you can construct examples which are kind of special put-up jobs where you essentially have a universal computer inside but you've chopped off all its input output mechanisms enough that it can't act as a universal computer but can still have undecidability and I don't

think that's a I don't think that's a real real thing but yeah so those are undecidability is infinite time limits of irreducibility basically speaking of what's real or what's not real is infinity real who's infinity I mean the the you know, look, you can write down, you know, in Wolfram language there's a symbol infinity that represents infinity and one over it is zero and you can say lots of things about it. If you want to ask the question, can I make an infinite can I sort of actualize infinity this is a complicated question because you can certain kinds of infinities can be just made symbolic and reasoned in terms of to explicitly make infinity is a different

thing than to reason in terms of infinity. We can write down transfinite numbers and we can do all kinds of reasoning about transfinite numbers. That doesn't mean we can explicitly in our universe make a birthday cake that's a transfinite number, so to speak. I mean we can't... So the question of actualization in the universe versus symbolic representation is a little bit of a tricky question. Okay, forget about us making infinity. Is there a quality of the universe that's infinite at all? So for example, infinite space, infinite computational speed, infinite memory storage. And how can we enter even if there was an infinite? Is there a way that we could tell?

Is there an experiment that would let us know that infinity exists in some way, shape or form? Or is it somehow irreducible it would look like noise to us well i think we can wait for an infinite time we'll know in the infinite future we'll know if the universe is infinite i mean i think that before that we can um you know the the question for example is space you know infinitely divisible that would be a question we might ask I think our models look like they're going to make some very specific predictions about what happens in fast rotating black holes and things like this where they will kind of see through there'll be a microscope that kind of sees through down to the actual fabric of space-time

and actually sees these discrete things and were we to be able to use that microscope and were it to see you know were to just keep seeing you know finer and finer and finer detail you know in other words we look through a physical microscope and we're used to seeing, oh, the biological organism actually is made of cells. Oh, we look, it's actually made of molecules. The molecules are made of atoms. The atoms are made of whatever. And the question is space.

Right now, we might think our microscope for space, we just look and it keeps on looking the same. It's always indivisible. It's always divisible. And the question is what we're saying in this theory is no, at some point you'll see the atoms of space. Now, you don't really get to do that because you are embedded. Your microscope is made of the same atoms of space. So you don't really get to make a microscope that directly sees that. So you have to use more indirect techniques to be able to kind of sense the presence of these atoms of space but you could certainly imagine something where you know you could you could predict we don't know what scale precisely these atoms of space occur

but where you're kind of trying to you're sort of making the universe be in such an extreme condition that you kind of see through to the structure of space. It's very similar if you are going through a fluid. You know, a typical, you know, a car going through air doesn't know air is made of molecules. It just knows there's a flow of air. A hypersonic plane, missile or something going through air absolutely does know that air is made of molecules of oxygen and nitrogen and so on because at that speed you've kind of broken down this continuum structure of space or in that case of a fluid of the air you've broken down the continuum structure of the air and you are sensitive to the presence of individual molecules with particular properties

and so the question is can we find extreme situations in space-time, for example, where we're similarly sensitive to the underlying structure of space? And, you know, there's a decent chance that we may have examples of that. Usually when talking about whether or not space is discretized or on a lattice in some way, people say, well, we have these fluids. And then as you investigate further, you find out that they're atoms and we thought that they were continuous. But then as you investigate the atoms further, you'll, you find out that they're quantum fields. And obviously then you can say, well, those quantum fields are discretized. Do you think that

there's a place in your models for continuity underneath what seems like discrete points. So let me be a little bit more specific. Anything that I can think of as continuous, there's some way, maybe a simplicial decomposition to make it discrete. But then also the same, you can apply step functions of a certain width from something continuous to make something discrete so when someone says well this is obviously discrete well the argument can can be turned on its head the thing to understand the formalism of our models is probably most humanly stated in terms of hypergraphs and things like that but it is basically certainly the case that

there are for example algebraic formulations of what we're doing in fact some of the things from category theory look that way where you can think about it as features of some continuous space you know it is you know some algebraic geometry feature of some continuous space etc etc etc the net result is it's just the same as this hypergraph but it is presented as something that looks like you know topological you know aspects of the homotopies of continuous spaces or something but it looks like, but a different interpretation is there's just this hypergraph. So there's nothing particularly special about this hypergraph except that it's the most human relatable version of what's going on. I'll give you an analogy.

In theory of computation, you can think about lambda calculus, you can think about combinators, you can think about register machines, or you can think about Turing machines. Turing machines are the, you know, at least in the early such systems were the most human relatable, you know, way of thinking about computation. And I think that there are different formulations of our models that, some of them we can see now, some of them will probably emerge in the future, that look different with respect to that. Now, there's a more extreme possibility, which I don't know if it's the case. And I'm trying to not repeat mistakes of history,

so to speak, here. You know, when Einstein invented general relativity, one of the things that came up was the theory, as he first set it up implied that the universe expands and he was like that can't possibly be right you know surely that isn't right so let me add this extra cosmological term to prevent the cosmological constant and so on to prevent the universe from expanding well turned out it was true that the universe expanded and he shouldn't worry too much about it out it was true that the universe expanded and he shouldn't have worried too much about it. Well in our models the most obvious possibility is that this hypergraph is progressively subdividing itself. It's getting bigger and bigger and bigger and the distance one meter is corresponding to more and more and more sort of separate atoms of space if you line them up and looked at their connections and so on it will be a larger number of connections that would

have to be made to correspond to a meter of physical space so one thing which I have to say it does look in these models as if it's suggesting it's the way it happens is that in fact the amount of the number of atoms of space is rapidly increasing in the history of the universe and if that's the case one of the most bizarre possibilities is you say okay you say I've got an experiment it's going to test whether the universe is discrete as I run the experiment the universe is subdividing itself so if the experiment said I'm going to test is the universe discrete at the level of 10 to the minus 200 meters? By the time that experiment has been run, the universe will

have subdivided itself to be 10 to the minus 220 meters or something. And so in other words, it will always be running away from you. It will always be subdividing itself faster than you can detect its subdivision. It's kind of like the ultimate epsilon-delta proof in calculus or something. You're watching this channel because you're interested in theoretical physics, consciousness, and the ostensible connection between the two. What's required to follow some of these arguments is facility with mathematics as well as discernment of the underlying physical laws, and you may think that this is beyond you, but that's false.

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Try four of the lessons at least, don't stop before four, and I think you'll be greatly surprised at the ease at which you comprehend subjects you previously had trouble grokking. Links are in the description. Is there a way to test the discretization of space or time in the cosmic background radiation because of how quickly it inflated? Maybe. Or even that inflation. No, maybe. I mean, we've been looking at this what what if the universe starts infinite

dimensional um what um uh and gradually cools down to being three-dimensional we expect there to be some dimensional fluctuations left over they may have survived for hundreds of thousands of years they would lead to perturbations in the cosmic microwave background um and uh that we don't yet know what those perturbations are like. We're just trying to work out what the analog of the standard, you know, Robertson-Walker-Friedman-Robertson-Walker metric for a kind of a homogeneous universe, what that's like when the dimension changes. We don't know.

We did some live streams recently actually exploring that question. We don't know the answer yet. It changed from infinite to a finite. So infinity is real, or are you saying infinite as a standard for an extremely large dimensional space? More like extremely large. Because you can't even make a sense of a... If you have a graph that's sort of completely connected, there's no sense of dimension. Because dimension requires that you take limits of larger and larger distances in the graph. there is no if everything's connected everything is distance one away so there's no way

to get far away and talk about what the large scale limit of that is how do you get the dimension of time in your model because i can understand space and there's a haasdorf or a topological but with growing a ball of radius r but how do you grow a ball of radius time? Is the dimension of time defined? So time is multi, you know, time is going in this multi-way graph. So time, to begin with, has, in a sense,

it is an assumption that is a very consciousness-related assumption that time is one-dimensional. That is, that there is a very consciousness related assumption that time is one dimensional. That is that there is a single thread of experience is basically saying we're going to conflate time until it is one dimensional. That is our view of the universe. As soon as we put in these foliations, we are essentially assuming that time is one dimensional. It doesn't need to be. Time can be off with, you know, there can be many different paths, many different histories of the universe that never knit together.

The fact that those things are knitted together is an assumption that's closely related to kind of the generalized view of consciousness. I don't know what you call this metamathematical space, if it's proof space or what, but as I was imagining it, nodes on a graph and there's some diagrammatic rewriting rules. Does that mean that you can make rigorous the notion of what beauty is, you know, Erdos has the book, by saying that it's a geodesic in proof space or metamathematical space? Well, I don't know, that's a good question. or metamathematical space? Well, I don't know.

That's a good question. Whether Erdos' proofs from the book is going to be geodesic paths in theorem space, so to speak. My guess is not. My guess is most of the shortest proofs will be absolutely incomprehensible to us humans. So they may be, I mean, I think Erdos' view of the book

was kind of a God-given book the proofs may be well understandable to god but sorry the humans don't get to understand them i mean in other words it it the shortest it's like the shortest algorithm for something is usually not a human comprehensible algorithm so i see so it's a trade-off of of and this is very related to what what a mathematical consciousness really is because to say it's it's following geodesics is probably to say it's an optimized mathematician but not not something closely modeled by a human mathematician one time i heard you speculate and perhaps it's not perhaps it's worked out even farther than what i saw that particles are black holes in branchial space uh maybe we'll see not not properly worked out yet i mean i think that

black holes yeah i mean that that's a um the relationship between particles and black holes is an interesting one i'm i'm you know for for anybody younger who's who's paying attention to this, I have to tell a story. I was probably 1974, 1975. I was probably 14, 15 years old. I go to some talk by some fancy physicist and they're talking about black holes and whatever else. So I go up to this person afterwards and I say, could particles be small black holes, right? And the person says, oh, no, no, no, you don't understand anything. It's, you know, they're all completely different kinds of things. So, okay, now we're another 45 years later and turns out it might actually be true.

So don't listen to what the main moral of that is. You know, if you go to the talks by the fancy physicists and and I mean I wasn't you know at the time it just seemed like the feature of black holes there's no hair theorems for black holes the fact that black holes have this feature that there are only certain aspects of black holes that seem to be visible from the outside just seemed to me as the 14 year old me or something as being you know that seems awfully like what you find with particles that there are a limited number of kinds of particles that just as there are a limited number of kinds of black holes and turns out as I say the main the main takeaway from that is you, so I'm applying that to myself.

So just as I may say to somebody about some idea, you know, that couldn't possibly be that way, you know, wait another few decades and maybe you'll turn out to be right. What are snake states? Oh, this is a complicated story. And I'm running out of time. So we probably let's not let's not dive down that that um i mean i even even if even if that led to some wonderful puns about snakes on a plane and things like this do you have any feinman stories that you haven't told before that i haven't told before um or how about this you mentioned one time perhaps more that feinman

is misapprehended as someone who has an extreme understanding. He does, but he was great at calculation, and that calculation allowed him to understand and perceive, apprehend. What other misunderstandings or false impressions do people have about Feynman that you're able to see from the inside? the one that always drove him crazy was, and you know, you mentioned at the beginning of this, you know, people sort of ad hominem attacks that I may get, which I'm blissfully unaware of for the most part. But the, you know, people, one of the things that drove Feynman crazy was that people thought of him as you know the quintessential nice guy you know would listen to anything etc etc etc but in fact like all of us you know he got impatient he valued his time etc etc etc and so when people would kind of get close to him and he would be like kind of snarky with them and so on they would say oh my gosh you know you're supposed to be this this wonderfully nice you know positive person and actually you're kind of snarky that's terrible that's horrible

I'm I'm I'm you know that's that's very horrifying so so actually one of the things he always used to tell me is, don't appear to be too nice because it's actually a worse life than the other, so to speak. I'm not sure that I've intentionally taken that to heart, but it was one of those things. But I think here's the thing that, I talked a lot to Dick Feynman about quantum mechanics. And he would always say, you know, we don't really understand quantum mechanics.

You know, we can calculate this and that. We don't really understand it. We don't have an intuitive understanding of what's going on. It's a shame he's not still around because I would really have had a good time telling him about the stuff we figured out now. And it's, you know, one of the the things I remember just these endless conversations about why does thermodynamics e to the minus beta h quantum mechanics is e to the IHT why are they both exponentials like that why is and I think we now know the answer and it's it's pretty neat and it's I think that somehow I mean another thing that we don't yet know, it will be interesting to see how

it plays out. You know one of Dick Feynman's most famous, probably his single most famous invention was Feynman diagrams, this way of calculating things in quantum field theory. And one of the features of Feynman diagrams is the simple ones are pretty easy to compute, but there's this whole series of Feynman diagrams for any particular thing and they get more and more and more complicated and they get unbelievably more difficult to compute. So for example right now there's a big sort of flap because the anomalous magnetic moment of the muon which is computed using Feynman diagrams, there's a disagreement apparently between the experiment and the theory, that's sort of why is is that the case well you know it could be that one of the things that happens is these series of diagrams we don't

actually know that the ones that we can't compute yet are really as small as we think they are and anyway one of the things that I think may come out is we may have an actual method for doing computations in quantum field theory that avoids Feynman diagrams. And Feynman always thought that, he thought, said Feynman diagrams are a crazy idea, he would always say. And, you know, I can't believe people think, you know, that there's got to be a better way to do this. This is a crazy way to do it. There's got to be a better way to do it. Maybe we'll have such a way. I'm not sure. crazy way to do it. There's got to be a better way to do it. Maybe we'll have such a way. I'm not sure. There's also hints of better ways that involve the whole ADS-CFT business, which is

pretty closely related, I think, to correspondence between physical and branchial space in our models. So it may end up being the same idea in the end. Is there some relationship between the holographic principle and particles being associated with black holes in branchial space and ADS-CFT correspondence? That's probably a large question you don't have time to answer now. We don't know yet. I mean, it looks like the holographic principle is a story of the multi-way causal graph being able to be projected both in a spatial direction and in a branchial direction. And that it's basically the same graph but you're taking two different projections of that graph and the fact that it's

the same graph is why there's a holographic principle that relates those two different projections that's that's probably how it's going to work out that seems to be how it will work out ac felly dwi'n meddwl, ond rydw i'n cael i chi'n cael i mi ddewis fy mhenoriaeth i, rydw i'n ceisio meddwl am rhai o'r storïau Dick Fineman sy'n gysylltiedig â, dwi'n meddwl am bethau I mean I'm thinking about things that we now know so to speak that were things that I talked to him about um and uh yeah that he would dismiss um no I mean he always believed there was something funky about quantum mechanics that there was something more to understand that it really wasn't that what had been done to that time which is now early 1980s was just a calculational method wasn't a a real understanding so to speak I would say that yeah okay there's another thing I remember I talked to him at great length about the second law of thermodynamics which I finally understood in the 1990s and I remember we had a huge argument

at one point where he was claiming that the fact that the universe is as orderly as it is today is a fluctuation which I was just like that's a stupid thing to say our whole universe if you say our whole universe in its current stages of fluctuation, that's not a useful scientific theory because you're saying with respect to our theory everything about what exists today is an exception and then you don't have a theory of what you know of what exists today. But we, I remember we had a huge argument about this about this topic in which we we did both have to, I had to agree that there was a bunch that I didn't understand about thermodynamics

and nor did he. And I think finally we've understood how that works and it's a story of computational irreducibility. And I should have been able to tell that story actually even at that time. I just wasn't smart enough to see that connection for another probably 10 years after that. Okay, last fluff question has to do with cryptocurrencies and what you see is the

future of cryptocurrencies. Let me read it specifically because it came from one of the viewers. What is the future of cryptocurrencies? This is from Amjad. Many CEOs are buying crypto as a store of value. Your thoughts on it? Who is thing that is most ironic to me about the crypto world, which is back in the 1980s, you know, I had this idea about computational irreducibility, the idea that you might need to do computational irreducibility in the 1980s, I imagined it as this limitation on science, this principle about something formal and mathematical. I had no idea that decades later there would be, you know, whatever it is, some number of percentage points of the total energy production of the world would be burnt in computational irreducibility. It's an utterly bizarre, it's kind of like,

you know, for somebody like me, I build theories, I build tools, and then the world goes on and eventually uses those theories and those tools for things that are just, I mean, that one was something so far out of left field that I couldn't see coming, that it's remarkable that that idea of proof of work is completely crazy. I mean, it's a, to be fair, it's very amusing and completely crazy. And, you know, I have certainly thought about, is there a way to do something like proof of work that generates useful computation? And I have not yet figured out how to do that. But with respect to cryptocurrency, and for example, the question, why is there value in cryptocurrency? You know, I had thought, well, to get value in economics, you have to actually be

making something in the real world. And I had thought for a while, you know, we've been a lot involved in computational contracts, the idea of expressing what would otherwise be contracts written in legalese in computational language, because we have kind of the unique computational language that can talk about the real world and that is therefore capable of having, you know, contracts about the real world written in it. So we've done quite a bit of work on that. And I sort of imagine my belief as a few years ago was that when computational contracts are the dominant form of contracts that cryptocurrencies just become a convenient mechanism for sort of servicing

computational contracts. But then the question is is there intrinsic value in a cryptocurrency and so this relates to the question of well why is there intrinsic value in a cryptocurrency. And so this relates to the question of, well, why is there intrinsic value in anything in economics? And so that relates to, well, what is the foundational theory of economics? And so this is something I've been thinking about. And, you know, I think that the elementary actions in economics are transactions. And I think that what's happening is that this whole giant network of transactions. Why does this sound like something that's heard elsewhere? Well, because I think it maybe is. It's something not unlike the giant network of updatings of this spatial hypergraph and so on. It's all these different transactions happening in the world. And the story ends up being that what is value? What is price, for

example? Price is something related to, okay, so think about it this way. I've been using this thing the last few weeks at least. You know, somebody wants to buy a cookie. The person they want to buy it from eventually wants to rent a movie. The question is, is there in a certain world where it's AI bots all the way down, one could imagine that they arrange this network of transactions so that the person who wants to buy the cookie eventually is giving value to the person who wants to rent the movie. They botter everything. So that's what happens.

No money is involved. It's just bot to bot transactions. So the question is, what is money? What is price? And I think what it could be thought of as I think I don't know if this will really work out that it is just like you have all these sort of interactions in space and so on and in aggregate you can think about them as having certain gravitational fields certain this that and the other certain aggregate properties

that is a description of all of those microscopic microscopic processes that are going on so I have the slight guess that value and price are associated with sort of an aggregate version of all these microscopic processes that are going on and the most bizarre thing is that what leads those things to have a sort of a robust value is computational irreducibility. So the absolutely bizarre possibility is that the transactions that go on an economic system are sort of in aggregate, they are a whole story of computational irreducibility and the reason that they build up some definite sort of uh sort of solid sense of price or value is because you sort of can't unravel that

computational irreducibility and so in some sense that computational irreducibility is the source of robust value in economics and then that in a sense the bizarre thing then is proof of work is a is a crazy sort of in a bottle version of that process so to speak proof of work yes the proof of work is ends up being sort of the the bottled up version of that that idea although it's it's a it's a poor way to to think about that and i think that the so you know what I'm imagining is that that the very fact that so many people are doing things with cryptocurrencies is almost by definition a proof that they have value. That is it could be the case that you say well everybody is doing things as a speculator which might be close to true. But even so by the time there's a complicated enough network of transactions, that is in a sense building you up processes that are going on in this purely abstract cryptocurrency and in something that is

connected to the real world and buying cookies and so on in the real world? And the answer is, I'm increasingly coming to the belief that there is a notion of a store of value that doesn't have to do with sort of the details of that. Now, as a practical matter, what's going to happen with all this cryptocurrencies, I have no idea. We've been involved with the cryptocurrency world. So at this point I am the proud owner of a certain amount of cryptocurrency. And it's been interesting for me

because I've never done our technology, our open language and mathematical and so on, get widely used by quant finance people. But I've never personally done kind of, you know, trading of those things on any kind of serious kind of actual trading screens type basis. And so, you know, it's kind of a funny thing because, you know, I have a company with lots of people in it. But in the end, you know, we've gotten cryptocurrency from a bunch of companies that we work with. And it's like, what do we do with this cryptocurrency? My longtime CFO was like, you can't, you know, we can't accept this cryptocurrency. What the heck are we going to do with it? And, you know, how do we account for it?

And so anyway, we finally solved those problems. But so I have been, I did have an amusing time a few weeks ago when I was both spending some number of hours working on the question of why does the universe exist and multitasking between that and cryptocurrency trading. And that was kind of an interesting personal experience. You were actively trading crypto? What's that? You were actively trading crypto? Yes, because we got a bunch of cryptocurrency. And my calculation is, by the time it's... Well,

the real problem was that within my company, it was like, who do we delegate the cryptocurrency trading to? And generally, the general principle of companies is, you know, the CEO, it starts with the CEO, and then they try and find somebody to delegate it to. And if we have about 800 people, but, you know, if none of them was kind of volunteering, I'm going to be the cryptocurrency trader. It kind of sticks with the CEO. But I was also just interested to get some intuitive feeling for it, which I think I do have now a better feeling for. But it was just from a purely personal point of view, the couple of days that I happened to spend sort of multitasking between figuring out why the universe exists and figuring out how we should move this or that between cryptocurrencies was an interesting experience, let's say. I would say that we have all the apparatus in

Morphin language to build some very fancy analytics for understanding what happens with cryptocurrencies and we're just starting to do that. And, you know, it's so deeply analogous to what's happened in quantitative finance. It's, I think it's, you know, the question of, is there going to be some store of value in the world that isn't gold and isn't fiat currency? The answer is presumably yes, unless governments get so freaked out about it, they managed to presumably yes unless governments get so freaked out about it they managed to to to sort of smash it um i think that the uh uh you know is it good for the world though that's a more complicated question um is it uh um is it something where um you know where one can understand you know is there some way actually it's a good exercise you know in this theory of economics that I'm sort of slowly developing, there are going to be

analogs of things like time dilation and things like the Einstein equations. It's a necessary feature of this very aggregated thing of lots of these transactions. And so then the question is, well, one of the things I was joking with as we were working on this a bit, that inflation in economics might turn out to be bizarrely similar to inflation in cosmologies. What do you mean that there's an analog of the Einstein field equations in economics? Well, you've got a whole space of transactions, right? You've got all these transactions happening. And you've got, this question is, you've got all these transactions happening. And one thing is to say there's a

global price. But actually, that probably isn't true. You've got all these transactions happening, and they're all interwoven in certain ways. And you ask questions like, is that space, for example, arbitrage? You know, you go around a loop. It's like going around a loop in space-time. You go around a loop between this transaction and it goes in time it goes to that transaction and so on the question of whether there is an arbitrage opportunity becomes a question of whether there's curvature in this kind of economic space and so that's that's the beginning I haven't worked this theory out okay so I don't know how it's all going to work but that's sort of the beginning of the story and so that that's and you know these questions about you know economic activity and

and deflection of gd6 and so on I haven't worked all this stuff out but I have this feeling that there may be a correspondence and that correspondence will be very interesting because it allows one then to leverage both the intuition from finance and the intuition from physics and merge them together. I mean, I have a friend who's a long, well-known person who's spent a lot of time as a trader. And for him, sort of, you know, for me, things are functions. They increase, they decrease, whatever. For him, everything is a put or a call. And I always have to try to remember, remember you know what does it mean by put a call you know that's just some function that is you know some particular uh you know payoff function as a function of price but um so you know these different intuitions that you get in different places um have uh like you know the notion of

volatility that we're very familiar with in the financial case. How does that map into fluctuations in space time in a physics case or something? I don't know what the correspondence will be. But these are things that I think there was one other part to that question, which I perhaps now have forgotten, but about cryptocurrency. Look, I think that the thing that's interesting... Proof of work algorithms versus Ethereum and proof of stake. Yeah. I mean, look, there are many... We just actually did a little conference about distributed consensus, which is a story of... part of that story. There are a whole collection

of different ways to come to consensus about what has happened. And in fact, what we realized is that both work I did on cellular automata and other people did on cellular automata back a long time ago is deeply relevant. There's this blockchain called NKN that is some NKN, needless to say, sort of rhymes with NKS, my new kind of science thing. And their system is very much based on kind of ideas from NKS. And it's based on using a notion of consensus that is a distributed consensus based on graph cellular automata that is different from the sort of the proof of work, proof of stake type approach.

So it's a variety of differences. That one is, I think, a rather interesting one that some other people are trying to do as well. But NKN is probably the most broadly deployed version of that. I think that's an example of, I mean, the thing to realize about blockchain is computation's general idea. There are different form factors. There are different workflows in which computation is used. What's happening in blockchain is autonomous computation.

That's what computational contracts will be. They are purely autonomous computation that no human initiated it. It wasn't, you know, it's not, it isn't just living in a cloud. It's living in a way where something might happen in the real world that actuates what ends up being a giant chain of events in the kind of, in the sort of blockchain world. And this kind of autonomous computation is the AI's takeover type scenario because it's basically you end up with these giant chains of autonomous computations and that's an interesting situation to try to understand. And there are a lot of things that something like an NFT is a very simple kind of thing about autonomous computation, but there are vastly more complex versions of that and we're only at the very, very early stages of understanding sort of what's possible in this

world of autonomous computation. I think the thing maybe I can end with is the statement that you know, in just as all these sort of interactions in between atoms of space are kind of what knit together the structure of space. I think these transactions in economics are what kind of knit together the economic system and lead to sort of coherence in things like prices and economic systems.

And it's kind of interesting to see what, when you have a fork in a blockchain it's like an event horizon in physical space time and when you have you know these closed countries and so on that's another kind of event horizon type thing analogous to what happens in physical space time but these are these are things I'm just we're're just starting to explore. Hopefully, I don't know how long it'll be, next few months or something. I'm, you know, for me, it's always, it's a crazy thing because, you know, I work in these different fields and something like economics, I've sort of paid attention to it for decades, but don't really know it in great detail.

And here I am thinking about sort of reforming the foundations of this field. And it's a scary thing because it's kind of like, how much of the field should I really know? If I start knowing too many of the details, I'm already sunk in the mud. You know, it's very hard to think, you know, to stick your head out of the mud, so to speak, because you're already, oh, but I know that it's, you know, marginal utility of this and that and the other. But at the same time, you need to familiarize yourself. So how do you strike that balance? Yeah, well, it's a challenge, right? And for economics, I keep on sort of poking away. And I,

you know, I have friends who are economists, and I talk to them a bit. And, you know, I'm still at the stage with economics where everybody tells me something I didn't know already. Eventually, in most fields that I work on, there comes this moment where most things that I hear about are things that I can readily fit in to something I already know. And I'm still on the upward curve with economics. But it always helps me with understanding a field, particularly one as complicated as economics, to have my own kind of theory about it because then as I learn new things I have at least a chance to fit them into just to a framework that I've already built all right unfortunately I really have to go but this has been fun lots of interesting questions and I didn't get to perhaps 70 percent of the questions, maybe even 80%, maybe even more.

If some of you are more familiar with the technical aspects of Wolfram's theory, I was curious about if the global hyperbolicity condition means that there are no naked singularities or is he using that simply as a way of foliating into spatial surfaces to solve the Cauchy problem and then to derive the Einstein equations but he doesn't think global hyperbolicity is actually intrinsic to our universe it doesn't seem like it is because our universe is a decider space, not an anti-desider space. If any of you can help me out with that, that would be wonderful. Oh, right, I wanted to know if global confluence meant that at any two points on this manifold that represent our world, spatially at least,

that they will necessarily causally influence each other at some point, because he did seem to indicate that there's an expansion of the universe inherent in his models. But at the same time, any two points are going to be causally connected with global confluence, at least that's the way that I see it. So if anyone here can help me out with that, either you can email me, that would be great. And while I have you here, I'm curious why you think that there's such an averse reaction to Stephen's theories, when to me... I'm not quite sure about that, because it is rigorous.

It's not fluff, but at the same time, there are also, there is also resistance to even Penrose is not liked by other professors because he has outlandish ideas with regard to consciousness and the origins of the universe in his cyclical model. And then there's Weinstein who gets criticized too, and then there's Garrett Lisi. I was wondering why there are a couple people, one named Chiara, Chiara Marletto, and then another named Sabrina Gonzalez that have their own intriguing ideas about physics. And they don't get criticized. And I'm curious if that's because they're women. And so academia wants to show how diverse and equitable they are. And thus they don't criticize them. Or if it's something else, I'm not sure.

No, we didn't touch on Bell's inequalities, though. I believe Stephen has... See, plenty of what Stephen said, for example, that quantum mechanics and general relativity are unified in that the path, the way that the formalism that leads you to the path integral is the same that leads to the Einstein equations. They're just in different spaces.

As far as I can tell, that's not proven. It's just, it seems to be the case in the models or the simulations that they have tested. As for Bell's inequality, I also don't know if Stephen's ideas on that are proven or if they're just surmising, if they're just conjectures right now. Right, DC Adams, you can say that they're avoiding testable predictions, but that's false because Stephen isn't at all. He's actively looking for how he can test his theory. Same with Penrose. And I don't see any testable or falsifiable predictions coming from Chiara or Sabrina, at least not yet.

But I haven't studied their models much. So it can't simply be that. I don't know why there's vitriol toward Steven, Eric Weinstein, Penrose, to some degree even Julian Barber. But there's not toward Chiara and Sabrina. Is it because they're young? Is it because they're women? Is it because their models are just superlative compared to Lisi, Garrett Lisi, or Barber or Penrose? I don't know. Okay, for the people watching, if you want to continue conversations, especially about consciousness, theoretical physics, and the intersection between the two,

then there's a Discord. The Discord is in the description of all of the videos as well as in the YouTube page somewhere. You can click Discord. Right where there's a Twitter and a PayPal and and a patreon and so on there's a discord link join that this channel is meant to be more of a i know strange it's strange it's meant to be more of a community than it is well it's a mission rather than a podcast and i see that as what separates it and the mission is explicating

toes and advancing toes and furthering our understanding of the universe it's not a podcast per se like joe rogan or even lex friedman where they're interested in speaking to people and i don't mean this in any demeaning way because their podcasts are far far superior to mine there's a certain high level at which they operate. And that's because they're interested in many different topics. And they're generally interested in conversing with people. And I'm not particularly or this podcast isn't about conversing in that same way. It's more about office hours is one way that I described it. I'm trying to clarify my own thinking. But another is that we have a aim and the aim is the theory of everything. Explicating them because there are around 200 as far as I can

count. If you would like to further that aim, then please join the discord. If anyone is watching and is mathematically or physically inclined, when I say physically inclined, I mean mathematical physics. And you can tell me if the ADM decomposition from Wolfram's model is necessary in order for them to derive general relativity. That's as far as I can see it is. But at the same time, so the ADM decomposition requires you to be able to foliate your space-time into spatial dimensions, and then sequentially move forward or backward in time. And that doesn't seem to be what

characterizes our world, but it seems to be essential in Wolfram's models. And I'm wondering, is it essential? As well as even if it is. So this ADM decomposition, it's not as if that's on solid foundation. There's a disproof of the ADM decomposition from Kirushcheva and Kuzmin. But that disproof itself is contested. Okay, I gotta get going. I should eat and I should sleep and spend some time with my wife. If you all would like to see more conversations like this, then please do consider going to patreon.com slash KurtJaiMungle. I will leave a link right now. Every dollar indeed does help tremendously. So here's one. Here's one way that that was invested into this podcast i spent so much time sitting that i was able to get a standing desk which is what you're seeing right now using some of the funds and that i just got this recently that

helps tremendously because my legs and my, well, you can understand how a standing desk helps. So if you do want to see more conversations like this, if you, for whatever reason, want to make it easier on Kurt, or you would like to see more podcasts more frequently, then please do consider going to patreon.com slash Kurt Jaimungal and donating a dollar, $10, $50, whatever you feel like you can afford, or you would, whatever you feel like you would like to give. Thank you so much. Yeah, Grayson, that's correct. So when I asked a question that I expected an answer that would take three minutes, it would span the length of 10 minutes. I'm just thinking come on Steven time is money you know this

let's hurry this up because I have 150 questions to get to and that's not including the audience questions alright everyone thank you so much for watching and I hope that you All right, everyone. Thank you so much for watching, and I hope that you gleaned something positive from it. Have a great night.